Power law catchment‐scale recessions arising from heterogeneous linear small‐scale dynamics

Power law recession behavior has typically been attributed to the hydraulics of subsurface flows in the landscape (e.g., the Boussinesq equation). Many catchments exhibit enormous heterogeneity in their characteristics, such as the permeability of soils, hillslope length and gradient, and soil mantle thickness. In the paper we demonstrate using a simple linear flow model that the between‐hillslope heterogeneity alone can give rise to observed apparently nonlinear recession slope curves. The degree of nonlinearity (represented by the exponent fitted to the recession slope curve) is shown to increase with the degree of heterogeneity of catchment hydraulic properties. In sufficiently heterogeneous catchments, the recession is also sensitive to the history of recharge events, tending to increase when the past events have built up a storage of water in the ‘slow’ parts of the catchment. The models based on the catchment heterogeneity were fitted to data from the Panola Mountain Research watershed, yielding a good fit, and allowing us to infer how the heterogeneity in catchment properties varies with scale. The range of exponents explained by this theory overlaps with the range explained by the hydraulics of subsurface flow, which raises doubts about our ability to extract catchment hydraulic parameters on the basis of recession curves so long as the heterogeneity is not accounted for. In general the results presented here have enabled us to show how the heterogeneity of landscape characteristics is upscaled and manifested in the apparent nonlinear relationship at the catchment scale.