Measures of sensitivity and uncertainty with the fuzzy model of solute transport through groundwater

Sensitivity analysis addresses the most influential parameter of the model which is essential before uncertainty quantification of any model. Uncertainty analysis of any model is one of the main themes of recent trends of computation, modeling, and optimization. Uncertainty analysis is classified as two categories, aleatory and epistemic. Aleatory uncertainty is due to random variability of the model parameters which is irreducible in nature, whereas epistemic uncertainty is due to insufficiency or vagueness of the model parameters and this is reducible. Probabilistic uncertainty is quantified using Monte Carlo method; however, a large number of such uncertain parameters present in a model require sensitivity analysis. Probabilistic sensitivity analysis is carried out using spearman rank correlation method. However, if the model uncertain parameters are fuzzy due to their insufficiency or incompleteness or lack of information, the global sensitivity analysis with those fuzzy parameters is challenging in the sense that the computation scheme to extract the most important fuzzy parameter is based on information theory. The paper describes an approach of sensitivity analysis with the fuzzy parameters. Method of sensitivity analysis in this case is based on the imprecise probability. Hartley-like measure and fuzziness measure are claimed as sensitivity indicators. Details of the computation of Hartley-like measure and fuzziness measure are described in the paper. The paper also presents the uncertainty analysis with the fuzzy parameters of the model. Non-specificity was also computed in this paper to address the various measures of uncertainty. The computation scheme is illustrated with the help of the solute transport through groundwater.