Usage of Differential Evolution Algorithm in the Calibration of Parametric Rainfall-Runoff Modeling

Introduction

The parametric rainfall-runoff models are usually based on water budget equivalents developed by Thornthwaite and Mather (1955). These models could be used in a variety of areas, such as explaining precipitation-flow relationships of basins, deriving flows in gauged and ungauged catchments, modeling groundwater flow, projecting future streamflows under climate change scenarios, determining land use or effects of climate change on flows.

These models convert the precipitation inputs to the flows of the basin outlet with conceptualizing the hydrological components of the basin as evapotranspiration, infiltration, percolation, baseflow, and so on. When the internal structures of the parametric rainfall-runoff models are examined, it is seen that the models are composed of the hydrological processes transformed into conceptualized by means of the related parameters (Xu & Singh, 1986). The parameters integrated at the modeling phase could be the physical parameters (like roughness, basin area, land slope, etc.) measured in the basins or not measured directly so gaining from the conceptualization theory (Singh & Frevert, 2002). The values of all defined parameters like maximum soil moisture storage, base flow coefficient are required to be optimally determined. The optimization process of these parameters is called calibration in hydrology concept. In practice, calibrated parameters need to be also verified with other dataset belonged to the basin.

As the number of parameters utilized in the conceptualization of hydrological processes increases, the degrees of freedom of the models rise as well, and thus the calibration of the model parameters becomes more complicated. Therefore, this situation is not preferred in hydrological applications (Gan, Dlamini, & Biftu, 1997, Butts, Payne, Kristensen, & Madsen, 2004, Thorsten & Gupta, 2005). Hydrologic model calibration studies were firstly carried out with applying to the Newton based classical methods. The studies presented by Gupta and Sorooshian (1985) and Hendrickson et al. (1988) could be shown in this context. In recent years, researchers started to investigate the heuristic algorithms since classical optimization methods are sometimes insufficient at parameter estimation. Within the scope of meta-heuristic methods, firstly, calibration studies were performed with genetic algorithm (GA). Wang (1991) calibrated a seven parameter hydrologic model with GA and obtained very consistent results. Similarly, Wang (1997) implemented a GA application for different basins by adding a groundwater storage component to the hydrological model. Cheng et al. (2006) used the GA in the calibration of the Xinanjiang model which is such an intensive hydrological model and obtained very qualified results. Another calibration application of the Xinanjiang model is presented by Jiang et al. (2010). In their work, it is emphasized that the modified particle swarm optimization (PSO) algorithm based on hybrid style is superior to the standard particle swarm optimization algorithm. Duan et al. (1992) proposed an algorithm named shuffled complex evolution (SCE) for hydrological model calibration and examined the performance on the conceptual hydrological model named SIXPAR. According to findings presented in their paper, it is stated that this method is one of effective global optimization strategies. Cooper et al. (1997) calibrated the TANK hydrological model using GA, SCE and Annealing Simulation (SA) algorithms and tested the ability of the algorithms to produce global results. A similar comparison could be found in Zhang et al. (2009). In their work, they tested the performance of the Soil and Water Assessment Tool (SWAT) model on four basins and stated that the PSO algorithm is very practical in the calibration process. In a study prepared by Turan and Dogan (2015), hunting search, artificial bee colony and firefly algorithms were utilized for calibration of GR4J, GR2M conceptual hydrological models and the efficiency of the methods on the optimization problem were investigated by evaluating data from different observation stations. According to their results, artificial bee colony method is superior to others in calibration of GR2M model although hunting method results for GR4J model were pertinent. Arsenault et al. (2013) used ten different stochastic optimization methods for calibration of three hydrologic conceptual models. As a result of the study, the adaptive simulated annealing algorithm is the most suitable method among the compared methods implemented in their study.