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

Abstract

Hydrologists and engineers may choose from a range of semidistributed rainfall‐runoff models such as VIC, PDM, and TOPMODEL, all of which predict runoff from a distribution of watershed properties. However, these models are not easily compared to event‐based data and are missing ready‐to‐use analytical expressions that are analogous to the SCS‐CN method. The SCS‐CN method is an event‐based model that describes the runoff response with a rainfall‐runoff curve that is a function of the cumulative storm rainfall and antecedent wetness condition. Here we develop an event‐based probabilistic storage framework and distill semidistributed models into analytical, event‐based expressions for describing the rainfall‐runoff response. The event‐based versions called VICx, PDMx, and TOPMODELx also are extended with a spatial description of the runoff concept of “prethreshold” and “threshold‐excess” runoff, which occur, respectively, before and after infiltration exceeds a storage capacity threshold. For total storm rainfall and antecedent wetness conditions, the resulting ready‐to‐use analytical expressions define the source areas (fraction of the watershed) that produce runoff by each mechanism. They also define the probability density function (PDF) representing the spatial variability of runoff depths that are cumulative values for the storm duration, and the average unit area runoff, which describes the so‐called runoff curve. These new event‐based semidistributed models and the traditional SCS‐CN method are unified by the same general expression for the runoff curve. Since the general runoff curve may incorporate different model distributions, it may ease the way for relating such distributions to land use, climate, topography, ecology, geology, and other characteristics.

A new probability density function for spatial distribution of soil water storage capacity leads to the SCS curve number method

“…The Soil Conservation Service Curve Number (SCS-CN) method (Mockus, 1972) has been popularly used for direct runoff estimation in engineering communities. Even though the SCS-CN method was obtained empirically (Ponce, 1996;Beven, 2012), it is often interpreted as an infiltration excess runoff model (Bras, 1990;Mishra and Singh, 1999). Yu (1998) showed that partial area infiltration excess runoff generation on a statistical distribution of soil infiltration characteristics provided a similar runoff generation equation to the SCS-CN method.…”

A Clustering Preprocessing Framework for the Subannual Calibration of a Hydrological Model Considering Climate‐Land Surface Variations

“…Compared with data‐driven models, process‐driven hydrological models can better capture the physical processes in a catchment and are an important tool to estimate the elements of the water cycle (Bárdossy, ). In particular, on the daily scale, process‐driven hydrological models are usually superior to data‐driven ones (Bartlett et al, ; L. Wang et al, 2017). Therefore, this study applied data mining techniques to improving the performance of process‐driven hydrological models.…”

Reply to comment by Fred L. Ogden et al. on “Beyond the SCS‐CN method: A theoretical framework for spatially lumped rainfall‐runoff response”

“…However, O&C do not recognize the compatibility of their call with our framework, which accommodates different runoff mechanisms (including threshold-type runoff resulting from different hydrologic connections to the stream [e.g., Hewlett and Hibbert, 1967;McDonnell, 2006a, 2006b;McGuire and McDonnell, 2010]) as well as different data-derived distributions for describing soil and rainfall variability. Indeed, we are intrigued by the fact that previous process-based rainfall-runoff research may be converging on the idea that all runoff processes are ''the same,'' i.e., all threshold like via filling, spilling, loss along the flow path and ultimately connectivity of saturated areas [McDonnell, 2013;Ameli et al, 2015;Bartlett et al, 2016b]. If true, this could lead to interesting developments for dynamic and multiscale models and new guidance for what data to collect in the field.…”

“…C1-C5 and C7: A specific response to these points is made difficult by the fact that they, when correct, apply generically to most spatially implicit rainfall-runoff models. We only note that (i) obtaining data for the parameter distributions of our model is no more difficult than gathering the data (e.g., soil hydraulics) desired by O&C in their call to action, (ii) including rainfall intensity is certainly possible (as also stated in Bartlett et al [2016a]) and work is in progress to implement the time compression approximation [e.g., Rigby and Porporato, 2006;Liu et al, 1998] in this framework, (iii) capturing discontinuity of the rainfall field and systematic spatial nonuniformities is possible through mixed distributions [e.g., Sivapalan et al, 1997], and (iv) accommodating (nonrandom) heterogeneity is feasible as demonstrated by the framework adaptation to TOPMODEL [Bartlett et al, 2016b]. Figure 1.…”

“…But, more broadly and more importantly, our goal is to explore a theoretical underpinning to this method that was perhaps hitherto unnoticed. As detailed in a subsequent paper [Bartlett et al, 2016b], we have described a family of semidistributed models, of which the SCS-CN method is just one. Other models described by this framework include event-based versions of the Variable Infiltration Capacity (VIC) model [Liang et al, 1994] and TOPMODEL (Topography-based hydrologic MODEL) [Beven and Kirkby, 1979].…”