Spatial variability of groundwater flow fields caused by nonstationary random input parameter processes

Much of the stochastic analysis of flow fields in heterogeneous formations in the literature treats the random input parameters that appear in the stochastic differential equation for the groundwater flow perturbations can be characterized by a covariance function. However, it may be that the covariance functions of the input parameters cannot be identified with the limited field data or that the covariance functions of the parameters do not exist at the regional scale. It is therefore necessary to generalize the existing stochastic theories for the quantification of groundwater flow variability to the case of nonstationarity of input parameter processes, which is the goal of the present work. This work deals with the problem of steady-state flow in heterogeneous confined aquifers with variable thickness, where the spatial variability of hydraulic conductivity and aquifer thickness are considered as intrinsic (nonstationary) random input processes. The introduction of the intrinsic spectral representations for the log conductivity and log aquifer thickness leads to an intrinsic process for the perturbation of the depth-averaged head, and therefore nonstationary semivariograms of the depth-averaged hydraulic head and the integrated specific discharge are developed to quantify the variability of the flow fields. The stochastic theories developed here improve the quantification of the variability of flow fields in natural confined aquifers. The analysis clearly demonstrates that the unbounded increase of the semivariograms of depth-averaged head and integrated discharge with separation distance indicates that quantifying the variability of depth-averaged head and integrated discharge using the assumption of second-order stationarity for the input parameters may lead to a significant underestimation of the variability of head and discharge for the case of variation of random input parameters characterized by a linear semivariogram model. The parameters that appear in the linear semivariograms of the logarithmic conductivity and the logarithmic thickness of the aquifer play a role in increasing the variability of the depth-averaged hydraulic head and thus the variability of the integrated discharge.