Towards a more representative parametrisation of hydrologic models via synthesizing the strengths of Particle Swarm Optimisation and Robust Parameter Estimation

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

Robust multi-objective calibration strategies – possibilities for improving flood forecasting

Process-oriented rainfall-runoff models are designed to approximate the complex hydrologic processes within a specific catchment and in particular to simulate the discharge at the catchment outlet. Most of these models exhibit a high degree of complexity and require the determination of various parameters by calibration. Recently, automatic calibration methods became popular in order to identify parameter vectors with high corresponding model performance. The model performance is often assessed by a purpose-oriented objective function. Practical experience suggests that in many situations one single objective function cannot adequately describe the model's ability to represent any aspect of the catchment's behaviour. This is regardless of whether the objective is aggregated of several criteria that measure different (possibly opposite) aspects of the system behaviour. One strategy to circumvent this problem is to define multiple objective functions and to apply a multi-objective optimisation algorithm to identify the set of Pareto optimal or non-dominated solutions. Nonetheless, there is a major disadvantage of automatic calibration procedures that understand the problem of model calibration just as the solution of an optimisation problem: due to the complex-shaped response surface, the estimated solution of the optimisation problem can result in different near-optimum parameter vectors that can lead to a very different performance on the validation data. Bárdossy and Singh (2008) studied this problem for single-objective calibration problems using the example of hydrological models and proposed a geometrical sampling approach called Robust Parameter Estimation (ROPE). This approach applies the concept of data depth in order to overcome the shortcomings of automatic calibration procedures and find a set of robust parameter vectors. Recent studies confirmed the effectivity of this method. However, all ROPE approaches published so far just identify robust model parameter vectors with respect to one single objective. The consideration of multiple objectives is just possible by aggregation. In this paper, we present an approach that combines the principles of multi-objective optimisation and depth-based sampling, entitled Multi-Objective Robust Parameter Estimation (MOROPE). It applies a multi-objective optimisation algorithm in order to identify non-dominated robust model parameter vectors. Subsequently, it samples parameter vectors with high data depth using a further developed sampling algorithm presented in Krauße and Cullmann (2012a). We study the effectivity of the proposed method using synthetical test functions and for the calibration of a distributed hydrologic model with focus on flood events in a small, pre-alpine, and fast responding catchment in Switzerland

Agile tuning method in successive steps for a river flow simulator

Abstract: Scientists and engineers continuously build models to interpret axiomatic theories or explain the reality of the universe of interest to reduce the gap between formal theory and observation in practice. We focus our work on dealing with the uncertainty of the input data of the model to improve the quality of the simulation. To reduce this error, scientist and engineering implement techniques for model tuning and they look for ways to reduce their high computational cost. This article proposes a methodology for adjusting a simulator of a complex dynamic system that models the wave translation along rivers channels, with emphasis on the reduction of computation resources. We propose a simulator calibration by using a methodology based on successive adjustment steps of the model. We based our process in a parametric simulation. The input scenarios used to run the simulator at every step were obtained in an agile way, achieving a model improvement up to 50% in the reduction of the simulated data error. These results encouraged us to extend the adjustment process over a larger domain region

Impact of modellers' decisions on hydrological a priori predictions

In practice, the catchment hydrologist is often confronted with the task of predicting discharge without having the needed records for calibration. Here, we report the discharge predictions of 10 modellers using the model of their choice for the man-made Chicken Creek catchment (6 ha, northeast Germany, Gerwin et al., 2009b) and we analyse how well they improved their prediction in three steps based on adding information prior to each following step. The modellers predicted the catchment's hydrological response in its initial phase without having access to the observed records. They used conceptually different physically based models and their modelling experience differed largely. Hence, they encountered two problems: (i) to simulate discharge for an ungauged catchment and (ii) using models that were developed for catchments, which are not in a state of landscape transformation. The prediction exercise was organized in three steps: (1) for the first prediction the modellers received a basic data set describing the catchment to a degree somewhat more complete than usually available for a priori predictions of ungauged catchments; they did not obtain information on stream flow, soil moisture, nor groundwater response and had therefore to guess the initial conditions; (2) before the second prediction they inspected the catchment on-site and discussed their first prediction attempt; (3) for their third prediction they were offered additional data by charging them pro forma with the costs for obtaining this additional information. Holländer et al. (2009) discussed the range of predictions obtained in step (1). Here, we detail the modeller's assumptions and decisions in accounting for the various processes. We document the prediction progress as well as the learning process resulting from the availability of added information. For the second and third steps, the progress in prediction quality is evaluated in relation to individual modelling experience and costs of added information. In this qualitative analysis of a statistically small number of predictions we learned (i) that soft information such as the modeller's system understanding is as important as the model itself (hard information), (ii) that the sequence of modelling steps matters (field visit, interactions between differently experienced experts, choice of model, selection of available data, and methods for parameter guessing), and (iii) that added process understanding can be as efficient as adding data for improving parameters needed to satisfy model requirements