Stochastic modeling of complex nonstationary groundwater flow systems.

摘要

Although the "stochastic revolution" has produced an enormous number of theoretical publications and influenced significantly how we think about the aquifer heterogeneity, it has had relatively little impact on practical modeling community. A number of recent review articles provided the following reasons and the potential solutions: (1) Stochastic modeling is incompatible with the available measurement technologies. New measurement technologies, and new sources of data of much better resolution to characterize aquifer heterogeneity are urgently needed [9, 10, 59, 87, 57]. (2) Stochastic analytical theories are based on too many restrictive requirements to be practically useful. The assumptions of stationarity, ergodicity, mean uniform flow, Gaussian distribution, and small perturbation must be substantially relaxed [9, 47, 42, 43, 62, 59, 87, 19]. (3)Stochastic numerical theories are computationally impractical for most problems of realistic sizes. One must recognize and remove these tough computational bottlenecks before meaningful stochastic modeling applications are possible [9, 59].;Motivated by these critical assessments, this research addressed a number of conceptual, computational, and implementation issues in the modeling of subsurface heterogeneity. In particular, this study developed, tested, and implemented the conceptually improved, nonstationary stochastic methods for predicting velocity uncertainty in two-dimensional flows. An approximate and analytically-based spectral method was presented for predicting velocity variances under mildly nonstationary flow situations. This approximate spectral method (ASM) rely on a linearization of the groundwater flow equation but do not require the common statistical stationarity assumptions. To provide general insight into the ASM for mildly nonstationary flows, this study performed intensive numerical experiments to assess the accuracy of ASM under a number of nonstationary situations. The illustrative examples involved nonstationary situations caused by hydraulic conductivity trends, composite media, nonlinear head distributions in unconfined aquifers, transient flows, and deterministic sources and sinks applied in modeling areas. The surprising results in the assessment showed that ASM can reproduce well the solutions of corresponding first-order numerical analysis and Monte Carlo simulation except in the proximity of prescribed boundaries and well locations. These regions, however, are limited in 3 to 5lambdas (lnk correlation length) from boundaries and in 5 to 10lambdas from wells. (Abstract shortened by UMI.).