Evaluation of the basin hydrological response to the instantaneous storm process using the concepts of MATLAB software simulink control system

Introduction
Rainfall-runoff modeling is one of the most important components of hydrological processes in water resources management and accurate estimation of runoff and river flow in the short and long term can be of great help to various sectors of water engineering. In several types of rainfall-runoff models, the unit hydrograph methods are still a useful tool for flood estimation in many, except non-gauged, basins. The unit hydrograph is the same as the unit pulse response function of a linear hydrological system. The tank model is one of the hydrological models for analyzing river flow characteristics. In hydrological analysis, simulation models are often used to describe and predict basin response to rainfall events based on mathematical and physical knowledge. In this article, using the concept of linear system theory, the pulse response functions of the runoff components (surface runoff and base flow) using the reservoir model for several flood events related to the two Navrood basin in Gillan province and Liqvan basin in the East Azerbaijan province has been extracted. Since Simulink can schematically show the dynamic relationship between hydrological components such as rainfall, runoff, storage, evapotranspiration, and runoff, it can be useful for rainfall-runoff modeling. Therefore, Modeling is done in the Simulink MATLAB environment. The modular design and block library can help users focus on hydrological analysis, including modeling strategy development, parameter estimation, and model application.
 
Materials and Methods
In the present study, to evaluate the capability of the tank model in different climates, the model has been implemented for two regions with dry and wet climates to evaluate the effectiveness of the tank model by comparing the results. Therefore, the Navrood representative basin in Gilan province was selected for a wet climate, and the Liqvan representative basin in East Azerbaijan province for a dry and semi-arid climate. The response of the entire basin to the rainfall that fell on its surface has been determined using the conceptual model of the tank. In order to extract the unit pulse response function for the runoff caused by precipitation, the model of three tanks in series with holes on the side and bottom has been used to show the types of currents prevailing in the process of forming runoff. The internal dependence of reservoirs is described using exponential functions of model parameters. Estimating the model parameters was performed using the cluttered evolution optimization method or SCE-UA for short, a conceptual optimization method. In addition, to extract unit pulse response functions and evaluate the model's efficiency in predicting flood events, it was tried to select events that have rained in the entire basin and correspond to flood events in terms of occurrence time.
 
Results and Discussion
The results obtained in this research showed that the tank model provides good results in estimating the peak discharges and the time to reach the peak discharges in the two representative basins of Navrood and Liqvan with two different climates. The parameters of the model, which actually reflect the geomorphological characteristics of the basin, are almost constant, and only the changes in soil moisture storage are variable in the runoff calculations. Response functions as exponential functions of model parameters have simulated the different roles of flow components (quick surface, quick subsurface, delayed subsurface, and underground flow) in relation to the precipitation process. As can be deduced from the results obtained for the Navrood basin, the slow runoff accounts for a major part of the total runoff in the falling limb of the hydrograph. The relations extracted for the response functions of the unit pulse for ru as a unit input that happened in the duration of ∆t have been obtained parametrically, therefore, for different combinations of ru and ∆t, several unit pulse response functions can be extracted. Examining the parameters of the model obtained from the SCE-UA algorithm shows that due to the large value of the b₂ parameter compared to other parameters, a major part of the volley losses is penetration losses. In fact, the high permeability of the surface layers of the soil justifies the high value of the b₁ parameter compared to other parameters.
 
Conclusion
The performance results of the tank model showed that the model has a relatively good capability in predicting the runoff affected by the rainstorm. The comparison of the computational and observed hydrographs shows that the mentioned values have a good correlation. According to the results, it can be seen that the fast runoff, which usually appears in the form of surface flow and waterways in the basin, occupies a significant part of the entire flood hydrograph during the flooding process, and in terms of durability has a shorter duration than slow runoff. Slow runoff hydrograph is slowly affected by precipitation during the flooding process, but in terms of durability, it has a longer duration.