United States
Environmental Protection
Agency
Office of
Research and Development
Washington, DC 20460
EPA/600/2-91/062
December 1991
oEPA
A Model of Virus
Transport in
Unsaturated Soil
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EPA/600/2-91/062
December 1991
A MODEL OF VIRUS TRANSPORT IN UNSATURATED SOIL
by
M.V. Yates
Department of Soil & Environmental Sciences
University of California
Riverside, CA 92521
S.R. Yates
USDA/ARS
U.S. Salinity Laboratory
Riverside, CA 92501
Y. Ouyang
Department of Soil & Environmental Sciences
University of California
Riverside, CA 92521
Interagency Agreement No. DW12933820
Project Officer
David M. Walters
Processes and Systems Research Division
Robert S. Kerr Environmental Research Laboratory
Ada, OK 74820
ROBERT S. KERR ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U. S. ENVIRONMENTAL PROTECTION AGENCY
ADA, OKLAHOMA 74820
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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 interagency agreement no. DW-
12933820 to the United States Department of Agriculture United States Salinity
Laboratory. It has been subjected to the Agency's peer and administrative
review, and it has been approved for publication as an EPA document. Mention of
trade names or commercial products does not constitute endorsement or
recommendation for use.
All research projects making conclusions or recommendations based on
environmentally related measurements and funded by the Environmental Protection
Agency are required to participate in the Agency Quality Assurance Program. This
project did not involve environmentally related measurements and did not involve
a Quality Assurance Project Plan.
ii
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FOREWORD
EPA is charged by Congress to protect the Nation's land, air, and water
systems. Under a mandate of national environmental laws focused on air and water
quality, solid waste management and control of toxic substances, pesticides,
noise, and radiation, the agency strives to formulate and implement actions which
lead to a compatible balance between human activities and the ability of natural
systems to support and nurture life.
The Robert S. Kerr Environmental Research Laboratory is the Agency's center
of expertise for investigation of the soil and subsurface environment. Personnel
at the Laboratory are responsible for management of research programs to: a)
determine the fate, transport, and transformation rates of pollutants in the
soil, the unsaturated zone, and the saturated zones of the subsurface
environment; b) define the processes to be used in characterizing the soil and
subsurface environment as a receptor of pollutants; c) develop techniques for
predicting the effect of pollutants on ground water, soil, and indigenous
organisms; d) define and demonstrate the applicability and limitations of using
natural processes, indigenous to the soil and subsurface environment, for the
protection of this resource.
The model described herein can be used to predict the fate and transport
of disease-causing viruses in unsaturated soil. It can be used to help
researchers design experiments so that important transport parameters are
measured accurately. It can also be used in conjunction with a saturated flow
model to help determine placement of waste sources relative to drinking water
wells to minimize the potential for waterborne viral disease.
Clinton W. Hall
Director
Robert S. Kerr Environmental
Research Laboratory
iii
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ABSTRACT
As a result of the recently-proposed mandatory ground-water disinfection
requirements to inactivate viruses in potable water supplies, there has been
increasing interest in virus fate and transport in the subsurface. Several
models have been developed to predict the fate of viruses in ground water, but
few include transport in the unsaturated zone, and all require a constant virus
inactivation rate. These are serious limitations in the models, as it has been
well documented that considerable virus removal occurs in the unsaturated zone,
and that the inactivation rate of viruses is dependent on environmental
conditions. The purpose of this research was to develop a predictive model of
virus fate and transport in unsaturated soils that allows the virus inactivation
rate to vary based on changes in soil temperature. The model was developed based
on the law of mass conservation of a contaminant in porous media and couples the
flow of water, viruses, and heat through the soil. Model predictions were
compared to measured data of virus transport in laboratory column studies, and
were within the 95% confidence limits of the measured concentrations. The model
should be a useful tool for anyone wishing to estimate the number of viruses
entering ground water after traveling through the soil from a contamination
source. In addition, model simulations were performed to identify variables that
have a large effect on the results. This information can be used to help design
experiments so that important variables are measured accurately.
iv
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TABLE OF CONTENTS
Page
Disclaimer ii
Foreword iii
Abstract iv
List of Figures vii
List of Tables ix
Introduction 1
Transport Processes 2
Factors Affecting Transport Processes 3
Soil Water Content 3
Soil Temperature 3
Water Application and Evaporation 4
Soil Heterogeneity 4
Objectives 4
Development of Transport Equations 4
Water and Heat Transport in the Soil 6
Virus Transport in Soil 10
Boundary Conditions 11
Boundary Between the Atmosphere and the Soil Profile .... 11
Water 11
Heat 14
Viruses 18
Boundary Between the Soil Profile and the Water Table ... 18
Solution of Transport Equations 20
VIRTUS: a Model of Virus Transport in Unsaturated Soil 26
Model Applications and Limitations 26
Verification of VIRTUS 26
Input Parameters 27
Results 28
Model Simulations 28
Simulation 1. Virus Transport Through Loam Soil With
Temperature-Dependent Inactivation Rate 28
Input Parameters 28
Results 36
Simulation 2. Virus Transport Through Loam Soil With
Constant Inactivation Rate 42
Input Parameters 42
Results 42
Simulation 3. Virus Transport Through a Loam Soil With
Inactivation Rate Dependent Upon Adsorption State .... 45
Input Parameters 46
Results 46
Simulation 4. Virus Transport Through an Unsaturated Sand . 46
Input Parameters 48
Results 48
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Page
Model Testing 48
Example 1. Virus Transport in a Saturated Gravelly
Sand Column 55
Input Parameters 55
Results 55
Example 2. Virus Transport in an Unsaturated Loamy Sand . . 55
Input Parameters 55
Results
Discussion .
Conclusions
References .
Appendix I:
Appendix II:
55
60
62
63
SOLVING THE VIRUS TRANSPORT EQUATIONS 66
: DEFINITIONS OF MATHEMATICAL SYMBOLS AND UNITS 67
Appendix III: VIRTUS USER MANUAL 71
Appendix IV: LISTING OF INPUT AND OUTPUT FILES 93
Appendix V: DISTRIBUTION OF SOFTWARE 137
vi
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LIST OF FIGURES
Figure Page
1 Schematic diagram of a soil profile for which the model
is developed 5
2 Gaussian Pill Box concept for water flow at the
atmosphere-soil interface 12
3 Gaussian Pill Box concept for heat flow at the
atmosphere-soil interface 15
4 Gaussian Pill Box concept for virus flow at the
atmosphere-soil interface 19
5 Comparison of analytical and numerical solutions of
virus transport equation at 5 hours 29
6 Comparison of analytical and numerical solutions of
virus transport equation at 10 hours 30
7 Virus concentration as a function of soil depth using
a temperature-dependent inactivation rate in an Indio
loam soil, simulation 1 37
8 Virus concentration as a function of time using
a temperature-dependent inactivation rate in an Indio
loam soil, simulation 1 38
9 Soil-water content as a function of time in an Indio
loam soil, simulation 1 39
10 Surface evaporation or condensation as a function of
time in an Indio loam soil, simulation 1 40
11 Soil temperature as a function of time in an Indio
loam soil, simulation 1 41
12a Differences in predicted virus concentrations using
a temperature—dependent (Cet) vs. constant (C10)
inactivation rate in an Indio loam soil, simulation 2a . . . 43
12b Differences in predicted virus concentrations using
a temperature-dependent (Cct) vs. constant (C2s)
inactivation rate in an Indio loam soil, simulation 2b . . . 44
13 Effect of assuming no inactivation of adsorbed viruses
(Cnu«) vs. a non-zero inactivation rate of adsorbed
viruses (C^,) on model predictions for an Indio loam
soil, simulation 3 47
vii
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LIST OF FIGURES
Figure Page
14 Virus concentration as a function of soil depth using
a temperature-dependent inactivation rate in a Rehovot
sand soil, simulation 4 52
15 Virus concentration as a function of time using
a temperature-dependent inactivation rate in a Rehovot
sand soil, simulation 4 53
16 Soil-water content as a function of time in a Rehovot
sand soil, simulation 4 54
17 Comparison of model predictions to experimental data,
Example 1 57
18 Comparison of model predictions to experimental data,
Example 2 59
viii
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LIST OF TABLES
Table Page
1. Equations for water, heat, and virus transport through
the soil 21
2. Boundary conditions at: (1) the interface between the
atmosphere and the soil surface; and (2) the water table. . 22
3. Parameters for the virus properties in simulation 1 .... 31
4. General input parameters for simulations 1, 2, and 3 .... 32
5. Values of the soil parameters used for the Indio loam
soil that remain constant throughout the simulation .... 33
6. Values of the soil parameters used for the Rehovot sand
that remain constant throughout the simulation 49
7. Parameters for the virus transport properties in the
simulation 51
8. Data used for model testing, example 1 56
9. Data used for model testing, example 2 58
ix
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INTRODUCTION
The significance of viruses as agents of ground-waterborne disease in the
United States has been well documented (Craun 1986, 1990). The increasing
interest in preventing ground-water contamination by viruses and other disease-
causing microorganisms has led to new U.S. Environmental Protection Agency
regulations regarding ground-water disinfection (U.S.EPA, 1991), the development
of wellhead protection zones, and stricter standards for the microbiological
quality of municipal sludge (U.S.EPA, 1989) and treated effluent (California
Department of Health Services, 1990) that is applied to land. For many of the
new regulations, a predictive model of virus (or bacterial) transport would be
helpful in the implementation process. For example, such a model could be used
to determine where septic tanks could be placed or where land application of
sludge or effluent could be practiced relative to drinking water wells to
minimize negative impacts on the ground-water quality. Another application of
microbial transport models is related to the ground-water disinfection rule
(U.S.EPA, 1991). Water utilities wishing to avoid ground-water disinfection may
use a pathogen transport model to demonstrate that adequate removal of viruses
in the source water occurs during transport to the wellhead.
Several models of microbial transport have been developed during the past
15 to 20 years (Grosser, 1984; Harvey and Garabedian, 1991; Matthess et al.,
1988; Park et al., 1990; Teutsch et al., 1991; Tim and Mostaghimi, 1991; Vilker
and Burge, 1980; Yates and Yates, 1989). The models range from the very simple,
requiring few input parameters, to the very complex, requiring numerous input
parameters. For many of the more complex models, the data required for input are
not available except for very limited environmental conditions. They may be
useful for research purposes, but would be impractical for widespread use. The
potential applications of these models also range considerably, from being useful
only for screening purposes on a regional scale, to predicting virus behavior at
one specific location.
One limitation of almost all of these models is that they have been
developed to describe virus transport in saturated soils (i.e., ground water).
However, it has been demonstrated many times that the potential for virus removal
is greater in the unsaturated zone than in the ground water (Keswick and Gerba,
1980; Lance and Gerba, 1984; Powelson et al., 1990). Neglecting the unsaturated
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zone In any model of virus transport could lead to inaccurately high predictions
of virus concentrations at the site of interest. This omission would be
especially significant in areas with thick unsaturated zones, such as those in
many western states. The one transport model (Tim and Mostaghimi, 1991) that has
reportedly been developed for predicting virus transport in variably saturated
media is not specific for viruses, but can be used for any contaminant. In
addition, It has not been tested using data of virus transport in unsaturated
soil.
Another, and more important, limitation of published models of virus
transport is that none of them has been validated using actual data of virus
transport in unsaturated soils. Most models are developed based on theory, and
are fitted to data obtained from one or two experiments. Rarely are they tested
by applying the model to data collected under a variety of conditions and then
determining how well the model predicts what has been observed in the laboratory
or field without any fitting or calibration of the model.
TRANSPORT PROCESSES
The transport of viruses through a porous medium such as soil is affected
primarily by the following mechanisms and processes:
1. Advection. The advection of viruses or any other contaminants in
water is due to the average velocity of water as it flows. It
results in the entire mass of contaminant streaming from a zone of
higher potential to one of lower potential.
2. Hydrodynamic dispersion. Hydrodynamic dispersion is the spreading
of a contaminant caused by mechanical dispersion and molecular
diffusion. Dispersion is the nonsteady irreversible mixing of two
miscible fluids displacing one another. Diffusion is a random
motion of molecules caused by thermal kinetics.
3. Adsorption (and desorption). The adsorption of viruses to soil
particles is caused by a combination of electrostatic and van der
Waals forces and hydrophobic interactions between the virus and soil
particles. Adsorption reduces the concentration of viruses in the
soil water. Desorption occurs due to changes in the ionic strength
of the soil water.
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4. Filtration. The physical filtration of viruses during the transport
process occurs primarily by straining and sedimentation. Straining
occurs when the particles in suspension in the porous matrix cannot
pass through a smaller pore, and thus their transport is halted.
For very small particles such as viruses, filtration is generally
neglected (Corapcioglu and Haridas, 1986). However, if the viruses
are adsorbed onto a solid particle entrained in the water or are
present as aggregates, filtration can be an important removal
process. Sedimentation of viruses in the soil pores occurs when the
density of virus particles is higher than that of water.
5. Inactivation. Virus inactivation is the loss of infectivity toward
host cells, and therefore ability to causes disease. The
inactivation of viruses is caused by a variety of adverse chemical,
biological, and physical processes.
FACTORS AFFECTING TRANSPORT PROCESSES
The transport of viruses through soil is controlled by climatic conditions
such as the rate of rainfall (or water application) and evaporation and by soil
properties such as soil water content, soil temperature, adsorption and
desorption, filtration, soil pH, and salt concentration (Yates and Yates, 1988).
The properties of the specific virus of interest are also important in
determining its behavior in the subsurface. Some of the most important factors
that affect the transport of viruses through soil research include soil water
content, soil temperature, the rate of water application and evaporation, and
soil heterogeneity.
Soil Water Content
The amount of water in the soil (soil water content) influences the
movement of viruses through soil. Lance and Gerba (1984) found that saturated
flow through loamy sand resulted in 7% recovery of poliovirus at a depth of 10
cm, but unsaturated flow resulted in only 0.5% recovery. Powelson et al. (1990)
found that MS-2 virus was removed to a much greater extent under unsaturated flow
conditions as compared to that during saturated flow conditions.
Soil Temperature
Soil temperature affects the length of time that viruses remain infective
in the environment. At lower temperature, virus persistence is prolonged
3
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compared with that at higher temperature (Yates and Yates, 1988). Soil
temperature also affects the transport of soil water, thereby indirectly
affecting the transport of viruses through soils.
Water Application and Evaporation
Addition of water (e.g., by rainfall or irrigation) to the soil acts to
move viruses through the soil profile. It can also act to desorb previously
adsorbed viruses, thus allowing them to be transported deeper through the soil.
The evaporation of water out of the soil surface causes the changes in the soil
water content and soil temperature, thereby affecting the transport and fate of
viruses.
Soil Heterogeneity
Soil is a heterogeneous system whose properties change with soil depth.
At different soil layers, soil properties such as soil porosity, hydraulic
conductivity, and thermal conductivity, are different. Therefore, the transport
of viruses through soil, which is subjected to the soil properties, will change
with soil depth.
OBJECTIVES
The purpose of this research was to develop a model that can be used to
predict virus movement from a contamination source through unsaturated soil to
the ground water. Several model simulations were performed to -determine the
effects of different input variables on model predictions. The model was tested
by comparing model predictions to results of laboratory studies.
The specific objectives of this project were:
1. To develop a mathematical model to describe the transport of viruses
in unsaturated soil that includes factors specific to viruses, and
2. To test model predictions with experimental data of virus transport
in soil.
DEVELOPMENT OF TRANSPORT EQUATIONS
Transport equations were derived to describe the simultaneous transport of
water, viruses, and heat for a soil profile shown schematically in Figure 1. The
soil profile, which may contain soil with nonhomogeneous properties, is bound
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SOLAR RADIATION
! 1 1
RAINFALL
1 1
I* C'
BOUNDARY LAYER
(2.: ) T ( r. t ) C, i z. t )
TYPICAL SOIL LAYER
WATER TABLE
(ATMOSPHERE)
(SOIL SLAB)
£7
- Z
z = z
N
Figure 1. Schematic diagram of a soil profile for which the model
is developed
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below by a water table and above by the atmosphere.
The assumptions used in the development of transport equations pertaining to
the atmosphere are:
1. Diurnal changes in air temperature and relative humidity can be
characterized by a Fourier series;
2. Diurnal changes in solar intensity can be characterized by a
Gaussian normal distribution function;
3. The initial distributions of water and temperature in the atmosphere
are known;
A. The rate and duration of water application is prescribed.
The assumptions used in the development of transport equations pertaining
to the soil profile are:
1. The soil can be characterized by known parameters such as: the soil
porosity; the specific heats of solid, water, and air; the thermal
conductivities of solid, water, and air; the latent heat of
vaporization; the water potential function; the hydraulic
conductivity function; and the densities of solid, water, air, and
water vapor;
2. The atmosphere and soil surface are coupled for the water, virus,
and heat fields by heat and mass transport rules operating in the
boundary layer at the atmosphere-soil interface; and
3. The initial distributions of water content, temperature, and viruses
in the soil profile are prescribed.
WATER AND HEAT TRANSPORT IN THE SOIL
Water and heat transport equations derived by Ouyang (1990) are given as:
= -v [Pre V> + Pw (e-6)
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for water transport, and:
-A [ (i-e) Cfolid pgolid T + (e-6) c^r f>Mir T + 6 c
- -v • [ (i-e) if,. + 6 Htl + (e-6) H,v ] (2)
for heat transport, where t is the time (hr). pw is the density of water (g
cnf3), 6 is the volumetric water content (cm3 cm"3), ffi (T) is the density of
water vapor at saturation at temperature T (g vapor cm"3 air), h is the relative
humidity (dimensionless), c is the soil porosity (cm3 soil voids cm"3 soil)
^i and Vv are the velocity vectors of water in the liquid and vapor phases (cm
hr"1) , respectively, pm is the density of water vapor (g vapor cm"3 air). cBoLid
is the specific heat of soil particles (cal soil"1 particle "C"1) , ptoud *-s tne
density of soil particles (g cm~3 solids), T is the temperature (°C) , cair and cw
are specific heats of air and water (cal g"1 "C"1) , respectively, pair is the
density of air (g cm~3air) , H*,, is the vector of heat conduction through the soil
particles (cal cm"2 hr"1) . flsl is the vector of heat conduction and convection in
the liquid phase (cal cm"2 hr"1) , and tfsv is the vector of heat conduction in the
vapor phase and the latent heat flux (cal cm"2 hr"1) .
The velocity vectors, VL and Vv, in equation (1) are defined as:
Vj = - V"6 - $r/vr + *• (* - |f) - (3)
and
with
(6)
-------
(7)
tare [<-=
. (9)
where Dei Is the second rank tensor describing the diffusion coefficient of
water in the liquid phase (cm2 hr"1) . DT1 is the second tensor describing the
thermal diffusivity in the liquid phase (cn^hr"1) , K is the second rank tensor
describing the water conductivity (cm hr"1) , z~*is the unit vector normal to plane
z — 0 with positive orientation vertically downward, z is the soil depth (cm).
V1 is the water potential (cm), D^ is the second rank tensor describing the
diffusion coefficient of water in the vapor phase (cm2 hr"1) , Djy is the second
rank tensor describing the thermal diffusivity in the vapor phase (cm2 hr"1) ,
Uj is the second rank tensor describing the diffusion coefficient of water
affected by the water potential (cm2 hr"1) , Datm is the water vapor molecular
diffusion coefficient in air (cm2 hr"1) , atort is the tortuosity factor of the
soil, g is the gravitational constant (cm hr"1), R is the gas constant (cnf2 hr"2
++ sat
°C~1), E is the second rank identity tensor (dimensionless), and pm is the
density of water vapor at saturation (g vapor cm"3 air).
The vectors flss, "kgl, and flgv in equation (2) are defined as:
**
,* m ~ , olid *r ' (10)
Htl - - A.r vr+ C, prvj r
-------
and
**.y - - lDttm«toZt*Prv - X^r vT , (12)
where A.olid is the thermal conductivity of the solids (cal cm"1 hr"1 "C"1) , AM is
the thermal conductivity of water (cal cm"1 hr"1 "(T1), £ i-s tne latent heat of
evaporation (cal g"1), and Aair is the thermal conductivity of the air (cal cm"1
hr'1 "C"1).
The variables p^f, p^, h, and ^ in equations (1) and (12). which are
functions of temperature, are given as (Weast, 1986):
p"' = 0.004928 + 0. 0002581 T + 0.0000183T2 (13)
for 0 < T < 22.5°C, and
pJt' = 0.00493 + 0.000258T + 0.0000396T2 (14)
for 1 > 22.5°C,
(15)
and
(17)
= 598.88 - 0.547T .
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VIRUS TRANSPORT IN SOIL
According to the law of conservation of mass, the virus transport equation
in differential form can be expressed as:
_|j[PJ, c,. ec, j .-£I8B4| j
- I », c, . tt t.c. ] - Ofc, . <1S)
where t is the time (hr) . pb is the bulk density of soil (g cm"3 soil) , C, is the
concentration of viruses adsorbed onto the soil particles (mass g"1 solid), 8 is
the volumetric soil water content (cm3 cm"3), Cx is the concentration of viruses
in soil water (mass cm"3 water), z is the soil depth (cm) , D is the coefficient
of hydrodynamic dispersion of viruses (cm2 hr"1) , V is the flow velocity of water
(cm hr"1) , /*! and nt are the inactivation coefficients of viruses in liquid and
solid phases (hr"1) , respectively, and f is the filtration coefficient of viruses
(hr"1).
The adsorption of viruses onto soil particles, Cg, in equation (18) can be
expressed by using the Freundlich adsorption isotherm (Grosser, 1984; Corapcioglu
and Haridas, 1986):
C. = Kd Of , (19)
where Cs is the concentration of viruses adsorbed onto the soil particles (mass
g"1 solid) , Kj is the Freundlich constant (cm3 water g"1 solid) , n is the
exponential constant (dimensionless), and C± is the concentration of viruses in
the soil water (mass cm"3 water). For many systems, the empirical constant n is
not significantly different from unity and equation (19) reduces to a linear form
(Vilker and Burge, 1980; Yates and Yates, 1988):
(20)
10
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BOUNDARY CONDITIONS
Equations (1), (2), and (18) define the coupled transport of water, heat,
and virus, respectively. Boundary conditions must be defined to be able to solve
these equations.
Boundary Between the Atmosphere and the Soil Profile
Water
By using the "Gaussian Pill Box" concept (Figure 2) , the conservation of
mass law requires that:
3 - -z) - 0 , (21)
where qw is a vector describing the total water flux at the soil surface (g water
cm"2 hr"1) , n is the unit vector outward going normal to the simple closed
surface, z is the unit vector normal to plane z - 0 with positive orientation
vertically downward, q*rain is a vector describing rainwater flux into the soil (g
water cm""2 hr"1) , and q^vap is a vector describing evaporation flux or condensation
flux of water out of, or into, the soil (g water cm"2 hr"1) .
The total water flux vector q^, at the soil surface (z - 0) can be defined
as :
*» l..o - [8oPw?z + PvX] |,.0 , (22)
-*
the rainwater flux vector qrain is written as:
(23)
and the evaporation or condensation flux vector q.vap is given as:
11
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evao
'ram
n = - z
ATMOSPHERE
SOIL
t
iw
n = + z
Figure 2. Gaussian Pill Box concept for water flow at the
atmosphere-soil interface
12
-------
(T \ T -T
t ^t' Q / •*cj*«
* P-'^.x)] , (24)
where B0 is the water content at the atmosphere-soil interface (cm3 cm"3) , pv is
the density of water (g cm"3) , ^ is the velocity vector of liquid water (cm hr~
*) . c0 is the soil porosity at the atmosphere-soil interface (cm3 soil voids cm"3
soil) , pm is the density of water vapor (g cm"3) . V^ is the velocity vector of
water vapor (cm hr"1) , i^in is the vector describing the rainfall rate (cm hr"1) ,
*
D.tni is the the boundary layer wind-speed-dependent coefficient of dispersion of
water vapor (cm2 hr"1) , p"fc (Ta) is the density of water vapor at saturation at
temperature T. (g vapor cm"3) , T» is the temperature in the atmosphere (°C), 66
is the relative humidity in the atmosphere (dimensionless), T0 is the temperature
at the atmosphere-soil interface (°C) , 6z is the thickness of the boundary layer
at the atmosphere-soil interface (cm), and h is the relative humidity at the
atmosphere-soil interface (dimensionless).
Substituting equations (22), (23) and (24) into equation (21) yields:
n
. . (25)
Recall that equations (3) and (4) are written as:
(z-
Vv = -
13
-------
and n - z, substituting tfL and Vv into equation (25) leads to:
r.0
Krv ' "' *z ' ' (26)
which is the coupling upper boundary condition for water transport.
Heat
Analogous to the movement of water, again using the Gaussian Pill Box
concept (Figure 3), conservation of heat requires that:
+ qh»(n - z) = 0 , (27)
where qheatin is a vector describing heat flux into the soil surface via
rainwater (cal cm"2 hr"1), qhteVp is a vector describing heat flux out of
the soil surface due to evaporation or heat flux into the soil surface due to
condensation (cal cm"2 hr"1), qhtiwr is a vector describing heat flux into the
soil surface by short wave radiation (cal cm"1 hr"1) , qht§»i *s a vector describing
14
-------
heann
I bAMU^
IIIArr
htev
n = -
n = + 2
q q
^ htssi httwrs
htNvra
ATMOSPHERE
z = 0
SOIL
Hs
Figure 3. Gaussian Pill Box concept for heat flow at the
atmosphere-soil interface
15
-------
heat flux through the soil surface via sensible heat (cal cm"2 hr"1) ,
a vector describing heat flux into the soil surface via long wave radiation
(cal cm'2 hr"1) , qttiwr* *s a vector describing heat flux out of the soil
surface via long wave radiation (cal cm"2 hr"1) , and qj, is a vector describing
total heat flux into, or out of, the soil surface (cal cm"2 hr"1) .
The vectors in equation (27) are defined by (Lindstrom and Piver, 1985):
(28)
(29)
(e0-60)
T -T
1* / o • \
- *«*r( &z ) , (31)
[0.605 + 0.048] . (32)
- 60)] , (33)
+ «0 - 0,V , (34)
with
(35)
16
-------
(36)
Definitions of variables in equations (28) through (36) are in Appendix II.
Substituting equations (28) through (36) into equation (27) with subsequent
combination of variables leads to:
[(1 -
dT,
[(1 -ej (1 -
+ 60(1 -aMt.J
(e0-60)(l -
[0.605 * 0.048/e7n]
(37)
17
-------
which is the coupling upper boundary conditions for heat transport.
Viruses
Analogous to the transport of water and heat, and again using the Gaussian
Pill Box concept (Figure 4), the conservation of virus mass requires that:
qv»(n* z) + Gziijtf* -f) • 0 , (38)
where qv is a vector describing virus flux into the soil surface (mass cm'2 hr'1)
and qrain is a vector describing virus flux through the soil surface by
infiltration (mass cm'2 hr'1) .
The vectors in equation (38) are defined as:
(39)
and
Grain = C«n $r«in • (40)
where Cwin is the concentration of virus in water entering the soil (mass
cm'1 water) .
Substitution of equations (39) and (40) into equation (38) yields:
which is the coupling upper boundary condition for virus transport.
Boundary Between the Soil Profile and the Water Table
The boundary conditions at the interface between the soil profile and the
fixed elevation water table for water and heat transport are assumed to be
constant. These are:
(42)
Q(ZW, t) - e,,
and
18
-------
ATMOSPHERE
SOIL
'ran
t
n = - z
Z= 0
n- 4 2
Figure 4. Gaussian Pill Box concept for virus flow at the
atmosphere-soil interface
19
-------
, t) - Tg , (43)
where z, is the soil depth at the interface between the soil slab and the water
table (cm) , 6t is the saturated soil water content (cm3 cm"3) . and Tg is the
temperature at water table (°C) .
The boundary condition for the virus field at the interface between the
soil slab and the water table is not fixed. This boundary condition does not
occur except for short periods of time, insufficient for the viruses to be
transported from the top or from a buried source position to the water table.
The more realistic boundary condition is obtained by applying the Gaussian Pill
Box concept to virus transport at the interface between the soil and the water
table and is given as (Lindstrom et al., 1990):
r (* f\ - ' o * *' »" » /' + i
C2(zv, t) = ( —*- t- — )/(T*T~ + TT' '
AZ, AZHf *ZN* *Z.
where C].(zw, t) is the concentration of virus at the interface between the soil
profile and the water table at time t (mass cm*3 water) , Cg is the concentration
of virus in the ground water (mass cm*3 water). zw is the soil depth at the
interface between the soil and the water table (cm). and AzNz and Az* are the
depth intervals above and below the interface between the soil profile and the
water table, respectively (cm).
The water, heat, and virus transport equations and their boundary
conditions, discussed above, are summarized in Tables 1 and 2.
SOLUTION OF TRANSPORT EQUATIONS
Since the solution of the virus transport equation (18) requires a point-
wise knowledge of water and heat distributions in space and time, the water and
heat transport equations (1) and (2) must be solved prior to solving the virus
transport equation. The three transport equations were solved using the finite
difference method. Solution of the water and heat transport equations were
discussed and given in Ouyang (1990). Solution of the virus transport equation
is discussed below.
20
-------
Table 1. Equations for water, heat, and virus transport through the soil.
Water
(e-6) ] - -* • tpr e v, + Pw
Heat
T * (e-6) c.lr p.ir T * 6
6 Htl + (e-6) H.v
c.
21
-------
Table 2. Boundary conditions at: (1) the interface between the atmosphere and
the soil surface; and (2) the water table.
Interface Between the Atmosphere and the Soil Surface
Water
<-Jf )
- -fj) U
Tj +
-------
Table 2. Boundary conditions at: (1) the interface between the atmosphere and
the soil surface; and (2) the water table (continued).
(e0-00)(l -«^r)]g«T
eo + e-ir(e0 - 80)]
|[0.605 * 0.
Virus
Interface Between the Soil Profile and the Water Table
Water
e(*w, t) - e.
Heat
T(zw, t) - Tg
Virus
23
-------
Before approximating equation (18), define:
, (45)
and
A « 6jij Ca + pb M.C.
Putting equations (45) and (46) into equation (18) yields:
[P» C. + Be, ] -•£[«) -A. (47)
Following Varga's (1962) method of approximation, integration of both sides
of equation (47) over the rectangular subregion of space and time [ (Zi-iiz,
zi+1/2) x (tj,, t^) ] yields:
"
tp^c.+ecj tdz
- / / [A]dzdt. (48)
Applying the finite difference formulations in Appendix I, substituting
equations (45) and (46) into equation (48), and defining C, - Kj C1( obtains:
i.i/2
24
-------
Qf J^c/;1} . (49)
Multiplying both sides of equation (49) by 2/(&zi + Azi+1/2) and
rearranging terms into common coefficients yields:
rial?:?/, + /,
J
me,-/
j-. (50)
which is a useful form for setting up the computer program.
25
-------
VIRTUS: A MODEL OF VIRUS TRANSPORT IN UNSATURATED SOIL
The mathematical model developed herein was entitled VIRTUS (VJRus
Jransport in Jlnsaturated £oil) , and programmed in FORTRAN for use on IBM and IBM-
compatible PC's. A document describing the use of the program is contained in
Appendix III. Sample input and output data that can be used to test the model
are listed in Appendix IV. In this section, the mathematical model and
corresponding computer program, VIRTUS, will be demonstrated in a variety of
situations. The potential applications of this model and its limitations will
also be discussed.
MODEL APPLICATIONS AND LIMITATIONS
Some of the features of this model include its ability to simulate:
1. unsteady flow in variably-saturated media
2. transport in layered soils
3. variable virus inactivation rate (e.g., function of temperature)
A. different virus inactivation rates for adsorbed versus freely
suspended virus particles.
5. the flow of heat through soil (which affects water flow, virus
inactivation rate, etc.)
As the model was programmed, the viruses are applied to the soil surface. This
occurs when treated sewage effluent is used for irrigation purposes, where ground
water is recharged with effluent, and when sewage effluent is discharged to dry
stream beds (such as occurs in the southwest). If viruses are applied to the
soil from a buried source, such as a septic tank, the model may still be applied;
however, the boundary conditions in the program must be adjusted. VIRTUS also
assumes that there is a water table at the bottom of the soil profile, if there
Is not, the appropriate boundary conditions must be introduced.
VERIFICATION OF VIRTUS
The numerical solution of the virus transport equations was verified using
an analytical solution to the equations. The virus transport equation and
initial and boundary conditions used were:
IP* C. * 6Cj ] * -^ ( 6D-£ ]
(51)
- [ 6ti; Cj + pb \i,c, ] -
26
-------
Cj(z, 0) « 0 , (52)
C,(0. t) - Cc , (53)
and
Cj(«, t) - o . (54)
The analytical solution of equations (51), (52), (53), and (54) is:
(z t) m C°
jU, t) - _
6V-Z
' ^ ^
Equations (51). (52), and (53) were also solved using VIRTUS by a numerical
method (with C1(z1,t) - 0 at the lower boundary z - zx).
Input Parameters
Input parameters for the simulation were as follows:
1. Hydrodynamic dispersion coefficient: Dx - 4 cm2 hr"1;
2. Saturated soil water content: 0, - 0.3 cm3 cm"3;
3. Freundlich constant: K,, - -0.02 ml g"1 soil;
4. Inactivation coefficient: px - 0.001 hr'1;
5. Average linear flow velocity of water: vi - 0.1 cm hr"1;
6. Initial virus concentration: C0 - 105 PFU ml"1;
27
-------
7. Bulk density: pb - 1.65 g cm"3; and
8. Soil depth: z - 100 cm.
Results
Comparisons of predictions made using the analytical solution versus the
numerical solution of the virus transport equation are in Figures 5 and 6. These
figures show the relative virus concentration as a function of soil depth at
times of 5 and 10 hours. Good agreement was obtained between the analytical and
numerical solutions as shown in the Figures.
MODEL SIMULATIONS
The capabilities of VIRTUS to simulate the simultaneous transport of water,
viruses, and heat are demonstrated using data for two different soil types.
Several simulations were performed to show the effects different variables on
model predictions.
Simulation 1. Virus Transport Through Loam Soil With Temperature -Dependent
Inactivation Rate.
This simulation calculated virus concentration profiles during transport
through an unsaturated loam soil. The rate of virus inactivation changed as a
function of soil temperature throughout the course of the transport process .
Viruses adsorbed to soil particles were assumed to have an inactivation rate of
zero.
Input Parameters
The specific values of the variables related to virus fate and transport
are shown in Table 3. The values were chosen from published data of virus
transport obtained from experiments conducted under conditions similar to those
used in the simulation.
General input values for the simulation are shown in Table 4. The physical
properties of the Indio loam soil are listed in Table 5. Parameters that varied
as a function of time included air temperature, relative humidity of the air
above the soil surface, and solar radiation. These variables were represented
by the functions described below. These functions are only approximations of the
'daily changes measured in nature.
The daily course of air temperature can be characterized by a Fourier
series (Ouyang, 1990):
. (56)
28
-------
(J
Q_
0)
Q
O
00
0
20
40
60
80
100
0.2
C/Co
0.4 0.6
0.8
Numerical Solution
—» Analytical Solution
Figure 5. Comparison of analytical and numerical solutions of
virus transport equation at 5 hours
29
-------
C/Co
0.2
0.4
0.6
0.8
£
o
Q_
CD
O
O
00
20
40
60
80
100
Numerical Solution
— > Analytical Solution
Figure 6. Comparison of analytical and numerical solutions of
virus transport equation at 10 hours
30
-------
Table 3. Parameters for the virus properties in simulation 1.
Parameters
Values/Units
References
Dispersion
coefficient
Distribution
coefficient
Filtration
coefficient
Inactivation*
coefficient
in liquid phase
Inactivation
coefficient
in solid phase
- OtortDlo + Qdiip I VI
- 0.66 x 0.000324 +
10 I VI cm2 hr'1
- 0.27 ml g'1 soil
f - 0.0 cm'1
[(-0.181 + 0.0214 T)
LnlO]/24 hr'1
/*. - 0
Grosser, 1984,
Bales et al., 1989
Lindstrom et al., 1990
Powelson et al. , 1990
Yates and Yates, 1988
* T is soil temperature (°C).
31
-------
Table 4. General input parameters for simulations 1, 2, and 3.
Parameters
Values
Units
Simulation time
Simulation time
step
Simulation soil depth
Simulation depth
step
Surface infiltration
rate
Surface infiltration
duration*
Initial soil water
content
Initial soil
temperature
Initial soil virus
concentration
Virus concentration
in the surface
infiltration water
Initial virus
concentration in
ground water
Virus type
Soil type
120
0.025
100
1.0
0.1
0.25
8.7
0.0
105
0.0
MS-2 bacteriophage
Indio loam soil
hrs
hr
cm
cm
cm hr"1
hrs
cm3 cm"3
PFU ml"1
PFU ml
-i
PFU ml
-i
*Surface infiltration started at 0th hour and ended at 6th hour in the morning
of the first day.
32
-------
Table 5. Values of the soil parameters used for the Indio loam soil that
remain constant throughout the simulations 1, 2, and 3.
Symbol
a.ir
Q«oil
°tort.
«~t.r
"<
fit
c.ir
cel«y
c««nd
c«ilt
c..,..
£
£
Meaning
Albedo of air
Albedo of soil
Tortuosity factor
Albedo of water
Coefficient in
equation (59)
Coefficient in
equation (59)
Specific heat
of air
Specific heat
of clay
Specific heat
of sand
Specific heat
of silt
Specific heat
of water
Total porosity
Emissivity of air
Value /Units
0.05
0.09
0.66
0.07
1241.39
cm
0.7079
0.24 cal g"1
oc-i
0.175 cal g'1
oc-i
0.175 cal g-1
oc-i
0.175 cal g-1
oc-i
1.0 cal g-1
oc-i
0.55
0.9
Reference
Weast, 1986
Ghildyal and Tripathi, 1987
Hillel, 1982
Weast, 1986
Ouyang, 1990
Ouyang, 1990
Weast, 1986
Ghildyal and Tripathi,
1987
Ghildyal and Tripathi,
1987
Ghildyal and Tripathi,
1987
Weast, 1986
McCoy, et al . , 1984
Weast, 1986
above the soil
«.oll Emissivity of 0.5
coil surface
Emissivity of 0.95
water
Saturated 0.61
conductivity in cm hr"1
equation (60)
pmil Density of air 0.0011 g cm
-3
Ghildyal and Tripathi,
1987
Weast, 1986
Ouyang, 1990
Weast, 1986
33
-------
Table 5. Values of the soil parameters used for the Indio loam soil that
remain constant throughout the simulations 1, 2, and 3.
Symbol Meaning
Value/Units
Reference
f>b
Pcifj
Bulk Density of 1.2 g cm
soil
'3
P.ilt
7C
•olid
air
Density of clay
Density of sand
Density of silt
Density of water
Coefficient in
equation (60)
Thermal
conductivity
of solids
Thermal
conductivity
of water
Thermal
conductivity
of air
Residual soil
water content cm
Saturated soil
water content cm
2.64 g cm'3
2.66 g cm'3
2.65 g cm'3
1.00 g cm'3
6.5
18.9 cal
cm -1 hr'1
5.14 cal
cm'1 hr'1
0.2214 cal
cm'1 hr'1
0.029 cm3
'3
0.55 cm3
'3
McCoy, et al., 1984
Ghildyal and Tripathi, 1987
Ghildyal and Tripathi, 1987
Ghildyal and Tripathi, 1987
Veast, 1986
Ouyang, 1990
Ghildyal and Tripathi,
1987
Ghildyal and Tripathi,
1987
Ghildyal and Tripathi,
1987
Ouyang, 1990
Ouyang, 1990
34
-------
where T,lr(t) is the air temperature (°C) at time t, T is the mean air temperature
(°C) , N is the number of the Fourier frequency, A^^Cn) and Bt-np(n) are the
temperature coefficients, u^ is the n** temperature Fourier frequency, and t is
time (hr).
The relative humidity in the atmosphere can be characterized by a Fourier
series (Ouyang, 1990) :
RH^z(t) - RH + Y^.1 [Azb(n) COB (w^t) +5^(23) sin (to^t)] , (57)
where RHmlt (t) is the relative humidity (dimensionless) at time t,~RH is the
mean relative humidity (dimensionless), N is the number of the Fourier frequency,
Arh(n) and Brh(n) are the relative humidity coefficients, u^ is the nth relative
humidity Fourier frequency, and t is time (hr) .
The Gaussian normal distribution function of the form (Ouyang, 1990):
QSR(t) * ^expt-0.5 * ] . (58)
**i
was used to describe rate of solar radiation as a function of time of day, where
QSR(t) is the intensity of solar radiation (cal cm'2 hr"1) at time t; E:, E2, and
£3 are coefficients of the equation, and t is time.
The power law function proposed by van Genuchten (1980) was used to
describe the soil water potential as a function of water content:
(59)
where ^ is the water potential (cm), ae is a coefficient characterizing a
specific soil (cm), 0e *s a coefficient characterizing a specific soil
(dimensionless) , 6n is the saturated volumetric soil water content (cm3 cm"3), and
6X is the residual volumetric soil water content (cm3 cm"3). Values of constant
coefficients in equation (59) for the Indio loam soil are in Table 5.
35
-------
The Kozeny function
, e - e.
proposed by Mualem (1976) was used to describe hydraulic conductivity as a
function of soil water content. K is the hydraulic conductivity (cm hr"1), K,
is the hydraulic conductivity at saturation (cm hr"1), 6 is the volumetric soil
water content (cm3 cm"3), 6X is the residual volumetric soil water content at air
dry conditions (cm3 cm"3), 0. is the saturated volumetric soil water content (cm3
cm"3), and 7e is a coefficient characteristic for a specific soil. Values of
constant coefficients in equation (60) for the Indio loam soil are in Table 5.
Results
The virus concentration profiles predicted during the simulation are shown
in Figures 7 and 8. The concentration of viruses in the top few cm of soil
changed rapidly from an initial value of zero to more than 5 x 10* PFU/ml during
the 6 hours of infiltration (Figure 7). Figure 8 shows the change in virus
concentration with time at two soil depths. It can be seen that as the
concentration of viruses begins to decrease at the 5-cm depth after 48 h (as a
result of advection, adsorption, and inactivation). the concentration at 10 cm
begins to increase as a result of transport through the soil.
Changes in soil water content during 48 hours simulation are shown in
Figure 9. This simulation started with a water application period from 0 to 6
hours at a rate of 0.1 cm hr"1. The application rate was lower than the
infiltration capacity of the soil, so that the infiltration profiles at 6 hours
did not show the constant water content of a transmission zone followed by a
rapid decrease in water content in the wetting zone or wetting front. Following
the 6 hours of water application was a period of change in the water content of
the soil profile, due to evaporation (Figure 10) at the soil surface and further
penetration of the water into the soil due to a water potential gradient at the
wetting front.
Daily cycles of soil temperature at several depths are shown in Figure 11.
This figure shows that the temperature at the soil surface was close to the
temperature of the applied water (4 °C). This water, which completely wetted the
soil surface, decreased the temperature of the soil surface layer to the
temperature of water at about 6 hours. As soon as water application stopped at
36
-------
E
(J
CL
-------
-------
E
U
CL
(D
Q
O
Ul
Soil Water Content (cm3/cm~3 )
0.24 0.26 0.28 0.3 0.32
20
40
60
80
100
i X D
1 ^ 1
« x D
I \ I
T x ^"^"^
9 o'x D
T/ 1 /
-a
a
0
Ox
Ox
DX
1 /
IX
K
K
1
t
t
I
o-^"^"
^
ff.^^^"^^
^ — """^
*— o t = 0 hrs
e>— e> t = 6 hrs
D— a t = 24 hrs
x— x t = 48 hrs
Figure 9. Soil-water content as a function of time in an Indio
loan soil, simulation 1
39
-------
-0.02
Si
\
E
E
C
,2
03
6
CL
ro
L^J
CD
U
if} O
o
_g
03
en
c
CD
-0.011-
0.01
0
12
36
48
Time (hrs)
Figure 10. Surface evaporation or condensation as a function of
time in an Indio loam soil, simulation 1
40
-------
12
24
36
48
Time (h)
Figure 11. Soil temperature as a function of time in an Indio
loam soil, simulation 1
-------
6 hours, radiation started to warm the soil profile. The changes in soil
temperature during the period from 6 to 48 hours showed the characteristic
temperature cycle, with a decreasing temperature during the night followed by
warming during the day.
Simulation 2. Virus Transport Through Loam Soil With Constant Inactivation Rate.
Most models of contaminant transport consider the movement of water and the
transport of the contaminant in their development, and assume that the thermal
conditions in the soil remain constant. In reality, under field conditions, this
is not generally the case. Temperature fluctuations in soil can be considerable
throughout the course of a 24-hour period, especially near the soil surface.
Because the effects of temperature on virus inactivation rates in the environment
can be quite significant, it seems logical to use a model of contaminant
transport that also models heat flow.
This simulation demonstrates the effects of holding the inactivation rate
of the viruses constant at a) 0.033 Iog10 per day, which would be expected at a
soil temperature of 10 C; and b) 0.354 Iog10 per day, which would be expected at
a soil temperature of 25 C.
Input Parameters
The input parameters used for this simulation were the same as for
Simulation 1 and are shown in Tables 3, 4 and 5. The only exception is that the
virus inactivation rate was 0.033 for Simulation 2a and 0.354 for Simulation 2b,
rather than calculated as a function of temperature as shown in Table 3.
Results
The effects of allowing the virus inactivation rate to vary as a function
of soil temperature as compared to holding it constant are graphically shown in
Figures 12a and 12b. In the case where the virus inactivation rate was held
constant at 0.033 Iog10 day'1 (10 C), the model predicted higher concentrations
of viruses than would be predicted if the inactivation rate was allowed to vary
as a function of temperature (Figure 12a). The opposite predictions were
obtained in the case of a constant inactivation rate of 0.354 Iog10 day"1 (25 C)
'as shown in Figure 12b. Considering the inactivation rate to be a constant at
25 C resulted in an underprediction in the concentration of viruses as compared
with the temperature-dependent inactivation rate.
The reasons for these predictions become apparent upon observation of the
predicted change in soil temperature that occurs as applied water is infiltrated
42
-------
- C10 (PFU/ml)
-12000 -9000 -6000 -3000
0
t = 24 h
t = 72 h
t = 120 h
Figure 12a. Differences in predicted virus concentrations using
a temperature-dependent (Cet) vs. constant (C10)
inactivation rate in an Indio loam soil, simulation 2a
43
-------
CCT - C25 (PFU/ml)
2000 4000 6000 8000
30
t = 24 h
x—x t = 72 h
o-a t = 120 h
Figure 12b. Differences in predicted virus concentrations using
a temperature-dependent (Cct) vs. constant (C25)
inactivation rate in an Indio loam soil, simulation 2b
44
-------
through the soil column (Figure 11). At the soil surface, over a 24-hour period,
the soil temperature (which started at 8.7 C) decreased to 3 C at 6 h during the
addition of cold water and increased to 35 C at 12 h due to the effects of solar
radiation. Similar patterns would be expected at the 5- and 10-cm depths,
although the magnitude of the variation would not be as large. In Simulation 2a,
the virus inactivation rate was held constant at a value that would be expected
for constant 10 C soil conditions. The fact that the soil temperature rose above
10 C for more than 12 hours in a 24-hour period resulted in a prediction of virus
inactivation at relatively high rates (compared to the rate at a constant
temperature of 10 C) for that period. Overall, maintaining the inactivation rate
at a constant value had the effect of increasing the predicted concentration of
viruses that were transported through the soil column by more than 4 orders of
magnitude (Figure 12a).
In Simulation 2b, the soil temperature was considered to be constant at 25
C; consequently the virus inactivation was maintained at a relatively high rate
throughout the transport process. In actuality, the soil temperature was at or
above 25 C for a relatively short period of time (less than 6 hours), so viruses
were inactivated at or above that high rate for only six hours in the simulation
where the rate was temperature dependent. In this case (Figure 12b), assuming
a constant inactivation rate would lead to a prediction that thousands of viruses
fewer than the actual number (assuming that the variable inactivation rate
simulation predicts the actual number) would be transported through the column.
The sensitivity of model predictions to changes in the temperature-
dependent inactivation rate was determined by changing the inactivation rate
while keeping all other variables constant. This sensitivity analysis showed
that changing the value of the inactivation rate by 50% resulted in a 33% change
in the predicted concentration of viruses being transported through the soil.
A high sensitivity of model predictions to the virus inactivation rate has also
been observed by Tim and Mostaghimi (1991) and Park, et al. (1990). These
results demonstrate the need to accurately monitor virus inactivation and/or
temperature during experiments of virus transport in the subsurface.
Simulation 3. Virus Transport Through a Loam Soil With Inactivation Rate
Pependent Upon Adsorption State.
There have been reports in the literature of differences in measured rates
of virus inactivation for viruses that are adsorbed to soil particles as compared
45
-------
to viruses that are freely suspended In the liquid medium (Hurst et al., 1980;
Sobsey et al., 1980; Vaughn and Landry, 1983). Therefore, this model was
developed to allow the user to input different values for inactivation rates for
viruses in these two states. When a value for the inactivation rate of adsorbed
viruses is specified, the model calculates the number of viruses adsorbed at a
given time based on the adsorption coefficient specified by the user, and
determines the number inactivated accordingly.
Input Parameters
It is difficult to obtain a quantitative value for the relative difference
In inactivation rates for adsorbed as compared to freely suspended viruses. For
the purposes of illustration, this simulation used an inactivation rate for
adsorbed viruses equal to one-half that of free viruses. Inactivation rates for
viruses in the adsorbed and free state were allowed to change as a function of
the soil temperature. All other input values are as shown in Tables 3, 4, and
5.
Results
The model predictions made in Simulation 3 were compared to those of
Simulation 1, in which the inactivation rate for adsorbed viruses was zero
(Figure 13). As one would expect, the concentration of viruses transported
through the soil column is larger when the solid-phase inactivation rate is zero
than when it is one-half the liquid-phase rate. The difference increases with
time, as shown in Figure 13. In a system in which the inactivation rate of
adsorbed viruses is equal to that of free viruses, the differences would be even
greater.
This example demonstrates the importance of knowing the inactivation rate
for viruses in the adsorbed as well as in the liquid phase. If the inactivation
rate for adsorbed viruses is actually lower than that of suspended viruses, it
would be important to incorporate that information in a model so that accurate
predictions can be made of virus concentration profiles. If the model assumes
the same inactivation rate for all viruses, it would predict that fewer viruses
are being transported than the actual number.
Simulation 4. Virus Transport Through an Unsaturated Sand
This simulation predicts virus concentration profiles during transport
through an unsaturated Rehovot sand. This simulation was included to demonstrate
the large differences in the transport properties of different soil types.
46
-------
c - c
nus wus
(PFU/ml)
o
CL
CD
Q
10
i
i
~ 20*
CO
11
30
1000 2000 3000 4000 5000
—» t = 24 h
x-x t = 72 h
o-o t = 120 h
Figure 13. Effect of assuming no inactivation of adsorbed viruses
(Cnu») vs. a non-zero inactivation rate of adsorbed
viruses (C^,,) on model predictions for an Indio loam
soil, simulation 3
47
-------
Input Parameters
The general input values used for this simulation are shown in Table 3,
with the exception of a value of 0.1 cm3 cm"3 for the initial soil water content.
The soil physical properties are shown in Table 6, and the virus fate and
transport properties are listed in Table 7.
Results
This simulation illustrates the effects of soil properties on transport.
The Rehovot sand has a much higher hydraulic conductivity (see Table 6) than the
Indio loam (Table 5), thus water and contaminants can move through this soil more
rapidly. As shown in Figures 14 and 15, the viruses were transported more
rapidly and in higher concentrations in this soil as compared with the loam soil
of the previous examples. After 6 hours, the viruses in the loam soil had been
transported only 11 cm (Figure 7), as compared with more than 35 cm in the sandy
soil (Figure 14). The differences between the two columns become more apparent
at longer times: after 5 days approximately 30 viruses ml"1 had been transported
15 cm in the loam soil; whereas more than 102 viruses ml"1 were being recovered
in the sand column effluent after the same amount of time.
Changes in soil water content during 120 hours of simulation are shown in
Figure 16. This figure contrasts sharply with that for the loam soil (Figure 9).
Another reason for the relatively higher concentrations of viruses being
transported through this soil, in addition to the higher hydraulic conductivity,
is related to the adsorption coefficient. For this sand, based on reported
values for virus adsorption to other sandy soils, an adsorption coefficient of
zero was chosen. Thus, the rate at which the viruses were transported through
the soil was not decreased as a result of adsorption to the soil particles,
unlike the case for the loam soil.
MODEL TESTING
The model was tested for its ability to predict virus movement as measured
in laboratory column studies. Two data sets that contained sufficient
information about the soil properties for the model were obtained. In each case,
the model was run using input values measured or reported by the respective
investigator. No attempt was made to fit the model predictions to the measured
results. Model predictions were then compared with the virus concentrations
measured as a function of soil depth and time in the laboratory.
48
-------
Table 6. Values of the soil parameters used for the Rehovot sand that
remain constant throughout the simulation.
Symbol
«^
«.0il
atort
«..t.r
ae
fie
C.ir
-,
c»«nd
c«ilt
—
€
«.ir
Meaning
Albedo of air
Albedo of soil
Tortuosity factor
Albedo of water
Coefficient in
equation (59)
Coefficient in
equation (59)
Specific heat
of air
Specific heat
of clay
Specific heat
of sand
Specific heat
of silt
Specific heat
of water
Total porosity
Emissivity of air
Value /Units
0.05
0.35
0.66
0.07
8.8654
cm
1.5024
0.24 cal g-1
oc-i
0.175 cal g-1
oc-i
0.175 cal g-1
oc-i
0.175 cal g"1
oc-i
1.0 cal g-1
oc-l
0.4
0.9
Reference
Weast, 1986
Ghildyal and Tripathi, 1987
Hillel, 1982
Weast, 1986
Weast, 1986
Ghildyal and Tripathi,
1987
Ghildyal and Tripathi,
1987
Ghildyal and Tripathi,
1987
Weast, 1986
Ungs, et al. , 1985
Weast, 1986
4 soil
above the soil
Emissivity of
soil surface
Emissivity of
water
Saturated
conductivity in
equation (60)
Density of air
0.3
0.95
52.8914
en hr"1
Ghildyal and Tripathi,
1987
Weast, 1986
0.0011 g cm
-3
Weast, 1986
49
-------
Table 6. Values of the soil parameters used for the Rehovot sand that
remain constant throughout the simulation (continued).
Symbol Meaning
Value/Units
Reference
lb Bulk Density of
soil
Peitj Density of clay
/>««nd Density of sand
P»nt Density of silt
£w«t«r Density of water
-yc Coefficient in
equation (60)
*«oiid Thermal
conductivity
of solids
Thermal
conductivity
of water
Thermal
conductivity
of air
Residual soil
water content
Saturated soil
water content
1.595 g cnf3
2.64 g cm'3
2.66 g cm'3
2.65 g cm'3
1.00 g cm"3
3.3421
18.9 cal
cm -1 hr'1
5.14 cal
cm'1 hr'1
0.2214 cal
cnf1 hr"1
0.008 cm3
cm"3
0.4 cm3
cm'3
Ungs, et al., 1985
Ghildyal and Tripathi, 1987
Ghildyal and Tripathi, 1987
Ghildyal and Tripathi, 1987
Veast, 1986
Ghildyal and Tripathi,
1987
Ghildyal and Tripathi,
1987
Ghildyal and Tripathi,
1987
Ungs, et al., 1985
(adapted)
Ungs, et al., 1985
50
-------
Table 7. Parameters for the virus transport properties In the simulation.
Parameters
Values/Units
References
Dispersion
coefficient
Distribution
coefficient
Filtration
coefficient
Inactivation*
coefficient
in liquid phase
Inactivation
coefficient
in solid phase
Virus type
ni - <*tortDlo + «di.P I vl
- 0.66 x 0.000324 +
10 I Vl cm2 hr'1
Ke - 0.0 ml g'1 soil
f - 0.0 cnf1
Mi - [(-0.181 + 0.0214 T)
lnlO]/24 hr'1
- 0.0
MS-2 bacteriophage
Grosser, 1984,
Bales et al., 1989
Lindstrom et al., 1990
Powelson et al., 1990
Yates and Yates, 1988
* T is soil temperature (°C).
51
-------
E
o
d
CD
O
10
Virus Concentration (PFU/ml)
10C
101
10s
10-
io4
Figure 14. Virus concentration as a function of soil depth using
a temperature-dependent inactivation rate in a Rehovot
sand soil, simulation 4
52
-------
30000
120
Time (hrs)
Figure 15. Virus concentration as a function of time using
a temperature-dependent inactivation rate in a Rehovot
sand soil, simulation 4
53
-------
Water Content (cm3/cm3)
E
(J
Q_
CD
Q
O
00
o.c
0
20
40
60
80
100
)6 0.08 0.1 0.1
A \ \
• q x
\ \ \
• 0 X
\ \ \
• a x
\ Vo V
\ \ \
• D x
\ A \
• q x
\ \ \
• a x <
\ \ \
* q x
\ " \
* q x <
\ \ \
*\°\
• q *
\ \ \
* q x
/
E>
t>
/
1 O
/
O
/
O
/
t>
/
t>
/
O
/
> &
/
1 &
/
»
/
x>
\A \ \l
« t = 0 hrs V\ U
— t - 6 hrs \ I',
- x-x t = 24 hrs \t I
o-o t = 72 hrs \ 3J
p
1
^
1
»
»
•
VV 1 I
"— • t = 120 hrs \J
\
Figure 16. Soil-water content as a function of time in a Rehovot
sand soil, simulation 4
-------
Example 1. Virus Transport in a Saturated Gravelly Sand Column.
The data used for this example were obtained from virus transport
experiments using saturated soil columns conducted by Grondin at the University
of Arizona, Tucson (1987).
Input Parameters
The values used as input to VIRTUS are shown in Table 8. All of the values
were determined experimentally by Grondin or calculated by him during fitting of
his data to a model.
Results
When VIRTUS' predictions were compared to the results obtained by Grondin
(1987) using a saturated soil column, the model predictions were within the 95%
confidence limits of the measured virus concentrations (Figure 17).
Example 2. Virus Transport in an Unsaturated Loamy Sand.
Input Parameters
The data used as input for this example were obtained from virus transport
experiments using unsaturated soil columns conducted by Powelson at the
University of Arizona, Tucson and reported in Powelson et al. (1990). The input
values are listed in Table 9. All values were either measured by the
investigator or reported by him after model fitting.
Results
The virus concentration profiles predicted by VIRTUS are compared with the
measured data of Powelson in Figure 18. The model predictions were very close
to the measured virus concentration profiles, in all cases within the 95%
confidence limits of the measured virus concentrations.
55
-------
Table 8. Data used for model testing, example 1. (from Grondin, 1987)
Property
Soil type
Soil bulk density
Hydrodynamic dispersion
Soil water content
Average water velocity
Soil column length
Soil adsorption coefficient
Virus type
Virus inactivation rate
Filtration coefficient
Input virus concentration
Simulation time
Input Value
gravelly sand
1.65 g cm'3
78 cm2 h'1
0.26 cm3 cm"3
48.3 cm h'1
100 cm
-0.054 ml g'1 soil
MS2 coliphage
0.082 loglo day'1
0 cm'1
6.3 x 103 pfu ml'1
48 min
56
-------
Depth (cm)
tn
20
40
60 -
80
100
120
I 95% C.L.
Measured
-0- Predicted
0
2 3
Concentration (log pfu/ml)
Figure 17. Comparison of model predictions to experimental data,
Example 1
-------
Table 9. Data used for model testing, example 2. (from Powelson et al. (1990))
Property
Soil type
Soil bulk density
Hydrodynamic dispersion
Soil water content
Average water velocity
Soil column length
Soil adsorption coefficient
Virus type
Virus inactivation rate
Filtration coefficient
Input virus concentration
Simulation time
Input Value
loamy fine sand
1.54 g cnf3
92.24 cm2 h'1
variable with depth
1.54 cm h'1
100 cm
0 ml g"1 soil
MS2 coliphage
2.00 Iog10 day'1
0 cm'1
105 pfu ml'1
4 days
58
-------
Depth (cm)
20
40
60
80
100
120
I
95% C.L.
Measured
Predicted
4 5 (
Concentration (log pfu/ml)
Figure 18. Comparison of model predictions to experimental data,
Example 2
-------
DISCUSSION
The ultimate measure of a model's usefulness as a predictive tool is its
ability to accurately predict field observations of virus transport under a
variety of environmental conditions. However, most models that have been
developed to predict microbial transport have not been tested using field or
laboratory data. There are a few exceptions to this (e.g. , Teutsch et al. , 1991;
Harvey and Garabedian, 1991). However, both of these models were developed for
use by the investigators in order to simulate their own data. In the case of the
colloid filtration model of Harvey and Garabedian, extensive fitting of the
required input parameters was performed by calibrating different solutions of the
transport equation to the observed bacterial breakthrough curves. Thus, while
these models may be able to simulate the investigator's data reasonably well,
they may not be able to predict the results of other investigator's transport
experiments. If a model is to be used for purposes other than research, such as
for community planning or for making regulatory decisions, it must be able to
predict microbial transport using data obtained by anyone under a wide range of
environmental conditions.
In this research, a model to describe virus transport was developed based
on the factors known to affect virus fate in the subsurface. A survey of the
literature was conducted to locate data sets in which the investigators made
measurements of not only virus properties, but also soil and hydraulic
properties. Two data sets were located and used to test VIRTUS. No fitting or
calibration of the model was performed; the data and measurements as reported by
the respective investigators were used as model input. Model predictions
compared favorably to measured experimental data. However, only one example of
a comparison to one laboratory transport study in unsaturated soil using a single
soil type and a single virus type was performed.
In addition, the temperature-dependent inactivation rate capabilities of
the model could not be tested. This is due to the fact that the experiments were
conducted under constant temperature conditions in the laboratory, thus the virus
inactivation rate remained constant (theoretically) throughout the course of the
experiment. In order to test the model's capacity to calculate new virus
inactivation rates as a function of the changing soil temperature, data from a
laboratory study in which the temperature is allowed to change (and is closely
60
-------
monitored) or from a field study in which the temperature is monitored will be
required. This will allow an assessment of the model's capability to accurately
calculate heat flow through the soil, which affects water flow (and thus virus
transport) as well as the rate of virus inactivation during transport. More
testing of the nodel is required before using it for any purposes other than
research.
61
-------
CONCLUSIONS
This research project has resulted in the development of a mathematical
model that can be used to predict virus (or bacterial) transport in unsaturated
soils. The model allows the user to specify the virus inactivation rate as a
function of soil temperature. It will also allow the user to specify different
inactivation rates for adsorbed versus freely suspended virus particles, if that
information is available.
A sensitivity analysis of the model indicated that the inactivation rate
of the virus has a large effect on model predictions. The adsorption coefficient
and dispersivity also affect model predictions, although to a smaller extent.
Model predictions compared favorably to two data sets against which the
model was tested. However, there is a lack of data available for extensive model
testing. No complete data sets from field transport experiments were found that
could be used to test VIRTUS. Before the model can be used for any purposes
other than research, it should be extensively tested using actual field data.
In its present condition, the model requires the user to input several
pieces of information related to climatic conditions. It also requires a large
amount of information characterizing the physical properties of the soil, as do
most models of contaminant transport. Before VIRTUS could be used for purposes
other than research, a user interface, extensive help facilities, and a library
of soil and virus properties would have to be added to the model.
62
-------
REFERENCES
Bales, R. , C. Gerba, G. H. Grondin, and S. Jensen. 1989. Bacteriophage
transport in sandy soil and fractured tuff. Appl. Environ. Microbiol.
11:2061-2067.
Bitton, G., and C. P. Gerba. 1984. Groundwater pollution microbiology: The
emerging issue. pp. 1-7. In: Groundwater pollution microbiology. G.
Bitton and C. P. Gerba, eds. John Wiley & Sons, Inc., New York.
Brady, N. C. 1984. The nature and properties of soils. Macmillan
Publishing Company, New York.
California Department of Health Services. 1990. Initial statement of reasons
for proposed changes in the regulations of the Department of Health
Services pertaining to the use of reclaimed water other than for
groundwater recharge and pertaining to use of household gray water at
residences and text of proposed regulations. Sacramento.
Corapcioglu, M. Y. , and A. Haridas. 1986. Transport and fate of microorganisms
in porous media: A theoretical investigation. J. Hydrol. 72:149-169.
Craun, G. F. 1986. Vaterbome Diseases in the United States. CRC Press, Boca
Raton, Florida.
Craun, G. F. 1990. Review of the causes of waterborne disease outbreaks. In
G.F. Craun (ed.), Methods for the investigation and prevention of
waterborne disease outbreaks, USEPA, Washington D.C. publication no.
EPA/600/1-90/005a.
Frind, M. 0., W. H. Duynisveld, 0. Strebel, and J. Boettcher. 1990. Modeling
of multicomponent transport with microbial transformation in groundwater:
The Fuhrberg case. Water Resour. Res. 26:1707-1719.
Ghildyal, B. P., and R. P. Tripathi. 1987. Soil physics. John Wiley & Sons, New
York.
Grondin, G. H. 1987. Transport of MS-2 and f2 bacteriophage through saturated
Tanque Verde Wash soil. Master's thesis. Department of Hydrology and
Water Resources Administration, The University of Arizona, Tucson,
Arizona.
Grosser, P. W. 1984. A one-dimensional mathematical model of virus transport.
Proc. Second International Conference on Ground-Water Quality Research,
Tulsa, Oklahoma.
Harvey. R. W., and S. P. Garabedian. 1991. Use of colloid filtration theory in
modeling movement of bacteria through a contaminated sandy aquifer.
Environ. Sci. Technol. 21:178-185.
Hillel, D. 1982. Introduction to soil physics. Academic Press, Orlando,
Florida.
63
-------
Keswick, B. H., and C. P. Gerba. 1980. Viruses in groundwater. Environ. Sci.
Technol. 14:1290-1297.
Lance, J. C., and C. P. Gerba. 1984. Virus movement in soil during saturated
and unsaturated flow. Appl. Environ. Microbiol. 47:335-337.
Lindstrom, F. T. , L. Boersma, and S. Yingjajaval. 1990. CTSPAC: Mathematical
model for coupled transport of water, solutes, and heat in the soil-plant-
atmosphere continuum. Vol. 1. Mathematical theory and transport concepts.
Tech. Rept. Dept. of Soil Science, Oregon State University, Corvallis,
Oregon.
Lindstrom, F. T., and W. T. Piver. 1985. A mathematical model of the transport
and the fate of toxic chemicals in a simple aquifer. Tech. Rept. No. 52,
Oregon State University, Department of Mathematics, Corvallis, Oregon.
Matthess, G., A. Pekdeger, and J. Schroeter. 1988. Persistence and transport
of bacteria and viruses in groundwater-A conceptual evaluation. J.
Contain. Hydrol. 2:171-188.
McCoy, E. L. , L. Boersma, M. L. Ungs and S. Akratanakul. 1984. Toward
understanding soil water uptake by plant roots. Soil Sci. 137:69-77.
Moore, W. J. 1983. Basic physical chemistry. Prentice-Hall, Inc., Englewood
Cliffs, New Jersey.
Mualem, Y. 1976. A new model for predicting the hydraulic conductivity of
unsaturated porous media. Water Resour. Res. 12:513-522.
Ouyang, Y. 1990. Dynamic mathematical model of oxygen and carbon dioxide
exchange between soil and atmosphere. Ph.D. Thesis. Oregon State
University, Corvallis, Oregon.
Park, N., T. N. Blandford, M. Y. Corapcioglu, and P. S. Huyakorn. 1990. VIRALT:
A modular semi-analytical and numerical model for simulating viral
transport in ground water. Report to U.S. Environmental Protection
Agency, Office of Drinking Water, Washington, D.C.
Powelson, D. K., J. R. Simpson, and C. P. Gerba. 1990. Virus transport and
survival in saturated and unsaturated flow through soil columns. J.
Environ. Cnial. 1£:396-401.
Teutsch, G.f K. Herbold-Paschke, D. Tougianidou, T. Hahn, and K. Botzenhart.
1991. Transport of microorganisms in the underground - processes,
experiments, and simulation models. Wat. Sci. Tech. 24:309-314.
Tim, U.S., and S. Mostaghimi. 1991. Model for predicting virus movement through
soils. Ground Water 22:251-259.
64
-------
Ungs, M. J., L. Boersma, and S. Akratanakul. 1985. OR-Nature: The numerical
analysis of transport of water and solutes through soil and plants.
Volume IV. Examples. Special report 754. Agricultural Experiment
Station, Oregon State University, Corvallis, Oregon.
U.S. Environmental Protection Agency. 1989. Standards for the disposal of
sewage sludge; proposed rule. Fed. Regist. 54:5746-5902.
U.S. Environmental Protection Agency. 1991. Possible requirements of the
ground-water disinfection rule. (6/20/91). Office of Ground Water and
Drinking Water, Washington, D.C.
van Genuchten, M. Th. 1980. A close form equation for predicting the hydraulic
conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44:892-898.
Varga, R. S. 1962. Matrix iteration analysis. Prentice-Hall, Englewood Cliffs,
New Jersey.
Vilker, V. L. , and W. D. Burge. 1980. Adsorption mass transfer model for virus
transport in soils. Wat. Res. 14:783-790.
Weast, R. C. 1986. Handbook of Chemistry and Physics. CRC Press, Boca Raton,
Florida.
Yates, M. V., and S. R. Yates. 1988. Modeling microbial fate in the subsurface
environment. CRC Crit. Rev. Environ. Contr. 17:307-344.
Yates, M. V. and S. R. Yates. 1989. Septic tank setback distances: a way to
minimize virus contamination of drinking water. Ground Water 27: 202-
208.
65
-------
APPENDIX I: SOLVING THE VIRUS TRANSPORT EQUATIONS
The finite difference formulations used for solving the virus transport
equation were:
A(z,t)dzdt *
66
(2)
-------
APPENDIX II: Definitions of Mathematical Symbols and Units
For Equations (28) Through (36)
Symbol
<*.ir
a«oil
°w«t«r
°tort
finrp
Meaning
Albedo of air
Albedo of soil surface
Albedo of water surface
Tortuosity of the soil
Vaporization of water due
to wind speed
Loss of heat from soil due
to wind speed
Specific heat of water
Molecular diffusion
coefficient of water
vapor in air
Maximum value of the
dispersion coefficient of
water vapor in the boundary
layer of the atmosphere
Units
dimensionless
dimensionless
dimensionless
dimensionless
hr cm"1
hr cm"1
cal g"1 "CT1
cm2 hr"1
cm2 hr"1
•'•to
air
Logistic representation of
the boundary layer wind speed
dependent coefficient of
dispersion of water vapor
Saturated vapor pressure of
of the air
Soil porosity
Emissivity of the air
above the soil
cm2 hr
-i
mm Hg
cm3 soil voids
cm"3 soil
dimensionless
67
-------
Symbol
Meaning
Units
c»oil
Porosity of the soil
at the atmosphere-soil
interface soil
Emissivity of the soil
Emissivity of the water
Stefan-Boltzman constant
Infiltration of rainwater
Latent heat of evaporation
cm3 soil
voids cm'3
dimensionless
dimensionless
cal hr"1 cm"2
°C"*
cm hr"1
cal g"1
n,v
Transfer of heat by
conduction through
the soil particles
Transfer of heat by conduction
and convection in the liquid
phase water
Transfer of heat by
conduction in the vapor
phase water and by transport
in the form of latent heat
Relative humidity
at the atmosphere-soil
interface
Thermal conductivity of
the air
Maximum value of the
effective thermal
conductivity of the air
Thermal conductivity of
the solid
Thermal conductivity of
the water
The effective thermal
conductivity of the air at
the boundary of atmosphere-soil
interface
cal cm"2 hr"1
cal cm"2 hr"1
cal cm"2 hr"1
dimensionless
cal cm"1
hr"1 °C"1
cal cm"1
hr"1 "C"1
cal cm"1
hr"1 "C"1
cal cm"1
hr"1 °C"1
cal cm"1
hr"1 "C"1
68
-------
Symbol
Meaning
Relative humidity at the
atmosphere-soil interface
Water content at the
atmosphere-soil interface
Density of water
Units
dimensionless
cm3 cm"3
g cm
-3
•at
(T0)
Density of water vapor at
saturation at Tn
g cm
-3
Qh«atin
Heat flux into the soil
surface by rainwater
cal cm'2 hr"1
Heat flux out of the soil
surface due to evaporation
or heat flux into the soil
surface due to condensation
cal cm"2 hr"1
1htl»wr
Heat flux into the soil
surface by short wave
radiation
cal cm"1 hr"1
Qhtssl
Heat flux through the soil
surface via sensible heat
cal cm"2 hr"1
QhUwra
Heat flux into the soil
surface by long wave
radiation
cal cm"2 hr"1
-------
Symbol Meaning Units
T0 Temperature at the atmosphere °C
-soil interface
T, Temperature at the air °C
WS Wind speed cm hr'1
6z Thickness of boundary layer cm
at the atmosphere-soil
interface
z Soil depth cm
70
-------
APPENDIX III. VIRTUS USER MANUAL
This appendix describes the computer program, VIRTUS, developed from the
mathematical model described in the main body of the report. The model was
written to be run on an IBM XT, IBM AT or equivalent computer, which has 6AOK
memory and an 8087 math co-processor. This document begins with a description
of the program. A listing of FORTRAN variables for input with mathematical
symbols, meanings, and units is given next. This is followed by a section on the
preparation of input data files. The user is then guided through a section on
the running of the program and a discussion of the output files.
PROGRAM DESCRIPTION
Program Organization
The program is written in ANSI Standard FORTRAN 77. It implements the
mathematical model described in the main body of this report. The "include"
feature of Microsoft FORTRAN (version 5.0) is used for global Common Blacks.
There is one "include" file name: "COMMON.NEW" in the program. There are 12
FORTRAN source files, all with the extension ".FOR".
Flow Chart of the Program
Figure 1 shows the flow chart illustrating the modules in the execution of
the program. Each module contains many helpful comments and is compiled
separately, then the resulting object codes are linked together to create an
executable file called MIXMAIN.EXE. The functions of each of the modules is
described below.
Module Functions
MIXMAIN.FOR MAIN Program MIXMAIN
MIXREAD.FOR Reads in simulation input data
MIXUNCS.FOR Computes "universal porous media constants"
MIXWRTO.FOR Prints out input system parameters, calculated
system parameters, and initial distributions of
water, temperature, and viruses so that the user
knows what the run parameters are
MIXLRZV.FOR Makes decisions about starting and ending water
application and light cycles
MIXING.FOR Makes approximate time integrations of the water,
heat, and virus systems
71
-------
MIXWATR.FOR
MIXHEAT.FOR
MIXTHOM.FOR
MIXBNDY.FOR
MIXVIR.FOR
MIXCUM.FOR
Approximates soil water content distributions
Approximates soil temperature distributions
Solves resulting tri-diagonal systems of water
and heat transport equations (and later virus
transport equation)
Calculates all water- and heat-related variables
Approximates virus concentration distributions
Stores and prints simulation results
PROGRAM VARIABLES
This section contains a list of the program variables that are used in
input. The variables are listed in alphabetic order (Table Al). The
mathematical symbol corresponding to each variable is shown, with a brief
description of the meaning of the variable and its units.
DATA FILES
Format Instructions
To run the program, the data file must be created in proper format. The
user can create and modify the data file using a text editor or word processor.
A data file must be created in ASCII format using the following standard FORTRAN
formatting instructions.
Record 1 FORMAT (all of data files use
free format).
TO Initial time for the simulation
(usually set to zero).
TCUT Ending time for the simulation.
DTO Time step for the simulation.
Record 2 PRTIN(I) Nonevent print interval. The program
can print out the simulation results
at any time according to the data given
here.
Record 3 NPRINT(I) Index for print out. See example given
below for more information.
Record 4 NNSTRZ(I) Number of storage node indexes. These
72
-------
Record 5 NSLZM1
Record 6 DELTAZ
Record 7 DZ(I)
Record 8 ALBAIR
ALBWAT
ALBSOI
Record 9 EMSAIR
EMSWAT
EMSSOI
Record 10 LAMBHT
Record 11
Record 12
Record 13
Record 14
LAHSLD
SHTSAN
SHTSIL
SHTCLA
SHTWAT
SHTAIR
RHOSND
RHOC1A
RHOSIL
GAMTLI
indexes are used to print out simulation
results at a given time and soil depth
for checking the program.
Number of internal vertical soil nodes.
Top boundary layer thickness.
Soil depth step. See example given
below for more information.
Albedo of soil surface air which is used
for heat flux at the top boundary.
Albedo of water which is used for heat
flux at the top boundary.
Albedo of soil which is used for heat
flux at the top boundary.
Emissivity of air which is used for
heat flux at the top boundary.
Emissivity of water which is used for
heat flux at the top boundary.
Emissivity of soil which is used for
heat flux at the top boundary.
Coefficient due to wind speed affecting
on thermal conductivity of air.
Thermal conductivity of solids.
Specific heat of sand.
Specific heat of silt.
Specific heat of clay.
Specific heat of water.
Specific heat of air.
Density of sand.
Density of clay.
Density of silt.
Derivative of surface tension with
respect to temperature.
73
-------
BETATV
Record 15 NWVAIR
Record 16 DWVAR
Record 17
Record 18
RHOWAT
RHOAIR
WS
Record 19 NCFTHP
NCFFRH
Record 20 ATEMP(I)
Derivative of saturation water vapor
density with respect to temperature.
Number of characterizing parameters
for the effective water vapor
diffusivity in the top boundary
layer. See example given below for
aore information.
Effective water vapor diffusivity
parameters in the top boundary layer.
See example given below for more
information.
Density of water.
Density of air.
Vind peed at the atmosphere-soil
surface.
Number of coefficients in the Fourier
Series (equation 56) representing nth
term of air temperature.
Number of coefficients in the Fourier
Series (equation 57) representing nth
term of relative humidity.
Temperature coefficients in equation
(56). These values are generated by
fitting the daily air temperature data
to equation (56). See Table 1 to
identify the correspond mathematical
symbol in equation (56).
Temperature coefficients in equation
(56). These values are generated by
fitting the daily air temperature data
to equation (56).
OMEGTP(I) Temperature coefficients in equation
(56). These values are generated by
fitting the daily air temperature data
to equation (56).
BTEMP(I)
Record 21 ARHIN(I)
Relative humidity coefficients in
equation (57). These values are
generated by fitting the daily relative
humidity data to equation (57). See
Table 1 to identify the correspond
74
-------
mathematical symbol in equation (57).
BRHIN(I) Relative humidity coefficients in
equation (57). These values are
generated by fitting the daily relative
humidity data to equation (57).
OMGRHI(I) Relative humidity coefficients in
equation (57). These values are
generated by fitting the daily relative
humidity data to equation (57).
Record 22 TPINMU Mean air temperature in equation (56).
RHINMU Mean relative humidity in equation (57).
TPWAT1 Temperature in rainwater.
Record 23 CWIN Concentration of virus in infiltration
water.
CVGRD Concentration of virus in ground water.
DLO Diffusion coefficient of virus.
DISPLZ Dispersivity coefficient of virus.
KD Virus adsorption coefficient.
FILTRA Filtration coefficient of virus.
THTAST(J) Saturated soil water content at each
node of soil. These values are
generated by fitting the experimental
data (water content vs. water potential)
to equation (59).
Record 24 TORT(J) Tortuosity factor of soil.
Record 25 EPS(J) Soil porosity.
Record 26 PCTSAN(J) Percentage of sand.
Record 27 PCTCLA(J) Percentage of clay.
Record 28 PCTSIL(J) Percentage of silt.
Record 29 ALPTH(J) Parameter in equation (59). The values
are generated by fitting the experimen-
tal data to equation (59).
Record 30 BETATH(J) Parameter in equation (59). The values
75
-------
Record 31 GAMCNS(J)
Record 32 KTHSTS(J)
Record 38
Record 39
Record 40
Record 41
Record 42
are generated by fitting the experimen-
tal data to equation (59).
Parameter in equation (60). The values
are generated by fitting the experimen-
tal data to equation (60).
Saturated conductivity in equation (60).
These values are generated by fitting
the experimental data to equation (60).
Record 33 THTRES(J) Residual soil water content.
Record 34 DALPTZ Derivative of at with respect to soil
depth z. See example given below for
more information.
Record 35 DBETAZ
Record 36 DTHTSZ
Record 37 DTHREZ
THTAA
TEMPA
THTAS(J)
TEMPS(J)
CV(J)
QRAIN(J)
QSR(J)
NLIEV
NRAEV
TLION(I)
TLIOF(I)
Derivative of f)e with respect to soil
depth z. See example given below for
more information.
Derivative of saturated water content
with respect to soil depth z.
Derivative of residual water content
with respect to soil depth z.
Initial air relative humidity.
Initial air temperature.
Initial soil water content.
Initial soil temperature.
Initial soil virus concentration.
Parameters for rainfall rate. See
example given below for more
information.
Parameters for solar intensity. See
example given below for more
information.
Number of light events.
Number of rain events.
Time at which the light is turned on.
Time at which the light is turned off.
76
-------
Record A3 TRAON(I) Time at which the rain is turned on.
TRAOF(I) Time at which the rain is turned off.
Examples of Data Sets
Examples for input data files are presented and described in this section.
These data files, together with the executable program, are included on the
distribution diskette. It is recommended that these files be used as input to
the program to verify that the program is working properly. These files can be
modified to describe an actual scenario for model simulation.
Example Input Data File: WTV1.DAT
This section discusses the run control, upper boundary, and thermal
properties input data that are in the file: WTV1.DAT. These data are read in by
the subroutine MIXREAD in nodule MIXREAD.FOR. The data used by the program are
numerical, in either real or integer form. Real numbers are handled by the
program as double precision. The data is read using FORTRAN'S "list-directed"
input format. This is a free form input: numbers may occupy any number of
positions; they are separated by spaces. The following are the descriptions of
the actions of MIXREAD for the input file WTV1.DAT. The input data and the
corresponding FORTRAN codes are first listed, then discussed briefly.
As the program begins to execute, the following message
•E««din« IroB d«t« file WTV1.DAT'
is shown on the screen. It tells the user that the program is beginning to read
in data in the file: WTV1.DAT. Then it reads in the run control information in
the first line of WTV1.DAT as follows:
o.o 2.1 o.i
«EAD{2,*) TO.TCUT.DTO
It first reads in the time for beginning the simulation, then the time for ending
the simulation, and finally the time step for running the simulation. The time
step may vary for simulations. The user should try several time steps to decide
which is required for the purpose of achieving the desired accuracy.
i.o 5.BO 11.ee i7.es 23.ee ze.ee 3S.ee *i.se *7.ee 7i.ee ei.ee
lie.99 ise.ee i48.es iss.es ise.es i7s.se
77
-------
KEADC2,*) (F&TINU). 1-1,16)
The program reads in the number of times for printing the simulation results.
The first number in the above data file is the time for printing the simulation
results in output file: "test.out". The other numbers are times for printing the
simulation results in output file: "plrnfl". In order to print the results at
6 hours, the number 5.99 is used. This is to avoid possible numerical roundoff
which may cause the program to print the results before or after 6 hours.
00000000101010000010
SEADC2,*) (IPRIHTCI),1-1,20)
The program reads in the index for the print out. The user may not have to
change these numbers.
1 2 3 4 5 8 7 8 9 10 11 12 13 1* 13 16 17 16 IB 20 21 22
23 24 25
X£AD(2,«)(HKStR2(I),1-1.25)
The program reads in the number of storage node indexes for the output file:
TEST.OUT. In this example, the simulation results of the top 25 nodes for every
hour are saved in the file of TEST.OUT.
89
K£AD(2.*) HSLZM1
HSLZZZ-NSLZMl+1
XSLZF1-HSLZZZ+1
First, the number of internal vertical soil nodes is read in. Then, the upper
and bottom nodes are computed.
i.o
o.i
i.o
i.o
i.o
KEADC2.*) DELTA!
DO 16, I-l.HSLZZZ
EEAD(2,«) DZ(I)
IB CONTINUZ
The program reads in the upper boundary layer thickness and distance between
nodes. The depth step in this example is 1 cm although it is not necessary to
have equal space for all depth steps. However, it is recommended that the first
•oil layer (DZ(l)) should be kept small (0.1) for the purpose of obtaining
accurate results.
o.os 0.07 o.oe
0.90 0.9$ 0.50
78
-------
3.33000E-4
3.43
0.175 0.175 0.175 1.0 0.2*
SEAD(2,«) AIAAIR.ALBWAT.ALBSOI
XEADC2.*) mSAJR.EMSWAT.BCSOI
HEADC2.*) LAMEST
IEADC2.*) LAtCLD
*£AD<2,«> SBTSAH.SETSIL.SBTCLA.SBnUT.SHTAIR
The program reads In the albedos, emissivities, thermal conductivities, and
specific heats of air, water, and soil. All these coefficients may be kept
constant except the albedo coefficients of soil (ALBSOI). which may change for
different types of soil.
2.66 2.64 2.65
KEADC2.*) RHOSND.RBOCLA.RBOSIL
The program reads in soil particle densities, which are always constant.
-2.0900E-3 1.05600E-6
3
954.0 4770.0 3.33000E-4
HEADC2,*) GAMTLI.BETATV
KEAD(2.*) HWVAIR
BEAD (2. • ) (DWVAR (I). 1-1, FWVAIR)
The program reads in liquid and vapor phase water parameters. These parameters
may be kept constant for all the simulations.
i.o 0.0011
SEADC2.*) RHOHAI.HBQAIR
The program reads in the densities of water and air, which are always constant.
o.o
SEAD(2.*> MS
The program reads in wind speed constant. It is assumed to be zero in this
example.
2 5
-1.006722008 -2.356626766 0.261188
-0.371635705 1.000000000 0.523598
0.0371929656 0.0675873369 0.261198
-.0052916350 -.0274241549 0.523598
-.0094577665 0.0116668147 0.785367
O.C0637S2911 -.0043302556 1.047196
-.0061084983 0.0040792275 1.308895
READ<2.*> BCFTMF.IICFFBB
DO 13. I - l.HCFTKP
HEAD(2.«) ATEMPCD.BIEMFCD.CHEGTPd)
13 COHTimjE
DO 23, I - l.KFFKB
K£AD(2.*> ARHIN(I).BREIM(I),OMQRBI(I)
23 COHTIHUE
79
-------
The program reads in the number of air temperature coefficients (in equation 56)
and relative humidity coefficients (in equation 57). These coefficients are
generated by fitting the measurement data to equations (56) and (57).
8.7578 0.869 277.0
BZAD<2,«) TPnWU.BBHWU.TFWATI
The first two variables are the mean air temperature in equation (56) and mean
relative humidity in equation (57), respectively. The third variable is the
temperature in the applied water.
Example Input Data File: WTV2.DAT
This section discusses the virus transport properties input data in file:
VTV2.DAT. It is read in by subroutine MIXREAD in module MIXREAD.FOR. The
following are the descriptions of the actions of MIXREAD for the input file
WTV2.DAT.
As the program begins to execute, the following message
•R»«ding from file WTV2.DAT1
is shown on the screen. It tells the user that the program is beginning to read
data in the UTV2.DAT file. Then, it reads in the virus transport properties as
follows:
l.OE+5 0.0 0.00032* 200.0 0.27 0.0
SEADC3,*) CHIN, CVGRD, DLO, DISPLZ, KD, FILTRA
Table 1A lists the definitions and units of the above FORTRAN variables. The
user may need to change the values of the variables according to a specific
simulation.
Example Input Data File: WTV3.DAT
This section discusses the soil physical properties input data in file:
VTV3.DAT. It is read in by subroutine MIXREAD in module MIXREAD.FOR. The
following are the descriptions of the actions of MIXREAD for the input file
WTV2.DAT.
As the program begins to execute, the following message
•R«*din( Iron file WTV3.DAT1
is shown on the screen. It tells the user that the program is beginning to read
data in WTV3.DAT file. Then, it reads in the soil physical properties as
follows:
0.55 0.55 0.55 0.55 0.55 0.55 0.55
0.55 0.55 0.55 0.55 0.55 0.55 0.55
0.55 0.55 0.55 0.55 0.55 0.55 0.55
80
-------
0.55
O.SS
0.55
0.55
O.SS
0.55
0.55
0.55
O.SS
O.SS
0.55
O.SS
O.SS
0.55
O.SS
O.SS
O.SS
O.SS
O.SS
O.SS
O.SS
O.SS
e.ss
O.SS
O.SS
0.35
O.SS
O.SS
O.SS
O.SS
O.SS
O.SS
0.55
O.SS
O.SS
O.SS
0.55
0.55
O.SS
O.SS
0.55
0.55
0.55
0.55
O.SS
0.55
O.SS
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
O.SS
0.55
0.55
0.55
0.55
O.SS
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
READ(*,*>(THTAST(J),J"1,ISL2P1)
The progran reads In the saturated soil water content at each node of the soil
profile. The saturated soil water content varies for different types of soil.
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6500
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
B£AD(4.«HTORICJ),J-1.HSLZ!>1)
The program reads in the tortuosity factor at each node of the soil profile
These values nay be kept constant for most soils (Hillel, 1982).
0.55
0.55
0.55
O.SS
O.SS
0.55
0.55
O.SS
0.55
O.SS
O.SS
O.SS
0.55
0.55
O.SS
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
e.
0.
0.
0.
0.
55
55
55
55
55
55
55
55
55
55
55
55
55
55
35
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.55
.55
.55
.55
.55
.55
.55
.55
.55
.55
.35
.55
.55
.55
.55
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.55
.55
.55
.55
.55
.55
.55
.55
.55
.55
.55
.55
.35
.55
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.55
.55
.55
.55
.55
.55
.55
.55
.55
.55
.55
.55
.55
.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
O.SS
O.SS
0.55
0.55
READ(4.•)CEPSCJ),J-1,HSLZP1)
The progran reads in the soil porosity at each node of the soil profile. These
values vary for different types of soil.
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
81
-------
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
BEAD(4,•)(KTSAft (J),J-l.BSLZF1)
The program reads in the percentage of sand at each node of the soil profile.
These values are extracted from experimental measurements. If the values are not
available for a specific soil, the user can estimate them easily through the soil
textural triangle diagram, which is commonly shown in the soil science text book
(Brady. 1984).
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
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.1000
.1000
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.1000
.1000
.1000
.1000
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.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
mEAD(*.*)(PCTCLA(J),J-l,HSLZPl)
The program reads in the percentage of clay at each node of the soil profile.
As with the percentage of sand, if the values are not available for a specific
soil, the user can estimate them easily through the soil textural triangle
diagram.
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
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0.6
0.6
0.6
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0.6
0.6
0.6
0.6
0.6
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0.6
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0.6
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0.6
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0.6
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0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
SEAD(*.«)(PCTSIL(J),J-
The program reads in the percentage of silt at each node of the soil profile.
82
-------
Again, if the values are not available for a specific soil, the user can estimate
them easily through the soil textural triangle diagram.
1241.
1241.
1241.
1241.
1241.
1241.
1241.
1241.
1241.
1241.
1241.
1241.
1241
1241
1241
39 1241.39
39 1241.39
39 1241.39
38 1241.39
39 1241.39
39 1241.39
39 1241.39
39 1241.39
39 1241.39
39 1241.39
39 1241.39
39 1241.39
39 1241.39
39 1241.39
39 1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.
1241.
1241.
1241.
1241.
1241.
1241.
1241.
1241.
1241
1241.
1241.
1241.
1241.
39 1241.
39 1241.
39 1241.
39 1241.39
39 1241.39
39 1241.39
39 1241.39
39 1241.39
39 1241.39
39 1241.39
39 1241.39
39 1241.39
39 1241.39
39 1241.39
.39
.39
.39
BEAD(4,«)(ALPTH(J).J-l,HSLZP1)
The program reads in the parameter in equation (59) at each node of the soil
profile. These values are generated by fitting the experimental data to equation
(59). The user can identify the FORTRAN variable to the corresponding
mathematical symbol using Table 1A.
7079
7079
7079
7079
7079
7079
7079
7079
7079
7079
7079
7079
7079
7079
7079
.7079
.7079
.7079
.7079
.7078
.7079
.7079
.7079
.7079
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.7079
.7079
.7079
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.7078
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.7076
.7079
.7079
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.7079
.7078
.7078
.7079
.7079
.7079
.7079
.7079
.7079
.7078
.7078
.7078
.7078
.7079
.7079
.7079
.7079
.7079
.7078
.7078
.7078
.7078
.7078
.7078
.7078
.7078
.7078
.7079
.7078
.7079
.7078
.7079
.7073
.7078
.7078
.7078
.7078
.7078
.7079
.7078
.7079
.7078
.7078
.7078
.7078
.7078
.7078
.7078
.7078
.7079
.7079
.7078
.7079
.7079
.7079
.7078
.7078
SEAD(4,«)(BrTATH(J).J-l.KSl,ZPl)
The program reads in the parameter in equation (59) at each node of the soil
profile. These values are generated by fitting the experimental data to equation
(59).
.5
.5
.5
.5
.5
.5
.5
.5
.5
.5
.3
.5
.5
.5
.5
.5
.3
.5
.5
.5
.5
.5
.3
.5
.5
.5
.5
.3
.5
.5
.5
.5
.5
.5
.5
.5
.5
.3
.3
.5
.5
.3
.5
.5
.5
.5
.5
.5
.5
.5
.5
.3
.3
.5
.5
.5
.5
.5
.5
.5
.5
.5
.5
.5
.5
.5
.5
.5
.5
.5
.5
.5
.3
.5
.5
.5
.5
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.5
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.5
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.5
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.5
.5
.5
83
-------
6.S 6.5 6.5 6.5
«EAD (*. • ) (GMC8S (J). J-l. HSLZP1)
The program reads In the parameter In equation (60) at each node of the soil
profile. These values are generated by fitting the experimental data to equation
(60).
0.61
0.61
0.61
0.61
0.61
0.61
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0.61 1
0.61 I
0.61 1
0.61 1
0.61 1
0.61 1
.61
.61
.61
.61
.61
.61
.61
.61
.61
3.61
).61
).61
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«EAI>(4.*>(lCTHSTS(J),J-l,irSLZFl)
The program reads in the saturated conductivity at each node of the soil profile.
These values are generated by fitting the experimental data to equation (60).
0.029
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0.029
0.029
SEADC*.*)(IHTRES(J).J-l.HSLZP1)
The program reads in the residual soil water content at each node of the soil
profile. These values are generated by fitting the experimental data to equation
(59).
0.0
0.0
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84
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0.0
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O.D
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0.0
12AD(4,*)(DAI.PTZ(J).J-1,IISI.ZP1)
BEAD(4,*)(DBtTAZ(J),J-l.HSLZP1)
READ(4.*>(DTHTSZ(J).J"1,HSI.ZP1)
BZAD(4.«)(DTHREZ(J),J-1,KSLZF1)
The program reads in the derivatives of parameters in equations (59) and (60)
with respect to soil depth. Since these parameters are assumed to be constant
throughout the soil profile, the derivatives of parameters with respect to soil
depth should be all zero. The user may not have to change them.
Example Input Data File: WTV4.DAT
This section discusses the initial distributions of water, temperature, and
85
-------
virus Input data in file: WTV4.DAT. It is read in by subroutine MIXREAD in
nodule MIXREAD.FOR. The following are the descriptions of the actions of MIXREAD
for the input file WTV4.DAT.
As the program begins to execute, the following message
•R»»dim frca til* HTV4.DAT'
is shown on the screen. It tells the user that the program is beginning to read
data in WTV4.DAT file.
0.092 281.72
KEADCS.*) THIAA.TEMPA
The program reads in the initial relative humidity and air temperature at the
upper boundary layer. The user may change these values according to the location
and beginning season.
0.25 281.72 0.0
0.25 281.72 0.0
0.25 281.72 0.0
0.25 281.72 0.0
DO 127. J-l.KSLZPl
READCS,*) THTAS(J>,TBC'S(J),CV(J)
127 CONTINUE
The program reads in the initial soil water contents, temperatures, and virus
concentrations.
Example Input Data File: WTV5.DAT
This section discusses the rainfall rate, solar radiation, .rain and light
cycles input data in file: WTV5.DAT. It is read in by subroutine MIXREAD in
module MIXREAD.FOR. The following are the descriptions of the actions of MIXREAD
for the input file WTV5.DAT.
As the program begins to execute, the following message
•lUadias free. til. WTV5.DAT1
is shown on the screen. It tells the user that the program begins to read data
in WTV5.DAT file.
0.0 0.0
0.1 35.607219
0.0 6.6392*47
0.0 2.5100518
0.0 0.15
00 15, 1-1,5
KEADC6.*) ORAIHCI),QSRU>
15 CONTINUE
The program reads In the parameters for the rainfall rate and the solar
86
-------
intensity. The value in the second row of column one above is the rainfall rate.
The values in the second to fourth rows of column two are for the parameters in
equation (58). The value in the fifth row of column two is the solar intensity
factor during the rainy period, which is assumed to be 15% of the total solar
intensity AS compared to that of no rain. Other zero values are control indexes
which the user nay not have to change.
s 2
KEADC6.*) K.IZV.NKAEV
The program reads in the numbers of sunrise and sunset cycles and rain events .
e.o le.o
30.0 42.0
54 . 0 66 . 0
76.0 90.0
102.0 114.0
DO 16. I-l.Hl.IEV
HZAD(6,*) TLIOH(I),TLIOF(I)
16 CONTINUE
The program reads in the times for sunrise and sunset.
o.o e.o
130.0 140.0
DO 17. I-l.KRAEV
EEADC6.*) IRAON(I),TRAOF(I)
17 CONTINUE
The program reads in the times for rain start and rain stop.
RUNNING THE PROGRAM AND OUTPUT FILES
Instructions for Running the Program
The program can be run on IBM PC, IBM AT computer, or their equivalents,
which have 640K memory and an 8087 math co-processor. A hard disk is desirable,
but not absolutely necessary. The program was developed under DOS 4.0, using
Microsoft FORTRAN Version 5.0. The distribution diskette includes the executable
form of the program (MIXMAIN.EXE), input data files, and output files.
There is one Batch file on the distribution diskette: MIX.INP, which is
used to run the program. To start running the program, the user may just type:
If the user wants to type the input files from the screen, s/he may just type:
C:\XGXMMH
at this point, the computer will ask for one output file (see next section about
the output files), five input files, and two other output files consecutively by
displaying on the screen.
87
-------
When the program Is run, it will display information on the screen. First,
it will show the messages about the reading of input data, the writing of all
input data, the convergence checking (those ". . . ."on the screen), and the
times. If the program should stop due to a data error, or for some other
unexpected reason, the last messages displayed will give an indication of the
program that caused the error. If the program runs well, it will show how much
computing time is used at the end of running.
Output Files
File TEST.OUT shows the information read fromWTVl.DAT, WTV2.DAT, WTV2.DAT,
WTV3.DAT, WTV4.DAT, AND WTV5.DAT, together with computed data. This information
should be examined to be sure that the data were read in correctly. All the
numbers are labeled to indicate what they represent. Next, it shows some
simulation results at each hour, including simulation time, water content,
temperature, virus concentration, water potential, conductivity, water flow
velocity, and the upper boundary parameters. This information should also be
examined to be sure the right simulation results were generated mathematically
and scientifically.
File P1RNFL shows water content, temperature, and virus concentration at
all of the node points in the soil profile at selected print times. They are
used to draw graphs.
File P2RNFL shows soil temperature and surface evaporation rate at each
hour at the selected soil depths. They are also used to draw graphs.
88
-------
Table Al. Program Variables for Input Data
FORTRAN Hath
Variable Symbol
ALBAIR a.ir
ALBSOL o.oil
ALBWAT a,,,.,
ALPTH at
ARHIN A,,,
ATEMP At.
BATATH fig
BETATV dpj;1 /dT
BRHIN Brh
BTEMP BtM
CV G!
CVGRD Cg
CWIN C^
DALPTZ da,,/dz
DBETAZ d0v/dz
DELTAZ 6z
DISPLZ 0^.,,
DLO DXO
DTO At
Meaning
Albedo of surface air
Albedo of surface soil
Albedo of surface water
Parameter for equation
Unit
(59) cm
Relative humidity coefficient in
equation (57)
Temperature coefficient
(56)
Parameter for equation
Derivative of saturated
density with respect to
in equation
(59)
water vapor g/cm3 °K
temperature
Relative humidity coefficient in
equation (57)
Temperature coefficient
(56)
Concentration of virus
Concentration of virus
water
Concentration of virus
infiltration water
in equation
in soil water mass cm"3
water
in ground mass cm'3
water
in mass cm"3
water
Derivative of ae with respect to
soil depth z
Derivative of 0e with respect to
soil depth z
Upper boundary layer thickness cm
Dispersivity coefficient of virus cm
Diffusion coefficient of virus cm2/hr
Time step for running the model hr
89
-------
Table Al. Program Variables for Input Data (continued)
FORTRAN
Variable
Math
Symbol
Meaning
Unit
DTHREZ
DTHTSZ
DWVAR
DZ
EMSAIR
EMSSOI
EMSWAT
EPS
FILTRA
GAMCNS
Az
«ar
c»oil
£w«t«r
c
f
7C
GAMTLI d(surf.
tension)/dT
KD K^
KTHSTS
LAMBHT
LAMSLD
NCFFRH
NCFTMP
Derivative of 6t with respect to
soil depth z
Derivative of 0, with respect to
soil depth z
Effective water vapor diffusivity
parameters in boundary layer
Depth step of soil profile
Emissivity of air above soil
Emissivity of soil surface
Emissivity of water
Soil porosity
Filtration coefficient of virus
Parameter for equation (60)
Derivative of surface tension with
respect to temperature
Virus adsorption coefficient
Saturated conductivity of soil
Coefficient due to wind speed
effects on thermal conductivity of air
Thermal conductivity of solids
Number of coefficients in the
Fourier series (equation 56)
representing n"1 term of air
temperature
Number of coefficients in the
Fourier series (equation 57)
representing n** term of relative
humidity
cm
cm3/cm3
I/cm
ml/g
soil
cm/hr
cal/cm
hr °K
90
-------
Table Al. Program Variables for Input Data (continued)
FORTRAN Math
Variable Symbol
NLIEV
NNSTRZ
NPRINT
NRAEV
NSLZK1
NWVAIR
OMEGTP u^
OMGRHI wjn
PCTCLA
PCTSAN
PCTSIL
QRAIN
QSR
RHINMU RH
RHAIR ,.ir
RHOCLA pcl.y
RHOSIL P«iit
RHOSND p>Kld
RHOWAT *W.r
SHTAIR c^r
SHTCLA ceUy
SHTSAN c.md
Meaning Unit
Number of light events
Storage node indexes
Indices for print out
Number of rain events
Number of internal vertical soil
nodes
Number of characterizing parameters
for the effective water vapor
diffusivity in the boundary layer
Parameter in equation (56)
Parameter in equation (56)
Percentage of clay
Percentage of sand
Percentage of silt
Parameter for rainfall rate cm/hr
Light flux charactering parameters cal/cm2
hr
Parameter in equation (57)
Bulk density of air g cm'3
Bulk density of clay g cm'3
Bulk density of silt g cm"3
Bulk density of sand g cm'3
Bulk density of water g cm"3
Specific heat of air cal/g °K
Specific heat of clay cal/g °K
Specific heat of sand cal/g °K
91
-------
Table Al. Program Variables for Input Data (continued)
FORTRAN Math
Variable Symbol
SHTSIL c.ut
SHTWAT cv.^
TO
TCUT
TEMPA T^r
TEMPS T
THTAA 0mir
THTAS 8
THTAST 6.
THTRES 6;
TLIOF
TLION
TORT otort
TPINMU T
TPWATI
TRAOF
Meaning
Specific heat of silt
Specific heat of water
Start time for simulation
End time for simulation
Initial air temperature
Initial soil temperature
Initial air relative humidity
Initial soil water content
Saturated soil water content
Residual soil water content
in equations (59) and (60)
Time at which the light is
turned off
Time at which the light is
turned on
Tortuosity factor of soil
Parameter in equation (56)
Temperature of rain water
Time at which the rain is
Unit
cal/g °K
cal/g °K
hr
hr
°K
°K
cm3/cm3
cm3/cm3
cm3/cm3
hr
hr
°K
°K
hr
TRAON
turned off
Time at which the rain is
turned on
hr
US
Vind speed at the atmosphere-
soil surface
cm
92
-------
APPENDIX IV: LISTING OF INPUT AND OUTPUT FILES
Input Data File: vtvl.dat
0.0 6.1 0.1
1.0 2.99 5.99 17.99 23.99 29.99 35.99 41.99 47.99 71.99 95.99
119.99 139.99 149.99 159.99 169.99 179.99
00000000101010000010
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
23 24 25
99
1.0
0.1
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
93
-------
1,
1
1.
1.
1.
1,
1.
1.
1.
1,
1.
1.
1.
1.
1.
1.
1.
1.
1,
1,
1.
1.
1.
1.
1.
1,
1.
1.
1,
1
1.
1.
1.
1,
1.
1.
1.
1.
1,
1.
1.
1.
1.
1.
1.
1,
1,
1.
1,
1,
.0
.0
.0
,0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
,0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
,0
1.0
1.0
94
-------
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.05 0
0.90 0
3.33000E-4
3.43
0.175 0
2.66 2
.07
.95
.175
.64
0.09
0.50
0.175
2.65
954.0
1.0
0.0
2 5
-1.006722008
-0.371835795
0.0371929656
-.0052916350
-.0094577865
0.0063752911
-.0061084983
8.7578
4770.0
0.0011
1.0
0.24
-2.0900E-3 1.05600E-6
3
3.33000E-4
-2.356626769
1.000000000
0.0675873369
-.0274241549
0.0116668147
-.0043302556
0.0040792275
0.869
0.261199
0.523598
0.261199
0.523598
0.785397
.047196
.308995
1.
1.
277.0
95
-------
Input Data File: WTV2.dat
l.OE+5 0.0 0.000324 1.0 0.27 0.0
96
-------
Input Data File; WTV3.dat
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.3
0.3
0.3
0.3
0.3
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
.6600
.6600
.6600
.6600
.6600
.6600
.6600
.6600
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0.55
0.55
0.55
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0.55
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3
3
3
3
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6600
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0.3
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0.55
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0.55
0.55
0.55
0.55
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0.55
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0.55
0.55
0.55
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0.55
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0.55
0.55
0.55
0.55
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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.6600
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.6600
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.6600
.6600
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0
0
0
0
0
0
0
0
0
0
0
0
0
0.3
0.3
0.3
0.3
0.3
.55
.55
.55
.55
.55
.55
.55
.55
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.55
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0.
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3
3
3
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3
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
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.6600
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.6600
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.6600
.6600
.6600
.6600
.6600
97
-------
1241
1241
1241
1241
1241
1241
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
.1000
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.1000
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0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
1241.39
.39
1241.39
.39
1241.39
.39
1241.39
.39
1241.39
.39
1241.39
.39
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
3 0.3
3 0.3
3 0.3
3 0.3
3 0.3
3 0.3
3 0.3
3 0.3
3 0.3
3 0.3
.1000
.1000
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.1000
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.1000
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6 0.6
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6 0.6
6 0.6
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6 0.6
6 0.6
6 0.6
6 0.6
6 0.6
6 0.6
6 0.6
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
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0
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.6
.6
.6
.6
.6
.6
.6
.6
.6
.6
.6
.6
.6
1241.
1241.
1241.
1241.
1241.
1241.
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
.1000
.1000
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0.6
0.6
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0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
39
39
39
39
39
39
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
.1000
.1000
.1000
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0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.3
.3
.3
.3
.3
.3
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.1000
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.1000
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.1000
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.1000
.1000
.1000
.1000
.1000
.1000
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.6
.6
.6
.6
.6
.6
.6
.6
.6
.6
.6
.6
.6
.6
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
.1000
1241
1241
1241
1241
1241
1241
.39
.39
.39
.39
.39
.39
98
-------
1241.39 1241.39 1241.39
1241.39
1241.39 1241.39 1241.39
1241.39
1241.39 1241.39 1241.39
1241.39
1241.39 1241.39 1241.39
1241.39
1241.39 1241.39 1241.39
1241.39
1241.39 1241.39 1241.39
1241.39
1241.39 1241.39 1241.39
1241.39
1241.39 1241.39 1241.39
1241.39
1241.39 1241.39 1241.39
,7079 .7079 .7079 .7079
.7079 .7079 .7079 .7079
.7079 .7079 .7079 .7079
.7079 .7079 .7079 .7079
.7079 .7079 .7079 .7079
.7079 .7079 .7079 .7079
.7079 .7079 .7079 .7079
.7079 .7079 .7079 .7079
.7079 .7079 .7079 .7079
.7079 .7079 .7079 .7079
.7079 .7079 .7079 .7079
.7079 .7079 .7079 .7079
.7079 .7079 .7079 .7079
.7079 .7079 .7079 .7079
.7079
6.
6.
6.
6.
6.
6.
6.
6.
6.
6.
6.
6.
6.
6.
6.
0.
0.
0.
0.
0.
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
61
61
61
61
61
.7079
6.5
6.5
6.5
6.5
6.5
6.5
6.5
6.5
6.5
6.5
6.5
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6.5
6.5
6.5
0.61
0.61
0.61
0.61
0.61
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
1241.39
.7079
.7079
.7079
.7079
.7079
.7079
.7079
.7079
.7079
.7079
.7079
.7079
.7079
.7079
1241.39 1241.39
1241.39 1241.39
1241.39 1241.39
1241.39 1241.39
1241.39 1241.39
1241.39 1241.39
1241.39 1241.39
1241.39 1241.39
.7079 .7079
.7079 .7079
.7079 .7079
.7079 .7079
.7079 .7079
.7079 .7079
.7079 .7079
.7079 .7079
.7079 .7079
.7079 .7079
.7079 .7079
.7079 .7079
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0.61
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6
6
6
6
6
6
6
6
6
6
6
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6
0.61
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6
6
6
6
6
6
6
6
6
6
6
6
6
6
0.61
0.61
0.61
0.61
0.61
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0.61
0.61
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0.61
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-------
Input Data File: WTV4.dat
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281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
102
-------
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
281.72
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
103
-------
Input pqta File! WTV5.dat
0-0 0.0
0.1 35.607219
0.0 6.6392447
0.0 2.5100518
0-0 0.15
5 2
6.0 18.0
30.0 42.0
54.0 66.0
78.0 90.0
102.0 114.0
0.0 6.0
130.0 140.0
105
-------
Output Data File: P1RNFL
TIMEST- .3000E+01
LAYER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
NODE POSITION
( CM )
.OOOOE+00
. 1000E+00
.1100E+01
.2100E+01
.3100E+01
.4100E+01
.5100E+01
.6100E+01
.7100E+01
.8100E+01
.9100E+01
.1010E+02
.1110E+02
.1210E+02
.1310E+02
.1410E+02
.1510E+02
.1610E+02
.1710E+02
.1810E+02
.1910E+02
.2010E+02
.2110E+02
.2210E+02
.2310E+02
.2410E+02
.2510E+02
.2610E+02
.2710E+02
.2810E+02
.2910E+02
.3010E+02
.3110E+02
.3210E+02
.3310E+02
. 3410E+02
.3510E+02
.3610E+02
.3710E+02
.3810E+02
.3910E+02
.4010E+02
.4110E+02
.4210E+02
.4310E+02
.4410E+02
.4510E+02
WATER
(CM3/CM3 SOIL)
.2931E+00
.2926E+00
.2889E+00
.2849E+00
.2809E+00
.2770E+00
.2731E+00
.2694E+00
.2660E+00
.2629E+00
.2601E+00
.2578E+00
.2558E+00
.2543E+00
.2531E+00
.2522E+00
.2515E+00
.2510E+00
.2507E+00
.2505E+00
.2502E+00
.2502E+00
.2501E+00
.2501E+00
.2501E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
. 2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E-1-00
.2500E+00
. 2500E+00
.2500E+00
.2500E+00
.2500E+00
TEMP
(K)
.2772E+03
.2773E+03
.2781E+03
.2787E-K)3
.2793E+03
.2798E-t-03
.2802E+03
.2806E+03
.2809E+03
.2811E+03
.2813E+03
.2814E+03
.2815E+03
.2816E+03
.2816E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
TEMP
(K)
.2772E+03
.2773E+03
.2781E+03
.2787E-K)3
.2793E+03
.2798E-t-03
.2802E+03
.2806E+03
.2809E+03
.2811E+03
.2813E+03
.2814E+03
.2815E+03
.2816E+03
.2816E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
VIRUS
(PFU/ML)
.7458E+05
.6307E+05
.1059E+05
.1096E+04
.7991E+02
.4212E+01
.1636E+00
.4710E-02
.1003E-03
.1572E-05
.1799E-07
.1488E-09
.8829E-12
.3731E-14
.1119E-16
.2380E-19
.3610E-22
.3948E-25
.3167E-28
.1911E-31
.8955E-35
.3381E-38
.1070E-41
.2949E-45
.7331E-49
.1691E-52
.3702E-56
.7820E-60
.1612E-63
.3271E-67
.6564E-71
.1308E-74
.2593E-78
.5122E-82
.1009E-85
.1984E-89
.3893E-93
.7628E-97
.1493-100
.2917-104
.5693-108
.1110-111
.2160-115
.4201-119
.8161-123
.1583-126
.3069-130
RCV
.7458E+00
.6307E+00
.1059E+00
.1096E-01
.7991E-03
.4212E-04
.1636E-05
.4710E-07
.1003E-08
.1572E-10
.1799E-12
.1488E-14
.8829E-17
.3731E-19
.1119E-21
.2380E-24
.3610E-27
.3948E-30
.3167E-33
.1911E-36
.8955E-40
.3381E-43
.1070E-46
.2949E-50
.7331E-54
.1691E-57
.3702E-61
.7820E-65
.1612E-68
.3271E-72
.6564E-76
.1308E-79
.2593E-83
.5122E-87
.1009E-90
.1984E-94
.3893E-98
.7628-102
.1493-105
.2917-109
.5693-113
.1110-116
.2160-120
.4201-124
.8161-128
.1583-131
.3069-135
106
-------
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
.4610E+02
.4710E+02
.4810E+02
.4910E+02
.5010E+02
.5110E+02
.5210E+02
.5310E+02
. 5410E+02
.5510E+02
.5610E+02
.5710E+02
.5810E+02
.5910E+02
.6010E+02
.6110E+02
.6210E+02
.6310E+02
.6410E+02
.6510E+02
.6610E+02
.6710E+02
.6810E+02
.6910E+02
.7010E+02
.7110E+02
.7210E+02
.7310E+02
.7410E+02
.7510E+02
.7610E+02
.7710E+02
.7810E+02
.7910E-I-02
.8010E+02
.8110E+02
.8210E+02
.8310E+02
.8410E+02
. 8510E+02
.8610E+02
.8710E+02
.8810E+02
.8910E+02
.9010E+02
.9110E+02
.9210E+02
.9310E+02
.9410E+02
.9510E+02
.9610E+02
.9710E+02
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
,2500E-K)0
.2500E+00
.2500E+00
.2500E-1-00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E-»-00
.2500E+00
.2500E+00
.2500E+00
.2500E-t-00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
. 2500E+00
.2500E-t-00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
. 2500E+00
.2500E-KX)
.2500E+00
.2500E+00
. 2500E+00
. 2500E+00
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E-1-03
.2817E+03
.2817E+03
.2817E+03
.2817E-1-03
.2817E+03
.2817E+03
.2817E+03
.2817E-K)3
.2817E-K)3
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E-1-03
.2817E+03
.2817E-K)3
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.5940-134
.1149-137
.2219-141
.4281-145
.8252-149
.1589-152
.3056-156
.5873-160
.1127-163
.2162-167
.4141-171
.7924-175
.1515-178
.2893-182
.5521-186
.1053-189
.2005-193
.3814-197
.7250-201
.1377-204
.2613-208
.4954-212
.9383-216
.1776-219
.3357-223
.6343-227
.1197-230
.2258-234
.4255-238
.8011-242
.1507-245
.2833-249 '
.5321-253
.9985-257
.1872-260
.3508-264
.6569-268
.1229-271
.2297-275
.4291-279
.8010-283
.1494-286
.2785-290
.5186-294
.9653-298
.1795-301
.3336-305
.6196-309
.1150-312
.2133-316
.3957-320
.OOOOE+00
.5940-139
.1149-142
.2219-146
.4281-150
.8252-154
.1589-157
.3056-161
.5873-165
.1127-168
.2162-172
.4141-176
.7924-180
.1515-183
.2893-187
.5521-191
.1053-194
.2005-198
.3814-202
.7250-206
.1377-209
.2613-213
.4954-217
.9383-221
.1776-224
.3357-228
.6343-232
.1197-235
.2258-239
.4255-243
.8011-247
.1507-250
.2833-254
.5321-258
.9985-262
.1872-265
.3508-269
.6569-273
.1229-276
.2297-280
.4291-284
.8010-288
.1494-291
.2785-295
.5186-299
.9653-303
.1795-306
.3336-310
.6196-314
.1150-317
.2124-321
.OOOOE+00
.OOOOE+00
107
-------
100 .9810E+02
101 .9910E+02
TIHEST- .6000E+01
LAYER NODE POSITION
( CM )
1 .OOOOE+00
2 .1000E+00
3 .1100E+01
4 .2100E+01
5 .3100E+01
6 .4100E+01
7 .5100E+01
8 .6100E+01
9 .7100E+01
10 .8100E+01
11 .9100E+01
12 .1010E+02
13 .1110E+02
14 .1210E+02
15 .1310E+02
16 .1410E+02
17 .1510E+02
18 .1610E+02
19 .1710E+02
20 .1810E+02
21 .1910E+02
22 .2010E+02
23 .2110E+02
24 .2210E+02
25 .2310E+02
26 .2410E+02
27 .2510E+02
28 .2610E+02
29 .2710E+02
30 .2810E+02
31 .2910E+02
32 .3010E+02
33 .3110E+02
34 .3210E+02
35 .3310E+02
36 .3410E+02
37 .3510E+02
38 .3610E+02
39 .3710E+02
40 .3810E+02
41 .3910E+02
42 .4010E+02
43 .4110E+02
44 .4210E+02
45 .4310E+02
46 .4410E+02
47 .4510E+02
.2SOOE+00
.2500E+00
WATER
(CM3/CM3 SOIL)
.3059E+00
.3056E+00
.3026E+00
.2995E+00
.2964E+00
.2932E+00
.2899E+00
.2867E+00
.2835E+00
.2802E+00
.2771E+00
.2740E+00
.2710E+00
.2682E+00
.2655E+00
.2631E+00
.2609E+00
.2589E+00
.2572E+00
.2558E+00
.2545E+00
.2535E+00
.2527E+00
.2521E+00
.2516E+00
.2512E+00
.2509E+00
.2507E+00
.2505E+00
.2503E+00
.2503E+00
.2502E+00
.2501E+00
.2501E+00
.2501E+00
.2500E+00
.2500E-I-00
.2500E+00
.2500E+00
. 2500E+00
.2500E+00
.2500E+00
.2500E+00
. 2500E+00
.2500E+00
.2500E+00
.2500E+00
.2817E+03
.2S17E+03
TEMP
(K)
.2763E+03
.2764E+03
.2770E+03
.2776E+03
.2781E+03
.2786E+03
.2791E+03
.2795E+03
.2798E+03
.2802E+03
.2804E+03
.2807E+03
.2809E+03
.2810E+03
.2812E+03
.2813E+03
.2814E+03
.2815E+03
.2815E+03
.2816E+03
.2816E+03
.2816E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E-HD3
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.OOOOE+00
. OOOOE+00
VIRUS
(PFU/ML)
.1061E+06
.9794E+05
.3055E+05
.6254E+04
.9466E+03
.1097E+03
.1001E+02
.7306E+00
.4309E-01
.2063E-02
.8033E-04
.2540E-05
.6503E-07
.1342E-08
.2218E-10
.2918E-12
.3034E-14
.2478E-16
.1579E-18
.7813E-21
.2990E-23
.8835E-26
.2015E-28
.3559E-31
.4890E-34
.5274E-37
.4517E-40
.3119E-43
.1768E-46
.8399E-50
.3421E-53
.1222E-56
.3916E-60
.1149E-63
.3144E-67
.8153E-71
.2029E-74
.4893E-78
.1153E-81
.2672E-85
.6113E-89
.1386E-92
.3118E-96
.6981-100
.1557-103
.3460-107
.7669-111
.OOOOE+00
.OOOOE+00
RCV
.1061E+01
.9794E+00
.3055E+00
.6254E-01
.9466E-02
.1097E-02
.1001E-03
.7306E-05
.4309E-06
.2063E-07
.8033E-09
.2540E-10
.6503E-12
.1342E-13
.2218E-15
.2918E-17
.3034E-19
.2478E-21
.1579E-23
.7813E-26
.2990E-28
.8835E-31
.2015E-33
.3559E-36
.4890E-39
.5274E-42
.4517E-45
.3119E-48
.1768E-51
.8399E-55
.3421E-58
.1222E-61
.3916E-65
.1149E-68
.3144E-72
.8153E-76
.2029E-79
.4893E-83
.1153E-86
.2672E-90
.6113E-94
.1386E-97
.3118-101
.6981-105
.1557-108
.3460-112
.7669-116
108
-------
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
.4610E+02
.4710E+02
.4810E+02
.4910E+02
. 5010E+02
.5110E-f02
. 5210E+02
.5310E+02
. 5410E+02
.5510E+02
. 5610E+02
. 5710E+02
.S810E-M32
.5910E-f02
. 6010E+02
.6110E+02
.6210E+02
.6310E+02
.6410E+02
.6510E+02
.6610E+02
.6710E+02
.6810E+02
.6910E+02
.7010E+02
.7110E+02
.7210E+02
.7310E+02
. 7410E+02
.7510E+02
.7610E+02
.7710E+02
.7810E+02
.7910E+02
.8010E-I-02
.8110E+02
.8210E-I-02
.8310E+02
.8410E+02
.8510E+02
.8610E+02
.8710E+02
.8810E+02
.8910E+02
.9010E+02
.9110E+02
.9210E+02
.9310E^02
. 9410E-I-02
.9510E+02
.9610E+02
.9710E+02
.2500E+00
,2500E-fOO
.2500E+00
.2500E+00
.2500E-I-00
.2500E+00
,2500E-fOO
o 2500E-J-00
.2500E-fOO
.2500E+00
. 2500E+00
. 2SOOE+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
. 2500E+00
.2500E+00
. 2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
. 2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E-fOO
.2500E-»-00
.2500E-I-00
.2500E-fOO
.2500E+00
. 2500E+00
.2500E+00
. 2500E+00
.2500E+00
.2500E-K)0
.2500E+00
.2500E+00
. 2500E+00
. 2500E+00
.2817E+03
.2817E+03
.2817E+03
.2817E-4-03
.2817E+03
.2817E+03
.2817E+03
.2817E-K)3
.2817E+03
.2817E+03
.2S17E+03
.2817E+03
.2817E-f03
.2817E-K)3
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E-I-03
.2817E+03
.2817E+03
.2817E-»-03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E-K)3
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.1696-114
.3745-118
.8255-122
.1817-125
.3992-129
.8760-133
.1920-136
.4202-140
.9185-144
.2005-147
.4372-151
.9520-155
.2071-158
.4498-162
.9759-166
.2115-169
.4577-173
.9895-177
.2136-180
.4608-184
.9925-188
.2136-191
.4589-195
.9851-199
.2112-202
.4524-206
.9677-210
.2068-213
.4413-217
.9408-221
.2003-224
.4261-228
.9054-232
.1922-235
.4074-239
.8628-243
.1825-246
.3857-250
.8142-254
.1717-257
.3616-261
.7609-265
.1599-268
.3358-272
.7045-276
.1476-279
.3090-283
.6461-287
.1350-290
.2817-294
.5873-298
.1223-301
.1696-119
.3745-123
.8255-127
.1817-130
.3992-134
.8760-138
.1920-141
.4202-145
.9185-149
.2005-152
.4372-156
.9520-160
.2071-163
.4498-167
.9759-171
.2115-174
.4577-178
.9895-182
.2136-185
.4608-189
.9925-193
.2136-196
.4589-200
.9851-204
.2112-207
.4524-211
.9677-215
.2068-218
.4413-222
.9408-226
.2003-229
.4261-233
.9054-237
.1922-240
.4074-244
.8628-248
.1825-251
.3857-255
.8142-259
.1717-262
.3616-266
.7609-270
.1599-273
.3358-277
.7045-281
.1476-284
.3090-288
.6461-292
.1350-295
.2817-299
.5873-303
.1223-306
109
-------
100 .9810E+02 .2500E+00 .2817E+03 .2545-305 .2545-310
101 .9910E+02 .2500E+00 .2817E+03 .1435-305 .1435-310
110
-------
Output Data File: P2RNFL
TIME WATER EVAP. TEMPI TEMP5 TEMP10 TEMP20 TEMP50
.1000E+01-.6399E-03 .2784E+03 .2814E+03 .2817E+03 .2817E+03 .2817E+03
.2000E+01-.3555E-03 .2777E+03 .2808E+03 .2816E+03 .2817E+03 .2817E+03
.3000E+01-.2015E-03 .2772E+03 .2802E-1-03 .2814E+03 .2817E+03 .2817E+03
.4000E+01-.9010E-04 .2769E+03 .2798E+03 .2812E+03 .2817E-I-03 .2817E+03
.5000E+01-.1567E-04 .2766E+03 .2794E+03 .2809E+03 .2817E+03 .2817E+03
.6000E+01 .3717E-04 .2763E+03 .2791E+03 .2807E+03 .2816E+03 .2817E+03
111
-------
Output Data File: TEST.OUT
RUN CONTROL INFORMATION.
T0« .0000 TOUT- 6.1000 DTO- .1000
PRTIN(I)- 1.0000 2.9900 5.9900 17.9900 23.9900
29.9900 35.9900 41.9900 47.9900 71.9900
119.9900 139.9900 149.9900 159.9900
000000101010000010
169.9900
NPRINT(I)- 0
NNSTR2(I)« 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
24 25
LAYER, THICKNESS(CM), NODAL POSITION(CM).
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
. 1000E+00
.1000E+01
.1000E+01
. 1000E+01
.1000E+01
.1000E+01
.1000E+01
.1000E+01
.1000E+01
.1000E+01
.1000E+01
.1000E+01
.1000E+01
.1000E+01
.1000E+01
. 1000E+01
.1000E+01
.1000E+01
.1000E+01
.1000E+01
.1000E+01
.1000E+01
. lOOOE-f-01
.1000E+01
.1000E+01
. 1000E+01
. 1000E+01
. lOOOE-f 01
. 1000E+01
. 1000E+01
.1000E+01
. 1000E+01
.1000E+01
.OOOOE+00
. 1000E+00
.1100E+01
.2100E+01
.3100E+01
.4100E+01
.5100E+01
.6100E+01
.7100E+01
.8100E+01
.9100E+01
.1010E+02
.1110E+02
.1210E+02
.1310E+02
.1410E+02
.1510E+02
.1610E+02
.1710E+02
.1810E+02
.1910E+02
.2010E+02
.2110E+02
.2210E+02
.2310E+02
.2410E+02
.2510E-t-02
.2610E-J-02
.2710E-V02
.2810E+02
.2910E+02
.3010E+02
.3110E+02
112
-------
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
. 1000E+01
.1000E+01
.1000E+01
. 1000E+01
. 1000E+01
.1000E+01
.1000E+01
. 1000E+01
.1000E+01
.1000E+01
. 1000E+01
.1000E+01
. 1000E+01
.1000E+01
. 1000E+01
. 1000E+01
.1000E+01
.1000E+01
.1000E+01
.1000E+01
.1000E+01
.1000E+01
. 1000E+01
.1000E+01
.1000E+01
.1000E+01
.1000E+01
. 1000E+01
.1000E+01
.1000E+01
.1000E+01
. 1000E+01
.1000E+01
.1000E+01
. 1000E-I-01
.1000E+01
. 1000E+01
. 1000E+01
.1000E+01
. 1000E+01
. 1000E+01
.1000E-K)!
. 1000E+01
. 1000E+01
.lOOOE-t-01
.1000E+01
. 1000E+01
.1000E+01
. 1000E-K)!
. 1000EH-01
. 1000E+01
.1000E+01
.3210E+02
.3310E+02
.3410E+02
.3510E+02
.3610E+02
.3710E-I-02
.3810E+02
.3910E+02
.4010E+02
.4110E+02
.4210E-K)2
.4310E+02
.4410E+02
.4510E+02
.4610E+02
.4710E+02
.4810E+02
.4910E+02
.5010E+02
.5110E+02
.5210E+02
.5310E+02
.5410E+02
.5510E+02
.5610E+02
.5710E-t-02
.5810E+02
.5910E+02
.6010E+02
.6110E+02
.6210E+02
.6310E+02
.6410E+02
.6510E+02
.6610E+02
.6710E+02
.6810E+02
.6910E+02
.7010E+02
.7110E-I-02
.7210E+02
.7310E+02
.7410E+02
.7510E+02
.7610E+02
.7710E+02
.7810E+02
.7910E+02
.8010E+02
.8110E+02
.8210E+02
.8310E+02
113
-------
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
.1000E+01
.1000E+01
.1000E+01
. 1000E+01
. 1000E+01
. 1000E+01
. 1000E+01
. 1000E+01
. 1000E+01
.1000E+01
.1000E+01
.1000E+01
.1000E+01
.1000E+01
.1000E+01
.8410E+02
.8510E+02
.8610E+02
.8710E+02
.8810E-I-02
.8910E-I-02
.9010E+02
.9110E+02
.9210E-I-02
.9310E+02
.9410E+02
.9510E+02
.9610E+02
.9710E+02
.9810E+02
NUMBER OF INTERNAL SOIL NODES- 99 SOIL THICKNESS (CM)-
BOUNDARY LAYER THICKNESS- 1.0000
.2640E+01 RHOSIL-
.7000E-01 ALBSOI-
.9bOOE+00 EMSSOI-
RHOSND- .2660E+01 RHOCLA-
ALBAIR- .5000E-01 ALBWAT-
EMSAIR- .9000E+00 EMSWAT-
LAMBHT- .3330E-03
LAMSLD - .3430E+01
SHTSAN- .1750E+00 SHTSIL- .1750E+00 SHTCLA-
. lOOOE-t-01 SHTAIR- . 2400E+00
99.1000
.2650E+01
.9000E-01
.5000E+00
.1750E+00 SHTWAT-
GAMTLI- -.2090E-02 BETATV- .1056E-05
DWVAR(I)- .9540E+03 .4770E+04 .3330E-03
RHOWAT- .1000E+01 RHOAIR- .1100E-02 WS - .OOOOE+00
DRIVING FUNCTION PARAMETERS.
FOURIER COEFFICIENTS
NCFTMP - 2 NCFFRH - 5
INDEX ATEMP
1 -1.006722
BTEMP
-2.356627
114
-------
-.371836
1.000000
INDEX
1
2
3
4
5
ARHIN
.037193
-.005292
-.009458
.006375
-.006108
BRH1N
.067587
-.027424
.011667
-.004330
.004079
TPINMU - 8.757800 RHINMU -
.869000 TPWATI - 277.000000
INDEX
1
2
INDEX
1
2
3
4
5
INDEX
1
2
3
4
5
INDEX
1
2
3
4
5
INDEX
1
2
OMEGTP
.261199
.523598
OMGRHI
.261199
.523598
.785397
1.047196
1.308995
QRAIN QSR
.OOOOE+00
.1000E+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
TIME LIGHT ON
.6000E+01
. 3000E+02
. 5400E+02
.7800E+02
.1020E+03
TIME RAIN ON
. OOOOE+00
.1300E+03
OOOOE+00
3561E+02
6639E+01
2510E+01
1500E+00
TIME LIGHT OFF
.1800E+02
.4200E+02
.6600E+02
.9000E+02
.1140E+03
TIME RAIN OFF
.6000E+01
. 1400E+03
VIRUS PARAMETERS
115
-------
DISPLZ- .1000E+01 DLO- .3240E-03 CWIN- .1000E+06 CVGRD- .OOOOE+00
AIR R.H.
(PERCENT)
AIR TEMP-
(DEC. KELVIN)
.8920E+00
.2817E-4-03
INITIAL FIELD DISTRIBUTIONS
LAYER WATER
(CM3 WATER/CM-3 SOIL)
1 .2500E+00
2 .2500E+00
3 .2500E+00
4 .2500E+00
5 .2500E+00
6 .2500E+00
7 .2500E+00
8 .2500E+00
9 .2500E+00
10 .2500E+00
11 .2500E+00
12 .2500E+00
13 .2500E+00
14 .2500E+00
15 .2500E+00
16 .2500E+00
17 .2500E+00
18 .2500E+00
19 .2500E+00
20 .2500E+00
21 .2500E+00
22 .2500E+00
23 .2500E+00
24 .2500E+00
25 .2500E+00
26 .2500E+00
27 .2500E+00
28 .2500E+00
29 .2500E-I-00
30 .2500E+00
31 .2500E+00
32 .2500E+00
33 .2500E+00
34 .2500E+00
35 .2500E+00
36 .2500E+00
37 .2500E-I-00
38 .2500E-K)0
39 .2500E+00
40 .2500E+00
TEMPERATURE
(DEC. KELVIN)
.2817E+03
.2817E+03
.2817E-I-03
.2817E+03
.2817E+03
.2817E-I-03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E-K)3
.2817E+03
.2817E-I-03
.2817E-K)3
.2817E+03
.2817E+03
.2817E+03
VIRUS
(PFU/ML)
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
116
-------
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
.2500E+00
.2500E+00
.2500E4-00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
. 2500E-I-00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E-I-00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E-H03
.2817E+03
.2817E-K)3
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E-f03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E-I-03
.2817E+03
.2817E+03
.2817E+03
.2817E-J-03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E-KJ3
.2817E+03
.2817E+03
.OOOOE+00
.OOOOE+00
.OOOOE-l-00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
117
-------
93
94
95
96
97
98
99
100
101
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
UNIVERSAL CONSTANTS
GRAV - .1271E+11 R - .5981E+14 SIGMA
TABLES OF SOIL PROPERTIES
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.4896E-08
THTAST(I)
.5500E+00
5500E+00
.5500E+00
5500E+00
.5500E+00
5500E+00
.5500E+00
5500E+00
.5500E+00
5500E+00
.5500E+00
5500E+00
.5500E+00
5500E+00
.5500E+00
5500E+00
.5500E+00
5500E+00
.5500E+00
5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
. 5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
. 5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
. 5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
. 5500E+00
.5500E+00
.5500E+00
TORT(I)
.6600E+00
6600E+00
.6600E+00
6600E+00
.6600E+00
6600E+00
.6600E+00
6600E+00
.6600E+00
.6600E+00
. 6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
. 6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
. 6600E+00
.6600E+00
.6600E+00
. 6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
. 6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
118
-------
6600E+00
.6600E+00
6600E+00
.6600E+00
6600E+00
. 6600E+00
6600E+00
.6600E+00
6600E+00
.6600E+00
6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
. 6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
. 6600E+00
.6600E+00
.6600E+00
.6600E+00
. 6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E-f-00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
. 6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
. 6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
.6600E+00
EPS(I)
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
. 5500E-KOO
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E-I-00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E-1-00
.5500E+00
.5500E+00
.5500E+00
PCTSAN(I)
.3000E-I-00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
. 3000E-K)0
.3000E+00
.3000E+00
.3000E+00
. 5500E+00
5500E+00
.5500E+00
5500E+00
.5500E+00
5500E+00
.5500E+00
5500E+00
.5500E+00
5500E+00
.5500E+00
5500E+00
.5500E+00
5500E+00
.5500E+00
5500E+00
.5500E+00
5500E+00
.5500E+00
5500E+00
.3000E+00
3000E+00
. 3000E+00
3000E+00
. 3000E+00
3000E+00
. 3000E+00
3000E+00
. 3000E+00
3000E+00
. 3000E+00
3000E+00
. 3000E+00
. 5500E+00
. 5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
. 5500E+00
. 5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.3000E+00
. 3000E+00
. 3000E+00
. 3000E+00
. 3000E+00
.3000E+00
. 3000E+00
. 3000E+00
. 3000E+00
. 3000E+00
. 3000E+00
. 3000E+00
.3000E+00
.5500E+00
.5500E+00
,5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
. 5500E+00'
.5500E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.3000E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.5500E+00
.3000E+00
.3000E+00
. 3000E+09,
. 3000E+0'6
. 3000E+00
.3000E+00
.3000E+00
119
-------
3000E+00
„ 3000E-S-00
3000E+00
. 3000E4-00
300QE+00
„ 3000E+00
3000E-I-00
. 3000E+00
.300QE+00
. 3000E+00
. 3000E+00
. 3000E+00
. 3000E+00
„ 3000E+00
. 3000E+00
. 300GE+ 00
. 3000E+00
. 300QE-H30
. 3000E-J-00
. 3000E+00
„ 3000E+00
. 3000E-J-00
. 3000E-f 00
. 3000E+00
. 3000E-M30
.3000E-S-00
. 3000E-fOO
. 3000E-f 00
. 3000E-J-00
PCTCIA(I)
,10001-s-OO
1©OOE+00
. 1000E+00
1000E+00
. 1000E+00
iOOOE+OO
. lOOOE+00
1000E+00
. 1000E+00
1000E4-00
. 1000E+00
1000E+00
. 1000E+00
lOOOE+00
.lOOOE-s-00
lOOOE+00
.1000E+00
lOOOE+00
. 1000E+00
1000E-J-00
. 1000E+00
.10001^-00
. 1000E+00
. lOOOE^OO
. 1000E+00
. iOOOE-f 00
. lOOOE+00
„ 1000E+00
.1000E+00
.lOOOE-fOO
.1000E+00
.1000E+00
.1000E+00
. 1000E+00
.1000E+00
.lOOOE-fOO
.1000E+00
. lOOOE-t-00
.1000E+00
.1000E+00
. 1000E+00
.1000E+00
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. 1000E4-00
. 1000E+00
. 1000E+ 00
.1000E4-00
. 1000E+ 00
.1000E+00
.1000E+00
.1000E+00
. lOOOE-fOO
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.1000E+00
.1000E+00
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. 1000E+00
. lOOOE+00
. 1000E+ 00
. 1000E-S-00
. lOOOE+00
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. 1QOOE-H30
.lOOOE+00
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. lOOOE-s-00
. 1000E-I-00
. 1000E+ 00
.lOOOE+00
. lOOOE+00
. lOOOE+00
. lOOOE+00
.lOOOE+00
. lOOOE-f 00
. lOOOE+00
PCTSIL(I)
.6000E+00
6000E+00
.6000E-fOO
6000E+00
. 6000EHKOO
6000E+00
.6000E-fOO
6000E+00
. 6000E+00
SOOOE-i-00
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6000E+00
. 6000E4- 00
6000E+00
. 6000E* 00
6000E+00
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. 60QOE-K>0
. SOOOE-fOO
. 6000E+00
. 6000E+00
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. 6000E+00
. 6000E+00
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.6000E+00
. 6000E-fOO
. 6000E+00
. 6000E+00
. 6000E+00
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. 6000E+00
. 6000E-S-00
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. 6000E+00
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. 6000E+00
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. 6000E+00
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. 6000E-H30
.3000E+00
. 3000E-I-00
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. lOOOE+00
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.lOOOE+00
.6000E+00
.6000E+00
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, 6000E4-00
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.lOOOE+00
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.1000E+00
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.lOOOE+00
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.6000E+00
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.6000E+00
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.6000E+00
.6000E+00
.6000E+00
120
-------
6000E+00
. 6000E+00
6000E+00
. 6000E+00
. 6000E+00
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.6000E+00
.6000E+00
.6000E+00
.6000E+00
.6000E+00
.6000E+00
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.6000E+00
.6000E+00
RHOSOL(I)
.2652E-K)!
.2652E+01
.2652E+01
.2652E+01
.2652E+01
.2652E+01
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.2652E+01
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.2652E+01
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.2652E+01
.2652E+01
.2652E+01
.2652E+01
RHOB(I)
.1193E+01
.1193E+01
.1193E+01
.1193E+01
.1193E+01
.1193E+01
.1193E-I-01
.1193E+01
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.1193E+01
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2652E+01
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2652E+01
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.1193E+01
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.1193E-I-01
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1193E-I-01
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1193E+01
.1193E-K)!
1193E+01
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1193EH-01
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.2652E-KI1
.2652E-K)!
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.2652E+01
.2652E+01
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.2652E+01
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.1193E+01
.1193E^01
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.1193E+01
.2652E+01
.2652E+01
.2652E+01
.2652E+01
.2652E+01
.2652E+01
.2652E+01
.2652E+01
.2652E+01
.2652E-t-01
.1193E+01
.1193E+01
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.1193E-I-01
.1193E-1-01
.1193EH-01
.1193E+01
.1193E+01
.1193E+01
.2652E+01
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.2652E+01
.2652E+01
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.2652E+01
.2652E+01
.2652E+01
.2652E+01
,1193E+01
,1193E+01
.1193E+01
.1193E+01
.1193E+01
.1193E+01
.1193E+01
.1193E+01
.1193E+01
.1193E+01
121
-------
SHTSOL(I)
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.17SOE+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
LAMSOL(I)
.3A30E+01
.3430E+01
.3430E+01
.3430E+01
.3430E-t-01
.3430E-I-01
.3430E+01
.3430E-I-01
.3430E+01
.3430E+01
.3430E+01
.3430E+01
.3430E+01
.3430E+01
.3430E+01
,3430E-K)1
.3430E+01
.3430E-K)!
.3430E+01
.3430E-K)!
.3430E+01
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.3430E+01
.3430E+01
.3430E-H01
.3430E+01
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.3430E+01
.3430E+01
.1750E+00
1750E+00
.1750E+00
1750E+00
.1750E+00
1750E+00
.1750E+00
1750E+00
.1750E+00
1750E+00
. 1750E+00
1750E+00
.1750E+00
1750E+00
.1750E+00
1750E+00
.1750E+00
1750E+00
.1750E+00
1750E+00
.3430E+01
3430E+01
.3430E+01
3430E+01
.3430E+01
3430E+01
.3430E+01
3430E+01
.3430E+01
3430E+01
.3430E+01
3430E+01
.3430E+01
3430E+01
. 3430E+01
3430E+01
.3430E+01
3430E+01
.3430E+01
3430E+01
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E-I-00
.1750E+00
.1750E+00
. 1750E+00
.1750E+00
. 1750E+00
.1750E+00
. 1750E+00
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.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.3430E+01
.3430E+01
.3430E+01
.3430E+01
.3430E+01
.3430E+01
.3430E+01
.3430E+01
.3430E+01
.3430E+01
.3430E+01
. 3430E+01
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. 3430E+01
. 3430E+01
.3430E+01
. 3430E+01
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.3430E+01
.3430E+01
.1750E+00
.1750E+00
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.1750E-I-00
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.3430E+01
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. 3430E+01
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. 3430E+01
.1750E+00
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.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.1750E+00
.3430E+01
.3430E+01
.3430E+01
.3430E+01
.3430E+01
.3430E+01
.3430E+01
.3430E+01
.3430E+01
.3430E+01
ALPTH(I)
.1241E+04
.1241E-M34
.1241E+04
.1241E+04
.1241E+04 .1241E+04
.1241E+04 .1241E+04
.1241E+04
.1241E+04
122
-------
- 1241E+04
1241E+04
•1241E+04
1241E+04
•1241E+04
1241E+04
. 1241E+04
1241E+04
.1241E+04
1241E+04
. 1241E+04
1241E+04
.1241E+04
1241E+04
. 1241E+04
1241E+04
.1241E+04
1241E+04
. 1241E+04
. 1241E+04
. 1241E+04
. 1241E+04
.1241E+04
.1241E+04
.1241E+04
.1241E-K)4
.1241E-K)4
.1241E-I-04
. 1241E-I-04
. 1241E+04
. 1241E+04
.1241E+04
.1241E+04
.1241E-I-04
.1241E+04
. 1241E+04
. 1241E+04
. 1241E+04
. 1241E+04
. 1241E+04
.1241E+04
. 1241E+04
.1241E+04
.1241E+04
. 1241E-K)4
. 1241E+04
.1241E+04
. 1241E+04
.1241E+04
.1241E+04
.1241E+04
.1241E+04
.1241E+04
.1241E+04
.1241E+04
.1241E+04
.1241E+04
. 1241E+04
. 1241E+04
.1241E+04
. 1241E+04
. 1241E-K)4
. 1241E+04
. 1241E+04
. 1241E+04
.1241E-K)4
.1241E+04
. 1241E+04
.1241E+04
.1241E+04
. 1241E+04
.1241E+04
. 1241E+04
BETATH(I)
.7079E+00
7079E+00
.7079E+00
7079E+00
.7079E+00
7079E+00
.7079E+00
7079E+00
.7079E+00
7079E+00
.7079E+00
7079E+00
.7079E+00
7079E+00
.7079E+00
7079E+00
.7079E+00
7079E-I-00
.70192+00
7079E+00
.7079E+OO
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E-K)0
.7079E+00
.7079EH-00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E-HOO
.7079E+00
.7079E+00
.7079E+00
.7079E-K)0
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
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.7079E+00
.7079E+00
.7079E+00
.7079E-1-00
.7079E+00
.7079E+00
.7079E+00
GAMCNS(I)
.6500E+01
6500E+01
.6500E+01
6500E+01
.6500E+01
6500E+01
.6500E-J-01
.6500E+01
.6500E+01
. 6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E-KJ1
.6500E-»-01
.6500E+01
.6500E+01
.6500E+01
.1241E+04
.1241E+04
.1241E+04
.1241E+04
. 1241E+04
.1241E+04
.1241E+04
. 1241E+04
.1241E+04
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E-fOO
.7079E+00
.7079E+00
.6500E+01
.6500E+01
.6500E-t-01
.1241E+OA
.1241E+04
.1241E+04
.1241E+04
.1241E+04
.1241E+04
.1241E+04
.1241E+04
.1241E+04
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.7079E+00
.6500E+01
.6500E+01
.6500E+01
123
-------
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E-K)!
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
KTHSTS(I)
.6100E+00
.6100E+00
.6100E-fOO
.6100E+00
.6100E+00
.6100E+00
.6100E+00
.6100E+00
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.6100E+00
.6100E+00
.6100E+00
.6100E+00
.6100E+00
.6100E+00
.6100E+00
THTRES(I)
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
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.6500E+01
.6500E+01
.6500E-t-01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
. 6500E-I-01
.6500E+01
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.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6500E+01
.6100E+00
eiooE-t-oo
.6100E+00
6100E+00
.6100E+00
6100E+00
.6100E+00
6100E+00
.6100E+00
6100E+00
.6100E+00
6100E+00
.6100E+00
6100E+00
.6100E+00
6100E+00
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6100E+00
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6100E+00
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. 6100E+00
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.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
124
-------
.2900E-01
2900E-01
.2900E-01
2900E-01
.2900E-01
2900E-01
.2900E-01
2900E-01
.2900E-01
2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
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.2900E-01
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.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
.2900E-01
DALPTZ(I)
.OOOOE+00
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DBETAZ(I)
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
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125
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.OOOOE+00
.OOOOE+00
DTHTSZ(I)
.OOOOE+00
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DTHREZ(I)
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
.OOOOE+00
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126
-------
.OOOOE+00
-OOOOE+00
.OOOOE+00
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.OOOOE+00
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.OOOOE+00
OUTPUT DATA FOR DYNAMIC SYSTEM
*** WATER, TEMP., AND VIRUS CONC. , RESPECTIVELY, AT TIME T -1.0000 ***
(DTLAST- .1000)
LAYER WATER
(CH3/CM3 SOIL)
1 .2780E+00
2 .2774E+00
3 .2717E+00
4 .2663E+00
5 .2616E+00
6 .2578E+00
7 .2550E+00
8 .2531E+00
9 .2518E+00
10 .2510E+00
11 .2506E+00
12 .2503E+00
13 .2502E+00
14 .2501E+00
15 .2500E+00
16 .2500E+00
17 .2500E+00
18 .2500E+00
19 .2500E+00
20 .2500E+00
21 .2500E+00
22 .2500E+00
23 .2500E+00
24 .2500E+00
25 .2500E+00
FIELD DISTRIBUTIONS
TEMPERATURE
(DEC. KELVIN)
.2784E+03
.2785E+03
.2795E+03
.2803E+03
.2808E+03
.2812E+03
.2814E+03
.2816E+03
.2816E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
VIRUS
(PFU/ML)
.4090E+05
.2580E+05
.1508E+04
.4823E+02
.9113E+00
.1024E-01
.6823E-04
.2687E-06
.6259E-09
.8731E-12
.7494E-15
.4150E-18
.1588E-21
.4559E-25
.1070E-28
.2203E-32
.4196E-36
.7646E-40
.1360E-43
.2386E-47
.4159E-51
.7219E-55
.1250E-58
.2162E-62
.3734E-66
NODE
PS I
KONTHS
VLZZ
1
2
3
4
5
6
7
8
9
10
11
-.8527E+03
-.8563E+03
-.8905E+03
-.9246E+03
- . 9554E+03
-.9811E+03
- . 1001E+04
- . 1014E+04
-.1023E+04
- . 1029E+04
- . 1032E+04
.5014E-02
.4935E-02
.4254E-02
.3677E-02
.3230E-02
.2903E-02
.2679E-02
.2532E-02
.2441E-02
.2387E-02
.2355E-02
.1873E+00
.1833E+00
.1495E+00
.1230E+00
.9445E-01
.6859E-01
.4730E-01
.3136E-01
.2029E-01
.1305E-01
.8550E-02
127
-------
12
13
14
15
16
17
18
19
20
21
22
23
24
25
-.1034E+04
- . 1035E+04
-.1036E+04
-.1036E+04
- . 1036E+04
-.1037E+04
- . 1037E+04
-.1037E-K>4
- . 1037E+04
- . 1037E+04
-.1037E+04
-.1037E+04
-.1037E+04
-.1037E+04
.2336E-02
.2326E-02
.2321E-02
.2318E-02
.2316E-02
.2315E-02
.2315E-02
.2315E-02
.2314E-02
.2314E-02
.2314E-02
.2314E-02
.2314E-02
.2314E-02
.5848E-02
.4275E-02
.3382E-02
.2886E-02
.2616E-02
.2472E-02
.2395E-02
.2355E-02
.2335E-02
.2325E-02
.2319E-02
.2317E-02
.2316E-02
.2315E-02
IEVENT(1)- 0
IEVENT(2)-
RELATIVE HUMIDITY OF THE OUTER BOUNDARY LAYER AIR- .1000E+01
RELATIVE HUMIDITY AT THE SOIL SURFACE- .9993E+00
SATURATED WATER VAPOR DENSITY IN AIR- .6124E-05
SATURATED WATER VAPOR DENSITY AT AIR-SOIL INTERFACE- .6857E-05
EVAPORATIVE(-) OR CONDENSIVE(+) FLUX--.6399E-03
AIR TEMP. AT OUTER BOUNDARY LAYER EDGE- .2767E+03
SURFACE INFILTRATION RATE(CM/HR)- .1000E+00
TEMP, PAIN WATER- .2770E+03
SOLAR RADIATION- .OOOOE+00
EVAPORATIVE(-) OR CONDENSIVE(+) HEAT TRANSFER—.3794E+00
SENSIBLE HEAT TRANSFER--.3552E+00
TRANSFER OF HEAT OF RAIN WATER INTO SOIL- .4000E+00
*** WATER, TEMP., AND VIRUS CONC., RESPECTIVELY, AT TIME T - 2.0000***
(DTLAST- .1000)
LAYER WATER
(CM3/CM3 SOIL)
1 .2871E+00
2 .2866E+00
3 .2822E+00
4 .2776E+00
5 .2732E+00
6 .2689E+00
7 .2650E+00
8 .2615E+00
9 .2586E+00
10 .2562E+00
11 .2543E+00
12 .2529E+00
13 .2520E+00
14 .2513E+00
15 .2508E+00
16 .2505E+00
FIELD DISTRIBUTIONS
TEMPERATURE
(DEC. KELVIN)
.2777E+03
.2778E+03
.2786E+03
.2793E+03
.2799E+03
.2804E+03
.2808E+03
.2811E+03
.2813E+03
.2814E+03
.2815E-I-03
.2816E+03
.2817E-f03
.2817E+03
.2817E+03
.2817E+03
VIRUS
(PFU/ML)
.5940E+05
.4629E+05
.5336E+04
.3677E+03
.1700E+02
.5377E+00
.1175E-01
.1768E-03
.1818E-05
.1266E-07
.5921E-10
.1850E-12
.3862E-15
.5429E-18
.5222E-21
.3530E-24
128
-------
17
18
19
20
21
22
23
24
25
NODE
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
.2503E+00
.2502E+00
.2501E+00
.2501E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
.2500E+00
PS I
.8001E+03
.8029E+03
.8276E+03
.8544E+03
.8813E-I-03
.9079E+03
.9331E+03
.9561E+03
.9761E+03
.9927E+03
.1006E+04
.1015E+04
.1022E+04
.1027E+04
.1031E+04
.1033E+04
.1034E+04
.1035E+04
.1036E+04
.1036E+04
.1036E+04
.1036E+04
.1037E+04
.1037E+04
.1037E+04
lEVENT(l)- 0
KONTHS
.6333E-02
.6255E-02
.5601E-02
.4977E-02
.4426E-02
.3949E-02
.3547E-02
.3220E-02
.2963E-02
.2768E-02
.2625E-02
.2522E-02
.2451E-02
.2403E-02
.2371E-02
.2350E-02
.2336E-02
.2328E-02
.2322E-02
.2319E-02
.2317E-02
.2316E-02
.2315E-02
.2315E-02
.2315E-02
.2817E+03
.2817E-I-03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
VLZZ
.1826E+00
.1786E-J-00
.1499E+00
.1387E+00
.1228E+00
.1062E+00
.8912E-01
.7247E-01
.5707E-01
.4363E-01
.3249E-01
.2372E-01
.1710E-01
.1230E-01
.8914E-02
.6599E-02
.5050E-02
.4035E-02
-3381E-02
.2967E-02
.2709E-02
.2550E-02
.2454E-02
.2396E-02
.2361E-02
.1742E-27
.6576E-31
.2003E-34
.5187E-38
.1196E-41
.2550E-45
.5164E-49
.1012E-52
.1943E-56
IEVENT(2)-
RELATIVE HUMIDITY OF THE OUTER BOUNDARY LAYER AIR- .1000E+01
RELATIVE HUMIDITY AT THE SOIL SURFACE- .9994E+00
SATURATED WATER VAPOR DENSITY IN AIR- .6131E-05
SATURATED WATER VAPOR DENSITY AT AIR-SOIL INTERFACE- .6528E-05
EVAPORATIVE(-) OR CONDENSIVE(+) FLUX—.3555E-03
AIR TEMP. AT OUTER BOUNDARY LAYER EDGE- .2767E+03
SURFACE INFILTRATION RATE(CM/HR)- .1000E-*-00
TEMP. RAIN WATER- .2770E+03
SOLAR RADIATION- .OOOOE+00
EVAPORATIVE(-) OR CONDENSIVE(+) HEAT TRANSFER— . 2109E+00
SENSIBLE HEAT TRANSFER-- .1974E+00
TRANSFER OF HEAT OF RAIN WATER INTO SOIL- .4000E+00
129
-------
*** WATER, TEMP. , AND VIRUS CONC. , RESPECTIVELY, AT TIME T - 3.0000***
.1000)
(DTLAST-
LAYER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
NODE
WATER
(CM3/CM3 SOIL)
.2931E+00
.2926E+00
.2889E+00
.2849E+00
.2809E+00
.2770E+00
.2731E+00
.2694E+00
.2660E+00
.2629E+00
.2601E+00
.2578E+00
.2558E+00
.2543E+00
.2531E+00
.2522E+00
.2515E+00
.2510E+00
.2507E+00
.2505E+00
.2503E+00
.2502E+00
.2501E+00
.2501E+00
.2501E+00
FIELD DISTRIBUTIONS
TEMPERATURE
(DEC. KELVIN)
.2772E+03
.2773E+03
.2781E+03
.2787E+03
.2793E+03
.2798E+03
.2802E+03
.2806E+03
.2809E+03
.2811E+03
.2813E+03
.2814E+03
.2815E+03
.2816E+03
.2816E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
PSI
KONTHS
VLZZ
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
-.7673E+03
--7697E+03
-.7900E+03
-.8124E+03
-.8352E+03
-.8585E+03
-.8818E+03
- . 9047E+03
-.9267E-KJ3
-.9471E+03
-.9655E+03
-.9815E-I-03
-.9950E+03
-.1006E-K)4
- . 1014E+04
-.1021E+04
-.1026E+04
.7348E-02
.7269E-02
.6628E-02
.5994E-02
.5416E-02
.4889E-02
.4418E-02
.4003E-02
.3646E-02
.3345E-02
.3097E-02
.2898E-02
.2742E-02
.2623E-02
.2533E-02
.2468E-02
.2420E-02
.1798E+00
.1758E+00
.1481E+00
. 1414E+00
.1302E+00
.1188E+00
.1066E+00
.9383E-01
.8095E-01
.6834E-01
.5641E-01
.4556E-01
.3605E-01
.2803E-01
.2150E-01
.1635E-01
.1240E-01
VIRUS
(PFU/ML)
.7458E+05
.6307E+05
.1059E+05
.1096E+04
.7991E+02
.4212E+01
.1636E+00
.4710E-02
.1003E-03
.1572E-05
.1799E-07
.1488E-09
.8829E-12
.3731E-14
.1119E-16
.2380E-19
.3610E-22
.3948E-25
.3167E-28
.1911E-31
.8955E-35
.3381E-38
.1070E-41
.2949E-45
.7331E-49
130
-------
18 -.1029E+04 .2387E-02 .9440E-02
19 -.1031E+04 .2363E-02 .7276E-02
20 -.1033E+04 .2347E-02 .5722E-02
21 -.1034E+04 .2336E-02 .4626E-02
22 -.1035E+04 .2328E-02 .3863E-02
23 -.1036E+04 .2323E-02 .3341E-02
24 -.1036E+04 .2320E-02 .2987E-02
25 -.1036E+04 .2318E-02 .2751E-02
lEVENT(l)- 0 1EVENT(2)- 1
RELATIVE HUMIDITY OF THE OUTER BOUNDARY LAYER AIR- .1000E+01
RELATIVE HUMIDITY AT THE SOIL SURFACE- .9994E+00
SATURATED WATER VAPOR DENSITY IN AIR- .6131E-05
SATURATED WATER VAPOR DENSITY AT AIR-SOIL INTERFACE- .6355E-05
EVAPORATIVE(-) OR CONDENSIVE(-l-) FLUX--.2015E-03
AIR TEMP. AT OUTER BOUNDARY LAYER EDGE- .2767E+03
SURFACE INFILTRATION RATE(CM/HR)- .1000E+00
TEMP. RAIN WATER- .2770E+03
SOLAR RADIATION- .OOOOE+00
EVAPORATIVE(-) OR CONDENSIVE(+) HEAT TRANSFER—.1196E+00
SENSIBLE HEAT TRANSFER--.1126E+00
TRANSFER OF HEAT OF RAIN WATER INTO SOIL- .4000E+00
*** WATER, TEMP., AND VIRUS CONC., RESPECTIVELY, AT TIME T - 4.0000*** (DTLAST-
.1000)
131
-------
FIELD DISTRIBUTIONS
LAYER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
NODE
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
WATER
(CM3/CM3 SOIL)
.2980E+00
.2976E+00
.2942E+00
.2906E+00
.2870E+00
.2833E+00
.2797E+00
.2761E+00
.2726E+00
.2693E+00
.2662E+00
.2633E+00
.2608E+00
.2586E+00
.2567E+00
.2551E+00
.2539E+00
.2529E+00
.2521E+00
.2515E+00
.2511E+00
.2508E+00
.2505E+00
.2504E+00
.2503E+00
PSI
.7410E+03
.7430E-I-03
.7608E+03
.7804E+03
.8005E+03
.8212E-1-03
.8424E+03
.8637E+03
.8849E-H33
.9057E+03
. 9255E+03
.9442E+03
.9611E+03
.9762E+03
.9892E+03
, 1000E+04
.1009E-KJ4
. 1016E+04
.1022E+04
.1026E+04
KONTHS
.8296E-02
.8218E-02
.7570E-02
.6922E-02
.6321E-02
.5762E-02
.5247E-02
.4778E-02
.4358E-02
.3987E-02
.3663E-02
.3386E-02
.3154E-02
.2963E-02
.2808E-02
.2685E-02
.2589E-02
.2516E-02
.2460E-02
.2419E-02
TEMPERATURE
(DEC. KELVIN)
.2769E+03
.2770E+03
.2777E-»-03
.2783E+03
.278-9E+03
.2794E+03
.2798E+03
.2802E+03
.2805E+03
.2808E+03
.2810E+03
.2812E-f03
.2813E+03
.2814E+03
.2815E+03
.2816E+03
.2816E+03
.2816E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
.2817E+03
VLZZ
.1775E+00
.1740E+00
.1493E+00
.1443E+00
.1353E+00
.1263E-t-00
.1166E-1-00
. 1064E+00
.9578E-01
.8496E-01
.7416E-01
.6365E-01
.5370E-01
.4453E-01
.3634E-01
.2923E-01
.2323E-01
.1831E-01
.1435E-01
.1125E-01
VIRUS
(PFU/ML)
.8707E+05
.7689E+05
.1678E+05
.2310E+04
.2290E+03
.1687E+02
.9463E+00
.4087E-01
.1364E-02
.3514E-04
.6964E-06
.1054E-07
.1210E-09
.1044E-11
.6718E-14
.3206E-16
.1129E-18
.2930E-21
.5609E-24
.7967E-27
.8481E-30
.6870E-33
.4323E-36
.2167E-39
.8914E-43
132
-------
21 -.1029E+04
22 -.1031E+04
23 -.1033E+04
24 - . 1034E+04
25 -.1035E+04
lEVENT(l)- 0
.2389E-02
.2367E-02
.2351E-02
.2340E-02
.2332E-02
.8861E-02
.7053E-02
.5707E-02
.4717E-02
.4000E-02
IEVENT(2)-
RELATIVE HUMIDITY OF THE OUTER BOUNDARY LAYER AIR- .1000E+01
RELATIVE HUMIDITY AT THE SOIL SURFACE- .9994E+00
SATURATED WATER VAPOR DENSITY IN AIR- .6111E-05
SATURATED WATER VAPOR DENSITY AT AIR-SOIL INTERFACE- .6213E-05
EVAPORATIVE(-) OR CONDENSIVE(+) FLUX—.9010E-04
AIR TEMP. AT OUTER BOUNDARY LAYER EDGE- .2766E+03
SURFACE INFILTRATION RATE(CM/HR)- .1000E+00
TEMP. RAIN WATER- .2770E+03
SOLAR RADIATION- .OOOOE+00
EVAPORATIVE(-) OR CONDENSIVE(+) HEAT TRANSFER—.5350E-01
SENSIBLE HEAT TRANSFER—.5151E-01
TRANSFER OF HEAT OF RAIN WATER INTO SOIL- .4000E+00
*** WATER, TEMP., AND VIRUS CONC. , RESPECTIVELY, AT TIME T - 5.0000***
(DTLAST- .1000)
LAYER WATER
(CM3/CM3 SOIL)
1 .3022E+00
2 .3019E+00
3 .2987E+00
4 .2954E-t-00
5 .2920E+00
6 .2886E+00
7 .2852E+00
8 .2818E+00
9 .2784E+00
10 .2751E+00
11 .2719E+00
12 .2688E+00
13 .2660E+00
14 .2633E+00
15 .2610E+00
16 .2589E-I-00
17 .2571E+00
18 .2556E+00
19 .2543E+00
20 .2533E-I-00
21 .2525E+00
22 .2519E+00
23 .2514E-I-00
24 .2510E+00
25 .2507E+00
FIELD DISTRIBUTIONS
TEMPERATURE
(DEC. KELVIN)
.2766E+03
.2767E+03
.2773E+03
.2779E+03
.2785E+03
.2790E+03
.2794E+03
.2798E+03
.2802E+03
.2804E+03
.2807E+03
.2809E+03
.2811E+03
.2812E-1-03
.2814E-K03
.2814E+03
.2815E-I-03
.2816E-K)3
.2816E-t-03
.2816E-K)3
.2817E-K)3
.2B17E+03
.2817E-I-03
.2817E+03
.2817E+03
VIRUS
(PFU/ML)
.9741E+05
.8834E+05
.2353E+05
.4036E+04
.5056E+03
.4790E+02
.3525E+01
.2043E+00
.9399E-02
.3440E-03
.1001E-04
.2306E-06
.4185E-08
.5946E-10
.6563E-12
.5587E-14
.3642E-16
.1808E-18
.6808E-21
.1940E-23
.4183E-26
.6854E-29
.8589E-32
.8321E-35
.6327E-38
133
-------
NODE
PSI
KONTHS
VLZZ
1 -.7193E+03
2 -.7211E+03
3 -.7371E+03
4 -.7546E+03
5 -.7726E+03
6 -.7913E+03
7 -.8105E+03
8 -.8301E+03
9 -.8499E+03
10 -.8698E+03
11 -.8895E+03
12 -.9086E-K)3
13 -.9270E+03
14 -.9442E+03
15 -.9599E+03
16 -.9740E+03
17 -.9864E+03
18 -.9969E+03
19 -.1006E+04
20 -.1013E+04
21 -.1019E+04
22 -.1023E+04
23 -.1027E+04
24 -.1029E+04
25 -.1031E+04
lEVENT(l)- 0
.9178E-02
.9101E-02
.8446E-02
.7790E-02
.7172E-02
.6590E-02
.6045E-02
.5540E-02
.5075E-02
.4653E-02
.4273E-02
.3936E-02
.3641E-02
.3386E-02
.3170E-02
.2989E-02
.2841E-02
.2720E-02
.2624E-02
.2548E-02
.2489E-02
.2444E-02
.2409E-02
.2384E-02
.2364E-02
.1758E+00
.1725E+00
.1501E+00
.1462E+00
.1387E+00
.1313E+00
.1233E+00
.1148E+00
.1059E+00
.9667E-01
.8722E-01
.7769E-01
.6828E-01
.5917E-01
.5054E-01
.4256E-01
.3537E-01
.2904E-01
.2360E-01
.1903E-01
.1527E-01
.1223E-01
.9824E-02
.7939E-02
.6485E-02
IEVENT(2)-
RELATIVE HUMIDITY OF THE OUTER BOUNDARY LAYER AIR- .1000E+01
RELATIVE HUMIDITY AT THE SOIL SURFACE- .9994E+00
SATURATED WATER VAPOR DENSITY IN AIR- .6069E-05
SATURATED WATER VAPOR DENSITY AT AIR-SOIL INTERFACE- .6091E-05
EVAPORATIVE(-) OR CONDENSIVE(+) FLUX—.1567E-04
AIR TEMP. AT OUTER BOUNDARY LAYER EDGE- .2765E+03
SURFACE INFILTRATION RATE(CM/HR)- .lOOOE-MDO
TEMP- RAIN WATER- .2770E+03
SOLAR RADIATION- .OOOOE+00
EVAPORATIVE(-) OR CONDENSIVE(-l-) HEAT TRANSFER—.9309E-02
SENSIBLE HEAT TRANSFER—.1051E-01
TRANSFER OF HEAT OF RAIN WATER INTO SOIL- .4000E+00
WATER, TEMP., AND VIRUS CONC., RESPECTIVELY, AT TIME T -6.0000 ***
(DTLAST- .1000)
LAYER WATER
(CM3/CM3 SOIL)
1 .3059E+00
2 .3056E-I-00
3 .3026E+00
FIELD DISTRIBUTIONS
TEMPERATURE
(DEC. KELVIN)
.2763E+03
.2764E+03
.2770E+03
VIRUS
(PFU/ML)
.1061E+06
.9794E+05
.3055E+05
134
-------
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
NODE
.2995E+00
.2964E+00
.2932E+00
.2899E+00
.2867E+00
.2835E+00
.2802E+00
.2771E-I-00
.2740E+00
.2710E-K)0
.2682E+00
.2655E+00
.2631E+00
.2609E+00
.2589E+00
.2572E+00
.2558E+00
.2545E+00
.2535E+00
.2527E+00
.2521E+00
.2516E+00
PSI
KONTHS
.2776E+03
.2781E+03
.2786E+03
.2791E+03
.2795E+03
.2798E-»-03
.2802E+03
.2804E+03
.2807E+03
.2809E+03
.2810E+03
.2812E+03
.2813E+03
.2814E+03
.2815E-I-03
.2815E+03
.2816E+03
.2816E+03
.2816E+03
.2817E+03
.2817E+03
.2817E+03
VLZZ
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
-.7009E+03
-.7025E+03
-.7171E+03
-.7330E+03
- . 7494E+03
-.7663E+03
-.7839E+03
-.8019E+03
-.8203E-f-03
-.8390E+03
-.8578E+03
-.8766E+03
-.8950E+03
-.9129E+03
-.9299E+03
-.9459E+03
-.9606E+03
-.9738E+03
-.9855E+03
-.9955E-K03
- . 1004E+04
-.1011E-K)4
- . 1017E+04
-.1022E+04
-.1025E-K)4
.1001E-01
.9930E-02
.9272E-02
.8608E-02
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.1743E+00
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.1347E-t-00
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.8835E-26
.2015E-28
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.4890E-34
lEVENT(l)- 0
IEVENT(2)-
135
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RELATIVE HUMIDITY OF THE OUTER BOUNDARY LAYER AIR- .1000E+01
RELATIVE HUMIDITY AT THE SOIL SURFACE- .9995E+00
SATURATED WATER VAPOR DENSITY IN AIR- .6016E-05
SATURATED WATER VAPOR DENSITY AT AIR-SOIL INTERFACE- .5983E-05
EVAPORATIVE(-) OR CONDENSIVE(+) FLUX- .3717E-04
AIR TEMP. AT OUTER BOUNDARY LAYER EDGE- .2764E+03
SURFACE INFILTRATION RATE(CM/HR)- .1000E-1-00
TEMP. RAIN WATER- .2770E+03
SOLAR RADIATION- .OOOOE+00
EVAPORATIVE(-) OR CONDENSIVE(+) HEAT TRANSFER- .2208E-01
SENSIBLE HEAT TRANSFER- .1920E-01
TRANSFER OF HEAT OF RAIN WATER INTO SOIL- .4000E+00
136
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APPENDIX V: DISTRIBUTION OF SOFTWARE
The VIRTUS model software may be obtained from the Robert S. Kerr Environmental
Research Laboratory. Please send a written request with either a 3.5 inch low
density (720 KB) or a 5.25 inch low density (360 KB) diskette to the following
address. The diskette needs to be preformatted and MS-DOS compatible.
VIRTUS Distribution
Robert S. Kerr Environmental Research Laboratory
U. S. Environmental Protection Agency
P. 0. Box 1198
Ada, OK 74821-1198
USA
137
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing]
. REPORT NO.
EPA/600/2-91/062
3. RECIPIENT'S ACCESSION NO.
PB92- 119 957
TITLE AND SUBTITLE
A MODEL OF VIRUS TRANSPORT IN UNSATURATED SOIL
5. REPORT DATE
6. PERFORMING ORGANIZATION CODE
AUT.HORISI
M.V. Yates, S.R. Yates, and XY.-Ouyang
I. PERFORMING ORGANIZATION REPORT NO.
. PERFORMING ORGANIZATION NAME AND ADDRESS
Dept. of Soil & Environmental Sciences, University of
California, Riverside, CA 92501
^fSDA/ARS, U.S. Salinity Laboratory, Riverside, CA 92501
10. PROGRAM ELEMENT NO.
CBPC1A
11. CONTRACT/GRANT NO.
DW12933820
12. SPONSORING AGENCY NAME AND ADDRESS
Robert S. Kerr Environmental Research Laboratory
U.S. Environmental Protection Agency
P.O. Box 1198, Ada, OK 74820
13. TYPE OF REPORT AND PERIOD COVERED
Research Report
14. SPONSORING AGENCY CODE
EPA/600/15
15. SUPPLEMENTARY NOTES
Project Officer: David M. Walters
FTS: 743-2261
16. ABSTRACT
As a result of the recently-proposed mandatory ground-water
disinfection requirements to inactivate viruses in potable water supplies;
there has been increasing interest in virus fate and transport in the
subsurface. Several models have been developed to predict the fate of
viruses in ground water, but few include transport in the unsaturated zone,
and all require a constant virus inactivation rate. These are serious
limitations in the models, as it has been shown that considerable virus
removal occurs in the unsaturated zone, and inactivation rate of viruses is
dependent on environmental conditions. The purpose of this research was to
develop a predictive model of virus fate and transport in unsaturated soils
that allows the virus inactivation rate to vary based on changes in soil
temperature. The model was developed based on the law of mass conservation
of a contaminant in porous media and couples the flow of water, viruses,
and heat through the soil. Model predictions were compared to measured
data of virus transport in laboratory column studies, and were within the
95% confidence limits of the measured concentrations. Model simulations
were performed to identify variables that have a large effect on the
results.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
COSATi Field,Group
Virus Transport
Unsaturated Zone Modeling
Pathogens
Virus
Heat Transport
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS iTIm Report)
UNCLASSIFIED
21. NO. OF PAGES
148
20. SECURITY CLASS fTliu page-
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (R«T. <-77) PREVIOUS COITION n OBSOLETE
GOVERNMENT PJUNTlNGOmCE:! 9 92 Ji i a -003*0677
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