پیش‌بینی بارش ماهانه با استفاده از شبکه‌های عصبی مصنوعی (مورد: تهران)

Introduction
Forecasting precipitation in arid and semi-arid regions, in Iran for example, has particular importance since precipitation is the unique source of water in such regions. Precipitation is a complex phenomenon that varies both in time and space and affects other components of the hydrological cycle, including surface runoff, infiltration, groundwater, seepage, percolation, evaporation and transpiration. Temporal variation comes from the seasonality and inter-annual variability of the atmosphere, whereas spatial variation is due to the topographical heterogeneity of the earth surface at the local scales as well as the teleconnections at the global scale. Forecasting precipitation ahead of time has been an important problem in hydrological studies. The Artificial Neural Networks (ANNs) modeling has been used increasingly in various aspects of science and engineering because of its ability to model both linear and nonlinear systems without the need to make any assumptions as are implicit in most traditional statistical approaches. In most hydrological and water resources studies, precipitation is an important parameter to estimate. Since the numbers of precipitation gages are usually insufficient and there are high uncertainties in measurement, the estimated precipitation is not accurate. Forecasting precipitation is most important in estimating of runoff, drought, catchments management, agriculture and etc.

Materials and methods
In this paper, the usefulness of artificial neural networks as a suitable tool for the study of the medium and long-term climatic parameter variations is examined. The objective of this investigation was forecasting monthly precipitation with artificial neural networks. The monthly precipitation data of Tehran synoptic station for period of 1951 to 2003 obtained from Tehran Meteorology Center. Then artificial neural networks were used as a nonlinear method for forecasting precipitation. The samples were divided into two sets. The first set is the learning set for the ANN training, while the other set represents the holdout set for precipitation prediction to verify the efficiency and correctness of the model. With these collected data, the ANN system is ready to launch its training scheme. Then the year and month set as input layer and precipitation set as output layer. TanhAxon function which is the most important function in Back propagation method is used as irritates function. Neurosolutions for Matlab software is used for training artificial neural network. To reduce forecasting error, train and error on the network parameters carried out. The Multi-layer perceptron (MLP) model has been used. The ANN is composed of an input layer of neurons, one or more hidden layers and an output layer. Each layer composites multiple unites connected completely with the next layers.

Results and discussion
Precipitation is one of the main sources of water without which humankind cannot survive, so understanding, modeling, predicting or forecasting of precipitation has always been important. Among a host of modern nonlinear data-based techniques, artificial neural networks have been extensively applied in hydrology. The several ANN models with varying numbers of nodes have been trained. The results of this study after network testing with different hidden layers and training coefficient indicated that using of artificial neural network with 2 hidden layer perceptron, 0.1 training coefficient and 0.7 momentums has presentation comparatively a better model.

Conclusion
Although concerns and criticisms regarding ANN applications in hydrology remains, but there is no doubt anymore that ANNs are useful tools in hydrological, meteorological and climatological practices. The classic or linear models are used for trends that with increase of a parameter, another parameter increases or decreases. Thus, using of these models for nonlinear trends increases the error rate. The neural networks can be a useful tool to model the relation between variables because we can consider the ANN as being very general forms of non-linear regression models. In fact they can model time series very effectively and are employed when the classic methods do not work effectively. There is a nonlinear trend for precipitation. When network trained without genetic algorithm, the correlation and adjust coefficient are 0.87 and 0.77, respectively. So after testing network and training with different hidden layer and training coefficient in combination with genetic algorithm indicated that combination of network with mentioned characters with genetic algorithm decrease the error and increase speed of calculation and finally present a better model. When network trained with genetic algorithm the correlation and adjust coefficient are 0.91 and 0.83, respectively. In summery artificial neural networks forecast the nonlinear trend of monthly precipitation. The combination of genetic algorithm with artificial neural networks increases the speed of analyzing and processing accuracy which leads to decrease in error rate.