Extended Abstract
Introduction
Rain is one of the most important atmospheric phenomena affecting human life. Rainfall prediction is important for various purposes such as planning for agricultural activities, forecasting floods, monitoring drought and providing resources for consumable water. The rapid expansion of using artificial neural networks (ANNs) as an experimental and efficient model in various sciences including meteorology and climatology implies the high value of studying these types of models.
Materials and methods
The purpose of this paper is to predict the monthly rainfall in Iran, using the combination of artificial neural networks and extendedKalman filter. For this purpose, the monthly average rainfall data of about 180 synoptic stations spreading across the country were used during the years 1951 to 2016, then, the monthly rainfall was predicted for the year 2017 using the article’s method.  Artificial neural networks are a method for the approximation of the functions and prediction of the future state of various systems. Artificial neural networks discover the law latent in them and transfer it into the network by processing the experimental data. The smallest processing unit of information in the artificial neural network is neuron that builds the bases for the application of neural networks. Each neural network consists of a number of nodes which are the neurons, and the communication weights that connect the nodes together. Input data is multiplied by their corresponding weights, and their sum is entered into the neurons. Each neuron has a transfer function. This input data passes through the transfer function and specifies the output value of the neuron. The back propagation algorithm is one of the most commonly used algorithms for teaching these networks, but the back propagation algorithm depends on the selection of the number of hidden neurons. Also, the convergence speed of the back propagation algorithm is very slow comparing with the proposed method in this paper, and is very sensitive to the noises present in the input and output data set, which is used for teaching the neural network. In addition, it has a poor performance in modeling the complex processes. One of the most famous methods to eliminate the aforementioned defects is the use of the Kalman filter. The Kalman filter contains a set of mathematical equations that performs a repeated process, prediction and updates, and is also an optimal tool in minimizing the covarianceof the estimated error. The leading neural network can be considered as a nonlinear dynamic system with synaptic weights and equate the teaching of the neural network with the problem of estimating the state of the nonlinear system. Therefore, the extended version of the Kalman filter can be used to estimate the adjustable parameters of the artificial neural network like the neural network weights.
Results and discussion
The climatic zonation of Iran was used for the data separation by the method of Coupon-Geiger which has been conducted by other researchers, and Iran was divided into eight climatic zones. This zonation divides Iran into dry and hot desert, dry and cold desert, dry and hot semi-desert, dry and cold semi-desert, moderate with dry and hot summers, rainy moderate with warm summers, snowy with dry and hotarm summers, snowy with dry and warm summers climates. This artificial neural network which has been taught by the extended Kalmanfilter, was used for the prediction in each of the climatic zones. A multi-layered artificial neural network with two hidden layers has been used. There are 10 neurons in each of the hidden layers, and 7 neurons in the input layer, which are the same numbers as the network inputs. The methodology is that the year and number of months, the average monthly temperature, the average monthly wind speed and the geographic location of the synoptic stations are considered as the input parameters, and the average monthly precipitation as the output parameter. The difference between the observed and the predicted values of the monthly precipitation in 2017 was calculated ​​for all stations and was considered as an error. The Root Mean Square Error (RMSE) of these differences was calculated for the 8 climatic zones. The RMSE is lower for dry and hot desert climate than for dry and cold desert climate. This RMSE is lower for dry and cold semi-desert climate than for dry and hot semi-desert climate. The RMSE is lower for moderate climate with dry and hot summers than for moderate rainy climate with warm summers. The RMSE is lower for snowy climate with dry and hotsummers than for snowy climates with dry and warm summers.
Conclusion
In most cases, the RMSE for hot climates is less than others that represents the efficiency of the proposed method for the prediction of  monthly precipitation in hot climates.