Abstract
Abstract. The estimation of hydrological model parameters is a challenging task. With increasing capacity of computational power several complex optimization algorithms have emerged, but none of the algorithms gives a unique and very best parameter vector. The parameters of fitted hydrological models depend upon the input data. The quality of input data cannot be assured as there may be measurement errors for both input and state variables. In this study a methodology has been developed to find a set of robust parameter vectors for a hydrological model. To see the effect of observational error on parameters, stochastically generated synthetic measurement errors were applied to observed discharge and temperature data. With this modified data, the model was calibrated and the effect of measurement errors on parameters was analysed. It was found that the measurement errors have a significant effect on the best performing parameter vector. The erroneous data led to very different optimal parameter vectors. To overcome this problem and to find a set of robust parameter vectors, a geometrical approach based on Tukey's half space depth was used. The depth of the set of N randomly generated parameters was calculated with respect to the set with the best model performance (Nash-Sutclife efficiency was used for this study) for each parameter vector. Based on the depth of parameter vectors, one can find a set of robust parameter vectors. The results show that the parameters chosen according to the above criteria have low sensitivity and perform well when transfered to a different time period. The method is demonstrated on the upper Neckar catchment in Germany. The conceptual HBV model was used for this study.
Highlights
Hydrological models are used for different purposes such as water management or flood forecasting
It could be shown that observation errors can lead to very different optimal model parameters if the uniqueness of the www.hydrol-earth-syst-sci.net/12/1273/2008/
– Observational uncertainty of the input and the discharge leads to variability of the model performance
Summary
Hydrological models are used for different purposes such as water management or flood forecasting. Beven and Freer (2001) argue that there are no optimum parameters, there is a large set of parameter vectors which all perform reasonably and one cannot distinguish between them They call this an equifinality problem which leads to high uncertainties in the model predictions. In Kavetski et al (2006a,b) it was noted that the performance metric of hydrological models is a bumpy function of the model parameters They suggest different numerical procedures to smoothen parameter surfaces and to obtain optimal parameter vectors. The purpose of this paper is to investigate the reasons leading to very different near optimum parameter vectors and to investigate the properties of the set of good parameters in high dimensional spaces. Results are discussed and conclusions are drawn
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