Computation of stochastic wellhead protection zones by combining the first-order second-moment method and Kolmogorov backward equation analysis

Input parameters of groundwater models are usually poorly known and model results suffer from uncertainty. When conservative decisions have to be drawn, 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) analysis which directly propagates the uncertainty originating from input parameters 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 yields 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 second-moment analysis of solute concentrations is combined with the Kolmogorov backward equations and applied to the stochastic computation of wellhead protection zones for a pumping well group in Gambach (Germany). Unconditional and conditional simulation results are compared to corresponding Monte Carlo simulations. The unconditioned FOSM method reveals a computational advantage of a factor of 5–10 against the Monte Carlo method in terms of CPU time requirements. Conditioned FOSM shows an even larger advantage with a factor of 50–100 against the usual inverse stochastic modeling method based on Monte Carlo techniques.