Reconceptualizing threshold-mediated runoff responses: A case study from the Humber River watershed, Ontario, Canada

Watershed-scale runoff responses are driven by various factors including climate, geology, soils, topography and landcover. They are often threshold-mediated, expressing significant changes in hydrologic behaviour at critical moments in time or points in space. The influence of multiple explanatory variables on rainfall-runoff relationships is not adequately captured by commonly applied approaches portraying runoff responses as a function of one variable related to watershed storage. In this case study, a novel approach was borrowed from ecological research to quantify and better understand threshold-mediated runoff responses. Modelled three-dimensional surfaces depicting metrics of event runoff responses as a function of rainfall amount and intensity were analysed to quantify both the abruptness of potential thresholds (i.e., threshold strength) and the simultaneous influence of different rainfall characteristics on the response (i.e., diagonality). The approach was applied to sub-watersheds of the Humber River (Ontario, Canada), which have a nested configuration and a strong land use gradient, providing an opportunity to explore how the interplay between rainfall amount and intensity in determining runoff response is affected by sub-watershed physical features. The study revealed that threshold strengths and the simultaneous influence of rainfall amount and intensity varied, depending on the sub-watershed and event-specific conditions. There was evidence that sub-watershed slope and imperviousness along with the watershed position relative to prevailing weather patterns influences threshold strength and diagonality. This research extends threshold analyses in hydrology to encompass multiple explanatory variables: it aligns more closely with perceptual models of runoff generation and encourages a reimagining of thresholds as discontinuities in response across various combinations of explanatory variables. The threshold strength and diagonality parameters facilitate objective comparisons of thresholds across space and time and may be valuable tools for watershed classification and inter-comparison, and for evaluating and/or calibrating rainfall-runoff models. These promising lines of inquiry would be best served by applying this methodology across a broader range of spatial scales and hydroclimatic conditions.