An Examination of Response-Surface Methodologies for Uncertainty Analysis in Assessment Models

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.Two techniques of uncertainty analysis were applied to a mathematical model that estimates the dose-equivalent to man from the concentration of radioactivity in air, water, and food. The response-surface method involved screening of the model to determine the important parameters, development of the response-surface equation, calculating the moments using the response-surface model, and fitting a Pearson or Johnson distribution using the calculated moments. The second method sampled model inputs by Latin hypercube methods and iteratively simulated the model to obtain an empirical estimation of the cdf. Comparison of the two methods indicates that it is often difficult to ascertain the adequacy or reliability of the response-surface method. The empirical method is simpler to implement and, because all model inputs are included in the analysis, it is also a more reliable estimator of the cumulative distribution function of the model output than the response-surface method. Table 1. Input Parameters for SR Dose Model Standard Variable Distribution Mean Deviation Mode Minimum Maximum Dose Conversion Factor (DFI, rem/,u Sr) lognormal 1.575 .289 Weathering Loss Leaf (TW leaf, days) lognormal 12.795 4.5291 Nonleaf (TW nonleaf, days) lognormal 21.926 9.5982 Pasture (TW pasture, days) lognormal 12.799 4.5291 Interception Fraction Normalized for Biomass Leaf (RY leaf, m 2/kg) lognormal .1201 .0790 Nonleaf (RY nonleaf, m2/kg) lognormal .0725 .0486 Pasture (RY pasture, m 2/kg) lognormal 1.9523 .6911 Soil Surface Density (P, kg/m 2) lognormal 214.0159 23.6135

A review of techniques for parameter sensitivity analysis of environmental models

“…Many authors, when referring to the degree to which an input parameter affects the model output, use the terms 'sensitive', 'important', 'most influential', 'major contributor', 'effective', or 'correlated' interchangeably (Krieger et al, 1977;Downing et al 1985;Iman, 1987;Iman and Helton, 1988;Marguiles et al, 1991). Crick et al (1987) have made a distinction by referring to 'important' parameters as those whose uncertainty contributes substantially to the uncertainty in assessment results, and 'sensitive' parameters as those which have a significant influence on assessment results.…”

“…Inherent to this calculation are the assumptions that the higher ordered partials are negligible and there is no correlation between input parameters (Atherton et al, 1975;Gardner et al, 1981). For large sets of equations, the partial derivative can be approximated as a finite difference and output values calculated for small changes in the input parameter (Downing et al, 1985). Thus, if nonlinearities are neglected, the partial derivative can be approximated as, %AY ¢i-%AXi Gardner et al (1981) report that the partial derivative approach to sensitivity analysis may become so complex that implementation is impractical.…”

“…Conceptually, the simplest method to sensitivity analysis is to repeatedly vary one parameter at a time while holding the others fixed (Gardner et aI., 1980;O'Neill et aL, 1980;Downing et al, 1985;Breshears, 1987;Crick et aL, 1987;Yu et al, 1991). A sensitivity ranking can be obtained quickly by increasing each parameter by a given percentage while leaving all others constant, and quantifying the change in model output.…”

“…More than a dozen methods have been reviewed (Bellman and Asrrom, 1970;Cukier et al, 1973;Morisawa and Inoue, 1974;Kfieger et al, 1977;Box et al, 1978;Oblow, 1978;Conover, 1980;Demiralp and Rabitz, 1981;Gardner et al, 1981;Iman et al, 1981b;Hoffman and Gardner, 1983;Downing et al, 1985;Helton et al, 1985;Crick et aL, 1987;IAEA, 1989;Iman and Helton, 1991;Hamby, 1993). This paper is a comprehensive assessment of several of the more practical methods for conducting parameter sensitivity studies, ranging from one-at-a-time sensitivity measures to standardized regression coefficients to statistical tests based on partitioning of empirical input distributions.…”

“…The adjoint method has been demonstrated by several investigators in the fields of climatological modeling, reactor thermal hydraulics, and reactor safety (Koda et al 1979;Cacuci et al, 1980;Hall et al, 1982). In this approach, 'exact' (Downing et al 1985) sensitivities are calculated as defined by partial derivatives. The Fourier amplitude sensitivity test (FAST) (Cukier et al 1973(Cukier et al , 1978 has been used to solve coupled nonlinear rate equations by Schaibly and Shuler (1973) and Cukier et al, (1975).…”