The development of methods for estimating the parameters of hydrologic models considering uncertainties has been of high interest in hydrologic research over the last years. In particular methods which understand the estimation of hydrologic model parameters as a geometric search of a set of robust performing parameter vectors by application of the concept of data depth found growing research interest. Bárdossy and Singh (2008) presented a first Robust Parameter Estimation Method (ROPE) and applied it for the calibration of a conceptual rainfall-runoff model with daily time step. The basic idea of this algorithm is to identify a set of model parameter vectors with high model performance called good parameters and subsequently generate a set of parameter vectors with high data depth with respect to the first set. Both steps are repeated iteratively until a stopping criterion is met. The results estimated in this case study show the high potential of the principle of data depth to be used for the estimation of hydrologic model parameters. In this paper we present some further developments that address the most important shortcomings of the original ROPE approach. We developed a stratified depth based sampling approach that improves the sampling from non-elliptic and multi-modal distributions. It provides a higher efficiency for the sampling of deep points in parameter spaces with higher dimensionality. Another modification addresses the problem of a too strong shrinking of the estimated set of robust parameter vectors that might lead to overfitting for model calibration with a small amount of calibration data. This contradicts the principle of robustness. Therefore, we suggest to split the available calibration data into two sets and use one set to control the overfitting. All modifications were implemented into a further developed ROPE approach that is called Advanced Robust Parameter Estimation (AROPE). However, in this approach the estimation of the good parameters is still based on an ineffective Monte Carlo approach. Therefore we developed another approach called ROPE with Particle Swarm Optimisation (ROPE-PSO) that substitutes the Monte Carlo approach with a more effective and efficient approach based on Particle Swarm Optimisation. Two case studies demonstrate the improvements of the developed algorithms when compared with the first ROPE approach and two other classical optimisation approaches calibrating a process oriented hydrologic model with hourly time step. The focus of both case studies is on modelling flood events in a small catchment characterised by extreme process dynamics. The calibration problem was repeated with higher dimensionality considering the uncertainty in the soil hydraulic parameters and another conceptual parameter of the soil module. We discuss the estimated results and propose further possibilities in order to apply ROPE as a well-founded parameter estimation and uncertainty analysis tool.
Krauße, T., & Cullmann, J. (2012). Towards a more representative parametrisation of hydrologic models via synthesizing the strengths of Particle Swarm Optimisation and Robust Parameter Estimation. Hydrology and Earth System Sciences, 16(2), 603–629. https://doi.org/10.5194/hess-16-603-2012