Searching for Functional Simplicity of Stormflow Generation

Abstract

Our study proposes a data-driven framework that identifies the level of functional simplicity of catchment's stormflow generation during dormant/growing seasons, using daily scale observations of streamflow and precipitation. We classify 619 rain-dominated catchments across Canada, the United States, Great Britain, and Australia into three behavioral classes—simple, intermediate, and complex—based on the validity of (segmented) linear models in explaining the inter-event relationship between precipitation volume and stormflow volume. Results reveal that simple stormflow generation behavior occurs at 108 catchments during dormant seasons with the linear model explaining most variability of inter-event relationship between precipitation and stormflow volumes (median R² of 0.81). These simple catchments are typically steep with wet/out-of-phase climate and strong precipitation persistence. The functional simplicity of simple catchments is further explored using spectral (coherency) analysis, which indicates the level of synchronicity between daily scale precipitation and streamflow time-series. Simple catchments exhibit a strong coherency value at high frequencies, resembling the dynamic of a nearly Linear Time-Invariant system. Indeed, the portion of precipitation volume that becomes stormflow tends to remain constant during dormant seasons, since the transfer function translating precipitation pulses to the streamflow hydrograph is nearly linear and time-invariant. Complex catchments, in contrast, exhibit nonlinear relationships and time-variant transfer functions, with weak coherency between precipitation and streamflow time-series. Our results guide modeling frameworks to adjust the simplicity/complexity level with the catchment's “observation-based” functional behavior. By synthesizing the causes/drivers and empirical equations relevant to simple stormflow behavior, our study contributes to the development of a unified hydrologic theory of stormflow generation.