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

2012 ◽  
Vol 16 (10) ◽  
pp. 3579-3606 ◽  
Author(s):  
T. Krauße ◽  
J. Cullmann ◽  
P. Saile ◽  
G. H. Schmitz
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Model Performance ◽  
Data Depth ◽  
Automatic Calibration ◽  
Multi Objective ◽  
Robust Model ◽  
Robust Parameter ◽  
Robust Parameter Estimation ◽  
Single Objective

Abstract. 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.

scholarly journals Robust multi-objective calibration strategies – chances for improving flood forecasting

2011 ◽  
Vol 8 (2) ◽  
pp. 3693-3741 ◽  
Author(s):  
T. Krauße ◽  
J. Cullmann ◽  
P. Saile ◽  
G. H. Schmitz
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Particle Swarm ◽  
Model Performance ◽  
Data Depth ◽  
Particle Swarm Optimisation ◽  
Multi Objective ◽  
Optimisation Algorithm ◽  
Robust Parameter ◽  
Single Objective

Abstract. 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 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. One possible approach to estimate the Pareto set effectively and efficiently is the particle swarm optimisation (PSO). It has already been successfully applied in various other fields and has been reported to show effective and efficient performance. Krauße and Cullmann (2011b) presented a method entitled ROPEPSO which merges the strengths of PSO and data depth measures in order to identify robust parameter vectors for hydrological models. In this paper we present a multi-objective parameter estimation algorithm, entitled the Multi-Objective Robust Particle Swarm Parameter Estimation (MO-ROPE). The algorithm is a further development of the previously mentioned single-objective ROPEPSO approach. It applies a newly developed multi-objective particle swarm optimisation algorithm in order to identify non-dominated robust model parameter vectors. Subsequently it samples robust parameter vectors by the application of data depth metrics. In a preliminary assessment MO-PSO-GA is compared with other multi-objective optimisation algorithms. In the frame of a real world case study MO-ROPE is applied identifying robust parameter vectors of a distributed hydrological model with focus on flood events in a small, pre-alpine, and fast responding catchment in Switzerland. The method is compared with existing robust parameter estimation methods.

scholarly journals Towards a more representative parametrisation of hydrological models via synthesizing the strengths of particle swarm optimisation and robust parameter estimation

2011 ◽  
Vol 8 (2) ◽  
pp. 2373-2422 ◽  
Author(s):  
T. Krauße ◽  
J. Cullmann
Keyword(s):  
Monte Carlo ◽  
Parameter Estimation ◽  
Hydrological Model ◽  
Data Depth ◽  
Hydrological Models ◽  
Time Step ◽  
Good Parameter ◽  
Robust Parameter ◽  
Robust Parameter Estimation

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. In particular methods which understand the estimation of hydrological 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 proposal and applied it for the calibration of a conceptual rainfall-runoff model with daily time step. Krauße and Cullmann (2011) further developed this method and applied it in a case study to calibrate a process oriented hydrological model with hourly time step focussing on flood events in a fast responding catchment. The results of both studies showed the potential of the application of the principle of data depth. However, also the weak point of the presented approach got obvious. The algorithm identifies a set of model parameter vectors with high model performance and subsequently generates a set of parameter vectors with high data depth with respect to the first set. These both steps are repeated iteratively until a stopping criterion is met. In the first step the estimation of the good parameter vectors is based on the Monte Carlo method. The major shortcoming of this method is that it is strongly dependent on a high number of samples exponentially growing with the dimensionality of the problem. In this paper we present another robust parameter estimation strategy which applies an approved search strategy for high-dimensional parameter spaces, the particle swarm optimisation in order to identify a set of good parameter vectors with given uncertainty bounds. The generation of deep parameters is according to Krauße and Cullmann (2011). The method was compared to the Monte Carlo based robust parameter estimation algorithm on the example of a case study in Krauße and Cullmann (2011) to calibrate the process-oriented distributed hydrological model focussing for flood forecasting in a small catchment characterised by extreme process dynamics. In a second case study the comparison is repeated on a problem with higher dimensionality considering further parameters of the soil module.

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

2011 ◽  
Vol 8 (2) ◽  
pp. 2423-2476 ◽  
Author(s):  
T. Krauße ◽  
J. Cullmann
Keyword(s):  
Monte Carlo ◽  
Parameter Estimation ◽  
Hydrological Model ◽  
Flood Forecasting ◽  
Data Depth ◽  
Mcmc Methods ◽  
Model Parameters ◽  
Robust Parameter ◽  
Robust Parameter Estimation ◽  
Optimisation Algorithms

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 (AROPEMC). The AROPEMC algorithm is a modified version of the original robust parameter estimation algorithm ROPEMC developed by Bárdossy and Singh (2008). AROPEMC 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 AROPEMC 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.

scholarly journals Searching for an optimized single-objective function matching multiple objectives with automatic calibration of hydrological models

2016 ◽  
Author(s):  
Fuqiang Tian ◽  
Yu Sun ◽  
Hongchang Hu ◽  
Hongyi Li
Keyword(s):  
Objective Function ◽  
Power Function ◽  
Automatic Calibration ◽  
Efficiency Coefficient ◽  
Hydrological Models ◽  
Objective Functions ◽  
Multi Objective ◽  
Hydrological Variable ◽  
Flow Part ◽  
Single Objective

Abstract. In the calibration of hydrological models, evaluation criteria are explicitly and quantitatively defined as single- or multi-objective functions when utilizing automatic calibration approaches. In most previous studies, there is a general opinion that no single-objective function can represent all of the important characteristics of even one specific kind of hydrological variable (e.g., streamflow). Thus hydrologists must turn to multi-objective calibration. In this study, we demonstrated that an optimized single-objective function can compromise multi-response modes (i.e., multi-objective functions) of the hydrograph, which is defined as summation of a power function of the absolute error between observed and simulated streamflow with the exponent of power function optimized for specific watersheds. The new objective function was applied to 196 model parameter estimation experiment (MOPEX) watersheds across the eastern United States using the semi-distributed Xinanjiang hydrological model. The optimized exponent value for each watershed was obtained by targeting four popular objective functions focusing on peak flows, low flows, water balance, and flashiness, respectively. The results showed that the optimized single-objective function can achieve a better hydrograph simulation compared to the traditional single-objective function Nash-Sutcliffe efficiency coefficient for most watersheds, and balance high flow part and low flow part of the hydrograph without substantial differences compared to multi-objective calibration. The proposed optimal single-objective function can be practically adopted in the hydrological modeling if the optimal exponent value could be determined a priori according to hydrological/climatic/landscape characteristics in a specific watershed. This is, however, left for future study.

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

2012 ◽  
Vol 16 (2) ◽  
pp. 603-629 ◽  
Author(s):  
T. Krauße ◽  
J. Cullmann
Keyword(s):  
Parameter Estimation ◽  
Particle Swarm ◽  
Hydrologic Model ◽  
Data Depth ◽  
Particle Swarm Optimisation ◽  
Model Parameters ◽  
Calibration Data ◽  
Time Step ◽  
Robust Parameter ◽  
Robust Parameter Estimation

Abstract. 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.

Development of a Stepped Calibration Approach for XAJ Hydrological Model

2013 ◽  
Vol 405-408 ◽  
pp. 2222-2225
Author(s):  
Qian Li ◽  
Wei Min Bao ◽  
Jing Lin Qian
Keyword(s):  
Root Mean Square Error ◽  
Objective Function ◽  
Traditional Method ◽  
Hydrological Model ◽  
Model Performance ◽  
Layer By Layer ◽  
Mean Square ◽  
Objective Functions ◽  
Single Objective ◽  
Calibration Approach

This paper discusses the conceptual stepped calibration approach (SCA) which has been developed for the Xinanjiang (XAJ) model. Multi-layer and multi-objective functions which can make optimization work simpler and more effective are introduced in this procedure. In all eight parameters were considered, they were divided into four layers according to the structure of XAJ model, and then calibrated layer by layer. The SCA procedure tends to improve the performance of the traditional method of calibration (thus, using a single objective function, such as root mean square error RMSE). The compared results demonstrate that the SCA yield better model performance than RMSE.

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