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

Abstract

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.