Calibration Of Conceptual Rainfall-runoff Models Research Articles

Calibration of conceptual rainfall-runoff models by selected differential evolution and particle swarm optimization variants

The performance of conceptual catchment runoff models may highly depend on the specific choice of calibration methods made by the user. Particle Swarm Optimization (PSO) and Differential Evolution (DE) are two well-known families of Evolutionary Algorithms that are widely used for calibration of hydrological and environmental models. In the present paper, five DE and five PSO optimization algorithms are compared regarding calibration of two conceptual models, namely the Swedish HBV model (Hydrologiska Byrans Vattenavdelning model) and the French GR4J model (modèle du Génie Rural à 4 paramètres Journalier) of the Kamienna catchment runoff. This catchment is located in the middle part of Poland. The main goal of the study was to find out whether DE or PSO algorithms would be better suited for calibration of conceptual rainfall-runoff models. In general, four out of five DE algorithms perform better than four out of five PSO methods, at least for the calibration data. However, one DE algorithm constantly performs very poorly, while one PSO algorithm is among the best optimizers. Large differences are observed between results obtained for calibration and validation data sets. Differences between optimization algorithms are lower for the GR4J than for the HBV model, probably because GR4J has fewer parameters to optimize than HBV.

Optimization of the Multi-Start Strategy of a Direct-Search Algorithm for the Calibration of Rainfall–Runoff Models for Water-Resource Assessment

Calibration of conceptual rainfall–runoff models (CRRM) for water-resource assessment (WRA) is a complicated task that contributes to the reliability of results obtained from catchments. In recent decades, the application of automatic calibration techniques has been frequently used because of the increasing complexity of models and the considerable time savings gained at this phase. In this work, the traditional Rosenbrock (RNB) algorithm is combined with a random sampling method and the Latin hypercube (LH) to optimize a multi-start strategy and test the efficiency in the calibration of CRRMs. Three models (the French rural-engineering-with-four-daily-parameters (GR4J) model, the Swedish Hydrological Office Water-balance Department (HBV) model and the Sacramento Soil Moisture Accounting (SAC-SMA) model) are selected for WRA at nine headwaters in Spain in zones prone to long and severe droughts. To assess the results, the University of Arizona’s shuffled complex evolution (SCE-UA) algorithm was selected as a benchmark, because, until now, it has been one of the most robust techniques used to solve calibration problems with rainfall–runoff models. This comparison shows that the traditional algorithm can find optimal solutions at least as good as the SCE-UA algorithm. In fact, with the calibration of the SAC-SMA model, the results are significantly different: The RNB algorithm found better solutions than the SCE-UA for all basins. Finally, the combination created between the LH and RNB methods is detailed thoroughly, and a sensitivity analysis of its parameters is used to define the set of optimal values for its efficient performance.

Relationship Between Calibration Time and Final Performance of Conceptual Rainfall-Runoff Models

Various methods are used in the literature for calibration of conceptual rainfall-runoff models. However, very rarely the question on the relation between the number of model runs (or function calls) and the quality of solutions found is asked. In this study two lumped conceptual rainfall-runoff models (HBV and GR4J with added snow module) are calibrated for five catchments, located in temperate climate zones of USA and Poland, by means of three modern variants of Evolutionary Computation and Swarm Intelligence optimization algorithms with four different maximum numbers of function calls set to 1000, 3000, 10,000 and 30,000. At the calibration stage, when more than 10,000 function calls is used, only marginal improvement in model performance has been found, irrespective of the catchment or calibration algorithm. For validation data, the relation between the number of function calls and model performance is even weaker, in some cases the longer calibration, the poorer modelling performance. It is also shown that the opinion on the model performance based on different popular hydrological criteria, like the Nash-Sutcliffe coefficient or the Persistence Index, may be misleading. This is because very similar, largely positive values of Nash-Sutcliffe coefficient obtained on different catchments may be accompanied by contradictory values of the Persistence Index.

Calibration of Conceptual Rainfall-Runoff Models Using Global Optimization

Parameter optimization for the conceptual rainfall-runoff (CRR) model has always been the difficult problem in hydrology since watershed hydrological model is high-dimensional and nonlinear with multimodal and nonconvex response surface and its parameters are obviously related and complementary. In the research presented here, the shuffled complex evolution (SCE-UA) global optimization method was used to calibrate the Xinanjiang (XAJ) model. We defined the ideal data and applied the method to observed data. Our results show that, in the case of ideal data, the data length did not affect the parameter optimization for the hydrological model. If the objective function was selected appropriately, the proposed method found the true parameter values. In the case of observed data, we applied the technique to different lengths of data (1, 2, and 3 years) and compared the results with ideal data. We found that errors in the data and model structure lead to significant uncertainties in the parameter optimization.

Enhancing gradient-based parameter estimation with an evolutionary approach

Traditionally, the calibration of groundwater models has depended on gradient-based local optimization methods. These methods provide a reasonable degree of success only when the objective function is smooth, second-order differentiable, and satisfies the Lipschitz's condition. For complicated and highly nonlinear objective functions it is almost impractical to satisfy these conditions simultaneously. Research in the calibration of conceptual rainfall-runoff models, has shown that global optimization methods are more successful in locating the global optimum in the region of multiple local optima. In this study, a global optimization technique, known as shuffle complex evolution (SCE), is coupled to the gradient-based Lavenberg–Marquardt algorithm (GBLM). The resultant hybrid global optimization algorithm (SCEGB) is then deployed in parallel testing with SCE and GBLM to solve several inverse problems where parameters of a nonlinear numerical groundwater flow model are estimated. Using perfect (i.e. noise-free) observation data, it is shown SCEGB and SCE are successful at identifying the global optimum and predicting all model parameters; whereas, the commonly applied GBLM fails to identify the optimum. In subsequent inverse simulations using observation data corrupted with noise, SCEGB and SCE again outperform GBLM by consistently producing more accurate parameter estimates. Finally, in all simulations the hybrid SCEGB is seen to be equally effective as SCE but computationally more efficient.

Global optimization techniques for the calibration of conceptual rainfall-runoff models

In this study we present the results of the comparison of three different algorithms: the Genetic Algorithm coupled with Sequential Quadratic Programming (GA-SQP), the Pattern Search also coupled with SQP (PS-SQP) and the Shuffled Complex Evolution (SCE-UA). The analyses were conducted using a conceptual rainfall-runoff model applied both to a single basin and to a complex basin. For both types of basin, a theoretical case without model and data errors was considered, in which the true values of the parameters are known a priori, and several real-world cases where model and data errors exist. With reference to the single basin, the SCE-UA algorithm was the most reliable while the other two algorithms gave solutions equivalent to those of the SCE-UA in the theoretical case, but in the real-world cases they showed an increasing tendency (particularly the PS-SQP) to be trapped in local minima. With reference to the complex basin, none of the three algorithms identified the exact solution in the theoretical case. However, the SCEUA was the one which systematically approximated it better than the others. In the real-world case its solutions were stable but characterized by many parameter values set at the boundary of their own range. The other two algorithms produced a very unstable set of parameters.

Comparing several genetic algorithm schemes for the calibration of conceptual rainfall-runoff models

The Genetic Algorithm (GA) is often associated with local search optimisation techniques in the calibration process of Conceptual Rainfall-Runoff Models (CRRMs) (Wang, 1991; Franchini, 1996), i.e. the GA is used for approaching the region encompassing the global solution and then its results are used as a starting point for the local optimizer in the subsequent “fine-tuning” process. However, the GA can be formulated in very many ways. This study analyses various GA structures and their robustness and efficiency. In addition, a sensitivity analysis of the various schemes to their own parameters is performed. The analysis is conducted using an 11-parameter CRRM, called A Distributed Model (ADM), applied to both a theoretical case without model and data errors and two cases of the real world in which there are both model and data errors. Finally, assuming the same role as the GA for the “Pattern Search” (PS) method in a two-step optimisation technique (Hendrickson et al., 1988), the results of the two algorithms are compared, showing that, in the calibration of the ADM, the PS may give a slightly superior performance.

Automatic calibration of conceptual rainfall-runoff models: sensitivity to calibration data

The identification of hydrologic models requires that appropriate data be selected for model calibration. In the research presented here, the shuffled complex evolution (SCE-UA) global optimization method was used to calibrate the NWSRFS-SMA conceptual rainfall-runoff flood forecasting model of the US National Weather Service, using a 40-year record of historical data. Based on 344 calibration runs using different lengths of data from different sections of the historical record, we conclude that approximately 8 years of data are required to obtain calibrations that are relatively insensitive to the period selected. Further, the reduction in parameter uncertainty is maximal when the wettest data periods on record are used. A residual analysis is used to compare the performance of the daily root mean square (DRMS) and heteroscedastic maximum likelihood error (HMLE) objective functions. The results suggest that the factor currently limiting model performance is the unavailability of strategies that explicitly account for model error during calibration.

Use of a genetic algorithm combined with a local search method for the automatic calibration of conceptual rainfall-runoff models

Abstract Wang (1991) reported that a genetic algorithm (GA), combined with a local search method, is an efficient and robust means for the calibration of conceptual rainfall-runoff models. In this article Wang's genetic algorithm has been slightly modified in order to improve its efficiency. The “optimal parameter set” produced by the GA has then been used as the starting point for a local optimization procedure based on Sequential Quadratic Programming (SQP). The purpose of this paper is to investigate the ability of the resulting algorithm, GA-SQP, to find the optimal parameter values during calibration of a conceptual rainfallrunoff (CRR) model. Two types of analysis were performed. The first refers to a theoretical case free of model and data errors, while the second refers to a real case in which the rainfall and runoff data were affected by evaluation errors. Specifically, in the synthetic data study, where the real set of parameters was known a priori, a 100% success rate was observed, and in all cases the number of objective function evaluations remained relatively limited.

Automatic calibration of conceptual rainfall-runoff models: Optimization algorithms, catchment conditions, and model structure

Automatic calibration of conceptual rainfall-runoff models: Optimization algorithms, catchment conditions, and model structure