A method of multi-site calibration of distributed hydrological models based on the Nash-Sutcliffe efficiency

Abstract

Contemporary distributed hydrological models are detailed and mathematically rigorous, but their calibration and testing can be still an issue. Often it is based on the quadratic measure of the calculated and observed hydrographs proximity at one outlet gauge station, typically on the Nash-Sutcliffe model efficiency coefficient (NSE). This approach seems insufficient to calibrate a model with hundreds of spatial elements. This paper presents using a multi-dimensional estimator of modeling quality, being a natural generalization of the traditional NSE but which would aggregate data from several hydrological stations using Principal Component Analysis (PCA). The method was tested on the ECOMAG model developed for a sub-basin (24,400 km2, with 15 gauges) of the Ussuri River in Russia. The results show that the presented version of the multi-dimensional NSE with PCA in calibration of spatially-distributed hydrological models has a number of advantages compared to other methods: the reduced dimensionality without loss of important information, straightforward data analysis and the automated calibration procedure; objective separation of the deterministic signal from the noise, calibration using the “informational kernel” of data, leading to more accurate parameters’ estimates. Additionally, the introduced notion of the “compact” dataset allow to interpret physical-geographical homogeneity of the basins in mathematic manner, which can be valuable for hydrological zoning of the basins, hydrological fields analysis, and structuring the models of large basins. There is no doubt that further development and testing of the proposed methodology is advisable in solving spatial hydrological problems based on distributed models, such as managing a cascade of reservoirs, creating hydrological reanalyses, etc.