Uncertainty estimation of pathlines in ground water models

A method is proposed to estimate the uncertainty of the location of pathlines in two-dimensional, steady-state confined or unconfined flow in aquifers due to the uncertainty of the spatially variable unconditional hydraulic conductivity or transmissivity field. The method is based on concepts of the semianalytical first-order theory given in Stauffer et al. (2002, 2004), which allows estimates of the lateral second moment (variance) of the location of a moving particle. However, this method is reformulated in order to account for nonuniform recharge and nonuniform aquifer thickness. One prominent application is the uncertainty estimation of the catchment of a pumping well by considering the boundary pathlines starting at a stagnation point. In this method, the advective transport of particles is considered, based on the velocity field. In the case of a well catchment, backtracking is applied by using the reversed velocity field. Spatial variability of hydraulic conductivity or transmissivity is considered by taking into account an isotropic exponential covariance function of log-transformed values with parameters describing the variance and correlation length. The method allows postprocessing of results from ground water models with respect to uncertainty estimation. The code PPPath, which was developed for this purpose, provides a postprocessing of pathline computations under PMWIN, which is based on MODFLOW. In order to test the methodology, it was applied to results from Monte Carlo simulations for catchments of pumping wells. The results correspond well. Practical applications illustrate the use of the method in aquifers.