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.
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Kool, J.B., and M.Th. van Genuchten. 1991.
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including hysteresis and root water
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Riverside, California.
McCuen, R.H. 1973. The role of sensitivity
analysis in hydrologic modeling. J.
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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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