On the relationship between surface runoff and impervious area in the urban RPA (Receiving Pervious Area)-DIA (Disconnected Impervious Area) system: A simple equation expressing the sensitivity of runoff to changes in imperviousness

Abstract

The urban RPA (Receiving Pervious Area)-DIA (Disconnected Impervious Area) system is the sub-catchment with a typical land distribution pattern where the connectivity between impervious area and drainage is disconnected by pervious area in the context of Low Impact Development (LID). The rainfall-runoff response of the RPA-DIA system is complex and plays an important role in LID management, which is not yet fully understood. In this study, to systematically learn the rainfall-runoff response of the RPA-DIA system, an indoor rainfall simulation experiment was applied to a laboratory RPA-DIA system, and an integrated surface-subsurface flow model was used to simulate the hydrological processes of actual-scale RPA-DIA systems with consideration of numerous rainfall and underlying surface conditions. Both the laboratory experiment and the numerical simulations show a segmented linear runoff-imperviousness relationship for the RPA-DIA system. A threshold of impervious area exists in the runoff-imperviousness relationship, and when the impervious area is less than the threshold, the surface runoff coefficient is zero, otherwise the surface runoff coefficient increases with impervious area in a generally linear trend. We define the slope of the linear trend as the R-I sensitivity (sensitivity of runoff to imperviousness), which is the key metric to determine the runoff-imperviousness relationship. We further explored how the R-I sensitivity changes between different rainfall and RPA conditions (e.g., different LID facilities and initial soil moistures) and found that both the laboratory experiment and the numerical simulations suggest a very simple equation to express the R-I sensitivity (RISE, Runoff-Imperviosness Sensitivity Equation) in terms of rainfall depth and intensity, including three parameters indicating the specific RPA conditions. Based on the segmented linear relationship and RISE, we have established a framework that vividly presents the rainfall control behavior of a specific RPA under different rainfall events, which can be a simple tool to provide cost-effective guidelines for LID facilities adapting to current or future rainfall characters.