Application of Cross Wavelet - Kalman Filter and GIUH Methods in Modeling of rainfall-Runoff Events

The existence of high uncertainty and the nonlinearity of rainfall and runoff relationships signalize the vacancy of many studies in this direction. The present study is conducted with the aim of simulating and predicting the watershed’s behavior based on the recognition of a part of the relationships prevailing on this complex system. In this study, Cross wavelet transform methods, Kalman Filter and Linear Programming (KF-LP_CW) were used to analysis of 9 compound events of rainfall and runoff in the Sufi Chai watershed with about 250.65 km2 area. Then, to compare the performance of this method, the results were compared with geomorphologic unit hydrograph combination with Cross wavelet (GIUH-CW) and geomorphologic unit hydrograph based on Nash models combination with Cross wavelet (GIUH-Nash-CW). Considering the satisfactory performance of all three models, the final performance of these methods was finally discussed using the evaluation criteria used in the research. Results showed that the KF-LP_CW method simulated the compound events in the calibration and validation stage with a mean square error (MSE) of 2.47 and 3.2, respectively. In the case of time to peak, the mean average relative error (MARE) for the three studied methods was 0.05 and 0.037 for the calibration and validation stages, respectively. The same criteria for peak discharge and base time were 0.07 and 0.06 respectively for the two calibration stages, and 0.18 and 0.07 in the two validation stages. This indicates better performance of the methods in the estimation of time to peak, base time, and peak discharge, respectively.