Identification of hydrological model parameters for flood forecasting using data depth measures

Abstract. The development of methods for estimating the parameters of hydrological models considering uncertainties has been of high interest in hydrological research over the last years. Besides the very popular Markov Chain Monte Carlo (MCMC) methods which estimate the uncertainty of model parameters in the settings of a Bayesian framework, the development of depth based sampling methods, also entitled robust parameter estimation (ROPE), have attracted an increasing research interest. These methods understand the estimation of model parameters as a geometric search of a set of robust performing parameter vectors by application of the concept of data depth. Recent studies showed that the parameter vectors estimated by depth based sampling perform more robust in validation. One major advantage of this kind of approach over the MCMC methods is that the formulation of a likelihood function within a Bayesian uncertainty framework gets obsolete and arbitrary purpose-oriented performance criteria defined by the user can be integrated without any further complications. In this paper we present an advanced ROPE method entitled the Advanced Robust Parameter Estimation by Monte Carlo algorithm (AROPE_MC). The AROPE_MC algorithm is a modified version of the original robust parameter estimation algorithm ROPE_MC developed by Bárdossy and Singh (2008). AROPE_MC performs by merging iterative Monte Carlo simulations, identifying well performing parameter vectors, the sampling of robust parameter vectors according to the principle of data depth and the application of a well-founded stopping criterion applied in supervised machine learning. The principals of the algorithm are illustrated by means of the Rosenbrock's and Rastrigin's function, two well known performance benchmarks for optimisation algorithms. Two case studies demonstrate the advantage of AROPE_MC compared to state of the art global optimisation algorithms. A distributed process-oriented hydrological model is calibrated and validated for flood forecasting in a small catchment characterised by extreme process dynamics.