QUANTITIVE SENSITIVITY AND IMPORTANCE ANALYSIS OF PARAMETERS IN MONTE CARLO MODELS Page: 2 of 3
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parameters describing each distribution are given in Table
1. The solute of concern is Cesium (Cs) and the free water
diffusion coefficient, De, of Cs is held constant at 20.7x10-
The regulatory constraint for this example problem is
that the hypothetical site will "fail" if the time to a relative
concentration of 0.90 at the outlet is less than 100 years.
The equation above was solved for t when C/Co =0.90 for
each of the 10,000 parameter vectors and each of these
resulting times was compared to the regulatory limit. The
results show that 7768 vectors failed and 2232 passed the
GSA provides both qualitative and quantitative tech-
niques to examine the sensitivity of results to a given
parameter. The qualitative results are a graph of cumula-
tive density functions (cdf's) for each parameter where the
distribution of the parameter within the vectors that passed
the regulatory constraint is compared to the distribution
within the vectors that failed. If there is a large separation
between the two cdf's, then the results, in terms of the
decision point defined by the regulator, are sensitive to that
parameter. Example cdf's for both a relatively sensitive
(fracture width) and an insensitive (Kd) parameter are
shown in Figure 1, A and B.
GSA provides quantitative results by using a non-
parametric statistical test of the difference in cumulative
probability between two distributions. The test used here
is the Kolomogrov-Smirnov (K-S) test where the maxi-
mum difference between two cdf's, d, is determined. This
maximum can occur at any value of the selected parameter
(e.g., the entire range of values in Figure 1 A or B). The K-
S test also provides a determination of the probability, P,
that the maximum distance between the passing and failing
cdf's could have occurred if the two distributions were in
fact obtained from a single population. The lower this
probability, the more certainty there is that the cdf's are
significantly different. In order to demonstrate the effect of
the number of runs on parameter sensitivity and impor-
tance, results of the K-S test are given for each parameter
in Table 2 for runs with both 100 and 10,000 vectors.
GSA is a quantitative technique for determining the
sensitivity of Monte Carlo model results to the input
parameters. Importance of parameters is determined in
GSA by explicit consideration of the regulatory con-
straints. As exhibited by the results in Table 2, the calcu-
lated probability values (P's) are a function of the number
of Monte Carlo runs. Relative to regression techniques for
sensitivity analysis, GSA is focused on behavior about a
regulatory decision point and does not require the fitting of
a regression model to the resulting data. For the example
problem demonstrated here, fracture transport results are
sensitive to all six parameters for the given regulatory cut-
off (100 years to 0.90 relative concentration) when 10,000
vectors are analyzed. We are currently engaged in apply-
ing GSA to results of sub-site scale, saturated zone, trans-
port modeling at Yucca Mountain and suggest that GSA be
considered for sensitivity analysis of the final TSPA-VA
This work was supported by the Yucca Mountain Site
Characterization Office as part of the Civilian Radioactive
Waste Management Program which is managed by the U.S.
Dept. of Energy, Yucca Mountain Site Characterization
Project. Sandia is a multiprogram laboratory operated by
the Sandia Corp. a Lockheed Martin Company for the U.S.
Dept. of Energy under contract DE-ACO4-94AL85000.
'Wilson, M.L., 1993, Sensitivity Analyses for Total-Sys-
tem Performance Assessment, in Proceedings of the
Fourth Annual International High Level Radioactive
Waste Management Conference, Las Vegas, Nevada,
April 26-30, 1993, American Nuclear Society, La
Grange Park, IL, Vol. 1 pp. 14-21.
2Reeves, M., V.A. Kelley and J.F. Pickens, 1987, Regional
Double-Porosity Transport in the Culebra Dolomite:
An Analysis of Parameter Sensitivity and Importance
at the Wate Isolation Pilot Plant (WIPP) Site,
SAND87-7105, Sandia National Laboratories, Albu-
querque, New Mexico.
3Spear, R.C. and G.M. Hornberger, 1980, Eutrophication
in Peel Inlet. II. Identification of Critical Uncertain-
ties via Generalized Sensitivity Analysis, Water
Research, Vol. 14 (1), pp. 43-49.
4James, BR., J.-P. Gwo and L. Toran, 1996, Risk-Cost
Decision Framework for Aquifer Remediation
Design, Journal of Water Resources Planning and
Management, Vol. 122 (6), pp. 414-420.
5Carslaw, H.S. and J.C. Jaeger, 1959, Conduction of Heat
in Solids, Oxford Univ. Press, Oxford, 2nd Edition,
6Iman, R.L. and M.J. Shortencarrier, 1984, A FORTRAN
77 Program and User's Guide for the Generation of
Latin Hypercube and Random Samples for Use with
Computer Models, SAND83-2365, Sandia National
Laboratories, Albuquerque, New Mexico, 50 pp.
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McKenna, Sean A. & Arnold, Bill W. QUANTITIVE SENSITIVITY AND IMPORTANCE ANALYSIS OF PARAMETERS IN MONTE CARLO MODELS, report, February 18, 1998; Las Vegas, Nevada. (digital.library.unt.edu/ark:/67531/metadc724405/m1/2/: accessed February 17, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.