United States 

Environmental Protection 

Agency 

Predicting Attenuation of 

Viruses During 

Percolation in Soils 

2. User’s Guide to the 

Virulo 1.0 Computer Model 
EPA/600/R-02/051b 

August 2002 

Predicting Attenuation of Viruses


During Percolation in Soils


2. User’s Guide to the 

Virulo 1.0 Computer Model 

William G. Lyon


ManTech Environmental Research Services Corporation


Ada, Oklahoma 74820


Barton R. Faulkner


Subsurface Protection and Remediation Division


National Risk Management Research Laboratory


Ada, Oklahoma 74820


Faruque A. Khan


U.S. EPA Headquarters


Washington, D.C. 20460


Sandip Chattopadhyay


Battelle Memorial Institute


Columbus, Ohio 43230


Jerome B. Cruz


Washington State Department of Ecology


Toxics Cleanup Program, Northwest Regional Office


Bellevue, Washington 98008


EPA Contract 68-C-98-138


Project Officer


Georgia A. Sampson


Subsurface Protection and Remediation Division


National Risk Management Research Laboratory


Ada, Oklahoma 74820


National Risk Management Research Laboratory


Office of Research and Development


U.S. Environmental Protection Agency


Cincinnati, Ohio 45268

Notice 

The U.S. Environmental Protection Agency through its Office of Research 

and Development funded and managed the research described here through inhouse efforts and under Contract 68-C-98-138 to ManTech Environmental 

Research Services Corporation. It has been subjected to the Agency’s peer and 

administrative review and has been approved for publication as an EPA 

document. Use of trade names or commercial products does not constitute 

endorsement or recommendation for use. 

All research projects making conclusions or recommendations based on 

environmental data and funded by the U.S. Environmental Protection Agency are 

required to participate in the Agency Quality Assurance Program. This project 

was conducted under an approved Quality Assurance Project Plan. The procedures specified in this plan were used without exception. Information on the plan 

and documentation of the quality assurance activities and results are available 

from the Principal Investigator. 

Virulo and the user’s guide have been subjected to the Agency’s peer and 

administrative review and have been approved for publication as an EPA 

document. Virulo is made available on an as-is basis without guarantee or 

warranty of any kind, express or implied. Neither the United States Government 

(U.S. EPA), ManTech Environmental Research Services Corporation, Battelle 

Memorial Institute, Washington State Department of Ecology, nor any of the 

authors or reviewers accept any liability resulting from the use of Virulo, and 

interpretation of the predictions of the model are the sole responsibility of the 

user. 

ii 
Foreword 

The U.S. Environmental Protection Agency is charged by Congress with 

protecting the Nation’s land, air, and water resources. Under a mandate of 

national environmental laws, the Agency strives to formulate and implement 

actions leading to a compatible balance between human activities and the ability 

of natural systems to support and nurture life. To meet this mandate, EPA’s 

research program is providing data and technical support for solving environmental problems today and building a science knowledge base necessary to manage 

our ecological resources wisely, understand how pollutants affect our health, and 

prevent or reduce environmental risks in the future. 

The National Risk Management Research Laboratory is the Agency’s center 

for investigation of technological and management approaches for preventing and 

reducing risks from pollution that threatens human health and the environment. 

The focus of the Laboratory’s research program is on methods and their costeffectiveness for prevention and control of pollution to air, land, water, and 

subsurface resources; protection of water quality in public water systems; 

remediation of contaminated sites, sediments and ground water; prevention and 

control of indoor air pollution; and restoration of ecosystems. NRMRL collaborates with both public and private sector partners to foster technologies that 

reduce the cost of compliance and to anticipate emerging problems. NRMRL’s 

research provides solutions to environmental problems by: developing and 

promoting technologies that protect and improve the environment; advancing 

scientific and engineering information to support regulatory and policy decisions; 

and providing the technical support and information transfer to ensure implementation of environmental regulations and strategies at the national, state, and 

community levels. 

This publication has been produced as part of the Laboratory’s strategic longterm research plan. It is published and made available by EPA’s Office of 

Research and Development to assist the user community and to link researchers 

with their clients. 

EPA’s Office of Water is currently promulgating a Ground Water Rule that will 

place increased burden on public water systems to ensure water supplies are 

safe from contamination by viruses. States may be required to conduct 

hydrogeologic sensitivity assessments to predict whether a particular aquifer is 

vulnerable to pathogens. This work presents a User’s Guide for Virulo, a userfriendly predictive screening model for virus attenuation above aquifers. It is 

hoped this model will be a useful tool for state regulators, utilities, and 

development planners. 

Stephen G. Schmelling, Acting Director 

Subsurface Protection and Remediation Division 

National Risk Management Research Laboratory 

iii 
Abstract 

In the EPA document Predicting Attenuation of Viruses During Percolation in 

Soils 1. Probabilistic Model the conceptual, theoretical, and mathematical 

foundations for a predictive screening model were presented. In this current 

volume we present a User’s Guide for the computer model that implements the 

probabilistic model. The model is a predictive screening model called Virulo, so 

named because of its use of the Monte Carlo method for predicting virus fate and 

transport. This document presents a general overview of the parameters used 

and how they can be modified to suit a particular predictive modeling scenario. In 

addition, a non-technical overview of the conceptual modeling approach is given. 

Some example applications of Virulo are presented. 

iv 
Contents 

Foreword ....................................................................................................................................... iii


Abstract .........................................................................................................................................iv


Figures ..........................................................................................................................................vi


Tables........................................................................................................................................... vii


Acknowledgments ....................................................................................................................... viii


1 Introduction ............................................................................................................................. 1


1.1 What does Virulo do? ...................................................................................................... 1


1.2 What information is needed to run Virulo? ...................................................................... 1


2 The Virulo User Interface ....................................................................................................... 6


2.1 Soil and Flow Parameters ................................................................................................ 7


2.2 Virus Parameters .............................................................................................................8


3 Example Applications ............................................................................................................. 9


4 References ........................................................................................................................... 14


5 Website References ............................................................................................................. 14


v 
Figures 

1.1 Schematic depiction of physical role of microscopic parameters discussed 

in detail in Predicting Attenuation of Viruses During Percolation in Soils. 

1. Probabilistic Model. ................................................................................................... 3


1.2	 Schematic depiction of physical role of macroscopic parameters discussed 

in detail in Predicting Attenuation of Viruses During Percolation in Soils. 

1. Probabilistic Model. ................................................................................................... 3


1.3	 Schematic depiction of physical role of the equilibrium partitioning coefficient, 

discussed in detail in Predicting Attenuation of Viruses During Percolation in Soils. 

1. Probabilistic Model. .................................................................................................. 4


1.4	 Schematic depiction of how the Monte Carlo method works. Each realization is a


random sample of input parameters. The collection of all realizations is the


ensemble, from which inference is made on the output. ............................................. 5


2.1 Default flow parameters upon first opening Virulo (WindowsTM Version). .................. 6


2.2 Default virus parameters upon first opening Virulo (Linux (WindowMaker) Version). 7


2.3 Flow input panel showing pull-down list of soil textures (Mac OS X Version). .......... 8


2.4	 Virus input panel showing pull-down list of virus-texture defaults


(Linux (WindowMaker) Version). ..................................................................................... 8


3.1 Virus property panel showing start of simulation (Linux (WindowMaker) Version). .........10


3.2	 Histogram for a single simulation of default case Clay, Polio


(Linux (WindowMaker) Version). ................................................................................ 10


3.3	 Histogram for a single simulation of default loamy sand, hepatitis A-Clay


(Linux (WindowMaker) Version). ................................................................................ 11


3.4 Histogram for a single simulation of default sandy loam with θ mean set m 

to 0.2 and its standard deviation set to 0.05, hepatitis A-Clay


(Linux (WindowMaker) Version). ....................................................................................12


vi 
Tables 

1.1
 Summary of Notation Used in the Virulo Input Data Windows. .................................. 2 

3.1 Failures to Achieve 4-log10


Soil Textures for a Single Virulo Simulation Run of 106 Iterations..................................13


Attenuation Results for Various 

vii 
Acknowledgments 

The authors wish to acknowledge Martha Williams, Computer Sciences 

Corp., who typeset this document. We also thank Liping Pang, of the Institute of 

Environmental Science & Research Limited, Christchurch, New Zealand, for 

many helpful comments and suggestions which improved the utility of the Virulo 

model. 

viii 
Section 1. Introduction 

Understanding the fate and transport of viruses and pathogens in variably saturated soil and aquifer materials is 

important in predicting potential risk to human health from human and animal wastes. The U.S. EPA Office of Water 

proposed the Ground Water Rule (U.S. EPA 2000), which will reduce exposure to pathogenic viruses and bacteria 

associated with human and animal wastes that might contaminate Public Water Supply wells. As part of the Ground 

Water Rule, public water supply systems that do not meet disinfectant treatment requirements will be required to 

conduct source water monitoring if the system produces water from sensitive aquifers1

. 

The U.S. EPA Office of Research and Development has developed a virus fate and transport model (Virulo) that 

analyzes virus leaching from sorption sites in variably saturated soil and aquifer materials. Virulo predicts attenuation 

to total viruses as they pass through a soil layer. One use of the model could be to provide estimates of attenuation 

of viruses percolating through a candidate barrier layer of a particular soil textural type. However the model has many 

other potential uses such as predicting virus attenuation through land spreading of wastewater during ground-water 

recharge operations or for predicting the effects of high density septic tank discharge on ground-water quality. 

1.1 What does Virulo do? 

Virulo is a one-dimensional, variably saturated, ground-water flow and contaminant transport model. By computing 

analytical solution equations that describe advection, dispersion, viral sorption, inactivation, and mass transfer, 

ensembles of outputs are produced using random sampling of certain parameters over specified ranges and 

distributions through use of the Monte Carlo method. 

Virulo generates the number of cases in which a certain level2 of virus attenuation was or was not achieved. As 

discussed in detail in Predicting Attenuation of Viruses During Percolation in Soils. 1. Probabilistic Model (hereafter 

referred to as “Part 1"), attenuation is defined as the ratio of total mass leaving the layer to the total mass entering 

it (Figure 1.1). Part 1 contains a detailed description of the system being modeled and the theoretical development of 

Virulo. 

Virulo is a screening model only. It was developed to fill a niche for users who are expected to have only a small 

amount of information available for a site of interest. Default values, categorized by qualitative descriptions are 

emphasized. For more complete investigations of a site, numerical models such as Viralt (Park et al. 1992), Virtus 

(Yates et al. 1991), or Canvas (Park et al. 1991) should be considered. These models allow handling of heterogeneity, 

and other factors affecting transport and fate which are conceptually greatly simplified in Virulo. 

1.2 What information is needed to run Virulo? 

The transport component of the model primarily uses data from soil textural3 and thickness information (perhaps 

derived from boring logs) and soil survey reports for a particular site of interest. Human virus data at present are 

limited to polio, hepatitis A, reovirus 3, coxsackievirus, and echovirus. 

Many parameters can be defaulted to standardized values on the input panels. Default parameters can also be 

overridden by the user when more accurate values are available for a particular site. 

The default description of soil water content used internally is a climate-free estimate based on the assumption of a 

uniform random distribution of water content values chosen from values between the residual water saturation and 

complete water saturation for a given soil texture (Table 1.1). This distribution is used in the Virulo Monte Carlo 

calculations. The user currently has the option of overriding this distribution, and inserting a water content (e.g., the 

estimated field capacity or wilt point for the given soil texture) directly. This allows the user to gain a better 

appreciation for the effect of water content on virus breakthrough at the bottom of the soil layer of interest. 

1 Sensitive aquifers include karst, fractured bedrock, and gravel aquifers. 

2 The targeted level of attenuation is adjustable by the user. 4-log10 (99.99%) represents the current default level. 

3	 The 12 USDA textural categories are used in Virulo to supply default parameters. See, for example, http://www.agronomy.psu.edu/ 

Courses/SOILS101/Labs/texture.html. 

1 
Table 1.1 Summary of Notation Used in the Virulo Input Data Windows


Parameter Description Units 

Flow Parameters Window (given in sequence): 

�r Residual water content, the water content that is 

approached at highly negative capillary pressure, where the 

water remaining is that held by the soil’s capillary forces 

m 3 m -3 

�m Water content, the volume fraction containing water m 3 m -3 

�s Saturated water content, equal to the porosity m 3 m -3 

log10 (Ks) Saturated hydraulic conductivity, the hydraulic conductivity 

the soil would have if �m = �s 

log10 (m h-1) 

log10 (�) van Genuchten parameter * log10 (m-1) 

log10 (n) van Genuchten parameter * log10 

� Soil dry bulk density g m -3 

r p Mean soil particle radius m 

�z Hydrodynamic dispersivity m 

T Mean soil temperature, used for computing molecular 

dispersivity of the virus, a component of dispersion 

°C 

L Thickness of candidate barrier layer m 

Virus Parameters Window (given in sequence) 

� Exponential decay exponent in source term h-1 

log10 (�) Mobile virus inactivation rate constant, rate of inactivation of 

suspended viruses 

log10 (h-1) 

log10 (�*) Solid-sorbed virus inactivation rate constant, rate of 

inactivation of soil-adsorbed viruses 

log10 (h-1) 

� Mass transfer coefficient, mobile phase to solid-sorbed 

phase† 

m h-1 

�� Mass transfer coefficient, mobile phase to air-water 

interface sorbed ‡ 

m h-1 

r v Mean virus radius m 

C max Maximum virus concentration in source term, arbitrary units [e.g., PFU L-1] 

Kd Equilibrium partitioning coefficient for viruses sorbing onto 

soil particles 

m 3 g -1 

θ m −θr  1 1   = m , m = 1− *the van Genuchten relation is  θs −θr  1+ ( )n 

 

n 

 αh 

†

the rate itself is computed in Virulo by k = ��aT where a� is the water-solid interfacial area. 

‡

the rate itself is computed in Virulo by k� = ��aT 

� where a�� is the water-air interfacial area. 

2 
Figure 1.1 shows schematically, at the microscopic level, the interaction among the various parameters, and the 

descriptions of their physical basis are also described in detail in Part 1. 

Figure 1.1	 Schematic depiction of physical role of microscopic parameters discussed in detail in Predicting 

Attenuation of Viruses During Percolation in Soils. 1. Probabilistic Model. 

Figure 1.2 shows the macroscopic parameters that describe advective flux and dispersion of viruses as they pass 

through the soil layer of interest. Figure 1.3 illustrates the role of Kd

, the equilibrium partitioning coefficient. 

Figure 1.2	 Schematic depiction of physical role of macroscopic parameters discussed in detail in Predicting 

Attenuation of Viruses During Percolation in Soils. 1. Probabilistic Model. 

3 
Figure 1.3	 Schematic depiction of physical role of the equilibrium partitioning coefficient, discussed in detail in 

Predicting Attenuation of Viruses During Percolation in Soils. 1. Probabilistic Model. 

Virulo makes use of a conceptual model that simplifies the types and rates of natural processes that govern variably 

saturated ground water flow and virus transport. As noted in Part 1, Virulo employs the following simplifications and 

assumptions: 

• One-dimensional, vertical, uniform, variably saturated, ground-water flow 

• Gravity drainage only (no abrupt change in capillary pressure in the soil) 

• Random soil water content representing random, instantaneous recharge from precipitation 

•	 There is no soil water hysteresis and water content is random, rather than cyclical, wetting and drying (the results 

are very sensitive to the water content) 

• Variably saturated ground-water flow through uniform layers of porous media without preferential flow pathways 

•	 Virus transport may be simulated by linear sorption typical of dissolved contaminants rather than by colloidal 

filtration theory specific to colloidal particles 

• Measured laboratory, rather than field, values of virus transport and survival are suitable for use in the simulations 

•	 Parameter values are displayed with significant figures not warranted by the actual measurements available to the 

user to allow use of a variety of data sources with varying significant figures. The user should recognize that the 

results are suitable for informational purposes only; i.e., four log removal could be undistinguishable from two log 

removal or six log removal given available data and theory 

The figures are merely meant to illustrate the role of the parameters used in Virulo. For a complete description of the 

processes they represent, Part 1 should be studied. 

In order to quantify uncertainty in model outputs, Virulo employs the Monte Carlo method (Figure 1.4). The method 

works in Virulo by assuming the values of the parameters vary randomly in one of two possible ways: 

•	 the input parameters vary randomly and independently of each other, but they follow a normal distribution 

described by the mean and standard deviation; or, 

•	 the input parameters vary randomly, but dependently with a subset of the other parameters, and they follow a 

multivariate normal distribution described by their means and their variance-covariance matrix. 

The parameters in Virulo which vary according to the latter are the hydraulic parameters θ r, θ s

, log10 Ks, log10 a, log10 n. 

This is important to the user because their standard deviations cannot be modified because Virulo employs the 

variance-covariance matrix, computed a priori for each of the twelve USDA soil types. The current version does not 

allow the user to modify the underlying matrix used in the dependent conditional simulations for these input 

parameters. Furthermore, modifying the mean values of these five parameters is not recommended because it is 

dubious to assume the variance-covariance matrix would remain unchanged, and presumably the greater the 

magnitude of the adjustment in the mean, the greater the error in the existing variance-covariance matrix. The user 

is advised not to change these values unless they have a complete understanding of the way conditional dependence 

is simulated in Virulo, as described in Part 1, and they are completely able to justify the change made. 

4 
Figure 1.4	 Schematic depiction of how the Monte Carlo method works. Each realization is a random sample of 

input parameters. The collection of all realizations is the ensemble, from which inference is made on 

the output. 

The Monte Carlo method uses computer-generated random numbers. In models such as Virulo, the Monte Carlo 

method works as follows: 

I. A randomly generated set of input parameters is created and the model is run to produce an output. 

II. Step I is repeated many times, building up a list of output values corresponding to each random set of input 

parameters. 

III.	 After suitably many such runs (enough runs so that the user is confident the full range of possible inputs 

has been covered), inference is made on the output. 

In the case of Virulo, the outputs (attenuation values) are plotted on a logarithmic scale as a right-truncated histogram. 

The user is free to adjust any of the parameters provided they can justify doing so. Furthermore, a user may wish to 

run Virulo by assuming one or more of the parameters is deterministic (i.e., does not vary). This is done by simply 

setting the standard deviation for the parameter to zero. Note that some of the parameters are given as the log10 of 

its value. This is because these parameters are either known to follow, or are thought to follow the lognormal 

distribution, hence the user should be careful to note this if the values are adjusted from the defaults. 

In addition to the special case of the conditional dependence of some of the input parameters, another special case 

should be discussed here: The value of the water content will depend not only on soil type, but on many external 

factors, such as climate, time of year, presence of irrigation, and evapotranspiration. Indeed, for most sites users will 

not have definitive information about its value. Therefore, Virulo offers two ways to model its value: 

•	 it varies in a uniformly random manner between the residual water content at the lower end, and the saturated 

water content at the upper end (this is the default); 

• the user can input a value and a standard deviation, as is done with the other independent parameters. 

As is discussed in Part 1, the parameters to which the output is most sensitive are the hydraulic parameters. This may 

be viewed as fortunate, because these parameters and their variation are better studied and documented at present, 

than the parameters directly related to microscopic adsorption and decay. 

5 
6

Section 2. The Virulo User Interface 

The main data input windows for Virulo consist of two panels, one denoted “Flow Parameters,” and one denoted “Virus 

Parameters.” These two panels are displayed on the following two pages as Figures 2.1 and 2.2. Despite the names, 

both panels contain some parameters that straddle more than one category. For example, the Flow Parameters panel 

contains some soil parameters, and the Virus Parameters panel contains some virus properties that are specifically 

for a certain soil texture. Nevertheless, the rough subdivision into two panels clusters together parameters controlling 

flow, and parameters controlling virus inactivation and sorption. 

Figure 2.1 Default flow parameters upon first opening Virulo (WindowsTM Version). 

The input variables are denoted by symbols, which reflect common usage in the published literature. In case of doubt, 

resting the cursor on the symbol opens an identity box, which gives a short description of the variable denoted by the 

symbol. 

When first opened, Virulo has default values corresponding to clay, and polio-clay entered for each of the parameters, 

and for the standard deviation to be associated with the parameter values. On the far right side, the dimensions for 

the entered parameter are indicated. In order to run Virulo, appropriate values for the parameters expressed in the 

necessary units must be entered in each of the active boxes. This can be accomplished in one of two ways. 

Method One is simply the use of the built-in default options as they stand. At the bottom of each panel is a box that 

activates a pull-down list of default options for a given soil texture, selection of which will automatically fill in all the 

appropriate parameters. This makes the program very easy to run for simple cases. 

7 
Figure 2.2 Default virus parameters upon first opening Virulo (Linux (WindowMaker) Version). 

Method Two involves the more laborious filling in of the parameters one by one based on a detailed knowledge of the 

site. These parameters might be obtained independently (see Schijven and Hassanizadeh, 2000), from the 

compilation of Breidenbach et al., 20004 . Great care must be taken to convert all parameters into the exact units 

specified by the input panel. 

Finally, we should mention that Methods One and Two can be combined. Method One can be used to fill in most of 

the parameters, leaving only a few parameters to be changed to fit the particular situation prevailing on the site of 

interest. The parameters can be changed repeatedly, and are not finalized until the program is actually run. 

Note that in Figure 2.1 the "uniformly random" box opposite θ has been checked as the default. If this box is m 

unchecked, then the θ parameter and its standard deviation may be edited. Various water contents consistent with m

the values of θ and θ may be inserted here, e.g., values for the field capacity and wilt point for the given texture. r s 

It is recommended that the standard deviation be kept very small (e.g., 0.001) for benchmark calculations of this type. 

The value of the threshold attenuation can be set by the user by typing it in the text field at the right side of the toolbar 

of the main window frame. This is the level of attenuation being considered. Attenuation less than this value is 

considered an exceedance for that particular Monte Carlo run. In this way the user can set what constitutes an 

exceedance, for their purposes. A vertical red bar will be displayed in the histogram panel indicating the threshold 

attenuation chosen. By default, this value is set to 4, indicating a threshold of “4-log attenuation.” This value is often 

mentioned in the context of proposed hydrogeologic sensitivity assessments, as well as in Comprehensive 

Performance Evaluations for public water systems. In the future, such performance evaluations will consider groundwater systems. The value is completely arbitrary, and is offered as a way for the user to make judgments or inferences 

from the model runs. 

2.1 Soil and Flow Parameters 

In the following Figure 2.3, the flow input panel is shown with the pull-down list of default textures. The clay default 

option was selected, and the program has inserted all the appropriate parameters for an “average” clay. The basis 

for selecting these default values is given in Faulkner et al., 2002. 

The user will notice that when the model is running on their computer some of the parameter values are highlighted 

in red, some in regular black and white, and some of the standard deviations are grayed-out. Holding the cursor on 

4 We anticipate making a data compilation available in the future as a separate document. 

8 
any red-highlighted value will produce a message box indicating that “Modifying this mean value is not recommended. 

See model documentation.” Study has shown that the model results are highly sensitive to these red-highlighted 

parameters. The grayed-out standard deviations indicate that these values cannot be changed. Only those 

parameters and standard deviations appearing in regular black and white should ordinarily be changed. 

Figure 2.3 Flow input panel showing pull-down list of soil textures (Mac OS X Version).


9 
2.2 Virus Parameters 

In the following Figure 2.4, the virus input panel is shown with the pull-down list of virus and soil textures. The polioclay default option was selected, and the program has inserted all the appropriate parameters for an “average” clay. 

The basis for selecting these default values as well as guidance for selecting custom values for a real site are given 

in Breidenbach et al., 2000. 

Figure 2.4 Virus input panel showing pull-down list of virus-texture defaults (Linux (WindowMaker) Version). 

10 
Section 3. Example Applications 

Following entry of the default clay parameters, and the default polio-clay parameters, one can proceed to run the 

simulation. Figure 3.1 displays how the simulation is set to run, just after selection of the virus parameters. One can 

also proceed by clicking on the green arrow button. Typical run times are approximately 3 minutes5. 

The simulation generates two kinds of output. The graphical histogram output, which is displayed continuously 

developing during the simulation, is shown below in final form as Figure 3.2. The vertical red bar separates cases of 

failure to attenuate (left of the bar) from successfully attenuated cases (right of the bar). The horizontal axis is the 

negative base-10 logarithm of the attenuation (A). The negative is used merely to allow the user to intuitively view 

increasing attenuation to the right, decreasing attenuation to the left. In the simulation shown, zero cases of failure 

were calculated in 106

 iterations; thus, the probability of failure to achieve 4-log10 attenuation of poliovirus under all the 

prevailing assumptions about texture, water content, etc. is very low. If it were necessary to estimate this probability 

more precisely, further simulations could be run and accumulated until several cases of failure were seen. This is 

done by checking the Retain and Accumulate box on the histogram panel. When this box is checked, results from the 

simulation are included in the next simulation. This can be done as many times as needed in order to produce an 

acceptable histogram of outputs. 

Probability Output as text can also be obtained by clicking on the appropriate tab. The output contains a complete list 

of all parameter values assumed in the simulation. This text information can readily be clip-boarded into another 

program for formatting and printing. Below we display this text output information (edited to manuscript format) for 

the clay, polio-clay simulation, and random water content: 

Output from Virulo Model: 

Input parameters used: 

Parameter: Mean Value(Standard Deviation) units: 

Soil Parameters: 

Residual water content: 0.1(0.01) m3 m-3 

Water content: random between Residual water content and Saturated water content. 

Saturated water content: 0.52(0.09) m3 m-3 

Hydrodynamic dispersivity: 8.75E-5(1.0E-4) m 

Log van Genuchten’s alpha: 0.28(0.13) log10( m -

1 ) 

Log van Genuchten’s n: 0.11(0.02) log10( . ) 

Temperature of soil (for computing molecular diffusivity): 11.7(7.38) Celsius 

Soil bulk density: 1290000.0(168000.0) g m -

3 

Mean soil particle radius: 9.95E-5(6.15E-5) m 

Log Saturated hydraulic conductivity: -2.09(0.48) log10( m h -1 ) 

Thickness of proposed barrier: 0.5(0.1) m 

Virus Parameters: 

Coefficient of exponential decay of input concentration: 0.1(1.0E-11) h-1 

Log Mobile Virus Inactivation Rate: 0.605(0.608) log10( h-1 ) 

Log Solid-sorbed Virus Inactivation Rate: 0.304(0.608) log10( h-

1 ) 

5	 For the example above, run times were typically 2 minutes 43 seconds for 106

 iterations on a Pentium III system with 128 Mb RAM 

operating under Windows98, and no other programs running concurrently. 

11 
Figure 3.1 Virus property panel showing start of simulation (Linux (WindowMaker) Version).


Figure 3.2 Histogram for a single simulation of default case Clay, Polio (Linux (WindowMaker) Version).


12

 Mobile to solid-sorbed mass transfer coeff.: 0.00134(0.0018) m h -

1


Mobile to air-sorbed mass transfer coeff.: 0.00927(0.0018) m h -

1


Radius of virus: 1.375E-8(1.25E-9) m


Maximum virus concentration entering proposed barrier: 10.0(0.01) any


Mobile to solid-sorbed equilibrium partition coeff.: 7.2E-4(9.74E-4) m3 g -

1


The probability of failure to achieve 4.0-log attenuation from 1000000 Monte Carlo runs was 0:1000000. 

The last entry gives the probability of failure to achieve successful reduction of virus concentration. In the computed 

case, this is apparently a relatively low probability6

, and such a clay barrier would, therefore, under the assumed 

moisture conditions seem fairly adequate to prevent poliovirus contamination of an aquifer beneath it. 

Figure 3.3 shows the histogram result for a default loamy sand with hepatitis A, Kd

 value for clays. In this case the 

histogram shows a distinct mode in the neighborhood of 60-log attenuation. By observing the shape of the histogram 

the user can obtain information about the distribution of attenuation values and how they behave in the vicinity of the 

chosen threshold attenuation. The maximum of 300-log is close to the numerical double precision limit of most modern 

math processors. 

Figure 3.4 shows the output for hepatitis A with a default sandy loam soil. However, in this case the volumetric water 

content was set to 0.2, with a standard deviation of 0.05, instead of varying in a uniformly random way. It shows the 

dramatically different results that can be obtained if information is known about the water content. In this case the 

mode is very close to zero, and the probability of failure is very high. 

Figure 3.3	 Histogram for a single simulation of default loamy sand, hepatitis A-Clay (Linux (WindowMaker) 

Version). 

6	 Further accumulated simulations yielded ca. 1 chance in 1.2 million. Note that Virulo offers no guidance regarding what constitutes an 

“acceptable risk” in any given case. This judgment requires additional considerations well beyond the scope of the simple transport 

model described here. 

13 
Figure 3.4 Histogram for a single simulation of default sandy loam with θ mean set to 0.2 and its standard m 

deviation set to 0.05, hepatitis A-Clay (Linux (WindowMaker) Version). 

To estimate the ability of a clay layer to attenuate poliovirus under wetter conditions, the simulation was run with the 

water content set to the approximate field capacity of clay7. 

Further Output from Virulo Model with θ = Field Capacity m 

Input parameters used:


Parameter: Mean Value(Standard Deviation) units:


Soil Parameters: 

Log van Genuchten’s alpha: 0.28(0.13) log10( m -

1 )


Residual water content: 0.1(0.01) m3 m-3


Water content: 0.47 (0.00) m3 m-3


Saturated water content: 0.52(0.09) m3 m-3


Thickness of proposed barrier: 0.5(0.1) m


Hydrodynamic dispersivity: 8.75E-5(1.0E-4) m


Log van Genuchten’s n: 0.11(0.02) log10( . )


Temperature of soil (for computing molecular diffusivity): 11.7(7.38) 


Soil bulk density: 1290000.0(168000.0) g m -3


Mean soil particle radius: 9.95E-5(6.15E-5) m


Log Saturated hydraulic conductivity: -2.09(0.48) log10( m h -

1 )


Celsius


7 This was calculated as ca. 0.9091 xs

, where the value 0.9091 is the water saturation fraction at the field capacity for centroid clay 

texture (64.83% Clay, 16.55% Silt, 18.62% Sand) calculated using the method on the website, http://www.bsyse.wsu.edu/saxton/ 

soilwater/ 

14 
Virus Parameters: 

Coefficient of exponential decay of input concentration: 0.1(1.0E-11) 


Log Mobile Virus Inactivation Rate: 0.605(0.608) log10( h-

1 )


Log Solid-sorbed Virus Inactivation Rate: 0.304(0.608) log10( h-

1 )


Mobile to solid-sorbed mass transfer coeff.: 0.00134(0.0018) m h -

1


Mobile to air-sorbed mass transfer coeff.: 0.00927(0.0018) m h -1


Radius of virus: 1.375E-8(1.25E-9) m


Maximum virus concentration entering proposed barrier: 10.0(0.01) 


h-

1 

any 

Mobile to solid-sorbed equilibrium partition coeff.: 7.2E-4(9.74E-4) m3 g -1 

Saturated water content: 0.515332222 (0.085260028) m3 m-

3 

Thickness of proposed barrier: 0.5 (1.0E-4) m 

Hydrodynamic dispersivity: 8.75E-5 (1.0E-4) m 

Log van Genuchten’s n: 0.113751456 (0.015201357) log10( . ) 

Temperature: 11.7 (7.38) °C 

Soil bulk density: 1290000.0 (168000.0) g m-3 

Mean soil particle radius: 9.95E-5 (6.15E-5) m 

Log Saturated hydraulic conductivity: -2.085670553 (0.475140674) log10( m h-1 ) 

The probability of failure to achieve 4.0-log attenuation from 1000000 Monte Carlo runs was 60:1000000. 

Again, the last entry gives the probability of failure to achieve successful reduction of virus concentration. Here the 

choice of a water content constantly equal to the field capacity yields a substantially higher probability of failure to 

attenuate. 

Further Results 

Runs for the thirteen possible default data sets are summarized in the table below. For clay and sand textures, 

1000000 iterations were sufficient to estimate the probability of failure. For the silt texture, even the accumulated 

results from four simulations did not detect any failure cases. 

Other mixed cases are shown in the table. These were computed using the textural based, flow parameters with a 

set of virus parameters. For example, the clay loam flow parameters were used with the polio-clay virus parameters. 

Table 3.1 Failures to Achieve 4-log10 Attenuation Results for Various Soil Textures for a Single Virulo Simulation 

Run of 106

 Iterations 

Texture 

Clay, �m = UD 

Clay, �m = FC = 0.468


Clay loam, �m = UD


Loam


Loamy sand


Sand, �m = UD


Sand, �m = FC = 0.133 

Sand, �m =0.35 

Poliovirus Hepatitis A Reovirus 3 

0 11 13 

60 31009 68383 

0 7 

1 3 9 

35 158 265 

236 864 684 

0 1 0 

98,358 277,415 232,229 

6 

Coxsackievirus Echovirus

5 8 

79880 54778 

10 10 

332 219 

655 612 

228,397 220,645 

1 1

7 8 

0 0 

UD = Uniform Distribution between �r and �s 

FC = Field Capacity Moisture Content 

15 
16

Section 4. References 

Breidenbach, P., S. Chattopadhyay, and W.G. Lyon. 2000. Survival and Transport of Viruses in the Subsurface, An 

Environmental Handbook, a report prepared for WA-RE-1-5 under EPA Contract 68-C-98-138, September 15, 

2000, 273 pp. 

Faulkner, B.R., W.G. Lyon, F.A. Khan, and S. Chattopadhyay. 2002. Predicting Attenuation of Viruses During 

Percolation in Soils: 1. Probabilistic Model. EPA/600/R-02/051a. 

Park, N.S., T.N. Blandford, and P.S. Huyakorn. 1992. Viralt Version 2.1, A Modular Semi-Analytical and Numerical 

Transport Model for Simulating Viral Transport in Ground Water. Documentation and User’s Guide. 

Park, N.S., T.N. Blandford, and P.S. Huyakorn. 1991. Canvas Version 1.0, A Composite Analytical-Numerical Model 

for Viral and Solute Transport Simulation, Documentation and User’s Guide. 

Schijven, J.F., and S.M. Hassanizadeh. 2000. Removal of viruses by soil passage: overview of modeling, processes 

and parameters. Crit. Rev. Environ. Sci. Technol. 30(1):49-127. 

Yates, M.V., S.R. Yates, and Y. Ouyang. 1991. A Model of Virus Transport in Unsaturated Soil. EPA/600/2-91/062. 

U.S. EPA. 2000. National Primary Drinking Water Regulations: Ground Water Rule. Fed. Regis. 65(91) :30193-30274. 

Section 5. Website References 

Centroid Compositions http://www. epa.gov/superfund/programs/risk/airmodel/guide.pdf


Rosetta Database http://www.ussl.ars.usda.gov/MODELS/Rosetta/rosetta.htm


Soil Texture Calculator http://www.bsyse.wsu.edu/saxton/soilwater/


Soil Texture Triangle http://www.agronomy.psu.edu/Courses/SOILS101/Labs/texture.html


UNSODA and RETC http://www.ussl.ars.usda.gov/


17 
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