Comparing multi-objective optimization techniques to calibrate a conceptual hydrological model using in situ runoff and daily GRACE data

Hydrological models are necessary tools for simulating the water cycle and for understanding changes in water resources. To achieve realistic model simulation results, real-world observations are used to determine model parameters within a “calibration” procedure. Optimization techniques are usually applied in the model calibration step, which assures a maximum similarity between model outputs and observations. Practical experiences of hydrological model calibration have shown that single-objective approaches might not be adequate to tune different aspects of model simulations. These limitations can be as a result of (i) using observations that do not sufficiently represent the dynamics of the water cycle, and/or (ii) due to restricted efficiency of the applied calibration techniques. To address (i), we assess how adding daily Total Water Storage (dTWS) changes derived from the Gravity Recovery And Climate Experiment (GRACE) as an extra observations, besides the traditionally used runoff data, improves calibration of a simple 4-parameter conceptual hydrological model (GR4J, in French: modèle du Génie Rural à 4 paramètres Journalier) within the Danube River Basin. As selecting a proper calibration approach (in ii) is a challenging task and might have significant influence on the quality of model simulations, for the first time, four evolutionary optimization techniques, including the Non-dominated Sorting Genetic Algorithm II (NSGA-II), the Multi-objective Particle Swarm Optimization (MPSO), the Pareto Envelope-Based Selection Algorithm II (PESA-II), and the Strength Pareto Evolutionary Algorithm II (SPEA-II) along with the Combined objective function and Genetic Algorithm (CGA) are tested to calibrate the model in (i). A number of quality measures are applied to assess cardinality, accuracy, and diversity of solutions, which include the Number of Pareto Solutions (NPS), Generation Distance (GD), Spacing (SP), and Maximum Spread (MS). Our results indicate that according to MS and SP, NSGA-II performs better than other techniques for calibrating GR4J using GRACE dTWS and in situ runoff data. Considering GD as a measure of efficiency, MPSO is found to be the best technique. CGA is found to be an efficient method, while considering the statistics of the GR4J’s 4 calibrated parameters to rank the optimization techniques. The Nash-Sutcliffe model efficiency coefficient is also used to assess the predictive power of the calibrated hydrological models, for which our results indicate satisfactory performance of the assessed calibration experiments.