Theory of Recession Based on Concepts from Percolation Theory

Abstract. Using the definition of recession as the decline in streamflow following a rainfall event peak and before the next peak (provided evapotranspiration may be neglected), recession defines the relationship between catchment storage and outflow. The present analysis addresses the limiting processes absent in existing recession analysis, which are nonetheless treatable in the language of percolation theory. This includes: a) a universal decline in hydraulic conductivity as the percolation threshold is approached, and b) a universal decline in accessible moisture content beyond the simple decline in overall moisture content. The process of addressing these two time-dependent phenomena generates the basic structure of recession response: 1) linear response for an average of multiple events, 2) the corresponding time frame variation, 3) the specific characteristics of its non-linear response, specifically, its convexity.  The present approach results in an absolute value of the non-linearity that is still underestimated as compared to results published in the literature.