ﻣﺪلﺳﺎزي رواﻧﺎب ﺳﻄﺤﯽ ﺑﺎ اﺳﺘﻔﺎده از اﺗﻮﻣﺎﺗﺎي ﺳﻠﻮﻟﯽ

Cellular Automata Model for Simulating Surface Runoff

رواﻧﺎب ﺳﻄﺤﯽ از ﻣﻬﻢﺗﺮﯾﻦ ﺑﺨﺶﻫﺎي ﭼﺮﺧﻪ ﻫﯿﺪروﻟﻮژﯾﮑﯽ ﺑﻪ ﺷﻤﺎر ﻣﯽرود و ﺗﺨﻤﯿﻦ دﻗﯿﻖ آن ﻧﻘﺶ ﻣﻬﻤﯽ در ﻣــﺪﯾﺮﯾﺖ ﺣﻮﺿــﻪ آﺑﺮﯾﺰ و ﻃﺮاﺣﯽ ﺳﺎزهﻫﺎي آﺑﯽ دارد. از اﯾﻦرو اﺳﺘﻔﺎده و ﺗﻮﺳﻌﻪ روشﻫﺎي دﻗﯿﻖ و ﻗﺎﺑﻞ اﻋﺘﻤﺎد ﺟﻬﺖ ﻣﺪلﺳﺎزي رواﻧﺎب ﺣﻮﺿﻪﻫﺎ ﺿﺮوري اﺳﺖ. اﺗﻮﻣﺎﺗﺎي ﺳﻠﻮﻟﯽ ﯾﮏ روش ﺑﻨﯿﺎدي ﺑﺮاي ﺷﺒﯿﻪﺳﺎزي ﺳﯿﺴﺘﻢﻫﺎي ﭘﯿﭽﯿﺪه اﺳﺖ. ﺑﺮاي ﻣﺪلﺳﺎزي رواﻧﺎب ﺳﻄﺤﯽ ﺑﺎ اﺳﺘﻔﺎده از اﺗﻮﻣﺎﺗﺎي ﺳﻠﻮﻟﯽ، ﺣﻮﺿﻪ آﺑﺮﯾﺰ ﺑﻪ ﺻﻮرت ﺷﺒﮑﻪاي از ﺳﻠﻮلﻫﺎ ﺗﻌﺮﯾﻒ ﻣﯽﺷﻮد. ﺗﺮاز آب ﺑﻪ ﻋﻨﻮان ﺣﺎﻟﺖ ﺳﻠﻮل ﺑﯿــﺎن ﻣــﯽﺷــﻮد و ﺑــﺎ اﺳــﺘﻔﺎده از ﻗــﻮاﻧﯿﻦ اﻧﺘﻘــﺎل،ﺳﻠﻮلﻫﺎ از ﯾﮏ ﺣﺎﻟﺖ ﺑﻪ ﺣﺎﻟﺖ دﯾﮕﺮ ﺑﺎ ﮔﺬﺷﺖ زﻣﺎن ﺑﺮوزرﺳﺎﻧﯽ ﻣﯽﺷﻮﻧﺪ. در اﯾﻦ ﻣﻘﺎﻟﻪ رواﻧﺎب ﺣﺎﺻــﻞ از ﺑــﺎرش ﺑــﻪ روش اﺗﻮﻣﺎﺗــﺎي ﺳــﻠﻮﻟﯽ ﺷﺒﯿﻪﺳﺎزي ﺷﺪه اﺳﺖ. اﺑﺘﺪا رواﻧﺎب ﺳﻄﺤﯽ ﺑﺮ روي ﭼﻨﺪ ﻣﺪل ﻣﺴﺘﻄﯿﻠﯽ ﺑﺎ اﺳــﺘﻔﺎده از روش اﺗﻮﻣﺎﺗــﺎي ﺳــﻠﻮﻟﯽ ﻣــﺪلﺳــﺎزي ﺷــﺪه و ﺟﻬــﺖ ﺻﺤﺖﺳﻨﺠﯽ، ﻧﺘﺎﯾﺞ ﻣﺪل اﺗﻮﻣﺎﺗﺎي ﺳﻠﻮﻟﯽ ﺑﺎ روشﻫﺎي ﺗﺤﻠﯿﻠﯽ ﻣﻮﺟﻮد ﻣﻘﺎﯾﺴﻪ ﮔﺮدﯾﺪه اﺳﺖ. در اداﻣﻪ ﺑﺎ اﺳــﺘﻔﺎده از ﻣــﺪل اﺗﻮﻣﺎﺗــﺎي ﺳــﻠﻮﻟﯽ رواﻧﺎب در ﺣﻮﺿﻪ آﺑﺮﯾﺰ Con واﻗﻊ در ﮐﺸﻮر اﺳﭙﺎﻧﯿﺎ ﺷﺒﯿﻪﺳﺎزي ﺷﺪه و ﻣﻘﺎدﯾﺮ دﺑﯽ ﻣﺤﺎﺳﺒﺎﺗﯽ ﺑﺎ ﻣﻘﺎدﯾﺮ ﻣﺸﺎﻫﺪاﺗﯽ ﻣﻘﺎﯾﺴﻪ ﺷﺪه اﺳﺖ. ﻣﻘﺎﯾﺴﻪ ﻧﺘﺎﯾﺞ ﻣﺪل اﺗﻮﻣﺎﺗﺎي ﺳﻠﻮﻟﯽ و روشﻫﺎي ﺗﺤﻠﯿﻠﯽ ﻧﺸﺎن ﻣﯽدﻫﺪ ﮐﻪ ﻣﺪل اﺗﻮﻣﺎﺗﺎي ﺳﻠﻮﻟﯽ از دﻗﺖ ﺑﺎﻻﯾﯽ ﺑﺮﺧﻮردار اﺳــﺖ. ﻫﻤﭽﻨــﯿﻦ در ﻣــﺪل-ﺳﺎزي رواﻧﺎب ﺣﻮﺿﻪ آﺑﺮﯾﺰ Con ﻣﻘﺎدﯾﺮ ﺿﺮﯾﺐ ﻫﻤﺒﺴﺘﮕﯽ، ﺟﺬر ﻣﯿﺎﻧﮕﯿﻦ ﻣﺮﺑﻌﺎت ﺧﻄﺎ و ﺿــﺮﯾﺐ ﻧــﺶ-ﺳــﺎﺗﮑﻠﯿﻒ ﺑــﻪ ﺗﺮﺗﯿــﺐ 0/99، 0/11و 0/97ﻣﯽﺑﺎﺷﺪ. ﻧﺘﺎﯾﺞ ﺑﻪ دﺳﺖ آﻣﺪه ﻧﺸﺎن ﻣﯽدﻫﺪ ﮐﻪ روش اﺗﻮﻣﺎﺗﺎي ﺳﻠﻮﻟﯽ ﻣﯽﺗﻮاﻧﺪ ﺑﻪ ﻋﻨﻮان ﯾﮏ روش ﮐﺎرﺑﺮدي و دﻗﯿﻖ ﺑﺮاي ﻣﺪلﺳــﺎزي رواﻧﺎب اﺳﺘﻔﺎده ﺷﻮد.

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 for runoff modeling of the catchments is 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 create 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 that which neighboring cell can get water from 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 apply to all cells at each time step and as a result the output flow from each central cell to its neighbors is calculated. In the general view, each central cell is a neighbor of other cells, as a result a third rule must be used for calculation 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 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 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 correlation coefficient, mean 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.