Conceptual hydrological model calibration using multi-objective optimization techniques over the transboundary Komadugu-Yobe basin, Lake Chad Area, West Africa

O. E. Adeyeri, P. Laux, J. Arnault, A. E. Lawin, H. Kunstmann
A B S T R A C T Study Area: The discharge of the transboundary Komadugu-Yobe Basin, Lake Chad Area, West Africa is calibrated using multi-objective optimization techniques. Study focus: The GR5J hydrological model parameters are calibrated using six optimization methods i.e. Local Optimization-Multi Start (LOMS), the Differential Evolution (DE), the Multiobjective Particle the Swarm Optimization (MPSO), the Memetic Algorithm with Local Search Chains (MALS), the Shuffled Complex
more » ... ex Evolution-Rosenbrock's function (SCE-R), and the Bayesian Markov Chain Monte Carlo (MCMC) approach. Three combined objective functions i.e. Root Mean Square Error, Nash-Sutcliffe efficiency, Kling-Gupta efficiency are applied. The calibration process is divided into two separate episodes (1974-2000 and 1980-1995) so as to ascertain the robustness of the calibration approaches. Runoff simulation results are analysed with a timefrequency wavelet transform. New hydrological insights for the region: For calibration and validation stages, all optimization methods simulate the base flow and high flow spells with a satisfactory level of accuracy. For calibration period, MCMC underestimate it by -0.07 mm/day. The performance evaluation shows that MCMC has the highest values of mean absolute error (0.28) and mean square error (0.40) while LOMS and MCMC record a low volumetric efficiency of 0.56. In all cases, the DE and the SCE-R methods perform better than others. The combination of multi-objective functions and multi-optimization techniques improve the model's parameters stability and the algorithms' optimization to represent the runoff in the basin. Each hydrological model has its constraints in terms of the number of input data, spatial variability representation, calibration parameters and duration. In particular, some hydrological models have been developed to represent a simplified representation, relationship and transformation of precipitation into runoff (Singh and Woolhiser., 2002; Narasayya et al., 2013) . These so-called rainfall-runoff models are created to characterize the physical components of a basin by assuming a simplified rainfall-runoff relationship; without explicit representation of the spatial variability in topography, vegetation and soil properties. The advantage of these models is that they require fewer input data. Additionally, they are simpler to set up and have fewer calibration parameters. As a consequence, they are widely used for operational applications (Lampert and Wu, 2015; Narasayya et al., 2013) as well as for investigating the future changes in climate and land use (Beven, 2011) . In this type of model, the parameters selection is restricted to a predefined range in order to achieve a realistic representation of the basin properties (Sorooshian and Gupta, 1995) . Furthermore, these parameters are indirectly estimated using calibration and optimization procedures ). The best model parameter sets during the calibration procedures are benchmarked on objective functions which indicate the degree of numerical agreement between basin observations and model simulations. Previous researches (e.g. Lu et al., 2013; Duan, 2003) illustrate that calibrations based on a single-objective function are effective for emphasizing a definite characteristic of a system, however, causing increasing errors in other characteristics of the system (Wagener, 2003) . In hydrological simulations, for instance, a calibration based on an objective function fine-tunes the model simulation in favour of the predetermined objective function which does not assure a better simulation with other objective function. A multi-objective calibration method seeks to address this limitation by quantifying the adjustments in maximizing or minimizing a number of objective functions, finding a representative set of the Pareto optimal solutions, as well as defining a single solution that maximizes or minimizes a specific independent preference (Gupta et al., 2009; Van Werkhoven et al., 2009) . According to Yapo et al. (1998) , multi-objective calibrations are of great advantage as it ensures desired outcomes in hydrological applications. A detailed report of the advantages of this technique is summarized in Efstratiadis and Koutsoyiannis (2010). Thenceforth, many hydrological studies have applied this technique by weighing various objective functions (Foglia et al., 2009; Li et al., 2010) , population-based search method, and Pareto set search (Bekele and Nicklow, 2007; Dumedah et al., 2010) . In similar attempts, Rakovec et al. (2016) calibrated the mesoscale Hydrologic Model (mHM) (Kumar et al., 2013) over 83 European basins using the Multi-scale Parameter Regionalization approach for improved physiographic and hydrologic regimes. Ning et al. (2015) calibrated the Hydrological Predictions for the Environment model (Lindstrom et al., 2010) over the Da River Basin of Vietnam using the Differential Evolution Markov Chain Monte Carlo (Braak, 2006) step-wise calibration method. Werth et al. (2009) applied the multiobjective calibration framework of Non-Dominated-Sorting-Genetic-Algorithm-II (Deb et al., 2002, NSGAII) to calibrate the Wa-terGAP Global Hydrology Model (Doll et al., 2003) over the Congo basin in Africa, the Amazon basin in South America, and the Mississippi basin of North America. Xie et al. (2012) calibrated the Soil and Water Assessment Tool model (Arnold and Fohrer, 2005) using the NSGAII technique to assess the total water storage variability over Sub-Saharan Africa basins. While previous studies established the advantages of using multiple-objective functions over a single criterion, they do not consider the effect of using combined multi-optimization procedures and multiple-objective functions on model parameters set. The advantage of using various optimization methods lies in its ability to assess quality phases of the optimized solutions such as their accuracies, diversities and cardinalities (Riquelme et al., 2015) . In order to reduce the errors being propagated by the use of single objective function as well as generating good optimized solutions for the model parameter sets, this study attempts to calibrate a 5-parameter daily lumped rainfall-runoff model i.e. le modèle du Génie Rural à 5 paramètres au pas de temps Journalier (GR5J) (Coron et al., 2017) over the Komadugu-Yobe Basin (KYB) in West Africa using a combined multi-optimization procedures and multiple-objective functions. A detailed description of the study area is given in Section 2. The GR5J model, the calibration and optimization methods are presented in Section 3. Results are provided in Section 4, followed by a summary and conclusion in Section 5. Study area and data
doi:10.5445/ir/1000104779 fatcat:mbwfbalcufbjbc3xhb2mutaphu