Towards closure relations in the Representative Elementary Watershed (REW) framework containing observable parameters: Relations for Hortonian overland flow

Abstract

This study presents the derivation procedure of an integrated closure relation for infiltration and Hortonian overland flow in the Representative Elementary Watershed (REW) framework that contains directlyobservable parameters. A physically-based high resolution model is used to simulate the infiltration flux and discharge for 6 Â 10 5 set of synthetic REWs and rainstorms scenarios. This synthetic data set serves as a surrogate of real-world data to deduce the closure relation. The closure relation performance is evaluated against the results from the high resolution model. The results show that the closure relation is capable of predicting accurate hydrological responses for an independent set of synthetic REWs and rainstroms in terms of the Nash-Sutcliffe index, errors in total discharge volume, and peak discharge, especially in cases where a relatively large amount of runoff is produced with fast responses. For the estimation of parameters in the closure relation, a local method using inverse distance weighted interpolation in the parameter space is superior to the global method based on the multiple regression, resulting in a better reproduction of runoff characteristics.

Hortonian runoff closure relations for geomorphologic response units: evaluation against field data

“…They suggested using the units (or catchments) with uniform properties to allow imposing a number of assumptions essential in their formulation of the closure relation. The methodology proposed in Vannametee et al (2012) is somewhat similar to the works by Massuel et al (2011), in which they scaled up the surface runoff processes, using the detailed fine-scale, physically based model to derive the runoff coefficient as a basis to estimate the groundwater recharge over a large region.…”

“…A number of studies are dedicated to developing the closure relations for specific hydrological compartments that partly resolve the problems related to scale-dependent effects, process non-linearity, sub-unit heterogeneity, and hysteresis (e.g. Lee et al, 2007;Reggiani and Rientjes, 2010;Troch, 2003;Vannametee et al, 2012). The existing closure schemes require parameter values that are representative for the region that is lumped by the model, which typically has a size above 10 5 m 2 (e.g.…”

“…To address the issues discussed above, Vannametee et al (2012) defined a rigorous approach for identifying the closure relations in lumped precipitation-runoff models, focussing on the closure relations related to Hortonian runoff, in particular the infiltration flux to the unsaturated zone, and the runoff flux. Their closure relations use local-scale parameter values as inputs to derive the runoff flux generated at the scale of the modelling units.…”

“…To account for scale transfer, their closure relation explicitly includes scaling parameters, that are used to characterise the effects of geometry and process variability in the modelling units for Hortonian runoff generation. To avoid ad hoc estimation of these scaling parameters, Vannametee et al (2012) provided a parameter estimation scheme, which is based on empirical relations between the geometry, and locally observable properties of the modelling units, including boundary conditions and past trajectory of surface water storage. These relations were identified from an extensive set of precipitation-runoff responses generated by a distributed, physically based, high-resolution model.…”

“…This paper presents an evaluation of the closure relation for Hortonian runoff, proposed in Vannametee et al (2012), that incorporates a scaling component to explicitly account for the process heterogeneity and scale effects in runoff generation for the real-world case studies. We applied the closure relation, which was embedded in an eventbased lumped rainfall-runoff model, to a 15 km 2 catchment in the French Alps.…”