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[1] Groundwater inverse problems are concerned with the estimation of uncertain model parameters, such as hydraulic conductivity, from field or laboratory measurements. In practice, model and measurement errors compromise the ability of inverse procedures to provide accurate results. It is important to account for such errors in order to determine the proper weight to give to each source of information. Probabilistic descriptions of model and measurement errors can be incorporated into classical variational inverse procedures, but the computational demands are excessive if the model errors vary over time. An alternative approach based on representer expansions is able to efficiently accommodate time-dependent errors for large problems. In the representer approach, unknown variables are expanded in finite series which depend on unknown functions called representers. Each representer quantifies the influence of a given measurement on the estimate of a particular variable. This procedure replaces the original inverse problem by an equivalent problem where the number of independent unknowns is proportional to the number of measurements. The representer approach is especially advantageous in groundwater problems, where the total number of measurements is often small. This approach is illustrated with a synthetic flow and transport example that includes time-dependent model errors. The representer algorithm is able to provide good estimates of a spatially variable hydraulic conductivity field and good predictions of solute concentration. Its computational demands are reasonable, and it is relatively easy to implement. The example reveals that it is beneficial to account for model errors even when they are difficult to estimate.

Abstract. A stochastic approach is adopted for characterizing the uncertainty in timerelated well capture zones in heterogeneous formations. Transmissivity is modeled as a random space function, conditioned on regular grids of evenly distributed transmissivity measurements. Monte Carlo analysis is used to infer the probability distribution of the resulting stochastic capture zones. Three measures of conditioning performance are defined and evaluated for several combinations of conditioning density, transmissivity variance, and transmissivity integral scale. Furthermore, a connection is made with previous work on transport theory. Simulation results show that conditioning performance increases with an increasing conditioning density, an increasing transmissivity integral scale, and a decreasing transmissivity variance. However, there is a threshold combination of conditioning density and integral scale beyond which conditioning performance stagnates. The practical implications of the results in general and the threshold in particular are discussed.

Abstract. A stochastic approach is adopted for characterizing the uncertainty in well capture zones in heterogeneous formations. Transmissivity is modeled as a random space function and a Monte Carlo approach is used to infer the probability distribution of the resulting stochastic capture zones. Through several numerical experiments, the influence of the statistical parameters of transmissivity variation on the extent of uncertainty in the location of the capture zone is investigated. Two aquifer models are considered: a fully confined aquifer and a leaky-confined aquifer receiving recharge from above. A connection is made with previous work on transport theory, and the statistical parameters of the capture zone probability distribution are compared with those of a solute concentration plume.

[1] Different upscaling methods for groundwater flow models are investigated. A suite of different upscaling methods is applied to several synthetic cases with structured and unstructured porous media. Although each of the methods applies best to one of the synthetic cases, no performance differences are formed if the methods were applied to a real three-dimensional case. Furthermore, we focus on boundary conditions, such as Dirichlet, Neumann, and Cauchy conditions, that characterize the interaction of groundwater with, for example, surface water and recharge. It follows that the inaccuracy of the flux exchange between boundary conditions on a fine scale and the hydraulic head on a coarse scale causes additional errors that are far more significant than the errors due to an incorrect upscaling of the heterogeneity itself. Whenever those errors were reduced, the upscaled model was improved by 70%. It thus follows that in practice, whenever we focus on predicting groundwater heads, it is more important to correctly upscale the boundary conditions than hydraulic transmissivity.