Soil-aquifer-stream interactions — A reductionist attempt toward physical-stochastic integration

Abstract

The paper suggests an approach to describe the various interactions between soil, aquifer and stream in a simplified but essentially physical and integrated manner. For practical applications, the complex hydrological processes cannot be thoroughly described at the smallest scale in time and space, at which theoretical or empirical physical laws are known. The successful passage from a smaller to a larger scale requires: enlightened simplification, integration in many senses that is: (1) in time; (2) in space; (3) in an expectation sense; and (4) in a process sense, and finally enlightened coupling. The paper illustrates in a simple manner this processus of multiple integration for the processes of infiltration, moisture redistribution, aquifer recharge and aquifer return flow, with emphasis on the stream-aquifer interaction. The paper suggests that temporal patterns of rainfall, spacial variation in soil properties, temporal fluctuations in river stage, sharp turns in flow directions (e.g. from vertical to horizontal direction at the interface of two soil layers with contrasting hydraulic properties or in the vicinity of a water table) etc., can significantly affect the response of a watershed. The paper also suggests that simple techniques can be devised that account to a large extent for these influences and will provide satisfactory tools for watershed modeling. As a sort of parenthesis, the paper shows that the purely statistical ARMA approach to hydrologic modeling will lead to incorrect identification of a perfectly stationary linear system as a nonstationary one. The combined physical-stochastic approach eliminates this potential error.