Computationally efficient methods for the quantification of uncertainties in groundwater modelling

Abstract

When conservative decisions have to be made in water management questions, the quantification of uncertainties is necessary. Monte Carlo techniques are suited for this analysis but usually require a huge computational effort. An alternative and computationally efficient approach is the First Order Second Moment (FOSM) method which directly propagates the uncertainty originating from parameter uncertainty into the result. We apply the FOSM method to both the groundwater flow and solute transport equations. It is shown how calibration on the basis of measured heads and concentrations yield the Principle of Interdependent Uncertainty that correlates the uncertainties of feasible transmissivities and recharge rates. The method is used to compute the uncertainty of steady state heads and of steady state solute concentrations. The method is illustrated by application to the Palla Road aquifer in semiarid Botswana, for which the quantification of the uncertainty range of groundwater recharge is of prime interest. The uncertainty bounds obtained by the FOSM method correspond well with the results obtained by the Monte Carlo method. It is shown that at the planned abstraction rate the probability of exceeding the natural replenishment of the Palla Road aquifer by overpumping is 30%.