Multi-objective calibration by combination of stochastic and gradient-like parameter generation rules – the caRamel algorithm

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.

Simulation of long-term spatiotemporal variations in regional-scale groundwater recharge: contributions of a water budget approach in cold and humid climates

“…The model was simultaneously calibrated for all the gauging stations using the automatic calibration procedure of the R package caRamel (Monteil et al, 2020) to obtain a regionalized set of parameters. Up to 5000 model calls were used, with several successive optimizations to confirm the reproducibility of the results, as recommended by Monteil et al (2020).…”

“…The model was simultaneously calibrated for all the gauging stations using the automatic calibration procedure of the R package caRamel (Monteil et al, 2020) to obtain a regionalized set of parameters. Up to 5000 model calls were used, with several successive optimizations to confirm the reproducibility of the results, as recommended by Monteil et al (2020). Model performance was assessed using the Kling-Gupta efficiency (KGE) calculated with total monthly measured and simulated total flow (KGE q tot ) as well as monthly baseflow and monthly potential GWR (KGE q base ).…”

“…The caRamel algorithm (Monteil et al, 2020), a combination of the multi-objective evolutionary annealing simplex algorithm (MEAS; Efstratiadis and Koutsoyiannis, 2008) and the non-dominated sorting genetic algorithm II (ε-NSGA-II; Reed and Devireddy, 2004), automatically calibrated the eight HB parameters to maximize KGE q tot and KGE q base values. The algorithm produces an ensemble of parameter sets (called generation) to run the model, downscales the generation to the parameter sets that optimize the objective functions, and creates a new set of parameters that produces better results.…”

Simulation of long-term spatiotemporal variations in regional-scale groundwater recharge: Contributions of a water budget approach in southern Quebec

“…The model was simultaneously calibrated for all the gauging stations using the automatic calibration procedure of the R package caRamel (Monteil et al, 2020) to obtain a regionalized set of parameters. The eight HB parameters were optimized for each gauging station, grouped by river watershed to save computational time (from 51 individual optimizations to eight grouped optimizations), and averaged over the study area using the normalized density of stations per group (number of stations per km 2 ) as weights.…”

“…The caRamel algorithm (Monteil et al, 2020), a combination of the multi-objective evolutionary annealing simplex algorithm (MEAS; Efstratiadis and Koutsoyiannis, 2008) and the non-dominated sorting genetic algorithm II (ε-NSGA-II; Reed and Devireddy, 2004), automatically calibrated the eight HB parameters to maximize KGEqtot and KGEqbase values. The algorithm produces an ensemble of parameter sets (called generation) to run the model, downscales the generation to the parameter sets that optimize the objective functions, and creates a new set of parameters that produces better results.…”