Sensitivity analysis of the probability distribution of groundwater level series based on information entropy

Abstract

Information entropy is an effective method to analyze uncertainty in various processes. The principle of maximum entropy (POME) provides a guide line for the parameter estimation of probability density function (PDF). Mutual entropy analysis is well qualified for delineating the nonlinear and complex multivariable relationship. The probability distribution of model output is the element of model uncertainty analysis. In this paper, a synthetic groundwater flow field is build to produce groundwater level series (GLS). The probability distribution of GLS is obtained by the frequency analysis method based on POME and Chi-Squared test. The important uncertainty factors that affect the parameters of PDF of GLS are assessed by the sensitivity analysis methods, which include stepwise regression analysis and mutual entropy analysis. Results of this analysis indicate that most of the GLS follow normal distribution (or log-normal distribution), while a few obey others. The mean and variance of normal GLS are affected differently by the input variables of groundwater model. Mutual entropy analysis is more competitive and appropriate for delineating the nonlinear and nonmonotonic multivariable relationship than stepwise regression analysis.