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 r esults suffer from uncertainty. When conservative decisions have to be draw n, the quantification of uncertainties is necessary. Monte Carlo techniques are suited for this analysis but usually require a huge computational effo rt. An alternative and computationally efficient approach is the first-orde r second-moment (FOSM) analysis which directly propagates the uncertainty o riginating from input parameters into the result. We apply the FOSM method to both the groundwater flow and solute transport equations. It is shown ho w calibration on the basis of measured heads yields the "Principle of Inter dependent Uncertainty" that correlates the uncertainties of feasible transm issivities and recharge rates. The method is used to compute the uncertaint y of steady state heads and of steady state solute concentrations. The seco nd-moment analysis of solute concentrations is combined with the Kolmogorov backward equations and applied to the stochastic computation of wellhead p rotection zones for a pumping well group in Gambach (Germany). Unconditiona l and conditional simulation results are compared to corresponding Monte Ca rlo simulations. The unconditioned FOSM method reveals a computational adva ntage of a factor of 5-10 against the Monte Carlo method in terms of CPU ti me requirements. Conditioned FOSM shows an even larger advantage with a fac tor of 50-100 against the usual inverse stochastic modeling method based on Monte Carlo techniques. (C) 2000 Elsevier Science B.V. All rights reserved .