&EPA
United States
Environmental Protection
Agency
Office of Research and
Development
Washington, DC 20460
EPA/600/R-93/046
March 1993
PRZM-2, A Model for
Predicting Pesticide
Fate in the Crop
Root and Unsaturated
Soil Zones:
Users Manual for
Release 2.0
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EPA/600/R-93/046
March 1993
PRZM-2, A Model for Predicting Pesticide Fate
in the Crop Root and Unsaturated Soil Zones:
Users Manual for Release 2.0
by
J.A. Mullins.'R.F. Carsel,2
J.E. Scarbrough.'and A.M. Ivery1
AScI Corporation
Athens, GA 30605-2720
Environmental Research Laboratory
U.S. Environmental Protection Agency
Athens, GA 30605-2720
ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ATHENS, GA 30605-2720
iXO Printed on Recycled Paper
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DISCLAIMER
The information in this document has been funded wholly or in part by the United
States Environmental Protection Agency under Contract No. 68-CO-0054 to AScI It has
been subject to the Agency's peer and administrative review, and it has been approved for
publication as an EPA document. Mention of trade names of commercial products does
not constitute endorsement or recommendation for use by the U.S. Environmental
Protection Agency.
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FOREWORD
As environmental controls become more costly to implement and the penalties of
judgment errors become more severe, environmental quality management requires more
efficient analytical tools based on greater knowledge of the environmental phenomena to
be managed. As part of this Laboratory's research on the occurrence, movement, transfor-
mation, impact, and control of environmental contaminants, the Assessment Branch
develops management or engineering tools to help pollution control officials reach
decisions on the registration and restriction of pesticides used for agricultural purposes.
The pesticide regulatory process requires that the potential risk to human health
resulting from the introduction or continued use of these chemicals be evaluated.
Recently much of this attention has been focused on exposure through leaching of
pesticides to groundwater and subsequent ingestion of contaminated water. To provide a
tool for evaluating this exposure, the PRZM-2 model was developed. PRZM-2 simulates
the transport of field-applied pesticides in the crop root zone and the vadose zone taking
into account the effects of agricultural management practices. The model further provides
estimates of probable exposure concentrations by taking into account the variability in the
natural systems and the uncertainties in system properties and processes.
Rosemarie C. Russo, Ph.D.
Director
Environmental Research Laboratory
Athens, Georgia
111
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ABSTRACT
This publication contains documentation for the PRZM-2 model. PRZM-2 links two
subordinate models-PRZM and VADOFT-- in order to predict pesticide transport and
transformation down through the crop root, and unsaturated zone. PRZM is a one-
dimensional, finite-difference model that accounts for pesticide fate in the crop root zone,
This release of PRZM-2 incorporates several features in addition to those simulated in the
original PRZM code-specifically, soil temperature simulation, volatilization and vapor
phase transport in soils, irrigation simulation, microbial transformation, and a method of
characteristics (MOC) algorithm to eliminate numerical dispersion. PRZM is now capable
of simulating transport and transformation of the parent compound and as many as two
daughter species. VADOFT is a one-dimensional, finite-element code that solves the Rich-
ard's equation for flow in the unsaturated zone. The user may make use of constitutive
relationships between pressure, water content, and hydraulic conductivity to solve the
flow equations. VADOFT may also simulate the fate of two parent and two daughter
products. The PRZM and VADOFT codes are linked together with the aid of a flexible
execution supervisor that allows the user to build loading models that are tailored to site-
specific situations. In order to perform probability-based exposure assessments, the code
is also equipped with a Monte Carlo pre- and post-processor.
IV
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TABLE OF CONTENTS
Page
Disclaimer ii
Foreword iii
Abstract iv
Figures x
Tables xiv
Acknowledgments xix
Section
1.0 INTRODUCTION 1-1
1.1 Background and Objectives 1-1
1.2 Concept of Risk and Exposure Assessment 1-2
1.3 Overview of PRZM-2 1-7
1.3.1 Overview of PRZM 1-8
1.3.1.1 Features 1-8
1.3.1.2 Limitations 1-9
1.3.2 Overview of the Vadose Zone Flow and
Transport Model (VADOFT) 1-11
1.3.2.1 Features 1-11
1.3.2.2 Limitations 1-11
1.3.3 Overview of the Monte Carlo Simulation Module 1-12
1.3.4 Model Linkage 1-12
1.3.4.1 Temporal Model Linkage 1-12
1.3.4.2 Spatial Linkages 1-13
1.3.5 Monte Carlo Processor 1-13
1.3.6 Overview Summary 1-14
2.0 MODEL DEVELOPMENT, DISTRIBUTION, AND SUPPORT 2-1
2.1 Development and Testing 2-1
2.2 Distribution 2-2
2.3 Obtaining a copy of the PRZM-2 Model 2-3
2.3.1 Diskette 2-3
2.3.2 Electronic Bulletin Board System (BBS) 2-3
2.4 General/Minimum Hardware and Software
Installation and Run-Time Requirements 2-4
2.4.1 Installation Requirements 2-4
2.4.2 Run Time Requirements 2-4
2.5 Installation 2-4
2.6 Installation Verification and Routine Execution 2-5
2.7 Code Modification 2-5
2.8 Technical Help 2-5
2.9 Disclaimer 2-7
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TABLE OF CONTENTS (continued)
Section Page
2.10 Trademarks 2-7
3.0 MODULES AND LOGISTICS 3-1
4.0 INPUT PARAMETERS FOR PRZM-2 4-1
4.1 Input File Descriptions 4-1
4.1.1 Meteorological File 4-2
4.1.2 Execution Supervisor File..., 4-2
4.1.2.1 Example Execution Supervisor 4-3
4.1.2.2 Example Execution Supervisor 4-4
4.1.2.3 Execution Supervisor Input Guide 4-5
4.1.3 PRZM Input File 4-7
4.1.3.1 Example PRZM Input File 4-7
4.1.3.2 PRZM Input Guide 4-8
4.1.4 VADOFT Input File 4-24
4.1.4.1 Example VADOFT Input File 4-24
4.1.4.2 VADOFT Input Guide for FLOW 4-25
4.1.4.3 VADOFT Input Guide for TRANSPORT 4-32
4.1.5 MONTE CARLO Input File 4-39
4.1.5.1 Example MONTE CARLO Input File 4-39
4.1.5.2 MONTE CARLO Input Guide 4-40
5.0 PARAMETER ESTIMATION 5-1
5.1 EXESUP (Execution Supervisor) 5-1
5.2 PRZM (Pesticide Root Zone Model) 5-2
5.3 VADOFT Parameters 5-62
6.0 PRZM CODE AND THEORY 6-1
6.1 Introduction and Background (PRZM) 6-1
6.1.1 Introduction 6-1
6.1.2 Background 6-2
6.2 Features and Limitations 6-2
6.2.1 Features 6-2
6.2.2 Limitations 6-4
6.3 Description of the Equations 6-6
6.3.1 Transport in Soil 6-6
6.3.2 Water Movement 6-14
6.3.2.1 Option 6-20
6.3.2.2 Option 2 6-20
6.3.3 Soil Erosion 6-21
vi
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TABLE OF CONTENTS (continued)
Section Page
6.3.4 Volatilization 6-22
6.3.4.1 Soil Vapor Phase and Volat. Flux 6-23
6.3.4.2 Volat. Flux Through the Plant Canopy 6-25
6.3.4.3 Volat. Flux from Plant Surfaces 6-30
6.3.4.4 Soil Temperature Simulation 6-31
6.3.5 Irrigation Equations 6-40
6.3.5.1 Soil Moisture Deficit 6-41
6.3.5.2 Sprinkler Irrigation 6-41
6.3.5.3 Flood Irrigation 6-42
6.3.5.4 Furrow Irrigation 6-42
6.4 Numerical Solution Techniques 6-44
6.4.1 Chemical Transport Equations 6-44
6.4.2 Volatilization 6-46
6.4.3 Soil Temperature 6-49
6.4.4 Furrow Irrigation 6-50
6.5 Results of PRZM Testing Simulations 6-52
6.5.1 Transport Equation Solution Options 6-53
6.5.1.1 High Peclet Number 6-53
6.5.1.2 Low Peclet Number 6 53
6.5.2 Testing Results of Volatilization Subroutines 6-54
6.5.2.1 Comparison with Analytical Sol 6-54
6.5.2.2 Comparison with Field Data 6-67
6.5.2.3 Conclusions from Volatilization Model Testing ...... 6-65
6.5.3 Testing Results of Soil Temp. Simulation Subroutine 6-68
6.5.4 Testing of Daughter Products Simulation 6-69
6.6 Biodegradation Theory and Assumptions 6-79
7.0 VADOFT CODE AND THEORY 7-1
7.1 Introduction 7-1
7.2 Overview of VADOFT
7.2.1 Features 7-1
7.2.1.1 General Description 7-1
7.2.1.2 Process and Geometry 7-1
7.2.1.3 Assumptions 7-1
7.2.1.4 Data Requirements 7-2
7.2.2 Limitations 7-2
7.3 Description of the Flow Module 7-3
7.3.1 Flow Equation 7-3
7.3.2 Numerical Solution 7-6
7.3.2.1 Numerical Appr. of the Flow Eq 7-6
VII
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TABLE OF CONTENTS (continued)
Section Page
7.3.2.2 General Guidance on Selection of Grid Spacings
and Time Steps, and the Use of
Solution Algorithms 7-15
7.4 Description of the Transport Module 7-15
7.4.1 Transport Equation 7-15
7.4.2 Numerical Solution of the Transport Equation 7-16
7.4.2.1 Numerical Appr. of the Transport
Equation 7-16
7.5 Results of VADOFT Testing Simulations 7-19
7.5.1 Flow Module 7-19
7.5.1.1 Transient Upward Flow 7-19
7.5.1.2 Steady Infiltration 7-19
7.5.2 Transport Module 7-20
7.5.2.1 Transport in a Semi-Infinite
Soil Column 7-20
7.5.2.2 Transport in a Finite Soil Column 7-20
7.5.2.3 Transport in a Layered Soil Column 7-20
7.5.3 Combined Nonlinear Flow and Transport Modules 7-32
7.5.3.1 Transport During Absorption of
Water in a Soil Tube 7-32
7.5.3.2 Transient Infiltration and Contam-
inant Transport in the Vadose Zone 7-32
8.0 UNCERTAINTY PREPROCESSOR 8-1
8.1 Introduction 8-1
8.2 Overview of the Preprocessor 8-1
8.2.1 Description of the Method 8-2
8.2.2 Uncertainty in the Input Variables 8-3
8.3 Description of Available Parameter Distributions 8-4
8.3.1 Uniform Distribution 8-4
8.3.2 Normal Distribution 8-5
8.3.3 Log-Normal Distribution 8-6
8.3.4 Exponential Distribution 8-6
8.3.5 The Johnson System of Distributions 8-7
8.3.6 Triangular Distribution 8-7
8.3.7 Empirical Distribution 8-8
8.3.8 Uncertainty in Correlated Variables 8-8
8.3.9 Generation of Random Numbers 8-13
8.4 Analysis of Output and Estimation of Distribution
Quantizes 8-13
8.4.1 Estimating Distribution Quantizes 8-14
8.4.2 Confidence of up 8-16
viii
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TABLE OF CONTENTS (continued)
Section
9.0 REFERENCES
10.0 APPENDICES 10-1
10.1 Error Messages and Warnings 10-1
10.2 Variable Glossary 10-1
10.3 PRZM and VADOFT Example Input Files 10-70
IX
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LIST OF FIGURES
1.1 DECISION PATH FOR RISK ASSESSMENT 1-3
1.2 TIME SERIES PLOT OF TOXICANT CONCENTRATIONS 1-5
1.3 FREQUENCY DISTRIBUTION OF TOXICANT CONCENTRATIONS 1-5
1.4 CUMULATIVE FREQUENCY DISTRIBUTION OF TOXICANT
CONCENTRATIONS 1-5
1.5 TIME SERIES OF TOXICANT CONCENTRATIONS WITH MOVING
AVERAGE WINDOW OF DURATION!^ 1-6
1.6 LINKED MODELING SYSTEM CONFIGURATION 1-6
5.1 PAN EVAPORATION CORRECTION FACTORS 5-18
5.2 DIAGRAM FOR ESTIMATING SOIL EVAPORATION LOSS 5-19
5.3 REPRESENTATIVE REGIONAL MEAN STORM DURATION VALUES
FOR THE UNITED STATES 5-20
5.4 DIAGRAM FOR ESTIMATING SOIL CONSERVATION SERVICE SOIL
HYDROLOGIC GROUPS 5-21
5.5 NUMERICAL DISPERSION ASSOCIATED WITH SPACE STEP 5-22
5.6 PHYSICAL DISPERSION ASSOCIATED WITH ADJECTIVE TRANSPORT . . .5-23
5.7 AVERAGE TEMPERATURE OF SHALLOW GROUNDWATER 5-24
5.8 1/3-BAR SOIL MOISTURE BY VOLUME 5-25
5.9 15-BAR SOIL MOISTURE BY VOLUME 5-26
5.10 MINERAL BULK DENSITY 5-27
5.11 ESTIMATION OF DRAINAGE RATE AD VERSUS NUMBER OF
COMPARTMENTS 5-28
6.1 PESTICIDE ROOT ZONE MODEL 6-3
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LIST OF FIGURES
Figure Page
6.2 SCHEMATIC REPRESENTATION OF A SINGLE CHEMICAL IN A SOIL
LAYER [[[ 6-7
6.3 SCHEMATIC OF PESTICIDE VAPOR AND VOLATILIZATION PROCESSES . .6-24
6.4 VARIABILITY OF INFILTRATION DEPTHS WITHIN AN IRRIGATION
FURROW [[[ 6-43
6.5 SCHEMATIC OF THE TOP TWO SOIL COMPARTMENTS AND THE
OVERLYING SURFACE COMPARTMENT .............................. 6-48
6.6 COMPARISON OF SIMULATION RESULTS AT HIGH PECLET NUMBER ..... 6-55
6.7 COMPARISON OF SIMULATION RESULTS AT LOW PECLET NUMBER ...... 6-56
6.8 COMPARISON OF VOLATILIZATION FLUX PREDICTED BY PRZM AND
JURY'S ANALYTICAL SOLUTION: TEST CASES #1 AND #2 ................ 6-59
6.9 COMPARISON OF VOLATILIZATION FLUX PREDICTED BY PRZM AND
JURY'S ANALYTICAL SOLUTION: TEST CASES #3 AND #4 ................ 6-60
6.10 SENSITIVITY OF CUMULATIVE VOLATILIZATION FLUX TO
DECAY RATE, ............................................. 6-63
6.11 EFFECTS OF DELX ON VOLATILIZATION FLUX AND PESTICIDE
DECAY [[[ 6-64
6.12 COMPARISON OF CONSTANT AND TWO-STEP DECAY RATES ............ 6-66
6.13 EFFECTS OF TWO-STEP DECAY RATES ON VOLATILIZATION
FLUX AND PESTICIDE DECAY ................................. 6-67
6.14 COMPARISON OF SOIL TEMPERATURE PROFILES PREDICTED BY
ANALYTICAL AND FINITE DIFFERENCE SOLUTIONS (Time Step=l HR) . . . .6-70
6.15 COMPARISON OF SOIL TEMPERATURE PROFILES PREDICTED BY
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LIST OF FIGURES (Continued)
Page
6.17 CONVERSION OF d TO C$ TO Q WITH NO ADSORPTION
AND NO DECAY 6-76
6.18 CONVERSION OF CJ TO C2 TO Oj WITH DECAY BUT NO
ADSORPTION 6-77
6.19 CONVERSION OF ALDICARB TO ALDICARB SULFOXIDE TO
ALDICARB SULFONE 6-78
7.1 LOGARITHMIC PLOT OF CONSTITUTIVE RELATIONS FOR CLAY, CLAY
LOAM, AND LOAMY SAND 7-7
7.2 LOGARITHMIC PLOT OF CONSTITUTIVE RELATIONS FOR SILT, SILTY
CLAY LOAM, SILTY CLAY, AND SILTY LOAM 7-8
7.3 LOGARITHMIC PLOT OF CONSTITUTIVE RELATIONS FOR SANDY CLAY,
SANDY CLAY LOAM, SANDY LOAM, ND SAND 7-9
7.4 STANDARD PLOT OF RELATIVE PERMEABILITY VS. SATURATION FOR
CLAY, CLAY LOAM, LOAM, AND LOAMY SAND 7-10
7.5 STANDARD PLOT OF RELATIVE PERMEABILITY VS. SATURATION FOR
SILT, SILT CLAY LOAM, SILTY CLAY, AND SILTY LOAM 7-11
7.6 STANDARD PLOT OF RELATIVE PERMEABILITY VS. SATURATION FOR
SANDY CLAY, SANDY CLAY LOAM, SANDY LOAM, AND SAND 7-12
7.7 FINITE ELEMENT DISCRETIZATION OF SOIL COLUMN SHOWING NODE
AND ELEMENT NUMBERS 7-13
7.8 SIMULATED PRESSURE HEAD PROFILES FOR THE PROBLEM OF
TRANSIENT UPWARD FLOW IN A SOIL COLUMN 7-22
7.9 SIMULATED PROFILE OF WATER SATURATION FOR THE PROBLEM OF
TRANSIENT UPWARD FLOW IN A SOIL COLUMN 7-23
7.10 SIMULATED PRESSURE HEAD PROFILES FOR FIVE CASES OF
THE PROBLEM OF STEADY INFILTRATION IN A SOIL COLUMN 7-25
xn
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LIST OF FIGURES (Continued)
Figure Page
7.11 SIMULATED PROFILES OF WATER SATURATION FOR FIVE CASES
OF THE PROBLEM OF STEADY INFILTRATION IN A SOIL COLUMN 7-26
7.12 SIMULATED CONCENTRATION PROFILES FOR THE PROBLEM OF SOLUTE
TRANSPORT IN A SEMI-INFINITE SOIL COLUMN 7-27
7.13 SIMULATED CONCENTRATION PROFILES FOR TWO CASES OF
THE PROBLEM OF SOLUTE TRANSPORT IN A SOIL COLUMN OF
FINITE LENGTH 7-30
7.14 SIMULATED OUTFLOW BREAKTHROUGH CURVE FOR CASE 1
OF THE PROBLEM OF SOLUTE TRANSPORT IN A LAYERED
SOIL COLUMN 7-33
7.15 SIMULATED OUTFLOW BREAKTHROUGH CURVE FOR CASE 2
OF THE PROBLEM OF SOLUTE TRANSPORT IN A LAYERED
SOIL COLUMN 7-34
7.16 ONE-DIMENSIONAL SOLUTE TRANSPORT DURING ABSORPTION
OF WATER IN A SOIL TUBE 7-39
7.17 SIMULATED PROFILES OF WATER SATURATION DURING ABSORP-
TION OF WATER IN A SOIL TUBE 7-40
7.18 SIMULATED CONCENTRATION PROFILES FOR THE PROBLEM OF
ONE-DIMENSIONAL SOLUTE TRANSPORT DURING ABSORPTION
OF WATER IN A SOIL TUBE 7-41
7.19 PROBLEM DESCRIPTION FOR TRANSIENT INFILTRATION AND
TRANSPORT IN THE VADOSE ZONE 7-42
7.20 INFILTRATION RATE VS. TIME RELATIONSHIP USED IN
NUMERICAL SIMULATION 7-43
7.21 SIMULATED WATER SATURATION PROFILES 7-44
7.22 SIMULATED PRESSURE HEAD PROFILES 7-45
7.23 SIMULATED VERTICAL DARCY VELOCITY PROFILES 7-46
7.24 SIMULATED SOLUTE CONCENTRATION PROFILES 7-47
8.1 TRIANGULAR PROBABILITY DISTRIBUTION 8-9
xiii
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LIST OF TABLES
Table page
3-1 LIST OF SUBROUTINES AND FUNCTIONS AND A BRIEF DESCRIPTION OF
THEIR PURPOSE 3-2
3-2 LIST OF ALL PARAMETER FILES, PARAMETER DIMENSIONS, AND
A BRIEF DESCRIPTION 3-6
4-1 VARIABLE DESIGNATIONS FOR PLOTTING FILES 4-21
4-2 MONTE CARLO INPUT AND OUTPUT LABELS 4-43
5-1 TYPICAL VALUES OF SNOWMELT (SFAC) AS RELATED
TO FOREST COVER 5-29
5-2 MEAN DURATION (HOURS) OF SUNLIGHT FOR LATITUDES 0° TO 50° IN
THE NORTHERN AND SOUTHERN HEMISPHERES 5-29
5-3 INDICATIONS OF THE GENERAL MAGNITUDE OF THE
SOIL/ERODIBILITY FACTOR, K 5-30
5-4 INTERCEPTION STORAGE FOR MAJOR CROPS 5-30
5-5 VALUES OF THE EROSION EQUATION'S TOPOGRAPHIC FACTOR, LS,
FOR SPECIFIED COMBINATIONS OF SLOPE LENGTH AND STEEPNESS . .5-31
5-6 VALUES OF SUPPORT-PRACTICE FACTOR, P 5-32
5-7 GENERALIZED VALUES OF THE COVER AND WAGEMENT FACTOR, C,
IN THE 37 STATES EAST OF THE ROCKY MOUNTAINS ., 5-33
5-8 MEAN STORM DURATION (TR) VALUES FOR SELECTED CITIES 5-33
5-9 AGRONOMIC DATA FOR MAJOR AGRICULTURAL CROPS IN THE
UNITED STATES 5-37
5-10 RUNOFF CURVE NUMBERS FOR HYDROLOGIC SOIL-
COVER COMPLEXES 5-38
5-11 METHOD FOR CONVERTING CROP YIELDS TO RESIDUE 5-39
5-12 RESIDUE REMAINING FROM TILLAGE OPERATIONS 5-39
5-13 REDUCTION IN RUNOFF CURVE NUMBERS CAUSED BY
CONSERVATION TILLAGE AND RESIDUE MANAGEMENT 5-40
xiv
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LIST OF TABLES (Continued)
Table Page
5-14 VALUES FOR ESTIMATING WFMAX IN EXPONENTIAL
FOLIAR MODEL 5-40
5-15 PESTICIDE SOIL APPLICATION METHODS AND DISTRIBUTION 5-41
5-16 MAXIMUM CANOPY HEIGHT AT CROP MATURATION 5-41
5-17 DEGRADATION RATE CONSTANTS OF SELECTED PESTICIDES
ON FOLIAGE 5-42
5-18 ESTIMATED VALUES OF HENRY'S CONSTANT FOR SELECTED
PESTICIDES 5-43
5-19 PHYSICAL CHARACTERISTICS OF SELECTED PESTICIDES
FOR USE IN DEVELOPMENT OF PARTITION COEFFICIENTS
AND REPORTED DEGRADATION RATE CONSTANTS IN SOIL
ROOT ZONE 5-44
5-20 OCTANOL WATER DISTRIBUTION COEFFICIENTS AND SOIL
DEGRADATION RATE CONSTANTS FOR SELECTED CHEMICALS 5-47
5-21 ALBEDO FACTORS OF NATURAL SURFACES FOR SOLAR
RADIATION 5-49
5-22 EMISSMTY VALUES FOR NATURAL SURFACES AT NORMAL
TEMPERATURES 5-50
5-23 COEFFICIENTS FOR LINEAR REGRESSION EQUATIONS FOR
PREDICTION OF SOIL WATER CONTENTS AT SPECIFIC
MATRIC POTENTIALS 5-50
5-24 THERMAL PROPERTIES OF SOME SOIL AND REFERENCE
MATERIALS 5-51
5-25 HYDROLOGIC PROPERTIES BY SOIL TEXTURE 5-52
5-26 DESCRIPTIVE STATISTICS AND DISTRIBUTION MODEL FOR
FIELD CAPACITY 5-53
5-27 DESCRIPTIVE STATISTICS AND DISTRIBUTION MODEL FOR
WILTING POINT, 5-54
xv
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LIST OF TABLES (Continued)
Table Page
5-28 CORRELATIONS AMONG TRANSFORMED VARIABLES OF ORGANIC
MATTER, FIELD CAPACITY, AND WILTING POINT 5-55
5-29 MEAN BULK DENSITY FOR FIVE SOIL TEXTURAL
CLASSIFICATIONS 5-56
5-30 DESCRIPTIVE STATISTICS FOR BULK DENSITY 5-56
5-31 DESCRIPTIVE STATISTICS AND DISTRIBUTION MODEL FOR
ORGANIC MATTER 5-57
5-32 ADAPTATIONS AND LIMITATIONS OF COMMON IRRIGATION
METHODS 5-58
5-33 WATER REQUIREMENTS FOR VARIOUS IRRIGATION AND
SOIL TYPES 5-58
5-34 REPRESENTATIVE FURROW PARAMETERS DESCRIBED IN THE
LITERATURE 5-59
5-35 FURROW IRRIGATION RELATIONSHIPS FOR VARIOUS SOILS,
SLOPES, AND DEPTHS OF APPLICATION 5-59
5-36 SUITABLE SIDE SLOPES FOR CHANNELS BUILT IN VARIOUS
KINDS OF MATERIALS 5-60
5-37 VALUE OF "N" FOR DRAINAGE DITCH DESIGN 5-60
5-38 REPRESENTATIVE PERMEABILITY RANGES FOR SEDIMENTARY
MATERIALS 5-61
5-39 VALUES OF GREEN-AMPT PARAMETERS FOR SCS HYDROLOGIC
SOIL GROUPS 5-61
5-40 DESCRIPTIVE STATISTICS FOR SATURATED HYDRAULIC
CONDUCTIVITY 5-64
5-41 DESCRIPTIVE STATISTICS FOR VAN GENUCHTEN WATER
RETENTION MODEL PARAMETERS, a, & y 5-66
5-42 DESCRIPTIVE STATISTICS FOR SATURATION WATER CONTENT
AND RESIDUAL WATER CONTENT (65 5-67
xvi
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LIST OF TABLES (Continued)
Table Page
5-43 STATISTICAL PARAMETERS USED FOR DISTRIBUTION
APPROXIMATION 5-68
5-44 CORRELATIONS AMONG TRANSFORMED VARIABLES PRESENTED
WITH THE FACTORED COVARIANCE MATRIX 5-70
6-1 SUMMARY OF SOIL TEMPERATURE MODEL CHARACTERISTICS 6-33
6-2 INPUT PARAMETERS FOR THE TEST CASES - ANALYTICAL SOLUTION 6-58
6-3 TRIFLURALIN VOLATILIZATION LOSSES, AMOUNTS REMAINING IN
SOIL, AND ESTIMATED LOSSES VIA OTHER PATHWAYS FOR THE 120-
DAY FIELD TEST 6-62
6-4 INPUT PARAMETERS FOR THE TEST CASES - WATKINSVILLE SITE 6-62
6-5 SIMULATION RESULTS OF USING DIFFERENT COMPARTMENT DEPTH . . .6-65
6-6 SIMULATED SOIL TEMPERATURE PROFILE AFTER ONE DAY FOR
DIFFERENT COMPARTMENT THICKNESSES 6-72
7-1 SOIL PROPERTIES AND DISCRETIZATION DATA USED IN SIMULATING
TRANSIENT FLOW IN A SOIL COLUMN 7-21
7-2 SOIL PROPERTIES USED IN SIMULATING STEADY-STATE
INFILTRATION 7-21
7-3 ITERATIVE PROCEDURE PERFORMANCE COMPARISON 7-24
7-4 VALUES OF PHYSICAL PARAMETERS AND DISCRETIZATION DATA USED
IN SIMULATING ONE-DIMENSIONAL TRANSPORT IN A SEMI-INFINITE
SOIL COLUMN 7-24
7-5 CONCENTRATION PROFILE CURVES AT t = 25 hr AND t = 50 hr
SHOWING COMPARISON OF THE ANALYTICAL SOLUTION AND RESULTS
FROM VADOFT 7-28
7-6 VALUES OF PHYSICAL PARAMETERS AND DISCRETIZATION DATA USED
IN SIMULATING ONE-DIMENSIONAL TRANSPORT IN A FINITE
SOIL COLUMN 7-29
xvn
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LIST OF TABLES (Concluded)
Table page
7-7 CONCENTRATION PROFILE CURVES SHOWING COMPARISON OF THE
ANALYTICAL SOLUTION AND VADOFT 7-31
7-8 VALUES OF PHYSICAL PARAMETERS USED IN THE SIMULATION OF
TRANSPORT IN A LAYERED SOIL COLUMN 7-35
7-9 BREAKTHROUGH CURVES COMPUTED USING THE ANALYTICAL SOLUTION
AND VADOFT (CASE1) 7-36
7-10 BREAKTHROUGH CURVES COMPUTED USING THE ANALYTICAL
SOLUTION AND VADOFT (CASE 2) 7-37
7-11 VALUES OF PHYSICAL PARAMETERS AND DISCRETIZATION
DATA USED IN SIMULATING TRANSPORT IN A VARIABLY
SATURATED SOIL TUBE 7-38
7-12 VALUES OF PHYSICAL PARAMETERS AND DISCRETIZATION DATA
USED IN SIMULATING TRANSIENT INFILTRATION AND
CONTAMINANT TRANSPORT IN THE VADOSE ZONE 7-38
10-1 PRZM-2 ERROR MESSAGES, WARNINGS, AND TROUBLESHOOTING
APPROACHES 10-2
10-2 EXESUP PROGRAM VARIABLES 10-13
10-3 PRZM PROGRAM VARIABLES, UNITS, LOCATION, AND VARIABLE
DESIGNATION 10-16
10-4 VADOFT PROGRAM VARIABLES, UNITS, LOCATION, AND
VARIABLE DESIGNATIONS 10-55
10-5 MONTE-CARLO PROGRAM VARIABLES 10-68
XVIII
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ACKNOWLEDGMENTS
A number of individuals contributed to this effort. Their roles are acknowledged in the
following paragraphs.
Several components of PRZM-2 were excerpted from the RUSTIC model. The following
contributors to the RUSTIC model are acknowledged: Mr. K.A. Voos of Woodward-Clyde
Consultants (WCC) programmed the execution supervisor and linked the models. The linkage
was conceived by Mr. J.D. Dean and Dr. Atul Salhotra of WCC and Dr. P.S. Huyakorn of
HydroGeologic. Dr. Huyakorn and his staff wrote the time/space bridging subroutines for the
linkage. Mr. R.W. Schanz (WCC) and Ms. Meeks (WCC) wrote the irrigation and MOC
algorithms. The volatilization routines were written by Dr. J. Lin and Dr. S. Raju of Aqua
Terra Consultants, Mr. Dean wrote the daughter products algorithms that were implemented
by Dr. Lin. Mr. J.L. Kittle implemented modifications to allow multiple segment (zone)
simulation capability.
The original VADOFT code was written and documented by Dr. Huyakorn,
Mr. H. White, Mr. J. Buckley, and Mr. T. Wadsworth of HydroGeologic. The Monte Carlo pre-
and post-processors were written by Dr. Salhotra, Mr. P. Mineart, and Mr. Schanz of WCC.
Modifications were developed and implemented by the authors of this document.
Final assembly of the model code, documentation and model testing were performed by
AScI. The support of the graphics staff of AScI is appreciated. Also a special thanks to Ms. T.
Robinson (AScI) and Ms. S. Tucker (CSC) for their typing of text, equations, and tables.
The authors would like to acknowledge Mr. D.S. Brown, Chief, Assessment Branch,
ERL-Athens, for his suggestions, input, and helpful comments,
xix
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SECTION 1
INTRODUCTION
This publication contains documentation for a linked groundwater loading model, known as
PRZM-2, for organic chemical contaminant transport down through the crop in root and vadose
zones. A brief section on background and objectives for the model development effort follows in
this introduction (Section 1.1). Section 1.2 gives a synopsis of risk and exposure assessment
concepts. The reader who has sufficient background in these concepts may proceed to Section
1.3, which provides an overview of the PRZM-2 modeling system, including major features and
limitations.
1.1 BACKGROUND AND OBJECTIVES
The U.S. Environmental Protection Agency is continually faced with issues concerning the
registration and restriction of pesticides used for agricultural purposes. Each of these
regulatory processes requires that the potential risk to human health resulting from the
introduction or continued use of such chemicals be evaluated. Recently, much of this attention
has been focused on exposure through leaching of pesticides to groundwater and subsequent
ingestion of contaminated water.
The capability to simulate the potential exposure to pesticides via this pathway has two major
facets:
o Prediction of the fate of the chemical, after it is applied, as it is transported by water
down through the crop root and soil vadose zones.
o Evaluation of the probability of the occurrence of concentrations of various magni-
tudes at various depths.
Several models are capable of simulating the transport and transformation of chemicals in the
subsurface and in the root zone of agricultural crops. However, none of these models have
been linked together in such a way that a complete simulation package, which takes into
account the effects of agricultural management practices on contaminant fate is available for
use either by the Agency or the agricultural chemical industry to address potential groundwa-
ter contamination problems. Without such a package, the decision maker must rely on
modeling scenarios that are either incomplete or potentially incorrect. Each time a new
scenario arises, recurring questions must be answered:
o What models should be used?
o How should mass transfer between models be handled?
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The resolution of these issues for each scenario is both expensive and time consuming.
Furthermore, it precludes consistency of approach to evaluation of contamination potential for
various scenarios.
The modeling package described in this report seeks to overcome these problems by providing a
consistent set of linked unsaturated zone models that have the flexibility to handle a wide
variety of hydrogeological, soils, climate, and pesticide scenarios. However, the formulation of
the risk analysis problem requires more than a simple, deterministic evaluation of potential
exposure concentrations. The inherent variability of force, capacitance and resistance in
natural systems, combined with the inability to exactly describe these attributes of the system,
suggests that exposure concentrations cannot be predicted with certainty. Therefore, the
uncertainty associated with the predictions must be quantified. Consequently, this simulation
package also seeks to provide this capability by utilizing Monte Carlo simulation techniques.
Stated more concisely, the objectives of this model development effort were to provide a
simulation package that can:
o Simulate the transport and transformation of field-applied pesticides in the crop root
zone and the underneath unsaturated zone taking into account the effects of agricul-
tural management practices
o Provide probabilistic estimates of exposure concentrations by taking into account the
variability in the natural systems and the uncertainly in system properties and
processes
Furthermore, it was desirable that the simulation package be easy to use and parameterize,
and execute on IBM or IBM-compatible PCs and the Agency's DEC/VAX machines. As a
result, considerable effort has gone into providing parameter guidance for both deterministic
and probabilistic applications of the model and software development for facile model imple-
mentation.
1.2 CONCEPT OF RISK AND EXPOSURE ASSESSMENT
Exposure assessment, as defined in the Federal Register (1984) for human impacts, is the
estimation of the magnitude, frequency, and duration at which a quantity of a toxicant is
available at certain exchange boundaries (i.e., lungs, gut, or skin) of a subject population over a
specified time interval. Exposure assessment is an element of the larger problems of risk
assessment and risk management, as demonstrated in Figure 1.1. The concentration estimates
generated during an exposure assessment are combined with demographic and toxicological
information to evaluate risk to a population-which can be used, in turn, to make policy
decisions regarding the use or disposal of the chemical.
Major components of risk assessment are indicated below. Of these, the first three constitute
the important steps for exposure assessment and are discussed in detail here,
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REGULATORY CONCERN
SCIENTIFIC DATA
Population
Exposure
Product Ltf» Cycle
General Information Gathering
Preliminary Exposure
Assessement
Hazard Identification TOxldty
env. cone., etc.
Most Probable Areas of Exposure
Prallminaiy Exposur* Ass*«m«!it
1
Preliminary FUak Analysis
Decision
Exposure A99*»smant
In-Depth Exposure
I
No N*»d lor Future
Exposure Assessment
Mum-Disciplinary
Peer Review
Dontgn At««<«m«ot Stud/ Plan
Compt«h«nsV« Data Gaiharlng
Conduct Mlrwd Exposure Motteilng
Dvdstor
Regulatory Rsspcnss
HazarsJ Input
Formal Ptgk Asa*sorn»nt
D^islon
1
Regulatory Proposal
Examined Exposure*
Present No Umesenobto Risk
Figure 1.1 Decision path for risk assessment
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o Characterization and quantification of chemical sources
o Identification of exposure routes
o Quantification of contaminant movement through the exposure routes to the receptor
population/location
o Characterization of the exposed population
o Integration of quantified environmental concentrations with the characteristics of the
exposed populations to yield exposure profiles
Characterization of sources(s) requires in a broad sense the estimation of the loading of a
chemical into various environmental media. For the groundwater contamination problem, on a
regional scale, this requires data on chemical uses and distribution of those uses (spatially and
temporally). It also requires information on the crops being grown, registered or proposed
chemical uses of those crops, and regional management practices. For a specific field-scale
area, similar data would be needed to support an assessment; however, greater detail may be
necessary.
The identification of exposure pathways involves a qualitative (or semiquantitative) assessment
of how the chemical is thought to move from the source to the exposed population. Important
fate processes that may serve to reduce the concentration of the chemical (s) along various
pathways in different environmental media are also identified. For the case of groundwater
exposure, important pathways and processes are predefined to a large extent in the models to
be used. The quantification of concentrations in a medium, given the source strength,
pathways, and attenuation mechanisms along each pathway, is the next step, and is the major
benefit of using models such as PRZM-2. The guidelines are very specific in the requirement
that concentrations be characterized by duration and frequency as well as magnitude. These
characteristics can be determined through the analysis of time series exposure data generated
by the model.
PRZM-2 produces time series of toxicant concentrations such as appears in Figure 1.2. Each
time series can be compared to a critical value of the concentration y. This type of analysis
easily shows whether the criterion is exceeded and gives a qualitative feel for the severity of
the exccedance state. If we determine how often a contaminant is at a particular level or
within a specified range, a frequency distribution of the values of y (Figure 1.3) can be created.
If, in addition, we choose any value of y in Figure 1.2 and determine the area under the curve
to the right of that value, we can plot Figure 1.4, which is a cumulative frequency distribution
of the toxicant concentration. The cumulative frequency distribution shows the chance that
any given value y that we select will be exceeded. If the example time series is long enough,
then the "chance" approaches the true "probability" that y will be exceeded.
Thus far, only the concentration to which the organism will be exposed has been discussed and
nothing has been said concerning the duration of the event. If we take the same time series
and impose a window of length "t" on it at level j^ (Figure 1.5), and move it incrementally
forward in time, we can make a statement concerning the toxicant concentration within the
duration window. Normally, the average concentration within the window is used. The
resulting cumulative frequency distribution shows the chance that the moving average of
duration tQ will exceed the critical value of y, yc.
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Time (t)
Figure 1.2.
Time series plot of toxicant concentrations.
100-
a>
d
a
•n
o>
JJ
id
n
•H
i
o
»
Concentration (y)
Concentration (y)
Figure 1.3. Frequency distribution of toxi-
cant concentrations.
Figure 1.4. Cumulative frequency
distribution of toxicant
concentrations.
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Time (t)
Figure 1.5. Time series of toxicant concentrations with moving average window of duration
PRZM-2
(l-D Flow and Transport)
VADOSE
ZONE
MODEL
VADOFT
(1-D Flow and Transport)
Figure 1.6. Linked modeling system configuration.
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The moving average window should be the same length as that specified for yc. For instance,
in the case of cancer risk, a 70-year (lifetime) window is normally used to average the data in
the simulated time series, The use of the moving window for averaging the time series allows
us to compare both the concentration and duration against the standard. The chance or
probability that the moving average concentration exceeds the standard is the essence of the
exposure assessment. This type of information provides a precursor to the estimates of risk
taken in using this chemical under the conditions of the model simulation. The use of models
like PRZM-2 that provide data in environmental concentrations, duration and probability of
occurrence ends here.
The next step in exposure assessment involves the characterization of the exposed population.
Such factors as habits, age, sex, and location with respect to the source are of importance. The
integration of concentration estimates and population characteristics makes possible the count-
ing of the conditional events of concentration in an environmental medium and the opportunity
for the population to be exposed to these concentrations. The exposure assessment ends at this
point. The actual intake of chemicals, their fate within the human body (e.g., pharmaco-
kinetics, toxicology), and their effects on the exposed population are not considered. These,
however, are also elements of the risk assessment.
Although the concepts underlying an exposure assessment are relatively simple, the actual
application of these concepts is complicated because of large variations in source-specfic and
environment- specific characteristics and the necessity to integrate specialized knowledge from
a number of different fields. This variability underscores the need to use a model such as
PRZM-2 in the evaluation of exposure concentrations.
1.3 OVERVIEW OF PRZM-2
This section gives an overview of the PRZM-2 model highlighting the features and limitations
of the simulation package as a whole, and the component models PRZM and VADOFT. The
PRZM-2 code was designed to provide state-of-the-art deterministic simulation of the fate of
pesticides, applied for agricultural purposes, both in the crop root zone and the underlying
vadose zone. The model is capable of simulating multiple pesticides or parent/daughter
relationships. The model is also capable of estimating probabilities of concentrations or fluxes
in or from these various media for the purpose of performing exposure assessments.
To avoid writing an entirely new computer code, it was decided to make use of existing codes
and software to the extent possible. Thus, due to its comprehensive treatment of important
processes, its dynamic nature, and its widespread use and acceptability to the Agency and the
agricultural chemical industry, the Pesticide Root Zone model (PRZM) (Carsel et al. 1984) was
selected to simulate the crop root zone.
Having selected PRZM, two options were evaluated for developing the PRZM-2 linked model to
meet the objectives stated in Section 1.1. The first involved use of PRZM only. In this
configuration, PRZM would be used to simulate both the root zone and the vadose zone. This
option was rejected because the assumptions of the elementary soil hydraulics in PRZM (i.e.,
drainage of the entire soil column to field capacity in 1 day) were considered inadequate for
1-7
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simulating flow in a thick vadose zone. The second option involved PRZM linked to a to be
determined unsaturated zone model. The option finally selected is depicted in Figure 1.6. In
this configuration, an enhanced version of PRZM is linked to a one-dimensional vadose zone
flow and transport model. Both the vadose and PRZM models simulate water flow and solute
transport. Subsequently, a new code (VADOFT) was written to perform the flow and transport
simulation in the vadose zone.
1.3.1 Overview of PRZM
1.3.1.1 Features—
The Pesticide Root Zone Model (PRZM) is a one-dimensional, dynamic, compartmental model
that can be used to simulate chemical movement in unsaturated soil systems within and
immediately below the plant root zone. It has two major components- hydrology (and
hydraulics) and chemical transport. The hydrologic component for calculating runoff and
erosion is based on the Soil Conservation Service curve number technique and the Universal
Soil Loss Equation. Evapotranspiration is estimated either directly from pan evaporation data,
or based on an empirical formula. Evapotranspiration is divided among evaporation from crop
interception, evaporation from soil, and transpiration by the crop. Water movement is
simulated by the use of generalized soil parameters, including field capacity, wilting point, and
saturation water content. The chemical transport component can simulate pesticide applica-
tion on the soil or on the plant foliage. With a newly added feature, biodegradation can also be
considered in the root zone. Dissolved, adsorbed, and vapor-phase concentrations in the soil
are estimated by simultaneously considering the processes of pesticide uptake by plants,
surface runoff, erosion, decay, volatilization, foliar washoff, advection, dispersion, and retarda-
tion. Two options are available to solve the transport equations: (1) the original backwards-
difference implicit scheme that may be affected by excessive numerical dispersion at high
Peclet numbers, or (2) the method of characteristics algorithm that eliminates numerical
dispersion while slightly increasing model execution time.
PRZM has the capability to simulate multiple zones. This allows PRZM and VADOFT to
combine different root zone and vadose zone characteristics into a single simulation. Zones can
be visualized as multiple land segments joined together in a horizontal manner. There are
three reasons a user may choose for implementing multiple zones:
1) to simulate heterogeneous PRZM root zones with a homogeneous vadose zone
2) to simulate a homogeneous root zone with heterogeneous vadose zones
3) to simulate multiple homogeneous root zones with multiple homogeneous
vadose zones
Weighing multiple zones together and their use are discussed in detail in Section 5.
Another added feature is the ability to simulate as many as three chemicals simultaneously as
separate compounds or as a parent-daughter relationship. This gives the user the option to
1-8
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observe the effects of multiple chemicals without making additional runs or the ability to enter
a mass transformation factor from a parent chemical to one or two daughter products.
Predictions are made on a daily basis. Output can be summarized for a daily, monthly, or
annual period. Daily time series values of various fluxes or storages can be written to
sequential files during program execution for subsequent analysis.
1.3.1.2 Limitations--
There were significant limitations in the original (Release I) version of PRZM. A few were
obvious to the developers; others were pointed out subsequently by model users. These are
broken into four categories:
o Hydrology
o Soil hydraulics
o Method of solution of the transport equation
o Deterministic nature of the model
The Release II version of PRZM has been suitably modified to overcome many of these
limitations.
Hydrologic and hydraulic computations are still performed in PRZM on a daily time step even
though, for some of the processes involved (evaporation, runoff, erosion), finer time steps might
be used to ensure greater accuracy and realism. For instance, simulation of erosion by runoff
depends upon the peak runoff rate, which is in turn dependent upon the time base of the
runoff hydrography. This depends to some extent upon the duration of the precipitation event,
PRZM retains its daily time step primarily due to the relative availability of daily versus
shorter time step meteorological data. This limitation has been mitigated, in part, by
enhanced parameter guidance.
In PRZM, Release I, the soil hydraulics were simple-all drainage to field capacity water
content was assumed to occur within 1 day. (An option to make drainage time dependent also
was included, but there is not much evidence to suggest that it was utilized by model users to
any great extent.) This had 1-day drainage assumption the effect, especially in deeper soils, of
inducing a greater-than-anticipated movement of chemical through the profile. While this
representation of soil hydraulics has been retained in PRZM, the user has the option of
coupling PRZM to VADOFT. PRZM is then used to represent the root zone, while VADOFT,
with a more rigorous representation of unsaturated flow, is used to simulate the thicker vadose
zone. The VADOFT code is discussed in more detail in a subsequent section. For short
distances from the soil surface to the water table, PRZM can be used to represent the entire
vadose zone without invoking the use of VADOFT as long as no layers that would restrict
drainage are present.
The addition of algorithms to simulate volatilization has brought into focus another limitation
of the soil hydraulics representation. PRZM simulates only advective, downward movement of
water and does not account for diffusive movement due to soil water gradients. This means
that PRZM is unable to simulate the upward movement of water in response to gradients
induced by evapotranspiration. This process has been identified by Jury et al. (1984) as an
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important one for simulating the effects of volatilization. However, the process would seem
less likely to impact the movement of chemicals with high vapor pressures. For these
chemicals, vapor diffusion would be a major process for renewing the chemical concentration in
the surface soil.
Another limitation of the Release I model was the apparent inadequacy of the solution to the
transport equation in advection-dominated systems. The backward difference formulation of
the advection term tends to produce a high degree of numerical dispersion in such systems.
This results in overprediction of downward movement due to smearing of the peak and
subsequent overestimation of loadings to groundwater. In this new release, a new formulation
is available for advection-dominated systems. The advective terms are decoupled from the rest
of the transport equation and solved separately using the method of characteristics (MOC).
The remainder of the transport equation is then solved as before, using the fully implicit
scheme. This approach effectively eliminates numerical dispersion with only a small increase
in the computation time. In low-advection systems, the MOC approach reduces to the original
PRZM solution scheme, which becomes exact as velocities approach zero.
The final limitation is the use of field-averaged water and chemical transport parameters to
represent spatially heterogeneous soils. Several researchers have shown that this approach
produces slower breakthrough times than are observed using stochastic approaches. This
concern has been addressed by adding the capability to run PRZM-2 in a Monte Carlo
framework. Thus, distributional, rather than field-averaged, values can be utilized as inputs
that will produce distributional outputs of the relevant variables (e.g., flux to the water table).
The Special Actions option in PRZM-2 allows the user to output soil profile pesticide concentra-
tions at user-specified times during the simulation period and to change selected model
parameters to better represent chemical behavior and the impacts of agricultural management
practices. The required input format and parameters are specified in Section 4.
By using the 'SNAPSHOT' capability of Special Actions, the user can output the pesticide
concentration profile, i.e., the total concentration in each soil compartment, for any user-
specified day during the simulation period. In this way, the user can run PRZM-2 with only
monthly or annual output summaries and still obtain simulation results for selected days when
field data were collected. There is no inherent limit to the number of SNAPSHOTS that can be
requested in a single run. When more than one chemical is being simulated, the concentration
profiles are provided by the order of the chemical number, i.e., NCHEM.
To better represent the expected behavior of the chemical being simulated, or the impacts of
tillage or other agricultural practices, the following parameters can be reset to new values at
any time during the simulation period:
Solution Decay Rate (DWRATE)
Sorbed Decay Rate (DSRATE)
Partition Coefficient (KD)
Bulk Density (BD)
Curve Number (CN)
USLE Cover Factor (USLEC)
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Thus, for chemicals that demonstrate seasonal decay rates or partition coefficients, or different
values for the period following application compared to later in the crop season, the appropri-
ate parameters can be changed at user-specified times to mimic the observed, or expected,
behavior of the compound.
Similarly, for agricultural practices or specific tillage operations that affect the soil bulk
density, curve number, or cover factor, these parameter values can be altered during the
simulation in an attempt to better represent their impacts. The parameter guidance in Section
5 may help the user in determining adjustments for these parameters. Users should note that
adjustments to the bulk density, and possibly the partition coefficient, may affect the pesticide
balance calculation.
1.3.2 Overview of the Vadose Zone Flow and Transport Model (VADOFT)
VADOFT is a finite-element code for simulating moisture movement and solute transport in
the vadose zone. It is the second part of the two-component PRZM-2 model for predicting the
movement of pesticides within and below the plant root zone and assessing subsequent
groundwater contamination. The VADOFT code simulates one-dimensional, single-phase
moisture and solute transport in unconfined, variably saturated porous media. Transport
processes include hydrodynamic dispersion, advection, linear equilibrium sorption, and first-
order decay, The code predicts infiltration or recharge rate and solute mass flux entering the
saturated zone. The following description of VADOFT is adapted from Huyakorn et al.
(1988a).
1.3.2.1 Features—
The code, which employs the Galerkin finite-element technique to approximate the governing
equations for flow and transport, allows for a wide range of nonlinear flow conditions.
Boundary conditions of the variably saturated flow problems may be specified in terms of
prescribed pressure head or prescribed volumetric water flux per unit area, Boundary
conditions of the solute transport problem may be specified in terms of prescribed concentra-
tion or prescribed solute mass flux per unit area. All boundary conditions may be time
dependent. An important feature of the algorithm is the use of constitutive relationships for
soil water characteristic curves based on soil texture.
1.3.2.2 Limitations--
Major assumptions of the flow model are that the flow of the fluid phase is one-dimensional,
isothermal and governed by Darcy's law and that the fluid is slightly compressible and
homogeneous. Hysteresis effects in the constitutive relationships of relative permeability
versus water saturation, and water saturation versus capillary pressure head, are assumed to
be negligible.
Major assumptions of the solute transport model are that advection and dispersion are one-
dimensional and that fluid properties are independent of contaminant concentrations.
Diffisive/dispersive transport in the porous-medium system is governed by Pick's law. The
hydrodynamic dispersion coefficient is defined as the sum of the coefficients of mechanical
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dispersion and molecular diffusion. Adsorption and decay of the solute is described by a linear
equilibrium isotherm and a lumped first-order decay constant. Parent/daughter chemical
relationships may be simulated.
The code handles only single-phase flow (i.e., water) and ignores the presence of a second
phase-i. e., air. The code does not take into account sorption nonlinearity or kinetic sorption
effects that, in some instances, can be important. The code considers only single-porosity
(granular) soil media. It does not simulate flow or transport in fractured porous media or
structured soils.
1.3.3 Overview of the Monte Carlo Simulation Module
MCARLO performs all the functions necessary to execute a Monte Carlo simulation. It reads
special data for parameters to be varied (e.g., distribution types and moments) and output
variables to be observed, generates random numbers, correlates them and performs transfor-
mations, exchanges these generated values for PRZM-2 parameters, performs statistical
analysis on the output variables, and writes out statistical summaries for the output variables.
The MCARLO module makes use of an input and output file. Inputs to the MCARLO module
are discussed in Section 4. The user should be aware that many of the parameters entered in
the Monte Carlo input file once designated as constants will be used in lieu of that same
parameter value entered in the standard input file.
The final limitation is that only a small number of input variables may be changed at random
by invoking the Monte Carlo routines. It is not difficult to add additional variables, however.
1.3.4 Model Linkage
One of the more challenging problems in this model development effort was the temporal and
spatial linkage of the component models In the section which follows, these linkages are
discussed.
1.3.4.1 Temporal Model Linkage—
The resolution of the temporal aspects of the two models was straightforward. PRZM runs on
a daily time step. The time step in VADOFT is dependent upon the properties of soils and the
magnitude of the water flux introduced at the top of the column. In order for the nonlinear
Richards' equation to converge, VADOFT may sometimes require time steps on the order of
minutes.
For the linkage of PRZM-2, through VADOFT the resolution of time scales is also straightfor-
ward. VADOFT is prescribed to simulate to a "marker" time value, specifically to the end of a
day. The last computational time step taken by VADOFT is adjusted so that it coincides with
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the end of the day. PRZM's daily water fluxes are used as input to VADOFT. VADOFT
utilizes this flux as a constant over the day and adjusts its internal computational time step in
order to converge.
1.3.4.2 Spatial Linkages—
The spatial linkages utilized for the models are more complex. The principal problem is the
presence of a fluctuating water table. A second problem is that of the incompatibility between
the hydraulics in PRZM and VADOFT. Of course, any linking scheme utilized must provide a
realistic simulation of the flow of water and transport of solutes at the interfaces and must
ensure mass balance.
The major problem with the interfacing of these two models is that while VADOFT solves the
Richards' equation for water flow in a variably saturated medium, PRZM uses simple "drain-
age rules" to move water through the soil profile. Because of this incompatibility, there may be
times when PRZM produces too much water for VADOFT to accommodate within one day.
This is very likely to happen in agricultural soils, where subsoils are typically of lower
permeability than those of the root zone, which have been tilled and perforated by plant roots
and soil biota. The result of this would be water ponded at the interface which would belong
neither to PRZM or VADOFT.
The solution was to prescribe the flux from PRZM into VADOFT so that VADOFT accommod-
ates all the water output by PRZM each day. This eliminates the problem of pending at the
interface. However, it does force more water into the vadose zone than might actually occur in
a real system, given the same set of soil properties and meteorological conditions. The
consequence is that water and solute are forced to move at higher velocities in the upper
portions of the vadose zone. If the vadose zone is deep, then this condition probably has little
impact on the solution. If it is shallow, however, it could overestimate loadings to groundwa-
ter, especially if chemical degradation rates are lower in the vadose zone than in the root zone.
1.3.5 Monte Carlo Processor
PRZM-2 can be run in a Monte Carlo mode so that probabilistic estimates of pesticide loadings
to the saturated zone from the source area can be made. The input preprocessor allows the
user to select distributions for key parameters from a variety of distributions; the Johnson
family (which includes the normal and lognormal), uniform, exponential and empirical, If the
user selects distributions from the Johnson family, he or she may also specify correlations
between the input parameters. The Monte Carlo processor reads the standard deterministic
input data sets for each model, then reads a Monte Carlo input file that specifies which
parameters are to be allowed to vary, their distributions, the distribution parameters, and
correlation matrix. The model then executes a prespecified number of runs.
The output processor is capable of preparing statistics of the specified output variables
including mean, maximum values and quantiles of the output distribution. The output
processor also can tabulate cumulative frequency histograms of the output variables and send
them to a line printer for plotting,
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1,3.6 Overview Summary
A modeling system (PRZM-2) has been developed for the U.S. Environmental Protection
Agency that is capable of simulating the transport and transformation of pesticides, following
application, down through the crop root zone and underlying vadose zone. The modeling
system was designed to handle a variety of geometries likely to be encountered in performing
evaluations for pesticide registration or special reviews. A major objective was to keep the
model simple and efficient enough so that it could be operated on an IBM-PC or IBM-compati-
ble PC and used in a Monte Carlo mode to generate probabilistic estimates of pesticide
loadings or water concentrations. The model consists of two major computational modules-
PRZM, which performs pollutant fate calculations for the crop root zone and is capable of
incorporating the effects of management practices and VADOFT, which simulates one-
dimensional transport and transformation within the vadose zone.
Linkage of these models is accomplished through the use of simple bridging algorithms that
conserve water and solute mass.
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SECTION 2
MODEL DEVELOPMENT, DISTRIBUTION, AND SUPPORT
NOTE: Refer to the README file for the latest supplemental information,
changes, and/or additions to the PRZM-2 model documentation. A copy of
the RE AD.ME file is included on each distribution diskette set or it can be
down loaded from the Center for Exposure Assessment Modeling (CEAM)
electronic bulletin board system (BBS). It can be installed on a hard disk
using the INSTALL, (diskette) or INSTALP2 (BBS) program. It is an ASCII
(non-binary) text file that can be displayed on the monitor screen by using
the DOS TYPE command (e.g., TYPE READ.ME) or printed using the DOS
PRINT command (e.g., PRINT READ.ME).
The READ.ME file contains a section entitled File Name and Content that
provides a brief functional description of each PRZM-2 file by name or file
name extension type. Other sections in this document contain further
information about
o system development took used to build the microcomputer release of the
PRZM-2 model system
o recommended hardware and software configuration for execution of the
model and. all support programs
o routine program execution
o Minimum file configuration
o run time and performance
o program modification
o technical help contacts
2.1. DEVELOPMENT AND TESTING
The PRZW-2 model system was developed and tested on a Digital Equipment Corporation
(DEC) VAX 6310 running under version 5.4-2 of the VMS operating system (OS) and
version 5.5-98 of VAX VMS FORTRAN-77, and an Advanced Logic Research (ALR) 486/25
microcomputer running under version 4.00 of IBM PC DOS and version 2.51 of Salford
FORTRAN (FTN77/486).
The following FORTRAN tools also were used to perform static evaluations of the PRZM-2
FORTRAN code on an IBM PS/2 Model 8085-071 running under version 3.3 of IBM PC
DOS, MICRO EXPRESS (ME) 486/25 and 486/33 systems running under version 5.00 of
Microsoft (MS) DOS, and a Sun SPARCstation 1 +GX running version 4.1.1 of UNIX/Sun-
Os:
2-1
-------
o Lahey - F77L, F77L-EM/32 versions 5.01,
4.02 (DOS, ext DOS)
o Microsof - MSFORT version 5.00 (OS/2, DOS)
o Ryan-McFarland - RMFORT versions 2.45, 3.10.01 (DOS)
o Salford - FTN77/386 version 2.50 (DOS,
extended DOS)
o Silicon Valley
Systems - SVS-77/386 version 2.81 (DOS,
extended DOS)
o Sun - (UNIX/SunOS, version 1.4)
oWaterloo - Watcom-77/386 version 8.5E (DOS,
extended DOS)
In addition to the VAX and ALR systems, PRZM-2 has also been successfully executed on
a PRIME 50 Series minicomputer running under PRIMOS, the Sun SPARCstation, and
the IBM PS/2 Model 8085-071.
The distribution version of the PRZM-2 model system is built with the Lahey FORTRAN
F77L-EM/32) extended (i.e., protected) mode FORTRAN compiler and link editor, version
5.01. Refer to section 2.4.2 for specific hardware and software run time requirements for
the host system for the PRZM-2 model system.
2.2 DISTRIBUTION
The PRZM-2 model system and all support files and programs are available on diskette
from CEAM, located at the U.S. EPA Environmental Research Laboratory, Athens,
Georgia, at no charge. The CEAM has an exchange diskette policy. It is preferred that
diskettes be received before sending a copy of the model system (refer to section 2.3,
Obtaining a Copy of the PRZM-2 Model Systemz).
Included in a distribution diskette set are
o PRZM-2 general execution and user support guide (READ.ME) file
o interactive installation program (refer to section 2.5, Installation)
o test input and output files for installation verification
o executable task image file for the PRZM-2 model system
o FORTRAN source code files
o command and/or "make" files to compile, link, and run the task image file (PRZM2-
.EXE)
A FORTRAN compiler and link editor are NOT required to execute any portion of the
model. If the user wishes to modify the model, it will be up to the user to supply and/or
obtain
o an appropriate text editor that saves files in ASCII (non-binary) text format
o FORTRAN development tools to recompile and link edit any portion of the model
2-2
-------
CEAM cannot support, maintain, and/or be responsible for modifications that change the
function and/or operational characteristics of the executable task image, MAKE, or DOS
command files supplied with this model package.
The microcomputer release of the PRZM-2 model is a full implementation of the VAX/-
VMS version. The microcomputer implementation of this model performs the same
function as the U.S. EPA mainframe/minicomputer version.
2.3 OBTAINING A COPY OF THE PRZM-2 MODEL
NOTE: k=l,024; m=l,048,576; b=l byte
2.3.1 Diskette
To obtain a copy of the PRZM-2 distribution model system on diskette, send
o the appropriate number of double-sided, double-density (DS/DD 360kb) 5.25 inch,
or double-sided, high-density (DS/HD 1.44mb) 3.5 inch error-free diskettes
NOTE: To obtain the correct number of diskettes, contact CEAM at 706/-
546-3549.
o a cover letter, with a complete return address, requesting the PRZM-2 model to:
Model Distribution Coordinator
Center for Exposure Assessment Modeling
Environmental Research Laboratory
U.S. Environmental Protection Agency
960 College Station Road
Athens, GA 30606-2720
Program and/or user documentation, or instructions on how to order documentation, will
accompany each response.
2.3.2 Electronic Bulletin Board System (BBS)
To down load a copy of the PRZM-2 model system, or to check the status of the latest
release of this model or any other CEAM software product, call the CEAM BBS 24 hours
a day, 7 days a week. To access the BBS, a computer with a modem and communication
software is needed. The phone number for the BBS is 706/546-3402. Communication
parameters for the BBS are
o 300/1200/2400/9600 baud rate
o 8 data bits
o no parity
o 1 stop bit
2-3
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2.4 GENERA1L/MINIMUM HARDWARE AND SOFTWARE INSTALLATION AND RUN
TIME REQUIREMENTS
NOTE: Refer to the READ.ME file for the latest supplemental and more complete
information, changes, and/or additions concerning specific hardware and software
installation and run time requirements.
2.4.1 Installation Requirements
o 3.5 inch, 1.44mb diskette drive, or 5.25 inch, 360kb diskette drive
o hard disk drive
o approximately 4.5mb free hard disk storage
2.4.2 Run Time Requirements
o 386 or 486 compatible microcomputer
o MS or PC DOS version 3.30 or higher
o 640k base memory
o 4mb of extended (XMS) memory
o 4.5mb free hard disk storage
Refer to READ.ME file for suggested modification of the CONFIG.SYS and/or
AUTOEXEC.BAT DOS system configuration and start-up files.
2.5 INSTALLATION
To install the PRZM-2 model system and/or related support files on a hard disk, insert the
first distribution diskette in a compatible diskette drive (refer to section 2.4). Then type
A: \INSTALL or B: \INSTALL
at the DOS system prompt and press the key. Then follow instructions and
respond to prompts presented on the monitor screen by the interactive installation
program. Complete installation instructions are also printed on each external diskette
label.
NOTE: To install the PRZM-2 model system and/or related support files on a hard
disk from an interactive, self-extracting installation program down loaded from the
CEAM BBS or through Internet, type
INSTALP2
at the DOS system prompt then press the key. This assumes that the
current default drive and sub-directory is the same as the drive and sub-directory
where the file INSTALP2.EXE is stored. Then follow instructions and respond to
prompts presented on the monitor screen by the interactive installation program.
2-4
-------
The PRZM-2 distribution diskette sets and BBS files implement software product
installation standards to insure the most error-free, maintainable, and user-acceptable
distribution of CEAM products. It has a unique menu option, command, full-screen
(interactive), diagnostic, error-recovery, help, and selective installation capabilities using
state-of-the-art human-factors engineering practices and principles.
NOTE: The contents of the distribution diskettes can be copied to another set
of "backup" diskettes using the DOS DISKCOPY command. Refer to the DOS
Reference Manual for command application and use. The "backup" diskettes
must be the same size and storage density as the original source diskettes.
2.6 INSTALLATION VERIFICATION AND ROUTINE EXECUTION
Refer to the following sections in the RE AD.ME file for complete instructions concerning
installation verification and routine execution of the PRZM-2 model:
o File Name and Content
o Routine Execution
o Run Time and Performance
o Minimum File Configuration
2.7 CODE MODIFICATION
Included in the diskette set are
o an executable task image file for the PRZM-2 model system
o FORTRAN source code files
o command and/or "make" files to compile, link, and run the task image file (PRZM2-
.EXE)
If the user wishes to modify the model or any other program, it will be up to him or her to
supply and/or obtain
o an appropriate text editor that saves files in ASCII (non-binary) text format
o FORTRAN development tools to recompile and link edit any portion of the model
CEAM cannot support, maintain, and/or be responsible for modifications that change the
function of any executable task image (*, EXE), DOS batch command (*.BAT), and/or
"make" utility file(s) supplied with this model package.
2.8 TECHNICAL HELP
For questions and/or information concerning
2-5
-------
o installation and/or testing of the PRZM-2 model system and/or support programs or
files, call 706/546-3590 for assistance
o PRZM-2 model and/or program content, application, and/or theory, call 706/546-
3210 for assistance
o use of the CEAM electronic bulletin board system (BBS), contact the BBS system
operator (SYSOP) at 706/546-3590
o CEAM software and distribution Quality Assurance and Control, call 706/546-3125
o other environmental software and documentation distributed through CEAM,
contact the Model Distribution Coordinator at 706/546-3549
o other support available through CEAM, contact Mr. Dermont Bouchard, CEAM
Manager
o by mail at the following address
Center for Exposure Assessment Modeling (CEAM)
Environmental Research Laboratory
U.S. Environmental Protection Agency
960 College Station Road
Athens, Georgia 30605-2720
o by telephone at 706/546-3130
o by fax at 706/546-2018
o through the CEAM BBS message menu and commands. The CEAM BBS commu-
nication parameters and telephone number are listed above (section 2.3.2).
To help technical staff provide better assistance, write down a response to the following
topics before calling or writing. If calling, be at the computer, with the computer on, and
in the proper sub-directory (e.g., \PRZM2) when the call is placed.
o program information:
- describe the problem, including the exact wording of any error and/or warning
message (s)
- list the exact steps, command (s), and/or keyboard key sequence that will
reproduce the problem machine information:
o machine information:
- list computer brand and model
- list available RAM (as reported by DOS CHKDSK command)
- list extended memory present and free (XMS)
- list name and version of extended memory (XMS) manager (i.e., HIMEM,
VDISK, RAMDRIVE, etc.)
- list available hard disk space (as reported by DOS CHKDSK command)
- list the brand and version of DOS (as reported by DOS VER command)
- list the name of any memory resident (TSR) program(s) installed
printer brand and model
monitor brand and model
2-6
-------
NOTE: If contacting CEAM by mail, fax, or BBS, include responses to the above
information in your correspondence.
2.9 DISCLAIMER
Mention of trade names or use of commercial products does not constitute endorsement or
recommendation for use by the United States Environmental Protection Agency.
Execution of the PRZM-2 model system, and moditfications to the DOS system configura-
tion files (i.e., \CONFIG.SYS and \AUTOEXEC.BAT) must be used and/or made at the
user's own risk. Neither the U.S. EPA nor the program authors can assume responsibility
for model and/or program modification, content, output, interpretation, or usage.
CEAM software products are built using FORTRAN-77, assembler, and operating system
interface command languages. The code structure and logic of these products is designed
for single-user, single-tasking, non-LAN environment and operating platform for micro-
computer installations (i.e., single user on dedicated system).
A user will be on their own if he/she attempts to install a CEAM product on a multi-user,
multi-tasking, and/or LAN based system (i.e., Windows, DESQview, any LAN). CEAM
cannot provide installation, operation, and/or general user support under any combination
of these configurations. Instructions and conditions for proper installation and testing are
provided with the product in a READ.ME file. While multiuser/multitasking/LAN
installations could work, none of the CEAM products have been thoroughly tested under
all possible conditions. CEAM can provide scientific and/or application-support for
selected products if the user proves that a given product is installed and working
correctly.
2.10 TRADEMARKS
o F77L is a registered trademark of Lahey Computer Systems, Inc. All other Lahey
products are trademarks of Lahey Computer Systems, Inc.
o IBM, Personal Computer/XT (PC/XT), Personal Computer/AT (PC/AT), PC DOS,
VDISK, and Personal System/2 (PS/2) are registered trademarks of International
Business Machines Corporation
o DESQview is a trademark of Quarterdeck Office Systems, Inc.
o Sun and SunOS are registered trademarks of Sun Microsystems, Inc.
o SPARC is a registered trademark of SPARC International, Inc.
o UNIX is a registered trademark of American Telephone and Telegraph
o SVS FORTRAN-77 is a trademark of Silicon Valley Software
o PRIME and PRIMOS are trademarks of Prime Computers, Inc.
o Microsoft, RAMDRIVE, HIMEM, MS, and MS-DOS are registered trademarks of
Microsoft Corporation
o Windows is a trademark of Microsoft Corporation
o RM/FORTRAN is a trademark of Language Processors, Inc.
o DEC, VAX, VMS, and DCL are trademarks of Digital Equipment Corporation
2-7
-------
o 386 is a trademark of Intel Corporation
o US Robotics is a registered trademark and Courier HST is a trademark of U. S.Rob-
otics, Inc.
2-8
-------
SECTION 3
MODULES AND LOGISTICS
The PRZM-2 model consists of four major modules. These are:
o EXESUP, which controls the simulation
o PRZM, which performs transport and transformation simulations for the root
zone
o VADOFT, which performs transport and transformation simulations for the
vadose zone
o MONTE CARLO, which performs sensitivity analysis by generating random
inputs
In this section, Table 3-1 gives a listing of all subroutines and functions organized by
module calling routines. Table 3-2 gives a listing of all parameter files and their dimen-
sions. A brief description for each listing is also given.
3-1
-------
TABLE 3-1.
LIST OF SUBROUTINES AND FUNCTIONS AND A BRIEF DESCRIP-
TION OF THEIR PURPOSE.
MODULE
CALLING
ROUTINE
SUBROUTINE
FUNCTION PURPOSE
EXESUP
PRZM
INIT initializes common block CONST.INC
ECHOF echo names of files opened.
ENDDAY used to determine Julian day and simulation progress.
FILOPN opens and assigns file unit numbers.
ECHOGD echoes global data input.
DONBAR calculates percent complete bar.
ADDSTR add string to end of existing string.
INPREA reads and initializes program input.
BMPCHR converts character to uppercase.
CENTER centers string message on screen.
COMRD checks input for end of file.
COMRD2 checks input for comment lines.
COMRD3 checks input for END statement.
DISPLAY display data to echo file and screen.
ECHORD echoes line numbers read from input.
ELPSE add trailing string and fill middle.
ERRCHK write error messages.
EXPCHK check argument for exponential limits.
FILCLO closes open files.
OPECHO flags the printing utility.
RELTST checks argument as a real number.
SQRCHK gives square root with error checking.
SUBIN tracks entry into a subroutine.
SUBOUT tracks exit from a subroutine.
TRCLIN writes subroutine tracking to screen.
SCREEN controls display to screen.
LFTJUS left justifies a character string.
LNCHK takes natural log of a number.
LNGSTR returns length of a character string.
LOGCHK takes base 10 logarithm of a number with error checking
provided.
NAMFIX left justifies and capitalizes a string.
CLEAR clears the display screen.
FILCHK checks that necessary files are open.
EXESUP controls calls to PRZM, VADOFT ,and MONTE
CARLO.
INITEM determines global data.
FILINI initializes file unit numbers.
PRZM2 controls model calling routines.
LSUFIX performs internal reads.
BIODEG perform time dependant solution for microbiodegradation.
SLPST1 set up coefficient matrix for the solution of pesticide
3-2
-------
TABLE 3-1. (Continued)
MODULE
CALLING
ROUTINE
SUBROUTINE
FUNCTION PURPOSE
transport.
PRZMRD reads PRZM input file.
HYDR2 perform soil hydraulic calculations.
PLGROW determines plant growth parameters for use in other subrou-
tines.
FARM
insures pesticide application is applied during adequate
moisture conditions.
INIDAT provides common block CMISC.INC values.
TRDIAl solves tridiagonal maxtrix.
HYDROL calculates snowmelt, crop interception, runoff, and infiltra-
tion.
HFINTP determines boundary for head, concentration or flux.
PESTAP computes amount of pesticide application.
PLPEST determines amount of pesticide which disappears by first
order decay and pesticide washoff.
SLPSTO sets up the matrix for transport of pesticide.
CANOPY calculates the overall vertical transport resistance.
MOC solves the advection component of the pesticide transport
process.
MASBAL calculates mass balance error terms for both flow and transport.
PSTLNK provides linkage for transformation and source terms of
parent/daughter.
OUTCNC prints daily, monthly, and annual pesticide concentration
profiles.
TRDIAG solves tridiagonal matrix.
OUTRPT prints daily, monthly, and annual concentration profiles plus
snapshots.
VALDAT checks simulation dates against calendar dates.
XPRZM performs PRZM execution calls.
INITDK initializes amount of pesticide decay each chemical which
could have daughter products.
OUTPST prints daily, monthly, and annual pesticide flux profiles.
INITL initializes PRZM arrays.
OUTTSR prints daily, monthly, and annual time series data.
OUTHYD accumulates summaries for water flow.
HYDR1 performs hydraulic calculations assuming a uniform soil
profile.
PRZECH echoes PRZM input to files.
RSTPUT writes PRZM input to a restart file.
RSTGET reads PRZM input from a restart file.
RSTPT1 writes PRZM input to a restart file.
RCALC function to compute biodegradation.
RSTGT1 reads PRZM input from a restart file.
3-3
-------
TABLE 3-1. (Continued)
SUBROUTINE
MODULE
CALLING
ROUTINE
VADOFT
or
FUNCTION PURPOSE
PRZEXM creates input file for EXAMS moldel.
PRZDAY transfers start and end dates to common block.
THCALC computes moisture for PRZM.
INIACC initializes PRZM storage arrays.
KDCALC computes KD.
MCPRZ computes MONTE CARLO inputs for PRZM.
FNDCHM function to find a chemical number.
FNDHOR function to find a horizon number.
PZCHK checks horizonal values for consistency.
KHCORR corrects Henry's law constant.
ACTION performs special actions.
GETMET reads in meteorological data.
IRRIG performs irrigation algorithm.
FURROW computes furrow irrigation.
INFIL computes Green-Ampt infiltration.
EVPOTR computes evapotranspiration.
EROSN computes erosion losses,
SLTEMP calculates soil temperatures.
PRZM performs calls to PRZM routines.
TDCALC calculates total days in a simulation.
VADCAL calls relevant subroutines to compute nodal head and
concentration.
BALCHK mass balance calculation.
READTM reads in HVTM, TMHV, QVTM from input.
VADINP reads in flow and transport input.
TRIDIV performs tridiagonal matrix solution
VADOFT saves information between flow and transport.
IRDVC reads in integer vectors.
VSWCOM computes nodal values of water saturation and Darcy
velocities.
VADCHM transfers chemical specific data to VADOFT variables.
INTERP performs linear interpolation using tabulated data of
relative permeability versus water saturation.
SWFUN computes water saturation values for grid element.
PKWFUN computes relative permeability.
DSWFUN computes moisture capacity.
XTRANS controls transport calling routines.
RDPINT reads non-default nodes data.
VARCAL computes nodal head and concentration values.
ASSEMF assembly routine for flow.
VADPUT writes VADOFT input to restart file.
VADGET reads VADOFT input from a restart file.
ASSEMT assembly routine for transport.
XFLOW controls flow calling routines.
3-4
-------
TABLE 3-1. (Continued)
MODULE SUBROUTINE
CALLING or
ROUTINE FUNCTION PURPOSE
MCVAD determines MONTE CARLO variables for VADOFT.
READVC reads in vectors.
CONVER computes the limiting values of water saturation for each
material.
MONTE CARLO
MTPV calculates vectors.
OUTPUT write summary statistics.
INITMC initializes statistical summation arrays.
DECOMP decomposes the matrix BBT (N by N) into a lower triangular
form.
RANDOM controls random numbers generation.
NMB generates normal (0-1) random numbers.
UNIF generates uniform random numbers.
EXPRN generates exponentially distributed random numbers.
EMPCAL generates values from empirical distributions.
TRANSM converts normally distributed correlated vectors to the
parameter set returned to the model.
TRANSB transforms variables from normal space to SB space or vice-
versa.
OUTFOR writes tables and plots of cumulative distribution.
STOUT initializes the amount of pesticide decay.
FRQTAB prints tabular frequency output.
FRQPLT plots cumulative distributions.
MCECHO echoes MONTE CARLO input.
READM reads in MONTE CARLO input.
MAXAVG computes maximum daily average output.
STATIS performs summations for MONTE CARLO.
3-5
-------
TABLE 3-2.
LIST OF ALL PARAMETERS FILES, PARAMETER DIMENSIONS,
AND A BRIEF DESCRIPTION.
FILE
CTRACE.INC
PMXMAT.INC
PMXNLY.INC
PMXPRT.INC
PMXTIM.INC
PMXTMV.1NC
PMXVDT.INC
PCMPLR.INC
PARAMETER
MAXSUB=50
MAXLIN=10
MXMAT=5
MXNLAY=20
MXPRT=100
MXTIM=31
MXTMV-31
MXVDT=31
REALMX=1.0D+30
DESCRIPTION
maximum number of subroutines.
maximum number of lines for trace option.
maximum number of VADOFT materials.
maximum number of layers in VADOFT.
maximum number of VADOFT observation
nodes.
maximum number of VADOFT iterations
allowed.
maximum number of VADOFT time interpola
tion values.
maximum number of VADOFT time steps.
maximum real number.
PMXNOD.INC
PMXZON.NC
PPARM.1NC
PIOUNI.INC
PMXNSZ.INC
CMCRVR.INC
REALMN=1.0D-30
MAXINT=2147483647
MAXREC=512
EXNMX=-53.0
EXPMN=REALMN
EXPMX=53.0
WINDOW=. TRUE.
PCASCI=TRUE.
NONPC=.FALSE.
MXNOD=100
MXZONE=10
NCMPTS=100
NAPP=50
NC=5
NPII=800
NCMPP2=NCMPTS+2
MXCPD=100
KUOUT=6
NMXF1L=99
FILBAS=30
MXNSZO=lo
MCMAX=50
NMAX=10
NCMAX=10
NRMAX=1000
NEMP=20
MCSUM=MCMAX+NMAX
NPMAX=5
minimum real number.
maximum integer value.
maximum record length.
maximum negative exponential number.
minimum exponential real number.
maximum positive exponential number.
allows screen window on or off.
allows attributes for PC's for displays.
allows attributes for non-PC's for displays.
maximum number of VADOFT nodes allowed.
maximum number of PRZM zones.
maximum number of compartments in PRZM.
maximum number of applications in PRZM.
maximum number of crops allowed in PRZM.
maximum number of PRZM particles in MOC.
maximum number of compartments plus 2 for
top and bottom ends.
maximum number of cropping periods.in
PRZM.
screen unit number.
maximum number of file units open.
base file unit number.
maximum number of VADOFT zones allowed.
maximum number of random input variables.
maximum number of summary output
variables.
maximum number of CDF'S.
maximum number of MONTE CARLO runs.
maximum number of empirical distributions.
maximum number of random input and output
variables.
maximum length of MONTE CARLO averag-
ing periods.
3-6
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SECTION 4
INPUT PARAMETERS FOR PRZM 2
This section describes the development of the input data files used in the Execution
Supervisor (PRZM2.RUN), PRZM, VADOFT and MONTE CARLO. All of these fries,
except for the meteorological file, nay "have embedded comment lines. A comment line is
any line beginning with three asterisks (***), These lines are ignored by the code during
execution. For best accuracy and process time, a text or line editor is recommended for
inputing file records. To better understand record formats used in model input, an
example record format statement appears below:
FORMAT 3I2,2X,F8.0,EI0.3,1X2(I5,1XF8.0)
where input would look like:
010181 0.340 2.40EOO 1 0.340 1 0.340
The format identifier, 312, specifies there are three integers with 2 columns each. The
format identifier, 2X, specifies there are two blank spaces. The format identifier, F8.0,
specifies there is one floating point field with eight columns and also a decimal point with
no precision (although up to 7 seven of these columns may be points of precision with the
eighth column being the decimal point since this is a FORTRAN read statement). The
format identifier, E 10.3, specifies there is one field often columns that may include an
exponential suffix. The format identifier, 2(I5,1X,F8.0), specifies that there are two
sequential sets of I5,1X,F8.0 entered. All format specifiers should be right justified so that
unused columns in a field are assumed to be zeros by the code.
4.1 INPUT FILE DESCRIPTIONS
The Execution Supervisor (PRZM2.RUN) is used to define: 1) which modules are chosen
for simulation; 2) the number of zones used in a simulation; 3) input, output, and scratch
file names with optional path statements; 4) the starting and ending date of a simulation;
5) the number of chemicals (either separate or daughter); 6) weighting parameters
between PRZM and VADOFT zones; 7) and global echo and trace levels during execution.
PRZM, VADOFT, and MONTE CARLO input files consist of various title and FORTRAN-
formatted records. Each of these module files along with their examples are discussed in
the following pages. For further descriptions, see Section 5 on parameter estimation.
4.1
-------
4.1.1 Meteorological File
The PRZM-2 model requires use of a meteorological file that is specified in the execution
supervisor. Information on daily precipitation, pan evaporation, temperature, wind speed,
and solar radiation is included in each record of the meteorological file. These files are
from the National Oceanic and Atmospheric Administration (NOAA) and are available
from the Athens-ERL, An example file format is shown below:
RECORD FORMAT 1X,3I2,6F10.0
READ STATEMENT: MM, MD, MY, PRECIP, PEVP, TEMP, WIND, SOLRAD
where
MM = meteorological month
MD = meteorological day
MY = meteorological year
PRECIP = precipitation (cm day:l)
PEVP = pan evaporation data (cm day:l)
TEMP = temperature (celsius)
WIND = wind speed (cm see-1)
SOLRAD = solar radiation (Langleys)
4.1.2 Execution Supervisor File (PRZM2.RUN)
The PRZM-2 model requires existence of a control file (PRZM2.RUN) also known as the
execution supervisor file. This file specifies options by the user to control the overall
(global) parameters during model execution, The file must always be resident in the
current directory where the execution is performed. On the following pages are examples
of the execution supervisor input file.
4-2
-------
4.1.2.1 Example Execution Supervisor (PRZM2.RUN) input file
ONE ZONE
*** option records
PRZM
VADOFT
MONTE CARLO
TRANSPORT SIMULATION
*** zone records
PRZM ZONES
VADOFT ZONES
ENDRUN
*** Input file records
PATH
MCIN
METEOROLOGY 1
PRZM INPUT 1
VADOFTINPUT 1
*** output file records
PATH
TIME SERIES 1
PRZM OUTPUT 1
VADOFT OUTPUT 1
MCOUT
MCOUT2
*** scratch file records
PRZM RESTART 1
VADOFT FLOW RS 1
VADOFT TRANS RST 1
VADOFT TAPE 10 1
ENDFILES
*** global records
START DATE
END DATE
NUMBER OF CHEMICALS
PARENT OF 2
PARENT OF 3
ENDDATA
*** display records
ECHO
TRACE
ON
ON
OFF
ON
1
D:\PRZM2\INPUT\
MC.INP
MET.INP
PRZM3.INP
VADF3.INP
D:\PRZM2\OUTPUT\
TIMES. OUT
PRZM.OUT
VADF.OUT
MC. OUT
MC2.0UT
RESTART.PRZ
VFLOW.RST
VTRANS.RST
VADF.TAP
010181
311283
3
1
2
4
OFF
NOTE: Three asterisks (***) denote a comment line and are ignored by the program.
4-3
-------
4.1.2.2 Example Execution Supervisor (PRZM2.RUN) input file
TWO ZONES WITH MONTE CARLO OPTION
***0ptions
ON
ON
ON
ON
2
2
PRZM
VADOFT
MONTE CARLO
TRANSPORT SIMULATION
PRZM ZONES
VADOFT ZONES
ENDRUN
***Input files
MCIN
METEOROLOGY 1
METEOROLOGY 2
PRZM INPUT 1
PRZM INPUT 2
VADOFTINPUT 1
VADOFTINPUT 2
***0utput files
TIME SERIES 1
TIME SERIES 2
PRZM OUTPUT 1
PRZM OUTPUT 2
VADOFT OUTPUT 1
VADOFT OUTPUT 2
MCOUT
MCOUT2
***Scratch files
PRZM RESTART 1
PRZM RESTART 2
VADOFT FLOW RST 1
VADOFT FLOW RST 2
VADOFT TRANS RST 1
VADOFT TRANS RST 2
VADOFT TAPE10 1
VADOFT TAPE10 2
ENDFILES
START DATE
END DATE
NUMBER OF CHEMICALS
PARENT OF 2
PARENT OF 3
WEIGHTS
1.0 0.0
0.0 1.0
ENDDATA
ECHO
TRACE
MC.INP
MET.INP
METx.INP
PRZM.INP
PRZMx.INP
VADF.INP
VADFx.INP
TIMES. OUT
TIMESx.OUT
PRZM.OUT
PRZMx.OUT
VADF.OUT
VADFx.OUT
MC. OUT
MC2.0UT
RESTART.PRZ
RESTARTx.PRZ
VFLOW.RST
VFLOWx.RST
VTRANS.RST
VTRANSx.RST
VADF10.TAP
VADFlOx.TAP
010181
311281
3
1
2
ON
OFF
NOTE: Three asterisks (***) denote a comment line and are ignored by the program
4-4
-------
4.1.2.3 Execution Supervisor (PRZM2.RUN) Input Guide
RECORD 1 OPTIONS FORMAT A18,6X,A56
LABEL (Col. 1-18) EXECUTION STATUS (Col. 25-78)
PRZM ON or OFF (the root zone model execution)
VADOFT ON or OFF (the vadose zone model execution)
MONTE CARLO ON or OFF (Monte Carlo execution)
TRANSPORT ON or OFF (vadose zone transport execution)
RECORD 2- ZONES FORMAT A18,6X,I2
LABEL (Col. 1-18) ZONE NUMBER (Col. 25-78)
PRZM ZONES 1 to 10 (total number of PRZM land zones)
VADOFT ZONES 1 to 10 (total number of VADOFT land zones)
ENDRUN (specifies end of OPTIONS and ZONE
records)
RECORD 3- INPUT FILES FORMAT A18,1X,I2,3X,A56
LABEL (Col. 1-18) ZONE NUMBER (Col. 20-21) NAME (Col. 25-78)
PATH directory (optional)
METEOROLOGY 1 to 10 filename
PRZM INPUT 1 to 10 filename
VADOFT INPUT 1 to 10 filename
MCIN filename
RECORD 4 OUTPUT FILES FORMAT A18,1X,I2,3X,A56
LABEL (Col. 1-18) ZONE NUMBER (Col. 20-21) NAME (Col. 25-78)
PATH directory (optional)
TIME SERIES 1 to 10 filename
PRZM OUTPUT 1 to 10 filename
VADOFT OUTPUT 1 to 10 filename
MCOUT 1 to 10 filename
MCOUT2 1 to 10 filename
RECORD 5 SCRATCH FILES FORMAT A18,1X,I2,3X,A56
LABEL (Col. 1-18) ZONE NUMBER (Col. 20-21) NAME (Col. 25-78)
PATH directory (optional)
PRZM RESTART 1 to 10 filename
VADOFT FLOW RESTART 1 to 10 filename
VADOFT TRANS RESTART 1 to 10 filename
VADOFT TAPE 1 to 10 filename
ENDFILES (spectiles end of file name records)
4-5
-------
RECORD 6 GLOBAL RECORDS FORMAT A18,1X,3I2
LABEL (Col. 1-18) VALUE (Col. 20-25)
START DATE ddmmyy (starting day, month, year)
END DATE ddmmyy (ending day, month, year)
NUMBER OF CHEMICALS 1 to 3 (number of chemicals)
PARENT OF 2 1 (parent of the second chemical if TRANS-
PORT=ON and if more than one chemi-
cal)
PARENT OF 3 1 or 2 (parent of third chemical if TRANS-
PORT=ON and if more than one chemi-
cal)
WEIGHTS (indicates next values are weights)
NOTE: enter next lines only if PRZM or VADOFT have multiple zones.
Enter a line for every increasing PRZM zone containing a frac-
tional weight to each VADOFT zone. FORMAT 10(F8.2)
1.0 0.0 (PRZM zone 1 weight to VADOFT zone 1 and 2)
0.0 1.0 (PRZM zone 2 weight to VADOFT zone 1 and 2)
ENDDATA (specifies end of GLOBAL data)
RECORD 7 DISPLAY RECORDS FORMAT A18,6X,A56
LABEL (Col. 1-18) VALUE (Col. 25-78)
ECHO 1 to 9 (amount output increasingly displayed to
the screen and to files)
TRACE ON or OFF (tracking of subroutines for debugging)
EFFECT OF THE ECHO LEVEL ON MODEL OUTPUT
ECHO LEVEL
Percent bar graph
Simulation status to screen
Simulation status to files
Subroutine trace available
Warnings displayed
Results of linkage routines
Detailed water/solute data
Detailed head/concentration
Echo of line being read from
1 2
x X
X
data
input
3
X
X
X
4
X
X
X
X
5
X
X
X
X
X
6
X
X
X
X
X
X
7
X
X
X
X
X
X
X
8
X
X
X
X
X
X
X
X
X
Echo of image being read from input
9
X
X
X
X
X
X
X
X
X
X
4-6
-------
4.1.3 PRZM Input File
The PRZM-2 model requires a PRZM input file if the PRZM option is specified "ON" in
the execution supervisor file. The following page shows an example PRZM input file with
various options implemented as a reference.
4.1.3.1 Example PRZM.INP input file for PRZM-2
3 CHEMICALS, 2 HORIZONS, EROSION, IRRIGATION, PRZM INPUT FOR ZONE 1
HYDROLOGY PARAMETERS (CROP DATA FROM USDA NO.283 HANDBOOK)
0.72
9.6
15.1
1
0.15
1
1
110582
0.00
9.7
14.5
0.14
0.15
2
12.2
12.5
1.0
15.000
13.61
11.3
2.0
1
5.4
9.5
5.8
3
1
9.0
5.5
15.0 80.000
86 78 82 0.1 0.1 0.1 60.0
300982 151082
PESTICIDE TRANSPORT AND ^RS^(SffOiRMM36N AND APPLICATION PARAMETERS
ALDICARB
120582 0
120682 0
1 1
SOILS PARAMETERS
45.0 0.3
4.3E3 O.OEOO
3 0.25
0
ATRAZINE
2.5
2.5
CARBOFURAN
2.5
2.5
2.5
2.5
1.00
1.00
0
1.00 1.00
1.00 1.00
0
5.5E-3
1 1
5.5E-7
000
2.5E-7 O.OEOO 5.5E-7
0.55 .78
0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.97 10.0
8.3 8.3 8.3 8.3 8.3 8.3 8.3 8.3 8.3 8.3 8.3 8.3
0.0 0.0 0.0
0.014 0.0000.023
.1 1. .3
0.0
0
2
1
2
0
VATR
2
,FLX1
INFL
15.0
0.020
0.5
8.3
0.000
30.0
0.020
2.5
8.3
0.000
0
YEAR
YEAR
TSER
TCUM
1.45 0.233
0.000 0.000
.233 .050
10.0 60.0
0.000 0.000
1.45 0.233
0.000 0.000
.233 .050
10.0 60.0
0.000 0.000
0.0
0.014
1.0
0.0
0.0
0.007
0.1
0.0
1 PEST YEAR
1.0E05
31
0.0
0.007
0.1
0.0
0.0 0.0 0.0
0.007 0.0000.023
0. .1 0.
0.0
CONC
0.2300.000
0.0230.000
YEAR
SPECIAL ACTIONS
010782 SNAPSHOT
4-7
-------
4.1.3.2 PRZM input guide for PRZM-2
RECORD 1
col: 1-78
RECORD 2
col: 1-78
RECORD 3
col: 1-8
col: 9-16
col: 17-24
coll: 25-32
col: 33-40
col: 41-48
RECORD 4
col: 1-48
RECORD 5
col: 1-48
RECORD 6
col: 1-8
RECORD 7
col: 1-8
col: 9-16
col.k 17-24
FORMAT A78
TITLE: label for simulation title.
FORMAT A78
HTITLE: label for hydrology information title.
FORMAT 2F8.0,I8,F8.0,2I8
PFAC: pan factor used to estimate daily evapotranspiration.
SFAC: snowmelt factor in cm/degrees Celsius above freezing.
IPEIND: pan factor flag. 0 = pan data read, 1 = temperature
data read, 2 = either available used.
ANETD: minimum depth of which evaporation is extracted
(cm).
INICRP: flag for initial crop if the simulation date is before
the emergence date, (see record 10). 1 = yes, 0 = no.
ISCOND: surface condition of initial crop if INICRP = 1.1 =
fallow, 2 = cropping, 3 = residue.
Only if IPEIND = 1 or 2 (see record 3).
FORMAT 6F8.0
DT: monthly daylight hours for January - June.
Only if IPEIND = 1 or 2 (see record 3).
FORMAT 6F8.0
DT: monthly daylight hours for July - December.
FORMAT 18
ERFLAG: flag to calculate erosion. 1 = yes, 0 = no.
Only if ERFLAG = 1 (see record 6).
FORMAT 5F8.0
USLEK universal soil loss equation (K) of soil erodibilty.
USLELS: universal soil loss equation (LS) topographic factor.
USLEP: universal soil loss equation (P) practice factor.
4-8
-------
col: 25-32 AFIELD: area of field or plot in hectares,
col: 33-40 TR: average duration of rainfall produced by storms (hrs).
RECORD 8 FORMAT 18
col: 1-8 NDC: number of different crops in the simulation (1 to 5).
RECORD 9 Repeat this record up to NDC (see record 8).
FORMAT I8,3F8.0,I8,3(1X,I3),3(1X,I3),2F8.0
crop number of the different crop.
maximum interception storage of the crop (cm).
maximum rooting depth of the crop (cm).
maximum areal coverage of the canopy (percent).
surface condition of the crop after harvest date (see
record 11). 1 = fallow, 2 = cropping, 3 = residue.
runoff curve numbers of antecedent moisture condi-
tion 11 for fallow, cropping, residue (3 values).
universal soil loss cover management factors for
fallow, cropping ,residue (C value). Required if ERFL-
AG = 1 (see record 6) else set to 0.0 (3 values).
WFMAX maximum dry weight of the crop at full canopy (kg
mi). Required if FAM = 3 (see record 16) else set to
0.0.
HTMAX: maximum canopy height at maturation date (cm) (see
record 11).
FORMAT 18
NCPDS: number of cropping periods (sum of NDC for all
cropping dates in record 11).
col: 1-8
col: 9-16
col: 17-24
col: 25-32
col: 33-40
col: 42-52
col: 54-64
ICNCN:
CINTCP:
AMXDR:
COVMAX:
1CNAH:
CN:
USLEC:
col: 65-72
col: 73-80
RECORD 10
col: 1-8
RECORD 11 Repeat this record up to NCPDS (see record 10).
col: 3-4
col: 5-6
col: 7-8
col: 11-12
FORMAT 2X,3I2,2X,3I2,2X,3I2,I8
EMD: integer day of crop emergence,
EMM: integer month of crop emergence.
IYREM: integer year of crop emergence.
MAD: integer day of crop maturation.
4-9
-------
col: 13-14
col: 15-16
col: 19-20
col: 21-22
col: 23-24
col: 25-32
RECORD 12
col: 1-80
RECORD 13
col: 1-8
col: 9-16
col: 17-24
RECORD 14
col: 1-60
RECORD 15
col: 3-4
col: 5-6
col: 7-8
col: 9-16
FORMAT
PSTNAM:
Repeat this
FORMAT
APD:
APM:
IAPYR:
WINDAY:
col: variable
MAM: integer month of crop maturation.
IYRMAT: integer year of crop maturation.
HAD: integer day of crop harvest.
HAM: integer month of crop harvest.
IYRHAR: integer year of crop harvest.
INCROP crop number associated with NDC (see record 8).
FORMAT A78
PTITLE: label for pesticide title.
FORMAT 318
NAPS: total number of pesticide applications occuring at
different dates (1 to 50). Note: if two or more pesti-
cides are applied on the same date then NAPS = 1
for that day.
NCHEM: number of pesticide(s) in the simulation. This value
should equal the number in the execution supervisor
file(l to 3).
FRMFLG: flag for testing of ideal soil moisture conditions for
the application of pesticide(s) relative to the target
date (see record 15 for target date information). 1 =
yes, 0 = no.
3A20
names of pesticide (s) for output titles.
record up to NAPS (see record 13).
2X,3I2,I8,6F8.0
integer target application day.
integer target application month.
integer target application year.
number of days in which to check soil moisture val-
ues following the target date for ideal pesticide (s)
applications. Required if FRMFLG = 1 else set to 0.
DEPI: depth of the pesticide(s) application (cm). Note:
DEPI should be entered in the same order as in
PSTNAM (record 14) if NCHEM is greater than one.
4-10
-------
col: variable
RECORD 16
col: 1-8
col: 9-16
col: 17-24
RECORD 17
col: 1-8
col: 9-16
col: 17-24
RECORD 18
col: 1-78
RECORD 19
col: 1-8
col: 9-16
col: 17-20
col: 21-24
TAPP: total application of the pesticide(s) (kg ha:l). Note:
TAPP should be entered in the same order as in
PSTNAM (record 14) if NCHEM is greater than one.
FORMAT 2I8,F8.0
FAM: foliar application model flag. 1 = pest, application to
soil only, 2 = linear pesticide foliar application based
on crop canopy, 3 = pesticide foliar application using
nonlinear exponential filtration.
IPSCND: condition for disposition of foliar pesticide after har-
vest. 1 = surface applied, 2 = complete removal, 3 =
left alone. Required if FAM=2 or 3.
FILTRA: filtration parameter. Required if FAM = 3 else set to
0.0.
Only if FAM=2 or 3, repeat this record up to NCHEM.
FORMAT 3F8.0
PLVKRT pesticide volatilization decay rate on plant foliage
(days-1).
PLDKRT: pesticide decay rate on plant foliage (days-1).
FEXTRC: foliar extraction coefficient for pesticide washoff per
centimeter of rainfall.
FORMAT A78
STITLE: label for soil properties title.
FORMAT 2F8.0,9I4
CORED: total depth of soil core in cm. (must be sum of all
horizons thicknesses (THKNS)in record 33 and at
least as deep as the root depth in record 9).
UPTKF: plant uptake factor. 1 = uptake is equal to transpira-
tion * dissolved phase concentration, 0 = no uptake is
simulated, .001 to .99 = uptake is a fraction of tran-
spiration * dissolved phase concentration.
BDFLAG bulk density flag. 1 = mineral value entered, 0 =
apparent bulk density known and entered in record
33.
THFLAG field capacity and wilting point flag. 1 = calculated
by the model, 0 = water contents are entered.
4-11
-------
col: 25-28
col: 29-32
col: 33-36
col: 37-40
col: 41-44
col: 45-48
col: 49-52
RECORD 20
KDFLAG:
HSWZT:
MOC:
IRFLAG:
ITFLAG:
IDFLAG:
BIOFLG:
OnlyifBIOFLG
FORMAT
col: 1-8
col: 9-16
col: 17-24
col: 25-32
col: 33-40
RECORD 21
col: 1-8
col: 9-16
col: 17-24
col: 25-32
col: 33-40
AM:
AC:
AS:
AR:
KE:
OnlyifBIOFLG
FORMAT
KSM:
KCM:
KC:
MRS:
KR:
soil/pesticide adsorption coefficient. 1 = calculated by
the model, 0 = KD value entered in record 36.
drainage flag. 1 = restricted, 0 = free draining,
method of characteristics flag. 1 = yes, 0 = no.
irrigation flag. 0 = no, 1 = year round, 2 = during
cropping period only.
soil temperature simulation flag. 1 = yes, 0 = no.
thermal conductivity and heat capacity flag. 1 = yes,
0 = no.
biodegradation flag. 1 = yes, 0 = no.
= 1 (see record 19).
5F8.0
maintenance coefficient of the metabolizing X& popu-
lation (day-"]).
maintenance coefficient of the co-metabolizing X^
population (day:l).
maintenance coefficient of the sensitive X, population
(day:l).
maintenance coefficient of the non-sensitive Xj popu-
lation (day:l).
average enzyme content of the X;. population (dimen-
sionless).
= 1 (see record 19).
7F8.0
saturation constant of the metabolizing X^ popula-
tion with respect to pesticide concentration.
saturation constant of the metabolizing Xs popula-
tion with respect to carbon concentration.
saturation constant of the co-metabolizing X> popula-
tion.
saturation constant of the sensitive X^ population,
saturation constant of the non-sensitive Xj popula-
tion.
4-12
-------
col: 41-48
col: 49-56
RECORD 22
col: 1-8
col: 9-16
col: 17-24
col: 25-32
col: 33-40
col: 41-48
RECORD 23
col: 1-8
col: 9-16
KIN:
KSK:
OnlyifBIOFLG
FORMAT
KLDM:
KLDC:
KLDS:
KLDR:
KL1:
KL2:
OnlyifBIOFLG
FORMAT
USM:
UCM:
col: 17-24 MUC:
col: 25-32 us:
col: 33-40 UR:
RECORD 24
col: 1-8
OnlyifBIOFLG
FORMAT
YSM:
inhibition constant (mg g:1 dry soil).
carbon solubilization constant (day-1).
=1 (see record 19).
6F8.0
death rate of the metabolizing Xg population (day-').
death rate of the co-metabolizing Xj population
(day:l).
death rate of the sensitive J^ population (day:l).
death rate of the non-sensitive ^ population (day-').
second order death rate of the X^ population (mg g:l
day-\).
dissociation constant of the enzyme substrate com-
plex (day-1),
= 1 (see record 19).
5F8.0
growth rate of the metabolizing Xg, population with
respect to pesticide concentration (day-1).
specific growth rate of the metabolizing X^ popula-
tion with respect to carbon concentration
(day-').
specific growth rate of the co-metabolizing Xj popula-
tion (day-1),
specific growth rate of the sensitive 2%, population
(day-1).
specific growth rate of the non-sensitive X^ popula-
tion.
= 1 (see record 19).
5F8.0
true growth yield of the metabolizing EQ population
with respect to pesticide concentration (rngfdry wt.)/-
mg).
4-13
-------
col: 9-16
YCM:
true growth yield of the metabolizing X^ population
with respect to carbon concentration (mgfdry wt.)/m-
g).
col: 17-24
col: 25-32
col: 33-40
RECORD 25
col: 1-8
col: variable
col: variable
RECORD 26
col: 1-8
col: 9-16
col: 17-24
col: 25-32
RECORD 27
col: 1-8
col: 9-16
col: 17-24
YC:
YS:
YR:
FORMAT
DAIR:
HENRYK:
ENPY:
OnlyiflRFLAG
FORMAT
IRTYP:
PLEACH:
PCDEPL:
RATEAP:
OnlyiflRFLAG
FORMAT
QO:
BT:
ZRS:
true growth yield of the co-metabolizing X^ population
(mg(dry wt.)/mg).
true growth yield of the sensitive X, population (mg(-
dry wt.)/mg).
true growth yield of the non-sensitive X;. population
(mg(dry wt.)/mg).
7F8.0
diffusion coefficient for the pesticide (s) in the air.
Only required if HENRYK is greater than 0 else set
to 0.0
henry's law constant of the pesticide (s) for each NCH-
EM.
enthalpy of vaporization of the pesticide (s) for each
NCHEM.
= 1 or 2.
I8,3F8.0
type of irrigation. 1 = flood irrigation, 2 = furrow, 3
= over canopy, 4 = under canopy sprinkler.
leaching factor as a fraction of irrigation water depth.
fraction of water capacity at which irrigation is ap-
plied.
maximum rate at which irrigation is applied (cm
hr-i),
= 1 or 2 and IRTYP = 2.
7F8.0
flow rate of water entering the heads of individual
furrows (ni? s%
bottom width of the furrows (m) .
slope of the furrow channel walls
(horizontal/vertical).
4-14
-------
col: 25-32
SF:
col: 33-40
col: 41-48
col: 49-56
EN:
X2:
XFRAC:
RECORD 28
col: 1-8
col: 9-16
RECORD 29
col: 1-8
col: variable
RECORD 30
col: 1-60
col: 61-65
col: 66-70
RECORD 31
col: 1-60
slope of the furrow channel bottom (verti-
cal/horizontal) .
Manning's roughness coefficient for the furrow.
length of the furrow (m).
location in furrow where PRZM infiltration calcula-
tions are performed, as a fraction of the furrow
length (X2). If XFRAC = -1, average depths are used
in PRZM.
Only if IRFLAG = 1 or 2 and IRTYP = 2.
FORMAT 2F8.0
KS:
saturated hydraulic conductivity of the soil in which
furrows are dug (m s'-l).
HF: green-amp infiltration suction parameter (m).
Only if KDFLAG = 1 (see record 19).
FORMAT I8,3F8.0
PCMC: flag for which model is used to estimate KD (see
record 36). 1 = mole fraction, 2 = mg liter:l, 3 = micr-
omoles liter-1, 4 = KOC entered (dimensionless).
SOL: pesticide(s) volubility entered according to PCMC flag
above for each NCHEM.
Only if ITFLAG = 1 (see record 19).
FORMAT 1415
ALBEDO: monthly values of soil surface albedo (12 values).
EMMISS: reflectivity of soil surface to longwave radiation (frac-
tion) .
ZWIND: height of wind speed measurement above the soil
surface (m).
Only if ITFLAG = 1 (see record 19).
FORMAT 1215
BBT:
average monthly values of bottom boundary soil
temperatures in degrees Celsius (12 values).
4-15
-------
RECORD 32
col: 1-8
RECORD 33
col: 1-8
col: 9-16
col: 17-24
col: 25-32
col: 33-40
col: 41-48
RECORD 34
col: 9-16
col: 17-24
col: 25-32
col: 33-40
col: 41-48
col: 49-56
RECORD 35
col: variable
FORMAT
NHORIZ:
Repeat records
FORMAT
HORIZN:
THKNS:
BD:
THETO:
AD:
DISP:
OnlyifBIOFLG
FORMAT
Q:
CM1:
Yl:
Y2:
Y3:
Y4:
FORMAT
DWRATE:
18
total number of horizons (minimum of 1).
33 38 in data sets up to NHORIZ.
I8JF8.0
horizon number in relation to NHORIZ.
thickness of the horizon.
bulk density if BDFLAG = 0 or mineral density if
BDFLAG= 1.
initial soil water content in the horizon (cm? cmty.
soil drainage parameter if HSWZT = 1, else set to 0.0
(day:l).
pesticide (s) hydrodynamic solute dispersion coeffi-
cient for each NCHEM.
= 1 (see record 19).
8X,5F8.0
average carbon content of the population.
dimensionless.
mineralizable carbon (mg g;l).
concentration of metabolizing microbial population
concentration of co-metabolizing microbial population
(mg g:l).
concentration of sensitive microbial population (mg
concentration of non-sensitive microbial population
i -\\
(mg g-1).
8X,9F8.0
dissolved phase pesticide (s) hydrolysis decay rate for
col: variable
DSRATE:
each NCHEM (day-1).
adsorbed phase pesticide (s) hydrolysis decay rate for
each NCHEM (day-1).
4-16
-------
col: variable
DGRATE:
vapor phase pesticide(s) decay rate for each NCHEM
RECORD 36
col: 9-16
col: 17-24
col: 25-32
col: 33-40
col: variable
col: 9-16
col: 17-24
col: 25-32
col: 33-40
col: 41-48
RECORD 38
col: 9-16
col: 17-24
col: 25-32
FORMAT
DPN:
THEFC:
THEWP:
OC:
KD:
Note: set DWRATE and DSRATE equal to simulate
lumped first-order degradation.
8X7F8.0
thickness of compartments in the horizon (cm).
field capacity in the horizon (cm? cm3),
wilting point in the horizon (cm? cna^),
organic carbon in the horizon (percent).
pesticide (s) partition coefficient for each NCHEM.
Required if KDFLAG = 0, else set to 0.0 (cm$ g-1).
RECORD 37 Only if ITFLAG = 1 (see record 19).
FORMAT 8X,5F8.0
SPT: initial temp, of the horizon (celsius).
SAND: sand content in the horizon. Required if THFLAG =
1, else set to 0.0 (percent).
CLAY clay content in the horizon. Required if THFLAG =
1, else set to 0.0 (percent).
THCOND: thermal conductivity of the horizon (cm-"t day:l).
Required if IDFLAG = 0, else set to 0.0.
VHTCAP: heat capacity per unit volume of the soil horizon (cmn3
celstafr j. Required if IDFLAG = 0, else set to 0.0.
Only if NCHEM greater than 1. Note: this record is used for
parent/daughter-relationship. Set to zero for simulating inde-
pendent parent chemicals.
FORMAT 8X3F8.0
DKRT12: transformation rate for chemical 1 to 2.
DKRT13: transformation rate for chemical 1 to 3. If NCHEM =
2, set to 0.0.
DKRT23: transformation rate for chemical 2 to 3. If NCHEM =
2, set to 0.0.
4-17
-------
RECORD 39
col: 1-8
col: 9-16
RECORD 40
col: 1-80
RECORD 41
col: 5-8
col: 13-16
col: 17-24
col: 29-32
col: 37-40
col: 41-48
col: 53-56
col: 61-64
col: 65-72
col: 73-76
RECORD 42
col: 1-8
col: 13-16
FORMAT
ILP:
CFLAG:
Only if ILP = 1
SCO divided by
per line. Enter
FORMAT
PESTR:
FORMAT
ITEM1:
STEP1:
LFREQ1:
ITEM2:
STEP2:
LFREQ2:
ITEMS:
STEPS:
LFREQ3:
EXMFLG:
FORMAT
NPLOTS:
STEP4:
218
flag for initial pesticide (s) levels before simulation
start date. 1 = yes, 0 = no.
conversion flag for initial pesticide (s) levels, 0 =
mgAgl, 1 = kgfflatfh Leave blank if ILP = 0.
(see record 39). NOTE: number of lines = THKN-
DPN(I) where I = HORIZN. Maximum of 8 values
this record in data sets for each NCHEM.
8F8.0
initial pesticide(s) levels.
3(4X,A4,4X,A4,I8),I4
hydrologic hardcopy output flag. WATR is inserted
or leave blank.
time step of hydrologic output. DAY= daily, MNTH
= monthly, YEAR = yearly.
frequency of hydrologic output given by a specific
compartment number.
pesticide flux output flag. PEST is inserted or leave
blank.
same as STEP1.
same as LFREQ1.
pesticide concentration output flag. CONC is insert-
ed or leave blank.
same as STEP1.
same as LFREQ1.
flag for reporting output to file for EXAMS model. 1
= yes, 0 = no. If ERFLAG = 0, EXMFLG is automati-
cally set to 0.
I8,4X,A4
number of times series plots (max. of 7).
Time step of output. This option outputs pesticide
runoff and erosion flux and pesticide leaching below
core depth. Three options are available: DAY for
daily, MNTH for monthly, YEAR for yearly.
4-18
-------
RECORD 43
col: 5-8
col: 9-9
col: 13-16
col: 17-24
col: 25-32
RECORD 44
col: 1-78
RECORD 45
col: 3-4
col: 5-6
col: 7-8
col: 10-17
col: 19-21
col: variable
Only if NPLOTS is greater than 0 and ECHOLV greater than 2.
NOTE: repeat this record up to NPLOTS.
4X,A4,A1,3X,A4,I8,F8.0
name of plotting variable (see Table 4-1 on page 4-
23).
index to identify which pesticide if applicable. 1 =
first chemical, 2 = second chemical, 3 = third chemi-
cal.
plotting mode, enter TSER (daily) or TCUM (cumu-
lative) to plot to times series file.
argument value for PLNAME (see table 4-1),
constant with which to multiply for unit conversion.
Leave blank for default to 1.0.
FORMAT
PLNAME:
INDX:
MODE:
IARG:
CONST:
Only if special actions are desired (see record 45).
FORMAT A78
ATITLE: label for special actions title,
Only if special actions are desired. Repeat this record for each
special action required (up to 7).
FORMAT 2X,3I2,1X,A8,1X,I3,3F8.0
SADAY: day of special action.
SAMON: month of special action.
SAYR: year of special action.
SPACT: special action variable (see below).
NACTS: horizon or crop number affected by special actions
(see below).
SPACTS: new value(s) for the special action (see page 4-23),
4-19
-------
SPACT NACTS SPACTS
BD HORIZON NO. NEW VALUE(S) (F8.0)
CN CROP NO. NEW VALUES (318)
DSRATE HORIZON NO. NEW VALUE(S) (3F8.0)
DWRATE HORIZON NO. NEW VALUE (S) (3F8.0)
KD HORIZON NO. NEW VALUE (S) (3F8.0)
SNAPSHOT*
USLEC CROP NO. NEW VALUE (S) (3F8.0)
* Used to display pesticide concentration profile.
4-20
-------
TABLE 4-1. VARIABLE DESIGNATIONS FOR PLOTTING FILES
Variable
Designation
(PLNAME)
Water Storage
INTS
SWTR
SNOP
THET
Water Fluxes
PRCP
SNOF
THRF
INFL
RUNF
CEVP
SLET
TETD
Sediment Flux
ESLS
FORTRAN
Variable
CINT
SW
SNOW
THETN
PRECIP
SNOWFL
THRUFL
AINF
RUNOF
CEVAP
ET
TDET
SEDL
Description
Interception sto
rage on canopy
Soil water storage
Snow pack storage
Soil water content
Precipitation
Snowfall
Canopy throughfall
Percolation into
Runoff depth
Canopy evaporation
Actual evapotrans-
piration from each
compartment
Total daily actual
evapotranspiration
Event soil loss
Units
cm
cm
cm
cm cm:l
cm day:l
cm day:!
cm day:l
each soil com-
partment
cm day:l
cm day:l
cm day:l
Tonnes
day\
Arguments
Required
(IARG)
None
1-NCOM2
None
1-NCOM2
cm day:lNome
None
None
1-NCOM2
cm day:lNone
None
1-NCOM2
None
None
Pesticide Storages
FPST FOLPST
TPST
PESTR
Foliar pesticide
storage
Total soil pesticide
storage in each soil
compartment
gcmf
None
1-NCOM2
4-21
-------
TABLE 4-1. VARIABLE DESIGNATIONS FOR PLOTTING FILES (continued)
Variable
Designation
(PLNAME)
SPST
Pesticide Fluxes
TPAP
FPDL
WFLX
DFLX
AFLX
DKFX
UFLX
Pesticide Fluxes
RFLX
FORTRAN
Variable
SPESTR
TAPP
FPDLOS
WOFLUX
DFFLUX
ADFLUX
DKFLUX
UPFLUX
ROFLUX
Description
Dissolved pesticide
storage in 'each soil
compartment
Total pesticide
application
Foliar pesticide
decay loss
Foliar pesticide
washoff flux
Individual soil
compartment pesticide
net diffusive flux
Pesticide advective
flux from each soil
compartment
Pesticide decay flux
in each soil compart-
ment
Pesticide uptake
flux from each soil
compartment
Pesticide runoff flux
Units
g cmfi
g cm?
day:l
g cmf
day-'
gcmf
day-'
g cmi
dayl
gcnDh?
day:l
gcmi
day:l
g cmi
day:l
—4
g cmt£
day-'
Arguments
Required
(IARG)
1-NCOM2
None
None
None
1-NCOM2
1-NCOM2
1-NCOM2
1-NCOM2
None
EFLX
RZFX
TUPX
ERFLUX Pesticide erosion flux g cm%
RZFLUX Net pesticide flux g cntf
past the maximum root day:l
depth
SUPFLX Total pesticide uptake g cm-z
flux from entire soil day;l
profile
None
None
None
4-22
-------
TABLE 4-1. VARIABLE DESIGNATIONS FOR PLOTTING FILES (concluded)
Variable
Designation
(PLNAME)
TDKF
PCNC
VFLX
FPVL
FORTRAN
Variable
SDKFLX
TCNC
PVFLUX
FPVLOS
Description
Total pesticide decay
flux from entire profile
Pesticide concentration
in canopy
Soil pesticide
volatilization flux
Foliar pesticide
volatilization flux
Units
g cm,-z
gcm3
day:l
gcml?
day:l
Arguments
Required
(IARG)
None
None
None
None
Soil Temperature
STMP SPT
Canopy Height
CHGT HEIGHT
Soil temperature in °C
each soil compartment
Canopy height
cm
1-NCOM2
None
4-23
-------
4.1.4 VADOFT Input File
The PRZM-2 model requires a VADOFT flow input file if VADOFT is specified "ON" in
the execution supervisor (PRZM2.RUN) file. Also if TRANSPORT SIMULATION is
specified "ON", VADOFT transport input must follow.
4.1.4.1 Example of VADOFT FLOW and TRANSPORT input file for PRZM-2
************* **********************pkOW******************* *******************
3 CHEMICAL, 2 HORIZON, 1 MATERIAL, VADOSE ZONE FLOW SIMULATION FOR
ZONE 1
11 110
61 1
20 2
1 1
0.0
1
2
1 20
2 40
O.OEOO
0 1
7.12E02
0.045EOO
YEAR
1
1
1
0.0
1
1
0
0
.01
1
1.0
0
1
1.0
1
1.0
0
1.0
50.0
80.0
0.0
.43EOO
-l.OEOO
O.OEOO
O.OEOO
0.145EOO
0000
O.OEOO
2.68EOO 0.626EOO
5 10
************* *********************rj^^ysq-gpQjjrp ******* ***************************
3 CHEMICAL, 2 HORIZON, 1 MATERIAL, VADOSE TRANSPORT SIMULATION FOR
ZONE 1
61
0
1
2
1
2
0.
0
1
1
0.0
0.0
20
40
OEOO
0
1
1
1
1
0
1.30E01
l.OOEOO
1
1
1
5
1
0
1
0
1.0
50.0
80.0
0
0
1
.0
O.OEOO
0.0
1
1
1
0
0
.0
2
1
1.0
O.OEOO
.0
0
0
0
0
.43EOO
.01EOO
.0
2.000E-2
1
10
1
1
.OOEOO
.0
O.OOEOO
0.
0.
7.00E-3
OEOO
OEOO
0.0
O.OOEOO
COO O.OEOO
2.30E-2 O.OEOO
YEAR
4-24
-------
4.1.4.2 VADOFT
RECORD 1
col: 1-80
RECORD 2
col: 1-5
col: 6-10
col: 11-15
col: 16-20
col: 21-25
col: 26-30
col: 31-35
col: 36-40
col: 41-45
col: 46-50
Input Guide for Flow
FORMAT A80
TITLE: label for flow simulation title.
FORMAT 1015
NP: total number of Vadoft nodal points (max of 100).
NMAT: total number of different porous materials (maximum of 5).
NONU: flag to indicate if initial condition is non-uniform. 1 = yes, 0
= no.
ITRANS: flag to indicate if running in transient or steady-state. Must
be set to 1 if PRZM is ON. 1 = transient, 0 = steady-state.
IMODL: flag to indicate if running flow or transport model. 1 = flow,
0 = transport. Set to 1 here.
IKALL: time stepping index. 1 = backward difference, 0 = central
difference. This flag is automatically set to 1 in FLOW.
IMBAL: flag to indicate if mass balance computation is required. 1 =
yes, 0 = no.
INTSPC: flag to indicate initial conditions for head values. 1 = hydrau-
lic head, 0 = pressure head.
IHORIZ: flag to indicate if flow direction is horizontal. 1 = yes, 0 = no.
Set to 0 if PRZM is ON.
ICHAIN: flag to indicate if daughter products are used. 1 = yes, 0 =
no. Automatically set to 0 for flow.
RECORD 3 FORMAT
col: 1-5 NITMAX
col: 6-10
col: 11-15
col: 16-25
INEWT:
IRESOL:
HTOL:
3I5,E10.3
maximum number of iterations per time step. Sug-
gested value of 20.
flag to indicate nonlinear iterative procedure for
solving saturated flow equation. 0 = Picard, 1 =
standard Newton-Raphson, 2 = modified Newton-
Raphson. Suggested value of 2 if PRZM is ON.
maximum number of refinements each time step if
solution does not converge. Suggested value of 1.
head tolerance for the nonlinear solution (length).
Suggested value of 0.01.
4-25
-------
RECORD 4
col:: 1-5
col: 6-10
col: 11-15
col: 16-20
col: 21-25
col: 26-30
col: 31-35
col: 36-40
RECORD 5
col: 1-10
FORMAT
KPROP:
ITSGN:
ITMARK:
NSTEP:
NVPR:
IOBSND:
NOBSND:
IPRCHK:
OnlyiflTRANS
FORMAT
TIMA:
815
flag to indicate relationship between relative perme-
ability versus saturation and pressure head versus
saturation. 1 = functional parameters supplied in
record 15,0 = model calculated.
flag to indicate if output time values are to be model
calculated. 1 = yes, 0 = no.
flag to indicate if output time values differ from com-
putational time values (see records 6 and 7). 1 = yes,
0 = no.
value of which time step to output nodal values from.
When NSTEP = n, then output is printed. Must be
from 1 up to 31 (days).
value of which time step to output nodal velocities.
When NVPR = n, then output is printed. Must be
from 1 up to 31 (days).
flag to indicate if values are printed at certain obser-
vation nodes. 1 = yes, 0 = no. NOTE: Echo level
must be greater than or equal to 6 in PRZM2 .RUN
file.
number of observation node(s) to be printed. NOBS-
ND must not be greater than NP (see record 2). If
IOBSND = 0 then set NOBSND = 0.
flag to indicate if detailed information is generated in
the flow matrix. 1 = yes, 0 = no,
= 1 (see record 2).
4E10.3
initial time value (t). Suggested value if PRZM is
ON: 0.0
col: 11-20
col: 21-30
col: 31-40
TIN:
TFAC:
TMAX:
initial time step value (t). Suggested value if PRZM
is ON: 1.0. Omit if ITSGN = 0.
time step multiplier. Suggested value if PRZM is ON:
1.0. Omit if ITSGN = 0.
maximum time step value allowed (t). Suggested
value if PRZM is ON: 1.0 Omit if ITSGN = 0.
4-26
-------
RECORD 6 Only if ITGSN = 0 (see record 4) and ITRANS = 1.
FORMAT 8E10.3
col: 1-80 m e ( I ) : time values corresponding to the number of time
steps where I = 1...31 (t). Input up to 8 values per
line.
RECORD 7 Only if ITMARK = 1 and ITRANS = 1
col: 1-5
col: 6-15
col: 16-25
RECORD 8
col: 1-80
RECORD 9
col: 1-5
RECORD 10
col: 1-5
col: 6-10
col: 11-15
col: 16-25
RECORD 11
col: 1-10
FORMAT I5,2E10.3
ITMGEN: flag to indicate if backup file marker time values are
used, 1 = yes, 0 = no.
STMARK: starting marker time value (t). If PRZM and TRAN-
SPORT are ON, set to 0.0.
DTMARK: marker time value increment (t). If PRZM and TRA-
NSPORT are ON, set to 1.0.
Only if ITRANS = 1, ITMARK = 1 and ITMGEN = 0.
FORMAT 8E10.3
TMFOMT: output marker file time values (t) corresponding to
TMVEC(I) (see record 6). Input up to 8 values per
line,
FORMAT 15
NLAYRG: number of soil horizons to be discretized.
Repeat this record up to NLAYRG (see record 9).
FORMAT 3I5,E10.3
ILAYR: horizon number in relation to NLAYRG,
NELM: number of finite elements in ILAYR.
IMATL: porous material number related to NMAT (see record
2) in ILAYR.
THL: thickness of the horizon (ILAYR).
FORMAT EIO.3,15
CHINV: default initial values of pressure (1) or hydraulic head
(m 1s) for nodes in the matrix.
4-27
-------
col: 11-15
RECORD 12
col: 1-5
col: 6-10
col: 11-20
col: 21-30
col: 31-35
col: 36-40
col: 41-50
col: 51-60
CNPIN: number of non-default nodes in the matrix related to
the default initial values (CHINV) if NONU = 1 (see
record 2), else set to 0.
FORMAT 2I5,2E10.3,2I5,2E10.3
IBTND1 : type of boundary condition for the first node. 1 =
pressure head, 0 = water flux.
IBTNDN: type of boundary condition for the last node. 1 =
pressure head, 0 = water flux.
VALND1: value of the pressure head or water flux at the first
node. The value should be positive for influx and
negative for efflux. Set to 0.0 if PRZM is ON.
VALNDN: value of the pressure head or water flux at the last
node. The value should be positive for influx and
negative for efflux. Set to 0.0 if fluid is exiting the
last node.
ITCND1 : flag to indicate if the boundary condition at the first
node is transient. 1 = yes, 0 = no. Automatically set
to 0 if PRZM is ON.
ITCNDN: flag to indicate if the boundary condition at the last
node is transient. 1 = yes, 0 = no. Automatically set
to 0 if PRZM is ON.
FLX1: fluid flux injected into the first node (I3t). Automati-
cally set to 0.0 for FLOW if PRZM is ON.
FLXN: fluid flux injected into the last node (I3t). Automati-
cally set to 0.0 for FLOW if PRZM is ON.
RECORD 13 Repeat this record up to NMAT (see record 2).
FORMAT 4E10.3
col: 1-10 PROP1: saturated hydraulic conductivity of the material (use
cm day! if PRZM is ON).
col: 11-20 PROP2: effective porosity of the material.
col: 21-30 PROPS: specific storage of the material. For unsaturated
flow, set to 0.0.
col: 31-40 PROP4: air entry pressure head of the material.
4-28
-------
RECORD 14
RECORD 16
col: 1-10
col: 11-20
col: 21-30
col: 31-40
col: 41-50
RECORD 16
Omit for FLOW simulation.
Repeat this record up to NMAT if KPROP = 1.
FORMAT 6E10.3
FVAL1: residual water phase saturation of the material (re-
sidual water content / saturated water content).
FVAL2: parameter n of the relative permeability versus satu-
ration relationship. Suggested value of 0.0 or nega-
tive value.
FVAL3: leading coefficient of the saturation versus capillary
head relationship (alpha).
FVAL4: power index of the saturation versus capillary head
relationship (beta).
FVAL5: power index of the saturation versus capillary head
relationship (gamma). Suggested value of 1.- (l./FV-
AL4).
Repeat records 16-19 in data sets up to NMAT if KPROP - 0.
FORMAT 15
col: 1-5
RECORD 17
col: 1-10
col: 11-20
col: 21-30
col: 31-40
NUMK
Only if KPROP
FORMAT
SMV1:
PKRW1:
SMV2:
PKRW2:
number of entry pairs of relative
saturation of the material,
= 0.
8E10.3
permeability and
value of water phase saturation for point 1 of the
entry pairs related to NUMK.
value of relative permeability (I2)
entry pairs related to NUMK.
etc.
etc.
for point 1 of the
RECORD 18
col: 1-5
Only if KPROP = 0.
FORMAT 15
NUMP:
number of entry pairs of pressure head versus satu-
ration values for the material.
4-29
-------
RECORD 19 Only if KPROP = 0.
col: 1-10
col: 11-20
FORMAT
SSWV1:
HCAP1:
col: 21-30
col: 31-40
RECORD 20
col: 1-5
col: 6-15
RECORD 21
RECORD 22
RECORD 23
RECORD 24
SSWV2:
HCAP2:
8E10.3
value of water phase saturation for point 1 of the
entry pairs related to NUMP.
value of the pressure head (1) for point 1 of the entry
pairs related to NUMP.
etc.
etc.
OnlyifNONU = l.
NOTE: enter next two variables sequentially for every non-
default node (CNPIN).
FORMAT 5(I5,E10.3)
N: non-default node number relative to CNPIN (see
record 11).
PINT: non-default initial value of pressure head (1) or hy-
draulic head (m I3) of the node number (n).
Omit for FLOW simulation.
Omit for FLOW simulation.
Omit for FLOW simulation.
Only if ITCND1 = 1 and PRZM is OFF.
FORMAT 15
col: 1-5
RECORD 25
col: 1-80
NTSNDH1: number of selected time values of pressure head or
water flux for transient simulation at first node.
Only if ITCND1 = 1 and PRZM is OFF.
FORMAT 8E10.3
TMHV1:
time values in relation to NTSNDH1 at the first node
for pressure head or water flux (t). Enter up to 8
values per line up to NTSNDH1 lines,
4-30
-------
RECORD 26
col: 1-80
RECORD 27
RECORD 28
col: 1-5
RECORD 29
col: 1-80
RECORD 30
col: 1-80
RECORD 31
RECORD 32
col: 1-80
RECORD 33
col: 1-4
Only if ITCND1 = 1 and PRZM is OFF.
FORMAT 8E10.3
HVTM1:
values of pressure head or water flux corresponding
to TMHV1 at the first node (length), Enter up to 8
values per line up to NTSNDH1 lines.
Omit for FLOW simulation.
Only if ITCNDN =1 and PRZM is OFF.
FORMAT 15
NTSNDH2: number of selected time values of pressure head or
water flux for transient simulation at the last node.
Only if ITCNDN = 1 and PRZM is OFF.
FORMAT 8E10.3
TMHV2: time values in relation to NTSNDH2 at the last node
for pressure head or water flux (t). Enter up to 8
values per line up to NTSNDH2 lines.
Only if ITCNDN = 1 and PRZM is OFF.
FORMAT 8E10.3
HVTM2:
values of pressure head or water flux corresponding
to TMHV2 at the last node (length). Enter up to 8
values per line up to NTSNDH2 lines.
Omit for FLOW simulation.
OnlyifIOBSND = l.
FORMAT 1615
NDOBS: increasing sequential numbers of observation nodes.
Enter up to 16 per line up to NOBSND (see record 4).
FORMAT A4
OUTF: output time step for printing. Enter DAY for daily,
MNTH for monthly, YEAR for yearly.
4-31
-------
4.1.4.3 VADOFT Input Guide for TRANSPORT
RECORD 1 FORMAT A80
col: 1-80 TITLE: label for transport simulation title.
RECORD 2 FORMAT 1015
col: 1-5 NP: total number of Vadoft nodal points.
col: 6-10 NM-AT: total number of different porous materials (maximum
of 5).
col: 11-15 NONU: flag to indicate if initial condition is non-uniform. 1
= yes, 0 = no.
col: 16-20 ITRANS: flag to indicate if running in transient or steady-
state. Must be set to 1 if PRZM is ON. 1 = tran-
sient, 0 = steady-state.
col: 21-25 IMODL: flag to indicate if running flow or transport model. 1
= flow, 0 = transport. Set to 0 here.
col: 26-30 KALL: time stepping index. 1 = backward difference, 0 =
central difference. This flag is automatically set to 1
for steady-state simulation.
col: 31-35 IMBAL: flag to indicate if mass balance computation is re-
quired. 1 = yes, 0 = no.
col: 36-40 INTSPC: flag to indicate initial conditions for head values. 1 =
hydraulic head, 0 = pressure head. Automatically set
to 0 for transport.
col: 41-45 IHORIZ: flag to indicate if flow direction is horizontal. 1 =
yes, 0 = no. Set to 0 if PRZM is ON.
col: 46-50 ICHAIN: flag to indicate if daughter products are used. 1 =
yes, 0 = no.
RECORD 3
RECORD 4
col: 1-5
col: 6-10
Omit for transport simulation.
FORMAT 815
KPROP:
ITSGN:
flag to indicate relationship between relative perme-
ability versus saturation and pressure head versus
saturation. Set to 0 for Transport simulation.
flag to indicate if output time values are to be model
calculated. 1 = yes, 0 = no,
4-32
-------
col: 11-15 ITMARK: flag to indicate if output time values differ from com-
putational time values (see records 6 and 7). 1 = yes,
0 = no.
col: 16-20 NSTEP: value of which time step to output nodal values from,
When NSTEP = n, then output is printed. Must be
from 1 up to 31 (days).
col: 21-25 NVPR: value of which time step to output nodal velocities.
When NVPR = n, then output is printed. Must be
from 1 up to 31 (days).
col: 26-30 IOBSND: flag to indicate if values are printed at certain obser-
vation nodes. 1 = yes, 0 = no. NOTE: Echo level
must be greater than or equal to 6 in PRZM2.RUN
file.
col: 31-35 NOBSND: number of observation node(s) to be printed. NOBS-
ND must not be greater than NP (see record 2). If
IOBSND = 0 then set NOBSND = 0.
col: 36-40 IPRCHK: flag to indicate if detailed information is generated in
the flow matrix. 1 = yes, 0 = no.
RECORD 5 Only if ITRANS - 1 (see record 2).
FORMAT 4E10.3
col: 1-10
col: 11-20
col: 21-30
col: 31-40
RECORD 6
col: 1-80
TIMA
TIN:
TFAC:
TMAX:
initial time value (t). Suggested value if PRZM is
ON: 0.0
initial time step value (t). Suggested value if PRZM
is ON: 1.0. Omit if ITSGN = 0.
time step multiplier. Suggested value if PRZM is ON:
1.0. Omit if ITSGN = 0.
maximum time step value allowed (t). Suggested
value if PRZM is ON: 1.0 Omit if ITSGN = 0.
Only if ITGSN = 0 (see record 4) and ITRANS = 1.
FORMAT 8E10.3
TMVEC(I): time values corresponding to the number of time
steps where I = 1...31 (t). Input up to 8 values per
line.
4-33
-------
RECORD 7 Only if ITMARK = 1 and ITRANS = 1
FORMAT I5,2E10.3
col: 1-5 ITMGEN: flag to indicate if backup file marker time values are
used. 1 = yes, 0 = no.
col: 6-15 STMARK: starting marker time value (t). If PRZM and TRAN-
SPORT are ON, set to 0.0.
col: 16-25 DTMARK: marker time value increment (t). If PRZM and TRA-
NSPORT are ON, set to 1.0.
RECORD 8 Only if ITRANS = 1, ITM.ARK = 1 and ITMGEN = 0.
FORMAT 8E10.3
col: 1-80 TMFOMT: output marker file time values (t) corresponding to
TMVEC(I) (see record 6). Input up to 8 values per
line.
RECORD 9 FORMAT 15
col: 1-5 NLAYRG: number of soil horizons to be discretized,
RECORD 10 Repeat this record up to NLAYRG (see record 9).
FORMAT 3I5,E10.3
col: 1-5 ILAYR: horizon number in relation to NLAYRG.
col: 6-10 NELM: number of finite elements in ILAYR.
col: 11-15 IMATL: porous material number related to NMAT (see record
2) in ILAYR.
col: 16-25 THL: thickness of the horizon (ILAYR).
RECORD 11
col: 1-10
col: 11-15
RECORD 12
col: 1-5
FORMAT E10.3,I5 Repeat for each NCHEM.
CHINV: default initial values of concentration (m I3) for nodes
in the matrix.
CNPIN: number of non-default nodes in the matrix related to
the default initial values (CHINV) if NONU = 1 (see
record 2), else set to 0.
FORMAT 2I5,2E10.3,2I5,2E10.3
IBTND1: type of boundary condition for the first node. 1 =
concentration, 0 = solute flux.
4-34
-------
col: 6-10
col: 11-20
col: 21-30
col: 31-35
col: 36-40
col: variable
RECORD 15
RECORD 16
RECORD 17
RECORD 18
RECORD 19
IBTNDN:
VALND1:
VALNDN:
ITCND1:
ITCNDN:
type of boundary condition for the last node. 1 =
concentration, 0 = solute flux.
value of the concentration or solute flux at the frost
node. The value should be positive for influx and
negative for efflux. Set to 0.0 if PRZM is ON.
value of the concentration or solute flux at the last
node. The value should be positive for influx and
negative for efflux. Set to 0.0 if fluid is exiting the
last node.
flag to indicate if the boundary condition at the first
node is transient. 1 = yes, 0 = no. Automatically set
to 0 if PRZM is ON.
flag to indicate if the boundary condition at the last
node is transient. 1 = yes, 0 = no. Automatically set
to 0 if PRZM is ON.
col: 41-50
col: 51-60
RECORD 13
col: 1-10
col: 11-20
RECORD 14
col: variable
FLX1:
FLXN:
Repeat records
FORMAT
CPROP1:
CPROP2:
FORMAT
CPROP3:
fluid flux injected into the first node (1?
cally set to 0.0 if PRZM is ON.
fluid flux injected into the last node (1?
cally set to 0.0 if PRZM is ON.
13-14 in data sets up to NMAT.
2E10.3
longitudinal dispersivity of the material
effective porosity of the material.
3(2E10.3)
retardation coefficient for the material.
t). Automati-
t). Automati-
Enter this
CPROP4:
value up to NCHEM.
molecular diffusion for the material. Enter this val-
ue up to NCHEM.
Omit for TRANSPORT
Omit for TRANSPORT
Omit for TRANSPORT
Omit for TRANSPORT
Omit for TRANSPORT
4-35
-------
RECORD 20
Only if NONU = 1. Repeat this record up to NCHEM.
NOTE: enter next two variables sequentially for every non-
default node (CNPIN).
col: 1-5
col: 6-15
RECORD 21
col: 1-5
col: 6-15
col: 16-25
col: 26-35
RECORD 22
col: 1-5
col: variable
FORMAT
N:
PINT:
Repeat records
FORMAT
I:
VDFI:
SWDFI:
UWFI:
FORMAT
I:
CLAMDI:
5(I5,E10.3)
non-default node number relative to CNPIN (see
record 11).
non-default initial value of concentration (m 1?) of the
node number (n).
21-22 in data sets up to NMAT.
I5,3E10.3
porous material number in relation to NMAT.
default value of darcy velocity.
default value of water saturation.
value of upstream weighting factor. Set to 0.0 if no
upstream weighting is desired.
I5,6E10.3
porous material number in relation to NMAT.
decay coefficient of the material. Enter this value up
col: variable
RECORD 23
col: 1-5
col: 6-10
RECORD 24
col: 1-5
to NCHEM.
CRACMP: transformation mass fraction of the material. Enter
this value up to NCHEM.
FORMAT 215
NVREAD: flag to indicate if darcy velocities will be read from
internal scratch files. If PRZM and TRANSPORT are
ON, but not FLOW, then NVREAD is set to 1. 1 =
yes, 0 = no.
IVSTED: flag to indicate if the velocities are at steady-state.
This implies steady-state within each day, not the
entire simulation. 1 = yes , 0 = no. If PRZM is ON
then IVSTED is set to 1.
Only if ITCND1 = 1 and PRZM is OFF.
FORMAT 15
NTSNDH1: number of selected time values of concentration or
solute flux for transient simulation at first node.
4-36
-------
RECORD 25
col: 1-80
RECORD 26
col: 1-80
RECORD 27
col: 1-80
RECORD 28
col: 1-5
RECORD 29
col: 1-80
RECORD 30
col: 1-80
RECORD 31
col: 1-80
OnlyiflTCNDl
FORMAT
TMHV1:
= 1 and PRZM is OFF.
8E10.3
time values in relation to NTSNDH1 at the first node
for pressure head or water flux (t). Enter up to 8
values per line up to NTSNDH1 lines.
Only if ITCND1 = 1 and PRZM is OFF.
FORMAT 8E10.3
HVTM1:
OnlyiflBTNDl
FORMAT
QVTM1:
values of concentration or solute flux corresponding
to TMHV1 at the first node (length). Enter up to 8
values per line up to NTSNDH1 lines.
= 0 and PRZM is OFF.
8E10.3
volumetric fluxes corresponding to TMHV1 at the
first node. Enter 8 values per line up to NTSNDH1.
Only if ITCNDN =1 and PRZM is OFF.
FORMAT 15
NTSNDH2:
Only if ITCNDN
FORMAT
TMHV2:
number of selected time values of concentration or
solute flux for transient simulation at the last node.
= 1 and PRZM is OFF.
8E10.3
time values in relation to NTSNDH2 at the last node
for concentration or solute flux (t). Enter up to 8
values per line up to NTSNDH2 lines.
Only if ITCNDN = 1 and PRZM is OFF.
FORMAT 8E10.3
HVTM2:
values of pressure head or water flux corresponding
to TMHV2 at the last node (length). Enter up to 8
values per line up to NTSNDH2 lines.
Only if ITCNDN = 1 and PRZM is OFF.
FORMAT 8E10.3
QVTM2:
volumetric fluxes corresponding to TMHV2 at the
last node. Enter 8 values per lineup to NTSNDH2.
4-37
-------
RECORD 32 Only if IOBSND = 1.
FORMAT 1615
col: 1-80 NDOBS: increasing sequential numbers of observation nodes.
Enter up to 16 per lineup to NOBSND (see record 4).
RECORD 33 FORMAT A4
col: 1-4 OUTT: output time step for printing. Enter DAY for daily,
MNTH for monthly, YEAR for yearly.
4-38
-------
4.1.5 MONTE CARLO Input File
The PRZM-2 model requires a Monte Carlo input file when MONTE CARLO is specified
"ON" in the execution supervisor file. The following is an example Monte Carlo input file.
4.1.5.1 Example MONTE CARLO input file for PRZM-2
Title
MONTE CARLO TEST INPUT
H* H* ^IXTi im V^ar1 r\f r-iinc1 orirl r>r\r-»fir1 o
Number of runs and confidence level
**
• * r i • 9°;°
onte Carlo inputs
KOC1 1
FIELD CAPACITY 1
WILTING POINT 1
ORGANIC CARBON 1
FIELD CAPACITY 2
WILTING POINT 2
ORGANIC CARBON 2
DISPERSION 1 1
***Empirical Distribution Data
4
89.7 0.10
82.9 0.20
76.1 0.30
69.3 0.40
***Monte Carlo outputs
INFILTRATION 1 1
DISPERSION 1 1 1
END
***Correlations
FIELD CAPACITY 1 1
FIELD CAPACITY 1 1
FIELD CAPACITY 2 1
FIELD CAPACITY 2 1
END
800.1400.
10.10000.
1 .316
1 ,150
1 1.30
1 .288
1 .143
1 .110
1 50.0
.130 0.050.60
.066 0.030.30
.870 0.015.00
.110 0.04 .540
.076 0.03 .030
.070 0.011.00
15.0 10.090.0
&
5.
1.
5.
5.
1
7
CDFWRITE
CDFWRITE
WILTING POINT 1
ORGANIC CARBON 1
WILTING POINT 2
ORGANIC CARBON 2
0.757
0.609
0.757
0.170
NOTE: The above Monte Carlo input file contains lines beginning with three asterisks
(***). These are considered comment lines and will be ignored by the program.
4-39
-------
4.1.5.2 MONTE
RECORD 1
col: 1-80
RECORD 2
col: 1-5
col: 6-15
RECORD 3
col: 1-20
col: 21-25
col: 26-30
col: 31-40
col: 41-50
col: 51-60
col:61-70
col: 71-80
RECORD 4
col: 1-3
RECORD 5
CARLO Input
FORMAT
TITLE:
FORMAT
NRUN:
PALPH:
Repeat this
cords.
FORMAT
PNAME:
IND1:
INDZ:
VAR1 :
VAR2:
VAR3:
VAR4:
VAR5:
FORMAT
ENDIT:
Guide
A80
label for Monte Carlo simulation title.
I5,F10.0
number of Monte Carlo runs (1 to 1000).
confidence level for percentile confidence bounds.
Entered as a percent(%). Default of 90.
record for number of inputs desired up to 50 re-
A20,2I5,5F10.0
Monte Carlo input variable name (up to 20 charac-
ters). See Table 4-2 on page 4-47.
integer index for horizon, application, or material.
See Table 4-2 on page 4-47.
zone number (1 to 10).
the mean value of the distribution variable.
the standard deviation of the distribution variable.
the minimum value for the variable.
the maximum value for the variable.
flag to indicate the type of the variable distribution
0 = constant, 1 = normal
2 = log-normal, 3 = exponential
4 = uniform
5 = Johnson SU
6 = Johnson SB
7 = empirical, entered in record 4
8 = triangular
A3
enter "END" to indicate end of record 3
only if VAR5 = 7 (see record 3).
col: 1-5
NDAT:
number of data pairs in empirical cumulative distri-
bution (1 to 20).
4-40
-------
RECORD 6
col: 1-10
col: 11-20
RECORD 7
col: 1-20
col: 21-25
col: 26-30
col: 31-50
col: 51-70
col: 71-75
only if VAR5 = 7 (see record 3). Note: repeat record 5 for every
time VAR5 =7.
FORMAT 2F10.0
DIST1: value of quantile for data pair I where I = 1... .NDAT,
DIST2:
cumulative probability for data pair I where 1 = 1
NDAT.
repeat this record for number of outputs desired up to 10 re-
cords.
FORMAT A20,2I5,2(A20),I5
SNAME: Monte Carlo output variable name, See Table 4-2 on
page 4-47.
IND1: integer index for horizon, application, or material
number. See Table 4-2 on page 4-47.
INDZ: zone number (1 to 10).
SNAME2: enter "CDF" to indicate if cumulative distributions
are plotted.
SNAME3: enter "WRITE" to indicate if values are written as
output for each Monte Carlo run (NRUN).
NAVG: length of the averaging period (in days) for output
variables (1 to 5).
RECORD 8
col: 1-3
RECORD 9
col: 1-20
col: 21-25
col: 26-30
col: 31-50
FORMAT
ENDIT:
onlyifVAR5
to half of the
desired.
FORMAT
NAME1:
IND1:
INDZ:
NAME2:
A3
enter "END" to indicate end of output variables.
= 1, 2, 5, or 6 note: this record may be repeated up
number of inputs in record 3 if correlation is
A20,2I5,A20,2I5,F10.0
variable (PNAME) in record 3 to be correlated,
integer index for horizon, application, or material
number (1 to 10).
zone number (1 to 10).
variable (PNAME) in record 3 to be correlated with
NAME1.
4-41
-------
col: 51-55 IND1: same as IND1 above.
col: 56-60 INDZ: same as INDZ above.
col: 61-70 CORK: the value of the correlation coefficient for NAME1
and NAME2.
RECORD 10 FORMAT A3
col: 1-3 ENDIT: enter "END" to indicate end of correlation inputs.
4-42
-------
TABLE 4-2. MONTE CARLO INPUT AND OUTPUT LABELS (conclude]
Parameter
Monte Carlo Label Index
Random VADOFT Model Inputs
Volat. Flux, Chem 3 (kg/ha/day)
Plant Flux, Chem 1 (kg/ha/day)
Plant Flux, Chem 2 (kg/ha/day)
Plant Flux, Chem 3 (kg/ha/day)
Root Zone Flux, Chem 1 (kg/ha/day)
Root Zone Flux, Chem 2 (kg/ha/day)
Root Zone Flux, Chem 3 (kg/ha/day)
Hydraulic Conductivity
Residual Saturation
Van-Genuchten Alpha
Van- Genuchten N
Decay Rate Chemical 1
Decay Rate Chemical 2
Decay Rate Chemical 3
Dispersion Coefficient, Chemical 1
Dispersion Coefficient, Chemical 2
Dispersion Coefficient, Chemical 3
Retardation, Chemical 1
Retardation, Chemical 2
Retardation, Chemical 3
Random VADOFT Model Outputs
Total Water Flux
Advection Flux, Chemical 1
Advection Flux, Chemical 2
Advection Flux, Chemical 3
Dispersion Flux, Chemical 1
Dispersion Flux, Chemical 2
Dispersion Flux, Chemical 3
Decay Flux, Chemical 1
Decay Flux, Chemical 2
Decay Flux, Chemical 3
Concentration, Chemical 1
Concentration, Chemical 2
Concentration, Chemical 3
VOLAT. FLUX 3
PLANT FLUX 1 Comp.
PLANT FLUX 2 Comp.
PLANT FLUX 3 Comp.
ROOT FLUX 1
ROOT FLUX 2
ROOT FLUX 3
HYDRAULIC CONDUC Material
RESIDUAL SATURATION Material
V-G ALPHA Material
V-G POWER N Material
VADOFT DECAY 1 Material
VADOFT DECAY 2 Material
VADOFT DECAY 3 Material
VAD DISPC 1 Material
VAD DISPC 2 Material
VAD DISPC 3 Material
VAD RETARD 1. Material
VAD RETARD 2 Material
VAD RETARD 3 Material
VAD WATER FLUX
VAD ADVECTION 1.
VAD ADVECTION 2
VAD ADVECTION 3
VAD DISPERSION 1
VAD DISPERSION 2
VAD DISPERSION 3
VAD DECAY FLUX 1
VAD DECAY FLUX 2
VAD DECAY FLUX 3
VAD CONC 1 Node
VAD CONC 2 Node
VAD CONC 3 Node
4-44
-------
SECTION 5
PARAMETER ESTIMATION
This section describes estimation of the parameters established in Section 4 b provide the
user with an aid in inputing records for EXESUP, PRZM, and VADOFT modules. For
convenience to the user, all variables (or parameters) from Section 4 are categorized by
module name and alphabetized to ensure quick reference.
5.1 EXESUP (Execution Supervisor)
The Execution Supervisor generally consists of labels and options; therefore, only
parameters of obscure definitions are defined.
ECHO - This value can be entered as an integer value (1-9) to controlthe amount of
display sent to the screen and output files. Also entering "ON" or "OFF" rather than an
integer value defaults the echo level to 5 (ON) or a minimal display of 1 (OFF). For
MONTE CARLO simulations, the echo level defaults to 1 automatically to prevent
excessive output,
ENDDATE - A valid calendar date that specifies the day at which all of the simulation
processes stop. The user must choose this date with respect to meteorological file dates to
ensure adequate weather data exist for the total elapsed time (STARTDATE to ENDDAT-
E) of the simulation.
NUMBER OF CHEMICALS - This value (1-3) controls the number of pesticides being
simulated. As many as three separate chemicals are allowed per simulation. Whether
these multiple chemicals have a parent-daughter relationship depends upon transforma-
ion mass fractions entered in the PRZM and VADOFT input files.
PARENT OF 2- This value implies the NUMBER OF CHEMICALS is greater than 1
and that a possible parent-daughter relationship exists.
PARENT OF 3- This value implies the NUMBER OF CHEMICALS is greater than 2
and that a possible parent-daughter relationship exists.
PATH - A computer-specific drive and directory statement allowing any proceeding file
names to be read or written in this area.
STARTDATE - A valid calendar date that specifies the day at which all simulation
processes begin. The user must choose this date with respect to meteorological file dates
to ensure adequate weather data exists from this date forward to the ENDDATE.
5-1
-------
TRACE - Primarily a tool for code debugging. By entering "ON" or "OFF", the user has
the option to track subroutine calling processes during a simulation.
WEIGHTS - Values entered that specify a fractional percent of fluxes between PRZM and
VADOFT zones. These values are ordered into a matrix with a sum of 1.0 for each PRZM
zone.
5.2 PRZM (Pesticide Root Zone Model)
AC - Maintenance coefficient of the co-metabolizing X^ population, This value specifies
the amount of energy required to maintain co-metabolizing (inhibited growth) microorgan-
isms.
AD - Soil water drainage rate. This value is required if HSWZT = 1. It is an empirical
constant and dependent on both soil type and the number of compartments (DPN(I)/THK-
NS(I), where I = number of horizons) to be simulated. Although there is limited experi-
ence using this option, three soils were evaluated for testing AD. The analysis was
performed by comparing the storage of water in the soil profile following the infiltration
output from SUMATRA-1 (van Genuchten 1978). Each soil had a profile depth of 125 cm.
The amount of water moving out of the profile changed by only 1 to 2% over the range of
compartments (15-40). Calibrating PRZM by comparison was accomplished and estimates
of AD calculated. Suggested values of AD for clay loam, loamy sand, and sand as a
function of the number of compartments are given in Figure 5.11.
AFIELD - This is the erosion area or plot size in hectares.
ALBEDO - Soil surface albedo. To simulate soil temperatures, ALBEDO values for each
must be specified for each month. As the surface condition changes, the ALBEDO values
change accordingly. Values for some natural surface conditions are provided in Table 5-
21.
AM - Maintenance coefficient of the metabolizing IQ population. This parameter is used
in biodegradation processes to express the amount of energy required to maintain
metabolizing (enhanced) microorganism growth rates.
AMXDR - The maximum active rooting depth of crops. PRZM requires this parameter in
centimeters to estimate the measurement of root depth from the land surface. For ranges
on specific root depths, consult the USDA Handbook No. 283 (Usual Planting and
Harvesting Dates), or the local Cooperative Extension Service. For general information,
Table 5-9 shows the ranges for major crops.
ANETD - This value represents soil evaporation moisture loss during a fallow, dormant
period. Evaporation is initially assumed to occur in the top 10 cm of soil with remaining
moisture losses occurring below 10 cm up to the maximum rooting depth. Values for
ANETD apply when there is no growing season, allowing a reduced level of moisture loss
5-2
-------
through evaporation. For soils with limited drainage, set ANETD to 10 cm. Values for
free drainage soils are shown in Figure 5.2.
AR - Maintenance coefficient of the non-sensitive X,. population. This parameter specifies
the energy to sustain non-sensitive (indifferent) microorganisms.
AS - Maintenance coefficient of the sensitive X= population. This parameter specifies the
value of energy required to sustain sensitive (lethally affected) microorganisms
BD - Soil bulk density. This value is required in the basic chemical transport equations
of PRZM and is also used to estimate moisture saturation vilues. Two methods are
provided for estimating BD if site data are not available. Method one requires percent
sand, clay and organic matter. The procedure from Rawls (1983) is used, to estimate BD
in (5.1):
Method 1
100.0
BD= __ . (5.1)
%OM + 100,0 - %OM
OMBD MBD
where
BD = soil bulk density, g ami
OM = organic matter-content of the soil, %
OMBD = organic matter bulk density of the soil, g cm3
MBD = mineral bulk density, g cm:5-
Step 1. Locate the percent sand along bottom of Figure 5.10.
Step 2. Locate the percent clay along side of Figure 5.10.
Step 3. Locate the intersection point of the two values and read the mineral
bulk density.
Step 4. Solve the Rawls equation for BD.
Method 2
Step 1. Use Table 5-29 to locate the textural class.
Step 2. Read mean BD for the general soil texture.
Table 5-30 shows distributional properties of BD information.
BBT - Bottom boundary soil temperatures. BBT values for each month must be specified.
The BBT soil temperature for shallow core depths may vary significantly with time
throughout the year. For deep cores, BBT will be relatively constant. BBT can be
estimated from NOAA data reports, Department of Commerce. Depending on core depth
used in the simulation, the average temperature of shallow groundwater, as shown in
Figure 5.7, may be used to estimate BBT.
BDFLAG - Flag to indicate bulk density calculation.
BIOFLG - Biodegradation flag. This flag allows the user to simulate the degradation of
pesticides by microorganisms in the root zone. Parameters associated with biodegradation
5-3
-------
are very specific and may be difficult to obtain for soil conditions. As an alternative,
estimates of biological parameters can be found in literature on kinetics of microbial
growth in liquid culture.
BT - Bottom width of the furrows. BT will depend mostly upon the type of equipment
used to dig the furrow channels and the spacing between the furrows.
CFLAG - Conversion flag for initial pesticide levels. This flag is valid when ILP = 1. If
CFLAG = 0, then initial pesticide levels (PESTR) are in units of mgbjg-1. If CFLAG = 1,
then initial pesticide levels (PESTR) are in units of kgha:l. Leave CFLAG blank if ILP =
0.
CINTCP - The maximum interception storage of the crop (cm), This parameter estimates
the amount of rainfall that is intercepted by a fully developed plant canopy and retained
on the plant surface. A range of 0.1 to 0.3 for a dense crop canopy is reported by USDA
(1980). Values for several major crops are provided in Table 5-4.
CM - Mineralizable carbon (mg g:l). This value represents the carbon substrate in the soil
solution originating from a fraction of the carbon compounds of the solid phase.
CN - Runoff curve numbers of antecedent moisture condition II. The interaction of
hydrologic groups (Figure 5.4) and land use treatment (cover) is accounted for by assign-
ing a runoff curve number (CN) for average soil moisture condition (AMC II) to important
soil cover complexes for fallow, cropping, and residue parts of a growing season. Tables 5-
10 through 5-14 can be used to help estimate the correct curve numbers.
CORED - The total depth of the soil core in centimeters. This value specifies the
maximum depth in which PRZM simulates vertical movement. CORED must be greater
or equal to the active crop root depth (AMXDR). For simulation using PRZM and
VADOFT, the core depth (CORED) is usually equal to the root zone (AMXDR).
COVMAX - This is the maximum areal crop coverage. PRZM estimates crop ground cover
to a maximum value, COVMAX, by linear interpolation between emergence and maturity
dates. As a crop grows, its ground cover increases thus influencing the mass of pesticide
that reaches the ground from an above surface application event. For most crops, the
maximum coverage will be on the order of 80 to 100 percent.
DAIR - Vapor phase diffusion coefficient. When Henry's law constant (HENRYK) is
greater than zero, vapor phase diffusion is used to calculate equilibrium between vapor
and solution phases. Pick's first law defines the diffusion coefficient as the proportionality
between the chemical flux and the spatial gradient in its concentration (Nye 1979). In
soil, vapor phase diffusion occurs in the soil air space, Each chemical will have its own
characteristic diffusion coefficient depending on its molecular weight, molecular volume,
and shape (Streile 1984). Jury et al. (1983) has concluded that the diffusion coefficient
will not show significant variations for different pesticides at a given temperature; they
recommend using a constant value of 0.43 m?day:l for all pesticides. This value is
recommended unless other chemical-specific data are available. Note that DAIR is
entered in cm? day-'h The user should be sure to convert the above recommended value.
DEP1 - The depth(s) of pesticide incorporation. This variable is only needed if soil
application of a chemical is specified (FAM=1). Typical depths are 5 to 10 centimeters,
Representative values for several soil application methods are given in Table 5-15.
5-4
-------
DGRATE - Vapor phase degradation rate constant(s). Pesticides are degraded by
different mechanisms, and at different rates, depending upon whether they are in vapor,
liquid or absorbed phase (Streile 1984). A lumped first-order rate is assumed for DGRAT-
E. In general, a zero value of DGRATE is recommended, unless chemical-specific data are
available to justify a non-zero value. For example, if the user is calibrating for a highly
volatile and/or photo-sensitive chemical, vapor phase attenuation processes in the upper 1
to 2 mm of the soil surface may be very important. Field studies have shown that photo
chemical loss of organic chemicals may be rapid and substantial immediately following
application to the land surface, especially in the case of hydrophobic or cationic organics
that sorb to soil particles (Miller et al. 1987).
DISP - Dispersion of pesticide(s). The dispersion or "smearing out" of the pesticide as it
moves down in the profile is attributed to a combination of molecular diffusion and
hydrodynamic dispersion. Molecular diffusion, D£, in soils will be lower than free-water
diffusion and has been estimated by Bresler (1973)
Dm - m ae*3 (5.2)
where
TSU = molecular diffusion in free water, cm? day-1
a = soil constants having a range of 0.001 to 0.005
b = soil constants having an approximate value of 10
6 = volumetric water content, ami? att3
Hydrodynamic dispersion is more difficult to estimate because of its site-soil specificity
and its apparent strong dependence upon water velocity. Most investigators have
established an effective diffusion or dispersion coefficient that combines molecular and
hydrodynamic terms. Most notable among these is
D = 0.6 + 2.93 Vl'11 (5.3)
where
D = effective dispersion coefficient, CVB£ day:l
v = pore water velocity, cm day:l
by Biggar and Nielsen (1976). Note in equation 5.3 that D is a time and depth varying
function since v is both time and depth-varying. The problem remains to estimate the
assumed constant for DISP, the effective dispersion coefficient. As noted earlier, the
backward difference numerical scheme in PRZM produces numerical dispersion. This
dispersion is also related to the magnitude of the velocity term. Other variables that
influence the truncation error include the time and space steps. A sensitivity test was
performed to examine the influence of the spatial step, Ax. Results are given in Figure
5.5. For these runs, the DISP parameter was set to 0.0. The influence of DISP superim-
posed on the numerical dispersion created by the model at a AX value of 5.0 cm is shown
in Figure 5.6. A number of studies were performed to investigate the impact of model
parameters other than DISP on the apparent dispersion. From these, the following
guidance is offered:
1) A spatial step or compartment size of 5.0 cm will mimic the observed
field effective dispersion quite well and should be used as an initial
value.
2) No fewer than 30 compartments should be used in order to minimize
mass balance errors created by numerical dispersion.
5-5
-------
3) The DISP parameter should be set to 0.0 unless field data are available
for calibration.
4) If DISP calibration is attempted, the compartment size should be re-
duced to 1.0 cm to minimize numerical dispersion.
5) The Biggar and Nielsen (1976) equation previously noted can be used to
bound the values only should the need arise to increase dispersion
beyond that produced by the numerical scheme.
If the user chooses the MOC algorithm to simulate advection transport, then numerical
dispersion will be eliminated and a typical value for field-observed data dispersion should
be entered. Use of the MOC algorithm will result in increased model execution time.
DKRT12,DKRT13,DKRT23- Transformation rate from a parent chemical (1 or 2) to a
daughter chemical (2 and/or 3), When multiple chemicals are specified in PRZM2.RUN,
either a parent/daughter relationship exists or the chemicals are independent (chosen by
the user). For a parent/daughter relationship, DKRTxx is the mass fraction degrading
from parent x to daughter x. By setting DKRTxx to 0.0, the user is specifying that the
multiple chemicals (xx) are independent parents.
DPN - Thickness of the compartments in the horizon. The DPN parameter allows the
user to specify a different layer depth for each soil horizon. The value of each DPN can be
divided by each horizon thickness (THKNS) to obtain the total number of compartments
in PRZM. In general, a smaller DPN will generate more accurate results and provide
greater spatial resolution, but will also consume more CPU time. From a volatilization
viewpoint, a smaller DPN in the top horizon is required for better estimation of the
volatilization flux from the soil surface. In addition, since pesticide runoff is calculated
from the surface layer, a smaller layer depth allows a better representation of surface-
applied chemicals. For the surface horizon, DPN values in the range of 0.5 to 2.0 cm are
recommended; a 1.0 cm vallue for DPN is commonly used. Smaller values down to 0.1 cm
can be used for highly- volatile compounds where volatilization is a major loss mechanism.
For subsurface soil horizons, DPN values in the range of 5.0 to 30.0 cm are recommended
depending on the spatial resolution needed at lower depths.
DSRATK - Absorbed phase degradation rate constant(s). See DWRATE for guidance.
5-6
-------
DT - Daylight hours for each month in relation to latitude. These values are used to
calculate total potential ET if daily pan evaporation data do not exist. Table 5.2 lists
monthly daylight hours for the northern hemisphere.
DWRATE - Solution phase degradation rate constant(s). This rate constant contributes
to the disappearance of pesticide(s) through decay. For most cases, the same values
should be used for solution (DWRATE) and adsorbed (DSRATE) phases for all depths.
This will allow a lumped first-order degradation rate constant. The dissipation rate of
pesticides below the root zone, however, is virtually unknown. Several studies have
suggested the rate of dissipation decreases with depth; however, no uniform correction
factor was suggested between surface/subsurface rates. First-order dissipation rates for
selected pesticides in the root zone were tabulated in Tables 5-19 and 5-20.
EMMISS - Infrared Emissivity. Most natural surfaces have an infrared emissivities lying
between 0.9 and 0.99. Values for all natural surfaces are not well known, but it is usually
close to unity. Specific values of EMMISS for some natural surfaces are given in Table 5-
22.
EN - Manning's roughness coefficient. This is a well known measure of the resistance of
open channels to flow. Chow (1959) suggests the values of EN range from 0.016 to 0.033
in excavated or dredged earth channels. EN values for the furrows listed in Table 5-34
range from 0.01 to 0.048. Table 5-37 lists the values of EN suggested by the USDA Soil
Conservation Service for drainage ditches with various hydraulic radii (defined as the flow
area divided by the wetted perimeter).
ENPY - Enthalpy of vaporization. This parameter is used in the temperature correction
equation for Henry's Law constant. In a limited literature search, we could find only two
pesticides for which ENPY values reported: 18.488 kcal molel for lindane and 20.640 kcal
mole-'J for napropamide (Streile 1984), Chemical-specific values are needed for ENPY, but
it appears that a value of 20 kcal mole-1 is a reasonable first guess.
ERFLAG - Erosion flag used to determine whether erosion losses are to be calculated
during a simulation. The total mass of pesticide loss by erosion is determined using the
chemicals affinity for soil. The amount of pesticide loss by these means is quite small for
highly soluble pesticides. If the apparent distribution coefficient is less than or equal to
5.0, erosion can usually be neglected. For a compound having a greater distribution
coefficient, erosion losses should be estimated (ERFLAG = 1).
EXMFLG - Flag for reporting output into the EXAMS model file format. This flag allows
a user to create an input file for the EXAMS model through PRZM output if so desired.
The EXAMS input file created has the name PRZM2EXA.Dxx where xx is the year of
PRZM simulation.
FAM - Foliar application model flag. This flag specifies how the pesticide is applied to
foliage (if FAM = 2 or 3).
FEXTRC - Foliar washoff extraction coefficient. Washoff from plant surfaces is modeled
using a relationship among rainfall, foliar mass of pesticide, and an extraction coefficient.
The parameter (FEXTRC) is the required input parameter to estimate the flux of pesticide
washoff. Exact values are varied and depend upon the crop, pesticide properties, and
application method. Smith and Carsel (1984) suggest that a value of 0.10 is suitable for
most pesticides.
5-7
-------
FILTRA - The filtration parameter of initial foliage to soil distribution. This parameter
relates to the equation for partitioning the applied pesticide between foliage and the
ground. Lassey (1982) suggests values in the range of 2.3 to 3.3m? kg-i. Miller (1979)
suggested a value of 2.8 m kg-'t for pasture grasses. Most of the variation appears to be
due to the vegetation and not the aerosol. FILTRA only applies if FAM=3.
FLEACH - The leaching factor as a fraction of irrigation water depth. This factor is used
to specify the amount of water added by irrigation to leach salts from saline soil and is
defined as a fraction of the amount of water required to meet the soil water deficit. For
instance, a value of 0.25 indicates that 25 percent extra water is added to meet the soil
water deficit.
FRMFLG - Flag for testing of ideal soil moisture conditions. This flag specifies whether
to check preceding days (WTNDAY) after the target application date (API)) for moisture
levels being ideal for pesticide application. If a preceding date has adequate moisture
levels and the target date does not, then the application date is changed automatically. If
the soil moisture after a specified number of days (WINDAY) fails to meet ideal condi-
tions, execution is halted.
HENRYK - Henry's constant is a ratio of a chemical's vapor pressure to its volubility. It
represents the equilibrium between the vapor and solution phases. It is quite common to
express HENRYK as a dimensionless number. Specific values for HENRYK for selected
pesticides can be found in Table 5-18.
HF - Suction parameter. HF represents water movement due to suction in unsaturated
soils, and has units of length (meters). As with KS, HF has been correlated with SCS
hydrologic soil groups (Brakensiek and Rawls 1983) and are shown in Table 5-39.
HORKZN - Horizon number. The horizon number in relation to the total number of
horizons (NHORIZ) must be specified when inputing parameters for each of the PRZM
horizons,
HSWZT - Flag to indicate soil water drainage calculation. The HSWZT flag indicates
which drain age model is invoked for simulating the movement of recharging water.
Drainage model 1 (HSZWT = 0) is for freely draining soils; drainage model 2 (HSZWT = 1)
is for more poorly drained soils and requires the user to enter a soil water drainage rate
(AD).
HTMAX - Maximum canopy height of the crop at maturation in centimeters. Canopy
height increases during crop growth resulting in pesticide flux changes in the plant
compartment. Users should have site-specific information on HTMAX since it varies with
climate, crop species, and environmental conditions. General ranges for different crops
are listed in Table 5-16.
ICNAH - This is the surface condition after crop harvest. Three values are allowed-
fallow, cropping, and residue (foliage remains on ground).
ICNCN - The crop number of the different crop. This value is in relation to NDC
(number of different crops). This allows separate crop parameters to be specified for each
different crop in a simulation.
IDFLAG - Thermal conductivity and volumetric heat capacity flag. This flag allows a
user to simulate soil temperature profiles. If ID FLAG = 0, the user must enter thermal
5-8
-------
conductivity (THCOND) and volumetric heat capacity (VHTCAP). If IDFLAG = 1, the
model automatically simulates soil temperature profiles.
ILP - Initial pesticide levels flag. ILP should be set to 1 when evidence of pesticide is
present before the simulation start date (STARTDATE). See also CFLAG and PESTR.
1NCROP - The crop number associated with the number of different crops (NDC).
IN CROP should be an increasing integer from the first different crop to the last different
crop grown.
INICRP - Initial crop flag. This flag indicates that before the simulation date occurs, a
previous crop existed.
IRFLAG - Flag to simulate irrigation. If irrigation is desired, the user has a choice of
applying water for the whole year or during a cropping period whenever a specified deficit
exists.
IRTYP - Specifies the type of irrigation used. See Table 5-32.
IPEIND - Pan Factor flag. When this flag is set to 0, daily pan evaporation is read from
the meteorological file. When this flag is set to 1, pan data are calculated from daylight
hours according to latitude. When this flag is set to 2, pan data are calculated through
either the met file or daylight hours according to availability.
IPSCND - Flag indicating the disposition of pesticide remaining on foliage after harvest.
This flag only applies if FAM = 2 or 3. If IPSCND = 1, pesticide remaining on foliage is
converted to surface application to the top soil layer. If IPSCND = 2, remaining pesticide
on foliage is completely removed after harvest. If IPSCND = 3, remaining pesticide on
foliage is retained as surface residue and continues to undergo decay.
ISCOND - The surface condition for the initial crop if applicable.
ITFLAG - Flag for soil temperature simulation. This flag allows a user to specify soil
temperatures (BBT) for shallow core depths. For deep cores (CORED), temperatures will
remain relatively constant.
KC - Saturation constant of the co-metabolizing JS^ population. See KSM and KCM for
further explanation.
KCM - Saturation constant of the metabolizing X^ population with respect to carbon
concentration. This value represents an inhibition of growth rate in relation to soil
carbon. Lower saturation constants result in. decreased carbon content consequently
resulting in a lower growth rate.
KE - Average enzyme content of the Xj population. This parameter specifies the amount
of the enzyme necessary to allow the population to break a pesticide down.
KD - Pesticide soil-water distribution coefficient. The user can enter KD directly if
KDFLAG = 0 (see PCMC and SOL) or allow the model to calculate KD automatically
(KDFLAG= 1).
5-9
-------
KDFLAG - Flag to indicate soil/pesticide adsorption coefficient. A user may choose to
enter KD by setting this flag to 0 else the model automatically calculates the adsorption
coefficient.
KIN - Inhibition constant of the 3$ population. Evolution of the population requires a
finite value controlling growth. KIN accounts for natural variations found in metabolic
activities affecting growth rates.
KL1 - Second-order death rate of the Xj population.
KL2 - Dissociation constant of the enzyme substrate complex.
KLDC - Death rate of the co-iaae!ted]HdIiaii|g]!% population.
KLDM - Death rate of the mettrfhodlzziqgg^ population.
KLDR - Death rate of the non-sensitive X^ population.
KLDS - Death rate of the sensitive X, population.
KR - Saturation constant of the non-sensitive KT population. See KSM and KCM for
further explanation.
KS - Saturated hydraulic conductivity This parameter represents the limiting infiltration
rate when the soil column is saturated and suction pressure is no longer important. KS
depends upon soil mineralogy, texture, and degree of compaction. Ranges for various
unconsolidated materials are given in Table 5-38. KS has also been correlated with SCS
hydrologic soil groups (Brakensiek and Rawls 1983) shown in Table 5-39.
KSK - Carbon solubilization constant.
KSM - Saturation constant of the metabolizing Xa population with respect to pesticide
concentration. This value represents an inhibition of growth rate. Lower saturation
constants result in lower bacteria rates, consequently resulting in lower growth rates.
Higher saturation constants increase bacteria growth, resulting in higher growth rates.
MKS - Saturation constant of the sensitive X, population. See KSM and KCM for further
explanation.
MOC - Flag to indicate method of characteristics calculation. The MOC algorithm is a
two-pass solution technique used to simulate advection and dispersion. The solution
technique reduces truncation error, Because of the 24 hour time step in PRZM, this
method can lead to significant losses of mass under high velocity (greater than 120 cm per
day) conditions,
MUC - Specific growth rate of the co-metabolizing SQ population.
NAPS - Number of pesticide applications. This is the total number of application dates
specified during the simulation. It is possible to apply up to three chemicals on the same
application date, but for PRZM this still constitutes one application.
NCHEM - Number of chemicals in the simulation. PRZM and VADOFT allow up to three
chemicals to be specified. Using more than one chemical (i. e., NCHEM=3) indicates either
5-10
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a parent-daughter relationship or multiple separate chemicals (determined by transforma-
tion mass fractions). NCHEM should be consistent with the number of chemicals
specified in the Execution Supervisor file.
NCPDS - Number of cropping periods. This is entered as a sum of all cropping dates
from the beginning simulation date to the ending simulation date.
NDG - The number of different crops in the simulation, This value determines how many
separate crops will be grown during a simulation. If only one type of crop is grow-n (ex:
corn), then NDC = 1. This includes the crop type of the initial crop also (INICRP).
NHORIZ - Total number of horizons. PRZM allows the user to specify how many
horizons are to be simulated within the core depth (CORED). The horizon should serve as
a distinct morphologic zone generally described by layers (i.e., surface, subsurface,
substratum) according to soil pedon descriptions or soil interpretation records, if available.
NPLOTS - Number of time series plots. PRZM can report several output variables
(PLNAME) to a time series file. NPLOTS specifies how many are written in a single
simulation.
OC - Percent of soil organic carbon. OC is conventionally related to soil organic matter as
%OC = 960M/1.724. Guidance on estimating OM is found in Table 5-31. Information is
categorized by hydrologic soil group and by depth. Also shown are coefficients of variation
for each soil group and depth. Carsel et al. (1988) determined that the Johnson SB
distribution provides the best fit to this data. Rao and Wagenet (1985) and Nielsen et al.
(1983) have reported that these values are often normally distributed. Carsel et al. (1988)
noted that organic carbon is weakly correlated with field capacity and wilting point water
content with the correlation coefficients ranging from 0.1 to 0.74. Strength of correlation
decreases with depth, as shown previously in Table 5-28.
5-11
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PCDEPL - Fraction of available water capacity where irrigation is triggered, The
moisture level where irrigation is required is defined by the user as a fraction of the
available water capacity, This fraction will depend upon the soil-moisture holding
characteristics, the type of crop planted, and regional agricultural practices. In general,
PCDEPL should range between 0.0 and 0.6, where a value of 0.0 indicates that irrigation
begins when soil moisture drops to wilting point, and 0.6 indicates the more conservative
practice of irrigating at 60 percent of the available water capacity. Schwab et al. (1966)
recommend values between 0.45 and 0.55.
PCMC - Flag for estimating distribution coefficients (KD). PRZM allows the user to
estimate the KD by multiplying the organic carbon partition coefficient I|JKQ derived from
the volubility (SOL)- PCMC is the flag for using one of four different models for estimat-
ing EQ The four models are:
PCMC1 Log IQ = (-0.54 * Log SOL) + 0.44
K^. = organic carbon distribution coefficient
where SOL = water volubility, mole fraction
PCMC2 LogKSc= 3.64- (0.55 * Log SOL)
where SOL = water volubility, mg 1"-J
PCMC3 Logl^ = 4.40- (0.557 * Log SOL)
where SOL = water volubility, micromoles 1-1
PCMC4EOSOL
where SOL = K~, dimensionless
oc»
PESTR - Initial pesticide(s) levels. PESTR levels are required if evidence of pesticide(s)
is present before the simulation start date (ILP =1). PESTR is entered in units specified
by CFLAG for each compartment in each horizon and for all chemicals (NCHEM).
PFAC - The pan factor is a dimensionless number used to convert daily pan evaporation
to daily potential evapotranspiration (ET). Pan factor general ranges are between 0.60 to
0.80. See Figure 5.1 for specific regions of the United States.
PLDKRT - Foliage pesticide first-order decay rate. Pesticide degradation rates on plant
leaf surfaces is represented as a first-order process controlled by PLDKRT. The user must
be consistent in specifying PLDKRT and PLVKRT rates. If PLDKRT includes volatiliza-
tion processes, then PLVKRT should be zero. If PLVKRT is non-zero then PLDKRT
should include all attenuation processes except volatilization. Recent information (Willis
and McDowell 1987) is available for estimating degradation rates of pesticides on plant
foliage. In the work cited above, observed half-lives (days) were grouped by chemical
family. These were:
o Organochlorine 5.0 ±4.6
o Organophosphorus 3.0 4 2.7
o Carbamate 2.4 4 2.0
o Pyrethroid 5.3 £3.6
These mean half-lives correspond to degradation rates of 0.14,0.23,0.29, and 0.13 day-1,
respectively. These are in reasonable agreement with values in Table 5-17.
5-12
-------
PLNAME - Name of plotting variable. When creating a time series plot, PLNAME
specifies the variable in Table 4.1 for which that output data are written.
PLVKRT - Foliage pesticide first-order volatilization rate. Pesticide volatilization from
plant leaf surfaces is represented as a first-order process controlled by PLVKRT. For
organophosphate insecticides, Stamper et al. (1970) has shown that the disappearance
rate from leaf surfaces can be estimated by a first-order kinetic approach. Similar
observations for first-order kinetics were found for volatilization of 2,4-D iso-octyl ester
from leaf surfaces by Grover et al. (1985). Volatilization losses of toxaphene and DDT
from cotton plants decreased exponentially with time and were linearly related to the
pesticide load on these plants (Willis et al, 1983). Table 5-17 shows disappearance rates
for selected pesticides on plant foliage. These rates are applicable to estimation of
PLVKRT since the overall decay rate (PLDKRT) includes loss associated with volatiliza-
tion.
PSTN AM - Pesticide (s) name. This is a label used to identify pesticide output. Pesticide
names should be placed in order of chemical 1, chemical 2, and chemical 3 if applicable
(NCHEM=3).
Q - Average carbon content of the Xj population.
QO - Flow rate into a single furrow, QO is defined as the volume of water entering the
furrow per unit time. Flow rates are usually set so that sufficient water reaches the end
of the furrow without causing excessive erosion. Table 5-35 lists the maximum non-
erosion flow rates for various furrow channel slopes.
RATEAP - Maximum sprinkler application rate, RATEAP is used to limit sprinkler
applications to volumes that the sprinkler system is capable of delivering per time step.
This value is defined as a maximum depth (cm) of water delivered per hour. Table 5-33
lists sprinkler rates.
SF - Channel slope. SF is determined by regional topography and the design grades of
the furrows, and is defined as vertical drop in elevation per horizontal distance of the bed.
Furrows are usually used only in relatively level terrain, with slopes no greater than 0.03
(Todd 1970). A few representative slopes are listed in Table 5-34.
SFAC - The snowmelt factor is a used to calculate snowmelt rates in relation to temperat-
ure. Snow is considered any precipitation that falls when the air temperature is below 0
degrees Celsius. In areas where climatology prevents snow fall, SFAC should be set to 0.0.
Typical ranges for SFAC are provided in Table 5-1.
SOL - Pesticide water volubility. By specifying a water volubility (SOL) for pesticides, the
model can calculate the IQ and KD by using one of the models specified for PCMC. SOL
must be entered according to the PCMC model selected. Table 5-19 on page 5-45 provides
pertinent values for selected pesticides for obtaining SOL. Methods are also available to
calculate KJJ. (SOL if PCMC=4). The octanol-water distribution coefficient can be used for
calculating KJJJ. with a relationship to organic carbon (OC). Karickhoff et al. (1979)
proposed a relationship between ]§&, and KJJJ given by
Log Km- 1.00 (Log Kea) -0.21 (5.4)
where
= octanol-water distribution coefficient (cm? g1^
5-13
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Step 1. From Table 5-23 find the matric potential for field capacity and
wilting point .
Step 2. For each matric potential, find the regression coefficient (a-e) that
are in the Rawls and Brakensiek equation.
Step 3. For any given soil solve the equation for the -0.33 and -15.0 poten-
tial.
Method 2
Use Figure 5.8 for estimating the field capacity and Figure 5.9 for estimating
the wilting point, given the percent sand and clay.
Method 3
Use Table 5-25 to locate the textural class of the soil of choice. After locatin
the textural class, read the mean field capacity and wilting point potentials
, to the right of the textural class.
Guidance for estimating distributional properties for THEFC and THEWP is given in
Tables 5-26 and 5-27.
THETO - Initial water content of the soil. This value provides the model with a starting
calculation for moisture. If site-specific data are not available, field capacity value is
recommended for THETO.
THEWP - See THEFC for guidance.
THFLAG - Flag to indicate field capacity and wilting point calculation.
THKNS - Thickness of the horizon. This value is the depth (cm) of the horizon specified
(HORIZN) in relation to core depth (CORED).
TR - Storm duration peak runoff rate. TR is entered as an average, although in reality
this parameter changes seasonally as well as with each storm type. This value represents
the time period when storms occur producing peak runoff over a short duration. Table 5-8
provides estimates for TR for selected locations in the U.S. for both mean summer and
annual time periods while Figure 5.3 provides regionalized values for different areas in
the United States.
UPTKF - Plant uptake efficiency factor. This value provides for removal of pesticides by
plants. It is also a function of the crop root distribution and the interaction of soil, water,
and the pesticide. Several approaches to modeling the uptake of nutrients/pesticides have
been proposed ranging from process models that treat the root zone system as a distribu-
tion sink of known density or strength to empirical approaches that assume a relationship
to the transpiration rate. Dejonckheere et al. (1983) reported the mass of uptake into
sugarbeets for the pesticides aldicarb and thiofanox for three soils (sandy loam, silt loam,
and sandy clay loam). Mass removal expressed as a percentage of applied material for
aldicarb on sandy loam, silt loam, and clay loam ranged from 0.46 to 7.14%, 0.68 to 2.32%,
and 0.15 to 0.74%, respectively. For thiofanox, 2.78 to 20.22%, 0.81 to 8.70%, and 0.24 to
2.42% removals were reported for the respective soils. Other reviews have suggested
ranges from 4 to 20% for removal by plants. Sensitivity tests conducted with PRZM
indicate an increase in the uptake by plants as the crop root zone (AMXDR) increases and
5-15
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the partition coefficient (KD) decreases. For highly soluble pesticides and for crop root
zones of greater than 120 cm, values of greater than 20% were simulated. For initial
estimates, a value of 1.0 for UPTKF is recommended.
USLEC - The universal soil loss cover management factor (C value). Values for USLEC
are dimensionless and range from 0.001 (well managed) to 1.0 (fallow or tilled condition).
One value for each of the three growing periods (fallow, cropping, and residue) is required.
Specific values can be calculated by Wischmeier and Smith (1978) or obtained from a local
SCS office. Generalized values are provided in Table 5-7.
USLEK - The universal soil loss equation (K) of soil erodibilty. This is a soil-specific
parameter developed by the USDA. Specific values can be obtained from the local SCS
office. Approximate values are listed in Table 5-3.
USLELS - The universal soil loss equation (LS) topographic factor. This is a slope length
and steepness parameter developed by the USDA. The value is dimensionless and can be
estimated from Table 5-5.
USLEP - The universal soil loss equation (P) practice factor. This value is developed by
the USDA to describe conservative agricultural practices. Values are dimensionless and
range from 0.10 (extensive practices) to 1.0 (no supporting practices). Specific values can
be estimated in Table 5-6.
UCM - Specific growth rate of the metabolizing& population with respect to carbon
concentration.
UR - Specific growth rate of the non-sensitive 1%. population.
US - Specific growth rate of the sensitive X$, population.
USM - Specific growth rate of the metabolizing Xg, population with respect to pesticide
concentration.
VHTCAP - See THCOND for guidance.
WINDAY - An integer number of days. This specifies the number of days after the target
date (APD) that the code checks for ideal moisture conditions. For this value to be valid,
FRMFLG must equal 1. WINDAY should be less than the difference of the target date
(APD) to the next chronological target date,
WFMAX - The maximum dry foliar weight. This value is used only if a user desires to
have the model estimate the distribution between plants and the soil by an exponential
function when a pesticide is applied. WFMAX of the plant above ground (kg mtf) is the
exponent used in the exponential foliar pesticide application model. Estimates of WFMAX
for several crops are given in Table 5-14.
X2 - Length of the furrow. X2 will depend upon the size of the field and the local
topography. Table 5-35 lists maximum furrow lengths for various slope textures,
irrigation application depths, and furrow slopes.
XFRAC - Location of the furrow. XFRAC is a fraction of furrow length (X2) that specifies
where PRZM infiltration calculations are performed. To use the average depth of furrow
infiltration depths, set XFRAC to -1.
5-16
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Yl - Metabolizing (XQ microbial population.
Y2 - Co-metabolizing (3Q microbial population.
Y3 - Sensitive (2Q) microbial population.
Y4 - Non-sensitive (JQ microbial population.
YC - True growth yield of the co-metabolizing JS^ population.
YCM - True growth yield of the metabolizing& population with respect to carbon
concentration.
YR - True growth yield of the non-sensitive 3%. population.
YS - True growth yield of the sensitive % population.
YSM - True growth yield of the metabnliziog^^ population with respect to pesticide
concentration.
ZRS - Side slope of the furrows. This parameter is defined as the slope of the channel
walls, horizontal distance/vertical distance. ZRS will depend upon the cohesiveness of
soils and the type of equipment used to dig the furrows. Table 5-36 lists the suitable side
slopes for different types of soils, with values ranging from 1.5 to 3.0 for unconsolidated
materials,
ZWIND - Height of wind speed measuring instrument. The wind speed anemometer is
usually freed at 10 meters (30 feet) above the ground surface. This height may differ at
some weather stations such as at a class A station where the anemometer may be
attached to the evaporation pan. The correct value can be obtained from the meteorologi-
cal data reports for the station whose data are in the simulation.
5-17
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5-18
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figure 5.2
en
| | 10-15 cm
15-20 cm
20-30 cm
30-35 cm
Figure 5.2. Diagram for estimating soil evaporation loss.
-------
Figure 5.3
I
PERIOD
MEAN STORM DURATION (hour*)
ZONE
234567
ANNUAL
MEAN
C.V.
SIMMER
MEAN
C.V,
5.8
1.05
4. 4
l.U
5.9
1.05
4.2
1.09
€.2
1.22
4.9
1.J3
7.3
1.17
5.2
1.Z9
4.0
1.07
3.2
1.08
3.6
1.02
2.6
1,01
20.0
1.23
11.4
1.20
4.5
0.92
2,8
0.90
4.4
1.20
3.1
1.14
Maan - Man value
C.V. - Coefficient of variation
Source: Voodvard-Clyde Consultants. "Methodology for Analyti* of Detention
kilns for Control of Urban Runoff Quality, pr«p«rtd for U.S. EPA.
Offlea of Uatar, Honpolnc Source Division, Sapctsber, 1986.
Figure 5.3. Representative regional mean storm duration (hours) values for the U.S.
5-20
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Figure 5.4. Diagram for estimating Soil Conservation Service soil hydrologic groups, (from EPA Field Guide for Scientific
Support Activities Associated with Superfund Emergency Response. U.S. EPA, Corvallis, OR.
-------
figure 5.5
Pesticide concentration In total soil
(Kr7xg.cnT3)
0.0
Depth
(cm)
100-
150
Figure 5.5. Numerical dispersion associated with space step (Dx).
5-22
-------
100_
0.5% Organic matter
°'50 0.0% Porosity change
35
.10
0 10 20 30 40 50 60 70 80 90 100
Sand (%)
Figure 5.8. 1/3-bar soil moisture by volume, (provided by Dr. Walter J. Rawls, U.S.
Department of Agriculture, Agricultural Research Service, Beltsville, Maryland).
5-25
-------
100—,
9O—
0.40
O.35
0.5% Organic matter
0.0% Porosity change
0.30
0.25
30 40 50 60 eo 80 90
0.15
0.10
0.05
10 20
100
Sand (%)
Figure 5.9. 15-bar soil moisture by volume, (provided by Dr. Walter J. Rawls, U.S.
Department of Agriculture, Agricultural Research Service, Beltsville, Maryland).
5-26
-------
100
1 I I I ' I ' I
20 30 40 50 60
Sand ( % )
Figure 5.10. Mineral bulk density (g cm-3). (provided by Dr. Walter J. Rawls, U.S.
Department of Agriculture, Agricultural Research Service, Beltsville Maryland).
5-27
-------
2.&
1 . 2
15
20
Number of compartments
Figure 5.11. Estimation of drainage rate AD((tt^"f) versus number of compartments.
5-28
-------
TABLE 5-1. TYPICAL VALUES OF SNOWMELT (SFAC) AS RELATED TO FOREST
COVER
Snowmelt Factor, (cm £
FOREST COVER
Coniferous - quite dense
Mixed forest - coniferous,
deciduous, open
Predominantly deciduous forest
Open areas
K^day-1)
MINIMUM
0.08-0.12
0.10-0.16
0.14-0.20
0.20-0.36
MAXIMUM
0.20-0.32
0.32-0.40
0.40-0.52
0.52-0.80
Source: Anderson, E.A., "Initial Parameter Values for the Snow Accumulation and
Ablation Model", Part IV.2.2.1, National Weather Service River Forecast System
- User's Manual, NWS/NOAA, U.S. Dept. of Commerce, Silver Springs, MD.,
March 31, 1978.
TABLE 5-2. MEAN DURATION (HOURS) OF SUNLIGHT FOR LATITUDES IN THE
NORTHERN AND SOUTHERN HEMISPHERES*
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Ott
Nov
Dec
Days In
Month
31
28
31
30
31
30
31
31
30
31
30
31
00
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
10
11.6
11.7
12.0
12.4
12.5
12.7
12.5
12.4
12.2
11.8
11.8
11.5
20
11.0
11.6
12.0
12.6
13.1
13.3
13.2
12.9
12.2
11.6
11.2
10.9
Latitude North
30 35
10.5
11.2
12.0
13.0
13.7
14.0
13.9
13.2
12.4
11.4
10.7
10.2
10.1
10.9
12.0
13.1
14.1
14.5
14.3
13.5
12.4
11.3
10.3
9.9
*
40
9.8
10.7
12.0
13.3
14.4
15.0
14.7
13.7
12.5
11.1
10.0
9.4
45
9.3
10.4
11.8
13.6
14.9
15.5
15.2
14.1
12.5
10.9
9.5
8.7
50
8.6
10.0
11.8
13.8
15.4
16.3
15.9
14.5
12.7
10.7
9.1
8.1
9 - Criddle, W.D. Methods of Computing Consumptive Use of Water, Proceedings ASCE.
84(IR 1). 1958
* - Values for the southern hemisphere were assumed equal to the northern hemisphere
lagged by six months, e.g., the duration for January in the northern hemisphere is the
same as July in the southern hemisphere.
5-29
-------
TABLE 5-3. INDICATIONS OF THE GENERAL MAGNITUDE OF THE
SOIL/ERODIBILITY FACTOR, Ka
Organic Matter Content
Texture Class
<0.5%
2%
4%
Sand
Fine sand
Very Fine Sand
Loamy Sand
Loamy Fine Sand
Loamy Very Fine Sand
Sandy Loam
Fine Sandy Loam
Very Fine Sandy Loam
Loam
Silt Loam
silt
Sandy Clay Loam
Clay Loam
Silty Clay Loam
Sandy Clay
Silty Clay
Clay
0.05
0.16
.42
.12
.24
.44
.27
.35
.47
.38
.48
.60
.27
.28
.37
.14
.25
0.03
0.14
.36
.10
.20
.38
.24
.30
.41
.34
.42
.52
.25
.25
.32
.13
.23
0.13-0.29
0.02
0.10
.28
.08
.16
.30
.19
.24
.33
.29
.33
.42
.21
.21
.26
.12
.19
a The values shown are estimated averages of broad ranges of specific-soil values. When a
texture is near the borderline of two texture classes, use the average of the two K values.
For specific soils, Soil Conservation Service K-value tables will provide much greater
accuracy. (Control of Water Pollution from Cropland, Vol. I, A Manual for Guideline
Development. U.S. Environmental Protection Agency, Athens, GA. EPA-600/2-75-026a).
TABLE 5-4. INTERCEPTION STORAGE FOR MAJOR CROPS
Crop
Density
CINTCP (cm)
corn
Soybeans
Wheat
Oats
Barley
Potatoes
Peanuts
Cotton
Tobacco
Heavy
Moderate
Light
Light
Light
Light
Light
Moderate
Moderate
0.25-0.30
0.20-0.25
0.0 -0.15
0.0 -0.15
0.0 -0.15
0.0 -0.15
0.0 -0.15
0.20-0.25
0.20-0.25
5-30
-------
TABLE 6-6. VALUES OF SUPPORT-PRACTICE FACTOR, P"
Practice
Land Slope (percent)
1.1-2.0
2.1-7.0
7.1-12.0
(Factor P)
12.1 -18.0 18.1 -24.0
Contouring (PJ
Contour Strip
cropping
R-R-M-M
R-W-M-M
R-R-W-M
R-W
R-0
Contour listing
or ridge
planting (P
-------
TABLE 5-7. GENERALIZED VALUES OF THE COVER AND MANAGEMENT FAC-
TOR, C, IN THE 37 STATES EAST OF THE ROCKY
Line Crop, Rotation, and Management0
No.
Base value: continuous fallow, tilled up and down
corn
1 C, RdR, fall TP, conv (1)
2 C, RdR, spring TP, conv (1)
3 C, RdL, fall TP, conv (1)
4 C, RdR, we seeding, spring TP, conv (1)
5 C, RdL, standing, spring TP, conv (1)
6 C, fall shred stalks, spring TP, conv (1)
7 C(silage)-W(RdL, fall TP) (2)
8 C,RdL, fall chisel, spring disk, 40-30%rc(l)
9 C (silage), W we seeding, no-till pi in c-k(l)
10 C(RdL)-w)RdL, spring TP) (2)
11 C, fall shred stalks, chisel pi, 40-30%rc(l)
12 C-C-C-W-M, RdL, TP for C, disk for W (6)
13 C, RdL, strip till row zones, 55-40% re (1)
14 C-C-C-W-M-M, RdL, TP for C, disk for W (6)
15 C-C-W-M, RdL, TP for C, disk for W (4)
16 C, fall shred, no-till pi, 70-50% re (1)
17 C-C-W-M-M, RdL, TP for C, disk for W (5)
18 C-C-C-W-M, RdL, no-till pi 2nd & 3rd C (5)
19 C-C-W-M, RdL, no-till pi 2nd C (4)
20 C, no-till pi in c-k wheat, 90-70% re (1)
21 C-C-C-W-M-M, no-till pi 2nd& 3rd C (6)
22 C-W-M, RdL, TP for C, disk for W (3)
23 C-C-W-M-M, RdL, no-till pi 2nd C (5)
24 C-W-M-M, RdL, TP for C, disk for W (4)
25 C-W-M-M-M, RdL, TP for C, disk for W (5)
26 C, no-till pi in c-k sod, 95-80% re (1)
Cotton6
27 Cot, conv (Western Plains) (1)
28 Cot, conv (South) (1)
Meadow
29 Grass & Legume mix
30 Alfalfa, lespedeza or Sericia
3 1 Sweet clover
Sorghum, grain (Western Plains)6
32 RdL, spring TP, conv (1)
33 No-till pi in shredded 70-50% re
Productivity
Level"
High Mod.
C Value
1.00 1
0.54 0
.50
.42
.40
.38
.35
.31
.24
.20
.20
.19
.17
.16
.14
.12
.11
.087
.076
.068
.062
.061
.055
.051
.039
.032
.017
0.42 0.
.34
.004 0.
.020
.025
0.43 0.
.11
.00
.62
.59
.52
.49
.48
.44
.35
.30
.24
.28
.26
.23
.24
.20
.17
.18
.14
.13
.11
.14
.11
.095
.094
.074
.061
.053
49
.40
01
53
,18
5-33
-------
TABLE 5-7. GENERALIZED VALUES OF THE COVER AND MANAGEMENT FAC-
TOR, C, IN THE 37 STATES EAST OF THE ROCKY MOETMMHSSftf
Productivity Level11
Line Crop, Rotation, and Management0 High Mod.
No. C Value
Base value: continuous fallow, tilled up and down 1.00 1.00
Soybtesotrf
34 B, RdL, spring TP, conv (1) 0.48 0.54
35 C-B, TP annually, conv (2) .43 .51
36 B, no-till pi .22 .28
37 C-B, no-till pi, fall shred C stalks (2) .18 .22
Wheat
38 W-F, fall TP after W (2) 0.38
39 W-F, stubble mulch, 500 Ibs re (2) .32
40 W-F, stubble mulch, 1000 Ibs re (2) .21
41 Spring W, RdL, Sept TP, conv (N&S Dak) (1) .23
42 Winter W, RdL, Aug TP, conv (Kansas) (1) .19
43 Spring W, stubble mulch, 750 Ibs re (1) .15
44 Spring W, stubble mulch, 1250 Ibs re (1) .12
45 Winter W, stubble mulch, 750 Ibs re (1) .11
46 Winter W, stubble mulch, 1250 Ibs re (1) .10
47 W-M, conv (2) .054
48 W-M-M, conv (3) .026
49 W-M-M-M, conv (4) .021
a This table is for illustrative purposes only and is not a complete list of cropping systems
or potential practices. Values of C differ with rainfall pattern and planting dates,
These generalized values show approximately the relative erosion-reducing effectiveness
of various crop systems, but vocationally derived C values should be used for conserva-
tion planning at the field level. Tables of local values are available from the Soil
Conservation Service.
Control of Water Pollution from Cropland, Vol. I, A Manual for Guideline Development,
U.S. Environmental Protection Agency, Athens, GA. EPA-600/3-75-026a.
c Numbers in parentheses indicate number of years in the rotation cycle. No. (1) desig-
nates a continuous one-crop system.
High level is exemplified by long-term yield averages greater than 75 bu. corn or 3 tons
grass-and-legume hay; or cotton management that regularly provides good stands and
growth.
e Grain sorghum, soybeans, or cotton may be substituted for corn in lines 12, 14, 17-19,
21-25 to estimate C values for sod-based rotations.
5-34
-------
TABLE 5-7. GENERALIZED VALUES OF THE COVER AND MANAGEMENT FAC-
TOR, C, IN THE 37 STATES EAST OF THE ROCKY
Line Crop, Rotation, and Management'
No.
Productivity Level
High Mod.
C Value
Base value: continuous fallow, tilled up and down
1.00
1.00
Abbreviations defined:
B - soybeans F - fallow
C - corn M - grass & legume hay
c-k - chemically killed pi - plantconv - conventional
W - wheat cot - cotton
we - cover
Ibs re -
% re -
7-50% re -
RdR-
RdL-
TP-
pounds of crop residue per acre remaining on surface after new
crop seeding
percentage
70% cover for C values in first column; 50% for second column
residues (corn stover, straw, etc.) removed or burned
all residues left on field (on surface or incorporated)
turn plowed (upper 5 or more inches of soil inverted, covering
residues
5-35
-------
TABLE 5-8. MEAN STORM DURATION* (TR) VALUES FOR SELECTED CITIES
Great Lakes
Champaign-UrbanaJL
Chicago, IL
Davenport, IA
Detroit, MI
Louisville, KY
Minneapolis, MN
Stubenville, OH
Toledo, OH
Zanesville, OH
Lansing, MI (30 Yr)
Lansing, MI (21 Yr)
Storm
Mean
Annual
6.1
5.7
6.6
4.4
6.7
6.0
7.0
5.0
6.1
5.6
6.2
Duration (hrs) Storm Duration (hrs)
Summer Summer
(June- Mean (June-
Sept) Location Annual Sept)
4.6
4.5
5.3
3.1
4.5
4.5
5.9
3.7
4.3
4.2
5.1
Lower Mississippi Vallev
Memphis, TN
New Orleans, LA
Shreveport, LA (17)
Lake Charles, LA
Texas and Southwest
Abilene, TX
Austin, TX
Brownsville, TX
Dallas, TX
El Paso, TX
Waco, TX
Phoenix, AZ
Northwest
Portland, OR (2 Syr)
Portland, OR (lOyr)
Eugene, OR
Seattle, WA
6.9
6.9
7.8
7.7
4.2
4.0
3.5
4.2
3.3
4.2
3.2
5.4
15.5
29.2
21.5
4.7
5.0
5.3
5.9
3.3
3.3
2.8
3.2
2.6
3.3
2.4
4.5
9.4
15.0
12.7
Southeast
Greensboro, NC
Columbia, SC
Atlanta, GA
Birmingham, AL
Gainesville, FL
Tampa, FL
Rocky Mountains
Denver, CO (8 Yr)
Denver, CO (25 Yr)
Denver, CO (24 Yr)
Rapid City, SD
Salt Lake City, UT
Salt Lake City, UT
California
Oakland, CA
San Francisco, CA
Northeast
Caribou, ME
Boston, MA
Lake George, NY
Kingston, NY
Poughkeepsie, NY
New York City, NY
Mineola, LI, NY (2)
Upton LI, NY
Wantagh, LI, NY (2)
Long Island, NY
Washington, DC
Baltimore, MD
5.0
4.5
8.0
7.2
7.6
3.6
4.3
4.8
9.1
8.0
4.5
7.8
4.3
5.9
5.8
6.1
5.4
7.0
6.9
6.7
5.6
6.3
5.6
4.2
5.9
6.0
3.6
3.5
6.2
5.0
6.6
3.1
3.2
3.2
4.4
6.1
2.8
6.8
2.9
11.2
4.4
4.2
4.5
5.0
4.9
4.8
4.0
4.6
4.0
3.4
4.1
4.2
Source: Woodward-Clyde Consultants, "Methodology for Analysis of Detention Basins for
Control of Urban Runoff Quality", prepared for U.S. EPA, Office of Water,
Nonpoint Source Division, 1986.
These values may be misleading in arid regions or regions with pronounced
seasonal rainfall patterns.
5-36
-------
C6
IO
a
§
y
y)
on
uli
Ha
Mo
(Ju
I -
!ll
1-1
s §1
sss
o
CO
m
o
CO
c?
O
t-
:i ~j
^ 0
ajiM
_
£ co
en
o o
CO CO
o
CO
o
CO
o
TAB j]^ 5-9
IO IO
r-H r-H
10 ui
in
r-H
in
a
IO
m
i— i
in
~
831
is
II
•SB'S
sa
E
o
Soybeans
O
CO
8
O
CO
CN
CO
SJ «
13
2
o
m
g
in
i— i
ui
2
E
s
II
• rH
-------
TABLE 5-10. RUNOFF CURVE NUMBERS FOR HYDROLOGIC SOIL-COVER COMP-
LEX^ (ANTECEDENT MOISTURE CONDITION H, AND \ = 0.2 S)
Land Use
Fallow
Row crops
Small
grain
Close-
seeded
legunnnsesB1
or rota-
tion
meadow
Pasture
or range
Meadow
Woods
Farmsteads
Roads
(dirt)*
(hard surface)'
Cover
Treatment
or Practice
Straight Row
Straight Row
Straight row
Contoured
Contoured
Contoured and terraced
Contoured and terraced
Straight row
Straight row
Contoured
Contoured
Contoured and terraced
Contoured and terraced
Straight row
Straight row
Contoured
Contoured
Contoured and terraced
Contoured and terraced
Contoured
Contoured
Contoured
Hydrologic
Condition
—
Poor
Good
Poor
Good
Poor
Good
Poor
Good
Poor
Good
Poor
Good
Poor
Good
Poor
Good
Poor
Good
Poor
Fair
Good
Poor
Fair
Good
Good
Poor
Fair
Good
— -
—
—
Hydraulic Soil Group
A
77
72
67
70
65
66
62
65
63
63
61
61
59
66
58
64
55
63
51
68
49
39
47
25
6
30
45
36
25
59
72
74
B
86
78
78
79
75
74
71
76
75
74
73
72
70
77
72
75
69
73
67
79
69
61
67
59
35
58
66
60
55
74
82
84
C
91
85
85
84
82
80
78
84
83
83
81
79
78
85
81
83
78
80
76
86
79
74
81
75
70
71
77
73
70
82
87
90
D
94
91
89
88
86
82
81
88
87
87
84
82
81
89
85
85
83
83
80
89
84
80
88
83
79
78
83
79
77
86
89
92
fMockus, 1972.
ft Close-drilled or broadcast.
f Including right-of-way.
5-38
-------
TABLE 5-11. METHOD FOR CONVERTING CROP YIELDS TO RESIDUE'
Crtffljpij
Barley
corn
Oats
Rice
Rye
Sorghum
Soybeans
Winter wheat
Spring Wheat
Straw/Grain
Ratio
1.5
1.0
2.0
1.5
1.5
1.0
1.5
1.7
1.3
Bushel
Weight
(Ibs)
48
56
32
45
56
56
60
60
60
8 Crop residue = (straw/grain ratio) x (bushel weight in Ib/bu) x (crop yield in bu/acre).
15 Knisel, W.G. (Ed.). CREAMS: A Field-Scale Model for Chemicals, Runoff, and Erosion
from Agricultural Management Systems. USDA, Conservation Research Report No. 26,
1980.
TABLE 5-12. RESIDUE REMAINING FROM TILLAGE Operations
Residue
Tillagefe Remaining
Operation (%)
Chisel Plow 65
Rod weeder 90
Light disk 70
Heavy disk 30
Moldboard plow 10
Till plant 80
Fluted coulter 90
V Sweep 90
9 Crop residue remaining= (crop residue from Table 10) x (tillage factor(s),
6 Knisel, W.G. (Ed.). CREAMS: A Field-Scale Model for Chemicals, Runoff, and
Erosion from Agricultural Management Systems. USDA, Conservation Research
Report No. 26, 1980.
5-39
-------
TABLE 5-13. REDUCTION IN RUNOFF CURVE NUMBERS CAUSED BY CONSERVA-
TION TILLAGE AND RESIDUE Management
Large
Residue
Crapfr
(Ib/acre)
0
400
700
1,100
1,500
2,000
2,500
6,200
Medium
Residue
(Ib/acre)
0
150
300
450
700
950
1,200
3,500
Surface
Covered
by Residue
0
10
19
28
37
46
55
90
Reductive
in Curve
Numteiirf
0
0
2
4
6
8
10
10
a Knisel, W.G. (Ed.). CREAMS: A Field-Scale Model for Chemicals, Runoff, and Erosion
from Agricultural Management Systems. USDA, Conservation Research Report No. 26,
1980.
Large-residue crop (corn).
c Medium residue crop (wheat, oats, barley, rye, sorghum, soybeans).
Percent reduction in curve numbers can be interpolated linearly. Onlv apply 0 to 1/2 of
these percent reductions to CNS for contouring and terracing practice when they are
used in conjunction with conservation tillage.
TABLE 5-14. VALUES FOR ESTIMATING WFMAX IN EXPONENTIAL FOLIAR
MODEL
Crop
corn
Sorghum
Soybeans
Winter
wheat
YielaK
(Bu/Ac)
110
62
35
40
BushdH
dry wt.
(Ibs/Bu)
56
56
60
60
Straw/Grain
Ratio
1.0
1.0
1.5
1.7
Units
Conversion
Factor
1.1214X10-4
1.1214X10-4
1.1214X10-4
1.1214X10-4
WFMAX
1.38
0.78
0.59
0.72
10-year average
5-40
-------
TABLE 5-15. PESTICIDE SOIL APPLICATION METHODS AND DISTRIBUTION
Method of
Application
Common Procedure
Distribution
DEPI
Broadcast
Disked-in
Chisel-plowed
Surface banded
Banded -
incorporated
Spread as dry granules
or spray over the whole
surface
Disking after broadcast
application
Chisel plowing after
broadcast
Spread as dry granules
or a spray over a fraction
of the row
Spread as dry granules
or a spray over a
fraction of the row
and incorporated in
planting operation
Remains on the 0.0
soil surface
Assume uniform 10.0
distribution to
tillage depth
(10 cm)
Assume linear 15.0
distribution to
tillage depth
(15 cm)
Remains on soil 0.0
surface
Assume uniform 5.0
distribution to
depth of incor-
poration (5 cm)
TABLE 5-16. MAXIMUM CANOPY HEIGHT AT CROP MATURATION
Crop
References:
A. Szeicyetal. (1969)
B. Smith et al. (1978)
Height (cm)
Reference
Barley
Grain Sorghum
Alfalfa
corn
Potatoes
Soybeans
Sugarcane
20-50
90-110
10-50
80-300
30-60
90-110
100-400
A
B
A
A
A
B
A
5-41
-------
TABLE 5-17. DEGRADATION RATE CONSTANTS OF SELECTED PESTICIDES ON
FOLIAGE*
Class
Group
Decay Rate (days-1)
Organochlorine
Organophosphate
Fast
(aldrin, dieldrin, ethylan,
heptachlor, lindane,
methoxychlor).
slow
(chlordane, DDT, endrin,
toxaphene).
Fast
(acephate, chlorphyrifos-methyl,
cyanophenphos, diazinon, depterex,
ethion, fenitrothion, leptophos,
malathion, methidathion, methyl
parathion, phorate, phosdrin,
phosphamidon, quinalphos, alithion,
tokuthion, triazophos, trithion).
slow
azinphosmethyl, demeton, dimethoate,
EPN, phosalone).
0.231-0.1386
0.1195-0.0510
0.2772-0.3013
0.1925-0.0541
Carbamate
Pyrethroid
Pyridine
Benzole acid
Fast
(carbofuran)
slow
(carbaryl)
(permethrin)
(pichloram)
(dicamba)
0.630
0.1260-0.0855
0.0196
0.0866
0.0745
* Knisel, W.G, (Ed.). CREAMS: A Field-Scale Model for Chemicals, Runoff, and Erosion
from Agricultural Management Systems, USDA, Conservation Research Report No, 26,
1980.
5-42
-------
TABLE 5-18. ESTIMATED VALUES OF HENRYS CONSTANT FOR SELECTED
PESTICIDES
Compound
Alachlor
Aldrin
Anthracene
Atrazine
Bentazon
Bromacil
Butylate
Carbaryl
Carbofuran
Chlorpyrifos
Chrysene
Cyanazine
DDT
Diazinon
Dicamba
Dieldrin
Diuron
Endrin
EPTC
Ethoprophos
Fenitrothion
Fonofos
Heptachlor
Lindane
Linuron
Malathion
Methomyl
Methyl Parathion
Metolachlor
Metribuzin
Monuron
Napropamide
Parathion
Permethrin
Picloram
Prometryne
Simazine
Terbufos
Toxaphene
Triallate
Trichlorfon
Trifluralin
2,4-D (acid)
2,4,5-T (acid)
Henry's Constant
(dimensionless)
1.3E-06
6.3E-04
4.4E-05
2.5E-07
2.0E-10
3.7E-08
3.3E-03
1.1E-05
1.4E-07
1.2E-03
4.7E-05
1.2E-10
2.0E-03
5.0E-05
3.3E-08
6.7E-04
5.4E-08
1.8E-05
5.9E-04
6.0E-06
6.0E-06
2.1E-04
1.7E-02
1.3E-04
2.7E-06
2.4E-06
4.3E-08
4.4E-06
3.8E-07
9.8E-08
7.6E-09
7.9E-07
6.1E-06
6.2E-05
1.9E-08
5.6E-07
1.3E-08
1.1E-03
2.3E+00
7.9E-04
1.5E-09
6.7E-03
5.6E-09
7.2E-09
References
A
D
D
A
A
c
A
A
A
A
D
A
C
C
A
C
C
D
C
C
B
A
D
B
A
B
A
A
A
A
C
C
C
A
B
C
A
A
A
C
B
A
A
B
References: A. Donigian et al. (1986) B, Spencer et al. (1984) C, Jury et al. (1984) D.
Schnooretal. (1987)
5-43
-------
TABLE 5-19. PHYSICAL CHARACTERISTICS OF SELECTED PESTICIDES FOR USE IN DEVELOPMENT OF PARTITION COEFFICIENTS (USING WATER SOLUBILITY)
AND REPORTED DEGRADATION RATE CONSTANTS IN SOIL ROOT ZONE (Continued)
en
Chemical
Actellic
Alachlor
Antor
Aresin
Balan
Basalin
Baygon
Baygon Meb
Bayleton
Baythion
Baythion C
Betas an
Bromophos
Butachlor
Bux
Carbamult
Carbyne
Chlordimeform
Chlorfenvin-
phos
Chloro IPC
Chlorpyrifos
Co-Ral
Counter
DNOC
Dichlorprop
Dimetan
Dimethoate
Dinitramine
Dinoseb
Dazomet
Devrinol
Elocron
Evik
Far-Go
Fongarid
Common
Name
pirimiphosmethyl
alachlor
diethatyl ethyl
monol inuron
benefin
fluchloralin
propoxur
plifenate
triad! mefon
phoxim
chlorphoxim
bensulide
bromophos
butachlor
bufencarb
promecarb
barban
chlordimeform
chlorfenvinphos
chlorpropham
chlorpyrifos
coumaphos
terbufos
DNOC
dichlorprop
dimetan
dimethoate
dinitroamine
dinoseb
dazomet
napropamide
dioxacarb
ametryn
triallate
furalaxyl
Solubility
in water
20-25°C) Refer-
(mg/1) ence
5
220
105
735
70
0.7
2000
50
70
7
1.7
25
40
23
1
92
11
250
110
108
2
1.5
15
130
350
30000
X=25000
1
52
1200
73
6000
185
4
230
a
b
a
a
b
b
a
a
a
b
a
c
a
a
b
a
c
a
a
b
b
b
a
a
a
b
a
a
c
b
a
a
a
b
a
In-
sect-
icide
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Mode of Action
Nema-
Herb- Fungi- to- Acar-
icide cide cide icide
X
X
X
X
X
X
X
X
X
X
X
X
X X
X
X
X
XXX
X
X
X
X
Mole-
cular
weight
(g)
274
269.9
311.5
214.6
335.3
355.7
209
336.2
267.45
298
301.45
397.5
366
312
221.3
207
258.1
196.7
359.5
213.7
350.5
362.8
288
198.1
235
197.3
229.1
322.2
240.2
162.3
271.36
223
227
304.6
301
Partitioning Model
Refer-
ence
b
b
c
b
b
b
b
d
d
b
d
b
b
e
b
d
b
b
b
b
b
b
d
b
b
b
b
c
b
b
b
b
b
d
PCMCl PMCM2 PCMC3
(mole (mg/1) ((im/l)
fraction)
3.28xlO'7
1.47x10°
6.07x10-"
6.17x10-'
3.76x10-"
3.55x10*
1.72x10^
2.68x10-"
4.72x10'"
4.23xlO'7
1.02xl07
1.13x10'"
1.97x10'"
1.33x10-"
8.14x10*
8.01x10^
7.70x1 Q-7
2.30x10'°
5.51x10-*
9.11x10-"
1.03xlO'7
7.45x10-"
9.38xlO'7
1.18x10-'
2.68x10-"
2.74xlO'3
1.97xl03
5.60x1 0'8
3.90x10-"
1.33x10^
4.85x10-'
4.85x10^
1.47xlO'5
2.37x1 0'7
1.38x10-°
5
220
105
735
70
0.7
2000
50
70
7
1.7
25
40
23
1.0
92
11
250
110
108
2.0
1.5
15
130
350
30000
25000
1
52
1200
73
6000
185
4
230
18
815
337
3430
209
2
9600
149
262
24
5.6
63
109
74
5
444
43
1270
306
505
6
4
52
656
1490
152000
109000
3
217
7390
269
26900
815
13
764
Degradation
Rate Constant
in Soil
Root Zone Refer-
(days"1) ence
.0384
.0099-.0173
0.3349
0.0169
.0198
.0347
.0055
.0058-.00267
.0578-.0866
.0057
.0193-.0856
.0462-.0231
.3465-.0248
.0231-.0077
.0231-.0713
f
g
f
f
f
g
f
g
f
f
g
f
g
g
-------
TABLE 5-19. PHYSICAL CHARACTERISTICS OF SELECTED PESTICIDES FOR USE IN DEVELOPMENT OF PARTITION COEFFICIENTS (USING WATER SOLUBILITY)
AND REPORTED DEGRADATION RATE CONSTANTS IN SOIL ROOT ZONE (Continued)
en
Chemical
Fornothion
Fuji-one
Gardona
Gesaran
Goal
Guthion
Hoelon
TmiHnn
0>C
Linuron
Malathion
Mecoprop
MEMC
Merpelan AZ
Mesoranil
Mesurol
Methomyl
Methoxychlor
Meth-Para-
thion
Nemacur
Nortron
Orthene
Oxamyl
Parathion
Patoran
Phorate
Propachlor
Propanil
Prowl
Prynachlor
Quinalphos
Ronstar
Sancap
Semeron
Common
Name
fornothion
isoprothiolane
tetrachlorvin-
phos
methoprotryne
oxyfluorfen
azinphos-methyl
diclofop methyl
phosmet
propham
linuron
malathion
mecoprop
MEMC
isocarbamid
aziprotryn
mercaptodi-
methur
methomyl
methoxychlor
methyl Para-
thion
fenamiphos
ethofume&ate
acephate
oxamyl
parathion
metabromuron
phorate
propachlor
propanil
pendimethalin
prynachlor
quinalphos
oxadiazon
dipropetryn
desmetryn
Solubility
in water
20-25°C) Refer-
(mg/1) ence
2600
48
11
320
0.1
29
30
25
250
75
145
620
50000
13000
75
2.7xlOT
58000
0.1
X = 57.5
400
110
6.5x10"
2.8x10"
24
330
50
580
500
0.5
500
22
0.7
16
580
a
a
b
a
c
a
a
b
b
a
a
a
a
a
b
a
a
b
a
a
a
b
a
b
a
b
c
c
c
a
a
b
a
a
In-
sect-
icide
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Mode of Action
Nema-
Herb- Fungi- to- Acar-
icide cide cide icide
X
X
X
X
X
X
X
X
X
X
X
X
X
X X
X
X
X
X
X
X
X
X
X
Mole-
cular
weight
(g)
257
290
366
271
361.7
317.3
340.9
317.3
179.2
249.1
330.4
214.6
295
185
225
225.3
162.2
345.7
263.2
300
286
183.2
219
291.3
258.9
260.4
211.7
218
281.3
221.7
298
345.23
255.4
213
Refer-
ence
b
d
b
b
c
b
d
b
b
b
b
b
d
d
b
b
b
b
b
b
d
b
b
b
d
b
b
b
c
b
d
b
b
b
Partitioning Model
PCMCl PMCM2 PCMC3
(mole (mg/1) ((im/l)
fraction)
1.82x1 0"4
2.98x10-"
5.42x10'
2.13x10'"
4.98xlO'9
1.65x10'"
1.59x10'"
1.42x10'"
2.51x10-'
5.42x10"
7.91x10-"
5.21x10'"
3.05x10"
1.27xlO-3
6.01x10'"
2.16
6.44xlO'3
5.21x10
3.94x10'"
2.38x10-'
6.93x10'°
0.06 6.5x10"
0.023 2.8x10"
1.48x10"
2.30x10'"
3.46x10-"
4.94x10-"
4.13x10-'
3.20xlO-8
4.06x10''
1.33x10'°
3.65x10*
1.13x10"
4.91x10'
2600
48
11
320
0.1
29
30
25
250
75
145
620
50000
13000
75
2.7xl07
58000
0.1
57.5
400
110
650000
280000
24
330
50
580
500
0.5
500
22
0.7
16
580
10100
166
30
1180
0.3
91
88
79
1400
300
439
2890
169000
70300
333
1.2xlOe
358000
0.3
219
1320
385
3550000
1280000
82
1280
192
2740
2290
1.8
2260
74
2.0
63
2720
Degradation
Rate Constant
in Soil
Root Zone Refer-
(days"1) ence
.1732-1386
.0231-.0173
.0533-.0014
.0347-.0116
.0280-.0039
2.91-.4152
.0046-.0033
.2207
.0354-.0646
.2962-.0046
.0234
.0363-.0040
.0231-.0139
.693- .231
c
f
g
f
f
f
f
f
f
f
f
g
g
-------
i
'1U
s*
•e-s
.2 "S
•
co to
O iH
S 88S
8 8
0
00000
OlOlO'—I N C3 i-H 00
§
m m m in
'
X X
X
X
X XX
05 EH EH EH
-------
TABLE 5-20. OCTANOL WATER DISTRIBUTION COEFFICIENTS (log Kg)) AND SOIL
DEGRADATION RATE CONSTANTS FOR SELECTED CHEMICALS
Chemical Name
Alachlor
Aldicarb
Altosid
Atrazine
Benomyl
Bifenox
Bromacil
Captan
Carbaryl
Carbofuran
Chloramben
Chlordane
Chloroacetic Acid
Chloropropharn
Chloropyrifos
Cyanazine
Dalapon
Dialifor
Diazinon
Dicamba
Dichlobenil
Dichlorofenthion
2,4,-Dichloropheno-
acetic Acid
Dichloropropene
Dicofol
Dinoseb
Diuron
Endrin
Fenitrothion
Fluometuron
Linuron
Malathion
Methomyl
Methoxychlor
Methyl Parathion
Monolinuron
Monuron
MSMA
Nitrofen
Parathion
LogKgi
2.78
0.70
2.25
2.45
2.42
2.24
2.02
2.35
2.56
2.44
1.11
4.47
-0.39
3.06
4.97
2.24
0.76
4.69
3.02
0.48
2.90
5.14
2.81
1.73
3.54
2.30
2.81
3.21
3.36
1.34
2.19
2.89
0.69
5.08
3.32
1.60
2.12
-3.10
3.10
3.81
Degradation Rate
Constant (days:1)
0.0384
0.0322-0.0116
0.0149-0.0063
0.1486-0.0023
0.1420
0.1196-0.0768
0.0768-0.0079
0.0020-0.0007
0.0058-0.00267
0.0495
0.0462-0.0231
0.0330-0.0067
0.2140-0.0197
0.0116-0.0039
0.0693-0.0231
0.0462-0.0231
0.0035-0.0014
0.1155-0.0578
0.0231
0.0280-0.0039
02.91-0.4152
0.0046-0.0033
0.2207
0.0046-0.0020
0.2961-0.0046
Reference
A
A
A
A
A
A
A
D
C
D
A
A
D
D
D
A
C
A
A
A
A
D
A
5-47
-------
TABLE 5-20. OCTANOL WATER DISTRIBUTION COEFFICIENTS (log KM) AND SOIL
DEGRADATION RATE CONSTANTS FOR SELECTED CHEMICALS
(concluded)
Chemical Name
Degradation Rate
Constant (days-1)
Reference
Perrnethrin
Phorate
Phosalone
Phosmet
Picloram
Propachlor
Propanil
Propazine
Propoxur
Ronnel
Simazine
Terbacil
Terbufos
Toxaphene
Trifluralin
Zineb
2.88
2.92
4.30
2.83
0.30
1.61
2.03
2.94
1.45
4.88
1.94
1.89
2.22
3.27
4.75
1.78
0.0396
0.0363-0.0040
0.0354-0.0019
0.0231-0.0139
0.693 -0.231
0.0035-0.0017
0.0539-0074
0.0046
0.0956-0.0026
0.0512
E
A
A
D
D
D
A
E
A
A
Nash, R. G. 1980. Dissipation Rate of Pesticides from Soils. Chapter 17.
IN CREAMS: A Field Scale Model for Chemicals, Runoff, and Erosion from Agricultur-
al Management Systems. W. G. Knisel, ed. USDA Conservation Research Report No.
26. 643pp.
Smith, C. N. Partition Coefficients (Log K$) for Selected Chemicals.
Athens Environmental Research Laboratory, Athens, GA. Unpublished report, 1981.
Herbicide Handbook of the Weed Science Society of America, 4th ed. 1979.
Control of Water Pollution from Cropland, Vol. I, a manual for guideline development,
EPA-600/2-75-026a.
Smith, C. N. and R. F. Carsel. Foliar Washoff of Pesticides (FWOP) Model:
Development and Evaluation. Accepted for publishing in Journal of Environmental
Science and Health - Part B. Pesticides, Food Contaminants, and Agricultural Wastes,
B 19(3), 1984.
5-48
-------
TABLE 5-21. ALBEDO FACTORS OF NATURAL SURFACES FOR SOLAR RADIA-
TION*
Surface Reflectivity
Fresh Dry Snow 0.80-0.90
Clean, Stable Snow Cover 0.60-0.75
Old and Dirty Snow Cover 0.30-0.65
Dry Salt Cover 0.50
Lime 0.45
White Sand, Lime 0.30-0.40
Quartz Sand 0.35
Granite 0.15
Dark Clay, Wet 0.02-0.08
Dark Clay, Dry 0.16
Sand, Wet 0.09
Sand, Dry 0.18
Sand, Yellow 0.35
Bare Fields 0.12-0.25
Wet Plowed Field 0.05-0.14
Newly Plowed Field 0.17
Grass, Green 0.16-0.27
Grass, Dried 0.16-0.19
Grass, High Dense 0.18-0.20
Prairie, Wet 0.22
Prairie, Dry 0.32
Stubble Fields 0.15-0.17
Grain Crops 0.10-0.25
Alfalfa, Lettuce, Beets, Potatoes 0.18-0.32
Coniferous Forest 0.10-0.15
Deciduous Forest 0.15-0.25
Forest with Melting Snow 0.20-0.30
Yellow Leaves (fall) 0.33-0.36
Desert, Dry Soils 0.20-0.35
Desert, Midday 0.15
Desert, Low Solar Altitude 0.35
Water (0 to 300)" 0.02
Water (600)" 0.06
Water (850)" 0.58
* References:
Van Wijk, W.R. 1963. Physics of Plant Environment, p. 87. North-Holland Publishing
Co., Amsterdam.
Brutsaert, W. 1982. Evaporation into the Atmopshere: Theory, History, and
Applications. D. Reidel Publishing Co., Dordrecht, Holland.
a angle of solar incidence.
5-49
-------
TABLE 5-22. EMISSIVITY VALUES FOR NATURAL SURFACES AT NORMAL TEM-
PERATURES*
Surface Emissivity
Sand (dry-wet) 0.95-0.98
Mineral Soil (dry-wet) 0.95-0.97
Peat (dry-wet) 0.97-0.98
Firs 0.97
Tree Vegetation 0.96-0.97
Grassy Vegetation 0.96-0.98
Leaves 0.94-0.98
Water 0.95
Snow (old) 0.97
Snow (fresh) 0.99
References
Van Wijk, W.R. 1963. Physics of Plant Environment, p. 87. North-Holland Publishing
Co., Amsterdam.
Brutsaert, W. 1982. Evaporation into the Atmosphere: Theory, History, and Applica-
tions, D. Reidel Publishing Co., Dordrecht, Holland.
Table 5-23. COEFFICIENTS FOR LINEAR REGRESSION EQUATIONS FOR PRE-
DICTION OF SOIL WATER CONTENTS AT SPECIFIC MATRIC POTEN-
TML&
Sand
Matric Intercept (%)
Coefficient a b
-0.20
-0.33
-0.60
-1.0
-2.0
-4.0
-7.0
-10.0
-15.0
0.4180
0.3486
0.2819
0.2352
0.1837
0.1426
0.1155
0.1005
0.0854
-0.0021
-0.0018
-0.0014
-0.0012
-0.0009
-0.0007
-0.0005
-0.0004
-0.0004
Clay
(%)
c
0.0035
0.0039
0.0042
0.0043
0.0044
0.0045
0.0045
0.0044
0.0044
Organic
Matter
('%)
d
0.0232
0.0228
0.0216
0.0202
0.0181
0.0160
0.0143
0.0133
0.0122
Bulk
Density
(g cm-*)
e
-0.0859
-0.0738
-0.0612
-0.0517
-0.0407
-0.0315
-0.0253
-0.0218
-0.0182
R2
KT
0.75
0.78
0.78
0.76
0.74
0.71
0.69
0.67
0.66
Rawls, W. J., U.S. Department of Agriculture, Agricultural Research
Service, Beltsville, MD. Personal Communication.
5-50
-------
TABLE 5-25. HYDROLOGIC PROPERTIES BY SOIL TEXTURE!
Texture
Class
Sand
Loamy
Sand
Sandy
Loam
Loam
Silt Loam
Sandy Clay
Loam
Clay Loam
Silty Clay
Loam
Sandy Clay
Silty Clay
Clay
IRawls, W I
Range of
Textural Properties
(Percent)
Sand silt Clay
85-100
70-90
45-85
25-50
0-50
45-80
20-45
0-20
45-65
0-20
0-45
0-15
0-30
0-50
28-50
50-100
0-28
15-55
40-73
0-20
40-60
0-40
, D. L. Brakensiek, and
0-10
0-15
0-20
8-28
8-28
20-35
28-50
28-40
35-55
40-60
40-100
K. E. Saxton.
Water Retained at Water Retained at
-0.33 Bar Tension -15.0 Bar Tension
cmf cunt j cnw cast's
0.091"
(0.018-0.164)°
0.125
(0.060-0.190)
0.207
(0.126-0.288)
0.270
(0.195-0.345)
0.330
(0.258 - 0.402)
0.257
(0.186-0.324)
0.318
(0.250 - 0.386)
0.366
(0.304 - 0.428)
0.339
(0.245 - 0.433)
0.387
(0.332 - 0.442)
0.396
(0.326 - 0.466)
Estimation of Soil
0.033*
(0.007-0.059)°
0.055
(0.019-0.091)
0.095
(0.031-0.159)
0.117
(0.069-0.165)
0.133
(0.078-0.188)
0.148
(0.085-0.211)
0.197
(0.115-0.279)
0.208
(0.138-0.278)
0.239
(0.162-0.316)
0.250
(0.193-0.307)
0.272
(0.208 - 0.336)
Water Properties,
Transactions ASAE Paper No. 81-2510, pp. 1316-1320. 1982.
15 Mean value.
E One standard deviation about the mean,
5-52
-------
TABLE 5-26. DESCRIPTIVE STATISTICS AND DISTRIBUTION MODEL FOR FIELD
CAPACITY (PERCENT BY VOLUME)
Stratum
(m)
Class A
0.0-0.3
0.3-0.6
0.6-0.9
0.9- 1.2
Class B
0.0-0.3
0.3-0.6
0.6-0.9
0.9-1.2
Class C
0.0-0.3
0.3-0.6
0.6-0.9
0.9- 1.2
Class D
0.0-0.3
0.3-0.6
0.6-0.9
0.9- 1.2
Sample
Size
52
50
42
39
456
454
435
373
371
362
336
290
230
208
178
146
Mean
11.8
9.6
7.3
7.1
19.5
18.8
18.7
17.5
22.4
22.8
22.7
22.2
24.1
26.1
25.0
24.1
Original
Median
9.4
8.1
5.9
5.8
19.1
18.8
18.7
17.5
22.5
23.2
22.9
21.3
24.2
26.3
25.6
24.4
Data
s.d.
9.2
7.9
5.8
5.0
8.3
7.4
7.1
7.6
7.8
7.8
8.6
8.9
9.1
9.3
8.2
8.1
CV
Distribution Model
(%) Transform Mean
78
82
79
70
42
39
39
43
35
34
38
40
38
36
33
33
In
In
In
In
ty
STJ
£
Su
su
Su
Su
&u
§y
§y
§y
2.25
1.99
1.73
1.73
0.316
0.311
0.298
0.288
0.363
0.369
0.368
0.359
0.387
0.419
0.403
0.390
s.d.
0.65
0.73
0.73
0.71
0.13
0.12
0.11
0.12
0.12
0.12
0.13
0.13
0.14
0.14
0.13
0.12
CV = coefficient of variation
s.d. = standard deviation
Source: Carsel et al. (1988)
5-53
-------
TABLE 6-27. DESCRIPTIVE STATISTICS AND DISTRIBUTION MODEL FOR WILT-
ING POINT (PERCENT BY VOLUME)
Stratum
(m)
Class A
0.0-0.3
0.3-0.6
0.6-0.9
0.9- 1.2
Class B
0.0-0.3
0.3-0.6
0.6-0.9
0.6- 1.2
Class C
0.3-0.3
0.3-0.6
0.6-0.9
0.9- 1.2
Class D
0.0-0.3
0.3-0.6
0.6-0.9
0.9-1.2
Sample
Size
118
119
113
105
880
883
866
866
678
677
652
582
495
485
437
401
Mean
4.1
3.2
2.9
2.6
9.0
9.4
9.1
8.6
10.8
12.2
12.2
11.8
14.6
16.9
16.6
15.7
Original
Median
3.1
2.3
2.1
1.9
8.7
9.3
8.9
8.4
10.4
12.1
11.9
11.5
13.8
17.0
16.3
15.1
Data
s.d.
3.4
2.4
2.3
2.3
4.0
4.3
4.4
4.6
5.1
5.6
6.0
5.7
7.6
7.3
7.4
7.6
CV
(%)
82
75
81
87
45
46
48
53
48
46
49
48
52
43
45
48
Distribution
Transform
In
In
SB
SB
Su
Su
Su
Su
Su
Su
Su
Su
Su
Su
Su
Su
Model
Mean
1.83
0.915
3.32
3.43
0.150
0.156
0.151
0.143
1.63
0.202
0.201
0.194
1.26
0.277
0.271
0.257
s.d.
0.64
0.71
0.88
0.92
0.066
0.071
0.072
0.076
0.62
0.091
0.096
0.092
0.76
0.12
0.12
0.12
CV = coefficient of variation
s.d. = standard deviation
Source: Carsel et al. (1988)
5-54
-------
TABLE 5-28. CORRELATIONS AMONG TRANSFORMED VARIABLES OF ORGANIC
MATTER, FIELD CAPACITY, AND WILTING POINT
Stratum
(m)
OM+WP FC + OM
N Corr. N
Corr.
FC + WP
N
Corr.
Class A
0.0-0.3
0.3-0.6
0.6-0.9
0.9- 1.2
Class B
0.0-0.3
0.3-0.6
0.6-0.9
0.9- 1.2
Class C
0.0-0.3
0.3-0.6
0.6-0.9
0.9-1.2
Class D
118
119
111
98
877
870
844
780
673
664
627
543
0.738
0.630
0.487
0.456
0.545
0.372
0.375
0.392
0.495
0.473
0.457
0.434
52
49
42
38
459
446
419
347
369
355
321
264
0.624
0.404
0.427
0.170
0.609
0.384
0.336
0.412
0.577
0.409
0.434
0.456
51
49
42
39
455
450
429
370
370
361
334
289
0.757
0.759
0.811
0.761
0.675
0.639
0.714
0.762
0.745
0.775
0.784
0.751
0.0-0.3
0.3-0.6
0.6-0.9
0.9-1.2
488
472
420
384
0.538
0.434
0.456
0.415
228
201
171
137
0.496
0.454
0.369
0.106
226
204
174
145
0.847
0.845
0.782
0.687
OM = organic matter; WP = wilting point; FC = field capacity; N = sample size; Corr. =
correlation.
Source: Carsel et al. 1988.
5-55
-------
TABLE 5-29. MEAN BULK DENSITY (g cnt$ FOR FIVE SOIL TEXTURAL CLASSIFI-
CATION
Soil Texture
Mean Value
Range Reported
Silt Loams
Clay and Clay Loams
Sandy Loams
Gravelly Silt Loams
Loams
All soils
1.32
1.30
1.49
1.22
1.42
1.35
0.86-1.67
0.94-1.54
1.25-1.76
1.02-1.58
1.16-1.58
0.86-1.76
t Baes, C. F., Ill and R.D. Sharp. 1983. A Proposal for Estimation of Soil Leaching
Constants for Use in Assessment Models, J. Environ. Qual. 12(1): 17-28.
TABLE 5-30. DESCRIPTIVE STATISTICS FOR BULK DENSITY (g
Stratum
(m)
Class A
0.0-0.3
0.3-0.6
0.6-0.9
0.9-1.2
Class B
0.0-0.3
0.3-0.6
0.6-0.9
0.9-1.2
Class C
0.0-0.3
0.3-0.6
0.6-0.9
0.9-1.2
Class D
0.0-0.3
0.3-0.6
0.6-0.9
0.9-1.2
Sample
Size
40
44
38
34
459
457
438
384
398
395
371
326
259
244
214
180
Mean
1.45
1.50
1.57
1.58
1.44
1.51
1.56
1.60
1.46
1.58
1.64
1.67
1.52
1.63
1.67
1.65
Medium
1.53
1.56
1.55
1.59
1.45
1.53
1.57
1.60
1.48
1.59
1.65
1.68
1.53
1.66
1.72
1.72
s.d.
0.24
0.23
0.16
0.13
0.19
0.19
0.19
0.21
0.22
0.23
0.23
0.23
0.24
0.26
0.27
0.28
CV
(%)
16.2
15.6
10.5
8.4
13.5
12.2
12.3
12.9
15.0
14.5
14.2
14.0
15.9
16.0
16.3
17.0
CV = coefficient of variation
s.d. = standard deviation
Source: Carsel et al. (1988)
5-56
-------
TABLE 5-31. DESCRIPTIVE STATISTICS AND DISTRIBUTION MODEL FOR OR-
GANIC MATTER (PERCENT BY VOLUME)
Stratum
(m)
Class A
0.0-0.3
0.3-0.6
0.6-0.9
0.9-1.2
Class B
0.0-0.3
0.3-0.6
0.6-0.9
0.9-1.2
Class C
0.0-0.3
0.3-0.6
0.3-0.9
0.9-1.2
Class D
0.0-0.3
0.3-0.6
0.6-0.9
0.9-1.2
Sample
Size
162
162
151
134
1135
1120
1090
1001
838
822
780
672
638
617
558
493
Mean
0.86
0.29
0.15
0.11
1.3
0.50
0.27
0.18
1.45
0.53
0.28
0.20
1.34
0.65
0.41
0.29
Original
Median
0.62
0.19
0.10
0.07
1.1
0.40
0.22
0.14
1.15
0.39
0.22
0.15
1.15
0.53
0.32
0.22
Data
CV
s.d. (%)
0.79 92
0.34 114
0.14 94
0.11 104
0.87 68
0.40 83
0.23 84
0.16 87
1.12 77
0.61 114
0.27 96
0.21 104
0.87 66
0.52 80
0.34 84
0.31 105
Distribution
Mean
-4.53
-5.72
-6.33
-6.72
-4.02
-5.04
-5.65
-6.10
-3.95
-5.08
-5.67
-6.03
-4.01
-4.79
-5.29
-5.65
Model
s.d.
0.96
0.91
0.83
0.87
0.76
0.77
0.75
0.78
0.79
0.84
0.83
0.88
0.73
0.78
0.82
0.86
CV = coefficient of variation
s.d. = standard deviation
Source: Carsel et al. (1988)
"Johnson sfi transformation is used for all cases in this table.
5-57
-------
TABLE 5-32. ADAPTATIONS AND LIMITATIONS OF COMMON IRRIGATION METH-
ODS
Irrigation
Method
Adaptations
Limitations
Furrow Light, medium-and fine-
textured soils; row crops.
crops; 10 percent cross
Sprinklers
and hot climate.
Flood
than 2 percent.
All slopes; soils; crops.
Light, medium, and heavy
soils.
Slopes up to 3 percent in
direction of irrigation; row
slope.
High initial equipment cost;
lowered efficiency in wind
Deep soils; high cost of land
preparation; slopes less
Source: Adapted from Todd (1970).
TABLE 5-33. WATER REQUIREMENTS FOR VARIOUS IRRIGATION AND SOIL
TYPES
Typical Application Rate (Inches/Hour) bv Sprinklers
Slope
(%)
Sprinkling 0-2
2-5
5-8
8-12
Coarse
Sandy
Loam
2.0
2.0
1.5
1.0
Light
Sandy
Loam
0.75
0.75
0.50
0.40
Medium
silt
Loam
0.5
0.5
0.4
0.3
Clay
Loam
soils
0.20
0.20
0.15
Source: Adapted from Todd (1970).
5-58
-------
TABLE 5-36. SUITABLE SIDE SLOPES FOR CHANNELS BUILT IN VARIOUS KINDS
OF MATERIALS
Material Side slope
Rock Nearly vertical
Muck and peat soils !4:1
Stiff clay or earth with concrete lining l/2\\ to 1:1
Earth with stone lining, or earth for large channels 1:1
Firm clay or earth for small ditches IVz'.l
Loose sandy earth 2:1
Sandy loam or porous clay 3:1
Source: Adapted from Chow (1959).
TABLE 5-37. VALUE OF "N" FOR DRAINAGE DITCH DESIGN
Hydraulic radius (ft) EN
less than 2.50.040-0.045
2.5 to 4.0 .035-.040
4.0 to 5.0 .030-.035
more than 5.0 .025 -.030
Source: Adapted from U.S. Dept. of Agric. Soil Conservation Service.
5-60
-------
TABLE 5-38. REPRESENTATIVE PERMEABILITY RANGES FOR SEDIMENTARY
MATERIALS
Material
Clay
Silty clay
Sandy clay
Silty clay loam
Sandy loam sand
silt
silt loam
Loam
Sandy loam
Hydraulic
Conductivity
(In/s)
J0--H ; jftps
l&f .-lfe«
IP ,i$)6
10$ .-1$)6
Idff .lfb»
m> ,w
Material
Very fine sand
Find sand
Medium sand
Coarse sand
Gravel and sand
Gravel
Sandstone
Limestone*
Shale
Hydraulic
Conductivity
(m/s)
ifoe8 -HBO?
103.- m?
105-1D02
^ .-ifb-3
^ .-1^4
^"W
* Excluding cavernous limestone.
Source: Adapted from Todd (1970).
* See also Table 5-40.
TABLE 5-39. VALUES OF GREEN-AMPT PARAMETERS FOR SCS HYDROLOGIC
SOIL GROUPS
SCS
Hydrologic
Soil Group
A
B
C
D
Saturated Hydraulic^
Conductivity KS
(cm hr-1)
1.0 -10.0
.60 -1.0
.20 -0.60
.005 -0.20
Suction
Parameter HF
(cm)
10
10-20
15-10
20-150
Source: Adapted from Brakensiek and Rawls (1983).
"Also see Table 5-30.
5-61
-------
5.3 VADOFT PARAMETERS
Input data for variably saturated flow simulations include the following:
(1) System Geometry
• Soil column dimensions (L)
(2) Porous Medium Properties
• Saturated hydraulic conductivity, KB (LT1)
• Specific storage, S, (Lrt)
• Effective porosity, $
(3) Constitutive Relationships for Variably Saturated Flow
• Tabulated data of kpj versus SW, or values of parameters of analytic expres-
sions for kj^ versus SW
• Tabulated data of SW versus ty, or values of parameters of analytic expres-
sions for SW versus \p,
(4) Initial and Boundary Conditions
• Prescribed values of pressure head, f (L)
• Prescribed values of nodal fluid flux
(infiltration rate), I (LT1)
Input data for the transport model include the following:
(1) System Geometry
• Soil column dimensions (L)
(2) Porous Medium Properties
• Longitudinal dispersivity «£, (L)
• Molecular diffusion coefficients, D* (LlT1)
• Effective porosity, f
(3) Properties of Solute Species
• Decay coefficient, A (T-l)
5-62
-------
• i Retardation coefficient, R
(4) Darcy Velocity, V (LT)
(5) Water Saturation, SW
(6) Initial and Boundary Conditions
• Prescribed value of concentration, CO
• Prescribed value of solute flux,
Guidance for certain of these parameters is given in the following paragraphs.
Saturated Hydraulic Conductivity - represents the rate at which a porous medium
can transmit water under saturated conditions. Table 5-40 gives representative values for
various soil types. Also note the values of the coefficient of variation in column three.
These CVs are for many soils nationwide that fall into this texture category. CVs for a
single soil are likely to be lower. Jury (1985) gives a CV of 120% for this parameter,
which may be more representative. The most likely shape for the distribution is lognorm-
al.
Soil-Water Characteristic Data - The user is allowed two options: either to input these
data as a set of paired functions (water saturation |S^I versus relative conductivity l]Kj4]
and pressure head [vf] versus water saturation |S$J or to input parameters of the analytic
expressions for these functions in the code. The parameterization of the latter functions
is discussed here.
5-63
-------
TABLE 5-40. DESCRIPTIVE STATISTICS FOR SAT. HYDRAULIC CONDUCTIVITY
(cm hr-1)
Hydraulic Conductivity (K)*
Soil Type
Clay**
Clay Loam
Loam
Loamy Sand
silt
Silt Loam
Silty Clay
Silty Clay Loam
Sand
Sandy Clay
Sandy Clay Loam
Sandy Loam
X
0.20
0.26
1.04
14.59
0.25
0.45
0.02
0.07
29.70
0.12
1.31
4.42
s
0.42
0.70
1.82
11.36
0.33
1.23
0.11
0.19
15.60
0.28
2.74
5.63
CV
210.3
267.2
174.6
77.9
129.9
275.1
453.3
288.7
52.4
234.1
208.6
127.0
n
114
345
735
315
88
1093
126
592
246
46
214
1183
* n = Sample size, i = Mean, s = Standard deviation, CV = Coefficient of variation
(percent)
** Agricultural soil, less than 60 percent clay
Source: Carsel and Parrish (1988).
To provide a linkage for these parameters to widely known or easily obtained soils data
(such as soil texture), Carsel and Parrish (1988) fit these analytic functions to data from
soils all over the United States and tabulated corresponding parameter values by texture.
These are shown in Table 5-41. The required parameters are a, (5, and f of the van
Genuchten model (see Section 7). Mean values of these parameters are shown along with
CVs for each by soil texture. Other parameters required to use these relationships are
the air entry pressure head (\^g) and the residual water phase saturation (SW. The air
entry pressure head is normally taken to be zero. Values of the residual water phase
saturation are given in Table 5-42 along with their respective CVs. Table 5-43 from
Carsel and Parrish (1988) shows the types of probability density functions used to fit the
sample distributions of saturated hydraulic conductivity, residual water phase saturation,
and van Genuchten parameters a and 0,
Note that y is related to (3 by the relationship:
In addition, Table 5-44 gives the correlations between these parameters by soil textural
classification.
5-64
-------
Specific Storage - For unsaturated zone flow, set the specific storage to 0.
Effective Porosity - Mean values of saturated water content (Q) and residual water
content (6^ shown in Table 5-42 can be used to estimate effective porosity. The satura-
tion water content ($J) is equal to the total porosity of the soil. The effective porosity can
be roughly approximated as the difference of 6, and f)r in Table 5-43. CVs for soil texture
categories are also shown in Table 5-43. According to Jury (1985) the normal distribution
is an appropriate probability density function for this parameter.
Longitudinal Dispersivity - (The user should refer to the discussion in Section 5.2 of
the dispersion coefficient having units of era? day:l.) Dispersion coefficients are calculated
by the model as the product of the seepage velocity and the dispersivity input by the user.
In the absence of site-specific values it is recommended that the dispersivity be chosen as
one-tenth of the distance of the flow path or:
a = 0.1 x,
where
x^ = the thickness of the vadose zone.
Molecular Diffusion - See the discussion in Section 5.2.
5-65
-------
TABLE 5-43. STATISTICAL PARAMETERS USED FOR DISTRIBUTION APPROXIMA-
TION
Soil
Tex
ture**
s
s
s
s
SL
SL
SL
SL
LS
LS
LS
LS
SIL
SIL
SIL
SIL
SI
SI
SI
SI
c
c
c
c
SIC
SIC
SIC
SIC
sc
sc
sc
sc
SICL
SICL
SICL
SICL
CL
CL
CL
CL
Hydrau- Trans-
lie forma-
Variable tion
R
Qt
a
P
K.
9,
a
P
K.
er
a
P
K.
er
a
P
K,
er
a
P
K,
er
a
P
K.
er
a
P
K.
er
a
P
K.
er
a
P
K.
o.
a
P
SB
LN
SB
LN
SB
SB
SB
LN
SB
SB
NO
SB
LN
SB
LN
SB
LN***
ND***
NO
NO
SB
su**
SB**
LN**
LN
NO
LN
SB
LN
SB
LN
LN
SB
NO
SB
NO
gB***
SU
LN
SB
Limits of
Variation
A B
0.0 70.0
0.0 0.1
0.0 0.25
1.5 4.0
0.0 30.0
0.00 0.11
0.00 0.25
1.35 3.00
0.0 51.0
0.0 0.11
0.0 0.25
1.35 5.00
0.0 15.0
0.0 0.11
0.0 0.15
1.0 2.0
0.0 2.0
0.0 0.09
0.0 0.1
1.2 1.6
0.0 5.0
0.0 0.15
0.0 0.15
0.9 1.4
0.0 1.0
0.0 0.14
0.0 0.15
1.0 1.4
0.0 1.5
0.0 0.12
0.0 0.15
1.0 1.5
0.0 3.5
0.0 0.115
0.0 0.15
1.0 1.5
0.0 7.5
0.0 0.13
0.0 0.15
1.0 1.6
Mean
-0.39387
-3.11765
0.37768
0.97813
-2.49047
0.38411
-0.93655
0.63390
-1.26908
0.07473
0.12354
-1.11095
-2.18691
0.47752
-4.09937
-0.37036
-2.20
0.042
0.01688
1.37815
-5.75949
0.44537
-4.14805
0.00021
-5.68562
0.06971
-5.65849
-1.28378
-4.04036
1.72496
-3.76810
0.20209
-5.31256
0.08871
-2.75043
1.23640
-5.87171
0.67937
-4.21897
0.13248
Estimated*
Standard
Deviation
1.15472
0.22369
0.43895
0.10046
1.52854
0.70011
0.76383
0.08162
1.40000
0.56677
0.04345
0.30718
1.49414
0.58156
0.55542
0.52557
0.7000
0.0145
0.00611
0.03729
2.32884
0.28178
1.29310
0.11800
1.31421
0.02337
0.58445
0.82074
2.01721
0.70000
0.56322
0.07788
1.61775
0.00937
0.60529
0.06130
2.92220
0.06005
0.71389
0.72498
Truncation Limits
on Transformed
D*** Variable
0.045
0.053
0.050
0.063
0.029
0.034
0.044
0.039
0.036
0.043
0.027
0.070
0.046
0.073
0.083
0.104
0.168
0.089
0.252
0.184
0.122
0.058
0.189
0.131
0.205
0.058
0.164
0.069
0.130
0.078
0.127
0.100
0.049
0.056
0.082
0.082
0.058
0.061
0.052
0.035
-2.564 -0.337
0.013 0.049
0.0065 0.834
-5.01 0.912
0.00 0.315
-8.92 2.98
5-68
-------
TABLE 5-43. STATISTICAL PARAMETERS USED FOR DISTRIBUTION APPROXIMA-
TION (continued)
Soil
Tex
ture**
SCL
SCL
SCL
SCL
L
L
L
L
Hydrau- Trans-
lie forma-
Variable tion
Of-
a
0
K.
a
B
SB
SB***
SB
LN
SB
SB
SB
su
Limits of
Variation
A
0.0
0.0
0.0
1.0
0.0
0.0
0.0
1.0
B
20.0
0.12
0.25
2.0
15.0
0.12
0.15
2.0
Mean
-4.
1
-1.
0.
-3,
0.
-1.
0.
.03718
.65387
,37920
38772
,71390
63872
,27456
53169
Estimated*
Standard
Deviation
1
0,
0.
0,
1
0,
0.
0.
.84976
,43934
82327
,08645
.77920
,48709
78608
09948
Truncation Limits
on Transformed
D*** Variable
0,
0
0.
0,
0.
0.
0.
0.
,047
.077 0.928 2.94
048
,043
019
,064
039
036
**
***
For distribution of transformed variables.
S = sand, SL = sandy loam, LS = loamy sand, SIL = silty loam, SI = silt, C = clay,
SIC = silty clay, SC = sandy clay, SICL = silty clay loam, CL= clay loam, SCL =
sandy clay loam, L = loam.
Truncated form of the distribution.
**** Kolmogorov-Smirnov test statistic,
Source: Carsel and Parrish, 1988.
5-69
-------
TABLE 5-44. CORRELATIONS AMONG TRANSFORMED VARIABLES PRESENTED
WITH THE FACTORED COVARIANCE MATRIX*
Silt **(n = 61)
K.
er
a
0
Clay (n= 95)
K,
er
a
§
Silty Clay (n =
K,
9r
oc
0
Sandy Clay (n
K,
er
a
0
Sand (n- 237)
K,
9r
a
6
K.
0.5349258
-0.204
0.984
0.466
1.9614077
0.972
0.948
0.908
123)
1.2512845
0.949
0.974
0.908
= 46)
2.0172105
0.939
0.957
0.972
1.0370702
-0.515
0.743
0.843
Of
-0.0015813
0.0075771
-0.200
-0.610
0.0701669
0.0170159
0.890
0.819
0.0082067
0.0027392
0.964
0.794
0.8827527
0.3241979
0.937
0.928
-0.1092256
0.1816914
0.119
-0.858
a
0.0030541
0.0000021
0.0005522
0.551
0.5645309
-0.0798488
0.1716520
0.910
0.3143268
0.0404171
0.0608834
0.889
0.5391195
0.0634106
0.1501651
0.932
0.3276629
0.2583835
0.1429585
0.298
P
0.0128700
-0.0145118
0.0144376
0.0133233
0.0475514
-0.0142394
0.0021973
0.0164640
0.3674505
-0.0858769
0.0660396
0.1305065
0.0756103
0.0035688
0.0010668
0.0178225
0.0805436
-0.0471785
-0.0013674
0.0167064
SandyLoani(n=l 145)
K,
er
a
5
1.6026856
-0.273
0.856
0.686
-0.1529235
0.5378436
0.151
-0.796
0.0372713
0.0174500
0.0142626
0.354
0.2108253
-0.1943369
0.0193794
0.1084945
Loamy Sand(n= 313)
K,
0r
a
i
Silt Loam (n=
K.
9r
a
0
1.4754063
-0.359
0.986
0.730
1072)
1.4754063
-0.359
0.986
0.730
-0.2005639
0.5215473
-0.301
-0.590
-0.02005639
0.5215473
-0.301
-0.590
0.0372713
0.0174500
0.0142626
0.354
0.5245489
0.0300399
0.0820163
0.775
0.2108253
-0.1943369
0.0193794
0.1084945
0.3525548
-0.1696100
0.2341768
0.1583593
5-70
-------
TABLE 5-44. CORRELATIONS AMONG TRANSFORMED VARIABLES PRESENTED
WITH THE FACTORED COVARIANCE MATRIX* (continued)
Silty Clay Loam (n= 591)
K, 1.6177521
6r 0.724
a 0.986
B 0.918
Clay Loam (n= 328)
R
9,
a
1.9200165
0.790
0.979
0.936
Sandy Clay Loam (n= 212)
K, 1.8497610
6r 0.261
a 0.952
| 0.909
Loam (n= 664)
0.0056509
0.0053780
0.777
0.549
0.0395603
0.0307122
0.836
0.577
0.1020156
0.3775754
0.392
-0.113
0.5116521
0.0475299
0.0731704
0.911
0.5886263
-0.0619715
0.1060875
0.909
0.7838769
0.1223451
0.2198684
0.787
0.0486478
-0.0089569
0.0080399
0.0171716
0.5417671
-0.1536351
0.0653030
0.1159401
0.0766289
-0.0305588
-0.0078559
0.0155766
K.
9r
a
P
1.4083953
0.204
0.982
0.632
-0.0995016
0.4775039
-0.086
-0.748
0.6110671
0.0727710
0.0926351
0.591
0.0545016
-.0545793
0.0256843
0.0288861
Entries in the lower triangular portion of the matrix are sample Pearson product-
moment correlations given to three decimal places. The diagonal and upper
triangular entries form the triangular Cholesky decomposition of the sample
covariance matrix.
** n = Sample size.
Source: Carsel and Parrish, 1988.
Pesticide Decay Coefficients - See the discussion in Section 5.2.
Retardation Factors - In VADOFT, in contrast to PRZM, the user inputs the retarda-
tion factor R instead of the distribution coefficient,^ (cm? g:l). The retardation factor is
defined for saturated conditions in the input:
(5.5)
5-71
-------
and is adjusted internally for values of 6K 9§, In the above equation, p is the soil bulk
density (g cm?) and 0, is the saturation water content (cm? cutl). In making this calcula-
tion, the user should directly use the value for p, if known. If necessary, p can be
approximated according to:
p= 2.65(1-® (5.6)
The CV of the retardation factor, R, can be computed knowing the uncertainties in K^ p
and 8, (Taylor 1982). The fractional uncertainties add to give an upper bound error on R
nS? or are combined as a root mean square for independent random errors. Thus,
c«aaa = (eve. + ew^ + cvp> (5.7)
or
CV = 100
The uncertainty in the value of Kg will depend upon whether it is measured, calculated as
the product of Jty and % organic carbon, and whether the IQ is calculated from a
surrogate parameter such as octanol water partition coefficient (JKg^ or volubility (s).
Directly measured values would obviously have lower CVs. Assuming that Kj is calculat-
ed from a measured soluble concentration, then it is possible that the CV would be on the
order of 60 to 130% (Jury 1985). For Kg derived from KJQ or volubility, the CV could be on
the order of 1000%.
5-72
-------
SECTION 6
PESTICIDE ROOT ZONE MODEL (PRZM)
CODE AND THEORY
6.1 INTRODUCTION AND BACKGROUND (PRZM)
This section describes the theoretical background for a mathematical simulation model
(PRZM) that has been developed and partially tested to evaluate pesticide leaching from
the crop root zone under field crop conditions.
Following this short introduction, Section 6.2 describes the features and limitations of the
model. A description of the theory, including a detailed description of the equations
solved, is provided in Section 6.3. An outline of the numerical implementation techniques
used by the model to apply the theory to the simulation of physical problems follows.
This section concludes with a discussion of testing results for new algorithms that have
been added in this release.
6.1.1 Introduction
Pesticide leaching from agricultural fields as nonpoint source loads can lead to groundwa-
ter contamination. Nonpoint source contamination is characterized by highly variable
loadings, with rainfall and irrigation events dominating the timing and magnitude of the
loading of pesticides leaching below the root zone. The potentially widespread, areal
nature of resulting contamination makes remedial actions difficult because there is no
single plume emanating from a "point source" (the more common groundwater problem)
that can be isolated and controlled. In any case, a more prudent approach to prevention
or reduction of groundwater contamination by pesticides must be based on understanding
the relationships among chemical properties, soil system properties, and the climatic and
agronomic variables that combine to induce leaching. Knowledge of these relationships
can allow a priori investigation of conditions that lead to problems, and appropriate
actions can be taken to prevent widespread contamination.
Many investigators have studied the factors contributing to pesticide leaching. These
investigations have shown that chemical volubility in water, sorptive properties, volatility,
formulation, and soil persistence determine the tendency of pesticides to leach through
soil. Similarly, the important environmental and agronomic factors include soil proper-
ties, climatic conditions, crop type, and cropping practices. In short, the hydrologic cycle
interacts with the chemical characteristics to transform and transport pesticides within
and out of the root zone. Vertical movement out of the root zone can result in groundwa-
ter contamination and is the problem that the model is designed to investigate,
6-1
-------
Numerical models for the movement of solutes in porous media for steady-state, transient,
homogeneous, and multi-layered conditions have been previously developed. Included in
such studies have been linear and nonlinear sorption, ion exchange, and other chemical-
specific reactions. These investigations have proven valuable in interpreting laboratory
data, investigating basic transport processes, and identifying controlling factors in
transport and transformation. As noted in a recent review of models for simulating the
movement of contaminants through groundwater flow systems, however, the successful
use of such models requires a great deal of detailed field data. This unfortunate conclu-
sion arises from the scaling problems associated with laboratory experiments and the
traditional solution of the appropriate partial differential equations at points or nodes in a
finite-difference or finite-element grid network. Each spatial segment modeled must be
properly characterized-a most expensive, if not impossible, task for many modeling
problems.
Such problems in modeling pesticide leaching with existing procedures are discouraging
when one considers the need to evaluate future problems arising from pesticides not yet
widely distributed or used. Models used to perform such evaluations should conform to
the maximum possible extent to known theory, but must be structured to enable efficient
analysis of field situations with minimal requirements for specialized field data. In short,
the goal is to integrate the essential chemical-specific processes for leaching with reason-
able estimates of water movement through soil systems. Data input requirements must
be reasonable in spatial and temporal requirements and generally available from existing
data bases. This model attempts to meet these objectives.
6.1.2 Background
The Pesticide Root Zone Model (PRZM) (Camel et al. 1984, Carsel et al. 1985) was
selected as the code to provide the capability to simulate the transport and transformation
of agriculturally applied pesticides in the crop root zone. PRZM was initially designed for
this purpose and has attained a degree of acceptability in both the regulatory community
and in the agricultural chemical industry. Therefore, its utility in accomplishing the
objective of this model development effort is obvious.
6.2 FEATURES AND LIMITATIONS
6.2.1 Features
PRZM Release H is a one-dimensional, dynamic, compartmental model for use in simulat-
ing chemical movement in unsaturated soil systems within and immediately below the
plant root zone (see Figure 6.1). PRZM allows the user to perform simulations of
potentially toxic chemicals, particularly pesticides, that are applied to the soil or to plant
foliage. Dynamic simulations allow the consideration of pulse loads, the prediction of
peak events, and the estimation of time-varying mass emission or concentration profiles,
6-2
-------
Figure 6.1
Figure 6.1. Pesticide Root Zone Model.
6-3
-------
thus overcoming limitations of emission or concentration profiles, thus overcoming
limitations of the more commonly used steady-state models. Time-varying transport by
both advection and dispersion in the dissolved phase or diffusion in the gas phase are
represented in the program.
PRZM has two major components-hydrology and chemical transport. The hydrologic
component for calculating runoff and erosion is based on the Soil Conservation Service
curve number technique and the Universal Soil Loss Equation. Evapotranspiration is
estimated from pan evaporation data, or by an empirical formula if input pan data are
unavailable. Evapotranspiration is divided among evaporation from crop interception,
evaporation from soil, and transpiration by the crop. Water movement is simulated by
the use of generalized soil parameters, including field capacity, wilting point, and
saturation water content. Irrigation may also be considered.
Dissolved, adsorbed, and vapor-phase concentrations in the soil are estimated by simulta-
neously Considering the processes of pesticide uptake by plants, surface runoff, erosion,
decay, volatilization, foliar washoff, advection, dispersion, and retardation. The user may
elect to solve the transport equations using one of two finite-difference numerical
solutions, the original backwards-difference implicit scheme featured in the first release,
or a Method of Characteristics algorithm that greatly reduces numerical dispersion, but
increases model execution time.
The hydrologic components of pesticide transport equations (i.e., moisture content and
soil-water velocities) are decoupled, solved separately, and used to numerically integrate
the equation in succeeding time steps. Predictions are made on a daily basis. Output can
be summarized on a daily, monthly, or annual period. A daily time series value for
various fluxes or storages can be written to sequential files during program execution.
6.2.2 Limitations
There were severe limitations of the PRZM Release I Code, some that were obvious to the
developers and some that were pointed out subsequently by model users. These can be
broken into four categories:
• Hydrology
• Soil hydraulics
9 Method of solution of the transport equation
» Deterministic nature of the model
In Release II, many of these limitations to an extent, have been overcome.
Hydraulic computations are performed in PRZM on a daily time step; however, some of
the processes involved (evaporation, runoff, erosion) are clearly among those that might be
simulated on a freer time step to ensure greater accuracy and realism. For instance,
simulation of erosion by runoff depends upon the peak runoff rate, which is in turn
dependent upon the time base of the runoff hydrography. This depends to some extent
upon the duration of the precipitation event. PRZM retains its daily time step in this
release primarily due to the relative availability of daily versus shorter time step
6-4
-------
meteorological data. A portion of this limitation has been mitigated, we hope, by en-
hanced parameter guidance.
The method of computing potential evapotranspiration using Hamon's formula, in the
absence of some evaporation data, has also been retained. Evapotranspiration from
irrigated citrus in Florida was found to be substantially underpredicted when using this
method to estimate potential evapotranspiration (Dean and Atwood 1985). Users should
check the model's hydrologic simulation carefully when using this option.
The capability to simulate soil temperature has been added to PRZM-2 in order to correct
Henry's constant for the temperature occurring in various depths in the soil when
performing vapor-phase calculations. Removal of water by evaporation versus transpira-
tion from the profile may have a pronounced effect on soil temperature. This is due to the
fact that more heat is removed during the process of evaporation because the energy
necessary to vaporize water leaves the system, producing a cooling effect. No differentia-
tion is made between evaporation and transpiration in PRZM at this time.
In PRZM Release I, the soil hydraulics were simple-all drainage to field capacity water
content was assumed to occur within 1 day. (An option to make drainage time dependent
was also included, but there is not much evidence to suggest that it was utilized by model
users to any great extent). This had the effect, especially in larger soil cores, of inducing
a greater-than-anticipated movement of chemical through the profile. While this repre-
sentation of soil hydraulics has been retained in PRZM-2, the user has the option, with
the linked modeling system, of coupling PRZM to VADOFT. PRZM-2 is then used to
represent the root zone, while VADOFT, with a more rigorous representation of unsatu-
rated flow, is used to simulate the thicker vadose zone. The difficulties in parameterizing
the Richards equation for unsaturated flow in VADOFT is overcome by using the tech-
nique of van Genuchten to generate soil water characteristic curves using soil textural
information. For short soil cores, PRZM can obviously be used to represent the entire
vadose zone.
The addition of algorithms to simulate volatilization has brought into focus another
limitation of the soil hydraulics representation. PRZM-2 simulates only advective,
downward movement of water and does not account for diffusive movement due to soil
water gradients. This means that PRZM-2 is unable to simulate the upward movement of
water in response to gradients induced by evapotranspiration. This process has been
identified by Jury et al. (1984) as an important one for simulating the effects of volatiliza-
tion. However, the process would seem less likely to affect the movement of chemicals
with high vapor pressures. For these chemicals, vapor diffusion would be a major process
for renewing the chemical concentration in the surface soil.
Another limitation of the Release I model was the inadequacy of the solution to the
transport equation in advection-dominated systems. The backward difference formulation
of the advection term tends to produce a high degree of numerical dispersion in such
systems. This results in overprediction of downward movement due to smearing of the
peak and subsequent overestimation of loadings to groundwater. In this new release, a
new formulation is available for advection-dominated systems. The advective terms are
decoupled from the rest of the transport equation and solved separately using a Method of
6-5
-------
Characteristics (MOC) formulation. The remainder of the transport equation is then
solved as before, using the fully implicit scheme. This approach effectively eliminates
numerical dispersion, but with some additional overhead expense in computation time. In
low-advection systems, the MOC approach reduces to the original PRZM solution scheme,
which is exact for velocities approaching zero.
The final limitation is the use of field-averaged water and chemical transport parameters
to represent spatially heterogeneous soils. Several researchers have shown that this
approach produces slower breakthrough times than are observed using stochastic
approaches. This concern has been addressed by adding the capability to run PRZM in a
Monte Carlo framework. Thus, distributional, rather than field-averaged, values can be
utilized as inputs that will produce distributional outputs of the relevant variables (e.g.,
flux to the water table).
6.3 DESCRIPTION OF THE EQUATIONS
The mathematical description of the processes simulated by PRZM are broken down in
the following discussion into five categories:
• Transport in Soil
• Water Movement
• Soil Erosion
• Volatilization
• Irrigation
The first three categories were simulation options previously available in PRZM Release I.
Since the capability to simulate pending is new, the mathematical basis of the pending
algorithms is described in detail. The final process, volatilization, was not available in
the previous release of PRZM, and its theoretical basis is also described in detail.
6.3.1 Transport in Soil
The PRZM-2 model was derived from the conceptual, compartmentalized representation of
the soil profile as shown in Figure 6.2. From consideration of Figure 6.2, it is possible to
write mass balance equations for both the surface zone and the subsurface zones.
Addition of the vapor phase and ponded water compartments in PRZM-2 require the
consideration of additional terms. The surface zone expressions for each of the dissolved,
adsorbed, and vapor phases can be written as:
A A
6-6
-------
(Surface Layer:
Runoff)
(Surface L
JQR
(Wro )
Diflusion
fcK
ft \rf*r* ^ ----- 1
over, "*^
Erosion)
SOLIDS
c
P
S
s
Adsorption/
Desof]
?wm
(JDS )
j
I
I Diffusion /?„,*
Leaching ,
\ i
i'v
WATER
C
w
0
(J,
•DM )
Ml
-------
=_J _J
=j - j
where
A = cross-sectional area of soil column (cm?)
Az ~ depth dimension of compartment (cm)
(% = dissolved concentration of pesticide (g cm$)
6, ~ sorbed concentration of pesticide (g g:l)
Qg = gaseous concentration of pesticide (g cnml)
0 = volumetric water content of soil (cm? cm$)
a = volumetric air content of the soil (cm! ctm^j)
(% ~ soil bulk density (g cnm^
t = time (d)
JD = represents the effect of dispersion and diffusion of dissolved phase (g
day1)
Jy = represents the effect of advection of dissolved phase (g day!)
Jgg = represents the effect of dispersion and diffusion in vapor phase (g day!)
J0W = mass loss due to degradation in the dissolved phase (g day-i)
Jgg = mass loss due to degradation in the vapor phase (g day-1)
jy = mass loss by plant uptake of dissolved phase (g day-1)
= mass loss by removal in runoff (g day-!)
= mass gain due to pesticide deposition on the soil surface (g day-"!)
= mass gain due to washoff from plants to soil (g day:l)
Jg§ = mass loss due to degradation of sorbed phase chemical (g day-!)
Jgg = mass loss by removal on eroded sediments (g day-!)
= mass gain or loss due to parent/daughter transformations
Equations for the subsurface zones are identical to Equations 6-1, 6-2, and 6-3 except that
J^g, Jjpjjp, and JEE are not included. J^Jp applies to subsurface zones only when pesticides
are incorporated into the soil. For subsurface layers below the root zone, the term Jl^J is
also not utilized.
6-8
-------
Note that terms representing phase transfers (e.g., volatilization) are neglected in
Equations 6-1 through 6-3 because they cancel when the equations are added (see
Equation 6-19 below).
Each term in Equations 6-1 through 6-3 are now further defined. Dispersion and
diffusion in the dissolved phase are combined and are described using Pick's law as
(6_4)
where
Eli^ = diffusion-dispersion coefficient for the dissolved phase, assumed constant
(on£ day:1)
C} = dissolved concentration of pesticide (g
-------
4> = total porosity (cm? cmf*)
Da = molecular diffusivity of the chemical in air, assumed constant (cm? day!)
The mathematical theory underlying the diffusive and dispersive flux of pesticide in the
vapor phase within the soil and into the overlying air can be found in the section describ-
ing volatilization.
The advective term for the dissolved phase, JV, describes the movement of pesticide in the
bulk flow field and is written as
/LAz W , A Az (6-9)
Kg Cg a Az (6-10)
6-10
-------
where
|^ = lumped, first-order decay constant for solid and dissolved phases (day"r)
^ = lumped, first-order decay constant for vapor phase (day-1)
68 = solid-phase concentration of pesticide (g g:l)
Plant uptake of pesticides is modeled by assuming that uptake of a pesticide by a plant is
directly related to transpiration rate. The uptake is given by:
*=f CyJSoe AAz (6-11)
where
sKJ = uptake of pesticide (g day:l)
f = the fraction of total water in the zone used for transpiration (day:l)
& = an uptake efficiency factor or reflectance coefficient
(dimensionless)
Erosion and runoff losses as well as inputs to the surface zone from foliar washoff are
considered in the surface layer. The loss of pesticide due to runoff is
(6-12)
w
in which
J^S = pesticide loss due to runoff (g day:l)
Q = the daily runoff volume (cm& day:l)
Aw, = watershed area
and the loss of pesticide due to erosion is
Jfe-
where
JER = the pesticide loss due to erosion (g day;l)
Xe = the erosion sediment loss (metric tons day:l)
6-11
-------
r^ = the enrichment ratio for organic matter (g g-i)
p = a units conversion factor (g tons-1)
Soil erosion is discussed in more detail in Section 6.3.3.
Pesticides can be applied to either bare soil if pre-plant conditions prevail or to a full or
developing crop canopy if post-plant treatments are desired. The pesticide application is
an input mass rate that is calculated by one of the application/deposition models discussed
in Section 7.1. It is partitioned between the plant canopy and the soil surface, and the
rate at which it reaches the soil surface is designated
Pesticides applied to the plant canopy can be transported to the soil surface as a result of
rainfall washoff. This term, JBQEu is defined as:
MA (6-14)
where
E = foliar extraction coefficient (cm:l)
Pr = daily rainfall depth (cm day:l)
M = mass of the pesticide on the plant surface projected area basis (g cnaf)
The foliar pesticide mass, M, is further subject to degradation and losses through
volatilization. Its rate of change is given by
dt
(6- 1 5)
where
Kf = lumped first-order foliar degradation constant (day1!)
Aj. = application rate to the plant (gha-"I day:l)
It> =3= a units conversion factor (ha)
Adsorption and resorption in Equations 6-1 through 6-3 are treated as instantaneous,
linear, and reversible processes. Using this assumption, we can relate the sorbed phase
concentration to the dissolved-phase concentration by:
Q - K& OK (6-16)
6-12
-------
where
^g = partition coefficient between the dissolved and solid phases (cm? g:l)
A similar expression can be developed to express the vapor phase concentration in terms
of the dissolved-phase concentration as follows
Cg = K$3fy (6-17)
where
KH = Henry's constant, i.e., distribution-coefficient between liquid phase and
vapor phase (cm? cmi'3)
The transformation of parent to daughter is assumed to be first order and takes place
according to
C^vAAz 6 (6-18)
where
= the transformation rate constant (day:1)
When simulating an end-of-chain daughter, J^ may also be a source term equal to the
sum of the first-order transfers from any and all parents.
JIM = £ K^ C*A Az 6 (6-19)
in which the superscript k denotes a parent compound. For intermediate products, the
solute transport equation may contain terms such as those shown in both Equations 6-18
and 6-19. The transformation of parent to daughter compounds is discussed in detail in
Section 6.5.4. The section includes a description of the equations used to simulate this
process.
Summing Equations 6-1, 6-2, and 6-3 and utilizing equations 6-16 and 6-17, produces the
following expressions for the mass balance of pesticide in the uppermost soil layer:
6-13
-------
a
(6-20)
Equation 6-20 is solved in PRZM-2 for the surface layer with ffl = 0, and an upper
boundary condition that allows vapor phase flux upward from the soil surface to the
overlying air. This upper boundary condition is described more fully in the section on
volatilization. The lower boundary condition is one that allows advection, but no diffu-
sion, out of the bottom of the soil profile.
6.3.2 Water Movement
Because V and 0 are not generally known and not generally measured as part of routine
monitoring programs, it is necessary to develop additional equations for these variables.
In the general case, Darcy's law can be combined with the continuity equation to yield the
Richards equation (Richards 1931):
(6-21)
where
and
K(6) = hydraulic conductivity at various heads (cm see-ff
§ = soil water content (cm? cro3)
(6-22)
or, in simpler terms
i_ a*?
(6-23)
6-14
-------
where
6 = soil water content (cna? cmf)
V = soil water velocity (cm day:1)
Writing Equation 6-23 in an integrated backwards finite difference form yields
Az (BW1 (6-24)
or
fe * ft - KMt + 0'Az (6-25)
In these equations, t and t+1 denote the beginning and end of time step values, respec-
tively, and i is the soil layer index. These equations can be further simplified by substi-
tuting the nomenclature SW for $£z so that
£ (6-26)
where
SW= soil water content (cm)
The velocities in Equation 6-26 are a function of inputs to the soil (precipitation, infiltra-
tion) and outflows from the soil (evapotranspiration, runoff).
Water balance equations are separately developed for (a) the surface zone, (b) horizons
comprising the active root zones, and (c) the remaining lower horizons within the
unsaturated zone, The equations are:
Surface Zone
^1- E[-U( (6-27)
6-15
-------
Root Zone
Below Root Zone
(6-29)
where
($W)f = soil water in layer "i" on day "t" (cm)
EI = evaporation (cm day-1)
Uj = transpiration (cm day-1)
Ij = percolation out of zone i (cm day:l)
INF = infiltration into layer 1 (cm day:l)
Daily updating of soil moisture in the soil profile using the above equations requires the
additional calculations for infiltration, evaporation, transpiration, and percolation.
Infiltration is calculated as
<@-K (6-30)
where, assuming a unit area of 1 cm?,
P = precipitation as rainfall, minus crop interception (cm day:l)
SM = snowmelt (cm day-"l)
Q = runoff (cm day:l)
E = evaporation (cm day-1)
The calculations of precipitation, snowmelt, and runoff on a daily time step are described
below. The disaggregation of these values and the calculation of the change in the depth
of pending on a finer time step is included in Sections 6.3.5.4 and 6.4.4 describing the
simulation of furrow irrigation and ponded surface water.
6-16
-------
Input precipitation is read in and pan evaporation and/or air temperature are inputs from
which potential evapotranspiration (PET) is estimated, Incoming precipitation is first
partitioned between snow or rain, depending upon temperature. Air temperatures below
0°C produce snow and may result in the accumulation of a snowpack. Precipitation first
encounters the plant canopy and once the interception storage is depleted, the remaining
depth is available for the runoff or infiltration.
The runoff calculation partitions the precipitation between infiltrating water and surface
runoff. Infiltrating water may be ponded on the soil surface for a period of time before it
infiltrates, but this ephemeral process is described in a following section. Runoff is
calculated by a modification of the USDA Soil Conservation Service curve number
approach (Haith et al. 1979). Snowmelt is estimated on days in which a snowpack exists
and above freezing temperatures occur as
SM = CT (6-31)
where
Cjyi= degree-day snowmelt factor (cm 8C:1 day:1)
T = average daily temperature PQ
The precipitation and/or snowmelt are inputs to the SCS runoff equation written as
where S, the watershed retention parameter, is estimated by
s = ioeo/Rew -10 (6-33)
where
RCN = SCS runoff curve number
Curve numbers are a function of soil type, soil drainage properties, crop type, and
management practice. Typically, specific curve numbers for a given rainfall event are
determined by the sum of the rainfall totals for the previous 5 days, known as the 5-day
antecedent moisture condition. In this release of PRZM, as in the original version, the
curve numbers are continuously adjusted each day as a function of the soil water status in
the upper soil layers. These algorithms were developed and reported by Haith and Loehr
(1979).
6-17
-------
The daily evapotranspiration demand is divided among evaporation from canopy, ponded
surface water, soil evaporation, and crop transpiration. Total demand is first estimated
and then extracted sequentially from crop canopy storage, ponded surface water, and then
from each layer until wilting point is reached in each layer or until total demand is met.
Evaporation occurs down to a user-specified depth. The remaining demand, crop transpi-
ration, is met from the active root zone. The root zone growth function is activated at
crop emergence and increases stepwise until maximum rooting depth is achieved at crop
maturity.
Actual evapotranspiration from a soil layer is estimated as:
(6-34)
where
El\ = the actual evapotranspiration from layer T (cm)
fgj = depth factor for layer T
WHj = wilting point water content in layer T (cm)
ETp = potential evapotranspiration (cm)
This equation states that the transpiration from any layer T is the minimum of the
available water in layer T or the demand remaining after extracting available water from
layers above T in the profile.
The depth factor, &ij is internally set in the code. It linearly weights the extraction of ET
from the root zone with depth. A triangular root distribution is assumed from the surface
zone to the maximum depth of rooting, with the maximum root density assumed to be
near the surface. This algorithm essentially views the plant as a pump and assumes that
it will expend the minimum energy possible in pumping. As long as the soil water is
equally available, water closest to the surface meets this criterion.
Evapotranspiration may also be limited by soil moisture availability. The potential rate
may not be met if sufficient soil water is not available to meet the demand. In that case,
PRZM-2 modifies the potential rate by the following equations.
Elg = E2p tf SW k .06 FC
EBg = SMFAC Elfytfm* SW< 0.6 FC (6-35)
0; if mi^ W
where
6-18
-------
FC = soil moisture content at field capacity (cm)
WP = soil moisture content at wilting point (cm)
SMFAC = soil moisture factor
The SMFAC concept has been used in other similar water balance models (Haith et al,
1979, Stewart et al. 1976) and is internally set in the code to linearly reduce ETUjJ when
soil water becomes limited. Finally, if pan evaporation input data are available, ETC^ is
related to the input values as
• Ch PE (6-36)
where
PE = pan evaporation (cm day:l)
6p = pan factor (dimensionless)
The pan factor is constant for a given location and is a function of the average daily
relative humidity, average daily wind speed, and location of the pan with respect to an
actively transpiring crop.
In the absence of pan evaporation data, EUtj, is estimated by
14000 l (SRZD) (6-37)
where
L% = possible hours of sunshine per day, in 12-hour units
SVD = saturated vapor density at the mean air temperature (g cm:l)
SVD = 0.622 SVP/(Rg T^
where
SVP = saturated vapor pressure at the mean absolute air
temperature (rob)
R§ = dry-air gas constant
= absolute mean air temperature
The final term in the water balance equations that must be defined is the percolation
value, 1. Because the Richards equation is not solved in PRZM-2 utilizing soil water
characteristic curves to predict water movement, PRZM-2 resorts to "drainage rules"
keyed to soil moisture storages and the time available for drainage. Two options are
6-19
-------
included. Although these options are admittedly simplistic representations of soil
moisture redistribution, they are consistent with the objectives of PRZM-2 and its
intended uses.
6.3.2.1 Option 1-
Percolation, I, in this option is defined in the context of two bulk soil moisture holding
characteristics commonly reported for agricultural soils-field capacity and wilting point.
Field capacity is a somewhat imprecise measure of soil water holding properties and is
usually reported as the moisture content that field soils attain after all excess water is
drained from the system under influence of gravity, usually at tensions of about 0.3 bar.
The difficulty with this concept is the fact that some soils will continue to drain for long
periods of time, and thus field capacity is not a constant. Admitting the lack of theoreti-
cal and physical rigor, we believe that the concept remains a useful measure of soil
moisture capacity that has been successfully used in a number of water balance models
(Haith et al. 1979, Stewart et al. 1976). Wilting point is a function of both the soil and
plants growing in the soil. It is defined as the soil moisture content below which plants
are unable to extract water, usually at tensions of about 15 bar.
Field capacity and wilting point are used operationally to define two reference states in
each soil layer for predicting percolation. If the soil water, SW, is calculated to be in
excess of field capacity, then percolation is allowed to remove the excess water to a lower
zone. The entire soil profile excess is assumed to drain within 1 day. The lower limit of
soil water permitted is the wilting point. One outcome of these assumed "drainage rules"
is that the soil layers below the root zone tend to quickly reach field capacity and remain
at that value. When this condition is reached, all water percolated below the root zone
will displace the water within the lower soil layer simulated, and so on. There is no
allowance for lateral water movement. Water balance accounting in this manner should
be most accurate for sandy soils in which water movement is relatively unimpeded and is
least accurate for clay soils (Stewart et al, 1976).
6.3.2.2 Option 2—
The second option is provided to accommodate soils having low permeability layers that
restrict the "free drainage" assumed in Option 1. In the context of the field capacity
reference condition, two things may occur. First, conditions may prevail that raise the
soil moisture levels above field capacity for periods of time because the water is "backed
up" above a relatively impermeable layer. Second, the excess water may not drain during
the 1-day period assumed in Option 1. To accommodate these conditions, two additional
parameters are needed. Maximum soil moisture storage, 0,, is added to represent
moisture contents under saturated conditions. The drainage rate also must be modified to
allow drainage to field capacity over periods in excess of 1 day (one time step). The
drainage rate is assumed to be a first-order function of the water content above field
capacity and is modeled by
6-20
-------
dt
(6-38)
which has the solution
(6-39)
where
§ = soil layer water content (cml crof)
0£. = water content at field capacity (cm! cm/3)
a = drainage rate parameter (day"1)
In this equation, t and t+1 denote beginning and end of time step values, respectively, and
i is the soil layer index. The value t* denotes a value of time between the beginning and
the end of the time step. The variable 6fr here denotes current storage plus any percola-
tion from the next layer above, before the occurrence of any drainage from the current
layer. Because Equation 6-39 is solved independently for each layer in the profile, there
is a possibility of exceeding the storage capability (saturation water content, @^> of a low-
permeability layer in the profile if a more permeable layer overlies it. At each time step,
once redistribution is complete, the model searches the profile for any §i >GBL. If this
condition is found, the model redistributes water back into overlying layers, as if the
percolation of additional water beyond that necessary to saturate the low-permeability
layer had not occurred. This adjustment is necessary due to the nature of Equation 6-39
and the fact that these equations for each layer are not easily coupled. The difficulty in
coupling the equations for the entire profile arises from the dichotomy that one of two
factors limits percolation from a stratum in the profile: either the rate at which that
stratum can transmit water, or the ability of the stratum below it to store or transmit
water. This dichotomy leads to an iterative (or at least corrective) approach to the explicit
solution of a system of equations for §i represented by Equation (6-39). It should be
noted, however, that the value of a selected by this approach is only relevant if the
permeability of the soil materials, and not storage considerations in the profile (i.e., the
presence of a water table), is the limiting factor for percolation of water.
6.3.3 Soil Erosion
Removal of sorbed pesticides on eroded sediments requires estimates for soil erosion. The
Modified Universal Soil Loss Equation (MUSLE) as developed by Williams (1975) is used
to calculate soil loss:
6-21
-------
Xe=a (Vr qJ>*K LS C P (6-40)
where
2j^ = the event soil loss (metric tons day:l)
Vr = volume of event (daily) runoff (n$)
eh = peak storm runoff (ml see:J)
K = soil erodability factor
LS = length-slope factor
C = soil cover factor
P = conservation practice factor
a = units conversion factor
Most of the parameters in Equation 6-40 are easily determined from other calculations
within PRZM (e.g., V,J, and others are familiar terms readily available from handbooks.
However, the peak storm runoff value, qg, can vary widely depending upon rainfall and
runoff characteristics. A trapezoidal hydrography is assumed in PRZM-2. From the
assumed hydrography shape and the storm duration, a peak runoff rate is calculated.
The enrichment ratio, rjji, is the remaining term that needs to be defined to estimate the
removal of sorbed pesticides by erosion, Because erosion is a selective process during
runoff events, eroded sediments become "enriched" in smaller particles. The sediment
transport theory available to describe this process requires substantially more hydraulic
spatial and temporal resolution than used in PRZM-2, leading to the adoption of an
empirical approach (Mockus 1972). The enrichment ratio for organic matter is calculated
from
• 2 t 0.2 Iitfi (6-41)
6.3.4 Volatilization
As volatilization was not available in the previous release of PRZM, its theoretical basis is
discussed in detail here. The following key processes have been identified as being
important in volatilization algorithms to simulate vapor-phase pesticide transport within
the soil/plant compartments:
6-22
-------
• Vapor-phase movement of the pesticide in the soil profile
• Boundary layer transfer at the soil-air interface
• Vertical diffusion of pesticide vapor within the plant canopy
• Pesticide mass transfer between the plant (leaves) and the surrounding
atmosphere
• Soil temperature effects on pesticide volatilization
The discussion of the volatilization algorithms is presented in four parts: influence of
vapor phase pesticide in soil and volatilization flux, volatilization flux through the plant
canopy, volatilization flux from plant surfaces, and soil temperature modeling and effects.
Figure 6.3 is a schematic of the pesticide vapor and volatilization processes considered in
soil and plant compartments.
6.3.4.1 Soil Vapor Phase and Volatilization Flux-
The governing equations for chemical transport in the vapor phase were introduced
previously in the description of transport in the soil. Fluxes from the soil colunm in the
vapor phase are summarized in that discussion by Equations 6-3, 6-5, and 6-9. The terms
in these equations are summed with the other flux terms to produce the transport
Equation 6-20. In addition to these enhancements, the upper boundary of PRZM-2 was
changed from a zero-concentration boundary to a stagnant-layer boundary to allow
diffusive transport upward from the soil to the overlying atmosphere. This enhancement
is discussed in detail below.
Surface boundary condition- When a pesticide is incorporated into the soil, the initial
volatilization rate is a function of the vapor pressure of the chemical at the surface as
modified by adsorptive interactions with the soil. As the concentration at the surface of
the soil changes, volatilization may become more dependent on the rate of movement of
the pesticide to the soil surface (Jury et al., 1983b).
The soil surface layer can be visualized as a membrane that only allows water to pass
through and keeps the solute behind, Experimental results show that, within the top
centimeter of the soil surface, the pesticide concentration can increase as much as 10-fold
due to the accumulation of chemical at the surface layer, resulting in higher vapor
density. In order to describe these phenomena, Jury et al, (1983a, 1983b) proposed a
boundary layer model that states that the controlling mechanism for pesticide volati-
lization is molecular diffusion through the stagnant surface boundary layer.
The layer of stagnant air may or may not form a significant barrier to volatilization loss
for a given pesticide, depending on a variety of factors. In general, if the diffusion rate
through the air layer is able to match the upward flux to the soil surface without having
the surface concentration build up, then the stagnant layer is not acting as a barrier to
loss and the volatilization flux will not depend strongly on the thickness of the volatiliza-
tion flux will not depend strongly on the thickness of the boundary layer. Conversely, if
6-23
-------
the diffusion rate through the air is less than the flow to the surface by diffusion or mass
flow, then the concentration at the soil surface will not be close to zero, and the thickness
of the air layer will regulate the loss by volatilization. In other words, the significance of
the boundary layer model depends on the ratio of the magnitudes between the upward soil
pesticide flux and the boundary layer diffusion flux. Only downward, advective movement
of water is treated in PRZM Release I. In this case, the sources that contribute to the
upward soil pesticide flux are only the diffusion processes in the vapor and dissolved
phases, but not upward water advection,
The zero chemical concentration upper boundary condition in the first release was
modified in accordance with Jury's boundary layer model. The pesticide volatilization flux
from the soil profile can be estimated as follows:
(6'42)
where
JL = volatilization flux from soil (g day-lj)
Da = molecular diffusivity of the chemical in air (ctmi? day-"J;D
A = cross-sectional area of soil column (cnn$)
d = thickness of stagnant air boundary layer (cm)
6g^ = vapor-phase concentration in the surface soil layer (g ennui)
= vapor-phase concentration above the stagnant air boundary layer (g
The thickness of the stagnant boundary layer can be estimated using a water vapor
transport approach (Jury et al. 1983a). However, Wagenet and Biggar (1987) assumed a
constant value of 5 mm for this thickness, which is consistent with the values estimated
by Jury. Consequently, the same assumption of a 5-mm thickness for the stagnant layer
has been used here pending the results of further sensitivity analyses. The value of G-*^
can take on a value of zero if the soil surface is bare or can be positive if a plant canopy
exists,
6.3.4.2 Volatilization Flux Through the Plant Canopy —
In pioneering work on this topic, Parmele et al. (1972) discuss a number of micrometeoro-
logical techniques for calculating pesticide volatilization flux from observed aerial
pesticide concentrations. Their procedures are based on the assumption that the vertical
diffusivity coefficient (IQ for pesticide vapor is analogous to the vertical diffusivity for
water vapor, energy, or momentum. The pesticide volatilization flux can be computed by
Pick's first law of diffusion, as follows.
6-25
-------
(dPfd® (6-43)
where
= pesticide flux at height Z (g m$ s:l)
(dP/dZ) = pesticide concentration gradient (g m:2)
KJ!Z) = the vertical diffusivity at the height Z (m£ s:l)
The value of K± depends on the turbulent flow of the atmosphere into which the pesticide
vapor is dissipated. Therefore, it is a function of the prevailing meteorological conditions
and not of any physical or chemical property of the pesticide.
In order to apply these concepts, pesticide concentrations at two or more heights are
required to estimate the pesticide gradient and the subsequent flux. For the estimation of
vertical diffusivity;, more extensive meteorological information is also required. All of
these data requirements pose signficant limitations for a predictive modeling approach.
In developing this PRZM-2 module, the following approaches are proposed to circumvent
the intensive data requirements. First, a relationship for K^ is derived as a function of
height within the canopy. Then one need only consider the pesticide concentration
gradient (or a suitable surrogate) in order to compute the pesticide volatilization flux.
Estimation of Kt(Z) --Mehlenbacher and Whitfield (1977) present the following formula to
compute Kq, at various heights within the plant canopy.
* Kgfife) exp lO ~ - 1.0 (6-44)
» I/* Jk (Iffl - OM* (6-45)
(6-46)
where
= thermal eddy diffusivity at height Z (m? s-\)
= thermal eddy diffusivity at canopy height(m? s:l)
= canopy height (m)
Z0 = roughness length (m)
jQ = zero plane displacement height (m)
6-26
-------
von Karman's constant, 0.41
U* = friction velocity (m s-1)
— = stability function for sensible heat
= integrated momentum stability parameter as a function of
stability function for momentum
" "^ wind velocity at the canopy height (m S-1)
For agricultural applications, the canopy height is used as a reference height for calculat-
ing U*. The user is required to input the wind speed and the height where the measure-
ment was made. The wind speed at the canopy height (UQfl) is computed based on the
logarithm law. The relationship is:
(6-47)
measured
The friction velocity U* can be visualized as a characteristic of the flow regime in the
plant canopy compartment in which the logarithmic velocity distribution law holds. As
shown in Equation 6-44, U* is calculated as a function of U£H, Zgg, ZQ, D> and JJfjg.
Rosenberg (1974) describes ZQ + I) as the total height at which the velocity profile above
the canopy extrapolates to zero wind velocity. The values for both ZQ and D can be
estimated with the following equations presented by Thibodeaux (1979). For very short
crops (lawns, for example), ZQ adequately describes the total roughness length, and little
adjustment of the zero plane is necessary (i.e., Q = 0). Q is assumed to be zero in the
current code when Z^J is less than 5 cm. For tall crops, ZQ is related to canopy height
fag Ze = 0.997 % 2£$ -OC8B3 (6-48)
In tall crops, ZQ is no longer adequate to describe the total roughness length, and a value
of Dj the zero plane displacement, is needed. For a wide range of crops and heights, 0.02
m
-------
Strictly speaking, both Z^knndlBsfchniiDid be evaluated from experimental observations. In
the calculation of K,, the module uses these two equations for estimation of ZQ and Bj
since there is no method available to justify any variations for crop type, row spacing, or
canopy density.
With estimates of ZQ and D> U* (friction velocity) can be estimated if the values of the
stability parameters (^ and $$ are known. These two variables are closely related to Ri,
the Richardson number, which is the measure of the rate of conversion of convective
turbulence to mechanical turbulence. It is defined as follows (Wark and Warner 1976).
Ri = (6_5Q)
(dU/dZ)2
where
g = acceleration of gravity (m see?)
T = potential temperature (°K)
Z = elevation (m)
U = wind velocity (m s:l)
Potential temperature is defined as the temperature that a parcel of dry air would acquire
if brought adiabatically from its initial pressure to a saturated pressure of 1000 millibars
(Perkins 1974). In application of the model, the measured temperature is used in the
Richardson number estimation as suggested by Rosenberg (1974).
The sign of Ri indicates the atmospheric condition, and its magnitude reflects the degree
of the influence. There are several different formulas for relating Ri to the atmospheric
stability parameters; for these purposes, the sign of Ri is of greater concern than its
magnitude. When Ri is larger than 0.003, the atmosphere exhibits little vertical mixing,
reflecting stable conditions: when the absolute value of Ri, |Ri|l, is less than 0.003,
neutral stability conditions exist (Oliver 197 1); and when Ri is less than -0.003, convective
mixing becomes dominant and atmospheric conditions are unstable.
To relate the atmospheric stability parameters to the Richardson number, Thorn et al.
(1975) proposed the following formulas based on the work by Dyer (1974) and Dyer and
Hicks (1970).
For stable conditions -
For unstable conditions -
6-28
-------
For neutral conditions -
l (6-53)
The integrated momentum stability parameter, q?m<) can be evaluated based on the
following equation as derived by Lo (1977).
ln(8) + $m + 3 IK( based on the stability condition and associated Equations
6-51, 6-52, or 6-53.
4) Calculate tp~, from Equation 6-54.
5) Calculate ZQ and B. from canopy height using Equations 6-48 and 6-49.
6) Estimate K$Z) by applying Equations 6-46, 6-45, and 6-44.
The resistance approach for the estimation of volatilization flux from soil- The calculation
of the volatilization flux from the soil is based on a resistance-type approach. For pre-
plant pesticides, and time periods just after emergence and post-harvest, transport by
volatilization from plant surfaces is much less than vapor phase transport by other
mechanisms. For those conditions in which the plant leaves do not act as significant
sources or sinks for pesticide vapor, the resistances of the air for the whole plant compart-
ment can be estimated as follows (Mehlenbacher and Whitfield 1977).
6-29
-------
(6-55)
Ru = 4 (6-56)
*** I
-------
approach is possible that requires the user to input the first-order rate constant for
volatilization. The plant leaf volatilization flux can be estimated as follows.
Jpl= M Kf (6-59)
where
JIjJ = volatilization flux from the leaf (g cm? day:1)
M = foliar pesticide mass (g cm'ty
K| = first-order volatilization rate (day1*)
A resistance type approach is also applicable for volatilization flux estimation from plant
leaves. The current code employs the first-order kinetics approach to calculate volatiliza-
tion flux from plant leaf surfaces described above. This approach, which requires the user
to specify the first-order rates constant for plant leaf volatilization, was selected because
it is consistent with the foliar fate model in PRZM Release I.
Average pesticide concentration in plant canopy-Volatilization flux from plant leaves
will exist only after pesticide application to the plant foliage has been specified in the
model input. When a plant canopy exists, the average concentration in the air within the
plant canopy can be estimated as follows.
c; = (Jpc «• Jj £ ^ (6-60)
where
6^ = average concentration in the air between the ground surface and the plant
canopy height (g cnd'3)
= canopy resistance from half canopy height to the top of the canopy
_*_ (6-61)
'CH *
Equation 6-60 then calculates the mean plant compartment pesticide concentration as the
concentration at one-half of the canopy height. This approach assumes a linear concentra-
tion gradient from ground surface to canopy height.
6.3.4.4 Soil Temperature Simulation--
Soil temperature is modeled in order to correct the Henry's law constant, E^, for tempera-
ture effects. The interaction of its microclimate with the soil surface that results in a
given soil temperature regime is complex and dynamic. Soil surface configuration and
6-31
-------
plant residue cover, both affected by tillage, have significant impacts on soil heat flux and,
therefore, soil temperature. Studies of tillage and residue effects on soil temperature
have been dominated by qualitative observations and site-specific measurements. The
lack of mathematical evaluation and supporting field data has limited the ability of
researchers to predict, beyond qualitative terms, the tillage and residue effect on soil
temperature for soil and climatic conditions other than those under which data have been
collected.
The objective of the soil temperature model is to provide a scientifically sound and usable
approach: (i) to predict with reasonable accuracy the daily average soil temperatures at
the soil surface and in and below the root zone, utilizing basic soil physical and thermal
properties, and daily climatic measurements taken at weather stations; and (ii) to allow
consideration of the residue, canopy, and tillage effects on soil temperature.
Several models are available to predict soil temperature under various soil surface
conditions, but there are restrictions to the general use of these models because either
they need large data bases that are not available at many places, or they are site specific.
Existing soil temperature models form two general groups: (1) process-oriented models,
which require detailed information on soil and surface characteristics, initial and bound-
ary conditions, and inputs, and (2) semi- or non-process-oriented models, which often
utilize weather station information and soil temperature information at one depth to
develop empirical relationships.
Table 6-1 summarizes the key characteristics of the soil temperature models reviewed in
this work. For both the process and semi-process oriented models, the two primary
components are estimation of soil surface (or upper boundary) temperatures and soil
profile temperature utilizing the calculated or estimated surface temperature as the upper
boundary condition. A number of the models utilize the same procedure for calculating
temperature in the soil profile (Gupta et al. 1981, Wagenet and Hutson 1987) and differ
only in the procedures for specifying the surface boundary condition.
Van Bavel and Hillel (1975, 1976) developed a dynamic numerical procedure to link the
process-oriented simulations of heat movement in the soil and the partition of heat and
energy at the soil surface. Soil surface temperature, 1Q, is calculated as a factor in
predicting evaporation from a bare soil. Their technique utilized simultaneous solutions
of seven equations with seven unknowns: net radiative flux, evaporation rate, air sensible
heat flux, soil sensible heat flux, surface soil temperature, Richardson's number, and the
saturation humidity at the surface soil temperature. Heat and water (liquid) flows are
each coupled at the soil surface. An iterative procedure was used at each update to find
the proper soil surface temperature. Soil temperatures were then estimated (Wierenga
and de Wit 1970) by using these estimates of TQ as the surface boundary condition.
Inputs required for this model include solar radiation, air and dewpoint temperature,
wind speed, initial soil temperature profile, and the surface roughness evaluated by its
effect on the aerodynamic roughness parameter. No comparisons were made between
predicted and measured soil temperatures. Thibodeaux (1979) describes a similar energy-
balance procedure for calculating soil surface temperatures.
6-32
-------
TABLE 6-1. SUMMARY OF SOIL TEMPERATURE MODEL CHARACTERISTICS
o
CO
Model/
Author(s)
(1975)
1) Type of Model:
a) Process-Oriented
b) Semi-Process-Oriented
c) Non-Process-Oriented
2) Heat Flow Process
a) Conduction
b) Convection
c) Radiation
3) Upper Boundary Temperature
a) Est. by Energy Partitioning
b) Est. by Empirical Relationship
4) Soil Temperature Profile:
(Solving 1-D Heat Flow Eqn.
Using the Procedure of:)
a) Hanks et al. (1971)
b) Wierenga and de Wit (1970)
c) Curve Fitting
5) Input Data Required
a) Daily Max and Min Air Temp.
b) Daily Max and Min Soil
Surface Temperature
c) Hourly Air Temperature
d) Hourly Solar Radiation
e) Surface Albedo
f) Wind Velocity
g) Humidity /Dewpoint Temp.
h) Canopy Shadow/Ht. of Veg.
i) Soil Water Content
j) Soil Bulk Density
k) Soil Mineral Composition
1) Percentage Organic Matter
6) Soil Surface Condition
a) Residue Cover
b) Tillage Condition
c) Crop Canopy
7) Time Step
a) Hourly
b) Daily
* - Horton et al. (1984) used
Van Bavel Thibodeaux Gupta et al.
and Hillel
X
X
X
X
X*
X
X
X
X
X
X
X
X
X
X
X
X
X
a 2-D heat flow equation
** - Regression equation is fitted for soil temp at 5-cm
(1979)
'82, '83)
X
X
X
X
X
X
X
X
X
X
X
(1981,
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Parton
(1984)
X
X
X
EX
X
XX
X
X
Cruse et al. Hasfurther Williams Wagenet
(1980) and Burman
(1974) (1983)
X X
X
X
X" X
X X
XX
X
X
at 5 cm
X
X
X
X
X
X X
AVE • "Average" measured soil surface temperatures
depth.
DD - Damping depth parameter is used to predict soil
temperature at different
ME - Simplified mathematical
radiation, surface albedo,
depths.
etal.
(1987)
X
X
X
ME
DD
X
XX
X
X
X
X
X
X
and Hutson
(1983)
X
X
AVE
X
X
X
X
X
X
X
X
Chen
etal.
X
X
X
AT
X
X
X
X
X
100%
X
X
are used.
AT - Ambient air temperature is used as upper boundary
XX - Total daily solar
EX - Explicit
radiation.
temperature.
Finite Difference Scheme.
relationship involving solar
, and daily min and max air temperatures.
-------
For modeling soil profile temperatures, Hanks et al. (1971) used a numerical approxima-
tion for the one-dimensional soil-heat flow equation. This method requires the input of
initial and boundary conditions, as well as the soil thermal conductivity and heat capacity
as a function of depth and time. Predicted root zone soil temperature profiles were within
1°C of observed values for a 3-day period, but this model needs estimated or measured
soil surface temperatures as upper boundary condition.
Using the Hanks et al. (1971) procedure for the root zone, Gupta et al. (1981, 1982, 1983,
1984) developed a model for estimating hourly soil temperature by depth from meteorolog-
ic data. Inputs needed for this model include hourly air temperature at the 2-m height;
daily maximum and minimum soil temperatures; initial soil temperature with depth; and
soil thermal diffusivity, which may be estimated from soil mineral composition, organic
matter percentage, bulk density, and soil water content. The upper boundary tempera-
tures are estimated by a sine function. The amplitude of the function is equal to the
difference between daily maximum temperatures of air and soil surface or daily minimum
temperatures of air and soil surface. Empirical curves relating daily maximum air
temperature to daily maximum soil surface temperature, and daily minimum air tempera-
ture to daily minimum soil surface temperature, were developed for different residue and
tillage conditions for the specific application site. These relationships provided a means of
accounting for residue and tillage effects on soil temperature, but require site-specific
data.
The soil temperature model in PRZM-2 is derived from a combination of the work by van
Bavel and Hillel (1976) and Thibodeaux (1979) for estimating the soil surface/upper
boundary temperature. The soil profile temperature procedures were developed by Hanks
et al. (1971) and applied by Gupta et al. (1981, 1982, 1983) and Wagenet and Hutson
(1987),
Estimating upper boundary temperature-An energy balance procedure is used in PRZM-2
to estimate soil surface temperature (Thibodeaux 1979, van Bavel and Hillel 1976). The
same procedure is used in the POSSM model (Brown and Boutwell 1986), which employs
PRZM-2 as a framework for PCB fate simulation.
The basic energy-balance equation with terms having units of cal cnri? day-\ at the air/soil
interface may be described as:
Rn - Hs - i, - G3 = A7# (6-62)
where
Rn = net radiation (positive downward)
H, = sensible air heat flux (positive upward)
LE, = latent heat flux (positive upward)
G, = soil heat flux (positive downward)
ATH = change in thermal energy storage in the thin soil layer (cal
cmf day'})
6-34
-------
The term ATH can be evaluated as:
ATH - fe$ s - 1 (6-63)
where
Pb = bulk density of soil (g cnm3)
d = thickness of a thin, surface soil layer (cm)
s = the specific heat capacity of soil (cal g:l *CM)
T\jH,<4 = the representative temperature for the surface layer at two consecutive
time steps and can be represented as the average of temperatures at the
top and bottom of the soil layers.
For evaluating the heat exchange across the air/soil interface, the thickness, d, can be set
to a small value so that ATH may be neglected. As a result, the right side of Equation
6-62 is set equal to zero.
Net radiation flux at any surface can be represented as:
(6-64)
where
Rj, = the net radiation flux (cal cnmf day:l)
R8 = incident short-wave solar radiation (cal cm
K^ = reflected short-wave solar radiation (cal cmi day-l)
Rjj = incident long-wave atmospheric radiation (cal cmi day-!)
Rjaf = reflected long-wave atmospheric radiation (cal cmf dffljp-)
Rj, = long-wave radiation emitted by the soil (cal cum/? day:l)
The terms R, and E5$ include both the direct and diffuse short-wave radiation, and are
related as follows.
(6-65)
where
a = the albedo of the surface (dimensionless)
Therefore, the short-wave radiation component of the energy balance is
6-35
-------
- a) (6-66)
The incident short-wave radiation can either be measured directly using pyranometers or
else calculated using a variety of available empirical relationships or nomography. The
model requires input of a radiation time series, whether measured or calculated, in order
to simulate soil temperature,
The albedo of a canopy-covered land surface can be estimated as:
a(t) = og C(t) + «3 (1 - C(t)) (6-67)
where
a(t) = albedo on day t
a£ = albedo of canopy cover (0.23 for vegetation)
C(t) = canopy cover on day t (fraction)
a, = albedo of soil surface (dimensionless)
Since the albedo of soil surface changes with the soil surface condition, it is defined by the
user as 12 monthly values corresponding to the first day of each month; the albedo value
for each day is interpolated between the neighboring monthly values. For snow cover less
than 0.5 cm, the surface albedo is estimated using Equation 6-67, and for snow cover
above 0.5 cm, the surface albedo is set equal to the snow albedo value (0.80).
The incident long-wave atmospheric radiation, RJj, is represented as
where
e^j = emissivity of the atmosphere [dimensionless]
a = the Stefan-Boltzmann constant (11.7 *1GD$ cal om£ 8K4 day:ij
TE = the air temperature (°K)
Wunderlich (1972) has proposed a correction to Equation 6-68 for the effects of cloud
cover, which could increase Rjj, by up to 25 percent under overcast conditions. However,
this correction is not included in the model because it would require input of a cloud cover
timeseries, and the effect on the calculated soil surface temperature would be small.
The emissivity of the atmosphere varies from a low of 0.7 to almost unity. Numerous
empirical relationships for estimating ej have been proposed (Salhotra 1986). A simple
reliable method is the use of Swinbank's formula:
6-36
-------
0.936 *103 ^ (6-69)
The reflected long-wave radiation, R,ar, can be expressed as:
/ciflF
t-y) (6-70)
where
¥ = the reflectivity of the surface for long-wave radiation [dimensionless]
The resulting net atmospheric long-wave radiation component becomes:
- y) = 0.936 *103 2~ a (1 - y) (671)
The long-wave radiation component emitted by the soil surface is represented in an
analogous equation to the atmospheric component, as follows.
where
e, = infrared emissivity of soil (dimensionless)
T, = soil surface temperature (~K)
Since the soil emissivity and reflectivity are related as e,=l-5y, we can replace (1 - y) in
Equation 6-71 with e,..
Combining the radiation components from Equations 6-66, 6-71, and 6-72, the net
radiation flux is calculated as follows.
Ify = (1 - a) + 0.936 *10..§ a T% e, a T? (6-73)
The evaporative heat flux, LE^ is estimated by:
(6-74)
6-37
-------
where
# = latent heat of vaporization/unit quantity of water
(580.0 cal g-1)
E = evaporation rate (cm day:i)
Pw = density of water (1.0 g cmi)
The evaporation rate is obtained from the evapotranspiration (EVPOTR) subroutine of
PRZM. It is assumed that the calculated evapotranspiration from the top 5 cm of soil
represents the potential evaporation energy loss at the air/soil interface. However, only a
fraction of the evapotranspiration loss calculated by PRZM contributes to this heat flux.
This fraction is estimated as the portion of the land surface not covered by vegetation,
(i.e., 1.0- canopy cover).
The sensible air heat flux, H,, is given by:
X, = Pi % ft (T, - %) (6-75)
where
Pa = air density (g
= (-0.0042 Tfc * 1.2WJHKD3
Cjj£ = specific heat of air at constant pressure
(0.2402 Sd g-1 °K*)
h = heat transfer coefficient at air-soil interface (cm day-1)
Ta = the air temperature PC)
The air density is computed based on the daily air temperature using a simple linear
correlation Equation 6-73 developed from data in Thibodeaux (1979). The heat transfer
coefficient is given by:
h=Kl2V( in \-HL-Z\\ (6-76)
where
K! = Von Karman's number (0.41)
$% = wind velocity (cm day:l)
ZM = reference height at which V^ is measured (m)
iQ = zero plane displacement (m)
6-38
-------
Z0 = roughness height (m)
Equation 6-76 is valid only when the air temperature does not vary greatly with height,
as is often the case near sunrise or sunset or under cloudy skies or when canopy heights
are relatively small. It appears to be a reasonable approximation for most agricultural
crops. Correlations have been developed relating D and ZQ to the canopy height as
described previously in this section by Equations 6-48 and 6-49.
From the fundamental equation of heat conduction, the soil heat flux, G,, is given by:
Gs = (Ts - 7\) yz>t (6-77)
where
T! = temperature of the soil at bottom of layer 1 (SK)
T, = soil surface temperature (°K)
Aj. = thermal conductivity of layer 1 (cal cm'l dajy ~ °K-1)
H\ = thickness of layer 1 (cm)
Substituting Equations 6-71, 6-72, 6-73, and 6-75 into Equation6-68£ the flollowing fourth-
order equation in terms of T, results.
, - [(1 - a)*. + 0.936*10-' « if e,
ID-to)
- o
The value of T, at each time step is estimated by solving the above equation using an
iterative solution based on the Newton- Raphson method. The initial estimate of soil
surface temperature is taken to equal measured air temperature, and R~s LE,,, Hs» and Gft
are calculated as explained above. The value for T\ is obtained from the previous time
step. These calculations are repeated until the difference between two consecutive
estimates for soil surface temperature is less than the convergence criteria (set to 0, 1 fjl(f)i
Simulation of heat flow through soil profile- The soil profile temperature model is based
on the one-dimensional partial differential equation describing heat flow in soils:
(6-79)
where
d = the thermal diffusivity.
6-39
-------
The thermal diffusivity is equal to the ratio of thermal conductivity and heat capacity of
the soil. The procedures used to estimate soil thermal conductivity and heat capacity are
taken from de Vries (1963). They are calculated from basic soil properties-soil water
content, mineral composition, texture, and thermal conductivity of the individual soil
particles. These parameters are either input or supplied by the model in the simulation.
The thermal diffusivity is given by:
d = W (6-80)
where
d = thermal diffusivity of the soil layer (cnni? day:l)
A = thermal conductivity of the soil layer
(cal cm^1 day-1 °C-\)
c = heat capacity per unit volume of the soil layer
(cal cm$ °C-\)
Temperature effect-- A detailed discussion of the temperature effect on the volatilization
behavior of pesticides is presented by Streile (1984). Two parameters that influence the
vapor-phase transport in the soil profile are Henry's constant and the vapor diffusion
coefficient.
The equation used to correct Henry's constant for temperature effects is (Streile 1984):
- *„., exp 1 - A (6-81)
where
= Henry's constant at the reference temperature T[
= patial molar enthalpy of vaporization from solution
(J mole!)
The temperature effect on the vapor phase diffusion coefficient can be estimated from the
Fuller correlation as presented in Liley and Gambill (1973). However, it is not imple-
mented in the code due to the general lack of information required to use it.
6.3.5 Irrigation Equations
PRZM-2 irrigation algorithms determine depths of irrigation water to be applied at the
soil surface. These depths are computed from the soil water deficit and are added as
infiltration to the frost PRZM soil compartment. Above- and below-canopy sprinklers,
6-40
-------
flooding, and furrow irrigation can be simulated. Methods for computing water applica-
tion depths for each type of irrigation are described in the following paragraphs.
6.3.5.1 Soil Moisture Deficit--
Irrigation is triggered when the average root-zone soil moisture volume falls below a level
fe defined by the user as a fraction of the available water capacity. The soil moisture
deficit, D, is then given by:
D = - S Z (6"82)
where
D = soil moisture deficit (cm)
6k = average root-zone soil moisture content
Q; = average root-zone soil moisture content at field capacity (cm?om3)
Zr = root zone depth (cm)
D is the depth of water over the unit area that must be added to the soil by irrigation to
bring the soil water content up to field capacity.
6.3.5.2 Sprinkler Irrigation-
Irrigation water from sprinklers may be applied either above or below the crop canopy.
When applied above the crop canopy, irrigation water is intercepted by the canopy and
may run off when it reaches the soil surface. The depth of water applied during a daily
PRZM-2 time step by overcanopy sprinklers is estimated from the soil moisture deficit:
-zi (6-83)
where
Da = depth of irrigation water applied to the field (cm)
If = crop canopy interception capacity (cm)
LF = a factor specified by the user to allow for the practice in saline soils of
adding water to leach salts out of the root zone (fraction of Da)
The water depth Da is applied as precipitation above the crop canopy, and canopy
interception is computed for the current crop in the PRZM-2 crop growth subroutines.
Sprinkler runoff from the soil surface is estimated using the SCS curve number approach,
assuming that runoff characteristics of sprinkler water are similar to those of precipita-
tion. Water that does not run off infiltrates into the first PRZM-2 soil compartment.
6-41
-------
Irrigation water applied below the crop canopy is not subject to canopy interception losses,
The depth of water applied by undercanopy sprinklers is therefore, is given by:
(6-84)
The irrigation water depth APDEP is applied as throughfall to the soil surface, and
sprinkler runoff is estimated using the SCS curve number approach.
In some instances, the sprinkler system may be unable, due to hydraulic limitations, to
deliver water at the rate needed to meet the required daily application depth. In these
cases, the sprinkler application depth Da is set equal to the maximum depth that the
system can deliver. The user, therefore, is required to input the maximum water
application rate E^ (cm hr-~) for the sprinkler system.
6.3.5.2 Flood Irrigation--
Flood irrigation, in this case, refers to the practice of flooding entire fields with irrigation
water. Flood-irrigated fields are diked around the edges to allow water to pond and
infiltrate into the soil. In the PRZM irrigation algorithm, it is assumed that this water
ponds uniformly over the entire field. The amount of water applied to the soil surface is
then :
= Dflh-LEf) M5)
Since the field is assumed to be diked around the edges, no water is allowed to run off
from the field.
6.3.5.4 Furrow Irrigation--
Furrow irrigation involves the release of water into numerous small channels that cut
across the planted field. Infiltration depths within furrows vary due to differences in
times at which water reaches various locations down the furrow, with less water infiltrat-
ing at the dowstrem end (Figure 6.4), Hydraulic characteristics of the furrow deter-
mine how quickly water moves down the channel, while soil characteristics determine the
rate of infiltration once water reaches a location in the furrow.
The PRZM-2 furrow irrigation model computes daily infiltration depths at various
locations down the length of the furrow. This requires solution of the open channel flow
equations of motion coupled with a soil infiltration model. Model developers have made
numerous attempts to solve the furrow-irrigation advance problem, ranging in complexity
from empirical volume-balance solutions (Wilke and Smerdon 1965, Fok and Bishop 1965)
to numerical solutions of the full open channel flow equations of motion (Bassett and
Fitzsimmons 1974). In general, solutions of the full equations of motion are too computa-
tionally intensive for this application, while simpler empirical models involve infiltration
parameters that are not easily related to physical soil characteristics.
6-42
-------
DISTANCE ALONG THE FURROW
Inflow
End
Outflow
End
Figure 6.4 Variability of iniltration depths within an irrigation furrow.
The PRZM-2 furrow advance model uses the kinematic wave simplification of the
equations of motion coupled with the Green-Ampt infiltration model to determine furrow
infiltration depths. Kinematic-wave theory neglects inertial accelerations and assumes
that the water surface slope is equal to the ground slope. The equations of motion then
reduce to:
6-43
-------
dz dt dt
where
Q = flow rate in the channel (m? s4)
A = cross-sectional area of flow (m?J
x = distance down the fin-row (m)
q = volume infiltrated per unit length of channel (mf m:l)
The flow area A is related to the flow rate Q by Manning's equation:
Q = i AR2* S1/2 (6-87)
n
where
n = Manning's roughness coefficient
R = the hydraulic radius of flow (m)
s = the channel slope (vertical/horizontal)
Section 6.4.4 explains how the solution of the horizontal furrow irrigation equation is
applied to PRZM-2.
6.4 NUMERICAL SOLUTION TECHNIQUES
This section describes the numerical techniques that are used to solve the differential
equations introduced in the preceding section. Section 6.4.1 discusses the two numerical
techniques available to solve the chemical transport equations-a backwards-difference
implicit scheme and a method of characteristics algorithm. The additional terms and the
adjustment in the upper soil boundary that are added into these transport equations to
simulate volatilization are described in Section 6.4.2. The numerical approximations used
to calculate soil temperature are presented in Section 6.4.3 and the numerical solution for
furrow infiltration depths are presented in Section 6.4.4.
6.4.1 Chemical Transport Equations
The second-order partial differential equation outlined in Section 6.3 must be solved with
appropriate boundary conditions. The calculations for moisture contents, air contents,
pore velocities, erosion, and runoff are decoupled from, and solved in advance of, the
transport equation. The resulting values, treated as constant for each specific time step,
are then used as coefficients in a discretized numerical approximation of the chemical
transport equation.
6-44
-------
Two techniques are currently available to solve the discretized chemical transport
equation for the new dissolved pesticide concentration at the end of the time step. The
available techniques are:
• A backward-difference, implicit scheme to simulate all chemical transport
processes
• A method of characteristics (MOC) algorithm that simulates diffusion, decay,
erosion, runoff, and uptake by the backward-difference technique, but uses the
method of characteristics to simulate advective transport
The user is allowed to select the desired solution technique in the input sequence. Details
of these techniques are provided below. Results from test simulations are provided in
Section 6.5.1.
Identical discretizations and initial and boundary conditions are used with both numerical
simulation techniques. A spatial and temporal discretization step is used equal to those
applied in the water balance equations. For boundary conditions at the base of the soil
column, the numerical technique uses
(6-88)
Az
in which the subscripts "i" refer to soil layer numbers.
This condition corresponds to a zero concentration gradient at the bottom of the soil
profile. The upper boundary condition is discussed in more detail in Section 6.4.2.
A backwards-difference solution algorithm was the only solution option available in the
original PRZM model. In this method, the first derivative in space, the advection term, is
written as a backward difference (i.e., involves the difference C[i,j]-C[i-l,j]). The second
spatial derivative, the diffusion term, is centered in space (i.e., based on the terms C[i-
l,j]+C[i+l,j]-2C[i,j]). The time derivative is also calculated as a backward difference in the
original code, (C[i,jl-C[i,j-l]). The equations are then made implicit by writing each
concentration for the (j+l)th time step. The advantage of this numerical scheme is that it
is unconditionally stable and convergent. However, the terms truncated in the Taylor's
series expansion from which the finite difference expression are formulated lead to errors
that, in the advection terms, appear identical to the expressions for hydrodynamic
dispersion. In the simulation results, these terms manifest themselves as "numerical
dispersion," which is difficult to separate from the physical dispersion that is intentionally
simulated. In systems exhibiting significant advection (i.e., high Peclet number), the
artificial numerical diffusion may dominate the physical dispersion. It can be larger by
orders of magnitude, leading to difficulty in the interpretation of simulation results.
To minimize the effects of numerical dispersion in systems having high Peclet numbers, a
method of characteristics solution was added as an option to PRZM-2. This solution
method avoids the backwards-difference approximation for the advection term and the
associated numerical dispersion by decomposing the governing transport equation. In
advection-dominated systems, as the dispersion term becomes small with respect to the
6-45
-------
advection term, the advection-dispersion equation approaches a hyperbolic equation.
According to the MOC theory, advection of the solute can be simulated separately from
the other processes governing the fate of that advected solute. M. Baptista et al. (1984)
state that no error is introduced by this decomposition provided that the advection
equation is solved first by an explicit procedure, and the diffusion equation is solved next
by an implicit technique. This order was preserved in the PRZM-2 model by utilizing a
new explicit algorithm for advection that is always called first, and is immediately
followed by execution of a modified version of the existing implicit algorithm for simula-
tion of other processes. The advection algorithm employed was adapted from those
described by Khalell and Reddell (1986) and Konikow and Bredehoeft (1978). These
techniques were modified to allow simulation of changes in saturation and adsorption of
the pesticide and variable compartment size,
In the new explicit advection algorithm, in addition to the fixed grid system, a set of
moving points is introduced. These points can be visualized as carrying the chemical
mass contained within a small region in space surrounding the point. Initially, these
points are uniformly distributed throughout the flow domain, At each time interval, these
moving points are redistributed according to the local solute velocity in each compart-
ment. New points may enter the top of the flow domain, while old points may move out
the bottom. When the moving points are transported in horizons where the compartment
size is larger and numerical resolution is less, the points may be consolidated to conserve
computational effort. After the new locations have been assigned to each point, the
average concentration in each compartment is computed based on the number and mass
carried by the points contained within the compartment at that time. This temporary
average concentration is returned to the main program, and a subroutine that assembles
the terms in the transport equation (without advection) is called. Changes in concentra-
tion due to all other transport and transformation processes (diffusion, decay, sources,
etc.) are calculated for each compartment exactly as in the original version of PRZM.
These values are then returned to the main program, and one transport step is complete.
When the MOC algorithm is called during the next time step, the exact location of each
moving point has been saved. The first task is to update the masses carried by each
moving point using the changes calculated during the last time step. Increases in mass
are simply added equally to each point in the compartment, while decreases are weighted
by the actual value at each point before subtraction to avoid simulating negative masses.
The updated moving points are then relocated and the two-step process is repeated again
until the end of the simulation.
6.4.2 Volatilization
The numerical techniques discussed in section 6.4.1 are the basis of the simulation of
chemical transport in all phases. However, some modifications have been made to the
upper boundary condition in order to model volatilization of chemical from the soil
surface.
In order to simulate vapor-phase pesticide movement past the soil surface, the zero
concentration upper boundary conditions used in the original PRZM code has to be
modified. Jury's boundary layer model (1983a, 1983b) has been incorporated into the
PRZM-2 code. The model states that the controlling mechanism for pesticide volatiliza-
tion is molecular diffusion through the stagnant surface boundary layer. The volatiliza-
tion flux from soil profile can be estimated by:
6-46
-------
(6"89)
where
$\ = volatilization flux from soil (g day:l)
Dj = molecular diffusivity of the chemical in air
QjT} — ~ vapor-phase concentration in the surface soil layer
(gorfS)
= vapor-phase concentration above the stagnant air boundary layer (= 0,
for the no-canoy field condition) (g cms)
d~ === thickness of stagnant air boundary layer (cm)
This equation defines the new flux-type boundary condition for the volatilization simula-
tion. In order to incorporate the new flux-type boundary condition into the
PRZM-2 code, new mass balance equations were derived for the surface soil and stagnant
air layers. Figure 6. 5 (a) is a schematic of the top two soil layers and the stagnant surface
boundary layer when no plant canopy exists. Zero concentration is assumed for 0^a under
the no-canopy field condition.
A mass balance equation for the uppermost soil compartment is
***
where
Dg = molecular diffusivity of pesticide in air filled pore space
V = volume of the compartment (cm?)
A = area of the compartment (cm?)
a = volumetric air content (cnoi? cnm3)
1^ = first-order reaction rate constant (day-1)
The first term of the right side of Equation 6-90 represents the gas diffusive flux into the
surface soil layer, and the second term denotes the gas diffusive output as governed by
the stagnant boundary layer above the soil surface. By using backward implicit finite
differencing, the following is derived.
6-47
-------
-
9,3
(a) without plant canopy
c* —^
(b) with plant canopy
Figure 6.5. Schematic of the top two soil compartments and the overlaying surface
compartment (a) without plant canopy, (b) with plant canopy.
6-48
-------
-l] KB CJM-1] = - - Dg[2ji] KH
(6-91)
where
n = time index
By substituting Equation 6-91 into the overall (i.e., all phases) mass balance equation for
the uppermost soil layer, a flux-type upper boundary condition is obtained. Figure 6.5(b)
reflects the field situation when a plant canopy exists. Zero concentration is now assumed
to exist above the top of the canopy compartment. The volatilization flux from the plant
canopy is defined as follows.
(6'92)
where
J^ = volatilization flux through the plant canopy (g cm? day:l)
ZR = vertical transfer resistance (day cm-1, described in
Section 6.3.4.3)
C* = concentration above the plant canopy (assumed to be zero)
By carrying out a similar mass balance using finite differences, the boundary condition
that describes the field with canopy existing is obtained.
6.4.3 Soil Temperature
Soil temperature is solved for numerically. Section 6.3.4.4 describes the theoretical basis
for the simulation of soil temperature. The distribution of temperature within the soil
profile is summarized by Equation 6-79. This equation is solved numerically for soil
temperature, T, as a function of depth, Z, and time, t, based on the input thermal
diffusivity, d, for each soil compartment, and the following initial and boundary condi-
tions.
Initial Condition:
6-49
-------
rv = TXz) (6-93)
Boundary Conditions:
Tpj = r,(t» (6-94)
(6-95)
where
T(z) = initial soil temperature in each soil compartment (°C)
T,(t) = calculated soil surface temperature for each time step (8C)
Tr(t) = lower boundary temperature condition at the bottom of the soil core (!€)
The lower boundary temperature is defined by the user as 1 2 monthly values correspond-
ing to the first day of each month; the value for each day is interpolated between the
neighboring monthly values.
The following numerical approximation used in the model is taken from Hanks et al.
(1971).
At
(6_96)
Equation 6-96 is solved using a modified numerical solution procedure of Hanks et al.
(1971), which involves the same finite difference technique and tridiagonal matrix solver
(Thomas algorithm) used in PRZM (Carsel et al. 1984).
6.4.4 Furrow Irrigation
To simplify the algebra required to calculate the furrow infiltration volume as Manning's
equation is substituted into the kinematic wave model (equation 6-86), Manning's
equation is approximated as follows.
A = a Qm (6-97)
a and m are constants that are estimated by the model from the parameters of Manning's
equation as follows.
where
6-50
-------
md. (6-98)
\n(Qj ^ w$)
(6-99)
A[, j8§ = cross-sectional areas (iri?) at depths y\ and y£
Qi; Q2 = flow rates (m3 s"-1) computed from Manning's equation [(Equation 6-75)] at
depths y\ and y$
yi = 1 cm
y2 = 10 cm
The depths yj. and y£ were chosen to represent the range of depths likely to occur in
furrows.
Substituting Equation 6-97 into Equation 6-86 produces:
dQ + d«tQM) = _ dq (6_100)
dz dt dt
No closed-form solution to the above equation is known when infiltration is time-variable.
Equation 6-88 therefore, is, solved for Q using the backwards-space, backwards-time
finite-diHerence solution described by Li et al, (1975). Writing Equation 6-100 in finite-
difference form producers:
(6-101)
Az At At
where
Q^ = flow rate at time k, station i
A2 = spatial step
At = time step
Infiltration volumes are computed using the Green-Ampt model:
at
6-51
-------
where
I* = infiltration depth at time k (m), station i
—= saturated hydraulic conductivity of the soil (m s:l)
3= ponded water depth (m)
HB = suction parameter (m)
= available porosity (fraction)
11 =s= total volume of infiltrated water (m)
The Green-Ampt model has long been accepted as a model of the advance of the wetting
front through the soil column, and involves parameters that can be related to well-known
soil properties. The volume of infiltration is computed assuming I* is an average infiltra-
tion depth for the channel at location i:
ak = Wk!k (6-103)
where
= volume infiltrated at location i (m? mf)
= current flow width at location i (m)
Furrow channels are assumed to be trapezoidal in shape. E uation 6-87 is solved at each
station at the end of each time step for teh new flow rateQ^+i • Because the equation is
non-linear with respect to Q, the new value of flow is found using second-order Taylor
series iteration. Given the flow rate in the furrow, infiltration depths at each location are
then computed using the Green-Ampt model (Equation 6-90).
The PRZM-2 furrow irrigation model determines infiltration depths at various locations in
the furrow. Irrigation continues until the depth of water infiltrated at the downstream
end of the furrow is sufficient to meet the soil moisture deficit SMDEF. The depth of
water applied as irrigation to the first PRZM-2 soil compartment is then set equal to
either the average furrow infiltration depth or the infiltration depth at a specific location
in the furrow, depending upon options selected by the user. This depth of water then
infiltrates through the root zone as determined by the PRZM-2 soil hydraulic algorithms.
6.5 RESULTS OF PRZM TESTING SIMULATIONS
This section includes the results of testing the two solute transport solution techniques
and the volatilization algorithm. Simulated results are compared with those from
analytic solutions. Sensitivity analyses also were performed to evaluate the effects of key
model parameters on the prediction of volatization rates. A test comparison of the model
with field data from Georgia (soybeans) concludes the section.
The PRZM model has undergone additional performance testing with field data in New
York and Wisconsin (potatoes), Florida (citrus), and Georgia (corn) (Carsel et al., 1985;
Jones 1983; Jones et al., 1983). The results of these tests demonstrate that PRZM is a
6-52
-------
usefiul tool for evaluating groundwater threats from pesticide use. Please refer to these
references for information regarding the further testing of PRZM-2 under field conditions.
6.5.1 Transport Equation Solution Options
Currently, two numerical solution options are available to the PRZM-2 user for the
chemical transport equation. As discussed in Section 6.4.1, the finite difference option
(utilizing subroutine SLPSTO) is unconditionally stable and convergent, but may result in
excessive numerical dispersion in high Peclet number systems. The method of character-
istics algorithm (utilizing subroutines MOC and SLPST1) eliminates or reduces that
numerical dispersion. Two examples are provided that compare the alternate solutions
methods at high Peclet number (greater than 5.0) and at low Peclet number (less than
0.5).
6.5.1.1 High Peclet Number--
Figure 6.6 presents the analytical solution (Hunt 1978) together with the SLPSTO and
MOC/SLPST1 solutions at 6 days for the transport of a 69 mg cm pesticide application
in the uppermost compartment. The physical parameters are as presented in the figure--
notably the Peclet number is 5.1. The following table details pertinent features of the
simulation:
Method
Analytical
SLPSTO
MOC/SLPST1
Location
of
Peak
5.8
4$5
5.5
Value
of Peak
(mgfara^)
11.2
5.07
12.09
% Error
at Peak
--
-54
+7
Runtime
(sec)
-
88.5
112.4
At this relatively high Peclet number, the SLPSTO algorithm shows excessive numerical
dispersion, capturing only about half the amplitude of the peak concentration, while
showing excessive mass in both tails. In addition, the SLPSTO algorithm does not predict
the location of the peak precisely. (It is logged behind the location of the peak given by
the analytical solution and the MOC/SLPST1 solution.) The MOC/SLPST1 algorithm
requires 27% more runtime, but errs by only 7% in the peak and shows good agreement in
the tails.
6.5.1.2 Low Peclet Number--
Figure 6.7 illustrates the results of a SLPSTO and MOC/SLPST1 simulation 8 days after
an incorporation of 69 mgfanri? in the sixth compartment using the parameters listed. The
predicted concentrations at this lower Peclet number, 0.46, are very similar in the peaks
and the tails, and apparently little additional resolution is gained from utilizing the MOC
algorithm. However, the additional computational burden associated with the MOC
algorithm is only 7%.
6-53
-------
6.5.2 Testing Results of Volatilization Subroutines
To test and validate the operation of the volatization algorithms, model results were
compared with Jury's analytical solution (Jury et al., 1983a), and against field data for
trifluralin from Watkinsville, GA, Sensitivity analyses were also performed to evaluate
effects of key parameters on model predictions. The intent of this preliminary model
testing was to evaluate model operation by comparing the results for the volatization flux
from a soil surface application.
6.5.2.1 Comparison with Analytical Solution--
Jury et al. (1983a) presented a mathematical model for describing volatile loss and
movement of soil-applied organic chemicals. By making the following assumptions, they
derived an analytical solution for evaluating the chemical concentration profile within the
soil and the volatization flux at the soil surface:
1) Uniform soil properties consisting of a constant water content, bulk density,
liquid water flux (either upward, downward, or zero), and a constant organic
carbon fraction
2) Linear equilibrium adsorption isotherm
3) Linear equilibrium liquid-vapor partitioning (Henry's law)
4) Uniform incorporation of a quantity of chemical to a specified depth below the
surface
5) Pesticide loss by volatilization through a stagnant air boundary layer at the
soil surface
6) Infinite depth of uniform soil below the depth of incorporation
Assumptions 2 to 5 are satisfied by the current PRZM-2 code. Assumption 6 defines zero
concentration for the bottom layer, which is somewhat different from PRZM's zero
gradient bottom boundary condition. However, as long as no chemical reaches the bottom
layer, these two types of boundary conditions produce identical results. Our test runs for
volatization were designed to satisfy this requirement. In order to comply with assump-
tion 1, the hydrological computation subroutines in PRZM were bypassed and replaced
with a constant value for water flux. A positive flux value indicates a leaching condition,
whereas a negative flux value indicates an evaporating condition. The hydrological
subroutines in PRZM-2 are based on a moisture-routing method in which daily accounting
of water inflow and outflow is recorded. One limitation of the moisture-routing method is
that it is unable to properly describe the upward movement of evaporating water.
Evaporation loss is removed from specific surface soil layers without accounting for
movement between layers.
The pesticide 2,4-D was chosen as the test compound for our simulation; the input
parameters are listed in Table 6-2 and were obtained from Jury et al. (1983a). The test
run results for daily volatilization flux are presented in Figures 2.8(a), 2.8(b), 2.9(a), and
2.9(b), corresponding to the four test cases listed at the bottom of Table 6-2. Two different
6-54
-------
5 7 9 11 13 15
COMPARTMENT NUMBER
17 19
Figure 6.6 Comparison of simulation results at high Peclet number.
6-55
-------
COMPARTMENT NUMBER
Figure 6.7 Comparison of simulation results at low Peclet number.
Velocity = 1.82 cm/day
Diffcoef=4.0cm!/day
Retardation Coef = 11.74
Decay = 0.1/day
Delta x = 1 cm
Delta t = 1 day
Core Length =20 cm
Peclet = 0.46
6-56
-------
soil compartment depths (DE LX) of 1.0 and 0.1 cm were used to investigate the sensitivity
of the volatilization algorithms to the spatial discretization in the surface soil horizon.
Figure 6.8(a) shows the steady state situation (i.e., no evaporation and no leaching)
without any advective movement. The daily volatilization flux values predicted by the
two different DELXS are almost identical. In this case, the magnitude of DELX is
relatively unimportant. The simulation results with a leaching rate of 0.01 cm day:l are
shown in Figure 6.8(b). Because of the leaching influence, the predicted daily flux is
smaller than the corresponding daily value shown in Figure 6.8(a), The differences
between the analytical solution and the PRZM-2 predictions are due to the finite differ-
ence solution technique and the occurrence of advective movement by leaching. The
simulation results using the smaller DELX (0.1 cm) more closely match the analytical
solution results, and an even smaller DELX would have improved the agreement further.
The slope of both DELX curves is the same as the analytical solution, and the maximum
differences (for the 1.0 cm DELX) from the analytical solution are 10% or less.
Figure 6.9 shows the simulation results under evaporating conditions with the upward
advective velocity at 0.01 (Figure 6.9(a)) and 0.25 (Figure 6.9(b)) cm day-"h The "wick
effect" phenomenon (described in Section 6.3.4) leading to enhanced upward movement of
the pesticide can be observed in these two figures, The maximum daily flux occurs on the
first day for the leaching conditions. Depending on the magnitude of the evaporating
water velocity, the maximum daily flux no longer occurs on the first day of the pesticide
application. Also the magnitude of the maximum daily flux is enhanced by the magnitude
of the evaporating water velocity. The effect of DELX becomes more critical as the
influence of advective movement increases. For simulations using a 1.0-cm DELX, Figure
6.9(a) shows stable numerical behavior with a small discrepancy when compared to the
analytical solution result. As the advective movement becomes larger, the numerical
behavior becomes more unstable, as shown in Figure 6.9(b). The smaller 0.1-cm DELX
showed good agreement with the analytical solution for both test cases shown in Figure
6.9.
Based on these test cases, it appears that a freer DELX, in the range of 0.1 to 0.5 cm, is
needed for top soil layers when volatilization processes are simulated with PRZM-2.
However, this finer DELX requirements poses an additional computational burden for
PRZM-2 applications due to the increase in the number of soil compartments. To
circumvent this burden, the PRZM-2 code was modified to allow a variable compartment
depth, which allows the user to select a smaller DELX for the top horizon (or any other
horizon) and a bigger DELX for the rest of the soil profile. By selecting this variable
compartment depth capability, a significant saving in CPU time may be achieved while a
better representation is provided for calculation of the surface volatilization flux. In
conjunction with field data comparisons (presented below), the results of model runs and
CPU time are presented for simulation runs both uniform and variable compartment
depth.
6.5.2.2 Comparison with Field Data--
Preliminary model testing with field observations also was performed to assess the ability
to predict the general magnitude of volatilization losses and daily fluxes under field
conditions. Based on a review of available volatilization field data sets, a USDA experi-
mental watershed site in north-central Georgia was selected because of its use of a
6-57
-------
TABLE 6-2. INPUT PARAMETERS FOR THE TEST CASES - ANALYTICAL SOLU-
TION
T
%
8
a
M
L
KH
Air diffusion coefficient
Water diffusion coefficient
Porosity
Bulk density
Temperature
Organic carbon fraction
Water content
Air content
Pesticide applied
Depth of incorporation
Henry's constant for 2,4-D
Organic carbon partition
coefficient for 2,4-D
Decay coefficient for 2,4-D
Total depth of soil column
Simulation period
Water flux
Evaporation flux
0.43 (m2 day-!)
4.3xlO"§(m2day-})
0.5
1.35 (kgm§)
25°C
0.0125
0.3
0.2
1 (kghtl)
0.1 m
5.5 x 10-9
0.02(m?kg-1)
4.62 x 10"i (day-1)
0.3 m
30 days
Test case #1: no evaporation and no leaching ($j[ = E = 0)
Test case #2: with leaching (A| = 0.01 cm day"-1?
Test case #3: with evaporation (E = 0.01 cmday:l)
Test case #4: with evaporation (E = 0.25 cmday:1)
6-58
-------
( E - 6 Kg/ ha-day )
20
3 15
I
jj 10
5J
"c
5
— Analytic Sol'n
PRZM Results
« DBLX - 0.1 cm
* DBLX - 1 cm
i i i i
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
(days)
No Evaporation & No Leaching
( E - 6 Kg/ ha-day )
20
I
R
o
>
10
— Analytic Sol'u
PRZM Results
« DELX - 0.1 cm
* DELX - 1 cm
i i i _ i
i _ i i i
i i i
2 46 8 10 12 14 16 18 20 22 24 26 28 30
(days)
Leaching Rate - 0.01 cm/ day
Figure 6.8 Comparison of volatilization flux predicted by PRZM and
Jury's analytical solution: Test cases #1 and #2.
6-59
-------
( E - 6 Kg/ ha-day )
— Analytic Sol'n
PRZM Results
» DELX - 0.1 cm
DELX - 1 cm
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Evaporation Rate • 0.01 cm/ day
so
( E - 6 Kj/ hft-day )
I
40
20
— Analytic Sol'n
PRZM Results
o DELX - 0.1 cm
DELX - 1 cai
2 46 8 10 12 14 16 18 20 22 24 26 28 30
(day)
Evaporation Rate - 0.25 cm/ day
Figure 6.9 Comparison of volatilization flux predicted by PRZM and
Jury's analytical solution: Test cases #3 and #4.
6-60
-------
volatile pesticide (trifluralin), surface-applied to a major crop (soybeans), with a compre-
hensive micrometeorological and soil sampling plan.
The study site was located at Watkinsville, GA, on a 1.26-ha watershed comprised of Cecil
soil (63.9% sand, 23.6% silt, and 12.5% clay) with 0.55% organic carbon, a pH of 6.5, and a
slope of 3.0%. Harper et al. (1976) present a detailed description of the site, the equip-
ment, and the installation procedures required for collecting microclimate data. They also
summarize the method, assumptions, and calculations used for determining pesticide
volatilization flux rates. Trifluralin was surface-applied as a spray to a bare soil surface,
using a ground sprayer equipped with flat-fan nozzles, at a rate of 1.12 kg/ha between
1220 and 1247 eastern daylight time (EOT) on 15 June 1973.
The field results shown in Table 6-3 were obtained from White et al. (1977). The values
in columns 2, 4 and 5 of Table 6-3 provide the cumulative volatilization flux, remaining
pesticide in soil, and total cumulative decay losses, respectively. A discrepancy is noted
for the data in column 4 of Table 6-3; the pesticide remaining in soil at the 35th day is
smaller than that at the 49th day. This discrepancy is most likely due to sampling
variations, although data were not available to establish accuracy limits on the data
points. Meteorological data required for applying PRZM to the site, which include daily
precipitation and pan evaporation, were obtained from Smith et al. (1978).
The PRZM-2 input parameters for trifluralin and the Watkinsville site are listed in Table
6-4. Two additional key parameters which influence the volatilization results are the
decay rate and the adsorption partition coefficient. The magnitude of the decay rate can
be estimated from the data in column 5 of Table 6-3, assuming that decay accounts for all
losses from the soil other than volatilization. A value of 0.0206 per day for the frost-order
decay rate constant obtained from these data points is consistent with the value of 0.0198
per day used by Donigian et al. (1986) after reviewing the literature. An initial value for
Kg was obtained from the organic carbon content of 0.55% and an organic-carbon partition
coefficient (Koc) value of 13,700, resulting in a Kg of 75 ml/g. Figure 6.10 shows the
results of sensitivity analyses runs for Kg and the decay rate; the observed data for
trifluralin from Table 6-3 are also included for comparison. Figure 6.10(a) shows a good
representation of the observed cumulative volatilization curve. Figure 6.10(b) shows that
a value of 40 for K$, and a decay rate of 0.02 per day provides the best representation of
the decay rate values analyzed.
The simulation results for cumulative volatilization flux and cumulative pesticide decay
are shown in Figure 6.11 for four different DELX combinations. For these simulations,
DELX values of 1.0, 0.5, 0.25, and 0.1 cm were chosen for the first horizon and 5-cm
DELX for the rest of the profile. The field data are also included in the figures for
comparison. Table 6-5 shows the total volatilization flux for each of the four combinations
using variable DELX, as well as for a simulation using simulations, a constant 1.0-cm
DELX throughout the whole soil profile. The CPU requirements for each run are also
included in Table 6-5. The predicted total volatilization flux using the smallest DELX of
0.1 cm is closest to the field-measured value; the values for DELX of 0.25 cm and 0.50 cm
are also quite close to the field value. The saving of CPU time can be observed from
Table 6-5. The simulation requires 129 seconds using 1.0-cm DELX for the whole soil
profile, compared with only 39 seconds for the simulation using 1.0 cm for the top horizon
and 5.0 cm for the rest of the profile. The results in Table 6-5 indicate that a DELX of
0.25 to 0.50 cm for the top horizon may be a reasonable compromise between simulation
accuracy and CPU costs.
6-61
-------
TABLE 6-3. TRIFLURALIN VOLATILIZATION LOSSES, AMOUNTS REMAINING IN
SOIL, AND ESTIMATED LOSSES VIA OTHER PATHWAYS FOR THE
120-DAY FIELD TEST
Time, (day)
Application
1
2
6
18
35
49
63
76
120
Cumulative
% of Total
Applied
3.5
3.8
5.3
10.9
20.5
23.4
24.4
25.1
25.4
25.9
Volatilized
% of Total
Applied
13.3
14.8
20.3
42.2
79.1
90.2
94.1
96.9
98.2
100.0
Remaining*
in Soil,
% Applied
-
89
72
64
51
33
35
23
20
11
Estimated
Other Losses,
% of Applied
-
7.2
22.7
25.1
28.5
43.6
40.6
48.9
54.6
63.1
Source: White et al. (1977).
* Based on amount remaining in soil at a 0- to 7.5-cm depth as compared with an
initial 1.0 pg/g level at application (rate was 1.12 kg/ha).
TABLE 6-4. INPUT PARAMETERS FOR THE TEST CASES - WATKINSVILLE SITE
Simulation start date
Simulation end date
Trifluralin: Henry's constant
Diffusion coefficient in air
Application date
Amount applied
Incorporation depth
14 June 1973
31 December 1973
6.7 X103
0.43m?day:l
15 June 1973
1.12kgha-l
5 cm
Horizon
Content
1
2
3
4
Thickness
(cm)
5
10
15
60
DELX
(cm)
0.1
5.0
5.0
5.0
Field
Capacity
.207
.207
.339
.320
Wilting
Point
.095
.095
.239
.239
Initial
Water
0.166
0.217
0.318
0.394
6-62
-------
1
1
40
30
20
10
12 24 36 4* 60 72 84 96 108 120
(day)
Sensitivity of KD
I
o
"
M 20
§•
of applied)
Field Data
PRZM Results
K - 0.01
K-0.02
K • 0.03
sfc 4s fc ii to
Sensitivity of Decay Rate
120
(day)
Figure 6.10 Sensitivity of cumulative volatilization flux to Kjj and decay rate.
-------
40
30
20
10
(% of applied)
Field Data
PRZM Results
DELX - 0.1 * 5 cm
DELX - 0.25 & 5 cm
DELX - 0.5 & 5 cm
DELX = 1.0 ft 5 cm
12 24 36 48 60 72 84 96
Effect of DELX on Volatilization Flux
10B
120
(day)
(% of applied)
Field Data
PRZM Results
DELX - 0.1 & 5 cm
DELX - 0.25 A S cm
DELX - 0.5 & 5 cm
DELX - 1X)& 5 cm
12 24 36 48 60 72 84 96 108
Effect of DELX on Pesticide Decay
120
(day)
Figure 6.11 Effects of DELX on volatilization flux and pesticide decay.
6-64
-------
TABLE 6-5. SIMULATION RESULTS OF USING DIFFERENT COMPARTMENT
DEPTH (DELX)
Constant DELX
Horizon Depth DELX
(cm) (cm)
1 5
2 10
3 15
4 60
Total
Volatilization
Flux (kg/ha)
1.0
1.0
1.0
1.0
0.393
DELX
(cm)
1.0
5.0
5.0
5.0
0.398
Variable
DELX
(cm)
0.5
5.0
5.0
5.0
0.338
DELX
DELX
(cm)
0.25
5.0
5.0
5.0
0.317
DELX
(cm)
0.1
5.0
5.0
5.0
0.316
Field
Value
0.290
CPU (See)
129
39
46
67
106
Figure 6.12(a) reveals significant differences between the observed pesticide decay and the
simulated values during the first few weeks following application. In fact, the observed
data appear to indicate a much higher attenuation rate during the first few days following
application, with a lower rate for the remaining period. To better match the decay
characteristics, and evaluate the potential impact on the volatilization simulation, a two-
step decay procedure was used with a rate of 0.1 per day for 5 days following application
and a rate of 0.01 per day for the remaining period. The results of these simulations in
terms of pesticide remaining in the soil, shown in Figure 6.12, indicate a much better
agreement with the observed field values in Figure 6.12(b). The impact of the two-step
decay on both cumulative decay and volatilization flux is shown in Figure 6.13. The
cumulative pesticide decay shown in Figure 6.13(a) improves considerably (compared to
Figure 6.11(b)), while the results for cumulative volatilization flux (Figure 2.13(b)) are
slightly better than those in Figure 2. n(a).
6.5.2.3 Conclusions from Volatilization Model Testing-
The primary conclusions derived from this preliminary model testing are as follows.
1) Comparisons with Jury's analytical solution indicate that the volatilization
algorithms are operating correctly, and that, with a very small DELX (0.1 cm or
less), the results are in excellent agreement.
2) The preliminary field testing results with trifluralin in Watkinsville, GA,
indicate good agreement between measured and predicted volatilization flux
when measured decay rates and adjusted KD values are used.
6-65
-------
90
80
70
60
50
40
30
20
10
(% of applied)
FWdData
PRZM Results
DELX - 0.1 & 5 cm
DELX - 0.25 A 5 cm
DELX - 0.5 & 5 cm
DELX - 1.0 A- 5 cm
12 24 36 48 60 72 84 96 108 1
Simulations with Constant Decay Rate
90
80
70
60
50
40
30
20
10
(% of applied)
(b)
Field Data
PRZM-2 Results
DELX - 0.1 & 5 cm
DELX - 0.25 & 5 cm
DELX - 0.5 & 5 cm
DELX - 1.0 & 5 cm
12
24
36 48 (50 72 84 96 108
Simulations with Two-Step Decay Rates
Figure 6.12 Comparison of constant and two-step decay rates.
6-66
-------
i
80
70
60
50
40
30
20
10
Field Data
PRZM Results
DELX - 0.1 & 5 cm
DELX - 0.25 & 5 cm
DELX - 0.5 & 5 cm
DELX 1.0 & 5 cm
12 25 3e 48 GO 728455"
Simulation with Two-Step Decay Rate
(day)
40
I 30
20
10
(% of applied)
Field Data
PRZM Results
DELX -0.1* 5 cm.
DELX - 0.25 & 5 cm
DELX - 0.5 & 5 cm
DELX 1.0 ft 5 cm
12 24 36 48 60 72 84 96 108 120
(day)
Simulations with Two-Step Decay Rates
Figure 6.13 Effects of two-step decay rates on volatilization flux and pesticide
decay.
6-67
-------
3) Small soil layer depths-in the range of 0.25 and 0.50 cm-are needed to provide
the best presentation of volatilization flux at reasonable CPU times, based on the
Watkinsville testing.
4) A two-step decay rate best represents the attenuation behavior of trifluralin
using a higher rate for the period immediately following application and a lower
rate for the remaining period.
Further testing of the volatilization model should be performed to evaluate its capabilities
for different compounds, different regions, and other crops. In addition, the vapor
transport and concentration calculations for the plant compartment should be tested with
the additional data available from the Watkinsville site and from other field data sets
(e.g., Grover et al. 1985, Willis et al. 1983).
6.5.3 Testing Results of Soil Temperature Simulation Subroutine
Preliminary testing of the simulation subroutine for the soil profile temperature was
performed by comparing predicted values with values obtained by an analytical solution to
the governing heat flow equation. These testing results are discussed in this section.
Testing of the soil surface/upper boundary temperature simulation, estimated by the
energy balance procedure in the model, was not performed due to problems in obtaining
observed meteorological and soil temperature data for the Watkinsville, GA, test site.
An analytical solution presented in Kreysig (1972) for the classical one-dimensional heat
flow partial differential equation (described in Section 6.3.4.4) was used to calculate
changes in the soil temperature profile with time, due to a change in the upper boundary
temperature. In order to develop a valid comparison between the analytical and finite
difference methods, three assumptions were made:
a) Uniform properties throughout the soil profile
b) Constant lower-boundary temperature
c) Uniform initial temperatures throughout the profile
To compare the results of the analytical solution with the finite difference solution from
the soil temperature model, the following parameters were used.
Depth of the soil profile =100 cm
Compartment thickness (DELX) =1.0 cm
Diffusivity of the soil profile = 864 cnoi? day lf
Upper-boundary temperature, I^J = 30°C
Lower-boundary temperature, T^ = 20eC
Initial temperature, f^jj ' = 20°C
Figures 6.14 and 6.15 show the comparison of soil temperature profiles predicted by both
the analytical solution and the finite difference soil temperature model after 1 day and 5
days of simulation. In Figure 6.14 the finite difference solution is obtained by using a i^
hour time step, while in Figure 6.15 a 1-day time step is used. The following observations
are evident from these testing results.
6-68
-------
1) Comparison of the soil temperature profiles predicted by both methods indicate
excellent agreement when the smaller, 1-hour time step is used in the finite
difference procedure, as shown in Figure 6.14.
2) The finite difference solution obtained by using the daily time steps deviates from
the analytical solution by about 1*C, in the upper and middle portions of the soil
profile (Figure 6.15). This deviation is due to the assumption of a constant initial
temperature profile and the abrupt change in the upper-boundary temperature
from 20°C to 300(2 for the first daily time step.
3) As the steady-state condition is approached, irrespective of the time step used in
the finite difference solution, the soil temperature profiles predicted by both
methods are in good agreement (Figures 6.14(b) and 6.15(b)).
Table 6-6 shows that reducing the depth of the compartment from 1 cm to 0.1 cm does not
produce any significant change in the finite difference solution. These depths bracket the
range of values for DELX (i.e., compartment thickness) likely to be used for the surface
soil horizon.
These test results show that, for smaller time steps, the finite difference solution will be
in complete agreement with the analytical solution. For a daily time step as used in
PRZM-2, under expected environmental conditions, with a non-uniform initial tempera-
ture profile, non-uniform soil characteristics, and smaller daily changes in the upper-
boundary temperature, the soil temperature profile estimated by the finite difference
method used in the model is expected to be capable of providing close agreement with
observed temperature profile data. In addition to further testing of the soil profile
temperature model with field data, the procedure to estimate the upper-boundary
temperature should be tested to evaluate and demonstrate the validity of the entire soil
temperature simulation model.
6.5.4 Testing of Daughter Products Simulation
The fate of pesticides in soils is a complex issue. Many processes (i.e., volatilization,
degradation, etc.) must be considered in order to adequately address this issue. One of
these processes, which has been largely neglected in pesticide leaching models, is that of
the transformation of the parent compound to various toxic daughter products. The
tendency has been to lump all the toxic family into a "total toxic residue" and to model the
fate of this composite as a single chemical. This assumption may not be acceptable,
especially if the daughters have very different decay rates or adsorption partition
coefficients from the parent or from each other.
Algorithms have been included in PRZM-2 to simulate parent/daughter relationships. An
analytical solution to the decay and transformation model was derived to check the
numerical model.
6-69
-------
30T
24..
21"
18-
15
Profile Initial Temp - 20 C
Upper Boundary Temp - 30 C
Lower Boundary Temp = 20 C
Time Step - 1 hr
Analytical Sola.
Finite Diff. Sdbi. ~™ • ~~ • —
0 iC 20 30 40 50 60 70 80 90 100
Depth of Soil Profile in cm
27--
24=-
21--
iS--
IJ
Piofite Initial Ttenp - 20 C
Upper Boundary Temp - 30 C
Lower Boundary Temp - 20 C
Time Step - 1 hr
Analytical Serin.
Finite Diff. Soln.
-J-
1020304050607080
Dep
-------
30
27
24
21
IS
\ X
Profile Initial Temp. - 20 C
Upper Boundary Temp. - 30 C
Lcw«r Boundary Twnp- - 20 C
Time Step • 1 day
Analytical Scdn. _ _ _
Ptoto Diff. Soln,
0 10 20 30 40 50 60 70 80 90 100
Depth, of Soil Profile in cm
30
27--
24--
21.-
18--
15
Profile Initial Temp = 20 C
Upper Boundary Temp • 30 C
Lower Boundary Temp - 20 C
Time Step - 1 day
Analytic! Soln. — — —
Finite Diff. Sota.
ffj 2\) lo Jo ^0 GO 70
Depth of Soil Profile in cm
Figure 6.15 Comparison of soil temperature profiles predicted by
analytical and finite difference solutions (Time Step=l day).
6-71
-------
TABLE 6-6. SIMULATED SOIL TEMPERATURE PROFILE AFTER ONE DAY FOR
DIFFERENT COMPARTMENT THICKNESSES (TIME STEP = 1 DAY)
Depth (cm)
0.0
1.0
2.0
3.0
4.0
5.0
10.0
20.0
30.0
40.0
50.0
60.0
75.0
99.0
100.0
DELX = 1 cm
30.000
29.665
29.341
29.028
28.725
28.432
27.109
25.048
23.577
22.524
21.766
21.215
20.638
20.023
20.000
DELX = 0.1 cm
30.000
29.664
29.340
29.026
28.723
28.431
27.106
25.045
23.574
22.520
21.760
21.206
20.627
20.020
20.000
The system that was modeled is shown in Figure 6.16. The Q are dissolved concen-
trations and the C[ are adsorbed concentrations. The K| are adsorption partition coeffi-
cients, the kj are decay and transformation rates in the dissolved species, the k[ are
adsorbed phase decay coefficients and 0 and p are the water content and soil bulk
densities, respectively. Notice that only the dissolved forms may be transformed from one
toxic form to another. A system of first order differential equations describing this system
can be written as:
&
d
(6-104)
&
(6-105)
(6-106)
6-72
-------
k *
1
k *
2
C1
C2
C3
k *
3
ADSORBED PHASE
DISSOLVED PHASE
Figure 6.16 Schematic of a system of parent and daughter pesticide.
(6-107)
(6-108)
dt
(6-109)
dt
Making use of C\ K| = Q* we can reduce the six equations above to three equations in
three unknowns, namely:
6-73
-------
in which
e +
aA =
(6-HO)
l=a4C2+a5C3 (6-H2)
dt 4253
(6-114)
(6-116)
4 e + A:SP
7 1 * V
*» " *» 3p (6-117)
6 + K, p
These ordinary differential equations with constant coefficients can be solved analytically
for C|, G§ and C% using the initial conditions Cjl= C^ when t = 0 and C/£ = C$ = Oatt = 0.
The solutions as given in Dean and Atwood (1985) are:
C{ = Credit (6-H8)
and
6-74
-------
In PRZM-2, the equations are solved numerically as part of the general advection-
dispersion equation for a solute in a porous medium by using an implicit scheme. A new
subroutine was added to set up the transformation (source and sink) terms for the system.
The relationship Ql-o C$ -> C$ may be modeled or the system can be configured for $\ -4
Cj and G! —> C% or for independent C\, Cg and Cg simply by selecting zero or positive
values for the appropriate transformation rate constants.
Figures 6.17 through 6.18 show the results of a series of tests performed on the numerical
model and checked by the analytical model. In these figures, the solid line represents the
"true" or analytical solution, and the dashed line represents the approximate numerical
solution. In Figure 6.17, there was no decay of the dissolved phase chemicals and no
adsorption of any species. The rate of transformation from C\ to Q, was 0.2 day:l and that
from C$ to G| was 0.5 day:l. After 20 days nearly all the chemical is in formCj. The
numerical model traces the decay and formation of each constituent closely, being poorer
in those regions where the rate of change of the concentrations are more rapid. Figure
6.18 shows the same system with a decay rate of 0.01 day:l in the dissolved phase.
Using the analytical model, the assumption of modeling the "total toxic residue" decay as
a first-order process was tested. Adsorption coefficients for aldicarb, aldicarb sulfoxide and
aldicarb sulfone in a Woburn sandy loam (KJ = 0.55, Kj = 0.16 and K% = 0.185) and decay
and transformation rate constants (kj = 0.07, lq = 0.55, fcg = 0.01, fcj = 0.031 and fc§ =
0.0152) were taken from Bromilow et al. (1980). A soil bulk density of 1.45, a water
content of 0.27 cm? cm ? and an initial aldicarb parent mass of 100 mg were also used.
The model was run for 90 days and the results are shown in Figure 6.19.
The results show that the decay of the sum of the dissolved aldicarb concentrations does
not follow first-order kinetics. The reason for this is the conversion of aldicarb parent to
aldicarb sulfoxide. Because the sulfoxide has a lower partition coefficient, the dissolved
concentration increases until most of this conversion is complete. Once this happens,
however, the sum of the sulfoxide and the sulfone concentrations does follow a first-order
decay curve.
6-75
-------
I I I I I I I I I I I I I
18 20
flME,INDAYS
Figure 6.17 Conversion of Q to C| to Cg with no adsorption and no decay.
-------
100.
8
I
u
§
u
I I I I I I I
I I I I I I
II
2 4 6 8 10 12 14 16 18 20
TIME, IN DAYS
Figure 6.18 Conversion of C\ to C^ to Q with decay but no adsorption,
6-77
-------
X PARENT ALDICARB
• SULFOXDE
OSULFONE
0 TOTAL
I I L I I I I I ..... I
30 40 50 60
TIME, IN DAYS
90
Figure 6.19 Conversion of aldicarB to al'dicarB sulfbxide to aldicarb sulfone.
6-78
-------
6.6 Biodegradation Theory and Assumptions
The biodegradation model is based on the: Mathematical Model for Microbial Degradation
of Pesticides in the Soil. Soil Biol. Biochem. V.I4 pp. 107-1 15 (Soulas 1982). The soil is
divided into two phases: the solid phase, consisting of the dry soil including the organic
matter, and the aqueous phase dispersed within it, consisting of the soil moisture, various
organic substrates, and all the biomass. Some of the organic and inorganic components
constituting the solid phase can adsorb the pesticide. This adsorption is represented as a
linear isotherm, instantaneous and without hysteresis.
The microbial population is divided into four groups. The first two are responsible for the
degradation of the pesticide. These are the metabolizing and co-metabolizing populations.
The former corresponds to normal metabolic utilization, whereas the latter represents
that fraction of the microflora which degrades without energy recovery.
The non-degrading population was divided into microorganisms that are sensitive to the
lethal action of the chemical and those that are indifferent.
In the original development of the equations, all concentrations were expressed with
respect to the soil solution. Soulas (1982) reports that these concentrations are somewhat
theoretical when considering the different biomasses and are not easy to evaluate by
experiment. Thus, all concentrations were expressed with respect to the weight of the
moist soil. For these biomasses, the simple proportionality
»», r
was chosen where
X; = concentration of the $i population in the moist soil
e
Xj = concentration of the X[ population in the soil solution
and
where
H = weight of the aqueous phase (soil solution)
P = weight of the solid phase (dry soil)
For the metabolizing population, growth is described by
6-79
-------
(6.122)
This represents growth at the expense of both the pesticide (S) and the carbon (C) in the
soil solution. The population decreases as a result of a first-order death process with a
death rate constant kj~.
For the co-metabolizing population,
Xc
~ k* *c (6-123)
PCCWK '^-y 'k&xc
This reflects growth only at the expense of soil carbon. Allowance was also made for
possible antagonistic effects by the non-degrading portion of the soil microflora. These
antagonisms were assumed to result only in a reduction of the growth rate of the co-
metabolizing population. Michaelis-Menten kinetics with non-competitive inhibition were
used to simulate these conflicts.
For the sensitive population,
— = u C ^-kWSX-k X (6-124)
This includes a supplementary death term following second-order kinetics.
For the non-sensitive, non-degrading population,
This is the basic relation of growth term and death term.
The equation concerning the pesticide concentration,
(6-126)
6-80
-------
has two parts. The first term concerns the degradation due to the metabolizing popula-
tion, while the second deals with the action of the co-metabolizing population. The
equation for the concentration of carbon in the moist soil,
Cm
(6-127)
-is derived from the basis that the concentration is the difference between two reaction
rates-the solubilization rate of carbon compounds from solid soil organic matter and the
rate of microbial consumption. It is assumed that soluble carbon in the soil solution is, in
first approximation, sufficiently low to be neglected when compared to the saturation
constant.
N.B. There are some minor differences between the equations as developed by Soulas and
as reported in his Appendix 3. In addition, some slight changes were made to the
equations to correct what were assumed to be some typographical errors. These changes
include:
Definitions:
Xj = Concentration of the X| population in the moist soil (i = m, c, s, r)*
St= Pesticide concentration in the moist soil
Cty = Carbon concentration in the moist soil
PJ = Maximum specific growth rate of the \ population (i = sm, cm, c, s, r)*
K|j = Saturation constant of the Xj population (i= sm, cm, c, s, r)*
fcaj = Death rate of the Xj population (i= m, c, s, r)*
YI = True growth yield of the X| population (i = sm, cm, c, s, r)*
k| = Second-order death rate of the X^ population
kj, = Dissociation constant of the enzyme-substrate complex
= Inhibition constant
6-81
-------
In addition,
T+W
-^ (6-128)
where
Kj = distribution coefficient
and
Wv~£ (6-129)
P
with
H = weight of soil solution (aqueous phase)
P = weight of dry soil (solid phase)
These equations are to be solved simultaneously, and the results used to determine the
amount of pesticide in the soil that is degraded biologically over the timestep interval.
These equations are solved in PRZM-2 using a fourth-order Runge-Kutta method.
This subprogram uses the carbon concentration and the pesticide concentration in the
moist soil of each compartment as input. Using the populations of organisms in each
compartment, which is saved between calls, the subprogram solves the degradation
algorithm to determine the new pesticide amount, and thus the amount degraded, over
the PRZM-2 time step. Also, the changes to the organism populations are calculated and
saved for use in the subsequent timestep.
6-82
-------
SECTION 7
VADOSE ZONE FLOW AND TRANSPORT MODEL (VADOFT)
CODE AND THEORY
7.1 INTRODUCTION
VADOFT is a finite-element code for simulating moisture movement and solute transport
in the vadose zone, It is the second part of the Iwo-component PRZM-2 model for
predicting the movement of pesticides within and below the plant root zone and assessing
consequent groundwater contamination. The VADOFT code simulates one-dimensional,
single-phase moisture movement in unconfined, variably saturated porous media. The
code considers only single-porosity media and also ignores the effects of hysteresis.
Transport of dissolved contaminants may also be simulated within the same domain.
Transport processes accounted for include hydrodynamic dispersion, advection, linear
equilibrium sorption, and first-order decay. VADOFT also simulates solute transforma-
tions in order to account for parent/daughter relationships,
7.2 OVERVIEW OF VADOFT
7.2.1 Features
7.2.1.1 General Description-
The VADOFT code can be used to perform one-dimensional modeling of water flow and
transport of dissolved contaminants in variably or fully saturated soil/aquifer systems.
VADOFT can be operated as a stand-alone code or operated in conjunction with the root
zone model, PRZM. In the latter case, boundary conditions at the interfaces of the
modeled domains are established via model linkage procedures.
7.2.1.2 Process and Geometry-
VADOFT performs one-dimensional transient or steady-state simulations of water flow
and solute transport in variably saturated porous media. The code employs the Galerkin
finite-element technique to approximate the governing equations for flow and transport.
It allows for a wide range of nonlinear flow conditions, and handles various transport
processes, including hydrodynamic dispersion, advection, linear equilibrium sorption, and
first-order decay. Steady-state transport can not be simulated when decay is considered.
Boundary conditions of the variably saturated flow problems are specified in terms of
prescribed pressure head or prescribed volumetric water flux per unit area. Boundary
conditions of the solute transport problem are specified in terms of prescribed concentra-
tion or prescribed solute mass flux per unit area. All boundary conditions may be time
dependent.
7.2.1.3 Assumptions—
7-1
-------
The VADOFT code contains both flow and solute transport models. Major assumptions of
the flow model are:
• Flow of the fluid phase is one-dimensional and considered isothermal and
governed by Darcy's law,
• The fluid considered is slightly compressible and homogeneous.
• Hysteresis effects in the constitutive relationships of relative permeability
versus water saturation, and water saturation versus capillary pressure head,
are assumed to be negligible.
Major assumptions of the solute transport model are:
• Advection and dispersion are one-dimensional.
• Fluid properties are independent of concentrations of contaminants.
• Diffusive/dispersive transport in the porous-medium system is governed by
Pick's law. The hydrodynamic dispersion coefficient is defined as the sum of
the coefficients of mechanical dispersion and molecular diffusion.
• Adsorption and decay of the solute may be described by a linear equilibrium
isotherm and a first-order decay constant.
• Vapor transport can be neglected.
7.2.1.4 Data Requirements--
Data required for the simulation of variably saturated flow include values of the saturated
hydraulic conductivity and specific storage of the porous media, the geometry and
configuration of the flow region, as well as initial and boundary conditions associated with
the flow equation. Soil moisture relationships are also required. These include relative
permeability versus water phase saturation and capillary head versus water phase
saturation. These relationships may be supplied to the code using tabulated data or
functional parameters,
Data required for the simulation of solute transport in variably saturated soil include
dispersivity and porosity values, retardation and decay constants, Darcy velocity and
water saturation values, as well as initial and boundary conditions associated with the
transport equation.
7.2.2 Limitations
Major limitations of the VADOFT code are:
• In performing a variably saturated flow analysis, the code handles only single-
phase flow (i.e., water) and ignores the flow of a second phase (i.e., air) which,
in some instances, can be significant,
7-2
-------
• The code ignores the effects of hysteresis on the soil moisture constitutive
relations.
• The code does not take into account sorption nonlinearity or kinetic sorption
effects which, in some instances, can be important.
• The code considers only single-porosity (granular) soil media. It cannot handle
fractured porous media or structured soils.
• The code does not take into account transverse dispersion, which can be
important for layered media.
7.3 DESCRIPTION OF FLOW MODULE
7.3.1 Flow Equation
VADOFT considers the problem of variably saturated flow in a soil column in the vadose
zone of an unconfined aquifer. The code solves the Richards' equation, the governing
equation for infiltration of water in the vadose zone:
"f
(7-D
where
z
t
n
the pressure head (L)
the saturated hydraulic conductivity (LTJ)
the relative permeability
the vertical coordinate pointing in the downward direction (L)
time (T)
an effective water storage capacity (Li) defined as:
(7-2a)
where
specific storage (L'f), SW is water saturation
the effective porosity.
7-3
-------
Specific storage is defined by
8i~pgftcf=Ml-4»cJ (7-2b)
where
cf = the fluid compressibility
-------
To solve the variably saturated infiltration problem, it is also necessary to specify the
relationships of relative permeability versus water saturation and pressure head versus
water saturation. Two alternative function expressions are used to describe the relation-
ship of relative permeability versus water saturation. These functions are given by
Brooks and Corey (1966) and by van Genuchten (1976):
k™ = Se" (7-6a)
and
S^fl-d-S/n2 (7-6b)
where
manbdly= empirical parameters
§i = the effective water saturation defined as Se= (SJ[ - S^)/(l - S$), with
S$ being referred to as the residual water saturation.
The relationship of pressure head versus water saturation is described by the following
function (van Genuchten 1976, Mualum 1976):
for * < +
y V Va (7-7)
1 for !|r fc i|»a
where
a and £ = empirical parameters
y^ = the air entry pressure head value (L)
= the residual water phase saturation.
7-5
-------
The parameters P and y are related by y = 1- 1//0.
Descriptive statistical values for a, [?, and y have been determined by Carsel and Parrish
(1987) for 12 soil classifications (see section 5). Using the mean parameter values, the
relationships of effective saturation versus capillary head and relative permeability versus
effective saturation are plotted. Logarithmic plots are shown in Figures 7.1 through 7.3.
To show more vividly the high degree of nonlinearities, the relationships of relative
permeability versus effective saturation are also plotted on arithmetic scales and present-
ed in Figures 7.4 through 7.6. It is important that the finite element flow module be
capable of handling such high nonlinearities to be successful in performing a Monte Carlo
study of infiltration in the unsaturated zone.
Equation 7-1 is solved using the Galerkin finite element subject to the initial and
boundary conditions given in Equations 7-3 through 7-5. After the distributions of tp and
% have been determined, the Darcy velocity is computed from
I) (7-8)
7.3.2 Numerical Solution
7.3.2.1 Numerical Approximation of the Flow Equation-
A numerical approximation of the one-dimensional flow equation in the vadose zone is
obtained using a Galerkin finite-element formulation with spatial discretization performed
using linear elements. Time integration is performed using a backward finite difference
approximation. This leads to a system of nonlinear algebraic equations. For a typical
node i in the finite-element grid (see Figure 7.7), the equation may be expressed as
7-6
-------
figure 7.1
to-"
CAPILLARY HEAD, cm
(a)
SATURATION
(b)
Figure 7.1. Logarithmic plot of constitutive relations for clay, clay loam, and loamy sand:
(a) saturation vs. capillary head and (b) relative permeability vs. saturation.
7-7
-------
(Figure 7.2
I
I.D
I 0
Ifl-l
IB'*
II '*
.«*-
p .c-»
w
10'
SfLTY CLAY
SILTY CLAY LOAM
SILT
SILT LOAM
10]
CAPILLARY HEAD, cm
(a)
!«•*
I*"*
SATURATION
(b)
t 0
Figure 7.2. Logarithmic plot of constitutive relations for silt, silty clay loam, silty clay, and
silty loam.
7-8
-------
figure 7.a
1 C
i.e
CAPILLARY HEAD, cm
(a)
Figure 7.3. Logarithmic plot of constitutive relations for sandy clay, sandy clay loam, sandy
loam, and sand.
7-9
-------
'igure 7.4
I
t
UJ
5
oc
UJ
LU
oc
0.4 0,6
SATURATION
0.8
1.0
Figure 7.4 Standard plot of relative permeability vs. saturation for clay, clay loam, loam and
loamy sand.
7-10
-------
'igure 7.5
1.0
0.8 •-
3 0.6 4-
3
UJ
5
QC
UJ
a 0.4--
UJ
UJ
QC
0.2-
0.0
SILT LOAM
SILT
SILTY CLAY LOAM
SILTY CLAY
0.0
0.2
0.4 0.6
SATURATION
Figure 7.5 Standard plot of relative permeability vs. saturation for silt, silt clay loam, silty
clay and silty loam.
7-11
-------
ITgure 7.6
1.0
0.8
S 0.6.
IU
ae
UJ
*• 0.4
UJ
(X
0.2"
0.0 ^
0.0
SAND
SANDY LOAM
SANDY CLAY LOAM
SANDY CLAY
0.4 0.6
SATURATION
0.2
Figure 7.6 Standard plot of relative permeability vs. saturation for sandy clay, sandy clay
loam, sandy loam and sand.
7-12
-------
figure 7.7
z - 0
NP « Total number of nodes
NE « Total number of elements
1-1
'1-1
1+1
z - L
Figure 7.7 Finite element discretization of soil column showing node and element numbers.
7-13
-------
(7-9)
where k+1 is the current time level, and 8j, Pi) Yij and dj are given by
(7-10a)
AVi
(7_10b)
(7-100
and &4 and A% are the spatial and time increments, respectively. Note that the braces
({}) are used in the equations above (and below) to denote the value of the enclosed
quantity at the element centroid. The nonlinear system of equations is solved for each
time step. Three nonlinear schemes are provided in the VADOFT code. The first scheme
is a Picard type iteration scheme, the second scheme is a Newton-Raphson scheme, and
the third is a Newton-Raphson scheme modified by Huyakorn (1988, personal communica-
tion) .
In the Picard scheme, the matrix coefficients, % &« ¥}) and d}, are first evaluated using an
initial estimate of pressure head values, ^. The resulting system of linearized
equations is then solved for yffi using the Thomas algorithm. Updating of the matrix
coefficient is performed by recomputing values of nonlinear soil parameters. Iterations
are performed until the successive change in pressure head values is within a prescribed
tolerance.
In the Newton-Raphson scheme, the nonlinear system of equations is treated by applying
the Newton-Raphson technique (see Huyakorn and Finder 1983, pp. 159-162) to Equation
7-9. This leads to the following system of linearized algebraic equations.
(7-11)
7-14
-------
where superscript r is used to denote the r-th iterate; &\, Pi? Yi? and di are as defined
previously; and Q.*it li, yi, and dj are given by
where Ij =
The initial solution and subsequent iterations of the Newton-Raphson scheme are
performed in the same manner as that described for the Picard scheme.
7.3.2.2 General Guidance on Selection of Grid Spacings and Time Steps, and
the Use of Solution Algorithms-
In designing a finite-element grid for variably saturated flow simulations, one should
select nodal spacings that will yield reasonable approximations to the expected moisture
profiles.
In the analysis of the given variably saturated flow problem, small nodal spacings should
be used in the zones where head gradients or moisture fronts are steep. The nodal
spacings may be gradually increased in the zone where no abrupt changes in hydraulic
conductivities occur and the head gradients are gradually sloping. The variably saturated
flow simulation can be performed using either the Picard algorithm or one of the Newton-
Raphson solution algorithms. For one-dimensional cases where convergence difficulties
are not expected, the efficiencies of these algorithms have been found to be similar. For
certain steady-state cases involving highly nonlinear soil moisture characteristics, the use
of either of the Newton-Raphson algorithms is preferable, particularly when the Picard
algorithm fails to converge within a reasonable number of iterations (say between 10 and
20).
7.4 DESCRIPTION OF THE TRANSPORT MODULE
7.4.1 Transport Equation
The governing equation for one-dimensional transport of a nonconservative solute species
in a variably saturated soil takes the form
where D is the apparent dispersion coefficient (L^F'f), c is the solute concentration (ML"
§), 6 is the volumetric water content (@=<$§w), R is the retardation coefficient, and A is the
frost-order decay constant (T:l). Note that the apparent dispersion coefficient is defined as
7-15
-------
D • aEV + Yi} and dj are given by
o, = TCC* + {OR},.! AZiV(6Atk) (7- 1 8a)
Pi = T0* + [{0R}i Azf + {ORJi.! AZiJ/OAtg (7- 1 8b)
Yi = tyl + {6R}; Az/(6Atk) (7- 1 8c)
7-16
-------
*+1 + 2c*)AZj (7-18d)
X{6R}U Az,!
m.i ^
(7_18e)
with T and «J denoting the time weighting factor and the upstream weighting factor,
respectively.
To obtain a second-order temporal approximation, the value of T is set equal to 1/2. This
corresponds to using the Crank-Nicholson central difference time stepping scheme. The
upstream weighting factor w is introduced in the above numerical approximation to curb
numerical oscillations that may occur when the selected finite-element grid is not
sufficiently refined for a given value of longitudinal dispersivity. For each time step, the
linear system of algebraic equations is solved using the Thomas algorithm.
Transport of a daughter species in a decay chain can also be handled by the VADOFT
code. In this case, the right side of the governing equation for single species transport (7-
13) is modified by adding a source term accounting for transformation of parent compo-
nents. This source term is given by
m = -L $ Sw e, X, R, c( (7-19)
where
subscript { = the parent species
_rr the number of parent species
§t = the mass fraction of parent component that is transformed into the
daughter species under consideration
The numerical solution of the modified transport equation can be performed in the same
manner as that described previously for a single species. The source term from Equation
7-19 is incorporated into the finite element matrix equation by adding d^ to the right side.
The term d; is given by
7-17
-------
(7-20)
**1
In performing the solute transport analysis, the selection of nodal spacing
(Az) and time step value (At) should follow the so-called Peclet number and Courant
number criteria where possible. These two criteria are given as follows.
4 (7-21)
AtfAzSl (7-22)
= VZBR (7-23)
where
«£ = the longitudinal dispersivity
» the solute velocity
= Darcy velocity
=^= water content
= retardation coefficient
The VADOFT code also provides the user with the option of using upstream weighting to
curb numerical oscillations that may occur in solving the advective-dispersive transport
equation, The recommended value of Ifl, the weighing factor, is determined by using the
following formulae:
u - 1 - 4a^/f, \ > 4ax (7-24)
W^(£|, | < 4at (7-25)
7-18
-------
where
04 = the longitudinal dispersivity
fi = the length of the element.
7.5 RESULTS OF VADOFT TESTING SIMULATIONS
Three sets of benchmark problems were used to test the VADOFT code. The first set
consists of two steady and transient problems designed to test the variably saturated flow
component of the code. The second set consists of four transient one-dimensional
transport problems. The third set consists of two coupled flow-transport problems.
Numerical results obtained from VADOFT are compared with analytical solutions and
results obtained using two other finite-element codes, UNSAT2 and SATURN. These test
problems were simulated using VADOFT before it was linked in PRZM-2.
7.5.1 Flow Module (Variably Saturated Flow Problems)
7.5.1.1 Transient Upward Flow in a Soil Column-
This problem concerns transient, vertically upward moisture movement in a 20 cm long
soil column. The soil column is subject to zero pressure head at the base and zero flux at
the top. The initial distribution of pressure head is hydrostatic: (t = 0) = -90 + z cm,
where z is the depth below the top of the soil column. Soil properties and discretization
data used in the simulation are presented in Table 7-1. The simulation was performed for
15 time steps with constant time step value oft = 0.01 d. Numerical results given by the
Picard and the Newton-Raphson schemes are virtually identical. Both schemes require
between 2 and 3 iterations per time step to converge to a head tolerance of 0.01 cm. The
simulation results obtained from VADOFT are compared with those obtained from
UNSAT2 and SATURN (the two-dimensional finite-element codes described by Davis and
Neuman [1983], and Huyakorn et al. [1984]) respectively, Shown in Figures 7.8 and 7.9
are plots of distributions of pressure head and water saturation, respectively. As can be
seen, the results of VADOFT are in good agreement with the results of the other two
codes.
7.5.1.2 Steady Infiltration in a Soil Column-
This problem concerns steady-state infiltration in a soil column. The column is 550 cm in
length and is subject to an infiltration rate of 4.07 cm day-1 at the top and zero pressure
head at the bottom. Soil properties used in the simulation are presented in Table 7-2.
Five cases of varying degree of nonlinearity of relative permeability function ($&= Sgn)
were simulated. Both the Picard and the Newton-Raphson schemes were used in
conjunction with a finite-element grid having constant nodal spacing, z = 10 cm. The
performance of the two iterative schemes are illustrated in Table 7-3. Note that the
Newton-Raphson scheme converges for all cases, whereas the Picard scheme fails to
converge when the nonlinear exponent n exceeds 4. Simulated distributions of pressure
head and water saturation are shown in Figure 7.10 and 7.11, respectively. These results
of the VADOFT code are virtually identical to corresponding results obtained using the
SATURN code.
7-19
-------
7.5.2 Transport Module
7.5.2.1 Transport in a Semi-Infinite Soil Column-
This problem concerns one-dimensional transport of a conservative solute species in a
saturated soil column of infinite length. The solute is introduced into the column at the
inlet section where z = 0. The initial concentration is assumed to be zero, and the
dimensionless constant inlet concentration is prescribed as 1. Values of physical parame-
ters and discretization data used in the numerical simulation are given in Table 3-4. The
finite-element grid representing the soil column was 400 cm in length. The simulation
was performed for 20 time steps. Thus the duration of the simulation time of transport in
the soil column was 50 hours. For this duration, the selected grid length is sufficient to
avoid the end boundary effect. The numerical solution obtained from the VADOFT code
was checked against the analytical solution of Ogata and Banks (1961). Shown in Figure
7.12 and Table 7-5 are concentration values at t = 25 hours and t = 50 hours. As can be
seen, the numerical and analytical solutions are in excellent agreement.
7.5.2.2 Transport in a Finite Soil Column-
n this problem, downward vertical transport of dissolved contaminants in a soil column
above the water table of an unconfined aquifer is considered. The length of the soil
column is 20 m and the Darcy velocity and water content are assumed to be constant and
equal to 0.25 m day:l and 0.25, respectively. The initial concentration is zero, and water
with dimensionless solute concentration of 1 enters the soil surface at a rate of 0.25 m
day:l. At the water table, a zero dispersive-flux boundary condition is assumed. A list of
physical parameter values and discretization data used in the simulation is provided in
Table 7-6. Two cases involving conservative and nonconservative species were simulated.
Results obtained from the VADOFT code are compared in Figure 7.13 and Table 7-7 with
the analytical solution given by van Genuchten and Alves (1982). There is excellent
agreement between the numerical and analytical solutions for both cases.
7.5.2.3 Transport in a Layered Soil Column-
This problem concerns one-dimensional transport of a conservative solute species in a soil
column consisting of three layers. The initial concentration in the soil column is assumed
to be zero, and the two boundary conditions prescribed are a unit concentration at the top
and a zero dispersive flux boundary condition at the bottom. A list of physical parameter
values and discretization data used in the simulation is provided in Table 7-8. Two cases
corresponding to those considered by Shamir and Harleman (1967) were simulated. Both
cases have contrasting longitudinal dispersivity values among the three layers. The
dispersivity values of the second case are ten times those of the first case for the same
layers. The intention here is to test the numerical scheme used in the VADOFT code, as
well as to check the validity of an approximate analytical solution presented by Shamir
and Harleman (1967) and Hadermann (1980). It should be noted here that the approxi-
mate solutions by Shamir and Harleman (1967) and Hadermann (1980) are valid only for
relatively small values of dispersivity. Therefore, for a small dispersivity value, the
solutions can be employed to verify the VADOFT code. Then with appropriate discretiza-
tion, the VADOFT code could be used to determine the validity of the analytical solutions
at large dispersivity values.
7-20
-------
TABLE 7-1. SOIL PROPERTIES AND DISCRETIZATION DATA USED IN SIMULAT-
ING TRANSIENT FLOW IN A SOIL COLUMN
Parameter Value
Length of soil column, L 20 cm
Saturated hydraulic conductivity, K 10 cm d:l
Porosity, $ 0.45
Residual water phase saturation, S$ 0.333
Air entry value, V. 0-0 cm
Constitutive relations:
)= (1 - SJOL -
where > = -100 era.
Az = 0.5 cm
At = 0.01 d
TABLE 7-2. SOIL PROPERTIES USED IN SIMULATING STEADY-STATE
INFILTRATION
Parameter Value
Length of soil column, L 550 cm
Saturated hydraulic conductivity, K 25 cm dl
Porosity, $ 0.331
Residual water saturation, S\^ 0.0
Air entry value, vpa 0.0 cm
Constitutive relations:
[1
where Se = (M - S^)/(l - S=j>, a ^ 0.014 cm-1, ^ » 0 cm,
M 1.51, y= 0.338
7-21
-------
Figure V.8
ie
UNSAT2
O VADOFT
X SATURN
12
-20
-40
PRESS WE HEAD, em
-to
-100
Figure 7.8 Simulated pressure head profiles for the problem of transient upward flow in a
soil column. (Adapted from Battelle and GeoTrans, 1988).
7-22
-------
b'igure 7.9
IWSAT2
O VADOFT
X SATURN
0.4 o.e
WATtft PHASE SATURATION
Figure 7.9 Simulated profile of water saturation for the problem of transient upward flow
in a soil column.
7-23
-------
TABLE 7-3. ITERATIVE PROCEDURE PERFORMANCE COMPARISON
Number of Nonlinear Iterations
Case
n
n
n
n
n
= 3
= 4
= 6
= 8
= 10
Newton-
Raphson
12
13
19
27
31
Picard
33
56
n.c.*
n.c.
n.c.
No convergence. Head tolerance = 0.0001 cm. Grid spacing z = 10 cm.
TABLE 7-4. VALUES OF PHYSICAL PARAMETERS AND DISCRETIZATION DATA
USED IN SIMULATING ONE-DIMENSIONAL TRANSPORT IN A SEMI-
INFINITE SOIL COLUMN
Parameter Value
Darcy velocity, V 1 cm hr4
Porosity, $ 0.25
Longitudinal dispersivity, e^ 5 cm
Concentration at the source, CO 1
Az = 10 cm
7-24
-------
'igure 7.10
-to
-!•
»»• -«»
HEAD tern)
Figure 7.10 Simulated pressure head profiles for five cases of the problem of steady
infiltration in a soil column. (Adapted from Springer and Fuentes, 1987).
7-25
-------
Figure 7.11
t»o
* n
•+ n
x n
• 10
- •
- e
* 4
- 3
v
tu
o
too
400
too
ft.o
.t
.4 .•
SATURATION
1.D
Figure 7.11 Simulated profiles of water saturation for five cases of the problem of steady
infiltration in a soil column. (Adapted from Springer and Fuentes, 1987).
7-26
-------
TABLE 7-6. VALUES OF PHYSICAL PARAMETERS AND DISCRETIZATION DATA
USED IN SIMULATING ONE-DIMENSIONAL TRANSPORT IN A
FINITE SOIL COLUMN
Parameter Value
Thickness of soil column, L 20m
Darcy velocity, V 0.25 m d:l
Water content, 0 0.25
Retardation coefficient, R 1
Longitudinal dispersivity, % 4m
Source leachate concentration, 6} 1
Case 1:
Decay constant, A a
Case 2:
Decay constant, A 0.25 d:f
Az= 1.0m
Att=0.5 d
7-29
-------
figure 7.13
— Analytic So1n
VADOFT
12. 16. X
(») X » 0 d'1
Analytic Soln.
C VAMFT
0. 12.
Distance, m
(b) ^ • 0.25 d"1
Figure 7.13 Simulated concentration profiles for two cases of the problem of solute transport
in a soil column of finite length, (a) X = 0 d:l, and (b) X = 0.25 d:L
7-30
-------
TABLE 7-7. CONCENTRATION PROFILE CURVES SHOWING COMPARISON OF
THE ANALYTICAL SOLUTION AND VADOFT
Distance
z, (m)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
t =
Analytical
0.764
0.638
0.502
0.371
0.256
0.164
0.097
0053
0.027
0.013
0.009
5d
VADOFT
0.751
0.624
0.489
0.360
0.247
0.158
0.094
0.052
0.027
0.014
0.009
t
Analytical
0.884
0.820
0.742
0.655
0.561
0.466
0.375
0.293
0.224
0.176
0.157
Case 1: h =
= 10d
VADOFT
0.878
0.812
0.733
0.645
0.552
0.457
0.367
0.286
0.219
0.171
0.152
Od^1
t =
Analytical
0.963
0.942
0.914
0.881
0.841
0.796
0.748
0.698
0.652
0.617
0.602
20 d
VADOFT
0.961
0.939
0.911
0.877
0.837
0.791
0.742
0.692
0.646
0.610
0.595
Distance
z, (m)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
t =
Analytical
0.593
0.416
0.283
0.186
0.116
0.069
0.038
0.020
0.009
0.004
0.002
5d
VADOFT
0.588
0.411
0.279
0.182
0.113
0.067
0.037
0.019
0.009
0.004
0.002
t
Analytical
0.615
0.449
0.326
0.236
0.169
0.119
0.083
0.057
0.039
0.028
0.024
Case 1: h =
= 10d
VADOFT
0.613
0.447
0.325
0.234
0.167
0.118
0.083
0.057
0.039
0.028
0.024
Od^1
t =
Analytical
0.618
0.453
0.333
0.244
0.179
0.131
0.096
0.071
0.053
0.042
0.038
20 d
VADOFT
0.617
0.452
0.332
0.243
0.178
0.131
0.096
0.071
0.053
0.042
0.038
Using the discretization data given in Table 7-8, the VADOFT code was run for 180 time
steps. Simulated breakthrough curves at the bottom end of the column (z = 86.1 cm) are
presented in Figures 7.14 and 7.15 and in Tables 7-9 and 7-10. As can be seen, the
numerical solution of the VADOFT code compares very well with the analytical solution
for case 1: The small dispersivity case, where the analytical assumption of infinite ratio
of layer thickness to layer dispersivity-i.e., each layer extends to infinity-is fairly
accurate, There is a slight discrepancy of the analytical solution from the numerical
solution for case 2, where the analytical assumption is less accurate.
7-31
-------
7.5.3 Combined Nonlinear Flow and Transport Modules
7.5.3.1 Transport During Absorption of Water in a Soil Tube-
This problem is selected to provide simultaneous testing of the flow and the transport
modules of VADOFT. The problem is depicted schematically in Figure 7.16. A conserva-
tive solute species has a uniform initial concentration and moisture content. The initial
con-centration is assumed to be zero, and the inlet concentration CO is assumed to be 1
ppm. The solute is transported by dispersion and advection. Note that the solute front
and the wetting front advance at different rates. The solute velocity, Yy., was previously
defined as Equa-tion 7-23. The velocity of the wetting front is dependent upon the rate of
water sorption into the soil, which is dependent on moisture diffusivity; thus, calculation
of the wetting front velocity requires integration of the mass balance equation. For the
sake of convenience, all physical data pertaining to the geometry of the soil tube and the
physical parameter values are kept the same as those used in the paper by Huyakorn et
al. (1985). The complete set of data is listed in Table 7-11. The simulation was per-
formed in two stages. In the first stage, the transient water flow problem was analyzed to
determine the distributions of Darcy velocity and water saturation for each time level.
These results are written on an output file. In the second stage, the transient solute
transport problem was analyzed to determine con-centration distributions using the
velocity and water saturation data file obtained from the flow simulation.
The spatial and temporal discretization data used in running the VADOFT code are also
given in Table 7-11. Both the flow and the transport analyses were performed for 50 time
steps. Results of the flow analysis are plotted in Figure 7.17. The water saturation
profiles given by VADOFT compare well with those obtained using the semi-analytical
solution of Phillip (1955) and the UNSAT2 finite-element flow code. Results of the
transport analysis are plotted in Figure 7.18. The concentration distributions given by
VADOFT also compare well with those obtained using the semi-analytical solution of
Smiles et al. (1978) and the FEMWASTE finite-element transport code documented by
Yeh and Ward (1981).
7.5.3.2 Transient Infiltration and Contaminant Transport in the Vadose Zone-
This problem, schematically depicted in Figure 7.19, involves variable infiltration and
contaminant transport in a layered system in which layer permeabilities differ by more
than two orders of magnitude. The problem was chosen to demonstrate the capability of
VADOFT to handle a higher nonlinear situation involving soil materials with sharp
contrast in drainage properties. Shown in Table 7-12 are values of physical parameters
and discretization data used in the flow and transport simulations. For the unsaturated
flow simulation, the transient infiltration rates illustrated in Figure 7.20 were used.
7-32
-------
Figure 7.14
c
o
c
o*
u
c
o
QJ
oc
CASE 1
—Analytic Soln
VADOFT
700. 750.
Time, s
850.
Figure 7.14 Simulated outflow breakthrough curve for case 1 of the problem of solute
transport in a layered soil column.
7-33
-------
''igure 7.15
1.6
.6 ••
e
o
CJ
u
O)
o:
.4 •-
.2 -
0.0
CASE 2
—A Analytic Solution
O VADOFT
\ \ 1
S6Z.
£02. 700.
Time, s
eac.
1B00
Figure 7.15 Simulated outflow breakthrough curve for case 2 of the problem of solute
transport in a layered soil column,
7-34
-------
TABLE 7-8. VALUES OF PHYSICAL PARAMETERS USED IN THE SIMULATION OF
TRANSPORT IN A LAYERED SOIL COLUMN
Value for Layer i
Parameter Layer 1 Layer 2 Layer 3
Layer thickness, (| 25.48 30.31 30.31 cm
Seepage velocity, Bi 0.127 0.123 0.121 cm si
Retardation coeff., Rj 1.0 1.0 1.0
Decay constant, hi 0 0 ° §
Source concentration, 6Q 1.0
Case 1:
Dispersivity, ay 0.076 0.174 0.436 cm
Case 2:
Dispersivity, eft 0.76 1.74 4.36 cm
Az = 0.6888 cm
7-35
-------
TABLE 7-11. VALUES OF PHYSICAL PARAMETERS AND DISCRETIZATION DATA
USED IN SIMULATING TRANSPORT IN A VARIABLY SATURATED
SOIL TUBE
Parameter Value
Length of soil column, L 20 cm
Saturated hydraulic conductivity, K 1 cm d"t
Initial pressure head, vpj -83.33 cm
Remaining flow parameters See Table 3-2
Initial concentration, 6j 0 ppm
Longitudinal dispersivity, a^ 0 cm
Molecular diffusion, D* \ qrp? d-1
Decay constant, A
Retardation coefficient, R 1
Az = 0.25 cm
Alt-0.0025 d
TABLE 7-12. VALUES OF PHYSICAL PARAMETERS AND DISCRETIZATION DATA
USED IN SIMULATING TRANSIENT INFILTRATION AND
CONTAMINANT TRANSPORT IN THE VADOSE ZONE
Material 1 Material 2
Property (Sand) (clay loam)
Saturated conductivity, K 713 6.24 cm d:l
Porosity, f 0.43 0.41
Residual Water Saturation, % 0.105 0.232
Air entry value, ipa 0.0 0.0 cm
Soil moisture parameter, a 0.145 O.OlBonntl1
Soil moisture parameter, |3 2.68 1.31
Soil moisture parameter, y 0.63 0.24
Longitudinal dispersivity, a^ 1.0 1.0 cm
Retardation coefficient, R 1.1 1.5
Decay coefficient, A 0.00274 0.00274 d-1
7-38
-------
ir'igure 7.Id
SOLUTE WETTING
FRONT | ] FRONT
J I
/ y y X
/ s s s s s
«
1
!
FLOW
••83.33 cm
d*
}- 20 em
c or g
SU.tJ
Figure 7.16 One-dimensional solute transport during absorption of water in a soil tube.
(Adapted from Huyakorn et al., 1985).
7-39
-------
figure 7.17
i.o
VADOFT
UMSATX
• EMI-ANALYTIC SOLUTION
II
Figure 7.17 Simulated profiles of water saturation during absorption of water in a soil tube.
(Adapted from Huyakorn et al., 1984a).
7-40
-------
figure 7.1b
0 VADOFT
— »•— FEMWASTE
SEMI-ANALYTIC
SOLUTION
Figure 7.18 Simulated concentration profiles for the problem of one-dimensional solute
transport during adsorption of water in a soil tube. (Adapted from Huyakorn, et al., 1985).
7-41
-------
b'igure 7.19
20 cm
120 cm
280 cm
l,cm/d
I I II 1 i I
SAND Ksat - 713 cm/d
CLAY LOAM
6,24 cm/d
SAND
Ksat" 713 cm/d
WATER TAB!
Figure 7.19 Problem description for transient infiltration and transport in the vadose zone.
7-42
-------
''igure 7.20
5
4 ••
3-
E
o
JO
^5
n
1
ll
8 12
time , days
20
Figure 7.20 Infiltration rate vs. time relationship used in numerical simulation.
7-43
-------
'igure 7.21
604-
120-
I «0T
0-
O 240T
300"
360+
420
0.2
0.4 0.6
SATURATION
10
Figure 7.21 Simulated water saturation profiles.
7-44
-------
[Figure 7.22
420
-100 -200 -300
PRESSURE HEAD, cm
-400
Figure 7.22 Simulated pressure head profiles.
7-45
-------
SECTION 8
UNCERTAINTY PREPROCESSOR
8.1 INTRODUCTION
In recent years, the use of quantitative models to assess the transport and transformation
of contaminants in the environment has increased significantly. Typically these models
include a set of algorithms that simulate the fate of a contaminant within a medium (e.g.,
unsaturated zone, saturated porous media, air or a surface water body) based on a
number of user-specified parameters. These parameters describe the properties of the
chemical, the transport medium, and the effects that man has on the system.
Unfortunately, the values of these parameters are not known exactly due to measurement
errors and/or inherent spatial and temporal variability. Therefore, it is often more
appropriate to express their value in terms of a probability distribution rather than a
single deterministic value and to use an uncertainty propagation model to assess the
effect of this variability on the transport and transformation of the contaminant.
This section describes the Monte Carlo method of uncertainty propagation and a Monte
Carlo shell that is coupled with the PRZM-2 model (subsequently referred to as the
deterministic code in this report). The composite code (i.e., the uncertainty shell coupled
with the deterministic code) can be used for the quantitative estimate of the uncertainty
in the concentrations at the monitoring point due to uncertainty in the (fate) model input
parameters.
8.2 OVERVIEW OF THE PREPROCESSOR
The objective of the uncertainty analysis/propagation method is to estimate the uncertain-
ty in model output (e.g., the concentration at a monitoring point) given the uncertainty in
the input parameters and the transport and transformation model. Alternatively stated,
the objective is to estimate the cumulative probability distribution of the concentration at
a receptor location given the probability distribution of the input parameters. If G|
represents the concentration at the receptor, then
(8-1)
where the function g represents the fate model and X represents the vector of all model
inputs. Note that some or all of the components of X may vary in an uncertain way, i.e.
they are random variables defined by cumulative probability distribution functions. Thus
the goal of an uncertainty propagation method is to calculate the cumulative distribution
function Fgw(C^) given a probabilistic characterization of X, Note that F£W(£$ is defined
as:
8-1
-------
) = Probability (Cl * Q (8-2)
where C£ is a given output concentration.
8.2.1 Description of the Method
Given a set of deterministic values for each of the input parameters, Xl, $3? . . . ^, the
composite model computes the output variable (e.g., a downgradient receptor well
concentration G$) as:
(8-3)
Application of the Monte Carlo simulation procedure requires that at least one of the
input variables, XI ... X^ be uncertain and the uncertainty represented by a cumulative
probability distribution. The method involves the repeated generation of pseudo-random
number values of the uncertain input variable (s) (drawn from the known distribution and
within the range of any imposed bounds) and the application of the model using these
values to generate a series of model responses i.e. values of C%. These responses are then
analyzed statistically to yield the cumulative probability distribution of the model
response. Thus, the various steps involved in the application of the Monte Carlo simula-
tion technique involve:
i) Selection of representative cumulative probability distribution functions for describing
uncertainty in the relevant input variables.
ii) Generation of pseudo-random numbers from the distributions selected in (i). These
values represent a possible set of values for the input variables.
iii) Application of the model to compute the derived inputs and output(s).
iv) Repeated application of steps (ii) and (iii) .
v) Presentation of the series of output (random) values generated in step (iii) as a cumula-
tive probability distribution function (CDF).
vi) Analysis and application of the cumulative probability distribution of the output as a
tool for decision making.
8-2
-------
8.2.2 Uncertainty in the Input Variables
The parameters required by a transport and transformation model can be broadly
classified into two different sets that exhibit different uncertainty characteristics. These
are:
• ' Chemical parameters. Examples of these variables include the octanol-water partition
coefficient, acid, neutral, and base catalyzed hydrolysis rate, soil-adsorption coefficient,
Henry's Law Constant, etc.
• Media parameters. Examples of these variables include the groundwater velocity, soil
porosity, organic carbon content, dispersivity values, etc.
• ] Meteorological parameters. Examples include precipitation, evaporation, solar radiation.
•'. Management parameters. Examples include irrigation timing, pesticide application
timing, well pumping rates, etc.
Uncertainty in chemical parameters primarily arises due to laboratory measurement
errors or theoretical methods used to estimate the numerical values. In addition to
experimental precision and accuracy, errors may arise due to extrapolations from
controlled (laboratory) measurement conditions to uncontrolled environmental (field)
conditions. Further, for some variables, semi-empirical methods are used to estimate the
values. In this case, errors in using the empirical relationships also contribute to
errors/uncertainty in the model outputs.
Uncertainty in the second and third sets of parameters, identified above, may include both
measurement and extrapolation errors. However, the dominant source of uncertainty in
these is the inherent natural (spatial and temporal) variability. This variability can be
interpreted as site-specific or within-site variation in the event that the fate model is used
to analyze exposure due to the use and/or the disposal of a contaminant at a particular
site. Alternatively it can represent a larger scale (regional/national) uncertainty if the
model is used to conduct exposure analysis for a specific chemical or specific disposal
technology on a generic, nation-wide or regional basis. Note that the distributional
properties of the variables may change significantly depending upon the nature of the
application. Uncertainty in the fourth set of parameters may arise from a complex variety
of factors including climate, sociology, economics, and human error.
Whatever the source of uncertainty, the uncertainty preprocessor developed here requires
that the uncertainty be quantified by the user. This implies that for each input parame-
ter deemed to be uncertain, the user select a distribution and specifies the parameters
that describe the distribution.
The current version of the preprocessor allows the user to select one of the following
distributions.
8-3
-------
i) Uniform
ii) Normal
iii) Log-normal
iv) Exponential
v) Johnson SB distribution
vi) Johnson SU distribution
vii) Empirical
viii) Triangular
Depending on the distribution selected, the user is required to input relevant parameters
of the distribution. The first requires minimum and maximum values. The second and
third distributions require the user to specify the mean and the variance. The fourth
distribution requires only one parameter - the mean of the distribution. For the empirical
distribution, the user is required to input the coordinates of the cumulative probability
distribution function (minimum 2 pairs, maximum 20 pairs) which is subsequently treated
as a piece-wise linear curve. For the triangular distribution the user is required to input
the minimum, maximum and the most likely value. Finally, the Johnson SB and SU
distribution requires four parameters — mean, variance, and the lower and upper bounds.
In addition to the parameters of the distribution, the user is required to input the bounds
of each model parameter. These bounds may be based on available data or simply
physical considerations, e.g., to avoid the generation of negative values. Values generated
outside these bounds are rejected.
Of the above eight distributions, the characteristics of the majority are easily available in
the literature (Benjamin and Cornell 1970). The triangular distribution has been
discussed in Megill (1977). Details of the Johnson system of distributions are presented
in McGrath and Irving (1973) and Johnson and Kotz (1970). Additional details for each of
these distributions are presented in the following discussion.
In some cases, it may be desirable to include correlations among the variables. For
example, there may be correlation between hydraulic conductivity and particle size or
between adsorption and degradation coefficients. The uncertainty processor allows the
generation of (linearly) correlated variables for cases where the underlying distribution of
the variables is either normal and/or lognormal.
8.3 DESCRIPTION OF AVAILABLE PARAMETER DISTRIBUTIONS
The Monte Carlo shell has the ability to generate data from a number of probability
distributions listed above. A description of each of these distributions is provided in the
following paragraphs, including parameters of the distributions, equations for the
probability and cumulative density functions, and a brief discussion of the properties of
each distribution.
8.3.1 Uniform Distribution
A uniform distribution is a symmetrical probability distribution in which all values within
a given range have an equal chance of occurrence. A uniform distribution is completely
described by two parameters: 1) the minimum value (lower bound) A, and 2) the maxi-
mum value (upper bound) B. The equation for the uniform probability density distribu-
tion of variable x is given by:
8-4
-------
fu(x) - 1/(B - A) (8-4)
where
fu(x) = the value of the probability density function for x
The cumulative distribution F(x) is obtained by integrating Equation (8-4). This yields
the probability distribution:
Fu(x) = (x - A)/(B - A) (8-5)
where
F(x) = the probability that a value less than or equal to x will occur
8.3.2 Normal Distribution
The term "normal distribution" refers to the well known bell-shaped probability distribu -
tion. Normal distributions are symmetrical about the mean value and are unbounded,
although values further from the mean occur less frequently. The spread of the distribu-
tion is generally described by the standard deviation. The normal distribution has only
two parameters) -the mean and the standard deviation. The probability density function
of x is given by:
/,(*) = — ~ «SP
-0.5
(8-6)
where
S, = the standard deviation
ni = the mean of x
8-5
-------
The cumulative distribution is the integral of the probability density function:
Fn(x) = J fn(x)dx (8-7)
The above integration must be performed numerically, but tables of numerically-integrat-
ed values of Fn(x) are widely available in the statistical literature.
8.3.3 Log-Normal Distribution
The log-normal distribution is a skewed distribution in which the natural log of variable x
is normally distributed. Thus, if y is the natural log of x, then the probability distribution
of y is normal with mean ir^, and standard deviation Sy and a probability density function
similar to Equation 8-10. The mean and standard deviation of x (ir^ and Sx) are related to
the log-normal parameters niy and Sy as follows.
+ 0.5(Sy)2] (8-8)
ll (8-9)
To preserve the observed mean and standard deviation of x, the parameters of the log-
normal distribution (rtiy and Sy) are selected such that the above relationships are
satisfied. Note that niy and Sy do not equal the natural logs of m^ and Sx, respectively.
Log-normal distributions have a lower bound of 0.0 and no upper bound, and are often
used to describe positive data with skewed observed probability distributions.
8.3.4 Exponential Distribution
The probability density function for an exponential distribution is described by an
exponential equation:
expC-x/m,)
= (8-10)
m,
where m, is the mean of x. The cumulative distribution is given by:
F.OO = 1- exp(-x/nO (8-11)
The exponential distribution is bounded by zero; the probability density function peaks at
zero and decreases exponentially as x increases in magnitude.
8-6
-------
8.3.5 The Johnson System of Distributions
The Johnson system involves two main distribution types-SB (log-ratio or bounded) and
SU (unbounded or hyperbolic arcsine). These two distribution types basically represent
two different transformations applied to the random variable such that the transformed
variable is normally distributed. The specific transformations are:
(8-12)
SB: Y = In
fl-x
(8-13)
where
in = natural logarithm transformation
x = untransformed variable with limits of variation from. A to B.
Y = the transformed variable with a normal distribution
Selection of a particular Johnson distribution for sample data set is accomplished by
plotting the skewness and kurtosis of the sample data. The location of the sample point
indicates the distribution for the sample data.
For additional details of the Johnson system of distributions, the reader is referred to
McGrath and Irving (1973) and Johnson and Kotz (1970).
8.3.6 Triangular Distribution
A triangular distribution is a relatively simple probability distribution defined by the
minimum value, the maximum value, and the most frequent value (i.e., the mode). Figure
8.1 shows an example triangular probability density function. The cumulative distribu-
tion for values of x less than the most frequent value, xm, is given by:
(x - Xl)2
where
Xi = the minimum value
and
8-7
-------
Xg = the maximum value
For values of x greater than the most frequent value, the cumulative distribution is:
(8-15)
8.3.7 Empirical Distribution
At times it may be difficult to fit a standard statistical distribution to observed data. In
these cases, it is more appropriate to use an empirical piecewise-linear description of the
observed cumulative distribution for the variable of interest.
Cumulative probabilities can be estimated from observed data by ranking the data from
lowest (rank = 1) to highest (rank= number of samples) value. The cumulative probabi-
lity associated with a value of x is then calculated as a function of the rank of x and the
total number of samples. The cumulative probabilities of values between observed data
can be estimated by linear interpolation.
8.3.8 Uncertainty in Correlated Variables
In many cases model input variables are correlated due to various physical mechanisms.
Monte Carlo simulation of such variables requires not only that parameters be generated
from the appropriate univariate distributions, but also that the appropriate correlations
be preserved in the generated input sequences. The Monte Carlo module currently has
the ability to generate correlated normal, log-normal, Johnson SB, and Johnson SU
numbers; the procedures used are described in the following paragraphs.
8-8
-------
Kigure 8.i
f(X)
t
1.0 -1
0.0 ->•
m
Figure 8.1. Triangular probability distribution.
8-9
-------
The correlation coefficient is a measure of the linear dependence between two random
variables and is defined as:
Vxy D n \y >•»>
H* Py
where
piy = the correlation coefficient between random variables x any y
cov(x,y) = the covariance of x and y as defined below
p,, py = the standard deviation for x and y.
The covariance of x and y is defined as:
cov(x,y) = E
+00
= JI (x-mj (y-my) fxy(X)y) dx dy (8-17)
-OO
where
E = the expected value
m,, iriy = the mean of the random variables x and y
f^ (x,y) = the joint probability distribution of x and y.
Note that the linear correlation coefficient between x and y can be computed using
£ x, y, - nxy
'=1 (8-18)
To generate correlated random variables, three steps are required. First uncorrelated,
normally distributed random numbers are generated. This vector is then transformed to
a vector of normally distributed numbers with the desired correlation. Finally, the
normally distributed numbers are transformed to numbers with the desired distribution.
The transformation of uncorrelated to correlated normal numbers consists of multiplying
the uncorrelated vector of numbers with a matrix B:
= Be (8-19)
8-10
-------
where
e = the vector of uncorrelated, normally distributed random numbers.
B = and N by N matrix
Y* = a vector of standard normal deviates of mean zero and standard
deviation of unity.
The matrix B is related to the variance-covariance matrix S as follows.
S = B BT (8-20)
where BT is the transpose of the B matrix. Since the normal variables V have means of
zero and unit variances, the variance-covariance matrix is equivalent to the correlation
matrix.
Thus, if the correlation matrix S is known, B can be found from Equation 8-20 by using a
Choleski decomposition algorithm. This algorithm will decomposes a symmetric positive
definite matrix, such as S, into a triangular matrix such as B (de Marsily 1986, p. 381).
Having generated a vector of correlated normally distributed random numbers, the user
can convert vector Y', through appropriate transformations, to the distribution of choice.
Thus for parameters Xj that have a normal distribution, the Y' numbers are transformed
as follows.
X, = m, + ox(YJ) (8-21)
For parameters that follow the lognormal distribution, the following transformation
applies.
Xi = exp[(Yp (a^) + ^,1 (8-22)
where
M-inj = the log mean of the 1th parameter
ain.i = the log standard deviation of the 1th parameter
For parameters with Johnson SB and SU distributions, the Y are first transformed to
normally distributed variables Y with mean My and standard deviation ay:
Y, = My + ay YI (8-23)
Johnson SB numbers are then computed from Yj as follows.
8-11
-------
X, - (B expCYj) - A)/(l + expC^)) (8-24)
Johnson SU numbers are computed by:
X; = A + (B-A) [exp(Y.) . expC-Yi)]^ (8-25)
Other distributions can be easily incorporated into the analyses at a later time when
suitable transformations from the normal distribution can be found. It is important to
note that, in using this technique, the correlations are maintained in normal space, so if
these correlations are estimated using actual data, the data should be transformed to a
normal distribution before correlation coefficients are estimated.
For two correlated variables, one with a normal distribution (xg) and the other with a log
normal distribution (xl), the following equation is used to transform correlations to normal
space (Meija and Rodriguez-Iturbe, 1974).
(8-26)
where
av v = the correlation coefficient between the two variables in the
ylJ2
normal space
crx f = the correlation coefficient between the two variables in the
1 &
arithmetic space
o
ay = the variance of y1 derived from Equation (8-9)
If both x1 and x2 are log-normally distributed then the correlation coefficient is trans-
formed using Meija and Rodriguez-Iturbe (1974):
ln
(8-27)
8-12
-------
where the relationships between S, (SIf>) and Syi(Syo) are given by Equations (8-8)
i o r\ \ £t L &
and 8-9.
Thus, for log-normal variables, the user enters the values of the correlation coefficients in
log-normal space; Equations 8-26 and 8-27 are then used to transform the correlation
coefficients into normal space.
No direct transformation of Johnson SB or SU correlations to normal correlations is
currently known. For these distributions, the user must supply the correlation coeffi-
cients between normal-transformed numbers. This may be accomplished by first trans-
forming Johnson SB and SU data to normal data using Equations 8-12 and 8-13. The
covariance matrix S is then derived using only normal, log-normal, and normal-trans-
formed SB and SU data.
8.3.9 Generation of Random Numbers
Having selected the distribution for the various input parameters, the next step is the
generation of random values of these parameters. This requires the use of pseudo-
random-number-generating algorithms for Normal and Uniform numbers. Numerous pro-
prietary as well as non-proprietary subroutines can be used to generate random numbers.
Many of these are comparable in terms of their computational efficiency, accuracy, and
precision. The performance of the algorithms included in this preprocessor has been
checked to ensure that they accurately reproduce the parameters of the distributions that
are being sampled (Woodward-Clyde Consultants 1988).
8.4 ANALYSIS OF OUTPUT AND ESTIMATION OF DISTRIBUTION QUANTILES
Model output generally will consist of a volume of data that represents a sample of
outcomes. Given the natural variability and the uncertainty of various model compo-
nents, there will be variability in the output. All of the factors that were allowed to vary
within the model contribute to variability in model predictions. Taken as a whole, the
model output depicts possible events in terms of their relative frequency of occurence.
Values produced by the model generally are treated as if they were observations of real
field events, In interpreting these values, it is important to maintain the perspective
dictated by the design and scope of the study.
Model output can be analyzed in various ways depending upon current objectives. Many
features of the distribution may be characterized. Quite often, for example, it is of
interest to estimate certain quantiles or percentiles of the distribution. Since the model
output is treated as a sample from an unknown parent population, the methods of
8-13
-------
statistical inference normally are used to estimate distribution parameters and to
associate measures of uncertainty with these parameters.
One of the most frequently asked questions concerns the number of samples required for
some given purpose. In modeling, this translates into the number of model runs needed.
For the most part, since methods of basic inference are being applied in a Monte Carlo
framework, resulting model output values are treated as observations forming a random
sample. The sample size required to estimate a given parameter depends on a number of
factors. These include the nature of the parameter that is being estimated, the form of
the underlying distribution, the variability in the observations, the degree of precision
and/or accuracy desired, the level of confidence to be associated with the estimate, and the
actual statistical estimator used to provide the estimate.
Generally, if the output distribution is to be accurately characterized with respect to its
many features, the number of model runs needed will be higher than if only a few
parameters are to be estimated. The simulation strategy should be determined by the
issues addressed by the modeling effort. It may be important, for example, to estimate
the extreme upper percentiles of the output distribution. In this case, the choice of
simulation design should account for the relative difficulty of obtaining such estimates. If
it is not known exactly how the data will be utilized, then the problem becomes one of
establishing a distributional representation that is as good as possible under the most
extreme usage or estimation scenario. For example, if only a distribution mean were to be
estimated, the sample size required could be determined without concern for estimating,
say, the 99th percentile.
8.4.1 Estimating Distribution Ouantiles
In the following section, a summary is given for statistical techniques used to estimate
distribution quantiles. Many such methods are available to estimate a given percentile of
an unknown distribution on the basis of sample data. In the PRZM-2 code, four such
methods can be used. Among these are distribution-free or nonparametric techniques as
described below. Others include methods specific to certain distributions that assume a
knowledge of the distributional form. First, the point estimators are given, then the
method for constructing a confidence interval is briefly described.
The order statistics of a sample are merely the ordered values denoted by x(1), x^,,.... x(n),
where n represents the sample size. The empirical cdf can be defined simply as
f 0, if x(1) < x,
g(x) = \ 1/n, if x(i) < x < xa+1), for i=l,..., n-1 (8-28)
I 1, if x > x^.
Mathematically, g(x) is a step function, discontinuous at each value x(i).
By definition, the lOOp-th percentile (i.e., the p-level quantile) is given by up where
p = Pr{X
-------
p = F(Up) and up = F'Hp) (8-30)
When only sample information is available, UP is unknown, but it can be estimated by
forming an appropriate function of the observations.
Nonparametric point estimates of Up can be constructed as linear combinations of the
order statistics. In particular, each of Yt through Y3 below is an estimator of Up. Let [z]
denote the largest integer less than or equal to z. Define
j = [np], g = np-J (8-31)
i = [np + 0.5], r = (np + 0.5) - i (8-32)
k = Kn+l)p], h = (n+l)p - k (8-33)
Then,
Y! = (1-h) X^ + h X^u (8-34)
Y2= - ,ifg=0 (8-35)
2
= XO+D , if gX)
Y3 = (0.5+i-np) Xa) + (0.5 -i+np) X(i+1) (8-36)
= (1 - r) X
-------
in which i is the rank of the outcome in the sample. The specific quantile of interest is
then determined by interpolation.
8.4.2 Confidence of u^
Approximate confidence statements can be placed on up by selecting appropriate order
statistics to serve as the upper and lower confidence bounds. The rationale is given as
follows.
For a given distribution, the value up is such that exactly 100p% of all values of this
distribution are less than up, and 100(l-p)% exceed this value. An individual value
selected randomly from the distribution has probability p of being less than up. In a
random sample of size n from this distribution, the probability of not exceeding up
remains constant for each individual element of the sample. Thus, the number of values
in the sample that are less than or equal to up is distributed binomially. The probability
that the random interval (X^, X^y) will contain up is equivalent to the probability that
exactly i of the n elements of the sample will be less than up. Hence, this probability is
' (1 -Prl (8-38)
which is a simple binomial probability.
This expression can be calculated for each pair of consecutive order statistics X^,, X^, for
i=l, . .., n-1. However, it is more convenient to deal with these several intervals by
calculating cumulative probabilities of the form
(8-39)
For practical convenience, the normal approximation
F {[(i+0.5)-np]/V [np(l-p)]} (8-40)
can be used, where F represents the cdf of the standard normal distribution.
All of this is utilized for determining two order statistics, denoted below with subscripts i
and j, with the property
PriX,,, < up < Xg)} = 1 - a (8-41)
where 1-a is the predetermined confidence coefficient; typically, 1-cc = 0.95. Computation-
ally, i and j can be determined by solving the equations
8-16
-------
a/2 = F{[(i+0.5)-np]A/ [np ( 1-p) ]} (8-42)
and
l-a/2= F{[(j+0.5)-np]/\/ [np(l-p)]} (8-43)
This results in
i = (np-0.5) + V[np(l=p)Tp-1