Unlike traditional groundwater hydrology textbooks, this book integrates classical principles of flow through porous media with recently developed stochastic analysis to provide new insight into subsurface hydrology. It is not a collection of “cookbook” recipes for solving groundwater flow problems as are many currently available textbooks. On the contrary, it examines classical principles of groundwater flow in geologic media in a stochastic framework; it explains their limitations to real-world problems and provides improved solutions and a better understanding of the underlying principles.

We believe that there is a lack of understanding of scale issues related to observations, theories, and processes, as well as uncertainty in hydrogeologic science. Likewise, there is a fundamental knowledge gap between the stochastic groundwater theory and its applications to applied, real-world problems. As a result, this book is designed to illustrate to readers what different laws and conceptual models tell us in relation to our observation scales, why we should care about stochastic theories, and why we need to consider using stochastic subsurface hydrology principles for real-world problems.

Specifically, this book starts in Chapter 1, with a discussion the fundamental fluid mechanic concepts, built upon the control volume (CV) at a scale that is larger than many molecules, but still smaller than a pore in porous media. By expanding the CV to scales larger than many pores, we then discuss in Chapters 2 and 3 Darcy's law under variably saturated conditions, and we define hydraulic properties for flow through porous media at laboratory scales, using the fluid mechanics principles. New concepts of spatial REV (representative elementary volume) and ensemble REV are introduced. Because of the average nature of the CV, spatial REV, and ensemble REV concepts, the importance of scale consistency among our interests, observations, hydraulic properties, and Darcy's law is then emphasized.

In order to quantify multiscale spatial variability of the laboratory-scale hydraulic properties in a field, stochastic processes or random field concepts are presented in Chapter 4. These concepts facilitate a quantitative method to describe spatially varying hydraulic properties of a field in terms of their spatial statistics (i.e., the most likely value, their standard deviation, as well as their spatial fabrics–sizes of layers or stratifications). In Chapter 5, different conceptual models are discussed for characterizing and modeling a heterogeneous porous medium, including equivalent homogeneous, geologic, and highly parameterized heterogeneous conceptual models, satisfying different scales of our interests.