Total Risk Integrated Methodology
TRIM.FaTE Technical Support Document
Volume II: Description of Chemical Transport and
Transformation Algorithms
F M vi ion in en Uil rule,
rransport, & Kcolo«ical
-------
EPA-453/R-02-011b
September 2002
TRIM
Total Risk Integrated Methodology
TRIM.FaTE
Technical Support Document
Volume II: Description of Chemical Transport and Transformation Algorithms
U.S. Environmental Protection Agency
Office of Air Quality Planning and Standards
Emissions Standards & Air Quality Strategies and Standards Divisions
Research Triangle Park, North Carolina
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DISCLAIMER
DISCLAIMER
This document has been reviewed and approved for publication by the U.S.
Environmental Protection Agency. It does not constitute Agency policy. Mention of trade
names or commercial products is not intended to constitute endorsement or recommendation for
use.
SEPTEMBER 2002 i TRIM.FATETSD VOLUME II
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ACKNOWLEDGMENTS
ACKNOWLEDGMENTS
As described in this report, the Office of Air Quality Planning and Standards (OAQPS) of
the U.S. Environmental Protection Agency (EPA) is developing the Total Risk Integrated
Methodology. Individuals and organizations who have been involved in the TRIM.FaTE
development effort and in the preparation of this report are listed below.
Steve Fine, EPA, Office of Research and Development
Robert G. Hetes, EPA, Office of Air Quality Planning and Standards
John Langstaff, EPA, Office of Air Quality Planning and Standards
Thomas McCurdy, EPA, Office of Research and Development
Deirdre L. Murphy, EPA, Office of Air Quality Planning and Standards
Ted Palma, EPA, Office of Air Quality Planning and Standards
Harvey M. Richmond, EPA, Office of Air Quality Planning and Standards
Amy B. Vasu, EPA, Office of Air Quality Planning and Standards
Deborah Hall Bennett, Lawrence Berkeley National Laboratory
David Burch, ICF Consulting
Rebecca A. Efroymson, Oak Ridge National Laboratory
Alison Eyth, MCNC-Environmental Modeling Center
Baxter Jones, ICF Consulting
Daniel S. Jones, Oak Ridge National Laboratory
Mark Lee, MCNC - Environmental Modeling Center
Bradford F. Lyon, University of Tennessee
Thomas E. McKone, Lawrence Berkeley National Laboratory & University of
California, Berkeley
Margaret E. McVey, ICF Consulting
Randy Maddalena, Lawrence Berkeley National Laboratory
SEPTEMBER 2002 iii TRIM.FaTE TSD VOLUME II
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ACKNOWLEDGMENTS
The following external experts reviewed a previous draft of this document.
Science Advisory Board Reviewers
Chair
Mitchell Small, Professor, Department of Civil Engineering & Public Policy,
Carnegie Mellon University, Pittsburgh, PA
Members
Steven M. Bartell, Senior Associate,
Cadmus Group, Inc., Oak Ridge, TN
Calvin Chien, Senior Environmental Fellow,
E.I. DuPont Company,
Wilmington, DE
Kai-Shen Liu, Epidemiologist, California
Department of Health Services,
Environmental Health Laboratory Branch,
Berkeley, CA
Paulette Middleton, Associate Director,
Environmental Science and Policy Center,
RAND Corporation, Boulder, CO
Ishwar Murarka, Chief Scientist and
President, ISHInc., Cupertino, CA
Consultants
M. Bruce Beck, Professor & Eminent
Scholar, Warnell School of Forest
Resources,
University of Georgia, Athens GA
Linfield Brown, Professor, Department of
Civil and Environmental Engineering,
Tufts University, Medford, MA
Arthur J. Gold, Professor, Department of
Natural Resources Science,
University of Rhode Island, Kingston, RI
Helen Grogan, Research Scientist, Cascade
Scientific, Inc., Bend, OR
Wu-Seng Lung, Professor, Department of
Civil Engineering,
University of Virginia, Charlottesville, VA
Jana Milford, Associate Professor,
Department of Mechanical Engineering,
University of Colorado, Boulder, CO
Thomas Theis, Professor & Chair,
Department of Civil and Environmental
Engineering, Clarkson University,
Potsdam, NY
SEPTEMBER 2002
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TRIM.FaTE TSD VOLUME II
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ACKNOWLEDGMENTS
The following EPA individuals reviewed a previous draft of this document.
EPA Models 2000 TRIM Review Team
Robert F. Carousel
National Exposure Research Laboratory
Office of Research and Development
*S. Steven Chang
Office of Emergency and Remedial Response
Office of Solid Waste and Emergency
Response
Ellen Cooler
National Exposure Research Laboratory
Office of Research and Development
Stan Durkee
Office of Science Policy
Office of Research and Development
Harvey Holm
National Exposure Research Laboratory
Office of Research and Development
John S. Irwin
Office of Air Quality Planning and Standards
Office of Air and Radiation
Team Leader
Linda Kirkland
National Center for Environmental Research
and Quality Assurance
Office of Research and Development
Matthew Lorber
National Center for Environmental
Assessment
Office of Research and Development
Haluk Ozkaynak
National Exposure Research Laboratory
Office of Research and Development
William Petersen
National Exposure Research Laboratory
Office of Research and Development
Ted W. Simon
Region 4
Amina Wilkins
National Center for Environmental
Assessment
Office of Research and Development
Review by Other Program Offices
Pam Brodowicz, Office of Air and Radiation, Office of Mobile Sources
William R. Effland, Office of Pesticide Programs
John Girman, Office of Air and Radiation, Office of Radiation and Indoor Air
Steven M. Hassur, Office of Pollution Prevention and Toxics
Terry J. Keating, Office of Air and Radiation, Office of Policy Analysis and Review
Russell Kinerson, Office of Water
Stephen Kroner, Office of Solid Waste
David J. Miller, Office of Pesticide Programs
SEPTEMBER 2002
TRIM.FaTE TSD VOLUME II
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PREFACE
PREFACE
This document, the TRIM.FaTE Technical Support Document, is part of a series of
documentation for the overall Total Risk Integrated Methodology (TRIM) modeling system.
The detailed documentation of TRIM's logic, assumptions, algorithms, equations, and input
parameters is provided in comprehensive Technical Support Documents (TSDs) and/or user's
guidance for each of the TRIM modules. This report, which supersedes earlier versions (U.S.
EPA 1998a, U.S. EPA 1999a,b), documents the Environmental Fate, Transport, and Ecological
Exposure module of TRIM (TRIM.FaTE) and is divided into two volumes. The first volume
provides a description of terminology, model framework, and functionality of TRIM.FaTE, and
the second volume presents a detailed description of the algorithms used in the module.
Comments and suggestions are welcomed. The OAQPS leads on the various modules are
provided below with their individual roles and addresses.
TRIM coordination
and TRIM.FaTE
TREVI.Expo
[Inhalation]
TREVI.Expo
[Ingestion]
TREVl.Risk
Deirdre L. Murphy
REAG/ESD/OAQPS
C404-01
RTF, NC 27711
[murphy. deirdre@epa.gov]
Ted Palma
REAG/ESD/OAQPS
C404-01
RTF, NC 27711
[palma.ted@epa.gov]
Amy B. Vasu
REAG/ESD/OAQPS
C404-01
RTF, NC 27711
[vasu.amy@epa.gov]
Terri Hollingsworth
REAG/ESD/OAQPS
C404-01
RTF, NC 27711
[hollingsworth.terri@epa.gov]
Harvey M. Richmond
HEEG/AQSSD/OAQPS
C404-01
RTF, NC 27711
[richmond.harvey@epa.gov]
SEPTEMBER 2002
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ACRONYMS, ABBREVIATIONS, AND SYMBOLS
ACRONYMS, ABBREVIATIONS, AND SYMBOLS
ACRONYMS
BAF Bioaccumulation Factor
B(a)P Benzo(a)pyrene
BASS Bioaccumulation and Aquatic System Simulator
BCF Bioconcentration Factor
BMR Basal Metabolic Rate
BW Body Weight
D Dust
DOC Dissolved Organic Carbon
EPA United States Environmental Protection Agency
FIR Free-living Inhalation Rate
GI Gastrointestinal
GIS Geographic Information Systems
GW Ground Water
HAP Hazardous Air Pollutant
IEM Indirect Exposure Methodology
KAW Air/Water Parition Coefficient
KOA Octanol/Air Partition Coefficient
Kow Octanol/Water Partition Coefficient
LSODE Livermore Solver for Ordinary Differential Equations
NERL National Exposure Research Laboratory
OAQPS EPA Office of Air Quality Planning and Standards
OPPT Office of Pollution Prevention and Toxics
ORD Office of Research and Development
OW Office of Water
PAH Polycyclic Aromatic Hydrocarbon
R-MCM Regional Mercury Cycling Model
SAB Science Advisory Board
SCF Stem Concentration Factor
SW Surface Water
TF Transfer Factor
TOC Total Organic Carbon
TRIM Total Risk Integrated Methodology
TRIM.Expo TRIM Exposure-Event module
TRIM.FaTE TRIM Environmental Fate, Transport, and Ecological Exposure module
TRIM.Risk TRIM Risk Characterization module
TSCF Transpiration Stream Concentration Factor
TSD Technical Support Document
WASP Water Quality Analysis Simulation Program
SEPTEMBER 2002
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ACRONYMS, ABBREVIATIONS, AND SYMBOLS
UNIT ABBREVIATIONS
°C
°K
g
hr
kg
L
m
degrees Centigrade
degrees Kelvin
gram
hour
kilogram
liters
meter
ng
mm
mol
nmol
nM
Pascals
yr
microgram
nanogram
millimeter
mole
nanomole
nanomolar
Pa
year
SYMBOLS USED FOR VARIABLES
Greek
a (alpha) proportion of equilibrium value
K (kappa) von Karmen's constant
KJ the equilibrium ratio between the concentration in phasey and the phase to
which one is normalizing
e (epsilon) volume fraction gas/vapor/pure air
6 (theta) volume fraction liquid
4> (phi) porosity (volume fraction not solid)
x|/(psi) volume fraction of compartment
p (rho) density
(p (alternate phi) fraction sorbed to solids
Y(gamma) gradient of soil concentration change
5 (delta) boundary layer thickness
0 (Theta) temperature correction factor
X (lamda) dimensionless viscous sublayer thickness
A; removal rate constant for soil compartment /
|J, (mu) viscosity
v (nu) velocity
u (upsilon) volumetric flow rate
(o (omega) volume fraction occupied by a fluid (where fluid = air or water)
Roman
A area
AE assimilation efficiency
BW body weight
C concentration
d depth
D diffusion coefficient
DSP dispersion coefficient (between surface water compartments)
E elimination (wildlife)
/ fraction
FIR free-living inhalation rate (not normalized to body weight)
g conductance
H Henry's law constant
/ interception fraction
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ACRONYMS, ABBREVIATIONS, AND SYMBOLS
IN ingestion, inhalation, or intake (normalized to body weight)
IR inhalation rate (not normalized to body weight)
k rate constant
k transfer coefficient (Chapter 3)
K partition coefficient
L characteristic mixing length
m mass of an organism
M mass of chemical
Mw molecular weight
n number
nas number of stomata in leaf multiplied by the area of a single stomata divided by
the area of the leaf
N chemical inventory (mass)
p proportion
P permeance
P pressure (Pvapor)
Q flux
R universal gas constant
R[sub] resistance [subscript]
rh relative humidity
fML fraction mass disolved/volume fraction liquid
fMS fraction mass solid particle-phase/volume fraction solid particles
fMV fraction mass vapor-phase/volume fraction gas
S rate of sediment deposition (or resuspension)
T transfer factor or
T temperature
U mass transfer coefficient
V volume
v velocity
ve effective velocity
WI water ingestion (not normalized to body weight)
Z fugacity capacity
SEPTEMBER 2002 xi TRIM.FaTETSD VOLUME II
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ACRONYMS, ABBREVIATIONS, AND SYMBOLS
ABBREVIATIONS USED IN VARIABLE SUBSCRIPTS
ace
adv
Al
Arth
ASF
avail
B
BI
C
d
D
dep
dep
dif
e
ef
eg
ET
f
ff
Fbo
Fh
Fwch
Fwco
G
G
L
L
lact
m
m
met
Mp
N
oc
accumulation
advection
Algae
Arthropod
Allometric Scaling Factor
available
Boundary layer
Benthic Invertebrates
Conductance
drag
Diet
depuration (fish)
deposition (abiotic media)
diffusion
effective
excretion via urine/feces
excretion from gills
total elimination
unspecified fish
fur, feathers (or hair)
Fish, benthic omnivore
Fish, herbivore
Fish, water column
herbivore
Fish, water column
omnivore
Growth (fish algorithms)
Gas (air algorithms)
load (e.g., DL = Dust load)
liquid (e.g., RL = liquid
phase resistance)
lactation
melting; or
mesophyl
metabolism
Macrophyte
normalized
organic carbon
ow
P
Ph
r
rV
R
Rev
res
S
Sed
SSed
Send
Snk
Sr
Ss
Sv
St
SWD
t
T
Tprey
Twl
uf
U
fuSs
fuSW
W
WD
v
VAF
Worm
WV
Xy
octanol water
Particle
Phloem
ratio
ratio for Vapor
Root
Receiving
resuspension/resuspend
Soil (e.g., As = soil area);
or
Stomatal (e.g., gs = total
stomatal conductance)
Sediment
Suspended sediments
Sending
Sink
root-zone Soil
surface Soil
vadose-zone Soil
Stem
dissolved in surface water
time
Temperature
Terrestrial prey
Terrestrial wildlife
urine/feces
Uptake
eliminated to surface soil
eliminated to surface water
Water
dissolved in water
volatilization
vegetation attenuation
factor
Earthworm
Wet Vapor
Xylem
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TABLE OF CONTENTS
TABLE OF CONTENTS
DISCLAIMER i
ACKNOWLEDGEMENTS iii
PREFACE vii
ACROYNMS, ABBREVIATIONS, AND SYMBOLS ix
TABLE OF CONTENTS xiii
1. INTRODUCTION 1-1
2. ALGORITHM OVERVIEW 2-1
2.1 Phase-Distribution Calculations 2-1
2.1.1 Assumed Chemical Equilibrium 2-2
2.1.2 Normalization to Liquid Phase 2-3
2.1.3 Concentrations of Chemical in Each Phase 2-5
2.1.3.1 General Form 2-5
2.1.3.2 Fugacity-based Notation 2-7
2.2 Application to Soil, Surface Water, and Sediment Compartment Types .2-10
2.2.1 General Form 2-10
2.2.2 Fugacity-based Notation 2-12
2.3 Approach for Air 2-12
2.3.1 Multiphase Partitioning in the Air Compartment Type 2-13
2.3.1.1 General Approach 2-13
2.3.1.2 Fugacity-based Notation 2-14
2.3.2 Calculation of the Fraction of Chemical Bound to Air Particles 2-15
2.3.2.1 KOA-based Method 2-15
2.3.2.2 Junge's Method 2-16
2.4 General Fate and Transport Processes 2-17
2.4.1 Advective Processes 2-17
2.4.2 Diffusive and Dispersive Processes 2-19
2.4.3 Reaction and Transformation Processes 2-19
2.4.4 Biotic Processes 2-20
2.5 Converting Equations with Equilibrium Relationships to Dynamic Form 2-20
2.6 Relating Fugacity and Equilibrium Notations 2-21
2.7 TRLVLFaTE Code for Distribution of Chemical Among Phases 2-24
3. AIR ALGORITHMS 3-1
3.1 Air-to-Air Algorithms 3-1
3.2 Air-to-Soil Algorithms 3-4
3.3 Air-to-Surface-Water Algorithms 3-4
3.3.1 Deposition 3-4
3.3.2 Diffusion and Volatilization 3-4
3.3.2.1 Diffusion and Volatilization Transfer Between Air and
Surface Water 3-5
3.3.2.2 Calculation of Volatilization Transfer Rates for the
Whitman Two-layer Resistance Model 3-8
SEPTEMBER 2002 xiii TRIM.FaTETSD VOLUME II
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TABLE OF CONTENTS
3.4 Air-to-Plant Algorithms 3-8
3.5 Transformations and Degradation 3-8
3.6 Air Boundary Contributions 3-8
4. SURFACE WATER AND SEDIMENT ALGORITHMS 4-1
4.1 Conceptualization of the Surface Water and Sediment Compartments 4-1
4.2 Advective Processes 4-6
4.2.1 Advective Processes Between Air and Surface Water 4-6
4.2.1.1 Dry Deposit!on of Particles to Surface Water 4-6
4.2.1.2 Wet Deposition of Particles to Surface Water 4-8
4.2.1.3 Wet Deposition of Vapor-phase Chemical to Surface Water . . 4-9
4.2.2 Advective Processes Between Sediment and Surface Water 4-10
4.2.2.1 Sediment Deposition and Resuspension 4-12
4.2.2.2 Sediment Deposition and Resuspension Rates 4-13
4.2.2.3 Algal Deposition Rates 4-15
4.2.3 Advective Processes Between Sediment/Surface Water and
Advective Sinks 4-16
4.2.3.1 Outflow from Flowing Water to Surface Water Advection Sink
(Total Phase) 4-16
4.2.3.2 Outflow from Lake or Pond to Surface Water Advection Sink
(Total Phase) 4-17
4.2.3.3 Movement of Sediment from Sediment Bed to Sediment Burial
Sink (Solid Phase) 4-17
4.2.4 Advective Processs from Surface Soil to Surface Water 4-18
4.3 Derivation of River Compartment Transfer Factors 4-18
4.4 Diffusive Processes 4-19
4.4.1 Diffusive Exchange Between Surface Water and Air 4-19
4.4.2 Diffusive Exchange Between Surface Water and Sediments 4-19
4.4.2.1 Transfer Factors Based on Fugacity Approach 4-19
4.4.2.2 Transfer Factors Based on the WASP Model 4-21
4.4.3 Diffusive Exchange Between Algae and Surface Water 4-23
4.5 Dispersive Processes 4-23
4.6 Transport Between Sediment Compartments 4-24
4.7 Transformations and Degradation 4-25
5. SOIL ALGORITHMS 5-1
5.1 Soil Compartments and Transport Processes 5-1
5.2 Transformations and Degradation 5-5
5.3 Vertical Transport Algorithms 5-8
5.3.1 Theoretical Basis for the Transport Algorithms 5-8
5.3.2 Relationship Between Inventory, Nt, and Peak Concentration, Ct(0) .5-11
5.3.3 Vertical Mass Exchange Between Air and the Surface Soil
Compartment 5-11
5.3.3.1 Diffusive Processes 5-11
5.3.3.2 Wet and Dry Deposition of Particles 5-15
5.3.3.3 Wet Deposition of Vapor-phase Chemical 5-17
5.3.3.4 Dry Resuspension of Dust from Soil to Air 5-18
SEPTEMBER 2002 xiv TRIM.FaTE TSD VOLUME II
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TABLE OF CONTENTS
5.3.4 Vertical Mass Exchange Between Two Vertically Adjacent
Soil Compartments 5-19
5.3.4.1 Vertical Diffusive Transfers 5-20
5.3.4.2 Downward Advective Transfer (Percolation) 5-22
5.4 Storm-Water Runoff Algorithms 5-24
5.4.1 Aqueous-phase Transport Processes 5-24
5.4.2 Solid-phase Transport Processes 5-26
5.5 Ground-Water Algorithms 5-28
6. AQUATIC BIOTA ALGORITHMS 6-1
6.1 Aquatic Biota Compartment Types 6-1
6.2 Aquatic Plants 6-4
6.2.1 Algae 6-4
6.2.2 Macrophytes 6-5
6.2.2.1 Transfers between Macrophytes and Surface Water 6-5
6.2.2.2 Transformations and Degradation 6-7
6.3 Benthic Infauna 6-8
6.3.1 Transfers Between Sediment Interstitial Water and Benthic
Invertebrates 6-8
6.3.2 Transfers Between Bulk Sediment and Benthic Invertebrates 6-11
6.3.3 Transformations and Degradation 6-12
6.4 Fish 6-13
6.4.1 Bioenergetic-based Kinetic Model 6-14
6.4.1.1 General Model 6-14
6.4.1.2 Nonionic Organic Chemicals 6-19
6.4.1.3 Mercury 6-20
6.4.1.4 Bioenergetic Model Transfer Factors 6-21
6.4.1.5 Transformations and Degradation 6-22
6.4.2 Time-to-equilibrium-based Kinetic Model 6-23
6.4.3 Other EPA Models for Bioaccumulation by Fish 6-26
7. TERRESTRIAL BIOTA ALGORITHMS 7-1
7.1 Terrestrial Biota Compartment Types 7-1
7.2 Algorithms for Terrestrial Plants 7-2
7.2.1 Transfers Between the Air, Particles, and Plant Leaves 7-7
7.2.1.1 Dry Deposition of Particles to Surface of Plant Leaves 7-7
7.2.1.2 Blow Off of Particles on Leaf to Air 7-9
7.2.1.3 Wet Deposition of Particles to Surface of Plant Leaves 7-10
7.2.1.4 Wash-off of Chemical from Plant Surface 7-11
7.2.1.5 Transfer of Chemical to Leaf from Particles on Leaf 7-12
7.2.1.6 Transfer of Vapor-phase Chemical to Leaf from Air during
Rain 7-13
7.2.2 Uptake of Gaseous Chemical into Foliage 7-15
7.2.2.1 Air Boundary-layer Conductance 7-16
7.2.2.2 Stomatal Conductance 7-16
7.2.2.3 Conductance of Mesophyll 7-18
7.2.2.4 Total Conductance of the Stomatal Pathway 7-18
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TABLE OF CONTENTS
7.2.2.5 Cuticular Conductance 7-19
7.2.2.6 Transfer Factors for Diffusion 7-20
7.2.3 Uptake from Soil by Root 7-21
7.2.3.1 Uptake from Bulk Soil 7-22
7.2.3.2 Uptake from Soil Pore Water 7-23
7.2.4 Transfers Involving the Stem 7-25
7.2.4.1 Contribution from Soil Pore Water via Transpiration
Stream (Xylem) 7-25
7.2.4.2 Alternative Algorithm for Soil/Stem Transfers 7-27
7.2.4.3 Contribution from Leaves via Phloem 7-28
7.2.4.4 Loss from Leaf to Stem via Xylem 7-29
7.2.4.5 Loss from Phloem to Fruit 7-30
7.2.5 Uptake by Wood and Tree Bark 7-31
7.2.6 Transformations and Degradation 7-31
7.2.7 Litter Fall 7-31
7.2.8 Senescence 7-33
7.2.9 Other Seasonal Issues 7-33
7.3 Soil Detritivores 7-34
7.3.1 Earthworms 7-34
7.3.1.1 Uptake of Chemicals from Bulk Soil 7-34
7.3.1.2 Uptake of Chemicals from Soil Pore Water 7-38
7.3.2 Soil Arthropods 7-40
7.3.3 Flying Insects 7-42
7.3.4 Transformations and Degradation 7-42
7.4 Terrestrial Wildlife 7-42
7.4.1 Generalized Model for Terrestrial Mammals and Birds 7-43
7.4.2 Transfer-factor Algorithms 7-48
7.4.2.1 Surface Water to Terrestrial Vertebrate Wildlife 7-48
7.4.2.2 Surface Soil to Terrestrial Vertebrate Wildlife 7-50
7.4.2.3 Plant Leaf to Terrestrial Vertebrate Wildlife 7-51
7.4.2.4 Particles on Leaf Surface to Terrestrial Vertebrate 7-52
7.4.2.5 Earthworm to Terrestrial Vertebrate Wildlife 7-52
7.4.2.6 Soil Arthropod to Terrestrial Vertebrate 7-53
7.4.2.7 Terrestrial Vertebrate to Terrestrial Vertebrate Wildlife 7-53
7.4.2.8 Fish to Terrestrial Vertebrate Wildlife 7-54
7.4.2.9 Benthic Invertebrate to Terrestrial Vertebrate Wildlife 7-54
7.4.2.10 Air to Terrestrial Vertebrate Wildlife 7-55
7.4.2.11 Terrestrial Vertebrate Wildlife to Surface Soil 7-57
7.4.2.12 Semi-aquatic Vertebrate Wildlife to Surface Water 7-57
7.4.3 Transformations and Degradation 7-58
7.4.4 Seasonality 7-58
7.4.5 Use of Terrestrial Wildlife Compartments 7-59
7.4.6 Assimilation Efficiency and Elimination 7-60
7.4.6.1 Efficiency of Chemical Assimilation from the Diet 7-61
7.4.6.2 Efficiency of Chemical Assimilation from Air 7-62
8. REFERENCES 8-1
SEPTEMBER 2002 xvi TRIM.FaTETSD VOLUME II
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TABLE OF CONTENTS
APPENDICES
A. Derivation of Mercury-specific Algorithms A-l
A.I Mercury-specific Transfer Algorithms A-l
A. 1.1 Dry Vapor Deposition of Divalent Mercury A-l
A.1.2 Algae A-2
A. 1.3 Mercury Excretion By Fish A-4
A. 1.4 Accumulation of Mercury By Fish A-4
A. 1.5 Plant Mesophyll Resistance A-5
A.2 Mercury Transformation Algorithms A-6
A.2.1 Abiotic Mercury Transformation Rate Constants A-7
A.2.2 Biotic Mercury Transformation Rate Constants A-16
A.2.2.1 Plants A-16
A.2.2.2 Soil Detritivores A-17
A.2.2.3 Terrestrial and Semi-aquatic Wildlife A-17
A.2.2.4 Aquatic Species A-18
A.4 References A-19
B. Derivation of PAH-specific Algorithms B-l
B.I Exchanges Between Sediment and Benthic Invertebrates B-l
B.2 Bioaccumulation by Fish B-3
B.3 References B-4
C. Steady-state Mode C-l
C. 1 Steady-State Solution Feature C-l
C.I.I Changing Time-varying Input Data To Constants C-l
C.I. 1.1 Advective Air-to-air Transfers C-3
C.I. 1.2 Dry Interception Fraction C-5
C.I. 1.3 Wet Interception Fraction C-6
C. 1.1.4 Diffusive Transfer Across Air/Stomata Interface and
Across Air/Cuticle Interface C-8
C.I.1.5 Litter Fall andRiverFlow C-8
C.I.1.6 Wildlife Plant Ingestion Rates C-9
C.I.2 Switching Advective Air Transport Algorithms C-9
C.I.3 Disabling Links with Ground Water C-10
C.2 Applications of the Steady-state Mode C-10
D. Tables of TREVLFaTE Input Parameters D-l
Non-chemical-dependent — Abiotic D-3
Non-chemical-dependent — Biotic D-l 1
Chemical-dependent — Independent of Compartment Type D-20
Chemical-dependent — Abiotic D-21
Chemical-dependent — Biotic D-27
Source, Meteorological, and Other Input Parameters D-37
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CHAPTER 1
INTRODUCTION
1. INTRODUCTION
This volume of the TRIM.FaTE Technical Support Document (TSD) presents the
equations available in the current TRIM.FaTE library that can be used to describe the transport
and transformation of chemicals in TRIM.FaTE simulations. These equations are used to
simulate the physical, chemical, and biological processes that drive chemical transport and
transformation in the environment. As explained in Volume I of this report, the TRIM.FaTE
modeling framework can incorporate first-order and higher order equations. At the present time,
however, only first-order equations have been included in the TRIM.FaTE library and applied
using the model.
First-order transfer between compartments in TRIM.FaTE is described mathematically
by transfer factors, referred to as T-factors or TFs. This volume documents all of the TF
algorithms currently included in the TRIM.FaTE library. A T-factor is the instantaneous flux of
the chemical into the receiving compartment normalized by the amount of chemical in the
sending compartment (see Section 4.2 in TRIM.FaTE TSD Volume I (U.S. EPA 2002a) for more
discussion about T-factors and related issues). That is, T x N(t) is the instantaneous flux at time
t in units of chemical amount/time, where N(t) is the chemical amount in the sending
compartment at time t. Thus, the unit for a T-factor is inverse time (in TRIM.FaTE, per day).
Because it is a normalized flux, a large T-factor in itself does not imply that the flux is
large; the actual flux also depends on the amount of chemical in the sending compartment. The
T-factor is not the same as the fraction of mass transported from the sending to receiving
compartment (or transformed or degraded from one chemical form to another) in a given time
interval, although the two quantities are related. When the fraction of mass lost is small, these
two quantities are approximately the same, but they differ significantly when the fraction of mass
lost is larger. In particular, T= -ln(l-/?), wherep is the proportion (fraction) of mass lost in one
simulation time step, and the units of time are the same as those for T.
The remainder of this volume is organized in seven chapters. Chapter 2 describes the
general methods and assumptions used to model fate and transport in TRIM.FaTE, focusing on
advection algorithms and the equations to estimate the fraction of the total chemical in a
compartment that occurs in each phase (i.e., solid, liquid, vapor) within the compartment.
Chapters 3 through 5 present the abiotic transfer factor algorithms for air (Chapter 3), surface
water and sediment (Chapter 4), and soil and ground water (Chapter 5). For simplicity, the T-
factor algorithms used to describe intermedia transport are presented in only one of the relevant
chapters and referenced in the other. Chapters 6 and 7 present the algorithms for transfers
between biotic compartment types and between biotic and abiotic compartment types. Chapter 6
describes the algorithms associated with aquatic biota, while Chapter 7 describes those
associated with terrestrial biota. Chapters 3 through 7 begin with (or begin each major
subsection with) a brief summary of the T-factor algorithms described in the chapter and then
explain each algorithm in greater detail. Each chapter also describes supporting equations that
are located in the compartment sections of the TRIM.FaTE code library instead of in the T-factor
algorithm sections. Chapter 8 provides the references cited in this volume.
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CHAPTER 1
INTRODUCTION
This volume includes four appendices. Appendix A presents chemical-specific
algorithms for mercury, and Appendix B presents chemical-specific algorithms for poly cyclic
aromatic hydrocarbons (PAHs). Appendix C describes key aspects of running TRIM.FaTE
using the steady-state solution feature. Appendix D lists and describes the input parameters in
the current library.
The derivation of T-factors begins in different ways in some chapters, reflecting
differences in typical presentations of transfer or partitioning models in the literature among the
related disciplines. An effort has been made, however, to use a standard set of variable names
throughout this volume (see Acronyms, Abbreviations, and Symbols on pages ix to xii.)
SEPTEMBER 2002 1 -2 TRIM.FATE TSD VOLUME II
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2. ALGORITHM OVERVIEW
As described in TRIM.FaTE TSD Volume I, Chapter 4, TRIM.FaTE includes algorithms
to model several types of transport and fate processes, including bulk advection, diffusion,
dispersion, biotic processes, and chemical reactions and transformations. Because some of these
algorithms are dependent on what phase (e.g., liquid, solid) a chemical is in, TRIM.FaTE also
contains equations to estimate phase distribution in abiotic compartments.1 This chapter
provides an overview of the general types of algorithms used by TRIM.FaTE, including those
used to model phase distribution.
The main focus of this chapter is the methods and assumptions used to develop the
advection algorithms, i.e., the T-factors used to describe advective transport of a chemical
between adjacent compartments. Mathematically, all that is required to calculate an advective
transfer is the velocity of the moving phase and the amount of the chemical that is in the moving
phase. Thus, the fraction of the total chemical in a compartment that is in the moving phase
(e.g., water) must be estimated. To estimate the fraction in the moving phase, the fraction of the
total chemical that will be found in each phase (i.e., the partitioning of the chemical among all
phases within a compartment) must be estimated. Both fugacity and non-fugacity related
approaches are used in TRIM.FaTE to model the partitioning of a chemical among phases within
a compartment.
The remainder of this chapter is organized into six main sections. Section 2.1 focuses on
multiphase calculations and how TRIM.FaTE estimates the fraction of the total chemical in a
compartment that occurs in each phase within the compartment. Section 2.2 describes the
general phase-distribution equations of Section 2.1 as they apply to soil, surface water, and
sediment compartment types and different moving phases as modeled in TRIM.FaTE. Section
2.3 describes the general phase-distribution equations for the air compartment type. Section 2.4
then indicates, in general terms, how the various T-factors are estimated in TRIM.FaTE for the
different fate and transport processes. Section 2.5 describes how some algorithms related to
equilibrium processes (e.g., diffusion between biotic and abiotic media) were modified from a
steady-state equilibrium form to a time-dependent form that is suitable for use in TRIM.FaTE.
Section, 2.6 demonstrates the equivalence of certain fugacity-based expressions to non-fugacity-
based expressions. The last Section, 2.7, provides descriptions of the code in the TRIM.FATE
library used to estimate the distribution of chemical among phases for each type of abiotic
compartment. Table 2-1 at the end of this chapter summarizes the advective algorithms included
in TRIM.FaTE.
2.1 PHASE-DISTRIBUTION CALCULATIONS
This section describes how the distribution of a chemical among multiple phases within a
compartment is currently modeled in TRIM.FaTE. The most common phases considered for the
Although termed "abiotic" compartments, chemical transformations that may be biologically mediated
(e.g., by bacteria) can be simulated in these compartments. Additionally, in the current TRIM.FaTE library, algae is
represented as an explicit phase of surface water rather than as a separate compartment.
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abiotic compartments are liquid, gas, and solid. In the current TRIM.FaTE library, the liquid
phase of the abiotic compartments is aqueous (i.e., water and chemicals dissolved in water).
Other phases included in some TRIM.FaTE compartments may include biotic phases (e.g., algae
in surface water). Section 2.1.1 describes the equations that result from assuming chemical
equilibrium among the phases within a compartment. Section 2.1.2 illustrates how
concentrations of a chemical in other phases are normalized to its concentration in the liquid
phase to allow calculation of its concentration in each phase. Section 2.1.3 describes two general
forms of equilibrium partitioning calculations: general and fugacity-based forms.
2.1.1 ASSUMED CHEMICAL EQUILIBRIUM
A fundamental assumption of the TRIM.FaTE algorithms is that within a single
compartment, all phases are at chemical equilibrium with each other at all times. Because
chemical equilibrium is assumed, the ratios of the concentrations among the individual phases
are constant over time, and mass balance need only be tracked for the total amount of the
chemical in a compartment. The amount of chemical in the compartment in a particular phase
can be determined from the total amount in the compartment (described in the following text),
characteristics of the chemical, and the relative volume fraction of the compartment that consists
of that phase. It is possible that, in future versions of TRIM.FaTE, chemical equilibrium among
phases in the same compartment will not be assumed, in which case the amount of chemical in
different phases will need to be tracked as separate compartments.
As pointed out in Section 4.2 of TSD Volume I, TRIM.FaTE tracks the amount of
chemical in each compartment using moles (actually conserved units, which are related to
moles). The resultant molar quantities in each compartment are then used to estimate the
modeling results in terms of mass or concentration by using a chemical's molecular weight. For
the sake of simplicity, however, most of the equations in this chapter refer to the amount of
chemical in compartments in units of mass, not moles. Exceptions include discussion of the gas
laws, in which moles are used.
In any given compartment, the total amount of chemical is the sum of the amounts in the
different phases:
NTotal = Amount _in_ gas _ phase +
Amount _in_aqueous_liquid_ phase + Amount _in_solid_ phase
= C xV + C xV + C xV (Ecl- 2-l)
^ gas A y gas T *- liquid A Y liquid T ^ solid A y solid
where:
NTotai = total mass of chemical in the compartment (g[chemical]);
Cgas = concentration of chemical vapor in gas phase of the compartment
(g[chemical vapor]/m3[gas]);
Vgas = volume of gas in the compartment (m3[gas]);
Cnquid = concentration of chemical in aqueous liquid phase of the compartment
(g[chemical]/m3[water]);
Viiquid = volume of aqueous liquid phase in the compartment (m3[water]);
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*— sW,W
-solid
solid
concentration of chemical in solid phase of the compartment
(g[chemical]/m3[solids]); and
volume of solid in the compartment (m3[solids]).
As noted earlier, because chemical equilibrium among phases within the same
compartment is assumed, the ratios of the concentrations between phases are constant over time.2
However, care must be used in specifying the units of the concentration. This is because, in
general practice, it is more common to present concentration ratios on a mass-by-mass basis
rather than on a mass-by-volume basis, as in TRIM.FaTE.
2.1.2 NORMALIZATION TO LIQUID PHASE
This section describes the relevant formulas when the concentrations of a chemical in
other phases are normalized to the concentration in the liquid phase. Normalization to the liquid
phase means that the concentrations in other phases are to be expressed in terms of concentration
in the liquid phase. This normalization is used for all soil, surface water, and sediment
compartments (including the cases where additional phases are considered). Using the
equilibrium assumptions, the following equations describe the concentration of the chemical in
the solid and gas phases, respectively:
Csolld = (Pso!ld x Kd x CF) x CUqmi
liquid
(Eq. 2-2)
C =
gas
H
x C
liquid
(Eq. 2-3)
where:
Psolid
Kd
CF
H
R
T
density of a solid phase in the compartment (kg[solid phase]/m3[solid
phase]);
equilibrium partition coefficient; ratio of concentration in solid phase
(g[chemical] /kg[solid phase]) to that in liquid phase
(g[chemical]/liters(L)[liquid phase]);
10"3 (m3/L), unit conversion factor
from m3 to L[liquid phase];
Henry's law constant for chemical
(Pascal (Pa)-m3/mol) in liquid
phase;
ideal gas constant (8.314 m3-
Pa/mol-°K); and
temperature (°K).
UNIT CONVERSIONS
1 Pascal (Pa) = 9.869E-06
atmospheres or 7.5E-03 mm Hg
1 atmosphere = 760 mm Hg
1 m3 = 1000 liters (L)
0°K = -273.15°C
Assuming a constant temperature.
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Equation 2-2 expresses the equilibrium partitioning for a solid in contact with water. The
density of the solid is included in the equation, because the concentrations Csolidand Cliquid are
expressed on a mass-by-volume basis rather than on a mass-by-mass basis (see Equation 2-1).
Equation 2-3 is derived from the ideal gas law and Henry's law. The ideal gas law states:
PgasxV=nxRxT (Eq.2-4)
where:
Pgas = gas pressure (Pa);
V = volume (m3); and
n = number of moles.
Henry'slaw states:
Pair = HxCUqmd (Eq. 2-5)
where:
Pair = partial pressure in air (Pa); and
Cnquid = concentration of the chemical in a liquid phase (moles[chemical]/
m3[liquid]).
Combining Equations 2-1, 2-4, and 2-5, with Pair = Pgas, yields Equation 2-6, from which
Equation 2-3 can be derived because Cgas = n/V:
-=HxCliqmd (Eq.2-6)
Applying Equations 2-2 and 2-3 to Equation 2-1 yields:
( H \
^TTOM = CUqmd x (-j^-j; x Vgas + VUqmd + psolld xKdxCFx Vso!ldj (Eq. 2-7)
The volumes of the various phases in the compartment can be expressed as fractions of
the total volume of the compartment, in which case the previous equation yields:
( HxV Vr -a V ,.d]
^ Total = Cliqmd x VTotal x 7 + 1T~ + P*OM *KdxCFx -^- (Eq. 2-8)
^ K X 1 X V Total V Total V Total j
where:
VTotal = VgaS + Vl,qu,d + VSoM (Eq. 2-9)
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The term CTotal = NTota/VTotal is the total concentration of the chemical in the compartment.
Using the assumed equilibrium relationships, the concentrations in the individual phases can be
recovered from the total amount of mass in the compartment, as follows:
liquid
Total
* Total
TT V
ti gas
X
liquid
Y Total
PSOM x Kd x
Total
(Eq. 2-10)
H
H ^ Total
?x T V
^A1 V Total
V V
gas liquid
x —— + — + psolid x Kd x
Rx T" V ' V
JY A ± V Totd V Tofal
solid
(Eq.2-11)
^ solid Psolid ^ ^d
r
liquid
Total
V liquid
Total
•** Total
Total
solid
* Total
(Eq.2-12)
For cases in which the concentration in the water phase is negligible (e.g., when the
compartment is air, or the chemical has a very low solubility), the concentrations must be
normalized to another phase.
2.1.3 CONCENTRATIONS OF CHEMICAL IN EACH PHASE
TRIM.FaTE includes two types of equations for estimating concentrations in multiple
phases: the general form of the equilibrium approach (Section 2.1.3.1) and the fugacity form
(Section 2.1.3.2). As discussed earlier, all of the equations assume that the phases are in
equilibrium with each other.
2.1.3.1 General Form
If a chemical is in equilibrium among several phases within a compartment, it is
straightforward to calculate the concentration of the chemical that is in each phase. If there are n
phases in equilibrium, the concentration of the chemical in each phase can be calculated using
the following equations:
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J=l ~ j=\
: (Eq. 2-13)
r - TC y r
^-j=n j=n ^ ^norm
where:
C = the concentration of the chemical in phasey (g[chemical]/m [phase/]);
Cnorm = the concentration in the phase to which one is normalizing; and
KJ = the equilibrium ratio between the concentration in phasey and the phase to
which one is normalizing, with units of (g[chemical]/m3[phase
y'])/(g[chemical]/m3[phase to which one is normalizing]).
The KJ ratios are generally expressed in terms of other environmental and/or chemical
parameters. The total mass of chemical in the compartment, denoted by NTotab is:
A' Total ^
V, X Kj X Cm (Eq. 2-14)
7=1
= Cnorm x IX x Kj
7=1
Where Vj is the volume of phasey in the compartment and the sum of the Vj values for all n
compartments equals VTotal. The fraction of mass of chemical in phasey is then given by:
Mass of chemical in phase j in compartment
Total mass of chemical in compartment j j' Total
V X K X C
Cm x 2, Vj. x KJ. (Eq. 2-15)
/=!
Vf x *•/
7'=1
When applied to the previous section (and using the notation introduced there), we have
that Cnorm= Cwater, and the A"terms are given by:
Kwater = 1 (Eq. 2-16)
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TT
K = (Eq. 2-17)
gas R x T
(Eq. 2-18)
2.1.3.2 Fugacity-based Notation
The concept of fugacity often is used to simplify the algorithms needed to describe the
partitioning of a chemical among phases within a compartment. Fugacity is defined as a
substitute for pressure in the real gas system so that the ideal gas equation (i.e., PX V = nx Rx T)
can be applied to the real gas system (Mackay 1991).
The fugacity of a chemical in a phase other than the gas phase is defined as the fugacity
of the chemical in the gas phase that is in equilibrium with the phase of interest. Fugacity
represents the escaping tendency of a chemical from a phase or compartment. When chemical
equilibrium is reached within a compartment, the fugacities of the chemical in each phase are
equal.
The concentration of a chemical in a phase can be linearly related to fugacity using the
following equation:
CJ = fj x ZJ (Eq. 2-19)
where:
Cj = concentration of a chemical in phasey (mol/m3);
fj = fugacity of the chemical in phasey (Pa); and
Zj = fugacity capacity of the chemical in phasey (mol/m3-Pa).
At equilibrium within a compartment,/! =f2 = ... fy Thus, when two phases achieve
chemical equilibrium, the chemical fugacities are equal and partitioning can be described in
terms of their Z values, which are essentially "half partition coefficients as shown below.
C, /, x Z, Z,
t=i^t-t-K* (Eq-2-20)
where:
C,, C2 = concentration of a chemical in phases 1 and 2, respectively (mol/m3);
Zj, Z2 = the fugacity capacity of the chemical in phases 1 and 2 (mol/m3-Pa);
f,,f2 = the fugacity of the chemical in phases 1 and 2, where/ =f2 (Pa); and
K12 = partition coefficient (ratio of concentrations in phase 1 to phase 2)
(g[chemical]/m3[phase 1] per g[chemical]/m3[phase 2] or m3[phase
2]/m3[phase 1]).
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ALGORITHM OVERVIEW
When concentrations are relatively low, as for most environmental contaminants, the
fugacity of a chemical in air (fair) is equal to the partial pressure of the chemical in air (Pair).
Thus, at equilibrium:
f air = Pair (Eq.2-21)
which equals the fugacity in the other phases (e.g., phase/), so that f j - fair - Pair . Thus:
Zj^j/P^ (Eq.2-22)
According to Henry's law, C liquid/Pair = 1/H. Thus, letting phasey = water:
Zwater=^/H (Eq. 2-23)
Substituting Henry's law Cwater = Pair/H'mto equations (2-2) and (2-3), respectively, and
solving for C, /P air leads to the definition of fugacity capacities for the chemical in water, air,
and solid phases:
(Eq. 2-24)
(Eq.2-25)
Zsolld = PsoM XK.XCFX Zwater (Eq. 2-26)
where:
Zwater = fugacity capacity of chemical in the liquid phase, i.e., water (mol/m3-Pa);
Zair = fugacity capacity of chemical in the gas phase, i.e., air (mol/m3-Pa);
Zsolid = fugacity capacity of chemical in the solid phase (mol/m3-Pa);
psolid = density of solid phase in compartment (kg[solid phase]/m3[solid phase]);
Kd = equilibrium partition coefficient; ratio of concentration in solid phase
(g [chemical]/kg[solid phase]) to that in liquid phase (g[chemical]/L[liquid
phase]); and
CF = 10"3 (m3/L), conversion factor to convert m3 to L[liquid phase].
Substituting Henry's law, C water = P air/H, into equation (2-9), solving for CTotal/P gas, and
inserting Zmr, Zmter, Z solld, and Z Total yields:
'air V t 'solid
ZTotai = Zair x — - + Zwater x -f^ + ZsoM x — - (Eq. 2-27)
' Total ' Total ' Total
Since the fugacity of a chemical in phase 1 and phase 2 within a compartment at
equilibrium is equal:
SEPTEMBER 2002 2^8 TRIM.FATE TSD VOLUME II
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CHAPTER 2
ALGORITHM OVERVIEW
C phase, _ Zphasei (Eq 2-28)
C 7
phase2 phase2
Applying these relationships shows that:
T Z
water _ _ _ water c
X " X ^ Total (Eq. 2-29)
water "7 y
^ Total ' Total
Total
n Lair .. Total Lair .. ^ /T-, OOAN
Cair = - - X — - = - - X CTotal (Eq. 2-30)
^ Total * Total CTotal
.Z ,., * v Total 7^
C~i sotla sotla /~i /-r-i r\ o 1 \
• S0,,d = 7 - X ~T7 - = 7 - X CTotal (Eq. 2-3 1 )
CTotal V Total CTotal
where:
CTotal = total concentration of the chemical in the compartment (g[chemical]/
m3[total compartment]).
From these relationships, in general, the amount of mass in the different phases is given by:
7
water - water
\T - 77 v C - 77 v water v - T/ v water v r1 /-"Co, o TO\
7V water ~ V water X ^water ~ ^ water X 7 X T/ ~ V water X 7 X CTotal (^q. 2-32)
^Toto/ KToto/ CTotal
7 N 7
Nair =VairxCair =Vairx-^x-^- =Vairx-^xCTotal (Eq.2-33)
CTotal V Total CTotal
7 N 7
AT 17 ,, /^ T7 ., ^xofij ,, r°to/ Tr ,, ^xofij ,, x-t /T- O T/l\
^,OM = ^^ X Ciojw = FrfJ x - - x — - = VsoM x - - x CTotal (Eq. 2-34)
CTotal 'Total CTotal
where:
Nwater = chemical mass in the liquid phase (i.e., water, excluding suspended
particles) (g[chemical]);
Nair = chemical mass in the gas phase (i.e., air, excluding suspended particles)
(g[chemical]); and
N Soiid = chemical mass in the solid phase (g[chemical]).
If there are other phases in equilibrium with the chemical dissolved in the water phase,
then the fugacity capacities of that phase can be defined in a manner consistent with that above.
For example, if Cother = Kother >
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CHAPTER 2
ALGORITHM OVERVIEW
and the total fugacity capacity of the chemical in the compartment is given by:
V • j/" j/" j/"
Zr-r alr r-r water , r-r solid , r-r other /T^ — "» x-\
Total = Za,r X y + Zwater X y + Z >oM X y + Z^ X y (E^ 2'36)
* Total * Total * Total * Total
where Vother is the volume of the other phase, in units of m3 [other phase].
In the following sections, the general equations presented in this section for multiple
phase calculations are applied to specific compartment types. The use of these equations in the
following sections generally adheres to notations commonly used in the literature for the
different media.
2.2 APPLICATION TO SOIL, SURFACE WATER, AND SEDIMENT
COMPARTMENT TYPES
For soil, surface water, and sediment compartment types, the concentrations are
normalized to the concentration in the liquid phase, and the same notation is used to represent
the relevant parameters. In a soil compartment, the solid phase consists of the soil particles. In a
surface water compartment, the solid phase consists of the sediment suspended in the water
column. In a sediment compartment, the solid phase consists of clay, silt, or sand particles as
opposed to the water phase that fills the interstitial space between the sediment solid particles.
Table 2-1 shows all of the phases modeled in TRIM.FaTE. Both the general form (Section
2.2.1) and the fugacity-based form (Section 2.2.2) are described below.
2.2.1 GENERAL FORM
Following common practice, the volume fractions of each phase are denoted as follows:
liquid
* Total
= 9 (Eq. 2-37)
gas
—=£ (Eq.2-38)
"
Total
77
' solid
T/
* Total
•=\-6-e=\-$ (Eq. 2-39)
where:
6 = (theta) volume fraction liquid (/.e., water) (unitless);
e = (epsilon) volume fraction gas ( i.e., air) (unitless);
\-6-e = volume fraction solid (i.e.., 1- 0) (unitless); and
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CHAPTER 2
ALGORITHM OVERVIEW
Table 2-1
Phases Explicitly Modeled in TRIM.FaTE by Abiotic Compartment Type
Type of Abiotic
Compartment
Air
Soil (surface,
root-zone, and
vadose zone
soils)
Ground water
Surface water
Sediment
Phases Modeled
in TRIM.FaTE
Solid
Gas
Solid
Liquid
Gas
Solid
Liquid
Solid-algae
Solid-other
Liquid
Solid
Liquid
Description
Airborne particles, where particles can
aerosols, or water droplets
be solids,
Vapors/gases in air
Soil particles
Soil pore water
Vapors/gases in soil air spaces
Soil particles
Soil pore water
Suspended algal cells/particles
Suspended sediments (particles other
than algae)
Water (excluding suspended sediments and algae)
Sediment particles
Sediment pore water
Using Equation 2-8, the equation for the total mass of chemical in the compartment and in the
different phases is then given by:
Tot
tal ~ ^liquid X V Total X
H
RXT
+ 0+ psolld*KdxCFx (1 -)
(Eq. 2-40)
If there are other phases in equilibrium with the chemical in the liquid (aqueous) phase, then the
previous equation is augmented as follows:
AT _ f y I/ Y
1V Total *- liquid A ' Toto/ A
/
H
(RXT
•x
psolld x Kd x Cf x 1 -
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CHAPTER 2
ALGORITHM OVERVIEW _
\l/j = volume fraction of compartment composed of phase 7 (m3[phase/|/
m3[total]).
2.2.2 FUGACITY-BASED NOTATION
If fugacity -based notation is to be used, then the total fugacity of the chemical in the total
compartment is given by:
ZTotal = Zair x e + Zmter x 0 + ZsoM x (1 - 0) (Eq. 2-42)
In the general case when there are additional equilibrium phases (up to m phases) considered:
ZTotal = Zair x e + Zwater x 0+ ZsoM x (1 - 0- ¥l) + Z, x ¥l (Eq. 2-43)
1=1 1=1
where:
Zt = fugacity capacity of the chemical in phase / (mol/m3-Pa).
NOTE: For the ground water, surface water, and sediment compartment types, the volume
fractions in the gas phase (e) are assumed to be zero.
The soil/water partition coefficients (Kd) in each compartment (the various soil, ground
water, surface water, and sediment compartments) may be either input or calculated. At present,
they are input for mercury species and calculated for nonionic organic chemicals (Karickhoff
1981) by:
Kd = Koc x foc (Eq. 2-44)
where:
Kd = soil/water partition coefficient (g[chemical]/kg[soil wet wt] per
g[chemical]/L[water] or L[water]/kg[soil wet wt]);
Koc = organic carbon/water partition coefficient (g[chemical]/kg[organic carbon]
per g[chemical]/L[water]); and
foc = fraction of organic carbon in the total compartment (kg[organic
carbon]/kg[soil wet wt].
2.3 APPROACH FOR AIR
Because the volume of water in an air compartment is so small relative to the volumes of
the solid and gas phases, there has not been a historical development of Kds (i.e., ratio of
concentration in the solid phase to that in the dissolved phase) for the atmosphere, although the
concept still applies. Instead, often the solid and gas phases only are addressed for the air
compartment. In TRIM.FaTE, solid particles and water (or chemical) droplets in clouds or mists
are all modeled as solid particles in the air (i.e., dust).
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Section 2.3.1 describes the equations for multiphase partitioning in the air compartment
type, and Section 2.3.2 describes two different approaches to calculating the fraction of chemical
that is bound to air particles.
2.3.1 MULTIPHASE PARTITIONING IN THE AIR COMPARTMENT TYPE
If chemical equilibrium is assumed between the solid and gas phases in air (liquid phase
is considered absent), then a normalization other than to the liquid concentration is required.
Section 2.3.1.1 describes the general approach, while Section 2.3.1.2 describes the fugacity-
based approach.
2.3.1.1 General Approach
At present, the volume fractions in each phase in an air compartment are given by:
liquid
~ =0 (Eq.2-45)
V Total
* solid DL
VTotal PP
V r>
gas LJ T
* Total Pp
(Eq. 2-46)
(Eq. 2-47)
where:
DL = atmospheric dust particle load in the air compartment (kg[dust particles]/
m3[air]), where dust could include any type of aerosol; and
pp = density of dust particles (kg[particles]/m3[particles]).
The dust load and density are specified properties of each air compartment. To normalize
to either the gas or solid phase, the equilibrium ratio of the concentrations in the two phases must
be estimated. The fraction of the chemical bound to particles is denoted by f here and by
Fraction Mass Sorbed in the air compartment of TRIM.FaTE. It is estimated using a method
developed by Junge (1977) for organic chemicals, and a more recent method developed by
Harner and Bidleman (1998) that is applied for mercury, both of which are discussed in Section
2.3.2. Use of this term in the current notation yields:
solid X C solid (0
where:
SEPTEMBER 2002 2-13 TRIM.FATE TSD VOLUME II
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(p = fraction of chemical in the air compartment that is sorbed to particles in
air (unitless).
From this, the equilibrium ratio of the concentration in the solid phase to that in the gas phase in
an air compartment is given by:
CSoUd
gas
(Eq. 2-49a)
. 2_49b)
(Eq.2-49c)
(l- V T j. 1 /> » A -/—' r / jL/r> * ~ /> I .i-j' 7- / jL/n M \ 1 x
./ Oft?/ 5''-*^' ^ OIGL IV L, I 1 r / /^i §&S V L, I i r / I
/ >V1 \/ / 1 / ) / y^ \ 1
= ^ga, x Froto/ X (1 - DL jpp ) + ——— L — X (DL /pp ) (Eq. 2-50b)
= Cgas x VTotal x\(l-DL/pp)+ ^X Q_^PP } (Eq. 2-50c)
= C,a, X Froto/ X (1 - DL lpp ) X ^ 1 + ~^—^ (Eq. 2-50d)
2.3.1.2 Fugacity-based Notation
For the air compartment, the fugacity capacity in the solid phase can be determined by
use of the relationship as follows:
z«*d = Za,r x -^ (Eq. 2-5la)
where:
SEPTEMBER 2002 2-14 TRIM.FATETSD VOLUME II
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Zair
3
R = ideal gas constant (8.3 14 m3-Pa/mol-K); and
T = temperature (°K).
The total fugacity in the air compartment is then given by:
V T/
7 7 •- g"S . 7 .. V solid
z Total = za,r X T7 - + Zsoi,d x y - (Eq. 2-52a)
' Total ' Total
= Zair x(\-DL/Pp) + ZsoM X (DL lpp ) (Eq. 2-52b)
2.3.2 CALCULATION OF THE FRACTION OF CHEMICAL BOUND TO AIR
PARTICLES
The fraction of chemical bound to particulate in the air compartment, denoted by (p, can
be calculated using one of two methods. The first method is the KOA-based method discussed in
Harner and Bidleman (1998) (Section 2.3.2.1), while the second is from Junge (1977) (Section
2.3.2.2). The current TRIM.FaTE library includes the method of Harner and Bidleman (1998).
Note that in each of these methods, a chemical with extremely low or essentially zero vapor
pressure (e.g., cadmium, lead) is assumed to be 100 percent bound to parti culate matter in the
air.
2.3.2.1 KoA-based Method
In Harner and Bidleman (1998), a "KOA adsorption model" is shown to fit to PCB data
better than a Junge-Pankow model similar to the Junge (1977) model. Further, the parameters
needed are considered to be more easily measurable than the parameters for the Junge-Pankow
model. This KOA model is in the current TRIM.FaTE library. Using the notation of Harner and
Bidleman (1998), the KOA model first estimates the particle/gas partition coefficient (KP) in terms
of the octanol/air partition coefficient and the fraction of organic matter attached to particles. It
then calculates the fraction of chemical in the particle phase via the relationship:
Kp x TSP
where:
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CHAPTER 2
ALGORITHM OVERVIEW
Using the notation of this section, the following relationship exists:
TSP=\09xDL (Eq. 2-54)
where:
DL = the dust load for the air compartment (kg[particles]/m3[air]).
The particle/gas partition coefficient, KP, is calculated via the regression-based equation:
log(^) = \og(KOA) + \og(fom) - 11.91 (Eq. 2-55)
where:
KP = particle/gas partition coefficient (g[chemical]/kg[particles] per
g[chemical]/m3[air] or m3[air]/kg[particles]);
KOA = octanol/air partition coefficient (g[chemical]/m3[octanol] per
g[chemical]/m3[air] or m3[air]/m3[octanol]); and
fom = fraction of dust comprised of organic material (on a weight basis;
unitless).
In the current TRIM.FaTE library representation of the formula for KP, \og(fom) is replaced by
\og(fom + IE-10) to prevent a log(zero) computer error if the user inputs zero as the value for the
fraction of organic matter in the particles.
If the octanol/air partition coefficient is not available, it can be calculated from the
octanol/water partition coefficient Kow (g[chemical]/kg[octanol] per g[chemical]/L[water] or
L[water]/kg[octanol]) via the relationship:
KOA = Kow x —^ (Eq. 2-56)
RxT
H
where the of R, T, and H are such that the quantity R*T/His unitless.
2.3.2.2 Junge's Method
This method has been used in multimedia models, including prototype versions of
TRIM.FaTE. It is not included in the TRIM.FaTE library for the reasons listed at the beginning
of Section 2.3.2.1. The following discussion is based on that presented in CalTOX (McKone
1993a,b,c). With this method, the fraction of chemical bound to dust particles (or aerosol) is
calculated via the formula:
_ ex SA
where:
Pvapor = vapor pressure or subcooled vapor pressure of the chemical (Pa);
c = empirical constant set to 0.173 (m-Pa) as in Junge (1977); and
SEPTEMBER 2002 2^16 TRIM.FATE TSD VOLUME II
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ALGORITHM OVERVIEW
SA = total surface of aerosols per volume of dust or aerosol particles
(m2[surface]/m3[particles]) (denoted by 6 in CalTOX).
There is a range of values for SA. Whitby (1978) reported a range of 4.2xlO"5 m2/m3 for a
"clean" continental site to l.lxiO"5 m2/m3 for urban sites.
Following CalTOX (McKone 1993a,b,c), the subcooled vapor pressure (i.e., vapor
pressure of subcooled liquid) is used if the temperature is below the melting point (Tm~) of the
chemical. In particular:
{D '-f T T
vapor J m ^ ~ ™x
exp[6.79(7;/r-l)] if T < Tm W-**)
where:
Pvapor = vapor pressure or subcooled vapor pressure of the chemical (Pa);
T = temperature (°K); and
Tm = melting point (°K).
2.4 GENERAL FATE AND TRANSPORT PROCESSES
This section provides a brief overview of the forms of the algorithms used to calculate the
T-factors in TRIM.FaTE for advective processes (Section 2.4.1), diffusive and dispersive
processes (Section 2.4.2), reaction and transformation processes (Section 2.4.3), and biotic
processes (Section 2.4.4).
2.4.1 ADVECTIVE PROCESSES
In general, the advective flux for a given phase (e.g.., attached to particles, or dissolved in
water) from compartment /' to compartment y is given by:
Advective flux from compartment i to compartment] =
(Volume of phase that moves from compartment i to compartment j per unit time) x ^ o sg\
(Amount of chemical in phase per volume of phase in compartment i)
or:
Advective Flux Compartment i -» Compartment j = Q(phase) x —' '— (Eq. 2-60a)
= T°?j (phase) x N, (f) (Ecl- 2-60b)
where:
Q(phase) = volumetric flow of phase from compartment /to compartment 7
(m3[phase]/day);
Nt(t) = amount of chemical in compartment /' at time (g[chemical]);
SEPTEMBER 2002 2^17 TRIM.FATE TSD VOLUME II
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f/phase) = fraction of chemical in compartment /' that is in the moving phase
(g [chemical in phase]/g[chemical in compartment /']);
Vt(phase) = volume of phase that is in compartment / (m3[phase]); and
T°fj (phase) = phase transfer factor for advective flux from compartment / to
receiving compartment y' (/day), given by:
x f, (phase)
' (Eq.2-61)
This formula for the transfer factor is valid for all advective processes from one
compartment to another, and it does not rely on the fugacity concept.
Application of the concept of fugacity (as presented in Section 2.1.3.2) shows that:
Z, ( phase) V, ( phase)
where:
Zt(phase) = fugacity capacity for moving phase (mol/m3 [phase]-Pa);
Zt(Total) = total fugacity capacity for compartment /' (mol/m3[sending compartment
/]-Pa); and
Vt(Total) = total volume of compartment / (sum of volumes of each phase in
compartment) (m3[compartment /']).
Applying this shows that the fugacity-based form for the transfer factor for advective flux
is:
T"* (phase) =
Vt(Total)xZt(Totat)
(Eq. 2-63)
vtj (phase) x Atj x Z. (phase)
Vt(Total) xZ,(Total)
where:
vtj = volumetric flow rate per unit area or flow velocity (m3[phase]/m2[relevant
area]-day or m/day); and
AJJ = area of interface between compartments / andy (m2)-
In most advective transfers between compartments, the volumetric flow rate Q(phase) of
the phase is calculated as the product of a relevant area (Ay) and the volumetric flow rate per unit
area, or a flow velocity (vfj). Usually the relevant area is the interfacial area between the sending
and receiving compartments, but this is not always the case; e.g., erosion from surface soil to
SEPTEMBER 2002 2^18 TRIM.FATE TSD VOLUME II
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ALGORITHM OVERVIEW
surface water is usually reported in units of mass[soil]/area[soil layer]-time, in which case the
relevant area is the surface area of the surface soil layer. Table 2-2 at the end of this chapter
summarizes the advective volumetric flows included for compartment types in TRIM.FaTE.
These flows are discussed in more detail in the chapters describing the specific compartment
types.
2.4.2 DIFFUSIVE AND DISPERSIVE PROCESSES
In TRIM.FaTE, dispersion is explicitly addressed as a first-order process in transfers
between surface water compartments and applies to the chemical in both liquid and solid phases.
Modeling of dispersion has not been implemented for transfers between air compartments or for
movement of a chemical through soils, either vertically or horizontally.
Diffusive processes are modeled in TRIM.FaTE for transfers between many different
compartment types (see TSD Volume I). T-factors developed for diffusive processes between
compartments often apply to the chemical found in only one of the phases in a compartment
(e.g., diffusion from air to surface water applies only to the vapor phase of the chemical in air).
T-factors developed for diffusion between abiotic and biotic compartments also depend on
characteristics, including the conductance, of the boundary layers between the two
compartments.
2.4.3 REACTION AND TRANSFORMATION PROCESSES
At present, all reaction and transformation processes are modeled using a first-order rate
constant k (units of I/day). The reaction/transformation flux within a compartment is then given
by kN(t), where N(t) is the mass of chemical in the compartment. There are a variety of ways in
which the rate constant is determined, with the details depending on the compartment types and
chemicals involved. The simplest is the case where the rate constant is an input (e.g., for the
current mercury species transformation algorithms).
In other cases, the rate constant for an organic chemical reaction can be calculated from
other environmental and/or chemical parameters (e.g., from a half-life input by the user). In the
current TRIM.FaTE library, a "degradation" rate constant, kdegradation (/day), for organic chemicals
is calculated as:
k degrade = to(2) / half-life (Eq. 2-64)
Whenever a chemical is transformed into reaction products that are no longer tracked in
TRIM.FaTE, the mass of the chemical is transferred to a "reaction/degradation sink" for the
compartment in which the transformation occurs. This is accomplished by setting a one-way
transfer factor from the compartment to the compartment degradation sink as equal to the
degradation rate constant, kdegradation.
Comp^Comp_Sink ~ degradation \ )
SEPTEMBER 2002 2-19 TRIM.FATE TSD VOLUME II
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ALGORITHM OVERVIEW
where:
Tcomp^comp sink = transfer factor from compartment to compartment degradation sink
(/day).
2.4.4 BIOTIC PROCESSES
The biotic processes in TRIM.FaTE are well characterized by the descriptions of abiotic
processes and conversions. Diffusive processes and advective processes are both included. The
primary instance of advection is dietary uptake. Another prominent example is litter fall.
Fugacity is used as a descriptor in algorithms where it is convenient (e.g., in the uptake of
contaminants by foliage from air). Because mechanisms of uptake of contaminants by some
organisms are not well understood or are difficult to parameterize, some partitioning processes
are assumed to be equilibrium relationships according to the form described in Section 2.5 (next
section). These processes may be combinations of diffusion, active transport, and/or advection
(e.g., transport of contaminants into the plant root), and it is not necessary for the user to specify
the mechanistic process, only the empirical relationship (e.g., partition coefficient and time to
equilibrium).
As with abiotic reactions and transformations (Section 2.4.3), biotic transformation rates
are also described as first-order processes with respect to the average chemical concentration in
the particular compartment of concern.
2.5 CONVERTING EQUATIONS WITH EQUILIBRIUM
RELATIONSHIPS TO DYNAMIC FORM
In the course of converting equations to a form suitable for use within the intended
TRIM.FaTE framework, it is possible to convert some algorithms that represent steady-state
equilibrium relationships into time-dependent ones. This can be accomplished if an estimate of
the time required for the concentration to reach some fraction of the equilibrium value is
available. In particular, if the concentration in one compartment C, is related to the
concentration in another compartment C2 by an equilibrium relationship of the form C, = K *C2,
where K is known and it is known that it takes time ta in order to reach 100 a percent of the
equilibrium value when C2 is approximately constant, then:
2xC2)-(MQ) (Eq.2-65)
Ull
where:
_ - ln(l - a) (Eq. 2-66)
k2 = K x k1 (Eq. 2-67)
and where:
SEPTEMBER 2002 2^20 TRIM.FATE TSD VOLUME II
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CHAPTER 2
_ ALGORITHM OVERVIEW
a = proportion of the equilibrium concentration reached in time ta (unitless);
ta = time required to reach lOOa percent of equilibrium value (days); and
K = ratio of the concentration of the chemical in compartment 1 to its
concentration in compartment 2 (g[chemical]/m3[compartment 1] per
g[chemical]/m3[compartment 2]).
The value for a used as a default in TRIM.FaTE is 0.95, meaning that ta is the time to
reach 95 percent of the equilibrium concentration value. The precision and accuracy of
empirical data available to estimate ta decreases with increasing values for a.
The solution of the previous differential equation with initial condition Cj(0) = 0 is given
by:
Q(0 = 7^(1-^) (Eq.2-68)
R\
The steady-state equilibrium solution is C^ft) = (k2/k-J C2, and so K = k2/kl. The
assumption that 1 00 x a percent (e.g., 95 percent) of the equilibrium value is reached at time ta
means that:
l-e-^" = a (Eq. 2-69)
Solving for k\ yields:
kl = -\n(\-a)/ta (Eq. 2-70)
When kl is determined, given K, k2can be determined (i.e., Equation 2-67, k2 = klx K).
2.6 RELATING FUGACITY AND EQUILIBRIUM NOTATIONS
In developing code for TRIM.FaTE, there were some equations that were most easily
developed using fugacity notation and others that were most easily developed using ratios of
fractions related to phases in a compartment. This section demonstrates the equivalence of
certain fugacity expressions to certain phase-related ratios that are commonly used in the
TRIM.FaTE code. Specifically, this section demonstrates that:
Mass Fraction Sorbed/Volume Fraction Solid = Zsolic/ZTotal (Eq. 2-71)
Mass Fraction Dissolved/Volume Fraction Liquid = ZvatJZTotal (Eq. 2-72)
Mass Ft -action Vapor '/Volume Ft -action Vapor = Zai/ZTotal (Eq. 2-73)
where:
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Mass Fraction Sorbed = fraction of the chemical mass in the total compartment
that is sorbed to the solid phase material in the
compartment (unitless);
Volume Fraction Solid = volume fraction of the total compartment that is solid or
particulate (unitless);
Mass Fraction Dissolved = fraction of the chemical mass in the total compartment
that is dissolved in the liquid-phase material (i.e.,
water) in the compartment (unitless);
Volume Fraction Liquid = volume fraction of the compartment that is liquid (i.e.,
water) (unitless);
Mass Fraction Vapor = fraction of the chemical mass in the total compartment
that is in vapor phase (unitless); and
Volume Fraction Vapor = volume fraction of the compartment that is vapor/gas
phase (i.e., air) (unitless).
Starting with:
( Dr]
Z,M = Zmr X —^ (Same as Eq. 2-51)
PP
an equation for ZOT>can be derived:
DT
Zair = ZsoM X -, -^- (Eq. 2-74)
0x 1- L}
Pp)
where:
Zair = fugacity capacity of chemical in gas-phase air (mol/m3-Pa);
Zsolid = fugacity capacity of chemical in solid-phase (mol/m3-Pa);
DL = atmospheric dust load in the air compartment (kg[dust]/m3[air
compartment]), where dust could include any type of aerosol;
pp = density of dust particles (kg[dust]/m3[dust]); and
(p = fraction of chemical in the air compartment that is sorbed to particles in
air (unitless).
It is also true that:
L L
ZTotal = Zair x 1 - -^ + Zsohd x -±-\ (Eq. 2-75)
V v Pp') \ Pp'
Using Equation 2-74 to replace Zair in Equation 2-75 yields:
SEPTEMBER 2002 2-22 TRIM.FATETSD VOLUME II
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ALGORITHM OVERVIEW
P DL DL
ZTotal = Zsolld X - -( - y X 1 - -f- + ZsoM X -M (Eq. 2-76)
x LAJ v /v v /v
I pp)
The term (l-DL/pP~) divided by (\-DL/pp) equals one; therefore, Equation 2-76 can be rewritten
as:
A A
X —- X -f + -f
PP PP
= Z x LX (Eqs- 2-77b, 2-77c)
= z xx (Eq.2-77d)
sohd pp = Mass Fraction Sorbed; and
(DL/PP) = Volume Fraction Solid.
Thus:
Zsolid/ZTotal = Mass Fraction Sorbed / Volume Fraction Solid. (same as Eq. 2-7 1 )
Similar derivations demonstrate that:
Zwate/ZTotal = Mass Fraction Dissolved / Volume Fraction Liquid. (same as Eq. 2-72)
and:
Zai/ZTotal = Mass Fraction Vapor/Volume Fraction Vapor (same as Eq. 2-73)
where:
7 =7
air vapor'
SEPTEMBER 2002 2^23 TRIM.FATE TSD VOLUME II
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ALGORITHM OVERVIEW
To simplify equations in Chapters 3 through 7, the variables^, fML, and^Fare defined
as follows:
fMS = Mass Fraction Sorbed / Volume Fraction Solid (Eq. 2-79)
fML = Mass Fraction Dissolved/ Volume Fraction Liquid (Eq. 2-80)
fMV = Mass Fraction Vapor/Volume Fraction Vapor (Eq. 2-81)
To ensure clarity in the presentation of equations throughout the remainder of this TSD,
the following naming conventions have been used:
Zpure air = Zair for fugacity capacity of the chemical vapor in gas-phase air
excluding atmospheric dust particles;
ZTotal Air = total fugacity capacity of chemical in bulk air, including
atmospheric dust particles;
Zpure water = Zwater f or fugacity capacity of the chemical dissolved in liquid-
phase water excluding suspended sediment particles;
Z Total sw = total fugacity capacity of chemical in bulk surface water, including
suspended sediment particles;
ZpUre Soiid = Zsolidfor fugacity capacity of the chemical in or sorbed to solid
particles; and
Z Total s* = total fugacity of chemical in a bulk soil compartment, including the
gas/vapor (air) and liquid (water) phases in the interstitial spaces,
where the subscript Sx equals Ss for surface soil, Sr for root-zone
soil, and Sv for vadose-zone soil.
2.7 TRIM.FaTE CODE FOR DISTRIBUTION OF CHEMICAL AMONG
PHASES
Tables 2-3a and 2-3b at the end of this chapter provide the equations in the current
TRIM.FaTE library for calculating the distribution of chemical mass among phases in each
abiotic compartment type, i.e.:
Fraction Mass Dissolved, the fraction in the aqueous liquid phase;
Fraction Mass Sorbed, the fraction in the solid phase;
Fraction Mass Vapor, the fraction in the vapor phase; and
Fraction Mass Algae, the fraction in algae.
All abiotic compartment types include a solid phase and hence the property
Fraction Mass Sorbed. The property Fraction Mass Algae is included only in the surface
water compartment. The air compartment does not include a liquid phase or the property
Fraction Mass Dissolved. The surface water, sediment, and ground water compartments do not
include a vapor/gas phase or the property Fraction Mass Vapor.
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ALGORITHM OVERVIEW
Each of the equations in Tables 2-3a and 2-3b are simply compartment-specific versions
of the general equations developed earlier in this chapter. The definitions of the parameters in
both tables are listed below:
as:
1000
Vsw
VSed
vs
6
KP
Kd
RatioConc
Psed
Ps
AC
Algae
Z,
pure_air
-'pure^vater
= units conversion factor (L/m3);
= volume of the surface water compartment (m3);
= volume of the sediment compartment (m3);
= volume of the soil (or ground water) compartment (m3);
= volume fraction liquid (i.e.., water) (unitless);
= total porosity (i.e. 0+ e) (unitless);
= volume fraction gas (i.e., air) (unitless);
= particle/gas partition coefficient (m3[air]/kg[particles]);
= soil/water partition coefficient (L[water]/kg[soil wet wt]);
•Mgae = ratio of the concentration of chemical in algae to the concentration
of chemical in surface water (excluding suspended sediments)
(unitless);
= density of sediment particles (kg[particles]/m3[particles]);
= density of soil particles (kg[particles]/m3[particles]);
= atmospheric dust load in the air compartment (kg[dust particles]/
m3[air]);
= algal concentration (density) in the water column
(g [algae]/m3 [water]);
= volume fraction of the surface water compartment comprised of
algae (unitless), i.e., Volume Fraction Algae;
= fugacity capacity of chemical in air (excluding atmospheric dust
particles) (mol/m3-Pa); and
= fugacity capacity of chemical in water (excluding suspended
sediment particles) (mol/m3-Pa).
The volume fraction of the surface water compartment that consists of algae is estimated
M
Algae
(Eq. 2-82)
where:
VjAlgae
CA =
1000 =
volume fraction of surface water compartment that is algae
(m3[algae]/m3[surface water], unitless);
algae concentration (density) in water column (g[algae]/L[water]);
density of algae (g[algae]/m3[algae]); and
conversion factor (L/m3).
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Table 2-2
Summary of Advective Volumetric Flows Included in TRIM.FaTEab
Source/
Sending
Compartment
Soil
Receiving
Compart-
ment
Soil
or Soil Sink
Moving
Phase
Liquid
Solid
Description of
Advective
Process
Runoff
(surface soil
only)
Precipitation
driven
percolation
Erosion (surface
soil only)
Units of
Moving Phase
m3[water]/day
m3[water]/day
m3[soil
particles]/day
Method for Calculation of
Volumetric Flow (Q)
= ASs x runoff
where:
ASs = Area of surface soil layer (m2)
runoff = Amount of runoff that reaches adjacent downgradient
surface soil parcel per unit area of sending soil parcel
(m3[water]/m2[area]-day)
= A x vliquid
where:
A = Area of soil/soil interface (m2)
vuquid = Velocity of water (vertical) in sending soil compartment
(m3[water]/m2[area]-day)
Calculated from mass-based areal erosion rate and soil density:
= ASs x erosion / pp
where:
ASs = Area of surface soil layer (m2)
erosion = erosion rate to adjacent downgradient surface soil parcel
(kg [soil]/m2[area]-day)
pp = density of eroding soil particles (kg[particles]/m3[soil])
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ALGORITHM OVERVIEW
Source/
Sending
Compartment
Soil
Ground Water
Receiving
Compart-
ment
Air
Surface
Water
Ground Water
Surface
Water
Moving
Phase
Solid
Solid
Liquid
Liquid
Liquid
Description of
Advective
Process
Resuspension
Erosion
Runoff
Percolation
Recharge
Units of
Moving Phase
m3[soil
particles]/day
m3[soil
particles]/day
m3[water]/day
m3[water]/day
m3[water]/day
Method for Calculation of
Volumetric Flow (Q)
It is assumed that volumetric flow of particles from soil is the same as
that to soil. Volumetric resuspension rate is then
= volumetric flow to soil = A x vdry x (DL/ pp)
where:
A = Area of soil/soil interface (m2)
vdry = Dry deposition velocity of particles (m/day)
DL = Atmospheric dust load in air compartment type
(concentration of dust in air) (kg[particles]/m3[air])
pp = Density of dust particles (kg[particles]/m3[particles])
Calculated from mass-based areal erosion rate and soil density:
= ASs x erosion / pp
where:
ASs = Area of surface soil layer (m2)
erosion = Erosion rate to surface water (kg[soil]/m2[area]-day)
pp = Density of eroding soil particles (kg[particles]/m3[soil])
= ASs x runoff
where:
A = Area of soil layer (m2)
runoff = Amount of runoff that reaches water body per unit area of
watershed (m3[water]/m2[area]-day)
= A x percolation
where:
A = Area of vadose-zone soil interface with the ground
water compartment ( m2)
percolation = Volume of water flow per unit area of interface
(m3[water]/m2[area]-day)
= A x recharge
where:
A = Area of ground water soil/surface water interface ( m2)
recharge = Volume of water flow per unit area of interface
(m3[water]/m2[area]-day)
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Table 2-2 (continued)
Summary of Advective Volumetric Flows Included in TRIM.FaTEab
Source/
Sending
Compartment
Air
Air
Receiving
Compart-
ment
Surface Soil
or Surface
Water
Air or Air
Advection
Sink
Plant Leaf
(no rain)
Moving
Phase
Solid
Gas and
solid
Solid
Description of
Advective
Process
Dry and Wet
deposition of
particles
Wind advection
Dry deposition
of particles
Units of
Moving Phase
m3[dust
particles]/day
m3[air]/day
m3[dust
particles]/day
Method for Calculation of
Volumetric Flow (Q)
= A x i/dryx DL /pp (dry dep.); =A* i/wdx DL / pp (wet dep.);
where:
ASs = Area of surface soil layer (m2)
vdiy = Dry deposition velocity of particles (m/day)
Kvet = Wet deposition velocity of particles (m/day)
DL = Atmospheric dust load in air compartment type
(concentration of dust in air) (kg[particles]/m3[atmosphere])
pp = Density of dust particles (kg[particles]/m3[particles])
= A x i/w/nd
where:
A = Area of air/air interface (m2)
Kif/nd = Wind velocity from sending to receiving air compartment
(m/day)
= As x ldry x vdry x (DL/ pp)
where:
As = Area of soil layer containing plant (m2)
ldry = Interception fraction for dry-depositing chemical (see
Section 7.2 for description of algorithm)
vdry = Dry deposition velocity of particles (m/day)
DL = Atmospheric dust load in air compartment type
(concentration of dust in air) (kg[particles]/
m3[atmosphere])
pp = Density of dust particles (kg[particles]/m3[particles])
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ALGORITHM OVERVIEW
Source/
Sending
Compartment
Surface Water
Surface Water
Sediment
Receiving
Compart-
ment
Plant Leaf
(during rain)
Sediment
Surface
Water
Surface
Water
Moving
Phase
Solid
Solid
Liquid and
solid
Solid
Description of
Advective
Process
Wet deposition
of particles
Sediment
deposition
Water flow
Sediment
resuspension
Units of
Moving Phase
m3[dust
particles]/day
m3[suspended
sediment
particles]/day
m3[water]/day
m3[benthic
sediment
particles]/day
Method for Calculation of
Volumetric Flow (Q)
= As x lwet x i/wefx (DL/ pp)
where:
As = Area of soil layer containing plant (m2)
lwet = Interception fraction for wet-depositing chemical (see
Section 7.2 for description of algorithm)
Kvet = Wet deposition velocity of particles (m/day)
DL = Atmospheric dust load in air compartment type
(concentration of dust in air) (kg[particles]/
m3[atmosphere])
pp = Density of dust particles (kg[particles]/m3[particles])
~ ^SW-sed * Sdep / Pssed
where:
Asw-sed = Area of surface water-sediment interface (m2)
Sdep = Deposition rate of suspended sediment particles to
sediment bed (kg[suspended sediment]/m2[area]-day)
Pssed = Density of suspended sediment (kg[suspended sediment]/
m3[suspended sediment])
= /\x VR
where:
A = Area of river parcel interface (m2)
VR = River velocity from sending to receiving river compartment
(of same interfacial areas) (m/day), OR
= Flow , where
Flow = volumetric bulk water flow rate (m3[water]/day) for
connecting water bodies of different interfacial areas
~~ "sed-SW * ^resusp ' Pbs
where:
ASed-sw = Area of sediment-surface water interface (m2)
Spesusp = Resuspension rate of benthic sediment particles to water
column (kg[benthic sediment particles]/m2[area]-day)
pbs = Density of benthic sediment (kg[benthic sediment
particles]/m3[benthic sediment particles])
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Table 2-2 (continued)
Summary of Advective Volumetric Flows Included in TRIM.FaTEab
Source/
Sending
Compartment
Receiving
Compart-
ment
Sediment
Burial Sink
Moving
Phase
Solid
Description of
Advective
Process
Sediment burial
Units of
Moving Phase
m3[(benthic
sediment
particles]/day
Method for Calculation of
Volumetric Flow (Q)
Calculated so that amount of sediment buried is equal to maximum of 0
and amount deposited minus amount resuspended:
= Ased_sw x max{ 0, Sde/pss - Sresus/pBSed}
where:
ASed-sw = Area of sediment-surface water interface (m2)
Sdep = Deposition rate of suspended sediment particles
to sediment bed (kg[suspended sediment]/m2[area]day)
pss = Density of suspended sediment (kg[suspended
sediment]/m3[suspended sediment])
SKSUSP = Resuspension rate of benthic sediment to water column
(kg[benthic sediment]/m2[area]-day)
Pasea = Density of benthic sediment (kg[benthic
sediment]/m3[benthic sediment])
" Advection of chemicals to and from plants in particles and rain water and advection of chemicals to and from wildlife in dietary and excretory materials are not
included. See Chapter 7.
b Equations for estimating chemical partitioning among phases are not included in this table. See individual chapters related to each type of transfer.
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Table 2-3a
Equations for Estimating Chemical Mass Distribution Among Phases: Air and Surface Watera
Compartment Property
Fraction Mass Dissolved
Fraction Mass Sorbed
Fraction Mass Vapor
fraction Mass Algae
GenericDenominatorfor
PhaseCalculations, or
GenDenom
AIR
NA, assume no liquid phase in air
/ \
1
[l+(^xZ)LxlE9(//g/kg))J
=1 -Fraction Mass Sorbed
NA, no algae in air
NA, not used
SURFACE WATER
vsw*o
GenDenomsw
Vsw x(l-0)xKdx psed x 0.001 (m3/L)
GenDenomsw
NA, assume no gas/vapor phase in surface water
Vsw x JVAlgae x RatioConcAlgae(g/m3)x 0.001(m3/L)
GenDenomsw
= Vsw X (JVAlgae X RatioConcAlgae X ^C(g/m3) X 0.001 (m3/L)
+ (1 - 0} X Kd X psed X 0.001 (m3/L) + 0}
a For parameter symbol definitions, see text of Section 2.7.
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Table 2-3b
Equations for Estimating Chemical Mass Distribution Among Phases: Sediments, Soil, and Ground Water"
Compartment Property
Fraction Mass Dissolved
Fraction Mass Sorbed
Fraction Mass Vapor
Fraction Mass Algae
GenericDenominatorfor
PhaseCalculations, or
GenDenom
SEDIMENT
Vsed x 0
GenDenomSed
vsed x (1 - 0) x Kd x psed x 0.001 (m3/L)
GenDenomSed
NA, assume no gas/vapor phase in sediments
NA, assume no algae in sediments
= Vsed x (1 - 0) x Kd x psed x 0.001 (m3/L)
+ V x 9
+ V Sed X ^
SOIL and GROUND WATER
Vs X 0X 1000
GenD*,™,,
F5 x(Kdxps)x(l- 6- e)
GenDenoms
( Zp,re ., }
77 v> f.^, '\c\c\r\^'
v s X £ X 1UUU X
V pure water J
GenDenoms
NA, no algae in soil or ground water
Z
( n^' 1 OOO^ -L ^ c?" P"re_air AArVi^
(^ I/ A 1 UUUj + (^ £ A A 1 UUUJ J
pure water
' For parameter symbol definitions, see text of Section 2.7.
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3. AIR ALGORITHMS
In this chapter, the algorithms for the horizontal transport of chemical species between air
compartments and those for diffusion/volatilization between air compartments and surface water
are presented. A description of deposition from air compartments to surface water can be found
in Chapter 4, and a description of the transport processes between air compartments and soil can
be found in Chapter 5. The text box on the next page provides a summary of the T-factor
algorithms developed in this chapter and definitions of the parameters used in those algorithms.
3.1 AIR-TO-AIR ALGORITHMS
For a given wind speed and direction, there are two types of transfer processes that
account for the majority of chemical mass that moves from one air compartment to another:
• Advective transfer (bulk) due to the component of the wind vector normal to the
boundary between the compartments; and
• Dispersive transfer (bulk) calculated from the component of the wind vector
parallel to the boundary between the compartments.
The total transfer factor from one air compartment to an adjacent air compartment is the sum of
these two transfers.
The current TRIM.FaTE library incorporates only the advective transfer due to the wind
vector normal to the boundary between compartments. This is because of the complexity and
technical challenges related to the representation of dispersive transfers in a compartment-based
modeling system such as TRIM.FaTE. Note that diffusion between air compartments is
considered negligible and thus is not included in TRIM.FaTE.
Let Air Rev and Air Send denote the adjacent receiving and sending air compartments.
If the boundary between the two air compartments is composed of n distinct line segments, then
the transfer factor from the sending to the receiving air compartment is calculated as:
4 x (u^ +u(tL}) (Eq. 3-1)
TT
*Send t=l
where:
Vsend = volume of the sending air compartment (m3);
Ai = interfacial area across /'th boundary (m2);
u/D) = direct (D) advective wind velocity across the /'th boundary (m/day); and
u{L> = lateral (L)/dispersive wind velocity across the /'th boundary (m/day).
The direct wind flow across an air compartment boundary (notation u/D) is used above) is
calculated by finding the projection of the wind vector onto the normal vector to the boundary
between the air compartments.
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Summary of Transfer Factors for Air in TRIM.FaTE
AIR ADVECTION
Air compartment to air compartment: (TF 3-1)
1 "
Tadv - yV
1 Air _Send^ Air _Rcv ~ rr X Li
-IT
* Air _Send i=l
AIR DIFFUSIONA/OLATILIZATION
Diffusion from air compartment to surface water compartment: (TF 3-2)
If
SW y^ H/(RXT)
Volatilization from surface water compartment to air compartment: (TF 3-3)
Tvol _ ASWA k r
1SW^Air ~ T A Kv A J ML
SW
LIST OF SYMBOLS USED IN AIR TRANSFER FACTOR ALGORITHMS
VAir send = volume of the sending air compartment (m3).
A, = interfacial area across /th boundary (m2).
u/D; = direct advective wind velocity across the ;th boundary (rn/day).
ASWA = interfacial area between the surface water and air compartments (m2).
VM = volume of air compartment (m3).
kv = volatilization transfer rate (m/day).
H = Henry's law coefficient for the air-water partitioning of the chemical (atm-m3/mole).
R = universal gas constant (8.206x10"5 atm-m3/mole °K).
T = water temperature (°K).
fMV = fraction of chemical mass in the air compartment that is in the vapor phase divided by
the volume fraction of the compartment that is air (i.e., excluding particles) (unitless).
Vsw = volume of the surface water compartment (m3).
fML = fraction of chemical mass in the surface water compartment that is dissolved in water
divided by volume fraction of the surface water compartment that is water (i.e.,
excluding suspended sediments and algae) (unitless).
Let/1; = (x}, y,} andP2= (x2, y2) be the points defining the line that is the projection of the
boundary onto the xy-plane (i.e., the view from above the vertical plane defining the boundary).
It is assumed that the points P, and P2 are ordered so that the receiving compartment is on the
right side of the directed line segment starting atPj and ending at P2. The unit
vector v perpendicular to this line segment that is in the direction of the receiving compartment
is given by:
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(Eq. 3-2)
where:
(p = the angle measured clockwise from due north.
If the wind is blowing with speed u toward the direction ^(measured clockwise from due north),
then the wind vector, denoted by vP, can be written:
w = (u x cos(^/2 - t?), M x sin(^/2 - #)}
(Eq. 3-3)
= w^sin ^, cos ^/
The projection of the wind vector w onto v is just the dot product (w • v ) of the two
vectors, which is given by:
vP • v = i x [(_y2 - _yt) sin z? - (jc2 - jCj) cos z?J
I- 3-4)
!
cosz/cos^J
Since v is a unit vector, the dot product in this case is the component of the vector w in
the direction of v . The wind flow rate from the sending compartment to the receiving
compartment is defined to be the dot product if it is positive; otherwise, it is zero. In other
words:
Wind speed perpendicularto compartmentboundary = UL = max{0,«cos(^- (p)\ (Eq. 3-5)
If the wind is blowing perpendicular to the boundary (i.e., Air Rev ~ y " L-t ^i " \"i > (TF 3~1)
V Air Send i=l
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CHAPTER 3
AIR ALGORITHMS
TAi?_send^Air_Rcv = advective transfer factor for wind in air from sending (Send) to
receiving (Rev) air compartments (/day);
VSend = volume of sending air compartment (m3);
At = interfacial area across the /th boundary (m2); and
ui ^ = direct (D) advective wind velocity across the /'th boundary (m/day).
The advective transport can occur both horizontally, based on the horizontal component
of the wind speed, and vertically, based on the vertical component of the wind speed and the
stability class assigned to the air layers. The advective transport Equations 3-1 through 3-5 are
hard coded in the main TRIM.FaTE program. The transfer factor in the TRIM.FaTE library
passes the information on wind speed and direction to the main TRIM.FaTE program to solve
the equations. In initial applications of TRIM.FaTE involving only one layer of air
compartments, any chemical transported vertically out of the compartments goes to an air sink.1
If there is to be no vertical loss of chemical due to vertical advection to the air sink, the user can
set the vertical wind speed to zero.
Advective transport in air also can carry the chemical horizontally beyond the boundary
of the modeling domain to an air sink for the chemical mass. The transfer factor would be the
same as TF 3-1, except that the receiving compartment would be the air sink.
3.2 AIR-TO-SOIL ALGORITHMS
The algorithms describing the transfer of chemical mass between air and soil are
presented in Section 5.3.3.
3.3 AIR-TO-SURFACE-WATER ALGORITHMS
Several processes can move chemical mass between the air and surface water
compartments, including deposition (Section 3.3.1) and diffusion and volatilization (Section
3.3.2).
3.3.1 DEPOSITION
The algorithms describing the deposition of chemical mass from air to surface water are
presented in Section 4.2.1.
3.3.2 DIFFUSION AND VOLATILIZATION
Transfer of chemical between an air compartment and a surface water compartment can
occur by advection (i.e., wet and dry deposition of particle-bound chemical and wet deposition
of vapor-phase chemical). The advective transfers between air and surface water are described
in the surface water chapter (Chapter 4). The diffusion (and volatilization) transfer factors are
The single air layer can vary in height (i.e., mixing height) depending on environmental conditions.
SEPTEMBER 2002 3^4 TRIM.FATE TSD VOLUME II
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described in Section 3.3.2.1. Section 3.3.2.2 includes several methods available to calculate the
gas-phase transfer coefficient and the liquid-phase transfer coefficient.
3.3.2.1 Diffusion and Volatilization Transfer Between Air and Surface Water
The following describes the method used for estimating volatilization transfer between
air and surface water for any chemical that has a non-zero Henry's law constant. The method is
a two-layer resistance model first presented by Whitman (1923) and incorporated into the EPA
Water Quality Analysis Simulation Program (WASP) (Ambrose et al. 1995). The following
discussion is based primarily on the WASP model documentation.
Volatilization is the movement of a chemical across the air/water interface as the
concentration of the dissolved chemical tends toward equilibrium with its vapor-phase
concentration. Equilibrium occurs when the partial pressure exerted by the chemical in solution
equals the partial pressure of the chemical in the overlying atmosphere. The rate of exchange is
proportional to the gradient between the dissolved concentration and the concentration in air.
With the approach described in Whitman (1923), the dissolved concentration in the
surface water is assumed to attempt to equilibrate with the gas-phase concentration in the
atmosphere via the general equation:
^•**—' ^7,V
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CHAPTER 3
AIR ALGORITHMS
The term Vsw/dwwi\\ be equal to the surface area of the water compartment, if the depth of the
water compartment is approximately constant. This area is also the interfacial area between the
air and water compartments, so that:
Net Flux air to water =
Fraction _ Mass_ Dissolved
Volume _ Fraction _ Liquid
Fraction _ Mass_ Vapor
N
sw
sw
N
Air
1
Volume _Fraction_Vapor VAir (H/(RxTJ),
(Eq. 3-8)
or, using the notation of transfer factors and Equations 2-81 and 2-80:
SWA . , "'v . , _c
77-
dif
VAtr (H/(RxT)) MV
(TF 3-2)
where:
Tml ^-x k x f
1SW^Air - v * Kv X JML
V SW
(TF 3-3)
Air^SW
transfer of chemical from air to surface water via diffusion (/day);
interfacial area between the surface water and air compartments (m2);
volume of air compartment (m3);
volatilization transfer rate (m/day) [see below for details];
Henry's law coefficient for the air/water partitioning of the chemical
(Pa-m3/mole).
universal gas constant (8.314 m3-Pa/mole-°K);
water temperature (°K);
fraction of chemical mass in the air compartment that is in the vapor
phase divided by the volume fraction of the compartment that is gas
(i.e.., excluding particles);
transfer of chemical from surface water to air via volatilization (/day);
volume of surface water compartment (m3); and
fraction of the chemical mass in the water compartment that is
dissolved in water divided by the volume fraction of the compartment
that is water (i.e., excluding suspended sediments or algae) (unitless).
The two-layer resistance method assumes that two "stagnant films" are bounded on either
side by well mixed compartments. Concentration differences serve as the driving force for
volatilization from the water. Pressure differences drive the diffusion from the air layer. From
mass balance considerations, it is obvious that the same mass must pass through both films; thus,
the two resistances combine in series, so that the conductivity is the reciprocal of the total
ASWA
VAir
H
R
T
JMV
-
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CHAPTER 3
AIR ALGORITHMS
resistance. Thus, the volatilization transfer rate is estimated in the current TREVI.FaTE library
as:
kv = (RL + RG)~I =
H ^
(Eq. 3-9)
J RxT.
where:
RL = liquid-phase resistance (day/m);
kL = liquid-phase transfer coefficient (m/day);
RG = gas-phase resistance (day/m); and
kG = gas-phase transfer coefficient (m/day).
There is actually yet another resistance involved, the transport resistance between the two
interfaces, but it is assumed to be negligible (although this may not be true in very turbulent
conditions or in the presence of surface-active contaminants).
The value of kv, the volatilization transfer rate, or conductivity, depends on the intensity
of turbulence in a water body and in the overlying atmosphere. Mackay and Leinonen (1975)
have discussed conditions under which the value of kv is primarily determined by the intensity of
turbulence in the water. As Henry's law coefficient increases, the conductivity tends to be
increasingly influenced by the intensity of turbulence in water. As Henry's law coefficient
decreases, the value of the conductivity tends to be increasingly influenced by the intensity of
atmospheric turbulence.
Henry's law coefficient generally increases with increasing vapor pressure of a chemical
and generally decreases with increasing solubility of a chemical. Thus, highly volatile low-
solubility chemicals are more likely to exhibit mass-transfer limitations in water, and relatively
nonvolatile high-solubility chemicals are more likely to exhibit-mass transfer limitations in the
air. Volatilization is usually of relatively lower magnitude in lakes and reservoirs than in rivers
and streams.
In cases where it is likely that the volatilization rate is regulated by the turbulence level
in the water phase, estimates of volatilization can be obtained from results of laboratory
experiments. As discussed by Mill et al. (1982), small flasks containing a solution of a pesticide
dissolved in water that have been stripped of oxygen can be shaken for specified periods of time.
The amount of pollutant lost and oxygen gained through volatilization can be measured and the
ratio of conductivities (KVOG) for pollutants and oxygen can be calculated. As shown by
Tsivoglou and Wallace (1972), this ratio should be constant irrespective of the turbulence in a
water body. Thus, if the reaeration coefficient for a receiving water body is known or can be
estimated and the ratio of the conductivity for the pollutant to reaeration coefficient has been
measured, the pollutant conductivity can be estimated.
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The volatilization rate constant is for a temperature of 20°C. It is adjusted for segment
temperature using the equation:
^r = ^2oX®v"2° (Eq. 3-10)
where:
&Vj2o = calculated volatilization transfer rate (m/day) at 20°C;
61~20 = temperature correction factor for volatilization (unitless); and
T = water temperature (°C).
3.3.2.2 Calculation of Volatilization Transfer Rates for the Whitman Two-layer
Resistance Model
There are a variety of methods for estimating the transfer rates kG and kL for stagnant and
flowing water bodies, many of which are available in the current TRIM.FaTE library. These
methods are summarized in Tables 3-1 and 3-2 at the end of this chapter.
3.4 AIR-TO-PLANT ALGORITHMS
The algorithms describing the transfer of chemical mass between air and plants are
presented in Sections 7.2.1 (advection processes) and 7.2.2 (diffusion processes).
3.5 TRANSFORMATIONS AND DEGRADATION
Transformations of chemicals into compounds that will no longer be tracked in
TRIM.FaTE (e.g., non-toxic degradation products) are called general degradation processes. In
TRIM.FaTE, the degradation of a chemical in air due to all mechanisms that might apply (e.g.,
oxidation, photolysis) is reflected by the user input for the half-life of the chemical in air. The
algorithm relating the degradation rate constant to the chemical half-life in the air compartment
is presented in Chapter 2 (Equation 2-64), and the corresponding transfer factor is TF 2-1. The
degradation transfer factor moves the chemical mass to a degradation sink.
TRIM.FaTE has the capability to track the newly formed compounds, when they are of
particular interest to the user. Transformations of a chemical into another form(s) that is tracked
in TRIM.FaTE are named for the processes (e.g., oxidation, methylation, reduction of mercury
species). In the TRIM.FaTE air compartments, all transformations are modeled as first-order
processes; that is, linear with inventory (i.e., the quantity of chemical contained in a
compartment). The rate of mass removal in a first-order transformation is calculated as the
product of the total inventory of chemical in the compartment and the transformation rate
constant specified in the corresponding transfer factor.
3.6 AIR BOUNDARY CONTRIBUTIONS
The TRIM.FaTE library includes algorithms to allow transport of chemical into the
modeling region from the ambient air located outside the modeling area. For many of the
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chemicals that will be modeled using TREVI.FaTE, so-called "background" concentrations in the
absence of the modeled source(s) are not zero. Trace or higher concentrations of a chemical of
interest might be found in ambient air due to natural causes or due to releases from other
facilities outside the modeling region.
To model chemical inputs to the modeling region via advection of ambient levels of
chemical in air from beyond the boundary of the modeling region in TREVI.FaTE, the user can
set a boundary concentration for any outside interface of an air compartment located just inside
the boundary of the modeled region. In the TREVI.FaTE definition of properties for each of the
outside air volume elements, there is a property called the BoundaryConcentration_g_per_m3 for
which the user may specify an ambient air concentration of the chemical in the absence of the
source(s) being modeled.
Chemical mass enters the air compartments located just inside the boundary of the
modeling region via an air advection algorithm that incorporates wind speed, wind direction, and
the boundary concentration of the chemical (see above). The use of wind speed and wind
direction in this algorithm is identical to the approach that is used for the air-to-air advection
algorithm.
Note that TRIM.FaTE does not model changes in chemical concentrations in the air
external to the modeling region that might occur as a consequence of emissions from the
modeled source. Losses of chemical via air advection from the modeling region to areas external
to that region are modeled as transfers of the chemical to an air sink.
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Table 3-1
Methods for Determining Gas-Phase Transfer Coefficient kGa for the
Whitman Two-Layer Resistance Volatilization Model Between Air and Surface Water
Water Body Type
Stagnant Pond or Lake
Stagnant Pond or Lake
Flowing Water or Estuary
Flowing Water or Estuary
Flowing Water or Estuary
Method
1*
2
1*
2
3*
ke. Gas phase transfer coefficient (m/day)
f*-"'33
where:
u' = the shear velocity (m/day) computed from u" = Cf'5 W10 x 86,400
where:
Ca = drag coefficient (= 0.001 1 ),
W10 = wind velocity 10 m above water surface (m/sec), and
86,400 = unit conversion factor (sec/day);
K = von Karmen's constant (= 0.74) (unitless);
A2 = dimensionless viscous sublayer thickness = (4) (unitless); and
- 10000 xD^
where:
/na!r = viscosity of air, internally calculated from air temperature (cm2/sec),
(l.32 + 0.009 T,irc)
10
where: Ta!rC = air temperature (°C), and
. . . 2 1.9X10'4
where: Mw = molecular weight of compound (g/mole).
See Method (1) for definition of terms.
kG =10'3+ 0.0462 x u'x Sc^0'67
Same as Method (1) for stagnant water body.
Same as Method (2) for stagnant water body.
Input value of 1 00 m/day.
Reference
O'Connor (1 983), Ambrose
et al (1995)
Mackay and Yeun (1983),
Ambrose etal. (1995)
Ambrose etal. (1995)
' Used in the calculation of the volatilization transfer rate kr kv = (RL + RG)
~L + \k0 x
H
RxT,,
*Available in current TRIM.FaTE Library.
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Table 3-2
Methods for Determining Liquid-Phase Transfer Coefficient kL a for the
Whitman Two-Layer Resistance Volatilization Model Between Air and Surface Water
Water Body Type
Method
kL, Liquid phase transfer coefficient (m/day)
Reference
Stagnant Pond or Lake
1*
if - if x K
KL ~ "a 'Vo
where:
fca (user input) = reaeration velocity (m/day); and
Kvo (user input) = ratio of volatilization rate to reaeration rate (unitless).
Ambrose etal. (1995)
Stagnant Pond or Lake
2*
= k, * (32/Mw)° 5 where: Mw = molecular weight
Ambrose etal. (1995)
Stagnant Pond or Lake
k, = u" x ——
-^ y-»
K
where:
u"
Pa
P,
K
the shear velocity (m/day) computed from «* = Q05 x fF,0 x 86,400
where:
Cd = drag coefficient (= 0.0011),
W10 = wind velocity 10 m above water surface (m/sec), and
86,400 = unit conversion factor (sec/day);
= density of air, internally calculated from air temperature (kg/m3);
= density of water, internally calculated from water temperature (kg/m3);
= von Karmen's constant (= 0.74) (unitless); and
= dimensionless viscous sublayer thickness (= 4) (unitless).
= water Schmidt Number, computed from
Sc- =^T/T
= viscosity of water, internally ™ «
calculated from water
temperature (kg/m-sec)
10A(-3.30233 + 1301/(998.333+8.1855(7w-20) + 0.00585 (7W-20)2),
where: Tw = water temperature (°C)
pw
Dw
where:
= diffusivity of chemical in water (m2/sec)
Mw = molecular weight of compound
(g/mole).
O'Connor (1983),
Ambrose etal. (1995)
SEPTEMBER 2002
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CHAPTER 3
AIR ALGORITHMS
Table 3-2 (continued)
Methods for Determining Liquid Phase Transfer Coefficient kL for the Whitman Two-Resistance Volatilization Model
Between Air and Surface Water
Water Body Type
Stagnant Pond or Lake
Flowing Water or Estuary
Flowing Water or Estuary
Flowing Water or Estuary
Flowing Water (e.g., stream,
river) or Estuary
Method
4*
1*
2
3*
4*
kL, Liquid phase transfer coefficient (m/day)
kL = 1CT6+ 0.00341 xu" xScn-" if «' >0.3m/s
kL = 1CT6+ 0.0144 xu""2 xScw-°'5 if u" <0.3m/s
See Method (3) for definition of terms.
Same as Method (1 ) for stagnant water body.
Same as Method (2) for stagnant water body.
Same as Method (3) for stagnant water body.
kL = ka x Kvo , where:
u"'61
dw
V dw
u0'969
ka - 5.049 x 0673 else
aw
rir
\MW
where:
u = velocity of water (m/sec); dw = water compartment depth (m);
Dw = diffusivity of chemical in water (m2/sec) (= 22E-9/ Mw2'3);
KTO = input = ratio of volatilization rate to reaeration rate (unitless); and
ka = input = reaeration velocity (m/day).
Reference
Mackay and Yeun
(1983), Ambrose et al.
(1995)
Covar(1976),
Ambrose etal. (1995)
a Used in the calculation of the volatilization transfer rate kr kv = (R£ + RG)
* = Available in current TRIM.FaTE Library.
kG x
H
RxTe
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CHAPTER 4
SURFACE WATER AND SEDIMENT ALGORITHMS
4. SURFACE WATER AND SEDIMENT ALGORITHMS
The surface water compartment is assumed to be well-mixed and composed of three
phases: water, suspended sediment particles, and algae.1 Thus, chemicals can be dissolved in the
water phase, sorbed to the sediment particles, or contained in algae. The sediment compartment
is modeled as well-mixed and consisting of a benthic-solids phase and benthic pore or interstitial
water. Chemicals can either be dissolved in the interstitial pore water or sorbed to the benthic
sediment particles. The gas phase of the surface water and sediment compartments is considered
to be negligible in terms of its impact on the movement of chemicals and is not modeled. The
text box beginning on the next page provides a list of the transfer-factor algorithms developed in
this chapter and defines all parameters used in those algorithms.
4.1 CONCEPTUALIZATION OF THE SURFACE WATER AND
SEDIMENT COMPARTMENTS
The behavior of chemicals in surface waters is determined by three factors: the rate of
input, the rate of physical transport in the water system, and chemical reactivity. Physical
transport processes are dependent to a large extent on the type of water body under consideration
i.e., oceans, seas, estuaries, lakes, rivers, or wetlands. Schnoor (1981) and Schnoor and McAvoy
(1981) have summarized important issues relating to surface-water transport. Fugacity models
have been developed for lakes and rivers by Mackay et al. (1983a,b).
At low concentrations, contaminants in natural waters exist in both a dissolved and a
sorbed phase. In slow-moving surface waters (e.g., lakes), both advection and dispersion are
important. In rapidly moving water systems (e.g., rivers), advection controls mass transport, and
dissolved substances move at essentially the same velocity as the bulk water in the system. A
water balance is the first step in assessing surface-water transport. A water balance is
established by equating gains and losses in a water system with storage. Water can be stored
within estuaries, lakes, rivers, and wetlands by a change in elevation. Water gains include
inflows (both runoff and stream input) and direct precipitation. Water losses include outflows
and evaporation.
The accuracy of modeling fresh-water systems depends on the ability to simulate the
movement of water and sediment to and from the system (Schnoor 1981). There are two primary
categories for fresh water: rivers and lakes. This model is based on that described in Mackay et
al. (1983a,b). Table 4-1 summarizes the chemical gains and losses for the surface water
compartment that are addressed in the current TRIM.FaTE library. Losses or changes due to
transformation or degradation reactions also are modeled in TRIM.FaTE. Losses from the
sediment due to colloidal diffusion and bioturbation are not addressed in the current TRIM.FaTE
library.
Because of data limitations, in the current TRIM.FaTE library, algae are modeled as a third phase of the
surface water compartment, instead of as a stand-alone biotic compartment.
SEPTEMBER 2002 ~\ TRIM.FATE TSD VOLUME II
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CHAPTER 4
SURFACE WATER AND SEDIMENT ALGORITHMS
Summary of Surface Water and Sediment Transfer Factors in TRIM.FaTE
ADVECTIVE TRANSFERS
Dry deposition of particles to surface water (solid phase):
Tdry_dep _
1 Air^SW
X V
dry
-17
*
ry f
A J 1
MS
Air
Wet deposition of particles to surface water (solid phase):
rr^wet_dep _
1Air^,SW ~
V
J MS
Air
ramx
Total air
•xrainxwryxfM
Deposition of suspended sediment to sediment bed (solid phase):
A
•**• e,, ,-7eR7
r^dep _ SedSW dep r
1-SW^Sed -17 A USed A J MS
V SW
Resuspension of sediment to surface water (solid phase):
rpres _ SedSW res v r
1Sed^SW ~ T7 X VSed X J MS
Sed
Algal deposition rates (algal phase):
A
Tdep _ "-SedSW Al r
*- Al^tSed ~ y A uSed A J MAI
' SW
Outflow from flowing river to surface water advection sink (total phase):
Tsw-sw_smk = outflow I Vsw
Outflow from lake or pond to surface water advection sink (total phase):
lake (flushes I yr)
W sink
365
TF 4-1 b
TF 4-2b
Wet deposition of vapor-phase from air to surface water during rain (fugacity approach): TF 4-3a
Wet deposition of vapor-phase from air to surface water during rain (partitioning approach): TF 4-3b
TF4-4
TF4-5
TF4-6
TF 4-7a
TF 4-7b
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CHAPTER 4
SURFACE WATER AND SEDIMENT ALGORITHMS
Summary of Surface Water and Sediment Transfer Factors in TREVLFaTE (cont.)
ADVECTIVE TRANSFERS (cont.)
Sediment burial (solid phase):
A,
*
burial_rate x ft
MS
Sed
Advection from one river compartment to another river or lake compartment:
T^ (total) = flow IV,
DIFFUSIVE/DISPERSIVE TRANSFERS
Diffusion from sediment to surface water compartments:
•X
- +
TJ y
u SedSW A
Total _Sed
U
SWSed
y
^Total _SW
Diffusion from surface water to sediment compartments:
( \-1
A
Sed^SW
SedSW
Sed
X
1
1
TJ y
'-' SWSed A
Total _SW
Total Sed
Dispersive exchange flux between two surface water compartments:
L^V,
Sedi
Sedj
L
Sedij
TF4-8
TF4-9
TF4-10a
TF4-11a
TF4-12
Diffusive exchange between sediment compartment; and sediment compartmenty below: TF 4-13
A,,. DSP,f]x
-ndif Sedij Sed
^ Sedi ^ Sedj ~ T/ J
r e.
Diffusive exchange between sediment compartmenty and sediment compartment; above: TF 4-14
ASedlJ DSPSed x ^
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CHAPTER 4
SURFACE WATER AND SEDIMENT ALGORITHMS
Summary of Surface Water and Sediment Transfer Factors in TREVLFaTE (cont.)
LIST OF SYMBOLS USED IN TRANSFER FACTOR ALGORITHMS
w,
rV
r
MV
'MS
rain
pure_wat&
Vsw
, dep
U.aA
V,
V
Sed
res
Sed
'MAI
outflow
flushes/yr
burial_rate
flow
"Sed
UsWSed
UsedSW
Sedij
DSPS
'-Sedij
'MLi
'MLj
vapor washout ratio (m3[air]/m3[rain]).
fraction chemical mass in air compartment that is vapor-phase divided by
volume fraction of the air compartment that is gas-phase (unitless).
area of surface water/air interface (m2[interface]).
volume of the air compartment (m3[air]).
fraction mass of chemical sorbed to sediment particles divided by the volume
fraction of the compartment (surface water or sediment) that is solid particles
(unitless).
rainfall rate (m/day).
fugacity capacity of chemical in the aqueous phase (mol/m3-Pa).
total fugacity capacity of chemical in the air compartment (mol/m3-Pa).
area of surface water/sediment interface (m2[interface]).
volume of surface water compartment (m3[water]).
volumetric deposition rate of suspended sediment to sediment bed
(m3[suspended sediment particles]/m2(area)-day).
volume of sediment compartment (m3).
volumetric resuspension rate of benthic sediment to water column (m3[benthic
sediment particles]/m2 [benthic sediment]-day).
volumetric algal deposition rate to benthic sediments (m3[algae]/m2[sediment/
water interface]-day).
fraction mass of chemical in algae divided by the volume fraction of the
surface water compartment that consists of algal cells (unitless).
volumetric outflow of water from surface water compartment to advection sink
(nf/day).
outflow measured as number of complete changes (flushes) of water per year.
sediment burial rate (m3[sediment particles]/m2[sediment]-day).
volumetric flow of water from one river compartment to another river or lake
compartment (m3/day).
area of the sending sediment compartment (m2).
mass transfer coefficient between surface water and sediment (m/day).
mass transfer coefficient between sediment and surface water (m/day).
dispersion coefficient for exchange between water compartments / and j
(m2/day).
interfacial area between water compartments / and j (m2).
characteristic mixing length between water compartments / and j (m).
volume of water compartment/ (m3).
interfacial area between sediment compartments / and j (m2);
volume of the sending sediment compartment/ (m3);
volume of the sending sediment compartmenty (m3);
diffusive exchange coefficient between sediment compartments (m2/day);
average porosity at the interface between sediment compartments /and j
(unitless);
characteristic mixing length between sediment compartments / and j (m);
fraction of the chemical mass in sediment compartment /that is dissolved in
water divided by volume fraction sending sediment compartment /that is liquid
(unitless).
fraction of the chemical mass in sediment compartmenty that is dissolved in
water divided by volume fraction sending sediment compartment j that is liquid
(unitless).
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CHAPTER 4
SURFACE WATER AND SEDIMENT ALGORITHMS
Table 4-1
Summary of the Chemical Gains and Losses for Surface Water Compartments
Addressed in TRIM.FaTE
Gains
Type of Process
Relevant
Phase
From Surface Soil
Erosion
Runoff
Advection (TF5-11)
Advection (TF5-10)
Solid
Aqueous
From Air
Diffusion from air
Dry deposition of
particles/
aerosols from air
Wet deposition of
particles/
aerosols from air
Wet deposition of
vapor from air
Diffusion (TF 3-2)
Advection (TF 4-1)
Advection (TF 4-2)
Advection (TF 4-3)
Vapor
Solid
Solid
Vapor
From Sediment
Diffusion from
sediment
Resuspension of
sediment
Diffusion (TF4-10a,b)
Advection (TF 4-5)
Aqueous
Solid
From Rivers
Compartment to
compartment flow
Advection (TF 4-9)
Total
From Aquatic Biota
Elimination from fish
Elimination from
macrophytes
Advection (TF 6-8)
Diffusion (TF6-1)
Total
Aqueous
From Terrestrial Birds and Mammals
Elimination from semi-
aquatic wildlife
Advection (TF 7-32)
Total
From Surface Water Transformations
Losses
Type of
Process
Relevant
Phase
To Air
Diffusion to air
Diffusion
(TF 3-3)
Aqueous
To Sediment
Diffusion to sediment
Deposition to
sediment
Diffusion
(TF4-11a,b)
Advection
(TF 4-4)
Aqueous
Solid
To Lake
River to lake
advective flow
Advection
(TF 4-9)
Total
To Aquatic Biota
Uptake by fish via
gills
Uptake by
macrophytes
Ingestion of algae by
fish
Advection
(TF 6-5)
Diffusive
(TF 6-2)
Advection
(TF 6-6)
Total
Aqueous
Algae
To Terrestrial Birds and Mammals
Ingestion by wildlife
Advection
(TF7-21)
Total
To Sink(s)
Decay to reaction
sinks
Outflow to advection
sink
Degradation
(TF2-1)
Advection
(TF 4-7)
Total
Total
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CHAPTER 4
SURFACE WATER AND SEDIMENT ALGORITHMS
The general manner in which the algorithms are presented below is intended to provide
model flexibility and to facilitate implementing different algorithms to describe specific
processes.
4.2 ADVECTIVE PROCESSES
This section describes the advective processes between different compartment types as
follows:
• Between air and surface water (Section 4.2.1);
• Between sediment and surface water (Section 4.2.2);
• From sediment/surface water to advection sinks (Section 4.2.3); and
• From surface soil to surface water (Section 4.2.4).
4.2.1 ADVECTIVE PROCESSES BETWEEN AIR AND SURFACE WATER
The advective processes considered between air and surface water are wet and dry
deposition of solid-phase particles and wet deposition of vapor that is dissolved into the water
phase.2 For all of these processes, the air compartment is the sending compartment and the
surface water compartment is the receiving compartment.
The following subsections describe the transfer algorithms for advective processes
between air and surface soil and surface water:
dry deposition of particles to surface water (Section 4.2.1.1);
• wet deposition of particles to surface water (Section 4.2.1.2); and
• wet deposition of vapor-phase to surface water (Section 4.2.1.3).
4.2.1.1 Dry Deposition of Particles to Surface Water
A unidirectional flux equation that expresses dry deposition of particles from air to
surface water, from van de Water (1995), follows. Note that the boundaries of the surface water
and air parcels may not be congruent; that is, the area of the surface water and the area
associated with a contiguous air compartment may be different. The change in the chemical
mass in the surface water from dry deposition of chemical sorbed to atmospheric dust particles
can be estimated as:
NAi DL ^ pure solid . __,
- = TT^X vdty X -^X -^- X ASWA (Eq. 4-1)
V Air PP *~'Total Air
where:
Nsw = mass of chemical in the surface water compartment (g[chemical]);
NAir = mass of chemical in the air compartment (g[chemical]);
See Appendix A for a description of a net dry vapor deposition algorithm for divalent mercury.
SEPTEMBER 2002 4^6 TRIM.FATE TSD VOLUME II
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SURFACE WATER AND SEDIMENT ALGORITHMS
VAir
DT
PP
Z,
'pure_solid
Z.
Total Air
A
SWA
= volume of air compartment (m3);
= dry deposition velocity of particles (m/day);
= atmospheric dust load in air compartment (kg[particles]/m3[air]);
= density of dust particles (kg[particles]/m3[particles]);
= fugacity capacity of the chemical in or sorbed to solid particles (mol/m3-
Pa);
= total fugacity capacity of chemical in bulk air, including atmospheric dust
particles (mol/m3-Pa); and
= area of the interface between surface water and air (m2).
Thus, the transfer factor for dry deposition of chemical associated with air particles can
be estimated using the fugacity approach:
where:
Air^SW
7 =
pure_solid
7 =
^Total_Air
It is also true that:
A
—^-x v, x
T7 dry
V Air
Z
pure _solid
Air
PP X ^Total Air
(TF 4-la)
advective transfer (dry deposition) of chemical sorbed to particles from air
to surface water (/day);
fugacity capacity of chemical in the solid phase (mol/m3-Pa); and
total fugacity capacity of chemical in the air compartment (mol/m3-Pa).
PP
(Eq. 4-2)
where:
"dry
and:
where:
IMS
volumetric dry deposition rate (m3[dust]/m2[surface water/air interface]-
day);
7j pure _soiid Mass_ Fraction _ Sorbed
7 ~ Volume Fraction Solid ~ MS
(Eq. 4-3)
Total Air
mass fraction of the chemical sorbed to atmospheric dust particles divided
by the volume fraction of the air compartment that consists of particles
(see Equations 2-71 and 2-79) (unitless).
Therefore, the transfer factor for dry deposition of particles in air to surface water can
also be expressed as the following equation, which is coded in the current TRIM.FaTE library:
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A
rpctry _dep _ an A v v r
1A,r^SW ~ ir X Vdry X Jl
MS
(TF 4-lb)
4.2.1.2 Wet Deposition of Particles to Surface Water
Nonionic organic chemicals in the atmosphere can be either in the vapor phase, attached
to particles or aerosols, or as fine aerosols. TF 4-3a (see Section 4.2.1.3) is used for wet
deposition of vapor. TF 4-2a is used for the wet deposition of aerosols, regardless of whether the
chemical is attached to the aerosol or particle or is present as a fine aerosol of the chemical itself.
The change in the chemical mass in the surface water from wet deposition of chemical
sorbed to atmospheric dust particles during a rain event can be estimated as:
•*• *
Air
dt
Air
U j pure solid .
x w xramx x = x A,
pp Z,
(Eq. 4-4)
~ 'Total Air
where:
NAir
V
Air
wr
rain
DL
PP
7
pure_solid
7
^ Total Air
mass of chemical in the surface water compartment (g[chemical]);
mass of chemical in the air compartment (g[chemical]);
volume of air compartment (m3);
scavenging or washout ratio for particles in air (ranges from 50,000 to
200,000) (m3[air]/m3[rain]);
rate of rainfall (m/day);
dust load, i.e., density of dust particles in air (kg[particles]/m3[air]);
density of dust particles (kg[particles]/m3[particles]);
fugacity capacity of the chemical in or sorbed to solid particles (mol/m3-
Pa);
total fugacity capacity of chemical in bulk air, including atmospheric dust
particles (mol/m3-Pa); and
area of surface water/air interface (m2).
Thus, the transfer factor for wet deposition of chemical associated with air particles can be
estimated as follows:
r> Y 7
*-^L A ^ pure soli
pure _solid
Air
Pp
(TF 4-2a)
Total Air
where:
rj-
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CHAPTER 4
SURFACE WATER AND SEDIMENT ALGORITHMS
Using the same relationships described in Section 4.2.1.1, algorithm TF 4-2a can be
rearranged to TF 4-2b, which reflects the code in the TRIM.FaTE library:
T
1
A
wet_dep _ SWA
Air
MS
(TF 4-2b)
where:
and:
JMS
t» ,
A,
A>
(Eq. 4-5)
Zpure soiic/^Totai Airas described for Equation 4-3 above (unitless); and
volumetric wet deposition rate (m3[dust particles]/m2[surface water/air
interface]-day).
4.2.1.3 Wet Deposition of Vapor-phase Chemical to Surface Water
There also is advective flux of vapor-phase chemical from rainfall. As the rain falls, it
gathers chemical from the air, coming into equilibrium with the fugacity of the air compartment.
* * *
K
pure water
.
x ASWA =>
Air
Total Air
< WVdep
A
SWA
7
pure _water
7
*-'Total Air
(Eq. 4-6)
(TF 4-3 a)
where:
N
sw
NA,r
VAir
rain
7
pure^vater
7
^
A
^-
total mass of chemical in the surface water compartment
(g[chemical]);
total mass of chemical in the air compartment (g[chemical]);
volume of air compartment (m3);
rainfall rate (m/day);
fugacity capacity of the chemical in aqueous phase of surface
water (i.e.., excluding suspended sediments) (mol/m3-Pa);
total fugacity capacity of the chemical in the air compartment
(mol/m3-Pa);
area of surface water/air interface (m2); and
advective transfer factor for wet deposition of vapor from air to
surface water (/day).
SEPTEMBER 2002
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The fugacity approach and TF 4-3a are well suited for nonionic organic chemicals. For
inorganic chemicals for which vapor washout ratios have been determined empirically, the
transfer factor is calculated in the current TRIM.FaTE library as:
T^PSW (rain) = - x rain x wrV x fMV (TF 4-3b)
VAir
where:
wrV = vapor washout ratio (g[chemical dissolved]/m3[rain] per g[chemical vapor-
phase]/m3[air]); and
fMV = the fraction of the chemical mass in the air compartment that is in the
vapor phase divided by the volume fraction of the air compartment that is
gas/vapor (i.e., the fraction that is not particulate (see Equation 2-73 in
Chapter 2).
Note that wrV= l/KAW, where:
KAW = air/water partition coefficient (g[chemical]/m3[air] per g[chemical]/
m3[ water]).
4.2.2 ADVECTIVE PROCESSES BETWEEN SEDIMENT AND SURFACE WATER
The two advective processes between sediment and surface water involve the transport of
the chemical from the surface water to the sediment and from the sediment to the surface water
via movement of sediment particles. "Sediment deposition" refers to the transport of the
chemical sorbed to sediment particles from the surface water to the benthic sediment bed, and
"sediment resuspension" refers to the reverse process. Both processes involve only the solid-
phase chemical; thus, it is necessary to estimate the partitioning of a chemical among the phases
in the surface water compartment and in the sediment compartment. Section 2.7 provides the
equations in the current TRIM.FaTE library that implement the general equilibrium approach to
calculating the chemical distribution among phases. The fugacity-based equations in the
TRIM.FaTE library are described below.
As indicated above, there are three surface-water phases in the current TRIM.FaTE
library: liquid-phase water, suspended particle solids, and algae. Thus, to calculate the total
fugacity of a chemical in the surface water compartment, it is necessary to add the fugacity
capacity of those three components:
_ _
where:
Z Total sw = total fugacity capacity of chemical in surface water compartment
(mol/m3-Pa);
Zpure water = fugacity capacity of chemical in liquid phase, i.e., water (mol/m3-
Pa);
Zpure solid = fugacity capacity of chemical in the solid phase (mol/m3-Pa); and
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ZAlgae = fugacity capacity of chemical in algae (mol/m -Pa).
Thus, the total fugacity of the chemical in the surface water compartment is estimated in the
current TRIM.FaTE library as:
ZTotal_sw = (zpure_water X Volume _ Fraction _ Liquid] +
[zpure_solld x Volume_Fraction_Solid) + (Eq. 4-8)
igae x Volume _ Fraction _ Algae]
Aiga
The fugacity capacity in algae, ZAlgae, is calculated as:
~- X x Zuremter (Eq. 4-9)
where:
C Aigae = chemical concentration in algae (g[chemical]/m3[algae]);
Csw = concentration of chemical dissolved in the liquid phase of surface water
(g[chemical]/m3[water]);
CA = concentration (density) of algae in surface water (g[algae wet wt]/
m3[water]); and
1000 = units conversion factor (g/kg).
Note that CA!ga/Csw is equivalent to a bioconcentration factor (BCF) of the chemical in algae and
is represented in the TRIM.FaTE library as RatioOfCondnAlgaeToConcDissolvedlnWater.
The sediment compartment in the current TRIM.FaTE library consists of two phases:
liquid-phase water and solid sediment particles. Thus, to calculate the total fugacity of a
chemical in the sediment compartment, it is only necessary to add the fugacity capacity of those
two components:
where:
ZTotal Sea = (Zpure Water X Volume_ FrOCtiOn_ Liquid +
(Eq. 4-10)
zPure_Soi,d x Volume Fraction Solid
sed = total fugacity capacity of chemical in the sediment compartment
(mol/m3-Pa).
SEPTEMBER 2002 4-11 TRIM.FATE TSD VOLUME II
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The following subsections describe the sediment deposition and resuspension transfer
factors (Section 4.2.2. 1), the equations used to calculate the phase flow velocities (Section
4.2.2.2), and algal deposition rates (Section 4.2.2.3), since living and dead algal cells can settle
out of the water column onto the sediment bed.
4.2.2.1 Sediment Deposition and Resuspension
The algorithms for sediment deposition and resuspension are similar and are described
below.
Deposition of suspended sediment to sediment bed (solid phase):
(TF 4-4a)
SW sed Total _SW
where:
Tsw^sed = advective transfer factor for deposition of suspended sediment in surface
water to sediment bed (/day);
ASedsw = area °f surface water/sediment interface (m2);
Vsw = volume of surface water compartment (m3);
Sdep = deposition rate of suspended sediment to sediment bed (kg[suspended
sediment]/m2[surface water/sediment interface] -day)
pSed = density of solid sediment particles (kg[sediment particles]/m3[sediment
particles]);
Zpu.™ solid = fugacity capacity of the solid phase (mol/m3-Pa); and
Z Total sw = total fugacity capacity of the surface water compartment (mol/m3-Pa).
In the TREVI.FaTE library:
vfepd = volumetric sediment deposition rate (m3[sediment]/m2[surface
water/sediment interface] -day) (see Section 4.2.2.2 below);
and:
fMS = mass fraction of chemical sorbed to suspended sediment particles divided
by the volumetric fraction of the surface water compartment that is
suspended sediments (unitless) (i.e., Mass Fraction Sorbed/
Volume Fraction Solid), which:
^pur^ou^Tota^r (see Equations 2-7 1 and 2-79).
Thus, the transfer factor for deposition of suspended sediments to the sediment bed is
represented in the TRIM.FaTE library as:
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fMS (TF 4-4b)
sw
Resuspension of sediment to surface water (solid phase):
A V 7
rpres ^-SedSW s/ ^ res s/ pure _solid
Tsed^sw = —^ x -— x 7 (TF 4-5a)
* Sed Psed ^ Total _Sed
As for Equations TF 4-4a and 4-4b above, TF 4-5a is coded in the TRIM.FaTE library as
the equivalent expression shown in TF 4-5b:
"-SedSW res .. r /r™ . ,-, x
-T7 ^ vsed x fMS (TF 4-5b)
ySed
where:
T™d^sw = advective transfer factor for resuspension of sediment to surface water
(/day);
ASedsw = area °f sediment/surface water interface (m2);
VSed = volume of sediment compartment (m3);
Sres = resuspension rate of benthic sediment to water column (kg[benthic
sediment particles]/m2[sediment/surface water interface]-day);
pSed = density of solid sediment particles (kg[particles]/m3[particles]);
Zpure SOHd = fugacity capacity of the chemical in solid phase (mol/m3-Pa);
ZTotal sed = total fugacity capacity of the chemical in the sediment compartment
(mol/m3-Pa);
vseesa = volumetric sediment resuspension rate (m3[sediment]/m2[sediment/surface
water interface]-day) (see Section 4.2.2.2 below); and
fMS = mass fraction of chemical sorbed to sediment bed particles divided by the
volume fraction of the sediment bed that is solid particles (unitless).
4.2.2.2 Sediment Deposition and Resuspension Rates
The volumetric sediment deposition and resuspension rates are estimated using similar
equations in TRIM.FaTE. The equation for volumetric sediment deposition is:
dep _ S^P (Eq. 4-9)
'Sed
PSed
where:
vf/d = volumetric sediment deposition rate (m3[sediment particles]/m2[surface
water/sediment interface]-day);
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Sdep = deposition rate of suspended sediment to sediment bed (kg[suspended
sediment particles]/m2[surface water/sediment interface]-day); and
pSed = density of suspended sediment particles (kg[particles]/m3[particles]).
The sediment deposition rate, Sdep, is calculated as:
Sdep = vdepxTSS (Eq.4-10)
where:
vdep = sediment deposition velocity (m/day); and
TSS = total suspended sediment concentration (kg[suspended sediment
particles]/m3[surface water compartment]);
The equation for volumetric sediment resuspension is similar to Equation 4-7:
where:
vseSd = volumetric sediment resuspension rate (m3[sediment particles]/m2[surface
water/sediment interface]-day);
Sres = resuspension rate of benthic sediment to surface water (kg[benthic
sediment]/m2[sediment/surface water interface]-day); and
pSed = density of solid sediment particles (kg[sediment particles]/m3[sediment
particles]).
In this case, the sediment resuspension rate, Sres, is calculated as:
Sres = vres x BSC (Eq. 4-12)
where:
vres = sediment resuspension velocity (m/day); and
BSC = benthic solids concentration (kg[sediment particles]/m3[sediment
compartment]).
In the TRTM.FaTE library:
BSC=Psedx(l-0) (Eq.4-13)
where:
(f) = porosity, which for the sediment compartment is equal to the volume
fraction liquid , i.e., water (m3[pore water]/m3 [sediment compartment]).
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4.2.2.3 Algal Deposition Rates
Algal cells, both living and dead, can settle out of the water column onto the sediment
bed. The transfer factor for that deposition process in TRIM.FaTE is similar in form to TF 4-4b:
Tdl>P - SedSW y 1}deP y f CYC A f.\
J Algae^Sed ~ y A uAlgae A J MAI \Lr ^~V)
* SW
where:
TAigae-* sed = deposition transfer factor for algae settling to the sediments (/day);
ASedsw = interfacial area between the surface water and sediment
compartments (m2);
Vsw = volume of the surface water compartment (m3);
^Mgae = algal deposition rate (m3[algae]/m2[sediment/surface water
interface]-day); and
fMAl = mass fraction of chemical in algal cells divided by the volume
fraction of the surface water compartment comprised of algal cells
(unitless).
The volumetric algal deposition rate can be estimated as:
d = ep (Eq. 4-14)
Algae
where:
ASdep = algal deposition rate (g[algae]/m2[sediment/surface water interface]-day);
CA = algae concentration (density) in water column (g[algae]/L[water]); and
1000 = units conversion factor (L/m3).
The mass-based algal deposition (sedimentation) rate can be estimated from:
dep
(Eq.4-15)
'~ Almcx(l-/WAlgae)
where:
CSdep = carbon sedimentation rate (g[carbon]/m2[sediment/surface water
interface]-day);
AITOC = dry weight total carbon content of algae (g[carbon]/g[algae dry wt]); and
rAigae = mass fraction of the algae that consists of water (unitless).
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Based on Baines and Pace (1994), the carbon sedimentation rate is estimated from the
following formula:
0.62xln(CC) ,
where:
CSdep = 10 ™ X — (Eq. 4-16)
CC = chlorophyll concentration in water (mg[chlorophyll]/m3[surface water]);
and
1000 = units conversion factor (mg/g).
Values for CC, AITOC , andJWAlgae can be obtained from the literature.
4.2.3 ADVECTIVE PROCESSES BETWEEN SEDIMENT/SURFACE WATER AND
ADVECTIVE SINKS
The surface water advection sink represents outflow of the chemical from the study area.
For sediment, the advection sink represents the burial of the chemical beneath the sediment
layer. Following is a summary of the following advective processes between sediment/surface
water and advective sinks:
• outflow from flowing river to surface water advection sink(s) (Section 4.2.3. 1);
outflow from a lake or pond to a surface water advection sink (Section 4.2.3.2);
and
transfer of bulk sediment from the sediment bed to a sediment burial sink (Section
4.2.3.3).
4.2.3.1 Outflow from Flowing Water to Surface Water Advection Sink (Total Phase)
For flowing waters (e.g., rivers and streams), chemical sorbed to suspended sediments
and dissolved in the water can be carried downstream with the bulk water flow beyond the
boundary of the modeling area, modeled as a transfer to a surface water advection sink. The
transfer factor is based on the volumetric flow of the water body:
T^sw_smk = outflow /Vsw (TF 4-7a)
where:
TSW^SW sink = advective transfer factor from surface water compartment to
surface water advection sink (downstream direction only) (/day);
outflow = volumetric outflow of bulk water (water and suspended sediments)
from surface water compartment to advection sink (m3[bulk
water]/day); and
Vsw = volume of surface water compartment (m3 [water]).
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Note that inflow of chemical from outside the boundary of the study area is possible if
there are background concentrations of the chemical in the water upstream of the study area.
That transfer is estimated using an inflow rate that is equal to the outflow rate for the surface
water compartment just inside the modeling boundary and a user-specified concentration of the
chemical upstream of the study site.
4.2.3.2 Outflow from Lake or Pond to Surface Water Advection Sink (Total Phase)
For non-flowing waters (e.g., lakes and ponds), chemical in water can be lost from the
surface-water body to one or more outflows that are not modeled in TREVI.FaTE:
(flushes I yr)
TSW^SW_s,nk = ^ (TF 4'7b)
where:
TSW^SW Smk = advective transfer factor from surface water compartment to
surface water advection sink (/day);
flushes/yr = outflow of water measured as number of complete flushes per year
from surface water compartment to advection sink (m3[bulk
water]/day); and
365 = unit conversion factor (days/year).
4.2.3.3 Movement of Sediment from Sediment Bed to Sediment Burial Sink (Solid
Phase)
The burial of chemical mass below the sediment compartment (i.e., in the sediment burial
sink) is a function of the sediment deposition rates and sediment resuspension rates.
Conceptually, as sediment particles suspended in the surface water settle, with their associated
chemical mass, to the top sediment layer, there is a simultaneous burial of sediment particles and
associated chemical from the bottom sediment layer into a sediment burial sink. The chemical
mass in TRIM.FaTE sinks does not move back into the modeled system. Transfer of chemical
mass from sediment to a sediment sink is then modeled as follows:
T£ZM smk = ^ x burial _ rate x fMS (TF 4-8)
V Sed
where:
Tsed^sed Smk = transfer factor for chemical mass in lower-most modeled sediment
layer to the sediment burial sink (/day);
ASed = area of the sending sediment compartment (m2);
VSed = volume of the sending sediment compartment (m3);
burial rate = sediment burial rate (m3[sediment particles] /m2[sediment]-day, or
m/day); and
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fMS = fraction of chemical mass sorbed to sediment particles divided by
volume fraction of the sediment compartment that is solid (unitless).
In the current library, burial rate is derived as a non-negative value as follows:
burial_ rate = max(0, vdjd - v% ) (Eq. 4-17)
where:
vfej = sediment deposition rate (m3[sediment]/m2-day) (see Eq. 4-9); and
v™d = sediment resuspension rate (m3[sediment]/m2-day) (see Eq. 4-11).
While the model could accommodate scouring (i.e., net resuspension of sediment from
the sediment layer up into the water column), the burial algorithm currently does not provide for
the transfer of chemical mass back into a sediment compartment from a sediment burial sink. To
accommodate a scouring situation in which chemical previously buried would become available
for resuspension, the user might consider using a more complex scenario involving multiple
sediment compartments positioned as layers above the burial sink, where the depth of the layers
(i.e., the upper most ones) could change depending on deposition and resuspension rates.
4.2.4 ADVECTIVE PROCESSES FROM SURFACE SOIL TO SURFACE WATER
The advective algorithms for runoff and erosion from surface soil compartments to a
surface water compartment are described in Chapter 5 (TF 5-1 Ob and TF 5-1 Ib, respectively).
4.3 DERIVATION OF RIVER COMPARTMENT TRANSFER FACTORS
The transfer factor from one river compartment to another, or to a lake compartment, was
derived based on advective flow rates of a total pollutant mass between two compartments, as
developed in Section 2.4. 1 . By substituting river flow for the total volumetric flow, the
following transfer factor is derived.
(TF4-9)
vi
where:
T^j (total) = advective transfer factor for bulk river flow between river
compartments / andy (/day);
flow = bulk volumetric water flow rate (m3[bulk water]/day); and
Vt = volume of compartment /' (m3[surface water]).
Because advection is being simulated for the total phase (i.e., both the water and the
suspended sediments), no phase partitioning is applied in this equation. This transfer factor is
specified for a particular link between surface water compartments.
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4.4 DIFFUSIVE PROCESSES
TREVI.FaTE models the diffusive exchanges of chemicals between surface water and air
(Section 4.4.1) and between surface water and sediments (Section 4.4.2). Diffusive exchanges
between surface water and algae are noted in Section 4.4.3.
4.4.1 DIFFUSIVE EXCHANGE BETWEEN SURFACE WATER AND AIR
The algorithms describing the diffusive exchange of chemical mass between surface
water and air are presented in Section 3.3.2.1 (see TF 3-2 and TF 3-3).
4.4.2 DIFFUSIVE EXCHANGE BETWEEN SURFACE WATER AND SEDIMENTS
The diffusive exchange of chemical between surface water and sediments is modeled
based on mass transfer coefficients between the two compartments. Transfer factors based on
the fugacity approach are developed in Section 4.4.2.1. The transfer factors for diffusion based
on the method described in the Water Quality Analysis Simulation Program (WASP) (Ambrose
et al. 1995) model are developed in Section 4.4.2.2.
4.4.2.1 Transfer Factors Based on Fugacity Approach
Diffusive transfers of dissolved chemical between sediment pore water and the overlying
surface water are estimated from chemical mass transfer coefficients as described in the
following set of equations. First:
U
De
SW
SWSed
U
%
De
Sed
SedSW
(Eq. 4-18a)
(Eq. 4-18b)
'Sed
where:
Desw =
Desed =
mass transfer coefficient from surface water to sediment (m/day);
mass transfer coefficient from sediment to surface water (m/day);
effective diffusivity of chemical in surface water (m2/day);
effective diffusivity of chemical in sediment (m2/day);
boundary layer thickness below water (m); and
boundary layer thickness above sediment (m).
The values of Desw and DeSed are calculated using equations (Millington and Quirk 1961):
/g 4-19)
SW - pum_v*ater
Desed -
D
pure_wa
. 4-20)
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where:
D.
pure_water
diffusivity of chemical in liquid phase, i.e., water (m2/day); and
porosity, or the volume fraction of the sediment compartment that is water
(i.e., 6, which = Volume Fraction Liquid given that e, or
Volume Fraction Vapor, in the sediment compartment = 0; unitless).
The value for 6Sed can be input by the user. The value for 6SW is estimated using the method from
CalTox (McKone 1993b, Equation 58, p. 44) as:
°-683
(Eq. 4-21)
The mass transfer coefficients are then used to estimate the diffusive transfer from
sediment to surface water:
T'
Sed^SW
A
^SedSW „
v» A
1 1
„ Z Total _SW USedsw
U SWSed A y
(TF 4-10a)
where:
Sed ^ SIT
Sed
= diffusive transfer factor from sediment to surface water (/day);
= interfacial area between the sediment and surface water compartments
(m2);
= total fugacity capacity of chemical in the surface water compartment
(mol/m3-Pa); and
= total fugacity capacity of chemical in the sediment compartment (mol/m3-
Pa).
The diffusive transfer from surface water to sediment is estimated by the same equations,
but with the identity of the sending and receiving compartments reversed:
rpdif
± SIT ^ Sed
A
^SedSW „
vsw A
1 1
Z TJ
„ 'Total _Sed U SWSed
U SedSlT A 7
(TF4-lla)
where:
diffusive transfer factor from surface water to sediment
compartments (/day);
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ASedsw = interfacial area between the sediment and surface water
compartments (m2);
USedsw = mass transfer coefficient from sediment to surface water
compartments (m/day);
Uswsed = mass transfer coefficient from surface water to sediment
compartments (m/day);
Z Total sw = total fugacity capacity of the chemical in the surface water
compartment (mol/m3-Pa); and
Z Total sed = total fugacity capacity of the chemical in the sediment
compartment (mol/m3-Pa).
4.4.2.2 Transfer Factors Based on the WASP model
An alternative to the fugacity approach described in Section 4.4.2.1 is the diffusive
method described in WASP (Ambrose et al. 1995). Diffusive transport between surface water
and sediment compartments can be approximated as a first-order process using the method
described for WASP. Based on the WASP model, the net diffusive exchange flux between a
surface water compartment and a sediment compartment is modeled by:
_ DSPSWSed x ASWSed x (/)SWSed ^ (fDsed x CSed _ fDsw x Csw^ ^
LSWSed I SWSed \ Sed SW ) ^
DSPSWSed x ASWSed x < SW )
where:
NSed = chemical mass in the underlying sediment compartment
(g[chemical]/day);
DSPSWSed = diffusive exchange coefficient between surface water and sediment
compartments (m2[surface water/sediment interface]/day);
^swsed = interfacial area between surface water and sediment compartments
(m2);
Lswsed = characteristic mixing length between surface water and sediment
compartments (m);
Csw> CSed = bulk concentration of chemical in surface water compartment and
sediment compartment, respectively
(g [chemi cal ]/m3 [compartment] )
Nsw, NSed = mass of chemical in surface water compartment and sediment
compartment, respectively (g[chemical]);
Vsw> Vsed = volume of surface water and sediment compartments, respectively
(m3[compartment]);
fosw fosed = dissolved fraction of chemical in surface water and sediment
compartments, respectively (calculated);
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'Psw' 'Psed = porosity of surface water and sediment compartments, respectively
(= volume fraction water, 0, for these compartments, see Chapter
2); and
< tsvsed ( A* }
X I _
Sed X
f r \
^x sw (TF4-llb)
SW X
Following the method used in WASP (Ambrose et al. 1995, p. 25), the sediment
compartment height is used as the characteristic mixing length LSWSed. The porosity of the
sediment compartment (
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CHAPTER 4
SURFACE WATER AND SEDIMENT ALGORITHMS
1995). Dispersive water column exchanges significantly influence the transport of dissolved and
particulate pollutants in such water bodies as lakes, reservoirs, and estuaries.
Based on the WASP model, the net dispersive exchange flux between two surface water
compartments / andy at a given time is modeled by:
(Eq. 4-25a)
DSP, x A^
*
L* {Vj
where:
Nj = chemical mass in surface watery (g[chemical] /day);
DSPjj = dispersion coefficient for exchange between surface water compartments /
andy (m2/day);
AJJ = interfacial area between surface water compartments / andy (m2);
LJJ = characteristic mixing length between surface water compartments /' andy
(m);
Cj, Cj = concentration of chemical in surface water compartments / andy,
respectively (g/m3);
Nj, Nj = mass of chemical in surface water compartments /' andy, respectively
(g[chemical]/m3[water]); and
Vj, Vj = volume of surface water compartments / andy, respectively (m3).
In TRIM.FaTE, the dispersive transfer factor between surface water compartments is:
DSR x A
rpdisp _ 1J_ y /'TTT A 10^
SW^J ~ Lv X V>
where:
TSWP^ = dispersive transfer factor from the ith to they* surface water compartment
(/day).
The distance between the midpoints of the two water compartments is used for the
characteristic mixing length, Lif Values for dispersion coefficients can range from 10'10 m2/sec
(8.64 x icr6 m2/day) for molecular diffusion to 5x 102 m2/sec (4.32x 107 m2/day) for longitudinal
mixing in estuaries (Ambrose et al. 1995, p. 35).
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4.6 TRANSPORT BETWEEN SEDIMENT COMPARTMENTS
A chemical can be transported between vertically adjacent sediment compartments via
the sediment pore water and bioturbation. Although applications of TRIM.FaTE to date have
involved only one sediment bed layer (above the sediment sink), a user might specify more than
one sediment layer with differing characteristics (e.g., porosity) above the sediment sink. In this
case, transport of a chemical between the layers can occur. In the current TRIM.FaTE library,
the only process modeled for this transfer is diffusion of the liquid-phase chemical across
compartments via the interstitial water. Bioturbation is not included in the TRIM.FaTE library at
this time.
The transfer factor for pore-water diffusion of chemical from one sediment compartment
to another located below it is:
= *^*/» (W4-13)
' Sedi Sedij
where:
Sedj = transfer factor for diffusion between sediment compartment /' and
sediment compartment y' below it (/day);
ASedij = interfacial area between sediment compartments /' andy (m2);
VSedi = volume of the sending sediment compartment /' (m3);
DSPSed = diffusive exchange coefficient (m2/day);
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The current TRIM.FaTE does not include algorithms for horizontal diffusion between
sediment compartments in the same sediment layer.
4.7 TRANSFORMATIONS AND DEGRADATION
The transformation of chemicals in surface water and sediments can affect their
persistence and environmental partitioning. Transformations of chemicals into compounds that
will no longer be tracked in TRIM.FaTE (e.g., non-toxic degradation products) are called general
degradation processes. In TRIM.FaTE, the degradation of a chemical in surface water due to all
mechanisms that might apply (e.g., hydrolysis, photolysis, and aerobic degradation by
microfauna) is reflected by the user input for the half-life of the chemical in a surface water
compartment. Similarly, the degradation of a chemical in sediments due to all mechanisms that
might apply (e.g.., aerobic and anaerobic bacterial degradation) is reflected by the user input for
the chemical half-life in the sediment compartment. The algorithm relating the degradation rate
constant to the chemical half-life in the soil compartment is presented in Chapter 2 (Equation 2-
64), and the corresponding transfer factor is TF 2-1.
Transformations of a chemical into another form of the chemical that is tracked in
TRIM.FaTE are named for the processes (e.g., oxidation, methylation, reduction of mercury
species). In the TRIM.FaTE surface water and sediment compartments, all transformations are
modeled as first-order processes, that is, linear with inventory (i.e., the quantity of chemical
contained in a compartment). The rate of mass removal in a first-order transformation is
calculated as the product of the total inventory of chemical in the compartment and the
transformation rate constant specified in the corresponding transfer factor. The transformation
rate constant is the inverse of the residence time with respect to that reaction.
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CHAPTER 5
SOIL ALGORITHMS
5. SOIL ALGORITHMS
In this chapter, the T-factors for the transport and transformation of chemical species
within and among soil compartments, including the ground-water stratum, are described. In
addition, algorithms for the transport of a chemical between soil compartments and the lower
atmosphere and between soil compartments and surface water are presented. The text box on the
next page and continued on the following pages provides a summary of the T-factor algorithms
developed in this chapter and defines all parameters used in those algorithms.
The remainder of this chapter is divided into five subsections. The first outlines the four
soil compartment types and the general transport processes that apply to each (Section 5.1). The
next (Section 5.2) describes the transformation and degradation processes that apply to the soil
compartments. The third subsection develops the T-factor algorithms for vertical-transport
between compartments (Section 5.3), while the fourth subsection describes the horizontal-
transport algorithms that apply to the surface soil compartments (Section 5.4). Finally, the
algorithms related to the ground-water compartment are described (Section 5.5).
5.1 SOIL COMPARTMENTS AND TRANSPORT PROCESSES
In TRIM.FaTE, soil is modeled as four distinct compartment types: surface soil, plant
root-zone soil, vadose-zone soil above the saturated zone, and the saturated zone or ground
water. In TRIM.FaTE, the root-zone and vadose-zone soils can be sub-divided into one or more
vertically stacked compartments for the purpose of assessing mass transfer. Tables 5-1 and 5-2
summarize the gains and losses for surface and subsurface soil compartments, respectively, that
are addressed in the current TRIM.FaTE library.
As indicated in Table 5-1, the uppermost surface soil compartment exchanges mass with
the lowest compartment of the atmosphere by a combination of diffusion and advection
processes. There are two advective processes addressed in TRIM.FaTE that can potentially
transport a chemical from a surface soil compartment to down-gradient surface soil
compartments or to surface water: erosion of surface soil particles and runoff of water from
surface soil. Erosion applies to the solid phase, while runoff and recharge apply to the dissolved
phase.
As indicated in Table 5-2, two of the primary transport processes in subsurface soils are
exchanges by diffusion and advection. Transport can occur both in the gas and liquid phases.
The predominant transport mechanism in the aqueous phase is advection, and that in the gas
phase is diffusion. The advective transport of contaminants in the liquid or gas phase depends
on the velocity of that phase. There currently is only one advective process included in the
TRIM.FaTE library that can potentially transport a chemical from the vadose-zone soil
compartment to ground water, that is percolation. Recharge of ground water to surface water also
is included. Important physicochemical properties include solubility, molecular weight, vapor
pressure, and diffusion coefficients in air and water. The important landscape properties include
temperatures of air, rainfall rates, soil properties (i.e., bulk density, porosity), and the depth of
each soil compartment.
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Summary of Transfer Factors for Soil in TRIM.FaTE
VERTICAL EXCHANGES BETWEEN SURFACE SOIL AND ATMOSPHERE
Diffusion of vapor-phase from air to surface soil: (TF 5-1)
- +
lr 7 Y V \ 7 Y TJ 7 Y TI\
^Total_Ss A * Ss \^pure_air A ^ Air ^ Total _Ss A ^ Ss J
Diffusion of vapor-phase from surface soil to air: (TF 5-2)
Air->Ss 7 y T/ 7 y 7-7 7
^ Total_Air A ' A> \^pure_air A ^ A> ^ Total_Ss ^ ^ Ss
Dry deposition of particle-phase from air to surface soil: (TF 5-3b)a
7) Y H - T \ Y A
isi A I 1 I , I A ^1?
rpdry_dep _ ary ^ ary ' ^f_ y ^>
1 AirP^Ss ~ Y X J MS
V Air
Wet deposition of particle-phase from air to surface soil during rain:
(TF 5-4)
v , x (1- / ,) x A,
Twet_deP viet_ V wet J Ss_ r
J AirP^rSs ~ y A J MS
'Air
Wet deposition of vapor-phase from air to surface soil during rain (fugacity approach): (TF 5-5a)
X
Total _Air
Wet deposition of vapor-phase from air to surface soil during rain (partitioning approach): (TF 5-5b)
T^-Sr = ^ x Wrv x ram x (l - Iwet ) x /MF
'Air
Dry resuspension of particle-phase to air from surface soil compartment: (TF 5-6)
res ASs reS pure_solid
X X
Total Ss
3 TF 5-5a represents the same basic equation, but uses the fugacity notation. TF 5-5b is the
expression of the equation in the current TRIM.FaTE library.
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Summary of Transfer Factors for Soil in TRIM.FaTE (cont.)
VERTICAL EXCHANGES BETWEEN SOIL COMPARTMENTS
Diffusion downward from soil compartment /to the soil compartment j directly below it:
Y
rpdif Sij
1st^sj - j 7
USi A ^Total_Si
Diffusion upward from soil compartment j to the soil compartment /immediately above it:
Y
rpdrf Sij
1Sj^Si ~ J 7
U.gj A ^Total_Sj
Percolation downward from soil compartment /to soil compartment j:
rriperc V£Si X ysi
* ~ (e+rsXds - l)
HORIZONTAL EXCHANGES ACROSS SURFACE SOIL COMPARTMENTS
Runoff during rain from surface soil compartment /to surface soil compartment j:
^
r^runoff -mmnfr V f ( CVV _A Cc-7\ V Ssi V f
'ss^ssj - runoff x Jrmoff (bsi -> bsj) x x j ML
" Ssi
Erosion during rain from surface soil compartment /to surface soil compartment j:
A f
rrerosion -j-i-j-ic-ij-i-n -' -f ( CVi • CrW' Ssi " MS
1 &*-+!% ~ ei osion A J emsion(^si -t 057) A A
V Ssi PP
Runoff during rain from surface soil compartment /to surface soil sink, same as TF 5-1 Oa
but with Ss_sink replacing Ssj\
Erosion during rain from surface soil compartment / to surface soil sink, same as TF 5-1 1 a
but with Ss_sink replacing Ssj:
HORIZONTAL TRANSFER FROM SURFACE SOIL TO SURFACE WATER
Runoff during rain from surface soil compartment /to surface water compartment:
^
rprunoff TnivtnfT V f ( CcV ^ CT/TA V f V Ssi V f
i-s^sw ~ runoff x J^ff^si -» t>W) x Javail_mnoff x x /ML
Erosion during rain from surface soil compartment /to surface water compartment:
A f
rrerosion -j-i-j-ic-ij-t-n -' -f f Vci - CTTA" f " &! " M5
7&,^sw - erosion/, Jemsion(^si -t ^ ) ^ J mml erosion A A
^ PP
(TF 5-7)
(TF 5-8)
(TF 5-9)
(TF5-10a)
(TF5-11a)
(TF5-10c)
(TF5-11C)
(TF5-10b)
(TF 5-1 1 b)
SEPTEMBER 2002 5-3 TRIM.FATE TSD VOLUME II
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SOIL ALGORITHMS
Summary of Transfer Factors for Soil in TRIM.FaTE (cont.)
VERTICAL EXCHANGES WITH GROUND WATER
Percolation from vadose-zone soil to ground water:
VC X 'Y
T~r Sv I Sv
(TF5-12)
Recharge from ground water to surface water:
(TF5-13)
vow
pure_water 7
• x x recharge
^ Total OW
LIST OF SYMBOLS USED IN TRANSFER FACTOR ALGORITHMS
Ss
-Total_Ss
~
pure_air
u~
"dry
'dry
'wet
rain
-pure_water
w,
rV
res
PP
pure_solid
Ys:
fraction of area available for vertical diffusion (from 0 to 1.0);
horizontal area of the surface soil compartment (m2). (This is the area assumed to be
shared between the top soil compartment and the atmosphere.)
total fugacity capacity of surface soil compartment (mol/m3-Pa).
volume of surface soil compartment (m3).
fugacity capacity of chemical in pure air, = 1/RT (mol/m3-Pa).
mass transfer coefficient on the air side of the air/soil boundary (m/day). (It is typical
to represent the mass transfer coefficient in air as the ratio of the diffusion coefficient
in air, Dair, divided by the turbulent boundary compartment thickness, 5air. For many
compounds, Dair is on the order of 0.4 m/day and 5air is on the order of 0.0005 m, so
that Ua!r is on the order of 800 m/day.)
volume of the air compartment (m3).
total fugacity capacity of chemical in the air compartment (includes gas and particle
phase of the atmosphere) (mol/m3-Pa).
volumetric dry particle deposition rate (m3[dust particles]/m2[surface water]-day).
fraction of dry particle deposition that is intercepted by plants (unitless).
fraction of total chemical mass in compartment that is sorbed to solid particles
divided by volume fraction of the compartment that consists of particles (unitless).
volumetric wet particle deposition rate (m3[dust particles]/m2[surface water]-day).
fraction of wet particle deposition that is intercepted by plants (unitless).
rate of rainfall (m3[rain]/m2[surface soil]-day).
fugacity capacity of chemical in the moving phase, water (mol/m3-Pa).
vapor washout ratio (g[chemical dissolved]/m3[rain] per g[chemical vapor-
phase]/m3[air]).
fraction chemical mass in air compartment that is in vapor-phase divided by the
volume fraction of air compartment that is gas (unitless).
rate of resuspension of dust particles from soil to air (kg[dust particles]/m2[surface
soil]-day).
density of dust or soil particles in air (kg[particles]/m3[particles]).
fugacity capacity of chemical in the moving phase, dust particles (mol/m3-Pa).
gradient of soil concentration change in soil compartment; (/m).
thickness of surface soil compartment; (m).
fugacity-capacity adjusted mass transfer coefficient between soil compartments /and
j (mol/m2-Pa-day), and is given by:
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Summary of Transfer Factors for Soil in TRIM.FaTE (cont.)
LIST OF SYMBOLS USED IN TRANSFER FACTOR ALGORITHMS (cont.)
Si) + \£Total Si x DeSj x Ysi)
7s,- Ysj
runoff =
avail_runo
'ML
erosion
avail_
'SWGW
GW
_
recharge =
2x
thickness of soil compartments /and j, respectively (m).
total fugacity capacity of chemical in soil compartment; (mol/m3-Pa).
total fugacity capacity of chemical in soil compartmenty (mol/m3-Pa).
gradient of soil concentration change in soil compartments /and/ respectively (/m).
effective diffusion coefficient in soil compartment; (m2[soil]/day].
effective advection velocity of a chemical in the soil compartment; (m/day), and equal
to the rate of soil-solution movement, v, (see below), multiplied by the fugacity capacity
of the moving phase (water) divided by the total fugacity capacity of the soil
compartment /; ve, = (v, x Zp_ure_wa J/ZTotal_s,
average velocity of the moving phase (assumed to be water) in soil compartment;
(/m).
flux of water transported away from surface soil compartment;
(m3[water]/m2[soil]-day).
= fraction of water that runs off of surface soil compartment; that is transported
to surface soil compartmenty (unitless).
= fraction of surface soil available for runoff (between 0 and 1.0).
= fraction of chemical in compartment that is dissolved in water divided by the
volume fraction of the compartment that is liquid (water).
= flux of soil particles transported away from surface soil compartment;
(kg[soil particles]/m2[soil]-day).
= fraction of soil that erodes from surface soil compartment; that is transported
to surface soil compartmenty (unitless).
= fraction of surface soil available for erosion (between 0 and 1.0).
effective advection velocity of a chemical in the vadose-zone soil compartment
(m/day).
gradient of soil concentration change in vadose-zone soil compartment (/m).
interfacial area between ground-water and surface-water compartments (m2).
volume of ground-water compartment (m3).
total fugacity of chemical in the ground-water compartment (mol/m3-Pa).
average daily recharge from ground water into surface water (m/day).
A future version of the TRIM.FaTE library could include algorithms for diffusive transfers
between the vadose-zone soil compartment and the ground-water compartment.
5.2 TRANSFORMATIONS AND DEGRADATION
The transformation of chemicals in soil layers can have a profound effect on their
potential for persistence. Chemical transformations, which may occur as a result of biotic or
abiotic processes, can significantly reduce the concentration of a substance in soil.
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Table 5-1
Summary of the Chemical Gains and Losses for Surface Soil
Compartments Addressed in TRIM.FaTE
Gains
Type of
Process
Relevant
Phase
From Air
Diffusion from air
Dry deposition of particles/
aerosols from air
Wet deposition of particles/
aerosols from air
Wet deposition of vapor from
air
Diffusion
(TF5-1)
Advection
(TF 5-3)
Advection
(TF 5-4)
Advection
(TF 5-5)
Vapor
Solid
Solid
Vapor
From Surface Soils
Erosion from upgradient soils
Runoff from upgradient soils
Advection
(TF5-10a)
Advection
(TF5-11a)
Solid
Aqueous
From Plants
Deposition of leaves during
litter fall
Deposition of particles on
leaves during litter fall
Advection
(TF7-15)
Advection
(TF7-16)
Solid
Solid
From Surface Water
From Terrestrial Birds and Mammals
Elimination from terrestrial
and semi-aquatic wildlife
Advection
(TF7-31)
Total
From Root-Zone Soil
Upward diffusion
Diffusion
(TF 5-8)
Aqueous
& Vapor
From Surface Soil Transformations
Losses
Type of
Process
Relevant
Phase
To Air
Diffusion to air
Dry resuspension of
particle phase
Diffusion
(TF5-2)
Advection
(TF 5-6)
Vapor
Solid
To Surface Soils
Erosion to downgradient
soils
Runoff to downgradient
soils
Advection
(TF5-10a)
Advection
(TF5-11a)
Solid
Aqueous
To Plants
To Surface Water
Erosion
Runoff
Advection
(TF5-11b)
Advection
(TF5-10b)
Solid
Aqueous
To Terrestrial Birds and Mammals
Ingestion by wildlife
Advection
(TF 7-22)
Total
To Root-Zone Soil
Percolation
Diffusion
Advection
(TF 5-9)
Diffusion
(TF 5-7)
Aqueous
Aqueous
& Vapor
To Sink(s)
Runoff off-site to sink
Erosion off-site to sink
Decay to reaction sinks
Advection
(TF5-10c)
Advection
(TF5-11c)
Degradation
(TF2-1)
Aqueous
Solid
Total
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Table 5-2
Summary of the Chemical Gains and Losses for Sub-surface Soil
Compartment./ Addressed in TRIM.FaTEa
Gains
Type of
Process
Relevant
Phase
From Vertically Adjacent Soil Compartment
Downward diffusion from soil
compartment /
Upward diffusion from soil
compartment /
Percolation downward from
soil compartment /
Diffusion
(TF 5-7)
Diffusion
(TF 5-8)
Advection
(TF 5-9)
Aqueous
Aqueous
Aqueous
Release from plant roots
Diffusion
(TF7-11)
From Ground Water
From Surface Water
From Soil Transformations
Losses
Type of
Process
Relevant
Phase
To Vertically Adjacent SoilCompartment
Downward diffusion from
soil compartment./
Upward diffusion from
soil compartment j
Percolation downward
from soil compartment j
Diffusion
(TF 5-7)
Diffusion
(TF 5-8)
Advection
(TF 5-9)
Aqueous
Aqueous
Aqueous
To Plants
Uptake from root-zone
soil by plant roots
Uptake by plant stems
from root-zone soil via
flow of transpired water
Diffusion
(TF7-10)
Advection
(TF7-12a)
Aqueous
Aqueous
To Ground Water
Percolation from vadose-
zone soil
Advection
(TF5-12)
Aqueous
To Surface Water
Recharge from ground
water
Advection
(TF5-13)
Aqueous
To Sink(s)
Decay to reaction sinks
Degradation
(TF2-1)
Total
aSub-surface soil compartment /' is higher than7 is higher than /.
Transformations of chemicals into compounds that will no longer be tracked in
TRIM.FaTE (e.g., non-toxic degradation products) are called general degradation processes in
the model. In TRIM.FaTE, the degradation of chemicals in soil due to all mechanisms that
might apply (e.g., degradation by soil microfauna, photolysis at the soil surface, hydrolysis in
the saturated zone) is reflected by the user input for the half-life of the chemical in the particular
soil compartment. The algorithm relating the degradation rate constant to the chemical half-life
in a soil compartment is presented in Chapter 2 (Equation 2-64).
Transformations of a chemical into another form of the chemical that is tracked in
TRIM.FaTE are reflected in algorithms that are named for the process (e.g., oxidation,
methylation, reduction of mercury species). In the TRIM.FaTE soil layers, all transformation
processes are modeled as first-order processes, that is, linear with inventory (i.e., the quantity of
chemical contained in a compartment). The rate of mass removal in a first-order transformation
is calculated as the product of the total inventory and the transformation rate constant. The
transformation rate constant is the inverse of the residence time with respect to that reaction.
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5.3 VERTICAL TRANSPORT ALGORITHMS
The transfer factors in the subsurface are a function of the advective flux (gas phase plus
liquid phase) and the diffusive flux (gas phase plus liquid phase). In the subsections below,
upward and downward transfer factors are developed for the top three soil compartments (i.e.,
excluding ground water). No provisions are made for preferential flow regions in the vadose
zone that could lead to higher concentrations in the ground water, because in most cases, the
proportion of exposure from ground water is minimal for air pollutants.
5.3.1 THEORETICAL BASIS FOR THE TRANSPORT ALGORITHMS
The algorithms below are developed by assuming that chemical concentration in each
compartment decreases exponentially with depth in that compartment. This type of
concentration gradient has been demonstrated as the correct analytical solution of the one-
dimensional, convective-dispersive, solute-transport equation in a vertical layer with a steady-
state concentration maintained at its upper surface (ARS 1982). With the assumption of
exponentially decreasing vertical concentration for each soil compartment, /', the variation in
concentration with depth in that compartment is given by:
C;.(*)=C;.(0)xexp(-y;.*) (Eq. 5-1)
where:
x = distance into the soil compartment measured from the top of the soil
column (m);
Ct(0) = peak chemical concentration in soil compartment / (g[chemical]/m3[soil]),
which is related to the total inventory Nt (g[chemical]) in this soil
compartment (this relationship is provided below); and
Yi = the gradient of soil concentration change in soil compartment /' (/m),
which is obtained from the inverse of the normalized or characteristic
depthJf*, which is yf = 1/X*.
X* can be input by the user. If the user does not provide a value, a value for X* is calculated as
follows. Let:
/?,- = removal rate constant for a chemical in soil compartment /', based on
chemical transformation (/day); then
If A, > 0 then X* = Minimum (DX,, DX2\
Otherwise (i.e., 2, = 0), thenX* = DX2. (Eq. 5-2)
DXj is the Damkoehler distance (the distance at which the soil concentration falls by 1/e
based on the aggregate results of diffusion, advection, and reaction) in units of meters and is
given by:
SEPTEMBER 2002 5-8 TRIM.FATE TSD VOLUME II
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ve + Jve + 4De<,
DX, = ' V ' S- (Eq. 5-3a)
2/1,
Equation 5-3a can be rearranged as follows to arrive at Equation 5-3d, which is the form of the
equation in the TRIM.FaTE library:
(Eq5-3b)
+ (Eq"d)
2/1. yv2/t.y V /t, J
Ifve, = 0, then:
In Equations 5-3a through 5-3e, the following parameter definitions apply:
DeSi = effective diffusion coefficient in soil compartment /' (m2[soil]/day), which
is derived below in Equation 5-7; and
vei = the effective advection velocity of a chemical in the soil compartment, /'
(m/day), and equal to the rate of soil-solution movement, vt, multiplied by
the fugacity capacity of the moving phase and divided by the fugacity
capacity of soil compartment /':
ve, = (v, x Zpure_water) /ZTotal_Sl (Eq. 5-4)
where:
vt = average velocity of the moving liquid phase (assumed to be water)
in the soil column /' (m/day);
Zpure water = fugacity capacity of chemical in the moving phase, water
(mol/m3-Pa); and
Zrotai si = total fugacity capacity of chemical in soil compartment /' (mol/m3-
Pa).
DX2 is the depth that establishes the concentration gradient in soil in the absence of any
reaction or transformation processes, in units of meters. It is obtained as follows:
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live, > 0, thenDX, = Minimum [(4 x De/ve,), (2d, x /TI)]
Otherwise (i.e., ve, = 0), DX2 = (2d, x /TI) (Eq. 5-5)
where:
dt = the thickness of soil compartment /' (m).
As an average, the property vt (m/day), the average velocity of the moving liquid phase
(assumed to be water) in the soil column /', is intended to be representative of the range of
velocities occurring, and not be limited only to the velocity during rainfall events. The user
should check that the value used for vi in the TRJJVI.FaTE library is consistent with the
precipitation data in the scenario (adjusted for infiltration) (see the TRIM.FaTE user guidance).
Compartments such as soils and sediments are neither homogeneous nor single phase.
When air and water occupy the tortuous pathways between stationary particles in a porous
medium such as a soil or sediment, Millington and Quirk (1961) have shown that the effective
diffusivity is given by:
De=(a10/3/02-)xDpure (Eq.5-6)
where:
De = effective diffusivity of a chemical in either the air or water phase of the
mixture (m2[fluid]/day);
(o = volume fraction occupied by that fluid (either air or water) (unitless);
(f) = porosity or total void fraction in the medium (the volume occupied by all
fluids) (unitless); and
Dpure = diffusion coefficient of the chemical in the pure fluid (m2[fluid]/day).
Jury et al. (1983) have shown that the effective tortuous diffusivity in the water and air of a soil
compartment /', such as the root-zone soil(s), is given by:
Des, = ^ x tf- / 0? ) x Dair + -f x (6T / $ ) x Dmter (Eq. 5-7)
^ Total _Si ^ Total _Si
where:
DeSi = the effective tortuous, mixed-phase diffusion coefficient in the soil
compartment / (m2[soil]/day);
et = volume fraction of soil compartment /' that is air (unitless);
6t = volume fraction of soil compartment /' that is water (unitless);
Zpure_air = fugacity capacity of chemical in the gas-phase of air (mol/m3-Pa);
ZPU™ water = fugacity capacity of chemical in the soil water (mol/m3-Pa);
Z Total si = total fugacity capacity of chemical in soil compartment / (mol/m3-Pa);
Dair = the diffusion coefficient of the chemical in air (excluding atmospheric dust
particulates) (m2[air]/day); and
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Dwater = the diffusion coefficient of the chemical in water (excluding suspended
sediments (m2[water]/day).
5.3.2 RELATIONSHIP BETWEEN INVENTORY, N^ AND PEAK
CONCENTRATION, Csi(0)
The assumptions of a peak chemical concentration and an exponential gradient of
chemical concentration within a soil compartment make it possible to define CSi(0) in terms of
the inventory, NSi:
NSl = Asi x j CSl (0) x exp(- r^dx (Eq. 5-8)
0
N,, = A,,x [CL (0) / r,, 1 x [1 - exp(- y„. x d,,)] (Eq 5-9)
Jl Jl •- Jl \ / * Jl -J L 1 \ ' Jl Jl / -> \ T. /
where:
NSi = inventory of chemical in soil compartment /' (g[chemical]);
ASi = horizontal area of the soil compartment /' (m2);
CSi = chemical concentration in soil compartment /' (g[chemical]/m3[soil]);
ysi = the gradient of soil concentration change in soil compartment /' (/m) (see
Equation 5-1); and
dsi = thickness of soil compartment /' (m).
Solving Equation 5-9 for CSi(0) yields:
c«(°) = A ~n !»/!' ^ M (Eq-5-10)
5.3.3 VERTICAL MASS EXCHANGE BETWEEN AIR AND THE SURFACE SOIL
COMPARTMENT
Both diffusive and advective processes can transfer a chemical between the air and the
surface soil compartment. The diffusive process can result in a two-way exchange of vapor-
phase chemical between the surface soil and air above it (Section 5.3.3.1). The advective
processes are one-way, from air to surface soil. These include the wet and dry deposition of
particle-bound chemical (i.e.., solid phase) (Section 5.3.3.2) and the wet deposition of vapor-
phase chemical scavenged from the air during rain.
5.3.3.1 Diffusive Processes
The algorithm for representing diffusion exchange at the air/soil interface is based on
defining the flux from air to soil in terms of the concentration gradient at the point of contact
between air and soil (Eq. 5-11) and the flux from soil to air in terms of the bulk chemical
concentration in the surface soil layer (Eq. 5-12):
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Flux (air side) = UAir x
z
pure _air
'Total Ss
(Eq.5-11)
Flux (soil side) = USs x [c&(0) - CSs]
(Eq. 5-12)
where:
Flux
UAir
CAir
7
pure_air
7
z'Total Ss
uss
CSs(bulk) =
transfer rate per unit area (g[chemical]/m2[air/soil interface]-day);
mass-transfer coefficient on the air side of the air/soil interface (m/day) (It
is typical to represent the mass transfer coefficient in air as the ratio of the
diffusion coefficient in air, Dair, divided by the turbulent boundary
compartment thickness, 6air. For many compounds, Dair is on the order of
0.4 m/day, and 6air is on the order of 0.0005 m, so that UAir is on the order
of 800 m/day.);
concentration of the chemical in the gas phase of the lowest compartment
of the atmosphere (g[chemical]/m3[gas-phase air]), derived in Equation 5-
16 below;
chemical concentration at the top of the uppermost (i.e., surface) soil
compartment in a vertical set of soil compartments (g[chemical]/m3[soil]),
as given for C,-(0) in Equation 5-10;
fugacity capacity of chemical in air, = 1/RT (mol/m3-Pa);
total fugacity capacity of chemical in surface soil compartment (mol/m3-
Pa);
mass-transfer coefficient on the soil side of the air/soil interface (m/day);
and
total chemical concentration in bulk surface soil (g[chemical]/ m3[soil]).
Rearranging Equations 5-11 and 5-12 yields Equations 5-13 and 5-14, respectively:
Flux
7 x TJ
pure air ^ Air
C C (0}
Air Ss \ /
7 7
pure air Total Ss
(Eq. 5-13)
Flux
7 y U
^ Total Ss A ^ Ss
CSs(0) CSs(bulk}
Total _Ss
Total _Ss
(Eq. 5-14)
Adding Equations 5-13 and 5-14 together yields:
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Fluxx
1
pure air
U Air ^ Total _Ss X ^ Ss
CAir
pure air
CSs(bulk}
^ Total _Ss
(Eq. 5-15)
Flux =
CAir
pure air
C^bulk)
^ Total _Ss
y
1
pure air
U Air ^ Total
1
_& X Us, _
1 -1
(Eq. 5-16)
The bulk concentration of the chemical in the lowest compartment of the atmosphere is given by:
where:
Air Total _Air
(Eq. 5-17)
pure_air
VAir
7 =
^Total Air
inventory of chemical in the air compartment above the soil (g[chemical]);
fugacity capacity of chemical in gas-phase air (mol/m3-Pa);
volume of the air compartment (m3[air]); and
total fugacity capacity of chemical in air compartment (including gas and
particle phases of the air) (mol/m3-Pa).
The bulk concentration of the chemical in the surface soil layer is given by:
Ss 77
V L
Ss
(Eq. 5-18)
Ss
where:
VSs
inventory of chemical in the surface soil compartment (g[chemical]); and
volume of the surface soil compartment (m3[soil]).
Finally, the chemical flow between the air and surface soil compartments is determined from the
flux and the area of the air/soil interface (as well as the fraction of that area that is not covered by
an impervious material):
where:
Flow = Flux xfAxASs
(Eq. 5-19)
Flow = diffusive flow (g[chemical]/day);
fA = fraction of area available for vertical diffusion (unitless, ranges from 0 to
1); and
ASs = area of surface soil compartment (m2).
Making the appropriate substitutions, the net flow of chemical mass between the air and surface
soil compartments by diffusion is calculated as:
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Net Diffusion Flow (Air^Ss) (g[chemical]/day) = (TAir^ x NAir) -(TSs^Air x NSs) =
-i
..
\ ^ Total_air ^ V Air ^ Total_Ss ^ V Ss J \ ^ pure _air A ^ Air ^ Total_Ss A ^ Ss
where:
(Eq. 5-20)
Zpare air = fugacity capacity of chemical in pure air (mol/m3-Pa);
VAir = volume of the air compartment (m3);
ZTotal ss = total fugacity capacity of chemical in surface soil compartment (mol/m3-Pa);
VSs = volume of the surface soil compartment (m3);
UAir = mass transfer coefficient on the air side of the air/soil boundary (m/day); and
USs = mass transfer coefficient on the soil side of the air/soil boundary (m/day).
This implies the following:
( \-1
f x A \ 1 1 1
Ss^Air ~ 7 y V \ 7 y TJ 7 y TJ \
*-'Total_Ss A ' Ss \^pure_air A ^ Air ^Total_Ss A ^ Ss J
where:
T^Atr = transfer factor for diffusion of chemical from surface soil compartment to air
(/day).
It also implies:
f
d. J A
Air^Ss ~ 7 x V 7 x U 7 x T7
^Total_air A ' A> \ ^ pure _air A ^ A> ^ Total _Ss A ^ 5x
where:
TAIT^SS = transfer factor for diffusion of chemical from air to surface soil compartment
(/day).
The mass transfer coefficient for the soil side of the air/soil boundary, USs, can be
estimated as follows:
Dess
USs = —^ (Eq. 5-21)
USs
where :
DeSs = effective diffusion coefficient in surface soil compartment (m2/d) (derived
in Equation 5-7); and
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d.
•Ss
the thickness of the surface soil compartment (m).
It is important to ensure that the area used to calculate the flux, ASs, is the area of the
surface soil compartment that is shared with the lowest atmosphere compartment. This is not
necessarily the surface area of the lowest atmosphere compartment.
Note: In the current TRIM.FaTE library, these transfer factor algorithms apply to all
chemicals except divalent mercury, which is reactive in air. Therefore, a separate algorithm
representing net diffusion from air to surface soil is used for divalent mercury (see vapor dry
deposition algorithms for Hg(2) described in Appendix A, Section A. 1.1).
5.3.3.2 Wet and Dry Deposition of Particles
For wet and dry deposition of particles from air to surface soil, the rate of mass flow is
given by:
A
Ss
DT
•= ^x v x(l- 7)x
dt VA,r PP ZToM Alr
(Eq. 5-22)
where:
inventory of chemical in surface soil compartment (g[chemical]);
area of contact between the surface soil compartment and the lowest air
compartment (m2[soil]);
volume of the air compartment (m3[air]);
air-to-soil deposition velocity, where the velocity is different for wet and
dry deposition of particles (m/day);
fraction of deposition that is intercepted by plants, where the interception
fraction is different for wet and dry deposition of particles (unitless);
dust load (i.e., particulate matter concentration) in air (kg[dust
parti cles]/m3[air]);
density of dust particles (kg[dust particles]/m3[dust particles]);
fugacity capacity of chemical in dust particles (mol/m3-Pa);
total fugacity capacity of chemical in air compartment (including dust
particles) (mol/m3-Pa); and
total inventory of chemical in air compartment, vapor- and solid-phase
(g[chemical]).
Dry deposition of particle-phase chemical:
Thus, the transfer factor for dry deposition of chemical sorbed to air particles to the
surface soil is as follows:
ASs
v
/
DL
PP
7
pure_solid
7
^Total Air
D
PP
L pure _solid
''Total Air
(TF 5-3a)
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where:
vdry = air-to-soil dry deposition velocity (m/day); and
rdty = fraction of dry deposition that is intercepted by plants (unitless) (see
Equation 7-2).
It is also true that:
where:
v,
dry
and:
PP
volumetric dry deposition rate (m3[dust]/m2[air]-day);
(Same as Eq. 4-1)
"*'pure _solid
z
Total Air
Mass_ Fraction _ Sorbed
Volume Fraction Solid MS
(Eq. 5-23)
where:
IMS
mass fraction of the chemical sorbed to solid particles in air divided by the
volume fraction of the air compartment that consists of solid particles
(unitless) (see Equations 2-71 and 2-79).
Therefore, the transfer factor can be calculated as:
j^dry _dep _
1AirP^Ss ~
dry ) X ASS
x/,
MS
(TF 5-3b)
where:
rj-<
J-
-------
where:
rj-
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CHAPTER 5
SOIL ALGORITHMS
Iwet = fraction of wet deposition that is intercepted by plants (unitless) (see
Equation 7-4); and
NAir = total chemical inventory in the air compartment, both vapor- and solid-
phase (g[chemical]).
Therefore, the transfer factor for wet deposition of vapor-phase chemical to surface soil can be
calculated as:
ram x (1 - Iwet ) x ^ (TF 5-5a)
Air Total _Air
where:
Tv^-^ = transfer factor for wet vapor deposition from air to surface soil
compartment /' during a rainfall event (/day).
In the current TRIM.FaTE library, TF 5-5a is used for organic chemicals. For the
mercury species, a slightly different algorithm is used:
V x rain x (l - Iwet ) x fMV (TF 5-5b)
where:
wrV = vapor washout ratio (g[chemical dissolved]/m3[rain] per g[chemical vapor-
phase]/m3[air]) = \IKAW, where:
KAW = air/water partition coefficient (g[chemical/m3[air] per
g[chemical]/m3[water]); and
fMV = the fraction of the chemical mass in the air compartment that is in the
vapor phase divided by the volume fraction of the air compartment that is
gas/vapor (i.e., fraction that is not particulate) (see Equation 2-81 in
Chapter 2).
The derivation of these algorithms is explained in more detail in Chapter 7, Section 7.2.1.6.
5.3.3.4 Dry Resuspension of Dust from Soil to Air
For resuspension of dust from the first surface soil compartment to the lower
compartment of the atmosphere, the chemical transfer from soil to air is given by:
.. ..
SS^A,rP ~ V n
' Ss Pp Total _Ss
where:
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res = rate at which dust particles are resuspended from the soil surface
(kg[particles]/m2[soil surface]-day);
pp = density of the dust particles (kg[particles]/m3[particles]);
Zpure_so!id = fugacity capacity of chemical in dust particles (mol/m3-Pa); and
ZTotal ss = total fugacity capacity of chemical in surface soil compartment
(including dust particles) (mol/m3-Pa).
If a value cannot be determined for res, then it can be estimated using the equation:
res= vdtyxpp (Eq. 5-25)
where:
vdry = volumetric dry deposition rate (m3[particles]/m2[surface soil]-day).
5.3.4 VERTICAL MASS EXCHANGE BETWEEN TWO VERTICALLY ADJACENT
SOIL COMPARTMENTS
The vertical exchange of a chemical substance between two vertically adjacent soil
compartments occurs through advection and diffusion. Only the net advection in the downward
direction is considered due to long-term infiltration of rain water. This percolation occurs only
in the downward direction, and not laterally. Diffusion in the current TRIM.FaTE library is
represented in both an upward and downward direction, but not horizontally. The focus is on
vertical diffusion because it is assumed that the vertical transport of chemicals in soils exceeds
the horizontal transport when the major source of contamination is from the air.
5.3.4.1 Vertical Diffusive Transfers
According to Equation 5-1, the concentration in each soil compartment /' is given by:
cs, O) = cs, (°) exP(- 7Six) (same as Eq. 5-1)
where:
x = distance into the soil compartment measured from the top of the soil column
(m);
CSi(0) = peak chemical concentration in soil compartment / (g[chemical]/m3[soil]),
which is related to the total inventory NSi (g[chemical]) in this soil
compartment (this relationship is provided below in Equation 5-30); and
ysi = the gradient of soil concentration change in soil compartment /' (/m), which is
obtained from the inverse of the normalized or characteristic depth X*, which
is Ysi = 1/X*.
Thus, the diffusive flow at the lower boundary of soil compartment / to compartment./ is given
by:
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dC
Diffusion Flow = - ASij x Desi x ——
\A,J\
= ASl] x DeSl x Cfl.(0) x 7si x e~r**d* (Eq. 5-26)
where:
Diffusion Flow = movement of chemical mass from soil compartment / toy
(g [chemi cal ]/day);
S'j
Des,
Ys,
ds,
area of interface between soil compartments /' andy (m2[interface]);
effective diffusion coefficient in soil compartment /' (m2/day);
the gradient of soil concentration change in soil compartment / (/m); and
the thickness of soil compartment / (m).
Conservation of mass requires that the flow specified by Equation 5-26 out of soil
compartment /' must equal the flow into soil compartment y at the upper boundary of
compartment j, that is:
Diffusion Flow = - ASl] x DeS] —
dC
dx
(Eq. 5-27)
where:
DeSj
effective diffusion coefficient in soil compartment ji (m2/day);
the gradient of soil concentration change in soil compartment y' (/m); and
the thickness of soil compartment y' (m).
Combining Equations 5-26 and 5-27 gives:
Diffusion Flow = ASjj x
[Desi x Ca.(0) x r, x e^** + DeSj x CSj(0) x ysj\
(Eq. 5-28)
Cs(0) is found from the condition:
NSl = ASIJ x j Q»(0) x e-^dx = ASIJ x -J^x (l -
(Eq. 5-29)
where:
Rearranging gives:
total chemical inventory in soil compartment /' (g[chemical]).
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In order to conserve concentration equilibrium at the boundary between two soil
compartments, the following condition must hold:
7 7
C,(0)= ^x C,(0)x -
'Total _Si *- 'Total _Si
where:
Zrofa/ # = total fugacity capacity of the chemical in soil compartment y (mol/m3-Pa); and
ZTotai_si = total fugacity capacity of the chemical in soil compartment / (mol/m3-Pa).
Substituting Equations 5-30 and 5-31 into Equation 5-28 gives:
n.~ . ^ Ns x ysi ( Des, x 7si x ZTotal Sl + DeSj x yS] x ZTotal }
Diffusion Flow = - - x - — - — (Eq. 5-32)
Then in order to express mass transfer between two compartments, the diffusion flow is
represented in the following form:
Diffusion Flow = ASlJ x YSlJ x N* - ^ (Eq. 5-33)
\^ Total _Si X '« ^ Total _Sj X 'S//
where:
TVy, = the total chemical inventory in soil compartment y' (g[chemical]);
VSi = volume of soil compartment / (m3);
VSi = volume of soil compartment y' (m3); and
YSij = fugacity-capacity adjusted mass transfer coefficient between soil
compartments /' andy, mol/(m2-Pa-day).
The total chemical inventory, NSj, in soil compartment y, is given by:
NSj = ASJ x j CSj (0) x e~r*xdx = ASj x ^— x (l - e~7sjXdsj ) (Eq. 5-34)
0 7sj
Substituting Equation 5-31 in Equation 5-34 gives:
oa
= oa, - , , -
J Z XY x(e+rs'xdsi - l)
^Total_Si A I SJ A \K 1/
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An expression for YSij is obtained by substituting Equation 5-35 for NSj in Equation 5-33 and then
setting Equation 5-33 equal to Equation 5-32:
NSi x ysi ( Des, x yst x ZTotal_st + DeSj x ysj x ZTotal_^
" X
7 y (p^^dsi _ -1}
L Total_Si X \e V
,\77 r-j \ 1 1
ZT0tai_Sl (ds, dsjxysjx
Rearranging gives:
(7 x DP x v \ 4- (7 x DP "y. v \
\^Total_Si A •L^c'Si A /5; / T \^Total_Sj A •LycS/ A /Sj)
7,.. =
2x
The definition of 7&> in Equation 5-37 completes the definition of all terms in Equation 5-33.
For the diffusive transfer of chemical from the higher soil compartment / (e.g., root-zone
soil) to the soil compartment y' below (e.g., vadose-zone soil), the transfer factor can be
calculated as follows:
(TF 5'7)
For the diffusive transfer of chemical from the lower soil compartment y' (e.g., vadose-
zone soil) to the soil compartment /' above (e.g., root-zone soil), the transfer factor can be
calculated as follows:
(TF 5'8)
Note that both TF 5-7 and TF 5-8 assume that the normalized depth of the higher soil
compartment i is thinner than the lower soil compartment y' (i.e., dsi x ysi < dsj x ysj). The
variable ysi, the soil penetration gradient (/m), is used to normalize depth in each soil
compartment as shown above.
5.3.4.2 Downward Advective Transfer (Percolation)
The advection flow (i.e., percolation) from soil compartment /' toy at the lower end, dt, of
compartment /' is given by:
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Advection Flow(Si -> Sj) = ASlJ x ve, x Cffi(0) exp(- /a. x rfa.) (Eq. 5-38)
where:
Advection Flow = movement of chemical mass from soil compartment /' toy
(g[chemical]/day);
vei = the effective advection velocity of a chemical in the soil compartment /'
(m/day), which is equal to the rate of soil-solution movement, v;,
multiplied by the fugacity capacity of the moving phase and divided by
the total fugacity capacity of soil compartment /':
v x 7
i pure_water
ve, = (Eq. 5-39)
^ Total _Si
where:
vt = the average downward velocity of the moving phase (assumed to be water)
in the soil compartment /' (m/day).
Substituting Equation 5-30 for C,(0) in Equation 5-38 gives:
7W x Y*. x ve
where:
NSj = chemical inventory in soil compartmenty' (g[chemical]); and
NSi = chemical inventory in soil compartment /' (g[chemical]).
From this equation, we can derive terms for the advective transfer of chemical downward
from soil compartment / to soil compartment./ below as:
ve x Y
Tperc _ v^i ^ I Si
5.4 STORM-WATER RUNOFF ALGORITHMS
Horizontal transport processes included in TRIM.FaTE include runoff (Section 5.4.1) and
erosion (Section 5.4.2) due to rainfall.
5.4.1 AQUEOUS-PHASE TRANSPORT PROCESSES
During a rainfall event, some of the water travels laterally across the soil as runoff. As
the water travels over the soil, the concentration of the water approaches that of the soil pore
water beneath it. Although the water flowing over the soil does not necessarily reach
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equilibrium instantaneously, some researchers use an approximation that runoff is in equilibrium
with the soil pore water (Wallach et al. 1989). Currently in TRIM.FaTE, an equilibrium
relationship between the runoff water and the soil pore water is used. Runoff water is considered
a phase of the surface soil compartment at each spatial location. A mass-balance approach is
used to determine the concentration in runoff water that moves from one surface soil
compartment to a horizontally adjacent compartment.
Runoff transport is assumed to carry chemical from the surface soil compartment of one
land unit to the next. During a rain event the surface soil compartment is assumed to be
saturated with rain water and this water is assumed to be in equilibrium with the soil solids on
the surface. It should be recognized that at times (e.g., short rain events, during very dry periods
of the year) the soil will not necessarily be fully saturated with rain water. However, the
assumption of saturation by rain is not expected to have a large impact on results for events
when the soil is not saturated. Moreover, a lack of information on the extent to which soil is
saturated during rain makes this a convenient starting point. The assumption of chemical
equilibrium between the surface soil water and surface soil solids has more uncertainty and
needs further research.
During periods of no rain, the total fugacity capacity of the ith surface soil compartment,
ZTotai_s,i, is given by:
ZTotai_Ss, = ^x Zpure_air + 0x Zpure_water + (1 - 0) x Zpure_soM (Eq. 5-41)
During periods of rain, when the soil becomes saturated with water, we account for the different
composition of the soil by writing the fugacity capacity of the chemical in the surface soil
compartment as follows:
^x dSsi)xZpure_mter + (1- 0x dssi)x Zpure_solid]x dssi (Eq. 5-42)
where:
ZTotal ssi = total fugacity capacity of the chemical in the ith surface soil compartment
(mol/m3-Pa);
ZpUre air = fugacity capacity of chemical in air (excluding suspended particles)
(mol/m3-Pa);
ZpUre_water = fugacity capacity of chemical in water (excluding suspended sediments)
(mol/m3-Pa);
Zpure solid = fugacity capacity of the chemical in solid phase in the surface soil
compartment (mol/m3-Pa);
e = volume fraction of the surface soil compartment that is gas (unitless);
6 = volume fraction of the surface soil compartment that is water (unitless);
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CHAPTER 5
SOIL ALGORITHMS
The hydraulic radius, Rh, for flow of water on top of the soil surface is site specific and
depends on the hydraulic gradient (slope of the flow), the rainfall rate, and the recharge rate. It
is considered an uncertain variable. A hydraulic balance is needed to determine the flow of the
water and the depth of the runoff stream. From the Geographic Information System (GIS) data,
the runoff is estimated.
Although runoff occurs only during rain events, in the current TRIM.FaTE library, it is
modeled as a continuous process based on an annual average runoff value divided by 365 days.
The horizontal advective flow of chemical in water from surface soil compartment /' to adjacent
compartment y is given by:
Runoff Flow (Ssi -» &/) =
runoff x fmnoff (^i -> Ssj) x fmafl_rmu,ff x Zpure_water (Eq. 5-43)
7 x d X Ssi
*-'Total Ssi A uSsi
where:
Runoff Flow (Ssi->Ssj) = average daily horizontal transfer of chemical carried in
surface soil pore water down-gradient from surface soil
compartment / to surface soil compartment7
(g[chemical]/day);
runoff = aereal flux of water that is transported away from surface soil
compartment /' (m3[water]/m2[surface soil]-day);
frunof/^si ~>Ssj) = fraction of water that runs off of surface soil compartment /' that is
transported to compartment y (unitless);
favaii runoff = fraction of surface soil compartment / that is available for runoff
(unitless);
ZTotal sSi = total fugacity capacity of the chemical in the ith surface soil
compartment (mol/m3-Pa) as determined in Equation 5-42;
ZpUre water = fugacity capacity of chemical in water (excluding suspended
sediments) (mol/m3-Pa); and
NSsi = total chemical inventory in the surface soil compartment /
(g[chemical]).
Using substitutions for \/dSsi and Zpure_wate/ZTotal_Ssi as indicated below, Equation 5-43 is
equivalent to:
dN A
SSJ
• = runoff x / (Ssi -> Ssj) x /_, x -*- x /ML x 7V&! (Eq. 5-44)
ui J - VSsi
where:
l/<5?&; = ASs/VSsi (m), /'.e., the area of surface soil compartment /' (m2) divided by the
volume of the surface soil compartment /' (m3);
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and:
Mass Fraction Dissolved
pure_water _ _ =^ (Eq. 5-45)
Total sSi
Volume _ Fraction _ Liquid
as described in Chapter 2, Equation 2-80 (i.e.,fML equals the fraction of the mass of total
chemical in surface soil compartment /' that is dissolved in water divided by the volume fraction
of the surface soil compartment that is liquid (water)) (unitless).
From Equation 5-44, the expression for TSsi^Ssj(runoff) that is in the TREVI.FaTE library
can be obtained:
A
Trs7fss] = runoff x fmnoff (Ssi -> Ssj) x /_7_ra^ x —^ x fML (TF 5-10a)
T£?sv = ™™ff >< frunoff (&' ~> SW) X /_, ^ X -f- X f^ (TF 5-10b)
'Ssi
Runoff from a surface soil compartment might flow into an adjacent to a surface water
(SW) body. The equation for that transfer is the same as for runoff to an adjacent surface soil
compartment, except that the receiving compartment is the surface water compartment instead:
Finally, for a surface soil compartment adjacent to the boundary of the modeling region,
runoff from the compartment can move out of the modeling region, which is modeled as a
transfer to the surface soil sink (Ss sink). The equation for runoff to a surface soil sink is similar
to the previous equation:
T™fss_sM = runoff x fmnoff (Ssi -> Ss_sink) x fwail_moff x -^ x fML (TF 5-10c)
Ssi
It is possible for all three of these different runoff algorithms to apply to a given surface
soil compartment /'. The sum of the/^^values across all of the runoff algorithms applied to the
same surface soil compartment cannot exceed 1.0.
5.4.2 SOLID-PHASE TRANSPORT PROCESSES
The algorithm for erosion runoff is based on knowledge of the erosion factor for the
region being modeled. Similar to solution runoff, erosion is also applied only to the surface soil
layer. Although erosion is most likely to occur during rain events, erosion can be modeled as a
continuous event. The flow of chemical (mol/d) from one surface soil compartment to another
by erosion is represented by the following expression:
Erosion Flow (Ssi -» Ssj) =
erosion x femsion (Ssi -» Ssj) x f^^^^ x Zpure_solld x N^ (Eq. 5-46)
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where:
Erosion Flow (Ssi -> Ssj) = average daily horizontal transfer of chemical carried in
surface soil particles down-gradient from surface soil
compartment /' to surface soil compartment y
(g[chemical]/day);
erosion = erosion factor (kg[soil solids]/m2[surface soil]-day);
ferosion(Ssi^-Ssj) = fraction of soil eroded from surface soil compartment /' that is
transported to surface soil compartment y' (unitless);
favaii erosion = fraction of surface soil compartment / that is available for erosion
(e.g., not paved or otherwise covered by non-soil surfaces);
Zpure_solid = fugacity capacity of chemical in the solid phase in the ith surface
soil compartment (mol/m3-Pa);
ZTotal ssi= total fugacity capacity of chemical in the ith surface soil compartment
(mol/m3-Pa);
pp = density of the soil particles (kg[particles]/m3[particles]);
dSsi = depth of the surface soil compartment (m); and
NSsi = the total chemical inventory in soil compartment /' (g[chemical]).
Substituting for \/dSsi and Zpure_solic/ZTotal_Ssi as indicated below, Equation 5-46 is equivalent
to:
dN A f
—^ = erosion x /„ (Ssi -> &/) x /_, erosion x -f- x ^f- x N^ (Eq.5-47)
at vssi pp
where:
l/<4,- = ASs/VSs, (m);
ASsi = area of surface soil compartment /' (m2);
VSsi = volume of the surface soil compartment/' (m3);
and:
Zpure_soiid Mass_ Fraction _ Sorbed
MS ^ Total Air Volume _ Fraction_ Solid
(same as Eq. 5-23)
as described in Chapter 2, Equation 2-79 (i.e., fraction of the mass of total chemical in surface
soil compartment /' that is sorbed to solid particles divided by the volume fraction of the surface
soil compartment that is solid particles) (unitless).
From Equation 5-47, the expression for TSsi^Ssj(erosion) can be obtained:
A« /^
^™ = erosion x ferosion (Ssi -> Ssj) x fmatt erosion x — x —- (TF 5-1 la)
VSsi PP
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Erosion from a surface soil compartment might flow into an adjacent to a surface water
body. The equation for that transfer is the same as for erosion to an adjacent surface soil
compartment, except that the receiving compartment is the surface water body instead:
ZZr = erosion x feroston (Ssi -> SW) x /_, eroston x x - (TF 5-1 Ib)
Ssi
Finally, for a surface soil compartment adjacent to the boundary of the modeling region,
erosion from the compartment can move out of the modeling region, which is modeled as a
transfer to the surface soil sink (Ss sink). The equation for erosion to a surface soil sink is
similar to the previous equation:
= erosion x /_ (Ssi -> SW) x /_, _ x x - (TF 5-1 Ic)
Ssi
It is possible for all three of these different erosion algorithms to apply to a given surface
soil compartment /'. The sum of the ferosion values across all of the erosion algorithms applied to
the same surface soil compartment cannot exceed 1.0.
5.5 GROUND- WATER ALGORITHMS
The horizontal flow of pollutants in the saturated zone (ground water) is not expected to
be a significant pathway when considering air pollutants. Downward advective transport from
the vadose zone to ground water has been simulated because it is a more significant process than
diffusion/dispersion. However, the relative importance of diffusive/dispersive transfer compared
with advective transport between the vadose zone and the ground-water zone needs to be
investigated further.
In the current version of TRIM.FaTE, ground water is modeled as a receiving
compartment for percolation from the vadose zone. The same equation used to estimate the
transfer of chemical via percolation from one soil compartment to another soil compartment
immediately below it (i.e., TF 5-9) is used to estimate the transfer factor for percolation from the
vadose-zone soil (Sv) compartment to ground water (GW):
veSv x
(e+J
where:
(TF 5-12)
transfer factor from vadose-zone soil to ground water (/day);
veSv = the effective advection velocity of a chemical in the vadose-zone soil
compartment (m/day), which is equal to the rate of soil-solution
movement, vh multiplied by the fugacity capacity of the moving phase
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_ SOIL ALGORITHMS
(water) and divided by the total fugacity capacity of the vadose-zone soil
compartment;
ySv = the gradient of soil concentration change in the vadose-zone soil
compartment (/m); and
dSv = thickness of vadose-zone soil compartment (m).
The transfer factor from ground water to surface water is based on aqueous-phase advec-
tion only. It can be calculated as:
where:
TGW->SW = transfer factor from ground-water to surface-water compartments (/day);
ASWGW = interfacial area between the surface-water and ground-water compartments
(m2);
VGW = volume of the ground-water compartment (m3);
Zpure water = fugacity capacity of the chemical in pure water (mol/m3-Pa);
Z Total GW = total fugacity capacity of the chemical in the ground-water compartment
(mol/m3-Pa);
recharge = annual average daily recharge from ground water into surface water
(m/day); and
x
^^ x recharge (TF 5-13a)
GW Total GW
SWGW
* GW
x fML x recharge (TF 5-13b)
/ML = Zpurewate/ZTotal_GW, which equals Mass_Fraction_Dissolved/
Volume Fraction Liquid (i.e., fraction of the mass of total chemical in the
ground-water compartment that is dissolved in water divided by the
volume fraction of the ground-water compartment that is liquid water, see
Equations 2-72 and 2-80) (unitless).
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CHAPTER 6
AQUATIC BIOTA ALGORITHMS
6. AQUATIC BIOTA ALGORITHMS
In this chapter, algorithms for transfers among aquatic biotic compartment types and
other biotic or abiotic compartment types are presented. The aquatic biotic components include
algae, macrophytes, benthic invertebrates, and several trophic groups offish. The transfer factor
algorithms are based on diffusive or advective transfer.
Most of the algorithms in this chapter apply to all air pollutants, although some are
applicable only to mercury species and others that involve octanol-water partition coefficients
are only applicable to nonionic organic chemicals. Some of the equations represent dynamic
processes, while others are simple models for which a time-to-equilibrium is calculated. The
text box on the next page and continued on the following pages provides a summary of the
transfer-factor algorithms developed in this chapter and defines all parameters used in those
algorithms. The derivation of chemical-specific algorithms and input parameters is presented in
Appendix A for mercury and in Appendix B for polyaromatic hydrocarbons (PAHs).
The remainder of this chapter is organized in four sections. Section 6.1 briefly discusses
the process of selecting aquatic compartments for use in a TRIM.FaTE scenario. Section 6.2
addresses algorithms associated with aquatic plants. Section 6.3 covers the algorithms for
benthic infauna (animals living in sediment), which are represented in the current TREVI.FaTE
library by a single compartment type. Section 6.4 develops and describes the transfer factor
algorithms associated with the fish compartments.
6.1 AQUATIC BIOTA COMPARTMENT TYPES
The aquatic compartments in the current TRIM.FaTE
library are listed in the text box to the right. Trophic level 1,
the primary producers, are represented by algae1 and
macrophytes. The 2nd trophic level is represented by
herbivorous fish and benthic infauna, while the 3rd and 4th
levels are represented by two fish trophic levels (omnivores,
that might feed on a combination of plant and animal material,
and carnivores).
Use of aquatic biotic compartment types in a
TRIM.FaTE scenario is described in Section 3.2.2 of
TRIM.FaTE TSD Volume I. Additional guidance on how to
select aquatic biota for compartments is provided in more
detail in the TRIM.FaTE user guidance.
AQUATIC BIOTA
COMPARTMENT TYPES
Algae (actually represented as a
phase of the surface water)
Macrophyte
Water column herbivore (fish)
Water column omnivore (fish)
Water column carnivore (fish)
Benthic herbivore (invertebrate)
Benthic omnivore (fish)
Benthic carnivore (fish)
Algae are represented as a phase of the surface water compartment than as a separate compartment.
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Summary of Transfer Factors for Aquatic Biota in TREVLFaTE
AQUATIC PLANT AND BENTHIC INVERTEBRATE TRANSFERS
Surface water to macrophytes (nonionic organic chemicals): F 6-1 a
k y V
_, n'Mp,acc-W ^ v Mp ,
TSW^MP = y x fML where kMp-acc_w = Eq. 6-3
* sw
Macrophytes to surface water (nonionic organic chemicals): TF 6-2a
Mp^>SW Mp:dep-W Mp,dep-W
Surface water to macrophytes (other chemicals): TF 6-1 b
-ln(l- a)
t
MpW
x
KMP-W X
r ST/T/
' ML
SW
Macrophytes to surface water (other chemicals): TF 6-2b
_ -ln(l-or)
M.p^SW jM.pW
la
Sediment water (interstitial or overlying) to benthic invertebrates: TF 6-3a
y* y jyt y ]f
IIBI A "1BI A "'BI, acc-SedW -
1 SedW^BI ~ -IT X JML
* Sed
Benthic invertebrates to sediment water (interstitial or overlying): TF 6-4a
T -If
1 BI^ SedW a BI, dep-SedW
Bulk sediment to benthic invertebrates: TF 6-3b
nm x mm x KBI c_Sed
Sed^BI~ vSed*Psed
Benthic invertebrates to bulk sediment: TF 6-4b
BI^>Sed ~ BI, dep-Sed
FISH TRANSFERS
Gill uptake by fish, bioenergetic-based kinetic model: TF 6-5
nf x mf x k
* sw
fML x 1000
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Summary of Transfer Factors for Aquatic Biota in TRIM.FaTE (cont.)
FISH TRANSFERS (cont.)
Ingestion with food by fish, bioenergetic-based kinetic model:
nf x m
TF6-6
"diet X
Ingestion with algae by water column herbivorous fish, bioenergetic-based kinetic model:
TF6-7
TA
t Fwch
nFwck >< mFwc
J MA ' m Algae
Fish excretion to surface water via gills, feces, and urine, bioenergetic-based kinetic model: TF 6-8
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Summary of Transfer Factors for Aquatic Biota in TRIM.FaTE (cont.)
LIST OF SYMBOLS USED IN AQUATIC BIOTA TRANSFER FACTORS (cont.)
kB/ dep.sedw = benthic invertebrate depuration rate constant to interstitial water in the sediment
compartment (/day).
k& acc-sed = benthic invertebrate uptake rate constant from bulk sediment (/day).
psed = bulk density of sediment (kg[sediment wet wt]/m3[sediment]).
k& dep-sed = benthic invertebrate depuration rate constant to bulk sediment (/day).
nf = number offish in fish compartment (unitless).
mf = mass per individual fish (kg[fish wet wt]/individual).
ku = fish gill uptake rate constant for chemical dissolved in water (/day).
ndiet = number of individuals in diet compartment (unitless).
mdiet = mass per individual in diet compartment (kg[organism]/individual).
IND = food (diet) ingestion rate for fish (kg[food wet wt]/kg[fish wet wt]-day).
AED = assimilation efficiency of chemical from the diet (unitless).
fMA = fraction of chemical mass in surface water compartment that is in the algal phase
(unitless).
nFwch = number of water column herbivorous fish in that fish compartment (unitless).
mFwch = mass per individual water column herbivorous (kg[fish wet wt]/individual).
mAigae = total mass of algae in the surface water compartment (kg[algae wet wt]).
PAigae = proportion of total fish diet that consists of algae on a wet-weight basis (unitless).
kE = total chemical excretion rate constant (/day).
a = proportion of equilibrium value reached (default = 0.95).
ta = time to reach 100xa percent of equilibrium value (days).
Krish-diet = fish/diet partition coefficient (kg[diet wet wt]/kg[fish wet wt]).
KFwch_Algae = fish(water column herbivore)/algae partition coefficient (kg[algae wet wt]/kg[fish
(water column herbivore) wet wt]).
6.2 AQUATIC PLANTS
Aquatic vegetation is included as two separate components, algae (modeled as a phase of
surface water in the current TRIM.FaTE library) and macrophytes (modeled as a separate
compartment). Water is assumed to be the primary source of chemical to both vegetation types,
and thus, uptake from water is the only pathway for which algorithms are currently included in
the TRIM.FaTE library.
6.2.1 ALGAE
As mentioned previously, algae are modeled as a phase of the surface water
compartment.2 For modeling transfer of dissolved chemical from surface water to algae for
nonionic organic chemicals or chemicals for which empirically based partition coefficients are
available, Equation 4-24 can be used. A more detailed approach has been developed for mercury
(see section A. 1.2 of Appendix A), and is available in the current TRIM.FaTE library.
The surface water compartment consists of three phases: liquid (dissolved), solid (particles), and algae.
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6.2.2 MACROPHYTES
Although rooted macrophytes can derive some nutrients and chemicals from sediments,
direct uptake from water is the primary pathway (Ribeyre and Boudou 1994). Transfers of
chemical between macrophytes and surface water are described in Section 6.2.2.1. Limited
chemical transformation by macrophytes is described in Section 6.2.2.2.
6.2.2.1 Transfers Between Macrophytes and Surface Water
Net uptake of chemicals dissolved in surface water by aquatic macrophytes (only the
dissolved portion of the chemical is available for bioaccumulation by macrophytes) is given by
the following concentration-based equation for the chemical flux rate:
FlowMp = (kMptacc_w x VMp x pMp x Csw x fML) - (kMpt dep_w x VMp x pMp x CMp) (Eq. 6-1)
where:
FlowMp = net flow of chemical into the macrophyte (g[chemical]/day);
^MP, acc-w = macrophyte bioaccumulation rate constant from water (/day);
VMp = volume of the macrophyte compartment (L[macrophyte]);
pMp = density of macrophyte (kg[macrophyte wet wt]/L[macrophyte]);
Csw = total chemical concentration in surface water (g[chemical]/L[bulk
water]);
fML = mass fraction of chemical dissolved in surface water (unitless)
divided by the volume fraction of the surface water compartment
that is liquid, i.e., water, (unitless, value close to 1.0), i.e.,
Fraction Mass Dissolved / Volume Fraction Liquid (see
Equations 2-72 and 2-80);
^MP, dep-w = macrophyte depuration rate constant to water (/day); and
CMp = chemical concentration in macrophyte (g[chemical]/L[macrophyte
wet wt]).
Note that:
Volume_Fraction_Liquid = 1 - \VfSSed + VfAlgae) (Eq. 6-2)
where:
Vfssed = volume fraction of the surface water compartment that is suspended solid
sediment particles (unitless); and
VfAigae = volume fraction of the surface water compartment that is algae (unitless).
The rate constants kMpi acc_sw and kMfj dep_sw, for nonionic organic chemicals are estimated
using the following equations (Gobas et al. 1991):
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500
= 0.0020+ — (Eq. 6-3)
,dep_w = 1.58 + 0.000015 Km (Eq. 6-4)
where:
Km = the octanol-water partitioning coefficient for the chemical
(g[chemical]/kg[octanol] per g[chemical]/L[water] = L[water]/kg[octanol]
or kg[water]/kg[octanol]).
The rate constants kMpi acc_w and kMfi dep_w for chemicals other than nonionic organic pollutants
were derived from bioconcentration factors using the time-to-equilibrium conversion (see
Section 2.5) as follows:
-ln(l-a)
k,
acc-W
,MpW
KMp_w (Eq. 6-5)
- ln(l- a)
kMP, deP-w = —F (Eq. 6-6)
where:
fMpW
1a = time (days) required to reach lOOxa percent of the macrophyte/water
interaction equilibrium when the concentration in water is approximately
constant with time;
a = fraction of equilibrium value attained (default = 0.95) (unitless); and
KMp_w = macrophyte/water partition coefficient (g[chemical]/kg[macrophyte] per
g[chemical]/L[water] = L[water]/kg[macrophyte] or
L[water]/L[macrophyte] assuming that the density of macrophytes equals
that of water).
The transfer of chemical mass from water to the macrophyte is given by:
—J7~ = ^MP, acc-w X /ML X VMP X PMP x TT^ ~ (kMp, dep-w X NMp ] (Eq. 6-7)
ui \ y sw j
where:
NMp = mass of chemical in the macrophyte (g[chemical]);
VMp = volume of the macrophyte (L);
Nsw = mass of chemical in the surface water compartment (g[chemical]); and
= volume of the surface water compartment (L[water]).
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In the current TRIM.FaTE library, the chemical transfer factors for nonionic organic
chemicals from water to macrophytes and for macrophytes to water are given by:
^Mp,acc-W X ' Mp X Pup
LSW^Mp
SW
y V
'Mp, acc-W A ' Mp
SW
'ML
' ML
(TF 6-la)
and:
T - k
^ "'
Mp.dep-W
(TF 6-2a)
where:
TSW^MP = transfer factor from surface water to macrophyte (/day);
pMp = wet density of macrophyte (kg[macrophyte wet wt]/L[macrophyte]
equals same density as water, i.e., 1 kg/L);
1 = unit conversion factor (L[water]/kg[water]); and
= transfer factor from macrophyte to surface water (/day).
The macrophyte/surface water transfer factors for other chemicals, including mercury,
use Equations 6-5 and 6-6 to replace the rate constants kMp< acc_wand kMpi dep_w in TFs 6-la and 6-2a.
Thus, the transfer factors for other chemicals, including mercury, are:
T
*- SW^Mp
- O)
KMp.w X VMp X p X 1
x - - x fML
sw
(TF 6-lb)
T =
* Mp^SW
- ln(l - 0)
fMPW
(TF 6-2b)
6.2.2.2 Transformation and Degradation
Although the TRIM.FaTE library supports macrophyte transformation of mercury species
(see below), it does not currently accommodate biodegradation of any chemicals (i.e.,
transformation into chemicals that are not tracked in TRIM.FaTE) in macrophytes.
Biotransformation of elemental to divalent mercury in macrophytes is included in the
TRIM.FaTE library and is described as a rapid (almost instantaneous) first-order rate constant
(i.e., 106 to 109). This is assumed because elemental mercury can be taken up by macrophytes
but is not accumulated in macrophytes in the elemental form (i.e., data showing Hg(0) in
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macrophytes were not found). Because data demonstrating methylation of divalent mercury or
demethylation of methylmercury in macrophytes were not found, those transformations are not
included for macrophytes in the current TRIM.FaTE library.
6.3 BENTHICINFAUNA
The benthic community is typically comprised of many different classes and species of
organisms, including those from the phyla Mollusca (e.g., clams and snails), Annelida (e.g.,
oligochaete worms), and Arthropoda (e.g., crustaceans and larval insects). Several trophic levels
are represented within this community. That is true even within some families of insects, such as
the mayflies and chironomids. In the current TRIM.FaTE library, benthic infauna are considered
to represent the lowest heterotrophic level of the benthic food chain, which includes those
species that feed on algae and/or detritus, which is assumed to be derived largely from plant
material.
An explicit dietary uptake component is not practical, given the highly variable diet
among benthic infauna. Rather, uptake is modeled based on the extraction of chemical from
water (interstitial or overlying) or bulk sediment. It should be noted that at this time only one
chemical source (water or bulk sediment) is considered for a given chemical. Selection of the
primary source of contamination is chemical dependent. Neutral organic chemicals (e.g., PAHs)
are typically evaluated based on uptake from water. If interstitial water is used, the results often
are considered representative of total sediment exposures. Uptake of metals (e.g., mercury) is
based on uptake data from bulk sediments. Sediment chemical concentrations are not
apportioned to separate inorganic and organic (living and detrital matter) compartments in
TRIM.FaTE. Thus, uptake from sediment implicitly includes transfers from algal and detrital
matter to the benthic invertebrate herbivores.
Algorithms describing the general case for uptake of chemicals by benthic invertebrates
from sediment interstitial (i.e., pore) water are presented in Section 6.3.1. The chemicals to
which these algorithms apply are those for which the measured partition coefficient between
sediments and benthic invertebrates is based on the chemical concentration in sediment water
only, not bulk sediment. An algorithm specific to PAHs that is available in the TRIM.FaTE
library is described in Appendix B. Algorithms for chemicals for which the measured partition
coefficient is based on bulk sediment rather than sediment pore water (e.g., mercury) are
presented in Section 6.3.2.
6.3.1 TRANSFERS BETWEEN SEDIMENT INTERSTITAL WATER AND BENTHIC
INVERTEBRATES
Uptake of chemical by benthic invertebrates from sediment pore water is given by the
following equation:
dC
BI
dt
dep_w m
x Cm (Eq. 6-8)
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where:
CBI = chemical concentration in benthic invertebrates
(g[chemical]/kg[invertebrates wet wt]);
CWD = chemical concentration in liquid phase of sediment (i.e., sediment pore
water) (g[chemical dissolved]/L[water]);
km, acc-w = uptake rate constant for chemical from water (/day); and
ksi, dep-w = depuration rate constant for chemical to water (/day).
The rate constants kBlacc_w and kBIjdep_w are derived from the bioconcentration factors using
the time-to-equilibrium conversion described in Section 2.5:
"-ln(l-a)
k,
, acc-W
tBIW
KBI_W (Eq. 6-9)
- ln(l- a]
- ~B^ - (Eq. 6- 1 0)
where:
tfw = time (days) required to reach 100* a percent of the benthic invertebrate/water
interaction equilibrium when the concentration in water is approximately
constant with time;
a = fraction of equilibrium attained (default = 0.95) (unitless); and
KBI-W = benthic invertebrate/sediment pore water partition coefficient (L[water]/
kg[invertebrates wet wt]).
Converting to mass units (N) yields the following equation:
Oi i WD \li ~\ r \ /T"1 s~ 11^
\ TJ v M-I V If V I If V A/ I I H n n - I I
Jt ~ \tlBI *mBI A KBI,acc-W A T/ \K BI, dep-W A 7 V BI } W4'U ii,
ill \ Vw J
where:
NBI = mass of chemical in organisms comprising the benthic invertebrate
compartment (g[chemical]);
nBI = number of organisms comprising the benthic invertebrate compartment
(unitless);
mm = average mass per individual benthic invertebrate (kg[invertebrates wet
wt]/individual);
NWD = mass of dissolved chemical in sediment compartment (g[chemical
dissolved]);
Vw = volume of water in the sediment compartment (L) = VSed x-6, where:
VSed = volume of sediment compartment (L); and
6 = Volume Fraction Liquid (water) (unitless); i.e.:
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6.3.2 TRANSFERS BETWEEN BULK SEDIMENT AND BENTHIC INVERTEBRATES
Uptake of chemicals by benthic invertebrates from bulk sediment (e.g., mercury) is given
by the following equation:
dCm / \ / \
—-llr y r \-\lf y C \ fFn 6-1^
Jj ~ \KBI,acc-Sed A ^Sed} \KBI,dep-Sed A ^ BI } ^^ ° 1J^
where:
CBI = chemical concentration in benthic invertebrates (g[chemical]/
kg[invertebrates wet wt]);
CSed = chemical concentration in bulk sediments (g[chemical]/kg[sediment wet
wt]);
kBl acc_Sed = benthic invertebrate uptake rate constant from sediment (/day); and
^BI, dep-sed = benthic invertebrate depuration rate constant to sediment (/day).
The rate constants kBl acc_Sed and kBl dep_Sed are derived from bioconcentration factors using
the time-to-equilibrium conversion (see Section 2.5):
I, acc-Sed
-ln(l-a)
, BISed
*KBI_Sed (Eq.6-14)
-ln(l-a)
* BI, dep-Sed ~ .BISed
where:
KBi-sed = benthic invertebrate/bulk sediment partition coefficient (kg[sediment wet
wt]/kg[invertebrates wet wt]);
t msed _ ^me ^ayS-j required to reach lOOxa percent of the benthic
invertebrate/bulk sediment interaction equilibrium value when the
concentration in water is approximately constant with time; and
a = fraction of equilibrium attained (default = 0.95) (unitless).
Converting to mass units (N) yields the following equation:
dNBI ( Nsd } i \
——= nm xmBI x kBLacc_Sed x — - (kBLdep_Sed x NBI\ (Eq. 6-16)
Ul ^ y Sec! X Psed J
where:
NBI = mass of chemical in organisms comprising the benthic invertebrate
compartment (g[chemical]);
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nBI = number of organisms comprising the benthic invertebrate compartment
(unitless);
mm = average mass per individual benthic invertebrate (kg[invertebrate wet
wt]/individual);
NSed = total mass of chemical in sediment compartment (g[chemical]);
VSed = volume of sediment compartment (L[sediment]); and
pSed = bulk density of sediment (kg[sediment wet wt]/L[sediment]).
Thus, the transfer factors for bulk sediment to benthic invertebrates and for benthic
invertebrates to bulk sediment are given by:
flr>T X A/7DT X /CDT ci J
BI BI BI,acc-Sed
TSed^BI = 7^-— (TF 6-3b)
V Sed X Psed
*Bl^Sed = K-BI.dep-Sed (TF 6-4b)
where:
Tsed->Bi = transfer factor for chemical in bulk sediment to benthic invertebrates
(/day); and
TBi^sed = transfer factor for chemical in benthic invertebrates to the bulk sediment
(/day).
For a given chemical, the user would specify either algorithms TF 6-3a and TF 6-4a (or,
for PAHs, algorithms TF B-l and TF B-2 from Appendix B) or algorithms TF 6-3b and TF 6-4b,
but not both. The most appropriate algorithm depends on whether the available data on the
partition coefficients were measured with respect to water only (e.g., sediment pore water) or
with respect to bulk sediments.
6.3.3 TRANSFORMATIONS AND DEGRADATION
Metabolic transformations of chemicals into different compounds that are tracked in
TREVI.FaTE (e.g., mercury species) can be included for biotic compartments. However,
biotransformation from one chemical to another that is tracked in TREVI.FaTE is not included for
benthic invertebrates in the current TREVI.FaTE library. Appropriate transformation rate data
were not identified during initial applications of the model.
Transformations of chemicals into compounds that will no longer be tracked in
TREVI.FaTE (e.g., non-toxic degradation products) are called general degradation processes. In
TRIM.FaTE, the metabolic degradation of chemicals is determined from the user-input value for
the half-life of the chemical in the benthic invertebrate compartment. The algorithm relating the
general degradation rate constant to the chemical half-life in a compartment is presented in
Chapter 2 (Equation 2-64), and the transfer factor is TF 2-1. The metabolic half-life reflects
metabolic degradation only, and not excretion or elimination of the parent chemical to the
sediment compartment.
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6.4 FISH
The current TRIM.FaTE library includes two alternate approaches to estimate chemical
uptake by fish: a bioenergetic-based kinetic model or a time-to-equilibrium-based kinetic model.
Each model has strengths and weaknesses, which may weigh differently for different chemicals.
The bioenergetic-based model is ideal for explicitly incorporating multiple exposure pathways,
but finding data to assign values to some of the fish parameters may be difficult (e.g., gill and
fecal elimination rates). Data to set parameter values for the time-to-equilibrium-based kinetic
model are generally available, but multiple pathways cannot be incorporated explicitly at the
same time and the time required to reach equilibrium may be uncertain for strongly
bioaccumulated chemicals. In applications to date, the bioenergetic model has been
parameterized for PAHs and mercury, whereas the time-to-equilibrium model is parameterized
for mercury only.
In comparison to the time-to-equilibrium model, the bioenergetic model provides the user
greater flexibility in the specification of the fish compartments and associated diets for a given
scenario. For example, the user may employ the five fish compartments currently available in
the TRIM.FaTE library, assigning their diets as deemed appropriate to the modeling scenario, or
the user may develop a different "set" of trophic compartments and diets to represent the fish
community in a particular water body. For each fish compartment, the user can assign more than
one diet item (e.g., 20 percent of the diet consists of benthic invertebrates, 70 percent is benthic
omnivorous fish, and 10 percent consists of omnivorous fish in the water column), creating a
web-like set of trophic relationships, with some fish feeding from more than one trophic level or
microenvironment. This approach is essentially the same as that used to model exposure via
food ingestion for terrestrial wildlife (see Section 7.4). This approach is described in Subsection
6.4.1 below.
Another approach which has been used in initial TRIM.FaTE applications with both of
the two bioaccumulation models, but which is particularly suited to the time-to-equilibrium
model (which was developed to use input derived from measured chemical concentrations in fish
at different trophic levels in the same water body) involves the adherence to a strict stepwise
trophic structure with separate benthic and water column derived food chains. In this design,
the existing five fish compartment types are presented as two separate food chains, one for
water-column organisms and one for benthic organisms (see the conceptual model in Figure 4-1
of TSD Volume I), with each fish compartment feeding on only the compartment below it in the
food chain. That is, water-column carnivores would consume only water-column omnivores,
water-column omnivores consume only water-column herbivores (planktivores), water-column
herbivores consume only algae (phytoplankton), benthic carnivores consume only benthic
omnivores, and benthic omnivores consume only benthic invertebrates. In this type of design,
both the benthic invertebrate (i.e., feeding on algae and detritus, which is derived largely from
plant material) and the herbivore compartments might be considered equivalent to trophic-level-
2 organisms of other models (e.g., Gobas 1993, Ambrose et. al. 1995). The
"omnivore"compartments might be considered equivalent to the trophic-level-3 fish, and the
carnivore compartments equivalent to the trophic-level-4 fish of the other models.
In initial TRIM.FaTE applications, a littoral food web (i.e., including linkages between
water-column and benthic food chains) was created from the linear benthic and pelagic food
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chain design described above by representing individual species as a combination of multiple
compartments. For example, a given carnivore (e.g., largemouth bass) may consume omnivores
from both the water column and the benthos (e.g., consume 50 percent water-column omnivores
and 50 percent benthic omnivores). This diet can be accounted for in the simulation by
assigning 50 percent of the bass biomass to each food chain (i.e., 50 percent to the water-column
carnivore and 50 percent to benthic carnivore compartments). The mass offish to be assigned to
each trophic level within each food chain may thus be derived from studies of the biomass of
individual species in various aquatic ecosystems and studies of feeding strategies of those
species. This method is described in detail in Subsection 6.4.2 below. When this approach is
employed, interpretation of the model results with regard to individual species requires revisiting
these data and calculations.
Regardless of the bioaccumulation model or food chain design employed, the entire fish
biomass in the surface water body being modeled should be distributed among the modeled
compartments. This will facilitate "realistic" partitioning of the modeled chemical within the
biotic and abiotic compartments of the aquatic ecosystem. In addition, the relative distribution
of biomass among the different fish compartment types should be as realistic as possible.
6.4.1 BIOENERGETIC-BASED KINETIC MODEL
This section describes the bioenergetic-based kinetic model for fish developed for use in
TREVI.FaTE. First, the development of the full model is described (Section 6.4.1.1). Next,
specific adaptations of the general model for nonionic organic chemicals (Section 6.4.1.2) and
mercury (Section 6.4.1.3) are described. Then the equations for the transfer factor algorithms in
the TRIM.FaTE library are presented (Section 6.4.1.4). Section 6.4.1.5 describes the
TREVI.FaTE algorithms for chemical transformation and degradation by fish.
6.4.1.1 General Model
The following model for estimating chemical concentrations in fish is based on the model
developed by Thomann (1989) and used in the derivation of the transfer factors associated with
the fish compartment type in the bioenergetic model:
^~= (UglU x CSWD)+(AED x X Pi.x CDJ)- (Emet + Eeg + Eef + EG)x Cf (Eq. 6-17)
where:
Cf = chemical concentration in fish (g[chemical]/kg[fish wet wt]);
Ugitt = uptake from water via the gills (L[water]/kg[fish wet wt]-day);
CSWD = dissolved chemical concentration in surface water (g[chemical
dissolved]/L[water]);
AED = chemical assimilation (absorption) efficiency from diet (unitless);
Pi = proportion of the diet consisting of diet item /' (unitless);
CDii = chemical concentration in diet item /' (g[chemical]/kg[food /']);
Emet = metabolic degradation or transformation of the chemical (/day);
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Eeg = excretion of chemical in the fish (i.e., absorbed chemical) via the gills
(/day);
Eef = excretion of chemical in the fish via feces and urine (/day); and
EG = dilution of chemical concentration from growth (/day).
Assuming first-order rate constants to express both uptake and elimination, the following
relationships hold:
Ugill = kv = rate constant for uptake from water via the gills (L[water]/kg[fish wet
wt]-day);
Emet = kmet = rate constant for metabolic transformation of chemical (/day);
Eeg = keg = rate constant for excretion of chemical via the gills (/day);
Eef = kef = rate constant for excretion of chemical via feces and urine (/day); and
EG = kG = rate constant for dilution of chemical concentration from growth
(/day).
This comprehensive model can be simplified consistent with the approach used in
Thomann(1989)to:
iv-r
-^-= (kv x CSWD)+(AED x X Pi x CD1)- (kET + kG)xCf (Eq. 6-18)
where:
kET = rate constant for total elimination via all excretory systems and via
metabolic degradation to chemicals no longer tracked (/day);
keg + kef + kmet(in Thomann 1989).
This simplification is appropriate in TRIM.FaTE for chemicals that are not lost via
metabolic degradation, only transformed among different species or compounds with a
conserved element (e.g., mercury) that is tracked individually in TRIM.FaTE. For those
chemicals, kmet = 0; all metabolic reactions are tracked via transformations between species (e.g.,
between elemental and divalent mercury and methylmercury).
For organic chemicals, that are metabolized to chemicals that are currently not tracked in
TRIM.FaTE, such as PAHs, loss of chemical from the modeling system via metabolic
degradation should be tracked separately from elimination of the parent chemical from fish back
into the surface water compartment. Loss of chemical from the modeling system is simulated in
TRIM.FaTE by transfers to a compartment sink, in this case, the fish degradation sink, that
accumulates the mass of chemical lost from the system via this pathway. Thus, for use in
TRIM.FaTE with organic chemicals that can be degraded, the "elimination" rate constant kET in
Equation 6-18 would need to be separated into kE, for the excretory pathways for transfer of the
chemical back to surface water (i.e., keg + ke^), and kmet, for loss (transfer) of chemical to the fish
degradation sink.
It is important to note that the equations in their present form exclude dermal uptake as a
significant exposure route. Also, growth dilution (kG) is not included in TRIM.FaTE, because a
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constant biomass for the entire fish population is assumed and growth of individual fish is not
included in the current TRIM.FaTE library.
The bioenergetic-based kinetic model generally is used to estimate concentrations in
individual fish of a species. Following is the derivation of the fish model for the entire fish
population. Initially the model is derived for a population of two fish and then generalized for
the case of n fish, where n is the fish population size. Thus, for two fish with concentrations Cfl,
and C.p, Equation 6-18 can be rewritten as:
dCfl
~dT
(AED x £ /?,. x CDI) - (kETl x cfl)
(Eq. 6-19)
dC
/2
dt
CSWD
(AED x X Pl .x cDl ) - (kET2 x c/2
(Eq. 6-20)
To convert the concentrations to masses, it is assumed that:
SWD
(Eq. 6-21)
,
C
fi ~
J m
Cf2 =
(Eq. 6-22)
(Eq. 6-23)
where:
6
m1
m
Note that:
concentration of dissolved chemical in surface water (g[chemical
dissolved]/L[water]);
mass of chemical dissolved in water (g[chemical dissolved]);
volume of surface water compartment (L);
volume fraction of surface water compartment that is water (unitless,
1.0);
mass offish 1 (kg[fish wet wt]);
mass offish 2 (kg[fish wet wt]);
mass of chemical in fish 1 (g[chemical]); and
mass of chemical in fish 2 (g[chemical]).
(Same as Eq. 6-2)
where:
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Vfssed = volume fraction of the surface water compartment that is suspended
sediment particles (unitless); and
VfAlgae = volume fraction of the surface water compartment that is algae (unitless).
Substituting yields:
d(NJm,) Nwn
' — -
x
m
\A,t ¥ or?/
,
Pi x CDI ) - kETl x - (Eq. 6-24)
Nwn / _, \ N7
= kU2 x —EL- + (AED x^p,x CD1 ) - kET2 x -2- (Eq. 6-25)
U2 D , D1 ET2
ill V SW 2
Adding Equations 6-24 and 6-25 yields the mass transfer equations for the total fish
compartment type, as follows:
df V
ui v sw
d(Nl/ml + N2/m2) NWD
' sw X "
,TN (Eq.6-26)
-k X+k
ETl fiET2
\ ETV ml ET2
Making the simplifying assumptions that individual fish mass is represented by a
population average mf(m, = m2= m^ and that ku} = kU2 = kv, and kET1 = kET2 = kET, yields:
d^
mf ( Nwn , ^ ^ (7V, + AU (Eq. 6-27)
l 1 2|
dt
This equation can be generalized from 2 to w^fish, with Nf(= jV;+jV2) being the total
chemical mass in the fish compartment type, to yield the following generalized chemical mass-
transfer equation for a fish compartment type:
diet
X Nf (Eq. 6-28)
where:
NWD = Nsw x Fraction _ Mass _ Dissolved ( ,
Fraction _ Mass_ Dissolved
*ML ~ Volume _ Fraction _ Liquid (Ecl- 6'30)
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and:
nf = total number of fish in surface water compartment;
IND = food (diet) ingestion rate constant (kg[food wet wt]/kg[fish wet wt]-day);
AED = assimilation (absorption) efficiency of chemical from the diet (unitless);
Nsw = total chemical inventory in the surface water compartment (both dissolved
and sorbed to suspended sediment particles) (g[chemical]);
fML = fraction of chemical mass in surface water compartment that is dissolved
in water divided by the volume fraction of the surface water compartment
that is liquid, i.e., water (unitless); and
6 = Volume Fraction Liquid (unitless).
Note that anAED of less than 1.0 implies that the fraction of chemical not absorbed was
effectively left in the diet compartment(s). A future enhancement of TRIM.FaTE might be to
transfer the unassimilated chemical to the suspended sediment phase of the surface water
compartment or directly to the sediment bed to simulate the fecal elimination of unabsorbed
chemical implied by the AED.
The food ingestion rate (IN^) of an individual fish is given by the following bioenergetic
model presented in Gobas (1993):
IND = 0.022 x m0*5 x e(0'06xT) (Eq. 6-31)
where:
mf = mass of the fish (kg); and
T = temperature (°C).
To illustrate how the dietary transfer calculation would differ between the different fish
trophic groups, an equation for a benthic omnivore (Fbo = fish, benthic omnivore) is illustrated
below.
dNpb ( Nw }
—— = npbo x mpbo x kpbo x -—x fML
at v vw )
Ar \ NMP Nph NBI
™Pbo x IND xAEDx\ pMp x -—+ pph x —— + pm x
(Eq. 6-32)
', WD X /LBD X I pMp X -—t Pph X —- t PBI X —I
V "lMp "lFh "1BI J )
-(kETxNFbo)
where:
npbo = number of benthic fish omnivores in the surface water
compartment (unitless);
mpho = mass per individual benthic omnivore fish (kg[fish wet
wt]/individual);
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Npbo = chemical inventory in the benthic omnivore fish compartment
(g[chemical]);
PMP> Pph< FBI = proportion of the benthic omnivore fish's diet that is comprised of
macrophytes, herbivorous fish, and benthic invertebrates,
respectively (unitless);
NMp, NFh, NBI = chemical inventory in the macrophyte, herbivorous fish, and
benthic invertebrate compartments, respectively (g[chemical]); and
mMp, mFh, mm = total biomass of the macrophyte, herbivorous fish, and benthic
invertebrate compartments, respectively (kg[biomass wet wt]).
Implicit in the previous equation is the assumption that the mass of an individual fish is
constant over the time of the simulation. The dilution-due-to-growth factor (kG) is not included
in the equation because kG is based on concentrations, while the mass transfer equations are in
mass units.
6.4.1.2 Nonionic Organic Chemicals
For nonionic organic chemicals (e.g., PAHs), the chemical uptake rate constant A^for
fish gills is estimated using the following formula in TRIM.FaTE if measured values are not
available:
3 -
lipid
= 103 x - - x AEg (Eq. 6-33)
where:
kv = chemical uptake rate constant (L[water]/kg[fish wet wt]-day);
mf = fish body mass (kg[fish wet wt]);
yASF = allometric scaling factor (e.g., 0.2 (Thomann 1989)) (unitless);
flipid = fraction lipid (kg[lipid]/kg[fish wet wt]); and
AEg = chemical assimilation (absorption) efficiency of the gills (unitless).
There is an apparent increase in assimilation efficiency for smaller organisms; therefore,
organisms have been divided into two weight groups: 10 to 100 g (wet) and more than 100 g
(wet) weight (Thomann 1989). The chemical assimilation efficiency of the gills (AEg) can be
approximated for these two size classes of organisms as follows. For smaller organisms, the
following equations should be used to estimate AEg, where Km is the octanol/water partition
coefficient (g[chemical]/kg[octanol] per g[chemical]/L[water] = L[water]/kg[octanol]):
For chemicals with log^) = 2.00-4.99, \og(AEg) = -2.6 + 0.5 log^);
For chemicals with log^J = 5.00-5.99, AEg = 0.8; and
For chemicals with log&J = 6.00-10, log(AEg) = 2.9 - 0.5 log(^J.
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For larger organisms, the following equations should be used to estimate AEg.
For chemicals with log^) = 2.00-2.99, \og(AEg) = -1.5 + 0.4 log^);
For chemicals with log^J = 3.00-5.99, AEg = 0.5; and
For chemicals with log^J = 6.00-10, log(AEg) = 1.2- 0.25 log(Km).
There is a similar relationship between chemical assimilation efficiency from dietary
items (AED) and Km (Thomann 1989). However, there does not appear to be an increase in the
dietary assimilation efficiency for smaller organisms; therefore, the^E^ can be approximated for
all size classes of organisms as follows:
For chemicals with logCK^) = 2.00-4.99, \og(AED) = -2.6 + 0.5 log^,);
For chemicals with log^J = 5.00-5.99, AED = 0.8; and
For chemicals with log^J = 6.00-10, log(AED) = 2.9 - 0.5
Note that this is the same set of equations used to estimate AEg for smaller organisms.
Thomann (1989) gives the total excretion rate constant (kEJ) for nonionic organic
chemicals using the following equation:
kET = -f- (Eq. 6-34)
Km
Note that in a subsequent publication, Thomann et. al. (1992a,b) state that kET accounts
for elimination via the gills and "other losses...for example, fecal loss and metabolism".
However, those publications (1) indicate that the simplified equation that includes a term for
elimination via the gills only is approximately representative of observed excretion data for fish
and (2) provide no data or formulas for estimating the values of the other types of losses (which
we interpret as meaning fecal loss of biliary secretions and excretion in urine). We interpret the
rate constant kET in Equation 6-34 as not including losses due to metabolism, because kET is set
directly proportional to the gill uptake rate divided by Km. Therefore, the simplified Equation 6-
35 from Thomann (1989) is used here to represent the total excretion rate constant for the
absorbed chemical, kE, excluding losses due to metabolism.
6.4.1.3 Mercury
For mercury (all forms), uptake from water is excluded from the transfer equations
because accumulation in fish is primarily as methylmercury, for which uptake from water is
negligible (Trudel andRasmussen 1997).
The mercury excretion rate constant (kE) (i.e., transfer of absorbed mercury back to
surface water) is given by a bioenergetic model from Trudel and Rasmussen (1997), as described
in Appendix A, Section A. 1.3. Trudel and Rasmussen (1997) based the excretion rate on the
clearance of methylmercury only, because greater than 95 percent of mercury in fish is
methylmercury, and the elimination of methylmercury is much slower than that of inorganic
mercury (i.e.., the overall rate is dominated by the elimination of methylmercury).
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6.4.1.4 Bioenergetic Model Transfer Factors
Using the bioenergetic model, the transfer factor for uptake of dissolved nonionic organic
chemicals from a surface water compartment via gill uptake for a fish compartment (/day) can be
expressed as:
nf x m, x ku
fML x 1000
(TF 6-5)
where:
nf
m
vsw
JML
1000
total number offish in surface water compartment;
mass per individual fish (kg[fish wet wt]);
fish gill uptake rate constant for chemical dissolved in water (/day);
volume of the surface water compartment (L[water]);
fraction of chemical mass in surface water compartment that is dissolved
in water divided by the volume fraction of the surface water compartment
that is liquid, i.e., water (unitless); and
unit conversion factor (L/m3) to match the units for all TREVI.FaTE
compartment volumes.
For mercury, the transfer from surface water to the fish via the gills is set to zero (0) (see
Appendix A, Section A. 1.3).
The generalized transfer factors for chemical uptake from dietary items to a specific fish
compartment are given by:
T,
fish
nf xmf
nd,et X md,et
x IND x AED
(TF 6-6a)
where:
m
diet
IND
AED
biomass
'fish
biomassdiet
biomass f,
jisn -_-,. T . 7_T
x INn x AEn
biomass^
(TF 6-6b)
'diet
number of individuals in the diet compartment (unitless);
mass per individual in the diet compartment
(kg[organism]/individual);
total diet (food) ingestion rate (kg[diet wet wt]/kg[fish wet wt]);
assimilation efficiency of chemical from diet (unitless);
total biomass of the fish compartment (= nf x way); and
total biomass of the diet compartment (= ndiet x mdiel).
Because algae is modeled as a phase of the surface water compartment in the current
TREVI.FaTE library, consumption of algae by herbivorous fish is represented by a slightly
different transfer factor algorithm:
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„ , „ , A r
X P Algae * AE
(TF 6-7)
where:
T
n
Algae^Fwch
Fwch
mFwch
fMA
mAlgae
pAlgae
transfer factor from algae to water column herbivore (/day);
number of water column herbivores in surface water compartment
(unitless);
mass per individual water column herbivore (g[fish wet wt]);
fraction of chemical mass that is in the algal-phase of the surface
water (kg[chemical]/kg[bulk surface water, including suspended
sediments and algae]);
total mass of algae in surface water compartment (kg[algae wet
wt]); and
proportion of the total diet that consists of algae on a wet-weight
basis (unitless).
Using the same bioenergetic model, the transfer of chemicals from the fish population
compartment to the surface water compartment can be expressed as:
where:
kE = rate constant for elimination of chemical from the fish to surface
water via the gills and in urine and feces (/day).
Note that kE applies only to the absorbed chemical in the fish compartment. Fecal loss of
unabsorbed chemical was accounted for by the AED parameter. As described in Section 6.4. 1 .4,
kE does not include losses due to metabolic transformation or degradation.
6.4.1.5 Transformations and Degradation
Transformations of organic chemicals into biodegradation by-products that are no longer
tracked in TRIM.FaTE are modeled as transfers to the fish degradation sinks. See the
TRIM.FaTE user guidance for recommendations on how to identify rate constants for
biodegradation separately from rate constants associated with chemical excretion from fish to
surface water. Equation 2-64 (Chapter 2) is used to estimate the metabolic degradation (in
TRIM.FaTE, called "general degradation") rate constant for an organic chemical from its
metabolic half-life.
Metabolic transformations of inorganic chemicals into different compounds containing
the same core chemical (e.g., mercury) can be included in the TRIM.FaTE fish models. For
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example, biotransformation of Hg(0) to Hg(2) in fish is included as a rapid (almost
instantaneous) first-order rate constant in the fish compartments. Thus, it is assumed that
elemental mercury can be taken up by fish but is not accumulated in the fish (i.e., data showing
Hg(0) in fish were not found). It is also assumed that inorganic mercury is not methylated by
fish. Demethylation in fish may occur as part of the excretory process, but it is not explicitly
modeled here. Rather, it is assumed to be insignificantly small compared to the relative masses
of the mercury species in the fish (i.e., receiving compartments).
6.4.2 TIME-TO-EQUILIBRIUM-BASED KINETIC MODEL
The time-to-equilibrium model is based on the assumption that one pathway accounts for
the vast majority of the chemical uptake. Thus, only one chemical "source" (e.g., food) is
explicitly considered for a given "receptor", (e.g., fish). The general form of the model is:
receptor
- ln(l - a)
t
a
x K x C
receptor- source
- ln(l - a)
t
a
x Creceptor (Eq. 6-35)
dt
where:
^receptor-source = receptor/source partition coefficient (e.g., fish/diet partition coefficient)
(g[chemical]/kg[receptor wet wt] per g[chemical]/kg[source wet wt]);
Creceptor = concentration in receptor (e.g., fish) (g[chemical]/kg[receptor wet wt]);
Csource = concentration in source (e.g., diet) (g[chemical]/kg[source wet wt]);
tras = time (days) required to reach 100* a percent of the receptor/source
equilibrium value when the concentration in the source is approximately
constant with time; and
a = fraction of the equilibrium value attained (default = 0.95; unitless).
If the sole chemical source is surface water, then Kreceptor_source is a bioconcentration factor
(BCF). Bioaccumulation factors (BAFs) implicitly include uptake from food and water, though
water is the identified source. This presumes that the concentration in the food item is
essentially constant relative to the concentration in the water. An alternative approach is the use
of diet as the primary source. Thus, empirically derived accumulation data are used to derive
factors for each trophic transfer, and uptake from water is implicitly, rather than explicitly,
included. This latter alternative is used here.
Following this approach requires that the dietary sources for a given fish compartment be
restricted to one other trophic group. Thus, intratrophic group transfers and multitrophic group
transfers are not explicitly included. These transfers are implicitly included to the extent that the
empirical data used to derive the transfer factors are from systems possessing those transfers.
Thus, the "fit" of the model results for any given case study will depend partly on how well the
food chains at the sites used to derive the transfer factors match the food chains at the case study
site (e.g., length of the food chains, number of interconnections, degree of intratrophic group
transfer, etc.).
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Restriction of the dietary pathway can be achieved within TRIM.FaTE by defining the
generic trophic compartment types to represent a straight food chain (e.g., of three or four
segments). As noted in Section 6.3, the benthic herbivore compartment type in initial
TRIM.FaTE applications has been represented by all benthic invertebrates and in the use of this
time-to-equilibrium approach, the bulk sediment (or interstitial water) is the chemical source.
The benthic omnivore fish compartment type is the next trophic level up from the benthic
invertebrates.
Like the benthic food chain, the chemical transfers in the water column food chain can be
set to be unidirectional from lower to higher trophic levels. In initial applications following this
design, it is important to note that zooplankton have been implicitly included in the transfers
from algae to water column herbivores. That is, the biomass and chemical mass associated with
zooplankton have not been explicitly tracked in TRIM.FaTE, but the dietary transfers were based
on concentration ratios for planktivorous fish and algae. Some studies provide the intermediate
transfer factors for algae to zooplankton, which might be used to include the zooplankton
compartment type within future TRIM.FaTE simulations.
For each trophic level transfer, the general concentration-based equation is converted to
the following mass-transfer equation:
dNf
= nf x mf x
dt f f
-ln(l- a)
tfl
^ fish-diet
-ln(l-a)
tfd
x Nf (Eq. 6-36)
where:
nf
mf
t:
fd
number offish in the compartment (unitless);
mass of individual fish (kg[fish wet wt]/individual);
time (days) required to reach lOQxa percent of the fish/diet interaction
equilibrium value when the concentration in the source is approximately
constant with time;
fish/diet partition coefficient (kg[diet wet wt]/kg[receptor wet wt]);
mass of chemical in items comprising the potential diet (g[chemical]);
number of contaminated items comprising the potential diet (unitless);
mass of individual items comprising the potential diet (kg[diet wet
wt]/individual); and
mass of chemical in the fish (receptor) compartment (g[chemical]).
As an example, the mass transfer equation for water-column omnivores eating water-
column herbivores is given as:
^-fish-diet
Ndiet
ndiet
dN
Fwco
dt
- ln(l - a)
1 Fwch
-ln(l-o)
tfd
(Eq. 6-37)
x TV
Fwco
where:
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Fwco
n
'Fwco
m
Fwco
K,
-Fwco-Fwch
yFwch
n
'Fwch
m
Fwch
mass of chemical in the fish water-column omnivore compartment
(g[chemical]);
number offish comprising the water-column omnivore
compartment (unitless);
mass per individual fish in the water-column omnivore
compartment (kg[fish wet wt]/individual);
fish (water-column omnivore)/fish (water-column herbivore)
partition coefficient (kg[Fwch wet wt]/kg[Fwco wet wt]);
mass of chemical in fish water-column herbivore compartment
(g[chemical]);
number offish comprising the water-column herbivore
compartment (unitless); and
mass per individual fish in the water-column herbivore
compartment (kg[fish wet wt]/individual).
For each trophic level transfer, the generalized transfer factors for dietary items to a
specific fish compartment type (i.e., benthic omnivore, benthic carnivore, water-column
herbivore, water-column omnivore, or water column carnivore) is given by:
T,
n
fish
- ln(l- a]
tfd
'•fish-diet
(TF 6-9)
Because algae is treated as a phase of the surface water compartment, the time-to-
equilibrium transfer factor from algae to the water-column herbivore fish compartment is slightly
different:
T
HFwch X mFwch
Algae—> Fwch
(/
MA
Alg
'ae J
-ln(l-flf)
t
FwchAlg
xK,
Fwch- Algae
(TF 6-10)
where:
* Algae -
IMA
m
'Algae
> FwchAlg
Fwch-Algae
,h = transfer factor from algae to fish (water-column herbivore) (/day);
= fraction of chemical mass that is in the algal phase of the surface water
compartment (unitless);
= total mass of algae in surface water compartment (kg[algae wet wt]);
= time (days) required to reach lOQxa percent of the fish/diet interaction
equilibrium value when the concentration in the source is approximately
constant with time; and
= fish (water-column herbivore)/algae partition coefficient (kg[algae wet
wt]/kg[fish wet wt]).
The generalized transfer factor in the other direction (to allow equilibirum) from a
specific fish compartment to its diet compartment is given by:
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- ln(l- a]
- ^ (TF6-11)
a
Transformations and degradation are modeled using the same approach as described for the
bioenergetic model (see Section 6.4.1.5).
6.4.3 OTHER EPA MODELS FOR BIO ACCUMULATION BY FISH
Aquatox is a general ecological risk model that estimates the fate and effects of chemical
and physical stressors in aquatic ecosystems (U.S. EPA 1998b). The model has been developed
by the Office of Pollution Prevention and Toxics (OPPT) and the Office of Water (OW). The
Bioaccumulation and Aquatic System Simulator (BASS), developed by the National Exposure
Research Laboratory (NERL) of the Office of Research and Development (ORD), also simulates
exposure and effects on fish (U.S. EPA 1999c).
Aquatox and BASS are designed to predict effects of chemical contaminants and
environmental factors on fish populations, whereas TRIM.FaTE is designed to estimate the fate
and transport of chemicals throughout aquatic and terrestrial environments, with an emphasis on
a collection of identical, individual fish. This difference in purpose results in several differences
in structure: (1) Aquatox and BASS include chemical toxicity data; TRIM.FaTE does not
(although TRIM.Risk is designed to include such a database); (2) the toxicological data in
Aquatox and BASS are used to predict mortality, which is used to modify the structures of the
models (e.g., age-class structure and predator-prey interactions); the biomass in the TRIM.FaTE
fish compartments remains constant; (3) in Aquatox, decomposition of dead fish and
contaminants are linked to the dissolved oxygen levels in water, which affect populations; in
TRIM.FaTE dissolved oxygen levels in surface water are not modeled; and (4) growth
estimation offish is fundamental to the population dynamics component of BASS, whereas
growth is not included in the current version of TRIM.FaTE.
BASS (U.S. EPA 1999c) and Aquatox (U.S. EPA 1998b) are bioenergetic models of a
multiple-trophic-level aquatic ecosystem. Aquatox, like TRIM.FaTE, provides an explicit time-
to-equilibrium model option, whereas BASS does not. Like TRIM.FaTE, Aquatox has a Monte
Carlo component to permit probabilistic estimates of exposure or risk. The developers of BASS
plan to include metabolism of organic compounds in future versions of the model, but, unlike
TRIM.FaTE, these transformations are not a feature of the current version (U.S. EPA 1999c).
Components of Aquatox or BASS could be integrated with TRIM.FaTE. The challenge would
be to preserve mass balance and to provide adequate links to all TRIM.FaTE compartment types
that are connected to surface water and/or fish.
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7. TERRESTRIAL BIOTA ALGORITHMS
In this chapter, algorithms for transfers between terrestrial biotic compartment types and
other biotic or abiotic compartment types are presented. The terrestrial biotic compartments
include terrestrial plants, soil detritivores, and wildlife (i.e., birds and mammals).
The algorithms in this chapter are based on diffusive or advective transfer, and the most
common instances of the latter are transfers via wildlife ingestion of chemicals in their diet.
Most algorithms apply to all air pollutants, although some apply only to mercury species, and
others (e.g., those that involve octanol/water partition coefficients) apply only to nonionic
organic chemicals. Some of the equations represent dynamic processes, while others are simple
models for which a time-to-equilibrium is calculated and used to estimate relevant transfer
factors.
After a brief introduction to the selection of terrestrial biotic compartments for a
TRIM.FaTE scenario (Section 7.1), the algorithms used to calculate the transfer factors for
chemical transfers in and out of terrestrial biota are developed and presented. General
algorithms for terrestrial plants, soil detritivores, and birds and mammals are presented in
Sections 7.2, 7.3, and 7.4, respectively. The derivations of chemical-specific algorithms for
mercury and polycyclic aromatic hydrocarbons (PAHs) are presented in Appendices A and B,
respectively.
7.1 TERRESTRIAL BIOTA COMPONENTS
The general approach for selecting biotic compartment types to include in a TRIM.FaTE
scenario is noted in Section 3.3 of TSD Volume I and described in more detail in the user
guidance document. All major trophic levels in terrestrial systems are represented in the current
TRIM.FaTE library. The user can select default, representative species, based on their
prevalence at the test location and/or the availability of data to estimate parameter values for
them. The user can also create compartments for additional species based on policy
considerations, such as the Endangered Species Act. There are some aspects of selecting biotic
compartments for the terrestrial environment that we emphasize here. For additional information
on these issues and more detailed guidance, see the TRIM.FaTE user guidance.
For terrestrial surface volume elements or parcels, the user can select one of a number of
land-use characteristics that influence the type of land cover and/or vegetation. There are four
types of plant communities that have already been incorporated into the TRIM.FaTE libraries:
deciduous forest, coniferous forest, grasses/herbs, and agricultural (e.g., crop) lands. Each plant
community type is represented in TRIM.FaTE by a plant composite compartment, which
includes particles on the leaf surface, leaf, stem, and root compartments and associated
parameter values for that type of plant community.
For biotic compartments in soil, the current TRIM.FaTE library includes two types of
soil organisms: earthworms and soil arthropods. Both types are detritivores (i.e., they feed on
the decaying organic materials found in soils). Chemical transformation and degradation
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processes that might be mediated by soil bacteria are accounted for in the soil compartment
transformation and degradation rates for a chemical.
Finally, the user can populate the vegetated surface volume elements with wildlife
species, depending on the goals and objectives of the project as well as considerations of
chemical mass distribution across wildlife biomass and trophic levels. Major herbivores at a site
should be included to facilitate appropriate partitioning of a chemical within the terrestrial
ecosystems. Higher trophic level birds and mammals would affect environmental partitioning to
a lesser extent. The current TRIM.FaTE library includes parameterized compartments for
several species of birds and mammals as described in Section 7.4.4.
For detailed guidance on how to select and parameterize terrestrial biotic compartments
and how to distribute them among surface soil and surface water parcels, see the TRIM.FaTE
user guidance.
7.2 ALGORITHMS FOR TERRESTRIAL PLANTS
The text box on the next page and continued on the following pages provides a summary
of the plant transfer-factor algorithms developed in this section and defines the parameters used
in those algorithms.
In TRIM.FaTE, terrestrial plants consist of four compartment types which, taken
together, represent an entire plant: leaf, stem, root, and particles on the leaf surface. All four
compartments, parameterized for a specific type of plant community (e.g., deciduous forest) are
linked together in a single plant composite compartment named for that community. Although
the particles on the leaf surface are not in the plant, it is useful to track this compartment type
separately from the leaf because: (1) it can provide a reservoir for chemical moving to leaves, (2)
herbivorous animals can ingest particulate matter on leaves, (3) particles can wash off leaves
during rain, (4) particles can be blown off leaves by wind, and (5) humans can wash most of
these particles off of leaves, prior to any consumption (e.g.., agricultural plants).
Several attributes of the plant compartments vary with time of day and with season. A
logical parameter named IsDay in TRIM.FaTE controls whether the plant stomata are open (1 for
"yes, it is day") or closed (0 for "no, it is night") for a specific simulation run. Diffusion of a
vapor-phase chemical between the air and plant leaves through the stomata occurs only during
the day when they are open. A logical parameter named AllowExchange is used to control
whether the plant is actively growing and has leaves (yes) or is dormant and without leaves for
the non-growing season (no). Chemical exchanges between the grasses and herbaceous and
deciduous plants occur only during the growing season (AllowExchange = 1). AllowExchange
always equals one (yes) for the coniferous plants.
There are, however, several problems that arise in modeling uptake and emissions of
chemicals by plants:
• Little information is available on the transformations of chemicals in plants.
SEPTEMBER 2002 7-2 TRIM.FATE TSD VOLUME II
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Summary of Transfer Factors for Plants in TREVLFaTE
ABOVE-GROUND EXCHANGES
Dry deposition of participate phase of air to particles-on-leaf compartment: TF 7-1
Vf, x /, x A.
rpdry_dep _ ary ary ±_ y f
*-Air^ LeafP y A J MS
'Air
Dry particles on leaf blown off to air: TF 7-2
rpblow_off _ dtV dtV s
* LeafP^> Air
v
v LeafP
Wet deposition of particles in air to the particles-on-leaf compartment: TF 7-3
rj^wet_dep _ wet wet S_ r
1 Air-^ LeafP ~ y X J MS
'Air
Wash off of particles on leaf to surface soil:
TF 7-4a
7> Y / x A
j^wash_off _ wet A •* wet A -^Ss
LeafP'->& "" -IT
'LeafP
Particles on leaf to leaf: TF 7-5
T - k
* LeafP ^ Leaf "" LeafP-Leaf
Leaf to particles on leaf: TF 7-6
T — 0 01 Y k
J-Leaf^LeafP w'w x A ^LeafP-Leaf
Wet deposition of vapor-phase chemical from air to the leaf (partitioning approach): TF 7-7a
*Air->~Leaf = ~Tr X WrV X ram X J- wet X J MV
V A,r
Wet deposition of vapor-phase chemical from air to the leaf (fugacity approach): TF 7-7b
A 7
rpVwet dep S • T pure_water
L « ~T /• — X YdTYl X y X
Air^Leaj T/" wet ^
Air Total Air
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Summary of Transfer Factors for Plants in TRIM.FaTE (cont.)
ABOVE-GROUND EXCHANGES (cont.)
Leaf to air (diffusion):
LAIxAsx
^ Leaf ^Total_Leaf
Air to leaf (diffusion):
T^Leaf = (2LAI xAsxgc + LAIxAsxgs)x
BELOW-GROUND EXCHANGES
Bulk root-zone soil to root:
V
T
^
-ln(l-a)
t
RSr
x -77^ x KRoot_Sr where KRoot_Sr = input value
V
Root
T
Sr
Root to bulk root-zone soil:
-ln(l-or)
1 Root^t Sr
t
RSr
Root-zone-soil pore water to root:
T
* SrW^Root
- ln(l - a)
t
RSrW
^Root-SrW
Sr
pure_water 7
x — where:
^ Total Sr
^Root-SrW ~ (J^Root + J^Root X J
Root to root-zone-soil pore water:
-Ml-tf)
x 0.001
Root^SrW
.
''
RSrW
PLANT STEM EXCHANGES
Bulk root-zone soil to stem:
Sr
TF 7-8a
TF 7-9a
TF 7-1 Oa
TF7-11a
TF7-10b
TF 7-11 b
TF7-12a
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Summary of Transfer Factors for Plants in TREVLFaTE (cont.)
PLANT STEM EXCHANGES (cont.)
Root-zone soil pore water to stem (simplification for nonionic organic compounds): TF 7-12b1
T
* cvrj/
Stem
- ln(l - a)
, StSrW
x pareastem x
SCF
PsrW >< sr
Stem to root-zone soil (simplification for nonionic organic compounds): TF 7-12b2
- ln(l - 0)
T
*
Sterna SrW .StSrW
a
* Leaf ^Stem (2
Leaf to stem: TF7-13
1
ph V Y K
* Leaf A ^LeafPh
Stem to leaf: TF7-14
* Sterna Leaf
v
' Stem
LITTER FALL
Leaf to surface soil: TF7-15
T -If
^Leaf^Ss ~ "-L
Particles on leaf to surface soil: TF 7-16
T -If
*-LeafP^Ss ~ "-L
LIST OF SYMBOLS USED IN PLANT TRANSFER FACTOR ALGORITHMS
vdry = volumetric dry deposition for particle-phase chemical (m3[particles]/m2[soil]-day).
ldry = fraction of dry-depositing chemical that is intercepted by plant canopy (unitless).
As = area of associated soil (m2).
VAir = volume of air compartment (m3).
fMS = mass fraction of chemical in the air compartment that is sorbed to solid particles divided
by the volume fraction of the air compartment that consists of particles (unitless).
VLeafp = volume of particles-on-leaf compartment (m3).
vwet = volumetric wet deposition rate of particle-phase chemical (m3[particle]/m2[soil]-day =
m/day),
lwet = plant interception fraction for wet deposition (unitless).
ASs = area of surface soil compartment (m2).
ki_eafp-Leaf = 1 "* -order rate constant for transfer of chemical from particles on leaf to leaf (/day).
wrV = vapor washout ratio (g[chemical]/m3[rain] per g[chemical]/m3[air]).
rain = rain rate (m/day).
fMV = mass fraction of chemical compartment that is in vapor phase divided by the volume
fraction of compartment that is gas/vapor phase (unitless).
Zpure_water = fugacity capacity of chemical in aqueous phase (mol/Pa-m3).
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Summary of Transfer Factors for Plants in TRIM.FaTE (cont.)
LIST OF SYMBOLS USED IN PLANT TRANSFER FACTOR ALGORITHMS (cont.)
ZTotai Air = total fugacity capacity of chemical in air compartment (mol/Pa-m3).
LAI = one-sided leaf-area index (m2[total leaf area]/m2[soil]).
gc = total conductance of the cuticular path, including the air boundary layer (m/day).
gs = total conductance of stomatal pathway, including mesophyll and air boundary layer
(m/day).
VLeaf = volume of leaf compartment (m3).
Zpure_air = fugacity capacity of chemical in gas phase of air (mol/Pa-m3).
ZTotal Leaf = total fugacity capacity of chemical in leaf compartment (mol/Pa-m3).
a = proportion of equilibrium value achieved (default = 0.95) (unitless).
ta = time required to reach 100xa percent of equilbrium value (days) (value depends on the
compartments and phases for which time-to-equilibrium is modeled).
VRoot = volume of root compartment (m3).
VSr = volume of root-zone soil compartment (m3[soil]).
K-Root-sr = root/bulk-soil partition coefficient (m3[soil]/m3[root]).
K-Root-srw = root/soil-pore-water partition coefficient (m3[water])/m3[root]).
ZTotai sr = total fugacity capacity of root-zone soil compartment (mol/Pa-m3).
fWRoot = fraction water content of root compartment (kg[water]/kg[root wet wt]).
fLRoot = fraction lipid content of root compartment (kg[lipid]/kg[root wet wt]).
Kow = octanol-water partition coefficient (g[chemical]/kg[octanol] perg[chemical]/L[water]).
b = correction exponent for the differences between octanol and lipids (unitless).
pRoot = density of fresh root (kg[root wet wt]/m3[root]).
QXy = flow of transpired water (m3[xylem]/day).
fML = mass fraction dissolved •*• volume fraction of soil compartment that is liquid (water)
(unitless).
TSCF = transpiration stream concentration factor (g[chemical]/m3[xylem] perg[chemical]/m3[soil
pore water]).
pareastem = areal density of stem on associated soil (kg[stem wet wt]/m2[soil]).
SCF = stem concentration factor (g[chemical]/kg[stem wet wt] per g[chemical]/kg[soil pore
water]).
psrw = density of soil pore water (kg[water]/m3[water] = 1 kg/m3).
c/Sr = depth of root-zone soil compartment (m3).
Qph = phloem flux into leaves (m3[phloem]/day) due to advection.
K-teafph = partition coefficient between leaves and phloem water (g[chemical]/m3[leaf] per
g[chemical]/m3[phloem])).
Vstem = volume of stem compartment (m3[stem]).
^StemXy
:L = litter-fall rate constant (/day).
K-stemxv = partition coefficient between stem and xylem water (m3[xylem]/m3[stem]).
The volatilization of chemicals from soils and uptake by plant foliage occurs at a scale
that is not easy to model in TRIM.FaTE.
Little is known about the rate at which chemicals enter plant leaves from particulate
matter or rain water on the leaf surface.
The transport of many chemical species within plants is not well understood.
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• The accumulation of chemicals by wood is not well understood; therefore, trees in
TRIM.FaTE currently consist of leaves only and not stems or roots, except to the extent
that stems are conduits of chemicals away from leaves.
Despite these limitations in understanding and available data, the potentially important
transfer processes have been modeled in TRIM.FaTE to the extent possible given the state of the
science and modeling efforts to date. The user can assess the importance of the limitations
identified above using the sensitivity and uncertainty analysis tools for any given scenario.
7.2.1 TRANSFERS BETWEEN THE AIR, PARTICLES, AND PLANT LEAVES
The particles on the leaf surface are represented by the particles-on-leaf compartment
type in the current TRIM.FaTE library. This compartment is comprised of particulate matter
deposited to the leaf by either wet or dry deposition. Deposition is defined here as the mass
transfer of suspended particulates from air to the plant surface. Elsewhere (e.g., Lindberg et al.
1992), the deposition of chemicals to plants is defined to include the gaseous fraction of the
pollutants that come into contact with plants. The uptake of gaseous pollutants in TRIM.FaTE is
described in Section 7.2.2.
Dry or wet deposition of particles to the parti cles-on-leaf compartment is calculated by
multiplying the particle-deposition velocity by the leaf-interception fraction. The leaf-
interception fraction (7) is the fraction of the depositing chemical mass that is intercepted and
initially retained on the leaf. Thus, the quantity (1-7) is the fraction of depositing chemical mass
that is transferred to the surface soil. The chemical mass that is transferred to the leaf surface via
particle deposition is assumed to join the particle-phase chemical in the parti cles-on-leaf
compartment. From there, transfers of chemical between the leaf itself and the particles on the
surface of the leaf occur via diffusion (see Section 7.2.1.5).
It is common for a concentration of a deposited particulate chemical to be estimated with
respect to the leaf or above-ground plant mass. However, when that concentration is estimated,
it is often forgotten that most of the chemical mass is still on the plant rather than in it. This
situation is treated explicitly in the current TRIM.FaTE library through the inclusion of a
separate compartment for particles on leaf.
In the TRIM.FaTE code, the transfer factors for exchanges between plant leaves and the
air or air particles include the variable AllowExchange, which must equal one (yes) for the
transfer to occur.
7.2.1.1 Dry Deposition of Particles to Surface of Plant Leaves
Dry deposition is estimated by multiplying the predicted air concentration of airborne
particles at ground level by the dry-particle-deposition velocity (U.S. EPA 1997a). A
unidirectional flux equation that expresses dry deposition to the leaf, from van de Water (1995),
follows. Note that, as the boundaries of the surface soil and air parcels may not be congruent,
that is the area of soil and the area associated with a contiguous air compartment may be
different. This algorithm describes the accumulation of chemical mass in the particles on leaves
SEPTEMBER 2002 7-7 TRIM.FATE TSD VOLUME II
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due to deposition from any air compartment to the area of the associated surface soil
compartment that it spatially overlaps.
x A, (Eq 7-1)
Air - 'Total _Air
where:
NLeafP = mass of chemical in particles-on-leaf compartment (g[chemical]);
NAir = mass of chemical in the air compartment (g[chemical]);
VAlr = volume of air compartment (m3);
vdry = volumetric dry deposition of particles (m3[particles]/m2[soil]-day);
Idry = fraction of dry-depositing chemical that is intercepted and initially
retained by the plant canopy (unitless, below);
Zpure solid = fugacity capacity of the chemical in or sorbed to solid particles (mol/m3-
Pa);
Z Total Air = total fugacity capacity in bulk air, including atmospheric dust particles
(mol/m3-Pa); and
As = area of associated soil (m2).
The volumetric dry deposition of particles is calculated as:
DL
Vdty = ydep x — (Same as Eq. 4-2)
PP
where:
vdep = dry deposition velocity of air particles (m/day);
DL = dust load in air compartment (kg[particles]/m3[air]); and
pp = density of dust particles (kg[particles]/m3[particles]).
The interception fraction for dry deposition (Idiy) of particles is calculated using the
following equation (Baes et al. 1984):
where:
JWLeaf = water content of leaf (kg[water]/kg[leaf wet wt]);
aVAP = vegetation attenuation factor (m2[leaf]/kg[plant dry wt]); and
parea = wet above-ground non-woody vegetation biomass inventory per unit area
of the surface soil (kg[plant wet wt]/m2[soil]).
Chamberlain (1970) describes the relationship between Idry and above-ground (dry)
biomass, and Prohl and Hoffman (1996) provide an excellent review of interception and loss
processes along with values (and ranges) for the constants used to estimate Idry.
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The water content adjusts parea to represent dry biomass. The equation was originally
derived for pasture grasses and hay and expanded to other crops. For this reason, the biomass
estimate should not include wood biomass in its calculation. The vegetation attenuation factor
(sometimes called the foliar interception constant) is sometimes equivalent to the surface area of
leaves divided by plant biomass (van de Water 1995) or the leaf biomass if the plant is woody.
Thus, TRIM.FaTE estimates the dry deposition of chemical mass associated with
airborne particles to the parti cles-on-leaf compartment as:
, , v^, x 7^, x As
X/MS (TF7-1)
v
'Air
where:
rp dry _dep
Air^ LeafP = transfer factor for dry deposition of particulate-phase chemical in air to
the particles on the surface of plant leaves when it is not raining (/day);
and
fMS = Zpure son/ZTotal Air, also the fraction of chemical mass in air compartment
that is sorbed to solid dust particles divided by the volume fraction of air
that consists of dust particles (see Equations 2-71 and 2-79) (unitless).
The implicit assumption in this algorithm is that depositing particles reach
thermodynamic (chemical) equilibrium with the surrounding air before contacting the leaf
surface. Accepting this assumption, the transfer to vegetation by dry deposition is related to the
total chemical mass in the air compartment (combined gas- and particle-phase) using the
particle/gas partition coefficient (normalized on a volume basis), K'p, which is the dimensionless
particle/gas partition coefficient (g[chemical]/m3[particles] per g[chemical]/m3[air
compartment]). The factor^/? is equivalent to K 'p.
7.2.1.2 Blow Off of Particles on Leaf to Air
The intent in the conceptual design of the leaf-particle transfer algorithms is to maintain a
constant (although unknown) mass of particles on the leaf. The algorithm below is based on
three assumptions: (1) particles are blown off the plant by wind at a rate that equals the
deposition rate to leaves; (2) the concentration in the particles blown off the leaf is equal to the
concentration in particles remaining on the leaf; and (3) all particles are dispersed in air.
7) X J X /\
where:
y
* LeafP
^Le^fAir = transfer factor for particle-phase chemical on surface of leaf blown off to
air (dry resuspension of particles) when it is not raining (/day)]; and
VLeafP = volume of the parti cles-on-leaf compartment (m3).
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The factor fMP is not needed in the algorithm TF 7-2 because all of the chemical mass
inventory in the parti cles-on-leaf compartment is sorbed to particles, and the compartment
consists only of the solid phase. The particles blown off leaves into the air are then available for
redeposition to leaves and the surface soil. Note that the algorithm for blow off of particles
from leaves includes a meteorological toggle that turns the process off during rain (the analogous
process during rain is wash off; see Section 7.2.1 .4).
7.2.1.3 Wet Deposition of Particles to Surface of Plant Leaves
Rain scavenges some of the parti culate-phase chemical from the air, depositing it on the
surface of leaves. The concentration in the rain drop is related to the fraction of the chemical in
the air that is associated with the particle and the scavenging ratio for particles in rain drops.
Thus, wet deposition resulting from this process can be modeled using equations similar to dry
deposition of particles. The rate of mass transfer of particle-phase chemicals from air to rain
water and to the parti cles-on-leaf compartment can be described as:
= ~ x M, x ram x L x , x = x As (Eq. M)
dt VA,r PP ZTotal_Alr
where:
Nieafp = mass of chemical in particles-on-leaf compartment (g[chemical]);
NAir = mass of chemical in the air compartment (g[chemical]);
VAir = volume of air compartment (m3);
wr = scavenging or washout ratio for particles in air (ranges from 50,000 to
200,000) (m3[air]/m3[rain]);
rain = rate of rainfall (m/day);
DL = dust load, i.e., density of dust particles in air (kg[particles]/m3[air]);
pp = density of dust particles (kg[particles]/m3[particles]);
IWet = w£t interception fraction (unitless);
Zpure solid = fugacity capacity of the chemical in or sorbed to solid particles (mol/m3-
Pa);
Z Total Air = total fugacity capacity in bulk air, including atmospheric dust particles
(mol/m3-Pa); and
As = area of associated soil (m2).
The washout ratio for particle-bound chemicals typically is restricted to empirical data on
particle scavenging ratios (Wania et al. 1998). The expression wr x Jmin x (DL/pdust) equals the
volumetric particle wet deposition velocity, vwet:
vwet = volumetric wet deposition rate of air particles (m3[particle]/m2[soil]-day =
m/day),
= wr x rain x (DL/pp).
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Thus, the transfer factor that describes chemical deposition to the particles-on-leaf
compartment from wet deposition of air particles is calculated as:
i) y / y A
rrLeafl> ~ TT J MS
'Air
where:
T^r'^Leafp = transfer factor for wet deposition of particulate-phase chemical in air to
the particles on plant leaves when it is raining (/day); and
fMS = the mass fraction of chemical in the particle-phase divided by the volume
fraction of the air compartment that is particulate (unitless).
The wet particle interception fraction in the preceding equations can be calculated using
the following equation from Muller and Prohl (1993). The value of the fraction depends on how
much water the leaf can hold, the total amount of rainfall during a rainfall event, and the ability
of the element or compound to stick to the leaf.
ram
(Eq. 7-4)
where:
LAI = one-sided leaf-area index (m2[total leaf area]/m2[underlying soil area]);
S = vegetation-dependent leaf-wetting factor (retention coefficient) (m); and
rain = amount of rainfall during a rainfall event (m).
With the current TRIM.FaTE library, however, the user must specify a value for the wet
deposition interception fraction or accept the default value of 0.2, which is based on five years of
meteorological data for a site in Maine. Because it is a fraction, the upper bound for Iwet is 1 .
7.2.1.4 Wash-off of Chemical from Plant Surface
During rain, the chemical sorbed to particles on the surface of the leaf can be washed off
and deposited to the surface soil. In TRIM.FaTE, this transfer is estimated by an equation that is
basically the same as TF 7-3, i.e.:
waSh_off _ Vwet X I vet X ASS
where:
TL£JP~?SS = transfer factor for wash off of particle-phase chemical from particles-on-
leaf compartment to surface soil (/day);
vwet = volumetric wet deposition rate of air particles (m3[particles]/m2[soil]-day);
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Iwet = fraction of wet-depositing particle-phase chemical that is intercepted by
plant canopy (unitless);
As = area of the associated soil (m2[soil]); and
VLeafP = volume of parti cles-on-leaf compartment (m3).
This equation has been implemented to ensure that the particle mass on the leaves does
not change (i.e., as much is wet-deposited as is washed off). The factorfMS is not needed in
algorithm TF 7-4a because all of the chemical mass inventory in the parti cles-on-leaf
compartment is sorbed to particles, and the compartment consists only of the solid phase. Note
that the algorithm for wash off of particles from leaves includes a meteorological toggle that
turns the process on during rain (the analogous process when it is not raining is blow off; see
Section 7.2.1.2).
There are some data available on wash off of particles from the surface of conifer leaves
during rain that indicate first-order kinetics with a rate constant of approximately 0.04 per min
(McCune and Lauver 1986). The rate of 0.04 per min is equivalent to 2.4 per hour or 57.6 per
day. It may be assumed that the particles deposited in rain water and the chemical dissolved in
rain water is washed off at the same rate. Thus, an alternative equation to estimate wash-off
from conifer leaves could be:
d^LeafP
(Eq.7-5)
and the associated transfer factor for the chemical wash off to the surface soil compartment is:
T^-fSs = 57.6 (TF 7-4b)
This algorithm is not included in the current TRIM.FaTE library, but is included here for users
who may prefer this value for coniferous forests.
7.2.1.5 Transfer of Chemical to Leaf from Particles on Leaf
The fraction of chemical sorbed to particles on the leaves that enters the leaf cuticle per
day is very uncertain. It depends on the relative concentrations in the plant and particles at
equilibrium (which is unknown), as well as the time to equilibrium. It is sometimes assumed
that chemicals attached to particles reach instantaneous solution equilibrium with plant tissues
when they land on the plant. If that assumption is made for some chemicals (e.g., mercury),
TRIM.FaTE is likely to overestimate the contribution of the particles to uptake of the chemical
by the plant (Lindberg 1999a). For a chemical that is tightly and chemically bound to particles
in air (e.g., mercury), an initial assumption of 0.2 per day may be appropriate (i.e., assume a half-
life of one week). Because particles cover only a small fraction of the surface of the plant, it is
assumed that the rate of transfer from leaves to particles is 1 percent of the rate constant for
transfer in the other direction (i.e., 0.002 per day). The rate may be higher for the transfer of
mercury from the plant to a dissolved state in rain water, but no information is available on this.
Note that these default values will change if units of time change. Thus, the transfer factors for
exchange between the leaf and parti cles-on-leaf compartments are:
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-* LeafP^Leaf * ' Leaf-Leaf (TF 7-5)
*W>-W (TF 7'6)
where:
Tiea/p^Leaf = transfer factor for transfer of chemical from parti cles-on-leaf
compartment to leaf compartment (/day);
^Leafp-Leaf = first-order rate constant for transfer of chemical from particles on
leaf to leaf (/day); and
TLeaf^LeafP = transfer factor for transfer of chemical from leaf to parti cles-on-
leaf compartment (/day).
In the current TRIM.FaTE library, these transfer factors are numeric constants set by the
user. Thus, to implement the relationship described here, the value of TLeaf_>Lea:fP should be set to
0.01 times that of TLeafP_>Leaf .
7.2.1.6 Transfer of Vapor-phase Chemical to Leaf from Air During Rain
The rate of mass transfer of the vapor-phase chemical from air to rain water and to the
plant leaf is described by the following equation (modified from van de Water 1995):
dNL , TV
— = — — x wrv x rain x As x Iwet x fMV (Eq. 7-6)
dt VAir
where:
NLeaf = mass of chemical in the leaf (g[chemical]);
NAir = mass of chemical in air (g[chemical]);
VAir = volume of air compartment (m3[air]);
wrV = vapor washout ratio (g[chemical dissolved]/m3[rain] per g[chemical vapor-
phase]/m3[air]);
rain = rain rate (m/day);
As = area of associated soil (m2);
Iwet = interception fraction for wet deposition (unitless); and
fMV = the fraction of the chemical mass in the air compartment that is in the
vapor phase divided by the volume fraction of the air compartment that is
gas/vapor (i.e., fraction that is not particulate).
It is difficult to know whether vapor-phase chemicals dissolved in rain and deposited to
leaves will partition into the particles on the surface of the leaf or into the leaf cuticle. The water
droplets on a leaf are small and persist for only a short period of time. The surface area of the
leaf that is actually in contact with the water also can be much larger or smaller than the
macroscopic surface of the leaf (Riederer 1995). Given the relative surface area of the leaf
versus the surface particles, we assume that all wet deposition of vapor that is intercepted and
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initially retained by the leaf will interact directly with the leaf compartment. Deposited chemical
can subsequently partition between the leaf and particles on the leaf (see Section 7.2.1.5).
The vapor wet interception fraction can be calculated using the same equation from
Muller and Prohl (1993) that was used to estimate the particle wet interception fraction
(Equation 7-4 above). As before, the value of the fraction depends on how much water the leaf
can hold, the total amount of rainfall during a rainfall event, and the ability of the element or
compound to stick to the leaf.
LAIxS
*
rain
(Same as Eq. 7-4)
The vapor washout ratio, wrV, is the equilibrium partition coefficient for a chemical
between rain water and the vapor phase in air; in other words, the chemical concentration in rain
divided by the chemical concentration in the gaseous phase. It can also be expressed as a ratio of
Z factors (see Chapter 2):
c 7 i
rain water pure water -*- ,
*rv = —^ - = ~^- - = -j— (Eq. 7-7)
^air ^pure_vapor ^ AW
where:
Crain water = concentration of chemical in rain water (g[chemical]/m3[rain]);
Cair = concentration of vapor-phase chemical in gas-phase air
(g[chemical]/m3[air]);
Zpum water = fugacity capacity of chemical in aqueous phase (mol/m3-Pa);
Zpure_air = fugacity capacity of vapor-phase chemical in air (excluding dust
particles) (mol/m3-Pa); and
KAW = air/water partition coefficient (g[chemical]/m3[air] per
g[chemical]/m3[water], unitless).
For some chemicals (e.g., the mercury species), the user can specify the washout ratio,
wrV, using an empirically derived equilibrium partition coefficient between the water and vapor
phases of the chemical, KWA. Thus, the transfer of vapor-phase chemical from air to plant leaves
during a rainfall event is calculated as:
x MV x rain x Iwet x fMV (TF 7-7a)
'Air
where:
^Ai^ieaf = transfer factor for wet deposition of vapor-phase chemical in air to the
leaf when it is raining (/day); and
wrV = \IKAW as described in Equation 7-7 above.
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For other chemicals (e.g., nonionic organic chemicals), the expression wrV x fMV can be
estimated from the expression Z^Hre wate/ZTotal Air as follows. From Equation 7-7 and the definition
offMV above:
•^'pure water MaSS Fraction VapOT
w X f = ——~ X ~ ~— rpfl 7-8^
rV MV Zpure vapor Volume_Fraction_Vapor
From Equation 2-73:
Z = Z
Total _ Air pure _ vapor
Mass_ Fraction _ Vapor
Therefore:
Volume _ Fraction _ Vapor
Total _Air
. 7-10)
Thus, an alternative algorithm for wet deposition of vapor-phase chemical to plant leaves
is calculated as:
ram x Iwet x ^ (TF 7-7b)
^ Total _Air
where:
^Air^Leaf = transfer factor for wet deposition of vapor-phase chemical in air to
the leaf (/day); and
Z Totd Air = total fugacity capacity of chemical in air compartment (mol/m3-
Pa).
7.2.2 UPTAKE OF GASEOUS CHEMICAL INTO FOLIAGE
The diffusion pathway between air and leaves is relevant for all gaseous forms of
chemicals, including organic compounds and mercury species. The diffusion from air to plants
is based on two resistances in parallel: (a) the series resistance of air boundary (Section 7.2.2.1),
stomata (Section 7.2.2.2), and mesophyll (Section 7.2.2.3), and (b) the series resistance of air
boundary (7.2.2. 1) and cuticle (Section 7.2.2.5). It is assumed that the chemical fraction that is
in the plant cuticle or mesophyll is inside of the plant, but that the chemical inside of the stomata
but outside of the mesophyll is outside of the plant. It should be noted that the resistance is the
inverse of the conductance. Damage to the plant (e.g., from insect herbivory) can also modify
the transport of nutrients from plant leaves (Hargrove 1999). However, the contribution of insect
or other sources of damage to the diffusion of mercury and other chemicals into and out of the
plant is unknown and not currently addressed in TRTM.FaTE.
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7.2.2.1 Air Boundary-layer Conductance
The air boundary-layer conductance is defined by the following equation:
pure_air , .
gB = —r (Eq. 7-11)
°AP
where:
gB = conductance of the air boundary layer (m/day);
Dpure air = diffusion coefficient of chemical through still, pure air (m2[air]/day); and
6AP = thickness of air boundary layer (i.e., still air) over leaf surfaces (m).
The boundary layer thickness (5^ in m) may be approximated by Equation 7-12 below
(Nobel 1999), or the value may be assumed (e.g., 0.001 m in Riederer 1995, 0.005 m in McKone
1993a,b,c). The constant of 0.00389 in the following equation is the square root of the viscosity
of air at 20° Celsius, 1.51 x 10'5 nrVsec (Wilmer and Fricker 1996).
SAP = 0.00389V/77 (Eq. 7-12)
where:
/ = length of flat leaf (m); and
v = wind velocity (m/sec).
7.2.2.2 Stomatal Conductance
The stomatal conductance of gaseous chemicals into the leaf is calculated in the
TREVI.FaTE library using the following equation (Riederer 1995):
Dpure a,r X ™ S X ^Doy X (Xg
g = (Eq. 7-13)
stomata xs + ys
where:
Sstomata = conductance of the chemical through the stomata (m/day);
Dpure air = diffusion coefficient of the chemical in pure, still air (m2[air]/day);
nas = number of stomata in leaf (n) times area of 1 stomata divided by area of
leaf (as) (unitless);
as = mean degree of opening of stomatal pores, between 0 and 1 (default =1)
(unitless);
IsDay = a time-varying parameter that equals 1 during the day and 0 at night, to
open and close the stomatal pores (unitless);
xs = depth of elliptical pore (m); and
ys = mean pore radius (m).
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In the field, the degree of opening of stomatal pores tends toward one during the day and
zero at night, unless the temperature is high and the humidity low, in which case the value of as
will be less than one during the day. The default value in the TREVI.FaTE library for as during
the day is one. The stomatal conductance is "turned off when IsDay equals zero.
Analysis of data reported by Wilmer and Flicker (1996, p. 18) indicates that the value for
the expression (nas)/(xs + ys) is relatively similar among plant species (i.e., coefficient of
variation -0.5). Thus, that expression in Equation 7-13 is replaced in the TREVI.FaTE library by
a single parameter:
na~
SN = — (Eq. 7-14)
*s + ys
where:
SN = stomatal area, normalized for effective diffusion path length (/m).
Thus, in the TREVI.FaTE library:
gstomata = DPure_a,r X $N X «s (Eq. 7-15)
If this algorithm for gstomatais used, it should be noted that a model limitation is that
conductance varies with temperature. In the 20° to 40°C temperature range, the vapor flux from
leaves has been observed to double with a 10° rise in temperature (Leonard et al. 1998), so
variability in temperature could contribute significantly to the uncertainty in this type of transfer.
If data on the effective diffusivity of the subject chemical in air, Dpure air, are lacking, the
following alternate equation can be used to estimate diffusivity (conductance) of the chemical
through stomata based on diffusivity of water through stomata (Trapp 1995). In other words, the
stomatal conductance of gaseous chemicals into the leaf may be approximated from the stomatal
conductance of water vapor. The only chemical-specific parameter that is required is the
molecular weight of the chemical:
gstamata = /Mw X gmter (Eq. 7-16)
where:
18 = molecular weight of water (g[water]/mol [water]);
Mw = molecular weight of chemical (g[chemical]/mol[chemical]); and
Swater = conductance of water through the stomata (m/day).
Conductance of water through the stomata may be calculated using the following
algorithm from Bennett et al. (1998):
461x7 / . 9x
gwater = 7.5(7-273) X (l kg X cT X HI j
(l-r/Ox611xlO(237+(r-273))
(Eq. 7-17)
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where:
rh = relative humidity (unitless); and
T = temperature (°K).
Note that Equation 7-16 for stomatal conductance, with Equation 7-17 substituted for gwaten
includes the resistance of the air-side boundary in series with the stomatal resistance. If those
equations were to be implemented in TREVI.FaTE instead of Equation 7-15, it would be
necessary to remove the air boundary-layer resistance from Equations 7-18 and 7-19 for total
conductance of the stomatal pathway (see Section 7.2.2.4 below).
7.2.2.3 Conductance of Mesophyll
It is suggested that for most organic chemical species and most plant species, the
stomatal or cuticular conductance is the rate-limiting pathway (Riederer 1995). Therefore, for
most chemicals, there is no need to consider the conductance of mesophyll (inner tissue).
However, some work with elemental mercury cited in Lindberg et al. (1992) suggests that
"resistance on or within mesophyll surfaces dominates the atmosphere-leaf diffusive path of
Hg°" (see Section A.I.5 of Appendix A). Thus, conductance of the mesophyll is included when
estimating the total conductance of the stomatal pathway for Hg(0), as described in the next
subsection.
7.2.2.4 Total Conductance of the Stomatal Pathway
The total conductance of the stomatal pathway is:
(Eq.7-18)
IP p- p y
^ o stomata om o B '
where:
gs = total conductance of stomatal pathway, including mesophyll (m/day);
gstomata = conductance of stomata (m/day);
gm = conductance of mesophyll (m/day); and
gB = conductance of the air boundary layer (m/day) (see Section 7.2.2.1).
However, of the chemicals evaluated for TREVI.FaTE to date, only elemental mercury encounters
significant resistance from the mesophyll (see Section 7.2.2.3). Thus, Equation 7-18 would be
used in full for elemental mercury, but the middle term for the resistance of the mesophyll would
be dropped from the equation for the two other mercury species (i.e., divalent and methyl). The
total conductance of the stomatal pathway for chemicals other than elemental mercury thus far
included in the TRIM.FaTE library is:
( ' 'r (E...7..9)
• O Stomata &B '
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7.2.2.5 Cuticular Conductance
The cuticular conductance (mass transfer coefficient for chemical transfer across the
cuticle side of the air/plant interface) is defined by the following equation (Riederer 1995):
where:
& cuticle
P =
cuticle
K
-AW
P
o cuticle
cuticle
K
(Eq. 7-20)
AW
conductance of the cuticle (m/sec);
permeance of the cuticle (m/sec); and
air/water partition coefficient, i.e., equilibrium ratio between the chemical
in water and in the vapor phase (g[chemical]/m3[air] per
g [chemi cal ]/m3 [water]).
Cuticular permeance is an experimentally derived value that describes the mass transfer
velocity from water into the leaf. The dimensionless air/water partition coefficient is used to
transform the chemical in the sending compartment from water-phase to the vapor-phase in air.
Cuticular permeance has been measured in Citrus aurantium leaves, and the following
relationship in Equation 7-21 (below) was derived from those data (Riederer 1995). The
variability of this relationship among plant species is unknown.
= 0.704X \oz(Kow-)- 11.2 (r = 0.91)
(Eq. 7-21)
We extend Equation 7-21 to estimate the conductance from bulk air, using ZTotalAir/
gcut.de =
7
Total Air pure water
86,400
(Eq. 7-22)
where:
Zpare water = fugacity capacity of chemical in aqueous phase (mol/Pa-m3);
ZTotd Air = total fugacity capacity of chemical in bulk air (mol/Pa-m3); and
86,400 = units conversion factor (sec/day).
The cuticular conductance must be put in series with resistance through the air boundary
on the leaf surface to yield the total cuticular conductance (air-to-plant), adjusted for the fugacity
capacity of the air and leaf. Thus:
1 1
-1
cuticle '
(Eq. 7-23)
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where:
gc
SB
& cuticle
total conductance of the cuticular path, including the air boundary layer
(m/day);
conductance of the boundary layer (m/day); and
conductance of the cuticle (m/day).
7.2.2.6 Transfer Factors for Diffusion
Riederer (1995) has derived a flux equation for diffusion in and out of plant leaves:
dN
Leaf
dt
' Air
va
AW
V:
Leaf
K
LeafW
(Eq. 7-24)
where:
NLeaf
ALeafA
NA,r
VAir
Leaf
^AW
K,
-LeafW
mass of chemical in leaves (g[chemical]);
effective interfacial area between leaf and air (m2);
mass of chemical in air (g[chemical]);
volume of air (m3);
volume of leaves (m3);
air/water partition coefficient (g[chemical]/m3[air] per
g[chemical]/m3[water]); and
leaf/water partition coefficient (g[chemical]/m3[leaf] per
g [chemi cal ]/m3 [water]).
If the Riederer (1995) equation (which is calculated with respect to one-sided leaf area;
i.e., Eq. 7-4) is used in TRIM.FaTE to estimate stomatal conductance, the following equation is
used to estimate diffusion of vapor-phase chemical from the plant leaf into the air:
= (2LAI:
LAIxAsxgs-)x-
1
Z
pure _air
Leaf
^ Total
(TF 7-8a)
Leaf
where:
Tdiff
* Leaf ^ Air
LAI
As
gc
Leaf
pure_air
'Total_Leaf
transfer factor for diffusion of vapor-phase chemical from leaf to the air
(/day);
one-sided leaf-area index (for the area of one side of a leaf) (unitless);
area of associated soil (m2);
total conductance of the cuticular pathway, including the air boundary
layer (m/day);
total conductance of the stomatal pathway, including the air boundary
layer (m/day);
volume of leaf compartment (m3);
fugacity capacity of chemical in gas-phase air (mol/m3-Pa); and
total fugacity capacity of chemical in the leaf compartment (mol/m3-Pa).
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The Riederer (1995) equation is the default implemented in the current TRIM.FaTE library.
If the alternative equation for stomatal conductance from Bennett et al. (1998) is used to
calculate stomatal conductance (i.e.., Equations 7-16 and 7-17), the transfer factor for diffusion
from leaf to air would be calculated as:
T^Air = (2 LAI x As x gc + As x gs ) x -^— x f""-flfr (TF 7-8b)
V Leaf ^ Total _Leaf
Note that the contact area associated with the cuticular pathway is double the LAI, because
cuticles cover the top and bottom of a leaf.
The total fugacity capacity of the chemical in the leaf compartment, ZTotal Leaf can be
calculated using Equation 7-25 (below), which represents plants as a mixture of air, water, and
nonpolar organic matter analogous to octanol (Paterson and Mackay 1995). It is assumed that
the fugacity capacity of the chemical in a plant leaf is equivalent to that in a generic plant that is
18 percent air, 80 percent water, and 2 percent nonpolar organic matter.
ZTotai_Lear= 0.18 x Zpure_air + 0.80 x Zpure_water + 0.02 x Kow x Zpure_water (Eq. 7-25)
Since the Riederer (1995) equation (which is calculated with respect to one-sided leaf
area, i.e., Equation 7-11) is used for the stomatal conductance in the current TRIM.FaTE library,
the transfer factor for diffusion of the chemical from the air into the leaf is calculated in the
library as:
= (2LAI xAsxgc + LAIxAsxgs)x-- (TF 7-9a)
Air
If the Bennett et al. (1998) equation is used for the stomatal conductance (i.e., Equations
7-16 and 7-17), the transfer factor for diffusion from air to leaf would be calculated as:
T^Leaf = (2LAI xAsxgc + Asxgs)x-^- (TF 7-9b)
V Air
7.2.3 UPTAKE FROM SOIL BY ROOT
The uptake of chemicals by plant roots is treated as an equilibrium process in the current
library. Two alternative algorithms may be used to calculate the accumulation of a chemical by
plants from soil: uptake from bulk soil (Section 7.2.3. 1) or uptake from soil pore water (Section
7.2.3.2). Both algorithms are derived from an equilibrium relationship, an estimated time to
equilibrium, and the assumption of a first-order rate of uptake. The selection of algorithms for
bulk soil or for soil pore water depends on the measured partition coefficient (i.e., whether it was
measured relative to bulk soil or estimated relative to soil pore water). Due to uncertainties
associated with modeling these root types, initial TRIM.FaTE applications have not applied
these algorithms to woody tree roots or tuber crops. Further consideration of compartment
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design, parameter values, etc. may lead to some use of these or other algorithms for those root
types.
7.2.3.1 Uptake from Bulk Soil
The uptake of chemicals from bulk soil by roots is described in TRIM.FaTE by an
equation in the form of time to equilibrium between the roots and soil. Because of the linear
relationships in TRIM.FaTE, uptake is described as proportional to the concentration of the
chemical in soil even though some studies suggest that a log-log regression between soil and root
concentrations is a more precise model of uptake (Efroymson et al. 2001).
The change in concentration of the chemical in the root over time can be estimated using
a time-to-equilibrium model (see Section 2.5):
dC,
Root
dt
-ln(l-o)
,RSr
-ln(l-a)
,RSr
xC,
'Root
(Eq. 7-26)
where:
CROOI =
a =
t™ =
K,
-Root-Sr
c,, =
concentration of chemical in the root compartment (g[chemical]/m3[roots]);
proportion of equilibrium value achieved (default = 0.95);
time (days) required for the root/bulk-soil interaction to reach lOOxa percent
(default a = 0.95) of equilibrium when CSr is approximately constant with
time;
user-specified value for the partition coefficient of the chemical between the
root and bulk wet soil (or uptake factor, g[chemical]/m3[root] per
g[chemical]/m3[soil wet wt]); and
concentration of the chemical in the root-zone soil (g[chemical]/m3[soil]).
If the areal density of roots is approximately constant with time, then:
dN
Root
dt
- d)
,RSr
x VRoot x KRoot_Sr x
Sr
- d)
,RSr
xN
Root
(Eq. 7-27)
where:
NRoot
v
y Root
Sr
mass of chemical in roots (g[chemical]);
volume of roots (m3[root]);
total mass of chemical in all phases of bulk root-zone soil (g[chemical]);
and
total volume of root-zone soil, which contains roots (m3[soil]).
Thus:
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T
Sr^fRoot
- ln(l - or)
fRSr
OS
v
„ ''Root „ ^
^
(TF 7-10a)
where:
TSr^Root = transfer factor for transfer of chemical from root-zone soil to root (/day).
The transfer in the other direction, from the root to the bulk root-zone soil is represented as:
- ln(l - a)
TRoot^Sr = -^ (TF 7-1 la)
a
where:
TKnnt^r = transfer factor for transfer of chemical from root to root-zone soil (/day).
I\OOl~'^ir \ J /
7.2.3.2 Uptake from Soil Pore Water
An alternative method by which to estimate the root concentration of a chemical is as an
equilibrium between root-tissue and soil-pore-water concentrations. Selection of the appropriate
method (i.e., for bulk soil or for soil pore water) depends on the experimental method used to
derive the partition coefficient, i.e., whether the data are reported based on pore water, bulk soil,
or dry soil and wet or dry roots. The equilibrium relationship is a generalization of the Briggs et
al. (1982) equation developed in Trapp (1995):
CRoot = KRoot_SrW x CSrW (Eq. 7-28)
where:
CRoot = concentration in roots (g[chemical]/m3[root wet wt]);
KRoot-srw = root/root-zone-soil-water partition coefficient (g[chemical]/m3[root] per
g[chemical]/m3[water] or m3[water]/m3[root]); and
C$rw = concentration in root-zone soil pore water (g[chemical]/m3[water]).
The root/root-zone-soil-water partition coefficient is determined as:
KRoot.SrW = (JWRoot + fLRoot X Kl) X pRoot X 0.001 (Eq. 7-29)
where:
JWRoot = fraction water content of root (kg[water]/kg[root wet wt]);
fLRoot = fraction lipid content of root (kg[lipid]/kg[root wet wt]);
K^ = octanol/water partition coefficient (g[chemical]/kg[octanol] per
g[chemical]/L[water] or L[water]/kg[octanol]);
b = correction exponent for the differences between octanol and lipids
(unitless);
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PRoot
0.001
= volumetric density of fresh root (kg[root wet wt]/m3[root]); and
= unit conversion factor (m3/L).
Thus:
dC.
Root
dt
- ln(l - a)
t«
- ln(l - a)
.RSrW
xC,
Root
(Eq. 7-30)
where:
.RSrW _
time (days) required for the root/soil-pore-water interaction to reach
lOQxa percent (default a = 0.95) of equilibrium when CSrW is
approximately constant with time.
The value of ta for the root/soil-pore-water interaction can be determined from empirical
studies using roots exposed to the chemical in water. In the absence of any data, this ta can be
estimated from the following equation:
RSrW 2x(l.62+glog(^)"L8)
24
(Eq.7-31)
That equation is based on the equation for the plant-root/soil-water interaction from Hsu
et al. (1990), and 24 is the unit conversion factor (hr/day). However, it is a rough estimate, and
the proportion of equilibrium that it might represent is not specified.
If the areal density of roots is approximately constant with time, then:
dN
Root
dt
- ln(l - a)
.RSrW
Root-SrW
Nsrw
SrW
- ln(l - a)
.RSrW
' Root
(Eq. 7-32)
where:
T/
'Root
NSrW
SrW
mass of chemical in roots (kg);
total volume of roots (m3[root]);
total mass of chemical in root-zone-soil water (kg), which
= NSr x Fraction Mass Dissolved (i.e., the total chemical mass in the soil
compartment multiplied by the fraction of it that is dissolved in water);
and
= volume of root-zone soil water (m3[water]), which
= VSr ^Volume Fraction Liquid (i.e., volume of the soil compartment
multiplied by 0, the fraction of the root-zone soil compartment that is
liquid (see Equation 2-37)).
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Making the substitutions for NSrW and VSrW and using Equation 2-72 (Chapter 2) to
substitute Z factors for the ratio of fractions, the transfer factors are:
T
±
-d)
j
RSrW
a
-d)
j
RSrW
a
VDnnt Fraction Mass Dissolved
Root
KOOt £
VSr Root~SrW Volume _ Fraction _ Liquid
V 7
Root -,r pure water
KOOl T£ £- _
T7- ^Root-SrW v \ l-i\J\J)
v
Sr ^ Total Sr
- ln(l - a)
LRoot^>SrW ~ fRSrW (TF7-llt>)
a
where:
Tsrw^Rooi = transfer factor for transfer of chemical from root-zone soil water to root
(/day);
T^Root^srw = transfer factor for transfer of chemical from root to root-zone soil water
(/day);
Zpure_water = fugacity capacity of the chemical in aqueous phase (mol/Pa-m3); and
ZTotai_sr = total fugacity capacity of the chemical in the root-zone soil compartment
(mol/Pa-m3); and
VSr = volume of the root-zone soil compartment (m3[soil]).
Note that the user specifies either equations TF 7-10a and TF 7-1 la (for transfers related
to bulk soil) or TF 7-1 Ob and TF 7-1 Ib (for transfers related to soil pore water only) for a given
chemical.
7.2.4 TRANSFERS INVOLVING THE STEM
The algorithms for the uptake of chemicals by the stem are taken from Trapp (1995), who
derived them for organic chemicals.
7.2.4.1 Contribution from Soil Pore Water via Transpiration Stream (Xylem)
Trapp (1995) derived an equation for the unidirectional flux of chemical from the soil
pore water into the stem driven by the plant transpiration stream through its xylem:
where:
dN N
—^ = Qxy x TSCF x -^ (Eq. 7-33)
Nstem = mass of chemical in stems (g[chemical]);
QXy = total flow of transpired water (m3[xylem]/day, derived below);
TSCF = transpiration stream concentration factor (g[chemical]/m3[xylem] per
g[chemical]/m3[soil pore water] or m3[water]/m3[xylem]);
NSrW = mass of chemical in root-zone-soil pore water (g[chemical]); and
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VSrW = volume of water in root-zone soil (m3[water]).
Using the equation of Hsu et al. (1990):
TSCF =
(Eq.7-34)
According to Crank et al. (1981):
QXy = 4.8 x 10~3 x LAI x As (Eq. 7-35)
where:
4.8 x 10"3 = empirical factor (m3[water]/m2[leaf]-day);
LAI = leaf-area index (m2[leaf]/m2[soil]); and
As = area of associated soil (m2[soil]).
The quantity (NSrW/VSrW) in Equation 7-33 equals the concentration of the chemical in the
root-zone soil pore water in g[chemical]/m3[water]. That quantity can also be expressed as the
fraction of the mass of the chemical in the root-zone soil compartment that is dissolved in water
divided by the volume of the root-zone soil compartment that is liquid, which equals
ZpvrevaJZTatoIJSr (SQQ SeCtOn 2.6):
N srw N Sr Mass _ Fraction _ Dissolved N Sr Zpure_water
q'
vsrw vsr Volume _Fmction_ Liquid VSr ZTotal Sr
Thus:
O x Z
rp _ *£Xy pure_water rTV(~'T7
Sr A ^ Total Sr
(TF7-12a)
r Sr
where:
Tsr^stem = transfer factor for transfer of chemical from root-zone soil to stem (/day);
Zpure water = fugacity capacity of chemical in pure water (mol/Pa-m3);
VSr = volume of the root-zone soil compartment (m3);
ZTotai sr = total fugacity capacity of chemical in bulk root-zone soil (mol/Pa-m3); and
fML = fraction of chemical mass that is dissolved in water divided by fraction of
the volume of the root-zone soil compartment that is water (unitless),
which
= Zpure_mte/ZTotal_Sr (see Equations 2-72 and 2-80).
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7.2.4.2 Alternative Algorithm for Soil/Stem Transfers
An alternative algorithm for uptake of nonionic organic chemicals by the stem from root-
zone soil is an equilibrium relationship between the soil pore water and stem taken from Briggs
etal. (1983):
Pstem
PsrW
(Eq. 7-37)
where:
C-Stem =
••"T
SCF =
Pstem ~
PsrW =
concentration of chemical in stem (g[chemical]/m3[stem]);
concentration in root-zone-soil pore water (g[chemical]/m3[water]);
stem concentration factor (g[chemical]/kg[stem wet wt] per
g[chemical]/kg[water] or kg[water]/kg[stem wet wt]) (see below);
density of stem (kg[stem wet wt]/m3[stem]); and
density of root-zone-soil pore water (kg[water]/m3[water]).
The SCF may be calculated using the following equation from Briggs et al. (1983):
SCF = (io°-95xl08^)-2-05 + 0.82) x 0.784 x
(Eq. 7-38)
Thus, the change in chemical concentration in the stem is estimated as:
dC.
Stem
where:
t.
dt
StSrW _
a
- ln(l - a)
, StSrW
PsrW
- ln(l - a)
t
StSrW
•'Stem
(Eq. 7-39)
time (days) required for the stem/root-zone-soil-pore-water interaction to
reach lOQxa percent of the equilibrium value when CSrWis approximately
constant with time.
If the areal density of stems is approximately constant with time, then:
dNstem
dt
where:
Nstem
v
" Stem
NSrW
-ln(l-etr)
, StSrW
= mass
total
total
.,v „ vrr^Pstem^NSrW
A ' Stem A OL-J A A y
PsrW V SrW
-ln(l-a)
, StSrW
x Nstem (Eq. 7-40)
of chemical in fresh stems (g[chemical]);
volume of stem compartment (m3[stem]);
mass of chemical in root-zone soil water (g[chemical]); and
VSrW = volume of root-zone soil water (m3[water]).
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The total volume of the stem compartment can be calculated as follows:
Vstem = /*?rga/f">< Sr (Eq. 7-41)
Pstem
where:
pareastem = areal density of stem on associated soil (kg[stem wet wt]/m2[soil]);
ASr = area of associated root-zone-soil compartment (m2[soil]); and
Pstem = w£t density of stem (kg[stem wet wt]/m3[stem]).
Thus, the transfer factors describing the transfer from root-zone-soil pore water to the
stem and from the stem to the root-zone-soil pore water are:
T =
SrW'—>Stem
-ln(l- Of)
ta
StSrW
SCF
x pareastem x —— (TF 7-12bl)
PsrW X "Sr
and:
-ln(l-flf)
Stem^SrW fStSrW (Ar 7-12b2)
la
where:
Tsrw^stem = transfer factor for transfer of chemical from root-zone soil water to stem
(/day);
Tstem^srw = transfer factor for transfer of chemical from stem to root-zone soil water
(/day); and
dSr = depth of root-zone soil compartment (m), which
= VSr(rr?)IASr(m2).
Note that this alternative algorithm for nonionic organic chemicals includes transfers in two
directions (TF 7-12bl and TF 7-12b2), whereas the default algorithm in the TRIM.FaTE library
(TF 7-12a) is a one-way transfer from root-zone-soil pore water to the stem. Note that TFs 7-
12bl and 7-12b2 are not in the current TRIM.FaTE library. They are provided here for those
users who may have data available for the SCF parameter but not one or more of the parameters
needed for TF 7-12a (e.g., TSCF, Qxy).
7.2.4.3 Contribution from Leaves via Phloem
During the growing season, the stem can gain dissolved chemical from the leaves via
phloem. Assuming that the chemical concentration in phloem sap is in equilibrium with that in
leaves:
nh=a,*F-7?— (*i.™>
Ul Leaf X ^LeafPh
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where:
Nstem = mass of chemical in stems (g[chemical]);
Qph = phloem flux into leaves (m3[phloem]/day), due to advection (assume 5 percent
of QXy [defined in Section 7.2.4.4], Paterson et al. 1991);
NLeaf = mass of chemical in leaves (g[chemical]);
Vieaf = volume of leaves (m3[leaf]); and
K-Leqfph = partition coefficient between leaves and phloem water (g[chemical]/m3[leaf]
per g[chemical]/m3[phloem] or m3[phloem]/m3[leaf])).
The following equation, adapted from an equation for sorption of contaminants to plant
roots (Trapp 1995), can be used to calculate KLeaJPh:
KLeqfPh = (fWLeaf + JLLeaf x O * ^ (Eq. 7-43)
where:
JWLeaf = fraction of leaves consisting of water (kg[water]/kg[leaf wet wt]);
JLieaf = fraction of leaves consisting of lipid (kg[lipid]/kg[leaf wet wt]);
K^ = octanol/water partition coefficient (g[chemical]/kg[octanol] per
g[chemical]/L[water]);
b = correction exponent for differences between foliage lipids and octanol
(unitless);
Pieaf = density of leaf (kg[leaf wet wt]/m3[leaf]); and
pph = density of phloem (kg[phloem]/m3[phloem]).
If the chemical in question is ionic, it may be assumed that Km is close to zero and that
the concentration of the ionic species in the phloem is the same as that in leaf water. Thus:
TLe^stem = QPh x — (TF 7-13)
Leaf A ^LeafPh
where:
Tieaf-^stem = transfer factor for leaf to stem (/day).
7.2.4.4 Loss from Stem to Leaf via Xylem
During the growing season, the stem can lose dissolved chemical to the leaves via the
xylem:
dNT f N
- = Q*y X TTT — (Eq- 7'44)
Stem StemXy
where:
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NLeaf = mass of chemical in leaf compartment (g[chemical]);
QXy = flow of transpired water (m3[xylem]/day);
Nstem = mass of chemical in stem compartment (g[chemical]);
Vstem = volume of stem (m3[stem]); and
Kstemxy = partition coefficient between stem and xylem water (m3[xylem]/m3[stem])).
The following equation, adapted from an equation for sorption of contaminants to plant
roots (Trapp 1995), may be used to calculate KStemXy.
Kstemxy = (jWstem + fLstem xK^x^L (£q ?.
HXy
where:
m = fraction water content of stem (kg[water]/kg[stem wet wt]);
fLstem = fraction lipid content of stem (kg[lipid]/kg[stem wet wt]);
Km = octanol/water partition coefficient (g[chemical]/kg[octanol] per
g[chemical]/L[water] or L[water]/kg[octanol]);
b = correction exponent for differences between foliage lipids and octanol
(unitless);
Pstem = density of stem (kg[stem wet wt]/m3[stem]); and
pXy = density of xylem fluid (kg[xylem]/m3[xylem]).
If the chemical in question is ionic, it may be assumed that Km is zero and that the
concentration of the ionic species in the xylem is the same as that in leaf water. Thus:
T Sterna Leaf = Qxy X „ - ~ ^ - (TF-7-14)
* Stem X ^StemXy
where:
Tstem^Leaf = transfer factor for stem to leaf.
7.2.4.5 Loss from Phloem to Fruit
Depending on the application, it may not be necessary to implement a fruit compartment
or this loss term in a TRIM.FaTE simulation. Things to consider may be the concentrations
expected in fruit and the portion of the diet (wildlife or human) expected to be comprised of
fruit. This algorithm has not yet been implemented in any applications of TRIM.FaTE. The
concentration of any chemical in the phloem running through the stem is at the same
concentration as xylem sap leaving the stem; both are in equilibrium with the stem. Thus:
N
Fruit j v Stem
"' v Stem
where:
, ,
(Eq- 7~46)
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NFruit = mass of chemical in fruit (g[chemical]);
QphF = phloem flux into fruit (m3[phloem]/day), due to advection (assume 5 percent
of QXy, Paterson et al. 1991);
Nstem = mass of chemical in stem (g[chemical]);
VStem = volume of stem (m3[stem]); and
Kstemxy = partition coefficient between stem and xylem water (m3[xylem]/m3[stem])).
7.2.5 UPTAKE BY WOOD AND TREE BARK
Wood is of interest in a mass-balanced chemical transport and fate model because of its
potential for serving as a large reservoir of chemical mass. The few studies that exist suggest
that there is some accumulation of air pollutants in bark and wood. Turner (1998) has collected
limited data on the accumulation of mercury in wood, but the mechanism of accumulation is not
understood. Simonich and Kites (1995) provide data on the accumulation of organochlorine
compounds in tree bark; PAHs would be expected to have similar properties. Algorithms for the
transfer of chemicals to wood and tree bark are not currently available in the TRIM.FaTE library
because of a general lack of information for persistent air pollutants.
7.2.6 TRANSFORMATIONS AND DEGRADATION
All transformations are assumed to be first-order processes in TRIM.FaTE. The
derivations of these values for mercury and PAHs are described in Appendices A and B of this
volume, respectively. Transformations of chemicals associated with particles on the surface of
plant leaves are assumed to occur with the same rate constants as transformations of chemicals
associated with particles in air.
Transformations of chemicals into other chemicals that are no longer be tracked in
TRIM.FaTE are called general degradation processes. In TRIM.FaTE, the degradation of a
chemical in particles on leaves and vegetation due to all mechanisms that might apply (e.g.,
photolysis, and metabolic activity) is reflected by the user input for the half-life of the chemical
in the plant leaf, stem, and root, and for the chemical associated with particles on the surface of
the leaf.
Transformations of a chemical into another form of the chemical that is tracked in
TRIM.FaTE are named for the processes associated with the transformation (e.g., oxidation,
methylation, reduction of mercury species). The transformation rate constant is the inverse of
the residence time with respect to that reaction.
7.2.7 LITTER FALL
The flux of chemical from leaves, including particles on leaves, to surface soil during
litter fall at the end of the growing season may be expressed by the equation:
dN
—f- = NLeaf + kL x NLeaJP (Eq. 7-47)
where:
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NSs = mass of chemical in surface soil in compartment (g[chemical]);
kL = litter-fall rate constant (/day);
NLeaf = mass of chemical in foliage in leaf compartment (g[chemical); and
NLeafp = mass of chemical in particles-on-leaf compartment (g[chemical]).
If it is assumed that 99 percent of the leaves of deciduous trees are dropped to surface
soil between the day of first frost and a date that is 30 days later, kL would be calculated
according to the equations:
.£. = e-^ (Eq. 7-48a)
ln(0.01)=-30£L (Eq. 7-48b)
where:
= ratio of concentration in the leaf compartment after 30 days of litter fall, C, to
the concentration in the leaf compartment at the beginning of litter fall, C0,
which equals 0.01 if 99 percent of the mass is lost in 30 days
(g[chemical]/m3[leaf] per g[chemical]/m3[leaf]).
Thus, kL would equal -ln(0.01)730 days which is 0.15 /day.
Litter fall for conifers, on the other hand, usually occurs more gradually, with a complete
turnover of leaves taking 2 to 10 or 11 years (Post 1999). Thus, if it is assumed for the purpose
of a TREVI.FaTE scenario that the leaf turnover is 6 years, kL would equal -ln(0.01)7 2190 days,
which is 0.002I/day. Moreover, that litter-fall rate could be set to a constant value for the year.
If it is assumed that herbaceous plants and grasses become "litter" on the surface of the
soil during the 30-day period beginning the day of first frost, again, kL would equal 0.15 /day.
If all of the plant material were harvested, the litter-fall rate constant would be set to
0/day and the chemical in the harvested plant compartments would need to be transferred to a
chemical sink or to another compartment (e.g., silage) for purposes of balancing mass in
TREVI.FaTE. If only a portion of the plant crop (half of the leaves for example) were harvested
and the remainder of the plant were allowed to remain in the "field", the user would need to
determine the fraction of the biomass that would be harvested. That fraction of the chemical in
the harvested plant biomass could be sent to a harvest sink while the remainder could be sent to
the surface soil compartment.
Thus:
TLeaf^Ss = kL (TF 7-15)
where:
TLeaf_^Ss = transfer factor for leaf to surface soil (/day).
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Also:
TLea^Ss = kL (TF 7-16)
where:
TLeafp^ss = transfer factor for the parti cles-on-leaf to surface-soil compartments
(/day).
Note that the transfer of chemical from litter to surface water is not implemented in
TRIM.FaTE at this time.
7.2.8 SENESCENCE
Senesence is not considered in the current version of the TRIM.FaTE library.
Senescence is the aging of plants, a process which affects the uptake of chemicals, growth, and
plant parameters such as water content. If a user of TRIM.FaTE wants to include the process of
senescence, candidate algorithms for changes in plant biomass may be found in Whicker and
Kirchner (1987). Senescence of plants is assumed to be negligible prior to the date of first frost.
7.2.9 OTHER SEASONAL ISSUES
Plants only take up chemicals during the growing season, i.e., the dates in the spring,
summer, and fall between last frost and first frost. Although there may be uptake by conifers
outside of the growing season, it is probably negligible for much of the non-growing season in
cold environments (e.g.., in the Maine case study) (Lindberg 1999b) and is not considered for
TRIM.FaTE modeling purposes. To limit plant uptake only to the growing season, the user must
specify the time period considered outside of the growing season.
During the 30-day period of litter fall for deciduous trees at the end of the growing
season, chemical mass is steadily decreased in the leaf compartment. Because the loss is
modeled using a rate constant, at the end of 30 days, a small amount of chemical remains in the
leaf compartment, and that amount remains throughout the winter. Note that in the current
TRIM.FaTE library, the volume of the leaf compartment goes to zero on the date at which
AllowExchange goes to zero, which is at the beginning of the 30-day litter-fall period. On that
date, the leaf compartment is no longer available as a food source for terrestrial herbivores and
omnivores.
An additional seasonal issue is deposition to the parti cles-on-leaf compartment type.
Tree foliage and grasses only intercept deposition when they are present. Like the leaf
compartment, the volume of the parti cles-on-leaf compartment is a function of AllowExchange,
and so the volume of parti cles-on-leaf drops abruptly to zero for the winter, starting on the first
day of litter fall. TRIM.FaTE assumes that no plant foliage is present in the non-growing
season, except for that associated with conifers or other user-created evergreen vegetation types.
All deposition in deciduous forests, old fields, and agricultural systems in the non-growing
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season goes directly to soil. Deposition to conifer foliage may continue in the winter, though
accumulation of chemicals from particles or wet deposition is assumed to be negligible.
Chemical transformation within the plant is also assumed to cease in the non-growing
season. There is no evidence to support or refute this assumption for most chemicals.
During the non-growing season, for herbivorous or omnivorous animals that do not
hibernate or engage in winter sleep, the user may want to consider the significance of
accumulation from alternative, non-plant dietary sources.
7.3 SOIL DETRITIVORES
In this section, the transfer factor algorithms associated with soil detritivores (i.e.,
earthworms, Section 7.3.1, and soil arthropods, Section 7.3.2) are developed. A list of these
algorithms is provided in the table on the next and following page.
7.3.1 EARTHWORMS
The uptake of chemicals by earthworms in TRIM.FaTE is described by an equation in the
form of time to equilibrium between the earthworms and soil (see Section 2.5). There are two
forms of the uptake equation in TRIM.FaTE: one for uptake of chemicals from an interaction
with bulk soil (Section 7.3.1.1) and one for uptake of chemicals dissolved in soil pore water
(Section 7.3.1.2). The choice of algorithm depends on the data available to derive the partition
coefficients. Empirical data on the uptake of chemicals from bulk soil by earthworms are
commonly available for inorganic chemicals and some organic compounds. Such empirical
ratios are not usually available for earthworm uptake from soil pore water; however, an
established relationship exists between octanol-water partition coefficients and earthworm/soil-
pore-water partition coefficients.
7.3.1.1 Uptake of Chemicals from Bulk Soil
For simplicity, uptake from bulk soil is described as being proportional to the
concentration of the chemical in soil, even though some studies suggest that a log-log regression
between soil and earthworm concentrations is a more precise model of uptake (Sample et al.
1999). The concentration of the chemical in the earthworm (dry -weight basis) is equal to the dry
worm/soil partition coefficient multiplied by the concentration of the chemical in the soil (dry-
weight basis):
(-Worm-dry = ^Worm-Sr-dry X ^Sr-dry (Eq. 7-49)
where:
^arm-dry
= dry-weight concentration of chemical in earthworm
(g[chemical]/kg[worm dry wt]);
K-worm-sr-dry = earthworm/dry-soil partition coefficient (kg[soil dry wt]/kg[worm dry
wt]); and
CSr.dry = dry-weight concentration of chemical in root-zone soil
(g[chemical]/kg[soil dry wt]).
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Summary of Transfer Factors for Soil Detritivores in TRIM.FaTE
DIFFUSIVE TRANSFERS
Bulk root-zone soil to earthworm:
1 Sr^Worm
.WSr
x ^ x K
^Worm-Sr
Earthworm to bulk root-zone soil:
T
^
.WSr
Root-zone-soil pore water to earthworm:
- ln(l - a)
T -
*- SrW^Worm
Earthworm to root-zone-soil pore water:
-ln(l-or)
-*- Worm-^ SrW . WSrW
Bulk soil to soil arthropod:
T
Arth
- ln(l - a)
.AS
^
M, Arth~s
Soil arthropod to bulk soil:
T
- ln(l - a)
Worm-SrW
TF7-17a
TF7-18a
TF7-17b
TF7-18b
TF7-19
TF 7-20
Arthur S .AS
''a
LIST OF SYMBOLS USED IN SOIL DETRITIVORE TRANSFER FACTOR ALGORITHMS
a
M,
M,
Worm
Sr
^Worm-Sr
fraction of equilibrium value achieved by time ta (default = 0.95 or 95%).
time required to reach the fraction a of equilibrium (days) (value depends on
the compartments and phases for which time-to-equilibrium is modeled).
total biomass of worms in root-zone soil compartment (kg[worm wet wt]).
total mass of root-zone soil compartment (kg[soil wet wt]).
earthworm/bulk-soil partition coefficient (kg[soil wet wt]/kg[worm wet wt]).
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Summary of Transfer Factors for Soil Detritivores in TRIM.FaTE (cont.)
LIST OF SYMBOLS USED IN SOIL DETRITIVORE TRANSFER FACTOR ALGORITHMS (cont.)
VSr = volume of root-zone soil compartment (m3).
0 = fraction root-zone soil compartment volume that is liquid (unitless).
K-worm-srw = earthworm/soN-pore-water partition coefficient ( L[water]/kg[worm wet wt]).
MMh = total biomass of arthropods in soil compartment (kg[arthropod wet wt]).
Ms = total mass of soil compartment (kg[soil wet wt]).
KArth-s = arthropod/bulk-soil partition coefficient (kg[soil wet wt]/kg[arthropod wet wt]).
If masses are converted to wet mass, then:
CWorm = (l-fWWorn} x CWorm-dry (Eq. 7-50)
where:
Cwarm = concentration of chemical in earthworm (g[chemical]/kg[worm wet wt]);
and
JWWorm = water content of earthworm (kg[water]/kg[worm wet wt]).
It is also true that:
xQ^ (Eq.7-51)
where:
Thus:
concentration of the chemical in the bulk root-zone soil
(g[chemical]/kg[soil]);
fraction water content of root-zone soil (kg[water]/kg[root-zone soil wet
wt]).
c^~ - Or (Eq. 7-52a)
,
Worm-sr-dty
Rearranging gives:
^Worm T^ „ \*-~ J*'Worm)
(Eq. 7-52b)
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Thus:
~JWWorm)
Worm-Sr
Worm_Sr _dry
(Eq. 7-53)
where:
K-worm-sr = eaithworm/bulk-soil partition coefficient (g[chemical]/kg[worm wet wt] per
g[chemical]/kg[soil wet wt] or kg[soil wet wt]/kg[worm wet wt]).
Using the approach described in Section 2.5, the change in chemical concentration in the
earthworm compartment over time can be described as:
dt
-ln(l-a)
-ln(l-a)
r
Worm
(Eq. 7-54)
where:
.WSr
= time (days) required for the earthworm/bulk-soil interaction to reach 100* a
percent (default a = 0.95) of equilibrium when CSr is approximately constant
with time. The value of ta must be determined from empirical studies
reported in the literature.
If the areal density of earthworms is approximately constant with time, then:
dNWorm
dt
tWSr
x pareaworm x ASr x KWorm_Sr x
M
Sr
- ln(l - a)
iWSr
(Eq. 7-55)
where:
NWorm = mass of chemical in earthworm compartment (g[chemical]);
pareaWorm = areal wet-weight density of earthworms in root-zone soil (kg[worm wet
wt]/m2[soil]);
ASr = area of root-zone soil compartment (m2[soil]);
NSr = total mass of chemical in all phases of bulk root-zone soil (g[chemical]);
and
MSr = bulk mass of root-zone soil compartment, including arthropods (kg[soil
wet wt]).
Note that the quantity (pareaWorm x ASr) is equal to the total biomass of worms (wet wt), MWorm, in
the soil compartment.
Thus, the transfer factors between the bulk root-zone soil and earthworm compartments
are estimated as:
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T =
2 Sr^fWorm
-ln(l- a)
M
Wonn
X KWorm-Sr (TF 7'17a)
- ln(l - a)
TWorn^Sr = ^r^- (TF 7-18a)
1a
where:
Tsr->warm = transfer factor for transfer of chemical from root-zone soil compartment to
earthworm compartment (/day);
Twarm->sr = transfer factor for transfer of chemical from earthworm to root-zone soil
compartments (/day); and
MWorm = total biomass of worms (kg[worm wet wt]) in the root-zone soil
compartment (= pareaWorm x Asr).
7.3.1.2 Uptake of Chemicals from Soil Pore Water
For simplicity, uptake of chemicals from soil pore water is described as being
proportional to the concentration of the chemical in soil pore water. This algorithm is used as an
alternative to uptake from bulk soil. All calculations can be done in original wet weights,
simplifying the derivation of the transfer factors. These equations are appropriate for any
chemicals for which partition coefficients have been reported on a pore-water basis:
CWorm = KWorm_SrW x CSrW (Eq. 7-56)
where:
Cwarm = wet-weight concentration of chemical in earthworm (g[chemical]/
kg[worm wet wt]);
Csrw = concentration of chemical in root-zone-soil pore water (g[chemical]/
L[water]); and
K-warm-srw = eaithworm/root-zone-soil-pore-water (or earthworm/water) partition
coefficient (L[water]/kg[worm wet wt]).
The partition coefficient for the lipophilic organic chemical between the earthworm and
the pore water of the root-zone soil can be calculated as:
fr = Y 73 og (En 7-57")
Wnrm-^rW OW —'•-•'*•' V^^^M * )
where:
Kow = the chemical's octanol-water partition coefficient (g[chemical]/kg[octanol]
per g[chemical]/L[water] or L[water]/kg[octanol]).
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Equation 7-57 was derived from studies of 32 lipophilic chemicals with \og(Kow) values
from 1.0 to 6.5 (Connell and Markwell 1990, Suter et al. 2000). As for uptake calculated with
respect to bulk soil, the equilibrium model for uptake from soil pore water can be changed to the
following equation to estimate the change in concentration of the chemical in the earthworm
over time:
dt
-ln(l-a)
.WSrW
V-
^
•'SrW
-ln(l-a)
.WSrW
(Eq. 7-58)
where:
.WSrW
= time (days) required for the worm/root-zone soil-pore-water interaction to
reach lOOxa percent (default a = 0.95) of equilibrium when CSrWis
approximately constant with time.
The value of this ta can be determined from empirical studies reported in the literature,
but these are rare. In the absence of any data, "^" can be estimated from the following equation
if the octanol/ water partition coefficient (Kow) is available:
.WSrW
2 x 1.62 + e
24
(Eq. 7-59)
This equation is based on the equation for the interaction of plant roots and soil water in
Hsu et al. (1990), which is a rough estimate of the time to equilibrium. An empirical relationship
derived from plant roots is used for earthworms because a model derived from earthworms is not
yet available and the diffusive processes are likely similar. The corresponding proportion of the
equilibrium concentration actually reached, however, is uncertain. Thus, the appropriate value to
use for a (e.g., 0.95, 0.99) is uncertain.
If the areal density of worms is approximately constant with time, then:
Worm
dt
- ln(l - a)
.WSrW
- ln(l - a)
.WSrW
^ SrW
L SrW
(Eq. 7-60)
where:
mass of chemical in earthworms (g[chemical]);
total biomass of worms (kg[worm wet wt]);
mass of chemical in root-zone-soil pore water (g[chemical]); and
mass of root-zone-soil pore water (kg[water]).
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It is also true that:
MSrW
= NSr x Fraction Mass Dissolved (i.e., the total chemical mass in the total
soil compartment multiplied by the fraction of the total chemical mass that
is dissolved in water); and
= VSrW (volume of root-zone soil water in m3) x 1 kg [water]/L [water] x 1000
L[water]/m3 [water]; where:
VSrw = Vsr (m3) x Volume Fraction Liquid (i.e., total volume of the root-
zone soil compartment multiplied by the volume fraction of the
root-zone soil compartment that is liquid).
Making the substitutions for NSrW, MSrW, and then VSrW, and using Equation 2-72 (Chapter 2) to
substitute Z factors for the ratio of fractions, the transfer factors are:
T
^
-a)
-a)
WSrW
MWorm x Fraction_Mass_Dissolved
VSr x 1000 x Volume_ Fraction_ Liquid
KWorm_SrW x
Pure
and:
F^xlOOO
- ln(l - a)
(TF 7-17b)
Total
,
i
WSrW
/-lot))
where:
Tsrw->warm = transfer factor for transfer of chemical from root-zone-soil pore water to
worm (/day);
Twarm->srw = transfer factor for transfer of chemical from worm to root-zone-soil pore
water (/day);
K-warm-srw = worm/soil-pore water partition coefficient (L[water]/kg[worm wet wt]);
= fugacity capacity of chemical in pure water (mol/m3-Pa); and
= total fugacity capacity of chemical in root-zone soil compartment
(mol/m3-Pa).
water
i sr
7.3.2 SOIL ARTHROPODS
An equation for the uptake of chemicals by soil arthropods may be derived similarly to
that for earthworms. Much of the available data relates the concentration of a chemical in the
fresh (wet weight) arthropod to that in its food. The food may be plant matter rather than soil,
but for the purposes of TRIM.FaTE, the uptake factor is assumed to apply to bulk soil. Bulk soil
includes all phases (i.e., solid, liquid, gas) of the soil compartment.
The user may include the soil arthropods in the root-zone or surface soil compartments or
both. In initial applications of TRIM.FaTE, soil arthropods were included in the surface soils.
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The concentration of the chemical in the arthropods equals the concentration in the bulk soil
multiplied by the arthropod/bulk-soil partition coefficient:
where:
Arth ~ ^Arth-S X ^ S
(Eq. 7-61)
CArth = concentration in arthropods (g[chemical]/kg[arthropod wet wt]);
KArth-s = arthropod/bulk-soil partition coefficient (kg[soil wet wt]/kg[arthropod wet
wt]); and
C.
Sr
Thus,
= concentration of the chemical in bulk soil (g[chemical]/kg[soil wet wt]).
dC
Arth
dt
- ln(l - a)
KArth_s x Cs -
- ln(l - a)
.AS
'Arth
(Eq. 7-62)
where:
.AS
= time (days) required for the arthropod/bulk-soil interaction to reach the
fraction a (default = 0.95) of the equilibrium value when Cs is
approximately constant with time.
If the areal density of arthropods is approximately constant with time, then:
dNArth
dt
-ln(l-a)
.AS
x pareaArth x As x KArth_s x
Ms
- ln(l - a)
.AS
xNArth (Eq.7-63)
where:
NArth = mass of chemical in arthropods (g[chemical]);
pareaArth = areal density of arthropod community in soil (kg[arthropod wet
wt]/m2[soil]);
As = area of soil compartment (m2);
Ns = total mass of chemical in all phases of the soil compartment (g[chemical]);
and
Ms = bulk mass of soil, including arthropods (kg[soil wet wt]).
Thus:
T
*-
- ln(l - or)
t
AS
(TF 7-19)
The corresponding algorithm for the release of chemical from the arthropods back to the soil is
estimated as:
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- ln(l - a)
7^-^ (TF 7-20)
' ,-
a
where:
Ts~Arth = transfer factor for transfer of chemical from soil to arthropods (/day);
TArth^s = transfer factor for transfer of chemical from arthropods to soil (/day); and
MArth = total biomass of arthropods (kg[arthropods wet wt]) in the soil
compartment; which
= pareaArth (kg[arthropods wet wt]/m2)x As (m2[soil]).
The transfer factors TF 7-19 and TF 7-20 apply to both organic and inorganic chemicals
in TRIM.FaTE at this time. The user must supply empirical data on the time to reach 95 percent
(or other selected proportion) of the equilibrium value between the bulk soil and arthropods.
7.3.3 FLYING INSECTS
Flying insects are the food of insectivores, particularly aerial feeding insectivores such as
tree swallows. In initial applications of TRIM.FaTE, these insects have been assumed to have
emerged from benthic aquatic larvae living in the surface water bodies. As a consequence, the
concentration of a chemical in flying insects was assumed to be equal to the concentration of that
chemical in the benthic invertebrate compartment in the surface water body to which the aerial
insectivore is linked in a given scenario (see Section 6.3).
7.3.4 TRANSFORMATIONS AND DEGRADATION
Transformations of organic chemicals into metabolic by-products that are no longer
tracked in TRIM.FaTE are not included in the current TRIM.FaTE library for soil detritivores.
Nor are metabolic transformations among chemicals containing the same core chemical (e.g.,
transformation among mercury species) included in the current TRIM.FaTE library for soil
detritivores. These processes are not included because no information could be found
concerning chemical transformations and degradation in soil detritivores.
7.4 TERRESTRIAL WILDLIFE
Terrestrial wildlife, including mammals and birds, can be exposed to chemicals through
food, soil, and water ingestion, and through inhalation of chemicals in air. In addition, chemicals
can be taken up dermally via contact with contaminants in surface water, soil, or air. The rate of
contact with water and soil, however, generally is unknown. In addition, sorption to the skin
surface is unknown, the rate of uptake into the organism is unknown, and the proportion
absorbed through the dermis is relatively low compared with the proportion absorbed through
the gastrointestinal tract or lungs. Thus, dermal uptake is not included in the current
TRIM.FaTE library. Elimination of chemicals from body tissues may occur through metabolic
transformation of the chemical or excretion of the parent compound through urine, feces, milk
(female mammals only), eggs (female birds and reptiles only), and excretion to fur, hair, or
feathers.
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In this section, terrestrial wildlife refers only to mammals and birds; no reptiles or
amphibians are included in the TRTM.FaTE library at this time. The phrase "terrestrial wildlife"
also includes the semi-aquatic species noted in the introduction to this chapter (e.g., mink, loon).
The text box on the next page and continued on the following pages provides a summary of the
transfer-factor algorithms developed in this section and defines the parameters used in those
algorithms.
7.4.1 GENERALIZED MODEL FOR TERRESTRIAL MAMMALS AND BIRDS
A generalized model for terrestrial wildlife (Twl), including all of the possible routes of
exposure and of elimination, is presented below. In addition, the equation below applies to semi-
aquatic populations, such as loons and raccoons. If particular rate constants are determined to be
insignificant relative to others for a particular implementation of TRIM.FaTE (e.g., excretion via
eggs compared to excretion in urine or feces), those may be set to zero. Similarly, if rate
constants for excretion and chemical transformation are determined with respect to the mass of a
contaminant that is taken up in the diet rather than the mass that is assimilated, the dietary
assimilation efficiencies may be ignored.
*- = [(INW x Csw xAEw) + (INSs x CSs xAEs) + Pplant(IND x CLeaf x AEplaJ +
*(WD x CLeafP xAEs) + pWorm(IND x CWorm x AEWorm)
(JN y C y AF \ 4- n (JN y C y AF \ (Eq- 7-64)
lrth\U^D X ^-Arth X ^^ Arth ) + Prwl-prey 177V ZJ X ^Twl-prey X ^^ Twl )
m(IND x Cflsh x AEfish) + pBI(IND x CBI x AEBI)+ (INAir x CAir x AEAir}~\
x (F + F + F + F + F ")1
Twl A V^rne^ T ^M/ T ^/arf T ^ egg T ^^/J
where:
CTwl = total, whole-body, internal concentration in the terrestrial wildlife
population (g[chemical]/kg[body wet wt]);
INW = water ingestion rate (m3[water]/kg[body wet wt]-day);
Csw = concentration of chemical in surface water ingested by wildlife
(g[chemical]/m3[water]);
AEW = assimilation efficiency of chemical from water (unitless);
INSs = surface soil ingestion rate (kg[soil dry wtl]/kg[body wet wt]-day);
CSs = concentration of chemical in surface soil (g[chemical]/kg[soil wet wt]);
AES = assimilation efficiency of chemical from soil (unitless);
Pplant = proportion of plant matter in diet (unitless);
IND = diet ingestion rate normalized to body weight (kg[diet wet wt]/kg[body
wet wt]-day);
CLeaf = concentration of chemical in leaf component of diet (g[chemical]/kg[leaf
wet wt]);
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Summary of Transfer Factors for Wildlife in TRIM.FaTE
ADVECTIVE TRANSFERS
Surface water to semi-aquatic terrestrial wildlife (i.e., bird or mammal):
TSW^T^I DiomassTwl A
* sw
Surface soil to terrestrial wildlife:
INSs x AES
TS^TWI DiomassTwl A
^Ss X Pss__wet
Plant leaf to terrestrial wildlife:
narea T ,
rp f lV/1 ,, ,, T-\T „ A JY
^Leaf^T^l ~ .-_„_,_ A P Plant A 77VZ3 A AL Plant
PClreaLeaf
Surface particles on plant leaf to terrestrial wildlife:
PLeafP >< WD X AES
^LeaJP^Twl ~ y y
' LeafP A PLeafP
Earthworm to terrestrial vertebrate:
narea T ,
rp r Tvil „ „ T-\T ^, ATT'
1Worm-^TWl ~ „„„„„ A Pworm A l^ D * ^^ Worm
/jareaWorm
Soil arthropod to terrestrial vertebrate:
pareaTv:ll
rp f JWt „ „ J-J.T ^, ,-r*
^Arth^T^l ~ A PArth A iN D A AL Arth
parva Arth
Terrestrial vertebrate to terrestrial vertebrate:
narea T ,
rp " Tvil , , „ riv r „ A JY
l^l-prey-,^1 ~ A Plprey-, A ^D A ^^ TV/
fjut cu. Tprey_j
TF 7-21
TF 7-22
TF 7-23
TF 7-24
TF 7-25
TF 7-26
TF 7-27
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Summary of Transfer Factors for Wildlife in TREVLFaTE (cont.)
ADVECTIVE TRANSFERS (cont.)
Fish to terrestrial wildlife (i.e., bird or mammal): TF 7-28
BiomassTwl
Benthic invertebrate or flying insect to terrestrial wildlife: TF 7-29
Biomass j^,,
X
LJ LJL
Air to terrestrial wildlife: TF 7-30
AE
4ir^rwi = BiomassTwl x -
VAir
Terrestrial wildlife to surface soil: TF 7-31
T - f y k
J-Twl^Ss J fuSs A nET
Terrestrial wildlife to water: TF 7-32
T - f Y If
J-Twl^SW J fuSW A ^ET
LIST OF SYMBOLS USED IN WILDLIFE TRANSFER FACTOR ALGORITHMS:
BiomassTwl = biomass of terrestrial wildlife species in a compartment (kg[wildlife wet wt]),
which
= pareaTwi (kg[wildlife wet wt]/m2]) x As(m2[soil]).
INW = water ingestion rate normalized to body weight (m [water]/kg[body wet wt]-
Vsw = volume of surface water compartment (m).
AEW = assimilation efficiency of chemical from water (unitless).
INSs = surface soil ingestion rate (kg[soil dry wt]/kg[body wet wt]-day).
VSs = volume of surface soil compartment (m3).
pss = density of soil particles (kg[soil dry wt]/m3[soil]).
AES = assimilation efficiency of chemical from soil (unitless).
pareaTwl = terrestrial wildlife biomass density per unit area (kg[wildlife wet wt]/m2[surface
parcel]), which
= Narea (number[individuals]/m2[soil]) x Bl/l/(kg[body wet wt]).
pplant = proportion of plant matter in diet (unitless).
IND = diet ingestion rate (kg[diet wet wt]/kg[body wet wt]-day).
AEplant = assimilation efficiency of chemical from plant in diet (unitless).
pareaLeaf = areal biomass density of foliage (kg[leaves wet wt]/m2[surface soil]).
pareaLeafP = areal biomass density of particles on leaf surface (kg[leaf particles]/m2[surface
parcel]).
pworm = proportion of earthworm in diet (unitless).
AEWorm = assimilation efficiency of chemical from earthworm in diet (unitless).
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Summary of Transfer Factors for Wildlife in TREVLFaTE (cont.)
LIST OF SYMBOLS USED IN WILDLIFE TRANSFER FACTOR ALGORITHMS (cont.)
pareaworm
PArth
A^Arth
Pjwl-prey-i
A^TwI-prey
pareaTwl_prey_i
Pflsh-i
nsw
PBI
AEBI
pareaBI
Aged
VAl
AE.
Air
I
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TERRESTRIAL BIOTA ALGORITHMS
Cfish = concentration of chemical in fish (by fish type) (g[chemical]/kg[fish wet
wt]; use correct size range);
AEfish = assimilation (absorption) efficiency of chemical from fish in diet
(unitless);
pBI = proportion of benthic invertebrates (or emergent flying insects) in diet
(unitless);
CBI = concentration of chemical in benthic invertebrates (or flying insects)
(g[chemical]/kg[invertebrates wet wt]);
AEBI = assimilation (absorption) efficiency of chemical from benthic invertebrates
or emergent flying insects in diet (unitless);
INAir = normalized inhalation rate (m3[air]/kg[body wet wt]-day);
CAir = concentration of chemical in the air, including vapor phase and particles
(g[chemcial]/m3[air]);
AEAir = assimilation (absorption) efficiency of chemical from air (unitless);
Emet = rate of metabolic transformation to another chemical(s) that is tracked in a
given scenario or "degradation" to another chemical(s) that is not tracked
in a given scenario (/day);
Euf = rate of chemical elimination through excretory processes (urine and feces)
(/day);
Elact = rate of chemical elimination through lactation (milk production, mammals
only) (/day);
Eegg = rate of chemical elimination through egg production, birds only (/day);
and
Eff = rate of chemical elimination to fur (hair) or feathers (/day).
Because the source of drinking water is not usually known and may include puddles, the
uptake of the chemical from water has been ignored in initial TRIM.FaTE applications for all
species except the semi-aquatic, which are associated with a single water body.
Thus, for a population:
dNTwl WwxNswxAEw INSsxNSsxAEs PPlant x IND x NLeaf x AEPlant
— - — = pareaTwl X As X [ - - - + - - - + - - -
^
Vsw
x NWorm x AEWorm | pArth x WD x NArth x AEArth
- _ ...
(Eq. 7-65)
P^l-prey X IN D X N T^- prey * AE^l Pfi* X ^D X N fish X AE fish P BI * IN D X N m X AE m
As X pareaTwl_prey Asw X pareafish ASed X paream
T Y J~ LJYrW A \^met T *V T -^farf T ^egg T ^^ ^J
j4/r
where:
7Vrw = mass of chemical in terrestrial wildlife species (g[chemical]);
pareaTwl = wildlife biomass density per unit area (kg[biomass wet wt]/m2[surface
volume element]);
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area of associated soil (m2);
mass of chemical in surface water source (g[chemical]);
volume of surface water (m3);
mass of chemical in surface soil (g[chemical]);
volume of surface soil (m3);
bulk density of soil (kg[soil wet wt]/m3[soil]);
mass of chemical in plant leaf (g[chemical]);
areal biomass density of foliage (kg[leaf wet wt]/m2[surface soil]);
mass of chemical in particles on leaf (g[chemical]);
volume of particles on leaf (m3[particles]);
density of particles on surface of leaf (kg[particles]/m3[particles]);
mass of chemical in earthworm (g[chemical]);
areal biomass density of earthworms (kg[worm wet wt]/m2[soil]);
mass of chemical in soil arthropods (g[chemical]);
areal biomass density of soil arthropods (kg[arthropod wet
wt]/m2[soil]);
mass of chemical in the wildlife prey species (g[chemical]);
areal biomass density of the wildlife prey species (kg[body wet
wt]/m2);
mass of chemical in the fish species (g[chemical]);
area of surface water (m2);
areal biomass density of the fish species (kg[fish wet wt]/m2[surface
water]);
mass of chemical in benthic invertebrates (emergent flying insects)
(g[chemical]);
area of sediment (m2);
areal biomass density of benthic invertebrates (kg[invertebrates wet
wt]/m2[sediment]);
total mass of chemical in air (g[chemical]); and
volume of air (m3).
Nsw
YSW
NSs
VSs
Pss we
pareaLeaf
NLeafP
T/-
* LeafP
PP
pareaworm
NArth
pareaArth
Nflsh
ASW
pareafish
N
BI
paream
NAir
V
Air
7.4.2 TRANSFER-FACTOR ALGORITHMS
In TRIM.FaTE, each route of exposure and elimination indicated in the previous section
is handled as a separate transfer factor, as described in subsections 7.4.2.1 through 7.4.2.12. In
the following subsections, the subscript Twl refers to terrestrial wildlife, including the semi-
aquatic wildlife species, because they breathe air.
7.4.2.1 Surface Water to Terrestrial Vertebrate Wildlife
The general transfer factor for ingesting a chemical while drinking surface water for a
specific semi-aquatic wildlife species, either a bird or a mammal, is given by:
= Biomass Twl x
IN xAE
w w_
(TF 7-21)
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where:
T =
± SW^Twl
BiomassTwl =
AEW
transfer factor for transfer of chemical from surface water to bird
or mammal (/day);
total biomass of wildlife compartment (kg);
water ingestion rate normalized to body weight (m3[air]/kg[body
wet wt]-day);
assimilation efficiency of chemical from water (unitless);
volume of surface water compartment from which the animal is
drinking (m3[water]);
and:
or:
where:
BiomassTwl = parearw! x A
Biomass Twl = PNTvl x
Twl
(Eq. 7-66)
(Eq. 7-67)
pareaTwl
A
terrestrial wildlife wet biomass density per unit area (kg[biomass
wet wt]/m2[surface parcel]);
area of associated surface water compartment (e.g., for loons and
ducks) or area of associated soil compartment that borders surface
water compartment (m2);
population size, or number of individuals in compartment
(unitless); and
body weight of the bird or mammal (kg).
(Note: In the current TRIM.FaTE library, the property PopulationSize in the wildlife
compartments is actually calculated as Number'oflndividualsPerSquareMeter x A.)
The water ingestion rates for birds and mammals can be estimated from allometric
equations that relate water ingestion rates to body weight, as described in Section 3.2 of EPA's
(1993) Wildlife Exposure Factors Handbook. The allometric equations for water ingestion by
mammals and birds are from Calder and Braun (1983):
0.90
WIbirds = 0.059 xBW
0.67
(Eq. 7-68)
(Eq. 7-69)
where:
WI
BW
water ingestion rate (L/day); and
body weight (kg[body wet wt]).
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Therefore, the water ingestion rate normalized to body weight in m3[water]/kg[body wet wt]-day
is estimated by:1
-dayj BW(kg)
0.0001
7.4.2.2 Surface Soil to Terrestrial Vertebrate Wildlife
The general transfer factor for incidental ingestion of chemical with surface soil by a
specific bird or mammal is given by:
«, x
, = Biomass Twlx —— - (TF 7-22)
Ss X yss wet
where:
TSs^Twl = transfer factor for transfer of chemical from surface soil to bird or
mammal (/day);
INSs = surface soil ingestion rate (kg[soil dry wt]/kg[body wet wt]-day);
AES = assimilation efficiency of chemical from soil (unitless);
VSs = volume of surface soil compartment (m3); and
pSs wet = bulk density of surface soil (kg[soil wet wt]/m3[soil]).
To estimate the soil ingestion rate from data on the estimated percent soil in the
consumed diet on a dry-weight basis (e.g., the data in Beyer et al. 1994), the following equations
can be used, where:
IND = diet (no soil) ingestion rate (kg[diet wet wt]/kg[body wet wt]-day);
INSs = ingestion rate of surface soil (kg[soil dry wt]/kg[body wet wt]-day);
IND dry = dry diet (no soil) ingestion rate (kg[diet dry wt]/kg[body wet wt]-day); and
INTotal dry = total intake of dry food plus dry soil (kg[food + soil, dry wt]/kg[body wet
wt]-day]).
Assuming the natural diet is 75 percent water:
IND_diy = INDx0.25 (Eq.7-71)
INTotaLdry = MSs + IND_dry (Eq. 7-72)
The data available in Beyer et al. (1994) and similar studies are in the form of:
The algorithm described in Equation 7-70 is associated with mammal and bird compartment types in the
current TRIM.FaTE library.
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Jintake_soil
Therefore:
fraction of total dry-weight intake that is soil (unitless).
^Total_dry ^D_dry ' (* ~ J intake _soil)
(Eq. 7-73)
Substituting Equation 7-73 for INTotal dry in Equation 7-72, using IND x 0.25 for IND dry, and
rearranging the equation yields:
INn x 0.25
77T7 -
\ J intake soil
x a25
(Eq. 7-74)
The transfer factor for surface soil to terrestrial vertebrates should only be used for birds
and mammals that forage on the ground (Beyer et al. 1994). For example, black-capped
chickadees are arboreal feeders and are rarely observed on the ground (Smith 1993), meaning
that soil ingestion for this species would be negligible. Representative species that ingest soil as
a consequence of their feeding habits include the mallard, mule deer, black-tailed deer, white-
tailed deer, long-tailed vole, raccoon, white-footed mouse, woodcock, and bobwhite quail.
Representative species that do not feed on the ground - and consequently ingest only negligible
amounts of soil or none at all - include the tree swallow, red-tailed hawk, long-tailed weasel,
mink, and black-capped chickadee.
7.4.2.3 Plant Leaf to Terrestrial Vertebrate Wildlife
The general transfer factor for bird or mammal ingestion of a chemical in plant leaves is
given by:
where:
pare a T .
/
pareaL
n y JN
P Plant X 77V
ZJ Plant
(TF 7-23)
,eaf
T
± Leaf-^Twl
Pplant
IND
AE.
'Plant
pareaL
,eaf
Note that:
transfer factor for transfer of chemical from plant leaf to bird or
mammal(/day);
proportion of plant matter in diet (unitless);
diet ingestion rate (kg[diet wet wt]/kg[body wet wt]-day);
assimilation efficiency of chemical from plant in diet (unitless);
and
areal biomass density of foliage (kg[leaves wet wt]/m2[surface
soil]).
pareaTvl = PNarea x BW
(Eq. 7-74)
and:
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Biomassrwl = PNarea x A x BW (Eq. 7-75)
where:
A = area of containing surface volume element (m2); and
PNarea = population size or number of individuals per unit area (/m2[soil]).
The transfer factor for plant leaf to terrestrial vertebrates is most relevant for herbivores,
which feed entirely on plant matter. It also is relevant for omnivores, for which plant matter
makes up a portion of their diet. This transfer factor is not relevant for carnivores or
predators/scavengers. The proportion of plant matter in the diet (pp!ant) varies by species, by
season, and by location of the population of interest. In initial applications of TRIM.FaTE, pplant
has varied by species.
7.4.2.4 Particles on Leaf Surface to Terrestrial Vertebrate Wildlife
Ingestion of plant materials generally results in the ingestion of the particles that have
settled on the plant surfaces. In some areas under some conditions, the coating of plants with
particulate matter (e.g., dust or soil particles) can be substantial. The general transfer factor for
particles on leaf surfaces to a specific bird or mammal is given by:
71._, = """ X 'N° X M- (TF7-24)
^VUJL —f L WL y \ /
V LeafP rLeafP
where:
TLeajp^Twl = transfer factor for transfer of chemical from parti cles-on-leaf
compartment to bird or mammal compartment via ingestion (/day);
AES = assimilation efficiency of chemical from soil (unitless);
VLeafP = volume of the parti cles-on-leaf compartment (m3); and
pLeafP = density of dust particles (kg[particles]/m3[particles]).
7.4.2.5 Earthworm to Terrestrial Vertebrate Wildlife
The general transfer factor for earthworms to a specific bird or mammal is given by:
parear ,
T £_ £H_ y r, y JM y AF fTTT 70^
J-Worm^Twl ~ Oarea Pworm X U V D X ^^ Worm l1^ ' ~^)
where:
Tworm^Twi = transfer factor for transfer of chemical from earthworm to bird or
mammal (/day);
pareaWorm = areal biomass density of earthworms (kg[worm wet wt]/m2 [soil]);
pWorm = proportion of earthworm in diet (unitless); and
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assimilation efficiency of chemical from earthworm in diet
(unitless).
This transfer factor is relevant in cases where the specific bird or mammal of interest is
known to consume earthworms. Examples of species that ingest earthworms include the
raccoon, short-tailed shrew, woodcock, and American robin.
7.4.2.6 Soil Arthropod to Terrestrial Vertebrate Wildlife
The general transfer factor for soil arthropods to a specific bird or mammal is given by:
parea T,
n
parea Arth
where:
TArth^Twi = transfer factor for transfer of chemical from soil arthropods to bird or
mammal (/day);
pareaArth = areal biomass density of soil arthropods (kg[arthropod wet wt]/m2[soil]);
pArth = proportion of soil arthropods in diet (unitless); and
AEArth = assimilation efficiency of chemical from arthropods in diet (unitless).
This transfer factor is relevant in cases where the specific bird or mammal of interest is
known to consume soil arthropods. Soil arthropods are invertebrates with segmented bodies and
jointed limbs as adults, such as ants, beetles, spiders, grasshoppers, and centipedes and include
their larval forms that dwell in the soil as well (e.g., beetle grubs). Examples of wildlife species
that consume soil arthropods include the shrew, woodcock, and white-footed mouse.
7.4.2.7 Terrestrial Vertebrate to Terrestrial Vertebrate Wildlife
The general transfer factor for bird or mammal ingestion of chemical in avian or
mammalian prey is given by:
parea T,
~ -
where:
pareaTwl
p Tprey-i
AETv>l
Tprey-i
transfer factor for the transfer of chemical from the ith terrestrial
vertebrate prey species to the bird or mammal predator species (/day);
areal biomass density of the consumer wildlife (i.e., bird or mammal)
species (kg[predator wet wt]/m2[soil]);
areal biomass density of the prey wildlife (i.e., bird or mammal) species
(kg[prey wet wt]/m2[soil]);
proportion ofith terrestrial vertebrate prey species in diet (unitless); and
assimilation efficiency of chemical from birds or mammals in diet
(unitless).
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The transfer factor for terrestrial vertebrate to terrestrial vertebrate is only applicable to
birds and mammals that are classified as terrestrial omnivores, carnivores, and
predators/scavengers. Examples of species to which this transfer factor would apply include the
red-tailed hawk, long-tailed weasel, and mink. Note that the assimilation efficiencies for a
chemical in either avian or mammalian prey consumed by avian or mammalian predators are
likely to be similar; hence, a single AETwl is specified.
7.4.2.8 Fish to Terrestrial Vertebrate Wildlife
The transfer factor for ingestion of a chemical in fish by a terrestrial vertebrate is relevant
in cases where the bird or mammal of interest is known to consume fish species (i.e., the bird or
mammal is classified as a piscivore or an omnivore). Several types or species offish can be
represented in TREVI.FaTE, including benthic herbivores, omnivores, and carnivores, and water
column herbivores, omnivores, and carnivores (see Chapter 6). Different species of piscivorous
wildlife are more likely to catch certain types and sizes offish than others (e.g., the belted
kingfisher is more likely to eat small water column herbivores and omnivores such as minnows
and bluegill than larger carnivorous species offish). The general transfer factor for fish to a
specific bird or mammal is given by:
BiomassT ,
T""-*™ = A xnarea X P*» X W D X ^ (TF 7'28)
ASW x pareafish_i
where:
Twi = transfer factor for transfer of chemical from ith type of fish to bird or
mammal (/day);
= proportion of ith type of fish in diet (unitless);
= assimilation efficiency of chemical from fish in diet (unitless);
Asw = area of surface of surface water body compartment (m2); and
pareafish_t = areal biomass density of the ith type offish (kg[fish wet wt]/m2[surface
water]).
7.4.2.9 Benthic Invertebrate to Terrestrial Vertebrate Wildlife
Benthic invertebrates include mayflies, dragonfly nymphs, crayfish, clams, and aquatic
snails, which dwell primarily at the bottom of water bodies. Examples of wildlife species that
consume benthic invertebrates are the mallard, raccoon, and belted kingfisher. The general
transfer factor for ingestion of a chemical in benthic invertebrates by a specific bird or mammal
is given by:
BiomassT ,
where:
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Tfl/^nw = transfer factor for transfer of chemical from benthic invertebrates to bird
or mammal (/day);
pBI = proportion of benthic invertebrates in diet (unitless);
AEBI = assimilation efficiency of chemical from benthic invertebrates in diet
(unitless);
ASed = area of the sediment compartment (m2); and
paream = areal biomass density of benthic invertebrates (kg[invertebrates wet
wt]/m2 [sediment]).
The same transfer factor is used to represent flying insects consumed by birds (or bats)
for species of insects with aquatic larval stages. For purposes of the model, the flying insects are
assumed to have the same chemical concentrations in their tissues as they had when living
underwater before metamorphosis into flying adults. Representative species that consume flying
insects include the black-capped chickadee and tree swallow.
7.4.2.10 Air to Terrestrial Vertebrate Wildlife
The general transfer factor for inhalation of a chemical in air (vapor- and parti culate-
phase) to a specific bird or mammal is given by:
INAir x AEAir
TAir^Twi ~ Biomass Twix T (TF 7-30)
Air
where:
^Air^rwi = transfer factor for transfer of chemical from air to bird or mammal (/day);
INAir = inhalation rate normalized to body weight (m3[air]/kg[body wet wt]-day);
AEAir = assimilation efficiency of chemical from air (unitless); and
VAir = volume of air compartment (m3).
The inhalation rates for birds and mammals are estimated from allometric equations that
relate inhalation rates of captive animals to body weight, as described in Section 3.3 of EPA' s
(1993) Wildlife Exposure Factors Handbook. The allometric equation for inhalation rate (IR)
by mammals is from Stahl (1967). For mammals:
IR = 0.5458 x BW° 80 (Eq. 7-76)
where:
IR = inhalation rate (m3[air]/day); and
BW = body weight (kg[body wet wt]).
The allometric equations for inhalation rate by birds are from Lasiewski and Calder
(1971). For nonpasserine birds (i.e.., birds other than the perching songbirds):
IR = 0.4089 X BW011 (Eq. 7-77)
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However, adjustments are required to estimate the inhalation rates of free-living animals
from these estimates, which are based on conditions used to measure standard metabolic rate of
captive animals. For example, it may be appropriate to multiply the predicted IR from these
allometric equations by a factor of 2 to 3 (USEPA 1993). The value used in initial TREVI.FaTE
applications is 2.5.
Also, the inhalation rate for birds is for nonpasserine species only. Passerines tend to
have a higher metabolic rate than nonpasserines for a given body weight. For example, the
equations for basal metabolic rate (BMK) developed by Lasiewski and Dawson (1967) from
almost 100 species of birds revealed the following differences:
For passerine birds: BMR = 128 x BW°™ (Eq. 7-78)
For nonpasserine birds: BMR = 77 6 x BW*-^ (Eq. 7-79)
where:
BMR = basal metabolic rate (kcal/day);
BW = body weight (kg[body wet wt]/day).
In other words, the BMR of passerine birds is about 1.65 times higher than that of non-
passerine birds. Similarly, the equations for free-living metabolic rate (FMR) developed by
Nagy (1987) for passerines (N = 26) and nonpasserines (N = 24) indicated that the FMR of
passerine birds is about 1.85 times higher than that of nonpasserine birds.
Thus, the equations for estimating the free-living inhalation rate (FIR) in m3/day for birds
and mammals may be derived as:
For all mammals: FIR = 0.5458 x BW°-80 x 2.5 (Eq. 7-80)
For nonpasserine birds: FIR = 0.4089 x BW077 x 2.5 (Eq. 7-81)
For passerine birds: FIR = 0.4089 x BW077 x 2.5 x 1.75 (Eq. 7-82)
Thus, INAir (in m3/kg[body wet wt]-day) in equation TF 7-30 is estimated by:
FIR
INAir = — (Eq. 7-83)
where:
FIR = free-living inhalation rate (m3/day).
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7.4.2.11 Terrestrial Vertebrate Wildlife to Surface Soil
The general transfer factor for elimination of a chemical from a bird or mammal to
surface soil is given by:
TTwl^Ss = ffuSs*kET (TF7-31)
where:
TTWI^SS = transfer factor for transfer of chemical from bird or mammal to surface
soil (/day);
ffuSs = fraction eliminated to surface soil (instead of surface water) (unitless); and
kET = first-order rate constant for total elimination of chemical in urine and feces
(£a/) plus feathers or fur (£^) (/day), i.e.,
= kuf+kff.
This single first-order elimination rate refers to the parent chemical (i.e., undegraded,
untransformed chemical). In addition to excretion in urine and feces, chemicals also can be
excreted by birds into feathers and eggs and by mammals into hair, or fur, and milk. For the
chemicals modeled in TRIM.FaTE to date, with the exception of methylmercury, this single
elimination rate constant will be dominated by elimination in urine and feces. For the excretion
of methylmercury from birds, feathers and eggs is similar in importance to urine and feces (see
Table A-17 in Appendix A). Thus, in the case of birds and methylmercury, the rate constant for
chemical elimination that reaches the soil, kET, is set equal to the rate constant for elimination in
urine and feces plus the rate constant for elimination in feathers. Note that in the current
TRIM.FaTE compartment design, excretion to eggs does not constitute movement of the
chemical out of the bird population compartment, nor does milk represent movement out of
mammal population compartment. A discussion of estimating elimination rate constants from
metabolic studies is presented in the TRIM.FaTE user guidance.
7.4.2.12 Semi-aquatic Vertebrate Wildlife to Surface Water
The general transfer factor for elimination of a chemical from semi-aquatic wildlife to
surface water is given by:
TT^SW = ffusw x kET (TF 7-32)
where:
TTwi^sw = transfer factor for transfer of chemical from bird or mammal to surface
water (/day);
ffuSW = fraction eliminated to surface water (unitless); which
~~ 1 ~JuSs-
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7.4.3 TRANSFORMATIONS AND DEGRADATION
Transformations of organic chemicals into metabolic by-products that are no longer
tracked in TRIM.FaTE are modeled as transfers to the wildlife degradation/reaction sinks. See
the TRIM.FaTE user guidance for discussion of identifying rate constants for metabolism
separately from rate constants associated with chemical excretion and elimination back to the
environment. Equation 2-64 (Chapter 2) is used to estimate the first-order metabolic degradation
(in TRIM.FaTE, called "general degradation") rate constant, kdegradation, for an organic chemical.
The transfer-factor algorithm for transfer of metabolic by-products to the wildlife
degradation/reaction sink is simply equal to kdegradation.
It has been observed that first-order degradation rate constants generally scale as a
function of body weight (BW) to a negative one quarter power (U.S. EPA 1992). Thus,
^degradation f°r a species of interest may be derived from kdegradation for a reference species using the
following equation:
BW(Twl)-°25
BW(reJ)~
degradation (Twl) = kdegradation (rSf> X DT^.^-0.25 (E^ 7'84)
where:
kdegradation(Twl) = metabolic degradation rate constant for the terrestrial wildlife
species in TRIM.FaTE (/day);
^degradation(ref) = metabolic degradation rate constant for the reference laboratory
animal (/day);
BW(Twl) = body weight for the terrestrial wildlife species in TRIM.FaTE
(kg[body wet wt]); and
BW(reJ) = body weight for the reference laboratory animal (kg[body wet wt]).
Metabolic transformations of chemicals among different compounds containing the same
core chemical (e.g., transformation among mercury species) are included in the TRIM.FaTE
wildlife models. See Appendix A, Section A.3, for a discussion of mercury transformations in
birds and mammals.
7.4.4 SEASONALITY
Seasonality of diet is partially reflected in the current TRIM.FaTE library algorithms.
Herbivorous or omnivorous wildlife consume leaves of deciduous trees, grasses/herbs, and
possibly agricultural crops only during the growing season, when such leaves are available.
During the non-growing season, those types of vegetation are no longer available to wildlife for
consumption. Applications to date have not included alternative dietary items (containing the
modeled chemical) for herbivorous wildlife in winter. Wildlife species could migrate out of the
area for the winter (e.g., American robin) or switch to other foods during the winter (e.g., deer
begin stripping bark and move from deciduous areas to coniferous forest).
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To reflect winter sleep, hibernation, or migration, the user may turn off wildlife
algorithms during relevant seasons. Additionally, it may be appropriate to seasonally vary the
diet of particular wildlife species.
7.4.5 USE OF TERRESTRIAL WILDLIFE COMPARTMENTS
The TRIM.FaTE model has been parameterized for many functional trophic groups of
wildlife species. These are listed in Table 7-1. The parameters for which input is needed in a
TRIM.FaTE simulation for these compartment types are presented in Appendix D.
Discussion on the selection of wildlife species for a TRIM.FaTE scenario and the
association of different species with appropriate volume elements is provided in the TRIM.FaTE
users guidance. The addition of wildlife populations to a TRIM.FaTE scenario will depend on
the goals and objectives of the project as well as the ecosystem being modeled. In addition, the
Table 7-1
Terrestrial and Semi-aquatic Vertebrate Compartment Types in
Current TRIM.FaTE Library
Functional Trophic Group
Semi-aquatic piscivorea/predator
Semi-aquatic predator/scavenger
Semi-aquatic aerial insectivore (i.e., feeding
on adults of emergent insects such as mayflies)
Semi-aquatic omnivore
Terrestrial omnivore
Terrestrial insectivore
Terrestrial predator/scavenger
Terrestrial herbivore
Terrestrial ground-invertebrate feeder
Compartment Type
Belted kingfisher
Common loon (water-based)13
Mink
Bald eagle
Tree swallow
Mallard (water-based)13
Raccoon
American robin
White-footed mouse
Black-capped chickadee
Long-tailed weasel
Red-tailed hawk
Black-tailed deer
Bobwhite quail
Long-tailed vole
Meadow vole
Mule deer
White-tailed deer
Short-tailed shrew
Trowbridge shrew
Woodcock
a Consumes fish.
b
The containing volume element is associated with surface water, and the species' population density represents the
number of individuals per unit surface water area.
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distribution of chemical mass (and transfers) across wildlife biomass and trophic levels in the
ecosystem needs consideration.
Exclusively terrestrial wildlife species may be associated with terrestrial surface volume
elements depending on the plant community represented by the volume element (e.g., deciduous
forest, coniferous forest, herbs/grasses). The containing volume element for semi-aquatic
wildlife species can either be a surface water volume element (i.e., water-based species, such as
loons, that spend most of their time on the water and feed entirely on aquatic organisms) or a
surface soil volume element (i.e., land-based species, such as mink that spend most of their time
on land and consume both aquatic and terrestrial foods) (see Table 7-1).
Several semi-aquatic wildlife species have been included in the current TRIM.FaTE
library. Each of these species must be linked to a specific surface water body from which they
can obtain their aquatic prey or food (e.g., fish, benthic invertebrates, macrophytes). This
generally is accomplished by including the wildlife species' compartment in a land parcel that is
adjacent to the surface water body and estimating the density and numbers of individuals present
based on the area of the land parcel. Alternatively, it might be appropriate to create two different
compartment types for these semi-aquatic wildlife (e.g., raccoons consuming aquatic prey and
raccoons consuming terrestrial prey), particularly for applications where aquatic species play a
substantive role (e.g., as focus in assessment, or significant source of pollutant to predators).
The densities of the land-based semi-aquatic wildlife in the containing surface soil volume
element should reflect only those individuals with foraging ranges that might realistically include
the water body. For species that defend feeding territories, the number of individuals per unit
length of shoreline would be the relevant density measure for those consuming aquatic prey.
The density of that species per unit area of the containing surface soil volume element would
equal the number of individuals that might forage along the interface between the surface water
compartment and containing surface soil volume element divided by the area of the surface soil
volume element. Otherwise, the simulation might reflect an unrealistic consumption of aquatic
organisms by their land-based predators. For species that forage in flocks or herds far from
nesting or breeding sites, such as tree swallows, the number of individuals per unit area of the
terrestrial environment generally would be the relevant density measure.
Predators/scavengers with large home ranges (e.g., bald eagle) can be modeled as
consuming prey from a number of different surface parcels or volume elements. A TRIM.FaTE
variable called TheLink.Fraction-SpecificCompartmentDiet in the transfer factor algorithm used
for the ingestion link from the prey (and its associated surface parcel) to the predator would be
used to partition the diet among different surface parcels.
7.4.6 ASSIMILATION EFFICIENCY AND ELIMINATION
The TRIM.FaTE user guidance discusses the types of data from published studies that
may be appropriate to use for chemical assimilation (absorption) efficiencies from the diet (AED),
from drinking water (AEW), from air via inhalation (AEAit), and for elimination rate constants
(kE1). Nonetheless, some explanation is warranted here to assist the user in understanding
differences in the fish and wildlife values for AE and kET properties in the current TRIM.FaTE
library. A simplified explanation ofAED, AEW, and kET for mammals and birds is presented in
Section 7.4.6.1. A simplified explanation ofAEAir is provided in Section 7.4.6.2.
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7.4.6.1 Efficiency of Chemical Assimilation from the Diet
AnAED for dietary intake of a chemical (or an AEWfor intake of a chemical with drinking
water) of 1.0 implies complete absorption from the diet/drinking water, while anAED of 0.2, for
example, indicates that 80 percent of the chemical passed through the wildlife unabsorbed and
hence, must have been eliminated in the feces. For the chemical that was absorbed (e.g., 20
percent in the current example), there are several possible elimination routes listed below, the
first three of which may be considered "excretory processes":
• excretion in urine (via the kidney);
• excretion in bile, which is eliminated in the feces;
transfer to fur or feathers, to eggs, or to milk;
exhalation via the lungs (considered a diffusive process of negligible magnitude for
compounds of interest and not included in the current TREVI.FaTE library); and
• metabolic degradation to other chemicals.
Depending on the organism, available data by which to estimate one or more of these
processes might be predominantly of one type or another. Many toxicokinetic studies using
birds or mammals, where both feces and urine are fairly easy to collect and analyze, estimate
"elimination" rates or rate constants based on those data. Those data account for (a) fecal
elimination of the unabsorbed chemical, and excretion of the absorbed chemical (b) in urine and
(c) in the bile. Many such studies also measure dose as the concentration of the chemical in the
diet multiplied by the quantity of food eaten. With these types of measurements, one would not
need to estimate anAED (or AEW) for the chemical. Instead, all of the chemical ingested with
food (and water) would represent the chemical gain rate for the wildlife compartment and
chemical elimination in urine and feces would represent the loss rate. In this case, the AED (or
AEW) would be set equal to 1.0. Given that the mercury loss (elimination) rates for wildlife
modeled in an initial mercury application were based on measurements of the quantity of
chemical in urine and feces compared with the quantity in the diet and water, we setAED and
AEW to 1.0 for that test case.
Toxicokinetic studies of organic compounds often use radioactive labels to track the
elimination of metabolites of organic compounds in urine and feces as well as elimination of the
parent compound. In TRIM.FaTE, if the metabolites are not tracked further by the model, the
mass of parent chemical that was degraded into metabolites should be transferred to a wildlife
sink. Only the parent chemical that is excreted in urine and feces should be transferred back to
the environment (either surface soil or surface water) via the "elimination" transfer factors.
Thus, only those studies in which the investigator quantifies the radioactive metabolites
separately from the radioactive parent chemical can be used to set a rate constant for transfer to
the degradation sink separately from the rate constant for elimination to the environment.
Another type of data often reported in the literature are elimination rate constants based
on measurements of body burdens of a chemical over time following a single administration.
Suppose that a group of animals were administered an organic chemical one time by intravenous
injection. Suppose further that the body burdens of the chemical in different subsets of those
animals were measured at weekly intervals after that. From those data (i.e., body burden at time
0, 7 days, 14 days, etc.), the estimated elimination rate constant would account for (a) excretion
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in urine, (b) excretion in bile (in feces), and (c) metabolic degradation to other chemicals. That
is, these data (from an intravenous injection study) do not provide information on assimilation or
absorption from the diet that is needed to estimate AED^ For additional discussion of these topics,
see the TRIM.FaTE user guidance.
7.4.6.2 Efficiency of Chemical Assimilation from Air
In a very simple inhalation model, the efficiency of assimilation of a chemical from air can be
calculated from the estimated inhalation dose (i.e., the chemical concentration in air multiplied
by the animal's inhalation rate, measured in volume of air per unit time) compared with the body
burden of the chemical in the animal after a specified exposure duration. The estimated AEAir,
representing a net absorption, would account for transfers from the air in the lungs to the
bloodstream and from the bloodstream to the air in the lungs.
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REFERENCES
8. REFERENCES
Ambrose, R.A., Jr., T.A. Wool, and J.L. Martin. 1995. The water quality analysis simulation
program, WASPS. Part A: Model documentation. Athens, GA: U.S. EPA National Exposure
Research Laboratory, Ecosystems Division.
ARS (Agricultural Research Service). 1982. Analytical Solutions of the One-dimensional
Convective-dispersive Solute Transport Equation. Washington, D.C.: U.S. Department of
Agriculture.
Baes, C.F., III, R.D. Sharp, A.L. Sjoreen, and R.W. Shor. 1984. A Review and Analysis of
Parameters for Assessing Transport of Environmentally Released Radionuclides Through
Agriculture. ORNL-5786. Oak Ridge, TN: Oak Ridge National Laboratory.
Baines, S. B., and M.L. Pace. 1994. Relationships between suspended particulate matter and
sinking flux along a trophic gradient and implications for the fate of planktonic primary
production. Canadian Journal of Fisheries and Aquatic Sciences. 51:25-36.
Bennett, D.H., T.E. McKone, M. Matthies, and W.E. Kastenberg. 1998. General formulation of
characteristic travel distance for semivolatile organic chemicals in a multimedia environment.
Environmental Science and Technology. 32:4023-4030.
Beyer, W.N., E.E. Connor, and S. Gerould. 1994. Estimates of soil ingestion by wildlife.
Journal of Wildlife Management. 58:375-382.
Briggs, G.G., R.H. Bromilow, A.A. Evans, and M.R. Williams. 1983. Relationships between
lipophilicity and the distribution of non-ionised chemicals in barley shoots following uptake by
the roots. Pesticide Science. 14:492-500.
Briggs, G.G., R.H. Bromilow, and A.A. Evans. 1982. Relationship between lipophilicity and
root uptake and translocation of non-ionised chemicals by barley. Pesticide Science. 13:495-
504.
Calder, W.A., and E.J. Braun. 1983. Scaling of osmotic regulation in mammals and birds.
American Journal of Physiology. 244:R601-R606.
Chamberlain, A.C. 1970. Interception and retention of radioactive aerosols by vegetation.
Atmospheric Environment 4: 57-78.
Connell, D.W., and R.D. Markwell. 1990. Bioaccumulation in the soil to earthworm system.
Chemosphere. 20:91-100.
Covar, A.P. 1976. Selecting the proper reaeration coefficient for use in water quality models.
Presented at the U.S. EPA Conference on Environmental Simulation Modeling, April 19-22,
Cincinnati, OH.
SEPTEMBER 2002 8-1 TRIM.FATE TSD VOLUME II
-------
CHAPTER 8
REFERENCES
Crank, 1, N.R. McFarlane, J.C. Newby, G.D. Paterson, and J.B. Pedley. 1981. Diffusion
processes in environmental systems. In: Paterson et al. 1991. London: Macmillan Press, Ltd.
Di Toro, D.M., and J.P. Connolly. 1980. Mathematical Models of Water Quality in Large Lakes,
Part 2: Lake Erie. Washington, D.C.: U.S. Environmental Protection Agency. EPA-600/3-80-
056; pp. 28-30.
Efroymson, R.A., B.E. Sample, and G.W. Suter II. 2001. Bioaccumulation of inorganic
chemicals by soil from plants: regressions of field data. Environ. Toxicol. Chem. 20:2165-2571.
Gobas, F.A.P.C. 1993. A model for predicting the bioaccumulation of hydrophobic organic-
chemicals in aquatic food-webs - application to Lake Ontario. Ecological Modeling. 69:1-17.
Gobas, F.A.P.C., E.J. McNeil, L. Lovettdoust, and G.D. Haffner. 1991. Bioconcentration of
chlorinated aromatic-hydrocarbons in aquatic macrophytes. Environmental Science &
Technology. 25:924-929.
Hargrove, W.W. 1999. Personal communication. University of Tennessee. January.
Harner and Bidleman. 1998. Octanol-air coefficient for describing particle/gas partitioning of
aromatic compounds in urban air. Environmental Science and Technology. 32:1494-1502.
Hsu, F.C., R.L. Marxmiller, and A.Y.S. Yang. 1990. Study of root uptake and xylem
translocation of cinmethylin and related compounds in detopped soybean roots using a pressure
chamber technique. Plant Physiology. 93:1573-1578.
Junge, C.E. 1977. Basic considerations about trace constituents in the atmosphere as related to
the fate of global pollutants. In: Suffet, I.H., ed. Fate of Pollutants in the Air and Water
Environments. New York, NY: Wiley and Sons; pp. 7-26.
Jury, W., W. Spencer, and W. Farmer. 1983. Behavior assessment model for trace organics in
soil: I. Model description. Journal of Environmental Quality. 12:558-564.
Karickhoff, S.W. 1981. Semi-emperical estimation of sorption of hydrophobic pollutants on
natural sediments and soils. Chemosphere. 10:833-846.
Lasiewski, R.C., and W.A. Calder. 1971. A preliminary allometric analysis of respiratory
variables in resting birds. Respiration Physiology. 11:152-166.
Lasiewski, R.C., and W.R. Dawson. 1967. A reexamination of the relation between standard
metabolic rate and body weight in birds. Condor. 69:12-23.
Leonard, T.L., G.E. Taylor, Jr., M.S. Gustin, and G.C. J. Fernandez. 1998. Mercury and plants
in contaminated soils: 2. Environmental and physiological factors governing mercury flux to
the atmosphere. Environmental Toxicology and Chemistry. 17:2072-2079.
Lindberg, S. 1999a. Personal communication. Oak Ridge National Laboratory. January.
SEPTEMBER 2002 8~3TRIM.FATE TSD VOLUME II
-------
CHAPTER 8
REFERENCES
Lindberg, S. 1999b. Personal communication. Oak Ridge National Laboratory. September.
Lindberg, S.E., T.P. Meyers, G.E. Taylor, Jr., R.R. Turner, and W.H. Schroeder. 1992.
Atmosphere-surface exchange of mercury in a forest: results of modeling and gradient
approaches. Journal of Geophysical Research. 97:2519-2528.
Mackay, D. 1991. Multimedia Environmental Models: The Fugacity Aproach. Chelsea, MI:
Lewis Publishers.
Mackay, D., M. Joy, and S. Paterson. 1983a. A quantitative water, air, sediment interaction
(QWASI) fugacity model for describing fate of chemicals in lakes. Chemosphere. 12:981-997.
Mackay, D., S. Paterson, and M. Joy. 1983b. A quantitative water, air, sediment interaction
(QWASI) fugacity model for describing fate of chemicals in rivers. Chemosphere. 12:1193-
1208.
Mackay, D., and P.J. Leinonen. 1975. Rate of evaporation of low-solubility contaminants from
water bodies to atmospheres. Environmental Science and Technology. 7:611-614.
Mackay, D., and A.T.K. Yeun. 1983. Mass transfer coefficients correlations of volatilization of
organic solutes from water. Environmental Science and Technology. 17:211-216.
McCune, D.C., and T.L. Lauver. 1986. Experimental modeling of the interaction of wet and dry
deposition on conifers. In: Lee, S. F., T. Schneider, L. D. Grant, and P. J. Verkerk, eds.
Aerosols: Research, Risk Assessment, and Control Strategies. Proceedings of the Second U.S.-
Dutch International Symposium, Williamsburg, VA; pp. 871-878. May 1985.
McKone, T.E. 1993a. CalTOX, A Multimedia Total-exposure Model for Hazardous-wastes
Sites, Parti: Executive Summary. UCRL-CR-111456PtI. Livermore, CA: Lawrence
Livermore National Laboratory.
McKone, T.E. 1993b. CalTOX, A Multimedia Total-exposure Model for Hazardous-wastes
Sites, Part II: The Dynamic Multimedia Transport and Transformation Model. UCRL-CR-
111456PtII. Livermore, CA: Lawrence Livermore National Laboratory.
McKone, T.E. 1993c. CalTOX, A Multimedia Total-exposure Model for Hazardous-waste
Sites, Part III: The Multiple-pathway Exposure Model. UCRL-CR-111456PtIII. Livermore,
CA: Lawrence Livermore National Laboratory.
Mill, T., W.R. Mabey, P.C. Bomberger, T.W. Chou, D.G Herdy, and J.H. Smith. 1982.
Laboratory Protocols for Evaluating the Fate of Organic Chemicals in Air and Water. EPA-
600/3-82-0220. Athens, GA: U.S. Environmental Protection Agency.
Millington, R.J. and J.M. Quirk. 1961. Permeability of porous solids. Transactions of the
Faraday Society. 57:1200-1207. In: Wallach, R., W.A. Jury, and W.F. Spencer. 1989. The
concept of convective mass transfer for prediction of surface-runoff pollution by soil surface
SEPTEMBER 2002 8-3 TRIM.FATE TSD VOLUME II
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CHAPTER 8
REFERENCES
applied chemicals. Transactions of the American Society of Agricultural Engineers. May-June.
1989.
Muller, H., and G. Prohl. 1993. Ecosys-87: A dynamic model for assessing radiological
consequences of nuclear accidents. Health Physics. 64:232-252.
Nagy, K.A. 1987. Field metabolic rate and food requirement scaling in mammals and birds.
Ecological Monograph. 57:111-128.
Nobel, P.S. 1999. Physiochemical and Environmental Plant Physiology. Second Edition. New
York, NY: Academic Press.
O'Connor, DJ. 1983. Wind effects on gas-liquid transfer coefficients. Journal of
Environmental Engineering. 109(9):731-752.
Paterson, S., and D. Mackay. 1995. Interpreting chemical partitioning in soil-plant-air systems
with a fugacity model. In: Trapp, S. and J.C. McFarlane, eds. Plant Contamination: Modeling
and Simulation of Organic Chemical Processes. Boca Raton, FL: Lewis Publishers; pp. 191-
214.
Paterson, S., D. Mackay, and A. Gladman. 1991. A fugacity model of chemical uptake by
plants from soil and air. Chemosphere. 23:539-565.
Post, W.M. 1999. Personal communication. Oak Ridge National Laboratory. January.
Prohl, G., Hoffman, F.O. 1996. Radionuclide interception and loss processes in vegetation. In:
Modeling of Radionuclide Interception and Loss Processes in Vegetation and of Transfer in
Semi-natural Ecosystems. Vienna. IAEA-TECDOC-857, pp. 9-46.
Ribeyre, F., and A. Boudou. 1994. Experimental study of inorganic and methylmercury
bioaccumulation by 4 species of fresh-water rooted macrophytes from water and sediment
contamination sources. Ecotoxicology and Environmental Safety. 28(3):270-286.
Riederer, M. 1995. Partitioning and transport of organic chemicals between the atmospheric
environment and leaves. In: S. Trapp and J.C. McFarlane, eds. Plant Contamination: Modeling
and Simulation of Organic Chemical Processes. Boca Raton, FL: Lewis Publishers; pp. 153-
190.
Sample, B.E., G.W. Suter II, J.J. Beauchamp, and R.A. Efroymson. 1999. Literature-derived
bioaccumulation models for earthworms: development and validation. Environmental
Toxicology and Chemistry. 18:2110-2120.
Schnoor, J.L. 1981. Fate and transport of dieldrin in Coraville Reservoir: residues in fish and
water following a pesticide ban. Science. 211:840-842.
Schnoor, J.L., and D.C. McAvoy. 1981. A pesticide transport and bioconcentration model.
Journal of Environmental Engineering. 107:1229-1246.
SEPTEMBER 2002 8^4 TRIM.FATE TSD VOLUME II
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CHAPTER 8
REFERENCES
Simonich, S.L,. and R.A. Kites. 1995. Global distribution of persistent organochlorine
compounds. Science. 269:1851-1854.
Smith, S.M. 1993. Black-capped chickadee. In: A. Poole, P. Stettenheim, and F. Gill, eds., The
Birds of North America. No. 39. Philadelphia, The Academy of Natural Sciences; Washington
D.C., The Ornithologists Union.
Stahl, W.R. 1967. Scaling of respiratory variables in mammals. Journal of Applied Physiology.
22:453-460.
Suter, G.W., II, R.A. Efroymson, B.E. Sample, and D.S. Jones. 2000. Ecological Risk
Assessment for Contaminated Sites. Boca Raton, FL: Lewis Publishers.
Thomann, R.V. 1989. Bioaccumulation model of organic-chemical distribution in aquatic food-
chains. Environmental Science and Technology. 23:699-707.
Thomann, R.V., J.P. Connolly, and T.F. Parkerton. 1992a. An equilibrium-model of organic-
chemical accumulation in aquatic food webs with sediment interaction. Environmental
Toxicology and Chemistry. 11:615-629.
Thomann, R.V., J.P. Connolly, and T.F. Parkerton. 1992b. Modeling accumulation of organic
chemicals in aquatic food webs. In: Gobas, F.A. and J.A. McCorquodale, eds. Chemical
Dynamics in Fresh Water Ecosystems. Boca Raton, FL: Lewis Publishers; pp. 153-186.
Trapp, S. 1995. Model for uptake of xenobiotics into plants. In: Trapp, S. and J.C. McFarlane,
eds. Plant Contamination: Modeling and Simulation of Organic Chemical Processes. Boca
Raton, FL: Lewis Publishers; pp. 107-151.
Trapp, S., and M. Matthies. 1995. Generic one-compartment model for uptake of organic
chemicals by foliar vegetation. Environmental Science and Technology. 29:2333-2338.
Trudel, M., and J.B. Rasmussen. 1997. Modeling the elimination of mercury by fish.
Environmental Science and Technology. 31:1716-1722.
Tsivoglou, E.E., and J.R. Wallace. 1972. Characterization of Stream Reaeration Capacity.
EPA-R3-72-012. Washington, DC: U.S. Environmental Protection Agency.
Turner, R. 1998. Personal communication. Frontier Geosciences. August.
U.S. EPA (U.S. Environmental Protection Agency). 2002a. TRIM.FaTE Technical Support
Document Volume I: Description of Module. EPA-453/R-02-011a. Research Triangle Park,
NC: Office of Air Quality Planning and Standards. September.
U.S. EPA (U.S. Environmental Protection Agency). 2002b. Evaluation of TRIM.FaTE Volume
I: Approach and Initial Findings. EPA-453/R-02-0012. Research Triangle Park, NC: Office of
Air Quality Planning and Standards. September.
SEPTEMBER 2002 8-5 TRIM.FATE TSD VOLUME II
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CHAPTER 8
REFERENCES
U.S. EPA (U.S. Environmental Protection Agency). 1999a. The Total Risk Integrated
Methodology: TRIM.FaTE Technical Support Document. Volume I: Description of Module.
External Review Draft. EPA-453/D-99-002A. Research Triangle Park, NC: Office of Air
Quality Planning and Standards. November.
U.S. EPA (U.S. Environmental Protection Agency). 1999b. The Total Risk Integrated
Methodology: TRIM.FaTE Technical Support Document. Volume II: Description of Chemical
Transport and Transformation Algorithms. External Review Draft. EPA-453/D-99-002B.
Research Triangle Park, NC: Office of Air Quality Planning and Standards. November.
U.S. EPA (U.S. Environmental Protection Agency). 1999c. Bioaccumulation and Aquatic
System Simulator (BASS) User's Manual Beta Test Version 2.0. Internal Draft as supplied by
Craig Barber. Research Triangle Park, NC: Office of Research and Development.
U.S. EPA (U.S. Environmental Protection Agency). 1998a. The Total Risk Integrated
Methodology: Technical support document for the TRIM.FaTE module. Draft. EPA-452/D-98-
001. Office of Air Quality Planning and Standards.
U.S. EPA (U.S. Environmental Protection Agency). 1998b. AQUATOX for Windows: A
Modular Toxic Effects Model for Aquatic Ecosystems. Internal Draft. Washington, D.C.:
Office of Pollution Prevention and Toxics.
U.S. EPA (U.S. Environmental Protection Agency). 1997. Mercury Study Report to Congress.
Volume III: Fate and Transport of Mercury in the Environment. EPA-452/R-97-005. Research
Triangle Park, NC, and Washington, D.C.: Office of Air Quality Planning and Standards and
Office of Research and Development.
U.S. EPA (U.S. Environmental Protection Agency). 1993 Wildlife Exposure Factors
Handbook, Volume I. EPA/600/R-93/187a. Washington, D.C.: Office of Water and Office of
Research and Development. December.
U.S. EPA (U.S. Environmental Protection Agency). 1992. Draft Report: A Cross-Species
Scaling Factor for Carcinogen Risk Assessment Based on Equivalence of mg/kg3/4/day; Notice.
Federal Register. June 5. 57(109): 24152-24173.
van der Leeden, F., F.L. Troise, and O.K. Todd. 1991. The Water Encyclopedia. Chelsea, MI:
Lewis Publishers.
van de Water, R.B. 1995. Modeling the transport and fate of volatile and semi-volatile organics
in a multimedia environment. Ph.D. Dissertation. Chemical Engineering, University of
California, Los Angeles.
Wallach, R., W.A. Jury, and W.F. Spencer. 1989. The concept of convective mass transfer for
prediction of surface-runoff pollution by soil surface applied chemicals. Transactions of the
American Society of Agricultural Engineers. May-June. 1989.
SEPTEMBER 2002 8-6 TRIM.FATE TSD VOLUME II
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CHAPTER 8
REFERENCES
Wania, F., J. Axelman, and D. Broman. 1998. A review of processes involved in the exchange
of persistent organic pollutants across the air-sea interface. Environmental Pollution. 102:3-23.
Whicker, F.W., and T.B. Kirchner. 1987. Pathway: A dynamic food-chain model to predict
radionuclide ingestion after fallout deposition. Health Physics. 52:717-737.
Whitby, K.T. 1978. The physical characteristics of sulfur aerosols. Atmospheric Environment.
12:135-159.
Whitman, R.G. 1923. A preliminary experimental confirmation of the two-film theory of gas
adsorption. Chemical and Metallurgical Engineering. 29:146-148.
Wilmer, C., andM. Flicker. 1996. Stomata. Seconded. New York, NY: Chapman and Hall.
p. 121.
Wilson, R., and J.D. Spengler, eds. 1996. Particles in Our Air: Concentrations and Health
Effects. Cambridge, MA: Harvard School of Public Health.
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APPENDIX A
DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
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APPENDIX A
DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
APPENDIX A
DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
This appendix contains derivations of mercury-specific transfer algorithms (Section A.I)
and transformation algorithms (Section A.2).
A. 1 MERCURY-SPECIFIC TRANSFER ALGORITHMS
The algorithms/equations included in the current TRIM.FaTE library that are specific to
mercury are described below. These include:
• dry deposition of divalent mercury vapors to surface water, plants, and soil (Section
A.1.1);
exchange of mercury between algae and surface water (Section A. 1.2);
mercury excretion by fish (Section A. 1.3);
time-to-equilibrium-based mercury accumulation by fish (Section A. 1.4); and
resistance of the plant leaf mesophyll to diffusion of elemental mercury (Section
A.I.5).
A.1.1 DRY VAPOR DEPOSITION OF DIVALENT MERCURY
Some of the algorithms used to transfer mercury from air to surface water, surface soils,
and plants (and the algorithms used for transfers in the opposite direction) depend on the
mercury species. The algorithms for diffusion between air and surface water, surface soils, and
plant leaves apply only to Hg(0) and CH3Hg, but not Hg(2). The net diffusion of Hg(2) vapors
from air to surface water, surface soils, and plant leaves is described in a single algorithm called
dry vapor deposition to distinguish it from the other diffusion algorithms noted above. The dry-
vapor algorithm uses an empirical value for net Hg(2) vapor deposition velocity to account for
diffusive processes, as described below. Thus, the net dry transfer factors for diffusion of Hg(2)
vapors in air to the compartments listed above and are expressed as:
dry_dep .. A
TDVdep ™P°r ASW (
LAir^SW ~ y X JMV ^ >
'Air
dry_dep j A
TDVdep _ vaP°r dfy ASs „ f
rr X JMV
VAir
— —XfMV (TFA-3)
Air
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APPENDIX A
DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
where:
rpDVdep
1 Air^SW
rj-<
*
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APPENDIX A
DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
Mason et al. (1996). The D^s for divalent mercury and methylmercury in TRIM.FaTE were
estimated based on those curves.
Uptake of inorganic mercury (divalent) and methylmercury by algae is given by the
following equation (Mason et al. 1996):
(Eq. A-2)
where:
U
R
P
total mercury concentration in algae (nmol[Hg]/g[algae wet wt]);
total dissolved mercury concentration in water (nM[Hg]);
overall Km for neutral mercury complexes at specified pH and chloride
concentrations (unitless);
algal surface area-specific uptake rate constant (nmol[Hg]/|j,m2[algal
surface] -day-nM [Hg]);
average radius of algae (|-im);
average algal cell density (g[algae wet wt]/|_im3[algae]); and
algal growth rate constant (/day).
Within TRIM.FaTE, the uptake of mercury by algae is characterized using the ratio of
ae to Hgwater. To transform the previous equation to this ratio, the units ofHgwater should be
converted from nM to nmol/g by dividing the right side of the equation by 1000 g/L. If both
sides are then divided by Hgwater:, the equation can be simplified to:
algae
xt/x3
Hgwater
(Eq. A-3)
Note that this equation uses moles. Gram weights are derived by multiplying the moles
per gram or liter by the chemical-specific molecular weight. Table A-l shows the molecular
weights of mercury and methylmercury in the units appropriate for converting the above algae
(nmol/g) and water (nM) concentrations.
Table A-l
Molecular Weights of Mercury and Methylmercury
Chemical
Hg
CH3Hg
Molecular Weight
g/mol
200.59
215.62
|jg/nmol
2.0059 x10'1
2.1562X 10'1
mg/nmol
2.0059 x 1C'4
2.1562X 10'4
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APPENDIX A
DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
The uptake process appears to be relatively fast, i.e., hours rather than days (Mason et al.
1996). Also, uptake of elemental mercury by algae is assumed to be insignificant in
TRIM.FaTE, based on the findings of (Mason et al. 1996) that the accumulation rates were less
than 1 amol/cell-hr-nM, where amol equals 1 x 10"18 moles.
A.1.3 MERCURY EXCRETION BY FISH
The mercury excretion rate constant (kE) (i.e., transfer of absorbed mercury back to
surface water) is given by the following bioenergetic model (Trudel and Rasmussen 1997):
\n(kE) = 0.066X.T- 0.20X \n(mf ) + 0.73X ED- 6.56 (£q. A-4)
where:
kE = total mercury excretion rate constant (/day);
T = temperature (°C);
mf = body mass fish (g[fish wet wt], note units are not kg); and
ED = exposure duration; 0 = acute (<90 days), 1 = chronic (>90 days).
For the chronic exposures for which TRIM.FaTE may be most frequently applied, the
mercury excretion rate constant is reduced to:
\n(kE ) = 0.066 x T - 0.20x \n(mf ) - 5.83 (Eq. A-5)
The transfer factor for mercury from fish to the surface water is simply:
sw = kE (TF A-4)
Trudel and Rasmussen (1997) based the excretion rate on the clearance of methylmercury
only, because greater than 95 percent of mercury in fish is methylmercury and the elimination of
methylmercury is much slower than that of inorganic mercury (i.e., the overall rate is dominated
by the elimination of methylmercury). Trudel and Rasmussen (1997) found the clearance of
inorganic mercury by fish to be about three times faster than the clearance of methylmercury.
Thus, to estimate kE for elemental and divalent mercury, the equation to estimate kE for
methylmercury is multiplied by a factor called HowMuchFasterHgElimination IsThanForMHg,
which is set equal to three in the current TRIM.FaTE library.
A.1.4 ACCUMULATION OF MERCURY BY FISH
Mercury concentrations in fish are ultimately determined by methylmercury
accumulation at the base of the food chain (Mason et al. 1995, 1996). Therefore, one algorithm
for the uptake of mercury in fish based on the general equation for the time-to-equilibrium food-
chain model is presented in Section 6.4.2. Intertrophic level concentration ratios (Kreceptor_diet)
were obtained from studies of natural populations offish, zooplankton, and phytoplankton.
Based on studies using methylmercury/nitrogen ratios in whole fish, the concentration ratio
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APPENDIX A
DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
between two adjacent trophic levels was found generally to be around 3 to 4 (studies cited in
Lindqvist et al. (1991)). As noted in Section 6.4.2, mercury transfers from algae to water-
column herbivores in TRIM.FaTE implicitly include the intermediate transfer from algae to
zooplankton. Concentration ratios between planktivorous fish and phytoplankton were between
9 and 16 (Lindqvist et al. 1991, Watras and Bloom 1992). That is, zooplankton were an
intermediate trophic level and the transfers between each trophic level were approximately
equal. Taking the geometric mean results in approximate concentration ratios for methylmercury
of 3.5 for one trophic-level transfer and 12 for two trophic-level transfers (Mason et al. 1996).
Inorganic mercury (divalent) transfer factors between phytoplankton and zooplankton
and between zooplankton and planktivorous fish are given by Watras and Bloom (1992). In the
absence of similar factors for fish-to-fish transfers of inorganic mercury, the zooplankton-to-
planktivorous-fish transfer factor was used to estimate the concentrations in the water-column
omnivore, water-column carnivore, benthic omnivore, and benthic carnivore compartment types.
In other words, in the current TRIM.FaTE library, the mercury partition coefficient between
adjacent trophic levels in the time-to-equilibrium model for bioaccumulation by fish is set as
follows:
^fish-diet = 3.5.
A.1.5 PLANT MESOPHYLL RESISTANCE
A general plant algorithm for mesophyll resistance was added to TRIM.FaTE to
accommodate the behavior of mercury in plants. For most organic chemicals and most plant
species, the stomatal or cuticular conductance is the rate-limiting pathway (Riederer 1995).
Therefore, for many chemicals, there is no need to consider mesophyll (inner tissue)
conductance. However, some work with mercury cited in Lindberg et al. (1992) suggests that
"resistance on or within mesophyll surfaces dominates the atmosphere-leaf diffusive path of
Hg(0)."
For herbaceous species, Lindberg et al. (1992) indicate that this mesophyll resistance for
elemental mercury is a factor of 2.5 x stomatal resistance and that mesophyll conductance is a
factor of 1/2.5 or 0.4 x stomatal conductance. TRIM.FaTE therefore uses the following equation
for elemental mercury (only):
gm = gstomataxOA (Eq.A-6)
where:
gm = conductance of chemical through mesophyll (m/day); and
gstomata = conductance of chemical through stomata (m/day).
Note that the high mesophyll resistance of elemental Hg might be due to its assimilation
in mesophyll tissue (Lindberg et al. 1992). It has previously been assumed that the mesophyll
resistance for divalent mercury is 0.0 (U.S. EPA 1997a); i.e., thatgm is infinite.
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DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
A.2 MERCURY TRANSFORMATION ALGORITHMS
Since there are three species of mercury, there are six possible transformation routes from
one species to another. All but one of these routes will be considered:
• Reduction Hg(2)^ Hg(0);
• Oxidation Hg(0) ->• Hg(2);
• Methylation Hg(2)^ CH3Hg;
• Demethylation CH3Hg -> Hg(2); and
• Mer cleavage demethylation CH3Hg -> Hg(0).
The route not considered is methylation of Hg(0), for which little information has been reported.
In the case of mercury, the transformation from one chemical species to another is
modeled using a first-order rate constant. In particular, the following general equations may be
used to model transformation:
i n dM,
Reduction, Hg2+ -» Hg°: - L = kR x M2(t)
(iiq. A-/)
n T ,
Oxidation, Hg° -» Hg2+ : —- = k0xM, (f)
(£q A_g)
dM,
Methylation, Hg2+ -» CH3Hg: —£- = kMx M2(t} (Eq A.9)
Demethylation, CH3Hg -» Hg2+ : —^ = kDm x M3 (t) (Eq. A- 1 0)
n
Mer cleavage demethylation, CH3Hg -* Hg° : —- = kMC x M3 (t)
(A-l
where:
Mj = mass of elemental mercury in a compartment type (g[Hg(0)]);
M2 = mass of divalent mercury in a compartment type (g[Hg(2)]);
M3 = mass of methylmercury in a compartment type (g[CH3Hg]);
kR = reduction rate in compartment type (/day);
k0 = oxidation rate in compartment type (/day);
kM = methylation rate in compartment type (/day);
kDm = demethylation rate in compartment type (/day); and
kMC = mer cleavage demethylation rate in compartment type (/day).
The transformation rates may be input directly or calculated based on other parameters.
If both algorithms and input values are available, then the user will be able to choose which
method to use. The corresponding transfer factors for Equations A-7 through A-10, respectively,
are listed below:
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DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
rpreduction
Hg(2)—>Hg(Q)
T~> oxidation
rpmeihylation
rr< demethylation
(TF A-5)
(TF A-6)
(TF A-7)
A.2.1 ABIOTIC MERCURY TRANSFORMATION RATE CONSTANTS
The information in Tables A-2 through A-13 is taken primarily from the 1997 Mercury
Report to Congress (U.S. EPA 1997a) and model documentation for EPRI's R-MCM Mercury
Cycling Model (Hudson et al. 1994).
Table A-2
Issues Related to Reduction of Hg(2) to Hg(0) in Soil, Surface Water, and Sediment
Soil
Decreases in decreasing
sunlight
Abiotic reduction (transfer
of electrons from humic
acid to Hg(2)) is
dependent on pH
Strong stability complex
between Hg(2) and humic
acid
Surface Water
Decreases with decreasing sunlight and
temperatures
Has been observed to increase with decreasing
dissolved organic carbon (DOC) conditions
(Amyot et al. 1997), and vice versa, due to
reduced light penetration and increased
complexation of Hg(2)
Sediment
Sparse literature on
subject
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DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
Table A-3
Reduction (k^ in Surface Water: Inputs
Input Values (1/day)
5E-1to 3.5
5E-3 to 1 E-1
2E-2 to 4E-2
1E-2
<5E-3
1.4E-1
2E-1 to 4E-1
2E-2 to 1 .4E-1
1E-1
5E-2
7.5E-3
Comment
Experimental value using simulated
sunlight, after normalizing to sunlight in
Stockholm, Sweden
Based on mass balances in Wisconsin
seepage lakes
Epilimnion
9 m depth
17m depth
high Arctic lake during 24 hour sunlight
period
high Arctic lake, low DOC conditions
high Arctic lake, high DOC conditions
July-August, upper 3 m
July August, upper 6 m
Value in current TRIM.FaTE library
Reference(s)
U.S. EPA (1997a), Xiao etal.
(1995)
U.S. EPA (1997a), Mason etal.
(1994)
Mason etal. (1995)
Mason etal. (1995)
Mason etal. (1995)
Amyotetal. (1997)
Amyotetal. (1997)
Amyotetal. (1997)
Vandal etal. (1995)
Vandal etal. (1995)
U.S. EPA(1997a)
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Table A-4
Reduction (k^ in Sediment: Inputs
Input Values (1/day)
1E-6
0.216
1E-6
Comment
Inferred value calculated based on
presence of Hg(0) in sediment porewater
Derived from humic acid from farm pool
sediment. pH did not appear to affect the
rate of reaction, but does seem to influence
the amount of mercury reduced
Value in current TRIM.FaTE library
Reference(s)
U.S. EPA (1997a), Vandal et al.
(1995)
Alberts et al. (1974)
U.S. EPA (1997a), Vandal et al.
(1995)
Table A-5
Reduction (k^ in Soil: Inputs
Equations to Calculate Input Values
Comment
Reference(s)
where
Ss
reduction rate constant normalized by
soil water content in the surficial 5 mm
of soil (L[soil]/L[water]-day); values
range from 1E-4 for forest site to 1.3E-3
for field site;
soil water content ( L[water]/L[soil]);
depth of soil surface layer to which
reduction rate is normalized, 5E-3 (m);
and
soil layer depth (m).
Formula is derived
from evasion flux
measurements
U.S. EPA (1997a), Carpi
and Lindberg (1997)
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Table A-6
Issues Related to Methylation in Soil, Surface Water, and Sediment
Soil
Anaerobic conditions favor
higher methylation rates3
Biotic methylation may occur
due to bacteria; abiotic
methylation may occur by
transmethylation from other
organometals or by humic
substances'3
Increases with increasing
organic carbon content and
BHTf
Generally occurs for Hg(2)
dissolved in soil pore water
Abiotic methylation is
proportional to temperature and
Hg(2) concentration. Also, it is
inversely proportional to pH (at
pH > 5)g
Surface Water
Anaerobic conditions favor
higher methylation rates3
Photodegradation at surface
can lower the gross methylation
ratec
Positively correlated with DOCd
(dissolved organic carbon)
Generally occurs for Hg(2)
dissolved in water columnd
Positively correlated with
temperatured
Potentially positively correlated
with sulfate concentration in
water column8
Sediment
Anaerobic conditions favor
higher methylation rates3
Highest rates may occur at the
sediment surface (sulfate-
reducing bacteria may be
important mediators of the
reaction), Gilmour and Henry
(1991)
Positively correlated with TOC
(total organic carbon)d
Generally occurs for Hg(2)
dissolved in sediment pore
waterd
Positively correlated with
temperatured
Potentially positively correlated
with sulfate concentration in
sediment pore water8
a This is generally due to increased bacterial reactions in anaerobic conditions.
b: U.S. EPA (1997a), Gilmour and Henry (1991).
c: Initial reference is Bob Ambrose's discussion of methylation in water column in U.S. EPA (1997a).
d: Hudson etal. (1994).
e: Watrasetal. (1995).
f: Nagase et al. (1984); BHT = 2,6, di-tert-butyl-methyl phenol.
g: Bodeketal. (1988).
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Table A-7
Methylation (kM) in Surface Water: Inputs
Input Values (1/day)
1 E-4 to 3E-3
6E-4 to 6E-3
5E-4 to 1 E-3
1 E-2 to 3E-2
4E-3 to 1 E-2
1 E-2 to 4E-2
1E-3
Comment
reported as maximum
potential methylation rate
Depth of 3 - 9m
Oxic portion of four forest
lakes in Finland
At seasonally-anoxic
depth of 15 m
Anaerobic layers of
hypolimnion
0.5 - 1.0 m layer of
bacterioplankton near the
top of the anoxic
hypolimnion
Value in current
TRIM.FaTE library
Reference(s)
Gilmour and Henry (1991)
U.S. EPA (1997a), based on
Henry et al. (1995a, 1995b) and
Jacobs etal. (1995)
Matilainen (1995)
U.S. EPA(1997a), based on
Henry et al. (1995a, 1995b) and
Jacobs etal., (1995)
Matilainen (1995)
Watrasetal. (1995)
U.S. EPA(1997a)
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APPENDIX A
DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
Table A-7
Methylation (kM) in Surface Water: Inputs (cont.)
Equations to Calculate Input Values
Comment
Reference
ksw
KM
where:
T
Tb
'dissolved
K
Su
(r~ra)x0-1
fHg(2)
ma
f
A J di
Hg(2)
issolved
K.
Su
methylation rate constant in the water column, based on DOC
(L/mg[DOC]-day);
term to adjust methylation rate for temperature (implied value in
R-MCM documentation is 2, so that methylation rate doubles for
every 10 degree increase in temperature above the base
temperature);
water column temperature (degrees Celsius);
base temperature at which methylation rate constant kMW applies
(degrees Celsius);
DOC concentration in water column (mg[DOC]/L);
fraction of the dissolved Hg(2) in the water column available for
methylation (unitless);
fraction of the Hg(2) in the water column that is dissolved
(unitless);
concentration of sulfate in the water column
(ueq[sulfate]/L[water]); and
half-saturation constant for the effect of sulfate on methylation
(u eq [s u Ifate]/L[wate r[).
Hudson etal. (1994)].
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APPENDIX A
DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
Table A-8
Methylation (kM) in Sediment: Inputs
Input Values (1/day)
Comment
Reference(s)
1E-5 to 1E-3
Reported as maximum
potential methylation rate
Gilmour and Henry (1991)
8E-4to2.5E-2
Above intact sediment
cores
Stordal and Gill (1995)
8E-5 to 2E-5
Upper 4 cm of Little Rock
Lake sediments
Calculated in U.S. EPA (1997a) from
methylation rates in units of ug/m2/day
(Gilmour and Riedel 1995) and assumed
dry density of 1.2 g/cm3
1E-4
Value in current
TRIM.FaTE library
U.S. EPA(1997a)
Equations To Calculate Input Values
Comment
Reference(s)
Sed
MS
v f v fHS\^> v f "£(•<•) v
A L-TOC A J ma A J dissolved A
((9, - 9b}x 0.5)x Cspwsu * (Cspwsu + Ksu)
where:
Q,,
T
Tb
'dissolved
methylation rate constant in the sediment, based on TOC (m3/g[TOC]-
day);
term to adjust methylation rate for temperature (implied value in R-
MCM documentation is 2, so that methylation rate doubles for every 10
degree increase in temperature above the base temperature);
sediment temperature (degrees Celsius);
base temperature at which methylation rate constant KMS applies
(degrees Celsius);
TOC concentration in water column (g[organic carbon]/m3);
fraction of the dissolved Hg(2) in the sediment pore water available for
methylation (unitless);
fraction of the Hg(2) in the sediment that is dissolved (unitless);
volume fraction water of the sediment at the sediment/water interface
(unitless);
volume fraction water of the bottom of the sediment (unitless);
concentration of sulfate in the sediment pore water (|Jeq/L); and
half-saturation constant for the effect of sulfate on methylation (|jeq/L).
Hudson etal. (1994), p.5-22
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APPENDIX A
DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
Table A-9
Methylation (kM) in Soil: Inputs
Input Values (1/day)
2E-4
1E-3
7E-5 to 9.7E-4
9.2 E-3
1E-3
Comment
minimum value for average maximum potential
methylation rate constant under aerobic conditions
for 120-day experiment
maximum value for average maximum potential
methylation rate constant under anaerobic
conditions for 120-day experiment
Range for median aerobic reaction rate (from peat,
humus layer, and soil samples, respectively)
Anaerobic median rate of four inundated soil
samples (range = 4.2E-3 to 1 .2E-2/day)
Value in current TRIM.FaTE library
Reference(s)
Porvari and Verta
(1995)
Porvari and Verta
(1995)
Verta et al (1994)
Verta et al. (1994)
Porvari and Verta
(1995)
Table A-10
Issues Related to Demethylation in Soil, Surface Water, and Sediment
Soil
May increase with increasing
anaerobic conditions
Surface Water
Negatively correlated with light
Sediment
May depend on bacteria
processes
Has been reported as
maximal at the
sediment/water interface
(Gilmouretal. 1992)
Table A-ll
Demethylation (kDm) in Surface Water: Inputs
Input Values (1/day)
Value
1E-3to2.5E-2
in current TRIM.FaTE library = 0.013
Equations Used to Calculate Input Values
ksw - (k
KDm ~ \K
where:
kaa
<-ext =
ds/Lext-)x(\-e-L^}/dsw
demethylation rate constant at the lake
surface (/day)
light extinction coefficient for use in
demethylation calculations (/m)
mean depth of water column (m)
Comment
Maximum potential
demethylation rate
constants
Comment
Reference(s)
Gilmour and Henry
(1991)
Reference(s)
Hudson et al.
(1994)
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APPENDIX A
DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
Table A-12
Demethylation (kDm) in Sediment: Inputs
Input Values (1/day)
Comment
Reference(s)
2E-4to1E-1
Value in current TRIM.FaTE library = 0.0501
Reported maximum
potential
demethylation rate
constants
Gilmour and Henry
(1991)
Equations to Calculate Input Values
Comment
Reference(s)
kSed - k
KDm ~ KL
where
DmS
fMHg
6
0
/"" A4Hg . .
d' Id
demethylation rate in the sediment, based
on TOC (m2/g[TOC]-day)
TOC concentration in sediment (g[organic
carbon]/m2)
fraction of the methylmercury in the
sediment that is dissolved (unitless)
porosity of the sediment at the
sediment/water interface (unitless)
porosity of the bottom of the sediment
(unitless) _
Hudson et al.
(1994)
Table A-13
Demethylation (kDm) in Soil: Inputs
Input Values (1/day)
3E-2
6E-2
3.6E-2, 7.6E-2, 1.1 E-1
8.9E-2
6E-2
Comment
Average of maximum potential demethylation rate
constants in aerobic conditions
Average of maximum potential demethylation rate
constants in anaerobic conditions
Median aerobic rates for 15 inundated soil samples,
15 humus layer samples, and five peat samples,
respectively.
Median anaerobic rate for 15 inundated soil samples.
Value in current TRIM.FaTE library
Reference(s)
Porvari and Verta
(1995)
Porvari and Verta
(1995)
Verta et al. (1994)
Verta et al. (1994)
Porvari and Verta
(1995)
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APPENDIX A
DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
A.2.2 BIOTIC MERCURY TRANSFORMATION RATE CONSTANTS
A.2.2.1 Plants
Fortmann et al. (1978) observed that some plants can change the mercury species
accumulated from the environment. However, few studies are available from which to determine
transformation rates.
Hg(0) ^Hg(2)
The oxidation of elemental mercury to divalent mercury (transformation listed above)
occurs in leaves; elemental mercury is probably not taken up by the root. This oxidation rate is
apparently very rapid and may be assumed to be instantaneous (U.S. EPA 1997a). No instances
have been found where elemental mercury was measured in plants (e.g.., Cappon 1987). Thus,
elemental mercury in air or on the surface of the leaf can be directly transferred to divalent
mercury in the leaf.
Hg(2)->CH3Hg
It is assumed that the methlyation of Hg(2) to methylmercury (CH3Hg) does not occur in
plants. Although the in vivo transformation of inorganic mercury to methylmercury was
observed in Pisum sativum (peas) in one study (Gay 1975), the chemical was ephemeral and
quickly (several hours) decayed to low parts per billion levels. Methylmercury residues were not
detected in mature crops following the addition of mercuric chloride to soil (Bache et al. 1973).
Indeed, most mercury in plants is usually in inorganic form (Lindberg 1998).
CH3Hg->Hg(2)
It is assumed that demethylation of methylmercury to Hg(2) (above) occurs in leaves and
stems, but not in roots (because transformations interfere with the equilibrium assumption in
roots). We assume that methylmercury is transformed to Hg(2) according to first-order kinetics,
where the first-order rate constant is 0.03 /day, based on the following information.
Only one study is available in which methylmercury was added to soil and the forms of
mercury (methyl and total) were measured after a defined period of exposure (Bache et al. 1973).
In the few other studies of speciation of mercury within plants, either it is not known which
species were present in soil (e.g., Heller and Weber 1998), or multiple Hg species were present
in soil and it is not known which were initially taken up by the plant (Cappon 1987).
Using data from Bache et al. (1973) (see Table A-14 below), we assume that the
methylmercury is readily taken up through the roots or foliage, that equilibrium between soil and
plant is achieved quickly, that methylmercury is not appreciably transformed in soil during a
crop season, that all methylmercury is only transformed to ionic mercury, and that crops were
harvested after 40 days. Under these assumptions, lst-order rate constants for the transformation
of methylmercury to Hg(2) vary by almost two orders of magnitude in a single study. No
mechanistic explanation is available for
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APPENDIX A
DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
Table A-14
Concentrations of Methylmercury in Foliage and Stems of Crops from Bache et al. (1973)
and Associated First-order Rate Constants, Using Assumptions in Text
Plant Species
Bush bean
(Phaseolus
vulgaris)
Bush bean
(Phaseolus
vulgaris)
Carrot (Daucus
carota)
Potato (solanum
tuberosum)
Potato (solanum
tuberosum)
Tomato
(Lycopersicon
esculantum)
Soil
gravelly
loam
gravelly
loam
gravelly
loam
silt loam
silt loam
gravelly
loam
Application
to Soil
(mg/kg)
1
10
10
1
10
10
Total Mercury
in Foliage and
Stem
52
90
214
86
58
341
Methylmercury
in Foliage and
Stem
46
28
1
27
17
3
1st Order Rate
Constant (d 1)
0.003
0.03
0.1
0.03
0.03
0.1
this high degree of variability. The default value of 0.03 /day in the TREVI.FaTE library for
demethylation of methylmercury to Hg(2) in plants is one of the mid values in the range.
A.2.2.2 Soil Detritivores
No information is available for transformations of mercury in soil detritivores. In
addition, transformation algorithms cannot be implemented if the mercury in these organisms is
in equilibrium with mercury in root-zone soil.
A.2.2.3 Terrestrial and Semi-aquatic Wildlife
Little quantitative information is available on the transformation of mercury in mammals
and birds. Where information is available, calculations of rate constants assume first-order
transformations and are calculated on the basis of the total mercury ingested by the organism but
not necessarily absorbed. (The exception is the inhalation pathway, where rate constants are
derived based on the absorbed fraction.)
Hg(0)
No information is available from which to derive transformation rate constants for the
oxidation of elemental mercury to the mercuric ion. Based on the following information, we
assume that the rate is rapid, and 1.0 /day is a rough estimate of the first-order rate constant.
Elemental mercury is readily oxidized to the inorganic divalent species in most tissues via the
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APPENDIX A
DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
hydrogen peroxidase-catalase pathway. This oxidation primarily occurs in the red blood cells,
and hydrogen peroxide is probably the rate-limiting reactant (ATSDR 1997, U.S. EPA 1997b).
Hg(2)-HIg(0)
Mercuric salts primarily remain in their divalent form. However, a small fraction of the
inorganic divalent cation can be reduced to elemental mercury and exhaled as a vapor (ATSDR
1997). Given the lack of information on the rate of this transformation, the transformation is
assumed not to occur.
Organic mercury ->Hg(2)
Forms of organic mercury are the most studied species of mercury. The short-chain alkyl
mercury compounds (e.g. methylmercury) are relatively stable and are more slowly metabolized
to the inorganic form than the longer-chain compounds (U.S. EPA 1997b) The longer-chain
compounds may be more readily metabolized to the mercuric ion (U.S. EPA 1997b). Takeda
and Ukita (1970) dosed Donryu rats with 20 [ig Hg/kg body weight as ethyl-mercuric chloride
via intravenous injection. After 8 days, 58.1 percent of the mercury excreted in the urine was
inorganic mercury and 35 percent of the mercury excreted in feces was inorganic (Table A-15).
If it is assumed that (1) the excreted chemicals reflect the transformation rate in the animal
(transformation occurred immediately prior to excretion) and (2) the first-order transformation
rate reflects a weighted average of the amount of dose excreted in urine (10.52 percent) and that
excreted in feces (6.01 percent), then the transformation rate may be estimated to be 0.09 /day.
Table A-15
Transformation Rate (/day) of Organic Mercury to the Inorganic Divalent Form
in Mammals (Takeda and Ukita 1970)
Elimination Type
urine
feces
assumed transformation
for whole animal
Dose Route
injection
injection
% Organic
after 8 days
41.9
65.0
% Inorganic
after 8 days
58.1
35.0
Transform
Rate
Constant
0.1084
0.0539
0.09
Hg(2) ->• organic mercury
No information is available on this transformation. Therefore it is assumed to be zero.
A.2.2.4 Aquatic Species
Transformations of mercury in algae, macrophytes, and benthic organisms are assumed
not to occur with one exception. It is assumed that elemental is transformed to divalent mercury
in macrophytes, and the transformation is described as a rapid (almost instantaneous) first-order
rate constant (i.e., 106 to 109). Thus, it is assumed that elemental mercury can be taken up by
SEPTEMBER 2002
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APPENDIX A
DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
macrophytes but is not accumulated in macrophytes (i.e., data showing Hg(0)) in macrophytes
were not found). Data demonstrating methylation of divalent mercury or demethylation of
methylmercury in macrophytes also were not found.
Very little is known about the rate at which transformation of mercury species occurs in
aquatic organisms. A large body of field data suggests that most (> 90 percent) of mercury in
fish is in the form of methylmercury and other organic species (represented here simply as
CH3Hg); however, methylation of inorganic mercury has not been demonstrated in fish. For this
reason, it is assumed that methylation of divalent mercury does not to occur in fish.
Hg(0)
Oxidation of elemental mercury is assumed to occur instantaneously in fish.
Hg(0) ~>CH3Hg
Methylation of inorganic mercury is assumed not to occur directly in fish.
Hg(2)->Hg(0)
Reduction of divalent mercury is assumed not to occur in fish.
CH3Hg^Hg(2)
Demethylation is assumed not to occur in fish.
CH3Hg^Hg(0)
Mer cleavage demethylation is assumed not to occur in fish.
A.4 REFERENCES
Alberts, J.J., I.E. Schindler, and R.W. Miller. 1974. Elemental mercury evolution mediated by
humicacid. Science. 184: 895-897.
Amyot, M., G. Mierle, D. Lean, and DJ. McQueen. 1997. Effect of solar radiation on the
formation of dissolved gaseous mercury in temperate lakes. Geochemica et
Cosmochimica Acta. 61(5):975987.
ATSDR. 1997. Agency for Toxic Substances and Disease Registry. Toxicological Profile for
Mercury. Draft for public comment (Update). ATSDR-7P-97-7 (Draft). U.S.
Department of Health and Human Services.
SEPTEMBER 2002 A-19 TRIM.FATE TSD VOLUME II
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APPENDIX A
DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
Bache, C.A., WJ. Gutenmann, L.E. St. John, Jr., R.D. Sweet, H.H. Hatfield, and D.J. Lisk.
1973. Mercury and methylmercury content of agricultural crops grown on soils treated
with various mercury compounds. J. Agr. Food Chem. 21:607-613.
Bodek, I, W.J. Lyman, W.F. Reehl, et al. 1988. Environmental Inorganic Chemistry:
Properties, Processes, and Estimation Methods. Elmsford, NY: Pergammon Press.
Cappon, C.J. 1987. Uptake and speciation of mercury and selenium in vegetable crops grown
on compost-treated soil. Water, Air, Soil Pollut. 34:353-361.
Carpi, A.., and S.E. Lindberg. 1997. Sunlight mediated emission of elemental mercury from
soil amended with municipal sewage sludge. Environmental Science and Technology.
31(7):2085-2091.
Fortmann, L.C., D.D. Gay, and K.O. Wirtz. 1978. Ethylmercury: Formation in Plant Tissues
and Relation to Methylmercury Formation. EPA600/378 037. U.S. EPA Ecological
Research Series.
Gay, D.D. 1975. Biotransformation and chemical form of mercury in plants. International
Conference on Heavy Metals in the Environment. Symposium Proceedings, pp. 87-95.
Vol. II, Parti. October 1975.
Gilmour, C.C. and G.S. Riedel. 1995. Measurement of Hg methylation in sediments using high
specific activity 203Hg and ambient incubation. Water, Air, and Soil Pollution. 80:747-
756.
Gilmour, C.C, E.A. Henry, and R. Mitchell. 1992. Sulfate stimulation of mercury methylation
in freshwater sediments. Environmental Science and Technology. 26(ll):2281-2287.
Gilmour, C.C. and E.A. Henry. 1991. Mercury methylation in aquatic systems affected by acid
deposition. Environmental Pollution. 71:131-169.
Heller, A.A., and J.H. Weber. 1998. Seasonal study of speciation of mercury(II) and
monomethylmercury in Spartina alternaflora from the Great Bay Estuary, NH. Science
of the Total Environment. 221:181-188.
Henry, E.A., L.J. DodgeMurphy, G.N. Bigham, S.M. Klein, and C.C. Gilmour. 1995a. Total
mercury and methylmercury mass balance in an alkaline, hypereutrophic urban lake
(Onondaga Lake, NY). Water, Air, and Soil Pollution. 80:509-518.
Henry, E.A., L.J. DodgeMurphy, G.N. Bigham, and S.M. Klein. 1995b. Modeling the transport
and fate of mercury in an urban lake (Onondaga Lake, NY). Water, Air, and Soil
Pollution. 80:489-498.
Hudson, R., S.A. Gherini, C.J. Watras, and D. Porcella. 1994. Modeling the biogeochemical
cycle of mercury in lakes: the Mercury Cycling Model (MCM) and its Application to the
SEPTEMBER 2002 A-20 TRIM.FATE TSD VOLUME II
-------
APPENDIX A
DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
MIL Study Lakes. In: C.J. Watras and J.W. Huckabee, eds. Mercury Pollution
Integration and Synthesis. Lewis Publishers; pp. 473-523.
Jacobs, L.A., S.M. Klein, and E.A. Henry. 1995. Mercury cycling in the water column of a
seasonally anoxic urban lake (Onondaga Lake, NY). Water, Air, and Soil Pollution.
80:553-562.
Lindberg, S.E. 1998. Personal communication. Oak Ridge National Laboratory. December.
Lindberg, S.E., T.P. Meyers, G.E. Taylor, Jr., R.R. Turner, and W.H. Schroeder. 1992.
Atmosphere-surface exchange of mercury in a forest: Results of modeling and gradient
approaches. Journal of Geophysical Research. 97:2519-2528.
Lindqvist, O., K. Johansson, M. Aastrup, A. Andersson, L. Bringmark, G. Hovsenius, L.
Hakanson, A. Iverfeldt, M. Meili and B. Timm. 1991. Mercury in the Swedish
environment - recent research on causes, consequences and corrective methods. Water
Air and Soil Pollution. 55(1-2):R11.
Mason, R.P., J.R. Reinfelder and F.M.M. Morel. 1996. Uptake, toxicity, and trophic transfer of
mercury in a coastal diatom.. Environmental Science & Technology. 30(6): 1835-1845.
Mason, R.P., J.R. Reinfelder and F.M.M. Morel. 1995. Bioaccumulation of mercury and
methylmercury. Water Air and Soil Pollution. 80(1-4):915-921.
Mason, R.P., W.F. Fitzgerald, and F.M.M. Morel. 1994. The biogeochemical cycling of
elemental mercury: Anthropogenic influences. Geochemica et Cosmochimica Acta.
58(15):3191-3198.
Matilainen, T. 1995. Involvement of bacteria in methymercury formation in anaerobic lake
waters. Water, Air, and Soil Pollution. 80:757-764.
Nagase, H, Y Ose, T Sato, et al. 1984. Mercury Methylation by Compounds in Humic Material.
The Science of the Total Environment. 32: 147-156.
Porvari, P. and M. Verta. 1995. Methylmercury production in flooded soils: a laboratory study.
Water, Air, and Soil Pollution. 80:765-773.
Riederer, M. 1995. Partitioning and transport of organic chemicals between the atmospheric
environment and leaves. In: Trapp, S. and J. C. McFarlane, eds. Plant Contamination:
Modeling and Simulation of Organic Chemical Processes. Boca Raton, FL: Lewis
Publishers; pp. 153-190.
Stordal, M.C. and G.A. Gill. 1985. Determination of mercury methylation rates using a 203Hg
radiotracer technique. Water, Air, and Soil Pollution. 80:529-538.
Takeda, Y. and T. Ukita. 1970. Metabolism of ethylmercuric chloride-203Hg in rats. Toxicol.
Applied Pharm. 17:181-188.
SEPTEMBER 2002 A~3lTRIM.FATE TSD VOLUME II
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APPENDIX A
DERIVATION OF MERCURY-SPECIFIC ALGORITHMS
Trudel, M., and J.B. Rasmussen. 1997. Modeling the elimination of mercury by fish.
Environmental Science and Technology. 31:1716-1722.
U.S. EPA (Environmental Protection Agency). 1997a. Mercury Study Report to Congress.
Volume III: Fate and Transport of Mercury in the Environment. EPA-452/R-97-005.
U.S. EPA Office of Air Quality Planning and Standards, and Office of Research and
Development.
U.S. EPA (Environmental Protection Agency). 1997b. Mercury Study Report to Congress.
Volume V: Health effects of mercury and mercury compounds. EPA-452/R-97-007.
U.S. EPA Office of Air Quality Planning and Standards, and Office of Research and
Development.
Vandal, G.M., W.F. Fitzgerald, K.R. Rolfhus, and C.H.Lamborg. 1995. Modeling the elemental
mercury cycle in Pallette Lake, Wisconsin, USA. Water, Air, and Soil Pollution.
80:789-798.
Verta, M, T Matilainen, P Porvari, et al. 1994. Methylmercury sources in boreal lake ecosystem.
In: CJ. Watras and J.W. Huckabee, eds. Mercury Pollution Integration and Synthesis.
Lewis Publishers Inc., MI; pp. 119-136.
Watras, CJ. andN.S. Bloom. 1992. Mercury and methylmercury in individual zooplankton -
Implications for bioaccumulation. Limnology and Oceanography. 37(6): 1313-1318.
Xiao, Z.F., D. Stromberg, and O. Lindqvist. 1995. Influence of humic substances on photolysis
of divalent mercury in aqueous solution. Water, Air, and Soil Pollution. 80:789-798.
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APPENDIX B
DERIVATION OF PAH-SPECIFIC ALGORITHMS
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APPENDIX B
DERIVATION OF PAH-SPECIFIC ALGORITHMS
APPENDIX B
DERIVATION OF PAH-SPECIFIC ALGORITHMS
This appendix contains includes derivations of algorithms and parts of algorithms
specific to polyaromatic hydrocarbons (PAHs). Section B.I covers exchanges of PAHs between
benthic invertebrates and sediments. Section B.2 includes provides a note about
bioaccumulation in fish which can metabolize PAHs. Section B.3 provides a note about dry
deposition of PAHs sorbed to airborne particles to plant leaves. The references are provided in
SectionB. 4.
B.I EXCHANGES BETWEEN SEDIMENT AND BENTHIC
INVERTEBRATES
Uptake of contaminants from water by benthic invertebrates (e.g., mayfly nymphs,
amphipods) is primarily based on respiratory processes. Stehly et al. (1990) found that the
clearance rate of benzo-a-pyrene (B(a)P) and phenanthrene from water by the mayfly (i.e.,
mayfly net uptake of the chemical from water) is analogous to the clearance rate (i.e., net uptake
rate) of oxygen during mayfly respiration. The uptake of these two PAHs can, therefore, be
estimated similarly to the ratio of oxygen clearance to the volume of water passing over
respiratory surfaces. With a known or assumed volume of water passing over respiratory
membranes with known concentrations of B(a)P and phenanthrene, the extraction efficiency of
these PAHs can be calculated. The following concentration algorithms and mass derivatives
were adopted from the model of Stehly et al. (1990) for estimating PAH uptake and loss for
benthic invertebrates. The equations are based on the clearance rate driven by the volume of
water cleared and the bioconcentration factor (BCF). Uptake rates, as measured by a clearance
constant (CLu), as well as the BCF for 30-, 60-, and 120-day-old mayflies for B(a)P and
phenanthrene were provided by Stehly et al. (1990).
(EqB-l)
at pc
where:
CMaxfiy = concentration of chemical compound in the organism expressed on a wet
weight basis (ng[chemical]/g[mayfly wet wt] = mg[chemical]/kg[mayfly
wet wt]);
CLU = clearance constant (equivalent to ku) (mL[water cleared]/g[mayfly wet wt]-
hour = L[water cleared]/kg[mayfly wet wt]-(day/24);
Cw = concentration of the chemical in the interstitial water
(ng[chemical]/mL[water] = mg[chemical]/L[water]); and
pc = proportionality constant that relates the concentration of chemical in the
organism to the concentration in the exposure water (equivalent to the
bioconcentration factor (BCF)) (mg[chemical]/kg[mayfly wet wt] per
mg[chemical]/L[water] = L[water]/kg[mayfly wet wt]).
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APPENDIX B
DERIVATION OF PAH-SPECIFIC ALGORITHMS
We substitute generic benthic invertebrates (BI) for the mayflies in Stehly et al. (1990). Thus, an
estimation of the PAH concentrations in benthic invertebrate populations (i.e.., compartments) is
as follows:
Nw 24
vw x looo,
- CL. x
N
BI
PC
x24
(Eq. B-2)
where:
"BI
n
'BI
m
m
Vw
1/1000
24
Note that:
where:
SedW
6
Also note that:
where:
mass of chemical in benthic invertebrates (g[chemical]);
number of benthic invertebrates (unitless);
mass of individual benthic invertebrate organisms (g[BI wet
wt]/individual);
mass of chemical dissolved in interstitial pore water (g[chemical]);
volume of the interstitial pore water (L[water]);
units conversion factor (kg/g); and
units converstion factor (hr/day).
SedW
Sed'
6
(Eq. B-3)
volume of the pore water in the sediment compartment (m3);
volume of the sediment compartment (m3);
volume fraction of the sediment compartment that is liquid (i.e., water)
(unitless).
Fraction Mass Dissolved = Nw x N-,
Total
(Eq. B-4)
Fraction Mass Dissolved = the fraction of the chemical mass in the sediment
compartment that is dissolved in the interstitial water
(unitless);
Nw = chemical inventory dissolved in the interstitial water (g[chemical]); and
= total chemical inventory in the sediment compartment, both dissolved and
associated with sediment particles (g[chemical]).
' Total
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APPENDIX B
DERIVATION OF PAH-SPECIFIC ALGORITHMS
As described in Chapter 2, Equation 2-81:
Fraction Mass Dissolved
. B-5)
Note that for sediments:
0 = 1 - Volume _ Fraction _ Solid (Eq. B-6)
where:
Volume Fraction Solid = fraction of sediment compartment that consists of solid
sediment particles (unitless),
because the fraction of the sediment compartment that is vapor/gas-phase is assumed to be zero.
From those equations, transfer factors can be derived as:
U
TSedw^BI = nBI x mBI x - - x — — x 24 x fML (TF B- 1)
V SedW 1UUU
TBI^Sedw = — -X24 (TFB-2)
PC
where:
TSedw^BI= transfer factor for PAHs from sediment pore water to benthic invertebrates
(/day); and
TBi^sedw= transfer factor for PAHs from benthic invertebrates to sediment pore water
(/day).
B.2 BIO ACCUMULATION BY FISH
It is possible to use the time-to-equilibrium-based model (Section 6.4.2) for estimating
bioaccumulation of nonionic organic chemicals in fish. As described in Section 2.5, some
algorithms that represent steady-state equilibrium relationships can be turned into time-
dependent ones for use in TRIM.FaTE if an estimate of the time required for the concentration to
reach some fraction of the equilibrium value is known. In this case, the concentration of a
nonionic organic chemical in a fish compartment at one trophic level (e.g., water-column
carnivore, Fwcc) can be related to the concentration of the chemical in the next lower trophic level
(e.g., water-column omnivore Fwco) by the equilibrium relationship of the form CFwcc = K x CFwco.
The value of K, also known in this context as the bioacumulation factor (BAF), and the time ta
required to reach lOO^r percent of the equilibrium must be known or estimated (default a = 0.95).
SEPTEMBER 2002 B-3 TRIM.FATE TSD VOLUME II
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APPENDIX B
DERIVATION OF PAH-SPECIFIC ALGORITHMS
For PAHs, which are readily metabolized by fish, it is appropriate to use a measured wet-
weight BAF for the PAH chemicals and a measured time to reach lOOx a percent of the
equilibrium ratio of concentrations in the transfer factor equations TF 6-9 and 6-10. BAF values
for PAHs can be estimated from Kow values only if the empirical model used (i.e., regression
equation) for relating BAF to Kow values was derived for fish from a series of PAHs.
B.3 REFERENCE
Stehly, G. R., Landrum, P. F., Henry, M. G. & Klemm, C. (1990). Toxicokinetics of PAHs in
Hexagenia. Environmental Toxicology and Chemistry, 9, 167-174.
SEPTEMBER 2002 B-4 TRIM.FATE TSD VOLUME II
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APPENDIX C
STEADY-STATE MODE
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APPENDIX C
STEADY-STATE MODE
APPENDIX C
STEADY-STATE MODE
TRIM.FaTE can be run in two modes: dynamic or steady-state. This appendix describes
implementation of the TRIM.FaTE steady-state mode (Section C.I) and potential user
applications of that feature (Section C.2). The advantage of the steady-state mode is that the run
time is very short compared with typical dynamic runs that use hourly-to-daily simulation time
steps over the course of many years (e.g., 30-year). The short run-time allows the user to
quickly test new approaches and to conduct sensitivity or Monte Carlo analyses that would be
require much greater run times if the dynamic mode were used.
C.I STEADY-STATE SOLUTION FEATURE
The description of TRIM.FaTE in Chapters 1 through 8 apply to both dynamic and
steady-state modes except where noted below. The remainder of this section describes important
differences between the steady-state and dynamic modes.
Section C. 1.1 describes how to develop constant values for time-varying model inputs.
Section C. 1.2 describes changing the air transfer factors in the dynamic mode to implement the
steady-state mode. Section C. 1.3 notes changes that are needed with respect to the ground-water
transfer factors. Finally, Section C.I.4 describes other differences in the TRIM.FaTE code setup
for the steady-state versus dynamic modes.
C.1.1 CHANGING TIME-VARYING INPUT DATA TO CONSTANTS
Generating steady-state results with the model requires representative steady-state values
for the time-varying inputs in the current version of the TRIM.FaTE library. The primary time-
varying inputs include:
wind speed;
• wind direction;
• mixing height;
rain;
• IsDay (0 at night; = 1 during the day);
• AllowExchange (0 during non-growing season; = 1 during growing season);
• litter fall (e.g., deciduous forest and grasses/herbs); and
• river flow.
Many of these time-varying inputs combine and interact to influence specific transfer
factors within TRIM.FaTE, and the different time-varying inputs interact/combine in different
ways when used in different algorithms. For example, wind speed and direction influence the
relative magnitude of the advective air transfers along the interfaces between air compartments.
Other transfer factors are influenced in a discontinuous fashion, as for example the transfer
factors that include the variable Iwep the proportion of the wet deposition of chemical sorbed to
dust particles (or in vapor phase) that is intercepted and retained on the plants. The variable Iwet
is a function of the leaf area index (LAI), mixing height, rain, and AllowExchange. When
SEPTEMBER 2002 CM TRIM.FATE TSD VOLUME II
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APPENDIX C
STEADY-STATE MODE
AllowExchange is zero, the wet interception fraction is zero. Thus, it is not appropriate to simply
assign an average value for each of the time varying inputs and assume that would result in
appropriate values for the calculated transfer factors. In addition to providing representative
values for the time-varying inputs, a number of calculated transfer factors need to be assigned
steady-state values.
The calculated steady-state variables (or distributions) that need to be considered include:
• Advective transfers across each air-to-air interface including external boundaries of the
system (calculated as function of wind speed, wind direction, mixing height, and parcel
coordinates) (Section C. 1.1.1);
Dry interception fraction for vegetation (calculated as function of AllowExchange,
mixing height, and the wet biomass of the vegetation per unit area) (Section C. 1.1.2);
• Wet interception fraction (calculated as function of AllowExchange, rain, mixing height,
and LAI) (Section C. 1.1.3);
Diffusive transfer across air/stomata interface (calculated as function of LAI, IsDay, and
mixing height) and diffusive transfer across air/cuticle interface (calculated as function of
LAI and mixing height) (Section C. 1.1.4);
Litter fall (e.g., deciduous forest and grasses/herbs) and river flow (Section C.I. 1.5); and
• Plant intake rates for wildlife, which are modified by the AllowExchange variable
(Section C.I. 1.6).
Steady-state models have typically used long-term arithmetic mean (AM) values for the
inputs, but we are not aware of any research that has evaluated whether those AM inputs are
more appropriate than other indications of central tendency (e.g., median, geometric mean, etc.)
for estimating steady-state output in a spatially segmented dynamic model. Fortunately, this
problem should not affect a steady-state uncertainty or sensitivity analysis because the user is
generally most interested in the relative propagation of uncertainty/variability through the model
for a given set of inputs. To maintain consistency with the other TRIM.FaTE inputs, we
recommend using the AM input values (and distributions) for the calculated time-varying inputs
and for the transfer factors in the steady-state scenario. For hourly meteorological data, the AM
value for each year of meteorological data can be calculated. The annual average values can
then be used to estimate a long-term average, and an appropriate statistical model can be used to
describe the set of annual average values.
SEPTEMBER 2002 C-2 TRIM.FATE TSD VOLUME II
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APPENDIX C
STEADY-STATE MODE
C.I. 1.1 Advective Air-to-air Transfers
A challenge that arises in calculating steady-state inputs for use in the advective air
transfers is that the time-varying inputs from the meteorological data files per unit time are not
normally distributed. As a result, the long-term average transfer factor estimated at the
simulation time steps from the transfer factors may differ from that estimated from the long-term
average inputs for a given mass-transfer process. We use an example to illustrate this challenge
below.
In its simplest form, the advective transfer factor (/day) across an interface between two
neighboring air parcels is given by:
C-l)
V.
5
where fluxs^r is the flux of air across the interface (m3/d) from sending compartment s, to
receiving compartment r, and Vs is the volume of the sending compartment. Assuming that the
long-term arithmetic mean (AM) transfer factor is a good surrogate for steady state, we can
calculate the AM\TAs^Ar] in two ways. The first way calculates a value of TAs^Ar for each hour of
meteorological data and then estimates the long-term average transfer factor from this set of
hourly values:
As->Ar (Eq. C-l)
n "
where y' represents the hour and n is the total number of hours (i.e., n = 8760 for one year of
meteorological data). The second way calculates the average values offluxs^rand Vs from the set
of hourly values for these variables, then estimates the steady state TAs^Ar as the quotient of the
two average values such that:
However, if the hourly values for flow and/or volume are not normally distributed (which
they are not) then the two approaches give different answers:
~ „„.
(Eq. C-3)
^ 4 ;
r -i
AM[V]
In other words, the arithmetic mean (AM) of the set of hourly transfer factors does not equal the
quotient of the AM \fluxs^r] and the AM [Vs] .
To illustrate the difference, we use the first year's hourly meteorological data prepared
for the mercury test case to calculate advective transfer across one of the segments of the parcel
that included the source facility. The AM[TAs_>Ar] calculated from the 8760 hourly transfer factors
SEPTEMBER 2002 (X3 TRIM.FATE TSD VOLUME II
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APPENDIX C
STEADY- STATE MODE
(excluding the zeros) was 19.9 /hr. The transfer factor calculated from the quotient of average
flow and volume was 12.7 /hr, a difference of about 40 percent.
The steady-state input for transfer across an air-to-air interface is dependent on wind
speed, wind direction, mixing height, and the coordinates of the interface (length and angle). In
addition, the actual transfer also depends on the volume of the sending compartment, which in
turn depends on the atmospheric mixing height. In the mercury test case, we actually calculated
the transfer factor for each interface using both of the methods described earlier (i.e., Equations
C-l andC-2).
For Eq. C-2, the value of TAs_>Ar for the/A hour of the meteorological data is given by:
- (x2 - xjcostfjx y (TF c.
2)
where u is the wind speed (m/day) towards the direction ft across the compartment boundary
during the/A hour, At is the area of the interface given by the time-varying mixing height fy (m),
and length of compartment interface, Lt (m). The volume of the sending compartment, Vsj, is also
a function of the time-varying mixing height. The Li is constant over time and is defined by two
Cartesian coordinates (Pl = (xl5 yx), P2 = (x2, y2)) where the coordinates of each segment of a
polygon are evaluated in clockwise order and the length is:
TF C-2 can be simplified for each hourly time step to give the following transfer-factor
algorithm:
A \\s 2. si/ vz "i/ | ^Ir-Lx-jJ
Evaluating the coordinates in clockwise order around a given polygon results in a
negative value for transfer out of the polygon and a positive value for transfer into the polygon
(wind direction is also reported as degrees clockwise from North). In estimating steady-state
transfer factors, the user is only interested in transfers out of a given polygon across a given
interface. Thus, the positive values can be ignored and the absolute values of transfers out of the
polygon (i.e., from the sending compartment) are used. In the example for the mercury test case,
we calculated values of AM[TAs_>Ar] for each of the five years of meteorological data, which
resulted in a distribution of AM[TAs_>Ar] values for each line segment and direction.
We also calculated the transfer factor for each year by summing the annual volumetric
flux across the interface and using the long-term average mixing height and constant area of the
SEPTEMBER 2002 C-4 TRIM.FATE TSD VOLUME II
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APPENDIX C
STEADY-STATE MODE
Comparison of Calculation Method for Steady State
Advection T-Factors
O)
400
300
IB
= | 200
o re
x LJ_
c
•S 100
o>
re
CD
0
0
100
200
300
400
Based on Total Annual Volumetric Flux Normalized to Average
Sending Cell Volume
Figure C-l. Comparison of long-term average advective transfer factors calculated using the
daily average volumetric flux normalized to sending compartment (cell) volume (x-axis) and
the average of the hourly transfer factors (y-axis).
sending compartment to estimate the transfer factor using Eq. C-2. The difference between the
two methods is illustrated in Figure C-l. The overall difference in the results of the two methods
was not great. (In the mercury test case, we combined the two sets of results to provide a single
estimate of the transfer factor for each interface).
It is important to remember that the steady-state value (or distribution) for a given
transfer factor represents a long-term average transfer, not day-to-day or hour-to-hour variation
in the transfer.
C.I.1.2 Dry Interception Fraction
For deciduous plants and grasses/herbs, the dry interception fraction is a function of
Allow Exchange., mixing height, and biomass (wet wt) of the vegetation per unit area. For
coniferous plants that do not loose their leaves seasonally, the dry interception fraction is
assumed to be a constant value throughout the year.
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APPENDIX C
STEADY-STATE MODE
The dry interception fraction, Idry^ is calculated for deciduous plants and grasses/herbs as
receiving compartments per Eq. 7-2 of TSD Volume II, as modified to accommodate a steady-
state AllowExchange variable:
ldry
= 1 - exp (l - JWLeafj(- (XVAF X AllowExchange X parea]
(Eq. C-5)
where, for both grasses/herbs and deciduous plants,/PFLea/is the water content of the plant (0.8,
unitless), aVAF is the vegetation attenuation factor (-2.9 m2[leaf]/kg[plant dry wt]), and parea is
the areal density of above-ground non-woody vegetation (0.6 kg[plant wet wt]/m2[surface soil]).
AllowExchange is used as a seasonal on/off switch for the interception fraction. When
AllowExchange is one, Idry is calculated by Eq. C-5, but when AllowExchange is zero, Idry is zero.
The volume of the sending air compartment, Vs, is also used to calculate the transfer
factor for dry deposition (see TF 7-1 in TSD Volume II). Due to hourly changes in the mixing
height, the long-term average Vs can differ during times when AllowExchange is on and when it
is off, as illustrated in Figure C-2. Therefore, the steady-state value of Idry needs to be
normalized to a sending compartment volume that is relevant to the time when leaves are
intercepting particles (i.e., when Allow Exchange = 1). The factor used to normalize the steady-
state interception fraction is the long-term (annual) average mixing height divided by the average
mixing height when AllowExchange is equal to 1. In summary, the steady-state Idry value for
each of the five years is given by:
SS.I
dry,]
h(AE=V)
n
(Eq. C-6)
where h (AE=1,0) represents the average over the full year and h (AE=1) represents average
mixing height when AllowExchange is set to 1.
C.I.1.3 Wet Interception Fraction
The wet interception fraction, Iwet, is a function of total rain for each rain event, the
seasonal LAI (calculated from the average leaf area interface and the AllowExchange variable)
and, as with the dry interception fraction, a normalization factor to the appropriate average air
mixing height. Wet interception is calculated by Equation 7-4 of the TSD Volume II as modified
to accommodate the AllowExchange variable and the cumulative rain for a given rainfall event.
We define a rainfall event as the cumulative time over which rain occurs, which is bracketed
(before and after) by at least one hour with no rain. Given this definition of rain, the wet
interception fraction for rain event k is:
AllowExchange x LAI x S
wet.k
ram
1 - expl
- H2)
3xS
•x ram\
(Eq. C-7)
SEPTEMBER 2002
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APPENDIX C
STEADY-STATE MODE
Distribution of Mixing Height
100%
-All Data
- Allow/Exchange & IsDay = 1
-AllowExchange=1
-AllowExchange=0
0 500 1000 1500 2000
Rural Mixing Height (m)
2500
3000
Figure C-2: Distributions of hourly mixing height reported for different conditions where
AllowExchange controls seasonality and IsDay is used in the model to modify stomata
diffusion.
where k indicates the k"1 rain event, S is the leaf wetting factor (0.0003 m) and LAI is the leaf
area index (grasses/herbs = 5, deciduous forest = 3.4 and coniferous forest = 5). The Iwet for the
k"1 event is multiplied by the cumulative amount of rain for that event to give the volume of
intercepted rain. The event-specific volume of intercepted rain is summed over the year to give
the total volume of "intercepted" rain. The long-term interception fraction is then estimated as
the intercepted volume for the given year divided by the cumulative rain for that year.
As with Idry, the final steady-state value for wet interception (for each year) is normalized
to account for differences between the overall average mixing height of the sending compartment
and the average mixing height when it is both raining and the AllowExchange variable is 1 such
that:
h(AE=l,0)
' wet h(AE= \&rain> 0)
n
(Eq. C-8)
J=1
where AE=l&rain>0 indicates that both the AllowExchange variable = 1 and it is raining.
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APPENDIX C
STEADY-STATE MODE
C.I.1.4 Diffusive Transfer Across Air/Stomata Interface and Across Air/Cuticle
Interface
This diffusive transfer combines two process where the stomata transfer is controlled by
the LAI (AllowExchange)., IsDay, and the relative mixing height during exchange (i.e., when LAI
and IsDay are both 1) and where the cuticle transfer is influenced only by LAI (AllowExchange)
and relative mixing height. The two parts of the equation need to be treated separately so that
each mass transfer process can be independently modified by either the AllowExchange variable
(cuticle) or the combined Allow Exchange.IsDay variable (stomata).
The first AllowExchange variable, the one that modifies cuticle exchange, is the same
height-normalized value that is used for Idry. In this case, we derive a single steady-state value
for AllowExchange that modifies bothldry and the cuticle side of the air-to-plant diffusion
equation.
The steady-state modification factor for the stomata diffusion is calculated as the long-
term average of the product of IsDay, input as a fraction representing the average number of
daylight hours per 24-hr period, and AllowExchange, adjusted for height of the sending
compartment, using the following normalization factor:
h(AE= 1,0)
NormalizationFactor = — (Eq. C-9)
h(AE = \&ID= 1)
where AE=1&ID=1 indicates that both AllowExchange and IsDay are equal to one.
These two steady-state modification factors are incorporated into the equation for total
diffusive transfer across the air/plant interface so that both the stomata pathway and the cuticle
pathway are transformed to steady state.
C.l.1.5 Litter Fall and River Flow
In the current TRIM.FaTE library, the litter-fall rate constant, kL, for deciduous forests
and for grasses/herbs is set such that 99 percent of the mass is transferred to soil in
approximately one month.1 To run TRIM.FaTE in the steady-state mode, this litter-fall rate is
transformed such that 99 percent of the mass is transferred to soil on an annual basis (365 days):
0.01 = QXp(-kL X 365) (Eq. C-10)
Solving Equation C-10 for kL gives a steady-state litter-fall rate constant of 0.013 /day. The litter-
fall rate for coniferous plants does not change from the rate used for TRIM.FaTE in the dynamic
mode. The user can set a date for harvest of agricultural plants or allow them to become litter.
In the current TRIM.FaTE library, the litter-fall rate constant for coniferous forest is set to a value that is
constant throughout the year. For the agricultural plants, the user can set the date of harvest, and the chemical mass
in the harvested biomass can be transferred to a sink.
SEPTEMBER 2002 C^8 TRIM.FATE TSD VOLUME II
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APPENDIX C
STEADY-STATE MODE
The steady-state flow of a river is simply the time-weighted average flow (or velocity).
C.l.1.6 Wildlife Plant Ingestion Rates
The wildlife plant ingestion rates (i.e., total ingestion rate * fraction of diet that consists
of plants on a wet weight basis) are multiplied by AllowExchange to ensure that wildlife only
consume plant leaves during the growing season. For a steady-state run, AllowExchange is set to
a fractional value equal to the number of days it is equal to 1 divided by 365 days per year to get
an annual average.
C.1.2 SWITCHING ADVECTIVE AIR TRANSPORT ALGORITHMS
Switching from the dynamic to the steady-state advective air transport algorithms
involves three steps:
(1) Enabling the steady-state algorithms;
(2) Disabling the dynamic algorithms; and
(3) Setting up the steady-state advective transfer factors.
The steady-state air advective transfer factors are used to calculate air advection (see
Section C. 1.1.1). Two transfer factors (two directions) are calculated for each interface between
one air volume element and an adjacent air volume element. In addition, the user should
calculate transfer factors across each interface from air volume elements bounding the exterior of
the modeling domain to the air sinks (i.e., moving chemical mass from the boundary air volume
elements into the air sinks). These transfer factors can be calculated by hand (in a spreadsheet)
using the meteorological data set and information about the spatial relationships of the air
volume elements. The number of years of meteorological data to average for each interface
depends on the number of years associated with any apparent cycle or pattern of meteorologic
conditions that is repeated at intervals (e.g., five years in the mercury test case). The steady-state
air advective transfer factors are simply set equal to the calculated value for a particular link.
The use of the steady-state air advection transfer factors for each air/air compartment
interface results in a more accurate representation of the average advective flows between air
compartments than simply using average values for all of the meteorological properties and
allowing the model to use those values in the existing dynamic air advection transfer algorithms.
The use of steady-state air advection transfer factors (see Section C. 1.1) retains information on
correlations among the meteorological properties (e.g., a certain wind direction may be
associated with higher wind speeds) that would be lost in an overall averaging process.
At the moment, the steady-state air advection transfer factors for each air/air
compartment interface must be calculated outside of TRIM.FaTE (e.g., using spreadsheets). We
expect that future versions of TRIM.FaTE will include the ability to calculate these transfer
factors internally, thus reducing the time required of the user to set up a steady-state simulation.
SEPTEMBER 2002 C-9 TRIM.FATE TSD VOLUME II
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APPENDIX C
STEADY-STATE MODE
C.1.3 DISABLING LINKS WITH GROUND WATER
A limitation of applying the steady-state mode is the inability to accommodate ground
water. Thus, the final step in setting up a steady-state simulation is disabling all of the links
from groundwater to other compartments (i.e., vadose-zone soil and surface water). This step is
required because the groundwater compartments lose mass so slowly that the steady-state solver
cannot find a solution. After disabling the dynamic-mode links to and from groundwater, the
ground-water compartment basically acts as a sink for chemical mass. Then, the steady-state
solver is able to calculate a solution.
C.2 APPLICATIONS OF THE STEADY-STATE MODE
The speed of the steady-state solution makes it attractive for several types of applications
(e.g.., diagnostic and uncertainty analyses).
As a diagnostic tool, the steady-state mode, with its short run time, can be used in
evaluating the impact of changes to the set-up of a simulation, as well as parameter values and
algorithms. The ability to perform a large number of realizations in reasonable run time (as
provided in the steady-state mode) gives the user the opportunity to investigate model behavior.
If the results from TRIM.FaTE appear inconsistent with expectations or with existing data, the
user can quickly test different hypotheses about how those results were produced. During this
exercise, the user can modify certain input parameters or assess different formulas for transfer
factor algorithms (or for various compartment properties) and quickly assess the response of the
model results to those changes.
In uncertainty and sensitivity analyses, the steady-state mode is also a valuable tool. For
large and/or complex parcel layouts, sensitivity analyses of the many property values in a
simulation when run in dynamic mode (e.g., involving simulations of many years) can involve
substantial run times. Similarly, dynamic simulations involving Monte Carlo assignment of key
property values can also be time consuming. The steady-state mode can be used to provide a
Monte Carlo sampling-based sensitivity analysis of many properties in a reasonable run time.
This enables examination of the sensitivity of the model results to a much larger number of
variables than would be possible using the sensitivity analysis feature in the dynamic mode in
the same amount of run time.
Information from sensitivity/Monte Carlo analyses conducted using the steady-state
mode can then be used to select a small number of input parameters for which the user can run a
dynamic-mode uncertainty analysis. The final uncertainty analysis could then be a set of fully
dynamic runs that produce a family of time-series curves (or an uncertainty band around an
outcome curve). Results from the steady-state uncertainty/sensitivity analysis might also be
evaluated as to their use to predict the outcome variance in the dynamic runs.
SEPTEMBER 2002 C-10 TRIM.FATE TSD VOLUME II
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Appendix D
TABLES OF TRIM.FaTE INPUT PARAMETERS
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Appendix D
Tables of TRIM.FaTE Input Parameters
Appendix D
TABLES OF TRIM.FaTE INPUT PARAMETERS
This appendix contains the following sets of tables listing and describing the input
parameters used in TRIM.FaTE:
non-chemical-dependent parameters for abiotic compartment types;
non-chemical-dependent parameters for biotic compartment types;
• chemical-dependent (i.e., value varies by chemical) parameters independent of
compartment type;
chemical-dependent parameters for abiotic compartment types;
chemical-dependent parameters for biotic compartment types; and
• source, meteorological, and other input parameters.
For each parameter listed, the parameter name and symbol, exact TRIM.FaTE code name, input
units, and a brief description are given; for chemical-specific parameters, the applicable
chemicals (e.g., all, organics, mercury) also are given. Values for parameters are not listed
here, but the values used should be documented for individual model applications.
Within the framework of the TRIM.FaTE computer model, several different kinds
of "properties" are defined and used. The input parameters described in this appendix fall into
the following categories of TRIM.FaTE properties:
compartment properties (includes by far the largest number of input parameters);
• volume element (VE) properties;
• link properties;
chemical properties;
source properties; and
• scenario properties.
In the following tables, the property type is identified for all input parameters that are not
compartment properties.
This appendix is intended to document only input parameters that are TRIM.FaTE
computer model properties, i.e., those parameters for which a user needs to supply a value (or
confirm that an existing TRIM.FaTE library value is appropriate) in order to apply TRIM.FaTE.
There are many other parameters, described throughout this Technical Support Document
(TSD), that are calculated from these inputs and used in various chains of equations in the
model. These intermediate parameters are not listed in the following tables, but they are
described in the other parts of this document.
September 2002 D-l TRIM.FaTE Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
In addition to the input parameters listed here, the transfer factor algorithms and other
equations described in the body of this document also include some parameters for which the
user may want to set different values (e.g., gill assimilation efficiency in fish, or "overall KOW"
(Dow) in surface water). Although these parameters are considered part of the TRIM.FaTE
algorithms/equations, rather than TRIM.FaTE properties, they and the algorithms/equations
themselves are available to the user to modify as appropriate and scientifically defensible for the
application at hand. These parameters are described along with the transfer factor algorithms
and other equations in the other parts of this document, and are not listed in this appendix.
Finally, for a TRIM.FaTE application, "off-line" calculations generally are needed to
develop some of the input parameters listed in these tables (e.g., meteorological data
preprocessing, calculation of surface water flows, calculation of runoff fractions for overland
flow). Inputs for such "off-line" calculations, which may vary considerably across model
applications, are not listed in this appendix.
Note that the units listed in these tables are the units in which model input values
need to be expressed. In a few cases, these computer model input units do not match the units
used for the same parameter in equations and derivations in the other parts of this TSD. In such
cases, there are internal units conversions in the computer model that account for the
differences.
For most of the input parameters listed in the following tables, the symbol used in
the other parts of this TSD is included. For a few input parameters (e.g., initial concentration of
a chemical, boundary concentration of a chemical), no symbol is included because no symbol is
used in the other parts of this TSD.
September 2002 D-2 TRIM.FaTE Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Non-Chemical-Dependent - Abiotic
Air Compartment Type
Parameter Name
(TSD Symbol)
Atmospheric dust particle load (DL)
Density of air (pa)
Density of dust particles (pp)
Fraction organic matter on particulates
(/cm)
Height [VE Property]3
Particulate washout ratio (wr)
TRIM FaTE Code Name
DustLoad
AirDensity_g_cm3
DustDensity
FractionOrganicMatteronParticulat
es
top, bottom3
WashoutRatio
Input Units
kg[dust particles]/m3[air
compartment]
g/cm3
kg[dust particles]/m3[dust particles]
unitless (wet wt)
m
m3[air]/m3[rain]
Description
Concentration of atmospheric dust particles in the
air compartment
Mass of air per unit volume of air
Mass of atmospheric particulate per unit volume of
atmospheric particulate
Mass fraction of air particulates that is organic
material
Height (i.e., vertical dimension) of the air volume
element
Precipitation scavenging ratio for particles in air
(ratio of concentration of particles in rain to
concentration of particles in air); used in estimating
wet deposition of particles
Height of air volume elements is set in TRIM.FaTE using two properties named "top" and "bottom."
September 2002
D-3
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Non-Chemical-Dependent - Abiotic
Soil Compartment Types
Parameter Name
(TSD Symbol)
TRIM FaTE Code Name
Input Units
Description
Surface Soil Compartment Type
Air content (eSs)a
Average vertical velocity of water
(percolation) (V;)b
Boundary layer thickness above surface
soil (5Ss)
Density of soil solids (dry weight) (p)a
Depth [VE Property] (dSs)c
Erosion fraction (ferosion(Ssi — »• Ssj)) [Link
property]
Fraction of area available for erosion
vavail erosion/
Fraction of area available for runoff
vavail runoff/
Fraction of area available for vertical
diffusion (/A)
Organic carbon fraction (/oc)
Runoff fraction (frunoff(Ssi — >• Ssj)) [Link
property]
Total erosion rate (erosion) b
Total runoff rate (runoff) b
VolumeFraction_vapor
AverageVerticalVelocity
AirSoilBoundaryThickness
rho
top, bottom0
FractionofTotal Erosion
Fractionofareaavailableforerosion
FractionofAreaAvailableforRunoff
Fractionofareaavailableforverticaldif
fusion
OrganicCarbonContent
FractionofTotal Runoff
TotalErosionRate_kg_m2_day
TotalRunoffRate_m3_m2_day
volume[air]/volume[compartment]
m/day
m
kg[soil]/m3[soil]
m
unitless
m2[area available]/m2[total]
m2[area available]/m2[total]
m2[area available]/m2[total]
kg [organic carbon]/kg[soil wet wt]
unitless
kg[soil solids]/m2[surface soil]-day
m3[water]/m2[surface soil]-day
Volumetric pore space occupied by air in
surface soil compartment (fraction of total
volume that is air)
Average speed of water movement in
downward vertical direction through soil column
Boundary layer thickness above surface soil
Dry soil density (or dry weight of surface soil
particles per unit volume of surface soil
particles)
Depth (i.e., vertical dimension) of the surface
soil volume element
Fraction of total eroded soil mass moving from
a given sending compartment to a given
receiving compartment or sink
Fraction of the total surface area for which
erosion can occur
Fraction of the total surface area for which
runoff can occur
Fraction of the total surface area for which
vertical diffusion can occur
Organic carbon mass fraction for surface soil
Fraction of total runoff volume moving from a
given sending compartment to a given
receiving compartment or sink
Mass of eroded surface soil particles per unit
surface area per day
Volume of liquid runoff from surface soil per
unit surface area per day
September 2002
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TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Non-Chemical-Dependent - Abiotic
Soil Compartment Types
Parameter Name
(TSD Symbol)
Water content (6 Ss)a
TRIM FaTE Code Name
VolumeFractionJJquid
Input Units
volume[water]/volume[compartment]
Description
Volumetric pore space occupied by water in
surface soil compartment (fraction of total
volume that is water)
Root Zone Soil Compartment Type
Air content (GSr)a
Average vertical velocity of water
(percolation) (V;)b
Density of soil solids (dry weight) (p)a
Depth [VE Property] (dSr)c
Organic carbon fraction (/oc)
Water content (6 Sr)a
VolumeFraction_vapor
AverageVerticalVelocity
rho
top, bottom0
OrganicCarbonContent
VolumeFraction_Liquid
volume[air]/volume[compartment]
m/day
kg[soil]/m3[soil]
m
kg [organic carbon]/kg [soil wet wt]
volume[water]/volume[compartment]
Volumetric pore space occupied by air in root
zone soil compartment (fraction of total volume
that is air)
Average speed of water movement in vertical
direction through soil column (downward)
Dry soil density (or dry weight of root zone soil
particles per unit volume of root zone soil
particles)
Depth (i.e., vertical dimension) of the root zone
soil volume element
Organic carbon mass fraction for root zone soil
Volumetric pore space occupied by water in
root zone soil compartment (fraction of total
volume that is water)
Vadose Zone Soil Compartment Type
Air content (C^f
Average vertical velocity of water
(percolation) (V;)b
Density of soil solids (dry weight) (p)a
Depth [VE Property] (d&f
Organic carbon fraction (/oc)
VolumeFraction_vapor
AverageVerticalVelocity
rho
top, bottom0
OrganicCarbonContent
volume[air]/volume[compartment]
m/day
kg[soil]/m3[soil]
m
kg [organic carbon]/kg [soil wet wt]
Volumetric pore space occupied by air in
vadose zone soil compartment (fraction of total
volume that is air)
Average speed of water movement in vertical
direction through soil column (downward)
Dry soil density (or dry weight of vadose zone
soil particles per unit volume of vadose zone
soil particles)
Depth (i.e., vertical dimension) of the vadose
zone soil volume element
Organic carbon mass fraction for vadose zone
soil
September 2002
D-5
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Non-Chemical-Dependent - Abiotic
Soil Compartment Types
Parameter Name
(TSD Symbol)
Water content (6 Sv)a
TRIM FaTE Code Name
VolumeFraction_Liquid
Input Units
volume[water]/volume[compartment]
Description
Volumetric pore space occupied by water in
vadose zone soil compartment (fraction of total
volume that is water)
Ground Water Compartment Type
Depth [VE Property]0
Organic carbon fraction (/oc)
Porosity (0)
Recharge rate to surface water
(recharge) [Link property]
Solid material density in aquifer (p)
top, bottom0
OrganicCarbonContent
Porosity
RechargeRate
rho
m
kg [organic carbon]/kg [soil wet wt]
volume[total pore
space]/volume[compartment]
m3[water]/m2[area]-day
kg[soil]/m3[soil]
Depth (i.e., vertical dimension) of the ground
water volume element
Organic carbon mass fraction for ground water
Ratio of pore space volume to total ground
water compartment volume
Volume of ground water moving into surface
water per unit interfacial area per day
Dry particle density (or dry weight of solid
material in ground water compartment per unit
volume of solid material in ground water
compartment)
Interdependent parameters - user is responsible for making sure input values are consistent (also interdependent with soil bulk density, which is not an input
parameter in TRIM.FaTE but for which data are often available).
Interdependent parameters with precipitation - user is responsible for making sure input values are consistent.
cSet using the volume element properties named "top" and "bottom."
September 2002
D-6
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Surface Water Compartment Type
Non-Chemical-Dependent -- Abiotic
Parameter Name
(TSD Symbol)
Algae carbon content (fraction) (AITOc)
Algae density in water column (AC)
Algae growth rate constant (u)
Algae radius (R)
Algae water content (fraction) (/WA|gae)
Average algae cell density (per vol cell,
not water) (pA!gae)
Boundary layer thickness above
sediment (5Sed)
Bulk water flow (flow) [Link property]a'b'c
Chloride concentration
Chlorophyll concentration (CC)
Current velocity (u)c'd
Depth (dw) [VE property]0'8
Dispersion coefficient for exchange
between surface water compartments
(DSPij) [Link property]3
TRIM FaTE Code Name
AlgaeCarbonContentDryWt
AlgaeDensityinWaterColumn_g_L
AlgaeGrowthRate
AlgaeRadius
AlgaeWaterContent
AlgaeDensity_g_m3
Boundary LayerThicknessAboveSedi
ment
BulkWaterFlowRate_Volumetric
ChlorideConcentration_mg_L
ChlorophyllConcentration_mg_L
CurrentVelocity
top, bottom8
DiffusiveExchangeCoefficient
Input Units
g[carbon]/g[algae dry wt]
g[algae wet wt]/L[water]
1/day
um
unitless
g[algae]/m3[algae]
m
m3[water]/day
mg/L
mg[chlorophyll]/L[water]
m/s
m
m2/day
Description
Mass fraction of algae that is carbon (dry wt
basis)
Mass of algae per unit volume of surface water
First-order rate constant for increase of algae
mass
Average size of algae cell
Mass fraction of algae that is water
Weight of algae per unit volume of algae cells
Thickness of surface water above sediment
within which molecular diffusion between media
can be significant (defines boundary between
the well mixed portion, where turbulent mixing is
rapid and continuous, and the stable portion at
the very edge of the interface)
Volume of water movement per unit time across
a link (i.e., at a compartment-compartment
interface)
Concentration of chloride ion in surface water
compartment
Concentration of chlorophyll in surface water
compartment
Average speed of moving water in flowing
surface water compartments
Depth (i.e., vertical dimension) of the surface
water volume element
Coefficient used to calculate dispersive transport
between two horizontally adjacent surface water
compartments
September 2002
D-7
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Surface Water Compartment Type
Non-Chemical-Dependent -- Abiotic
Parameter Name
(TSD Symbol)
Dimensionless viscous sublayer
thickness (A2)
Distance between midpoints (Ly) [Link
property]3
Drag coefficient for water body (Cd)
Flush rate (flushes/yr)f
Generic diffusive exchange coefficient
with sediment (DSPSed)
Organic carbon fraction in suspended
sediments (/oc)
PH
Suspended sediment density (Psed)
Suspended sediment deposition velocity
(Vdep)
Total suspended sediment concentration
(TSS)
Water temperature (T) [VE property]
TRIM FaTE Code Name
DimensionlessViscousSublayerThick
ness
DistanceBetweenMidpoints
DragCoefficient
Flushes_per_year
GenericDiffusiveExchangeCoefficient
WithSediment
OrganicCarbonContent
PH
rho
SedimentDepositionVelocity
SuspendedSedimentconcentration
WaterTemperature_K
Input Units
unitless
m
unitless
1/year
m2/day
unitless
unitless
kg[sediment particles]/m3[sediment
particles]
m/day
kg[suspended sediment
particles]/m3[surface water
compartment]
degrees K
Description
Parameter used in calculating gas and liquid
phase transfer coefficients, which are used in
calculating volatilization transfers between
surface water and air
Linear distance between the midpoints of two
connected surface water compartments; used as
characteristic mixing length for dispersion
calculations
Coefficient used to calculate the shear velocity
of wind, which is used in calculating volatilization
transfers between surface water and air
Number of times surface water compartment
volume is completely turned over (flushed) in a
year
Coefficient used to calculate diffusive exchange
between adjacent surface water and sediment
compartments
Organic carbon mass fraction for suspended
sediment
Negative logarithm (base 10) of concentration of
hydrogen ion in surface water compartment
Dry suspended sediment density (or dry weight
of suspended sediment particles per unit volume
of suspended sediment particles)
Speed that suspended sediment moves
downward through water column
Concentration of suspended sediment in water
column
Average water temperature of the surface water
compartment
aApplies to all surface water compartments connected to other surface water compartments.
Interdependent parameters with precipitation - user is responsible for making sure input values are consistent.
Interdependent parameters - user is responsible for making sure input values are consistent.
September 2002
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Surface Water Compartment Type
Non-Chemical-Dependent -- Abiotic
Parameter Name
(TSD Symbol)
TRIM FaTE Code Name
Input Units
Description
Applies to flowing water bodies only (i.e., rivers, streams).
eSet using the volume element properties named "top" and "bottom."
'Applies to all surface water compartments connected to a flush rate sink (i.e., all or part of discharge modeled to a sink).
September 2002
D-9
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Sediment Compartment Type
Non-Chemical-Dependent - Abiotic
Parameter Name
(TSD Symbol)
Depth (dsed) [VE Property]3
Organic carbon fraction (/oc)
Porosity of the sediment zone (0)b
Solid material density in sediment (pSed)b
TRIM FaTE Code Name
top, bottom3
OrganicCarbonContent
Porosity
rho
Input Units
m
kg[organic carbon]/kg[soil wet wt]
m3[pore water]/m3[sediment
compartment]
kg[sediment particles]/m3[sediment
particles]
Description
Depth (i.e., vertical dimension) of the sediment
volume element
Organic carbon mass fraction for bottom
sediment
Ratio of pore space volume to total sediment
compartment volume
Dry sediment density (or dry weight of bottom
sediment per unit volume of bottom sediment)
3Set using the volume element properties named "top" and "bottom."
Interdependent parameters with benthic
making sure input values are consistent.
Interdependent parameters with benthic solids concentration (kg[sediment]/m 3[sediment compartment]; not a TRIM.FaTE input parameter) - user is responsible for
September 2002
D-10
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Non-Chemical-Dependent -- Biotic
Terrestrial Plant Compartment Types3
Parameter Name 1
(TSD Symbol) | TRIM FaTE Code Name
Input Units
Description
Leaf Compartment Type
Allow exchange13
Average leaf area index (LAI)C
Calculate wet dep interception fraction
Correction exponent, octanol to lipid (b)
Degree stomatal opening (as)
Density of wet leaf (pLeaf)c
Leaf wetting factor (S)
Length of leaf (1)
Lipid content (/LLeaf)
Litter fall rate (KL)b
Stomatal area, normalized for effective
diffusion path length (SN)
Vegetation attenuation factor (aVAp)
Water content (/WLeaf)
AllowExchange
AverageLeafArealndex_No_Time_D
ependence
CalculateWetDeplnterceptionFracti
on_1_Means_Yes_Else_No
CorrectionExponent
DegreeStomatalOpening
WetDensity
LeafWettingFactor
LengthofLeaf
LipidContent
LitterFallRate
StomatalAreaNormalizedEffectiveDi
ffusionPathLength
AttenuationFactor
WaterContent
1=yes, 0=no
m2[total leaf area]/m2[underlying soil
area]
1=yes, 0=no
unitless
unitless
kg[leaf wet wt]/m3[leaf]
m
m
kg[lipid]/kg[leaf wet wt]
1/day
1/m
m2/kg
unitless (kg[water]/kg[leaf wet wt])
1 if exchange can occur with another compartment,
0 if not (can be made seasonal by setting allow
exchange start and stop dates)
Average area of leaf per unit surface area (no time
dependence)
Switch used to allow use of input value or model
calculations
Correction exponent for the differences between
octanol and lipids
Mean degree of opening of stomatal pores,
between 0 and 1
Density of wet plant leaf
Vegetation-dependent leaf-wetting factor (retention
coefficient)
Length of flat leaf
Mass fraction of leaf that is lipid (wet wt basis)
First-order rate constant for fall of plant leaves to
soil (can be made seasonal by setting litter fall start
and stop dates)
Portion of total leaf surface area comprised of
stomatal pores divided by the effective path length
for a diffusing molecule through a pore; value is
relatively similar across plant species
Effective attenuation by plant leaves of dry
depositing particles per unit dry weight of the plant
species; used to calculate interception fraction
Mass fraction of leaf that is water (wet wt basis)
September 2002
D-ll
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Non-Chemical-Dependent -- Biotic
Terrestrial Plant Compartment Ty
Parameter Name
(TSD Symbol)
Wet dep interception fraction (Iwet)
Wet mass of leaf per unit area
(pareaLeaf)c
pesa
TRIM FaTE Code Name
WetDeplnterceptionFraction_lnput_
Used_Only_lf_OptionSet
WetMassperArea
Input Units
unitless
kg[fresh Ieaf]/m2[area]
Description
Fraction of wet deposition intercepted by leaves
(input used only if option set)
Freshweight mass of leaf per unit surface area
Particle-on-Leaf Compartment Type
Allow exchange13
Volume particle per area leaf
AllowExchange
VolumeParticlePerAreaLeaf
1=yes, 0=no
m3 [leaf particles]/m2 [leaf]
1 if exchange can occur with another compartment,
0 if not (can be made seasonal by setting allow
exchange start and stop dates)
Volume of leaf particles per unit area of leaf; used
to calculate compartment volume
Root Compartment Type - Nonwoody Plants Only"
Allow exchange13
Correction exponent, octanol to lipid (b)
Lipid content of root (/LRoot)
Water content of root (/WRoot)
Wet density of root (pRoot)
Wet mass per area (pareaRoot)
AllowExchange
CorrectionExponent
LipidContent
WaterContent
WetDensity
WetMassperArea
1=yes, 0=no
unitless
kg[lipid]/kg [root wet wt]
kg[water]/kg[root wet wt])
kg[leaf wet wt]/m3[root]
kg[root wet wt]/m2[soil]
1 if exchange can occur with another compartment,
0 if not (can be made seasonal by setting allow
exchange start and stop dates)
Correction exponent for the differences between
octanol and lipids
Mass fraction of root that is lipid (wet wt basis)
Mass fraction of root that is water (wet wt basis)
Density of wet plant root
Freshweight mass of root per unit surface area
September 2002
D-12
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Non-Chemical-Dependent -- Biotic
Terrestrial Plant Compartment Types3
Parameter Name 1
(TSD Symbol) | TRIM FaTE Code Name
Input Units
Description
Stem Compartment Type - Nonwoody Plants Only"
Allow exchange13
Correction exponent, octanol to lipid (b)
Density of phloem fluid (pph)
Density of xylem fluid (pXy)
Flow rate of transpired water per leaf
area
Fraction of transpiration flow rate that is
phloem rate
Lipid content of stem (/Lstem)
Water content of stem (/W^J
Wet density of stem (Pstem)
Wet mass per area (paree^^)
AllowExchange
CorrectionExponent
PhloemDensity
XylemDensity
FlowRateofTranspiredWaterperAre
aofLeafSurface
FractionPhloemRatewithTranspirati
onFlowRate
LipidContent
WaterContent
WetDensity
WetMassperArea
1=yes, 0=no
unitless
kg[phloem]/m3[phloem]
kg[xylem]/m3[xylem]
m3[water]/m2 [leaf]-day
unitless
kg[lipid]/kg [stem wetwt]
kg[water]/kg[stem wet wt]
kg[stem wet wt]/m3[root]
kg[stem wet wt]/m2[soil]
1 if exchange can occur with another compartment,
0 if not (can be made seasonal by setting allow
exchange start and stop dates)
Correction exponent for the differences between
octanol and lipids
Density of phloem fluid
Density of xylem fluid
Empirical factor used to estimate total flow of
transpired water based on leaf surface area
Fraction of total transpiration flow rate that is the
phloem rate
Mass fraction of stem that is lipid (wet wt basis)
Mass fraction of stem that is water (wet wt basis)
Density of wet plant stem
Freshweight mass of stem per unit surface area
aTRIM.FaTE currently includes four kinds of terrestrial plants: deciduous forest, coniferous forest, grasses/herbs, and agricultural.
blf modeled as seasonal processes, on/off dates are interdependent - user is responsible for making sure input values are consistent.
Interdependent parameters - user is responsible for making sure input values are consistent.
dRoots and stems are not modeled for deciduous and coniferous forest in the current version of TRIM.FaTE.
September 2002
D-13
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Aquatic Plants Compartment Type
Non-Chemical-Dependent - Biotic
Parameter Name
(TSD Symbol)
TRIM FaTE Code Name
Input Units
Description
Macrophyte Compartment Type
Biomass per water area
Density of macrophytes (pMp)
BiomassPerArea kg m2
Density
kg/m2
kg/L
Mass of macrophytes per unit surface water
area (wet wt basis)
Mass of macrophytes per unit volume of
macrophytes (wet wt basis)
September 2002
D-14
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Terrestrial Animal Compartment Types
Non-Chemical-Dependent -- Biotic
Parameter Name
(TSD Symbol)
TRIM FaTE Code Name
Input Units
Description
Soil Detritivore Compartment Type - Earthworm
Density
Density per soil area (pareaWorm)
Water content of worm (/W^J
Density_Freshweight
ArealDensity_Freshweight
Water_content
kg[worm]/L[worm]
kg[worm wet wt]/m2[soil]
unitless
Density of worm (wet wt basis); used to calculate
compartment volume
Mass of worm per unit surface area of soil
Mass fraction of worm that is water
Soil Detritivore Compartment Type - Soil Arthropod
Biomass per soil area (pareaArth)
Body weight (BW)
BiomassPerArea_kg_m2
BW
kg[arthropod wet wt]/m2[soil]
kg
Mass of soil arthropods per unit surface area of soil
Mass of individual animal
All Other Terrestrial Animal Compartment Types3
Body weight (BW)
Food ingestion rate (IND)
Fraction diet- american robin (pAmerican
robin \
Fraction diet- black-capped chickadee
/pChickadee\
Fraction diet- bobwhite quail (pBobwhite
quaik
Fraction diet- mallard (pMallard)
Fraction diet- mouse (RMouse)
Fraction diet- plants (Pplants)
Fraction diet - short-tailed shrew (pshort-
tailed shrew\
BW
FoodlngestionRate
FractionDietAmericanRobin
FractionDietChickadee
FractionDietBobwhiteQuail
FractionDietMallard
FractionDietMouse
FractionDietPlant
FractionDietshorttailedshrew
kg
kg[dietwet wt]/kg BW-day
unitless
unitless
unitless
unitless
unitless
unitless
unitless
Mass of individual
Total amount of food eaten per day, scaled to body weight
Fraction of food diet comprised of american robin
Fraction of food diet comprised of black-capped chickadee
Fraction of food diet comprised of bobwhtie quail
Fraction of food diet comprised of mallard
Fraction of food diet comprised of mouse
Fraction of food diet comprised of plant
Fraction of food diet comprised of short-tailed shrew
September 2002
D-15
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Terrestrial Animal Compartment Types
Non-Chemical-Dependent -- Biotic
Parameter Name
(TSD Symbol)
Fraction diet- soil (/mtakesoN)
Fraction diet- soil arthropod (RArth)
Fraction diet- vole (PVole)
Fraction diet- worm (PWorm)
Fraction excretion to soil (fuSs)
Fraction excretion to water (fusw)
Fraction specific compartment diet
[Link property]
Population per soil area (PNarea)
Scaling constant A - inhalation rate
Scaling constant B - inhalation rate
Scaling constant A - water ingestion
rate
Scaling constant B - water ingestion
rate
Soil ingestion rate (INSs)
TRIM FaTE Code Name
FractionDietSoilb
FractionDietSoil Arthropod
FractionDietvole
FractionDietWorm
FractionExcretiontoSoil
FractionExcretiontoWater
FractionSpecificCompartmentDiet
NumberoflndividualsPerSquareMeter
lnhalationProps_A
lnhalationProps_B
WaterlngProps_A
WaterlngProps_B
SoillngestionRate
Input Units
unitless, dry wt basis
unitless
unitless
unitless
unitless
unitless
unitless
#/m2
unitless
unitless
unitless
unitless
kg[soil]/kg BW-day
Description
Fraction of total dry weight intake comprised of soil (used
to calculate soil ingestion rate, when necessary)
Fraction of food diet comprised of soil arthropod
Fraction of food diet comprised of vole
Fraction of food diet comprised of worm
Fraction of total excretion that goes to surface soil
Fraction of total excretion that goes to surface water
Fraction of food diet originating from a specific
compartment; must sum to 1.0 across all links
Number of individuals per unit surface area
Allometric scaling constant used to calculate inhalation
rate based on body weight
Allometric scaling constant used to calculate inhalation
rate based on body weight
Allometric scaling constant used to calculate water
ingestion rate based on body weight
Allometric scaling constant used to calculate water
ingestion rate based on body weight
Total amount of soil eaten per day, scaled to body weight
(used if data available - otherwise calculated from fraction
diet-soil and food ingestion rate)
aTRIM.FaTE currently includes the following terrestrial animal compartment types: Terrestrial Ground-invertebrate Feeder - American Woodcock, Terrestrial Ground-
invertebrate Feeder - Black-capped Chickadee, Terrestrial Ground-invertebrate Feeder - Short-tailed Shrew, Terrestrial Ground-invertebrate Feeder - Trowbridge Shrew,
Terrestrial Herbivore - Bobwhite Quail, Terrestrial Herbivore - Cow, Terrestrial Herbivore - Long-tailed Vole, Terrestrial Herbivore - Meadow Vole, Terrestrial Herbivore -
Mule Deer/Black-tailed Deer, Terrestrial Herbivore - White-tailed Deer, Terrestrial Insectivore - Tree Swallow, Terrestrial Omnivore - American Robin, Terrestrial Omnivore
- Mouse, Terrestrial Predator/Scavenger- Long-tailed Weasel, and Terrestrial Predator/Scavenger- Red-tailed hawk.
bParameter and equations using it are in process of being added to TRIM.FaTE as of publication date.
September 2002
D-16
TRIM.FaTE TSD Volume II
-------
Appendix D
Tables of TRIM.FaTE Input Parameters
Semi-aquatic Animal Compartment Types
Non-Chemical-Dependent -- Biotic
Parameter Name
(TSD Symbol)
TRIM FaTE Code Name
Input Units
Description
All Compartment Types3
Body weight (BW)
Food ingestion rate (IND)
Fraction diet- algae (PAlgae)
Fraction diet- american robin
/p American robin \
Fraction diet- benthic carnivores
(PFbc)
Fraction diet- benthic invertebrates
(PBI)
Fraction diet- benthic omnivores
(PFb°)
Fraction diet- black-capped
chickadee (PChickadee)
Fraction diet- bobwhite quail
/pBobwhite quaiU
Fraction diet- macrophyte (PMp)
Fraction diet- mallard (pMallard)
Fraction diet- mouse (RMouse)
Fraction diet- plants (Pplants)
Fraction diet - short-tailed shrew
/pShort-tailed shrew\
Fraction diet- soil (/mtakesoN)
Fraction diet- soil arthropod (PArth)
BW
FoodlngestionRate
FractionDietAlgae
FractionDietAmericanRobin
FractionDietFishbenthiccarnivore
FractionDietBenthiclnvertebrate
FractionDietFishbenthicomnivore
FractionDietChickadee
FractionDietBobwhiteQuail
FractionDietMacrophyte
FractionDietMallard
FractionDietMouse
FractionDietPlant
FractionDietshorttailedshrew
FractionDietSoilb
FractionDietSoilArthropod
kg
(kg[diet wet wt]/kg[body wet wt]-
day)
unitless
unitless
unitless
unitless
unitless
unitless
unitless
unitless
unitless
unitless
unitless
unitless
unitless, dry wt basis
unitless
Mass of individual animal
Total amount of food eaten per day, scaled to body
weight
Fraction of food diet comprised of algae
Fraction of food diet comprised of american robin
Fraction of food diet comprised of benthic carnivore
Fraction of food diet comprised of benthic invertebrate
Fraction of food diet comprised of benthic omnivore
Fraction of food diet comprised of black-capped
chickadee
Fraction of food diet comprised of bobwhite quail
Fraction of food diet comprised of macrophyte
Fraction of food diet comprised of mallard
Fraction of food diet comprised of mouse
Fraction of food diet comprised of plant
Fraction of food diet comprised of short-tailed shrew
Fraction of total dry weight intake comprised of soil (used
to calculate soil ingestion rate, when necessary)
Fraction of food diet comprised of soil arthropod
September 2002
D-17
TRIM.FaTE TSD Volume II
-------
Appendix D
Tables of TRIM.FaTE Input Parameters
Semi-aquatic Animal Compartment Types
Non-Chemical-Dependent -- Biotic
Parameter Name
(TSD Symbol)
Fraction diet- vole (PVole)
Fraction diet - water-column
carnivores (pFwcc)
Fraction diet - water-column
herbivores (PFwch)
Fraction diet - water-column
omnivores (PFwc°)
Fraction diet- worm (PWorm)
Fraction excretion to soil (fuSW)
Fraction excretion to water (fuss)
Fraction specific compartment diet
[Link property]
Population per soil area (PNarea)
Scaling constant A - inhalation rate
Scaling constant B - inhalation rate
Scaling constant A - water ingestion
rate
Scaling constant B - water ingestion
rate
Soil ingestion rate (INSs)
TRIM FaTE Code Name
FractionDietvole
FractionDietFishcarnivore
FractionDietFishherbivore
FractionDietFishomnivore
FractionDietWorm
FractionExcretiontoSoil
FractionExcretiontoWater
FractionSpecificCompartmentDiet
NumberoflndividualsPerSquareMeter
lnhalationProps_A
lnhalationProps_B
Wate r 1 n g P ro ps_A
WaterlngProps_B
SoillngestionRate
Input Units
unitless
unitless
unitless
unitless
unitless
unitless
unitless
unitless
#/m2
unitless
unitless
unitless
unitless
kg[soil]/kg BW-day
Description
Fraction of food diet comprised of vole
Fraction of food diet comprised of water-column carnivore
Fraction of food diet comprised of water-column
herbivore
Fraction of food diet comprised of water-column omnivore
Fraction of food diet comprised of worm
Fraction of total excretion that goes to soil
Fraction of total excretion that goes to surface water
Fraction of food diet originating from a specific
compartment; must sum to 1.0 across all links
Number of individuals per unit area
Allometric scaling constant used to calculate inhalation
rate based on body weight
Allometric scaling constant used to calculate inhalation
rate based on body weight
Allometric scaling constant used to calculate water
ingestion rate based on body weight
Allometric scaling constant used to calculate water
ingestion rate based on body weight
Total amount of soil eaten per day, scaled to body weight
(used if data available - otherwise calculated from fraction
diet-soil and food ingestion rate)
aTRIM.FaTE currently includes the following semi-aquatic animal compartment types: Semi-aquatic Omnivore
Omnivore - Raccoon, Semi-aquatic Piscivore - Common Loon, Semi-aquatic Piscivore - Kingfisher, and Semi-
bParameter and equations using it are in process of being added to TRIM.FaTE as of publication date.
- Mallard, Semi-aquatic Omnivore - Mink, Semi-aquatic
aquatic Predator/Scavenger - Bald Eagle.
September 2002
D-18
TRIM.FaTE TSD Volume II
-------
Appendix D
Tables of TRIM.FaTE Input Parameters
Aquatic Animal Compartment Types
Non-Chemical-Dependent -- Biotic
Parameter Name
(TSD Symbol)
TRIM FaTE Code Name
Input Units
Description
Benthic Invertebrate Compartment Type
Biomass per water area
Body weight (BW) or (mB|)
BiomassPerArea_kg_m2
BW
kg/m2
kg[inv wet wt]
Mass of benthic invertebrates per unit surface
water area
Mass of individual organisms comprising the
benthic invertebrate compartment
All Fish Compartment Types3
Body weight (BW) OR (mf)
Fraction diet - algae (RAlgae)
Fraction diet - benthic carnivores (PFbc)
Fraction diet - benthic invertebrates (PBI)
Fraction diet - benthic omnivores (PFb°)
Fraction diet - macrophyte (PMp)
Fraction diet - water-column carnivores
(PFwcc)
Fraction diet - water-column herbivores
/pFwchK
Fraction diet - water-column omnivores
,pFwco>
Fraction lipid weight (/|ipid)
Population per water area
BW
FractionDietAlgae
FractionDietFishbenthiccarnivore
FractionDietBenthiclnvertebrate
FractionDietFishbenthicomnivore
FractionDietMacrophyte
FractionDietFishcarnivore
FractionDietFishherbivore
FractionDietFishomnivore
FishLipidFraction
NumberofFishperSquareMeter
kg [fish wet wt]
unitless
unitless
unitless
unitless
unitless
unitless
unitless
unitless
kg[lipid]/kg[fish wet wt]
#/m2
Mass of individual fish
Fraction of food diet comprised of algae
Fraction of food diet comprised of benthic
carnivore
Fraction of food diet comprised of benthic
invertebrate
Fraction of food diet comprised of benthic
omnivore
Fraction of food diet comprised of macrophyte
Fraction of food diet comprised of water-
column carnivore
Fraction of food diet comprised of water-
column herbivore
Fraction of food diet comprised of water-
column omnivore
Mass fraction of fish that is lipid (wet wt basis)
Number of fish per unit surface water area
TRIM.FaTE currently includes the following fish compartment types: Benthic Carnivore,
Water-column Omnivore.
Benthic Omnivore, Water-column Carnivore, Water-column Herbivore, and
September 2002
D-19
TRIM.FaTE TSD Volume II
-------
Appendix D
Tables of TRIM.FaTE Input Parameters
Chemical-Dependent -- Independent of Compartment Type
Parameter Name3
(TSD Symbol)
Diffusion coefficient in pure air (Dair)
Diffusion coefficient in pure water
(Dwater)
Henry's Law constant (H)
Melting point (Tm)
Molecular weight (Mw)
Octanol-water partition coefficient
(KOW)
Reference bird body weight
(BW(Ref))
Reference bird chemical degradation
rate(kdegradation)
Reference bird elimination rate
Reference mammal body weight
(BW(Ref))
Reference mammal chemical
degradation rate (kdegradation)
Reference mammal elimination rate
Vapor pressure (Pvapor)
Vapor washout ratio (wrV)
TRIM FaTE Code Name
D_pureair
D_purewater
Henry LawConstant
MeltingPoint
molecularWeight
K_ow
ReferenceBird_BodyWeight
ReferenceBird_GeneralDegradation
Rate
TerrestrialBird_EliminationRate
ReferenceMammal_BodyWeight
ReferenceMammal_General Degrade
tionRate
TerrestrialMammal_EliminationRate
VaporPressure
VaporWashoutRatio
Input Units
m2[air]/day
m2[water]/day
Pa-m3/mol
°K
g/mol
L[water]/kg[octanol]
kg
1/day
1/day
kg
1/day
1/day
Pa
m3[air]/m3[rain]
Description
Coefficient that (when combined with chemical
concentration) predicts how quickly a chemical spreads
out in gas phase due to diffusion
Coefficient that (when combined with chemical
concentration) predicts how quickly a chemical spreads
out in aqueous phase due to diffusion
Ratio of the aqueous-phase concentration of a chemical
to its equilibrium partial pressure in the gas phase
Temperature at which a solid becomes a liquid at
standard atmospheric pressure
Weight of 1 mole of the chemical
Equilibrium ratio of concentration dissolved in octanol to
concentration dissolved in water
Mass of individual reference bird used for allometric
scaling of degradation rate
First-order rate constant for chemical degradation in
reference bird used for allometric scaling of degradation
rate
First-order rate constant for elimination of chemical from
the body (terrestrial birds)
Mass of individual reference mammal used for allometric
scaling of degradation rate
First-order rate constant for chemical degradation in
reference mammal used for allometric scaling of
degradation rate
First-order rate constant for elimination of chemical from
the body (terrestrial mammals)
Pressure exerted by a vapor in equilibrium with its solid
or liquid phase
Precipitation scavenging ratio for vapors (ratio of
concentration in rain to concentration in vapor form in
air); used in estimating wet deposition of vapors
Applicable
Chemicals
all
all
all
all
all
all
organics
organics
organics
organics
organics
organics
organics
Hg species
All parameters in this table are TRIM.FaTE chemical properties.
September 2002
D-20
TRIM.FaTE TSD Volume II
-------
Appendix D
Tables of TRIM.FaTE Input Parameters
Chemical-Dependent -- Abiotic
Air Compartment Type
Parameter Name
(TSD Symbol)
Initial concentration
Boundary concentration [VE property]3
Particle dry deposition velocity (Vdry)
Demethylation rate (kDm)
Methylation rate (kM)
Oxidation rate (k0)
Reduction rate (kR)
Half-life (half-life)
TRIM FaTE Code Name
initialConcentration g per m3
boundaryConcentration_g_per_m3
vdep
DemethylationRate
Methylation Rate
OxidationRate
ReductionRate
Halflife
Input Units
g/m3
g/m3
m/day
1/day
1/day
1/day
1/day
day
Description
Bulk air concentration at beginning of modeling
period
Air concentration at the outer boundary of the
modeling region (i.e., concentration in air flowing
into the modeling region)
Speed at which chemical in particle form in air
moves downward; used in estimating dry
deposition of particles
First-order rate constant for demethylation (MHg-
>Hg2)
First-order rate constant for methylation (Hg2-
>MHg)
First-order rate constant for oxidation (HgO->Hg2)
First-order rate constant for reduction (Hg2->HgO)
Length of time for chemical amount to be reduced
by one-half by degradation reactions
Applicable
Chemicals
all
all
all
MHg
Hg2
HgO
Hg2
organics
aOnly used in model runs specified as including non-zero air boundary contributions.
the modeling region (zero boundary contribution for all internal air compartments).
Only applicable for air volume elements with at least one boundary on the outer edge of
September 2002
D-21
TRIM.FaTE TSD Volume II
-------
Appendix D
Tables of TRIM.FaTE Input Parameters
Chemical-Dependent - Abiotic
Soil Compartment Types
Parameter Name
(TSD Symbol)
TRIM FaTE Code Name
Input Units
Description
Applicable
Chemicals
Surface Soil Compartment Type
Initial concentration
Input characteristic depth (X*)
Soil/water partition coefficient (Kd)
Use input characteristic depth
Vapor dry deposition velocity (vvapor)
Demethylation rate (kDm)
Methylation rate (kM)
Oxidation rate (k0)
Reduction rate (kR)
Half-life (half-life)
initialConcentration_g_per_m3
lnputCharacteristicDepth_m
Kd
UselnputCharacteristicDepth_0_Mea
nsNo_ElseYes
VaporDryDepositionVelocity_m_day
DemethylationRate
MethylationRate
OxidationRate
ReductionRate
Halflife
g/m3
m
L[water]/kg[soil wet
wt]
0 = no , Else = yes
m/day
1/day
1/day
1/day
1/day
day
Bulk surface soil concentration at beginning of
modeling period
Distance from top of the soil compartment at
which soil concentration has dropped to 36.79%
(1/e * 100%) of the concentration at top of
compartment
Equilibrium ratio of concentration sorbed to
solids and concentration dissolved
If = 0, use model-calculated characteristic depth,
else use user-provided characteristic depth
Speed at which chemical in vapor form in air
moves downward; used in estimating dry
deposition of vapors to soil
First-order rate constant for demethylation (MHg-
>Hg2)
First-order rate constant for methylation (Hg2-
>MHg)
First-order rate constant for oxidation (HgO-
>Hg2)
First-order rate constant for reduction (Hg2-
>HgO)
Length of time for chemical amount to be
reduced by one-half by degradation reactions
all
all
all
all
Hg2
MHg
Hg2
HgO
Hg2
organics
Root Zone Soil Compartment Type
Initial concentration
Input characteristic depth (X*)
Soil-water partition coefficient (Kd)
initialConcentration_g_per_m3
lnputCharacteristicDepth_m
Kd
g/m3
m
L[water]/kg[soil wet
wt]
Bulk root zone soil concentration at beginning of
modeling period
Distance from top of the soil compartment at
which soil concentration has dropped to 36.79%
(1/e * 100%) of the concentration at top of
compartment
Equilibrium ratio of concentration sorbed to
solids and concentration dissolved
all
all
all
September 2002
D-22
TRIM.FaTE TSD Volume II
-------
Appendix D
Tables of TRIM.FaTE Input Parameters
Chemical-Dependent - Abiotic
Soil Compartment Types
Parameter Name
(TSD Symbol)
Use input characteristic depth
Demethylation rate (kDm)
Methylation rate (kM)
Oxidation rate (k0)
Reduction rate (kR)
Half-life (half-life)
TRIM FaTE Code Name
UselnputCharacteristicDepth_0_Mea
nsNo_ElseYes
DemethylationRate
MethylationRate
OxidationRate
ReductionRate
Halflife
Input Units
0 = no , Else = yes
1/day
1/day
1/day
1/day
day
Description
If = 0, use model-calculated characteristic depth,
else use user-provided characteristic depth
First-order rate constant for demethylation (MHg-
>Hg2)
First-order rate constant for methylation (Hg2-
>MHg)
First-order rate constant for oxidation (HgO-
>Hg2)
First-order rate constant for reduction (Hg2-
>HgO)
Length of time for chemical amount to be
reduced by one-half by degradation reactions
Applicable
Chemicals
all
MHg
Hg2
HgO
Hg2
organics
Vadose Zone Soil Compartment Type
Initial concentration
Input characteristic depth (X*)
Soil-water partition coefficient (Kd)
Use input characteristic depth
Demethylation rate (kDm)
Methylation rate (kM)
Oxidation rate (k0)
Reduction rate (kR)
Half-life (half-life)
initialConcentration_g_per_m3
lnputCharacteristicDepth_m
Kd
UselnputCharacteristicDepth_0_Mea
nsNo_ElseYes
DemethylationRate
MethylationRate
OxidationRate
ReductionRate
Halflife
g/m3
m
L[water]/kg[soil wet
wt]
0 = no , Else = yes
1/day
1/day
1/day
1/day
day
Bulk vadose zone soil concentration at beginning
of modeling period
Distance from top of the soil compartment at
which soil concentration has dropped to 36.79%
(1/e * 100%) of the concentration at top of
compartment
Equilibrium ratio of concentration sorbed to
solids and concentration dissolved
If = 0, use model-calculated characteristic depth,
else use user-provided characteristic depth
First-order rate constant for demethylation (MHg-
>Hg2)
First-order rate constant for methylation (Hg2-
>MHg)
First-order rate constant for oxidation (HgO-
>Hg2)
First-order rate constant for reduction (Hg2-
>HgO)
Length of time for chemical amount to be
reduced by one-half by degradation reactions
all
all
all
all
MHg
Hg2
HgO
Hg2
organics
September 2002
D-23
TRIM.FaTE TSD Volume II
-------
Appendix D
Tables of TRIM.FaTE Input Parameters
Chemical-Dependent - Abiotic
Soil Compartment Types
Parameter Name
(TSD Symbol)
TRIM FaTE Code Name
Input Units
Description
Applicable
Chemicals
Ground Water Compartment Type
Initial concentration
Soil-water partition coefficient (Kd)
Demethylation rate (kDm)
Methylation rate (kM)
Oxidation rate (k0)
Reduction rate (kR)
Half-life (half-life)
initialConcentration_g_per_L
Kd
DemethylationRate
MethylationRate
OxidationRate
ReductionRate
Halflife
g/L
L[water]/kg[soil wet
wt]
1/day
1/day
1/day
1/day
day
Ground water concentration at beginning of
modeling period
Equilibrium ratio of concentration sorbed to
solids and concentration dissolved
First-order rate constant for demethylation (MHg-
>Hg2)
First-order rate constant for methylation (Hg2-
>MHg)
First-order rate constant for oxidation (HgO-
>Hg2)
First-order rate constant for reduction (Hg2-
>HgO)
Length of time for chemical amount to be
reduced by one-half by degradation reactions
all
all
MHg
Hg2
HgO
Hg2
organics
September 2002
D-24
TRIM.FaTE TSD Volume II
-------
Appendix D
Tables of TRIM.FaTE Input Parameters
Chemical-Dependent - Abiotic
Surface Water Compartment Type
Parameter Name
(TSD Symbol)
Initial concentration
Algal surface area-specific uptake rate
constant (U)
BCF-algae
Dow ("overall Kow") (Dow)
Soil-water partition coefficient (Kd)
Vapor dry deposition velocity (vvapor)
Demethylation rate (kDm)
Methylation rate (kM)
Oxidation rate (k0)
Reduction rate (kR)
Half-life (half-life)
TRIM FaTE Code Name
initialConcentration g per L
AlgaeUptakeRate
RatioOfConcinAlgaeToConcDissolv
edin Water
D_ow
Kd
VaporDryDepositionVelocity_m_da
y
DemethylationRate
MethylationRate
OxidationRate
ReductionRate
Halflife
Input Units
g/L
nmol/[um2-day-nmol]
L[water]/kg[algae wet
wt]
unitless
L[water]/kg[soil wet
wt]
m/day
1/day
1/day
1/day
1/day
day
Description
Surface water concentration at beginning of
modeling period
Surface area-specific rate constant for uptake into
algae of a chemical in water
Ratio of concentration in algae to concentration
dissolved in surface water (bioconcentration
factor)
Weighted (by mass fraction) sum of individual Kow
values for all chemical species present
Equilibrium ratio of concentration sorbed to solids
and concentration dissolved
Speed at which chemical in vapor form in air
moves downward; used in estimating dry
deposition of vapors to surface water
First-order rate constant for demethylation (MHg-
>Hg2)
First-order rate constant for methylation (Hg2-
>MHg)
First-order rate constant for oxidation (HgO->Hg2)
First-order rate constant for reduction (Hg2->HgO)
Length of time for chemical amount to be reduced
by one-half by degradation reactions
Applicable
Chemicals
all
Hg species
organics
Hg species3
all
Hg2
MHg
Hg2
HgO
Hg2
organics
aFor Hg2 and MHg, Dow is included in TRIM.FaTE as a Formula Property (calculated within TRIM.FaTE) rather than a Constant Property (supplied as an input) because
the value is dependent on surface water pH and chloride concentration. However, the relationships between Dow and pH and chloride are a user input.
September 2002
D-25
TRIM. FaTE TSD Volume II
-------
Appendix D
Tables of TRIM.FaTE Input Parameters
Chemical-Dependent -- Abiotic
Sediment Compartment Type
Parameter Name
(TSD Symbol)
Initial concentration
Soil-water partition coefficient (Kd)
Demethylation rate (kDm)
Methylation rate (kM)
Oxidation rate (k0)
Reduction rate (kR)
Half-life (half-life)
TRIM FaTE Code Name
initialConcentration g per m3
Kd
DemethylationRate
MethylationRate
OxidationRate
ReductionRate
Halflife
Input Units
g/m3
L[water]/kg[soil wet
wt]
1/day
1/day
1/day
1/day
days
Description
Bulk sediment concentration at beginning of
modeling period
Equilibrium ratio of concentration sorbed to
solids and concentration dissolved
First-order rate constant for demethylation (MHg-
>Hg2)
First-order rate constant for methylation (Hg2-
>MHg)
First-order rate constant for oxidation (HgO-
>Hg2)
First-order rate constant for reduction (Hg2-
>HgO)
Length of time for chemical amount to be
reduced by one-half by degradation reactions
Applicable
Chemicals
all
all
MHg
Hg2
HgO
Hg2
organics
September 2002
D-26
TRIM.FaTE TSD Volume II
-------
Appendix D
Tables of TRIM.FaTE Input Parameters
Chemical-Dependent - Biotic
Terrestrial Plant Compartment Types3
Parameter Name
(TSD Symbol)
TRIM FaTE Code Name
Input Units
Description
Applicable
Chemicals
Leaf Compartment Type
Initial concentration
Transfer factor to leaf particle (TLeaf^LeafP)
Demethylation rate (kDm)
Methylation rate (kM)
Oxidation rate (k0)
Reduction rate (kR)
Half-life (half-life)
initialConcentration_g_per_kg
TransferFactortoLeafParticle
DemethylationRate
MethylationRate
OxidationRate
ReductionRate
Halflife
g/kg
1/day
1/day
1/day
1/day
1/day
day
Leaf concentration at beginning of modeling
period (wet wt basis)
First-order rate constant for transfer from leaf to
leaf particle
First-order rate constant for demethylation (MHg-
>Hg2)
First-order rate constant for methylation (Hg2-
>MHg)
First-order rate constant for oxidation (HgO->Hg2)
First-order rate constant for reduction (Hg2->HgO)
Length of time for chemical amount to be reduced
by one-half by degradation reactions
all
all
MHg
Hg2
HgO
Hg2
organics
Particle-on-Leaf Compartment Type
Initial concentration
Transfer factor to leaf (TLeafP^Leaf)
Demethylation rate (kDm)
Methylation rate (kM)
Oxidation rate (k0)
Reduction rate (kR)
Half-life (half-life)
initialConcentration_g_per_kg
TransferFactortoLeaf
DemethylationRate
MethylationRate
OxidationRate
ReductionRate
Halflife
g/kg
1/day
1/day
1/day
1/day
1/day
day
Particle on leaf concentration at beginning of
modeling period (dry wt basis)
First-order rate constant for transfer from leaf
particle to leaf
First-order rate constant for demethylation (MHg-
>Hg2)
First-order rate constant for methylation (Hg2-
>MHg)
First-order rate constant for oxidation (HgO->Hg2)
First-order rate constant for reduction (Hg2->HgO)
Length of time for chemical amount to be reduced
by one-half by degradation reactions
all
all
MHg
Hg2
HgO
Hg2
organics
September 2002
D-27
TRIM.FaTE TSD Volume II
-------
Appendix D
Tables of TRIM.FaTE Input Parameters
Chemical-Dependent - Biotic
Terrestrial Plant Compartment Types3
Parameter Name
(TSD Symbol)
TRIM FaTE Code Name
Input Units
Description
Applicable
Chemicals
Root Compartment Type - Nonwoody Plants Only"
Initial concentration
Alpha for root-root zone bulk soil (a)
Alpha for root-soil water interaction (a)
Root/root-zone-soil-water partition
coefficient (KRoot.SrW)
talpha for root-root zone bulk soil (ta)
Demethylation rate (kDm)
Methylation rate (kM)
Oxidation rate (k0)
Reduction rate (kR)
Half-life (half-life)
initialConcentration_g_per_kg
Root_RootZonePartitioningBulkSoil
_AlphaofSteadyState
RootSoilWaterlnteraction_Alpha
Root_RootZonePartitioningBulkSoil
_PartitionCoefficient
Root_RootZonePartitioningBulkSoil
_TimetoReachAlphaofSteadyState
DemethylationRate
MethylationRate
OxidationRate
ReductionRate
Halflife
g/kg
unitless
unitless
m3[water]/m3[root]
day
1/day
1/day
1/day
1/day
day
Root concentration at beginning of modeling
period (wet wt basis)
Proportion of equilibrium value reached
Proportion of equilibrium value reached
Equilibrium ratio of concentration in root to
concentration in root zone
Time to reach 100a percent of equilibrium
First-order rate constant for demethylation (MHg-
>Hg2)
First-order rate constant for methylation (Hg2-
>MHg)
First-order rate constant for oxidation (HgO->Hg2)
First-order rate constant for reduction (Hg2->HgO)
Length of time for chemical amount to be reduced
by one-half by degradation reactions
all
Hg species
organics
Hg species
Hg species
MHg
Hg2
HgO
Hg2
organics
Stem Compartment Type - Nonwoody Plants Only"
Initial concentration
Transpiration stream concentration factor
(TSCF)
Demethylation rate (kDm)
Methylation rate (kM)
Oxidation rate (k0)
initialConcentration_g_per_kg
TSCF
DemethylationRate
MethylationRate
OxidationRate
g/kg
g[chemical]/m3[xylem]
per
g[chemical]/m3[soil
pore water])
1/day
1/day
1/day
Stem concentration at beginning of modeling
period (wet wt basis)
Ratio of concentration dissolved in xylem fluid to
concentration dissolved in soil pore water
First-order rate constant for demethylation (MHg-
>Hg2)
First-order rate constant for methylation (Hg2-
>MHg)
First-order rate constant for oxidation (HgO->Hg2)
all
Hg species
MHg
Hg2
HgO
September 2002
D-28
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Chemical-Dependent - Biotic
Terrestrial Plant Compartment Types3
Parameter Name
(TSD Symbol)
Reduction rate (kR)
Half-life (half-life)
TRIM FaTE Code Name
ReductionRate
Halflife
Input Units
1/day
day
Description
First-order rate constant for reduction (Hg2->HgO)
Length of time for chemical amount to be reduced
by one-half by degradation reactions
Applicable
Chemicals
Hg2
organics
aTRIM.FaTE currently includes four kinds of terrestrial plants: deciduous forest, coniferous forest, grasses/herbs, and agricultural.
bRoots and stems are not modeled for deciduous and coniferous forest in the current version of TRIM.FaTE.
September 2002
D-29
TRIM.FaTE TSD Volume II
-------
Appendix D
Tables of TRIM.FaTE Input Parameters
Chemical-Dependent - Biotic
Aquatic Plant Compartment Type
Parameter Name
(TSD Symbol)
TRIM FaTE Code Name
Input Units
Description
Applicable
Chemicals
Macrophyte Compartment Type
Initial concentration
Alpha for macrophyte (a)
Macrophyte/water partition coefficient
(KMP-W)
Oxidation rate (k0)
talpha (ta)
Half-life (half-life)
initialConcentration_g_per_kg
WaterColumnDissolvedPartitioning
_Alphaof Equilibrium
WaterColumnDissolvedPartitioning
_PartitionCoefficient
OxidationRate
WaterColumnDissolvedPartitioning
_TimeToReachAlphaofEquilibrium
Halflife
g/kg
unitless
L[water]/kg[macroph
yte]
1/day
day
day
Macrophyte concentration at beginning of
modeling period (wet wt basis)
Proportion of equilibrium value reached
Equilibrium ratio of concentration in macrophyte to
concentration dissolved in water
First-order rate constant for oxidation (HgO->Hg2)
Time to reach 100a percent of equilibrium
Length of time for chemical amount to be reduced
by one-half by degradation reactions
all
Hg species
Hg species
Hg species
Hg species
organics
September 2002
D-30
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Chemical-Dependent -- Biotic
Terrestrial Animal Compartment Types
Parameter Name
(TSD Symbol)
TRIM FaTE Code Name
Input Units
Description
Applicable
Chemicals
Soil Detritivore - Earthworm
Initial concentration
Alpha for earthworm-soil pore water (a)
Alpha for worm-bulk soil (a)
Earthworm/dry-soil partition coefficient
v'xJworm-Sr-dry/
talpha for earthworm-soil pore water (ta)
talpha for worm-bulk soil (ta)
Half-life (half-life)
initialConcentration_g_per_kg
WormSoilWaterlnteraction_alpha
WormSoillnteraction_alpha
WormSoil Parti tionCoefficient_drywe
ight
WormSoilWaterlnteraction_t_alpha
WormSoil lnteraction_t_alpha
Halflife
g/kg
unitless
unitless
kg [soil dry
wt]/kg[worm dry wt]
day
day
day
Earthworm concentration at beginning of modeling
period (wetwt basis)
Proportion of equilibrium value reached
Proportion of equilibrium value reached
Equilibrium ratio of concentration in earthworm to
concentration in soil (dry wt basis)
Time to reach 100a percent of equilibrium
Time to reach 100a percent of equilibrium
Length of time for chemical amount to be reduced
by one-half by degradation reactions
all
organics
Hg species
Hg species
organics
Hg species
organics
Soil Detritivore - Soil Arthropod
Initial concentration
Alpha for arthropod-soil (a)
Arthropod/bulk-soil partition coefficient
(KArth-Sr)
talpha for arthropod-soil (ta)
Half-life (half-life)
initialConcentration_g_per_kg
ArthropodSoilPartitioning_AlphaofE
quilibrium
Arthropod_SoilPartitionCoefficient
ArthropodSoilPartitioning_TimetoRe
achAlphaofEquilibrium
Halflife
g/kg
unitless
kg[soil wet
wt]/kg[arthropod wet
wt])
day
day
Soil arthropod concentration at beginning of
modeling period (wetwt basis)
Proportion of equilibrium value reached
Equilibrium ratio of concentration in arthropod to
concentration in soil
Time to reach 100a percent of equilibrium
Length of time for chemical amount to be reduced
by one-half by degradation reactions
all
all
all
all
organics
All Other Terrestrial Animal Compartment Types3
Initial concentration
Assimilation efficiency for inhalation
(AEAir)
Assimilation efficiency from arthropods
(AEArth)
initialConcentration_g_per_kg
InhalationAssimilationEfficiency
AssimilationEfficiencyFromArthropo
ds
g/kg
unitless
unitless
Terrestrial animal concentration at beginning of
modeling period (wetwt basis)
Fraction of amount of chemical breathed that is
actually absorbed by the animal
Fraction of amount of chemical in arthropods
eaten that is actually absorbed by the animal
all
all
all
September 2002
D-31
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Chemical-Dependent -- Biotic
Terrestrial Animal Compartment Types
Parameter Name
(TSD Symbol)
Assimilation efficiency from food (AETw!)
Assimilation efficiency from plants
(AEp|ant)
Assimilation efficiency from soils (AES)
Assimilation efficiency from water (AEW)
Assimilation efficiency from worms
(AEyvorm)
Total elimination rate (kET)
Demethylation rate (kDm)
Methylation rate (kM)
Oxidation rate (k0)
Reduction rate (kR)
TRIM FaTE Code Name
AssimilationEfficiencyFromFood
AssimilationEfficiencyFromPlants
AssimilationEfficiencyFromSoils
AssimilationEfficiencyFromWater
AssimilationEfficiencyFromWorms
TotalExcretionRate
DemethylationRate
MethylationRate
OxidationRate
ReductionRate
Input Units
unitless
unitless
unitless
unitless
unitless
1/day
1/day
1/day
1/day
1/day
Description
Fraction of amount of chemical in food eaten that
is actually absorbed by the animal
Fraction of amount of chemical in plants eaten
that is actually absorbed by the animal
Fraction of amount of chemical in soils eaten that
is actually absorbed by the animal
Fraction of amount of chemical in drinking water
that is actually absorbed by the animal
Fraction of amount of chemical in worms eaten
that is actually absorbed by the animal
First-order rate constant for elimination of
chemical from the body (in urine, feces, feathers,
fur)
First-order rate constant for demethylation (MHg-
>Hg2)
First-order rate constant for methylation (Hg2-
>MHg)
First-order rate constant for oxidation (HgO->Hg2)
First-order rate constant for reduction (Hg2->HgO)
Applicable
Chemicals
all
all
all
all
all
Hg species
MHg
Hg2
HgO
Hg2
aTRIM.FaTE currently includes the following terrestrial animal compartment types: Terrestrial Ground-invertebrate Feeder - American Woodcock, Terrestrial Ground-
invertebrate Feeder - Black-capped Chickadee, Terrestrial Ground-invertebrate Feeder - Short-tailed Shrew, Terrestrial Ground-invertebrate Feeder - Trowbridge Shrew,
Terrestrial Herbivore - Bobwhite Quail, Terrestrial Herbivore - Cow, Terrestrial Herbivore - Long-tailed Vole, Terrestrial Herbivore - Meadow Vole, Terrestrial Herbivore -
Mule Deer/Black-tailed Deer, Terrestrial Herbivore - White-tailed Deer, Terrestrial Insectivore - Tree Swallow, Terrestrial Omnivore - American Robin, Terrestrial Omnivore
- Mouse, Terrestrial Predator/Scavenger- Long-tailed Weasel, and Terrestrial Predator/Scavenger- Red-tailed Hawk.
September 2002
D-32
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Chemical-Dependent - Biotic
Semi-aquatic Animal Compartment Types3
Parameter Name
(TSD Symbol)
Initial concentration
Assimilation efficiency for inhalation
(AEAir)
Assimilation efficiency from arthropods
(AEArth)b
Assimilation efficiency from food
(AETwl)(AEFish)c
Assimilation efficiency from plants
(AEPlant)b
Assimilation efficiency from soils (AES)
Assimilation efficiency from water (AEW)
Assimilation efficiency from worms
(AEyvorm)
Total elimination rate (kET)
Demethylation rate (kDm)
Methylation rate (kM)
Oxidation rate (k0)
Reduction rate (kR)
TRIM FaTE Code Name
initialConcentration_g_per_kg
InhalationAssimilationEfficiency
AssimilationEfficiencyFromArthropods
AssimilationEfficiencyFromFood
AssimilationEfficiencyFromPlants
AssimilationEfficiencyFromSoils
AssimilationEfficiencyFromWater
AssimilationEfficiencyFromWorms
TotalExcretionRate
DemethylationRate
MethylationRate
OxidationRate
ReductionRate
Input Units
g/kg
unitless
unitless
unitless
unitless
unitless
unitless
unitless
1/day
1/day
1/day
1/day
1/day
Description
Semiaquatic animal concentration at beginning of
modeling period (wet wt basis)
Fraction of amount of chemical breathed that is
actually absorbed by the animal
Fraction of amount of chemical in arthropods eaten
that is actually absorbed by the animal
Fraction of amount of chemical in food eaten that is
actually absorbed by the animal
Fraction of amount of chemical in plants eaten that
is actually absorbed by the animal
Fraction of amount of chemical in soils eaten that is
actually absorbed by the animal
Fraction of amount of chemical in drinking water that
is actually absorbed by the animal
Fraction of amount of chemical in worms eaten that
is actually absorbed by the animal
First-order rate constant for elimination of chemical
from the body (in urine, feces, feathers, fur)
First-order rate constant for demethylation (MHg-
>Hg2)
First-order rate constant for methylation (Hg2-
>MHg)
First-order rate constant for oxidation (HgO->Hg2)
First-order rate constant for reduction (Hg2->HgO)
Applicable
Chemicals
all
all
all
all
all
all
all
all
Hg species
MHg
Hg2
HgO
Hg2
aTRIM.FaTE currently includes the following semi-aquatic animal compartment types: Semi-aquatic Omnivore - Mallard, Semi-aquatic Omnivore - Mink, Semi-aquatic
Omnivore - Raccoon, Semi-aquatic Piscivore - Common Loon, Semi-aquatic Piscivore - Kingfisher, and Semi-aquatic Predator/Scavenger - Bald Eagle.
bParameter applies only to Semi-aquatic Omnivore - Mallard.
CTSD uses two symbols, one for terrestrial wildlife and one for fish.
dParameter applies only to Semi-aquatic Omnivore - Raccoon.
September 2002
D-33
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Chemical-Dependent -- Biotic
Aquatic Animal Compartment Types
Parameter Name
(TSD Symbol)
TRIM FaTE Code Name
Input Units
Description
Applicable
Chemicals
Benthic Invertebrate Compartment Type
Initial concentration
Alpha (a)
Benthic invertebrate-bulk sediment
partition coefficient (KB|.Sed)
Clearance constant (CLU)
talpha (U
Proportionality constant (pc)
Half-life (half-life)
initialConcentration g per kg
SedimentPartitioning_AlphaofEquilibri
um
SedimentPartitioning_PartitionCoeffic
lent
ClearanceConstant
SedimentPartitioning_TimeToReachA
IphaofEquilibrium
V_d
Halflife
g/kg
unitless
kg[sediment wet
wt]/kg[invertebrates
wetwt]
L[water
cleared]/kg[BI wet wt]
hr
day
L[water]/kg[BI wet
wt]
day
Benthic invertebrate concentration at beginning of
modeling period (wet wt basis)
Proportion of equilibrium value reached
Equilibrium ratio of concentration in benthic
invertebrate to concentration in sediment
Rate of water passing over respiratory surface
scaled to benthic invertebrate mass
Time to reach 1 0Oa percent of equilibrium
Ratio of concentration in benthic invertebrates to
concentration in water
Length of time for chemical amount to be reduced
by one-half by degradation reactions
all
Hg species
Hg species
organics
Hg species
organics
organics
All Fish Compartment Types3
Initial concentration
Gamma_fish (YASF)
Demethylation rate (kDm)
Methylation rate (kM)
Oxidation rate (k0)
Reduction rate (kR)
Half-life (half-life)
initialConcentration g per kg
Gamma_fish
DemethylationRate
Methylation Rate
OxidationRate
ReductionRate
Halflife
g/kg
unitless
1/day
1/day
1/day
1/day
day
Fish concentration at beginning of modeling period
(wet wt basis)
Allometric scaling factor used in estimating gill
uptake
First-order rate constant for demethylation (MHg-
>Hg2)
First-order rate constant for methylation (Hg2-
>MHg)
First-order rate constant for oxidation (HgO->Hg2)
First-order rate constant for reduction (Hg2->HgO)
Length of time for chemical amount to be reduced
by one-half by degradation reactions
all
organics
MHg
Hg2
HgO
Hg2
organics
September 2002
D-34
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Chemical-Dependent -- Biotic
Aquatic Animal Compartment Types
Parameter Name
(TSD Symbol)
TRIM FaTE Code Name
Input Units
Description
Applicable
Chemicals
Water-column Carnivore Compartment Type
Alpha for water-column carnivore (a)
Assimilation efficiency from food (AED)
Elimination adjustment factor
Fish(water-column carnivore)-fish(water-
column omnivore) partition coefficient
\"^Fwcc-Fwco/
talpha for water-column carnivore (ta)
OmnivorePartitioning_AlphaofEquilibr
ium
AssimilationEfficiencyFromFood
HowMuchFasterHgEliminationlsThan
ForMHg
OmnivorePartitioning_PartitionCoeffic
lent
OmnivorePartitioning_TimeToReach
AlphaofEquilibrium
unitless
unitless
unitless
kg[Fwco wet
wt]/kg[Fwcc wet wt]
day
Proportion of equilibrium value reached
Fraction of amount of chemical in food eaten that
is actually absorbed by the fish
Factor used to adjust experimental data on
elimination rate for MHg to HgO and Hg2
Equilibrium ratio of concentration in water-column
carnivore to concentration in water-column
omnivore
Time to reach 1 0Oa percent of equilibrium
Hg species
all
Hg species
Hg species
Hg species
Water-column Herbivore Compartment Type
Alpha for algae (a)
Assimilation efficiency from food (AED)
Elimination adjustment factor
Fish (water-column herbivore)-algae
partition coefficient (KFwch.Aigae)
talpha for algae (ta)
AlgaePartitioning_AlphaofEquilibrium
AssimilationEfficiencyFromFood
HowMuchFasterHgEliminationlsThan
ForMHg
AlgaePartitioning_PartitionCoefficient
AlgaePartitioning_TimeToReachAlph
aofEquilibrium
unitless
unitless
unitless
kg[algae wet
wt]/kg[Fwch wet wt]
day
Proportion of equilibrium value reached
Fraction of amount of chemical in food eaten that
is actually absorbed by the fish
Factor used to adjust experimental data on
elimination rate for MHg to HgO and Hg2
Equilibrium ratio of concentration in water-column
herbivore to concentration in algae
Time to reach 1 0Oa percent of equilibrium
Hg species
all
Hg species
Hg species
Hg species
Water-column Omnivore Compartment Type
Alpha for water-column herbivore (a)
Assimilation efficiency from food (AED)
Elimination adjustment factor
Fish (water-column omnivore)-fish (water-
column herbivore) partition coefficient
(Kpwco-Fwch)
HerbivorePartitioning_AlphaofEquilibr
ium
AssimilationEfficiencyFromFood
HowMuchFasterHgEliminationlsThan
ForMHg
HerbivorePartitioning_PartitionCoeffic
lent
unitless
unitless
unitless
kg[Fwch wet
wt]/kg[Fwco wet wt]
Proportion of equilibrium value reached
Fraction of amount of chemical in food eaten that
is actually absorbed by the fish
Factor used to adjust experimental data on
elimination rate for MHg to HgO and Hg2
Equilibrium ratio of concentration in water-column
omnivore to concentration in water-column
herbivore
Hg species
all
Hg species
Hg species
September 2002
D-35
TRIM.FaTE TSD Volume II
-------
Appendix D
Tables of TRIM.FaTE Input Parameters
Chemical-Dependent -- Biotic
Aquatic Animal Compartment Types
Parameter Name
(TSD Symbol)
talpha for water-column herbivore (ta)
TRIM FaTE Code Name
HerbivorePartitioning_TimeToReach
AlphaofEquilibrium
Input Units
day
Description
Time to reach 1 0Oa percent of equilibrium
Applicable
Chemicals
Hg species
Benthic Carnivore Compartment Type
Alpha for benthic omnivore (a)
Assimilation efficiency from food (AED)
Elimination adjustment factor
Fish(benthic carnivore)-fish(benthic
omnivore) partition coefficient (KFbc.Fbo)
talpha for benthic omnivore (ta)
BenthicOmnivorePartitioning_Alphaof
Equilibrium
AssimilationEfficiencyFromFood
HowMuchFasterHgEliminationlsThan
ForMHg
BenthicOmnivorePartitioning_Partitio
nCoefficient
BenthicOmnivorePartitioning_TimeTo
ReachAlphaofEquilibrium
unitless
unitless
unitless
kg[Fbo wet
wt]/kg[Fbc wet wt]
day
Proportion of equilibrium value reached
Fraction of amount of chemical in food eaten that
is actually absorbed by the fish
Factor used to adjust experimental data on
elimination rate for MHg to HgO and Hg2
Equilibrium ratio of concentration in benthic
carnivore to concentration in benthic omnivore
Time to reach 1 0Oa percent of equilibrium
Hg species
all
Hg species
Hg species
Hg species
Benthic Omnivore Compartment Type
Alpha for benthic omnivore (a)
Assimilation efficiency from food (AED)
Elimination adjustment factor
Fish(benthic omnivore)-benthic
invertebrate partition coefficient (KFbo.B|)
talpha for benthic omnivore (ta)
BenthiclnvertebratePartitioning_Alph
aofEquilibrium
AssimilationEfficiencyFromFood
HowMuchFasterHgEliminationlsThan
ForMHg
BenthiclnvertebratePartitioning_Partit
ionCoefficient
BenthiclnvertebratePartitioning_Time
ToReachAlphaofEquilibrium
unitless
unitless
unitless
kg[BI wet wt]/kg[Fbo
wt wt]
day
Proportion of equilibrium value reached
Fraction of amount of chemical in food eaten that
is actually absorbed by the fish
Factor used to adjust experimental data on
elimination rate for MHg to HgO and Hg2
Equilibrium ratio of concentration in benthic
omnivore to concentration in benthic invertebrate
Time to reach 1 0Oa percent of equilibrium
Hg species
all
Hg species
Hg species
Hg species
aTRIM.FaTE currently includes the following fish compartment types: Benthic Carnivore,
column Omnivore.
Benthic Omnivore, Water-column Carnivore, Water-column Herbivore, and Water-
September 2002
D-36
TRIM.FaTE TSD Volume II
-------
Appendix D
Tables of TRIM.FaTE Input Parameters
Source, Meteorological, and Other Input Data and Settings
Parameter Name
(TSD Symbol)
TRIM FaTE Code Name
Input Units
Description
Source Inputs (all TRIM.FaTE source properties)3
Emission rate (needed for each
chemical emitted)
Source location
Source height
emissionRate
X, Y
elevation
g/day
x and y spatial coordinates
m
Quantity of chemical emitted from the source per
unit time
X-and Y-coordinates of the source (can be
designated as UTM or latitude/longitude)
Height of the emission point(s) above ground level
Meteorological Inputs (all TRIM.FaTE scenario properties)0
Air temperature (T)
Horizontal wind speed (v or u)c
Wind direction (•&)
Rainfall rate (rain)
Day/night (IsDay)
Ai rTe m pe ratu re_K
horizontalWindSpeed
windDirection
Rain
isDay
degrees K
m/sec
degrees clockwise from N (blowing
from)
m3[rain]/m2[surface area]-day
1=day, 0=night
Temperature of the air
Wind speed horizontally between volume elements
Direction from which the wind is blowing (degrees
clockwise from due north)
Amount of precipitation per unit surface area and
unit time
Day/night switch; used for certain plant algorithms
Other Settings (all TRIM.FaTE scenario properties)
Start of simulation
End of simulation
Simulation time step
Output time stepd
simulationBeginDateTime
simulationEndDateTime
simulationTimeStep
N/A
date/time
date/time
hr
hr
The starting date and time for the modeling period
The inclusive ending date and time for the modeling
period
The duration (hours) of each time increment at
which the model calculates and stores a new
moles/mass distribution; must be an integer value
The time increment at which the model reports a
new moles/mass distribution (based on distributions
calculated at simulation time steps); must be an
integer value and evenly divisible by the selected
simulation time step
Separate source inputs are needed for each source modeled.
September 2002
D-37
TRIM.FaTE TSD Volume II
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Appendix D
Tables of TRIM.FaTE Input Parameters
Source, Meteorological, and Other Input Data and Settings
Parameter Name
(TSD Symbol)
TRIM FaTE Code Name
Input Units
Description
The meteorological parameter "mixing height" is not required for any algorithms, but can be used to set the vertical boundary (top) of a layer of air volume elements. The
meteorological parameter "stability class" is not currently used in any algorithms, but may be in the future and is a required model input (named stabilityClass, input as an
integer value of 1 through 6, representing stability classes A through F, respectively). (Because it is not currently used in any algorithms, dummy values may be used as
inputs, if desired).
'When multiple layers of air compartments are modeled, vertical wind speed (m/sec, positive for up and negative for down) is also an input parameter. To date, the
modeling of multiple air layers in TRIM.FaTE has not been fully implemented and tested.
dNot a direct model input, but set using the scenario property, simulationStepsPerOutput (simulationStepsPerOutput is determined by dividing the desired output time step
by the selected simulation time step).
September 2002
D-38
TRIM.FaTE TSD Volume II
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TECHNICAL REPORT DATA
(Please read Instructions on reverse before completing)
1. REPORT NO.
EPA-453/R-02-011b
2.
4. TITLE AND SUBTITLE
Total Risk Integrated Methodology. TRIM. FaTE
Technical Support Document. Volume II: Description of
Chemical Transport and Transformation Algorithms.
7. AUTHOR(S)
9. PERFORMING ORGANIZATION NAME AND ADDRESS
U.S. Environmental Protection Agency
Office of Air Quality Planning and Standards
Emissions Standards &
Air Quality Strategies and Standards Divisions
Research Triangle Park, NC 2771 1
12. SPONSORING AGENCY NAME AND ADDRESS
3. RECIPIENT'S ACCESSION NO.
5. REPORT DATE
September, 2002
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NO.
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
13. TYPE OF REPORT AND PERIOD COVERED
Technical Report
14. SPONSORING AGENCY CODE
EPA/200/04
15. SUPPLEMENTARY NOTES
Supplements EPA-453/R-02-0 11 A; Supercedes EPA-452/D-98-001 and EPA-453/D-99-002B.
16. ABSTRACT
This report is part of a series of documentation for the Total Risk Integrated Methodology (TRIM). TRIM
is a time series modeling system, with multimedia capabilities, designed for assessing human health and
ecological risks from hazardous and criteria air pollutants. The detailed documentation of TREVI's logic,
assumptions, equations, and input parameters is provided in comprehensive technical support documents for
each of the three TRIM modules, as they are developed. This report documents the Environmental Fate,
Transport, and Ecological Exposure module of TRIM (TREVI.FaTE) and is divided into two volumes. The
first volume provides a description of terminology, model framework, and functionality of TRIM.FaTE, and
the second volume presents a detailed description of the algorithms used in the module.
17.
a. DESCRIPTORS
Risk Assessment
Multimedia Modeling
Exposure Assessment
Air Pollutants
18. DISTRIBUTION STATEMENT
Release Unlimited
KEY WORDS AND DOCUMENT ANALYSIS
b. IDENTIFIERS/OPEN ENDED TERMS
Air Pollution
19. SECURITY CLASS (Report)
Unclassified
20. SECURITY CLASS (Page)
Unclassified
c. COSATT Field/Group
21. NO. OF PAGES
298
22. PRICE
EPA Form 2220-1 (Rev. 4-77) PREVIOUS EDITION IS OBSOLETE
-------
United States Office of Air Quality Planning and Standards Publication No. EPA 453/R-02-01 Ib
Environmental Protection Emissions Standards & Air Quality Strategies and Standards Divisions September 2002
Agency Research Triangle Park, NC
------- |