Persistent questions of heterogeneity, uncertainty, and scale in subsurface flow and transport

When Water Resources Research was launched in 1965, heterogeneity, uncertainty, and scale issues in subsurface hydrology were in the backburner. Only about 10 years later, under the stimulus of dealing with solute transport problems, these problems received attention. The stochastic approach brought tools to deal both with problems of upscaling, also known as homogenization and coarse‐graining, and uncertainty quantification. Effective conductivity and effective dispersion, also known as macrodispersion, coefficients in statistically homogeneous formations were extensively studied. Mixing, in its role of affecting reaction rates, started receiving attention. While in the dispersion problem emphasis was on Fickian representations, more sophisticated models have also been studied. Uncertainty quantification in the inverse problem has also made progress and geostatistical ideas, as well as ideas originating in signal processing, influenced how we approach problems of inference like interpolation and inverse modeling. My view is that we should emphasize information aspects, i.e., the collection of more and better data, their correct assimilation, the quantification of uncertainty associated with predictions, and the selection of designs or policies that accurately reflect what we actually know and thus manage risk. Progress in this department has been hampered by ingrained ideas, inadequate training, and inadequate resources. Research in problems of upscaling will continue to shed new light and provide better tools to deal with onerous problems. At the same time, no cure is more universally potent than using a more refined grid. Finally, although research is active, the diffusion of research results to education and practice has been slow.