Abstract
Abstract. Environmental modelling is complex, and models often require the calibration of several parameters that are not able to be directly evaluated from a physical quantity or field measurement. Multi-objective calibration has many advantages such as adding constraints in a poorly constrained problem or finding a compromise between different objectives by defining a set of optimal parameters. The caRamel optimizer has been developed to meet the requirement for an automatic calibration procedure that delivers not just one but a family of parameter sets that are optimal with regard to a multi-objective target. The idea behind caRamel is to rely on stochastic rules while also allowing more “local” mechanisms, such as the extrapolation along vectors in the parameter space. The caRamel algorithm is a hybrid of the multi-objective evolutionary annealing simplex (MEAS) method and the non-dominated sorting genetic algorithm II (ε-NSGA-II). It was initially developed for calibrating hydrological models but can be used for any environmental model. The caRamel algorithm is well adapted to complex modelling. The comparison with other optimizers in hydrological case studies (i.e. NSGA-II and MEAS) confirms the quality of the algorithm. An R package, caRamel, has been designed to easily implement this multi-objective algorithm optimizer in the R environment.
Highlights
Environmental modelling is complex, and models often require the calibration of many parameters that cannot be directly estimated from a physical quantity or a field measurement
This paper aims to describe the principles of the caRamel algorithm via an analysis of its results when used for the parametrization of hydrological models
Four aspects are considered with respect to the results of the case studies: the shape of the final Pareto fronts, the dynamics of the optimizations, the distribution of the calibrated parameters and the consequences of the latter on simulated discharges for the hydrological case studies
Summary
Environmental modelling is complex, and models often require the calibration of many parameters that cannot be directly estimated from a physical quantity or a field measurement. As models’ outputs exhibit errors whose statistical structure may be difficult to characterize precisely, it is frequently necessary to use various objectives to evaluate the modelling performance. Efstratiadis and Koutsoyiannis (2010) list other advantages of multi-objective calibration such as ensuring parsimony between the number of objectives and the parameters to optimize, fitting distributed responses of models on multiple measurements, recognizing the uncertainties and structural errors related to the model configuration and the parameter estimation procedure, and handling objectives that have contradictory performance. Evolutionary algorithms have been widely used to explore the Pareto-optimal front in multi-objective optimization problems that are too complex to be solved by descent methods with classical aggregation approaches.
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