United States
Environmental Protection
Agency
EPA-452/D-98-001
March 1998
Air
THE TOTAL RISK INTEGRATED METHODOLOGY
TECHNICAL SUPPORT DOCUMENT
FOR THE TRIM.FaTE MODULE
DRAFT
Environmental Fate
6 Transport Module
(TRIM.FaTE) / AB
nra
Office of Air Quality Planning & Standards
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Disclaimer
This document was developed by the U.S. Environmental Protection Agency, in conjunction with
the Lawrence Berkeley National Laboratory (through Interagency Agreement DW89937865601),
Oak Ridge National Laboratory (through Interagency Agreement DW8993786601), IT
Corporation (through Contract No. 68-D-30094, Work Assignment No. 4-18), and TRJ
Environmental, Inc. (as a subcontractor to IT Corporation, under Contract No. 68-D-30094,
Work Assignment No. 4-18). Any opinions, findings, conclusions, or recommendations are
those of the authors and do not necessarily reflect the views of reviewers, individuals named in
the acknowledgments, the U.S. Environmental Protection Agency, the U.S. Department of
Energy, Lawrence Berkeley National Laboratory, Oak Ridge National Laboratory, FT
Corporation, or TRJ Environmental, Inc. Comments on this document should be addressed to
Amy Vasu, U.S. Environmental Protection Agency, Office of Air Quality Planning and
Standards, MD-15, Research Triangle Park, North Carolina 27711.
^K***1**1
Ctuca&o,
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Table of Contents.
Page
List of Tables vi
List of Figures viii
List of Acronyms x
Acknowledgment xii
1.0 Introduction 1-1
1.1 OAQPS Modeling Needs 1-2
1.2 TRIM Model Design 1-2
1.3 Review of Existing Fate and Transport Models 1-5
1.4 The Need for an Improved Fate and Transport Modeling Tool: TRIM.FaTE ... 1-9
1.5 Uniqueness of TRIM.FaTE 1-10
2.0 Conceptual Framework for TRIM.FaTE 2-1
2.1 TRIM.FaTE Terminology and Basic Concepts 2-1
2.2 Governing Mass Balance Equations 2-5
2.3 Modeling Approach 2-10
2.3.1 Problem Definition 2-12
2.3.2 Link Setup 2-12
2.3.3 Simulation Setup 2-13
2.3.4 Simulation Implementation 2-13
2.3.5 Result Analysis 2-13
2.3.6 Sensitivity Analysis 2-13
2.4 Summary of TRIM.FaTE Approach 2-14
3.0 TRIM.FaTE Prototype Development 3-1
3.1 Implementation of Prototypes 3-1
3.2 Prototype Development 3-2
3.2.1 Prototype 1 3-2
3.2.2 Prototype 2 3-4
3.2.3 Prototype 3 3-6
3.2.4 Prototype 4 3-8
3.3 Prototype Features 3-8
3.3.1 Abiotic Domains 3-8
3.3.2 Biotic Domains 3-9
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Table of Contents (Continued).
Page
3.3.3 Links 3-10
4.0 Algorithm Generalizations 4-1
4.1 Fate and Transport Processes 4-1
4.2 Multiple-Phase Calculations 4-2
4.2.1 Normalization to Liquid Phase 4-3
4.2.2 Application to Soil, Surface Water, and Sediment Domains 4-7
4.2.3 Multiphase Partitioning in the Air Domain 4-8
4.2.4 Calculation of the Fraction of Contaminant Bound to Aerosol 4-10
4.3 Converting Equations with Equilibrium Relationships to Dynamic Form 4-11
4.4 Advective Processes 4-12
4.5 Diffusive Processes 4-13
4.6 Reaction and Transformation Processes 4-21
5.0 Pollutant Transport in Soil and Groundwater 5-1
5.1 Conceptualization of the Soil Domain Type 5-1
5.2 General Mass-Transfer Issues 5-1
5.3 Derivation of Soil Transfer Factors 5-3
5.3.1 Advective Processes 5-3
5.3.2 Diffusive Processes 5-3
5.3.3 Total Transfer Factors 5-5
5.3.4 Lateral Runoff 5-5
5.3.5 Erosion 5-8
5.4 Groundwater 5-9
6.0 Pollutant Transport in Air 6-1
6.1 Conceptualization of the Air Domain 6-1
6.2 Calculation of Air Cell Dimensions 6-3
6.3 Calculation of Air Cell Horizontal Wind Velocities 6-5
6.4 Calculation of Air Cell Vertical Wind Velocities 6-6
6.5 General Mass-Transfer Issues Between Air and Air 6-6
6.6 Derivation of Air-to-Air Transfer Factors 6-7
6.7 Derivation of Air-to-Soil Transfer Factors 6-7
6.8 Derivation of Soil-to-Air Transfer Factors 6-10
7.0 Pollutant Transport in Surface Water and Sediment 7-1
11
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Table of Contents (Continued).
Page
7.1 Conceptualization of the Surface Water (Lake) and Sediment Domains 7-1
7.2 Advective Processes 7-2
7.2.1 Advective Processes Between Air and Surface Water 7-3
7.2.2 Advective Processes Between Sediment and Surface Water 7-4
7.2.3 Advective Processes Between Sediment/Surface Water and Advective
Sinks 7-5
7.2.4 Advective Process Across a Thermocline 7-7
7.3 Derivation of River Parcel Transfer Factors 7-8
7.4 Transformation Chemical Losses 7-8
7.5 Diffusive Processes 7-9
8.0 Pollutant Transport in Plants 8-1
8.1 Conceptualization of the Plant Domain 8-1
8.2 Leaf Cell 8-3
8.2.1 Transfer from Air 8-1
8.2.2 Diffusion Between Leaf and Air 8-5
8.3 Root Cell 8-6
8.4 Xylem Liquid Cell 8-8
8.5 Stem Cell 8-10
8.6 Litterfall 8-12
8.7 Summary of Important Limitations of Plant Model in the Prototype 8-13
8.7.1 Plant Growth 8-13
8.7.2 On the Plant vs. In the Plant 8-13
8.7.3 Plant Domains 8-13
9.0 Pollutant Transport in the Aquatic Food Web 9-1
9.1 Conceptualization of the Aquatic Food Web System 9-1
9.2 Benthic Community Transfers 9-3
9.3 Water Column Transfers 9-6
9.4 Food Chain Transfer Equations for Fish Domain 9-7
9.5 Derivation of Aquatic Macrophyte Transfer Equations 9-11
9.6 Ongoing Development 9-12
10.0 Contaminant Transport in Terrestrial Food Chain 10-1
10.1 Terrestrial Wildlife Algorithms 10-1
10.2 Earthworm Model 10-3
iii
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Table of Contents (Continued).
Page
10.2.1 Implementation of Earthworm Model if Concentrations are in
Equilibrium with other Soil Phases 10-4
10.2.2 Implementation of Earthworm Model if Steady-State Equations are
Converted to Time-Dependent Form 10-7
11.0 Code and Data Structures 11-1
11.1 Basic Code Features 11-1
11.2 General Program Flow 11-3
11.3 Data Structures 11-3
11.4 Implementation of the Volume Element Structure 11-3
11.5 Implementation of Algorithm Library 11-6
11.6 Necessity of Sinks 11-7
11.7 Lessons Learned 11-7
12.0 Test Case Application of the TRIM.FaTE Prototype 12-1
12.1 Description of Environmental Setting 12-1
12.2 Mapping the Ecosystem for the TRIM.FaTE Prototype 12-4
12.3 Input Data 12-8
12.4 Description of Model Runs 12-8
12.5 Results of Phase Calculations 12-9
12.6 Results of Constant Meteorology Runs 12-9
12.6.1 Results for No Precipitation, East Wind Direction Scenario 12-10
12.6.2 Results for Precipitation, East Wind Direction Scenario 12-14
12.6.3 Comparative Analysis 12-15
12.6.4 Results for All Runs - Constant Meteorology 12-17
12.6.5 Mass and Concentration Distribution in Biota 12-19
12.7 Variable Meteorology 12-25
13.0 Evaluation of TRIM.FaTE 13-1
13.1 Comparison with Other Models (SimpleBOX and CalTOX) 13-1
13.2 Sensitivity Analysis for TRIM.FaTE 13-2
13.3 Overall Capabilities 13-6
13.3.1 Time Scales 13-6
13.3.2 Spatial Scales 13-7
13.3.3 Chemical Classes 13-7
13.4 Limitations 13-7
iv
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Table of Contents (Continued).
Page
13.5 Conclusions from Developmental Work on TRM.FaTE 13-9
13.5.1 Prototype Algorithms and Mathematical Structure 13-10
13.5.2 Input Data Needs, Verification, and Validation 13-10
14.0 Bibliography 14-1
Appendices to the TSD Report
A Glossary
B Data Inputs Selection/Justification
B.I Data Table and References
B.2 Distribution Data for Terrestrial Wildlife
C. Results from TRIM.FaTE Prototype 2 and 3 Simulations
D Algorithm Library
E User's Guide
E. 1 User's Guide Outline
E.2 Prototype 4.0 Implementation
F Documentation of Software and Routines
F. 1 Properties of Class Modules
F.2 LSODE Steady State
F.3 Spatial Routines Implemented
F.4 Alpha Version
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List of Tables.
Number Title Page
3-1 Types of Abiotic Domains and Number of Volume Elements Modeled 3-9
3-2 Biotic Domains Modeled 3-11
3-3 Examples of Links Associated with Domains 3-12
4-1 Summary of Volumetric Advective Flow Velocities Considered in
TRIM.FaTE Prototype 4-14
4-2 Summary of Diffusion Mass Transfer Coefficients Considered in TRIM.FaTE
Prototype 4-22
5-1 Summary of the Processes by Which Contaminants are Exchanged
Between Soil Cells in The TRIM.FaTE Prototype 5-2
7-1 Summary of the Gains and Losses for Surface Water Cells Considered
in the Prototype 7-2
8-1 Summary of Gains and Losses for Plant Model Cells Implemented in the
Prototype 8-2
8-2 Parameters for Leaf Cell of Plant Model 8-3
8-3 Parameters for Root Cell of Plant Domain 8-8
8-4 Parameters for Xylem Cell of Plant Domain 8-10
8-5 Parameters for Stem Cell of Plant Model 8-12
9-1 Summary of Gains and Losses for Aquatic Biota Cells Implemented in the
TRIM.FaTE Prototype 9-2
9-2 Aquatic Population Assumptions 9-3
9-3 Aquatic Biota Assumptions 9-4
9-4 The Prototype Aquatic Food Web in the TRIM.FaTE Prototype 9-4
10-1 Terrestrial Wildlife Defined for TRIM.FaTE Prototype 10-1
11-1 Features of Implementation of the TRIM.FaTE Prototype 11-1
11 -2 Domains Considered in the TRIM.FaTE Prototype 11 -2
11 -3 Outline of General Program Flow to Create Transition Matrices in the
TRIM.FaTE Prototype 11 -4
11 -4 Primary Hierarchy of Data Structures in the TRIM.FaTE Prototype 11 -5
11 -5 Lessons Learned with the TRIM.FaTE Prototype 11 -8
12-1 Domains Simulated in the TRIM.FaTE Prototype 12-5
12-2 Links Associated with Domains in the TRIM.FaTE Prototype 12-6
12-3 Databases Consulted in Developing the TRIM.FaTE Prototype 12-7
VI
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List Of Tables (Continued).
Number Title Page
12-4 Predicted Phase Distribution for B(a)P and Phenanthrene in Abiotic Media
for Equilibrium 12^9
12-5 Predicted Steady-State Results (No Precipitation, East Wind Direction
Scenario) 12-14
12-6 Predicted Steady-State Results (Precipitation, East Wind Direction Scenario) 12-14
12-7 Predicted Distribution by Domain Type (No-Precipitation Scenario) 12-18
12-8 Predicted Distribution by Domain Type (Precipitation Scenario) 12-18
12-9 Prediced Distribution in Biota by Domain Type (No Precipitation Scenario) 12-20
12-10 Predicted Distribution in Biota by Domain Type (Precipitation Scenario) 12-22
12-11 Uptake Fractions for Specialized Fish Domains in Parcel Q (Precipitation,
East Wind Direction Scenario) 12-24
13-1 Parameters with High Sensitivity Scores for B(a)P 13-5
vn
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List of Figures.
Figure Title Follows Page
1-1 Conceptual Overview 1-4
2-1 Conceptual Blueprint for TRIM.FaTE 2-2
2-2 First Order Transfer Process for Two Cells 2-6
2-3 Simplified Ecosystem 2-9
2-4 Structure of TRIM.FaTE 2-11
3-1 Conceptual Site Model for Prototype 1 3-3
3-2 Conceptual Site Model for Prototype 2 3-5
3-3 Conceptual Site Model for Prototype 3 3-7
6-1 Typical Boundary Layer During High Pressure 6-2
6-2 TRIM.FaTE Boundary Layer Representation 6-4
12-1 Plan View for Study Area in the TRIM.FaTE Prototype 12-2
12-2 Cross Sectional View for Land, River, and Lake Parcels in the TRIM.FaTE
Prototype 12-3
12-3 Predicted Steady State Spatial Distribution of B(a)P and Phenanthrene
Wind Due East, No Precipitation 12-11
12-4 Transfer Factors for Select Parcels in the TRIM.FaTE Prototype 12-12
12-5 Predicted Steady State Spatial Distribution of B(a)P and Phenanthrene
Wind Due East, Precipitation 12-16
12-6 Steady State Concentrations of B(a)P in Biota and Soil in a Forested
Parcel, No Precipitation 12-22
12-7 Steady State Concentrations of Phenanthrene in Biota and Soil in a Forested
Parcel, No Precipitation 12-22
12-8 Wind Direction (degrees) Profile for TRIM.FaTE Prototype, Clockwise
from Due North Towards Direction of Wind 12-26
12-9 24-Hour Precipitation (mm/hr) Profile for TRIM.FaTE Prototype 12-26
12-10 B(a)P Fraction of Mass Distribution for Parcels in TRIM.FaTE Prototype,
Variable Meteorologist Conditions 12-27
12-11 Phenanthrene Mass Distribution for Select Domains in TRIM.FaTE Prototype,
Variable Meteorological Conditions 12-27
12-12 Phenanthrene Fraction of Mass Distribution for Parcels in TRIM.FaTE
Prototype, Variable Meteorological Conditions 12-28
12-13 B(a)P Mass Distribution in Biota for TRIM.FaTE Prototype, Variable
Meteorological Conditions 12-28
vm
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List Of Figures (Continued).
13-1 Model Comparison for B(a)P 13-3
13-2 Model Comparison for Phenanthrene 13-3
IX
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List of A crony mi
B(a)P
BCF
BL
CAA
CalTOX
CRARM
CSM
DLL
DISC
EPA
g
GIS
ISMCM
IT
kg
KOC
L
LSODE
Mg
m2
m^
MCM
mL
ML
NAS
ng
NWS
OAQPS
PI
P2
P3
P4
PAH
PC
benzo(a)pyrene
bioconcentration factor
boundary layer
Clean Air Act
California Department of Toxic Substance Control's model
Congressional Risk Assessment and Risk Management
conceptual site model
dynamic link libraries
Department of Toxic Substance Control
U.S. Environmental Protection Agency
gram
Geographic Information System
Integrated Spatial Multimedia Compartmental Model
IT Corporation
kilogram
soil adsorption coefficient
liter
Livermore Solver for Ordinary Differential Equation
microgram
square meter
cubic meter
multimedia compartment model
milliliter
mixed layer
National Academy of Sciences
nanogram
National Weather Service
Office of Air Quality Planning and Standards
Prototype 1
Prototype 2
Prototype 3
Prototype 4
polyaromatic hydrocarbon
personal computer
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List Of Acronyms (Continued).
RL residual layer
SAB Scientific Advisory Board
SBL stable boundary layer
SMCM spatial multimedia compartment model
TRIM Total Risk Integrated Methodology
TRIM.FaTE TRIM Environmental Fate, Transport, and Exposure
XI
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A cknowledgments
The U.S. Environmental Protection Agency (EPA) would like to acknowledge the significant
contributions of individuals from the following organizations to the development of the Total
Risk Integrated Methodology (TRIM) and the TRIM.FaTE Module: Lawrence Berkeley National
Laboratory, Oak Ridge National Laboratory, International Technology Corporation, and TRJ
Environmental, Inc.
xn
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1.0 Introduction
The Office of Air Quality Planning and Standards (OAQPS) of the U.S. Environmental
Protection Agency (EPA) is responsible for the evaluation of health risks associated with air
pollutants and for the regulation of those pollutants, if needed. To date, OAQPS has not
consistently estimated multimedia impacts of air pollutants and has used distinctly different .
methodologies to estimate risks from hazardous air pollutants (HAP) and criteria air pollutants.
While numerous models exist for use in risk assessment, there is no one model or modeling
system which meets the needs of OAQPS. As a result, OAQPS is developing the Total Risk
Integrated Methodology (TRIM), a multimedia, time-series simulation modeling system for the
assessment of human and ecological risks resulting from hazardous and criteria air pollutants.
TRIM represents an improved risk assessment tool which:
• Meets the requirements of the Clean Air Act of 1990 (CAA).
• Meets the scientific requirements/capabilities identified by the National Academy
of Sciences (NAS), the Presidential/Congressional Commission on Risk Assess-
ment and Risk Management (CRARM), and the EPA.
TRIM will provide a framework that is scientifically defensible, flexible, and user-friendly, for
characterizing human health and ecological risk and exposure to hazardous and criteria air
pollutants.
The TRIM status report summarizes the work performed during the first phase in the develop-
ment of the TRIM modeling system for review by the EPA's Scientific Advisory Board (SAB).
The first phase of the developments is a significant milestone for this project and includes the
conceptualization and implementation of an overall modeling infrastructure for TRIM, quanti-
fication of the mathematical structure of the Environmental Fate, Transport, and Exposure
(TRIM.FaTE) component of the TRIM modeling system, and testing and validation of these
concepts. The status report for the SAB provides detailed information about the overall structure
TRIM and the various steps undertaken to test TRIM.FaTE. This technical support document to
the status report for the SAB review provides more of the technical details related to
TRIM.FaTE.
This chapter presents the conceptual approach for TRIM, a review of current models and
discusses the need for TRIM.FaTE. The conceptual approach to TRIM.FaTE and its prototypes
are discussed in Chapters 2.0 and 3.0, respectively. Chapter 4.0 describes the algorithm genera-
1-1
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lizations and mathematical rules underlying the TRIM.FaTE mathematical structure. Chapters
4.0 through 10.0 describe the development of the algorithms for each environmental media. The
outputs, the comparison of the outputs, and overall result evaluations are presented in Chapter
12. Appendices A through F contain a glossary, input parameter information, results of
TRIM.FaTE prototypes, the algorithm library, a user's guide outline and information on how to
run the prototype, and the alpha version of the prototype with supporting information, respec-
tively.
1.1 OAQPS Modeling Needs
Based on the recommendations of the NAS and the CRARM, as well as the current EPA guide-
lines and policies, in combination with the CAA requirements, OAQPS recognized the need for
improvements in risk and exposure assessment tools. OAQPS currently has a variety of tools for
HAP and criteria air pollutant exposure and risk assessments, although several significant
features were determined to be lacking in the current models. To be consistent with the recom-
mendations of the NAS and the CRARM, as well as EPA guidelines and policies, OAQPS needs
modeling tools that: (1) have multimedia assessment capabilities; (2) have ecosystem risk and
exposure modeling capabilities; (3) can perform multi-pollutant assessments (e.g., assess
mixtures of pollutants, track chemical transformations); (4) can explicitly address uncertainty and
variability; and (5) are readily available and user-friendly, so that they can be used by EPA, state
and local agencies, and other stakeholders. OAQPS also needs HAP exposure and risk models
that adequately estimate temporal and spatial patterns of exposures and that maintain mass-
balance. While many current OAQPS criteria air pollutant exposure and risk models have these
advanced features, the HAP models do not. Finally, OAQPS and others recognize the
importance of having modeling tools with the capability to model pollutant uptake, biokinetics,
and dose-response for HAPs and criteria air pollutants where possible and relevant.
A risk and exposure assessment model, or set of models, with all of the previously noted features
does not exist. Although individual models that perform individual functions do exist, none of
these, separately or in combination with other models, provide an integrated system that could
function to meet the modeling needs previously described. Therefore, to meet the specific
modeling needs of OAQPS, the conceptual framework for TRIM was developed.
1.2 TRIM Model Design
TRIM will provide a framework for assessing human health and ecological risks resulting from
multimedia contamination (in air, water, soil, and food) and multipathway exposure (via
inhalation, ingestion, and absorption exposure routes) to HAPs and criteria pollutants. TRIM
1-2
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will be a dynamic modeling system that tracks the movement of pollutant mass through a
comprehensive system of compartments, providing an inventory of a pollutant throughout the
entire system. The compartments will be able to represent possible locations of the pollutant in
the physical and biological environments of a defined study area or species. Receptors may
move through these compartments for the estimation of exposure. Uptake, biokinetics, and dose-
response models may be used to determine dose and health impacts. The model will address
uncertainty and variability issues by evaluating a range of parameters.
The goal in developing TRIM is to create a modeling system that is complex enough to appro-
priately characterize human health and ecological risk and exposure, yet simple enough to be
useful in performing risk analyses for use in regulatory decision making. An extremely simple
modeling approach may be too restrictive to support risk and exposure assessments across the
CAA programs. An extremely complex model may be too difficult to initialize or may require
prohibitive amounts of data. The aim of developing TRIM is to suppress the less necessary
details and to focus on the processes that have the most significant impact on human health and
ecological risk.
For the development of TRIM, existing models and tools will be adopted, where possible.
Incorporating existing models or model features into a modeling tool that meets OAQPS needs is
preferable because it is most efficient and cost-effective approach.
As shown in Figure 1-1, TRIM is designed to be modular and will be an assembly of six primary
modules. Depending on the user's need for a particular assessment, it may be possible to use any
one or more of these modules for an assessment. The first TRIM module, TRIM.FaTE, accounts
for movement of the pollutant mass through the ecosystem and determines the pollutant concen-
tration in media and biota. Exposures will be evaluated within the TRIM Exposure Event
Module by tracking small population groups of humans and/or other organisms, referred to as
"cohorts," through time and space. Also included in TRIM will be a Pollutant Uptake Module,
which will determine the quantity of a pollutant entering an organism during a specific exposure
event; a Biokinetics Module, which will determine the quantity of a pollutant delivered to a
target organ; and a Dose-Response Module, which will estimate health effects caused by the
pollutant quantity delivered to a target organ. The final module of TRIM, the Risk Characteri-
zation Module, will present the risk estimates, assumptions, and uncertainties. A brief summary
of each module follows.
1-3
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Figure 1-1
Conceptual Overview of TRIM
Air Quality Models
(e.g., ISC3, AERMOD)
Monitoring Data
Environmental Fate
and Transport
(TRIM.FaTE)
Physical, Chemical,
Properties
Site Specific Data
GIS Data
Temporal and Spatial
Distribution of
Pollutant Concentration
Activity Data
(e.g., CHAD)
Population Data
(e g., 1990 BOC)
GIS Data
Other Multimedia Models
(e.g., MEND-TOX,...)
Temporal and Spatial
Distribution of
Exposure Level
within Exposed
Population
55"
Biokinetics
Temporal and Spatial
Distribution of
Absorbed Dose
Pollutant Uptake
Temporal and Spatial
Distribution of Target
Dose
Temporal and Spatial
Distribution of
Responses
Population Risk Estimates
Measure of Uncertainty
Limitations Description
Risk Characterization
1-4
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1.3 Review of Existing Fate and Transport Models
The first step in the model development process was to evaluate EPA and non-EPA approaches
already existing in the fields of non-inhalation exposure assessment that may meet or contribute
to the needs of the TRIM approach. In April 1996, a review of existing models and approaches
was undertaken as part of the initial step in the TRIM development effort. The report, entitled
Evaluation of Existing Approaches for Assessing Non-Inhalation Exposure and Risk with Recom-
mendations for Implementing TRIM (Mosier, et al., 1996), examined several multimedia models.
Two additional EPA studies (EPA, 1997a,b) conducted in 1997 have updated the 1996 study.
The literature searches identified several models/approaches for multimedia, multipathway
modeling for evaluation, including EPA's Indirect Exposure Methodology (IEM2), the California
Department of Toxic Substance Control's Multimedia Risk Computerized Model (CalTOX), the
Integrated Spatial Multimedia Compartmental Model (ISMCM), and the Multimedia Environ-
mental Pollutant Assessment System (MEPAS).
Efforts to assess human exposure from multiple media date back to the 1950s, when the need to
assess human exposure to global fallout led rapidly to a framework that included transport both
through and among air, soil, surface water, vegetation, and food chains (Wicker and Kirchner,
1987). Efforts to apply such a framework to non-radioactive organic and inorganic toxic
chemicals have been more recent and have not as yet achieved the level of sophistication that
exists in the radioecology field. In response to the need for multimedia models in exposure
assessment, a number of multimedia transport and transformation models have recently appeared.
Thibodeaux (1996, 1979) proposed the term "chemodynamics" to describe a set of integrated
methods for assessing the cross-media transfers of organic chemicals. The first widely used
multimedia compartment modeling for organic chemicals were the "fugacity" models proposed
by Mackay (1991, 1979) and Mackay and Paterson (1982, 1981). Cohen and his co-workers
applied the concept of multimedia compartment modeling as a screening tool with Multimedia
Compartment Model (MCM) (Cohen and Ryan, 1985), followed by the Spatial Multimedia
Compartment Model (SMCM) (Cohen, et al., 1990), and more recently with ISMCM, which
allows for non-uniformity in some compartments. Another multimedia screening model, called
GEOTOX (McKone and Layton, 1986) was one of the earliest multimedia models to explicitly
address human exposure. The CalTOX program (McKone, 1993a,b,c) has been developed for
the California EPA as a set of spreadsheet models and spreadsheet data sets to assist in assessing
human exposures for toxic substances releases in multiple media. More recently, SimpleBOX,
Version 2.0 (Brandes, et al., 1997) has been developed for the National Institute of Public Health
and the Environment in the Netherlands in order to evaluate the environmental fate of chemicals.
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Results can be for a level 3 (non-equilibrium, steady state) or quasi-dynamic level 4 (non-
equilibrium, non-steady state) system. All phases within the compartments are assumed to be in
a state of thermodynamic equilibrium at all times.
A brief summary of each of the multimedia models evaluated for its applicability to the TRIM
effort follows:
• Indirect Exposure Methodology (IEM2). With an interim final document
completed in 1990 (EPA, 1990) and with an addendum completed in 1993 (EPA,
1993), the IEM incorporates current EPA guidance. Descriptions of the fate and
transport, exposure pathways, and dose algorithms are presented in this methodo-
logy. This methodology sets out procedures for estimating the indirect (i.e., non-
inhalation) human exposures and health risks that can result from the transfer of
emitted pollutants to soil, vegetation, and water bodies. The methodology
addresses exposures via inhalation; food, water, and soil ingestion; and, dermal
contact. There appear to be several shortcomings in the methodology. For
example, the methodology, as currently implemented, can be applied only to
chemicals that are emitted to the air. This methodology is not a comprehensive
environmental audit, but is best regarded as an evolving and emerging process that
moves EPA beyond the analysis of potential effects associated with only one
medium (air) and exposure pathway (inhalation) to the consideration of other media
and exposure pathways. Most importantly, it is crucial in the development of
TRIM that a sense of continuity be maintained between the existing (IEM2) and
proposed (TRIM) methodologies. IEM2 has undergone extensive scientific review.
The SAB has identified several major limitations of IEM, which can be useful in
focusing efforts in TRIM development. While IEM represents the current EPA
guidance on multimedia multipathway modeling, it does not meet the needs of
OAQPS. One of the major limitations of IEM is that it consists of a one-way
process through a "train" of linked models or algorithms and is based on annual
average air concentrations, wet and dry deposition values from air dispersion
modeling. As a result, it is not a truly coupled multimedia model and thereby does
not have the ability to model "feedback" loops or secondary emissions and cannot
provide time-series estimation of media concentrations and concomitant exposure.
In addition, the methodology does not provide for flexibility in site-specific appli-
cations or in estimating population exposures. Significant site-specific adjustment
must be made to allow for spatially tracking differences in concentrations and
exposure. Much of the focus is on evaluating specific receptor scenarios (e.g.,
recreational or subsistence fisher) that may be indicative of high-end or average
exposures but does not allow for modeling the range of exposure scenarios within a
population. Therefore, IEM cannot estimate population exposure distributions.
More recent advances (Rice, et al., 1997) have addressed some of these limitations
to some degree, but have not been fully implemented.
1-6
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California Department of Toxic Substance Control's Multimedia Risk
Computerized Model (CalTOX). First issued in 1993 and updated in 1995,
with continual enhancements underway, CalTOX was developed as a spreadsheet
model for California's Department of Toxic Substance Control (DTSC), to assist in
human health risk assessments that address contaminated soils and the contami-
nation of adjacent air, surface water, sediment, and groundwater. CalTOX consists
of two component models: a multimedia transport and transformation (i.e., fate and
transport) model, which is based on both conservation of mass and chemical equili-
brium; and, a multipathway human exposure model that includes ingestion, inhala-
tion, and dermal uptake exposure routes. CalTOX is a fully mass balancing model
and also includes add-ins to quantify uncertainty and variability.
The multimedia transport and transformation model is a dynamic model that can be
used to assess time-varying concentrations of contaminants introduced initially to
soil layers or for contaminants released continuously to air, soil, or water. The
CalTOX multimedia model is a seven-compartment regional and dynamic multi-
media fugacity model. The seven compartments are (1) air, (2) ground surface soil,
(3) plants, (4) root-zone soil, (5) the vadose-zone soil below the root zone, (6)
surface water, and (7) sediment. The air, surface water, ground surface soil, plants,
and sediment compartments are assumed to be in quasi-steady state with the root-
zone soil, and vadose-zone soil compartments. Contaminant inventories in the
root-zone soil and vadose-soil zone are treated as time-varying state variables.
Contaminant concentrations in groundwater are based on the leachate from the
vadose-zone soil.
The multipathway exposure model encompasses 23 exposure pathways, which are
used to estimate average daily doses within a human population in the vicinity of a
hazardous substances release site. The exposure assessment process consists of
relating contaminant concentrations in the multimedia model compartments to
contaminant concentrations in the media with which a human population has
contact (personal air, tap water, foods, household dusts/soils, etc.). The explicit
treatment of differentiating environmental media pollutant concentration and the
pollutant concentration to which humans are exposed favorably distinguishes
CalTOX from many other exposure models. In addition, all parameter values used
as inputs to CalTOX are distributions, described in terms of mean values and a
coefficient of variation, rather than as point estimates or plausible upper values
such as most other models employ. This stochastic approach allows both sensiti-
vity and uncertainty to be directly incorporated into the model operation. This
model does not conserve mass.
As indicated in the literature review reports, the CalTOX model appears to be the
most promising existing model for application to the TRIM effort. Several of the
mathematical concepts and derivations used by the developers of CalTOX can be
directly applied to the TRIM approach. However, CalTOX does have several
limitations that prevent it from being entirely imported into the TRIM approach.
These limitations result from going beyond intended applications for CalTOX; for
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example, for landscapes in which there is a large ratio of land area to surface water
area, for a limited range of chemicals (e.g., non-ionic organic chemicals in a liquid
or gaseous state). As a result, the model does not provide adequate flexibility in
environmental settings and chemical classes (e.g., volatile metals such as mercury)
to be suitable for OAQPS needs. The most significant of these limitations, in terms
of application to TRIM, is the fact that the CalTOX model, as it currently exists,
does not allow spatial tracking of a pollutant as is required in the TRIM approach.
SimpleBox. SimpleBOX is a steady-state, non-equilibrium partitioning, mass
balance model. It consists of eight compartments, three of which are soils of
differing use and properties. It also produces quasi-dynamic (non-steady-state)
output by using an external numerical integrator. The model was developed as a
regional scale model for the Netherlands, so its default characteristics represent the
Netherlands. SimpleBOX uses the classical concentration concept to compute the
mass balance (van de Meent, 1993). Its goals are comparable to TRIM to the extent
that it simulates regional systems however its level of spatial and temporal
complexity does not match TRIM'S goals.
Integrated Spatial Multimedia Compartmental Model (ISMCM). ISMCM
has been under development with the School of Engineering and Applied Science at
University of California Los Angeles for approximately 15 years. A newer version
of ISMCM, called MEND-TOX, is currently under evaluation by the EPA Office of
Research and Development National Exposure Research Laboratory.
ISMCM considers all media, biological and non-biological, in one integrated
system. ISMCM includes both spatial and compartmental modules to account for
complex transport of pollutants through the ecosystem. Assuming mass conser-
vation, ISMCM is able to predict transport based on a sound mechanistic descrip-
tion of environmental processes, including estimation of intermedia transfer factors.
One of the limiting factors with the ISMCM system for use in the TRIM system is
that it is not structured to incorporate uncertainty/variability directly into the model
operation.
One of the limitations of the ISMCM model within the context of the goals for
TRIM (van de Water, 1995) is the fact that the links and compartments (spatial
configuration) of this model are predetermined. ISMCM was apparently not
designed from start with the necessary flexibility. Having this flexibility is not a
trivial thing to request, if the system is to be fully integrated.
Multimedia Environmental Pollutant Assessment System (MEPAS).
MEPAS was developed at the U.S. Department of Energy's (DOE) Pacific North-
west Laboratory to assess risks from mixed wastes at DOE facilities. MEPAS is a
model that can be run on IBM-compatible personal computers (PC). This model
consists of single-media transport models linked together under appropriate
boundary conditions. The model considers four primary pollutant pathways
(groundwater, overland, surface water, and atmospheric) in evaluating human
1-8
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exposure and health effects. The model also contains an exposure and risk module.
The model's ability to estimate multipathway risks for chemicals and radionuclides
makes it unique. The nature of its algorithms make it a screening tool, rather than a
detailed assessment tool. The model is updated periodically and the latest version
of MEPAS (Version 3.1) also contains a uncertainty and variability analysis module
(SUM) (Buck, et al., 1995). The mathematical design of this model does not
include mass balance and could not be integrated into TRIM.
As with EM2, MEPAS represents a "linked" model system that utilizes a one-way
process through a train of models that individually describe a specific environ-
mental process or media. These types of models are not mass conservative and do
not allow for appropriate temporal tracking of the pollutants and concomitant
exposure.
1.4 The Need for an Improved Fate and Transport Modeling Tool: TRIM.FaTE
Current OAQPS models for hazardous and criteria air pollutants do not address multimedia
exposures, and current OAQPS HAP models do not adequately estimate temporal and spatial
patterns of exposures. Adopting or incorporating existing models into a tool that meets OAQPS
needs represents the most cost-effective approach to developing the tools needed to support
regulatory decision making related to hazardous and criteria air pollutants. Based on the OAQPS
review of current multimedia models or modeling systems (described in Section 3.1), there is no
single model that meets the needs of OAQPS (outlined in Section 1.3) and that can be adopted as
part of TRIM. Most models are limited in the type of media and environmental processes
addressed. No single model can address the broad range of pollutants and environmental fate
and transport processes anticipated to be encountered by OAQPS in evaluating risks from
hazardous and criteria air pollutants. In addition, it is also not likely that one individual model
could be developed to address this wide range of concerns. Therefore, the TRIM framework
emphasizes a modular design. The lack of a flexible multimedia fate and transport model was
identified as a major limitation and has become the focus of the first phase implementation
efforts for TRIM.
Current multimedia models can be divided into three basic categories, each with its own
advantages and disadvantages: "linked" model systems, fugacity models, and compartmental
models. However, the identified limitations were considered critical and, therefore, deemed
unacceptable for incorporating such models into TRIM. "Linked" model systems (e.g., IEM2,
MEPAS) generally utilize a one-way process through a series of linked models that mathema-
tically describe distinct environmental media or processes (e.g., aquatic environment). These
types of models can never be truly mass conservative and cannot address feedback loops and
secondary pollutant movement (e.g., revolatilization and transport). Fugacity models (e.g.,
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CalTOX) typically are compartmental models without explicit spatial (zero-dimensional); thus,
they do not provide ability to spatially track pollutant movement. They are also applicable only to
a limited range of chemical classes (e.g., inappropriate to model volatile metals [e.g., mercury]).
Compartmental models (e.g., MCM) are also zero dimensional and do not allow for spatial
tracking of pollutant movement and concomitant exposures. Spatial compartmental models (e.g.,
ISMCM) represent the closest current models to an integrated multimedia system. However, as
previously described, it is does not meet the TRIM design goals for a flexible architecture.
In general, none of the current models are sufficiently coupled multimedia model that accounts for
inherent "feedback" loops or secondary emissions (i.e., re-emission of deposited pollution) or
releases to specific media, or that provides the temporal and spatial resolution critical in
estimating exposures. While it is unknown as to the degree to which modeled results would differ
between current models and a truly coupled multimedia model, models that are not truly coupled
have been considered to lack scientific credibility. Therefore, OAQPS determined it was
necessary to undertake efforts to develop a truly coupled multimedia model.
1.5 Uniqueness of TRIM.FaTE
Among the unique features of TRIM.FaTE are: (1) its flexibility to be formulated at different
spatial and temporal scales, (2) the ongoing development of an algorithm library, and (3) a full
accounting of all of the chemical mass that enters and leaves the environmental system.
TRIM.FaTE was developed to meet OAQPS modeling needs (Section 1.3) and fit the TRIM
design criteria ( Section 2.2). To meet these goals requires a multimedia framework. Also
required are true coupling of multiple media during a simulation (similar to Mackay-type models)
and a level of spatial and time-series resolution to date only obtained from linked single-media
numerical simulation models. The TRIM development team determined that TRIM must. (1)
address varying time steps (of one hour or greater) and provide sufficient spatial detail at varying
scales (site-specific to urban scale); (2) provide true "mass-conserving" results; (3) have the
transparency needed for use in a regulatory context; and, (4) be a truly coupled multimedia model
rather than a set of linked single media models. After reviewing currently available multimedia
models, the team determined that none of the available models offered all of these features. As a
result, the team engendered a new model framework that is distinct from other multimedia models
and unique among the current arsenal of EPA models.
TRIM.FaTE has a mathematical approach (Section 3.4), which makes possible: (1) different
mixes of compartment numbers, types, and links; (2) a unified approach to mass transfer based on
an algorithm library, which allows the user to change mass transfer relationships among
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compartments without creating a new program; and, (3) the flexibility to match a simulation to the
spatial and temporal scales needed for a broad range of pollutants and geographical areas.
Although some applications of TRIM.FaTE may resemble a simple fiigacity-based compartmental
model, it can be scaled to simulate time-series and spatial resolutions that current regional
fiigacity-type models could not handle. The mathematical Unking in TRIM.FaTE enables it to
simulate mass distribution within a system and attain a degree of precision not yet achieved by
other models.
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2.0 Conceptual Framework for TRIM.FaTE
The overall logic and terminology for TRIM.FaTE for expressing transport and transformation
of chemical contaminants in a multimedia environment is presented in this chapter. This chapter
also describes the processes being simulated in TRIM.FaTE, illustrates and discusses the mass
balance approach and the resulting system of differential equations for first-order systems, and
demonstrates the application of the TRIM mass-balance approach to a simple four-compartment
environmental system.
TRIM.FaTE Conceptual Blueprint. The development of TRIM.FaTE began with a
"conceptual blueprint" of the relationships and processes that describe chemical transport within
an ecosystem. This blueprint is shown in Figure 2-1. On this figure, the biota are represented by
squares, biota sinks are represented by diamonds, and the abiotic media are represented by ovals.
The various lines show possible chemical transfers occurring between each of the components of
the ecosystem. Any environment can be thought of as a complex system, and thus can be
represented using systems models that follow from the principles of system theory. All of the
different locations, geographical features, and ecosystems are then subsystems interacting with
each other. Lines may represent transfers of energy or matter, and in this case, the transfers
represent chemical contaminants.
2.1 TRIM.FaTE Terminology and Basic Concepts
Because the terminology used in the world of multimedia modeling can have multiple meanings
and implications, it is critical in the conceptualization of any complex model that terminology
used be defined specifically within the framework of that model. Multimedia models by nature
are multidisciplinary. Terminology can be confusing because a single term will have drama-
tically different meanings in different disciplines. To avoid confusion, discussion of TRIM.FaTE
terminology is presented in this section. Following the description of the terminology, a
summary is provided of the mathematical basis for TRIM.FaTE. In addition, a glossary is
included in Appendix A.
In the TRIM.FaTE model, the transport of multiple pollutant species in an ecosystem is set up as
a mass exchange among a set of systems used to represent spatial locations, collections of
environmental phases, and chemical species. The primary features of interest are the chemical
inventory and the chemical concentrations of the system as a function of time in the various
2-1
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components of the modeled system. These values are called state variables since they describe
the state of the system while it is varying (Odum, 1983).
The system being modeled is assumed to be partitioned into regions of three-dimensional space.
Each such region is referred to here as a volume element. Typically, only one type of abiotic
medium is contained in a volume element. This term is introduced as a matter of convenience
for organizing objects that have a natural spatial relationship. The region represented by a
volume element could be a cube or more complicated shape. A volume element usually shares a
surface with other volume elements. The spatial resolution of volume elements may vary from
application to application, and even within a single application.
Contained within volume elements are domains. The term "domain" is a loose equivalent of
what is referred to as "media" in environmental fate and transport modeling literature. However,
the term "media" was considered to be limited in its scope because it generally brings up images
of abiotic systems such as soil or air, while TRIM.FaTE includes both abiotic and biotic systems.
Therefore, the term domain was adopted for TRIM from the principles of systems theory to allow
for more flexibility in its definition. A domain is the material that contains a chemical(s). It is
currently assumed that, within any domain, a chemical is uniformly distributed throughout the
volume occupied by that domain. In addition, the various phases (gases, liquids, solids) that •
make up a domain are assumed to be in equilibrium with respect to chemical partitioning.
Domains can be thought of in both a general and specific sense within the TRIM.FaTE modeling
structure. In a general sense, a domain type is defined to classify overall system components
such as soil, water, or mouse, or more specific components such as surface soil or vadose zone
soil. A specific manifestation of a domain type is a domain instance. Domain instances belong
to the same domain type with similar attributes. One domain instance is distinguished from
another by the values that define its composition attributes at a given location. For example, any
"soil" domain type consists of the soil matrix, which is comprised of gas, liquid, and organic-
and mineral-solid phases. As a domain instance, a surface-soil domain instance typically has
more organic carbon than a vadose-soil domain instance. Moreover, a vadose-soil domain
instance will typically have a higher water-volume fraction than a root-soil domain instance.
Two different mouse domain instances may differ by the population size attribute. There can be
multiple domain instances within a volume element, i.e., a worm domain instance may exist
simultaneously with a surface soil domain instance in a volume element. Typically, one abiotic
domain type (soil, water, air), but multiple biotic domain types (worm, plants), can exist within a
2-3
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volume element. When there is no need for additional clarification between domain types and
domain instances, these will be referred as domains in TRIM.FaTE literature.
The set of all domain instances is assumed to contain all of the chemical mass within the eco-
system, excluding sources. A source is an external component that transfers chemical mass
directly into the domain instances. Examples of sources would include the factory emissions of a
chemical into an air domain, or the influx of chemical in a river from outside the modeled
system.
Associated with each domain instance is an inventory address or cell. A cell is a bin within the
computer code, and these cells collectively account for all potential locations of mass within the
ecosystem, and the pollutant sources and sinks outside the ecosystem that are required to balance
the overall mass flow. Each cell is uniquely defined by three indices. The first index is the
volume element. The second index identifies the domain containing the chemical at a given
location. The third index is the chemical species.
An important aspect that is tracked for each cell is the list of other cells in the system with which
it potentially exchanges chemical mass. It is necessary only to store in this list the cells from
which the cell receives mass. Elements of this list are referred to as links. With each link is
associated a sending cell and receiving cell. The sending cell is the cell from which the
chemical is potentially transported, and the receiving cell is the cell that receives the chemical.
Each specific link for any chemical may have unique properties, and hence must be considered as
an object separate from all other links. For example, a link between two particular soil cells may
contain information on the advective flow from the sending cell to the receiving cell. Another
example is the worm-to-soil cell link, which contains information on the ingestion rate of soil by
worms.
The link between domains includes information on the potential exchange of chemical between
the two domains. This information includes a transfer factor, which is the instantaneous flux
from the sending domain to the receiving domain per unit chemical mass in the sending domain.
Transfer factors are calculated based on transport and fate processes such as advection, diffusion,
dispersion, reaction, and bioaccumulation. The mathematical basis for these transfer factors is
discussed in Section 2.2. The transfer factor is determined by use of the methods in a central
repository of algorithms, called an algorithm library. Algorithms in TRIM.FaTE are equations
that expresses the transfer factor as a function of a set of variables. This function is specific to
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the locations, domains, and chemical species represented by the linked cells. Domain specific
transfer factors used in used in TRIM.FaTE are presented by domain in Chapters 5.0 through
10.0.
It is stressed that the algorithm library is not intended to consist of only documented methods;
instead, the methods must be properly entered in some standard manner so that they can be
accessed by other software. For first-order transfers, methods have been developed for conver-
ting typically encountered concentration-based equations to mass balance form. All major
methods of pollutant movement in the environment are frequently modeled with first-order
methods. These include advective processes, diffusive processes, and bioaccumulation.
2.2 Governing Mass Balance Equations
The TRIM.FaTE model is being developed with an emphasis on conserving chemical mass. This
means that the entire quantity of the chemical is tracked throughout the system being modeled.
When applied to a specific domain (e.g., soil or a mouse population), this implies that, over a
given time period, the amount of the chemical in the domain at the end of the period is equal to
the amount of the chemical in the domain at the beginning of the period, plus the gains of the
chemical that occurred during the time period, minus the chemical that was lost from the domain
during the time period.
Currently, the mass balance approach has been implemented primarily for first-order linear
processes. Therefore, this discussion is limited to models of this type. It is important to note that
higher order non-linear methods can also be implemented within this structure.
A simplification of a transfer process is shown in Figure 2-2 for a system of two volume
elements or cells, where it is assumed that the fluxes of chemical mass are first-order processes.
Denoting by Njt) and Nh(t) the mass of chemical in cells a and b, respectively (in units of mass),
it can be seen that:
Gains for cell a - Sa +
Lt)sses for cell a = T . N + R N
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and
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Tab = transfer factor for movement of chemical from cell a to cell b during time
interval, units of /time
Tba = transfer factor for movement of chemical from cell a to cell b, units of /time
Ra = reaction loss of chemical in cell a, units of /time
Rb = reaction loss of chemical in cell b, units of /time.
The constraint that mass balance must be preserved means that, over any time interval, the
change in mass in a cell is equal to the gains minus the losses in mass over the time interval. The
instantaneous change in mass with respect to time is the derivative with respect to time, denoted
by dNJdt. Thus, the mass balance constraint, when applied to the simple system discussed here,
yields a system of two linked differential equations:
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Additional terms are needed to properly account for the chemical mass. In particular, the fate of
the chemicals after reacting must be tracked. For this reason, two additional cells are added to
the system, and serve as the repository of the chemicals after reaction. These are referred to as
"sinks," since once the chemical is transferred into these cells, it no longer moves to any other
cells. While clearly the chemical would continue to move in its altered form throughout the
system, this history is not of interest. Denoting by Sinka and Sinkh, the mass in the reaction sinks
for cells a and b, respectively, the complete system is:
2-7
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Figure 2-3
Simplified Ecosystem
The ecosystem consists of:
•Two Air Cells
•Soil Cell
•Groundwater Cell (sink)
•Surface Water Cell
•Fish Cell
•Four sinks
TOTAL = 1 0 Cells
2-9
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where:
Sa, = source team for air Cell 1
T,j = transfer factors for Cell I to j
N, = mass of pollutant in Cell i
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Applying this same approach to a general system with M cells (including all sinks), and allowing
the transfer factors and source terms to depend on time as well, results in a system of linked
differential equations of the form:
dN/dt = A(t)N + s(t), N(to) = NO
where:
N(t) = an A/-dimensional vector whose /th entry is the mass in the /th cell
A(t) = an M x M time-dependent matrix
s(t) = an A/-dimensional vector accounting for the source terms in each cell.
The matrix A(t) is referred to as the transition matrix for the system. This term is borrowed from
Markov theory (Schneider and Barker, 1989), although the model is not strictly a Markov
process. The vector s accounts for pollutant sources located within specific cells. The vector N0
is the initial distribution of mass among the cells.
2.3 Modeling Approach
This section summarizes the general features of the application of the conceptual approach
previously described.
One of the primary features of the application of the TRIM approach is that it is to be an iterative
and flexible process. When the modeling process is first started, there is a general sequence that
must be followed. After the initial step, however, there is no fixed order in which the modeling
steps are necessarily performed. This process is shown in Figure 2-4. The boxes on the left side
of the figure represent a partitioning of the modeling sequence into five broad areas. These areas
include: basic problem definition, specification of links, setting up a run, performing a run, and
analysis of results. The particular division into five such areas is somewhat arbitrary, and in an
actual application, it may be that the progression is not quite as linear as that shown in the figure.
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Figure 2-4
Structure of TRIM.FaTE
PROCESS FLOW
PRIMARY TOOLS
^
w
^
k
Definition of problem
•specify volume elements
•specify domain instances
•specify data or data source(s)
for domains
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Specify links between domain
instances. For each link,
•specify algorithm to use from
available list
•specify data or data source(s)
for link
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•set initial conditions
•set source term(s)
•set output time periods of
interest
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Perform run
•Call algorithm library for each
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factors
•Calculate mass distribution in
system of domain instances at
requested time periods
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Analvsis of results
DATS"
•Spatial Data
•Flow data
•Chemical properties
•Source terms
ALGORITHM
LIBRARY
GENERAL CALCULATION TOOLS
•Differential equation solver
•Partial differential equation solver
2-11
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However, all of these steps are necessary. The vertical arrows between these boxes represent the
possible order of events in the modeling process. The arrows on the left side of the boxes
indicate the iteration that may be necessary or desired.
The shapes under the heading "Primary Tools" represent the primary tools used in the modeling
process. The arrows from these shapes to the flow boxes indicate where in the modeling process
these tools would be used. To focus on key aspects of the TRIM.FaTE approach, only selected
tools are shown. There are other tools that may be necessary that are not included in this figure.
Such tools would include pre/postprocessing software that may automate some aspects of the
process, and general user interface software.
2.3.7 Problem Definition
The first step requires the general problem definition. During this step, the chemical(s) to be
modeled and the initial spatial features of the ecosystem are determined. In the nomenclature
previously discussed, the volume elements and domain instances within the volume elements are
specified. For the first cycle through the simulation process, the spatial scales may be crude and
the number of domain instances may be small. It will be necessary at this step to specify various
types of data, or simply the sources of the data (e.g., a remote database). Data types include
spatial information about the ecosystem, chemical-specific environmental data (e.g., degradation
rates in various domain types), and data for the specified domain instances (e.g,. soil densities
and organic carbon content for soil domains).
2.3.2 Link Setup
The second step shown in Figure 2-4 specifies the links between the domain instances. Two
domains are considered "linked" if there is a direct means by which the chemical can be
exchanged. This definition does not include "indirect" links that result from a chain of direct
links (e.g., chemical is transported in eroding soil to a water domain, and subsequently taken up
by a fish population). The system of links is one of the most critical components of the model.
By specifying a link between two domains, it is assumed that some method exists by which to
estimate the transfer of chemical through the link. If this method is already included in the
algorithm library, then it is only necessary to specify the data (or data source) for this link and
which algorithm to use. These data may depend on both of the domains in the link (e.g., erosion
flow rate for link between a soil domain and a water domain). These data do not include
information about the mass of the chemical, as tracking the inventory of chemical mass with time
is the purpose of the model. If the algorithm is not in the algorithm library, then it must be
"added" so that it can be accessed by the underlying software.
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2.3.3 Simulation Setup
The third step shown in Figure 2-4 is the preparation of a simulation after the volume elements,
domain instances, and links have been specified. This involves specifying the initial distribution
of chemical mass in the domains, specifying any source terms considered within domains, and
specifying the output time period(s) of interest. The initial conditions may be specified as con-
centrations, which are then converted to mass form for the model. The "DATA" drum is connec-
ted to this step because data are necessary for the initial conditions and source term(s). The
initial conditions and source terms may be estimated from monitoring data available, or from the
results of another model.
2.3.4 Simulation Implementation
The fourth step is the actual running of the model, where the movement of the chemical(s)
through the domains is simulated for the specified time period(s). The exact manner in which
this is performed depends on the algorithms chosen. For each link between domains, a call is
made to the algorithm library to determine the transfer factors that indicate the potential
exchange of chemical mass. If all algorithms involve only first-order processes, then movement
of the chemical will be simulated with a system of linked differential equations, the solution of
which would be found using a differential equation solver. For more complicated algorithms,
other tools would be necessary (e.g., a method of solving partial differential equations).
2.3.5 Result Analysis
The last step shown in Figure 2-4 is the analysis of the results generated for the modeled system.
These results include the time history of the chemical mass and associated concentrations in the
domains. This step would also include postprocessing analysis of the results and use of the
results in other parts of the TRIM.
2.3.6 Sensitivity Analysis
An important aspect of the TRIM is the integration of sensitivity and uncertainty analyses
methods into the model framework. The reasons for a sensitivity analyses are to identify
important inputs with respect to outcome variance in order to direct efforts related to:
• Additional data collection
• Additional research
• Stratification of the population.
2-13
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Many of the parameters used in modeling of natural systems are uncertain or variable. It is
critical to confront sources and ranges of parameter variance for several reasons. Among them
are the need to determine the range of possible outcomes of the model, and the need to determine
what parameters are the important contributors to the range of outcome values generated by the
model.
The TRIM framework is designed to provide for a tiered uncertainty/sensitivity analyses in
several ways. All inputs to TRIM are entered in parameter tables where value distributions are
the default option and the labels "uncertain" or "variable" can be applied to make initial classi-
fications. The capability to conduct a joint uncertainty and variability analysis is a goal of TRIM.
Currently, the capability exists to conduct simple sensitivity analyses. Ultimately, Monte Carlo
assessments and uncertainty importance assessment capabilities will be an integral part of
TRIM.FaTE. Some limited assessment of model uncertainty is provided through the option of
selecting from alternate transport/transformation algorithms from an algorithm library.
2.4 Summary of TRIM.FaTE Approach
In this chapter, the TRIM.FaTE framework has been introduced by describing a unified
conceptual approach to multimedia mass-balance models. The term "unified" refers to the fact
that one approach has been generalized to all components of a multimedia environment,
including ecosystem components. The mass-balance approach for first-order systems reduces to
a set of linear ordinary differential equations as was illustrated in Section 2.2. However, the
approach is not limited to first-order linear methods. The modeling approach provides a flexible,
iterative process of simulating the movement of chemicals in a multimedia environment. This
makes the approach useful for addressing different types and aquatic and terrestrial ecosystems
and also for human exposure assessment. It is important to note that the approach used is not
based on linking different models for different compartments or domain instances. Instead, the
entire system is represented in a single informational structure, i.e., a large matrix. In the next
chapter, more specific examples are presented of the multimedia models that can be constructed
using this type of flexible and iterative process.
2-14
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3.0 TRIM.FaTE Prototype Development
This chapter provides a description of the process of applying the TRIM.FaTE methodology
(Chapter 2.0) to cases of increasing complexity (referred to as "prototypes"). Section 3.1
discusses the implementation of the prototypes; Section 3.2 describes the development process
for each prototype; Section 3.3 addresses the features of the prototypes, including the types of .
domains and links simulated; and Section 3.4 discusses the processes used to simulate links. The
goal of this chapter is to illustrate the flexibility of TRIM.FaTE for application at different levels
of spatial and temporal resolution. This chapter also serves to illustrate how different multimedia
configurations with TRIM.FaTE are set up.
3.1 Implementation of Prototypes
The concepts discussed in the previous chapter have been implemented in all the prototypes
using a combination of Microsoft Visual Basic™, Fortran, and Microsoft Excel™ software. These
implementations are introduced here briefly and are documented in greater detail in Chapter 11.0.
An object-oriented architecture was implemented using Visual Basic 5 application environment
imbedded within Excel 97 to model the hierarchy of components of TRIM.FaTE. This hierarchy
includes volume elements, domain types, domain instances in the volume elements, and links
between the domains. The coding architecture is not tied to any specific ecosystem configu-
ration. A preliminary algorithm library that utilizes this coding architecture was also imple-
mented.
If all transport processes are simulated as a first-order process, this results in a system of linear
ordinary differential equations as explained in Section 2.2. This system must be solved to
determine the redistribution of chemical mass as a function of time. For TRIM.FaTE, this
system is solved using the Livermore Solver for Ordinary Differential Equations (LSODE)
(Radhakrishnan and Hindmarsh, 1993), a Fortran program freely available via several online
numerical algorithm repositories.
The LSODE subroutine solves systems of first order ordinary differential equations of the form
(Hindmarsh, 1983):
dy/dt = F(t,y), y(to) = y0
where y is an n-dimensional time-dependent vector, i.e.,
3-1
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The system of differential equations can be stiff or non-stiff. In the stiff case, it treats the
Jacobian matrix (Schneider and Barker, 1989) as either a full or banded matrix. It uses Adams
(Schneider and Barker, 1989) methods (predictor-corrector) in the non-stiff case, and backward
differentiation formula methods in the stiff case. The linear systems that arise are solved by
direct methods. LSODE supersedes the older GEAR and GEARB packages.
The only restriction on the size of the system of differential equations is that imposed by
computer memory. This code was modified so that it could be accessed by Visual Basic 5 in
Excel 97. Another Fortran code was used, in a similar manner, to determine the steady-state
solution to the system of linear differential equations (Barrodole and Stuart, 1981).
Microsoft Excel spreadsheets were used for general preprocessing, postprocessing, and data
storage (additional databases for spatial data were also created using Visual Basic and accessed
by Excel). Excel spreadsheets also served as a convenient interface to the Visual Basic and
Fortran subroutines.
The approach taken for testing the methodology made it possible to investigate the implications
of draft algorithms and to work on the development of a flexible system for addressing concep-
tual site models with many domains. The pre- and postprocessing for the ultimate implementa-
tion of TRIM.FaTE may require a more sophisticated platform. However, with some modifica-
tion, much of the Visual Basic code, and all of the Fortran code, can be used in other computer
programming languages.
3.2 Prototype Development
Multiple prototypes were developed with increasing complexity to model the movement of a
pollutant through an ecosystem. This section describes features of the prototypes in increasing
order of complexity.
3.2.7 Prototype 1
Prototype 1 (PI) was set up to test the mass transfer methodology (Chapter 2.0) and the LSODE
utility. Air, soil, groundwater, surface water, and fish domains were simulated in PI as seen in
the conceptual site model shown in Figure 3-1. PI includes a uniform volume source emission
of benzene into the air volume. Benzene was selected because most of its transfer factors were
readily available from CalTOX (Maddalena, et al., 1995).
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Some transfer factors were derived independently of CalTOX for the air to air sink, soil to
groundwater, fish to water, and water to fish transfers. The remaining factors were taken directly
from CalTOX. The dimensions of the terrain were adapted from CalTOX to facilitate com-
parison of results. Chemical reaction was not simulated in this prototype.
The runs produced estimates of benzene mass throughout the system, and no problems were
experienced in running the LSODE subroutine. The resulting mass distribution of benzene in
various domains was examined qualitatively to ensure that the numerical routines were produc-
ing stable and realistic solutions. A quantitative analysis of the results were not performed
because the input parameters were selected only to test the implementation infrastructure. The
results were approximately commensurate with theoretical expectations with no unstable or
anomalous values. These results prompted further testing of the modeling approach on a more
complex ecosystem.
3.2.2 Prototype 2
Prototype 2 (P2) includes more spatial detail sophistication than PI in both the types and number
of domains used. Unlike PI, P2 included multiple volume elements for both the soil and air
domain types and included the use of plant and sediment domains. In addition, the links between
cells had multiple-phase (i.e., gas, liquid, and solid) mass transfers. P2 included a volume source
emission of benzo(a)pyrene (B[a]P) into only one of the air volumes. This made possible a very
simple representation of spatial transport. B(a)P was selected as a test chemical for this and
subsequent prototypes because of its persistence in the environment and because it is a HAP ( a
chemical of concern in the CAA). The derivation of the transfer factors are described in detail in
later chapters. The conceptual site model for P2 is shown in Figure 3-2.
Multiple-phase (liquid, gas, and solid) transport within a domain was introduced in P2. The
phases are assumed to be at chemical equilibrium, with the ratios of the concentrations in the
individual phases constant.
P2 was run for four different conditions that included constant source terms under pristine
conditions, a artificially lower organic carbon partioning coefficient (K^.) value for B(a)P, a
constant source term with non-pristine conditions in surface water, and a time-varying source-
term condition. The results and discussions of these runs are presented in Appendix C. In all
cases, under steady-state conditions, most of the B(a)P accumulated in the plants, with minimal
penetration into the subsurface. In the water column, most of the B(a)P was found in the
sediment sink, with minimal accumulation seen in the fish domain. Decrease of the K^ value
3-4
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resulted in corresponding increase in mass in subsurface soil. Only the air domain seemed to be
responsive to the varying source-term condition.
The transfer factors and steady-state outputs of P2 were compared to runs performed on CalTOX
(Maddalena, et al., 1995). Most of the transfer factors used in P2 were very similar to that in
CalTOX; the mass distributions of B(a)P were similar in the air, soil, and surface water domains
and differed by three orders of magnitude in the plant, sediment, and groundwater (aquifer)
domains. This lead to the refinement of the algorithms in the plant and sediment domains. The
difference in the groundwater masses was due to the fact that both TRIM and CalTOX have a
simple approximations to model transport in groundwater.
3.2.3 Prototypes
Prototype 3 (P3) focuses on code and input data structure refinements since the code and input
data are significantly more complex than either PI or P2. P3 was developed both to incorporate
lessons learned from P2, which has a refined set of abiotic algorithms, and to set up the
TRIM.FaTE model for the case study model run Prototype 4 (P4). P3 includes a conceptual site
that approaches the spatial scale (approximately 10-kilometer [km] radius) of the ecosystem used
for the testing the full prototype (P4). The conceptual site model for P3 is shown in Figure 3-3.
The vertical dimensions of individual air cells are not indicated because these dimensions were
allowed to vary with time according to a set of specified meteorological conditions. The soil and
surface water domains were split into finer grid structures relative to P2, and several new biotic
algorithms were added. The source term simulated in P3 was a volume-source emission of B(a)P
into only one of the four air volume elements. This was used to make an approximation to a
continuous point-source release.
The differences of P3 relative to P2 include:
• Addition of terrestrial earthworms, kingfisher, and mouse domains
• Addition of aquatic food-web system; addition of macrophyte domain
• Addition of cells with varying heights for the air domain to increase complexity
• Division of soil cells horizontally to add complexity to soil domain
• Introduction of "thermoclines" and refinement of mixing for surface water
• Refinement of plant domain algorithms
• Refinement of soil diffusion algorithms
• Addition of erosion in the soil domain
• Refinement of groundwater algorithm
• Introduction of flexible code design
• Introduction of temporal variation for a few key input parameters.
3-6
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As in the case of P2, several runs were performed for P3. The results, detailed in Appendix C,
showed that the plant, macrophyte, and sediment domains are major sinks of B(a)P in the
environment. The model showed that B(a)P mass distribution in the environment is sensitive to
total macrophyte volume in the water column. The model results were extremely responsive in
most domain to varying source-term conditions. Comparisons of P3 outputs with CalTOX
outputs showed that B(a)P mass distributions in the ecosystem being simulated were in closer
agreement than was seen in the case of P2. This was believed to be a result of refining the
algorithms as previously stated and implied that the prototype was appropriate for application to
a more complicated test case.
3.2.4 Prototype 4
Whereas PI through P3 used generic inputs and were intended for evaluation simulations, P4
was set up to be applied to an actual site. PI through P3 were used to develop and test the
TRIM.FaTE algorithms. Starting from Chapter 4.0, P4 is referred to as the TRIM.FaTE
prototype (the prototype) because P4 is a culmination of the knowledge acquired from PI
through P3 and is capable of simulating all these three cases. P4 was developed and used to
illustrate and evaluate the likely limits of TRIM.FaTE with respect to the number of land parcels
and length time steps used. This prototype had the shortest plausible time step (1 hours), a large
number of land units in the plan view (20 parcels), and 21 different biotic domain types. This
level of detail resulted in several hundred cells, including abiotic and biotic domain instances,
and the sinks needed to account for transformation and transport losses outside of the system
boundary. To test the model using a realistic ecosystem, P4 was applied to an area in the north-
western region of the United States. This prototype was developed as described in the setup
methodology in Chapter 2.0. The process of mapping the case study area into a form that is
usable in TRIM.FaTE is described in detail in the results section (Chapter 12.0).
3.3 Prototype Features
The specific features simulated in the prototypes are discussed in this section. Section 3.3.1
presents the types of abiotic domains modeled; Section 3.3.2 includes the types of biotic domains
modeled; and Section 3.3.3 discusses the abiotic and biotic links associated with the prototypes.
3.3.1 Abiotic Domains
In PI (Figure 3-1), the air, soil, and surface water each consist of a single volume element.
Groundwater was simulated simply as a sink to the soil domain. P2, as shown in Figure 3-2,
consists of an air domain that contained 4 volume elements (2 upper air and 2 lower air layers);
the soil domain, which was divided into 4 volume elements (surface soil, root zone, and vadose
3-8
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zones 1 and 2); and groundwater, surface water, and sediment, which were each simulated as a
single volume element. In P3, (Figure 3-3) the air domain consists of 6 volume elements (2
lower air and 2 upper air over soil, and a lower air and upper air over surface water); the soil
domain was divided into 32 volume elements (8 surface soil, 8 root zone, 8 vadose zone 1, and 8
vadose zone 2); groundwater and surface water were both simulated with 2 volume elements; and
sediment was simulated as a single volume element. P4 simulates 129 abiotic volume elements.
Parcels were defined in P4 and divided vertically based on domain type. The 129 abiotic domain
instances associated with the parcels in P4 are summarized in Table 3-1.
Table 3-1
Types of Abiotic Domains and Number of Volume Elements Modeled
Domain
finr
Boil
Surface Water
Sediment
TOTAL
MUMBER
Number of Volume Elements *
P1
1 - Air Layer
1 - Soil (general)
1 - Groundwater
1 - Surface
Water Layer
NA
4 Volume
Elements
P2
2 - Upper Air Layer
2 - Lower Air Layer
1 - Surface Soil
1 - Root Zone
1 - Vadose Zone 1
1 - Vadose Zone 2
1 - Groundwater
1 - Surface Water
Layer
1 - Interstitial Water
1 - Sediment
12 Volume Elements
P3
3 -Upper Air Layer
3 - Lower Air Layer
8 - Surface Soil
8 - Root Zone
8 - Vadose Zone 1
8 - Vadose Zone 2
2 - Groundwater
1 - Upper Surface
Water Layer
1 - Lower Surface
Water Layer
1 - Interstitial Water
1 - Sediment
44 Volume Elements
P4
20 -Upper Air Layer
20 - Lower Air Layer
14 -Surface Soil
14 - Root Zone
14 - Vadose Zone 1
14 - Vadose Zone 2
14 - Groundwater
1 - Upper Lake Layer
1 - Lower Lake Layer
5 - River Segments
6 - Interstitial Water
6 - Sediment
129 Volume Elements
*Reaction and advection sinks are not listed in this table.
3.3.2 Biotic Domains
In PI and P2, a single fish species is modeled and only uptake and loss of contaminant through
the gills is simulated. In the transition from P3 and P4, the number of biotic water column
domain instances was expanded from a single fish species to an aquatic food web represented by
several feeding trophic levels (domain instances). Bioaccumulation by herbivores, as well as
omnivores and carnivores, is accommodated within the P3 and P4 simulations. It is important to
note, however, that the trophic level representations were simplified to reflect primary uptake and
3-9
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loss from a single representative species from each trophic level. No natural variability specific
to individual populations or communities is accounted for in P3. In P4, distribution ranges for
parameters such as lipid content, ventilation rate, and individual size are included. For example,
the aquatic carnivore community is represented by a single finfish, the Largemouth Bass.
Both P3 and P4 include terrestrial wildlife as domain instances. Wildlife may be exposed to
contaminants through food, soil, and water ingestion, and through inhalation of contaminants in
air. Elimination of contaminants from body tissues may occur through metabolic breakdown of
the contaminant and excretion through urine, feces, milk (mammals only), and eggs (birds and
reptiles only). Terrestrial and semiaquatic biota were not considered in PI and P2. Two species
were introduced in P3: a white-footed mouse (Peromyscus leucopus) and the belted kingfisher
(Ceryle alcyon). These species were selected because they are taxonomically dissimilar
(mammal versus bird) and represent differing domains (terrestrial omnivore and semiaquatic
piscivore, respectively). P4 simulated a more complex terrestrial, aquatic, and semiaquatic
system, as summarized in Table 3-2.
P3 and P4 also simulated pollutant transfer to earthworms. The concentration in earthworms was
assumed to be in equilibrium with the solid, liquid, and vapor-phase concentrations of the
chemical in the root zone volume elements.
The plant domain was introduced to the TRIM.FaTE framework in P2. The plant component of
the ecological model implemented for P2 and subsequent prototypes is comprised of leaves,
roots, xylem, and stem. Plants are divided into these components (volume elements) because:
(1) the literature suggests that concentrations of non-ionic organic contaminants in foliage are
primarily related to those in air and that concentrations in roots are generally related to those in
soil (with stems serving as the conduit between the two), and (2) herbivores may eat part but not
all of a plant. The xylem is added for future versions of the model that may address exchanges
between volume elements in which the xylem plays a critical role. Currently, each volume
element is assumed to be homogeneously-mixed. The plant algorithms implemented in P2
through P4 are applicable for mature plants only, and do not yet address plant growth.
3.3.3 Links
If mass can move from one cell to another cell without first moving through intervening cells,
then the two cells are considered "linked." Each linkage is associated with an algorithm that
determines the direction and rate of mass flow between the two cells. Linkages may be between
adjacent volume elements or within a volume element. At a given spatial location, and within a
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Table 3-2
Biotic Domains Modeled
Domain
Aquatic
Ecosystem
Terrestrial
Ecosystem
Semi-
Aquatic
Ecosystem
P1
• Single
Fish
Species
NA
NA
P2
• Single
Fish
Species
NA
NA
P3
• Macrophytes (Benthic
Herbivores)
• Aquatic Herbivores
• Aquatic Omnivores
• Aquatic Carnivores
• White-footed Mouse
(Omnivore)
• Earthworm (Soil
Detritovore)
• Plant Leaves, Roots,
Xylem and Stem
• Belted Kingfisher
(Piscivore)
P4
• Macrophytes (Benthic
Herbivores)
• Mayfly (Benthic Herbivores)
• Bluegill (Modeled as
Herbivore)
• Channel Catfish (Omnivore)
• Bass (Carnivore)
• Mallard (Herbivore)
• Raccoon (Omnivore)
• Tree Swallow (Insectivore)
• White-footed Mouse
(Omnivore)
• Earthworm (Soil Detritovore)
• Black-capped Chickadee
(Insectivore)
• Red-tailed Hawk (Predator)
• Long-tailed Weasel (Predator)
• Black-tailed Deer (Herbivore)
• Long-tailed Vole (Herbivore)
• Mink (Piscivore)
• Trowbridge Shrew (Ground
Invertebrate Feeder)
• Insects
• Plant Leaves, Roots, Xylem
and Stem
• Belted Kingfisher (Piscivore)
• Wetland Plant Leaves, Roots,
Xylem and Stem
single volume element, more than one domain may exist and linkages may exist between these
domains. The mass transfer algorithm specific to each linkage was based on review of the
appropriate scientific literature and is discussed in detail in later chapters.
Table 3-3 shows examples of generalized linkages applied to PI through P4. This table is
generic and can be used in conjunction with Tables 3-1 and 3-2 to define a specific link. For
example, in P2 through P4, transfer of a pollutant can occur from an upper air cell to adjacent
upper air cells and to a lower air cell. This is represented in Table 3-3 by the air (sending
domain) to air (receiving domain) link. A more complex example is the links associated with the
kingfisher from the semi-aquatic ecosystem. As a receiving domain, pollutant(s) can transfer to
the kingfisher from air (i.e., lower air), soil (i.e., surface soil), surface water (i.e., upper lake
layer), and aquatic (i.e., bluegill) ecosystems.
3-11
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Table 3-3
Examples of Links Associated with Domains
Sending Domain
Air
Soil
Groundwater
Surface Water
Sediment
Terrestrial Ecosystem
Aquatic Ecosystem
Semi-Aquatic Ecosystem
Receiving Domain
Air
Soil
Surface Water
Terrestrial Ecosystem
Semi-Aquatic Ecosystem
Air
Soil
Groundwater
Surface Water
Terrestrial Ecosystem
Semi-Aquatic Ecosystem
Groundwater
Surface Water
Surface Water
Sediment
Aquatic Ecosystem
Semi-Aquatic Ecosystem
Terrestrial Ecosystem
Surface Water
Aquatic Ecosystem
Terrestrial Ecosystem
Air
Soil
Aquatic Ecosystem
Semi-Aquatic Ecosystem
Terrestrial Ecosystem
Surface Water
Terrestrial Ecosystem
Air
Soil
Surface Water
The links from sending domains to sinks are not shown in Table 3-3. Sinks refer to the cells of
pollutant mass leaving the ecosystem through a reaction or physical process(es). Section 4.1
describes these processes.
3-12
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4.0 Algorithm Generalizations
One of the goals of the TRIM modeling framework is to develop underlying generalizations,
estimation techniques or "rules," for application of algorithms. During the development of the
transfer factors for the prototypes, common rules were observed. These rules were functions of
the physics and chemistry of the transport processes rather than the domains. For example,
abiotic transport from one cell to another has the same mathematical form for all domains.
Some of these rules were refined after study of their documentation in the literature (McKone,
1993a,b,c; MacKay, 1991). This section documents these underlying rules for use in subsequent
prototypes in order to simplify algorithm development. These rules were observed as a conse-
quence of building the transfer factors for the different abiotic domains and are presented before
the domain specific algorithms because the rules are common across all the abiotic domains.
Primary processes used to simulate pollutant movement in the abiotic domains are diffusion and
advection. These are key components of the overall transfer rates. The transport occurs both in
the gas and liquid phase for organic chemicals.
4.1 Fate and Transport Processes
In the biotic domain, equilibrium relationships describing processes like bioaccumulation and
biomagnification were converted to a non-equilibrium form that could be used in the mass
transfer equations.
An advective process is one in which a chemical is transported within a given phase that is
moving from one cell to another (Mackay [1991]) refers to this as a piggyback process, in which
a chemical is "piggybacking" on material that is moving from one place to another for reasons
unrelated to the presence of the chemical). Mathematically, all that is required to calculate the
advective flux is the velocity of the moving phase, and the amount of the chemical that is in the
moving phase. Examples of advective processes considered for transport of a chemical from the
soil domain to the surface water domain are erosion of surface soil, runoff from surface soil, and
recharge from groundwater.
In a diffusion process, a chemical is transported from one cell to another as a result of the
magnitude and direction of the concentration differences between the two domain instances at the
interface between the two locations. This means that the direction of flux is not necessarily
constant with time. Estimates of effective diffusivity for a chemical species in gas and liquid-
phase diffusion were used to estimate the diffusive transfer rates.
4-1
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Reaction and transformation processes are modeled using either a specified reaction/transfor-
mation rate or transformation half-life. In all cases, the mass of chemical transformed in a given
cell is assumed to be lost from the system. To make possible a complete mass balance for the
entire environmental system being modeled, this sink is modeled as an additional cell that
receives input only from the particular cell.
Reaction transformation processes include such processes as biodegradation, photolysis,
hydrolysis, oxidation/reduction, and radioactive decay. These are processes that transform a
chemical species into another chemical species; they do not involve a change of location or a
change of domain.
It is also possible that a chemical species transfers from one domain instance to another at the
same location. Possible examples include the non-equilibrium transfer of a chemical from the
fluid (liquid/gas) phases of soil to the solid phase, the uptake of a chemical by fish from water, or
the uptake of a chemical by worms from soil. These processes do not involve a change of
location or a change of chemical species. These processes are typically expressed in terms of the
half-time to equilibrium. The half-time to equilibrium is typically measured in one direction, i.e.,
from water to fish or from soil to worm.
4.2 Multiple-Phase Calculations
This section describes how multiple phases within a domain are modeled in the prototype.
Phases considered in the prototype are liquid, gas, and solid, and are assumed to be at chemical
equilibrium. Because chemical equilibrium is assumed, the ratios of the concentrations in the
individual phases are constant, and mass balance need only be tracked for the total amount of the
chemical in all phases in a cell. The amount of chemical in the cell in a particular phase can be
determined from the total amount in the cell (described in the following text). It is possible that,
in later prototypes, chemical equilibrium will not be assumed, in which case the amount of
chemical in different phases will need to be tracked as separate cells.
In any cell, the total amount of chemical in a given cell is made up of the sum of the amounts in
the different phases:
4-2
-------
, °'a = Amount in gas phase + Amount in aqueous phase + Amount in solid phase
_ .-, gas-ii go* (-* water,, water ,-, solid,, solid
- C, K, + C, Vt C, V,
where:
N,Total = total amount of chemical in domain/cell, units of grams (g) (chemical)
C,gas = concentration of chemical in gas phase in domain/cell, units of g (chemical)/
cubic meter (m3) (gas) in domain
V,*" = volume of gas in domain/cell, units of m3 (gas) in domain
£ water _ concentration of chemical in aqueous phase in domain/cell, units of
g (chemical)/m3 (water) in domain
y water _ vo}ume of aqueous matter in domain/cell, units of volume (aqueous)] in
domain
£ solid _ concentration of chemical in solid phase in domain/cell, units of
g (chemical)/m3 (solid) in domain
V™''J = volume of solid in domain/cell, units of m3 (solid) in domain.
If it is desired that the units of N,Toial be in units of moles (chemical), then the preceding equation
must be multiplied by the molecular weight of the chemical (which has units of moles
[chemical]/g [chemical]).
Since chemical equilibrium is assumed, the ratios of the concentrations are constant. However,
care must be used in specifying what the units of the concentrations are. This is because, in
practice, it is more common to define notation for ratios of concentrations on a mass basis other
than that of mass by volume basis.
4.2.1 Normalization to Liquid Phase
This section describes the relevant formulas when the concentrations are normalized to the
concentration in the liquid phase. This normalization is utilized in the prototype for all soil,
surface water, and sediment cells. Using the equilibrium assumptions:
,, mlid _ . ]f f \ (" Hfl'er
C" = (HIRT)C*ater
4-3
-------
where:
Psoiid = density of solid phase in cell, units of kilograms (kg) (solid phase)/m3 (solid
phase)
Kd = equilibrium partition coefficient; ratio of concentration in solid phase (units
of kg[chemical]/kg[solid phase]) to that in liquid phase (units of
kg[chemical]/liters [L] [liquid phase])
Cf = 10~3 m3/L, conversion factor to convert m3 (liquid phase) to L (liquid phase)
H = Henry's law constant for chemical, units of Pa-m3/mol
R = ideal gas constant, 8.314 m3-Pa/mol-K
T = temperature, units of degrees K:
Applying these relationships to the general equation in the beginning of this section yields:
»r Total _ ^, wate rl H ,, gas y water n v /-• iftolid\
' ' ( ~RT '
The volumes of each phase in the domain can be expressed as fractions of the total volume of the
cell, in which case the previous equation yields:
Total_ ,-. water,,Total
,, #
-------
c
»r Total,, , Total
H V,
gas
,, Total ,, Total
i i
_ H .^ water _
~ ~RT '
,s»Ud\
Jsol,d"d^f vTola,
> J
(HIRT)N™IV™
solid
T r
H
gas
, water
j
, solid
Total
V ,
P solid Kj Cf :
/~*\ \r
^-
Total,-,, Total
^r vT<"al
•,, water
* i
y Total Ps°1'
,, solid
4 ti f
J ,. Total
For cases in which the concentration in the water phase is negligible (e.g., when domain is the
atmosphere, or the chemical has a very low solubility), the concentrations must be normalized to
another phase.
The preceding equation can be simplified by using the notation of fugacity. Fugacity has the
units of pressure and is linearly or nonlinearly related to concentration through the relationship
fugacity (f) = (fugacity capacity [Z])(concentrations), as defined by Mackay (1991). The fugacity
capacities for the pure phases are defined by Mackay, 1991.
'solid ~ P solid
-------
phase i z
i phase |
phase.,
where phase is either the solid, liquid, or gas phase.
Applying these relationships shows that:
7 M T"lal 7
,-, water _ water i _ water,-, total
^^ ^^^—~*—~ ^^™^~~ ~~ ^~~ v^ 0
7 f»/a/ r r 7Y>/a/ 7 ww/
A */ A
Z AT r°'a/ Z
C#as _ air i _ #aj f* total
— ~~—~— — ^
™ »»la/ , 7 Total ^r total
...,, 2
C
N Total y
solid_ ^solid "i _ ^solid total
™ ;«ia/ T > To/a/ ™ w/a/
Zi Vi Zi
where C,r'"a' is the total concentration of the chemical in the cell (units of g [chemical]/m3[total
cell]). From these relationships, in general, the amount of mass in the different phases is given
by:
7 ., /»/u( 7 7
, , water _, , water *-, water _ ,, water Hater i _,, water water water si total
' ' ' '7 total ,, Total ' 7 total 7 total '
L> V, Zi Lt
7 \f Total 7 7
A/ ^at = r **" V *"* = V Kas "tr ' = V*"* Kas Kas C '"'
' ' ' '7 total ,, Total ' 7 total 7 total '
A vi A A
7 », TVxa/ 7 7
,., solid_f,.solid,, solid_ ,, solid solid i _\/5"'"' .«»/«/ solid *-• total
' ' ' '7 fora/ ., Total ' 7 «>/a/ 7 total '
A v< A A
where N*""r, N,*1", and N,s"llJ are the mass in the water, gas, and solid phases, respectively.
In the following sections, these general equations are applied to the soil and surface water
domains. These "applications" involve only adhering to notation commonly used in the literature
for the different media.
4-6
-------
4.2.2 Application to Soil, Surface Water, and Sediment Domains
For soil, surface water, and sediment domains, the concentrations are normalized to the concen-
tration in the water phase, and the same notation is used to represent the relevant parameters. In
a soil cell, the solid phase consists of the soil particles. In a surface water cell, the solid phase
consists of the sediment suspended in the water column. In a sediment cell, 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. Following common practice, the volume fractions of each
phase are denoted as follows:
—=1-6-6=1-A.
10101 ' ' '
where:
0, = water volume fraction
e, = gas volume fraction
1-6,-e, = 1-4),= solid volume fraction.
where
-------
For the groundwater, surface water, and sediment domains, the volume fractions of the gas phase
(e,) are assumed to be zero.
In the prototype, the partition coefficients, soil-water, Kj in each cell (soil, surface water, and
sediment) are calculated in a manner applicable for nonionic organic chemicals (Karickhoff
1981, as cited in California Department of Toxic Substance Control's CalTOX model [McKone,
1993a,b,c,p. 25]) by:
where:
KIIC = organic-carbon partition coefficient
foc = fraction of organic carbon in the cell/domain.
4.2.3 Multiphase Partitioning in the Air Domain
Since the volume of water in an air domain is so small relative to the volume of the solid and the
gas phase, there has not been a historical development of Kd's (i.e., ratio of concentration in solid
phase to that in dissolved phase) for the atmosphere, although the concept still applies. Instead,
only the solid and gas phases are usually addressed. If chemical equilibrium is assumed between
the phases, then a normalization other than to the liquid concentration is required. In an air cell,
the solid phase consists of the paniculate matter in the atmosphere.
In the prototype, the volume fractions of chemical in each phase are given by:
-=0
• , imul
,, solid
where:
4-8
-------
DL = atmospheric dust load in air cell, kg (aerosol)/m3 (air cell)
Pjua = density of aerosols, kg (aerosol)/m3 (aerosol).
The dust load and aerosol density are specified in the prototype. To normalize to either the gas
or solid phase, the equilibrium ratio of the concentrations in the two phases must be estimated.
In the prototype, the fraction of the contaminant bound to particles, denoted by
-------
The fugacity capacity in the solid phase can be determined by use of the relationship as follows.
(-, solid
z =z — _
solid air
=z
air .
The total fugacity in the air cell is then given by:
T , gas ,, solid
r, total ™ i _ i
' airyTotal -s""a ,,Total
i
=Z (l-D./p ) + Z ,J)./p,
air^ L ~ust' solid L 'dust
4.2.4 Calculation of the Fraction of Contaminant Bound to Aerosol
In the prototype, the fraction of contaminant bound to paniculate in the air cell, denoted by cp,, is
calculated using the method of Junge (1977) as discussed in CalTOX (McKone, 1993a,b,c):
cs
where:
VP = vapor pressure or subcooled vapor pressure of the chemical, units of Pa
c - empirical constant set tp 0. 1 73 as in Junge ( 1 977), units of m-Pa
s = total surface of aerosols per volume of aerosol, units of square meters (m2)/m3.
There is a range of values for 8, with Whitby (1978) reporting a range of values of 4.2 x 10~5
nr/m3 for a "clean" continental site to l.lxlO5 m:/m3 for urban sites. In the prototype, the
average of these values is used for 0
Following CalTOX (McKone, 1993a,b,c), the subcooled vapor pressure (vapor pressure of
subcooled liquid)is used if the temperature is below the melting point of the chemical. In
particular:
i VP if T>Tm
VP = <
exp[6.79(r/r-l)] 1/7*7-
4-10
-------
4.3 Converting Equations with Equilibrium Relationships to Dynamic Form
In the course of converting equations to a form that is suitable for use within the intended
framework, it is possible to convert some algorithms that represent steady-state equilibrium
relationships into time-dependent ones. This can be performed if an estimate of the time required
for the concentration to reach some fraction of the steady-state value is available. In particular, if
the concentration in one domain/cell C, is related to the concentration in another domain/cell C2
by an equilibrium relationship of the form C, = K C2, where K is unknown and it is known that it
takes time t0 in order to reach 100a% of the steady-state value when C2 is approximately
constant, then:
dC.(t)
1 = k r - k C
K,^2 /Cj^,
where k2 and k, are defined as:
*, = -ln(l-a)/ra
*, =Kk2
The solution of the previous differential equation with initial condition C,(0) = 0 is given by:
C (t} = —r 11 -e k-
1 17 -"
AC-,
The steady-state solution is C,(t) = (k,/k2) C2, and so K = k,/k2. This assumption that 100a% of
the steady-state value is reached at time t0 means that:
1 -*->'«
\-e -"=0.
Solving for k: yields:
*, = -ln(l-a)/ra
When k2 is determined, k, = k2, from which the general result follows.
In the prototype, this conversion is performed only for the xylem, stem, and root cells of the plant
domain.
4-11
-------
4.4 Advective Processes
An advective process is one in which a chemical is transported within a given phase that is
moving from one cell to another (Mackay, 1991 refers to this as a piggyback process, in which a
chemical is "piggybacking" on material that is moving from one place to another for reasons
unrelated to the presence of the chemical). All that is required to estimate the advective flux is
the velocity of the moving phase, and the amount of the chemical that is in the moving phase. In
general, the advective flux in a given phase (e.g.,attached to particles, or dissolved in water) from
cell i to cell j is given by:
Advective flux from cell i to cellj= (Volume of phase that moves from cell i to cell j per unit time)
x (Amount of chemical in phase per volume of phase in cell i)
or
*f,(phase)
Advective flux Cell i~ Cell j - Q(phase) x
Vf(phase)
where:
Q (phase) = volumetric flux of phase from cell i to cell j, m3[phase]/day
N,(t) = amount of chemical in cell i at time , moles [chemical]
f,(phase) - fraction of chemical in cell i that is in the moving phase, moles
[chemical in phase]/moles [chemical in cell i],
VJphase) = volume of phase that is in cell i, m3[phase],
Tl '(phase) = transfer factor for advective flux from cell i to receiving cell, /day,
given by:
„.** , v Q(phase)xfl(phase)
T. ,(phase)=
' J Vt(phase)
This formula for the transfer factor is valid for all advective processes from one cell to another,
and does not rely on the fugacity concept. Application of the concept of fugacity shows that (see
Section 4.2.1):
Z (phase) V (phase)
/(phase) = — x
Z,(Total) V,(Total)
4-12
-------
where:
Z,(phase) = fugacity capacity for moving phase, mol/m3[phase]-Pa
Zt(Total) = total fugacity capacity for cell i, mol/m3[sending cell i]-Pa
VJTotal) = total volume of cell i (sum of volumes of each phase in cell), m3[cell i].
Applying this shows that the fugacity-based form for the transfer factor for advective flux is: .
-.«*, , , Q (Phase"> xZfjhase)
T. {phase)-
"J
v (phase) x A xZt(phase)
Vt(Total)xZt(Total)
In most applications, 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 (vtj). Usually
the relevant area is the interfacial area between the sending and receiving cells, but this is not
always the case; e.g., erosion from surface soil to surface water is usually reported in units of
mass (soil)/area (soil layer)-time, in which case the relevant area is the area of the surface soil
layer. Table 4-1 summarizes the implementation of all volumetric flows for domains in the
prototype. These flows are discussed in more detail in the sections describing the specific
domains.
4.5 Diffusive Processes
The net flux from diffusion from one cell to another cell depends on the difference in the
concentrations in the two cells. This means that the direction of flux is not necessarily constant
with time. However, it is possible to derive the general form for diffusion from one cell to
another and then break up defining net diffusion into a part proportional to the mass in one cell
and a part proportional to the mass in another cell. Although it is not known beforehand which is
the "sending" cell, if one is dealing with a fixed cell, then these terms take the mathematical form
of a "sending" component to the other cell and a "receiving" component from the other cell.
In all cases, diffusion across compartment boundaries is modeled in the prototype as a two-
resistance model through the boundary layers on either side of the domain interface (as discussed
in CalTOX [Mckone, 1993a,b,c], Vol. II, pp. 36-41). This is first done in a general manner that
simplifies the presentation, as characterization of diffusion between two cells reduces to
4-13
-------
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that to soil. Volumetric resuspension rate is ther
= Vol. Flow TO soil = A*vd * pA/ pp
where:
A = Area of soil-soil interface, m2(area)
vd = Dry deposition velocity of particles, m/day
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where:
A = Area of soil layer, m2
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where:
A = Area of soil layer containing plant
1 = Interception fraction (see Chapter 7.0 for description of
vd = Deposition velocity of particles, m/day
PA = Atmospheric dust load in air domain (concentration of
kg(particles)/m3(atmosphere)
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S,esusp = Resuspension rate of benthic sediment 1
kg(benthic sediment)/m2(area)-day
pbs = Density of benthic sediment,
kg(benthic sediment)/m3(benthic sediment)
Calculated so that amount of sediment buried is
and amount deposited minus amount resuspend
= A*max{ 0, S^p.. - Sresusp/pbs)
where:
A = Area of sediment-surface water interface, m;
Sdep = Deposition rate of suspended sediment to
kg(suspended sediment)/m2(area)-day
pss = Density of suspended sediment,
kg(suspended sediment)/m3(suspended s>
S,esusp = Resuspension rate of benthic sediment t
kg(benthic sediment)/m2(area)-day
pbs = Density of benthic sediment,
kg(benthic sediment)/m3(benthic sediment)
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specifying an interfacial area between the two cells and specifying the algorithm for calculating
the mass transfer coefficient for a particular domain.
In the two-resistance model for molecular and turbulent diffusion, the mass transfer between a
cell i to cell j depends on mass transfer through two distinct layers: the boundary in cell i and the
boundary in cell j. It is assumed that the net flux is equal on both sides of the boundary between
the two cells. This flux is assumed to be proportional to the difference in the bulk concentration
in the cell and the concentration at the cell-side of the boundary. The constant of proportionality
has units of m/day, and is called the mass transfer coefficient. Determination of the mass transfer
coefficient depends on the domain type of the cell, and in some cases on the domain type of both
cells.
The general form for the net diffusive flux between two cells is given by:
Net diffusive flux between cell i and cellj - FI =
where:
FtJ = net diffusive flux from cell i to cell j, mol/day
AtJ = interfacial area between cells i and j through which diffusion occurs, m
U,j = mass transfer coefficient for combined turbulent and molecular diffusion on
"i" side of boundary between cells i and j, m/day ( ={ mol/m2[area]-day}
/{moVm3[celli]})
Uj, = mass transfer coefficient for combined turbulent and molecular diffusion on
"j" side of boundary between cells i and j, m/day ( ={ mol/m2 [area]-day}
/{mol/nr[cellj]})
C,"""' = total concentration of chemical in cell i, mol/m3[cell i]
Ci' = total concentration of chemical in cell i at the boundary with cell j but in cell i,
mol/m3[cell i]
Cj""al = total concentration of chemical in cell j, mol/m3 cell j]
Cj = total concentration of chemical in cell j at the boundary with cell i but in cell j,
mol/m3 cell i]
To derive the general form for diffusion, the concept of fugacity is applied. Dividing the first
equation by Z,tot:" and the second by Z/0"1 yields:
2
4-18
-------
c;
F,i
z,o,a,
"S _
Z™al A..
, total
, total
If it is assumed that, at the boundary between the cells, the fugacities on both sides of the
boundary are equal; i.e., if f>C;/Z1total=CJ*/ZJlocaI=fJ*, where f is the fugacity of a cell, then:
, total
, total
, total
• total
Solving for F(J shows that:
I .r-, total f~, total
y total *j total
/
1
1 . -., total T ,
A Z. u
\ ' J } \ ~-iJ ' ~ 'J
/
Nt Nj
\ ' ' J J
f i
1 4 7 '"'"V/ A
1
. -7 WW/ T i
A Z, u
IJ J J1
1
™ total,.
-1
-1
where:
F,j = net diffusive flux from cell i to cell j, mol/day
U
N
= mass transfer coefficient for combined turbulent and molecular diffusion on
"i" side of boundary between cells i and j, m/day ( ={ mol/m2 [area] -day}
= mass transfer coefficient for combined turbulent and molecular diffusion on
"j" side of boundary between cells i and j, m/day ( ={ mol/m2[ area] -day}
/{mol/m3[cellj]})
= amount of chemical in cell i, moles (chemical)
V, = total volume of cell i, m3(cell i)
Z/""1' = total fugacity capacity for cell i, moles chemical]/m3(cell i)-Pa
The general form for the transfer factors can now be derived. In particular, the differential
equations for the amount of chemical in cells i and j are:
4-19
-------
dNt
~dT
dNj
~di~
N.
N }
total,, y total,
V
Y(iJ)Atj + other gains and losses
N, N, i
— Y(ij) Ati + other gains and losses
total,, ^ total,, I "
ry lUIUl-fT i-y lUIUt-wT
\ A v, A j
where
. Rearranging shows that:
dN±__ N y(/M,
dt
total
, ,
V
dN Y(iJ)A
• = N.
dt
total
,,
Y(iJ)A
N, + other gains and losses
' 7 total,, °
A v,
Y(ij}A,,
N, + other gains and losses
J r, total,.
From these equations, it can be seen that the general form for the transfer factor for diffusive
transport from cell i to cell j is:
-diff _
total
, ,
where:
1
y total , ,
> ' IJ
1
y total , ,
J J1
y total, ,
A V,
T = transfer factor for diffusive transport from cell i to cell j, /day
U,j = mass transfer coefficient for combined turbulent and molecular diffusion on
"i" side of boundary between cells i and j, m/day ( ={ mol/m2 [area]-day}
/{mol/m3[celli]})
Uj, = mass transfer coefficient for combined turbulent and molecular diffusion on
"j" side of boundary between cells i and j, m/day ( ={ mol/m2 [area]-day}
/{mol/m3[cellj]})
V, = total volume of cell i, m'(cell i)
Z'"'"' = total fugacity capacity for cell i, moles (chemical)/m3(cell i)-Pa
4-20
-------
This general form is used to model diffusive transport in the prototype. All that must be
determined for each such diffusive link between cells are the mass transfer coefficients and the
interfacial area between the cells through which diffusion occurs.
Table 4-2 summarizes how the mass transfer coefficients are estimated for all diffusive transfers
considered in the prototype. These are discussed in more detail in the sections describing the
specific domains.
4.6 Reaction and Transformation Processes
In the prototype, reaction and transformation processes are modeled using either a specified
reaction/ transformation rate or chemical half-life for each cell. In all cases, the mass of chemical
transformed in a given cell is assumed to be lost from the system into a sink cell which receives
input only from the particular cell. For a given cell i and an associated sink, the transfer factor
T,s'nk that represents the transformation/reaction process is simply the specified or calculated
reaction/ transformation rate.
4-21
-------
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5.0 Pollutant Transport in Soil and Groundwater
This section describes the specific application of the fugacity methodologies described by
Mackay (1991) to deriving the mass transfer equations for transport of an organic contaminant in
the subsurface. There are two types of transfers considered within the subsurface: diffusion
from higher to lower chemical potential, and advective transport (e.g., driven by precipitation).
Both of these processes occur for a contaminant in their aqueous and gas phase.
5.1 Conceptualization of the Soil Domain Type
For the purpose of the prototype, the soil domain type consists of three domain instances:
surface soil, root zone, vadose zone. The subsurface was divided into multiple cells horizontally
to capture variations in soil properties and achieve spatial resolution in the subsurface.
5.2 General Mass-Transfer Issues
Two of the primary processes in the subsurface are exchange by diffusion and advection. These
are key components of the overall rate constant. The transport occurs both in the gas and liquid
phase for organic chemicals. 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 is dependent on the darcy velocity of that phase. In this application, the total
contaminant mass is estimated for each soil layer. 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 (bulk
density, porosity), and depth of each soil layer.
There are three advective processes considered in the prototype that can potentially transport a
chemical from a soil domain to surface water: erosion of surface soil; runoff from surface soil;
and recharge from groundwater. Erosion applies to the solid phase, while runoff and recharge
applies to the dissolved phase. Table 5-1 summarizes the relevant area(s) and how the volu-
metric flow rates of the moving phase(s) are calculated. It is important to note that the concen-
tration in the eroded soil is higher than the concentration in the surface soil particles by a correc-
tion factor that varies between I and 2 because the lighter soil tends to be eroded and this soil has
a higher fraction of organic carbon.
5-1
-------
Table 5-1
Summary of the Processes by Which Contaminants are Exchanged
Between Soil Cells in The TRIM.FaTE Prototype
I.
Gains
Surface Soil
Type of
Process
Relevant
Phase
Losses
From Air
diffusion from air
deposition of
atmospheric particles
Diffusive
Advective
Gas
Solid
From Root Zone
Diffusion from Root
Zone
Diffusive
Cas&
Aqueous
II.
Root Zone
Type of
Process
Relevant
Phase
To Air
diffusion to Air 1
wind-induced resuspension
of soil
Diffusive
Advective
Gas
Solid
To Root Zone
Advective flow into Root
Zone
Diffusion into Root Zone
Advective
Diffusive
Aqueous
Gas&
Aqueous
To Surface Water
Erosion
Runoff
From Plant
Outflow from Roots,
Stem, and Xylem
Advective
Total
From Surface Soil
Diffusion
Advective inflow
Diffusive
Advective
Gas&
Aqueous
Aqueous
From Vadose Zone
Diffusion
Diffusive
Gas&
Aqueous
III
Vadose Zone
From Root Zone
Advective Inflow
Diffusion
Advective
Diffusive
Aqueous
Gas&
Aqueous
IV
. Groundwater
From Vadose Zone
Recharge
Aqueous
Advective
Advective
Solid
Aqueous
To Plants
Uptake from Roots, Stem,
and Xylem
Advective
Total
To Surface Soil
Diffusion to Surface Soil
Diffusive
Gas&
Aqueous
To Vadose Zone
Advective Flow
Diffusion
Advective
Diffusive
Aqueous
Gas &
Aqueous
To Root Zone
Diffusion
Diffusive
Gas&
Aqueous
To Groundwater
Advective flow
Advective
Aqueous
To Surface Water
Recharge
Aqueous
5-2
-------
5.5 Derivation of Soil Transfer Factors
The transfer factors in the subsurface is a function of the advective flux (gas phase plus liquid
phase) and the diffusive flux (gas phase plus liquid phase). For each cell in the subsurface, the
advective flux is loss mechanism. As noted in Table 5-1, the surface soil zone and the root zone
have gains and losses to other domains (air, plant, surface water). Transfer factors due to gains
and losses from soil to other domains are derived in the sections for those domains. The
following derivations are restricted to the subsurface only.
5.3.7 Advective Processes
The generalized equation for advective processes (Section 4.4) when applied specifically to the
aqueous phase in the subsurface yields the following transfer factor between soil cells i and j
used in the prototype:
A Z
rad\, N ii water
r,j (aqueous) = -
where:
u*ater = aqueous darcy velocity (m/h)
Ay = cross section area between the soil cells i and j (m2)
V, = volume of soil cell i (m1).
For the prototype, gas-phase advective transport was not simulated because B(a)P and
phenanthrene are not expected to have a significant gaseous darcy velocity.
5.3.2 Diffusive Processes
Jury etal. (1983, 1984a, 1984b, 1990) estimates of effective diffusivity for a chemical species in
gas and liquid phase diffusion were used in the prototype to estimate the diffusive transfer
factors. From Section 4.5, the general form of the diffusion transfer factor is given by:
5-3
-------
Therefore, the relevant pollutant phase for diffusion is the total phase. The mass transfer
coefficients are estimated by the method used in CalTOX (McKone, 1993a,b,c):
D*ff
U = ——
6
where:
Deff = total gas and liquid diffusivity for the chemical for a given cell i
6, = diffusion length for given cell i.
A simplified approach to estimate diffusion length used in multi-media compartment models
such as CHEMCAN (Mackay and Patterson, 1991), HAZCHEM (ten Berge, 1994), and
SIMPLEBOX (van de Meent, 1993), is to make use of a diffusion-path length that is independent
of chemical species. Mackay and Paterson (1991) use a diffusion-path length that is half the
depth of the soil. However, for the prototype, the effective diffusion distance is adopted from
CalTOX as:
6 = 16.64 x \jritnestep x De
0683
where timestep is the length of time between calling LSODE, not the actual time step being used
by LSODE.
For small spatial steps, modeling the flux of chemical in the soil is, by diffusion, based on the
effective diffusion coefficient and distance between the center point of the cells. However, this
method can only be used for a fine spatial grid and short timesteps. This model was developed
by matching the flux to the flux rate based on the appropriate timesteps and for a fine spatial grid
to the flux for longer time periods and a larger grid.
Jury, et al. (1983, 1984a, 1984b, 1990) have estimated an effective diffusivity for a chemical
species in gas and liquid-phase diffusion as follows:
5-4
-------
JO JO
air- T-y"' air water , •> water
where:
Dair = chemical diffusion coefficient in pure air, mVs
Dwater = chemical diffusion coefficient in pure water, mVs.
5.3.3 Total Transfer Factors
Combining the advective and diffusive transfer factors from the previous equation yields the total
transfer factor from cell i to j:
This transfer factor applies to vertical transport down (from surface soil to soil root for example),
because advective flow occurs from the surface soil down to the vadose zone cells (Table 5-1).
However, for transport upwards (soil root to surface soil), diffusion is the only transport
mechanism (capillary flow is neglected in the prototype); therefore, the first term in the
parentheses of the previous equation is zero.
5.3.4 Lateral Runoff
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. While some researchers use an approximation that runoff is in equilibrium with the soil pore
water, the process is most likely not instantaneous (Wallach, et al., 1989). Ideally, it should be
modeled as a time-dependent process. In this model, a steady-state relationship between the
runoff water and the pore water will be used. In the TRIM framework, runoff water will be
considered a separate domain in the surface soil layer at each spatial location. To understand
runoff, flow must first be characterized. If the runoff stream is shallow, it is likely to be laminar.
5-5
-------
As the rain increases the depth of the runoff stream, the flow is likely to be turbulent with a
laminar boundary close to the surface soil. One way to model the process is to assume that there
is a laminar boundary layer at the bottom of the runoff water. Chemical transport through this
stagnant layer is then by molecular diffusion. The water above the laminar layer is turbulent, and
thus assumed to be well mixed. It can further be assumed that the concentration in the runoff
water is equal to the concentration in the turbulent layer.
The flux from the surface soil to the runoff is a function of the following parameters (Wallach, et
al., 1989):
D = diffusion coefficient in water (mVs)
Cj-C,, = concentration difference between the soil pore water and the runoff water
(g/m3)
R = hydraulic radius (m), for planer flow, water depth over surface
um = mean velocity of the fluid (m/s)
r = fluid density (g/m3)
m = viscosity (kg/ms)
E = kinetic energy of the rainfall (gm/s2).
Using this model, the flux is related to the concentration difference as follows (Wallach, et al.,
1989):
r
Flux - - mol/m
6
where:
D = thickness of laminar boundary layer (m)
The derivation of Scan be found in Wallach, et al., (1989), but the result is:
6= ' JL
where:
n = Manning roughness coefficient, (unitless). One typical value might be .02
(Linsley, et al., 1982 for values).
J = hydraulic gradient (unitless). This should be taken from GIS data, default
value: 0.01
5-6
-------
R = hydraulic radius (m), for planer flow, water depth over surface. This is site
specific and depends on J, the rainfall rate, and the recharge rate (it will be
taken as an uncertain variable; with a default value of 1 centimeter [cm], an
investigation will be conducted on how sensitive the model is to this
parameter)
g = acceleration due to gravity (m/s2).
The mass transfer coefficient will increase with increases in roughness, hydraulic gradient, and
hydraulic radius, which is consistent with laboratory findings (Wallach, et al., 1989).
To solve the steady-state concentration in the runoff water as it travels from cell to cell, the soil
pore water concentration and runoff water concentration must be coupled. The water is only in
contact with the soil in each particular square for a limited time and this is taken into considera-
tion when solving for the steady-state concentration relationship.
The differential equation based on a constant hydraulic radius, mean flow velocity, and soil
concentration with boundary conditions that the water enters at an initial concentration when the
lateral distance (x) equals zero and the concentration approaches the soil pore water concentra-
tion as x equals infinity is defined as follows:
dCR_D(Cs-Cr)
dx buR
Boundary conditions applied to the previous equation are:
• X = 0
• c — c
*-R - *-RO
• X = infinity
Solving this equation under the specified boundary condition yields:
A hydraulic balance is needed to determine the velocity of the water and the depth of the runoff
stream. From the Geographic Information System (CIS) data, the runoff is estimated. The
runoff is related to the water depth and water velocity through the following relationship:
5-7
-------
n
Runoff = _2
However, for typical runoff rates, for cell lengths on the order of 1,000 m, the runoff water comes
to equilibrium with cell pore water, thus simplifying the equation.
During a runoff event, the volume of water in the surface soil is the volume fraction times the
thickness of the surface soil plus R.
Z =
Vfmr x bgasKbgas + R)
RT
H
R)
It should be noted that in a rainfall event, the volume fraction of air in surface and root should be
zero and the volume fraction of water should be the porosity; thus, the corresponding transfer
factor is:
Area
Groundsurafcesoil
£ , Volume . , ,+RxArea~ , , .,
total groundsurfacesoil (jroundsurafcesoil
The runoff to surface water uses the previous formula for the cell closest to the water.
5.3.5 Erosion
Based on the previous analysis for runoff, the eroded soil is assumed to be transferred from one
cell to the next and comes to equilibrium with the cell it is being transferred into.
The flux of chemical from erosion is:
erosion
Psolid I
j.,.
LW
Converting this to the transfer factor yields:
5-8
-------
„ _ erosion ^H ^ reaGroundsurafcesoil
prnsinn '71/7 DA
f solid ^total OiUmet>roundsurfacesoil+KxAreaGroundsurafcesoil
erosion
Again, this equation is applicable to ground surface soil to surface water transfer when the
ground surface soil cell is adjacent to the surface water.
5.4 Groundwater
The horizontal flow of pollutants in the saturated zone (groundwater) is not expected to be a
significant pathway when considering air pollutants. Transport has been simulated because it is a
more significant process than diffusion/dispersion. In the prototype, groundwater is modeled as a
receiving cell from the vadose zone and a sending cell to surface water. The transfer factors for
soil to groundwater and for groundwater to surface water are based on the aqueous phase advec-
tion only (Section 4.2.1) by substituting recharge for flow velocity:
and
A Z
sin! groundwater water r> i
- y - ^ - Recharge
still loml
A Z
_ xniundHaier surfarewater water
Xniundwuler surfuceHuler ~ y ~Z
f-r
-------
6.0 Pollutant Transport in Air
The prototype considers transfer of contaminants between the lower atmosphere and the soil
domain. The exchange of a contaminant from air to soil can occur by either diffusion from a
higher to lower chemical potential, particle (dry) deposition, wet deposition, or dust resuspen-
sion.
6.1 Conceptualization of the Air Domain
The troposphere extends from the ground up to an average height of 11 km. Generally, only the
lowest few km are directly modified by the underlying surface. The troposphere can be divided
into two parts, namely a boundary layer near the earths surface and the free atmosphere above the
boundary layer. We can define the boundary layer (BL) as that part of the troposphere that is
directly influenced by the earth's surface and responds to surface forces with a time scale on the
order of an hour or less. The BL depth is quite variable in time and space and ranges from a few
hundred m to several km.
Over oceans, the BL depth varies relatively little over time and space because the sea surface is a
relatively smooth surface and the temperature varies little with time. Most changes in the BL
depth over oceans are a result of movement of large-scale air masses.
Over land surfaces, especially during high pressure, the BL has a well-defined structure that
evolves with the diurnal cycle. The major components of the BL are the surface layer (SL), the
mixed layer (ML), the stable boundary layer (SBL), and the residual layer (RL). Figure 6-1
depicts these layers and their evolution during the diurnal cycle.
The SL is the region at the bottom of the BL where turbulent fluxes vary by less than 10 percent.
The depth of the SL is typically defined as 10 percent of the mixed layer. Pollutants emitted in
this layer are generally well mixed and are quickly brought down to ground level. The turbu-
lence in this region is primarily a result of mechanical mixing from wind forces acting upon
surface features.
The ML, as its name implies, is a well mixed region of the atmosphere. The turbulence in the
ML is primarily driven by convective forces resulting from surface heating. Because of this
dependency, on clear days, the ML growth is tied to the diurnal cycle. The ML begins its growth
about a half-hour after sunrise and reaches maximum depth in the late afternoon.
6-1
-------
CO
(A
Q)
D)
if
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6-2
-------
About a half-hour before sunset, the convective forces cease to form and a more neutrally
stratified layer called the RL begins to form. As night approaches, the bottom portion of the RL
is transformed by its contact with the ground into a SBL. Pollutants emitted in the SBL tend to
mix very little in the vertical.
To accurately depict the temporal and spacial relationship of these layers would take an effort
well beyond the scope of this project. However, by utilizing several existing BL models and
representative meteorological observations, and by making some simplifying assumptions, a
diurnal and annual behavior of the BL for use in TRIM.FaTE can be predicted.
In the prototype, the vertical structure of the atmosphere is represented by two vertical layers
representing the BL capped by the free atmosphere. During daytime, the BL is divided into two
vertical layers representing the SL (the lower air cell in the prototype) and the ML (the upper air
cell in the prototype). Air exchange between the SL and ML occurs at a rate determined as a
function of atmospheric stability and horizontal wind speed. During nighttime hours, the BL will
be divided into two layers representing the SBL (the lower air cell in the prototype) and the RL
(the upper air cell in the prototype). The vertical structure of the TRIM.FaTE air domains in the
prototype is shown in Figure 6-2.
6.2 Calculation of Air Cell Dimensions
The horizontal size of the grid cells will be determined on a run-by-run basis. A discussion of
the horizontal grid size are discussed in Chapter 11.0. In general, the horizontal size will be a
function of the expected gradient from the emission source, underlying surface features (i.e., land
or water), the model time-step, and the minimum horizontal wind speed. For example,
considering a minimum horizontal wind speed of 1 meter per second (m/s) and a 1-hour model
time-step, a maximum horizontal grid size of 3,600 m is suggested.
The vertical depth of BL was derived using the EPA's PCRAMMET meteorological prepro-
cessor. Using standard meteorological observations from National Weather Service (NWS) sites,
PCRAMMET can predict an hourly value of the "mixing height." In this model, the overall
depth of the BL has been conservatively set as equal to that of the mixing height as predicted by
PCRAMMET. Details on data requirements and model operation of PCRAMMET can be found
in the "PCRAMMET Users Guide" (EPA, 1995).
The depth of the SL is a function of the atmospheric stability. During unstable atmospheric
conditions, the depth of the SL is estimated to be approximately 10 percent of the BL (Stull,
6-3
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Figure 6-2
TRIM.FaTE Boundary Layer Representation
Free Atmosphere
Layer 2
t »
Layer 1
_^
i si
Layer Z
— ^ — *•
RL
Layer 1 y
, SBL
Surface Surface
Daytime Nightime
Time
6-4
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1993). During daytime neutral atmospheric conditions, it is assumed that the atmosphere is well
mixed and the height of SL is set equal to the depth of the BL. During nighttime neutral
atmospheric conditions, it is assumed that the atmosphere is also well mixed and there is no SBL
present, and the height of SBL is set equal to the depth of the BL. Stable atmospheric conditions
can only occur during nighttime hours during which the model predicts a SBL, in lieu of a SL.
The SBL is estimated to be approximately 30 percent of the BL:
Stability A, B, & C:
HSL=0.1 *HBL
Stability D:
Stability D:
"SBL = HBL
Stability E, F, and G:
HSBL = 0.3*HBL
Under all atmospheric conditions, the height of the ML and RL are set equal to the depth of the
BL;i.e.:
HRL= HBL
where:
HBL- HSL- HSBL HML, and HRL are the respective air cell heights in meters.
6.3 Calculation of Air Cell Horizontal Wind Velocities
The horizontal wind speed in each air cell can be predicted from NWS wind speed observations.
In the SL (lower air cell - daytime), the horizontal wind speed is approximated by fitting a log
wind profile to the NWS wind speed (WSW,S) observation (EPA, 1987). In the SBL lower air
cell - nighttime), the horizontal wind speed is set equal to the WS^s- In the ML (upper air cell -
daytime) and the RL (upper air cell - nighttime), horizontal wind speed is approximated by fitting
a log wind profile to the
• InSL:
• In SBL: WSH1 = WSN^.S
• In ML: WSH: = WSNWS*((HNU/2) / Hanem)p
• InRL: WSH, = WS^.s*((HRL/2) / Hanem)p
6-5
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where:
WSH1 is the horizontal wind speed in m/s in the lower air cell (SL or SBL)
WSH2 is the horizontal wind speed in m/s in the upper air cell (ML or RL)
WS^s is the measured hourly wind speed at the NWS
Hanem is the NWS anemometer height.
P is the Power-Law Exponent equal to:
• 0.07 (A&B Stability)
• 0.10 (CStability)
• 0.15 (D Stability)
• 0.35 (E Stability)
• 0.55 (F Stability).
6.4 Calculation of Air Cell Vertical Wind Velocities
The vertical wind speed between lower air cell (SL or SBL) and upper air cell (ML or RL) can be
predicted from horizontal wind velocity and the atmospheric stability. During unstable atmos-
pheric conditions, the vertical wind speed is estimated to be approximately 10 percent of the SL
horizontal wind speed in an upward direction. During neutral atmospheric conditions, it is
assumed that the atmosphere is well mixed and the heights of SL is set equal to the depth of the
BL; thus, there is no vertical wind speed between the two air cells (they are contiguous in space).
Stable atmospheric conditions can only occur during nighttime hours during which the model
predicts a gentle subsidence of the air mass from the upper air cell to lower air cell (downward
motion) at a rate equal to 1 percent of the SBL horizontal wind speed:
• Stability A, B, & C: WSV1.2 = 0.1 * WSH1
• Stability D:WSV1.2=0
• Stability E, F, and G: WSV1.2= -0.01 * WSHI
where:
WSV1.2 is the vertical wind speed in m/s between the lower air cell and upper air cell.
6.5 General Mass-Transfer Issues Between Air and Air
Both theory and observations suggest that the growth of a plume in the lower air cells of the
atmosphere conforms acceptably well to the gaussian form. EPA has developed many situation
specific air quality models which emulate the gaussian form to predict the growth and dispersion
of a plume. These models are excellent tools for predicting a pollutant concentration and
6-6
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gradients for a specific time period downwind of a source. The intent of the EPA model is not to
recreate a gaussian-type of air quality model, but to simply predict the mass transfer of a
pollutant from one air cell to another. Over long periods of time and at downwind distances on
the order of several km, a plume will tend to meander and lose its gaussian shape. The model
will assume that the pollutant mass is well mixed within a given air cell. Thus, no gradient will
be predicted within an air cell. If a tighter plume gradient is required, this can be achieved by
making the horizontal size of the air cells smaller.
In the TRIM.FaTE model, the mass of a pollutant in a given cell can be predicted with the
equation of continuity. Assuming the pollutant is well distributed within the air cell, the pollu-
tant mass will be transferred from cell to cell as a direct function of the air flow from one cell to
another. In addition, loss of pollutant mass through deposition on surface features must also be
considered in determining an air cell pollutant mass. Figure 6-2 depicts the suggested links
between air cells.
6.6 Derivation ofAir-to-Air Transfer Factors
The transfer factor from one air cell to another was derived based on advective flow rates of a
total pollutant mass between two cells as developed in Chapter 2.0 by substituting wind velocity
for the total volumetric flow velocity:
ut]
where:
u,j = annual averaged wind speed between air cells i and j (m/h).
Because advection is being simulated for the total phase, no phase partitioning is applied in this
equation.
6.7 Derivation of Air-to-Soil Transfer Factors
The transfer factor between the air and surface soil is a function of advective flux and diffusive
flux. In the prototype, the advective flow from air to surface soil is based on wet and dry
deposition.
Dry deposition of particles to surface soil (solid phase):
6-7
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V
"aTotal
where:
,dd
'aTotal
z
z
4>ap
PP
advective transfer factor of particles from air to surface soil (I/day)
= area of air-soil interface (m2)
= volume of air cell (m3)
= dry deposition velocity of particles, m/day
= total fugacity capacity for the air 1 cell (mol/Pa-m3)
= fugacity capacity of the solid in air (mol/Pa-m3)
= volumetric fraction of solid content in air (m3 of solid/ m3 of air)
= Pa/Pp
= atmospheric dust load in air domain (concentration of dust in air), kg
(particles)/m3 (atmosphere)
= density of air particles, kg (particles)/m3 (particles).
Wet deposition of particles to surface soil (solid phase):
V
wet.
"aSohd
"aTolal
4>
ap
where:
Vair
wetd
AiSolid
advective transfer factor of wet particles from air to surface soil (I/day)
area of air-soil interface (m2)
volume of air cell (m3)
wet deposition velocity of particles (m/day)
fugacity capacity of the solid in air (mol/Pa-m3).
Additionally, there is advective flux from rainfall. As the rain falls, it gathers chemical from the
air, coming into equilibrium with the fugacity of the air compartment. The flux is:
6-8
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fl i /Z,\ A ^aWaler i »,
flux(mass/h)=Aij — -- - — (J)^ Na
V L
_ , . . . Rain aWater .
T .(ram)=A -- avv = fraction water in air cell (unitless).
Therefore, the total advective transfer factor from air to soil is given by:
/t OM aWaier . A; ^aSolid , , \ A
= .4 q) + —^ (v ,+wet,) d)
y IT 7 TaM ., „ v d j/ fa
aTolal Vi
As developed in Section 4.4, the diffusive transfer factor is expressed as follows:
j.ff f\
VZ Z(7,
The relevant phase is the total phase; therefore, all the fugacity capacities are for total phases.
The total transfer factor from air to surface soil can, therefore, be expressed as:
11 1 Z ,., Z r i j
* s 1 1 \ -1 £> ' aWater A aSolid
, . — I -t- • ) "*" f\Qtn "••"•" CD *^ i v i ' rt-t.* j/ u/ j
"" ^2^;^ U,Z*rJ ZaTolal^ Za ^d d'^\
where:
Tass = total transfer factor from air to surface soil (1/d)
Aass = surface area between air cell 1 and surface soil (m3)
Va = volume of air cell 1 (m3)
6-9
-------
ssa
Uass = rnass transfer coefficient on air cell 1 side of air cell-surface soil
boundary, (m/d)
Ussa = mass transfer coefficient surface soil side of air cell-surface soil
boundary, (m/d)
= total fugacity capacity of surface soil (mol/Pa-m3)
vd = deposition velocity of air particles (m/d)
wetd = wet deposition velocity of air particles (m/d)
-------
7.0 Pollutant Transport in Surface Water and Sediment
The surface water cell is assumed to be well-mixed and composed of two phases: pure water and
suspended sediment material that contains the sorbed contaminants. Similarly, the sediment is
modeled as a well-mixed cell consisting of a phase sorbed to the benthic solids and a phase
dissolved in the benthic pore water or interstitial water.
7.1 Conceptualization of the Surface Water (Lake) and Sediment Domains
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 proces-
ses 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 MacAvoy (1981)
have summarized important issues relating to surface-water transport. Fugacity models have
been developed for lakes and rivers by Mackay, et al., (1983a and 1983b).
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 or stage. 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 accurately 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. The general TRIM.FaTE model, will have
the option of lake(s) and of being connected to river(s). This model is based on that described in
Mackay (1983a,b). Table 7-1 summarizes the gains and losses considered from the surface water
cell considered in the prototype. Losses from the sediment due to colloidal diffusion,
bioturbation, or reaction/transformation are not considered at this stage of the TRIM.FaTE
model.
The general manner in which the model is presented is intended to assist the flexibility of future
prototypes and to facilitate implementing different algorithms to describe specific processes. It is
also important to note that the fugacity concept is applied in this model, but it is only the
7-1
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Table 7-1
Summary of the Gains and Losses for Surface Water Cells
Considered in the Prototype
Gains
Type of
Process
Relevant
Phase
From Surface Soil
Erosion
Runoff
Advective
Advective
Solid
Aqueous
From Air
Diffusion from air
Dry deposition of aerosols from air
Wet deposition of aerosols from
air
Wet deposition of vapor from air
Diffusive
Advective
Advective
Advective
Vapor
Solid
Solid
Vapor
From Sediment
Diffusion from sediment
Resuspension of sediment
Diffusive
Advective
Aqueous
Solid
From Rivers
Cell to cell advective flow
Advective
Total
From Aquatic Biota
Elimination from fish
Exchange
Total
From Surface Water Cells
Losses
Type of
Process
Relevant
Phase
To Air
Diffusion to air
Diffusive
Aqueous
To Sediment
Diffusion to sediment
Deposition to sediment
Diffusive
Advective
Aqueous
Solid
To Lake
River to lake advective
flow
Advective
Total
To Aquatic Biota
Uptake by fish
Exchange
Total
To Sink(s)
Decay/transformation to
Reaction/Advection sink
Outflow to
Reaction/Advection sink
Transfer
mation
Advective
Total
Total
diffusion algorithms that make use of the fugacity assumptions. The use of the fugacity
terminology is used to describe the advective process for simplicity of notation and consistency.
7.2 Advective Processes
A generalized description of advective processes is provided in Section 4.4. This section focuses
on the advective processes simulated in the prototype specific to the surface water domain.
7-2
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7.2.1 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. For all of
these processes, the air cell is the sending cell and the surface water cell is the receiving cell.
Following is a summary of advective processes between air and surface water, and algorithms
used to calculate phase flow velocities:
Dry deposition of particles to surface water (solid phase):
j,dd _ Aalrsw PQ ^solid
airsw ,, d f
air rp \O{al
where:
Tairsw = advective transfer factor of particles from air to surface water (I/day)
Aairsw = area of surface water, m2
Vair = volume of air cell (m3)
vd = dry deposition velocity of particles, m/day
pa = atmospheric dust load in air domain (concentration of dust in air), kg
(particles)/m3 (atmosphere)
pp = density of air particles, kg (particles)/m3 (particles).
Wet deposition of particles to surface water (solid phase):
~-H'
-------
Additionally, there is advective flux from rainfall. As the rain falls, it gathers chemical from the
air, coming into equilibrium with the fugacity of the air compartment. The flux is:
^
n / n \ A KdlH water i »r
flux(mass/h)=A.. d> . , N
J ^ 'J V 7 ^w(a) a
Vi ^
. Rain %*
i Total
wh
ere:
rain = rainfall rate (m/h).
7.2.2 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 or from the sediment to the surface water via
movement of sediment particles. "Sediment deposition" refers to the transport of the chemical
from the surface water to sediment, and "sediment resuspension" refers to the reverse process.
Both processes involve only the solid phase.
Following is a summary of advective processes between sediment and surface water, and
algorithms used to calculate phase flow velocities:
Deposition of suspended sediment to sediment bed (solid phase):
«» 1 "Jj ^.
Td
s"sed
V o Z
^
where:
7"VK(^ = advective transfer factor for deposition of suspended sediment to sediment
bed (1/day)
Aswsed = area of surface water/sediment interface (m2)
Vsw = volume of surface water cell (m3)
7-4
-------
Sdep = deposition rate of suspended sediment to sediment bed, kg (suspended
sediment )/m2 (area)-day
pss = density of suspended sediment, kg (suspended sediment)/m3 (suspended
sediment).
Resuspension of sediment to surface water (solid phase):
A <\ 7
-r _ nsedsw Jr ^ solid
sedsw V o
v sed Vbs
where:
= advective transfer factor for resuspension of sediment to surface water
(I/day)
sedsw
Asedsw = area of surface water/sediment interface (m2)
Vsed = volume of sediment cell (m3)
Sr = resuspension rate of benthic sediment to water column, kg) benthic
sediment)/m2 (area)-day
pbs = density of benthic sediment, kg (benthic sediment)/m3 (benthic sediment).
7.2.3 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.
The outflow is calculated in the prototype so that the net flow into the lake is zero. This is done
by setting the outflow equal to the inflow from upstream, runoff, recharge, and precipitation,
minus the evaporation (all of these parameters are specified by the user in the prototype). In
subsequent versions, it may be worthwhile to let the outflow be calculated in a more sophisti-
cated manner (e.g., allow the volume of water in the surface water to change with time).
Similarly, burial is calculated so that the net flow of sediment into the sediment layer is 0. This,
is done by setting the amount of sediment buried equal to the sediment deposition rate minus the
sediment resuspension rate, both of which are specified input parameters. If the resuspension
rate is larger than the deposition rate, then the burial flow is set to 0. A more sophisticated
approach may be implemented in which the sediment layer depth could change, depending on the
deposition and resuspension rates. Further, the deposition rates can be calculated to correspond
to the suspended sediment concentration, which could change depending on the erosion of soil to
the water body and the outflow.
1-5
-------
Following is a summary of advective processes between sediment/surface water and advective
sinks, and algorithms used to calculate flow velocities:
Outflow from surface water to surface water advection sink (total phase):
M A
Tlvlul _ *' ylt/ ™ sssw n ff gwsw 13 i
S\VS T T T 7 *^*' t T O
y
xw vw w xw
where:
Tsws = transfer factor into advective sink for surface water
Inflow = volumetric water inflow (m3/day)
Asssw = area of surface soil and surface water interface, m2 (surface soil area)
Vsw = volume of surface water (m3)
Runoff = runoff from surface soil, m3 (water reaching surface water)/m2-day
(surface soil area)
A = area of surface water-ground water interface, m2 (interface)
Recharge = recharge from groundwater to surface water, m (water)/m (interface)
Aairsw = area of surface water and air interface (m2)
EV = evaporation (m3 [water]/m2 [surface water area]/day).
Resuspension of sediment to surface water (solid phase):
AS A S Z
~-total _ ,/-. serfs* dep _ sfdsvt r ,. Solid
5'*H' maX ' ^H PK ^ Pfa ^
where:
- net advective transfer factor for deposition and resuspension of sediment
to surface water (I/day)
= area of surface water/sediment interface (m2)
= volume of sediment cell (m3)
Sr = resuspension rate of benthic sediment to water column, kg (benthic
sediment)/nr (area)-day
pbs = density of benthic sediment, kg (benthic sediment)/m3 (benthic sediment)
Vsw = volume of surface water cell (m3)
S
-------
7.2.4 Advective Process Across a Thermocline
Lake movement results from wind, thermal gradients, diffusion and turbulent eddies. Lakes
potentially are thermally stratified, preventing chemicals from being mixed easily. Some lakes
are not thermally stratified, which tends to result in a more even chemical distribution
(Thibodeaux, 1996). Overturn in lakes (when the top and bottom waters of the lakes mix) occurs
only when there is no ice-cover and there is little difference in temperature between the surface
and bottom waters of the lake. Therefore, in summer, the temperature difference between the
surface and bottom waters of the lake is too great for mixing to occur.
To estimate the transfer factor by advective transfer, the primary parameters are the bulk flow
water velocity across the thermocline, the temperature differential between the upper and lower
surface water, and the interfacial areas. The interfacial area is determined from the conceptual
site model. A seasonal temperature profile of a typical lake and actual meteorological data from
a local airport were used to estimate upper and lower water temperatures for the prototype. The
bulk flow water velocity across the thermocline in surface water was estimated from Schnoor
(1981). Two independent methods were used to estimate bulk velocity and the results were
consistent as shown in the following text:
• Eddy Diffusivity Method. The bulk flow was first estimated from eddy
diffusivity as follows:
Bulk velocity = kz / boundary layer thickness (from conceptual site model [CSM])
where:
kz = vertical eddy diffusivity (Schnoor, 1981) = 0.0142 (Z) 149 mVday
Z = mean depth (CSM) = 5 m
Therefore, bulk velocity = 15 m/day.
• Dispersion Coefficient Method. The bulk flow is also estimated from range of
dispersion coefficients in Schnoor (1981). Vertical mixing ranges from 1 x 10"2 to
10 cnr/s. Assuming a boundary layer thickness of 1 cm, bulk velocities range from
10 to 10,000 m/day.
Comparison of the bulk velocities estimated from the eddy diffusivity factor yields a bulk
velocity in the lower end of the range estimated from the dispersion coefficients. Because the
bulk velocity of 15 m/day was derived by two independent methods, it was adopted as the
7-7
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advective flow velocity from the upper surface water to the lower surface water cells in the
prototype. When the temperature in the upper surface water varied more than 20°C, the bulk
velocity was assumed to be 0 m/day.
7.3 Derivation of River Parcel Transfer Factors
The transfer factor from one river cell to another, or to a lake cell, was derived based on advec-
tive flow rates of a total pollutant mass between two cells as developed in Section 4.2. By
substituting river flow velocity for the total volumetric flow velocity, the following transfer
factor is derived:
A
f"»
where:
u,j = annual averaged river flow between river cells i and j (m/h).
Because advection is being simulated for the total phase, no phase partitioning is applied in this
equation.
7.4 Transformation Chemical Losses
The chemical transformation loss rates in water and sediment should be specified in the chemical
database. The total losses are related to both the water losses and the sediment losses and are as
follows:
L - Sediment
Sediment
where:
RL
NL
waicr
transformation loss coefficient
moles of chemical in lake
volume fraction of water in lake
volume fraction of sediment in lake
lake fugacity capacity.
Converting the total losses to a transformation yields:
7-8
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water
Sediment
L-Sediment
7.5 Diffusive Processes
A general discussion of diffusive processes is provided in Section 4.5. Table 7-1 summarizes
how the mass transfer coefficients are calculated for diffusion between air and surface water and
between surface water and sediment. In some cases, algorithms are used that calculate the mass
transfer directly, while others make use of a diffusion coefficient and an assumed depth 6 in cell /
at the boundary of cells / andy. The diffusion transfer rates are obtained by substituting mass
transfer coefficients into the diffusive equation in Section 4.4.
Following is a summary of diffusion mass transfer coefficients for diffusion between air and
surface water.
Air to Surface Water (Southworth, 1979; p. 42 of CalTox manual, McKone, 1993b):
U
D'
where:
eff
D
L-'
Dair
6aw
Windspeed
MW
= 0.00316 * WindSpeed * (18/MW)172, if WindSpeed >0.5 m/s
= 0.00162 * WindSpeed * (18/MW)"2, if WindSpeed <0.5 m/s
- (Au/Aotal airf) Da,r
= mass transfer coefficient on air side of air-surface water boundary
(m/day)
= chemical diffusivity in air, m2/day
= boundary layer thickness in air above surface water, m
= wind speed, m/s
= molecular weight of chemical, g/mol.
Surface Water to Air (p. 41 of CalTox manual, McKone, 1993b)
= °'24
7-9
-------
where:
Uairsw = mass transfer coefficient on surface water side of air-surface water
boundary (m/day):
Surface Water to Sediment:
where:
D
eff
water
swsed
eff
D
Uswsed
Dwaler
6wd
= (Zwater/Ztotalwater)DwaIer
= mass transfer coefficient on surface water side of sediment-surface
water boundary, m/day
= diffusion coefficient in water, m2/day
= boundary layer thickness in surface water above sediment, m.
Specified.
Sediment to Surface Water (CalTox manual, McKone, 1993b, p. 36, based on Jury, et al. (1983):
U
dw
where:
D
cff
rnass transfer coefficient on sediment side of sediment-surface water
boundary, m/day
effective diffusivity in sediment, m2/day = (Zwale/Ztola|) Dwalcr 4/3 (CalTox
manual, McKone, 1993b, p. 44, Eq. 58 [based on Jury, et al., 1983])
where:
4>
fugacity capacity for water, mol/m3-Pa
tota' fugacity capacity for sediment layer, mol/m3-Pa
diffusion coefficient in pure water, m2/day
volumetric pore space filled with water in sediment layer, m3 (water)/m3
(sediment layer)
boundary layer thickness in sediment below surface water, m =3 18 Deff0683.
7-10
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8.0 Pollutant Transport in Plants
This section describes the development of the algorithms and the transition probabilities related
to the plant domain.
8.1 Conceptualization of the Plant Domain
The plant domain implemented in the prototype, for uptake of organic compounds, is comprised
of leaves, roots, xylem, and stem. The cells are assumed to each be homogeneously-mixed. A
summary of the gains and losses for the plant model is presented in Table 8-1. The leaf cell is
assumed to interact with the air domain (including gaseous and paniculate phases), while the
other cells interact with the root zone. The plant cells, the domains to which they are linked, and
the types of processes modeled are shown in Table 8-1. There is no direct interaction between
the leaves and other compartments in the current model; therefore, they are treated as separate
domains (i.e., there is a row in the transition matrix for each compartment). Only the leaf
compartment algorithms are originally in dynamic form. The time to equilibrium was estimated
for each of the other compartments to allow conversion of the steady-state partitioning relation-
ships to dynamic form. Plants are divided into these specialized domains because:
• Literature suggests that concentrations of nonionic organic contaminants in foliage
are primarily related to those in air and that concentrations in roots are generally
related to those in soil (with stems serving as the conduit between the two).
• Herbivores may eat part but not all of a plant. Contaminant mass in the xylem is
useful to keep track of because future versions of the model may address exchanges
between the plant cells, and the xylem plays a critical conduit.
8.2 Leaf Cell
The leaf compartment interacts with the air domain. Deposition of the particle-bound chemical
and exchange with the vapor phase of the chemical are addressed.
8.2.1 Transfer from Air
Transfer processes from air to the soil surface include dry deposition of particles, wet deposition
of particles, wet deposition of gases and diffusion of gases. The dry deposition velocity is the
ratio of contaminant flux (mol/[nr-h]) to contaminant concentration in air mol/m3. Dry
deposition of chemicals bound to fine particles (less than 5 micron) have a smaller deposition
velocity than chemicals bound to larger particles.
8-]
-------
Table 8-1
Summary of Gains and Losses for Plant Model Cells
Implemented in the Prototype
Cell
Leaf
Root, Stem, Xylem
Liquid Compartments
Relevant
Gains Type of Process Phase
From Air
Uptake from air Exchange Vapor
Wet gaseous Advective Vapor
deposition
Dry and wet Advective Solid
deposition onto
leaf
From Soil Root
Zone
Uptake from soil "Steady-state" Liquid
pore water converted to
Exchange
Losses
Type of
Process
Relevant Phase
To Air
Elimination
to air
Blowotf to
air
Washoff to
soil
Exchange
Advective
Advective
Total
Total
Total
To Sink(s)
Decay
Transformation
total
To Soil
Root Zone
Elimination
"Steady-state"
converted to
Exchange
Total
Wet deposition, which occurs during precipitation, is proportional to the rate of precipitation
(i.e., rain in m/h), but differs in both the relative magnitude and nature between particles and gas-
phase chemicals. For all deposition processes, there is a competition between vegetation and soil
surfaces as receptors for deposited materials. An interception factor is used to determine the
relative fraction of particles landing on soil surface and vegetation surface. Interception factors
differ between wet and dry deposition.
Dry deposition velocity is defined by a deposition velocity, v^, found in Table 8-2. The dry
deposition plant interception fraction is defined as:
lFd - \-e"BI
where:
IFU = plant interception fraction
BI = dry biomass inventory per unit area
a = vegetation attenuation factor.
8-2
-------
Table 8-2
Parameters for Leaf Cell of Plant Model
Parameter
VL
vd
Bl
a
rain
Wr
sbl
LAI
^r
rh
Pa
P,
Description
Total volume of the leaf compartment
for the area under deposition
Dry velocity
Dry biomass inventory per unit area
Vegetation attenuation factor
Rainfall rate
Washout ratio
Vegetation dependent leaf wetting
factor
Leaf area Index
Boundary layer thickness of air on
plants
Relative turbidity
Atmospheric dustload
Soil particle density
Algorithm for Calculation
Specified
43.2 m/s
Specified
2.3
Specified
200,000
.3
Specified
Specified
Specified
Specified
Reference/Com ment
van de Water, 1995
Bidleman, 1988
van de Water, 1995
Whicker and Kirchner,
1987
Bidleman, 1988
Muller & Prohl, 1993
Assumed to be the
same as 6 of air on
soil
Wet deposition velocity (m/s) is defined as:
Wetd = Wr x rain
where:
Wetd = wet deposition velocity
rain = rainfall rate
Wr = washout ratio.
The washout ratio is a unitless factor relating particle washout to rainfall rate. The washout ratio
is an emperical measure that depends on the chemical and level of pollution in the air.
8-3
-------
The wet deposition plant interception fraction is defined as:
-//i2 x rain
IFW = Su x LAI x e\ 3 * S"'
where:
IFW = wet plant interception factor
SM = vegetation dependent leaf wetting factor
LAI = leaf area index.
The other factors in the equation are imperical factors (Muller and Prohl, 1993).
These equations are applied such that deposition to plants is the deposition velocity times the
interception factor, and the deposition to soil is the deposition velocity times one minus the
interception factor. The equations are then converted into fugacity-based transfer factors by the
methods being used in this project as described in Section 4.2.
It is assumed that chemicals attached to particles reach instantaneous solution equilibrium with
plant tissues when they land on the plant. Particles are either washed off the plant with rain or
blown off the plant with wind at a rate that equals the deposition rate to the leaves. Studies that
quantify the relative rate of washoff to blowoff were not available, and representative values
were used. It was assumed that 5 percent of the paniculate mass was blown back into the air and
95 percent was washed off into the soil.
From these relations, we define the transfer factors due to deposition from air:
IF x rain x Z , x (IF x wet, xIf,xv,)xZ x —
H' vtufrr v H a J a a' op
Td = L
(W ~-m §
ZaXda
where:
T* - transfer factor from air to plant from deposition.
8-4
-------
.05 x (lFd x v, + Ifw x wet,) x Zap x
Tf°" z, * <*,
where:
Tpa = transfer from plant leaves back into the air.
This equation accounts for 5 percent of the particles re-entering the air as a result of being blown
off the leaves. The equation below accounts for the remaining 95 percent being washed off into
the soil.
.95 x (IF, x v, + //H. x wet,) x Zap x -^
T = - PL
where:
Tpg = transfer factor from plant leaves to the ground.
8.2.2 Diffusion Between Leaf and Air
The diffusion from plants to air is based on two resistances in parallel: the stomata and the series
resistance of air and cuticle. The conductance of a gaseous contaminant through the stomata is
based on a correlation to the conductance of water vapor through the stomata. The conductance
varies with the relative humidity, reflecting that stomata close up during dry conditions.
Additionally, the stomata are only open during the day. If day/night patterns are used in
TRDvI.FaTE in the future, additional adjustments will be necessary.
461 x Temp
\-rh)x6ll x
8-5
-------
where:
Ssiomata = conductance through the stomata (Trapp, 1995)
rh = relative humidity
Temp = temperature (Kelvins).
where:
= conductance through the cuticle (Reiderer, 1995).
The conductance through the cuticle is then put in series with the resistance through the air on the
leaf surface to yield the overall conductance:
D Z t> , Z
air air o cuticle p
where:
Y0 = total conductance
pa = thickness of air boundary layer over the plant
Xap = thickness of air boundary layer over the plant.
The fugacity based transfer factor is then determined for a diffusive process:
.d,ff _ Yar, Ssto
'
where:
T^ = transfer factor for plant to air from diffusion.
8.3 Root Cell
The algorithm to describe soil-to-root transfer is derived from an equilibrium relationship, an
estimated time-to-steady state, and the assumption of a first-order rate of uptake. The equili-
brium relationship is a generalization of the Briggs, et al. (1982) equation developed in Trapp
(1995):
8-6
-------
where:
CR = concentration in roots (mg [chemical]/m3 [root fresh weight])
Csw = concentration in soil pore water (mg [chemical]/m3 [soil pore water])
WR = water content of root (mass/mass wet weight)
1R = lipid content of root (mass/mass wet weight)
b = correction exponent for the differences between octanol and lipids
pR = density of fresh root (g [root]/cm3 [root])
psw = density of soil pore water (g [soil pore water]/cm3 [soil pore water])
Assuming that it takes time ta in order to reach 100a% of the steady-state value when Csw is
approximately constant, then:
dCR(t)
di 2 sw ' R
where:
kr, = -ln(l-a)/ra
Let NK denote the total mass of the chemical in the roots, and VR (m3) the total volume of root in
the domain. Then NR= VRCR, and the previous equation in mass balance form is:
- k V C - k N
^2VR^s* VV/?
dt
Applying fugacity, this reduces to:
dN,(t) Z
K^ = i- v *ater
^T ' D
_ _
^T ' D *^ l ^
(it ' KV Z (total) '
rmnzone riHiizime^ '
where:
Z^Mei = fugacity capacity for pure water, mol (chemical)/m3(water)-Pa
8-7
-------
= total fugacity capacity for root zone, mol (chemical)/m3 (root zone)-
Pa
= Volume of TOOt ZOHC, m3(rOOt ZOHC).
The parameters for this algorithm are summarized in Table 8-3.
8.4 Xylem Liquid Cell
The algorithm used to calculate the concentration in the xylem liquid is derived from an equili-
brium relationship between the soil pore water and the xylem concentration, in conjunction with
an estimated time-to-steady state. The equilibrium relationship is (Bromilow and Chamberlain
1995, and Briggs, et. al., 1982):
C -TSCFxC, xp A,
Table 8-3
Parameters for Root Cell of Plant Domain
Parameter
a
ta
WR
IR
b
PR
Prw
Description
Fraction of steady-state which is reached
by time ta when concentration in soil pore
water is constant
Time to reach 100a% of the steady-state
value when concentration in soil pore
water is constant
Water content of root
Lipid content of root
Correction exponent for the differences
between octanol and lipids
Density of fresh root
Density of external solution (soil pore
water)
Units
None
hour
mass/mass
wet weight
mass/mass
wet weight
none
g/cm3
g/cm3
Value used in the Prototype
0.95
Used twice the value estimated from Hsu,
et al., 1990, for xylem liquid since solid
root is an additional compartment to get to
0.85; Value for bean root in Trapp (1995).
0.01 1 ; Value for bean root in Trapp (1 995).
0.76 ; Average of values for barley of
(0.77) and bean root (0.75) in Trapp
(1995)
0.9; assumed
1 .0; assumed
8-8
-------
where:
Cn = concentration of chemical in xylem liquid, mg (chemical)/m3(xylem
liquid)
Cw = concentration in soil pore water, (mg [chemical]/m3 [soil pore water]
TSCF = transpiration stream concentration factor (mg [chemical]/g
[xylem liquid] )/(mg [chemical]/g [soil pore water)
pxy = density of xylem liquid, g (xylem liquid)/cm3 (xylem liquid)
psw = density of soil pore water, g (pore water)/cm3 (pore water).
The densities are required because the TSCF is on a mass/mass basis.
Assuming that it takes time ta to reach 100 percent of the steady-state value when Csw is
approximately constant, then (Section 4.3):
where:
Let /Vn denote the total mass (in mg) of the chemical in the xylem liquid, and Vxy (m3) the total
volume of xylem liquid in the domain. Then Nxy= VxyCxy, and the previous equation in mass
balance form is:
Mn(t)
di
t,V C -k.N
2 rv .IH I jn
Applying the fugacity concept, this is equivalent to:
- - *,v, Z
Vrtzime(toial)
..
8-9
-------
where:
Z^,,,, = fugacity capacity for pure water, mol(chemical)/m3 [water)-Pa
zrootzone(total) = total fugacity capacity for root zone, mol(chemical)/m3 (root zone)-
Pa
= volume of root zone, m3(root zone).
The parameters for this algorithm are summarized in Table 8-4.
8.5 Stem Cell
The algorithm used to calculate the concentration in the stem is derived from an equilibrium
relationship between the soil pore water and the stem concentration, in conjunction with an
estimated time-to-steady state. The equilibrium relationship is (Briggs, et al., 1983):
Table 8-4
Parameters for Xylem Cell of Plant Domain
Parameter
a
t.
VR
TSCF
PR
Pw
Description
Fraction of steady-state at which
is reached by time t0 when
concentration m soil pore water
is constant
Time to reach 100a% of the
steady-state value when
concentration in soil pore water
is constant
The total volume of xylem liquid
in the domain
Transpiration stream
concentration factor
Density of xylem liquid
Density of external solution (soil
pore water)
Units
None
hour
m3
(mg
[chemicaiym31 xylem
')/(mg[chemi-
cal)J/m3 (soil pore
water)
g/cm3
g/cm3
Algorithm or Value used in Prototype
0.95
Calculated as (Hsu, et al., 1990 )
1.62+exp[logKow-1.8]
This is an estimate of the time-to-steady-state.
Assumed to be 4 percent of stem volume.
(Boersma, et al., 1991)
Calculated in Prototype 2.0 based on
Cinmethylin and analog chemicals (Bromilow
and Chamberlain, 1995)
0. 7 exp[- (log K^ -3. 07f/2. 78.
Formula is also available (Briggs, et al., 1982)
0. 784 exp[- (log Kow • 1.78^/2.44
Based on pesticides in barley shoots.
1.0 ; Paterson, et al. (1994) makes the same
assumption, but acknowledge that "the
presence of dissolved organic matter could
distort this relationship."
1.0
8-10
-------
where:
di
Astern = concentration of chemical in stem (mg [chemical]/m [stem)
Csw = concentration in soil pore water (mg/m3)
SCF = stem concentration factor
Pstem = density of stem, g (fresh stem)/cm3 (fresh stem)
psw = density of soil pore water, g (pore water)/cm3 (pore water).
The densities are required because the SCF is on a mass/mass basis.
Assuming that it takes time ta to reach 100a% of the steady-state value when Cm is
approximately constant, then:
= *,C -k.C
2 sw 1 stem
where:
*= -ln(l-a)/ra
Lei Nslem denote the total mass (in mg) of the chemical in the stem, and VSIcm (m3) the total
volume of stem in the domain. Then Nstem= V51(;mCslem, and the previous equation in mass balance
form is:
dN^(t} - k y c _kN
< "-2.swri.nv *V stem
Applying fugacity notation this is equivalent to:
dN (t) Z
"em = k V wiaer - k N
d{ 2 "em Vrl.im((total) ' *'em
8-11
-------
dt
where:
= fugacity capacity for pure water, mol (chemical)/m3 (water)-Pa
= total fugacity capacity for root zone, mol (chemical)/m3 (root zone)-
Pa
= volume of root zone, m3 (root zone).
The parameters for this algorithm are summarized in Table 8-5.
Table 8-5
Parameters for Stem Cell of Plant Model
Parameter
a
ta
"stem
SCF
Pslem
P
-------
In a simplified representation of the litterfall process for the initial testing of the prototype, a
constant litterfall rate is assumed. An appropriate estimate would be 1/180 days, or 1 over the
length of the growing season. Plant growth is often modeled as a dilution mechanism, but the
process is not being modeled here because a constant volume is used for the plant compartment;
thus, dilution occurs as a result of the removal of chemicals through litterfall. The transfer factor
is equal to the litterfall rate:
Tpg = Litterfall rate
where:
Tpg = fugacity based transfer rate from plant to ground
Litterfall rate = 1/180.
8.7 Summary of Important Limitations of Plant Model in the Prototype
As with any model, the plant model implemented in the prototype has limitations, some of which
should be eliminated, if possible, in subsequent versions.
8.7.1 Plant Growth
The plant algorithms implemented in the prototype are applicable for mature plants only, and do
not address plant growth. If resources permit, it may be worthwhile to incorporate this process
for subsequent prototypes or to input monthly biomass estimates into the model.
8.7.2 On The Plant vs. In The Plant
For wildlife that ingest pans of a plant, it may be important to keep track of the total amount of
chemical both on and in the plant. The diffusion algorithm implemented in the prototype is
designed to predict the amount in the plant; the deposition equations represent the sum of conta-
minant mass in and on the plant.
8.7.3 Plant Domains
There is not an algorithm implemented to predict the amount of chemical in wood. It is not clear
how critical this may be for subsequent prototypes, and it appears that there are few models that
have simulated this phenomenon.
Domain instances for seeds, fruits, bark, and wood have not been incorporated into TRIM.FaTE.
Seeds and fruits are important food for wildlife and humans. Few, if any, models have been deve-
loped to stimulate the transfer of chemicals to wood, although wood could be an important sink.
8-13
-------
9.0 Pollutant Transport in the Aquatic Food Web
Transfer of contaminants between the fish domain and surface water is presented in this section.
A simplified model approximating only the first order processes was used in the prototype. A
summary of the gains and losses for the aquatic biota is presented in Table 9-1.
9.1 Conceptualization of the Aquatic Food Web System
The biotic and abiotic mechanisms affecting the transfer of pollutants within aquatic systems are
extremely complex. It is, therefore, important to understand that attempts to model the transfer
and fate of pollutants within these systems are subject to varying levels of uncertainty related to
simplification of complex biotic and abiotic processes. The stochastic approach of TRIM.FaTE
relaxes the constraints of oversimplification by employing distributional data. Moreover,
TRIM.FaTE has been designed to readily accommodate new algorithms or parameters as
understanding of these processes improves over time.
In the prototype, simple biotic transfers within an unstratified fresh water system were modeled.
The system was assumed to be an industrialized region with a river feeding a larger slow-moving
embayment or lake system. The uptake of pollutants of concern, which in this case were B(a)P
and phenanthrene, was assumed to be via bioconcentration processes directly from the water
column or sediment particles during respiration or incidental ingestion, as well as biomagnifica-
tion during trophic level transfers. The biotic transfers were modeled with use of a few species
occupying key food chain levels.
The modeled benthic community was represented by the mayfly (Hexagenia limbata), and with
the eurasion milfoil macrophyte (Myriophyllum spicatum) anchored to the sediment extending up
into the upper reaches of the water column. In addition, the channel catfish (Ictalurus
punctatus), a bottom feeding omnivore, was employed to model direct transfers from benthic
invertebrates up through a top carnivore such as the kingfisher. Upper water column fishes
included the herbivorous bluegill (Lepomis machrochirus) and the carnivorous largemouth bass
(Micropterus salmoides). It is important to note that although the bluegill is generally an omni-
vorous animal, the prototype model assumes its diet to be 100 percent vegetative; thus it is
classification as an herbivore. Population density ranges were adopted based on assumptions of
varying habitats present within the aquatic systems, as well as natural characteristics such as
water flow rates, sediment grain sizes, depth, and the presence or absence of vegetation. The
9-1
-------
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aquatic population assumptions for the segments modeled in the prototype are shown in Table
9-2. Aquatic population assumptions were gathered from Bonar, et al (1993), Carpenter, et al.
(1995), Jackson (1995), Maciena, et al. (1995), and Mclnery and Degon (1993).
Table 9-2
Aquatic Population Assumptions
Model Segment
River Segment
River Segment
River Segment
River Segment
River Segment
Lake Segment
N
M
L
J
H
Q
Blue Gill
Herbivore
(No./ha)
31-100
80-150
100-250
100-250
100-250
250-600
Largemouth Bass
Carnivore
(No./ha)
6-50
25-75
40-80
40-80
40-80
50-100
Channel Cat
Omnivore
(No./ha)
50-150
50-175
40-150
40-150
40-150
20-100
Mayfly
(No./sq.m)
100-500
100-500
200-600
200-600
200-600
500-1000
Macrophyte
(g/sq.m)
1-10
5-20
20-50
20-50
20-50
50-200
The algorithms employed in the prototype model provide a means to estimate the uptake, seques-
tration, and loss of B(a)P and phenanthrene within the representative aquatic receptors. Uptake
parameters include deliberate and incidental ingestion of abiotic media such as water and sedi-
ment as well as the more obvious uptake via feeding. Factors affecting uptake and loss rates,
such as lipid concentrations within the receptors, body weight, ventilation rates are provided in
Table 9-3 as ranges. It is important to note that uncertainties associated with natural biological
variabilities are addressed, in part, with use of distributional databases as shown in Table 9-2.
For the prototype, the food web is summarized in Table 9-4.
9.2 Benthic Community Transfers
The sole infaunal benthic representative within the prototype was the immature mayfly
(Hexagenia limbata). The mayfly is a ubiquitous invertebrate indigenous to the Great Lakes, but
commonly found in fine, high organic sediment throughout the United States. It represents an
important fish forage resource and is frequently employed by ecologists and aquatic risk asses-
sors as a key sentinel organism for sediment toxicity studies. Uptake of contaminants from the
overlying water body is primarily based on respiratory processes. Stehly and others (1990) have
found that the clearance rate of B(a)P and phenanthrene from water by the mayfly is analogous to
9-3
-------
Table 9-3
Aquatic Biota Assumptions
Blue Gill
Largemouth Bass
Channel Catfish
1. Fish/water column accumulation
1 . Lipid Content (% of Wt.)
2. Ventilation Rate
(ml/min/kg)
3. Size Distribution (kg)
4. Population Density (/ha)
3.5-7.9
500 - 6,000
0.09-1.12
31 - 925
5.7-15.0
500 - 6,000
0.22-3.15
6- 143
7.0-19.0
500 - 6,000
0.22 - 6.75
10-205
II. Macroinvertebrate Densities: (Based on the Mayfly, Hexagenia)
1 . Size Distribution (kg)
2. Population Density
(/sq.m)
0.00001 - 0.0005
10-5,000
Table 9-4
The Prototype Aquatic Food Web in the TRIM.FaTE Prototype
Trophic Level
Aquatic Carnivore
Aquatic Omnivore
Aquatic Herbivore
Producer
Benthic Herbivores
Representative Species
Largemouth Bass
Catfish
Blue Gill
Macrophyte
Mayfly
Linked to Domains
Water
Omnivore
Herbivore
Macrophytes
Benthic Herbivores
Water
Herbivore
Macrophytes
Benthic Herbivores
Sediments
Water
Macrophytes
Water
Water
Feeds on (% diet)
Bluegill (80%)
Catfish (10%)
Mayfly (10%)
Bluegill (5%)
Mayfly (50%)
Algae (45%)
Algae (100%)
NA
Algae 000%)
the clearance rate of oxygen during 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 respira-
tory surfaces. With a known or assumed volume of water passing over respiratory membranes
9-4
-------
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 Stehly and others (1990) for estimating PAH uptake and loss within the benthic invertebrate
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 bioconcentration
factor for 30-, 60-, and 120-day-old mayflies for B(a)P and phenanthrene were provided by
Stehly and others (1990):
dC , C f
mf s-'j f _ /~-j mi
~ ~
dt u » u Vd
where:
Cmf = Amount of compound in the organism normalized on a weight basis
(nanogram [ng]/g)
Clu = Clearance constant (equivalent to kj (milliliters [mL] water cleared/g
organism - hour)
Cw = Concentration of the compound in the interstitial water (ng/mL)
Vd = Proportionality constant that relates the amount of compound in the organism
to the concentration in the exposure water (equivalent to BCF).
An estimation of pollutant concentrations in mayfly populations is as follows:
dN , N N ,
- - - -
dl m/ m} u V " V.
M d
where:
nmf = number of mayflies
= mass of individual mayfly.
From this equation, transfer factors can be derived as:
T CL«
I = n m , -
M -mf mf mf i/
9-5
-------
CLu
T = _ «
mf-w y
9.3 Water Column Transfers
The algorithm used to calculate concentrations in water column organisms is derived from
equilibrium partitioning based algorithm and is based on the assumption that organic carbon is
the only sink for neutral organics in the sediment, and lipids are the only source within the biotic
receptors. The equilibrium relationship is as follows:
C C
— = AF sed
L TOC
where:
C0 = omnivore tissue concentration at steady state (micrograms per gram [|Jg/g])
L = lipid content of organism (g lipid/ g organism)
TOC = total organic carbon in sediment (g carbon/g sediment)
Cscd = sediment concentration ((Jg/g)
AF = accumulation factor (g carbon/g lipid).
This equation is converted to the following non-equilibrium differential equation following the
conversion scheme outline in Section 4.3:
dC
<1 - if c -k C
, *•:.«•
at
where:
k, = -In(l-a)/t0./day
a = Value between 0 and 1 (0.90)
ta = Time required in order to reach 100a% of the steady-state value when Csw is
approximately constant with time (96 hours)
k: = (k,)(AF)(L)/TOC.
9-6
-------
When converted to mass units (N), the nonequilibrium form looks like:
= n m I - s—-k. No
°f "f 2v
Vsed
where:
nof = omnivore population
mof = mass of omnivore
Vsed = volume of sediment volume element
Psed = bulk sediment density.
Thus the transfer factors for omnivore to sediment transfer and sediment to omnivore transfer are
given by:
_ "of
sed-o y
Vsed
9.4 Food Chain Transfer Equations for Fish Domain
The following model for estimating pollutant concentrations in fish (Thomann, 1989) was used
as a starting point in the derivation of the transfer probabilities associated with the fish domain:
dC
where:
CF = concentration in fish (ug/kg)
ku = uptake rate from water via the gills (1/kg-day)
CWD = dissolved chemical concentration in water (ug/L)
kD = chemical uptake from food (kg food/kg fish/day)
P, = proportion of the diet consisting of food item I
CD, = chemical concentration in food item I (ug/kg)
k,.g = elimination via the gills (I/day)
9-7
-------
kE = elimination via fecal egestion (I/day)
RE = metabolic transformation of chemical (I/day)
kc = dilution contaminate concentration from growth (I/day).
This algorithm is generally 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. Initially, it is assumed that there is no uptake through other food items, and the
elimination via fecal egestion and the metabolic transformation factors were neglected as they
were considered second-order rates. Thus, for two fish with concentrations Cfl, and Cn, the
previous equation can be rewritten as:
dC{,
IL = b x/~ - k
, *u/AOWD *>
= I ~xC - k
A(~ *
,
To convert the concentrations to masses, it is assumed that:
N
c *=—'
Hrf y
H
c^
- N,
where:
m, = mass of fish 1 (kg)
m: = mass of fish 2 (kg)
N, = mass of contaminant in fish 1 (ug)
n: = mass of contaminant in fish 2 (ug)
Vfc = volume of surface water cell (L).
9-8
-------
Substituting yields:
dt
N
= k , —- -
m.
2 - k H - k l
dt ~ ~ "* V.., <*2 Z
Adding these equations yields the mass transfer equations for the total fish domain, as follows:
d ( N./m. + NJm^
dt
/n,
Making the simplifying assumptions that individual fish mass is represented by a population
average mf (m1=m2=mf), and that ku,=ku;=kuand kcg,=keg2=keg, yields:
m
dt
N
= 2 k —- - k
u y e
N.+ N,
m.
This equation can be generalized from 2 to nf fish, with Nf (= N,+N2) being the total mass in the
fish domain to yield the following generalized CMT equation for a fish domain:
dN
f H
- = n, k m( — - k Nr
dt f u f y 'K f
Generalizing this equation to include feeding (based on the diet shown in Table 9-3) yields the
following food chain mass transfer equations for the individual fish species.
It is important to note that the equations in their present form excludes dermal uptake as a
significant exposure route. The equations include gill uptake (bioconcentration) and food uptake
(biomagnification) as the two principal exposure routes. Following are the food web equations:
9-9
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Aquatic herbivore (fh = fish herbivores) (100 percent macrophyte diet):
N..
N_
dt
mp
where:
° °85
Fd = feeding rate = 0.022
T = temperature
E = efficiency of transfer of chemical.
(kg-prey/kg-predator day)
For smaller organisms, the following equations should be used to estimate E:
For chemicals with log Kow = 2-5
For chemicals with log K<,w = 5-6
For chemicals with log K^ = 6- 1 0
log E = -2.6 + 0.5 log K
log E = 0.8
log E = 2.9 - 0.5 log Kow
For larger organisms, the following equations should be used to estimate E:
For chemicals with log Kow = 2-5
For chemicals with log K^ = 5-6
For chemicals with log Kow = 6-10
log E = - 1 .5 + 0.4 log K,,
log E = 0.5
log E = 1 .2 - 0.25 log K
Aquatic omnivore (f0 = fish omnivore):
dNf,
~~di
N
— - k Nt
N
A7,
Aquatic carnivore (fc = fish carnivore):
dNt N
-JL = nfKmf— - k Nf
dt * ' A-V « /(
N N. N.
a -^ * a-£ + a. -
9-10
-------
Implicit in the previous equation is the assumption that the mass of an individual fish is constant
over the time of the simulation. It may be noted that the dilution due to growth factor (k^ is not
included in the equation because k^ is based on concentrations, while the mass transfer equations
are in mass units.
The chemical uptake rate ku is estimated using the following formula:
k = 103(oTY/p)£
where:
ku = chemical uptake rate [L/day-kg(w)]
co = body weight [g(wet)]
Y = 0.2 (Thomann, 1989)
p = fraction lipid weight [kg(lp)/kg(wet)]
E = efficiency of transfer of chemical.
The chemical assimilation efficiency (E) can be approximated as previously described. There is
an apparent increase in assimilation efficiency for smaller organisms; therefore, organisms have
been divided into two weight groups: less than 10 to 100 g (wet) and more than 100 g (wet)
weight.
Thomann (1989) gives the excretion rate from gills using the following equation:
9.5 Derivation of Aquatic Macrophyte Transfer Equations
Uptake by aquatic macrophytes were based on the simple assumption that the eurasion milfoil
was only uptaking PAHs from the water column, and not via its root system embedded in the
sediment.
Aquatic macrophytes:
F = k V C -k V C
' MP I MP .m ^2 MP MP
9-11
-------
where:
FMP = Net flux of chemical in the macrophyte, (jag/day)
k, = Bioaccumulation rate (day"1)
VMP = Volume of the macrophyte (L)
Csw = Chemical concentration in water (ug/L)
k2 = Depuration rate (day"1)
CMP = Chemical concentration in macrophyte (ug/L).
The flux rate can be adjusted for weight ((jg/day-kg plant) by dividing the flux rate given by the
weight of the plant. The rate constants k! and k2, are estimated using the following equations:
\lk. = 0.0020+500/A:
1 On
1/Jt, = 1.58 +0.000015 Ko
where the units for k, and k; are day'1.
Aquatic macrophyte (mp = macrophyte):
dN N
—IT. = K.V — - ^
I mp ? mp
9.6 Ongoing Development
Again, given the complexities associated with ecosystems, and the importance of these comple-
xities in affecting pollutant transfers, a much larger database is needed. For model users to
predict the fate, transport, and principal reservoirs of pollutant mass within their aquatic system
of interest, they will need a "library" of benthic and water column fresh and saltwater species
representing multiple trophic levels. This library should include basic data critical to uptake and
loss of organic and inorganic pollutants from a mass balance perspective. These include distribu-
tional data specific to ingestion and loss rates, respiration rates, body weights, lipid levels, popu-
lation sizes, habitat preferences, feeding preferences and species distribution. Such efforts could
be pan of an ongoing effort to improve the usefulness of TRIM.FaTE.
Within the prototype, biotic water column domain was expanded from a single fish species
preying on like species to a more realistic ecosystem represented by aquatic macrophytes and
9-12
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several feeding trophic levels. Bioaccumulation by herbivorous representatives as well as
omnivores and carnivores are accommodated within the prototype simulation. It is important to
note, however, that the trophic level representations are grossly oversimplified to reflect primary
uptake and loss from a single representative species from each level. No natural variability
specific to individual, populations or communities was accounted for in this simulation. The
aquatic plant community, for example, is simply represented by a single macrophyte (Myiio-
phyllum spicatrum). Other macrophytes as well as various algal populations were deliberately
excluded, with the intent of adding their biomass and uptake/loss variable to a later date.
9-13
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10.0 Contaminant Transport in Terrestrial Food Chain
This section describes the biotic algorithms that were included in the prototype.
10.1 Terrestrial Wildlife Algorithms
Several species of terrestrial wildlife are considered in the prototype as identified in Table 10-1.
These species were selected because they are taxonomically dissimilar and represent differing
domains. The basic algorithms utilized are the same for the all of the species in Table 10-1, with
different input parameters as identified in Appendix B.
Table 10-1
Terrestrial Wildlife Defined for TRIM.FaTE Prototype
Domain
Terrestrial omnivore
Semi-aquatic piscivore
Terrestrial insectivore
Aquatic mammalian herbivore
Terrestrial predator/scavenger
Aquatic insectivore
Terrestrial vertebrate herbivore
Piscivore
Aquatic mammalian omnivore
Terrestrial ground invertebrate feeder
Benthic invertebrate
Soil Detritivore
Insects
Specialized Domains
White-footed mouse
Belted kingfisher
Black capped chickadee
Mallard
Red tailed hawk
Long-tailed weasel
Tree swallow
Mule deer/Black-tailed deer
Long-tailed vole
Mink
Racoon
Trowbridge shrew
Mayfly
Earthworm
Insects
Associated Parcels
A, D, F, G, P
H, J, L-N, Q
A, D, F, G, P
H,J, L-N.Q
A, D, F, G, P
A, D, F, G, P
H, J, L-N, Q
A, D, F, G, P
A, D, F, G, P
H, J, L-N, Q
H, J, L-N, Q
A, D, F, G, P
H, J, L-N, Q
A, D, F, G, P
A. D, F, G. P
Wildlife may be exposed to contaminants through food, soil, and water ingestion, and through
inhalation of contaminants in air. Elimination of contaminants from body tissues may occur
through metabolic breakdown of the contaminant or excretion of the parent compound through
urine, feces, milk (mammals only), and eggs (birds and reptiles only). To account for these
multiple routes of exposure and elimination, the generalized model implemented is:
10-1
-------
dC, /dt = [(I. *CW * AJ + (I, *CS* AS) + £Pj(If *Cfj* Af) + (I. *Ca* A.)] - [C, * (Em + Eu + E, + Ee)J2)
where:
C, = total, whole body, internal concentration in animal (mg [chemical]/kg [body
weight])
^ = water ingestion rate (L/kg body weight/d)
Cw = concentration of contaminant in water ingested by animal (mg/L)
A^ = assimilation efficiency of contaminant from water (unitless)
Is = soil ingestion rate (kg/kg body weight/d)
Cs = concentration of contaminant in soil (mg/kg)
As = assimilation efficiency of contaminant from soil (unitless)
Pj = proportion of food type (j) in diet (unitless)
If = food ingestion rate (kg/kg body weight/d)
Cfj = concentration of contaminant in food type (j) (mg/kg)
Af = assimilation efficiency of contaminant from food (unitless)
^ = inhalation rate (mVkg body weight/d)
Ca = concentration of contaminant in air (mg/m3)
Aa = assimilation efficiency of contaminant from air (unitless)
Em = contaminant elimination through metabolic breakdown (d "')
Eu = contaminant elimination through excretory processes (urine and feces) (d "')
E, = contaminant elimination through lactation (milk production, mammals only)
(d-1)
Ec = contaminant elimination through egg production, birds only (d "').
To utilize this equation in TRIM.FaTE, it must be converted to mass balance form. For a given
animal of a particular species with body weight, BW, if we denote by N, the mass of chemical in
the animal (in mg), then the previous equation is equivalent to:
dN
The previous equation is for a single animal. For modeling animal populations, one can either
assume that the properties of each animal in the population are approximately constant across
individuals, or one can model distinct individuals. Modeling distinct individuals may be
advisable in populations with a wide variation in properties across individuals; in this case, there
would be a differential equation for each individual considered. If the amount of chemical in a
particular individual is not of interest, then the differential equations may be combined to a single
differential equation for the whole animal population if it can be assumed that an individual is a
random variate within a defined population distribution. For the purpose of the prototype, it is
10-2
-------
assumed that the properties are approximately the same across individuals, and hence all that is
required is an estimate of the number of individuals in the population. If there are n, individuals
in the animal population, and if Ntot is the amount of chemical in the total population, then N'°'=nt
Nt, and combining the n, differential equations for each individual (using the previous equation)
yields:
dN
dt
The number of individuals in the population is estimated in the prototype using parameters
identified in Appendix B.
10.2 Earthworm Model
Uptake of chemicals from soil by earthworms has been much better studied than uptake by other
soil invertebrates, but is still much less studied than aquatic invertebrates or vertebrates.
Although some information is available on the kinetics of earthworm uptake (Belfroid, et al.,
1994a,b), all available operational models are based on equilibrium partitioning with soil or soil
pore water. There is a small amount of information available on how long it takes for steady
state to be attained, from which it is possible to derive time-dependent equations. Whichever
method is used, the steady-state (equilibrium) partition coefficients are required. In terms of
implementation, if equilibrium is assumed, then a separate differential equation is not required
for the worm component of the soil. Instead, the worms constitute another "phase" of the soil,
analogous to the solid, liquid, and vapor phases of the soil.
It has been proposed that invertebrates are in equilibrium with the aqueous phase of soil. This
approach has been used for sediment by EPA and others (DiToro, et al. 1991). It is well
supported for sediment invertebrates and is supported by some evidence for earthworms, and
possibly other soil invertebrates (van Gestel and Ma, 1988; Connell, 1990a; Lokke, 1994).
However, it has been suggested that it will underestimate accumulation of a few chemicals for
which the dietary route is dominant (Belfroid, et al., 1994a,b). This approach has the advantage
that differences among site soils that are relevant to earthworm uptake may be accounted for in
the model of water/solid phase partitioning. In addition to potentially making extrapolations
between soils more accurate than soil/worm partitioning, it has the advantages of making
available for use the large literature on biota/water partitioning factors (bioconcentration factors)
and the numerous quantitative structural activity relationships for biota/water partitioning. It has
10-3
-------
been suggested that for lipophilic compounds, earthworm accumulation should also be a function
of lipid content of the worms (Connell and Markwell, 1990). This is not a component of the
standard sediment model, and makes no contribution to predictive accuracy in practice because
the site-specific lipid content of worms is unknown in nearly all cases, and would vary in an
unquantified manner seasonally and among species.
If the steady state partition coefficient between the concentration in the worm and the
concentration in the soil water is utilized, then at equilibrium:
C - K C
worm bw soil.hquid
where:
= concentration of chemical in the earthworm, mg (chemical)/kg (worm,
fresh weight)
= earthworm/water partitioning coefficient, L (soil pore water)/kg (worm,
freshweight)
.iiquid = concentration of chemical in soil pore water, mg (chemical)/L (soil pore
water).
The mass of the chemical in a worm population in a particular soil cell is given by:
where:
Nworm = mass of chemical in worm population in a particular soil cell, g (chemical)
10"3 = conversion factor to convert mg (chemical) to g (chemical)
A^ = area of soil cell containing worm population, m2 (area)
pwom = areal density of worm population in soil cell, kg (worm, fresh weight)/m2
(area)
Cwomi = concentration of chemical in the earthworm, mg (chemical)/kg (worm,
fresh weight).
10.2.1 Implementation of Earthworm Model if Concentrations are in Equilibrium
with other Soil Phases
If it is assumed that the concentration in worms is in equilibrium with the solid, liquid, and vapor
phase of the chemical in the soil cell, then the earthworms can be modeled as simply another
10-4
-------
"phase" of the soil cell. There is then no transfer factor between worms and other cells; only
certain factors used in other transition probabilities are affected. The implementation of the
worm model in this case is a generalization of the methods discussed in Section 4.2 (Multiple-
Phase Calculations). In particular, the total amount of chemical in the soil cell is given by (using
the notation of Section 4.2).
\jTotal _ f gas ]f gas+ f watery water+ y- wormy worm
where:
C*orm = concentration of chemical in worm phase of soil cell, g (chemical)/m3 (worm,
freshweight)
yworm _ vojume of Worm phase of soil cell, m3 (worm, freshweight).
Note that the concentration in the worms is on a volumetric basis (for consistency with other
phases) rather than a mass basis as previously used. The equilibrium relationship between the
concentration in worms and that in the soil pore water, on a volumetric basis, is:
Cworm _ J is /— water in"3
- " K L 1U
where:
dwortn = density of worm, g (worm)/m3 (worm)
10"3 = conversion factor to convert L (water) to m3 (water).
Assuming that the other phases are in equilibrium with the liquid phase and using the notation of
Section 4.2.1:
JT_yg,u + y vaur + ft y ;ol,d jQ-3 + j £ yworm jQ-3
r>rr "sulid d worm bw
AY ;
Defining:
yTotal _ ynos + yHater + ysolid + yworm
10-5
-------
the concentrations in the phases are then determined from the total mass in the soil cell by:
Toiahy Total
y aas y
«"'«'
RT y Total y
+ Total + Pjo'"/ a / Total + w>m
bw
_ ** f water
RT
y Total mrm °w y Total
(HIRT) N Tola'/V Tolal
( H V"" ,
1 RT yTolal
\r water
y Total Pjo
y irr3
i,dKd 1U
y solid
y Total *°n
„**, 'o-3
W Ht>f7n
i/ 7"o/a/
7 Total
irv
1U
- 3 /^ water _
( "
\/Stt!
i/ Two/
w water
y Tolal
^ solid
t io-3
\7 SOild
i/ Tow/
worm bw
io-3
i/ Ufjrrn
\7 Total
10
-3
Kbw 10'3 ) A' To'al/V Toml
H V*"
RT yTotal y Tot
y solid y worm
solid d y Total worm h" y Tolal
As before, these equations can be simplified using the concept of fugacity. In particular,
defining:
Zair = \I(RT)
s»l,d
and defining the total fugacity as:
7 —A ff 1 C\~^ 7
worm H t trm bw water
\r *ater i/ solid \r worm
7 + 7 _1 + 7
~airy Total *aler y Total ~s""a y Tolal worm y Tolal
10-6
-------
it is seen that:
Z \fTotal Z
f water _ water JV water .-, total
7 total Y Total 7 total
Z N Total Z
/-gas_ air •/v gas f, total
\^, — l^
7 total \7 Total 7 total
Z , , N Total Z
C solid _ solid £V solid s~i total
———— ^^—^——\_,
•7 total \7 Total y total
Z MTotal Z
f worm _ worm £» worm f-, total
7 total \r Total y total
where CTotal is the total concentration of the chemical in the soil cell (units of g [chemical]/m3
[total cell]).
10.2.2 Implementation of Earthworm Model if Steady-State Equations are
Converted to Time-Dependent Form
Using the method discussed in Section 4.3, the previous model can be converted to time-
dependent form if information is available on how long it takes to reach a specified fraction of
steady-state and it is assumed that chemical uptake is a first-order process. In this case, the
exchange between the soil pore water and earthworm population is modeled, yielding:
dC
—— =kK. C -kC
i bw M worm
where:
k = -ln(l-a)/ta,/day
a = Value between 0 and 1
ta = Time required in order to reach 100a% of the steady-state value when Cw is
approximately constant with time, day.
If it can be assumed that the areal density of worms is approximately constant with time, then the
previous equation is equivalent to the following differential equation:
dN
k\Q-*A ,p Kh C -kN
t<>// 'worm OH K w
i
worm
10-7
-------
If it is assumed that the solid, liquid, and vapor phases of the chemical in the soil cell are in
equilibrium, then using the relationships discussed in Section 2.1.1, the preceding equation can
be written.
dN
dt
, ,
'
\jso\l ytolal.soilcell
- kN
where the additional parameters are:
Nso,l
ysoil
z.,
z1
ater
total, soilcel]
= 10~3, conversion factor to convert 1/m3 (water) to 1/L (water)
= mass of chemical in soil cell (solid, liquid, and vapor phases), g
(chemical)
= Total volume of soil cell containing worms, m3
= Fugacity of pure water, moles (chemical)/m3 (water)-Pa
= Total fugacity capacity of soil cell containing worms, moles
(chemical)m3 (total volume)-Pa
The transition probabilities are then:
* *"
Mv
10
-3
water
V
sail
total,soilcell
T = -k
worm-will ell
Note that an additional conversion factor is necessary to convert mass to other units (e.g., moles);
this factor is multiplied through the whole equation and does not affect the form of the transition
probabilities.
10-8
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11.0 Code and Data Structures
The coding and data issues involved with the implementation of the prototype are described in
this section. The prototype basic code features and input data were significantly more complex;
thus, its implementation required a more sophisticated application of the Visual Basic-LSODE
environment. The details of these issues and the lessons learned for further development of
TRIM.FaTE are also outlined.
11.1 Basic Code Features
Flexibility of application is tremendously enhanced in the prototype; an object-based prototype
data structure is developed to facilitate this flexibility, and a preliminary algorithm library is
implemented (Table 11-1). Nontrivial data structures are necessary due to the variability of the
Table 11-1
Features of Implementation of the TRIM.FaTE Prototype
Feature
Flexibility
Implementation of initial
algorithm library
Comment
Internal object-based structure implemented that can
address arbitrary conceptual models of domains and links.
Limitations are due to computer memory and execution
time.
Central repository of equations for calculating transition
probabilities between two domains. Implemented in
manner that allows easily adding new algorithms. Written
in style intended to facilitate readability and debugging.
types of properties associated with any given type of domain (Table 11-2), and in order to store
the links between domains so as to permit the use of an algorithm library. This is not to be
confused with the (external) indexing of various aspects of the data structures themselves. The
general approach taken is to use collections of domains at each geographic location; these collec-
tions are referred to here as volume elements. The use of such collections allows the most
general arrays possible, but without the (usual) restriction that the elements of the arrays must be
of the same data type. This approach simplifies the programming , readability, and scalability of
the code. The use of objects also facilitates centralization of the algorithm library.
KN/4OO9/4OO9 11/OV09-9XU 17 pm»/DO/E(.1-3-98l
11-1
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Table 11-2
Domains Considered in the TRIM.FaTE Prototype
Domain
Air (Abiotic)
Soil (Abiotic)
Groundwater (Abiotic)
Surface water (Abiotic)
Sediment (Abiotic)
Plant (Biotic)
Fish (Biotic)
Macrophyte (Biotic)
Terrestrial omnivore (Biotic)
Semiaquatic piscivore (Biotic)
Terrestrial insectivore (Biotic)
Aquatic Mammalian Herbivore
Terrestrial Predator (Biotic)
Aquatic insectivore (Biotic)
Terrestrial Vertebrate herbivore (Biotic)
Piscivore (Biotic)
Aquatic Mammalian Omnivore (Biotic)
Terrestrial ground invertebrate feeder
(Biotic)
Benthic Invertebrate (Biotic)
Worm (Biotic)
Insects (Biotic)
Sink
Possible Domain Subtypes
Upper air layer
Lower air layer
Surface soil
Root zone
Vadose zone
Groundwater
Upper lake
Lower lake
River
Sediment
Plant - leaf
Plant - root
Plant - xylem
Plant - stem
Bass (carnivore)
Bluegill (herbivore)
Channel Catfish (omnivore)
Macrophyte
White-footed mouse
Belted kingfisher
Black Capped Chickadee
Mallard
Red Tailed hawk
Long tailed weasel
Tree Swallow
Deer
Long tailed vole
Mink
Racoon
Shrew
Mayfly
Worm
Insects
Advection, reaction
KNM009/4009 11/0.1-09-98(1 17 pm>/DO/E(?--V98)
11-2
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As described in Section 1.1, the main structures in the prototype are the collection of volume
elements that comprise the region to be modeled and the collection of links between components
of the volume elements.
Using the collection of volume elements and links, for each time period of interest, a transition
matrix can be generated that represents the system of differential equations describing the move-
ment of the chemical(s). The size of this matrix depends on the volume element structure, links,
and equilibrium assumptions made.
11.2 General Program Flow
The main steps are reading in the input structure (volume elements and links), generating the
transition matrix(ices), and running LSODE. Due to concerns about memory and execution
times required, the first two steps are currently usually conducted separately from the last,
although this is not necessary. The outline in Table 11-3 summarizes the process by which the
input structure is read in and the transition matrices are calculated in the prototype. There is
comparatively little involved in running LSODE, and for this reason a similar program flow is
not included here. In particular, a run of LSODE only requires specification of initial conditions
and the time period(s) to simulate.
11.3 Data Structures
The primary hierarchy of objects in the prototype is summarized in the Table 11-4. One of the
fundamental challenges of the implementation of the TRIM.FaTE model is how to address the
system of links between domains, and the associated algorithm results ("T"-values) that consti-
tute the entries of the transition matrix. The last two data structures represent one method of
meeting this challenge in such a manner so as to restrict flexibility as little as possible. Proper-
ties of these objects are provided in Appendix F tables.
11.4 Implementation of the Volume Element Structure
A volume element consists of a part of three-dimensional space. It can contain various media
and biota. In the prototype, such a volume element will exist for each chemical. The idea is to
have an object that has all the information associated with it contained within the object itself.
This is not possible using standard arrays (such as in older versions of Fortran). Due to some
restrictions specific to the Office 97 version of Visual Basic for Applications (the main restriction
is that one cannot have arrays be public members of a class), the structures actually implemented
for the prototype have some memory-wasteful redundancies. These redundancies can be
KN/4O09/-1O09 I I/W-09-98(.1 00 pm)/DO/E< 1-3-98)
11-3
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Table 11-3
Outline of General Program Flow to Create Transition Matrices in the TRIM.FaTE
Prototype
Read in data on new volume elements until no more volume elements (noted by a "volume element
end" statement in input file).
Get volume element name/index (must be unique among volume elements for current time step and
chemical); create a new instance of a Volume element structure and add to collection of volume
elements for this time and chemical".
Get spatial properties, temperature, and precipitation rate for volume element.
Calculate pure fugacities for chemical in volume element.
Read basic information on domains in volume element until no more domains specified.
Get domain type, subtype, name/identification (ID) (must be unique within volume element).
Create new instance of domain class using default properties.
Add new domain to collection of domains in volume element.
If domain is a soil domain, then read if worm domains in volume element are in equilibrium with
domain.
Read if domain has reaction/metabolic sink; if it does, then create new instance of sink domain class
(reaction subtype) and add the new sink domain to the collection of input links for domain.
Read if domain has advection sink; if it does, then create new instance of sink domain class
(advection subtype) and add the new sink domain to the collection of input links for domain; read
advective phase velocity information for sink.
Read in information on input links between domains(cannot be done until all volume elements and
domains are specified).
For each domain ("receiving domain") in each volume element:
Read information on links until no more input links.
Read domain ID and volume element ID of domain that is sending mass.
Add sending domain to collection of input domains for receiving domain.
Read if link has diffusive transfer; if so, calculate interfacial area for diffusion and get relevant time
step for diffusion calculations.
Read if link has advective transfer; if so, calculate relevant interfacial area (method of calculation
depends on domain types of sending and receiving domains) and read advective phase velocities
(some additional manipulation of phase velocities may be necessary due to peculiarities of standard
inputs for various domain types).
Loop through domains and volume elements again, making sure diffusion links are always specified
both ways.
Calculate volumes and total masses (mass of domain, not chemical) for each domain for current
time step.
Calculate fugacities (for appropriate domain types) and equilibrium fraction of chemical mass in each
phase in each domain for current time step.
Determine which domains in each volume element earn a row in the transition matrix for current time
step (domain gets a row in transition matrix only if its set of input links is not empty for time step); if
domain gets a row, then store row number as property of domain, and add domain to Matrix
collection of domains that have rows in transition matrix.
For each domain in each volume element, loop through input links and call Algorithm Library to
calculate T-values for transition matrix.
Output transition matrix for later use by LSODE (in units specified by user).
•It is stressed that this manner of storing the volume element information separately for each time step
and chemical is a temporary compromise given the additional burden of creating arrays of properties of
class modules.
KN/4009/4009 11/0?-09-98<3 00 pm>/DO/E(.V?-98)
11-4
-------
Table 11 -4
Primary Hierarchy of Data Structures in the TRIM.FaTE Prototype
Structure
Volume Element
Domain class
LinkObject
Algorithm Result
Comment
Collection of domains associated with a given spatial location
Consists of properties and link information for a domain
There is an object of this type associated with every domain. Consists of
a collection of domains that exchange chemical mass with a given
domain.
There is an object of this type associated with every link. Contains
components of "T"-value describing potential exchange between
domains (e.g., diffusion component, advection component).
eliminated using separate structures that are referred to by many objects, but this was not
implemented to date in order to expedite implementation of the flexible structure. For later
applications with possibly thousands of cells, the redundancies can be eliminated if necessary by
defining additional classes that contain the chemical-independent information for each volume
element of domains. The same structure can be used because the chemical-independent
information can be referenced in a sub-property of the main volume element. The basic
properties of a volume element structure are spatial properties and the domains contained in the
volume element.
For a given application, an array of volume elements is used, denoted Volume elements(k_chem,
i_time), that consists of all of the volume elements for the time step and chemical. A particular
volume element can be specified using notation of the form Volume elements(k_chem,
i_time)(i_volume element) or
Volume elements(k_chem, i_time)(blockname), where blockname is the user-specified name for
the volume element from the input file. In the code itself, when a particular volume element is
being worked with, a variable called CurrentVolume element is used because the loops are
performed using a statement of the form For each Volume element in Volume
elements(k_chem,i_time)... CODE... Next Volume element.
A specific domain can be specified using Volume elements(k_chem, i_time)(i_volume
element).Domains (jjdomain), w\\ertj_domain is the index of the domain in the list of all
domains in the volume element (this index depends on when the domain was added to the list),
or Volume elements(k_chem, i_time) (i_volume element).Domains(domainname), where
KM MOW/4001) 11/OV09-98O 00 pmVDO/E(J->-9«) 11-5
-------
"domainname" is a name for the domain as specified by the user (this is a database "key"). All
of the properties of the domain, including the volume element in which the domain is contained
and other domains to which it is linked, are contained in the Domain structure (from a memory
standpoint, the actual objects are not contained in the domain itself, although this is invisible to a
reader of the code. Instead, within the domain there are "pointers" that tell where the information
is located). The types of properties that a specific domain has depends on the domain type. If a
procedure is passed a domain object, it can always tell what type of domain it is by checking the
property DomainType, which all domain objects have.
In all algorithms implemented to date, it is not necessary to dynamically track the phase that the
chemical is in. However, structures are incorporated to store this information, when necessary.
In particular, for each domain, there is a ChemicalPhase property. This property is unused for
the prototype. The mass or other properties of the phase in a particular volume element could be
accessed via (this can be considerably shortened in code using With statements):
Volume element(k_chem, i_time).Domain(j). ChemicalPhase.Props[k].Phase,
where Phase is the specific aspect of the phase k that is of interest (e.g., mass in the phase).
When algorithms are utilized that require particular chemical phase information, this feature can
be activated by defining the properties.
11.5 Implementation of Algorithm Library
After the information is read into the volume element structures and the systems of links between
domains is specified, for each link, a subroutine is called that calculates the associated "T"-value
for the link. This subroutine is referred to as an "Algorithm Library" because it is the central
repository for equations describing the transfer of chemical mass between any two domains.
Although there is currently at most one algorithm for any particular link, the subroutine is coded
so that additional algorithms can be added, if desired. In that case, there will be the additional
choice to the user to select the algorithm to use for a specific type of link.
The subroutine takes as input two domains (of any type) and calls the appropriate algorithm for
the types of domains using the properties of the domains and properties of the link specified by
the user. The result of the algorithm is an object that has several components for the different
factors that make up the transfer factor: advection component, diffusion component, reaction
component, and "other" component. (More categories will be implemented as necessary.
KN/4009/4009 I1/O.V09-9X(I 17 pml/DO/E(.1-3-9S)
11-6
-------
Further, additional properties will be added, if necessary, to characterize the transfer using the
concepts outlined by McKone and Hall [1997].)
11.6 Necessity of Sinks
In order to track the mass of a specific chemical as it moves through space and time, it is neces-
sary to include special types of domains called "sinks." A sink is a domain that receives input
from a domain, but does not output the chemical. In general, the sink is a "final" resting place
for the chemical, as far as the conceptual model is concerned. While the chemical of course
would continue to move in the environment outside of the site being modeled, this history is not
of interest. However, it is important to keep track of how much mass of chemical has left the
system in order to verify that mass balance is preserved; in fact, this serves as an important
method to assess the accuracy of the LSODE calculations. Examples of sinks would be the air
cells on the boundary of a modeled region, or the destination of chemical in the water body that
is lost due to outflow.
In the prototype, there are two types of sinks that a domain can have: advection and reaction. An
advective sink is one in which the chemical is transported via an advective process to a location
not being modeled (e.g., via wind or water flow). A reaction sink is one in which a chemical
degrades or is transformed into a chemical that is not being modeled. This includes metabolic
breakdown of a chemical in an organism.
In the prototype, the sinks associated with different domain instances are treated separately. This
essentially doubles the size of the system of differential equations, as almost every domain has a
reaction sink. It is not actually necessary to treat these sinks separately, as all sinks can be
combined; however, for preliminary execution and debugging, this is not performed.
11.7 Lessons Learned
The lessons learned for the prototype is summarized in Table 11-5.
KN/4009/4009 11/03-09-98(1 17 pm>/DO/E( '-3-98)
11-7
-------
Table 11 -5
Lessons Learned with the TRIM.FaTE Prototype
Lesson Learned
Greater flexibility implies more inputs
May not be as great a need to simultaneously
generate transition matrices and then run LSODE
as previously thought
Actual execution of LSODE a minimal component
of process
Plethora of results generated, even with simple
systems
LSODE is working well
Systems of differential equations become large
quickly
Outcome
Should continue to not restrict flexibility, but be
aware of implications
May be relic of slower computer resources utilized
to date
Should prioritize output results of interest
Mass balance is always being preserved,
indicating that neither numerical roundoff or other
instabilities are causing problems.
Will be more of an issue for later applications.
Investigate ways to reduce size of system (e.g.,
combine all sinks)
K.N/-MKN/4009 ll/OMN-WM 17 pmVDO/ECt-3-98)
11-8
-------
12.0 Test Case Application of the TRIM.FaTE Prototype
The TRIM.FaTE prototype was applied to the simulation of B(a)P and phenanthrene releases in a
realistic test case: a mixed use landscape surrounding an aluminum smelter. This chapter
presents the description and mapping of the test site, and the data inputs and model results for
various runs implemented in the prototype for the test site.
12.1 Description of Environmental Setting
The circular region containing all land within 50 km of an aluminum smelter was examined to,
define the boundaries of the study area. Precursory air dispersion modeling was performed and
results indicated that significant impacts of the emissions occurred within a radius of 5 km. The
land use within this 5-km area was evaluated from GIS information and it was determined that an
oval study area approximately 8.5 by 9.0 km would provide an instructive test case for the
TRIM.FaTE model. Figure 12-1 is the plan view and Figure 12-2 displays the cross-sectional
views of the study area used for the test case.
The test case facility is located near a bay in an area that is predominantly industrial in nature.
Much of the area immediately surrounding the smelter is used for storage of timber prior to ocean
shipment. The nearest residents (human) are located approximately 800 m east, north, and
northeast of the facility. Approximately 800 m north of the aluminum smelter is a ridge running
in a southeast-northwest direction, with a maximum elevation of approximately 120 m above sea
level.
The only other major industrial facility in the vicinity of the aluminum smelter that has been
identified as having a significant potential to emit air pollutants is a paper mill approximately 5
km due west of the smelter and on the bay. Nearby sources of polyaromatic hydrocarbons (PAH)
may also include residential wood smoke, emissions from automobiles (to air), and boats (to
water), among others. For purposes of the prototype, it was assumed that the aluminum smelter
was the only source of phenanthrene and B(a)P within the study area.
Although an actual location in the northwestern region of the United States was used as a rough
guide for constructing this system, the application of TRIM.FaTE to this system was not intended
to provide pollutant estimates for any existing facility in the United States.
12-1
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12-3
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12.2 Mapping the Ecosystem for the TRIM.FaTE Prototype
The plan view of the map resulting from the mapping process is shown in Figure 12-1. This
process also involved setting up the domains and associated links as described in Chapter 2.0.
The domains simulated by the prototype is presented in Table 12-1 and the associated links in
Table 12-2.
Determining the appropriate grid scale to use in this modeling effort is based on tradeoffs
between the desired level of detail in the results and the data computational requirements
necessary to run a detailed model. When determining the grid scale to use in the model, it is
desirable to include as much detail as necessary to capture the spatial resolution, both in terms of
land use and in order to capture the spatial change in chemical concentration. On the other hand,
it is undesirable to have so much detail as to increase the complexity of the model to the point
where it is difficult to set up and run. Ideally, there should be enough grids to capture the details
needed for the required task and no more. Based on this tradeoff and as shown in Figure 12-1,
the landscape was divided into 15 land units (parcels), and the water systems were divided into 5
water units (parcels). It is important to note that the embayment and other waters surrounding
the smelter were assumed to be fresh, not saline, for purposes of the modeling effort.
The GIS data for this area indicates that the land area is primarily forest and urban, with a patch
of agriculture and some very small parcels of grassy vegetation within the urban areas. GIS
databases accessed to characterize the study area are summarized in Table 12-3. Details on each
database are available in a separate report entitled Draft GIS and Spatial Data Report for the
Total Risk Integrated Model (TRIM) (Hunsacker and Simcock, 1997). The pattern of land use is
irregular and parcels were defined to be representative of the major land usage for the specific
parcel selected. Consequently, the location of each land use type does not correspond exactly
with the actual location of that type of land, but the total area of each type of land is represen-
tative of the total actual areas. In locating the different land types, an effort was made to repli-
cate the actual locations of each usage as much as feasible. The grids are either urban, forest, or
agriculture. The small amount of grassy vegetation was accounted for by assuming that the urban
parcels consist of grassy and paved areas.
12-4
-------
Table 12-1
Domains Simulated in the TRIM.FaTE Prototype
Domain Type
Air (Abiotic)
Soil (Abiotic)
Groundwater (Abiotic)
Surface water (Abiotic)
Sediment (Abiotic)
Plant (Biotic)
Fish (Biotic)
Macrophyte (Biotic)
Terrestrial omnivore (Biotic)
Semiaquatic piscivore (Biotic)
Terrestrial insectivore (Biotic)
Aquatic mammalian herbivore
Terrestrial predator (Biotic)
Aquatic insectivore (Biotic)
Terrestrial vertebrate herbivore
(Biotic)
Piscivore (Biotic)
Aquatic mammalian omnivore
(Biotic)
Terrestrial ground invertebrate
feeder (Biotic)
Benthic invertebrate (Biotic)
Benthic invertibrates (Biotic)
Insects
Domain Instance
Upper air layer
Lower air layer
Surface soil
Root zone
Vadose zone 1
Groundwater
Upper lake
Lower lake
River
Sediment
Plant - leaf
Plant - root
Plant - xylem
Plant - stem
Bass (carnivore)
Bluegill (herbivore)
Channel Catfish (omnivore)
Macrophyte
White-footed mouse
Belted kingfisher
Black Capped Chickadee
Mallard
Red Tailed hawk
Long tailed weasel
Tree Swallow
Deer
Long tailed vole
Mink
Racoon
Shrew
Mayfly
Earthworm
Insects
Associated Parcels
A-T
A-T
A-G, I, K, R-T, O, P
A-G, I, K, R-T, O, P
A-G, I, K, R-T, O, P
A-G, I, K, R-T, O, P
Q
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H, J, L-N, Q
A, D, F, G, P
A, D, F, G, P
A, D, F, G, P
A, D, F, G, P
H, J, L-N, Q (upper and lower)
H, J, L-N, Q (upper and lower)
H, J, L-N, Q (upper and lower)
H, J, L-N, Q (upper and lower)
A, D, F, G, P
H, J, L-N, Q
A, D, F, G, P
H, J, L-N, Q
A, D, F, G, P
A, D, F, G, P
H, J, L-N, Q
A, D, F, G, P
A, D, F, G, P
H, J, L-N, Q
H, J, L-N, Q
A, D, F, G, P
H, J, L-N, Q
A, D, F, G, P
A. D. F. G. P
12-5
-------
Table 12-2
Links Associated with Domains in the TRIM.FaTE Prototype
Sendina Domain
Air
Soil
Groundwater
Surface water
Sediment
Plant
Receivina Domain
air
air (react, sink)
soil
surface water
plant
macrophyte
mammal
bird
insect
air
soil
surface soil sink
soil reaction sink
groundwater
surface water
plant
worm
groundwater reaction sink
groundwater advection
sink
surface water
air
surface water
surface water reaction
sink
surface water advection
sink
sediment
fish
macrophyte
terr. Mammal
bird
insect
worm
surface water
sediment advection sink
sediment reaction sink
air
soil
groundwater
terr. omnivore
terr. herbivore
aquatic mamm. omnivore
insects
worm
Sendina Domain
:ish
Macrophyte
Terrestrial mammal
Bird
Aquatic mammal
Benthic invertebrates
Worm
nsects
Receivina Domain
surface water
fish
bird
mammal (mink)
surface water
sediment
fish
benthic invertebrate
air
soil
err. mammal
terr. mammal reaction sink
air
soil
terr. mammal
bird
air
soil
aquatic mammal
fish
air
fish
bird
insects
air
soil
fish
bird
air
soil
fish
err. omnivore
Dird
insects
12-6
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12.3 Input Data
The data selection process is summarized in this section and the data inputs used in this analysis
are described in detail in Appendix B. The advective flows of media that transport the chemical
throughout the system are a critical factor in the application of the model. Advective flows
include wind, precipitation, erosion, runoff, and surface water. To realistically model advective
flows, site-specific parameters were used to the extent possible. Meteorological data for 1 year
were obtained from a nearby airport. These data indicated approximately 80 cm of precipitation
annually, an average wind speed of 5.8 meters per second (m/s), and a dominant wind direction
toward the east. Soil properties were estimated with the assistance of GIS maps of the area.
Surface water flow rates were estimated using local river flow data. Due to the absence of site-
specific data for erosion and runoff flow, these parameters were estimated based on reasonable
assumptions. An erosion rate of approximately 1 kilogram per square meter per day (kg/m2/day)
was assumed when precipitation occurs. This value is higher than would occur on a yearly
average and is only used to demonstrate the type of results obtained. This estimate was made
based on information obtained from a data set (Purdue University web site, see Chapter 14.0),
which indicated that there is 11 percent total soil loss for precipitation events less than 1.5 inches
per hour. The runoff flow was estimated as 80 percent of the hourly precipitation rate.
For most species, the population sizes were estimated using information on the density of biota
per area of habitat. For the purpose of investigating the possible impact of the biota on the
distribution of chemical, biota were assumed to be located in all but the urban cells. Wildlife
densities were assumed to be identical on forested and agricultural parcels of land.
12.4 Description of Model Runs
Using the assumed parameter values discussed previously, numerous runs have been performed
investigating the predicted behavior of the modeled system. For brevity, selective results are
presented and analyzed in this section. The results reported here are categorized into three major
divisions as follows:
• Theoretical phase calculations for predictive analyses (Section 12.5).
• Constant meteorological conditions (Section 12.6). This category consists of
multiple runs under precipitation and no precipitation conditions
• Variable meteorological conditions (Section 12.8).
12-8
-------
To highlight key features of the model, results for constant meteorological conditions are
presented in greater detail than those obtained for variable conditions. By keeping meteoro-
logical conditions fixed, it is easier to discern key trends and responses of the model. For
varying meteorological conditions, only the resulting apportionment of mass across the domains
are compared and summarized at this time.
72.5 Results of Phase Calculations
As previously discussed, B(a)P and phenanthrene are assumed to be released from one source, an
aluminum smelter, and initially there is no B(a)P or phenanthrene in the system. The general
phase distribution of B(a)P and phenanthrene in abiotic media if equilibrium is assumed is shown
in Table 12-4.
Table 12-4
Predicted Phase Distribution for B(a)P and Phenanthrene
in Abiotic Media for Equilibrium
Domain Type
Air
Surface Soil
Surface Water
Sediment
Sorbed
B(a)P
9.7x10-'
1.0x 10°
7.7x10'
1.0x10°
Phenanthrene
9.9x10-'
9.9 x 10'1
2.0 x 10 2
9.8 x 10'
Dissolved
B(a)P
0.0x10°
5.0 x 10 5
2.3 x 10'
1.5x 107
Phenanthrene
0.0x10°
8.5 x10'3
9.8x10"'
2.0 x10-5
Vapor
B(a)P
3.3X192
0.0 x
W*
0.0x10°
0.0x10°
Phenanthrene
5.5 x10'3
0.0x10°
0.0x10°
0.0x10°
Results presented in Table 12-4, calculated only from chemical properties of B(a)P and phenan-
threne and the assumed properties of the media, indicate that B(a)P and phenanthrene will tend to
be sorbed to solids. The main difference between B(a)P and phenanthrene concentrations is in
surface water, where almost all of the phenanthrene is predicted to be dissolved. The fractions
dissolved in sediment and surface water are approximately two orders of magnitude higher for
phenanthrene than for B(a)P.
12.6 Results of Constant Meteorology Runs
Several test runs were performed to analyze the effects of precipitation and wind direction at
steady-state conditions. A total of eight runs were performed, each using a constant wind speed
of 5.8 m/s and a constant wind direction. Four of the runs did not include precipitation and had a
wind direction from either the east, west, north, or south. The additional four runs included a
12-9
-------
precipitation scenario, with a wind direction from either the east, west, north, or south. An emis-
sion rate of 216 grams per day (g/day) for B(a)P and 17,600 g/day for phenanthrene resulted in
different steady-state mass totals in the system for each run.
Results for runs with a due east wind direction are analyzed in detail in Sections 12.7.1 and
12.7.2 for purposes of discussing trends and model predictability relative to precipitation. A
comparative analysis of these runs is presented in Section 12.7.3. The results from all runs under
constant meteorological conditions are then compared and tabulated in Section 12.7.4. Separate
discussions on the ecological components are presented in Section 12.7.5.
12.6.1 Results for No Precipitation, East Wind Direction Scenario
For a due east wind direction and the given location of the source term, there is transport mecha-
nism by which the B(a)P or phenanthrene can enter the surface water if it is not raining. The
B(a)P and phenanthrene emitted in parcel I can accumulate only in the parcel with the smelter or
the parcels east of the facility (O and P). Because soil erosion or runoff is not assumed when
precipitation does not occur, the B(a)P deposited to soil can only be resuspended or flow verti-
cally through the soil layers. If resuspended, it is blown over the parcels to the east and/or out of
the system. Almost no vertical flow in soil is predicted due of the sorption properties of B(a)P.
The easterly wind flow will not bring the B(a)P over any surface water, and hence no dry depo-
sition to surface water will occur.
Spatially, as shown in Figure 12-3, the B(a)P and phenanthrene in the system are partitioned
relatively evenly among parcels I, O, and P, and there is an increase in the total mass of each
chemical as one moves east from the facility. The mass per unit area of B(a)P and phenanthrene
actually decreases as one moves east.
The presence of plants in parcel P (due to agricultural land use) is predicted to result in a magni-
fication of the B(a)P in the parcel. This can be seen by analysis of selected transfer factors for
parcel P, which are shown in Figure 12-4 (these transfer factors depend on the meteorological
conditions and input parameters, but are independent of any source terms or initial conditions
assumed).
If N,,Jt), Najt), and Nplanjt) denotes the mass of B(a)P in parcel P in surface soil, air, and plants,
respectively, then the values reported in the Figure 12-4 represent the following differential
equation:
12-10
-------
Figure 12-3
Predicted Steady State Spatial Distribution of B(a)P and Phenanthrene
Wind Due East, No Precipitation
9 km
-> Wind Direction East
8.5km
Source
Red - B(a)P
Blue- Phenanthrene
Not to scale
12-11
-------
Figure 12-4
Transfer Factors For Select Parcels in the TRIM.FaTE Prototype
—I
Parcel I
Parcel O
Parcel P
12-12
-------
<„ - (-0-003) N^ + 1.3 N^ + 0.01
ian, = (-0.37)^ + 15^
Note that this system is only one part of the larger system, which consists of approximately 500
such coupled differential equations. At steady state,N^oil=0 and Nplant=Q, and so
0 = (-0.003) A^,.,+1.3 Arfl,.r +0.01
0 =(-0.37)^ + 15^
Solving for Nsoll and Nplan, in terms of Nair shows that the steady-state values are given by:
1.3 AT _ +0.01 AT
air "'"' "plant
5'"' ~ 0.003
15 -N
N
plant r\ -i-i * 'air
Using both of these equations, the equation for Nsl>l, can then be written in terms of Nair as:
N . 1.3+(0.01) 15/0.37]
""' 0.003 - air
The first term in the parentheses is the result of the direct interaction of the air cell with the soil
cell; the second term is an indirect interaction, with the air cell influencing the soil cell by means
of the plants. This contribution accounts for more than 30 percent of the steady-state value in
soil, and is larger than the steady-state value in plants themselves of 40 Nair.
Plants are thus predicted to be a magnifier of B(a)P in the system. Plants themselves accumulate
only approximately 3 percent of the total B(a)P in the system, but approximately 10 percent of
the B(a)P in the system is directly due to the flux from the plant to surface soil through litterfall.
It can be seen from Figure 12-3 that 40 percent of total B(a)P is in parcel P (mostly in soil), 30
percent of which is accounted for by the litterfall flux from the plants.
Table 12-5 summarizes the steady-state distribution of B(a)P and phenanthrene by domain type.
12-13
-------
Table 12-5
Predicted Steady-State Results
(No Precipitation, East Wind Direction Scenario)
Distribution by
Domain Type
Total in System
Air
Soil
Sediment
Surface Water
Plants
Non-Plant Biota
B(a)P
Mass (g)
4.5 x IO3
2.1 x 10°
1.0 x IO3
0.0 x 10°
0.0 x 10°
2.8x 10'
<005
%
100
0.2
97.1
0
0
2.7
<0.01
Normalized
by Emission
Rate
(day)
4.6 x 10°
9.20 x IO'1
4.50 x 10°
0.00 x 10°
0.00 x 10°
2.00 x 10 2
<4.6x ID"1
Phenanthrene
Mass (g)
3.9 x IO4
2.0 xlO2
3.8 xlO4
0.0 x 10°
0.0 x 10°
5.5 x IO2
<4
%
100
0.5
98.2
0
0
1.4
<0.01
Normalized
by Emission
Rate
(day)
2.2 x 10°
1.0 x 10'2
2.16x10°
0.00 x 10°
0.00 x 10°
3.00 x 10 2
<2.2 x IO-4
12.6.2 Results for Precipitation, East Wind Direction Scenario
The predicted steady-state spatial distribution of chemicals is more complicated when precipita-
tion is occurring. When it is raining, there is enhanced atmospheric deposition, and erosion and
runoff transport the chemical to neighboring soil and water cells. As shown in Table 12-6, most
Table 12-6
Predicted Steady-State Results (Precipitation, East Wind Direction Scenario)
Distribution by
Domain Type
Total in System
Air
Soil
Sediment
Surface Water
Plants
Other
B(a)P
Mass (g)
4.5 x103
1.8x10°
7.6x10'
4.3x10'
7.6x10'
1.8x10'
<:0.2
%
100
0.04
1.7
96.2
1.7
0.4
<0.01
Normalized by
Emission Rate
(day)
2.0 x 10'
8.0x103
3.5x10'
2.0x10'
3.4x10'
8.0x102
<2.0x10-3
Phenanthrene
Mass (g)
1.5x104
1.7X102
7.1 x 103
5.1 x 103
2.3 x103
3.0 xlO2
<0.15
%
100
1.1
47.3
33.9
15.5
2.0
<0.1
Normalized by
Emission Rate
(day)
8.0x10''
8.8 X10'3
3.50x10'
2.9x10-'
1.2x10"'
1.6 x102
<8.0x10-"
12-14
-------
(98 percent) of the B(a)P is predicted to be in sediment (96 percent) and surface water (2
percent). Phenanthrene does not accumulate in sediment as much as B(a)P, and the total amount
of phenanthrene in the system, when normalized by the emission rate, is 20 times smaller than
that for B(a)P.
The spatial distribution of the chemicals is summarized in the Figure 12-5. The water bodies in
M and N receive the chemicals through erosion from parcels O and P, respectively. The water-
way in parcel L receives fluxes only through water flow from M. The water bodies north and
south of the facility, parcels H and J, have the smallest amount of both chemicals because the
erosion from the parcel containing the smelter is split evenly between these two parcels.
While much of the chemical is transported out of the system via wind or surface water outflow,
cycles of movement within the system are predictable. This result is illustrated by the fact that, at
steady-state, some mass of the chemical is predicted to be in the cells north of the facility, even
though, due to the easterly wind direction, there is no direct interchange between the cell contain-
ing the smelter (parcel I) and the cells north of it. This results from the mass-balance nature of
the model, as the cells to the north of the facility receive the chemicals through a chain of inter-
domain transfers. For example, the B(a)P emitted in parcel I is predicted to deposit in the soil
cells east of the facility (parcels I, O, and P). After deposition, the B(a)P is advected via erosion
into the waterways (H, J, M, and N), whereupon some is carried with the water flow into the
water bodies L and Q. Some of this B(a)P is then predicted to diffuse into the air column above
the water body. At this point, the chemical has been transported opposite to the wind direction,
and will be blown back across the region containing the cells north of the smelter. Once
deposited, it will undergo erosion and runoff back to the waterway H, to begin the cycle again.
Such cycling cannot be predicted by models that do not fully integrate mass-balance across
media. Environmental cycling, as discussed in Section 127.2, is expected under the precipitation
scenario and is predicted by the simulation. For the no-precipitation, this is not expected or
predicted.
12.6.3 Comparative Analysis
Using normalized emission rates to compare results, both meteorological cases predict B(a)P to
accumulate in the environment more than phenanthrene. When precipitation is not occurring,
most of the B(a)P accumulates in soil. There is a significant difference when precipitation is
occurring due to accumulation in sediment. The difference between B(a)P and phenanthrene
accumulation in sediment is due to the difference in their sorption properties (Table 12-4) and the
12-15
-------
Figure 12-5
Predicted Steady State Spatial Distribution of B(a)P and Phenanthrene,
Wind Due East, Precipitation
Wind Direction East
8.5 km
Source
Red - B(a)P
Blue- Phenanthrene
Not to scale
12-16
-------
The precipitation scenario results in a higher mass accumulation of B(a)P in the system than for
the no precipitation scenario. The B(a)P mass in air, soil, and plants is higher in both magnitude
and as a fraction in the system when there is no precipitation. This result indicates the impor-
tance of washout on the amount of B(a)P contained in these media and within the system.
Phenanthrene, unlike B(a)P, is predicted to accumulate more mass in the no-precipitation
scenario. The mass in air, soil, and plants is higher in magnitude when there is no precipitation.
For the precipitation scenario, both the magnitude and fraction of mass in the system increased in
the sediment and surface water.
12.6.4 Results for All Runs - Constant Meteorology
Tables 12-7 and 12-8 show the steady-state distribution of B(a)P and phenanthrene by domain
type for different wind directions.
Qualitatively, almost all of the chemicals are predicted to be in soil or sediment, with the mass in
sediment positively correlated with precipitation. The differences in the results for different
wind directions are due to the spatial distribution of the domain types and assumed erosion and
runoff flows.
When the wind is blowing north, the forest and urban cells north of the facility accumulate the
chemicals in soil; the large fraction in soil in this case is due to the negligible erosion rates
assumed for the urban cell farthest north from the facility. The summary results for the western
and southern wind directions are similar; however, when the wind is blowing west, most of the
B(a)P is transported to parcels J and Q, while when the wind is blowing south, most of the B(a)P
is transported to parcels L and Q. Since parcel J is located south of parcel I, it may seem unusual
that B(a)P would be transported to parcel J when the wind is blowing due west; however, the
B(a)P is homogeneously distributed in parcel I, and the wind speed from one cell to another
depends on the angle of the boundary with respect to the wind direction.
For all wind directions except east, B(a)P is predicted to accumulate in sediment even in the
absence of precipitation. In contrast, little phenanthrene accumulates in sediment unless precipi-
tation is occurring. This difference is due to a combination of factors. First, the estimated
transfer factors from air to water is approximately six times larger for B(a)P than for phenan-
threne. This ratio is approximately the same as the ratio of the vapor-phase fraction of B(a)P
(0.033) to that of phenanthrene (0.0055). This indicates that the diffusion to water from air is
being predicted to be an important process. Another factor that accounts for these differences is
12-17
-------
Table 12-7
Predicted Distribution by Domain Type
(No-Precipitation Scenario)
Wind Direction
Pollutant
Total Mass in Ecosystem (g)
Mass in system normalized
by emission rate
Soil
Air
Surface Water
Sediment
Plants
East
B(a)P
1000
4.6
97%
0%
0%
0%
3%
Phenanthrene
3.9x10"
2.2
98%
0%
0%
0%
1%
North
B(a)P I Phenanthrene
1100
5.1
84%
0%
0%
9%
7%
3.3x10*
1.9
95%
1%
0%
0%
4%
West
B(a)P
940
4.4
44%
0%
3%
54%
0%
Phenanthrene
1.7x10*
0.9
98%
1%
1%
0%
0%
South
B(a)P
8.8 x102
4.1
80%
0%
1%
19%
0%
Phenanthrene
2.9x10*
1.6
99%
1%
0%
0%
0%
Note: Nonplant biota is less than 0.1 percent of total mass in system.
Table 12-8
Predicted Distribution by Domain Type
(Precipitation Scenario)
Wind Direction
Pollutant
Total Mass in Ecosystem (g)
Mass in system normalized
by emission rate
Soil
Air
Surface Water
Sediment
Plants
East
B(a)P
4.5 x
103
20.8
2%
0%
2%
96%
0%
Phenanthrene
1.5x10*
0.8
47%
1%
16%
34%
2%
North
B(a)P I Phenanthrene
4900
22.7
53%
0%
1%
44%
2%
1.2 x105
6.8
95%
0%
1%
2%
2%
West
B(a)P | Phenanthrene
2500
11.6
1%
0%
4%
95%
0%
7.2 x103
0.4
41%
2%
27%
30%
0%
South
B(a)P| Phenanthrene
2500
11.6
2%
0%
3%
95%
0%
9.9 x 103
0.6
52%
1%
19%
28%
0%
Note: Nonplant biota is less than 0.1 percent of total mass in system.
that the reaction rate in water is approximately four times larger for phenanthrene than that for
B(a)P. Finally, the calculated transfer factors for deposition of B(a)P to the sediment bed is more
than 30 times larger than that for phenanthrene. This is due to the predicted phase distribution of
the chemicals in the water body. Seventy-seven percent of the B(a)P is sorbed to suspended sedi-
12-18
-------
ment, and hence is susceptible to deposition, while only approximately 2 percent of phenanthrene
is sorbed:^
72.6.5 Mass and Concentration Distribution in Biota
The mass distribution of B(a)P and phenanthrene within biota domains is based on steady-state
conditions. The steady-state distributions of B(a)P and phenanthrene for four wind directions is
shown in Tables 12-9 and 12-10 for conditions of precipitation and no precipitation, respectively.
It should be noted that the mass distribution presented in these tables represent only the biotic
portion of the total mass in the ecosystem. The mass in a particular biotic domain depends on the
size of the population as well as its diet. A few general terrestrial and aquatic biota trends are
discussed separately in the following paragraphs.
Most of the chemical mass is predicted to accumulate in plants when the wind direction blows
towards the parcels containing plants. The mass in the system is highest when the wind is
blowing north toward the forested areas, and lowest when blowing south toward the urban areas
without precipitation. After plants, fish and macrophytes accumulate most of the B(a)P and
phenanthrene. Relatively little of either chemical is predicted to accumulate in the terrestrial
species, although terrestrial wildlife species that consume fish (e.g., raccoon) accumulate the
most chemical mass. Note that this analysis is based on mass, not concentration. High
concentrations of pollutants may be seen in some wildlife domains due to low population
biomass.
Concentrations in Terrestrial Biota. Estimated steady-state concentrations for B(a)P and
phenanthrene in the terrestrial ecosystem are presented in Figures 12-6 and 12-7, respectively.
The concentrations do not include background concentrations of the contaminants in any media.
The wind direction in the scenario depicted is due north, and there is no precipitation. As
previously stated, the emission rate for B(a)P is 216 g/day (1,000 g at steady-state), and the
emission rate for phenanthrene is 17,600 g/day (39,000 g at steady-state). The concentration of
B(a)P in surface soil (the top 1 millimeter) is approximately six orders of magnitude higher than
that in root zone soil (the next 1 m) (Figure 12-5). The concentration of phenanthrene in root
zone soil is substantially higher than that of B(a)P, as would be expected given the higher emis-
sions rate of the former chemical.
12-19
-------
Table 12-9
Predicted Distribution in Biota by Domain Type
(No Precipitation Scenario)
Wind Direction
Pol utant
Mass total (g)
in Biota
Mass in system
normalized by
emission rate
Black-capped
Chickadee
Redtailed Hawk
Tree Swallow
Mule Dee
Blackballed
Deer
Lonqtailed Vole
Longtailed
Weasel
Mink
Raccoon
Trowbndge
Shrew
Mallard
Bluegill,
Herbivore
Catfish,
Omnivore
Largemouth
Bass, Carnivore
Mice
Kingfisher
Insect
Insect, Mayfly
Macrophyte
Plant, Leaf
East
2.84x10'
1.32x10"'
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
100%
Phenanthrene
5.28x10*
3.00 x10'2
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
100%
North
BMP
7.36x10'
3.41 x10'1
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
100%
Phenanthrene
1.40x10'
7.95 X10*
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
100%
West
B
-------
Table 12-10
Predicted Distribution in Biota by Domain Type
(Precipitation Scenario)
Wind Direction
Pollutant
Total Mass (g)
in Biota
Mass in system
normalized by
emission rate
Black capped
Chickadee
Redtailed Hawk
Tree Swallow
Mule Deer
Blacktailed
Deer
Longtailed Vole
Longtailed
Weasel
Mink
Raccoon
Trowbndge
Shrew
Mallard
Bluegill,
Herbivore
Cattish,
Omnivore
Largemouth
Bass, Carnivore
Mice
Kingfisher
Insect
Insect, Mayfly
Macrophyte
Plant, Leaf
East
B(a1P
2.08x10'
9.62 x10'2
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
5%
0%
0%
0%
0%
2%
93%
Phenanthrene
3.03 x102
1.72X10'2
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
1%
0%
2%
0%
0%
0%
0%
0%
97%
North
B(alP
7.73x10'
3.58x10''
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
1%
0%
0%
0%
0%
0%
98%
Phenanthrene
1.93 x103
1.10x10''
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
100%
West
1.70x10°
7.89 x10'3
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
3%
1%
69%
0%
0%
0%
0%
27%
0%
Phenanthrene
8.09x10°
4.59x10"*
0%
0%
0%
0%
0%
0%
0%
1%
0%
0%
19%
2%
70%
0%
0%
0%
1%
6%
0%
South
B(a^P
1.57x10°
7.26 x 10 3
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
3%
1%
70%
0%
0%
0%
0%
26%
0%
Phenanthrene
9.52x10°
5.40 x10J
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
20%
2%
71%
0%
0%
0%
1%
6%
0%
12-21
-------
Figure 12-6
Steady State Concentrations of B(a)P in Biota and Soil in a Forested
Parcel, No Precipitation
D>
1 .OOE+00
1 .OOE-02 i
1 .OOE-04 -
1 .OOE-06 -
1 .OOE-08
Surf Soil
Chickadee
Vole
Insect
Figure 12-7
Steady State Concentrations of Phenanthrene in Biota and Soil in a Forested
Parcel, No Precipitation
0>
o
1
§
1 .OOE+00 -
1 .OOE-02
1 .OOE-04 -
1 .OOE-06 -
1 .OOE-08
Surf Soil Plant Leaf Hawk
Vole
Shrew
Mouse
12-22
-------
Even though wildlife domains do not contribute significantly to the mass balance of PAHs,
concentrations of the chemicals in wildlife are generally within two orders of magnitude of the
concentrations in plant leaves and surface soil. The transfer from surface soil is the largest
contributor to the mass in wildlife. Because of the large difference in contaminant concentrations
in surface and root zone soil, the wildlife results are sensitive to the fraction of soil assumed to be
incidentally ingested from each of these domains. Future modifications of the model will focus
on improving the accuracy or expressing the uncertainty in the soil-to-wildlife transfers as
represented here. Because of the low concentrations of PAH in earthworms and plant roots,
these domains are not represented in the figures. For example, the estimated concentrations of
B(a)P in earthworms and plant roots are 4 x 10~16 and 4 x 10"", respectively.
Despite the higher emission rate of phenanthrene, the estimated steady state concentrations of the
chemical in individual domains are often lower than those for B(a)P. Specifically, the con-
centrations of phenanthrene in surface soil, plant leaf, deer, vole, weasel, shrew, and mouse are
somewhat lower than those for B(a)P. The estimated concentration of phenanthrene in the insect
is approximately three orders of magnitude lower than that of B(a)P in the insect.
Concentrations in Aquatic Biota. At this point in its development, TRIM.FaTE represents
very simplified transfers between abiotic and biotic domains. Although the model is being tested
on two PAHs emitted from an aluminum smelter located in a coastal northwestern setting, the
aquatic system was assumed to be unstratified freshwater and not estuarine with complex salinity
and density regimes. It was also assumed that the freshwater bluegill population would feed
exclusively on plant matter (algae) and thus represent herbivorous creatures. In reality, these fish
are omnivorous; however, they represented a suitable species to occupy the water column
herbivore trophic level.
Table 12-11 shows the contribution to the steady-state values for the fish species in the water
body in parcel Q. Comparing the mass normalized by emission rate, more B(a)P than phenan-
threne is predicted to accumulate in all fish species. For carnivores and herbivores, the dominant
uptake pathway is through interaction with the water column for both chemicals. There is a
marked difference in the accumulated mass of each chemical for the omnivores (catfish). Most
of the B(a)P is accumulated from the sediment, while most of the phenanthrene is taken up
through the water column.
12-23
-------
Table 12-11
Uptake Fractions for Specialized Fish Domains in Parcel Q
(Precipitation, East Wind Direction Scenario)
Species
Uptake Fractions
(% of total in specialized domain)
B(a)P
Phenanthrene
Carnivore (Largemouth Bass)
Normalized mass of chemical in fish
(g/g emission/day)
Water
Herbivore
Omnivore
2.0 x10-3
61
38
1
5.6 x10'5
86
14
0.2
Herbivore (Bluegill)
Normalized mass of chemical in fish
(g/g emission/day)
Water
Macrophyte
9.7x10's
97
3
1.6x1Q-5
100
0
Omnivore (Catfish)
Normalized mass of chemical in fish
(g/g emission/day)
Water
Sediment
Herbivore
Macrophyte
1.2X1CT5
1.3
99
0.1
0.1
6.8 x10'7
90
9
1
0
It is also important to note that the distribution within biotic domains of B(a)P and phenanthrene
predicted by the model suggests a surprisingly high percentage of PAH mass concentrated within
the carnivorous largemouth bass (Microplerus salmoides) population as opposed to the other
terrestrial and aquatic receptors (Tables 12-9 and 12-10). A few factors contributing to the
apparent imbalance in PAH distribution among biotic receptors include diet and associated
biomagnification tendencies, as well as the fact that the model segment Q was assumed to be a
large lake or slow-moving embayment with a significant bass population of 50 to 100 individuals
per hectare. While this density range is supported in the literature for slower moving waters such
as lakes (Macina, et al., 1995), when combined with lipid level estimates and assumptions of 80
percent of its diet being bluegills, the bass is inaccurately being predicted as the ultimate biotic
sink. Further sensitivity analysis on the model and subsequent adjustments should result in a
more accurate prediction of PAH distribution within the aquatic biota domains.
12-24
-------
In addition, Table 12-11 indicates that the bottom-dwelling catfish uptakes 99 percent of its B(a)P
from the sediment. Given the partitioning characteristics of B(a)P and the bottom-scouring habits
of catfish, this may be fairly accurate. This uptake is driven by the assumption that 96 hours are
required to reach steady state. This assumption may be inaccurate; the sensitivity of the model
estimates to this assumption will be tested in subsequent model runs.
12.7 Variable Meteorology
In this section, the results for time-dependent meteorology are discussed. The emitted chemical is
modeled for a 24-hour period. The factors that depend on time are the wind speed, wind
direction, and precipitation. The wind direction and precipitation time profiles used in this
analysis are shown in Figures 12-8 and 12-9.
Figures 12-10 through 12-13 show the predicted mass of each chemical in various domain types
for variable meteorological conditions. After 12 hours, each chemical is predicted to begin
accumulating to some degree in almost all domain types. An exception to this is seen for
phenanthrene in surface water. When precipitation stops (starting approximately the 19th hour),
there is no longer any erosion or runoff load to the water bodies. It can be seen in Figure 12-10
that phenanthrene mass in surface starts decreasing marginally. At this point, the phenanthrene in
the water bodies begins to either settle into the sediment or be flushed out, eventually reaching the
outflow sink for the water domain in parcel Q.
The air domain is predicted to be most sensitive to the hourly fluctuations in meteorological
conditions. This can be seen by looking at the first few hours, where the rapidly fluctuating
profile of precipitation is reflected in the clearly observable oscillations in the chemical mass in the
air domains (Figure 12-11). When precipitation is occurring, the chemical is removed from the
atmosphere; when precipitation is not occurring, less chemical is removed, resulting in the small
"peaks" during the second and fourth hours. After the fourth hour, the precipitation rate, when
precipitation occurs, is lower than that in the first four hours. This results in smaller oscillations.
Further, the chemical in the air domains will begin cycling as the wind direction changes from
hour to hour.
The plant domains are predicted to have a noticeable increase in chemical mass at the fourth hour
(Figure 12-13). This is a result of the wind blowing north for the first time, as most of the plants
are located north of the facility. The increase is more gradual for later hours. Similarly, there is a
sharp increase for the aquatic domains (water column, sediment, fish) during the first few hours
(Figure 12-13), with the mass in sediment and fish following the same general trend as that of the
12-25
-------
Figure 12-8
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12-26
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Figure 12-10
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12-28
-------
water column. There is comparatively little chemical mass predicted to accumulate in the biotic
domains.
12-29
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13.0 Evaluation of TRIM.FaTE
As a process for iterative discovery, science does not reward advocates; it rewards those who find
truth. Many models are assembled through dialectic interactions among advocacy groups, i.e.,
those who favor complex models versus those who favor simple models; those who want to
represent the highest plausible exposure versus those who want to represent central tendency;
those who favor an environmental perspective versus those who favor an industry perspective,
etc. TRIM and TRIM.FaTE aspire to a science-based model process, which requires that the goal
be to model what is real. If the reality is that exposure cannot be modeled without large uncer-
tainties, then this should be reflected in the model process. TRIM is designed to provide EPA
and other users with a tool that can be used in a flexible and iterative manner to explore human
and ecosystem exposures and provide insight in addition to risk estimates. The statistician
George Box has noted that "All models are wrong, but some models are useful" (Box and Tiao,
1973). To make TRIM "useful" and scientifically defensible, it has been designed with
flexibility, iterative analyses, and explicit treatment of sensitivity and uncertainty as core
components of the model building and model implementation process.
In this chapter, conclusions and evaluations based on the current work on TRIM.FaTE are
provided. The chapter is divided into five major sections that compare the TRIM.FaTE prototype
to other multimedia models; identify the capabilities, limitations, and important sensitivities of
the current TRIM.FaTE prototype; and summarize the important conclusions that derive both
from prototype development process and from the application of the prototype to a study site.
13.1 Comparison with Other Models (SimpleBOX and CalTOX)
To compare the results of TRIM.FaTE to other models, two widely-used multimedia models
were applied with the same landscape and chemical input data that were used for the TRIM.FaTE
model case study. The models used for this comparison were CalTOX (Version 2.3) (McKone,
I993a,b,c) and SimpleBOX (Version 2.0) (Brandes, et al., 1997). Comparisons among the three
models were made for the distribution of mass in multiple environmental media for the
chemicals B(a)P and phenanthrene. The descriptions of CalTOX and SimpleBOX are provided
in Section 1.3.
To make the comparison tractable, and to make TRIM.FaTE results consistent with the type of
information produced by the much less complex CalTOX and SimpleBOX models, an emission
13-1
-------
rate of 9 g/day to the air compartment of the case study site was considered. A steady-state mass
distribution was obtained from each model.
Figures 13-1 and 13-2 compare the results of mass distribution predictions for B(a)P and phenan-
threne obtained for similar landscape data sets using CalTOX, SimpleBOX, and TRIM.FaTE.
From Figure 13-1, it can be seen that for B(a)P, TRIM.FaTE, SimpleBOX, and CalTOX all give
similar distributions of mass in soil, water, sediment, and plant compartments. In the air com-
partment, TRIM.FaTE and CalTOX produce similar results and SimpleBOX is a factor of 10
lower. The results in Figure 13-2 show that for phenanthrene, which has a higher vapor pressure
than B(a)P, all three models give similar distributions of mass in soil. For water and sediment,
TRIM.FaTE and CalTOX produce similar results. For air and plants, all three models appear to
yield a large variation in results. This variation appears to be due in large part to the differences
in air/plant uptake factors among the models. This comparison indicates that TRIM.FaTE yields
similar results to CalTOX and SimpleBOX for some media, but different results for others, based
on different algorithms. However, without actual measured concentrations in a controlled
system, it cannot be determined which model more accurately reflects reality.
13.2 Sensitivity Analysis for TRIM.FaTE
Five factors that determine the precision or reliability of an environmental transfer model
(International Atomic Energy Agency, 1989): specification of the problem (scenario
development); formulation of the conceptual model (the influence diagram); formulation of the
computational model; estimation of parameter values; and calculation and documentation of
results, including uncertainties.
It should be recognized that there are some important inherent uncertainties in the TRIM.FaTE
multimedia approach. At this time, only a simplified sensitivity analysis for TRIM.FaTE has
been completed. The method used considers the range of uncertainty in the parameter value and
the linear elasticity of predicted organism concentration with respect to each input parameter.
This method identifies parameters with both relatively high sensitivity and a large range of
uncertainty. The method is used to identify parameters for which decreasing uncertainty would
have the largest impact on reducing output uncertainty.
13-2
-------
Figure 13-1
Model Comparison for B(a)P
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The technique used in this preliminary method uses a sensitivity score, defined as:
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sensitivity score - x CV.
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where:
dX, = change in output Y per change in input X
CV, = coefficient of variation of 1th input
X,°/Y0 = ratio of nominal values of input and output.
The sensitivity score was calculated for all of the inputs to the TRIM.FaTE model, and the
sensitivity to the change in inputs was determined for the following outputs: chemical
concentrations in a carnivorous fish, macrophytes, a vole, a chickadee, and a hawk. The
calculation was made for B(a)P in a steady-state condition. The coefficients of variation used
were estimated based on both reasonable judgment and coefficients of variation developed for
the California EPA for similar parameters used in the CalTOX model. Of the 400 inputs, Table
13-1 presents the 20 inputs that have relatively large sensitivity scores.
As discussed in Section 13.4.5, the mass distribution in the carnivorous fish (bass) was predicted
to be unusually high. The results of this analysis shows that the parameters with high sensitivity
scores for the macrophytes and fish appear to be reasonable, relative to our expectations. B(a)P
binds to particles in the air; therefore, exposure is influenced by how much B(a)P is transported
to the surface water during wet deposition, based on the wash-out ratio, thus increasing the
surface water concentration. Parameters that influence the concentration in the surface water also
have a strong effect on the results because aquatic exposure is through surface water. Decay
constants are highly uncertain because the model is sensitive to the decay content and the effects
of varying them score high. B(a)P is likely to partition into the organic carbon in suspended
sediment in water; thus, the amount of organic carbon suspended in water is an important factor.
The carnivorous fish is also dependent on sediment properties, as its food comes primarily from
the sediment. The assimilation efficiencies are highly uncertain for wild species.
13-4
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Table 13-1
Parameters with High Sensitivity Scores for B(a)P
Parameter
Washout-ratio
Octanol-water partition coefficient
Organic carbon partition coefficient
Decay constants in air
Decay constants in surface water
Decay constants in sediment
Decay constants in fish
Suspended sediment in surface
water
Organic carbon in suspended
sediment
Sediment organic carbon fraction
Porosity of sediment zone
Assimilation efficiencies
Accumulation factor
Fraction of lipids in fish
Fish diet
Water mgestion rate for the
chickadee
Inhalation rate of the chickadee
Water mgestion rate of the vole
Food mgestion rate of the vole
Inhalation rate of the vole
Carnivorous
Fish
X
X
X
X
X
X
X
X
X
X
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X
X
Macrophytes
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X
X
X
X
X
X
X
X
X
Chickadee
X
X
X
X
X
X
X
X
X
Vole
X
X
X
X
X
Hawk
X
X
X
X
X
X
X
The parameters with high sensitivity scores for the three terrestrial species (chickadee, vole, and
hawk) included many of the same parameters as the aquatic species. The terrestrial species are
sensitive to the chemical concentration in the surface water because they use the surface water in
large pan as their drinking water supply. The hawk also eats fish, whose chemical concentration
13-5
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is dependent on the concentration in surface water. Additionally, the chickadee and hawk are
sensitive to the water ingestion rate and inhalation rate of the chickadee. The chickadee is
obviously sensitive to its own intake rates, but the hawk is also sensitive to them because it feeds
on the chickadee. Similarly, both the vole and hawk are sensitive to the water ingestion rate,
food ingestion rate, and inhalation rate of the vole.
The model results were found to be highly dependent on the chemical properties of the chemical
species being modeled. Nonetheless, in all cases, the model was very sensitive to source terms.
All model predictions were directly proportional to the initial inventory or input rates used. For
many applications of a model such as TRIM.FaTE, source data are variable and/or uncertain,
particularly for contaminant measurements in soils. For most chemicals, the model is sensitive to
the magnitude of the transformation rates in soils, air, surface water, and/or sediment. These rate
constants can have a large impact on the predicted persistence of any chemical species and are
often the most uncertain inputs to the model. For volatile chemicals, the model is sensitive to the
magnitude of the air-water partition coefficient. For semivolatile chemicals and inorganic
species, the model is more sensitive to the soil-water partition coefficients. Researchers typically
assume that these partition processes are linear and reversible. When this assumption is not
valid, the reliability of the model is reduced because of the uncertainties about the degree to
which soil partition processes diverge from ideal behavior. The transformation of contaminants
in the environment can have a profound effect on their potential for persistence.
13.3 Overall Capabilities
TRIM.FaTE is a model that explicitly represents time and spatial resolution by the number of
cells and links among its compartments. In descending order of reliability, the model is capable
of handling non-ionic organic chemicals, radionuclides, fully dissociating organic and inorganic
chemicals, and solid-phase metal species. Limitations in reliability derive from relevance and
availability of data. With careful attention to inputs and selection of the appropriate algorithms,
the mathematical structure of TRIM.FaTE can be used to model partially dissociated organic and
inorganic species. As better data and scientific understanding become available, TRIM.FaTE can
be used for such difficult-to-model agents as surfactants, inorganic chemical species with high
vapor-pressure-to-solubility ratios, and volatile metals. As a result, TRIM.FaTE will be applic-
able to most chemicals of concern from a multimedia, multipathway perspective.
13.3.1 Time Scales
The TRIM.FaTE model was designed to be applied over time periods ranging from 1 hour to 1 or
more days, months, or years, when seasonally and yearly averaged partition factors apply.
13-6
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13.3.2 Spatial Scales
Spatial resolution is implicitly linked to the time-step size selected. When short time steps are
selected, TRIM.FaTE can provide spatial information on scales of hundreds of meters. The
assumption that compartments are well-mixed requires that compartment dimensions be less than
the distance traveled by a chemical in one time-step. Because TRIM.FaTE is a compartmental-
type model, there are no explicit vertical or horizontal dimensions in the cells used to represent
various components of the environment.
In addition to the time-step considerations, other factors should determine the appropriate
horizontal cell size. These include: (1) resolution of input data sets and (2) similarity of habitat
(e.g., vegetation cover) and soils within a cell.
73.3.3 Chemical Classes
There are many classes of chemicals that must be addressed in environmental transport/transfor-
mation models, including organic chemicals, metals, inorganic chemicals, and radionuclides.
These chemical species can also be categorized according to the physical state in which they are
introduced to the environment (gas, liquid, or solid), according to whether they dissociate in
solution (ionic or nonionic), and the charge distribution on the molecule (polar or nonpolar). The
traditional fugacity-type approach is most appropriate for nonionic organic chemicals in a liquid
or gaseous state. However, with modifications for condensation of solids on air particles, this
approach can be made appropriate for solid-phase organic chemicals. Additional adjustments
make possible the treatment of inorganic species, metals, and fully ionized organic species.
Metals (such as mercury) and inorganic chemicals with a relatively large vapor pressure pose
special problems not addressed in most multimedia models, but TRIM.FaTE provides the poten-
tial for addressing such species. In addition, TRIM.FaTE can handle special modeling problems,
such as those that occur with mixed polarity and dissociating organic species, such as surfactants.
73.4 Limitations
TRIM.FaTE is being designed to simulate pollutant movement within these complex ecosystems.
Given the complexity of processes dictating the transfer of pollutants within these systems, it
must be understood that the model's predictive capability is presently limited to gross transfers of
pollutants between sources, receptors, and sinks. The model's overall predictive capabilities
depend on: (1) the explicit transfer links built into the model; (2) available databases for which it
is possible to derive distributions of parameters; and (3) the current understanding of ecological
and abiotic transfers.
13-7
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The model is designed to accommodate new information in scientific understanding, so that its
precision and usefulness will improve with time. Factors that contribute to the uncertainty in
outputs of TRIM.FaTE include:
• Limitations on the number of receptor species representing terrestrial and aquatic
trophic levels and the mass (number) associated with those species;
• Limitations on our understanding of pollutant synergistic interactions, and their
effect on transfer, uptake, and loss rates;
• Limitations on our understanding of pollutant biotransformation processes and our
ability to quantify such processes;
• Limitations on our understanding of biotic interactions at the population, com-
munity, and ecosystem level;
• Limitations on our understanding of pollutant assimilation processes, as well as
depuration/egestion rates for aquatic and terrestrial receptors; and
• Limitations on our understanding of population dynamics and seasonal biomass
fluctuation for certain receptor species.
Because of the complexity, the current TRIM.FaTE generates enormous amounts of output.
There are more than 1,500 links in the TRIM.FaTE prototype in which transition rates are
calculated for each time period. Each link contains important information regarding the process
being simulated. Proper evaluation of the model requires that the generated information be
explored and assessed. This information includes:
• The contribution of various components to the total transition rate (e.g., diffusion
versus advection, solid phase advection versus liquid phase advection);
• The contribution of intermediate processes to specific components of the transition
rate (e.g., cuticle conductance versus stomatal conductance in calculating diffusion
component of the air-to-plant transition rate); and
• The partitioning of the flow of chemical through particular domains.
Limited model verification has been performed to date, but more verification is needed. This
may best be accomplished with simple applications that focus on a particular subset of domains.
The driving forces in TRIM.FaTE are the flows of air, water, and solids throughout the system.
The modeled chemical(s) will be transported primarily via these mechanisms. While such flows
13-8
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are considered external to the basic structure of the model, rather than part of the model itself, it
would be worthwhile to allow the inclusion of additional flow models within the model
framework. Numerous models exist for long-term flow (e.g., the Universal Soil Loss Equation
for erosion flow), but their application in a dynamic, multi-compartment context must be
carefully investigated. Currently, the flow model for air transport is also overly simplistic and
other appropriate models or algorithms need to be investigated.
13.5 Conclusions from Developmental Work on TRIM.FaTE
Detailed single-media models, such as Gaussian-plume models, subsurface transport models, and
surface water models, exist for a variety of applications. Some multimedia models are based on
the linking of these detailed single media models; MEPAS is one example (Whelan, et al., 1992).
However, it is extremely difficult to impose strict mass balance relationships, implement
thermodynamics of partition processes, and carry out comprehensive sensitivity and uncertainty
analyses with these "linked-model" systems (Thibodeaux, 1996). In contrast, the Mackay-type
multimedia models provide strict mass balance relationship, use fugacity capacities (that is the
capacity of a compartment to contain a chemical on a unit volume-basis) to define the kinetics
and limits of mass transfer, and provide a tractable and scientifically defensible framework for
assessing pollutant behavior in complex systems (McKay, 1991; Cowan, et al., 1995).
TRIM.FaTE was designed to fill the middle ground between the more spatially complex single-
media models and the comprehensive but often low-resolution multimedia mass-balance models.
TRIM.FaTE is a Mackay-type multimedia model based on the following criteria: it uses a series
of fully interacting compartments to represent all components of an environmental system; and it
is fully mass-balancing, and uses fugacity-based relationships to define the kinetics and
limitations of mass transfer processes.
However, unlike any Mackay-type multimedia model to date (for examples see The Multimedia
Fate Model: A Vital Tool for Reducing the Fate of Chemicals) (Cowen, et al., 1995).
TRIM.FaTE is designed to accommodate relatively short time steps and high spatial resolution.
In addition, unlike most multimedia models, TRIM.FaTE has the capability of simulating non-
reversible liquid-solid sorption processes in soil and of simulating the coupled transport and
transformation of multiple chemical species.
TRIM.FaTE currently has a spreadsheet interface with compiled FORTRAN modules used as
equation-solving routines. This arrangement facilitates sensitivity and uncertainty analyses and
makes possible the analysis of alternate algorithms for linking compartments.
13-9
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73.5.1 Prototype Algorithms and Mathematical Structure
Tests of a prototype version of TRIM.FaTE indicate that the multimedia approach produces
realistic mass distributions in ecosystems containing representative air, water, soil, plant, and
animal compartments.
TRIM uses a dynamic mass-balance approach to provide estimates of the exposure and dose
profile received by selected receptors. The TRIM.FaTE module accounts for the movement of
pollutant mass through a user-defined, bounded systems model that includes both biotic and
nonbiotic (abiotic) compartments. The compartments have index addresses that represent the
spatial location, domain type, and chemical species of the pollutant. The model uses mass
balance relationships, fugacity capacities, and biokinetics to determine the movement of pollutant
mass among the compartments. A system of linked differential equations describing pollutant
mass transfer rates between pairs of addresses is at the heart of this model.
The features that make the mathematical structure of TRIM.FaTE (Chapter 3.0) unique are: (1)
its system of linked differential equations across all locations, environmental domains, and
chemical species; and (2) the estimation of transfer factors between cells based on a library of
algorithms. These features provide flexibility in defining the complexity of a simulation.
73.5.2 Input Data Needs, Verification, and Validation
Data sets needed to carry out TRIM.FaTE assessments include: chemical properties data,
including basic chemical properties and transformation rates; landscape data, including eco-
system, land use, hydrology, and climate data; and nonchemical-specific biotic parameters.
TRIM.FaTE concentration estimates are to be as spatially and temporally explicit as is feasible.
The data needed for the spatial explicitness of TRIM.FaTE will be provided by a GIS containing
readily available national or regional data sets for required model parameters such as land cover,
soil characteristics, roads, water bodies, presence and abundance of species or biomass, and
climate variables. A default set of spatial data for biotic and abiotic parameters has been
identified.
13-10
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Blackadar, 1996, Turbulence and Diffusion in the Atmosphere, Springer, New York.
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McFarlane, eds., Lewis Publishers, Boca Raton, Florida.
Trapp, S., M. Matthies, I. Scheunert, and E. M. Topp, 1990, Modeling the Bioconcentration of
Organic Chemicals in Plants, Environ. Sci. Technol. 24:1246-1252.
Travis, C. C. and A. D. Arms, 1988, Bioconcentration ofOrganics in Beef, Milk, and
Vegetation, Environ. Sci. Technol., 22: 271-274.
Turner, D. B., 1970, Workbook of Atmospheric Dispersion Estimates, Office of Air Programs,
U.S. Environmental Protection Agency, Research Triangle Park, North Carolina.
U.S. Environmental Protection Agency (EPA), 1997a, Guiding Principles for Monte Carlo
Analysis, Office of Research and Development, Washington, DC, EPA/630/R-97/001.
14-12
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U.S. Environmental Protection Agency (EPA), 1997b, Guidance on Cumulative Risk
Assessment.
U.S. Environmental Protection Agency (EPA), 1996, Technical Background Document for Soil
Screening Guidance, EPA 540/R-95/128, May.
U. S. Environmental Protection Agency (EPA), 1995, PCRAMMET Users Guide, OAQPS,
RTP, NC, October 1995.
U. S. Environmental Protection Agency (EPA), 1994, Revised Draft of Risk Assessment
Implementation Guidance for Hazardous Waste Combustion Facilities, Memorandum from M.
H. Shapiro, EPA Office of Solid Waste to Waste Management Division Directors, Regions I-X,
May 5, as cited in WTI report.
U.S. Environmental Protection Agency (EPA), 1993, Addendum to Methodology for Assessing
Health Risks Associated with Indirect Exposure to Combustor Emissions, External Review
Draft, Office of Health and Environmental Assessment, EPA/600/AP-93/003, Washington DC,
November.
U.S. Environmental Protection Agency (EPA), 1990, Methodology for Assessing Health Risks
Associated with Indirect Exposure to Combustor Emissions, Interim Final, Office of Health and
Environmental Assessment, EPA/600/6-90/003, Washington DC, January.
U.S. Environmental Protection Agency (EPA), 1987, On-Site Meteorological Guidance for
Regulatory Modeling Applications, EPA-450/4-87-013, OAQPS, RTP, North Carolina.
U.S. Environmental Protection Agency (EPA), 1986, Guidelines for Carcinogenic Risk
Assessment, Federal Register 51:33992-34003.
van de Meent. D., 1993, SIMPLEBOX: A Generic Multimedia Fate Evaluation Model,
National Institute of Public Health and Environmental Protection (RFVM) Report No. 672720
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14-13
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Predict Radionuclide Ingestion After Fallout Deposition, Health Phys. 52, pp. 717-737.
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Env. 102:229-240.
14-14
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APPENDIX A
GLOSSARY
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Glossary,
Advection - Process in which a chemical is transported within a given phase that is moving
from one cell to another. Calculation of advective flux requires velocity of and amount of
chemical in the moving phase. Mac Kay (1991) refers to advection as the "piggyback" process, in
which a chemical "piggybacks" on material moving from one place to another for reasons
unrelated to the presence of the chemical.
Atmospheric Half-Life - The time required for one-half of the quantity of an air pollutant to
react and/or break down in the atmosphere.
Bioaccumulation - Progressive increase in amount of chemical in an organism or part of an
organism that occurs because the rate of intake exceeds the organism's ability to remove the
substance from the body.
Bioconcentration - Same as bioaccumulation; refers to the increase in concentration of a
chemical in an organism.
Biological Half-Life - The time required for the concentration of a chemical present in the
body or in a particular body compartment to decease by one-half through biological processes
such as metabolism and excretion.
Block Structure - Part of a three-dimensional space that can contain various media and biota.
Boundary Layer - Part of the trophosphere that is directly influenced by the earth's surface and
responds to surface forces with a time scale on the order of an hour or less. The major
components are the surface layer, the mixed layer, the stable boundary layer, and the residual
layer
Carcinogenic - Able to produce malignant tumor growth. Operationally, most benign tumors
are usually included also.
Cell - A uniquely defined address, within the computer code, which accounts for all potential
locations of mass within the ecosystem. The three indices that make up an inventory address in
A-l
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TRIM.FaTE are volume element, domain, and species. There is no concentration gradient within
an inventory address; the chemical is uniformly mixed. An informal synonym for this term is
"cell."
Chemodynamics - A set of integrated models for assessing the cross-media transfers of
organic chemicals.
Clean Air Act of 1990 - This amendment to the Clean Air Act of 1970 contains several provi-
sions requiring the EPA to evaluate effects to humans and the environment caused by exposure to
hazardous air pollutants and criteria air pollutants.
Cohort Study - A study of a group of persons sharing a common experience (e.g., exposure to
a substance) within a defined time period: this experiment is used to determine if an increased
risk of a health effect (disease) is associated with that exposure.
Compartmental Systems Model - A model that is represented by a series of cells, each with
a state variable, which interact through transfer factors. In this model, the transport of multiple
pollutant species in a multimedia region is set up as a mass exchange among a set of systems
used to represent spatial locations, collections of environmental phases, and chemical species.
Criteria Pollutant - Six common pollutants, used as indicators of air quality, regulated by EPA
on the basis of human and/or environmental adverse effects.
Dermal - Absorption through the skin membrane.
Dermal Uptake - Absorption through the skin membrane.
Diffusion - Movement of a chemical substance from areas of high concentration to areas of low
concentration. Biologically, diffusion is an important means for toxicant deposition for gases
and very small particles in the pulmonary region of the lungs.
Dispersion Model - A mathematical model or computer simulation used to predict the
movement of airborne pollution. Models take into account a variety of mixing mechanisms
which dilute effluents and transport them away from the point of emission.
A-2
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Domain - The domain refers to the composition of material in which the chemical is dissolved,
sorbed, or otherwise held. What distinguishes one domain from another at a given location is the
requirement that all phases of a single domain must attain equilibrium within a single calculation
time step. There is a hierarchical system of domain, i.e., different levels of domain. At a more
general level, a domain is a collections of volume elements, such as all of the root zone soil. For
example, an instance of the domain is the root zone soil within a volume element.
Dose - The amount of chemical absorbed by an organism usually expressed as mass of
substance per unit body weight of organism per unit time.
Dose Assessment - The determination of the relation between the magnitude of exposure and
the probability of occurrence of the health effects in question.
Dose Response - Determination of the magnitude of toxic response to dose.
Dry Deposition - A transfer process from air to soil. Dry deposition velocity is the ratio of
contaminant flux (mol/[nr-h]) to contaminant concentration in air (mol/m3).
Ecological Toxicity Database - A database in which the user inputs a chemical name and the
name of plant, animal, or aquatic species whose adverse effect is being sought; a list of "major
effects" is supplied by the database. Serves as a source of important information for TRIM
effort.
Environmental Fate - The destiny of a chemical or biological pollutant after release into the
environment. Environmental fate involves temporal and spatial considerations of transport,
transfer, storage, and transformation.
Equilibrium - The state in which opposing forces are exactly counteracted or balanced. Types
of equilibrium include acid-base, colloid, dynamic, homeostatic, and chemical. Used in risk
assessment of toxic air pollutants to generally describe the chemical equilibrium between a
pollutant in the inhaled air and the level in the body.
Exposure Assessment - Measurement or estimation of the magnitude, frequency, duration
and route of exposure of animals or ecological components to substances in the environment.
A-3
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The exposure assessment also describes the nature of exposure and the size and nature of the
exposed populations, and is one of four steps in risk assessment.
Fugacity - Fugacity has the units of pressure and is linearly or non-linearly related to
concentration through the relationship fugacity (f) = (fugacity capacity [Z])(concentrations). The
fugacity capacity of a chemical is equivalent to the concept of heat capacity or temperature. Just
as a chemical will flow from higher temperatures to lower temperatures, it will also flow from an
area of higher to lower fugacity capacity.
Gaussian Model - A widely used wind dispersion model based on the analytical solution to the
air pollutant transport differential equation under specific boundary conditions.
GEOTOX - Multimedia screening model; one of the earliest multimedia models to explicitly
address human exposure.
Half-Life - See atmospheric half-life and biological half-life. Also, the period of time
characteristic of a radionuclide in which one-half of the activity has decayed.
Hazard Identification - The determination of whether a particular chemical is or is not
causally liked to particular health effect(s).
Hazardous Air Pollutant- Any air pollutant listed pursuant to Section 112(b) of the Clean Air
Act of 1990. Those pollutants known or suspected to cause serious health problems.
Indices - There are three indices used in the inventory address and state variable used as a
tracking and auditing system to clarify the volume element, domain, and species in the
TRIM.FaTE framework.
Indirect Exposure Methodology - This methodology sets out procedures for estimating the
indirect (i.e., non-inhalation) human exposures and health risks that can result from the transfer
of emitted pollutants to soil, vegetation, and water bodies. This methodology is not a compre-
hensive environmental audit, but is best regarded as an evolving and emerging process that
moves the EPA beyond the analysis of potential effects on only one medium (air) and exposure
pathway (inhalation) to the consideration of other media and exposure pathways.
A-4
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Ingestion Uptake - Intake via the mouth, with transfer to the GI tract.
Inhalation Uptake - Intake via the nose and mouth, with transfer to the lungs.
Inhalation - Absorption through the lungs.
Inventory Address - A uniquely defined address, within the computer code, which accounts
for all potential locations of mass within the ecosystem. The three indices that make up an
inventory address in TRIM.FaTE are volume element, domain, and species. There is no
concentration gradient within an inventory address; the chemical is uniformly mixed. An
informal synonym for this term is "cell."
Lateral Runoff- during a rainfall event, some of the water travels laterally across the soil as
runoff. As the water travels over the soil, the water concentration approaches that of the soil pore
water beneath it.
Leaf Model - The total mass of chemical in the leaf is based on the interaction of the leaf with
both the vapor and paniculate phases.
Links - If mass moves without first moving through intervening cells, the two cells are
considered linked. Each linkage is associated with an algorithm determining the direction and
rate of mass flow between the two cells.
Lipophilic Compounds - Chemicals that have a strong affinity for lipids such as fats, proteins
etc.
Litterfall - The process of plant death resulting in the plant falling to the soil; this process adds
chemical to the surface soil compartment. Different tree types have different litterfall rates
determined by whether or not they shed their leaves.
Macrophyte - A large aquatic plant.
Microenvironment - The immediate local environment of an organism.
A-5
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Mixed Layer - A well-mixed layer of the atmosphere in which the turbulence is primarily
driven by convective forces resulting from surface heating; therefore, growth is tied to the diurnal
cycle. Growth begins approximately one-half hour after sunrise and reaches maximum depth in
the late afternoon.
Model - A mathematical representation of a natural system intended to mimic the behavior of
the real system, allowing description of empirical data, and predictions about untested states of
the system.
Models-3 - EPA's third generation of air quality management/modeling system to be used as a
tool for decision making by federal, state and the industry environmental analysts. It is a layered
modeling system providing various kinds of services at various levels of complexity. The most
important layers are the User, Management, Computational Modeling, and Data Access layers.
Molecular Diffusion - The process by which molecules intermingle as a result of their thermal
motion.
Moles - The amount of matter that contains 6.023 x 1023 atoms or molecules. For example, 1
gram mole of any element contains 6.023 x 1023 atoms.
Multi-Pathway Exposure - Exposure through inhalation, ingestion, and adsorption routes.
Multimedia Contamination - Contamination in air, water, soil, and food.
Multimedia Environmental Pollutant Assessment- A PC-based system that considers
four pathways: groundwater, overland, surface water, and atmospheric in evaluating human
exposure and health effects.
Multiple-Phase Calculations - Liquid, gas, and solid; these are assumed to be at chemical
equilibrium. Ratios of concentrations in individual phases are constant. Mass balance is only
tracked for the total amount of the chemical in all phases in a cell; the amount in the cell in a
particular phase can be determined from the total amount in the cell.
Overturn - Occurs when the top and bottom waters of lakes mix; only occurs when there is no
ice cover, and there is little difference in temperature between surface and bottom waters of the
A-6
-------
lake. Therefore, in summer, the temperature difference between the surface and bottom waters of
the lake are too great for mixing to occur.
Pharamacokinetics - The concentration obtained in the target organ depending on the
disposition of the chemical, that is, its absorption, distribution, biotransformation, and excretion.
Ultimately, the toxicity of an agent is determined by the concentration of the toxic chemical in
the target organ.
Phase - The building blocks of which everything else is composed (gas, liquid, solid, lipid, and
other material). Each domain consists of multiple phases.
Reaction or "R" Factor - Used for chemical reactions or transformation processes. Used for
transfer from one species to another (e.g., radioactive decay), or for transfers out of the system
(e.g., chemical degradation to a chemical not being tracked). As an example, consider an address
that represents a soil layer contaminated with trichloroethylene (TCE). This address will be at
the same location and represent the same domain, but differs in the last entry from the address
that represents the inventory of vinyl chloride (VC), which is a decay product of TCE. Both
addresses are at the same location and domain, but TCE must undergo a transformation to move
from the address with the TCE/soil layer to the VC/soil layer address.
Species - Chemical compound state/phase (i.e., form of the chemical and phase of the chemical
- physical properties of the chemical) This index is useful for representing radioactive decay or
chemical decay, (e.g., TCE to vinyl chloride).
Reaction Transformation - Process that transforms a chemical species into another chemical
species, but does not include a change of location or domain. Biodegradation, photolysis,
hydrolysis, oxidation/reduction, radioactive decay, etc., are reaction transformation processes.
Residual Boundary Layer- A more neutrally stratified layer that forms when convective
forces cease approximately one-half hour before sunset.
Risk Assessment - The scientific activity of evaluating the toxic properties of a chemical and
the conditions of human exposure to it in order both to ascertain the likelihood that exposed
humans will be adversely affected, and to characterize the nature of the effects they may
experience. May contain some or all of the following four steps:
A-7
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Risk Characterization - The description of the nature and often the magnitude of human risk,
including attendant uncertainty.
Risk Management - The decision-making process that uses the results of risk assessment to
produce a decision about environmental action. Risk management includes consideration of
technical, scientific, social, economic, and political information.
Sediment Disposition - The transport of the chemical from the surface water to sediment;
sediment resuspension refers to the reverse process. Both processes involve only the solid phase.
Sink - A domain that receives input from a domain, but does not output the chemical. Once a
chemical enters a sink, its mass is not tracked in the model; it is a final "resting place" for the
chemical.
Species - Chemical compound state/phase (i.e., form of the chemical and phase of the
chemical-physical properties of the chemical). This index is useful for representing radioactive
decay or chemical decay, (e.g., TCE to vinyl chloride).
Stable Boundary Layer - This layer forms in the atmosphere when the bottom portion of
residual boundary layer contacts with the ground.
State Variable - Values that describe the state of the system as a function of time in the various
components of the modeled system.
Steady State - When the pollutant concentration in a domain does not change with time.
Subcooled Vapor Pressure - Vapor pressure of a subcooled liquid.
Subsurface Transfer Factors - A function of the advective flux (gas phase + liquid phase)
and the diffusive flux (gas phase + liquid phase); for each cell in the subsurface, the advective
flux is loss mechanism.
Surface Layer - Region at the bottom of the boundary layer where turbulent fluxes vary by less
than 10 percent; depth is typically defined as 10 percent of the mixed layer.
A-8
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Total Human Environmental Relational Database and Advanced Simulation
Environment - A database containing both microenvironmental and human activity data which
can be used in the exposure assessment of the TRIM. Will be included in the Consolidated
Human Activity Database, which is currently under development by the Office of Research and
Development National Exposure Research Laboratory.
Transfer Factors - The rate at which a chemical will be transferred from one inventory address
to another inventory address for a given mass in that inventory address. The units of this factor
are fraction of total inventory per unit time. When a transfer rate factor is multiplied by an
inventory expressed as mass, the mass transferred per unit time is obtained. There are two types
of transfer factors: "T" factor and "R" factor, for transport and reaction, respectively. It should
be noted that the magnitude of transfer rates do not define the magnitude of the transfer because
if there is very little mass in a cell, there will be very little transferred.
Transformation - Alteration of a chemical substance from one chemical form to another
through a chemical, physical, or biological reaction.
Transport - To move or be conveyed from one place to another. In the context of environ-
mental contamination, a containment is transported from one location to another by dispersion,
advection (e.g., wind), or diffusion(e.g., dilution in air) processes.
Transport or "T" Factor- This transfer rate can be used in several ways. First, it can be used
for transport from one location to another. This is further broken down into transport processes
involving the change of location by advection or by diffusion. At a minimum, there will be a
change in the first index, the spatial location for this type of process, i.e. diffusion in the soil.
Sometimes, there will be both a change of domain and spatial location, i.e. diffusion from air to
soil. An alternate use is for transfer from one domain to another at the same spatial location, in
which case the second index changes. For example, if we decide that sediment particles should
not be in equilibrium with water, then the water and the particles would have to be separate
domains at the same volume element and a "T" factor would be used to express the exchange
between these phases.
Turbulent Diffusion - The intermingling of molecules in matter as a result of turbulent motion
such as wind gusts.
A-9
-------
Two-Resistance Model for Diffusion - For molecular and turbulent diffusion, the mass
transfer between a cell i to cell j depends on mass transfer through two distinct layers: the
boundary in cell i and the boundary in cell j. Net flux is assumed equal on both sides of the
boundary between the two cells. This flux is assumed proportional to the difference in the bulk
concentration in the cell and the concentration at the cell-side of the boundary. Constant of
proportionality has units of m/day, and is called the mass transfer coefficient. Determination of
mass transfer coefficient depends on domain type of cell, and in some cases, the domain type of
both cells.
Volume Element - An entity characterized by a total spatial volume (m ) completely enclosed
by a contiguous surface. This surface may be shared by one or more neighboring volume
elements. The volume element has a unique spatial location, which can be defined with a set of
x-y-z coordinates. The volume is occupied by all domains at this location. For example, if there
are two domains at a volume element, the sum of the volumes of these two domains must sum to
the volume of the volume element. When two domains occupy the same volume location, these
two domains are assumed to be well mixed.
Volumetric Flow Rate - In most applications, the product of a relevant area (Ay) and the
volumetric flow rate per unit area, or a flow velocity (vy). Usually the relevant area is the
interfacial area between the sending and receiving cells, but this is not always the case; e.g.,
erosion from surface soil to surface water is usually reported in units of mass(soil)/area(soil
layer)-time, in which case the relevant area is the area of the surface soil layer.
Water Balance - The first step in assessing surface-water transport; established by equating
gains and losses in a water system with storage. Gains include inflows (both runoff and stream
input) and direct precipitation. Losses include outflows and evaporation.
Wet Deposition - Transfer process from air to soil. Occurs during precipitation and is
proportional to the rate of precipitation (i.e., rain in m/h), but differs in both the relative
magnitude and nature between particles and gas-phase chemicals.
A-10
-------
APPENDIX B
DATA INPUTS SELECTION/JUSTIFICATION
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8.2 Distributional Data for Terrestrial Wildlife
Domain:TerrestriaI Insectivore
Species: Black-capped Chickadee (Parus atricapillus)
Parameter: Body weight (BW)
Value or Algorithm: BW,+,= 0.0108 ±0.00138
(mean ± SD; N=1880; range: 0.0082 - 0.0136)
Units: kg
Notes: Values are summaries from multiole locations throughout Pennsylvania
Reference: Dunning 1993
Parameter: Food ingestion rate (If)
Value or Algorithm: If = 0.74
Units: kg food/ kg BW/d
Notes: Smith (1993) reports that while no data on nutrition and food ingestion by black-capped chickadees
are available, parids of comparable size require 10 kcal /d (41.84 kJ/d). Assuming that the chickadee diet
consists 100% of insects, the body weight is 0.0108 kg (Dunning 1993), and energy and water content of
insects are 22.09 kJ/g dry weight and 76.3%, respectively (Bell 1990), daily food ingestion by chickadees
would be 0.74 kg food (wet weight) /kg BW/d.
Reference: NA
Parameter: Soil ingestion rate (Is)
Value or Algorithm: Is = 0
Units: kg soil/ kg BW/d
Notes: Blackcapped chickadees are reported to be arboreal foragers for insects and are rarely observed on
the ground (Smith 1993). Consequently, soil ingestion is assumed to be negligible
Reference: Smith 1993
Parameter: Water ingestion rate (Iw)
Value or Algorithm: Iw = (0.059*(BW)067)/BW
Units: L water/ kg BW/d
Notes: Allometric equation from Calder and Braun (1983) estimates water consumption in
mL/individual/day. Units converted to L water/ individual/d. Water ingestion normalized to body weight
using body weights reported in Dunning 1993.
Reference: Calder and Braun 1983
Parameter: Inhalation (IJ
Value or Algorithm: I, = (0.40896*(B W)° 8)/BW
Units: m3 air/ kg BW/d
Notes: Allometric equation from Lasiewski and Calder (1971) estimates inhalation in mL/individual/min.
Units converted to m3/ individual/d. Inhalation normalized to body weight using body weights reported in
Dunning 1993.
Reference: Lasiewski and Calder 1971
Parameter: Diet Composition (p;)
Value or Algorithm: ?,„«„,*«„ = 70
Pplam = ' ' Pinveiwbrates)
Units: N/A
Notes: Averaged over a full year, the diet of black-capped chickadees consists 70% of invertebrates
(insects, spiders) and 30% plant (seeds and berries) (Bent 1946). In summer, the diet is 80-100%
invertebrates (primarily Lepidoptera larvae) and 0-20% plant (Sample et al. 1993, Smith 1993). In winter,
the diet is approximately 50% invertebrate and 50% plant (Martin et al. 1951).
Domain: Aquatic Herbivore
Species: Mallard (Anas platyrhynchos)
B-25
-------
Parameter: Body weight (BW)
Value or Algorithm: BW,,= 1.225 (mean; N=3963; max=1.81)
BW,= 1.043 (mean;N=3169;max=1.63)
Units: kg
Notes: Values are summaries from multiple locations throughout North America
Reference: Neslon and Martin 1963
Parameter: Food ingestion rate (lf)
Value or Algorithm: I, = 0.1
Units: kg food/ kg BW/d
Notes: Heinz et al. (1987) report that mallards maintained in the laboratory consumed 0.1 kg dry mash
diet/kg BW/d. The water content of this diet ranged from 7-10%. Because the plant material consumed by
mallards consists largely of seeds, and the mean water content of seeds is 9.3% (EPA 1993), the food
ingestion rate reported by Heinz et al. (1987) may be used without adjusting for water content.
Reference: Heinz et al. 1987
Parameter: Soil ingestion rate (Is)
Value or Algorithm: Is = 0.033*Ir
Units: kg soil/ kg BW/d
Notes: Beyer et al. (1994) report the mean estimated soil ingestion rate from 88 mallard ducks from
Minnesota to be 3.3% of their food consumption rate.
Reference: Beyer et al. 1994
Parameter: Water ingestion rate (Iw)
Value or Algorithm: Iw= (0.059*(BW)067)/BW
Units: L water/ kg BW/d
Notes: Allometric equation from Calder and Braun (1983) estimates water consumption in
mL/individual/day. Units converted to L water/ individual/d. Water ingestion normalized to body weight
using body weights reported in Dunning 1993.
Reference: Calder and Braun 1983
Parameter: Inhalation (Ia)
Value or Algorithm: I, = (0.40896*(BW)° 8)/BW
Units: m' air/ kg BW/d
Notes: Allometric equation from Lasiewski and Calder (1971) estimates inhalation in mL/individual/min.
Units converted to mV individual/d. Inhalation normalized to body weight using body weights reported in
Dunning 1993.
Reference: Lasiewski and Calder 1971
Parameter: Diet Composition (pf)
Value or Algorithm: pftM = 0.665
PinvcnctxMM = ( ' ~ Pplanl)
Units: N/A
Notes: Martin et al. (1951) report that plant material (primarily marsh and aquatic plants) constitute 91%,
827c, and 93% of the diet in winter, spring and fall, respectively. Aquatic invertebrates (primarily insects)
constitute the remainder of the diet (9%. 18%, and 7% in winter, spring and fall, and approximately 100%
in summer). Averaged over the whole year, plants comprise 66.5% of the diet with aquatic invertebrates
accounting for the remainder.
Domain: Terrestrial Predator/Scavenger
Species: Red-tailed Hawk (Buteo jamaicensis)
Parameter: Body weight (BW)
Value or Algorithm: BW,,= 1.028 (mean;N=108)
BWS= 1.224 (mean; N= 100)
Units: kg
B-26
-------
Notes: Values are summaries from multiple locations throughout North America. Preston and Beane
(1993) report that body weight of males ranges from 0.69-1.3 kg and that for females ranges from 0.9-1.46
kg.
Reference: Means: Dunning (1993)
Parameter: Food ingestion rate (If)
Value or Algorithm: If = 0.12*BW
Units: kg food/ kg BW/d
Notes: Estimates of food ingestion rates for red-tailed hawks range from a low of 7% of body weight/d in
summer to as much as 17% of body mass/d in winter. The median of these estimates (12% of body weight)
is recommended to represent typical foraging across all seasons.
Reference: Preston and Beane (1993)
Parameter: Soil ingestion rate (Is)
Value or Algorithm: Is = 0
Units: kg soil/ kg BW/d
Notes: While soil may be attached to prey that may be ingested, the amount consumed is assumed to be
negligible.
Reference: NA
Parameter: Water ingestion rate (Iw)
Value or Algorithm: Iw = (0.059*(BW)067)/BW
Units: L water/ kg BW/d
Notes: Allometric equation from Calder and Braun (1983) estimates water consumption in
mL/individual/day. Units convened to L water/ individual/d. Water ingestion normalized to body weight
using body weights reported in Dunning 1993.
Reference: Calder and Braun 1983
Parameter: Inhalation (Ia)
Value or Algorithm: Ia = (0.40896*(BW)° 8)/BW
Units: m3 air/ kg BW/d
Notes: Allometric equation from Lasiewski and Calder (1971) estimates inhalation in mL/individual/mtn.
Units converted to m3/ individual/d. Inhalation normalized to body weight using body weights reported in
Dunning 1993.
Reference: Lasiewski and Calder 1971
Parameter: Diet Composition (p,)
Value or Algorithm: pmimroil =0.7013
Phlrt =0.1843
Preplllc = 0.0724
French™ = 0-0387
Units: N/A
Notes: The diet of red-tailed hawks is highly variable, differing across seasons, regions, and among
individuals (Preston and Beane 1993). In general, small to medium sized mammals, birds, and reptiles are
consumed. Sherrod (1978) summarized the results of 10 red-tailed hawk diet studies. In general, the diet
consisted of 70.13%, 18.43%, 7.24%, and 3.87% of small mammals, birds, reptiles and amphibians, and
invertebrates, respectively.
Domain: Aquatic Insectivore
Species: Tree Swallow (Tachycineta bicolor)
Parameter: Body weight (BW)
Value or Algorithm: BWrf,e= 0.0201+0.00158 (mean±STD; N=88)
Units: kg
Notes: Values are summaries from Pennsylvania. Body weights ranged from 0.0156-0.0254 kg.
Reference: Dunning (1993)
B-27
-------
Parameter: Food ingestion rate (If)
Value or Algorithm: If = 0.198+0.048
Units: kg food/ kg BW/d
Notes: Female tree swallows in New Brunswick, Canada, were observed to require 5.73+1.40 kJ/g/d
(mean+STD; n=10; Williams 1988). Using body wights reported in Williams (1988; 22.6 g), assuming that
the diet consists exclusively of insects (Quinney and Ankney 1985) and that the energy and water content
of insects is 22.09 kJ/g dry weight and 76.3%, respectively (Bell 1990), daily food consumption by tree
swallows is 0.198+0.048 kg/kg/d.
Reference: NA
Parameter: Soil ingestion rate (Is)
Value or Algorithm: Is= 0.01*If
Units: kg soil/ kg BW/d
Notes: Grit was found in 35 and 20% of the stomachs of nestling and adult tree swallows, respectively
(Mayoh and Zach 1986). The number of particles and the mass of grit was greater in nestings than adults:
the number of particles was 10.2+2.2 (mean+SE) in nestlings vs 0.8±0.8 in adults and mass (mg) was
17.2±2.6 in nestlings vs 6.1+6.1 in adults. Data relating grit ingestion to food ingestion rate was not found
in the literature, however. Consequently estimation of a soil ingestion rate from these data is problematic; a
soil ingestion rate of 1% of food ingestion was therefore assumed.
Reference: NA
Parameter: Water ingestion rate (Iw)
Value or Algorithm: Iw = (0.059*(BW)067)/BW
Units: L water/ kg BW/d
Notes: Allometric equation from Calder and Braun (1983) estimates water consumption in
mL/individual/day. Units converted to L water/ individual/d. Water ingestion normalized to body weight
using body weights reported in Dunning 1993.
Reference: Calder and Braun 1983
Parameter: Inhalation (Ia)
Value or Algorithm: I, = (0.40896*(B W)° 8)/B W
Units: m3 air/ kg BW/d
Notes: Allometric equation from Lasiewski and Calder (1971) estimates inhalation in mL/individual/min.
Units converted to m3/ individual/d. Inhalation normalized to body weight using body weights reported in
Dunning 1993.
Reference: Lasiewski and Calder 1971
Parameter: Diet Composition (pj)
Value or Algorithm: p,nvem!h«e = 1
Units: N/A
Notes: The diet of swallows consists primarily of insects; however, some plant matter may be
consumed (Beal 1918). Flies (Diptera) are generally very important food items for swallows, comprising as
much as 40% of the diet of some species (Quinney and Ankney 1985; Blancher and McNicol 1991).
Chironomid midges are an important food item of tree swallows, accounting for 33% of the diet of nestlings
(Blancher and McNicol 1991). Blancher and McNicol (1991) found prey of aquatic origins to account for
64.9, 71, and 54.9% of the diet of nestling, egg-laying female, and other adult tree swallows, respectively.
Swallows generally consume small insects. Quinney and Ankney (1985) report that 99% of the insects
consumed by tree swallows are <. 10 mm in length. Blancher and McNicol (1991) observed that-90% of
prey were s25 mm in length.
Domain:Terrestrial Vertebrate Herbivore
Species: Mule Deer/Black-tailed Deer (Odocoileus hemionus columbianus)
Parameter: Body weight (BW)
B-28
-------
Value or Algorithm: B Wrf = 72.9±3.0 (mean ± SE)
BW, = 59.4± 1.2 (mean ±SE)
Units: kg
Notes: Values are summaries from Colorado
Reference: Alldredge et al. 1974
Parameter: Food ingestion rate (I,)
Value or Algorithm: If = 0.0219 ± 0.0011 (mean ± SE)
Units: kg food/ kg BW/d
Notes: Data represent estimated food ingestion rate for 87 mule deer. Value derived based on known Cs-
137 concentrations in deer and forage. Value represents ingestion of air-dried food. Ingestion rate should
be adjusted for water content if fresh forage is consumed.
Reference: Alldredge et al. 1974
Parameter: Soil ingestion rate (Is)
Value or Algorithm: Is = 0.02(If)
Units: kg soil/ kg BW/d
Notes: Soil ingestion rates were calculated for mule deer in north central Colorado feeding in a grassland-
shrub community (Arthur and Alldredge 1979). The intake varied by season, with a year-round average of
16.1 g/individual/d. The soil ingested ranged from 0.6 to 2.1% of the deers' diets (dry matter intake).
Beyer et al. (1994) report soil ingestion by mule deer to be <2% of their diet.
Reference: Beyer et al. 1994
Parameter: Water ingestion rate (Iw)
Value or Algorithm: Iw = 0.024-0.035 (range; winter)
Iw = 0.047-0.070 (range; summer)
Units: L water/ kg BW/d
Notes: Mule deer obtain much of their water through succulent forage or as dew on forage plants. This is
sufficient to meet their metabolic needs during the spring, summer, and fall; in the winter snow is ingested
(Mackie et al. 1982). Observations of mean water intake by penned mule deer range from 0.024-0.035
L/kg/d in winter and 0.047-0.070 L/kg/d in the summer (Anderson and Wallmo 1984). Water consumption
by black-tailed deer ranges from 0.053 L/kg/d in winter to 0.104 L/kg/d in summer (Anderson and Wallmo
1984).
Reference: NA
Parameter: Inhalation (IJ
Value or Algorithm: Ia= (0.54576*(BW)08)/BW
Units: m3 air/ kg BW/d
Notes: Allometric equation from Stahl (1967) estimates inhalation in mL/individual/min. Units converted to
m3/ individual/d. Inhalation normalized to body weight using body weights reported in Alldredge et al.
1974.
Reference: Stahl 1967
Parameter: Diet Composition (p,)
Value or Algorithm: pplim = 1.0
Units: N/A
Notes: It is difficult to generalize the typical forage of mule deer; foods eaten vary dramatically in kind,
quantity, and nutritional quality as well as in digestibility from one season to another, from one year to the
next, and from place to place (Mackie et al. 1982). Mule deer may use many different plants at different
times, some may be eaten only in certain seasons, and some parts of plants may be selected over others. In
general, diets of mule deer consist mostly of browse, whereas the diets of elk, cattle, and wild horses consist
mainly of sedges and grasses (Hansen and Clark 1977). Both rumen and fecal analysis have been used to
describe deer diets, and both methods give similar results (Anthony and Smith 1974).
B-29
-------
Domain:Terrestrial Vertebrate Herbivore
Species: Long-tailed Vole (Microtus longicaudus)
Parameter: Body weight (BW)
Value or Algorithm: BWrf = 0.0465 (0.0369-0.0569; mean, range)
BW, = 0.0469 (0.042-0.0512; mean, range)
Units: kg
Notes:
Reference: Smolen and Keller 1987
Parameter: Food ingestion rate (If)
Value or Algorithm: If = 0.097 (mean of values reported for other Microtus species)
Units: kg food/ kg BW/d
Notes: While no data concerning feeding rates in long-tailed voles were found, data are available for
related species. Among meadow voles, food intake when exposed to 14-h days was 0.095±0.002
(mean±SE) g/g/d; intake by individuals exposed to 10-h days was 0.085±0.005 g/g/d (Dark et al. 1983).
Mean food consumption by prairie voles (assumed to weigh 35 g; Burt and Grossenheider 1976) was 0.088
g/g/d and 0.12 g/g/d when ambient temperatures were 21 ° and 28°C, respectively (Dice 1922). Laboratory
study of shrews fed a diet of beef brains and Purina cat chow.
Reference: NA
Parameter: Soil ingestion rate (Is)
Value or Algorithm: Is = 0.024(1,)
Units: kg soil/ kg BW/d
Notes: Data on soil ingestion by long-tailed voles was unavailable. Ingestion was assume to be comparable
to that reported for meadow voles (2.4% of diet; Beyer et al. 1994 ).
Reference: Beyer et al. 1994
Parameter: Water ingestion rate (Iw)
Value or Algorithm: Iw = (0.099*(BW)09)/BW
Units: L water/ kg BW/d
Notes: Allometric equation from Calder and Braun (1983) estimates water consumption in
mL/individual/day. Units converted to L water/ individual/d. Water ingestion normalized to body weight
using body weights reported in Smolen and Keller 1987.
Reference: Calder and Braun 1983
Parameter: Inhalation (Ia)
Value or Algorithm: Ia = (0.54576*(BW)° 8)/BW
Units: m3 air/ kg BW/d
Notes: Allometric equation from Stahl (1967) estimates inhalation in mL/individual/min. Units converted to
m3/ individual/d. Inhalation normalized to body weight using body weights reported in Smolen and Keller
1987.
Reference: Stahl 1967
Parameter: Diet Composition (Pj)
Value or Algorithm: pplams = 1.0
Units: N/A
Notes: Diet consists exclusively of plant material (green foliage, bark, seeds; Smolen and Keller 1987).
Domain: Terrestrial Predator/Scavenger
Species: Long-tailed Weasel (Mustela frenata)
Parameter: Body weight (BW)
Value or Algorithm: BW, = 0.200 ± 0.054 (mean ± SD)
BW 9 = 0.094 ± 0.010 (mean ± SD)
Units: kg
B-30
-------
Notes: Values for individuals from Indiana
Reference: Mumford and Whitaker 1982
Parameter: Food ingestion rate (If)
Value or Algorithm: If = 0.067 (males)
If = 0.080 (females)
Units: kg food/ kg BW/d
Notes: Brown and Lasiewski (1972) report the mean (±SD) metabolism of male and female long-tailed
weasels to be 1.36 ±0.2 and 0.84 ±0.12 kcal/hr, respectively. Assuming that male and female weasels
weigh 0.297 kg and 0.153 kg (Brown and Lasiewski 1972), respectively, the diet consists exclusively of
small mammals with an energy content of 5163 kcal/kg dry weight (Golley 1961), and the water content of
small mammals is 68% (EPA 1993), male and female weasels consume 0.067 and 0.080 kg food/kg BW/d.
Reference: NA
Parameter: Soil ingestion rate (Is)
Value or Algorithm: Is = 0
Units: kg soil/ kg BW/d
Notes: Data on soil ingestion by long-tailed weasels was unavailable and therefore was assumed to be
negligible.
Reference: NA
Parameter: Water ingestion rate (Iw)
Value or Algorithm: I, = (0.099*(BW)09)/BW
Units: L water/ kg BW/d
Notes: Allometric equation from Calder and Braun (1983) estimates water consumption in
mL/individual/day. Units convened to L water/ individual/d. Water ingestion normalized to body weight
using body weights reported in Mumford and Whitaker 1982.
Reference: Calder and Braun 1983
Parameter: Inhalation (Ia)
Value or Algorithm: Ia= (0.54576*(BW)08)/BW
Units: m3 air/ kg BW/d
Notes: Allometric equation from Stahl (1967) estimates inhalation in mL/individual/min. Units converted to
mV individual/d. Inhalation normalized to body weight using body weights reported in Mumford and
Whitaker 1982.
Reference: Stahl 1967
Parameter: Diet Composition (pt)
Value or Algorithm: psma,imammai =1-0
Units: N/A
Notes: While the diet of long-tailed weasels consists predominantly of small rodents (Peromyscus and
Microtus) and rabbits, birds may occasionally be taken (Poeldboer et al. 1941, Quick 1944, Fitzgerald
1977, Svendsen 1982). Fitzgerald (1977) reports that voles made up 99.1% of the diet of weasels in
California.
Domain: Piacivore
Species: Mink (Mustela vison)
Parameter: Body weight (BW)
Value or Algorithm: BWJ= 1.111 ±0.137 (mean ± SD)
BW, = 0.552 ± 0.094 (mean ± SD)
Units: kg
Notes: Values for individuals from Indiana
Reference: Mumford and Whitaker 1982
B-31
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Parameter: Food ingestion rate (I,)
Value or Algorithm: 1, = 0.12±0.012 (mean ± SD; males)
If = 0.16 ± 0.018 (mean ± SD; females)
Units: kg food/ kg BW/d
Notes: Food ingestion rates observed for male and female mink in captivity
Reference: Bleavins and Aulerich 1983
Parameter: Soil ingestion rate (Is)
Value or Algorithm: Is = 0
Units: kg soil/ kg BW/d
Notes: Hamilton (1940) observed sand in 1.3% of mink scats. This amount did not account for any
measurable scat volume. Soil ingestion is therefore assumed to be negligible.
Reference: NA
Parameter: Water ingestion rate (Iw)
Value or Algorithm: I, = (0.099*(BW)09)/BW
Units: L water/ kg BW/d
Notes: Allometric equation from Calder and Braun (1983) estimates water consumption in
mL/individual/day. Units converted to L water/ individual/d. Water ingestion normalized to body weight
using body weights reported in Mumford and Whitaker 1982.
Reference: Calder and Braun 1983
Parameter: Inhalation (Ia)
Value or Algorithm: Id = (0.54576*(BW)° 8)/BW
Units: m3 air/ kg BW/d
Notes: Allometric equation from Stahl (1967) estimates inhalation in mL/individual/min. Units converted to
m3/ individual/d. Inhalation normalized to body weight using body weights reported in Mumford and
Whitaker 1982.
Reference: Stahl 1967
Parameter: Diet Composition (p,)
Value or Algorithm: Pwull mammll = 0.46
Pn* =0.16
Pamphihu* = 0. 1 3
Ph.nl = 0.08
Units: N/A
Notes: Diets are diverse, varying among individuals, by locations, and by time of year. The values reported
represent the mean proportions of different prey types from 4 studies (Hamilton 1940, Sealander 1943,
Korsgen 1958, Burgess and Bider 1980).
Domain: Aquatic Omnivore
Species: Raccoon (Procyon lotor)
Parameter: Body weight (BW)
Value or Algorithm: BW^ = 6.76 (mean; n=5371)
BW8 = 5.94 (mean; n=2809)
Units: kg
Notes: Values for individuals from Missouri
Reference: Lotze and Anderson 1979
Parameter: Food ingestion rate (If)
Value or Algorithm: I, = 0.52 ±0.018 (mean ± SD)
Units: kg food/ kg BW/d
Notes: Teubner and Barrett (1983) report that captive yearling raccoons consumed 457 ± 10 (mean ± SD)
kcal/kg/d. Assuming a diet composed of molluscs (44%), Crustacea (25%), fish (9 %) and marine worms
B-32
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(21%) as reported by Tyson (1950) and fresh weight energy content of 0.8, 1, 1.2, and 0.83 kcal/g for
molluscs, crustacea, fish, and worms, respectively (EPA 1993), raccoons are estimated to consume 0.52 ±
0.018 (mean ± SD) kg/kg/d.
Reference: NA
Parameter: Soil ingestion rate (Is)
Value or Algorithm: Is = 0.094*If
Units: kg soil/ kg BW/d
Notes:
Reference: Beyer et al. 1994
Parameter: Water ingestion rate (Iw)
Value or Algorithm: Iw= (0.099*(BW)09)/BW
Units: L water/ kg BW/d
Notes: Allometric equation from Calder and Braun (1983) estimates water consumption in
mL/individual/day. Units converted to L water/ individual/d. Water ingestion normalized to body weight
using body weights reported in Lotze and Anderson 1979.
Reference: Calder and Braun 1983
Parameter: Inhalation (Ia)
Value or Algorithm: Ia= (0.54576*(BW)08)/BW
Units: m3 air/ kg BW/d
Notes: Allometric equation from Stahl (1967) estimates inhalation in mL/individual/min. Units converted to
m3/ individual/d. Inhalation normalized to body weight using body weights reported in Lotze and Anderson
1979.
Reference: Stahl 1967
Parameter: Diet Composition (PJ)
Value or Algorithm: pmonuxi = 0.44
Pcnmacca = 0.25
Pr,sh = 0.09
Pw«n» =0.21
Units: N/A
Notes: Raccoons are omnivorous, consuming a wide variety of plant and animal foods (Lotze and Anderson
1979). They may be highly selective when food is abundant and consume whatever is available when food
is scarce. Values reported above represent the diet composition observed among raccoons of the coastal
mudflats of SW Washington (Tyson, 1950).
Domain: Terrestrial Ground Invertebrate Feeder
Species: Trowbridge Shrew (Sorex trowbridgeii)
Parameter: Body weight (BW)
Value or Algorithm: BWrf= 0.00449 (mean; Oregon)
Units: kg
Notes: Weight range of 0.004-0.0055 kg is reported for CA (Silva and Downing 1995). Rust (1978)
reports mean (± SE) BW of breeding and non-breeding adults to be 7.24 ± 0.48 g and 6.13 ± 0.23 kg,
respectively.
Reference: Silva and Downing 1995
Parameter: Food ingestion rate (If)
Value or Algorithm: Ir = 0.91 ± 0.03 (mean ± SE; breeding)
I, = 1.43 ± 0.10 (mean ± SE; non-breeding)
Units: kg food/ kg BW/d
B-33
-------
Notes: Laboratory study of shrews fed a diet of beef brains and Purina cat chow.
Reference: Rust 1978
Parameter: Soil ingestion rate (Is)
Value or Algorithm: Is = 0.13(If)
Units: kg soil/kg B W/d
Notes: Data on soil ingestion by Trowbridge shrews was unavailable. Ingestion was assume to be
comparable to that reported for short-tailed shrews (13% of diet; Talmage and Walton 1993).
Reference: Talmage and Walton 1993
Parameter: Water ingestion rate (Iw)
Value or Algorithm: Iw = (0.099*(BW)09)/BW
Units: L water/ kg BW/d
Notes: Allometric equation from Calder and Braun (1983) estimates water consumption in
mL/individual/day. Units converted to L water/ individual/d. Water ingestion normalized to body weight
using body weights reported in Silva and Downing 1995.
Reference: Calder and Braun 1983
Parameter: Inhalation (Ia)
Value or Algorithm: Ia = (0.54576*(BW)° 8)/BW
Units: m3 air/ kg BW/d
Notes: Allometric equation from Stahl (1967) estimates inhalation in mL/individual/min. Units converted to
m3/ individual/d. Inhalation normalized to body weight using body weights reported in Silva and Downing
1995.
Reference: Stahl 1967
Parameter: Diet Composition (p,)
Value or Algorithm: p,nvcncbralcs = 1.0
Units: N/A
Notes: Data from the Sierra Nevada of California indicate that the diet consists almost exclusively of
arthropods (George 1989).
Domian: Terrestial Omnivore
Representative Species: White-footed Mouse (Peromyscus leucopus)
Parameter: Body weight (BW)
Value or Algorithm: BWrf = 0.0216 ± 0.0009 (mean ± SE)
BW9= 0.0208 ±0.0011 (mean ±SE)
BW_,S= 0.0212 ±0.0006 (mean ± SE)
Units: kg
Notes: Values are summaries from multiple locations throughout North America.
Reference: Silva and Downing 1995
Parameter: Food ingestion rate (If)
Value or Algorithm: 1, = 0.1513 ± 0.0054 (mean ± SE)
Units: kg food/ kg BW/d
Notes: Laboratory study of mice fed Purina rat chow. Body weights and gut dimensions of male and
female mice did not differ, so data were combined. Data reported as g food consumed /individual/d. Food
ingestion normalized to body weight using body weights reported in study.
Reference: Green and Millar 1987
Parameter: Soil ingestion rate (Is)
Value or Algorithm: I,. = 0.02*(If)
Units: kg soil/ kg BW/d
Notes: Based upon data from field collected mice, soil consumption is estimated to be <2% of diet.
B-34
-------
Reference: Beyer et al. 1994
Parameter: Water ingestion rate (I J
Value or Algorithm: Iw= [(99*(BW)09)*1/1000]/BW
Iw= (0.099*(BW)09)/BW
Units: L water/ kg BW/d
Notes: Allometric equation from Calder and Braun (1983) estimates water consumption in
mL/individual/day. Units converted to L water/ individual/d by multiplying by the following conversion
factor: IL/lOOOmL. Water ingestion normalized to body weight using body weights reported in Silva and
Downing 1995.
Reference: Calder and Braun 1983
Parameter: Inhalation (Ia)
Value or Algorithm: Ia= [(379*(BW)08)*60*24*1/1000*1/1000 ]/BW
I, = [(379*(BW)08)*0.00144 ]/BW
Ia = (0.54576*(BW)08)/BW
Units: m3 air/ kg BW/d
Notes: Allometric equation from Stahl (1967) estimates inhalation in mL/individual/min. Units converted to
m3/ individual/d by multiplying by'the following conversion factors: 60 minutes/hr, 24 hr/d, IL/lOOOmL,
ImVlOOOL. Inhalation normalized to body weight using body weights reported in Silva and Downing 1995.
Reference: Stahl 1967
Parameter: Diet Composition (p,)
Value or Algorithm: p,,,ven(;brales = 0.5
Pplam = 0.5
Units: N/A
Notes: White-footed mice forage opportunistically, consuming a wide variety of foods. In Virginia, on
average throughout the year, 57.1 % of the diet consisted of arthropods and 38.6% was plant material (fruits,
seeds, and green vegetation; Wolff et al. 1985. Study contains data on seasonal variability of diet). In
Indiana, diets were approximately 30% invertebrates and 67% plant material (Whitaker 1966; Study
contains data on variability of diet over seasons and among three habitat types). The diet of mice in Illinois
was found to be 50% invertebrates and 48% seeds, fruit and other plant material (Batzli 1977; Study
contains data on variability of diet over seasons and among two habitat types). The results of these studies
indicate that while diet composition varies among habitats and over seasons, on average approximately 50%
consists of invertebrates and 50% consists of plant material (fruits-, seeds, and green vegetation).
Domian: Semi-aquatic Piscivore
Representative Species: Belted Kingfisher (Ceryle atcyon)
Parameter: Body weight (BW)
Value or Algorithm: BW^,= 0.148 ±0.039 (mean ± SE)
Units: kg
Notes: Weights for males and females overlap. In spring in MN, male weights ranged from 0.138-0.150 kg
while female weights ranged from 138-169 kg (Hamas 1994). Values are summaries from multiple locations
throughout North America.
Reference: Dunning 1993
Parameter: Food ingestion rate (If)
Value or Algorithm: If = 0.5(BW)
Units: kg food/ kg BW/d
Notes: Food consumption in MI estimated to be approximately 50% of body weight/d.
Reference: Alexander 1977
Parameter: Soil ingestion rate (I,)
B-35
-------
Value or Algorithm: 0
Units: kg soil/ kg BW/d
Notes: Because kingfishers forage from perches near water or by hovering over water (Hamas 1994)
incidental ingestion of soil is assumed to be negligible
Reference:
Parameter: Water ingestion rate (!„)
Value or Algorithm: Iw= [(59*(BW)067)*1/1000]/BW
Iw= (0.059*(BW)067)/BW
Units: L water/ kg BW/d
Notes: Allometric equation from Calder and Braun (1983) estimates water consumption in
mL/individual/day. Units converted to L water/ individual/d by multiplying by the following conversion
factor: IL/lOOOmL. Water ingestion normalized to body weight using body weights reported in Dunning
1993.
Reference: Calder and Braun 1983
Parameter: Inhalation (Ia)
Value or Algorithm: Ia= [(284*(BW)077)*60*24*1/1000*1/1000 ]/BW
Ia = [(284*(BW)077)*0.00144 ]/BW
Ia= (0.40896*(BW)08)/BW
Units: m3 air/ kg BW/d
Notes: Allometric equation from Lasiewski and Calder (1971) estimates inhalation in mL/individual/min.
Units converted to m3/ individual/d by multiplying by the following conversion factors: 60 minutes/hr, 24
hr/d, IL/lOOOmL, ImVlOOOL. Inhalation normalized to body weight using body weights reported in
Dunning 1993.
Reference: Lasiewski and Calder 1971
Parameter: Diet Composition (pj)
Value or Algorithm: pfish =0.866
Pcrayfish =0.133
Units: N/A
Notes: The diet of belted kingfishers consists primarily of small fish, but may also include molluscs,
crustaceans, insects, amphibians, reptiles, young birds and small mammals (Hamas 1994). Davis (1982)
reports the diet of kingfishers in Ohio to consist of crayfish (13.3%) and small fish (86.6%; minnows
(12.7%), non-minnow fish (10.2%), stonerollers (37.6%), and unidentified cyprinids (26.1%)) In Michigan,
fish accounted for 46-86% of the diet, with crustaceans, insects, and amphibians accounting for the
remainder (Alexander 1977). All fish were <12.7 cm in length. In Ohio, the size distribution offish
consumed ranged from 4 to 14 cm, with 87% falling between 6 and 12 cm (Davis 1982). For the purposes
of this study, the diet of kingfishers is assumed to be best represented by the results of Davis (1982)
B-36
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B-38
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APPENDIX C
RESULTS FROM TRIM.FaTE
PROTOTYPE 2 AND 3 SIMULATIONS
-------
Table of Contents.
Page
C.l.O TRIM.FaTE Prototype 2 C-l
C. 1.1 Run 1: Pristine Cells at Initial time (t0) with a Constant Air Source Term . C-l
C. 1.2 Run 2: Decrease in Organic Carbon partition Coefficient (K^.) C-2
C. 1.3 Run 3: Nonpristine Surface Water Cell at Initial Time (t0) with a
Constant Air Source Term C-3
C.I.4 Run 4: Pristine Initial Conditions with a Varied Air Source Term C-4
C. 1.5 Run 5: Nonpristine Surface Water Cell at Initial Time (t0) with a Varied
Air Source Term C-5
C. 1.6 Comparison of Prototype 2 and CalTOX Transfer Factors C-5
C. 1.7 Comparison of Prototype 2 Results with CalTOX C-6
C.2.0 TRIM.FaTE Prototype 3 C-8
C.2.1 Steady-State Scenario C-8
C.2.2 Annual Steady-State Emissions Scenario C-10
C.2.3 One-Hour Puff Emission Single Day Scenario C-10
C.2.4 Comparison of Prototype 3 and CalTOX Transfer Factors C-11
C.2.5 Comparison of Prototype 3 Results with CalTOX C-12
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Appendix C
Results from Trim.FaTE Prototype 2 and 3 Simulations
C. 1.0 TRIM.FaTE Prototype 2.
This section presents the outputs of TRIM.FaTE Prototype 2 (P2) simulations and comparisons
of these outputs with CalTOX. Features of P2 are described in Chapter 3.0. The simulations
described in the following subsections used constant input parameters unless otherwise indicated
and used a time period of 500 days with a 50-day increment. Run 1 was used as the "control
run," which was used for comparison to other runs that varied inputs such as the organic carbon-
water partition coefficient (K^), initial concentration in surface water, and/or the air source term
concentration.
C. 1.1 Run 1: Pristine Cells at Initial Time (tg) with a Constant Air Source Term
A constant air source term of 4.32 grams per hour for 500 days was used. All cells were given an
initial pristine concentration of 1 x 10'8.
Results
Plant Domain. The leaf concentration increased 6.5 orders of magnitude within
the first time increment and then remained constant with time. Although the air
source term continued to release contaminant throughout the 500 days, the leaf
reached a point of equilibrium within the first time increment. The leaf weathering
sink also showed an immediate increase in concentration within the first time
increment and continued to increase throughout the entire 500 days to a level of
approximately 8 orders of magnitude higher than the initial pristine condition.
The stem decreased almost 5 orders of magnitude in the first time increment,
decreased again slightly in the second time increment, and then increased with time
to a level 4 orders of magnitude less than the initial pristine level of 1 x 10"8. The
xylem decreased about 8 orders of magnitude in the first, second, and third time
increments, and then slightly increased with time to a level 7 orders of magnitude
less than the initial pristine level of 1 x 10"8. The plant root decreased in the first
time increment and then increased with time to a level almost 1 order of magnitude
less than the initial pristine level of 1 x 10"8.
The results of the plant domain indicate that the leaf is very susceptible to
benzo(a)pyrene (B[a]P) and that it takes more than 500 days for concentration to
accumulate in the stem, xylem, and root.
C-l
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• So/7 Domains. Surface soil concentration increased within the first time
increment more than 8.5 orders of magnitude. The concentration continued to
increase slightly over the remaining 500 days to just over 9 orders of magnitude.
The soil root zone concentration increased approximately 4.5 orders of magnitude
within the first time increment and continued to increase over the remaining 500
days to a level more than 6 orders of magnitude higher than the initial pristine
condition. Soil zone 1 concentration remained at the pristine condition until the
fourth time increment and continued to increase less than an order of magnitude.
Soil zone 2 and groundwater reacted identically and remained at pristine conditions
until the fourth increment, when their concentrations decreased over the remaining
time to a concentration level slightly less than the pristine level.
• Water, Sediment, and Fish Domains. The surface water, sediment, fish, and
associated sinks associated with these domains showed concentrations increasing
mainly within the first time increment and then slightly for the remaining time
increments. The sediment and surface water reaction sink concentrations increased
the most significant to a level approximately 9.5 orders of magnitude higher than
the initial pristine level. The sediment reaction sink increased over the 500 days
approximately 8.5 orders of magnitude and the sediment burial sink remained
unchanged from the initial concentration. The surface water concentration leveled
out at 7 orders of magnitude higher than initial concentration. The fish concentra-
tion increased 3.5 orders of magnitude.
• Air Domains. Air 1, air 2, upper air 1, and upper air 2 domains each had concen-
tration increases during the first time increment and then remained constant for the
remaining increments. The concentrations increased between 6.5 and 7.5 orders of
magnitude higher than initial conditions.
The corresponding air domain sinks showed concentrations increasing mainly
during the first increment and then slightly for the remaining 450 days. The final
concentration increased 9 to 11 orders of magnitude higher than the initial
concentrations.
C. 1.2 Run 2: Decrease in Organic Carbon Partition Coefficient (Koc)
The Kx value was decreased from 2.5 x 10"6 to 2.5 x 103. The air source term was constant at
4.32 grams per day for 0 to 500 days. All cells had an initial pristine concentration of 1 x 10"8.
Run 2 was compared to Run 1 to identify the affects of decreasing the K^. value.
Results
Plant Domain. The leaf and leaf weathering sink have no noticeable affect from
the decrease in the K^. value. The root, stem, and xylem concentrations increased
approximately 5 orders of magnitude.
C-2
-------
• So/7 Domains. The surface soil and groundwater have no noticeable change with
respect to K^.. The soil root zone concentration increased linearly with the decrease
in KO,. value (3 orders of magnitude). Soil zone 1 concentration increased 5 orders
of magnitude. Soil zone 2 nearly increased 2 orders of magnitude.
With respect to time, the surface soil, root zone and soil zone 1 were affected immediately and
soil zone 2 showed an increase at approximately 100 days. Without the decrease in K^ value
(Run 2), soil zone 2 showed a decrease in concentration from the 1 x 10"8 initial value, indicating
partitioning to soil zone 1.
The soil reaction sinks reacted identical to that previously described.
• Water, Sediment, and Fish Domains. The surface water concentration
decreased approximately a half an order of magnitude, while the surface water
reaction sink decreased almost a half an order of magnitude. The sediment and
sediment reaction sink concentrations increased 2 orders of magnitude and the
sediment burial sink remained unchanged. The fish concentration increased slightly
(less than half an order of magnitude).
• Air Domains. Air domains remained unaffected by the change in K^, value.
C.1.3 Run 3: Nonpristine Surface Water Cell at Initial Time (tg) with a Constant
Air Source Term
A constant air source term of 4.32 grams per hour for 500 days. The surface water cell had an
initial concentration of 1 x 103 grams. All other cells have an initial pristine concentration of 1 x
10'8 grams.
Results. As expected, the plant, soil, and air domains remained unaffected by the initial
concentration increase in surface water. The surface water concentration decreased within the
first time increment over 2 orders of magnitude. The concentration from the surface water
transferred directly to the sediment. At time equal to 50 days, the sediment concentration is
approximately 1 x 103 grams (the surface water initial concentration). The sediment
concentration decreased over the remaining time increments almost an order of magnitude.
The fish, surface water, and sediment reaction sink concentrations increased identical to the
patterns observed in Run 1, but had final concentrations 1.5 orders of magnitude higher than
those observed in Run 1. The sediment burial sink remained at initial pristine conditions.
C-3
-------
C.I A Run 4: Pristine Initial Conditions with a Varied Air Source Term
A varied air source term was used:
• Time 0-10 days: concentration was 0 grams per day
• Time 10-100 days: concentration was 4.32 grams per day
• Time 100-500 days: concentration was 0 grams per day.
All cells have an initial pristine concentration of 1 x 10"8.
Results
• Plant Domain. During the first time increment, the leaf, root, xylem, and stem
decrease from the initial concentration. The leaf weathering sink increases less than
a 0.5 order of magnitude. By the second time increment, the leaf obtains its
apparent equilibrium concentration identical to Run 1. After the second time incre-
ment (100 to 500 days), the leaf concentration decreases to just above the initial
pristine condition.
The root, stem, and xylem react identical to Run 1, but have final concentrations
approximately 0.5 order of magnitude less than Run 1.
• Soil Domains: The second increment shows the surface soil concentration
identical to the concentration in Run 1 after the first increment. The remaining time
(100 to 500 days) shows concentrations reflecting no air source term (a decrease in
concentration). The soil root zone shows a concentration increase within the first
increment of 0.5 order of magnitude. From 50 to 100 days, the concentration
increases 4 more order of magnitudes. After 100 days, the concentration increases
slightly and levels off approximately 5 orders of magnitude higher than the initial
pristine concentration. As expected, the soil zones and groundwater show rela-
tively no change from the initial pristine condition.
• Water, Sediment, and Fish Domains. The varied air source appears to have
little affect on the final concentrations in the water, sediment, and fish domains.
Although surface soil concentrations drop almost 2 orders of magnitude within the
first time increment, by the second time increment, the concentration is identical to
Run 1 and then continues to slowly drop to a level approximately 1 order of magni-
tude less than results of a continuous air source. Sediment, fish, and surface water
reaction sink concentrations increase minimal within the first time increment and
then maintain the same concentration as in Run 1 by the second time increment.
The final concentrations are approximately 0.5 order of magnitude less than the
final concentration of Run 1. The sediment burial sink is unaffected.
• Air Domains. The air domains appear to be responsive to the air source term
more than other domains. The air concentrations drop approximately 7 orders of
C-4
-------
magnitude by the first time increment and increase by 13 orders of magnitude by
the second time increment. After 100 days (when the source term is 0 grams/day),
the concentrations drop to nearly pristine conditions. This is noticeable more with
the upper air domains. Air 2 domain final concentration is approximately 0.5
orders of magnitude higher than the air 1 domain. The sinks maintain the concen-
trations found in Run 1 after the first time increment.
C. 1.5 Run 5: Nonpristine Surface Water Cell at Initial Time (tj with a Varied Air
Source Term
A varied air source term was used:
• Time 0-10 days: concentration was 0 grams per day
• Time 10-100 days: concentration was 4.32 grams per day
• Time 100-500 days: concentration was 0 grams per day.
The surface water cell had an initial concentration of 1 x 103. The remaining cells have an initial
pristine concentration of 1 x 10~8. This run was compared to Run 4, which had an identical air
source term.
Results. As expected, the plant, soil, and some air domains remained unaffected by the initial
concentration increase in surface water. The surface water concentration decreased within the
first time increment over 2 orders of magnitude. The concentration from the surface water
transferred directly to the sediment. At time equal to 50 days, the sediment concentration is
approximately 1 x 103 grams (the surface water initial concentration). The sediment
concentration decreased over the remaining time increments almost an order of magnitude. The
air 2 and upper air 2 domains did not drop in concentrations as with Run 4, but increased
continually until the air source term was 0 grams/day (greater than 100 days). Because these two
air domains are above the surface water, their final concentrations are approximately 2 orders of
magnitude higher than in Run 4.
The fish, surface water, and sediment reaction sink concentrations increased identically to the
patterns observed in Run 4, but had final concentrations 1.5 orders of magnitude higher than
those observed in Run 4. The sediment burial sink remained at initial pristine conditions.
C. 1.6 Comparison of Prototype 2 and CalTOX Transfer Factors
CalTOX and P2 were compared to find similarities and differences between the models (Table
C-l). Many of the transfer processes in P2 were modeled after CalTOX; thus, the two models
should yield similar results for the transfer factors. Differences should be expected in the masses
C-5
-------
Table C-1
Comparison Between Prototype 2 and CalTOX Transfer Factors
Diffusion
CalTOX TRIM
7.15 x10'1 1.43x10°
5.07 X1Q-4 5.27 x 10"4
5.40 x10'2 1.01X10'1
2.29 X1Q-6 2.15 X1Q-6
2.57 X10"6 3.79 x10'6
6.90 x10'8 1.01X10'7
0.00x10° 1.50x10'1°
0.00x10° 0.00X10-0
2.49 X1Q-" 2.49x10-4
2.04 x10'6 2.15x10-6
Advection
CalTOX TRIM
1.02x10° 2.04x10°
0.00x10° 0.00x10°
1.02x10° 2.04x10°
1.40 x10'7 1.52 x10'7
1.55x1Q-7 1.40x10-7
0.00x10° 0.00x10°
4.17 x10'9 4.10 x10'9
7.73 x10'10 1.50x10'9
1.2 x101 1.24 X101
1.01x10'1 1.01X10'1
Total
CalTOX TRIM
1.73x10° 3.47x10°
5.07x10-" 5.27 x 10"4
1.07x10° 2.14x10°
2.43 X10"6 2.30 X10"6
2.72 xW6 3.93x10-*
6.90x10-* 1.01x10'7
4.17x10'9 4.25 x10'9
7.73x10'10 1.50x10'9
1.24 x101 1.24 x101
1.01x10'1 1.01x10'1
2.50 x10'5 0.00x10°
6.92 x101 6.92 x101
1.62X1Q-5 1.62x105
1.65X1Q-4 1.74x10'"
1.10x101 1.10x101
3.03 X10'3 3.03 x10-3
3.03 x10'3 3.03 x10'3
7.88 X10"4 7.88 X1Q-4
7.88 X1Q-4 7.88 x 10""
2.97x10'1 2.97 x10'1
5.91 x10'4 5.91 x10'4
Cell Interlace
air-water, T_aw
water-air, T_wa
air-ground, T_ag
ground-air, T_ga
ground-soil, T_gs
soil-ground, T_sg
soil-vadose, T_sv
vadose-aquifer, T_vq
water-setftment, T_wd
sediment-water, T_dw
sediment-out, T_do
air-out, T_ao
ground-water, T_gw
water-out, T_wo
Ra
Rg
Rs
Rv
Rq
Rw
Rd
in each cell because CalTOX models the root zone and vadose zone dynamically with other cells in
steady state while all cells are dynamic in P2. However, cells that come to steady state in less time
than the length of the model should yield similar results. The mass of B(a)P in each cell was
compared after a 5- and a 25-year simulation (Table C-2).
Most of the transfer factors are similar. The transfer from the vadose zone P2 to the aquifer is twice
as large in CalTOX, a result of using one vadose zone in CalTOX and two in TRIM. The air to
water and air to soil in P2 are twice as large as in CalTOX, a result of using one air cell in CalTOX
and two in P2.
The transfer factors for plants were not compared at this time because both CalTOX and the plant
cell is being updated. A comparison should be made for P3.
C-6
-------
Table C-2
Mass Distribution of B(a)P (grams) in CalTOX
and Prototype 2 At 5 and 25 Years*
Values Based on 5 Years Values Based on
CalTOX TRIM CalTOX/ TRIM CalTOX TRIM
air
plants
ground-soil
root-soil
vadose-zone
surface water
sediment
aquifer
2.9x10°
1.2 x103
3.1 x103
2.3x10°
5.2 x10'6
1.4 xlO1
1.7x103
2.0x10"*
4.9x10°
1.7x10°
1.7x103
1.7x 10°
3.7X1Q-6
2.4x10'
4.3x10°
5.9 x10"9
6.0x10'1
7.0 x102
1.9x10°
1.3x10°
1.4x10°
5.6x10"'
3.9 x102
3.4 x102
2.9x10°
1.2 x103
3.1 x103
2.7x10°
1.2x10"5
1.4x10'
1.7 x103
4.7 x10"6
4.9x10°
1.7x10°
1.9 x103
2.5x10°
1.1 x10'5
2.4x10'
8.8x10°
9.5 x10-10
25 Years
CalTOX/ TRIM
6.0 x10"'
7.0 X102
1.6x10°
1.1 x10°
1.1 x10°
5.6x10''
1.9 x102
4.9 x102
'Based on an air emission of 1 mole per day.
The sediment out term in CalTOX refers to the sediment burial rate. TRIM calculates sediment
burial rates based on the sediment deposition and sediment resuspension rates, which at this time
are set equal to each other. Changes to the sediment model are planned for Prototype 3 (P3) and a
comparison will be made at that time.
C.1.7 Comparison of Prototype 2 Results With CalTOX
The mass in each cell was calculated using each model. The masses were comparable except for
three notable differences: plants, sediment, and aquifer.
The sediment cell in CalTOX is in steady state with the surrounding cells. This cell acts like a
dynamic cell in reality and should be modeled as such. The predictions in TRIM reflect the effect
of having a dynamic cell. As the length of the simulation is increased, the difference between the
two models decreases.
There are extreme variations between the predicted mass in the aquifer cell. Aquifers are extremely
challenging to model and in both TRIM and CalTOX, simple approximations have been used.
CaJTOX uses one well mixed vadose zone cell, while TRIM uses two. The lower vadose cell in
TRIM has over three orders of magnitude less mass than the upper one, reflecting the gradients that
occur in soil. However, there could be breakthrough paths in a real environment enabling the
pollutant to reach the aquifer rather quickly, mimicking the setup in CalTOX. Refinements for the
C-7
-------
soil and aquifer cells in P3 include a review of the diffusion processes and calculation of a
retardation factor in determining the groundwater velocity. After the refinements, it might be more
appropriate to compare them to a model such as T2VOC, a fully dynamic subsurface model.
C.2.0 TRIM.FaTE Prototype 3
This section presents the outputs of TRIM.FaTE P3 simulations and comparisons of these outputs
with CalTOX. Features of P3 are described in Chapter 3.0 of the technical support document.
Three scenarios were run with P3 to test the validity of the outputs. The scenarios and resulting
outputs are discussed in the following sections.
C.2.1 Steady-State Scenario
This scenario included running P3 to obtain a long-term steady-state solution. P3 was run without
varying the input parameters with time, for 10 years with a constant source of 9 grams per hours
(g/hr) in lower air 1 cell. The steady-state concentrations are shown in Table C-3. The mass
distribution of B(a)P for a steady- state solution is shown in Figure C-l. This assumes that the total
macrophyte volume is significantly less than water volume. From this figure (where mass is in log
units), it can be seen that B(a)P predominantly accumulates in the soil and sediments. This is what
would be expected given the extremely high soil-water distribution coefficient of B(a)P (sorbs
preferentially to soil). Mass distribution outputs for P3 showed high degree of sensitivity to
macrophyte volume. The total macrophyte volume as a percentage of surface water volume was
varied between 0.001 percent to 10 percent and the resulting outputs are shown in Figure C-2.
From these figures, it can be concluded that within the context of the simplified ecosystem of P3,
macrophytes are a major sink for B(a)P and could mean that macrophytes could drive the final
destination B(a)P in the environment. A sensitivity analysis with the plant domain may also yield
similar results.
Table C-3
Steady-State Concentrations for Prototype 3
Volume Element
RZ(2), Worm
RZ(2), Root
RZ(2), Stem
RZ(2), Xylem
RZ(3). Worm
Concentration
2.13 X10'22
1.81 x10'16
1.81 xT'6
1.63X10"'6
2.13X1022
Units
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/L
arams B(a)P/kq
C-8
-------
Table C-3 (Continued)
Volume Element
RZ(3), Root
RZ(3), Stem
RZ(3), Xylem
RZ(4), Worm
RZ(5), Worm
RZ(6), Worm
RZ(6), Root
RZ(6), Stem
RZ(6), Xylem
RZ{7), Worm
RZ(7), Root
RZ(7), Stem
RZ(7), Xylem
RZ(8), Worm
SS(1), Mouse
SS(2), Leaf
SS(2), Mouse
SS(3), Leaf
SS(3), Mouse
SS(4), Mouse
SS(5), Mouse
SS(6), Leaf
SS(6), Mouse
SS(7), Leaf
SS(7), Mouse
SS(7), Kingfisher
SS(8), Mouse
LOWER AIR 1, Air
LOWER AIR 2, Air
UPPER AIR 1, Air
UPPER AIR 2, Air
SEDIMENT, Sediment
LOWER SW, Surface Water
LOWER SW, Macrophyte
LOWER SW. Herbivore
LOWER SW, Omnivore
LOWER SW, Carnivore
UPPER SW, Surface Water
UPPER SW, Macrophyte
UPPER SW, Herbivore
UPPER SW, Omnivore
UPPER SW, Carnivore
UPPER SW, Kingfisher
LOWER AIR 3, Air
UPPER AIR 3, Air
Concentration
1.81 x10'16
1.81 x10'16
1.63x10'16
2.13 X10'22
2.13 X10'22
2.13 X10'22
1.72x10'17
1.72X10-'7
1.54X10"17
2.13 X10'22
1.31 x10'17
1.31 x10"17
1.18x10'17
2.13 X10'22
1.03x10-"
7.86 x10'7
2.69x10"
7.86 x10'7
2.69 x10-6
3.45 x10-9
3.37 x10'10
7.23 x10-7
3.17x10'"
3.55 x10'6
1.06x10'7
4.07 x10'7
6.02 x10'9
1.61 x10'"
1.48x10'"
0.00x10°
0.00x10°
1.29x10-"
5.63 x 10 12
2.05x10"
8.47 x10'9
1.57x10'"
3.52 x ID"6
3.03 X10'11
1.10X107
4.55 x10'8
8.42x10'"
1.89x10'5
4.07 x 10 7
8.22x10'"
0.00x10°
Units
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/L
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/L
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/L
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/kg
grams B{a)P/kg
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/m3
grams B(a)P/m3
grams B(a)P/m3
grams B(a)P/m3
grams B(a)P/m3
grams B(a)P/L
grams B(a)P/kg
arams B(a)P/ka
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/L
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/kg
grams B(a)P/m3
grams B(a)P/m3
C-9
-------
To ensure that the observation regarding macrophytes was not a mathematical quirk, a quick
calculation of the steady-state solution for the macrophytes (Section 2.3.1) was performed. This
calculation shows that the concentration ratio between macrophytes and dissolved water
concentration should be approximately 15,000 for B(a)P, which is what can be seen from Table C-
3.
C.2.2 Annual Steady-State Emissions Scenario
This scenario included running P3 for 1 year, 1 day at a time using a constant source. The source
strength was 2.5 x 10"3 grams per second (g/s) in lower air 1 cell. The results of the residual mass
breakdown after a year are shown in Figure C-3. Due to the hydrophobicity of B(a)P, most of it is
seen in soils and sediment, as would be expected. The macrophyte volume for this run was less
than 0.01 percent of the surface water domain. It is interesting to observe that the residual mass
distribution is somewhat different from the steady-state case (Figure C-l), indicating that P3 is
sensitive to duration of the run and source conditions.
C.2.3 One-Hour Puff Emission Single Day Scenario
This scenario included running P3 for 1 day (24 hours) after 1-hour puff emission. The source
strength was 2.5 x 10"3 g/s. The outputs are shown in Figure C-4. From the mass distribution, it can
be seen that B(a)P is a minute later almost equally in soil, sediment, and surface water. At steady-
state, much less B(a)P is seen in surface water; however, in a 24-hour period, equilibration between
sediment and surface water would not be expected. The time series data shows the spike in the air
domain due to the puff, and then decline in mass. The mass in the soil stays mostly constant after
the puff. The mass in the surface water domain reduces with time as sediments are increasing as
B(a)P is sending towards equilibrium between surface water and sediment. Overall, these results
are encouraging and show that P3 is responsive to hourly changes.
C.2.4 Comparison of Prototype 3 and CalTOX Transfer Factors
Air/Soil and Air/Plant Concentration Ratios and Transfers. These values were compared
to the values from CalTOX and are on the same order of magnitude. The mass-transfer pathways in
CalTOX and TRIM.FaTE differ somewhat and thus slightly different values are to be expected.
However, since the algorithms in both models represent the same processes, they should produce
results on the same order of magnitude. In the TRIM.FaTE results, when compared to CalTOX,
there is less mass overall transferred to the plant than to the soil, because there is very little plant
biomass in TRIM.FaTE. This is, however, an input parameter issue as opposed to an algorithm
issue.
C-10
-------
Plants. After coming to equilibrium, the stem, roots, and xylem exchange equal mass to and from
the soil as expected.
Runoff and Erosion. The amount of runoff and erosion for a rainfall rate equal to that in
CalTOX produces very similar results.
Air-Water Interface. The air to water interface produces results that are comparable to CalTOX
results, as they should, since the same algorithms are used. The air to water is exactly the same,
while the water to air is higher because the surface water has been separated into two layers, and
thus, there is less mass in the upper layer; thus, the T factor needs to be higher for there to be the
same flux.
Sediment: Water Interface. For similar sediment deposition and resuspension rates, the T
factors are still comparable to CalTOX.
Groundwater to Surface Water. The T factor compares reasonably with CalTOX.
Plants to Ground and Plants to Air. The excepted T values were obtained for these
processes.
Air to Air. The values obtained for this T factor were comparable to CalTOX.
Air-Soil and Air-Plant. These values were compared to the values from CalTOX and were on
the same order of magnitude. The processes in the two are not exactly the same, and thus, slightly
different values are to be expected.
C.2.5 Comparison of Prototype 3 Results With CalTOX
The geometric factors and soil composition factors relating the soil exchange are all correct and
produce reasonable results. A checker has been added to make sure the Ts match up after soil
composition and geometric factors have been accounted for. Diffusion is an order of magnitude
less than advection, and thus, appears to be reasonable.
The time dependence of the T factors for soil diffusion comes about from the algorithm that was
used to match a multilayer box model of soil (that is, soil layers and resistances between them) to
C-ll
-------
the exact analytical solution that is used in the Jury et al. model. In a journal paper published by
McKone, it has been shown that the multilayer algorithm is reasonable when simulations are for
long periods of time (months to years). It is harder to compare these results to the exact (Jury)
solution for shorter time steps (1 hour to 1 month). Mass transfer and transformation are relatively
slow processes and the algorithm for extended time period simulations using short time steps has
not been checked. This is needed to determine how well the multilayer algorithm works for short
time periods. This issue needs to be revisited after the multilayer algorithm has been optimized for
a number of short time step long-term simulations. The reliability of the proposed algorithm for the
way it is being used in TRIM.FaTE can be tested after several linked, shorter time step simulations
are run.
C-12
-------
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APPENDIX D
ALGORITHM LIBRARY
-------
Appendix D
Algorithm Library
The algorithms, derived from literature or developed for TRIM.FaTE, that were the starting
algorithms in the development of intermedia transfer factors are listed in this appendix. The
visual basic source code implementation of this algorithm library is available upon request from
the U.S. Environmental Protection Agency (EPA).
Advective Transfer. The general form for the transfer factor for advective transport from cell
/ to cell j in any abiotic domain is:
-,«*, , , Q (Phase"> *Z (phase)
T._ .(phase) =
' J
v (phase) x At xZt(phase)
Vt(Totat)xZfTotat)
Diffusive Transfer. The general form for the transfer factor for diffusive transport from cell /
to cell j in any abiotic domain is:
T*ff =
•* i
V ^ lutul.,
A V,
total, , ~» total,
1 } ,o,a,v
where:
TtJ = transfer factor for diffusive transport from cell 7 to cell j, /day
UtJ = mass transfer coefficient for combined turbulent and molecular diffusion on
T' side of boundary between cells I andj, m/day ( ={ mol/m2 [area]-
day}/{mol/m'[cell/]})
Uj, = mass transfer coefficient for combined turbulent and molecular diffusion on
"j" side of boundary between cells / andy, m/day ( ={ mol/m2 [area]-
day}/{mol/m3 [cell;]})
D-l
-------
V, = total volume of cell /, m3 [cell /]
Z,""al = total fugacity capacity for cell /, moles chemical]/m3 [cell 7]-Pa.
Later Runoff in Soil
where:
D = diffusion coefficient in water (m2/s)
Cs = concentration in soil pore water (g/m3)
CR = concentration in runoff water (g/m3)
R = hydraulic radius (m), for planer flow, water depth over surface
um = mean velocity of the fluid (m/s)
r = fluid density (g/m3)
m = viscosity (kg/ms)
So/7 Erosion. The flux of chemical from erosion is:
_ c , erosion} LW
~ ^ solid I I>W
r solid )
Vertical Diffusion in Lakes. Vertical diffusion in lakes and is represented by:
*~ex epi *^ ex hypo
where:
J = net mass flux from epilimnion to hypolimnion due to vertical mixing, M/T
QM = exchange flow, L3/T
C = concentration of organic, M/L3.
Eddy Diffusivity in Lakes. Vertical eddy diffusivity is given by:
k, = 0.0142(Z)149 mVday
D-2
-------
where:
Z = mean depth (CSM).
Dry Deposition Plant Interception Fraction. The dry deposition plant interception
fraction (Ifd) is given by:
Ifd= 1 -exp(ccxbio_inv)
where:
bio-inv = dry biomass inventory per unit area
a = vegetation attenuation factor.
Wet Deposition Plant Interception Fraction. The wet deposition plant interception
fraction (Ifw) is given by:
-In2 x rain\
7/H. = Sblx LAI x e\ 3 * S"' '
where:
Sh] = vegetation dependent leaf wetting factor
LAI = leaf area index.
Wet Deposition Velocity lor Plants. Wet deposition velocity (Vdw) for plants is given by
x ran
where:
rain = rainfall rate
Wr = washout ratio, unitless factor relating particle washout to rainfall rate.
Diffusion Between Plants and Air. The diffusion from plants to air is based on two
resistances in parallel, the stomata and the series resistance of air and cuticle. The conductance
through the stomata is based on a correlation to the conductance of water vapor through the
D-3
-------
stomata. The conductance varies with the relative humidity, reflecting that the stomata closes up
during dry conditions. Additionally, the stomata are only open during the day and if day/night
patterns are ever used in TRIM, this should be taken into consideration.
g
461 x Temp
stomata
7.7 (7>m/>-273)
jc611 x 10(237 +
where:
rh = relative humidity.
"cuticle
jQ.704iogAT0w-M.2l
~Kaw
x 86400
The conductance through the cuticle is then put in series with the resistance through the air on the
leaf surface to yield the overall conductance:
1
1 ap
del
ap
air air o cuticle p
Soil to Root Transfer. Soil-to-root transfer is based on the following equilibrium
relationship:
where:
CR = concentration in roots (mg [chemical]/m3 [root fresh weight])
Cw = concentration in soil pore water (mg [chemical]/m3 [soil pore water])
WR = water content of root (mass/mass wet weight)
1R = lipid content of root (mass/mass wet weight)
b = correction exponent for the differences between octanol and lipids
pR = density of fresh root (g [root]/cm3 [root])
pw = density of soil pore water (g [soil pore water]/cm3 [soil pore water]).
Concentration in the Xylem Liquid
The algorithm used to calculate the concentration in the xylem liquid is the following:
D-4
-------
where:
TSCF
Pxy
Pw
= concentration of chemical in xylem liquid, mg (chemical)/m3 (xylem
liquid)
= concentration in soil pore water, (mg [chemicalJ/m3 [soil pore water])
= transpiration stream concentration factor (mg [chemical]/g
[xylem liquid])/(mg [chemical]/g [soil pore water])
= density of xylem liquid (g [xylem liquid]/cm3 [xylem liquid])
= density of soil pore water (g [pore water]/cm3 [pore water]).
Concentration in the Stem. The algorithm used to calculated the concentration in the stem
is the following:
where:
Astern
CH
SCF
Pstem
Pw
= concentration of chemical in stem (mg [chemical]/m3 [stem])
= concentration in soil pore water (mg/m3)
= stem concentration factor
= density of stem, g [fresh stem]/cm3 [fresh stem]
= density of soil pore water, g [pore water]/cm3 [pore water].
Benthic Community Transfers. The following concentration algorithm was used to
estimate the within the immature mayfly (benthic representative species):
mf _
'
where:
cmf =
CL, =
Vd-
Amount of compound in the organism normalized on a weight basis (ng/g)
Clearance constant (equivalent to kj (mL water cleared/g organism - hour)
Concentration of the compound in the interstitial water (ng/mL)
Proportionality constant that relates the amount of compound in the organism
to the concentration in the exposure water (equivalent to BCF).
D-5
-------
Water Column Transfers. The algorithm used to calculate concentrations in water column
organisms is as follows:
C C
sed
L TOC
where:
C0 = omnivore tissue concentration at steady state (ug/g)
L = lipid content of organism (g lipid/g organism)
TOC = total organic carbon in sediment (g carbon/g sediment)
Csed = sediment concentration (ug/g)
AF = accumulation factor (g carbon/g lipid).
Flux from Aquatic Macrophytes
The following algorithms was used to estimate flux of pollutant from macrophytes:
F = k V C -k V C
MP 1 MP H 2 MP^MP
where:
FMP = net flux of chemical in the macrophyte, (ug/day)
k, = bioaccumulation rate (day'1)
VMP = volume of the macrophyte (L)
Cw = chemical concentration in water (ug/L)
k2 = depuration rate (day"1)
CMP = chemical concentration in macrophyte (ug/L).
Food Chain Transfers for Fish. The following model for estimating pollutant concen-
trations in fish (Thomann, 1989) was used:
dt
where:
CF = concentration in fish (ug/kg)
k,, = uptake rate from water via the gills (1/kg-day)
D-6
-------
CWD = dissolved chemical concentration in water (ug/L)
kD = chemical uptake from food (kg food/kg fish/day)
P, = proportion of the diet consisting of food item I
CDl = chemical concentration in food item I (ug/kg)
keg = elimination via the gills (I/day)
kE = elimination via fecal egestion (1 /day)
KM = metabolic transformation of chemical (I/day)
KG = dilution contaminate concentration from growth (I/day).
Terrestrial Wildlife Algorithm. The following generalized algorithm was used to estimate
concentrations in terrestrial wildlife:
dC, /dt = [(^ *CW * AJ + (I, *CS* A,) + L^VCf/ A,) + (I, *Ca*Aa)] - [C, * (Em + Eu + E, + Ee)]
where:
C, = total, whole body, internal concentration in animal (mg[chemical]/kg[body
weight])
1^ = water ingestion rate (LVkg body weight/d)
Cw = concentration of contaminant in water ingested by animal (mg/L)
Aw = assimilation efficiency of contaminant from water (unitless)
Is = soil ingestion rate (kg/kg body weight/d)
Cs = concentration of contaminant in soil (mg/kg)
As = assimilation efficiency of contaminant from soil (unitless)
Pj = proportion of food type (j) in diet (unitless)
If = food ingestion rate (kg/kg body weight/d)
Cfj = concentration of contaminant in food type (j) (mg/kg)
Af = assimilation efficiency of contaminant from food (unitless)
Ia = inhalation rate (mVkg body weight/d)
Ca = concentration of contaminant in air (mg/m3)
Aa = assimilation efficiency of contaminant from air (unitless)
Em = contaminant elimination through metabolic breakdown (d'1)
Eu = contaminant elimination through excretory processes (urine and feces) (d"1)
E, = contaminant elimination through lactation (milk production, mammals only)
(d-1)
Ec = contaminant elimination through egg production, birds only (d'1).
Earthworm Model. If the steady state partition coefficient between the concentration in the
worm and the concentration in the soil water is utilized, then at equilibrium:
C = K C
Mum /»K stnl.liquid
D-7
-------
where:
Cworm = Concentration of chemical in the earthworm, mg (chemical)/kg (worm,
fresh weight)
Kj,w = earthworm/water partitioning coefficient, L (soil pore water)/kg (worm,
freshweight)
Cso,i iiqilid = Concentration of chemical in soil pore water, mg (chemical)/L (soil pore
water).
D-8
-------
APPENDIX E
USER'S GUIDE
-------
Appendix E
User's Guide
This appendix contains a suggested outline for the User's Guide Manual in Section E.1.0 and
step-by-step information on how to run and troubleshoot P4 in Section E.2.0.
E. 1.0 User's Guide Outline
This is a suggested outline for a user's guide that has not been written at this point in the TRIM
project. Without the knowledge of software and hardware platforms, it is difficult to be specific.
CHAPTER 1 Introduction
1.1 Background
1.2 TRIM.FaTE Approach
1.3 Regulatory Applicability
1.4 Model Limitations
CHAPTER 2 Getting Started
2.1 TRIM.FaTE Structure
2.2 Accessing TRIM.FaTE
2.3 Hardware and Software Requirements
CHAPTER 3 Simulation Setup
3.1 Main Menu
3.2 Setup Pathways
3.3 Input Data Requirements
3.3.1 Site Specific Data
3.3.2 Abiotic Parameters
3.3.3 Biotic Parameters
3.3.4 Chemical Specific Parameters
3.3.5 Uncertainty and Variability of Inputs
3.4 Data Format
3.4.1 Site Specific Data
3.4.2 Abiotic Parameters
3.4.3 Biotic Parameters
3.4.4 Chemical Specific Parameters
CHAPTER 4 Execution Modes
4.1 Batch
4.2 Sequential
4.3 Remote
4.4 Internet
E-l
-------
CHAPTER 5 Output Setup
5.1 Data
5.2 Graphics
5.3 Export/Import Capabilities
5.4 Output Reports
5.4.1 Domain Specific
5.4.2 Pollutant Specific
5.4.3 Time Dependent
CHAPTER 6 Customizing TRIM.FaTE Algorithm Library
CHAPTER 7 Technical Summary
APPENDICES
Appendix A - Default Data Sets
Appendix B - Data Collection Handbook
GLOSSARY
INDEX
E.2 Prototype 4 Implementation
Setting Up to Run Prototype 4
The program and datafiles implemented require Microsoft Excel 97 for Windows 95, with at
least 30MB of disk space. After downloading the zip file off the ftp site, unzip it (make sure to
set options so that directory structure is preserved), and run the program "setup.exe" in the
directory "trim\proto4\setupDLLs." This program will install the needed dynamic link libraries
(DLLs) to your "c:\windows\system" directory. Four of these DLLs are Visual Basic and Fortran
DLLs implemented for LSODE:
• "Trim Routines for P4.dll"
Visual Basic 5.0 DLL that contains needed geometry routines
• "convexhull.dll"
Fortran DLL to calculate smallest convex region containing a set of two-
dimensional points
• "varlsode.dll"
Fortran DLL to call LSODE
• "lineq.dll"
E-2
-------
Fortran DLL to solve the matrix equation needed to calculate steady-state
solution
The other DLLs are auxiliary files needed by the Visual Basic DLL. If some of the current DLLs
are out of date relative to these files, then the setup program may ask that you restart the machine
before proceeding with setup. Of the machines that we have installed the DLLs, overwriting the
existing files has not caused any problems.
Table E-1 summarizes the primary files needed. Note that paths will be different if the directory
structure on your machine is different than that assumed here.
Table E-1. Primary Files Used
Original Filename
Setup.exe
P4main.xls
Lsode Results Template.xls
P4timedata.xls
Set up file for p4.xls
Proto4FineGrid.xls
Blank Prototype4 Matrix
Template.xls
Debugging Output Template.xls
p4guts.xls
p4LSguts.xls
Description
Program to set up your system
with needed dynamic link
libraries (may require reboot of
machine). Run only when files
are first downloaded.
Has main sheet for generating
matrix and/or running LSODE
Output file for LSODE results.
Includes postprocessing graphs.
Contains time dependent data
Contains non-time-dependent
data
File with configuration
information for P4 (Volume
elements and links)
File for transition matrices
Contains intermediate
information from calculation of
transition matrices.
Programs to generate transition
matrices
Programs to run LSODE
Original Location
c:\trim\proto4\setupdlls
c:\trim\proto4
c:\trim\proto4\templates
c:\trim\proto4\Data files
c:\trim\proto4\Data files
c:\trim\proto4\configurationfiles
c:\trim\proto4\templates
C:\trim\proto4\templates
c:\trim\proto4\VBAFiles
c:\trim\proto4\VBAFiles
E-3
-------
Table E-1 . Primary Files Used
Original Filename
trim.mdb
Description
Database containing spatial
information on volume elements
Original Location
c:\trim\databases
The Main Excel File That Needs to be Opened
The main file that is needed is "p4main.xls" in the directory "c:\trim\proto4." This can be saved
as another name, but do not update format to Excel 97. Excel 97 will probably crash if this
file is updated (this is due to a problem with listboxes and drop-down boxes in Excel 97). This
file is linked to "p41sguts.xls" in the directory c:\trim\proto4\VBAFiles," which references the
file "p4guts.xls" in the directory "c:\trim\proto4\VBAFiles."
How to Do Specific Things
Modify Input Data
There are two input data files. One contains time-dependent data (wind speed and direction,
precipitation, temperature, erosion and runoff, water flow), and the other file contains all other
input data (Table E-2). The default file with time-dependent data is called "p4timedata.xls." The
Table E-2. Existing Data files that Can be Used
Filename
Setup file for P4,
DepthofRunoff=5cm.xls
Setup file for P4,
DepthofRunoff=0.05m.xls
p4timedata.xls
Comment
Depth of runoff for all
surface soil cells is
5cm
Depth of runoff for all
surface soil cells is
0.05m. This depth of
runoff was used for P4
runs prior to 11-8-97.
Time-dependent data
Path
c:\trim\proto4\D
ata files
c:\trim\proto4\D
ata files
c:\trim\proto4\D
ata files
Where in
"p4main.xls" it is
specified if to be
used
Cells to right of "Non-
time dependent data"
Cells to right of "Non-
time dependent data"
Cells to right of Time
dependent data"
default file with the other input data will start with the words "Setup file for P4," followed by a
date or descriptive text. The input parameters are spread out across several sheets, depending on
the dependence of the parameter. Since the inputs are read in by referencing the offset from the
E-4
-------
cell with the domain instance name, it is critical that the location of the data relative to the
domain instance name not change. There are several input files included in the zip file. These
can be modified as desired and saved under different names.
Choose a Chemical
The chemical-specific data will be obtained based on the value in the cell "Chemical" (1=BAP,
2=Phenanthrene). This value will be automatically set every time a matrix file is opened based
on the sheet selected. If the sheet has "bap" in the name, then it is assumed to be for BAP; if it
has "phen" in the name, then it is assumed to be phenanthrene.
Generate Transition Matrices
There are three manners in which transition matrices can be generated:
• Matrices generated without calling LSODE
• Matrices generated and LSODE called using generated matrices
• Sensitivity analysis performed, in which matrices are generated and LSODE run
for a specified number of times, with selected inputs modified each iteration (see
section on sensitivity analyses).
To generate matrices, one must specify the input and output files, and set the particular options
for the run. All of this is performed within the main spreadsheet "P4main.xls." Table E-3
summarizes the files that need to be specified and options selected in order to generate transition
matrices.
There are some matrix files already generated (Table E-4). These files can be used to run
LSODE if one does not want to regenerate new matrices. The existing matrix files can be quite
large (over 5MB), even though the matrices are stored in sparse form. A blank matrix file with
the proper formats is provided for new runs.
View Cell "T" Values
If a matrix file exists, then the input links for the cell and associated "T"-values can be viewed
from the file "P4main.xls" for any hour by selecting the desired cell in the list box under "Pick
Cell" and a time from the list box under "Pick Time." For the cell selected, various information
will be provided. This information includes: the parcel the cell is in, domain type and subtype,
E-5
-------
Table E-3. Files and Options for Generating Transition Matrices
Needed Pile (contains specific
formats for use)
Main file for calling routines
Time dependent data
Non-time-dependent data
Configuration information for P4
Transition matrices
Debugging output and
messages
Spatial database file
Option
Time for diffusion
Lstart for matrices
Lstop for matrices
Debug
Numberlterations
Existing Files (files in
"templates" directory should
be saved as different files)
P4Main.xls
p4timedata.xls
Setup file for P4,
DepthofRunoffs5cm.xls ;
Setup file for P4,
DepthofRunoff=0.05m.xls
Proto4FineGrid.xls
Initial Path
c:\trim\proto4
c:\trim\proto4\Data files
c:\trim\proto4\Data files
c:\trim\proto4\configurationfiles
See next table
Debugging Output Template.xls
trim.mdb
c:\trim\proto4\templates
c:\trim\proto4\databases
Description
Factor used in determining diffusion in soil. Default is one day.
There will be i_stop-istart+1 matrices created. The time-dependent
data will be read starting i_start+1 rows down from top of time-
dependent data set
If set to 1 , then extensive intermediate information on transition
matrices is generated and placed in the selected debugging file.
This information includes a breakdown of the "T values in terms of
diffusion and advection.
Only applicable for sensitivity analyses (see below)
Table E-4. Existing Files for Transition Matrices
FileName
Comment
Location
BlankPrototype4 Matrix
Template.xls
Can be used for new runs.
Open and save as desired file
name, and modify cells to right
of the cell "Matrix File" in
"p4main.xls" to refer to the new
file.
c:\trim\proto4\templates
E-6
-------
Table E-4. Existing Files for Transition Matrices
FileName
Prototype4 Matrix, 4 directions,
precip on and off, annual
averages for
temp.precip.wind.xls
Prototype4 Matrix, 1st 24
hours.xls
Comment
Contains 8 matrices for BAP
and phenanthrene: 4 wind
directions, precipitation on and
off (average annual
precipitation)
24 hours of transition matrices
for BAP and phenanthrene
Location
C:\TRIM\proto4\RunFilesforWrit
eup\4 Directions, annual
averages (precip off and on)
C:\TRIM\proto4\RunFilesforWrit
eup\1st24 hours
output "T" value for cell, number of input links, list of other cells that are linked to cell and
associated "T" values, population size (if biotic), and fraction of chemical in various phases.
General information on the matrix is also provided: units of transition matrix, size of matrix,
wind speed and direction, and precipitation.
Get LSODE/Steady-State Results
One can have LSODE run automatically after the transition matrices are generated, or one can
run LSODE using an existing transition matrix file. The transition matrix file is specified in the
columns to the right of the cell that contains "Matrix File." The options available for running
LSODE are summarized in Table E-5. Table E-6 shows the existing files with LSODE results.
Currently, it is assumed that there is initially no mass of the chemical in the system. Every time
that LSODE is called, the steady-state solution is also calculated.
Get Mass and Concentration Results for a Single Domain
After an LSODE run has been performed, the mass and concentration in a specific cell can be
examined by choosing the desired cell from the drop down box "Pick Cell." The masses and
concentrations are provided several rows down after a cell is selected. The value selected in the
"Pick Time" list box has no effect on these results.
Mass Distribution Graphs
All mass distribution graphs (by parcel, domain, and biotic breakdowns) are located in the
LSODE sheet selected.
Run Sensitivity Analyses
If a properly set up file is available, it is possible to perform "Elasticity"sensitivity analyses. In
addition to the options previously mentioned, the number of iterations desired are specified.
E-7
-------
Table E-5. Options for Running LSODE
Option
tstart
tstop
NumberofTimes
UseSameMatrix
Source term for lower air cell in
volume element 1
RelativeTolerance
MaxSteps
Comment
Time at which simulation starts
Time at which simulation stops
Number of outputs from LSODE between tstart and tstop. For
each each output time, a different transition matrix will potentially
be utilized
If set to 1 , then the same transition matrix is used for all times.
This is used to investigate the system reaching steady-state. If
set to 0, then a different transition matrix will be used for each
output time specified (starting with the first one in the matrix file)
Source term for the smelter, in grams/day
Relative tolerance LSODE will use in solving system
Maximum number of steps LSODE will allow for each interval.
Increase this value if "Istate" returns -3 in the LSODE output file
for any output time.
LSODE Results, 4directions, precip
on and off.xls
Phen LSODE Results, 4directions,
precip on and off.xls
BAP LSODE Results, 1st hour of
4directions, precip on and off
BAP LSODE Results, 1st 24 hours
Phen LSODE Results, 1st 24 hours
C:\TRIM\proto4\RunFilesforWriteup\4 Directions, annual averages
(precip off and on)
C:\TRIM\proto4\RunFilesforWriteup\4 Directions, annual averages
(precip off and on)
C:\TRIM\proto4\RunFilesforWriteup\4 Directions, annual averages
(precip off and on)
C:\TRIM\proto4\RunFilesforWriteup\1st 24 hours
C:\TRIM\Droto4\RunFilesforWriteup\1st 24 hours
TheMatrix - BaP
TheMatrix -
Phenanthrene
TheMatrix - BaP
TheMatrix - BaP
TheMatrix -
Phenanthrene
Prototype4 Matrix, 4 directions, precip on and off,
annual averages for temp.precip.wind.xls
Prototype4 Matrix, 4 directions, precip on and off,
annual averages for temp.precip.wind.xls
Prototype4 Matrix, 4 directions, precip on and off,
annual averages for temp.precip.wind.xls
Prototype4 Matrix, 1st 24 hours.xls
Prototype4 Matrix, 1st 24 hours.xls
C:\TRIM\proto4\RunFilesforWriteu
p\4 Directions, annual averages
(precip off and on)
C:\TRIM\proto4\RunFilesforWriteu
p\4 Directions, annual averages
(precip off and on)
C:\TRIM\proto4\RunFilesforWriteu
p\4 Directions, annual averages
(precip off and on)
C:\TRIM\proto4\RunFilesforWriteu
pYlst 24 hours
C:\TRIM\proto4\RunFilesforWriteu
D\1st24 hours
E-8
-------
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When the button "Sensitivity Runs" is clicked, the program will make multiple runs, generating a
transition matrix and calling LSODE each iteration. For each iteration, the iteration number will
be placed in the cell named "LookUp" in the "p4setup,....xls" file and all sheets will be
recalculated. If the file is configured appropriately, this will update all input parameters from a
master list, the particular values depending on the iteration number. After the transition matrix is
generated and LSODE called, the outputs are copied into another sheet, along with the iteration
number, for later postprocessing.
Open Algorithm Library
The implemented algorithm library is located in the module "P4Algorithm Library" in the file
"p4guts.xls." This is accessed by opening the Visual Basic editor from Excel and choosing the
module.
(Limited) Trouble-Shooting
Error Loading DLL (Error 48)
This error may occur even if one has had successful runs already. First, check and make sure that
there is plenty of disk space available. Windows will probably be caching things to disk, and if
disk space is very low, it cannot load the DLL. If there is plenty of space, then check and make
sure that the "dll" extension is all in lower case letters on the four P4-specific DLLs previously
discussed (this is a possible bug in Windows/Visual Basic).
Excel crashed when opening one of the files (or a version of one of the original
files saved under a different name)
For some files, this may happen if the file is saved in Excel 97 format, instead of Excel 5.0/95
format. You might be able to repair the file with Microsoft Access, but the best thing to do is
just open an Excel 5.0/95 version of this file, if this is an option. If the file is one of the VBA
files, then the problem may be with the references in the file "p4LSguts.xls". If this is the case,
then try renaming the file "p4guts.xls" and opening the file "p4LSguts.xls". If this file now
opens, then open the Visual basic editor and remove "TRIMDLL" and "P4Guts" from the
references. Exit Excel and then see if "p4LSguts.xls" can be opened. If so, then replace the
references.
E-ll
-------
Error 1004: Global Method of Range Failed
This usually means that the program was trying to locate a spreadsheet cell using a name, but the
name does not exist. The different types of files used (data files, output files, etc.) all are
assumed to have certain named ranges. For this reason, if you want new versions of these files
then it is necessary to specify a file that is created from an existing copy of one of the files. This
error may also occur if you halted the program execution and entered "Debug" mode, changed
the active sheet (e.g., you changed windows to look at another Excel file), and resumed execution
of the program. If you make "p4main.xls" the active sheet, then it will be possible to resume
execution if you enter "Debug" mode upon getting this particular error.
Error: Division by Zero
This can happen for a variety of reasons. If this error is obtained when generating transition
matrices, make sure that there are enough time-dependent data for the number of matrices to be
generated. For example, if "i_stop for matrices" is set to 24, this means that the last matrix
generated will use the data in the 25th row of data in the time dependent data sheet. If no data
are there, then 0 will be obtained for all values. This will cause a division by zero when it is
calculating fugacities since the temperature is in the denominator. If this is the case, then all
matrices previous to this matrix have already been generated, so the matrix file can be saved
without having to regenerate them.
E-12
-------
APPENDIX F
DOCUMENTATION OF SOFTWARE AND ROUTINES
-------
-------
Table of Contents.
Page
F. 1 Properties of Class Modules F-1
F.2 LSODE/Steady State F-5
F.3 Spatial Routines Implemented F-17
F.4 Alpha Version F-37
-------
Appendix F
Documentation of Software and Routines
This appendix contains documentation in support of the software developed for P4. Appendix
F. 1 is in tabular format describing the properties of the class modules; Appendix F.2 discusses
LSODE and steady state; Appendix F.3 discusses the intersection of planar regions; and,
Appendix F.4 supplies information on where to locate the alpha version and source code print-
out of P4.
F. 1 Properties of Class Modules
Table F-1
Properties of a BlockStructure in P4
Property
Name
SpatialProps
Domains
time_start
time_stop
Temperature
Rain
Z_pureair
Z_purewater
BasicChemProps
Comment
Name of block; can be used to get block in collection of all blocks
Spatial properties of block (location of lower left corner, length width
height)
and
Collection of domains in the block
Start time for this block (parameters in the block and its domains are valid
from time_start to time_stop; this information is also used to calculate
diffusive flows)
Stop time for this block
Temperature for the block (K)
Rainfall rate for the block (m/hr)
Fugacity in pure air for the block and chemical
Fugacity in pure water for the block and chemical
Object containing information on chemical properties for chemical(s)
block (see Table 10 below).
in the
Note: there is one of these for each chemical, time step, and geographic location1
'The memory (obviously) wasted by use of this type of structure for each geographic location and chemical (rather that having the
chemical-specific subpropemes be stored in arrays of objects within the block) is a temporary compromise given the time constraints and basic
objectives of the prototypes. In Visual Basic for Applications (the version of Visual Basic that comes with Office97), having arrays of properties
within an object requires some additional (tedious) code for each class module and property, and is implemented in only a limited number of cases
mP4
F-1
-------
Table F-2
Common Properties of All Domains in Prototype 4.0
Property
Domain type
Subtype
Keyname
BlockName
Indexinmatrix
Links
HasReactionSink
HasAdvectionSink
TheBlock
RowinExcelFile
IndexinDomains
BasicChemicalProperties
ChemicalPhase
Temperature
Spatial properties
TotalMass_tstart
TotalMassJstop
FractionMass
ConcentrationDenominator
ConcentrationUnits
Comment
Integer denoting the type of domain
Integer denoting subtype of domain. In P4, the domains that have
subtypes are:
Soil: Surface soil, root zone, vadose zone, groundwater
Fish: Carnivore, herbivore, omnivore
Sink: Reaction sink or advection sink
Unique name for domain in collection of domains in block
Name of the block containing the domain
Row in the transition matrix for this domain
Object containing information on the links between the domain to other
domains.
Whether or not domain has a reaction sink
Whether or not domain has an advection sink
Reference to the actual block containing the domain
Row in the Excel input file that contains base information for domain
(used for second pass through input file in order to read in input link
information)
Index for domain in the collection of all domains in the block
Object containing information on chemical properties for chemical(s) in
the domain (see T able 10 below). •
Information on actual phase of chemicaUs) in domain (will be utilized
when applicable algorithms are available).
Temperature of block containing domain
Object containing spatial information for block (see Table 10; this object
is also used for domains)
Total mass of chemical in domain at beginning of time step for which
parameters are valid
Total mass of chemical in domain at end of time step for which
parameters are valid (after LSODE is called)
Array containing information on the fraction of mass of chemical in
specific phases in domain. In P4 phases considered are: bulk (total),
sorbed, dissolved, vapor, worm (only used if domain is a soil domain and
worms domain are in equilibrium with soil)
Array of numbers to divide mass of chemical by in order to get
concentration in a specific phase in the domain. Depending on the
domain type and phase, this could be the volume of the domain (in m3 or
L) or the mass of domain (e.g., kg of soil if a soil domain)
Array of strings denoting the units of the denominator of concentration for
each phase.
F-2
-------
Table F-3
Properties of a BasicChemicalProperties Object
Property
Chemical name
Chemical index
K_ow
K_oc
Kaw
H
R
MW
VaporPressure
MeltingPoint
D_water
D_air
log10_K_ow
DefaultReactionHalflife
Comment
Integer ID for chemical
Octanol-water partitioning coefficient,
L[water]/L[octanol]
Octanol-carbon partitioning coefficient,
L[water]/kg[carbon]
Air-water partitioning coefficient
Henry's law constant
lideal gas constant, Pa-m3/mol-K
Molecular weight, g/mol
Vapor pressure, pa
Melting point (K)
Diffusion coefficient in pure water, m2/day
Diffusion coefficient in pure air, m2/day
Logarithm base 10 of K_ow
Default reaction half-life for chemical in each
domain and subtype of domain
F-3
-------
Table F-4
Properties of a Spatial Properties Object
Property
SinkFeaturelD
SinkFeatureArea
NameforDorhaininDataBase
dbData
GeometryRoutines
VolumeElement
Area
Volume
CrossSectionalArea
Comment
Array of IDs in spatial database for facets/features
of sinks for block/domain
Array of interfacial area with sink(s) with
block/domain
Keyname for domain in spatial database
Database containing spatial data
Object wrapper for geometry routines ("Exposed"
class; see Appendix A(?) of SAB report)
"CVolumeElement" class used for spatial
calculations (see Appendix A(?) of SAB report)
Area of horizontal plane in domain/block (m2)
Volume of domain/block (m3)
Area of vertical plane in domain/block (m2)
Table F-5
Properties of a LinkObject
Property
InputLinks
OutputLinks
Comment
Collection of GenericLinkObject objects (see
Table 11) detailing information on input links to
domain
Collection of generic link objects detailing
information on output links from domain
F-4
-------
Table F-6
Properties of a GenericLinkObject
(utilized for collections of input or output links of a domain)
Property
Domain
AlgorithmResult
Diffusion
Advection
Time_dependent_partition
IngestionRate
Comment
Object referencing the domain sending mass if link is an input link, or
referencing receiving domain is link is an output link
Object containing information on the algorithm result for the link (see
Table 12)
Object containing diffusion properties of link
Whether or not there is diffusion
Interfacial area for diffusion link (m2)
Boundary layer thickness on receiving side of link (m)
Boundary layer thickness on sending side of link (m)
Mass transfer coefficients for sending side of link (m/day)
Mass transfer coefficients for receiving side of link (m/day)
Object containing advection properties of link
Whether or not there is advection
Interfacial area for advection link (m2)
Areal velocities for each phase (m3[phase]/m2[interfacial area]-day
Area) bulk velocity (m3/m2[interfacial area]-day)
Object containing intermediate information on factors used to calculate
transfer for links in which an equilibrium relationship is converted to a
time-dependent form using the time to reach some fraction of steady-
state:
Fraction of steady-state reached (a) by time t_alpha
k, : = -ln(1-a)/t_alpha
k2 : =k, * Steady-state ratio
The ingestion rate if the link is one of ingestion of one domain by another
(e.g., ingestion of soil by mouse, ingestion of fish by kingfisher).
Table F-7
Properties of an AlgResult Object
Property
TValue
Diffusion
Advection
Reaction
Other
Comment
Sum of components; will be entry in the transition
matrix
Diffusion component of TValue
Advection component of TValue
Reaction component of TValue
Miscellaneous components of TValue
F-5
-------
Table F-8
Properties of a Soil Domain in P4
(in addition to properties shared by all domains)
Property
TotalPlantBiomass
InEquilwithWorm
WormProps
VolumeFractionlsWorm
Area
Volume
Height
theta
epsilon
phi
rho
OrganicCarbonContent
DepthofRunoff
Kd
D_Effective
Boundary_layer_Thickness_in_Air_Abov
e_Soil
Z
Zjotal
ErosionScaleFactor
Runoff ScaleFactor
EvaporationScaleFactor
Comment
Total plant biomass in soil domain, kgpdry plantym2[area]
Flag for if worms in domain are in equilibrium with domain
Properties of the worms in the domain; utilized only if
worms are in equilibrium
Fraction of total volume of domain that is worm; utilized
only if worms are in equilibrium
m2
m3
m
Volumetric water content
Volumetric air content
Total porosity
Density of soil particles (k3[soil]/m3[soil]
m; depth of runoff on soil; used only for surface soil
domains
Equilibrium partition coefficient for chemical, L/kg
Effective diffusion coefficient in domain, m2/day
Boundary layer thickness in air above soil (m); utilized if
diffusion is specified between the soil domain and an air
cell.
Fugacity in each relevant phase in domain
Total fugacity capacity in soil
Calculated erosion results are scaled by this term; used to
reflect fact that not all soil is susceptible to erosion
Calculated runoff results are scaled by this term; used to
reflect fact that not all soil is susceptible to runoff
Calculated evaporation results are scaled by this term;
used to reflect fact that not all soil is susceptible to
evaporation
F-l
-------
Table F-9
Properties of an Air Domain in P4
(in addition to properties shared by all domains)
Property
Area
Volume
Height
Junge_C
Temperature
Rain
RelativeHumidity
Dustload
DustDensity
SurfaceAreaperVolumeof Particles
VolumetricAirParticleContent
VolumetricAirAirContent
vdep
u_w
WashoutRatio
Z
Z total
Comment
m2
m3
m
Constant used in calculating partitioning between
air and particles
Temperature in air domain
Rainfall rate (m/day) in block
Mass of particles per volume of air domain, kg/m3
Mass of particles per volume of particles, kg/m3
m2[surface area]/m3[particles]
Ratio of volume of particles in domain to total
volume of domain
1 - VolumetricAirParticleContent
Dry deposition velocity (m/day)
Mass transfer coefficient on air side of air-water
boundary
Washout ratio for particles
Fugacity in each relevant phase in domain
Total f ugacity capacity of domain
F-2
-------
Table F-10
Properties of a Surface Water Domain in P4
(in addition to properties shared by all domains)
Property
Area
Volume
Height
Temperature
rho
SuspendedSedimentconcentration
VolumetricSolidsContent
OrganicCarbonContent
Kd
D_Effective
BoundaryLayerThicknessAboveSediment
WaterSide_AirWaterDiffusionMassTransferCoeffi
cient
CurrentVelocity
Evaporation
Waterlnflow
Outflow
Z
Z total
Comment
m2
m3
m
Temperature in surface water
Density of suspended sediment particles in
surface water, (k3[sediment]/m3[sediment]
Mass of suspended sediment per volume of
surface water, kg[sediment]/m3
Fraction of total volume of surface water domain
comprised of suspened sediment
Organic carbon content for suspended sediment
particles
Equilibrium partition coefficient for chemical, L/kg
Effective diffusion coefficient in domain, m2/day
Utilized only if surface water domain is linked to
sediment domain and diffusion is specified (m)
Utilized only if surface water domain is linked to
sediment domain and diffusion is specified
(m/day)
Velocity of water within domain; used for
estimating diffusion to air; m/day
Evaporation rate from surface water domain,
m/day
Inflow of water not from other surface water
domains in modeled system, m3/day
Outflow of water from surface water domain,
m3/day
Fugacity in each relevant phase in domain
Total f ugacity capacity in domain
F-3
-------
Table F-11
Properties of a Sediment Domain in P4
(in addition to properties shared by all domains)
Property
Area
Volume
Height
Temperature
phi
rho
Benthic_solids_concentration
OrganicCarbonContent
Kd
D_Effective
BoundaryLayerThicknessbelowWater
Z
Zjotal
Comment
m2
m3
m
Temperature in surface water
Total porosity of sediment (m3[pore
space]/m3[total volume]
Density of suspended sediment particles in
sediment, (k3[sediment]/m3[sediment]
Mass of sediment particles per volume of
sediment, kg[sediment]/m3
Organic carbon content for sediment particles
Equilibrium partition coefficient for chemical, LAg
Effective diffusion coefficient in domain, m2/day
Utilized only if sediment domain is linked to
surface water domain and diffusion is specified
(m)
Fugacity in each relevant phase in domain
Total fugacity capacity in domain
F-4
-------
TableF-12
Properties of Mouse, Kingfisher, and Animal Domains in P4
(in addition to properties shared by all domains)
Property
Diet
Excretionrate
Fraction Exc retionto W ater
FractionExcretiontoSoil
BW
PopulationSize_per_sq_meter
PopulationSize
Total Mass
WaterlngestionRate
WaterlngProps
InhalationRate
InhalationProps
FoodlngestionRate
FractionWorms
FractionPlant
SoillngestionRate
WormlngestionRate
FractionDietOmni
FractionDietCarn
FractionDietHerb
AssimilationEffinAir
Comment
FoodDiet object (see Table 19) containing
information on animal's diet
Loss rate of chemical from animal due to
excretion, /day
Fraction of excretion that goes to surface water
connected to animal
Fraction of excretion that goes to soil domain
connected to animal
Bodyweight of individual (kg)
Population size per square meter of abiotic
domain (domain depends on animal type)
Number of individuals in population
Total mass of population (kg)
Water ingestion rate, L[water]/kg[BW]-day
Parameters used in regression equatio to
calculate water ingestion rate from bodyweight
Inhalation rate, m3/kg[BW]-day
Parameters used in regression equatio to
calculate inhalation rate from bodyweight
Total food ingestion rate, kg[food]/kg[bodyweight]-
day
Fraction of food diet (on mass basis) comprised of
worms
Fraction of food diet (on mass basis) comprised of
plants
Soil ingestion rate, kg[soil]/kg[BW]-day
Worm ingestion rate, kg[worm]/kg[BW]-day
Fraction of food diet (on mass basis) comprised of
fish omnivores
Fraction of food diet (on mass basis) comprised of
fish carnivores
Fraction of food diet (on mass basis) comprised of
fish herbivores
Assimilation efficiency of chemical through
F-l
-------
Table F-12
Properties of Mouse, Kingfisher, and Animal Domains in P4
(in addition to properties shared by all domains)
(Continued)
Property
AssimilationEffinSoil
AssimilationEffinWater
AssimilationEffinFood
MetabolicBreakdownRate
Comment
Assimilation efficiency of chemical through
ingestion of soil
Assimilation efficiency of chemical through
ingestion of water
Assimilation efficiency of chemical through
ingestion of food
Breakdown rate of chemical in animal, /day
Table F-13
Properties of a FoodDiet Object
Property
FoodElement(i As Long)
DoesEat(Domam as Object)
colFoodDistribution
Numberltems
Comment
Returns rth domain instance consumed by animal;
return type is "FoodDietElement" (see Table 20)
Returns true if animal consumes Domain, else
false
Private collection of FoodDietElement objects
representing other domain instances consumed
by animal
Number of other domain instances consumed by
animal
TableF-14
Properties of a FoodDietElement Object
Property
DomamType
SubType
FractionofFoodDiet
Comment
Domain type consumed
Domain subtype consumed
Fraction of the total food diet made
domain instance
up of the
F-2
-------
Table F-15
Properties of Plant Domain in P4
(in addition to properties shared by all domains)
Property
Subtype
Volume_per_area
Volume_per_areaDryWeight
Volume
Density
WaterContent
LipidContent
DryBiomass
Total Mass
Stomata Properties
Cuticle properties
OverallConductance
dp
AttenuationFactor
DryDeplnterceptionFraction
WetDeplnterceptionFraction
Leaf area index
Leaf wetting factor
CorrectionExponent
kpa
kpa_part
Comment
Leaf, xylem, stem, or root
Volume of plant (fresh weight) per unit area of soil, m3/m2
Volume of plant (dry weight) per unit area of soil, m3/m2
Volume fresh weight of plant, m3
kg[freshweight]/m3[plant]
Water content of plant
Lipid content of plant
kg dryweight of plant
Total mass of plant (kg fresh weight)
Object that contains information about stomata for leaf
subtype. Currently only contains Conductance for stomata
Object that contains information about cuticles for leaf
subtype:
Conductance
Boundary layer thickness (m)
Total conductance based on stomata and cuticle
conductance
Plays same role as depth for spatial domains in diffusion
calculations; = DryBiomass/((1-WaterContent)*Density)
Used to calculate dry deposition fraction
Area of leaf per area of soil
Used to calculate wet deposition interception fraction
Used to calculate steady-state partitioning between root and
soil pore water
F-l
-------
Table F-15
Properties of Plant Domain in P4
(in addition to properties shared by all domains)
(Continued)
Property
LitterfallRate
alpha
t_alpha
TSCF
SCF
Z_total
Comment
/day
Factors used if steady-state partition relationships are
converted to time-dependent form using length of time
(t_a!pha) it takes to reach some fraction (a) of steady-state
Transpiration stream correction factor; steady-state ratio of
xylem concentration to concentration in soil pore water
Stem correction factor; steady-state ratio of stem
concentration to concentration in soil pore water
Total fugacity capacity for plant (only utilized for leaf subtype
inP4)
Table F-16
Properties of Worm Domain in P4
(in addition to properties shared by all domains)
Property
Volume
TotallMass
Density
ArealDensity
Worm_SoilPartitionCoefficient
alpha
t_alpha
Comment
m3[freshweight] of worm
kg[freshweight] of worm
wet weight, kg[worm]/m3[worm]
kg[worm]/m2[soil area]
L[soil pore water]/kg[worm, freshweight
Factors used if steady-state partition relationships
are converted to time-dependent form using
length of time (t_alpha) it takes to reach some
fraction (a) of steady-state
F-2
-------
Table F-17
Properties of Macrophyte Domain in P4
(in addition to properties shared by all domains)
Property
Volume
TotallMass
Density
DepurationRate
BioaccumulationRate
Comment
m3[freshweight] of macrophyte
kg[freshweight] of macrophyte
wet weight, kg[macrophyte]/m3[macrophyte]
TableF-18
Properties of Fish Domain in P4
(in addition to properties shared by all domains)
Property
NumberofFish
NumberofFishpersquaremeter
FishBodyweight
TotallMass
Diet
FeedingRate
FractionDietOmni
FractionDietHerb
FractionDietMacro
Gamma_fish
FishLipidFraction
GillEliminationRate
FishChemicalUptakeRateviaGill
ChemicalTransferEfficiencyinFish
BioaccumulationRate
Sedimentlnteraction
AccumulationFactor
Comment
Number of fish in population
Number of fish in population per square meter of
surface water area
kg
kg[f reshweight] of fish in population
FoodDiet object (see Table 19) containing
information on animal's diet
Fraction of diet comprised of fish omnivores
Fraction of diet comprised of fish herbivores
Fraction of diet comprised of macrophytes
Factor used in calculating bioaccumulation rate
TimeDependentPartition object (Table 24)for
catfish<->sediment links
g [carbon]/g[lipid], used for catfish<->sediment
F-3
-------
TableF-19
Properties of InsectDomain
(in addition to properties shared by all domains)
Property
Diet
Excretionrate
Fraction Exc retionto Wate r
FractionExcretiontoSoil
PopulationSize
BiomassperArea
TotalMass
SoillngestionRate
FoodlngestionRate
EliminationRate
ClearanceConstant
V_d
MetabolicBreakdownRate
DecayConstant
BW
Comment
FoodDiet object (see Table 19) containing
information on animal's diet
/day
kg/m2
for population, kg
kg[food]/kgBW-day
kg[food]/kgBW-day
/day
ml/g-hr, used for mayfly nymph
used for mayfly nymph, ml/g
/day
/day
kg
Table F-20
Properties of TimeDependentPartition Object
Property
kl
k2
alpha
t_alpha
Comment
Intermediate information on factors used to
calculate transfer for links in which an equilibrium
relationship is converted to a time-dependent form
using the time to reach some fraction of steady-
state:
Fraction of steady-state reached (a) by time
t_alpha
k, : = -ln(1-a)/t_alpha
k, : =k, * Steady-state ratio
F-4
-------
F.2 LSODE/Steady State
Introduction. The system of coupled differential equations that represent the flow of mass
between cells is (currently) assumed to be one of the form:
where y y(t) is the H-dimensional vector containing the amount of mass in each cell, A is the
n by n transition matrix for the current time step, and s is the source term vector for the time
step. The source term accounts for a possible source term in each cell considered. The
solution to this system is approximated using the Livermore Solver for Ordinary Differential
Equations (LSODE), available from the NetLib repository (http:\\www.netlib.org). A steady-
state solution of this system is one in which y 6; i.e., one in which Ay s 6. This equation
is solved using TOMS Algorithm 576 by I. Barrodale and G.F. Stuart (Barrodale and Stuart
1981). As part of the preprocessing, it is necessary to calculate intersections of polygonal
regions. An auxiliary subroutine utilized in this process calculates the convex hull for a set of
points. The convex hull of a set of points is determined using the subroutine CONVEX, which
is Algorithm 523 of the Association for Computing Transactions on Mathematical Software,
written by W.F. Eddy (1977). Details on the implementation of these programs is described
below.
Finding Solution to a System of Differential Equations
Background on Method Used. LSODE subroutine solves systems of first order ordinary
differential equations of the form:
>, y(r0) y0
where y is an n-d mensional time-dependent vector; i.e.,
y(t) (y,(0,y,(/) >„(/))
F-5
-------
and F is a vector-valued function of / and the vector y. The system of differential equations
can be stiff or nonstiff. The term "stiff, when applied to a system of differential equations,
essentially means that there are components of the solution that cause problems when the
solution is approximated. Generally this is due to components of the solution that are decaying
much faster than other components of the system. In the stiff case, it treats the Jacobian matrix
as either a full or banded matrix. It uses Adams methods (predictor-corrector) in the nonstiff
case, and backward differentiation formula methods in the stiff case. The linear systems that
arise are solved by direct methods. LSODE is intended to supersede the older GEAR and
GEARB packages (Hindmarsh 1983, Radhakrishnan and Hindmarsh 1993).
Implementation. The LSODE Fortran source code was downloaded from the NetLib
repository of algorithms (http:\\www.netlib.org). This code was compiled using Microsoft
Fortran PowerStation 4.0 as a 32-bit dynamic link library so that it could be accessed by Visual
Basic for Applications in Excel 8.0. An interface subroutine (Var_LSODE) was written in
Fortran that calls the LSODE routine. This interface subroutine accepts as input the transition
matrix, source term, and initial condition vector, in addition to various parameters concerning
the method of solution and numerical error tolerances. This subroutine can be called by any
other program that can call DLLs (e.g., Fortran, C, Visual Basic). In Visual Basic, the function
is made available by adding the following code to the top of a module:
Declare Sub Var_LSODE Lib "VarLsode" (MatrixSize As Long, MatrixSize_sq As
Long, Matrix_as_OneD_Array As Double, Initial Vector As Double,
SourceTennVector As Double, t_initial As Double, tout As Double, Output Vector As
Double, RelativeTolerance As Double, AbsoluteTolerance As Double, istate As
Long, Irw As Long, liw As Long, MethodFlag As Long, OutLine As Long, MaxSteps
As Long)
Explanation of the arguments is provided in Table 1. The subroutine is called by a statement of
the form:
Call Var_LSODE( MatrixSize, MatrixSize_sq, Matrix_as_OneD_Array(l),
InitialVectorfJ), SourceTennVector( 1), tjnitial, tout, OutputVector( 1),
RelativeTolerance, AbsoluteTolerancefJ), istate, Irw, liw, MethodFlag, OutLine,
MaxSteps)
where the arrays are properly dimensioned. In particular, the first index of the arrays must start
at 1, not 0. This is performed in Visual Basic as follows:
F-6
-------
ReDim A(l To MatrixSize, 1 To MatrixSize)
ReDim Matrix_as_OneD_Array(l To MatrixSize * MatrixSize)
ReDim InitialVector( 1 To MatrixSize)
ReDim Source Term Vector(l To MatrixSize)
ReDim OutputVectorf 1 To MatrixSize)
ReDim AbsoluteTolerance( 1 To MatrixSize)
Calculating Steady State Solution of a System of Linear Differential Equations
Background on Method Used. The system of coupled differential equations that represent
the flow of mass between cells is (currently) assumed to be one of the form:
y1 Ay s
wherey y(t) is the vector containing the amount of mass in each cell, A is the transition matrix
for the current time step, and s is the source term vector for the time step. A steady-state
solution of this system is one in which y 0; i.e., one in which Ay s 0. This equation is
solved (after some preprocessing) using TOMS Algorithm 576 by I. Barrodale and G.F. Stuart
(Barrodale and Stuart 1981). The method used is a modification of Gaussian elimination.
Implementation. The Fortran source code was obtained from the NetLib library of mathe-
matical, statistical and linear algebra routines (http:\\www.netlib.org) and compiled as a
Windows 95 32-bit dynamic link library using Microsoft Fortran Powerstation 4.0.
Before discussing the preprocessing performed, it is important to note some aspects of the
structure of the transition matrix A. The number of rows is equal to the number of distinct cells
where the chemical can be located. This includes all sinks. Assuming that the cells are ordered
from i=J to n, the numbers in the /th row off the diagonal correspond to input the /th cell
receives from other cells2. These numbers will always be nonnegative. The number in
diagonal in the /th row is always nonpositive, and is related to the total amount of chemical that
leaves the /th cell. The numbers in the /th column off the diagonal correspond to the mass of
chemical leaving the /th cell. This means that if cell / does not send mass to any other cells,
then all of the entries in the /th column of the transition matrix will be zero. In particular, all of
the entries in the columns corresponding to sinks will always be zero. This implies that if cell /
technically, these coefficients are the instantaneous fluxes from the sending cells to cell i per mass of chemical in the sending cells
F-7
-------
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additional string variable that would contain the error message, but thi
sometimes "unstable" when called by Excel, and causes frequent
crashing. The problem is that passing variable length string arrays
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is a sink, then y, (the mass of chemical in the sink) does not explicitly appear in the system
Ay s 0; i.e., the ith entry of the vector Ay is zero.
The preceding discussion shows that the rows and columns corresponding to the sinks can be
ignored when finding the steady state solution. For this reason, the actual system solved to find
the steady-state solution is the reduced system that does not include the sinks. This system is
obtained from the general system by deleting the rows and columns corresponding to the sinks.
In Visual Basic, the function is made available by adding the following code to the top of a
module:
Declare Sub Modge Lib "Lineq" (N As Long, NDIM As Long, A As Double, B As
Double, epsAs Double, tolerAs Double, P As Long, QAs Long, ZAs Double, XAs
Double, K As Long, OCODE As Long, OPIVOT As Long)
It is assumed that the file "lineq.dll" is located in the "c:\windows\system" directory. The setup
program will automatically copy this file. The actual calling of the subroutine is performed as:
CallModge(N, NDIM, A(l, I), B(l), eps, toler, P(l), Q(l), Z(l), X(l), K, OCODE, OPIVOT)
where the arrays are properly dimensioned. In particular, it is critical that the index of the first
element if 1, and not 0 (the default in Visual Basic is 0):
NDIM = N
ReDim A(J To N, 1 To N)
ReDim TA(I To N, 1 To N)
ReDim B(l To N)
ReDim P(I To N)
ReDim Q(l To N)
ReDim Z(I To N)
ReDim X(l To N)
On entry to the subroutine, the array A contains the matrix, and B contains the vector for which
a solution of AX=B is sought. If the algorithm is successful, then on return the array X will
contain the approximation to the solution.
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Calculating the Convex Hull for a Set of Points
Background on Method Used. Frequently it is necessary to calculate the smallest convex
region containing a set of two-dimensional points. This is primarily performed after finding
the points in the intersection of two convex polygons, where the points must be reordered to
preserve convexity. A convex region is one in which, for any two points in the region, the line
between the points is contained within the region. The smallest convex region containing a set
of points is called the "convex hull" for the points. The convex hull of a set of points is
determined using the subroutine CONVEX, which is Algorithm 523 of the Association for
Computing Transactions on Mathematical Software, written by W.F. Eddy (1977).
Implementation. The only modification made was to add the code to allow the subroutine to
be called by programs that can call DLLs (e.g., Visual Basic):
!MS$IF Defined(ForDLL)
!MS$ATTRBUTES dllexport:: MODGE
!MS$ATTRffiUTES alias: 'Modge'::MODGE
IMSSENDIF
To call the program from Visual Basic, the following code must be added at the top of the
module:
Declare Sub Convex Lib "ConvexHull" (N As Long, x As Double, M As Long, IN_I
As Long, I A As Long, IB As Long, IH As Long, NH As Long, IL As Long)
It is assumed that the file "convexhull.dll" is located in the "c:\windows\system" directory.
The setup program will automatically copy this file. The actual calling of the subroutine is
performed as:
Call Convex(N, x(l, 1), M, INJ(l), IA(1), IB(J), IH(J), NH, IL(J))
where the arrays are properly dimensioned. In particular, it is critical that the index of the first
element if 1, and not 0 (the default in Visual Basic is 0):
ReDim x(J To 2, 1 To N)
Re Dim IN_I(1 To N)
ReDim IA(J To N)
F-14
-------
ReDim IB(1 To N)
ReDim IH(1 To N)
ReDim IL(1 To N)
Before calling the routine, the vertices are placed in the x array; and IN(i) is set to i for i=l to
N. This is implemented here as:
For i = 1 To N
x(l, i) = Vertices(i).x
x(2, i) = Vertices(i).y
IN_I(i) = i'
Next i
After calling CONVEX, the variable NH will be equal to the number of vertices in the convex
hull, and the ordered points (referred to here as V_post) for the convex hull are obtained by the
following code (this uses the linked list in 7L):
IK = IL(1)
NumberVertices = NH
For i = 1 To NH
V_post(i).x = x(l, IH(IK))
V_post(i).y = x(2, IH(IK))
IK = IL(IK)
Next i
F-15
-------
Table F-23
Explanation of Arguments passed to CONVEX Dynamic Link Library Subroutine to Calculate
Convex Hull for a Set of Points
Variable
N
X
M
IN
IA
IB
IH
NH
IL
Variable Type
4-byte Integer
Double (2,N)
4-byte Integer
4-byte Integer array of
dimension M
4-byte Integer array of
dimension M
4-byte Integer array of
dimension M
4-byte Integer array of
dimension M
4-byte Integer
4-byte Integer array of
dimension M
Description
INPUT: Total number of data points
INPUT: (X,Y) co-ordinates of the data
INPUT: Number of points in the input subset
INPUT: Array (M) subscripts for array X of the points in the
input subset
WORK AREA: Array (M) subscripts for array X of left son
subsets
WORK AREA: Array (M) subscripts for array X of right son
subsets
OUTPUT: Array (M) subscripts for array X of the vertices of the
convex hull
OUTPUT: Number of elements in array IH and array IL. Same
as number of vertices of the convex polygon
OUTPUT: A linked list giving in order in a counter-clockwise
direction the elements of array IH
References:
Barrodale, I. and G.F. Stuart, ACM Transactions on Mathematical Software, September, 1981.
W. F. Eddy, Algorithm 523: CONVEX, A New Convex Hull Algorithm for Planar Sets, ACM
TOMS 3(1977) 411-412.
Alan C.Hindmarsh, ODEPACK, A systematized collection of ode solvers, in Scientific
Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983, pp. 55-64.
Radhakrishnan, K. and A.C. Hindmarsh, Description and Use ofLSODE, the Livermore Solver
for Ordinary Differential Equations, LLNL UCRL-ID-113855, 1993.
F-16
-------
F.3 Spatial Routines Implemented
Introduction. In order to facilitate the necessary spatial calculations, class modules and
subroutines were implemented in Visual Basic and Fortran. These were compiled into a 32-bit
dynamic link library (filename "TrimDLL for P4.dll"), which is referenced by the main sub-
routines that read the input files and generate the transition matrices. This DLL was created
using Microsoft Visual Basic Professional Edition 5.0, Service Pack 2.
A class module is essentially a user-defined "type", analogous to "Integer" or "Double
Precision" in standard Fortran. It is more general than a type, however, as it can have self-
contained properties and subroutines. The properties and subroutines can either be public
(readable/usable by any other subroutine) or private (available only to objects within the class
module itself). The code for a class module is a template or blueprint for creating instances of
the class module, as it is the instances that are utilized by programs making use of the class
modules. The instances can also be referred to as objects. The method of programming that
makes use of such objects is generally called object-oriented programming, although in its
strictest sense there are features that a programming language must have, that Visual Basic 5.0
does not, in order that it be referred to as being object-oriented1. An advantage of the use of
class modules is that it makes the logic flow of programs more transparent: coding details that
are extraneous to the program flow can be tucked inside objects. This simplifies programming,
compartmentalizes code to help reduce code redundancy, and facilitates code reuse.
A summary of the primary class modules implemented for the spatial calculations made in P4
are summarized in the table below. More detail on each of the class modules and associated
subroutines are summarized in subsequent tables.
'These include inheritance, in which objects can be created from existing objects, and polymorphism
F-17
-------
Table F-24
Summary of Main Class Modules Implemented for Spatial Calculations in P4
Class Module
Point2D
PolarVector2D
PointSD
Polygon2D
Facet3D
CVolumeElement
Exposed
Description
Contains x and y coordinates for a two-dimensional point. Used for polygon
calculations.
Contains polar form for a two-dimensional point. Used primarily for code
addressing wind vectors.
Contains information on a three dimensional point. Used primarily for
polyhedra calculations.
Two-dimensional polygon; vertices are Point2D objects
Consists of a two-dimensional polygon (Polygon2D object) rotated into three
dimensional space. Used for polyhedra calculations and windspeed
calculations across cells.
Polyhedron in three-dimensional space; boundary consists of FacetSD
objects.
Object wrapper for general spatial routines.
Calculating the Convex Hull lor a Set of Points. Frequently it is necessary to calculate
the smallest convex region containing a set of two-dimensional points. This is primarily
performed after finding the points in the intersection of two convex polygons, where the points
must be reordered to preserve convexity. A convex region is one in which, for any two points
in the region, the line between the points is contained within the region. The smallest convex
region containing a set of points is called the "convex hull" for the points. The convex hull of
a set of points is determined using the subroutine CONVEX, which is Algorithm 523 of the
Association for Computing Transactions on Mathematical Software, written by W.F. Eddy
(ACM TOMS 3(1977) 411-412. The Fortran source code for this program was downloaded
from the NeiLib repository (http://www.netlib.org). It was compiled as a dynamic link library
("convexhull.dll") using Microsoft Fortran Powerstation 4.0.
Calculation of Interfacial Areas. For diffusive and advective transfers between abiotic
cells, it is necessary to calculate the area of the interfacial region defining the boundary
between the cells. In P4, the cells are assumed to be three-dimensional polyhedra whose
boundaries consist of a finite number of planar regions. The planar regions are referred to here
as facets or features. The facets consist of points in three-dimensional space all of which are in
the same plane. The interfacial area between two cells is calculated by first determining the
pairs of facets in the two cells which are in the same plane. Then, for each such facet pair, the
facets are rotated so that they are both parallel to the xy-plane (this is done using the normal
F-18
-------
vector to the plane containing the facet). At this point the z-coordinates are not necessary, and
the interfacial area can be determined by finding the area of the intersection of the polygons
resulting after omitting the z-coordinates. The convex polygon resulting from the intersection
is determined by first calculating the finding the points in the intersection and then finding the
convex hull containing these points. This is performed using the routine CONVEX described in
the previous section.
Implementation of Wind Field. The wind flow across an air cell boundary is calculated by
finding the projection of the wind vector onto the normal vector to the boundary between the
air cells. In P4, it is assumed that the boundary between air cells is a vertical plane, but the
method described below can be extended to more general boundaries. Implementation of these
methods is performed in the subroutines in the module
GetWindSpeedBetween Volume Elements, has
Let P,=(x,,y,) and P2=(x2,y2) be the points defining the line that is the projection of the boun-
dary onto the ry-plane (i.e., the view from above of the vertical plane defining the boundary).
It is assumed that the points P, and P2 are ordered so that the receiving cell is on the right side
of the directed line segment starting at P, and ending at P2. The unit vector v perpendicular to
this line segment that is in the direction of the receiving cell is given by
r(v2v,, (A:,*,)) (simp, cos
-------
w • v
y,r (*2 .*,)-
5 [sinO sincp cosO cosq>]
- [(y2 y,) sinft (x, x,) cosft]
Since v is a unit vector, the dot product in this case is the component of the vectorv? in the
direction of v . The wind flow rate from the sending cell to the receiving cell is defined to be
the dot product if it is positive, otherwise it is zero; i.e.,
„,. , , r ,. ,, . . ,,
Wind speed from sending cell to receiving cell
-v w
„ ,
If the wind is blowing perpendicular to the boundary, then the wind flow rate is just the wind
speed; otherwise it is flowing with a velocity less than the wind speed, the magnitude of which
depends on the difference in the angles of the wind speed and the boundary.
Summary of Classes and Subroutines
Table F-25
Point2D Class Properties and Methods
Properties
/ Methods
X
y
Type
Double
Double
Public or
Private
Public
Public
Comment
Other Procedures
Called
F-20
-------
Table F-26
PointSD Class Properties and Methods
Properties/
Methods
X
y
z
phi
6
P
dx
dy
dz
dphi
dtheta
drho
SetXYZ
Type
Double
Double
Double
Double
Double
Double
Double
Double
Double
Double
Double
Double
NA
Public or
Private
Public
Public
Public
Public
Public
Public
Private
Private
Private
Private
Private
Private
Private
Comment
Spherical coordinates for point.
Phi is the angle measured from
the positive z-axis (will always be
between 0 and n), 0 is the angle
measured counterclockwise
from the positive x-axis in the xy-
plane, and p is the distance from
the origin to the point. The
relationship between Cartesian
and spherical points is:
p = (x2 + y2 + z2)1'2
tan(9) = y/x
cos(phi) = z/p
x = p * sin (phi) * cos( 6)
y = p * sin (phi) * sin( 8)
z = p * cos(phi)
If any of the properties x, y, z,
phi, 6, or pare modified, then all
of the other properties are
automatically updated, as
necessary.
Private copy of x
Private copy of y
Private copy of z
Private copy of phi
Private copy of 6
Private copy of p
Calculates dx, dy, and dzfrom
current values of dphi, dtheta,
and drho. Called whenever phi,
6, or pare modified
Other Procedures
Called
F-21
-------
Table F-26
PointSD Class Properties and Methods
(Continued)
Properties/
Methods
SetrhoTheta
andPhi
TheAngle(x
as double.y
as double)
Acos(x as
double)
Writeout(Opti
onal Verbose
as Boolean =
false,
optional polar
as boolean =
false)
Draw(Radius
as double,
ViewPt as
Point3D,
Theform as
Object,
optional
zscale as
double=1.0,
optional
thickness as
integer,
optional
Eraselt as
Boolean)
Type
NA
Double
Double
String
NA
Public or
Private
Private
Private
Private
Public
Public
Comment
Calculates dphi, dtheta, and
drho from current values of dx,
dy, and dz. Called whenever x,
y, or z are modified.
Calculates the angle in radians
counterclockwise form the
positive x-axis. There is
currently a separate copy of this
function in the module
BasicF 'unctions
Calculates the inverse cosine of
x, returning a number between 0
and n. There is currently a
separate copy of this function in
the module BasicFunctions
Returns a text string containing
values for either Cartesian or
spherical coordinates for point.
Draws the point with a circle
around it on the form Theform
using the specified (three
dimensional) viewpoint. The z-
values are scaled by zscale, the
line has thickness 1 if no
thickness is specified, and the
facet is drawn in the color of the
background of the form if Eraselt
is True.
Other Procedures
Called
TheAngle
F-22
-------
Table F-27
Polygon2D Class Properties and Methods
Properties/
Methods
Vertices
Sides
NumberVertices
Area
lsVertex(Pt as
Point2D,
Tolerance as
Double, Index
as long,
NumberVertices
as long)
ReorderVertices
toPreserveConv
exity
AddVertex(The
Point as
Point2D)
Draw(Theform
as Object,
Optional
Thickness as
Integer)
Type
Collection
Collection
Long
Double
Boolean
NA
NA
NA
Public or
Private
Public
Public
Public
Public read
only
Public
Public
Public
Public
Comment
Collection of Point2D objects. In
P4, a Polygon2D object will
always be convex.
Collection of LineSegment
objects that make up the sides
of the polygon
Returns the area of the polygon
(see CalcArea function below).
Returns true if the point Pt is
within Tolerance of a vertex of
the polygon. NumberVertices is
the number of vertices that the
point Pt is within Tolerance of,
and Index is the index in the
Vertices collection of the last
vertex that satisfies this criterion.
The purpose of this subroutine is
to reorder the Vertices collection
so that the polygon defined by
Vertices(1), Vertices(2),... is
convex. Generally this method
is called after a vertex is added
or after the intersection of two
polygons is calculated. This
routine will not be necessary if
additional subroutines are added
to allow nonconvex regions.
Adds the point ThePointto the
Vertices collection and updates
the Sides collection.
Draws the polygon on the form
Theform
Other Procedures
Called
CalcArea
Convex (calculates
convex hull of a set
of two dimensional
points)
F-23
-------
Table F-27
Polygon2D Class Properties and Methods
(Continued)
Properties/
Methods
CalcArea
Type
Double
Public or
Private
Public read
only
Comment
Calculates the area of the
polygon, assuming that it is
convex. The convexity implies
that the polygon can be
triangulated by the triangles
(V(1),V(2),V(3)),
(V(1),V(3),V(4)), ...
V(1),V(N-1),V(N), where V(i) is
the ith ordered vertex and N is
the number of vertices.
Other Procedures
Called
TriangleArea2D in
the module "Basic
Functions"
(calculates the area
of a triangle defined
by three arbitrary
two dimensional
points)
Table F-28
PolarVector2D Class Properties and Methods
Properties/
Methods
Direction
Length
X
y
Draw(Theform
as object,
Optional
Thickness as
Integer,
Optional
Eraselt as
Boolean)
Type
Double
Double
Double
Double
NA
Public or
Private
Public
Public
Public read only
Public read only
Public
Comment
Degrees clockwise of the
positive y-axis
Length of vector
Abscissa of the endpoint of the
vector
Ordinate of the endpoint of the
vector
Draws the vector on the form
Theform. If Eraselt is true, then
the line is drawn using the
background color of the form.
Other Procedures
Called
F-24
-------
Table F-29
CVolumeElement Class Properties and Methods
Properties/
Methods
Draw(ViewPt
as PointSD,
Theform as
Object,
Optional
zscale as
double
(default=1 ),
optional
Thickness as
integer,
optional
Eraselt as
Boolean)
IslnDataBase
Facets
ID
Name
TypelD
TypeName
Volume
IsConnectedto
Database
UnHookFrom
DataBase
Database
TimeStep
Type
None
Boolean
Collection
Long
String
Long
String
Double
Boolean
NA
Database
Long
Public or
Private
Public
Public
Public
Public
Public
Public
Public
Public read only
Public read only
Public
Public
Public
Comment
Draws all of the facets in the
volume element on the form
Theform using the specified
(three dimensional) viewpoint.
The z-values are scaled by
zscale, the line has thickness 1 if
no thickness is specified, and
the facet is drawn in the color of
the background of the form if
Eraselt is True.
Returns true if the volume
element is in the most recent
database pointed to, else false
Collection of the facets that
make up the volume element
ID of volume element in
database
Key for volume element in
database
Type volume element (e.g.,
urban, agriculture)
Name for volume element type
Returns the volume of the
volume element via a call to
CalcVolume
Returns true if the database
property is set to a database
Sets database property to
nothing
Sets database for volume
element and reads in data to
define facets. It is assumed that
either the ID or Name property
have been set.
Not utilized
Other Procedures
Called
CalcVolume
Load Facets
F-25
-------
Table F-29
CVolumeElement Class Properties and Methods
(Continued)
Properties/
Methods
Add
(ciFacetSd as
FacetSD)
CalcVolume
Load Facets
Type
Integer
Double
Integer
Public or
Private
Public
Private
Private
Comment
Adds a facet to the Facet
collection. Returns 0 if
successful
Calculates the volume of the
volume element, assuming that
it is bounded above and below
by horizontal facets of the same
shape. In this case, the volume
reduces to the product of the
area of the top and the height.
Reads in facets from database.
Returns 0 if facets successfully
loaded. Called whenever the
database is set.
Other Procedures
Called
Add
F-26
-------
Table F-30
Exposed Class Properties and Methods
Properties/
Methods
myWindSpeed
FromVolumeEleme
ntAtoB
(VolA_Sending as
CvolumeElement,
VolB_Receiving as
CvolumeElement,
WindVector as
PolarVector2D)
myWindSpeedAcros
sVerticalPlane
(VerticalPlane as
FacetSD,
VolA_Sending as
CvolumeElement,
WindVector as
PolarVector2D)
myW indSpeedTowa
rdsRightSide(
(WindVector as
PolarVector2D,
PointStart as
Point2D, PotntSTop
as Point2D)
mySidePointisOn(Z
_1 as Point2D, Z_2
as Pomt2D, p as
Point2D)
myFindProjection(W
indVector as
PolarVector2D,
PointStart as
Pomt2D, PointStop
as Point2D)
myGrabFacet(ID as
Long, iTimeStep as
Long, dbData as
DataBase)
myReorderFacetSD
Vertices(facet as
FacetSD)
Type
Variant
Variant
Variant
Variant
Double
Facet3D
FacetSD
Public or
Private
Public
Public
Public
Public
Public
Public
Public
Comment
Returns windspeed across
boundary of intersection of
volume elements
Returns windspeed from volume
element to a facet (returns 0 if
facet is not vertical)
Returns the wind speed from left
to right side of the directed line
segment starting at PointStart
and ending at PointStop
Returns "left" if point p is on the
left of the directed line segment
starting at Z_1 and ending at Z_2,
else "right"
Returns the projection of the
vector WindVector onto the vector
that is perpendicular to the
directed line segment starting at
PointStart and ending at
PointStop, and pointing to the
right of the segment.
Returns the facet in the database
dbData that has the specified ID
Returns convex hull containing
facet (this is the smallest convex
region containing the facet).
Other Procedures
Called
WindSpeedFromVolume
ElementAtoB in module
GetWindSpeedBetween
VolumeElements.bas
WindSpeedAcrossFacet
in module
GetWindSpeedBetween
VolumeElements. has
WindSpeedTowardsRigh
tSide in
modulePro/'ecf/ons.bas
SidePointisOn in module
WhichSidelsPoint.bas
FindProjection in module
Projections.bas
ReorderFacetSdVertices
F-27
-------
Table F-30
Exposed Class Properties and Methods
(Continued)
' Properties/
Methods
myCreateFacet3D(p
oly2d as
Polygon2D, Height
as double,
NormalVector as
pointSD)
myFacetSdlntersecti
on(Facet1 as
FacetSD, Facet2 as
FacetSd,
IntersectionSd as
Facets D,
intersection2D as
Polygon2D)
myVolumeElementl
nterfaces(VolumeEI
ementA as
CVolumeElement,
VolumeElementB as
CVolumeElement)
myFeaturelnterface
s(ciFacet3DA as
FacetSD,
ciFacetSDB as
FacetSd)
Type
Facet3D
Boolean
Collection
Facet3D
Public or
Private
Public
Public
Public
Public
Comment
Returns the facet generated as
follows:
-Creates a three dimensional
facet from the two dimensional
polygon poly2d by setting the x-
and y-coordinates of each vertex
to those of the polygon, and the
z-coordinate to Height
- Rotates the facet about the
origin so that it has normal vector
NormalVector
Calculates the convex hull of the
intersection of two coplanar
facets
Returns collection of all facets
that result from the intersection of
the facets in each volume
element
Calculates the convex hull of the
intersection of two coplanar
facets
Other Procedures
Called
CreateFacetSD
FacetSdlntersection in
the module
BasicFunctions
VolumeElementlnterface
s in Globals
Feature Interfaces in
Globals
F-28
-------
Table F-31
FacetSD Class Properties and Methods
Properties/
Methods
a
d
c
d
HasSPoints
arrVertices
iNumVertices
TheVertices
mJID
m_ciP3DMinZ
pSdBasePoint
pSdNormalvector
NormalVector
PolygoninXYPIan
ePositiveZView
Type
Double
Double
Double
Double
Boolean
Point3D
Long
Collection
Long
PointSD
PointSD
PointSD
PointSD
Polygon2D
Public or
Private
Public
Public
Public
Public
Public
Private
Private
Public
Private
Private
Private
Private
Public
Public
Comment
The equation for the plane
containing the points in the facet
is given by
ax + by + cz + d = 0
Returns true if there are at least
three points in the facet
Array containing the points in the
facet
Number of points in the facet
Collection containing the points
in the facet
ID for the facet in database (not
required if facet is not created
from a database)
Point in the facet that has the
minimum z-value
pSdNormalVector is a unit vector
normal to the plane containing
the facet, and pSdBasePoint is a
point in the plane (set equal to
the first point added to the.
facet).
The equation for the plane
containing the facet can be
written
pSdNormal.x * (x -
pSdBasePoint.x) +
pSdNormal.y * (y -
pSdBasePoint.y) +
pSdNormal.z " (z
- pSdBasePoint.z) = 0
Returns the point (0,0,0) if the
facet has less than 3 points, else
it returns pSDNormalVector
Returns the two-dimensional
polygon that results when the
facet is viewed from the normal
vector
Other Procedures
Called
DRotatePoint in
BasicFunctions
F-29
-------
Table F-31
FacetSD Class Properties and Methods
(Continued)
Properties/
Methods
Vertex(i as long)
NumVertices
ID
PointMinZ
AddVertex(p3dPt
as PointSD)
lnPlane(Pt as
Pomt3D,
testTolerance as
Double)
Type
Point3D
Long
Long
PointSD
Long
Boolean
Public or
Private
Public
Public
Public
Public
Public
Public
Comment
Returns or sets the Ah vertex of
the facet: arrVertices(i)
Returns the number of vertices
in the facet
Returns or sets the ID for the
facet in the database
returns the vertex point with the
minimum z-value
Adds a point to the facet, if it is
in the plane containing the points
already in the facet and is not
too close to points already in the
facet. The return value will be:
0 if point added to
facet
1 if point is not in
plane containing
the points already
in the facet (with
tolerance 1 E-4)
2 if point is too close
to points already in
the facet (with
tolerance 1 E-4)
If the point is successfully added
to the facet and the resulting
number of points in the facet is
three, then the normal vector
and the constants a, b, c, and d
are calculated.
Returns true if the point Pt is in
the plane containing the facet.
else false. A point is in the plane
containing the facet if there are
less than three points in the
facet, or if
la'Pt.x + b'Pt.y + c'Pt.z + dl <;
testTolerance
Other Procedures
Called
InPlane
F-30
-------
Table F-31
FacetSD Class Properties and Methods
(Continued)
Properties/
Methods
Draw(ViewPt as
PointSD,
Theform as
Object, Optional
zscale as double
(default=1),
optional
Thickness as
integer, optional
Eraselt as
Boolean)
Type
None
Public or
Private
Public
Comment
Draws the facet on the form
Theform using the specified
(three dimensional) viewpoint.
The z-values are scaled by
zscale, the line has thickness 1 if
no thickness is specified, and
the facet is drawn in the color of
the background of the form if
Eraselt is True.
Other Procedures
Called
DRotatePoint in
BasicFunctions
F-31
-------
Table F-32
Subroutines and Functions in the Module BasicFunctions.bas
Name(Arguments)
Convex(N as Long, x
»as Double, M as
Long, M as Long,
IN_I as long, 1 A as
Long, IB as Long, IH
as Long, NH as
Long, IL as Long)
ReorderFacetSdVerti
ces(facet as
FacetSD)
FindThetaandPhi(p
as PointSD, 9 as
Double, phi as
double)
CreateFacet3d(poly2
d as Polygon2D,
Zvalue as Double,
NormalVector as
PointSD)
Facet3dlntersection(
Facetl as FacetSD,
Facet2 as FacetSd,
IntersectionSd as
FacetSD,
intersection2D as
Polygon2D)
TheAngle(x a
Double, y as Double)
Acos(x as Double)
Type
NA
FacetSD
NA
FacetSD
Boolean
Double
Double
Comment
Fortran dynamic link library to calculate the
convex hull of an arbitrary array of two
dimensional points
Returns facet that is the convex hull for facet.
This is performed by
- using the normal vector of the facet, facet is
rotated about the origin so that it is in a
horizontal plane (i.e., z-coordinate is equal to
some Hfor all vertices
- this facet is projected onto the xy-plane to
obtain a two dimensional polygon
- the convex hull of the polygon is calculated,
then translated to height H, and finally rotated
about the origin so that it has same normal
vector as the original facet
Calculates spherical coordinates for the three
dimensional point p
Creates a facet as follows:
- create a facet by translating the polygon
poly2d\o height Zvalue
- rotating the facet about the origin so that it
has normal vector NormalVector
Calculates the convex hull of the intersection
of two coplanar facets
Returns the angle (in radians) of the point
(x,y), measured counterclockwise from the
positive x-axis
Returns the inverse cosine of x; result will be
in the range 0 to n
Other Procedures
Called
CreateFacetSD
UndoDRotatePt
VectorNorm,
1 nte rsection Polygons2
D in Globals,
CreateFacetSD
F-32
-------
Table F-32
Subroutines and Functions in the Module BasicFunctions.bas
(Continued)
Name( Arguments)
TriangleArea2D(p1
as Point2D, p2 as
Point2D, p3 as
Point2D)
VectorNorm (Vector
as Object)
DotProduct(a as
Point2D, b as
Point2D)
DotProduct3D(a as
Point3D, b as
PointSD)
Linelntersection(Line
1 as LineSegment,
Line2 as
LineSegment,
Optional
Tolerance=0)
Parallel(Line1 as
LineSegment, Line2
as LineSegment,
Optional Tolerance
as Double=0)
Vertical(Line as
LineSegment,
optional Tolerance as
Double=0)
Horizontal(Line as
LineSegment,
optional Tolerance as
Double=0)
Type
Double
Double
Double
Double
Point2D
Boolean
Boolean
Boolean
Comment
Calculates the area of the triangle with
vertices at the points p1, p2, and p3. If we
define three dimensional vectors by s*Plp2 and
£=/>,Pi, then the area of the triangle can be
calculated as
Area = (l/2)|jxfc|,
where-x- is the vector cross product, andi r is
the vector norm.
Calculates the norm of
Vector = U,-t,. j;J by
VfdorNorm = HP x~
Currently checks to make sure Vector is either
a Point2D or PointSD object
Returns a.x*b.x + a.y+b.y
Returns a.x*b.x + a.y+b.y+a.z*b.z
Determines the intersection of the lines
containing the two line segments. Currently it
is assumed that lines are not parallel (the
function Parallel is called before this function
is called).
Returns true if the lines are parallel, else false
Returns true if distance between x-
coordinates of starting and ending points of
the line segment is less than Tolerance
Returns true if distance between y-
coordinates of starting and ending points of
the line segment is less than Tolerance
Other Procedures
Called
CrossProduct
VectorNorm
Vertical
Vertical
F-33
-------
Table F-32
Subroutines and Functions in the Module BasicFunctions.bas
(Continued)
Name( Arguments)
Type
Comment
Other Procedures
Called
CrossProduct(u as
PointSD, v as
PointSD)
PointSD
Calculates cross product »• =«* v:
wx = u vv.z-v y*u z
w \ = -(u x*v.i-v x*u z)
H'.Z= U X'V \ -V.Jt»U V
RotatePt(Pt as
PointSD, ViewPt as
PointSD)
PointSD
Rotates the point Pt about the z-axis and then
about the y-axis in the same manner that
rotates ViewPt so that it lies on the positive x-
axis.
RotateAboutZAxis
RotateAboutYAxisD
DRotatePt(Pt as
PointSD, ViewPt as
PointSD)
PointSD
Rotates the point Pt about the z-axis and then
about the y-axis in the same manner that
rotates ViewPt so that it lies on the positive z-
axis. In particular, if the spherical coordinates
of ViewPt are given by (p,cp,9), then the point
Pt is subjected to two consecutive rotations:
- first rotated clockwise about the z-axis with
angle 8 (this rotation would move ViewPt so
that it lies in the xz-plane)
- next rotated counterclockwise about the y-
axis with angle cp (this rotation would move
ViewPt so that it lies in the yz-plane)
RotateAboutZAxis
RotateAboutYAxis
UndoDRotatePt(Pt as
PointSD, ViewPt as
PointSD)
PointSD
This is the inverse of DrotatePt:
UndoDRotatePt(DrotatePt(Pf, ViewPf))=Pt for
any Pt and any ViewPt.
It is used primarily to create facets from
polygons with prescribed normal vectors.
If the spherical coordinates of ViewPt are
given by (p,cp,9), then the point Pt is subjected
to two consecutive rotations:
- rotated clockwise about the y-axis with angle
-cp; this rotation would move the point (p,0,0)
to the point (p.cp.O)
-rotated counterclockwise about the z-axis
with angle -9; this rotation would move
(p.cp.O) to (p,cp,9)
RotateAboutZAxis
RotateAboutYAxis
F-34
-------
Table F-32
Subroutines and Functions in the Module BasicFunctions.bas
(Continued)
Name( Arguments)
RotateAbout2Axis(Pt
as Point3D, Angle as
Double)
RotateabdoutXAxis(P
t as PointSD, Angle
as Double)
RotateAboutYAxis(Pt
as PointSD, Angle as
Double)
Type
Point3D
PointSD
Comment
Rotates Pt clockwise by an angle Angle (in
radians) about the z-axis. This leaves the z-
coordinate unchanged; in particular, the
function returns the vector VP given by
H-J = Pi **cos( -Angle} - Pt\ •iin(-Anj?/f)
K i = Pi x-s\n(-Angle) • Pi \ *cos(-Angte)
Rotates Pt counterclockwise by an angle
Angle (in radians) about the y-axis. This
leaves the y-coordinate unchanged; in
particular, the function returns the vector *
given by
wx-Pii-coXAngM-Ptz-sirtAngle)
« \ = PM
H - = ftjfsinlAnjs/f) • Pi Z'Cos(Anelf)
Other Procedures
Called
F-35
-------
TECHNICAL REPORT DATA
(Please read Instructions on reverse before completing)
1. REPORT NO. 2.
EPA-452/D-98-001
4 TITLE AND SUBTITLE
The Total Risk Integrated Methodology: Technical Support
Document for the TRIM.FaTE Module, Draft
7. AUTHOR(S)
U.S. EPA
9. PERFORMING ORGANIZATION NAME AND ADDRESS
U.S. Environmental Protection Agency
Office of Air Quality Planning and Standards
AQSSD/REAG (MD-15)
Research Triangle Park, NC 27711
12. SPONSORING AGENCY NAME AND ADDRESS
Office of Air Quality Planning and Standards
Office of Air and Radiation
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
3. RECIPIENT'S ACCESSION NO.
5. REPORT DATE
March 1998
6. PERFORMING ORGANIZATION CODE
Office of Air and Radiation
8. PERFORMING ORGANIZATION REPORT NO.
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
13. TYPE OF REPORT AND PERIOD COVERED
Draft
14. SPONSORING AGENCY CODE
EPA/200/04
15. SUPPLEMENTARY NOTES
U.S. EPA Project Officer: Amy B. Vasu
16. ABSTRACT
The Total Risk Integrated Methodology (TRIM) is a modeling system for the assessment of human health
and ecological risk resulting from exposure to hazardous and criteria air pollutants. This report describes
the first phase of development of the TRIM.FaTE module (the environmental fate, transport, and exposure
module of TRIM) and provides detailed information (mathematical derivations, data inputs, justifications)
supporting the testing and implementation of the TRIM.FaTE module.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
Multimedia modeling; fate; transport; exposure;
risk assessment
18 DISTRIBUTION STATEMENT
Release Unlimited
b. IDENTIFIERS/OPEN ENDED TERMS
Air pollution
19. SECURITY CLASS (Report)
Unclassified
20. SECURITY CLASS (Page)
Unclassified
c. COSATI Field/Group
21. NO OF PAGES
356
22. PRICE
EPA Form 2220-1 (Rev. 4-77) PREVIOUS EDITION IS OBSOLETE
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Table F-33
Subroutines and Functions in the Module
GetWindSpeedBetweenVolumeElements.bas
Properties/ Methods
WindSpeedAcrossfacet(
VerticalPlane as
FacetSD, VolA_Sending
as CvolumeElement,
WindVector as
PolarVector2D)
WindSpeedFromVolume
ElementAtoB
(VolA_Sending as
CvolumeElement,
VolB_Receiving as
CvolumeElement,
WindVector as
PolarVector2D)
Type
Variant
Variant
Comment
Returns windspeed from volume
element to a facet (returns 0 if facet
is not vertical)
Returns windspeed across vertical
boundary of intersection of volume
elements
Other Procedures
Called
W indSpeed Acrossf acet
Table F-34
Subroutines and Functions in the Module Globals.bas
Properties/Methods
lntersectionPolygons2D(
Polyl as Polygon2D,
Poly2 as Polygon2D)
lnConvexPolygon(Pt as
Point2D, poly as
Polygon2D)
VolumeElementlnterface
s(VolumeElementA as
CvolumeElement,
VolumeElementB as
CVolumeElement)
Featurelnterfaces(ciFacet
3DA as FacetSD,
ciFacet3DB as FacetSd)
Type
Polygon2D
Boolean
Collection
Facet3 D
'Comment
Calculates the intersection of two
polygons. It is assumed that the
polygons are convex.
Returns true if the point Pt is in the
convex polygon poly, otherwise
false.
Returns collection of all facets that
result from the intersection of the
facets in each volume element
Calculates the convex hull of the
intersection of two coplanar facets
Other Procedures
Called
Convex
F-36
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Table F-35
Subroutines and Functions in the Module Projections.bas
Properties/Methods
WindSpeedTowardsRi
ghtSide( (WindVector
as PolarVector2D,
PointStart as Point2D,
PointSTop as
Point2D)
FindProjection(WindV
ector as
PolarVector2D,
PointStart as Point2D,
PointStop as Point2D)
Type
Variant
Double
Comment
Returns the wind speed from left to
right side of the directed line
segment starting at PointStart and
ending at PointStop
Returns the projection of the vector
WindVector onto the vector that is
perpendicular to the directed line
segment starting at Po/nfSfart and
ending at PointStop, and pointing to
the right of the segment.
Other Procedures
Called
FindProjection
MyDotProduct via
Routines. myDotProdu
ct, where Routines is
an Exposed object
instance
Table F-36
Subroutines and Functions in the Module WhichSidelsPoint.bas
Properties/Methods
SidePointisOn(Z_1 as
Point2D, Z_2 as
Point2D, p as Point2D)
Type
Variant
Comment
Returns "left" if point p is on the left
of the directed line segment starting
at Z_1 and ending at Z_2, else
"right"
Other Procedures
Called
TheAngle
References:
W. F. Eddy, Algorithm 523: CONVEX, A New Convex Hull Algorithm for Planar Sets, ACM
TOMS 3(1977) 411-412.
F.4 Alpha Version
The working alpha version of P4 for TRIM.FaTE can be downloaded from the following
World Wide Web site:
www.epa.gov/oar/oaqps
A printout of the source code is available upon request.
F-37
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