Simulation of Rainfall - Runoff Events by Applying Phase Differences Diagrams and Correcting Effective Rainfall Components

   The conversion of rainfall to runoff in basins includes nonlinear relations between the complex interactions of various hydrological processes. In this study, without considering of predetermined structure, relationship between input and output system was derived individually from the nature of the data recorded. Also, the phase difference occurred between rainfall and runoff signals using cross-wavelet transform analysis. Then phase difference diagram was plotted for the single and compound events of Lighvan basin. By applying these phases at the time of the rainfall signals, all errors resulting from considering average losses in basin was minimized that in this study was introduced as "minimum error time position"(METP). Also, discharge forecasting for basin was carried out by Kalman filter model and optimization in Lighvan basin state space, using calibration step events. By applying this phase difference to effective rainfall components, the error resulting from the considering of average infiltration losses and φ index decreases to the minimum. Also, using the linear programming optimization method, the unit hydrograph for Lighvan basin was used as Kalman filter measurement model. The results showed that by applying the phases difference between rainfall and runoff signals and integration with Kalman filtering and linear programming (KF-LP-CW), the corrected Nash-Sutcliff coefficient were obtained 0.94 in both Calibration and verification steps. These values were obtained 0.63 and 0.68 in calibration and validation steps respectively, as compared to the state that phase difference was not applied (KF-LP method). Therefore, in this study, significant improvement was observed with the application of phase differences in effective precipitation components.