United States
 Environmental Protection
 Agency
 Robert S. Kerr Environmental
 Research Laboratory
 Ada OK 74820
 Research and Development
 EPA/600/SR-93/184    May 1994
 Project  Summary
 Evaluation of  Unsaturated/Vadose
Zone  Models  for Superfund  Sites
D.L. Nofziger, Jin-Song Chen, and C.T. Haan
  Mathematical models of water and
chemical movement in soils are being
used as decision aids for defining ground-
water protection practices for Superfund
sites. Numerous transport models exist
for predicting movementand degradation
of hazardous chemicals through soils.
Many of these require extensive  input
parameters that involve uncertainty due
to soil variability and unknown future weather.
The impact of uncertain model parameters
upon the model output is not known. Model
users requirean understanding of this impact
so appropriate parameters are measured at a
site and model prediction uncertainty  is
incorporated  into decisions. This report
summarizes research findings that address
the sensitivity and uncertainty of model output
due to uncertain input parameters.
  The objective of  the research was to
determine the sensitivity and uncertainty
of travel time, concentration, mass loading
and pulse width of contaminants at the
water table due to  uncertainty in soil,
chemical, and  site  properties for four
models, RITZ, VIP, CMLS, and HYDRUS.
The models,  which  are all  designed to
estimate movement of solutes through
unsaturated soils, span a considerable
range in detail and intended use. Model
parameters investigated include soil
properties such as organic carbon content,
bulk density, water content, and hydraulic
conductivity.  Chemical  properties
examined include organic carbon partition
coefficient and degradation  half-life. Site
characteristics  such as  rooting depth,
recharge rate, weather, evapotranspiration
and runoff were examined when possible
in the  models. Model sensitivity was
quantified in the form of  sensitivity and
relative sensitivity coefficients.
  The study found that large uncertainty
exists in many model outputs due to the
combination  of sensitivity  and high
parameter variability.  In  addition,
predicted  movement  of contaminants
was greater when the natural variability
of rainfall was incorporated into the model
than when only average fluxes were used.
This is because major rainstorms that
result in large fluxes of water and high
leaching are essentially ignored when
average flux values are used. The study
reaffirms that uncertainty is pervasive in
natural systems and  that results of
modeling  efforts presented  in  a
deterministic fashion may be misleading.
  This Project Summary was developed
by EPA's Robert S. Kerr Environmental
Research Laboratory, Ada,  OK, to
announce key findings of the research
project that is fully documented in a
separate report of the same title (see
Project Report ordering information at
back).

Introduction
  Mathematical  models of  water  and
chemical movement in  soils are used as
decision aids  for defining remediation
practices for Superfund sites. To use models
in  making  decisions about remediation
practices appropriate for Superfund sites,
the model must predict the future behavior
of the contaminant. Numerous transport
models exist for predicting movement and
degradation of hazardous chemicals through
soils. Many of these require extensive input
parameters that are often not measured arid
that include uncertainty due to inherent
variability associated with the soil  and
weather conditions. Minimal information
exists on the impact of uncertain input data
on the outputs from these models. Given
these conditions, guidelines regarding the
selection and use of models are needed.
This report  summarizes research findings
                                                    Printed on Recycled Paper

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addressing two issues of  uncertainty  in
vadose modeling: (1) model sensitivity and
(2) incorporating uncertainty into decisions
using model predictions.
  Model sensitivity refers to the change in
model  output resulting from a specified
change in an input parameter. Sensitivity is
observed by examining differences in graphs
of the model outputs for different inputs in
the expected range. If differences in output
are large,  the output is sensitive to these
changes in inputs; if differences in output
are small, the output is not sensitive to these
changes in inputs.
  The use of models in a predictive manner
introduces  uncertainty. For example,
chemical  leaching  depends upon water
movementthrough the unsaturated soil. This
water movement is dependent upon the
amount and distribution of  water entering
the soil and hence upon future  weather.
Since future weather is unknown, uncertainty
exists in the model input. As a result, there
is inherent uncertainty in the model output.
Natural variability of the soil parameters is
an  additional source of input parameter
uncertainty. The second part of the full report
computes  the uncertainty in model outputs
due  to uncertainty  in one or more model
inputs.
  Results  of the sensitivity and uncertainty
analyses are presented for four  models:
RITZ, VIP, CMLS, and HYDRUS. RITZ, VIP,
and  CMLS were written as management
tools,  whereas  HYDRUS  is   more
appropriately suited for detailed  research
use by scientists.  The  models  differ
substantially in their intended use,
assumptions and processes, input  data
requirements, computer requirements, and
ease of use.

Model Descriptions
  The four models selected in the analysis
are  RITZ,  VIP, CMLS,  and HYDRUS. All
four models  include sorption of the
contaminant by soil  and  advection  or
movement of the contaminant with water.
RITZ and VIP include sorption  on an
immobile  oil  phase as  well as a  vapor
transport component. In addition, RITZ and
VIP  assume uniform soil  properties and
steady water flow. CMLS and HYDRUS can
simulate  layered  soils and unsteady,
unsaturated water  flow. HYDRUS  also
includes hydrodynamic dispersion. Each of
the models are described in greater detail
below.

RITZ Model: The Regulatory Investigative
Treatment Zone (RITZ) Model (Nofziger, et
a/., 1988) was developed to predict the fate
of contaminants mixed with oily wastes and
applied to  land treatment units.  RITZ
conceptualizes the vadose  zone  as
consisting of two zones: (1) the plow zone
where the sludge containing contaminant
and oil occurs uniformly mixed within the soil
and (2) the treatment zone, which contains
no oil. The  model simulates movement of
the contaminant through both zones. In this
study, the plow zone represents the portion
of soil  containing the contaminant at the
beginning of the simulation. The bottom of
the treatment zone represents  the water
table depth.
  RITZ  contains  many  simplifying
assumptions:  (1)  Soil properties are
assumed to be uniform throughoutthe profile.
(2)  The flux of water through the soil is
assumed to be constant  with depth and
time. (3) Oil is assumed to be immobile and
remains in the plow zone.  (4) Both oil and
contaminant  degrade  as first-order
processes. (5) Partitioning of the contaminant
between  phases is linear, instantaneous,
and reversible. (6) Dispersion in water phase
is small and can be ignored. (7) The soil
water content and  unsaturated  hydraulic
conductivity can be described by the Clapp
and Hornberger  equation (Clapp  and
Hornberger, 1978),
                    	i	
                    2b + 3
(D,
where 6^ is the soil water content, Ks is the
saturated  conductivity,  q is the average
recharge  rate,  9  is the soil porosity  or
saturated water content and b is the Clapp-
Hornberger constant (that depends on soil
properties).

VIP Model: The Vadose  Interactive
Processes (VIP) Model  (Stevens, et al.,
1989)  is  similar  to  RITZ   in  the
conceptualization of the  vadose zone but
consists  of more complex chemical
interactions. For example,  VIP considers
the  dynamics  of  sorption rather  than
assuming  instantaneous equilibrium
between phases. It also simulates oxygen
diffusion in the air-phase and oxygen-limited
degradation of the contaminant, and diffusion
of contaminant in the air phase. When oxygen
is not limiting, sorption is  instantaneous,
and diffusion of contaminant is negligible.
VIP solves the  differential  equations
numerically. As a result, the recharge rate or
flux  of water passing through the  soil can
change with time on a monthly basis.

CMLS Model: The Chemical Movement in
Layered Soils (CMLS) Model (Nofziger and
Hornsby, 1986) was originally developed as
a management tool to  simulate the
movement and degradation of pesticides in
layered soils. In CMLS, the soil profile  is
composed of up to 20 layers. Soil and
chemical properties are constant within a
layer but may change from layer to  layer.
Water balance is computed on a daily basis
to   account  for   infiltration    and
evapotranspiration.
  The following simplifying assumptions are
made in CMLS: (1) Chemicals move only in
the liquid (soil water) phase, and movement
in the vapor phase can  be ignored. (2)
Partitioning  of chemicals between the soil
solids and water is described by the linear,
reversible  model  with  instantaneous
equilibrium. (3) Dispersion and diffusion of
the chemical are ignored. (4) Degradation is
described as a first-order process. The
degradation  constant can  vary with  depth
but not with time. (5) Water moves through
the  soil  system  in a slug-like manner. All
water in the soil is  pushed ahead of new
water entering the soil. (6) The soil drains
instantly to the "field capacity" water content
after each infiltration event. (7) Water is
removed from each layer in the root zone in
proportion to the available water stored in
that layer. (8) Chemicals move downward in
the soil  system;  upward movement  of
chemicals is ignored. (9) No oil is present in
the soil system.
  The CMLS model estimates the amount
of chemical  at a particular position  as a
function  of  time. It does  not calculate
concentrations. If  concentrations are
needed, the user must estimate the mass of
water in which the chemical is mixed and
then calculate the concentration from this
mass of water and the mass of chemical
leached.

HYDRUS   Model:   HYDRUS:   One-
Dimensional Variably Saturated Flow and
Transport Model, Including Hysteresis and
Root Water  Uptake (Kool  and van
Genuchten, 1991) is a finite element model
and is the most computationally demanding
of the selected models. In HYDRUS soil and
chemical properties are assigned as a series
of points, and these properties can vary
from one point to another. As a result, the
user has great flexibility  to define  initial
conditions to represent the site of interest.
Assumptions incorporated into HYDRUS
include (1) partitioning of chemical between
solid and water is described by a linear,
reversible  model  with  instantaneous
equilibrium between phases; (2) movement
in the vapor phase is ignored; and (3) no oil
is present in the system.

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 Sensitivity and Uncertainty
   The sensitivity of a model refers to the
 change in a selected model output resulting
 from a specified change in a single input
 parameter. Mathematically the  sensitivity
 coefficient, S, is defined as
             ax
                                (2),
 where f represents the output of interest and
 x represents the input parameter (McCuen,
 1973). If the model output can be written in
 a nice symbolic form, the sensitivity can be
 applied by differentiating / symbolically.
 However, models are often too complex for
 this approach; in this case the sensitivity can
 be calculated using the difference equation
             Ax
                                (3).
   Model  sensitivity, S, as  defined by
 Equations 2 and 3 is the change in model
 response per unit change in  the  input
 parameter. The change in model output due
 to a small change in input parameter is given
 by
        A f = S A x
                        (4),
where A/is the change in output f due to a
change of Ax in the input parameter. That is,
the product of the sensitivity, S, and the
change in input parameter is the change in
model output.
  The value of  S calculated from these
equations has units, which makes it difficult
to compare sensitivities  for different input
parameters. This problem is overcome by
using the relative sensitivity, S,., given by
  or
c   _ u '
br  "37
        S  =
*  = S*-
f       f
                   x
              Ax
                           f
                                (5),
                        (6),
where /"is the value of the model output and
x is the value of the input parameter. The
relative change in model output, Af/f, can
then be estimated from the relative change
in input parameter, Ax/x, and the relative
sensitivity using the equation


        A f x  _ q  A x        m
        ~7~ 7  ~  f~7~        (  )-
         II        *

  Hence, the relative sensitivity is a measure
of  the relative  change  in  model output
 corresponding to a relative change in the
 input parameter.  In short,  Sr  gives  the
 percentage change in model response for
 each one percent change in  the  input
 parameter. If the absolute value of Sr is
 greater than  1, the absolute value of the
 relative change in model output will be greater
 than the absolute value of the relative change
 in input parameter. If the absolute value of Sr
 is less than 1, the absolute value of the
 relative change in model output will be less
 than the absolute value of the relative change
 in input.
  Uncertainty analysis is used to incorporate
 simultaneous changes in  more than one
 parameter and variability of the parameters.
 Two approaches are frequently used for
 defining  model uncertainty.  The  first
 approach, a deterministic approach, is most
 applicable to models in which  explicit
 equations can be written for model outputs
 as functions of input parameters. The first-
 order second-moment uncertainty analysis
 is a widely used technique in this  approach.
 It provides a method of calculating the mean,
 variance, and covariance of model outputs
 from  means, variances, covariances and
 sensitivity coefficients for the model inputs.
 First-order second-moment analysis is most
 appropriate when the model is not strongly
 nonlinear in  its  parameters  and  the
 coefficients of variation of the parameters
 are small.
  The second  approach  is a stochastic
 method, which is often used when the explicit
 formula for a complex system cannot be
 obtained or the equations are cumbersome.
 The Monle Carlo technique, which is an
 example  of this  approach,  requires
 knowledge of the frequency distribution of
 each input parameter and  the correlations
 among these parameters. Input parameters
 are generated at random from the parameter
 populations so that means and correlations
 are preserved. Each set of inputs is used in
 the model to compute the outputs of interest.
 This process is repeated many times  until
 the probability  distribution of the model
 outputs is defined. Summary statistics of the
 outputs are then computed or the entire
 distribution is used in the analysis.

 Physical Setting
  The  sensitivity of a particular  output to
 changes in model inputs depends upon the
 entire set of parameters used in the model
 and upon the total system being  analyzed.
 The general scenario simulated was from a
 benzene release near Perdido,  Alabama.
The soil in the area was the Norfolk sand
 (fine-loamy,  siliceous,  thermic Typic
 Paleudult)  At the beginning of the simulation,
 100  g  m-;> benzene was  assumed to be
uniformly distributed in the top 0.5 m of soil.
A water table was assumed to be present at
                                                                            a depth of 2 m. Soil properties for the top 2
                                                                            meters of the Norfolk sand were obtained
                                                                            from Quisenberry, era/. (1987) for the same
                                                                            soil in Blackville, South Carolina. Data on
                                                                            the organic carbon content (OC) of the soil
                                                                            were not available, and, as a result, percent
                                                                            organic carbon  content was  assumed  to
                                                                            decrease with  depth according  to the
                                                                            equation
                                                                              OC(d)  =1.35e
                                                                                                      -4.0d
                                (8),
where d is the soil depth (m). The organic
carbon content determined for the middle of
each soil layer was used for that entire layer.
The initial water content throughout the soil
profile was internally calculated by the RITZ
and VIP models from the specified recharge
rate,  the saturated conductivity, and the
Clapp-Hornberger constant. CMLS assumes
the initial water content of each soil layer is
the field capacity value. An initial water
content of 0.15 cm3 cm-3 throughout the soil
profile was used as the initial condition  in
HYDRUS. The  parameters for the  van
Genuchten closed-form hydraulic functions
(van Genuchten, 1980) were obtained from
the soil  water retention  and unsaturated
hydraulic conductivity data using the RETC
software (van Genuchten, era/., 1991)  Soil
porosity was computed from the bulk density.
The Clapp-Hornberger constant (Clapp and
Hornberger, 1978) required in the RITZ and
VIP models was determined by regression.
  Climatological data from the Perdido area
of Alabama were obtained for the nearby
sites  of  Fairhope  from  the  SE Regional
Climate Center. The only evaporation (ET)
data available were from Fairhope.. Daily
weather  data from the Fairhope site were
used in the simulation runs for HYDRUS and
CMLS models.  Average recharge rates
required  for RITZ and VIP were calculated
from total rainfall  and total evaporation data
at  these sites.  Average  rainfall  and
evaporation rates for the area were 5 and 4
mm per  day, respectively. Daily weather
data from Caddo County, Oklahoma, were
also used for some of the analyses using
CMLS since the data available for Perdido
were not sufficient for  the  Monte Carlo
simulations.
  The organic carbon partition coefficient
and degradation rates for benzene were
obtained from values  in  the literature.  A
value of 80 cm3 g-1 was used as the organic
carbon partition coefficient and a  half-life of
100 days was used as the rate of degradation.

Sensitivity Results
  Sensitivity analyses based on the physical
setting described above were conducted for
the selected models.  In particular,  the
sensitivity analysis focused on four primary
model  outputs: (1) the time  at which  the

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contaminant reaches the water table, (2)
the amount of contaminant entering the
saturated  zone, (3)  the width  of  the
contaminant pulse at the water table, and
(4) the concentration of the contaminant
entering the ground water.
  The results of the sensitivity analysis for
each of the models (RITZ, VIP, CMLS, and
HYDRUS) are summarized below. It should
be  recognized,  however, that although
these results reflect the specific model's
parameter sensitivity, the results are also
dependent upon the total system (physical
setting) that is conceptualized.

RITZ Model
  Results of the sensitivity analysis for the
RITZ model  indicate that  the  output
describing the  total amount  of pollutant
leached to ground water has  the highest
relative sensitivity parameter  values with
respect to the other model outputs. This
indicates that a relative change for most of
the parameters will result in a larger change
in the model  result for amount of pollutant
leached than travel time or  pulse  width.
Specifically,  for  the amount  of pollutant
leached, organic carbon content, saturated
water content,  treatment zone  depth,
partition coefficient, and degradation half-
life are sensitive parameters as these exceed
2.0 relative sensitivity. In contrast, the travel
time relative sensitivities range from -0.72 to
0.76 with  organic  carbon content, bulk
density, saturated water content, treatment
zone depth, recharge rate,  partition
coefficient, and  half-life of oil being the
principal sensitive parameters. The  relative
sensitivities for the pulse width model output
were the lowest values ranging from -0.46 to
0.60. The primary sensitive parameters for
this model output were recharge rate, sludge
application  rate,  oil-water partition
coefficient,   Henry's   law   constant,
concentration of oil in sludge, density of oil,
and half-life of oil.

 VIP Model
  VIP was written to model movement of a
chemical in a system similar to that used in
RITZ. VIP includes oxygen transport, oxygen
exchange, and oxygen  loss that are not
presentin RITZ. It also incorporates chemical
movement in the  vapor phase  for the
pollutant.
  The conditions modeled in this study
represent conditions  for which  vapor
movement is minimal and oxygen is not
limited so the two models would be expected
to agree. The time  at which the pollutant
reaches 2 m and the concentration in water
at that time are in good agreement between
the models. However,  the  end  of the
contaminant pulse is much more gradual for
VIP than for RITZ. Also, the concentration of
pollutant in water during the duration of the
pulse decreases more rapidly in VIP than in
RITZ. These results show that the travel
time and  pulse width increase as  the
recharge rate increases as was observed in
the analysis of RITZ. The impact of these
parameters upon concentration  is  nearly
identical to  those discussed for RITZ with
the following exceptions:

  1. The rate of decrease in concentration
      as a function of time during  the
      duration of the pulse is greater than
      that predicted by RITZ.
  2.  The pulse width predicted by VIP is
      somewhat greater than that predicted
      by RITZ due to the gradual decline in
      concentration at the trailing edge of
      the pulse.
  3.  When model parameters  are such
      that  substantial movement takes
      place in the vapor phase, radically
      different concentration functions are
      predicted  by VIP. VIP predicts low
      concentrations of pollutant at the 2-m
      depth  at very  small times   for
      simulations with  Henry's  constants
      exceeding 0.005.  RITZ  does  not
      predict  this  early  arrival  of  the
      contaminant.  Also, although  VIP
      predicts the end of the  pulse will
      occur at an earlier time, the change is
      not as large as that  predicted by
      RITZ. While VIP  shows a rapid
      increase in concentration at 2 m to a
      concentration of 0.01  g m3, RITZ
      predicts the pollutant never reaches
      that depth

  These results imply  that sensitivity
coefficients for VIP are approximately those
of RITZ for conditions when vapor movement
is of minor importance and oxygen-limiting
conditions do  not exist.  A thorough
examination  of the sensitivities  under
oxygen-limiting  conditions was not carried
out in this study.

CMLS Model
  When totally uniform  systems  are
simulated  using CMLS, the predicted
positions of the bottom of the chemical pulse
are in good agreement with RITZ. CMLS
predicts that the top of the chemical moves
more rapidly through the shallow soil layers
than does RITZ. Hence the duration of the
pulse entering the water table is less for
CMLS than for RITZ.  This  difference is
because RITZ assumes that the flux of water
at every depth m the soil is the same, and
therefore the top and bottom of the chemical
slug move at the same velocity (assuming
no  oil is present). In CMLS the flux of water
passing any depth on a particular day is the
difference between the flux entering the soil
surface and the amount of water stored in
the soil profile above that depth. Therefore,
the flux of water in the root zone decreases
with depth so chemicals near the soil surface
move more rapidly than chemicals  below
the root zone. (CMLS predicts that the top
and bottom of the chemical pulse move at
the same speed when the root zone depth is
zero and the soil properties are uniform with
depth.)
  CMLS allows the user to model movement
through layered soils where soil-water and
chemical properties change with depth,
When layers are  simulated, the chemical
reaches the 2-m depth approximately 150
days  earlier than when average soil
properties are used. The duration  of the
chemical pulse entering the water table is
greater for the layered soil  than for the
uniform soil. This is primarily due to a lower
velocity of chemical in the shallow soil layers
where the  sorption coefficient is greater
than in the uniform case.  For this soil, the
use of uniform soil properties causes CMLS
to overestimate  the travel  time and to
underestimate the  amount leached with
respect  to the layered  simulation. The
simulations described above for CMLS and
RITZ assumed  daily  infiltration and
evapotranspiration rates equal to the long-
term  average   values  derived   from
measurements taken at Fairhope, Alabama,
between  1983  to  1991.  Additional
simulations were conducted using daily water
fluxes from the same time period, January 1,
1983 to 1990. Results are shown in Table 1.
In particular, layered soils and daily fluxes
resulted in a mean travel time that was 47%
slower than the uniform soil - uniform flux
case. The amounts leached for the layered
soil with  uniform flux and the layered soil
with daily flux are 4 and  18 times greater
than the  uniform case, respectively.  These
leaching  amounts are based on a half-life of
100 days. If the half-life were less than 100
days  these factors would be larger. When
average  infiltration and evapotranspiration
rates are used in CMLS, solute leaching is
underestimated due to the impact of large
rainfall events and the resulting large water
fluxes being essentially ignored.
   Clearly the water fluxes or the weather
sequences used to drive the model have a
large impact upon the predictions. Therefore,
weather  will have a large impact  upon the
sensitivity coefficients. Since it is desired to
get an understanding  of the sensitivity for
any weather sequence, the model was run
many times for different weather sequences
characteristic of a site. Results from all of
the different simulations were summarized
and used in the sensitivity analysis. The site
chosen is near Fort Cobb, Oklahoma. Annual
rainfall there varied from  398 to 1034 mm
during the 1948 to 1975 time period. Average

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 Table 1.  Comparison of Predicted Travel Time, Duration of Loading, and Amount Leached for
         Benzene the Norfolk Soil with Different Levels of Simplification. Weather for Fairhope,
         Alabama. Model Used was CMLS.
                                    Travel Time
                                      (Days)
           Duration
            (Days)
Amount Leached
 Uniform Soil/Uniform Water Fluxes           699

 Layered Soil/Uniform Water Fluxes           541

 Layered Soil/Daily Water Fluxes

                  Beginning Year
                       1983             327
                       1984             573
                       1985             374
                       1986             423
                       1987             224
                       1988             276
                       1989             370
                       1990             395
                      Mean             370.2
              70

             115
      1.0

      3.8
242
152
72
5
87
28
58
320
120.5
32.9
3.6
9.9
5.4
29.9
16.3
9.6
33.0
17.6
annual rainfall was 709 mm during that time
period. Weather sequences were generated
using the weather generator developed by
Richardson  and  Wright (1984),  which  is
incorporated into the current version  of
CMLS. Probability distributions of travel time
and amount leached to ground water were
obtained and used in the sensitivity analyses.
  Results of the sensitivity analysis for the
designated model outputs indicate that all
CMLS parameters are  important as the
lowest  maximum value of the relative
sensitivity  coefficients for any  given
parameter and probability range was 0.54.
In particular, the relative sensitivities for the
amount leached are generally negative since
the amount leached decreases as the
parameter  value increases, and the
magnitudes  of these relative sensitivities
are much greater than those for travel time
or pulse width. Since the magnitudes  of
these relative sensitivities are greater than
1, the relative change in predicted amount
leached will be greater than the relative
change in the parameter itself. In  addition,
the relative sensitivity  values generally
increase by at least a factor of two, which
indicates that daily  weather is  a major
component of the total uncertainty  in  a
predicted value  for  amount  leached.  In
contrast to the sensitivities for the amount
leached, the sensitivity coefficients for travel
times and pulse width  are generally positive
and  of  much  lower  magnitude.  Further,
relative sensitivities are generally  constant
or decrease as probability levels increase.
HYDRUS Model
  Simulations using HYDRUS were  run
using three rainfall data sets, 1983, 1985,
and 1987. The percent of the total pollutant
predicted to be leached below the 2-m depth
was 27%, 3%, and 10% for 1983,1985, and
1987, respectively.  Clearly, weather
variability significantly impacts the predicted
pollutant leaching  results. The results for
1983 agree  well  with those of CMLS.
However, for 1985 and 1987, CMLS predicts
faster contaminant transport to the ground-
water table and greater amounts leached.
  As with  the other models,  results of the
sensitivity analysis for the HYDRUS model
indicate that the output describing the total
amount of pollutant leached to ground water
has higher relative sensitivity parameters
than travel time and pulse width. Specifically,
for this model output, HYDRUS is sensitive
to the values for the partition coefficient,
saturated water content,  and  the van
Genuchten 6 parameters. In contrast,  the
travel time relative sensitivities are lower in
magnitude and differ in sign from the amount
leached output sensitivity values. Travel time
is quite sensitive  to  van Genuchten  6,
saturated water content, partition coefficient,
root  uptake potential,  and  bulk density.
Relative sensitivities for pulse  width  are
high for saturated water content, bulk density,
dispersivity,  and the  van  Genuchten 6
coefficient. All three output parameters are
quite insensitive to residual water content
and diffusion coefficient.
Uncertainty Analysis
  Monte Carlo simulations were conducted
using RITZ for estimating uncertainty with
respect to soil and chemical properties. The
probability distributions of the soil parameters
were determined using soil data from 87 soil
profiles and 10  soil series of sand from
Florida. The bulk density, saturated
conductivity,  organic carbon  content,
saturated  water  content,  and Clapp-
Hornberger constant were best described
by log-normal distributions. The range of
values for the partition coefficient and half-
life of benzene were found in the literature.
Normal distributions were assumed for these
two parameters. Soil properties and chemical
properties were assumed to be uncorrelated.
If the generated saturated  water content
exceeded the soil porosity based on  the
generated bulk density, the set of generated
parameters was rejected and another set
was  generated. One hundred sets of input
parameters were generated for Monte Carlo
simulation.
  Results of incorporating the variability and
uncertainty of soil parameters into RITZ for
the standard scenario were defined for three
probability levels. At any instant of time, the
predicted concentration of pollutant at the 2-
m depth was less than the value for 95% of
the simulations. These results indicate that
the maximum  concentration  has values in
the range of 0.06 to 0.64 g rrr3 for 90% of the
simulations. Five percent of  the predicted
values are greater than 0.64  g nrr3 and 5%
are less then  0.06 g nr3. In addition,  the
uncertainty analysis indicates that the travel
time for  the pollutant ranges  from
approximately 940 to 1460 days with 90% of
the values  falling in the 980 to 1370 day
range. The computed  pulse  width varies
from 950 to 1050 days  with 90% of  the
values between  960 and 1020 days. The
predicted leaching varies from 0.009% to
0.2% of the amount applied with 90% of the
values in the range of 0.02% to 0.2% of the
amount applied. Clearly,  there is a large
uncertainty in model predictions due to only
soil properties.
  The results  of the uncertainty analysis
due to uncertainty in the partition coefficient
and  half-life of the pollutant indicate  the
maximum concentrations on the 95%, 50%,
and 5% probability curves are 0.7,0.21, and
0.008  g or3, respectively. This  range is
slightly larger than those for soil properties.
Specifically, the travel time varies from 970
to 1310 days for these simulations with 90%
of the values in the range of  1050 to 1220
days. Pulse width takes on values of 950 to
1010 days due to uncertainty  in these
chemical properties. Ninety percent of the
values are in the range of 970 to 1000 days.
The amount leached varies over more than

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4 orders of magnitude with 90% of  the
leaching amounts in the range of 0.004 to
0.4 % of the amount applied. In this case the
uncertainty in amount  leached  due  to
chemical properties exceeds that due to soil
properties.
  Simulations  for systems incorporating
uncertainty in both soil  and chemical
properties produced results that exceeded
those for soil and chemical properties
individually. Large differences in predicted
concentrations  have nearly 150-fold
differences  in concentration between  the
5% and 95% probabilities. Travel times take
on values from 950 to 1540 days with 90%
of the values in the 960 to 1350 day range.
Pulse widths vary from 950 to 1060 days
with 90% of the simulations between 955 to
1020 days. Calculated amounts  leached
beyond the 2-m depth have values of 0.0003
to 0.8%. Ninety percent of the values lie in
the range of 0.004 to 0.5%.
  The results of the uncertainty  analysis
indicate that uncertainties exist and must be
incorporated into the use  of models. In
particular, it is more realistic to think in terms
of the  probability that a certain  type of
behavior will take place rather than
attempting to say whether or not that behavior
will occur.  Moreover,  the  fact that  soil
properties vary spatially within a mapping
unit  must  be acknowledged.  Further,
modelers are  better served to simulate
movement in that unit for the many  different
sets of properties expected and to summarize
the model  predictions than to attempt to
derive  some  representative  set  of
parameters for the region hoping that the
model output for that set will describe the
entire region. By simulating results for many
sets of parameters expected in the area, it is
possibletodeterminethecontaminant leaching
for the area and gain knowledge of the likely
rangeof leaching possible. All of this information
can then be used  in the decision-making
process. Uncertainties must also be included
when validating models experimentally.
  Finally,  the uncertainty  in  model
predictions due to uncertainty in input
parameters represents only part of the overall
uncertainty. This analysis does  not
incorporate uncertainty due  to model
simplifications of real phenomena, errors in
understanding that phenomena, or errors in
solving the simplified problem.

References
Clapp,  R.B., and G.M. Hornberger. 1978.
    Empirical  equations for some  soil
    hydraulic properties. Water Resour.
    Res. 14:601-604.
Kool, J.B., and M.Th. van Genuchten. 1991.
    HYDRUS: One-dimensional variably
    saturated flow and  transport model,
    including hysteresis  and root water
    uptake. U.S. Salinity Lab., USDA-ARS,
    Riverside, California.
McCuen, R.H. 1973. The role of sensitivity
    analysis  in hydrologic modeling. J.
    Hydrol. 18:37-53.
Nofziger, D.L., and A.G. Hornsby. 1986. A
    microcomputer-based  management
    tool  for chemical movement  in soil.
    Applied Agric. Research 1:50-57.
Nofziger, D.L., J.R. Williams, and Thomas
    E. Short. 1988. Interactive simulation of
    the fate of hazardous chemicals during
    land treatment of oily wastes: RITZ
    user's guide.  Report No. EPA/600/8-
    88/001, U.S. Environmental Protection
    Agency. 61  pp.
Quisenberry, V.L., O.K. Cassel, J.H. Dane,
    and J.C. Parker.  1987. Physical
    characteristics of soils of the southern
    region Norfolk, Dothan, Wagram, and
    Goldsboro    series.     Southern
    Cooperative Series Bulletin 263. South
    Carolina Agricultural Experiment
    Station, Clemson University.
Richardson, C.W., and D.A. Wright. 1984. A
    model for generating daily weather
    variables.   U.S.  Department   of
    Agriculture,  Agricultural  Research
    Service, ARS-8, 83 pp.
Stevens, O.K., W.J. Grenney, and Z. Van.
    1989. VIP: A model for the evaluation of
    hazardous substances in the soil. Civil
    and Environmental Engineering
    Department,  Utah  State  University,
    Logan, Utah.
van Genuchten, M.Th. 1980. A closed-form
    equation  for  predicting the hydraulic
    conductivities of unsaturated soils. Soil
    Sci. Soc. Am. J. 44:892-898.
van Genuchten,  M.Th., F.J. Leij, S.R. Yates,
    and  J.R. Williams.  1991.  The RETC
    codes for quantifying the hydraulic
    functions of unsaturated soils. United
    States  Environmental  Protection
    Agency. EPA/600/2-91/065.

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   D.L Nofziger, Jin-Song Chen, and C.T. Haan are with Oklahoma State University,
     Stillwater, OK 74078-0507.
   Joseph Williams is the EPA Project Officer (see below).
   The complete report,  entitled "Evaluation of UnsaturatedA/adose Zone Models for
     Superfund Sites," (Order No. PB 94-157765; Cost:  $27.00, subject to change) will
     be available only from
          National technical Information Service
          5285 Port Royal Road
          Springfield, VA 22161
          Telephone: 703-487-4650
   The EPA Project Officer can be contacted at:
          Robert S. Kerr Environmental Research Laboratory
          U.S. Environmental Protection Agency
          Ada, OK 74820
United States
Environmental Protection Agency
Center for Environmental Research Information
Cincinnati, OH 45268
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