United States
Environmental Protection
Agenrv
Predicting Attenuation of
Viruses During
Percolation in Soils
1. Probabilistic Model
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EPA.'600;R-02.051a
August 2002
Predicting Attenuation of Viruses During Percolation in Soils:
1. Probabilistic Model.
Barton R Faulkner
U S EPA Office of Research and Development
National Risk Management Research Laboratory
Subsurface Protection and Remediation Division
Ada Oklahoma 74820
William G Lyon
ManTech Environmental Research Services Corp
Ada Oklahoma 78420
Famque A Khan
U S EPA Headquarters
Washington, District of Columbia 20460
Sandip Chattopadhyay
Battelle Memorial Institute
Environmental Restoration Department
Columbus Ohio 43230
Contract Number 68-C-98-138
Project Officer
Georgia A Sampson
National Risk Management Research Laboratory
Ofhce of Research and Development
U S Environmental Protection Agency
Cincinnati OH 45268
/T~~y Recycled/Recyclable
Printed with vegetable-based ink on
paper that contains a minimum of
50% post-consumer liber content
processed chlorine free
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Notice
The U S Environmental Protection Agency through its Office of Research and De-
velopment funded and managed the research described here through m-house efforts
and under Contract 68-C-98-138 to ManTech Environmental Research Services Cor-
poration 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
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All research projects making conclusions or recommendations based on environ-
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to participate in the Agency Quality Assurance Program This project was conduct-
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Virulo is made available on an as-is basis without guarantee or warranty of any kind,
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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 environ-
mental 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, under-
stand how pollutants affect our health and prevent or reduce environmental risks
in the future
The National Risk Management Research Laboratory (NRMRL) is the Agency's
center for investigation of technological and management approaches for prevent-
ing and reducing risks from pollution that threatens human health and the envi-
ronment The focus of the Laboratory's research program is on methods and their
cost-effectiveness for prevention and control of pollution to air land, water, and
subsurface resources protection of water quality in public water systems, remedi-
ation 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 so-
lutions to environmental problems by developing and promoting technologies that
protect and improve the environment advancing scientific and engineering informa-
tion 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
EPA's Office of Water is currently promulgating a Ground Water Rule 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 the conceptual and theoretical de-
velopment of a 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 Schmellmg Acting Director
Subsurface Protection and Remediation Division
National Risk Management Research Laboratory
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Abstract
We present a probabilistic model for predicting virus attenuation Monte Carlo
methods are used to generate ensemble simulations of virus attenuation due to
physical, biological and chemical factors The model generates a probability of
failure to achieve a chosen degree of attenuation We tabulated data from related
studies to develop probability density functions for input parameters, and utilized
a database of soil hydraulic parameters based on the 12 USDA soil categories
Regulators can use the model based on limited information such as boring logs,
climate data, and soil survey reports for a particular site of interest The model
may be most useful as a tool to aid in siting new septic systems
Sensitivity analysis indicated the most important mam effects on probability of
failure to achieve 4-log (99 99%) attenuation in our model were mean logarithm of
saturated hydraulic conductivity (+0 105) and the rate of microscopic mass transfer
of suspended viruses to the air-water interface (-0 099), where they are permanently
adsorbed and removed from suspension in the model Using the model, we predicted
the probability of failure of a 1-meter thick proposed hydrogeologic barrier to achieve
4-log attenuation Assuming a soil water content of 0 3 with the currently available
data and the associated uncertainty, we predicted the following probabilities of
failure sand (p - 22 '5697), silt loam (p =- 6/2000000), and clay (p - 0/9000000)
The model is extensible in the sense that probability density functions of param-
eters can be modified as future studies refine the uncertainty, and the lightweight
object-oriented design of the computer model (implemented in Java™) will facili-
tate reuse with modified classes, and implementation in a geographic information
system
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Contents
1 Introduction 1
2 Abridged Literature Review 1
3 Mathematical Description 2
3 1 Differential Equations 2
3 2 Proposed Solution for the Differential Equations 4
4 Mass Transfer and Inactivation Rates of Viruses 9
5 Modeling under Uncertainty 11
6 Sensitivity Analysis 14
7 Design of the Computer Model 19
8 Conclusions 20
9 List of Symbols and Notation Used 24
10 References 25
11 Internet References 27
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List of Figures
1 Processes Considered in the Model. 3
2 Plot illustrating correlations 12
3 Comparison of simulated and measured values 13
4 Frequency histogram of values of - Iog10.4 for poliovirus for
Rosetta sands. 15
5 Frequency histogram of values of - Iog1().l for poliovirus for Rosetta
silt loams 16
6 Frequency histogram of values of log|(,.4 for poliovirus for Rosetta
clays 17
7 Javadoc class documentation for Attenuator interface. 22
VI
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List of Tables
1 Hydraulic Properties of Sand, Silt and Clay 6
2 Parameters Used for Poliovirus 10
3 Main Effects on Probability of Failure 19
4 Classes Used in the Computer Model 21
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Acknowledgments
The authors would like to thank Mohamed Hantush, U S EPA, for his invaluable
suggestion to use the final value theorem modeling approach, and many other helpful
suggestions We would also like to thank John Wilson of the U S EPA for providing
compiled data, Kathy Tynsky (Computer Sciences Corp ) for designing the graphics
on the cover, and Joan Elliott (U S EPA) and Martha Williams (Computer Sciences
Corp ), for their advice in typesetting this document
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1 Introduction
Impending regulations m U 5 EPA s forthcoming Ground Water Rule (EPA, 2000)
will require public water systems (PWS) to more closely monitor their ground-water
systems for contamination by pathogenic viruses The Rule clarifies the conditions
that define risk to PWS from viruses Regulators can use the new definitions for
siting new septic systems If it can be shown that the risk is low due to the presence
of a hydrogeologic barrier, a proposed site may be acceptable The Rule defines a
hydrogeologic barrier as a subsurface region through which viruses must pass from
a source in order to reach PWS wells that provides at least a yet undetermined but
specific degree of attenuation of active pathogenic viruses The draft rule indicates
attenuation factors are "physical, biological, and chemical acting "singularly or in
combination "
In instances where the ground-water system in question is connected to potential
virus sources by karst fractured rock gravel or a soil exhibiting preferential flow
the system will be classified as high risk In other cases the assessment process will
benefit from prediction by mathematical modeling Therefore, regulators and utility
operators may benefit from simple, probabilistic quantitative models as tools in the
context of responding to the Ground Water Rule (GWR) This document presents
the development of a proposed model to evaluate attenuation as viruses are carried
with percolating water in an unsaturated, naturally existing soil layer The model
itself is a computer application At the time of this writing, a user's guide for this
model is imminent in a companion document Here we describe the conceptual
and mathematical development of the model, and highlight areas of much needed
research
2 Abridged Literature Review
Although several papers describing the modeling of virus transport in ground water
have recently been published, there is not yet a concensus on which factors have the
greatest impact on eliminating active viruses as they pass through natural porous
media Keswick and Gerba (1980) presented an early review of factors affecting
viruses in ground water More recently, Schijven and Hassamzadeh (2000) wrote a
valuable review that is fairly comprehensive, and Breidenbach et al (in review) have
produced an environmental handbook and extensive bibliography on the subject We
refer the reader to these works for a description of the available data from field and
laboratory studies
Current modeling approaches have been criticized Yates (1995) demonstrated
by using a numerical dynamic model to predict virus survival, that field data do not
agree well with model predictions In particular, their model-predicted attenuation
was dramatically greater than actual Yates and Jury (1995) have emphasized the
sensitivity of a numerical dynamic model to input parameters
Modeling approaches themselves have varied greatly depending on the scale of
the study and the specific interests of the investigators Some treat virus transport as
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a Fickian process, coupled with advection of ground water, others have incorporated
filtration theory, treating virus transport as a colloid filtration process
Field studies in which viruses were released into the subsurface have documented
early arrival times, with arrivals at monitoring wells sometimes preceding those of
dissolved tracers Viruses are more likely to be attenuated during percolation m the
unsaturated zone than during transport through the same distance in the saturated
zone (Lance and Gerba, 1984) Studies with unsaturated soils have shown that
hydrophobic colloids are adsorbed at the air-water interface in greater proportion
than the mineral-water interface (Wan and Wilson, 1994), and this is apparently
also the case with viruses (Thompson et al , 1998, Thompson and Yates. 1999)
Chu et al (2001) have shown that when sand column experiments were conducted
with reactive solids removed (metals and metal oxides) the effect of the air-water
interface was most pronounced, and suggested reactions at the solid-water interface
may be dominant when reactive solids are present Sim and Chrysikopoulos (2000)
developed a governing constitutive equation for unsaturated-zone virus transport
that considers partitioning of viruses to the air-water interface More recently Chu
et al (2001) expanded this model, more closely considering mterfacial reactions
using as yet untabulated parameters
3 Mathematical Description
3.1 Differential Equations
Sim and Chrysikopoulos (2000) developed the following governing equation which
can describe the transport of viruses in a porous medium as depicted in Figure 1
A6>,,,r A ,>(" A° #,„<"' (1)
where C - ( '(/.:) (ML ^) is the concentration of viruses m the mobile solution
phase, t is time : (L) is the downward distance from the top of the proposed
hydrogeologic barrier, ('"(/.;) (MM ') is the adsorbed virus concentration at
the liquid-solid interface C'"(/ :) (ML ~ '') is the adsorbed virus concentration at
the liquid-air interface q (LI ') is the specific discharge, H,n (Z,'/."') is the
moisture content, A (J "') is the mactivation rate coefficient for the viruses in
the bulk solution, A' (/ "'), the mactivation rate for the viruses that are sorbed
at the liquid-solid interface and A4' (7 ~'), the mactivation rate for the viruses
sorbed at the liquid-air interface, /> (.ML '') is the soil bulk density, and D
<>-<7/^iM - A (L2T~l) is the hydrodynamic dispersion coefficient, n (L) is the
vertical dispersivity, P, - P/r (L2T~ '), where T> (L2'l ') is the virus diffusivity
in water and r (LL~ ' greater than 1) is the tortuosity
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c(o,o
C(L,t)
inactivation
\ mass transfer
Figure 1 Processes Considered in the Model.
We assumed the following
• Steady-state flow
• Gravity drainage only
• The soil is homogeneous in terms of
hydraulic properties
virus properties
geochemistry
• The soil does not induce preferential flow
Sorption and inactivation of viruses at the various interfaces is described by Sim
and Chrysikopoulos (2000) by
(2)
where /. - /-,«/ "; - .<(! ^), ', is the liquid-solid interfacial area in units
of (L'l.~ () The symbol /. (1 ') \s the microscopic mass transfer rate and h
(LI ') is called the mass transfer coefficient In Eq 2 A,, (L^M ') is the
equilibrium partitioning coefficient /;, (I.) is the average radius of soil particles
and H^ (L''L '') is the saturated water content Analogously they derived the
change in concentration of viable viruses at the air-water interface,
(3)
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where /.c (1 ~') is the liquid to liquid-air interface mass transfer rate The mass
transfer rate for the liquid to liquid-air interface is described by
r H-a; (4)
where // (/.-'/.. ~ ^) is the mass transfer coefficient and a'} is the estimated area
of the air-liquid interface as a function of the moisture content Thompson et al
(1998) and Thompson and Yates (1999) have demonstrated dependence ol viral
mactivation rates on their sorption state A method for estimating
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Figure 1 is our conception of a proposed natural hydrogeologic barrier The
output consists of remaining viable viruses plus the amount destroyed due to the
attenuation factors of suspension and sorption coupled with virus-specific degrada-
tion rates
The initial and boundary conditions are
(8)
(9)
Mass continuity through the upper boundary requires the additional boundary
condition which states the input equals the supplying concentration subject to the
advection and dispersion constraints of the porous medium
DH,,,— -,/<" (10)
'
Since it is assumed that the flow is due to gravity only(t>/i '<): 0) then the
total head gradient is unity (/): <>:} and <\ --- K(f>,,,) To obtain K(Hl:i) van
Genuchten (1980) obtained the following
where A _ is the saturated hydraulic conductivity, d, is the residual water content
(//'/. !), W, is the saturated water content (//'/, !), and n is a well-tabulated
empirical curve fitting parameter (Table 1)
We consider the case where the supplying concentration results from percolation
of water containing viruses lasting for a period of time that is small compared to
the residence time in a proposed barrier Such a situation would result if a septic
tank temporarily overflowed and was then pumped or otherwise corrected thereby
stopping the virus source Arrival of viruses at the input may be approximated as a
relatively sharp concentration front followed by exponentially decreasing concentra-
tion of viruses such that the concentration of viruses immediately above the upper
boundary region of the barrier is ( ',,,,,, <>\p 11 Now we can write the attenuation
function
(12)
Having made the above assumptions, and assuming dispersion and bulk den-
sity of the soil are constant throughout the proposed barrier, taking the Laplace
transform of Eq 1 and applying the mtial conditions (Eq 8) yields
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Table 1 Hydraulic Properties of Sand, Silt, and Clay
Soil-
sand
silt loam
clay
Parameter
ft,
ft,
logi,,A\
logujO
login//
I1
rl>
n
1
0,
ft,
logn,A\
logion
login//
';<
n
r
ft,
ft,
logK,A,
IdgloM
login//
' ;'
n
1
X
308
308
99*J
308
308
168*
0!{
1
1944*
330
330
75*
330
330
133*,
O'i
1
1944'
84
84
22*
84
84
38*
0'",
1
1944*
Mean
0050
0 367
-0 691
05306
0482
1 r>,X X 10"
1.71 x 10- '
r) :><) x 10 *
11 7
0063
0406
-2 160
-0 207
0206
1 l:i x 10"
1 18 x 10 '
x 7") x 10 -"'
117
0 101
0 515
-2 085
0 276
0 114
1 2<) x 10"
().
000
738
0013
0050
-0 384
0075
0016
1 48 x 10"'
r> r)0 x If)' "'
000
7 38
0011
0085
00475
0 129
0015
1 (18 x 10 '
(>.r> x 10 "•
000
7 38
Units
L*L- "^
L^L !
log(/// // r j
!og(/// )
log((/////f // S/(,'/l/( SS 1
-------
- AX" - A H,,,C (13)
Likewise, the Laplace transform of Eq 2 is
(14)
Likewise the Laplace transform of Eq 3 is
(15)
Noting the boundary conditions given by Eq 8 and solving for (." in Eq 14
we obtain
We can solve for (' in Eq 15 to obtain
(17)
Now we insert the substitutions into Eq 13, which yields the following ordinary
differential equation, in terms of C
0 (18)
a ~ - ii :
where
(19)
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To solve Eq 18 we consider the homogeneous equation which has the character-
istic polynomial D Y1 - VY - - The general solution is f(.s. :) = ^\ rxpfFi (^)"-\ •
ri exp Fji ,s);j, where, by the quadratic formula
r \;
The Laplace transform of Eq 9 is dC( s x)/r/;, which implies
physically reasonable solution thus r'(s. ;) _ ^j ('xp[r_>(.s):
The Laplace transform of Eq 12 is
(20)
- 0 for a
Substituting for (" and its derivative we have
D
The Laplace transform of Eq 10 is
1 JT_,
(21)
(22)
(23)
or
^
(24)
Thus, we find the value of - > is
(25)
From Eq 22
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We now apply the final value theorem
Inn .We = /,) - Inn .V/(s. :) 'L^ll (28)
/ -- x ^ -0 ]
The attenuation factor 1 \s
To find -U(; - (II, we integrate the input flux in time
thus
.1 ,'-'- ' (31)
The average velocity of the percolating water is \"
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Table 2 Parameters Used for Poliovirus
Parameter
logioA
logi,)A'
h>
hc
'',
A',/ (sand)
A,/ (silt loam)
A,/ (clay)
N
12
0;
li
It
0'
87
23
39
Mean
().W).r)
o.:504
1 :i4 x K)- <
x 10""
2.4.5 x K)- '
,i 77 x K) '
7 20 x K)- '
Standard
Deviation
0 M)8
0 (>OM
l.MO x K)- ^
1 MO x 10 ''
1.2r» < 10"
r, (if) x HP '
7 K) x 10 '
().7i x 10 '
Units
\og(hr-1)
log(/i/-')
in hi' '
;» /// - '
;;/5 ,/- '
//; '' (, '
/» < y '
* Data complied by Breidenbach et al (2001) unless otherwise noted
1 From Chu et al (2001), see Appendix A for assumptions
| Yates and Ouyang (1992) assumed A* =: A _'
>t Mazzone (1998) p 114
soil and water, such as temperature, pH, organic matter, and presence of metals, or
other ions
Most of the work related to natural hydrogeologic barriers has been conducted
with bactenophages (viruses to bacteria), due to the restrictive conditions required
to obtain such data for human pathogenic viruses without posing a risk to re-
searchers The polio viruses are perhaps the most widely studied human pathogenic
viruses in this context Table 2 lists the relevant properties of the viruses, based
on Breidenbach et al (2001) The data cover a fairly wide range of geochem.cal
conditions, hence the high standard deviations Measured mass transfer rate data
is largely lacking Vilker and Burge (1980) did early work that included some mea-
surements for poliovirus More recently, Chu et al (2001) measured mass transfer
parameters with MS-2 bactenophage, which has comparable size and geometric
properties, using an inverse modeling approach
Due to the difficulty of obtaining good experimental control, and the corre-
sponding sparsity of data, a popular semi-empirical correlation to estimate h due
to W'lson and Geankophs (1966), /, - 1 00\' D'"2il,H, ' is often employed This
correlation can be used at low Reynolds numbers, however, comparison between this
expression and measured values shows very poor correlation (Pearson's correlation
coefficient,
I) O.'i'i A" = 2ii) The expression fails to account for major factors
that affect mass transfer of viruses at the molecular level, such as pH-dependent
e^ectrostatic interactions between the protein surfaces and soil particles and /or the
air-water interface Indeed the correlation was not developed for this purpose The
work of Chu et al (2000) highlighted the enormous effect of oxides on sand grains
in their soil column experiments Their work suggested the pH-dependent behavior
of oxide coatings has a stronger effect on mass transfer than the air-water interface
Much additional work is needed to develop realistic correlations to estimate mass
transfer of viruses The experimental control needed to conduct such studies can be
daunting Most soil column studies must rely on plaque assay methods that suffer
from virus aggregation effects and other sources of uncertainty
10
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As with h a correlation has not been established for t^ though we may now
rely on the results of Chu et al (2001) These are listed in Table 2
Rose and Bruce (1949) derived equations to estimate the air-water mterfacial
area by «-} - (/>,. t/liH,,,)/ rr In this expression, n (MLI ' ') is the surface tension
of water, /;„ is the density of water, // is the acceleration due to gravity Employing
the van Genuchten (1980) expression that relates «,„ to the capillary pressure head
// and expressing the effective saturation as S, - \H,,, - H, ) CV, 0, ) we obtain
the following
(33)
The benefit of using this expression is that it utilizes the well-tabulated fitting
parameters for which we have already developed multivanate distribution functions
which we will discuss in the next section
Virus diffusivity P (LJ7 ') is governed by Brownian motion and is described
by the Stokes-Emstem equation
(34)
in which /, i, is Boltzman's constant (MLI '-} I ( Celsius) is temperature,
// //( / ) is viscosity of water (.WZ. '/ ') and;, is the equivalent radius of the
virus
5 Modeling under Uncertainty
The draft Ground Water Rule states a specified degree of attenuation must occur in
order for a hydrogeologic medium to be considered a barrier Using the mathematical
model with as much information about the geochemistry and other factors that can
help in making a decision on the appropriate parameters we operate under the
premise that it is possible to obtain a prediction of attenuation that is more useful
than a qualitative expression of confidence that the barrier can or cannot attenuate a
particular virus It is essential to develop a probabilistic expression of the confidence
that -• log attenuation will occur encapsulating the possible sources of error in
the model parameters
Virus diffusivity P is a physical parameter that can be calculated if the tem-
perature / and corresponding viscosity of water are known Unfortunately the
tortuosity r, is less easily measured since it depends not only on the modal particle
diameter, but also the pore geometry and connectedness of the pores Tortuosity
for unsaturated soils is often predicted with (Schaefer et al 1995)
11
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UNSODA sands
simulated
0.05
'1 9
1 Z
/in
IU
4.
n
, ,*,* ,-,..
logK
i_ _ _
log n
log n
*•• * -
0.10
0.15 0.05
0.10
0.15
Figure 2 Plot illustrating correlation of logmA\, login//, #,, and logmn with
#, for sands in the UNSODA soils database and a corresponding multivariate
normal ensemble simulation.
(35)
—— otherwise
Although the data in Tables 1 and 2 list uncertainties that could introduce sig-
nificant error into the predicted attenuation, we needn't rely on these variabilities as
independent (orthogonal) sources of error Many of the parameters, when measured
in controlled experiments, are correlated Thus we can consider their space of vari-
ability as conditionally multivariate normal and ;or lognormal The five parameters
that display significant correlation (based on H(] //,,,, 0 //i //,,,, ^ 0) are shown
in Figure 2
We applied covariance- and histogram-honoring simulations using the Monte
Carlo approach Details of the Cholesky decomposition approach we used are de-
scribed by other authors (e g see Kitamdis, 1997, Appendix C3) For all the
other parameters, the Monte Carlo simulation used histograms from the parameters
independently The advantage of the Monte Carlo method is that it produces a
histogram of attenuation factors as output and it allows us to assign a probability
of failure to achieve ~ - log attenuation Figure 2 shows the space of variability for
the five (hydraulic) parameters which were significantly correlated The simulat-
ed values were generated by conditional simulation of multivariate normal density
functions parameterized by the vanance-covariance matrices of the parameters as
determined with the UNSODA database (Ley et al 1996) These are listed in
Appendix B
12
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00
•
^JUUU
4000
onfiA.
oUUU
onnn
iUUU
mnn-
0.
;: •• o~ '.V;"'»'>4-' '•.•»-i';' ,7'.-. ''•'.
, :-, i^^r^^^S^^.
»
^
rt
Kim etal. (1997) '
Anwar et al. (2000): !
25 mm,
iogKs =-0.165
>~! 50 mm,
log Ks = -0.082
log Ks = -0.029
simulated
, Baked blasting sand
i Glass micro beads of 3 different mean diameters listed
* Generated by setting mean U,n " ti It), std err (i _'
Figure 3 Comparison of values of
-------
Clearly, this simple model appears to underestimate u'-j when S, is less than
about 0 6 (0,,, less than about 0 25) The measurements themselves, may be subject
to considerable error, and there is no data for finer soils and soils containing clays
At low water contents «/' will apparently be underestimated for sandy soils, tnus
the model should not be used to test barriers which are proposed solely on account
of low water contents Other means of evaluation should be used in those cases
Figure 4 shows histograms of attenuation factors of polio 1 virus using the data
in Tables 1 and 2, for 1 meter thick soils at water content equal to 0 30 "he
histograms were generated with Monte Carlo simulations with soil hydraulic data
from the UNSODA soils database (Ley et al , 1996) for categorical sand and silt
loam soils (Table 1) The soil values themselves were generated in previous studies
using a bootstrap method (Schaap et al , 1999) The uncertainty associated with
hydraulic parameters is relatively well understood The higher standard deviations
for clay soil are due to the various clay mineralogies that can be present having large
effects on water retention characteristics On the other hand, the variation shown in
Table 2 is largely the result of the various geochemical conditions under which the
measurements were made Indeed, State regulators may not have comprehensive
data available for a proposed hydrogeologic barrier As more data become available,
the uncertainties may be reduced to primarily measurement error, assuming the
investigator knows relevant details about the geochemical environment
From the distribution of attenuations produced in the Monte Carlo simulations,
we simply compute the probability of failure to achieve a target attenuation factor
number of Monte Carlo runs that produced .1 < 10
p (f a 11 u re I =
total number of valid Monte Carlo runs
The probability of failure for poliovirus to achieve 4-!og attenuation was p=
22/.r>i»07 for the sands Model users would more likely be interested m tighter soils
more likely to be proposed as hydrogeologic barriers Figure 5 shows the results
for poliovirus for silt loams Probability of failure for the 1-meter thick barrier
was p— (> '2000000 For this particular set of data, the Rosetta clays produced a
probability of failure p- 0 ''1000000 for the data shown in Tables 1 and 2
6 Sensitivity Analysis
Beres and Hawkins (2001) listed the advantages of applying the Plackett-Burman
(Plackett and Burman 1946) method of sensitivity analysis These include the
ability to measure two-way interaction effects among parameters and the freedom
to apply any desired domain of plausiblility to input parameters The reader is
referred to Beres and Hawkins (2001) for a detailed description of how to apply
the method and Plackett and Burman (1946) gave the statistical foundation and
the optimum cyclic permutations (pattern of parameter variation) of parameter
combinations that may be used for a given number of variables
We considered the 17 input parameters that are used in the model solution
Table 3 lists each parameter and the plausible domains used, based on the means
14
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File Edit Run Help J> Start Simulation ^ Stop Threshold Attenuation
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File Edit Run Help |> Start Simulation |) Stop Threshold Attenuation <£): 4 (-loglG)
jJJgl Flow Parameters > ,','. Virus Parameters Jj| Histogram 7^ Probability
if Retain and Accumulate
Right Truncated Histogram
Vertical Axis is Count
Figure 5 Frequency histogram of values of log!0-4 for poliovirus for Rosetta
silt loams.
16
-------
File Edit Run Help p» Start Simulation ^ Stop Threshold Attenuation <£): 4 ( loglO)
yjsJK Flow Parameters ',", Virus Parameters jjjjj Histogram ZJ^ Probability
v Retain and Accumulate
Right Truncated Histogram
Vertical Asir i? Count
Figure 6 Frequency histogram of values of logm.4 for poliovirus for Rosetta
clays.
17
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and standard deviations shown in Tables 1 and 2 We used the following cyclic
permutation of the parameters, which was derived by Plackett and Burman (L946)
for a 20 parameter model
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Where the values in Table 3 are greater than zero, the effect is proportional to
the probability of failure, and parameters which produce effects less than zero are
inversely proportional to the probability of failure
We may interpret the effect as the expected amount and direction of change in
the response (probability of failure to achieve 4-log attenuation) that results from
changing the particular parameter by the + and - values given for the plausible
domains It is a resolution IV factorial design, on account of the foldover, the lower
half of the permutation matrix (Beres and Hawkins, 2001) It is not unexpected
that the probability of failure to achieve 4-log attenuation is sensitive to parame-
ters that affect water flow for the given plausible domains It should be noted the
effects of the correlated hydraulic parameters (logi()A\, Ws login//, M< • and logi()n)
listed in Table 3 are listed only to show the effect of a change in the mean value
A special vanance-covanance matrix was calculated for all the parameters of the
LINSODA database (see Appendix B) This matrix was used in the sensitivity anal-
ysis However, it was not adjusted for the effects in means resulting from the cyclic
permutations of the parameter mean values
For the given plausible domains, logarithm of saturated hydraulic conductivity
(logioAs) was the most important parameter In light of experimental evidence
that preferential flow plays an important role in unsaturated mass transfer, users
should do their best to obtain improved estimates of the effective logioA\ if there
is evidence of soils that could produce preferential flow The second most impor-
tant parameter was KC the rate of microscopic mass transfer from the suspended
phase to the air-water interface, where the viruses are adsorbed and effectively
removed from the system This result highlights the importance of estimating the
18
-------
Table 3 Main Effects on Probability of Failure
Parameter
h
L
logio "
';•
logio A
logio A'
A',/
(9,
6i m
/
logio n
/ ,
,,
Plausible
-2 12
00
0 5
023
6 233 x 10 "'
00
00
-305 ; 10 4
0 0647
0 15
432
975333
0 12
1 250 , 10 s
0 0
u 8 75 x 10 "'
^
0433
Domain' ^
042
0 023
20
031
1 997 > 10 '
1 213
0 912
1 20 * 10 ^
00753
040
19 08
1891333
0 28
1 500 x 10 s
3 14 x 10 <
5 59 < 10 '
0 376
Effect
+0 105
-0 099
-0039
+0030
-0026
-0025
+0 020
-0 017
+0015
+0012
+0007
+0006
+0 005
-0 004
+0002
-0001
+0001
air-water mterfacial area, a difficult endeavor and an important subject of research
for unsaturated-zone contaminant transport
Two-way interaction effects were also measured These are listed completely in
Appendix C Most notable among these include /. >< logniA (-0 072) which is not
surprising due to the increased residence time experienced by the viruses in thicker
soil layers. /, x A,, (+0054), and logn>/\. * /, (-0095 the parameters which
exhibit important (and opposing) mam effects
7 Design of the Computer Model
The Java programming language (Gosling et al 2000) was used to implement the
model This language allows object- oriented design to be relatively easily imple-
mented Table 4 lists the classes and interfaces used Java class documentation
will be available on-line and will be described in a forthcoming user's guide for the
model Some of the classes use the Matrix class of JAMA a Java matrix package
[2]
We consider these classes to be "lightweight,1 in this context, meaning that
they are high-level easily implemented with other applications abstracted from the
computer hardware and its operating system (i e , they are portable) they have a
small footprint and they require few memory and computational resources
19
-------
The model ("Virulo") can be implemented as an applet or application depending
on the launcher used (ViruloApplet java or Virulo java) The Swing graphical com-
ponents of the Java Foundation Classes were used in the Graphical User Interface
(GUI) The model and its source code can be found at
http://www.epa.gov/ada/
The classes were written using the Javadoc tool [5] The Javadoc tool uses
the philosophy of programming created by Professor Donald Knuth at Stanford
University Knuth advocates that programs should be written to be read not only
by machines, but also by humans (Knuth, 1992) He designed a programming
language called WEB Programs written in this language are parsed by an engine
that generates Pascal source code as well as source code that can be typeset with
Knuth's T[=X typesetting program
The Javadoc commenting system follows a similar philosophy It is natural to
make classes of an object-oriented program easier to read by other programmers
so they can be implemented in other programs This tool allows special comment
tags, embedded in the body of the source code, but ignored by the compiler, tc be
parsed by the Javadoc application It thus generates formated class documentation
that describes the structure and function of the class Programmers can use it to
implement classes without having to resort to reading the Java source code The
Javadoc system generates HTML code in a common style Much of the HTML
document comes from interpreting the Java source code, but the system also allows
commenting by the author Figure 7 shows the Javadoc documentation for the
Attenuator class of Virulo
8 Conclusions
We developed a probabilistic model to predict the effectiveness of a hydrogeologic
barrier to pathogenic viruses in the unsaturated zone It is based on physics, and
we can conclude that the following assumptions must be employed
• Viruses reach the top of the proposed barrier following release in an overlying
source, and following their arrival the input concentration decays exponen-
tially This condition corresponds to an accidental release, such as from an
overflowing septic tank, which is subsequently corrected
• Water flow in the proposed barrier is due to gravity only
• The virus of interest is approximately spherical in shape
• The proposed barrier does not contain significant numbers of predatory mi-
croorganisms (the model estimate is conservative in this sense)
• The percolating water does not contain significant amounts of surface active
agents, such as detergents that could change the hydraulic properties, decay
rates, or adsorption
20
-------
Table 4 Classes Used in the Computer Model
Class
Attenuator
Compare
DoubleCompare
FlowComboPanel extends JF'anel
FlowPanel extends JPanel
implements Observer
GasDev
Gossiper implements Observer
Histogram
HistoPlot
HistoPanel extends JPanel
HspBasicMath
HspMonteCarlo
ImageCanvas
JarLoadable
Medium implements Cloneable
Mvn
Normal implements Cloneable
IMormalF
Operandum implements Cloneable
OutputPanel extends JTextPane
Random
SoilStack
SortVector
StnngAsChars implements Cloneable
VarCov
VectorParser
Virulo (or ViruloApplet)
ViruloFrame extends JFrame
VirusComboPanel extends JF'anel
VirusStack
No of
Public
Methods
i 0
1
! i
2
1
1
0
1
7
1
1
0
1
Description
Computes the water flux and 1
Interface for sorting callback (due to Eckel 1998)
Subclass of Compare for sorting callback
Combo box for selecting soil type
Panel to display flow parameter text boxes
Java translation of the popular C program gasdev.c
(Press et al 1989)
Observer object (Gamma et al 1995) that notifies
subscribing objects of actions without violating
object-orientation bv creating unwanted dependencies
Polvmorphable class for generating histograms
Uses Histogram to create a Bufferedlmage for
display
Panel for displaying histogram image
Has useful static methods for oft-used math
operations
Conducts and manages the Monte Carlo Simulations
for Virulo
Polvmorphable image canvas of Geary (1999)
Allows image files to be retrieved on the flv from
a Java Archive (jar) file
Cloneable data structure for soil parameters
Generate a realization of a multivariate normal
distribution Behaves like the SAS' v macro
mvn. sas [3]
Cloneable data structure for a parameter in Virulo
Data structure for parameter text fields
Cloneable data structure for virus parameters
Prints dipboardable text output
Polvmorphable random deviate generator due to
Java Numerical Toolkit [4]
Holds necessarv parameters for each soil type
selectable with FlowComboPanel
Sorts a Java Vector object, due to Eckel (1998)
Cloneable data structure for a soil or virus name
Stores vanance-covariance matrices as computed with
Rosetta for each soil type
Useful oft-used static methods for use with Java
Vector objects
Launcher for the application (or applet)
GUI frame for Virulo
The analogv of FlowComboPanel but for
virus parameters
Analogy of SoilStack but for virus parameters
by virus name
i Names in italics represent Java interfaces
i Names in boldface represent classes that are part of the Java language
21
-------
File Edtt View Seated Go i<:ulrn*'Ki T3i* Help
V , ." '**->! |, litt ^ijp e-td't' -r;/H-.'3;"urrtjii u^'-tteni-a'^" i ltr( »| > Search •* -
da p3'> EESIXtee Deprecated Index Help
•FV :, a4;; NE- T c LA;; IJKAMM> NO t RAM[s» AJ o^
Interface Attenuator
i:iiDl.' ;.i'-r;-t"- Atlenuaior
Method Summary
J
Method Detail
get Medium
getOperandum
Figure 7 Javadoc class documentation for Attenuator interface.
22
-------
• The proposed barrier matrix consists of one of the 12 USDA soil types
• Provided distribution functions for saturated hydraulic conductivity do not
account for preferential flow, thus it must be assumed preferential flow will
not occur in the site of interest
We found that for a 1-meter thick proposed hydrogeologic barrier with a volu-
metric water content of 0 3, only soils classified as clays did not fail to produce the
4-log attenuation in the these simulations User s may have additional information
that could change the outcome of the probabilistic model
This study revealed several areas of much needed research These include
• Table 3 lists in order of magnitude the parameters that most strongly affect
the results of this model It suggests the parameters which should receive the
most research attention through experiments
• The issue of accurate estimation of the air-water interfacial area is an im-
portant one, not only for modeling transport of contaminants subject to hy-
drophobicity effects but also for unsaturated-zone virus transport modeling
• More experimentation is needed with real proteins or the ammo-acids that
have surfaces that behave like viruses, rather than artificial or inorganic col-
loids
• Geochemical effects can produce profound changes in the sorption and survival
of the viruses and more work is needed to identify the causes
• Although plaque assays are appropriate for testing of natural water for the
presence of viruses, the associated uncertainty when large numbers of viruses
are used lead to lack of experimental control at the level of accuracy needed
to study viruses in unsaturated soil columns For these types of studies more
accurate assay methods are needed
• Correlations need to be developed to predict mass transfer coefficients specifi-
cally for viruses which sorb at both the solid-water and the air-water interface
Current correlations are not relevant for viruses
• Out of about 36 soil column studies in the literature, only those of Jm et al
(2000) and Chu et al (2001) were done with unsaturated columns More
unsaturated column studies are needed
Because of the large uncertainty in parameters needed to predict virus transport
in the unsaturated zone probabilistic models that encapsulate and propagate the
uncertainty in those parameters in the predictions should be used
23
-------
9 List of Symbols and Notation Used
Symbol
Description
Water retention curve fitting parameter
Vertical hydrodvnamic dtspersivitv
Coefficient of exponential decav of virus concentration
Soil water content
Residual soil water content
Saturated soit water content
Measured water content equivalent to (),,
Suspended to solid sorbed virus mass transfer coefficient
Suspended to air-sorbed virus mass transfer coefficient
Suspended phase virus mactivation rate
Solid sorbed phase virus mactivation rate
Air sorbed phase virus mactivation rate
Viscosity of water
General Gaussian random variable
Soil bulk density
Pearson s correlation coefficient
Density of water
Surface tension of water
Variance operator
Unsaturated soil water tortuosity
Dummy variable of integration
The predicted attenuation factor ((',,(', , , }
Concentration of viruses in suspended phase
Concentration of viruses in the solid-sorbed phase
Concentration of viruses in the air-sorbed phase
Maximum (initial) concentration of viruses entering, top of proposed hvdrogeologic barrier
Concentration of viable suspended viruses exiting the proposed hydrogeologic barnei
Molecular virus diffusivitv
Effective molecular virus diffusi^ity
Vertical hydrodvnamic dispersion coefficient
Dahmkohler number for mass transfer suspended to solid water inlerface
Dahmkohler number for mass transfer suspended to air-water interface
Cumulative virus attenuation function
Laplace transform of cumulative virus attenuation function
Measured flux of percolating water equivalent to <(
Unsaturated hydraulic conductivity
Equilibrium distribution coefficient (solid-suspended)
Saturated hydraulic conductivity
Thickness of proposed hydrogeologic barrier
Number of observations
Effective soil water saturation
Temperature
Mean percolation velocity
Measured velocity of percolating water
Measured velocity of percolating water
Air water mterfacial area
Solid-water mterfacial area (soil specific surface area)
Virus attenuation function
Acceleration due to gravity
Soil capillary pressure head
Suspended to solid sorbed virus mass transfer rate
Suspended to air-sorbed virus mass transfer rate
Mass transfer rate equivalent to A
Mass transfer rate of equivalent to A
Boltzmann s constant
Water retention curve fitting parameter
Probability
Flux of percolating water
Vector of calculated mean soM particle diameters
Mean soil particle radius
Virus radius
Laplace domain variable
Ttme
General Gaussian random variable
General Gaussian random variable
Distance downward from top of proposed hydrogeologic barrier
24
-------
10 References
Anwar, A H M F , Bettahar, M , Matsubayashi, U 2000 A method for determining
air-water mterfacial area in variably saturated porous media J Contain Hydro/
43 129-146
Beres, D L , Hawkins, D M 2001 Plackett-Burman technique for sensitivity anal-
ysis of many-parametered models Ecol Modell 141 171-183
Boas M 1983 Mathematical Methods in the Physical Sciences, Second Edition
John Wiley & Sons New York 793 p
Breidenbach P Chattopadhyay, S Lyon, W G Survival and Transport of Viruses
in the Subsurface, An Environmental Handbook U S EPA Document in prepara-
tion
Chu Y . Jm Y Flury M Yates, M V 2001 Mechanisms of virus removal during
transport in unsaturated porous media Water Resour Res 37(2) 253-263
Eckel, B 1998 Thinking in Java Prentice Hall PTR, Upper Saddle River New
Jersey 1098 p
EPA 2000 National Primary Drinking Water Regulations Ground Water Rule
Fed Regis 65(91) 30193-30274
Gamma, E , Helm R Johnson, R Vlissides J 1995 Design Patterns, Elements
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Geary D M 1999 Graphic Java' w 2, Mastering the JFC, 3rd Edition, Volume
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Gosling, J Joy B Steele, G Bracha, G 2000 The Java1 w Language Spec-
ification, Second Edition Addison-Wesley, Boston 505 p
Hantush M M Marino M A Islam M R 2000 Models for leaching of pesti-
cides in soils and groundwater J Hydro 227 66-83
Jm, Y Chu, Y Yunsheng, L 2000 Virus removal and transport in saturated
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Jury W A Gardner W R , Gardner W H 1991 Soil Physics, Fifth Edition John
Wiley & Sons Inc New York 328 p
Kaczmarek M , Hueckel, T , Chawla V Imperiali P 1997 Transport through
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-------
Keswick, B H , Gerba, C P 1980 Viruses in groundwater Environ Sci Tech-
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11 Internet References
[1] Mount H R 2000 Remote Soil Temperature Network
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[2] JAMA A Java Matrix Package
http //math.nist gov/javanumerics/jama/
-------
[3] SAS Institute 2000 MVN macro Generating multivariate normal data,
http://ewe3.sas.com/techsup/download/stat/mvn.html
[4] NIST 1998 Java Numerical Toolkit
http://math.nist.gov/jnt/
[5] JAVADOC TOOL HOME PAGE
http://java.sun.com/j2se/javadoc/index.html
-------
Appendix A
Back-Calculation of Mass Transfer Coefficients of Chu et al (2001)
1 Assume Chu et al (2001) A i is our /,• and their A <, is our /, , based on Chu
et al Figure 1 Also their ./„ is our (in In
().()47.r) //, In
3 Experiment 1 obtained DH <, - 2 !)2 at \,,,.,, ,„,,,,,/ - 2.5.4 cm hr thus
/M^-> - V,,, ,,,„„,,,//)(/i//, = 12.4 .->(•/;/ //; 1(2.02) 'il(lr/;M -= (> M)/// '
Experiment 2 obtained Z9o i 121 at I ,,„,,, „„./,,,/ 1 7 1 cm, hr, thus
/, Ws j ~> 7i/u '
4 Let refer to values obtained from the sand centroid of the soil triangle Now
-• /, Ws _, --- ."i 7". 12.()r. = (I 1.44 cm hr^O 00134 m hr
J
if ft1,,, - ft1, ,r,<,., and other values taken from sand centroid then
a] ---- 7 .4:4.5 ( m ' -- 7.5.5 .4 /;/ '
and
(>Mi 7:5.4.4 (I 1)27 cm hr=-0 00927m hr
6 To compute the propagation of error let u1 {} be the variance operator Then
according to Boas (1983) p 734, consider a function c of 2 normally dis-
tributed variables i and // We use overlmes to denote the mean If they are
uncorrelated then
Var
From the UNSODA database, we estimated mean particle radii for each soil
classified as sand from sieve data as follows
a
sieve
size
particle
fraction
weighted
component
-------
With this we obtained an overall mean, rp = 1 73 x 10 ' ni, and a standard
deviation ,,„ - 0,
we obtained f> - 0 101, thus we cannot reject the null hypothesis, and con-
clude f^ and /,, are uncorrelated for soils classified as sand
Thus we may proceed using the propagation of error formula listed above
Var[«T]- (^
Noting that
And evaluating at the means, we obtain
Varl/;/]^ 3 33 x K)7
In a likewise manner, we obtain
= 3 2:5") x l()-fl
Due to the lack of data on h' we assume the only significant contributions to
the error in i^ are the lack of fit error in the Dahmkohler number as computed
by Chu et al plus the error in «c; is of similar magnitude as that of
-------
Appendix B.
Vanance-Covanance Matrices of Correlated Hydraulic Parameters
(I,
sand
(i,
H..
logni"
'ogio"
logi(lA\
silt loam
H,
/y.
-0 00001
+ 000003
-0 00009
-000012
^-0 00042
,000016
-0 00049
log,,," 1 -000015
login//
logioA",
clay
f>,
«.
login"
logm//
logm A" ..
everything"
^,
/;,
login"
logm//
>- 000000
-0 00050
-0 00011
, 0 00090
. 0 00110
-0 00006
- 0 00469
. 0 00034
-000103
-000262
-0 00099
logi,,A\ -000430
«„
• 0 00003
• 0 00103
-000021
-0 00038
000191
- 0 00049
-000251
-000146
• 0 00030
t 0 01017
- 0 00090
. 0 00727
000871
-0 00038
-003863
000103
- 0 00469
-0 00718
-000293
• 0 00016
logm"
-0 00009
-000021
- 0 00113
-000185
-0 00446
-000015
-0 00146
-000560
-0 00114
-001506
- 0 00110
-000871
- 0 01676
-000152
-0 04797
-0 00262
-000718
-0 09467
001776
• 0 12027
logm/;
-000012
-0 00038
-0 00185
^000593
i 0 01506
* 0 00000
- 0 00030
-000114
+-0 00026
-000425
-0 00006
-0 00038
-0 00152
-000023
-0 00179
-0 00099
-0 00293
-0 01776
-002035
. 0 08733
logioA\
- 0 00042
- 0 00191
-0 00446
-0 01506
004731
-0 00050
-001017
-001506
- 0 00425
,-0 14744
-0 00469
-0 03863
- 0 04797
-0 00179
0 22576
-0 00430
-000016
-0 12027
-008733
-0 52026
-------
o
o
Is- •*•
O ^H
O O
ac
o
ro
-------
-------
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