Development of possibilistic statistics and its application to quantify uncertainty of subsurface solute transport model

Imprecise information on any system is addressed by possibility theory wherein the system is modeled as a fuzzy set. Alpha level representation of a fuzzy set in the form of an interval defines the possibility theory. Uncertainty of any model in this context is quantified as mean value +/- standard deviation of a possibilistic (imprecise) parameter. This paper presents the possibilistic statistical techniques to estimate the mean and standard deviation of a possibilistic parameter of subsurface solute transport model. The solute transport model parameters, such as groundwater velocity, solute dispersion coefficient, etc., are sparse and imprecise in nature. Such parameters are characterized by the possibility distribution. In this paper, analytical expression of solute transport model is used to estimate the mean value and standard deviation of possibilistic spatial and temporal concentration of solute.