Développement d'approches de calage efficaces pour les modèles hydrologiques coûteux en temps de calcul, au moyen du modèle HYDROTEL

Abstract

The calibration of hydrological models is formulated as a blackbox optimization problem; i.e. the only information available is the objective function value which can be used by the optimizer to improve the calibration process. Running a single simulation may take several minutes in the case of distributed hydrological models, and the calibration process may require thousands of model evaluations; the computational time can thus easily expand to several hours or days, which can be an issue for many operational contexts. Calibration can therefore involve significant computational time and an effective optimization approach must be chosen. Based from previous works, this research aims first to propose a new promising automatic calibration approach for computationally-intensive hydrological models. The calibration approach is applied to the distributed and computationally-intensive HYDROTEL model on three different river basins located in Québec (Canada) and is developed by combining the efficient optimization strategies of two existing algorithms: the “Dynamically Dimensioned Search” algorithm (DDS) and the “Mesh Adaptive Direct Search” algorithm (MADS). First, the global exploration ability of the DDS algorithm is able to quickly obtained parameter sets which generate a good-quality value of the objective function (difference between observed and simulated streamflows at the watershed outlet). Then, the search strategies of the MADS algorithm provides a local refinement process based on the satisfaction of optimality conditions. Five transitional features are added to adequately merge both algorithms together. Average time savings of 70% of computational time on HYDROTEL with 10 parameters and 40% on HYDROTEL with 19 parameters were achieved by the new calibration approach in comparison with other algorithms traditionally used. In addition to this important reduction in computational times, final values of the objective function are similar to those obtained with existing optimization algorithms. The second phase aims to evaluate the potential to use different surrogate models that are low-cost and representative of the calibration problems. Three possibilities to construct reduced-fidelity surrogate models from the HYDROTEL model are examined: (1) the reduction of the number of “pseudo-meteorological” stations located on the territory, (2) the reduction of the calibration time-period and (3) the reduction of the watersheds spatial discretization by decreasing the number of simulation units within the modelling, called Relatively Homogenous Hydrological Units (RHHUs). Representativeness and computational time for each type of surrogate model and for the combination of all of them are evaluated and analysed. Results show that the combination of the three types of reducedfidelity models provides high-level of representativeness and good ratios of computational time between original and surrogate models. Representativeness of the polynomial functions and the Kriging models are also analysed for two variables: the Design of Experiments (DoE)size and the parametric domain size. Results demonstrate that both types of response surface functions can very well represent short parametric domain with a minimum of 100 evaluated solutions. Finally, the last part of this study focuses on the use of the low-cost and representative surrogate models previously developed within the DDS-MADS calibration approach and a range of calibration frameworks are proposed. Calibration frameworks are assessed and compared with one another and results demonstrate that exploiting reduced-fidelity models within the DDS-MADS calibration approach decreases the overall computational time while maintaining the quality of the final solutions. The tested frameworks provide a range of tradeoffs between computational time and objective function value, which offers the users the possibility to select the appropriate framework according to their calibration objectives and optimization constraints.

Date	18 Apr 2019
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	Annie Poulin (Supervisor) & Charles Audet (Co-supervisor)