Stochastic Hydrogeology: Chuck Newman Had a Good Idea About Where to Start

Abstract

Groundwater hydrology had reached a crisis by 1980 that Chuck Newman helped resolve. By then a large number of field observations had showed that contaminant transport was anomalously diffusive: the constant coefficient advection-diffusion equations that had been the basis for predictions of contaminant transport consistently under-predicted their spread on long time-scales. This anomalous diffusion appeared to have two sources. First, observations showed transport on small scales was not classically diffusive, as expected. Second, the material properties of natural porous media were not uniform in space or deterministic, but were in fact heterogeneous and uncertain. Both were fundamental assumptions of the classic approach. Chuck proposed and guided the development of an alternative model that views the large-scale behavior of transport in porous media as the convergent limit of a mesoscopic stochastic advection-diffusion process. This addressed both aspects of the crisis since the limit explained the transition from non-Fickian transport on mesoscopic scales to anomalous macroscale transport and the stochastic equation provided a means for quantifying uncertainty. We describe the development of the model, its setting in hydrology, and further developments in hydrology that sprung from it.