Discretization scale dependencies of the ensemble flow range versus catchment area relationship in distributed hydrologic modeling

Abstract

Summary Earlier research results have shown that the range of the ensemble flow simulations from a well-validated operational hydrologic model possesses a well-defined log-linear relationship to catchment area for which the ensembles are generated. The ensemble range is a function of both parametric and rainfall input uncertainty. In this paper the sensitivity of this scaling relationship for simulation uncertainty to the numerical discretization scale of the distributed model is quantified when the model is driven by WSR-88D (NEXRAD) radar data and for two catchments in the south-central United States. The distributed model used is subcatchment (rather than pixel) based, has components that are based on operational models employed in the US National Weather Service, and has been validated for the two application catchments of this work as part of the Distributed Model Intercomparison Project (DMIP). The approach taken develops a new parsimonious model for spatially correlated radar-rainfall errors with radar-pixel error variance that depends on the magnitude of the observed rainfall. Monte Carlo methods are used to translate parametric and radar-rainfall input uncertainty to ensemble flow simulations at a number of subcatchments of varying size. Selected events in the period from May 1993 to July 1999 were analyzed. The results confirm that the ensemble flow range is dependent on subcatchment scale with a well-defined log-linear relationship for both application catchments. This finding holds for all uncertainty scenarios examined and across all the scales of distributed model discretization. It is further found that a higher model discretization leads to a shorter range of simulation uncertainty for subcatchment spatial scales that are substantially larger than the average subcatchment size. Flow simulation uncertainty that is due to either parametric or input uncertainty alone scale in a way that is similar to the combined uncertainty scaling.