Comparing Techniques of Rosenbrock, GA, URS and SCE-UA Optimization to Determine the Parameters of SIMHYD Model to Simulate Discharge Flow

Abstract
The optimization of conceptual rainfall- runoff model parameters is important in calibration whose goal is determining the values of the model parameters providing the best fit between observed and estimated flows data. In this research, the performance of probabilistic optimization techniques was studied for calibrating the SIMHYD model in Khorramabad watershed with the area of 2467 square kilometers. These techniques for calibration are consist of genetic algorithms (GA), Shuffled Complex Evolution method developed at the University of Arizona (SCE-UA), Uniform Random Sampling (URS) and Rosenbrock algorithm. The results showed that changing the optimization algorithms has an important effect on the performance of conceptual model. So that, the values of Nash-Sutcliff (NS) coefficient for used algorithms were derived as 0.73, 0.72, 0.70 and 0.75, respectively. Compared with the others, the Rosenbrock algorithm had more performance, thus this algorithm was selected to simulate SIMHYD model for calibration during the period, from 2004 to 2008 and for validation during the period from 2009 to 2010. The values of coefficients NS, RMSE and R in calibration period were derived 0.73, 0.66 and 0.86, respectively and in validation period, they were 0.68, 0.80 and 0.83, respectively. The results showed that optimization algorithms in simulating SIMHYD model had high accuracy to identify the parameter values and they are suitable for the study area. Therefore using hydrological models and selecting the appropriate optimization techniques, we could simulate the watersheds flows with highly accuracy.
Extended Abstract
1-Introduction
The optimization of conceptual rainfall- runoff model parameters is important in calibration whose goal is determining the values of the model parameters providing the best fit between observed and estimated flows data. The evidence from previous conceptual rainfall runoff model calibration studies has indicated that the calibration problem should be solved by global optimization techniques (e.g., Johnston and Pilgrim, 1976; Sorooshian and Gupta, 1985). A large percentage of the rainfall volume in different areas of the country is transformed to surface runoff by the factors such as structure of geology, vegetation, land use, slope and the catchment shape. Therefore, the simulation of runoff in an area is influenced by several factors. Conceptual models are often preferred to other hydrologic models including models that are based on physics. In addition to providing acceptable responses, conceptual models need less computational efforts and input data than physical models. Depending on the purpose of the model implementation, these models have several parameters, which represent the catchment’s characteristics. Estimating the amount of runoff generated in a catchment as well as predicting numerous hydrological processes that is associated with certain complexity in some areas, is one the key issues in hydrological studies, which the required basis information for most of water resources projects, watershed projects as well as many related projects is established by obtaining these data. Thus, estimating runoff and necessary predictions for hydrological issues as well as a proper management of natural resources are very important.
2-Materials and Methods
The Khorramabad watershed with 2467 square kilometers area and 339 (km) perimeters is a sub watershed of Kharkhe watershed that located in the center of Lorestan province. This watershed is located in 48° 21' to 49° 8' east longitude and 33° 13' to 33° 44' north latitude geography range in the west part of the country.  In this area minimum elevation is 1102 (m) and the maximum elevation is 2545 (m) and with 405 average precipitation and 15 (C°) temperature have semi-arid climate.
This study investigated the performance of fore probabilistic optimization techniques for calibration the SIMHYD model in Khorramabad watershed with 2467 square kilometers. This techniques for calibration are consist of genetic algorithms (GA), Shuffled complex evolution method developed at the University of Arizona (SCE-UA).
Evaluation of model efficiency
To evaluate the model efficiency and to limit the answers to only one answer, sometimes it is needed to use several statistical criteria (Gassman et al, 2007; Santhi et al, 2001). In this research the SIMHYD model performance was used for assessment of NS, R, and RMSE Coefficients. RCoefficient (Correlation Coefficient) indicated that regression line between observation and simulation variable is near to maximum correlation between this tow Series that its ranges is between 0-1. The NS coefficient shows a relative different between observation and simulation value and the value of this factor is between -∞-1 (Moriasi et al, 2007). RMSE coefficient is different between simulation and observation value in which the little value of this coefficient shows high performance of model and if the value of this model increases the model performance will decreases.
3-Results and Discussion
The result showed that changing the optimization algorithms has important effect on performance of conceptual model. So that the value of the Nash-Sutcliff (NS) is used for algorithms performance in optimizing parameters that in GA, SCE-UA, URS and Rosenbrock algorithms was obtained 0.73, 0.72, 0.70 and 0.75 respectively. The URS algorithms with 0.70 NS coefficient in compare with other algorithms has less performance in determine value of parameters and the Rosenbrock algorithms with 0.75 NS coefficient have the more performance. Thus this algorithms for simulation SIMHYD model during 2004-2008 was calibration and in 2009-2010 was donned validation. Coefficient NS, RMSE and R² in calibration period was yield 0.73, 0.66 and 0.75 respectively and in validation period was yield 0.68, 0.80 and 0.69 respectively.
4- Conclusion
SIMHYD model is one of the conceptual hydrologic models in which the flow with daily time step was used for simulation. Various studies have used different methods to optimize parameters. The result showed that optimization algorithms in SIMHYD model have high performance to identify parameter values. In fact, the efficiency of the rainfall-runoff models depends on the accuracy and calibration parameters. In this study four optimization algorithms for the simulation of flow and calibration model parameters were compared in Khorramabad Basin. Rosenbrock algorithm between the used optimization algorithms have the highest accuracy. So the periods of this optimization algorithm was used to simulate. The results showed that SIMHYD model has suitable performance for simulation runoff during the time of the studies and this model can be used for simulation runoff in Khorramabad watershed.