Document Type : Research Article

**Authors**

Civil Engineering Department, Ferdowsi university

**Abstract**

Introduction: Understanding hydrological phenomena is essential for the optimal use of water resources. Surface runoff is an important part of the hydrological cycle. Accurate runoff estimation can make a significant role in water engineering and the proper utilization of resources for the various uses of agriculture, drinking, hydropower and the environment. Therefore, the use and development of accurate and reliable methods to model the runoff of the catchments are essential. One of the new methods of runoff calculations is cellular automata. Cellular automata is a fundamental method for simulating complex systems.

Methodology: In cellular automata, the lattice space is divided into a number of cells and creates a cellular space (Fig2). A set of cells adjacent to the central cell is called a neighborhood (Fig1). In the runoff production process, the cell state is the water level, which is the sum of the cell height and water depth. The height of the cell is determined from the digital elevation model and the determination of water depth is controlled by the effective precipitation at the present time step and the balance between inlet and outlet flow at the last time step. The transition rules in the cellular automata model determine the behavior of cells at different time steps and define the future state of the cell. The first transition rule determines which neighboring cell can get water from the central cell at each time step (Fig3). The second transition rule is used to calculate the amount of flow to neighboring cells, in which the Manning equation is used. The first and second transition rule applies to all cells at each time step and as a result, the output flow from each central cell to its neighbors is determined. In the general view, each central cell is a neighbor of other cells, as a result, a third rule must be used for calculating the total flow for each cell. The evaluation of the cellular automata model is performed using the statistical indicators of correlation coefficient and root mean square error and Nash-Sutcliffe efficiency coefficient.

Results and Discussion: First, the runoff is simulated on a uniform rectangular surface and the results of the cellular automata model are compared with the results of the Akan analytical solution. In order to evaluate the efficiency and accuracy of the cellular automata, the statistical parameters of the models were calculated. The results showed that the cellular automata model has high accuracy and efficiency (Fig 5). Then runoff in the Con catchment is simulated. This catchment is located in the northwest of Spain. (Fig 6). The results showed that the cellular automata model has been able to simulate runoff well in the catchment surface (Fig 7). At the outlet, the discharge is calculated based on the cellular automata and compared with the observed discharge. The results of the cellular automata model are shown with three different time steps (Fig 8). So far, various mathematical models for rainfall-runoff estimation have been proposed. In integrated models, the whole catchment is considered as a unit. These models have a simple structure and appropriate computation time, but are accompanied by many assumptions and the spatial distribution of variables is not considered. Therefore, integrated models are not suitable for large catchments. In semi-distributed models, the catchment is divided into a number of sub-catchments. In these models, important features of the catchment are shown, but for each sub-basin, moderate data is considered and the exact spatial distribution of data is not considered. In distribution models, spatial distribution data is considered, but the time required for computation and modeling is high. Therefore, it seems necessary to develop methods that have a simple structure and high accuracy at the same time. Due to the accuracy of the results and the ability to access the required information anywhere in the catchment, the cellular automata model can be used to predict runoff.

Conclusion: The results showed that the cellular automata model has a high accuracy compared to the Akan analytical solution. Also, in simulating the runoff of the con catchment, the runoff network at the catchment surface was well simulated. Comparing the computational discharge results from the cellular automata model and observational data, the values of the correlation coefficient, mean the square root of error and Nash-Sutcliffe coefficient were 0.99, 0.11 and 0.97. As the result, due to the accuracy of the results and the ease of implementation, the cellular automation model can be used to predict runoff in catchment without data and reliable results can be achieved.

Methodology: In cellular automata, the lattice space is divided into a number of cells and creates a cellular space (Fig2). A set of cells adjacent to the central cell is called a neighborhood (Fig1). In the runoff production process, the cell state is the water level, which is the sum of the cell height and water depth. The height of the cell is determined from the digital elevation model and the determination of water depth is controlled by the effective precipitation at the present time step and the balance between inlet and outlet flow at the last time step. The transition rules in the cellular automata model determine the behavior of cells at different time steps and define the future state of the cell. The first transition rule determines which neighboring cell can get water from the central cell at each time step (Fig3). The second transition rule is used to calculate the amount of flow to neighboring cells, in which the Manning equation is used. The first and second transition rule applies to all cells at each time step and as a result, the output flow from each central cell to its neighbors is determined. In the general view, each central cell is a neighbor of other cells, as a result, a third rule must be used for calculating the total flow for each cell. The evaluation of the cellular automata model is performed using the statistical indicators of correlation coefficient and root mean square error and Nash-Sutcliffe efficiency coefficient.

Results and Discussion: First, the runoff is simulated on a uniform rectangular surface and the results of the cellular automata model are compared with the results of the Akan analytical solution. In order to evaluate the efficiency and accuracy of the cellular automata, the statistical parameters of the models were calculated. The results showed that the cellular automata model has high accuracy and efficiency (Fig 5). Then runoff in the Con catchment is simulated. This catchment is located in the northwest of Spain. (Fig 6). The results showed that the cellular automata model has been able to simulate runoff well in the catchment surface (Fig 7). At the outlet, the discharge is calculated based on the cellular automata and compared with the observed discharge. The results of the cellular automata model are shown with three different time steps (Fig 8). So far, various mathematical models for rainfall-runoff estimation have been proposed. In integrated models, the whole catchment is considered as a unit. These models have a simple structure and appropriate computation time, but are accompanied by many assumptions and the spatial distribution of variables is not considered. Therefore, integrated models are not suitable for large catchments. In semi-distributed models, the catchment is divided into a number of sub-catchments. In these models, important features of the catchment are shown, but for each sub-basin, moderate data is considered and the exact spatial distribution of data is not considered. In distribution models, spatial distribution data is considered, but the time required for computation and modeling is high. Therefore, it seems necessary to develop methods that have a simple structure and high accuracy at the same time. Due to the accuracy of the results and the ability to access the required information anywhere in the catchment, the cellular automata model can be used to predict runoff.

Conclusion: The results showed that the cellular automata model has a high accuracy compared to the Akan analytical solution. Also, in simulating the runoff of the con catchment, the runoff network at the catchment surface was well simulated. Comparing the computational discharge results from the cellular automata model and observational data, the values of the correlation coefficient, mean the square root of error and Nash-Sutcliffe coefficient were 0.99, 0.11 and 0.97. As the result, due to the accuracy of the results and the ease of implementation, the cellular automation model can be used to predict runoff in catchment without data and reliable results can be achieved.

**Keywords**

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September 2022

Pages 121-135

**Receive Date:**31 January 2022**Revise Date:**07 April 2022**Accept Date:**11 April 2022**First Publish Date:**11 April 2022