Supplementary Documentation
DRAFT
GENII Version 2
Sensitivity/Uncertainty Multimedia
Modeling Module
For Advisory with
EPA's Science Advisory Board
Radiation Advisory Committee
April 25,2000
v>EPA
Supplementary Documentation
DRAFT
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GENH Version 2
Sensitivity/Uncertainty Multimedia
Modeling Module
User s Guidance
G. M. Gelston M. A. Pelton
K. J. Castleton B. L. Hoopes
R. Y. Toiro P. W. Eslinger
G. Wheton P. D. Meyer
B. A, Nopier
DRAFT December 1998
Prepared for
U.S. Environmental Protection Agency
under'Contract DE-AG06-76RLO 1830
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DISCLAIMER
This report was prepared as an account of work sponsored by an agency of the United States
Government. Neither the United States Government nor any agency thereof, nor Battelle
Memorial Institute, nor any of their employees, makes any warranty, expressed or implied, or
assumes any legal liability or responsibility for the accuracy, completeness, or usefulness
of any information, apparatus, product, or process disclosed, or represents that its use
would not infringe privately owned rights. Reference herein to any specific commercial
product, process, or service by trade name, trademark, manufacturer, or otherwise does not
necessarily constitute or imply its endorsement, recommendation, or favoring by the United
Stales Government or any agency thereof, or Battelle Memorial Institute. The views and opinions
of authors expressed herein do not necessarily state or reflect those of the United States
Government or any agency thereof.
PACIFIC NORTHWEST NATIONAL LABORATORY
operated by
BATTELLE MEMORIAL INSTITUTE
for the
UNITED STATES DEPARTMENT OF ENERGY
under Contract DE-AC06-76RLO1830
Printed in the United States of America
Available to DOE and DOE contractors from lite
Office of Scientific and Technical Information, P.O. Box 62, Oak Ridge, TN 37831;
prices available from (615) 576-8401.
Available to the public from the National Technical Information Service,
U.S. Department of Commerce, 5285 Port Royal R4, Springfield, VA 22161
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PNNL-12036
GENH Version 2
Sensitivity/Uncertainty Multimedia
Modeling Module
User's Guidance
G. M. Gelston M. A.Pelton
K. J. Castleton B. L. Hoopes
R. Y. Taira P. W. Eslinger
G. Whelan P. D. Meyer
B. A. Napier
October 1998
Prepared for
Center for Risk Modeling and Emergency Response
U.S. Environmental Protection Agency
under Contract DE-AC06-76RLO 1830
Pacific Northwest National Laboratory
Richland, Washington 99352
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Summary
The Framework for Risk Analysis in Multimedia Environmental Systems (FRAMES)
software is currently designed for deterministic environmental and human health impact models.
The Sensitivity/Uncertainty Multimedia Modeling Module (SUM3) software product was
designed to allow statistical analysis using the existing deterministic models available in
FRAMES. SUM3 is an available option under the Sensitivity/Uncertainty Module in FRAMES.
SUM3 randomly samples input variables and preserves the associated output values in an external
file available to the user for evaluation. This enables the user to calculate deterministic values
with variable inputs, producing a statistical distribution of results. A typical application of the
uncertainty analysis is to indicate the relative conservatism of the deterministic result. This
document serves as guidance for Version 2 of SUM3
Although SUM3 was originally developed as a sensitivity/uncertainty tool for use with the
Multimedia Environmental Pollutant Assessment System (MEPAS), it is not restricted to the
MEPAS models. SUM3 can now be used with other deterministic environmental models through
the FRAMES software package with other available tools, such as the GENII Version 2 software
system, which is a Hanford environmental dosimetry system. Within FRAMES, SUM3 allows
the user to conduct a sensitivity and/or uncertainty analysis to understand the influence and
importance of the variability/uncertainty input parameters on contaminant flux, concentration,
and human-health impacts. The sensitivity analysis can identify the key parameters that
dominate the overall uncertainty. Statistical methods used in SUM3 are based on Monte Carlo
sampling using Latin Hypercube random numbers. The file contains cumulative distribution
function (CDF) data and can be graphically displayed through the FRAMES Viewer option.
This document takes the user through a step-by-step process for setting up a statistical
analysis, running SUM3 software, and interpreting results. Examples of input screens and result
files are provided.
in
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Contents
1.0 Introduction 1.1
2.0 Using FRAMES Sensitivity/Uncertainty Module 2.1
3.0 Selecting Sampling Variables of Interest 3.1
4.0 Entering Statistical Parameters 4.1
4.1 Distribution 4.2
4.1.1 Uniform , 4.3
4.1.2 Log Uniform 4.5
4.1.3 Normal 4.5
4.1.4 Log Normal 4.7
3.1.5 Exponential 4.9
3.1.6 Triangular 4.9
3.1.7 Gamma 4.10
4.1.5 Beta 4.10
4.1.6 Weibull 4.10
4.1.7 Logistic 4.10
4.1.8 User Defined 4.10
4.2 Correlation 4.10
4.3 Equation 4.12
5.0 Selecting Output Variables of Interest 5.1
6.0 Running the Sensitivity Uncertainty Module and SUM3 6.1
6.1 Status Screen 6.2
6.2 SUM3 Sampling Technique 6.3
7.0 Interpreting Results 7.1
8.0 References 8.1
IV
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1.0 Introduction
An uncertainty analysis provides a quantitative estimate of the range of model outputs
that result from uncertainties in the structure of a software model or the inputs to that model. If
the analysis is carried out in an appropriate way, the range will likely contain the true value (or
values) that the model seeks to predict. The analysis can also be extended to identify the input
parameters that contribute the most to the overall uncertainty, so that priorities can be set for
work aimed at reducing the uncertainty. Sensitivity analysis allows the user to identifying the
parameters that impact the results the most. If uncertainty estimates are to be made meaningful
and practical, the analysis must be carried out systematically, with due regard to the purpose of
the model, the quality of the data, and the nature of the application. Uncertainty in model
predictions can arise form a number of sources, including specification of the problem,
formulation of the conceptual model, formulation of the computational model, estimation of the
parameter values, and calculation, interpretation and documentation of results. Of these sources
only uncertainties resulting from estimation of parameter values can be quantified in a
straightforward way by applying a statistical approach to deterministic models.
This document serves as guidance for the Sensitivity/Uncertainty Multimedia Modeling
Module (SUM3) Version 2. SUM3 is currently an option under the Sensitivity/Uncertainty
Module in Framework for Risk Analysis in Multimedia Environmental Systems (FRAMES)
Version 1.0. The FRAMES software is designed for deterministic models. Therefore, the SUM3
software product was designed to allow statistical analysis using the deterministic models.
SUM3 will randomly sample input variables and preserve the associated output values in an
external file available to the user for evaluation. The effect is calculating deterministic values
with variable inputs producing a statistical distribution of results. A typical application of the
uncertainty analysis is to indicate the relative conservatism of the deterministic result. Note that
within the FRAMES software, the SUM3 model is located in the Sensitivity/Uncertainty Module.
SUM3 can be used with deterministic environmental models through FRAMES. Within
FRAMES, SUM3 allows the user to conduct a sensitivity and uncertainty analysis of the input
parameter's variability/uncertainty on contaminant flux, concentration, and human health
impacts. The results of this analysis can be used to identify the key parameters that dominate the
overall uncertainty. Statistical methods used in SUM3 are based on Monte Carlo sampling using
Latin Hypercube random numbers. The file contains Cumulative Distribution Function (CDF)
data and can be graphically displayed through the FRAMES Viewer option.
This document takes the user through a step by step process for setting up, running, and
interpreting results from a sensitivity/uncertainty analysis simulation. Examples of user interface
screens and results files are provided.
1.1
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2.0 Using FRAMES Sensitivity/Uncertainty Module
The following section guides the user through the use of the Sensitivity/Uncertainty (SAJ)
Module option in the FRAMES user interface. There are four steps to starting the SAJ Module:
before using the SAJ Module, connecting the SAJ Module, choosing the SUM3 model and
opening the SUM3 user interface.
Before using the S/U Module:
First set up the deterministic FRAMES analysis (See FRAMES Tutorial), entering a value for
each parameter requested.
Run the deterministic model to ensure there are not errors in the base case.
There should be green lights on all module icons prior to running the SAJ Module. With the
exception of text or chart viewers.
i
Connecting the S/U Module:
Drag and drop a single SAJ Module icon onto the FRAMES conceptual model screen. The
SAJ Module Icon is a bell curve on a green background, Figure 2.1.
Using the right-click and drag feature of FRAMES, connect the SAJ Module icon to each
deterministic module icon containing an input variable of interest. Note the connection path
starts at the deterministic module icon and goes to the SAJ Module icon. (See Figure 2.2)
" Using the right-click and drag feature of FRAMES, connect the SAJ Module icon to each
deterministic module icon producing an output value of interest. Note the connection path
starts at the deterministic module icon and goes to the SAJ Module icon. Figure 2.2 is an
example a FRAMES conceptual model created for a multimedia transport and exposure case.
In this example two vadose zone icons and a saturated zone icon have been connected to the
SAJ module icon, thereby allowing all input and outputs produced by those modules to be
available for selection in the SUM3 user interface.
Figure 2.1. SensitivityAJncertainty Module Icon
2.1
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Figure 2.2. Connecting the S/U Module
Choosing the SUM3 Model:
Shift-Click on the S/U Module icon and choose the 'General Info' option.
From the General Info screen choose the 'Sensitivity/Uncertainty Multimedia Modeling
Module.' Figure 2.3 illustrates the model selection screen for FRAMES. The available
statistical models are listed in the left column, and a description and contact information for
the highlighted model is displayed in the right column.
Give the S/U Module icon a Label
« Click the OK button
2.2
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fe>^SlBsilffiifi|lii-Bl
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"ensitivitv/Uncertainty Multimedia Modeling Module
, «. ._., ,~.. .,,_»-,-,,,-_,» . .,_.,_»,-,«..«,-,
Thick of aquifer from Aquifer (aqu4)
Bulk density from Aquifer (aqu4)
Travel distance for flux, fcmS from Aquifer(aqu4)
Perpendicular distance for flux, fcmS from Aquifer{at
Vertical distance for flux, fcm5 from Aquifer(aqu4)
Longitudinal dispersivity for flux, fcmS from Aquife
Transverse dispersivity for flux, fcm5 from Aquifer(<
Vertical dispersivity for flux, fcmS from Aquifer(ae
Travel distance well, fcmS from Aquifer(aqu4)
Perpendicular distance well, fcmS from Aquifer(aqu4)
well, fcmS from Aquifer(aqu4)
Figure 2A. User Interface for SUM3
There are three main tabs in the SUM3 user interface: Variables, Parameters, and Outputs.
The Variables tab allows the user to select variables of interest. The Parameters tab allows the
user to describe and relate variables through distributions, correlation, and equations. The
Outputs tab allows the user to select the output values of interest. The following sections
describe each tab and it's use in more detail.
2.4
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3.0 Selecting Sampling Variables of Interest
The Variables tab enables the user to specify the stochastic parameters that are to be
randomly sampled and varied. A variable list is provided for the user with the description that is
consistent with the descriptions given in the deterministic module's input screen. This list of
variables is derived from all possible stochastic parameters found in all deterministic modules
connected to the S/U Module icon. The description provides the user with the variable name and
the associated module name (both the module name given by the user and the FRAMES icon.
name are displayed). Figure 3.1 demonstrates a portion of the listing of stochastic parameters
from two vadose zone modules and a saturated zone module that have been connected to the S/U
Module icon. A scroll bar is provided on the far right of the listing to enable the user to move
through the list when it is longer than the length.
Sensitivity/Uncertainty Multimedia Modeling Module - sen! 1
Soil total porosiV from Vadoze_1 (vad3)
conductivity
KsVadS
HVadQ
Soil bulk density from Vadoze_l(vad3)
Soil coefficient* from Vadoze I(vad3)
Lateral dispersivity from Tadoze_l(vad3)
Soil equilibrium coefficient, Antimony from
Soil equilibrium coefficient, STRONTIUM-90 from Vadoj
Soil equilibrium coefficient, YTTRIUM-90 from Vadoze J
Soil equilibrium coefficient, Tricbloroethylene from
Soil total porosity from Vadoze_2(vadB)
Soil field capacity from Vadoze_2 (vadB)
Soil hydraulic conductivity from Vadoze_2 (vadB)
Thick of vadose zone from Vadoze_2 (vadB)
Soil bulk density from Vadoze_2(vadB) g|
Figure 3.1. Variable Tab
3.1
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Adding an Alias:
In order to reduce this list to just those parameters the user wishes to vary, the user is
asked to provide a unique alias for each parameter of interest. A parameter of interest may be
one that is given a distribution, correlation, or used in an equation to describe another parameter
of interest. To add an alias, click on the white entry box to the right of the word "Alias." The
alias should be one word and is limited to eight (8) digits, capitalization is preserved but is not
used to distinguish between aliases, the underscore symbol (_ ) is not allowed. After typing the
alias, click the Add button to enter the alias into the variable list. The variable description list
will display the alias to the far left with a line (|) separating the alias from the description. This
alias will be used to create a selection list for distributions, correlation, and equations.
Changing an Alias:
To change an alias, the user must first delete the old alias then add hi the new alias.
Following the instructions given for deleting an alias the user should remove the alias from all
distributions and equations before selecting the alias to be deleted from the variables screen. A
warning will appear if any correlation or equation dependencies exist. To add the new alias
follow the guidance given for adding an alias.
Deleting an Alias:
To delete an alias the alias must first be removed from all parameter dependencies. The
user must first delete any correlation and/or equation where the alias has been assigned. A
Delete button is provided in the variables tab to remove the variable from the alias selection list.
A warning will appear if any correlation or equation dependencies exist By removing the alias
from the variable list, the variable will no longer be available for distributions, correlation, or
equations. This allows the user to reduce an alias listing to only those currently of interest.
3.2
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4.0 Entering Statistical Parameters
The Parameters Tab enables the user to describe the variables of interest. There are three
options for describing the variables statistically. Figure 4.1 demonstrates the Parameters Tab and
the three sub-tabs options found within it, distribution, correlation, and equation. There are
several combinations of these options to aid the user.in describing the variables of interest. Some
combinations available to the user are:
giving the variable a statistical distribution only,
* giving the variable a statistical distribution and correlating it to another variable of interest,
giving the variable a statistical distribution and using it in an equation to describe another
variable, and
using an equation to describe the variable.
This section provides guidance on using the distribution, correlation and equation
features.
^Sensitivity/Uncertainty Multimedia Modeling Module-sen11
Soil total porosity from VadozeJ (vad3)
BdVad3 (g/crn 3)
KsVadB (cm/day)
HVadB (cm)
SrKdVadS (ml/g)
Figure 4.1. Parameters Tab
4.1
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4.1 Distribution
To assign a distribution to a variable the user must first have assigned the variable an alias
(to learn how to assign an alias, go to Section 3.0 Selecting Sampling of Interest). The
distributions available in SUM3 are: Uniform, Log Uniform, Normal, and Log Normal
(Exponential, Triangular, Gamma, Beta, Weibull and Logistic distributions are not available in
this version of SUM3). Figure 4.2 gives an example shape for several of the distributions. Each
distribution will be discussed hi this section. Figure 4.3 .shows the dropdown menu of
distribution types available in SUM3. The listing of available variable aliases, with their default
units, is given in a selection listing on the far-left side of the screen. The variable description for
the highlighted alias is given at the top of the screen. The user will be given the option to select
preferred units for the distribution input parameters after a specific distribution is selected.
SUM3 will convert all units to the default units before initiating the simulation.
Selecting a distribution
In order to assign a distribution to an alias, the user must highlight the alias. Then click
the arrow in to the far left of the 'Type' box located on the distribution tab. This will bring down
a selection list. The user can select title distribution type by highlighting and clicking on it. The
user will be given the opportunity to enter the statistical input necessary for the selected
distribution. When the distribution parameters are entered they are preserved specifically for that
alias and distribution type.
Uniform
Normal
Log Normal
Triangular
Exponential
Beta
Figure 4.2. Distribution Curves
4.2
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C-j Sensitivity/Uncertainty Multimedia Modeling Module - sent 1
Soil total porosity from VadozeJ (vad3)
HVad3 (cm)
BdVad3
KsVad8 (onVday)
HVadS (cm)
SrKdVadB (ml/g)
I
Uniform
Log Uniform
Normal
Log Normal
Exponential
Triangular
Gamma
Beta '
Figure 4 J. Distribution Listing
4.1.1 Uniform
For the uniform distribution all values between the minimum value and ma-Kimnm value
are equally likely to be sampled. Figure 4.4 illustrates a Uniform distribution. In this example
distribution the variable is the soil hydraulic conductivity from the second vadose zone. The
variable is estimated to be somewhere between 100 cm/day and 700 cm/day. All values between
100 and 700 are equally likely to be selected for each simulation. Figure 4.5 is a view of the
input screen for a Uniform Distribution, where the Upper bound and Lower bound are entered in
linear space. Clicking to the right of the units box will activate a selection listing of units. The
user can select the units for the upper and lower bounds. Note that the user should be careful to
adjust both upper and lower bounds to the appropriate units to ensure consistency.
4.3
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I
£
0 0.5 I
Variable (SrKdVad8)
Figure 4.4. Unifonn Distribution Curve
: Sensitivity/Uncertainty Multimedia Modeling Module - senl 1
PorVad3 (percent)
HVad3 (on)
BdVad3 (g/cm
Soil hydraulic conductiviVfrom Vadoze_2(v«d8)
HVad8 (cm)
SrKdVadS (ml/g)
Figure 4.5. Uniform Distribution Input Parameters
4.4
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4.1.2 Log Uniform
The Log Uniform distribution is like the Uniform Distribution in that all values between
the lower bound and upper bound are equally as likely to be selected. The additional feature of
the Log Uniform distribution is the ability to sample the data in Log space or E space. The
Upper bound and Lower bound, however, are entered in the linear space. Figure 4.6 illustrates
the input screen for the Log Uniform distribution. This screen is similar to the uniform screen,
with the addition of the Log Base selection option at the bottom of the tab screen. To choose the
Base, click the arrow to the right of the Log Base box. A selection listing will be displayed.
Select the Base for the distribution.
iJ Sensitivity/Uncertainty Multimedia Modeling Module - senl 1
PorVad3 (percent)
II HVad3 (cm)
;!yBdVad3 fa/cm"
Soil hydraulic conductivity from Vadoze_2(v/ad8)
HVadS (cm)
SrKdVadB (ml/g)
cm/day
Figure 4.6. Log Uniform Distribution Input Parameters
4.1.3 Normal .
The Normal distribution is the most used distribution in probability theory because it
describes many natural phenomena and is useful in describing uncertain variables. This
4.5
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distribution, shown in Figure 4.7, is often described as the bell curve. There are several
assumptions common to a nonnal distribution. First, that here is a mean, (i.e. some value of the
variable is the most likely). Second, the value is symmetrical about the mean, and the uncertain
variable could as likely be above the means as it could be below the mean. And finally, the
uncertain variable is more likely to be in the vicinity of the mean than far away (i.e. 68% of the
values are within 1 standard deviation from the mean). Figure 4.7 illustrates a normal
distribution for the thickness of the second vadose Zone. In this example the mean of the
distribution is 213.36 cm with a lower bound of 200 cm and an upper bound of 225 cm. The
standard deviation for this distribution is given as 5 cm. Figure 4.8 displays the input screen for
the normal distribution, where the bounds, mean and standard deviation are entered.
p
r
o
b
a
b
I
1
i
t
y
200 213.36
Thickness of second Vadose Zoae
225
Figure 4.7. Nonnal Distribution Curve
4.6
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ill Sensitivity/Uncertainly Multimedia Modeling Module - senl!
iPorVad3
BdVad3
KsVadS (on/day)
HVadS (cm)
lick of vodose zone from VadozeJ (vad3)
1
Figure 4.8. Normal Distribution Input Parameters
4.1.4 Log Normal
The Log Normal distribution is widely used when most of the values occur near the
minimum value, or are positively skewed. Figure 4.9 depicts a Log Normal distribution, in linear
space, for the soil bulk density from vadose zone one. With a lower bound of 1 g/cm3 and an
upper bound of 2.65 g/cm3. The mean and standard deviation for the Log Normal distribution
should be calculated in log space. For this example the mean is 0.215 gm/cm3 and the standard
deviation is 0.014 g/cm3. There are some assumptions common to a normal distribution. The
variable cannot go below zero and the natural Logarithm of the variable is a normal distribution.
Figure 4.10 demonstrates the input screen for the Log Normal distribution. The required
parameters are upper bound, lower bound, mean, standard deviation, Log Base. The upper and
lower bounds are expected in the linear space. The Mean and Standard Deviation are expected in
the Log space. There are two choices for Base available Base 10 and Base £. To choose the
Base, click the arrow to the right of the Log Base box. A selection listing will be displayed.
Select the Base for the distribution
4.7
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Figure 4.9. Log Normal Distribution Curve
! Sensitivity/Uncertainty Multimedia Modelinq Module - sen 11
PorVadS (percent)
HVad3
Soil bulk density from Vadoze_1 (vod3)
KsVad8 (cm/day)
(cm)
SrKdVad8 (ml/g)
Figure 4.10. Log Normal Distribution Input Parameters
4.8
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3.1.5 Exponential
The Exponential distribution is widely used to describe events recurring at random in
time, such as the time between arrivals at a service booth or decay of a radionuclide over time.
The Exponential distribution has a memoryless property. This is an important characteristic that
allows the distribution to have the effect of timelessness. Therefore the future lifetime of given
parameter has the identical distribution, regardless when it occurred. Figure 4.11 is an
exponential distribution for radioactive decay of strontium-90.
Figure 4.11. Exponential Distribution Curve
This distribution not available in Version 2 of SUM3.
3.1.6 Triangular
To describe the Triangular distribution the miniTnumj maximum, and most likely values
to occur need to be known. This information is often gathered from records on similar events.
Figure 4.12 is a triangular distribution.
Figure 4.12. Triangular Distribution Curve
This distribution not available in Version 2 of SUM3.
4.9
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3.1.7 Gamma
The Gamma distribution applies to a wide-range of physical quantities. Environmentally
it is used in precipitation quantities or meteorological processes to represent pollutant
concentrations.
This distribution not available in Version 2 of SUM3.
4.1.5 Beta
The Beta distribution allows for flexibility over a range that is fixed. A common use of
this distribution is to describe empirical data and predict the random behavior of percentages and
fractions.
This distribution not available in Version 2 of SUM3.
4.1.6 Weibull
The Weibull distribution is widely used in the field of life phenomena, as the distribution
of the lifetime of some object, particularly when the "weakest link" model is appropriate for the
object. The "weakest link" model can be described as die instance when an object consists of
many parts, then suppose that the object experiences failures when any of its parts fail. Under
these type of conditions, it has been shone (both theoretically and empirically ) that the Weibull
distribution provides a close approximation of the distribution of the lifetime of the object.
Weibull distributions can also used to represent various physical quantities, such as wind speed.
This distribution not available in Version 2 of SUM3.
4.1.7 Logistic
Growth distribution can be described by the Logistic distribution. This distribution may
be used to describe the size of a population or individual, expressed as a function of the variable
time or to describe chemical reactions.
This distribution not available in Version 2 of SUM3.
4.1.8 User Defined
This distribution not available in Version 2 of SUM3.
4.2 Correlation
To assign a correlation to a set of variables the user must first have assigned the variables
aliases (to learn how to assign an alias go to Section 3.0 Selecting Sampling of Interest). A
correlation option is also available in SUM3 to account for dependencies (correlation) between
two parameters. The correlation of two variables allows the user to ensure the preservation of a
relationship between the variables. The correlation parameter is a ratio of one variable to the
4.10
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other. Therefore the correlation parameter can range from -1 to +1. A correlation of-1
represents a strong negative correlation, meaning one variable increases while the second
variable decreases. A correlation of+1 represents a strong positive correlation, meaning one
variable increases while the second variable increases. Likewise a correlation of 0 implies no
correlation between the variables. Figure 4.13 illustrates the input screen for variable correlation.
Assign a correlation
To assign a correlation, highlight the first alias to be correlated from the alias listing on
left of the screen. Then click the arrow on the alias box on the correlation tab. Select the second
variable from the drop down listing. Enter a correlation value in the space provided and click the
add button. The second variable alias and associated correlation will be displayed in the Current
Correlation box on the left.
A correlation from variable A to variable B will automatically be entered as a correlation
between variable B to variable A. This means, if a variable sequence A->B->C is assigned by
the user, then the correlation A->B, B->C, B->A, and C->B are all assigned, however, the
correlation A->C.
Sensitivity/Uncertainty Multimedia Modeling Module - se
HJPoiVadS (percent)
I HVad3 (cm)
ll8dVad3 fa/cm
Soil hydraulic conductivity from Vadoze_2(vad8)
HVadS (cm)
SrKclvacfS (ml/g)
Figure 4.13. Correlation Input Parameters
4.11
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Deleting a correlation
To delete a correlation, highlight the first alias to be correlated from the alias listing on
left of the screen. Then click the arrow on the alias box on the correlation tab. Select the second
variable from the drop down listing. Confirm the correlation to be deleted appears in the Current
Correlation box to the left and click the Delete the add button.
4.3 Equation
An Equation feature has been added to SUM3 to enable a user to relate two or more
variables. To assign an equation to a variable the user must first have assigned the variable, and
all variables used in the equation, an alias (to learn how to assign an alias go to Section 3.0
Selecting Sampling of Interest). This equation option allows the user to represent a variable as a
function of other variables. This feature is convent for equations relating several variables to a
single variable. All independent variables will be sampled, then the dependent variable will be
calculated. For example, Total Porosity can be computed as a function of Bulk Density. To
preserve this relationship throughout the simulation the equation can be entered. During the
simulation Bulk density will be sampled, then Total porosity will be calculated using the given
equation. Only the right side of the equation will be entered. Figure 4.14 demonstrates the
equation option, using the above example
Total Porosity = 1- (Bulk Density / 2.65)
Adding an Equation
To add an equation, first resolve the equation by solving for one variable in terms of the
others. Highlight the dependent variable to be represented by the equation from the alias listing
on left of the screen. Then enter the equation, the right side only, in the box labeled "Enter an
equation." Be sure that the equation has been resolved to match the units displayed next to the
dependent alias. The equation can contain most arithmetic operators (e.g. - + / * exp ). Click
the Add button.
Editing an Equation
To edit an equation, highlight the dependent variable represented by the equation from the
alias listing on left of the screen. Then edit the equation in the box labeled "Enter an equation."
Note that the current equation will be displayed in the "Current Equation" box. Be sure that the
equation has been resolved to match the units displayed next to the dependent alias. Click the
Add button.
4.12
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Sensitivity/Uncertainty Multimedia Modeling Module - senl 1
3a2bisratr»
3S2332SSSStii; »i£ -j"'^'^^!^^^''''^^^^
ijSoil total porosity from Vadoze_1 fwad3)
HVad3 (cm)
8dVad3 (g/cm"3)
KsVedS (cm/day)
HVadB (cm)
SrKdVadS (ml/g)
f|ff|l-(BdVad3/2.65)|
i:^s«sj-5*!!^S!Kia5KF-?riryiiS?s^«S3&^:!«af9;.»KK:==:=-^=i^fe
Figure 4.14.' Equation Input Parameters
Deleting an Equation
To delete an equation, highlight the dependent variable represented by the equation from
the alias listing on left of the screen. Confirm the equation to be deleted in the "Current equation"
box. Click the Delete button.
4.13
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5.0 Selecting Output Variables of Interest
The Output tab enables the user to specify the results to be preserved from the simulation.
An output list is provided for the user with descriptions describing what the results are and what
module it is output from. This list of outputs is derived from all possible results produced from
all media connected to the S/U icon. The description provides the user with the output name and
the module it is from (both the module name given by the user and the FRAMES icon name are
displayed). Figure 4.15 demonstrates a portion of the listing of outputs from the two vadose zone
modules and saturated zone module that have been connected to the S/U Module icon. A scroll
bar is provided on the far right of the listing to enable the user to move through the list when it is
larger than the window length.
i Sensitivity/Uncertainty Multimedia Modeling Module - senl 1
/anebtesli
lil
:luxSr8l
Water contaminant flux peak from Vadoze_2(vad8) for STT^NmUM-90S|liili
i,.^-^,...-.-..,..^.,..,^,.,--^..-.....^-^^.^,^^-*^-t**r«^s^&mzi9»#3
)escnc
Water contaminant Flux at year(s) #(,#...} from Vadt
Water contaminant flux peak from Vadoze_l(vad3) for
Water contaminant flux average years # to # from Vat
Water contaminant flux at year(s) #(,#...) from Vadoi
Water fl"T peak from Vadoze_2 ( vadS)
Water contaminant flux peak from Vadoze_2 (vadB) for
Water fline average years # to # from Vadoze_2 (vadS)
Water contaminant flux average years # to # from Vac
Water flux at year(s) #(,*...) from Vadoze_2(vad8)
Water contaminant flux at year (s) # ( ,#. . . ) from Vadoi;
Water contaminant flux peak from Vadoze 2(vad8) for
Water contaminant flux peak from Vadoze_2 (vad8) for
Water contaminant fluy average years # to # from Vad|
Water contaminant flux average years # to # from Vadl
Water contaminant flux at year(s) #(,#. . .) from Vadol|
Figure 5.1. Outputs Tab
5.1
-------
Adding an Alias:
The user is asked to provide a unique alias for each output of interest. To add an aims,
click on the white entry box to the right of the word "Alias". The alias should be one word and
is limited to eight (8) digits, capitalization is preserved but is not used to distinguish between
aliases, the underscore symbol (_) is not allowed. After typing the alias, click the Add button to
enter the alias into the variable list. The output list will display the alias to the far left with a line
( |) separating the alias from the description.
Changing an Alias:
The Add/Change button has been provided to allow a user to change an existing alias. First
select the output to be changed. The existing alias will appear in the alias box. Enter the new
alias, and click the Add/Change button. The variable list will be updated with the new alias.
Deleting an Alias:
A Delete button is provided to eliminate outputs from the alias list for distributions. By
removing the alias from the output list, the output will no longer be preserved. This allows the
user to reduce an alias listing to those currently of interest.
It is important to remember that only those outputs expected from the modules connected
to the S/U module will be listed in this screen (i.e. the user needs to be connected to the aquifer
icon if interested in waterbome concentration results from that media). In addition to the alias
information, the output screen also provides the user with the option to select the seed value to be
used in the random sampling algorithm. Thereby allowing the user to reproduce an analysis if
necessary. The number of iterations (realizations) to be run is selected in on this tab also. The
number of iterations is the number of sampling runs the user would like to make. The maximum
number of iterations for a single simulation is 500.
5.2
-------
6.0 Running the Sensitivity Uncertainty Module and SUM3
When all variable distributions, correlation, equations, and outputs have been selected
and entered, the SUM3 model user interface can be closed.
Closing SUM3 Module
To close the SUM3module user interface, click the file menu and choose the save & exit
option. Choosing the Exit only option will not save any data changes made since the last time
the users choose the exit & save option. This will return the user to the FRAMES interface,
Running the S/U Module
To run the S/U Module, shift click the S/U Icon and select Run, While running, the
SUM3 model a status screen will appear. Figure 6.1 illustrates tie status screen. Figure 6.2
illustrates the DOS screen that appears to indicate the Latin Hypercube sampling tool has been
activated and completed successfully. Close the DOS window to begin the calculation of the
sample iterations.
I
Initialize
Number of iterations to run 10
ReCopy C:\FUI\CASE1J3W.GID to C:\FUirsens.GID
FUeCoDvC:\FUftCASE1_GW.SUFtoC:\FUrsens.SUF
6.1
-------
Figure 6.1. Initial Status Screen
Figure 6.2. Latin Hypercube DOS Window
The FRAMES software is designed for deterministic models. Therefore, the SUM3
software product was designed to allow statistical analysis using the deterministic models.
SUM3 will randomly sample input variables and preserve the associated output values in an
external file available to the user for evaluation. The effect is calculating deterministic values
with variable inputs producing a statistical distribution of results. A typical application of the
uncertainty analysis is to indicate the relative conservatism of the deterministic result. Note that
within the FRAMES software, the SUM3 model is located hi the Sensitivity/Uncertainty Module.
6.1 Status Screen
The status screen will identify the number of iterations (or realizations) that have been
completed at the conclusion of each iteration. The statement "Iteration X of N with a statement
of OK or Error will appear. Figure 6.3 illustrates the status screen upon completion of the
SUM3run, The status box will indicate the completion of the simulation by displaying the word
"DONE" in the lower left comer.
6.2
-------
MEPAS Sensitivity/Uncertainty Module
FJf^Ki'Wt::*??^ .;r«fsKSJf T^"T;?
&S-:;--. :..''cv:a*'-'''.-'iK'X5fsiSw;r.:;v
i iil"in.ar»i«i«i»ii.i»wlimi»i;H»»^iy<
"Sensttivity/Uncertainiy Module for FFAMES"
"BetaTestversion"
6.1
"PoiVad3"."Soil total porosity from vad3"
"HVadS'VTrrick of vadose zone from vad3"
"Bdvad3","Soil bulk densiVfrom vad3"
"KsVad8","Soil hydraulic conductiviv from vad8"
"HVadB'VThickofvadose zone from vadB"
"SrKdVad8"."Soil equilibrium coefficient STROIsmUM-90 from vad8"
"PFIuxSr8","Water contaminant flux peak from vad8 for STRONTlUM-90"
10
'te
1,"0.527132"."2.0470E+OZ"."1.2S31E»00".lM.5a20E*OZ"."ES.3"."1.89832",733.09997S6.0.02646999992
2."0.523698"."2.1545E»02"."1.2822E*OD","4.2206E*02"."14.55"."2.54001 ".778.70001 Z2.0.007441999856
3."0.540792"."2.0825E+02","1.21 S9E+00"."5.9186E*02","21.75"."1.60784",724.S,0.03226999938
m
m
status OK
Running iteration 10 of 10
status OK
Cleani
Figure 63. Final Status Screen
6.2 SUM Sampling Technique
The FRAMES software is designed for deterministic models, therefore, the SUM3
software product was designed to allow statistical analysis using the deterministic models.
SUM3 randomly samples input variables following a Monte Carlo sampling method for
correlated variables and Latin Hypercube sampling method for uncorrelated variables. The
listing of sampled input values is stored in the "runname".SUF (Sensitivity/Uncertainty File) file.
Then SUM3 runs the deterministic models once for each iteration inserting the a sampled value
each time. After each deterministic run, the associated outputs of interest are preserved and also
stored in the "runname".SUF file. A typical application of the uncertainty analysis is to indicate
the relative conservatism of the deterministic result.
Monte Carlo Sampling Method
Latin Hypercube Sampling Method
6.3
-------
The Latin Hypercube method of sampling is a generalization of the Latin square
experimental design to K dimensions, which correspond to the number of input variables selected
of the model. Each input variable is assumed to be a random variable, which is governed by a
probability density function (PDF). The stratification is accomplished by dividing the range of
the input variable into N intervals of equal (1/N) probability. Each equally probable interval is
randomly sampled once for each variable. The output of the sampling can be considered an NxK
matrix, where the columns represent variables and the rows contain the sample values for the
appropriate interval. The values within a column are then randomly permuted, so that a row
represents a random vector of the input variables. The environmental model is then run N times
with the values of the input variables equal to the rows of the matrix. The advantages of Latin
Hypercube sampling over unconstrained sampling methods are that: 1) it provides an efficient
method for sampling the entire range of each variable in accordance with the assumed probability
distribution. And the estimate of the PDF of the model output variables is an unbiased estimate
of the true PDF. The Latin Hypercube sampling methodology assumes that the input variables
are uncorrelated: however, that is not always the case in practice, and a simple Latin Hypercube
sample may contain combinations of input variables that are physically unreasonable. Iman and
Conover (1982) developed a method to induce the desired dependence among variables in a Latin
Hypercube sampling using a rank correlation matrix. The method is very effective when rank
correlation among all pairs of variables can be obtained (Doctor et al. 1988). Figure 6.4
illiterates this concept in which a parameter's probability distribution is divided into intervals of
equal probability. Compared with conventional Monte Carlo sampling, Latin Hypercube
sampling is more precise because the entire range of the distribution is sampled in a more even
and consistent manner.
Figure 6.4. Example of Latin Hypercube Sampling Intervals
6.4
-------
7.0 interpreting Results
Results from a sensitivity/uncertainty analysis can be used to derive confidence limits and
intervals to provide a quantitative statement about the effect of varying a parameter on the model
prediction. The sampled variables along with their associated outputs of interest are stored in a
file. This data is stored in a comma separated format and can is stored in a file named
"runname".SUF. Where "runname" is the filename given to the FRAMES case analysis. Figure
7.1 illustrates an example SUF file with notations identifying key information.
senll
Sensitivity/Uncertainty Module for FRAMES
Beta Test version
6 1
PorVadS Soil total porosity from vad3
Thick of vadose zone from vad3
Soil bulk density from vad3
HVad3
BdVad3
KsVadS
HVadS
Soil hydraulic conductivity from vadS
Thick of vadose zone from vadS
SrKdVadS Soil equilibrium coefficient STRONTIUM-90 from vad8
PFIincSrfl Water contaminant flux peak from vadS for STRONTIUM-90
10
realization PorVad3 HVadS BdVadS KsVadS
1 0.527132 2.05E+02 1.25E+00 4.59E+02
0.523698 2.15E+02 1.26E+00 4.22E+02
0.540792 2.08E-HD2 1.22E+00 5.92E+02
0.531585 2.14E+02 1.24E+00 6.61 E+02
0.535472 2.11 E+02 1.23E+00 5.62E+02
0.529359 2.12E+02 1.25E+00 5.43E+02
0.538189 2.16E+02 1.22E+00 4.87E+02
8 0.522038 2.18E+02 1.27E+00 6.56E+02
9 0.532566 2.10E+02 1.24E+00 6.26E+02
10 0.537019 2.20E+02 1.23E+00 5.17E+02
HVadS SrKdVadB
25.3 1.89832
14.55 2.54001
21.75 1.60784
16.02 1.38078
1.65516
1.43606
1.73389
1.49371
1.88519
2.17862
17.86
14.09
11.86
19.51
10.29
PFIuxSrS peak time
733.0999756
778.7000122
724.5
780.4000244
734.7000122
738.2000122
744.5999756
801-0999756
739.5999756
764.9000244
PFIuxSrS
0.02647
0.007442
0.03227
0.01351
0.02
0.01427
0.013S8
0.005563
0.01854
0.007279
Figure 7.1. Example Sensitivity/Uncertainty File (SUF)
The file format for the SUF file is also consistent with the necessary information to
complete an r-squared analysis in a more sophisticated statistical tool such as SAS.
Example file
SUM3|s charting feature enables the user to view results. Cumulative Distribution
Function (CDF) curves are options for viewing results.
7.1
-------
-------
8.0 References
APHA. 1986. Selected Physical and Chemical Standard Methods for Students. American
Public Health Association, Port City Press, Baltimore, MD.
Buck, J. W., G. Whelan, J. G. Droppo, Jr., D. L. Strenge, K. J. Castleton, J. P. McDonald, C.
Sato, and G. P. Streile. 1995. Multimedia Environmental Pollutant Assessment System
(MEPAS): Application Guidance Guidelines for Evaluating MEPAS Input Parameters for
Version 3.1. PNL-10395. Prepared for the U.S. Department of Energy by Pacific Northwest
Laboratory, Richland, Washington.
Codell, R. B., K. T. Key, and G. Whelan. 1982. Radionuclide Dispersion Analysis. NUREG-
0868. Prepared by Pacific Northwest Laboratory for the Nuclear Regulatory Commission,
Washington, D.C.
Doctor, P.G., T.B. Miley, and C.E. Cowan. 1990. MnltitnHia Environmental Pollutant
Assessment System (MEPAS) Sensitivity Analysis of Computer Codes. PNL-7296, Pacific
Northwest Laboratory, Richland, Washington./ '
':-,', _ , .... ; ...IV
EPA. 1989. Risk Assessment Guidance for Superfund Volume 1 Human Health Evaluation
Manual (Part A). EPA/540/1-89/002, U.S. Environmental Protection Agency, Office of
Emergency and Remedial Response, Washington, D.C.
Meyer, P.D., M.L. Rockhold, G.W. Gee. 1997. Uncertainty Analyses of Infiltration and
Subsurface Flow and Transport for SDMP Sites. NUREG/CR-6565. PNNL-11705. U.S.
Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, Washington, DC.
USAF. 1993. Eielson Air Force Base. OU-2 Remedial Investigation/Feasibility Study. Remedial
Investigation Report. Table 5.7, Eielson Air Force Base, 343rd Wing, Eielson, Alaska.
Whelan, G., K.J. Castleton, J.W. Buck, G:M. Gelston, B.L. Hoopes, M.A. Pelton, D.L. Strenge,
and R.N. Kickert. 1997. Concepts of a Framework for Risk Analysis in Multimedia
Environmental Systems (FRAMES! PNNL-11748. Pacific Northwest National Laboratory,
Richland, Washington.
Whelan, G., J. W. Buck, D. L. Strenge, J. G. Droppo, Jr., B. L. Hoopes, and R. J. Aiken. 1992.
"An Overview of the Multimedia Assessment Methodology MEPAS." Haz. Waste Haz. Mat.
9(2): 191-
Doctor P.O., T.B. Miley, C. E. Cowan. 1990. Multimedia Environmental Pollutant Assessment
System (MEPAS) Sensitivity Analysis of Computer Codes, PNL-7296, Pacific Northwest
Laboratory, Richland, Washington.
8.1
L
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Cochran, W.G. 1963. Sampling Statistics. 2nd ed. John Wiley and Sons, New York.
Doctor, P. G., E. A. Jacobson, and J. A. Buchanan. 1988. A Comparison of Uncertainty
Analysis methods Using a Groundwater Flow Model. PNL-5649, Pacific Northwest Laboratory,
Richland, Washington.
Iman, R. L., J. M. Davenport, and D.K. Zeigler. 1980. Latin Hypercube Sampling (Program
User's Guide). SAND79-1473, Sandia national Laboratories, Albuquerque, New. Mexico.
Iman, R. L., and W. J. Conover. 1982. A Distribution-Free Approach to Reducing Rank
Correlation Among Input Variables. Communications in Statistics Bl 1(3):311-334.
US EPA Headquarters Library
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1200 Pennsylvania Avenue>NW
Washington, DC 20460
202-566-0556
8.2
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