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REVIEWS AND ANALYSES

Central Ideas of Buckingham (1907): A Century Later

Dep. of Materials Science and Engineering, Dep. of Environmental Science, Policy and Management, Earth Sciences Division, Lawrence Berkeley National Lab., 210 Hearst Mining Bldg., Univ. of California at Berkeley, Berkeley, CA 94720-1760
^* Corresponding author (tnnarasimhan{at}LBL.gov).

Received 22 April 2007.

A century ago, Edgar Buckingham presented data and a theoretical conceptualization of soil moisture movement. His work constitutes a milestone in the history of soil physics and more generally, of movement of multiple fluid phases in porous media. Starting from first principles, Buckingham formulated a conceptual model to make rational sense of long-term observations of evaporation from soil columns. Central to his model were the notion of a capillary potential, soil moisture retention curve, and potential-dependent hydraulic conductivity. Buckingham recognized that whereas heat capacity and thermal conductivity were independent of temperature in Fourier's heat equation, in the case of soil moisture, the slope of the soil-moisture retention curve (analogous to specific heat) and capillary conductivity were both strong functions of capillary potential. Noting that available solutions of Fourier's linear differential equation did not apply to moisture movement in soils, Buckingham was skeptical that the nonlinear problem could be solved mathematically. This is perhaps why he did not present a partial differential equation for soil-moisture movement. Such an equation would be gvien in 1931 by Richards. Despite considerable efforts, analytical solutions to Richards' equation can be obtained only under simplifying assumptions. While these solutions give valuable insights into patterns of soil moisture movement, they cannot adequately address problems of the natural soil environment. Although Buckingham's model remains the only workable physical-mathematical conceptualization for studying moisture movement in soils, his own skepticism of its ability to reliably describe moisture movement in soils is still valid. More profound, his skepticism captures the limitations inherent in precisely describing the behavior of earth systems. This paper examines Buckingham's central ideas in light of developments in groundwater hydrology and soil mechanics and reflects on the limits of our ability to quantitatively understand moisture movement in unsaturated soils.