Beyond the SCS‐CN method: A theoretical framework for spatially lumped rainfall‐runoff response

Abstract

Since its introduction in 1954, the Soil Conservation Service curve number (SCS‐CN) method has become the standard tool, in practice, for estimating an event‐based rainfall‐runoff response. However, because of its empirical origins, the SCS‐CN method is restricted to certain geographic regions and land use types. Moreover, it does not describe the spatial variability of runoff. To move beyond these limitations, we present a new theoretical framework for spatially lumped, event‐based rainfall‐runoff modeling. In this framework, we describe the spatially lumped runoff model as a point description of runoff that is upscaled to a watershed area based on probability distributions that are representative of watershed heterogeneities. The framework accommodates different runoff concepts and distributions of heterogeneities, and in doing so, it provides an implicit spatial description of runoff variability. Heterogeneity in storage capacity and soil moisture are the basis for upscaling a point runoff response and linking ecohydrological processes to runoff modeling. For the framework, we consider two different runoff responses for fractions of the watershed area: “prethreshold” and “threshold‐excess” runoff. These occur before and after infiltration exceeds a storage capacity threshold. Our application of the framework results in a new model (called SCS‐CNx) that extends the SCS‐CN method with the prethreshold and threshold‐excess runoff mechanisms and an implicit spatial description of runoff. We show proof of concept in four forested watersheds and further that the resulting model may better represent geographic regions and site types that previously have been beyond the scope of the traditional SCS‐CN method.

Framework for event‐based semidistributed modeling that unifies the SCS‐CN method, VIC, PDM, and TOPMODEL

“…A semidistributed model may be described by a joint distribution of the soil moisture deficit, c , and water storage capacity, w , which describe the potential retention S = cw [see Bartlett et al ., ]. In an event‐based representation, c and S are considered antecedent values immediately prior to the start of the storm, while the point values of rainfall, R , and runoff, Q , represent cumulative depths for the storm duration [see Bartlett et al ., , Figure ].…”

“…A semidistributed model may be described by a joint distribution of the soil moisture deficit, c , and water storage capacity, w , which describe the potential retention S = cw [see Bartlett et al ., ]. In an event‐based representation, c and S are considered antecedent values immediately prior to the start of the storm, while the point values of rainfall, R , and runoff, Q , represent cumulative depths for the storm duration [see Bartlett et al ., , Figure ]. The spatial variability of these values may be described by the probabilistic storage (ProStor) framework of the joint PDF where is the runoff PDF conditional on R , c , and w ; is the PDF of rainfall; and is the joint PDF of the antecedent soil moisture deficit and storage capacity.…”

“…If runoff at a watershed point is modeled as a deterministic function, i.e., then the joint PDF becomes where the conditional distribution is now represented by the point mass of probability , for which is the Dirac delta function. The PDF describing the spatial distribution of runoff is found by integrating equation over the remaining variables (i.e., R , c , and w ), while the lumped (unit area) runoff response (i.e., the runoff curve) is the average of equation [ Bartlett et al ., ]. Framework variables and parameters are listed in Table .…”

“…Based on the joint PDF of equation and the Bartlett et al . [] spatial description of threshold‐excess and prethreshold runoff at a point, we derive an event‐based model representation that is general to the PDFs of rainfall, , and storage capacity, (see Appendix ). This point runoff description of Bartlett et al .…”

“…This point runoff description of Bartlett et al . [] consists of both prethreshold and threshold‐excess runoff over the fraction of watershed area β , while over the complementary area, , the point response only consists of threshold‐excess runoff. The fraction β may represent riparian and lower hillslope areas with a persistent hydrologic connection to the stream that facilitates a prethreshold runoff before rainfall infiltration exceeds the storage capacity threshold.…”