Abstract
Mathematical models are utilized to approximate various highly complex engineering, physical, environmental, social, and economic phenomena. Model parameters exerting the most influence on model results are identified through a ‘sensitivity analysis’. A comprehensive review is presented of more than a dozen sensitivity analysis methods. This review is intended for those not intimately familiar with statistics or the techniques utilized for sensitivity analysis of computer models. The most fundamental of sensitivity techniques utilizes partial differentiation whereas the simplest approach requires varying parameter values one-at-a-time. Correlation analysis is used to determine relationships between independent and dependent variables. Regression analysis provides the most comprehensive sensitivity measure and is commonly utilized to build response surfaces that approximate complex models.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Atherton, R.W., Schainker, R.B., and Ducot, E.R.: 1975, ‘On the Statistical Sensitivity Analysis of Models for Chemical Kinetics’, AIChE. 21, 441–448.
Bauer, L.R., and Hamby, D.M.: 1991, ‘Relative Sensitivities of Existing and Novel Model Parameters in Atmospheric Tritium Dose Estimates’, Rad. Prot. Dosimetry. 37, 253–260.
Bellman, R., and Astrom, K.J.: 1970, ‘On Structural Identifiability’, Math. Biosci. 7, 329–339.
Box, G.E.P., Hunter, W.G., and Hunter, J.S.: 1978. Statistics for Experimenters: an Introduction to Design, Data Analysis, and Model Building. John Wiley & Sons. New York.
Breshears, D.D.: 1987, Uncertainty and sensitivity analyses of simulated concentrations of radionuclides in milk. Fort Collins, CO: Colorado State University, MS Thesis, pp. 1–69.
Cacuci, D.G., Weber, C.F., Oblow, E.M., and Marable, J.H.: 1980. ‘Sensitivity Theory for General systems of Nonlinear Equations’, Nuc. Sci. and Eng. 75, 88–110.
Cacuci, D.G., Maudlin, P.J., and Parks, C.V.: 1983, ‘Adjoint Sensitivity Analysis of Extremum-Type Responses in Reactor Safety’, Nuc. Sci. and Eng. 83, 112–135.
Cobelli, C., and Romanin-Jacur, G.: 1976, ‘Controllability, Observability and Structural Identifiability of Multi Input and Multi Output Biological Compartmental Systems’, IEEE Trans. Biomed. Eng. 23, 93.
Cobelli, C., and DiStefano, J.J.: 1980, ‘Parameter and Structural Identifiability Concepts and Ambiguities: A critical Review and Analysis’, Amer. J. Physiol. 239, R7-R24.
Conover, W.J.: 1980, Practical Nonparametric Statistics, 2nd edn. John Wiley & Sons, New York.
Cox, N.D.: 1977, ‘Comparison of Two Uncertainty Analysis Methods’, Nuc. Sci. and Eng. 64, 258–265.
Crick, M.J., Hill, M.D. and Charles, D.: 1987, ‘The Role of Sensitivity Analysis in Assessing Uncertainty. In: Proceedings of an NEA Workshop on Uncertainty Analysis for Performance Assessments of Radioactive Waste Disposal Systems, Paris, OECD, pp. 1–258.
Cukier, R.I., Fortuin, C.M., Shuler, K.E., Petschek, A.G. and Schaibly, J.H.: 1973, ‘Study of the Sensitivity of Coupled Reaction Systems to Uncertainties in Rate Coefficients. I. Theory J. Chem. Phys. 59, 3873–3878.
Cukier, R.I., Levine, H.B. and Schuler, K.E.: 1978, ‘Nonlinear Sensitivity Analysis of Multiparameter Model Systems’, J. Computational Phys. 26, 1–42.
Cukier, R.I., Schaibly, J.H. and Shuler, K.E.: 1975, ‘Study of the Sensitivity of Coupled Reaction Systems to Uncertainties in Rate Coefficients. III. Analysis of the Approximations’, J. Chem. Phys. 63, 1140–1149.
Cunningham, M.E., Hann, C.R., and Olsen, A.R.: 1980, ‘Uncertainty Analysis and Thermal Stored Energy Calculations in Nuclear Fuel Rods’, Nuc. Technol. 47, 457–467.
Dalrymple, G.J., and Broyd, T.W.: 1987, ‘The Development and Use of Parametric Sampling Techniques for Probabilistic Risk Assessment. IAEA-SR-111/54P’, In: Implications of Probabilistic Risk Assessment (M.C. Cullingford, S.M. Shah, and J.H. Gittus eds.), Elsevier, London, pp. 171–186.
Demiralp, M., and Rabitz, H.: 1981, ‘Chemical Kinetic Functional Sensitivity Analysis: Elementary Sensitivities’, J. Chem. Phys. 74, 3362–3375.
Dickinson R.P., and Gelinas, R.J.: 1976, ‘Sensitivity Analysis of Ordinary Differential Equation Systems — A Direct Method’, J. Computational Phys. 21, 123–143.
Downing, D.J., Gardner, R.H., and Hoffman, F.O.: 1985, ‘An Examination of Response-Surface Methodologies for Uncertainty Analysis in Assessment Models’, Technometrics. 27, 151–163. (See also Letter to the Editor, by R.G. Easterling and a rebuttal, Technometrics 28, 91–93, 1986.)
Dunker, A.M.: 1981, ‘Efficient Calculation of Sensitivity Coefficients for Complex Atmospheric Models’, Atmospheric Environment 15, 1155–1161.
Gardner, R.H.: Huff, D.D., O'Neill, R.V., Mankin, J.B., Carney, J. and Jones, J.: 1980, ‘Application of Error Analysis to a Marsh Hydrology Model’, Water Resources Res. 16, 659–664.
Gardner, R.H., O'Neill, R.V., Mankin, J.B. and Carney, J.H.: 1981, ‘A Comparison of Sensitivity Analysis and Error Analysis Based on a Stream Ecosystem Model’, Ecol. Modelling. 12, 173–190.
Hall, M.C.G., Cacuci, D.G., Schlesinger, M.E.: 1982, ‘Sensitivity Analysis of a Radiative-Convective Model by the Adjoint Method’, J. Atmos. Sci. 39, 2038–2050.
Hamby, D.M.: 1993, ‘A Probabilistic Estimation of Atmospheric tritium Dose’, Health Phys. 65, 33–40.
Hamby, D.M. 1995, ‘A Numerical Comparison of Sensitivity Analysis Techniques’, scheduled to appear in Health Phys. 68.
Helton, J.C., Garner, J.W., Marietta, M.G., Rechard, R.P., Rudeen, D.K. and Swift, P.N.: 1993. ‘Uncertainty and Sensitivity Analysis Results Obtained in a Preliminary Performance assessment for the Waste Isolation Pilot Plant, Nuc. Sci. and Eng. 114, 286–331.
Helton, J.C., Garner, J.W., McCurley, R.D. and Rudeen, D.K.: 1991, Sensitivity analysis techniques and results for performance assessment at the waste isolation pilot plant. Albuquerque, NM: Sandia National Laboratory; Report No. SAND90-7103.
Helton, J.C. and Iman, R.L.: 1982, ‘Sensitivity Analysis of a Model for the Environmental Movement of Radionuclides’, Health Phys. 42, 565–584.
Helton, J.C., Iman, R.L. and Brown, J.B.: 1985, ‘Sensitivity Analysis of the Asymptotic Behavior of a Model for the Environmental Movement of Radionuclides, Ecol. Modelling. 28, 243–278.
Helton, J.C., Iman, R.L., Johnson, J.D., and Leigh, C.D.: 1986, ‘Uncertainty and Sensitivity Analysis of a Model for Multicomponent Aerosol Dynamics, Nuc. Technol. 73, 320–342.
Hoffman, F.O. and Gardner, R.H.: 1983, ‘Evaluation of Uncertainties in Environmental Radiological Assessment Models’, in: Till, J.E.; Meyer, H.R. (eds) Radiological Assessments: a Textbook on Environmental Dose Assessment. Washington, DC: U.S. Nuclear Regulatory Commission; Report No. NUREG/CR-3332.
Horwedel, J.E., Worley, B.A., Oblow, E.M., Pin, F.G. and Wright, R.Q.: 1988, GRESS version 0.0 user's manual. Oak Ridge, TN: Oak Ridge National Laboratory; Report No. ORNL/TM-10835.
Iman, R.L.: 1987, ‘A Matrix-Based Approach to Uncertainty and Sensitivity Analysis for Fault Trees’, Risk Analysis. 7, 21–33.
Iman, R.L. and Conover, W.J.: 1979, ‘The Use of the Rank Transform in Regression’, Technometrics. 21, 499–509.
Iman, R.L. and Conover, W.J.: 1980 ‘Small Sample Sensitivity Analysis Techniques for Computer Models, With an Application to Risk Assessment’, Commun. Stats. — Theor. and Meth. A9, 1749–1842.
Iman, R.L. and Conover, W.J.: 1982, Sensitivity-analysis techniques: self-teaching curriculum. Albuquerque, NM: Sandia National Laboratories; Report No. NUREG/CR-2350.
Iman, R.L. and Helton, J.C.: 1985, A comparison of uncertainty and sensitivity analysis techniques for computer models. Albuquerque, NM: Sandia National Laboratory; Report No. NUREG/CR-3904.
Iman, R.L., and Helton, J.C. 1988, ‘An Investigation of Uncertainty and Sensitivity Analysis Techniques for Computer Models’, Risk Analysis. 8, 71–90.
Iman, R.L., and Helton, J.C., 1991; ‘The Repeatability of Uncertainty and Sensitivity Analyses for Complex Probabilistic Risk Assessments’, Risk Analysis. 11, 591–606.
Iman, R.L. Helton, J.C. and Campbell, J.E. 1978, Risk methodology for geologic disposal of radioactive waste: sensitivity analysis techniques. Albuquerque, NM: Sandia National Laboratories; Report No. NUREG/CR-0390.
Iman, R.L. Helton, J.C. and Campbell, J.E.: 1981a, ‘An Approach to Sensitivity Analysis of Computer Models: Part I — Introduction, Input Variable Selection and Preliminary Assessment’, J. Qual. Technol., 13, 174–183.
Iman, R.L. Helton, J.C. and Campbell, J.E.: 1981b, ‘An Approach to sensitivity Analysis of Computer Models: Part II — Ranking of Input Variables, Response Surface Validation, Distribution Effect and Technique Synopsis’, J. Qual. Technol. 13, 232–240.
Iman, R.L. and Shortencarier, M.J.: 1984, A FORTRAN 77 program and user's guide for the generation of Latin hypercube and random samples for use with computer models. Albuquerque, NM: Sandia National Laboratory; Report No. NUREG/CR-3624.
International Atomic Energy Agency (IAEA), ‘1989, Evaluating the reliability of predictions made using environmental transfer models. Vienna: Safety Series No. 100. Report No. STI/PUB/835; 1–106.
Kim, T.W., Chang, S.H. and Lee, B.H., 1988 ‘Uncertainty and Sensitivity Analyses in Evaluating Risk of High Level Waste Repository’, Rad. Waste Management and the Nuc. Fuel Cycle. 10, 321–356.
Kleijnen, J.P.C., van Ham, G., and Rotmans, J., 1992, ‘Techniques for Sensitivity Analysis of Simulation Models: A Case Study of the CO2 Greenhouse Effect’, Simulation. 58, 410.
Koda, M., Dogru, A.H., and Seinfeld, J.H.: 1979 ‘Sensitivity Analysis of Partial Differential Equations with Application to Reaction and Diffusion Processes’. J. Computational Phys. 30, 259–282. Koda, M. 1982, ‘Sensitivity Analysis of the Atmospheric Diffusion Equation’, Atmos. Environment, 16, 2595–2601.
Krieger, T.J., Durston, C., and Albright, D.C.: 1977 Statistical Determination of Effective Variables in Sensitivity Analysis’, Trans. Am. Nuc. Soc. 28, 515–516.
Liepmann, D., and Stephanopoulos, G., 1985, ‘Development and Global Sensitivity Analysis of a Closed Ecosystem Model,’ Ecol. Modelling. 30, 13–47.
Margulies, T., Lancaster, L., and Kornasiewicz, R.A.: 1991, ‘Uncertainty and Sensitivity Analysis of Environmental Transport Models for Risk Assessment’, In: Engineering Applications of Risk Analysis, Atlanta, GA: ASME, 11–19.
McKay, M.D., Beckman, R.J. and Conover, W.J.: 1979, ‘A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code, Technometrics. 21, 239–245.
Morisawa, S., and Inoue, Y. 1974, ‘On the Selection of a Ground Disposal Site by Sensitivity Analysis’, Health Phys. 26, 251–261.
Oblow, E.M.: 1978, ‘Sensitivity Theory for General Nonlinear Algebraic Equations with Constraints’, Nuc. Sci. and Eng. 65, 187–191.
O'Neill, R.V., Gardner, R.H., and Mankin, J.B. 1980, ‘Analysis of Parameter Error in a Nonlinear Model’, Ecol. Modelling. 8, 297–311.
Otis, M.D.: 1983, ‘Sensitivity and Uncertainty Analysis of the PATHWAY Radionuclide Transport Model’, Fort Collins, CO: Colorado State University, PhD Dissertation, pp. 1–86.
Reed, K.L., Rose, K.A., and Whitmore, R.C. 1984, ‘Latin Hypercube Analysis of Parameter Sensitivity in a Large Model of Outdoor Recreation Demand, Ecol. Modelling. 24, 159–169.
Rose, K.A.: 1983, ‘A Simulation Comparison and Evaluation of Parameter Sensitivity Methods Applicable to Large Models, in: Analysis of Ecological Systems: State-of-the-art in Ecological Modelling (Lauenroth, G.V. Skogerboe, M. Flug eds.), Proceedings of a meeting at Colorado State Universtiy, May 24–28, 1982 Elsevier, New York.
Schaibly, J.H., and Shuler, K.E. 1973, ‘Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. II. Applications’, J. Chem. Phys. 59, 3879–3888.
Stein, M.: 1987, ‘Large Sample Properties of Simulations Using Latin Hypercube Sampling’, Technometrics. 29, 143–151.
Summers, J.K., and McKellar, H.N.: 1981, ‘A sensitivity analysis of an Ecosystem Model of Estuarine Carbon Flow,’ Ecol. Modelling. 13; 283–301.
Whicker, F.W., and Kirchner, T.B.: 1987, ‘PATHWAY: A dynamic food-chain model to predict radionuclide ingestion after fallout deposition,’ Health Phys. 52; 717–737.
Whicker, F.W., Kirchner, T.B., Breshears, D.D., and Otis, M.D. 1990, ‘Estimation of radionuclide ingestion: the “Pathway” model’, Health Phys. 59; 645–657.
Worley, B.A., and Horwedel, J.E.: 1986. A waste package performance assessment code with automated sensitivity-calculation capability. Oak Ridge, TN: Oak Ridge National Laboratory; Report No. ORNL/TM-9976.
Yu, C., Cheng, J-J., and Zielen, A-J.: 1991, ‘Sensitivity Analysis of the RESRAD, a Dose Assessment Code,’ Trans. Am. Nuc. Soc. 64; 73–74.
Zirnmerman, D.A., Hanson, R.T., and Davis, P.A.: 1991, A comparison of parameter estimation and sensitivity analysis techniques and their impaet on the uneertainty in ground water flow model predictions. Albuquerque, NM: Sandia National Laboratory; Report No. NUREG/CR-5522.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hamby, D.M. A review of techniques for parameter sensitivity analysis of environmental models. Environ Monit Assess 32, 135–154 (1994). https://doi.org/10.1007/BF00547132
Issue Date:
DOI: https://doi.org/10.1007/BF00547132