Darcy’s Law and Structural Explanation in Hydrology

Abstract

According to a recent argument, models play two essential roles in the argumentative structure of solid state physics and chemistry (Hofmann 1990). On the one hand, models are the culmination of phenomenological description. That is, models are idealized representations of the molecular structures thought to be causally responsible for the processes experimentally monitored and measured. Secondly, dieoretical physicists and chemists require that models ultimately be cast in a mathematical form appropriate for the application of the Schroedinger equation. In this respect models become the means through which the Schroedinger equation gives a theoretical unity to what would otherwise be a disparate set of empirical phenomenological laws and descriptions with limited scope. That is, it is an important theoretical goal to show that experimentally generated phenomenological laws can be approximately derived through an application of the Schroedinger equation to a necessarily idealized and simplified mathematical description of the relevant system. The two functions of models are not incompatible, but they do reflect two distinct theoretical orientations toward the interpretation of data.

TOPMODEL: A critique

“…We therefore simplify on the basis of past hydrological theorizing, often in a way that we know is more convenient than true, blithely applying small-scale theories at the much larger scales where predictions are of interest (Beven, , 1996a. Such is true of TOPMODEL; such is also true of all other hydrological models applied at the catchment scale (for recent discussions with respect to the application of Darcy's law see Schrader-Frechette, 1989;Hofmann and Hofmann, 1992;Oreskes et al, 1994).…”

The Fact of Evolution: Implications for Science Education

“…Although Bogen and Woodward initially applied their distinction between data and phenomena to cases in physics and psychology, it has proved useful in solid state chemistry and hydrology as well (Hofmann 1990;Hofmann & Hofmann 1992). We argue that it is also pertinent to evolutionary biology.…”

Parameter estimation in flow through partially saturated porous materials

“…The expressions in the denominator are nodal fluid density fluxes at the upper ði ¼ 1Þ and lower ði ¼ NÞ boundaries of the spatial domain calculated using Darcy-Buckingham law [11,18,32].…”