Apportioning non-linearity in conceptual rainfall–runoff models: examples from upland UK catchments

Abstract

Rainfall–runoff modellers distinguish between flow generation and flow routing processes, and many models treat the two types of process independently. These models commonly assume that the dominant non-linearity in the rainfall–flow response resides in the flow generation process. This paper revisits three upland UK catchments where such an assumption has previously been made and explores the apportioning of non-linearity, its identifiability and how it is affected by catchment type, season, data time-resolution, objective function and model equations. The catchments showed stronger routing non-linearity than expected and comparatively little non-linearity in flow generation both in wet winter periods and in mixed wet-dry summer periods, although in one catchment this result was sensitive to a modification of the model equations. Aggregating data to time resolutions approaching the response times of the catchments makes the flow generation appear more non-linear that it actually is, less so if performance is assessed using log-transformed flows. In cases, using conceptually distinct models achieved similar Nash–Sutcliffe efficiency (NSE) performances; however, using a single non-linear routing function with a linear or near-linear loss model was considered the most efficient overall. Using this model, NSE values of up to 0.99 were obtained.