Application of time series model to estimate monthly rainfall in Kermanshah province

Introduction:
In recent years, limited water resources to supply water for agricultural and non-agricultural needs have caused many problems and rain is one of the important sources of water supply. On the other hand, rainfall is one of the most important components of input to hydrological systems that its study and measurement in most cases is necessary for studies of runoff, drought, groundwater, flood, sediment, etc. Therefore, forecasting and estimating rainfall for each region and watershed is considered as one of the important climatic parameters in the optimal use of water resources. One of the methods of estimating and predicting precipitation is the use of time series.
Materials and methods:
In this study, the statistical population includes the amount of precipitation in synoptic stations of Kermanshah, Kangavar, Sarpole-Zahab and Islamabad -Gharb provinces. The data has been prepared from the meteorological website at www.kermanshahmet.ir. The study method is cross-sectional and the sample size is all rainfall data during the years 1986 to 2018. In order to analyze the data in this study, spss16 and minitab18 statistical software for time series modeling fitting and finally after testing the existing models, the best model for predicting precipitation was determined.
Results and discussion:
In order to analyze the data from Arima method for fitting time series modeling and finally after testing the existing models, the best model for predicting precipitation was determined. The results showed that Arima time series model has the best performance and will have a decreasing trend of precipitation by 0.2. In the present studies, using 32-year data (1986-2018) of Kermanshah, Islamabad, Kangavar and Sarpole-Zahab stations as well as time series models, precipitation was modeled and predicted. Based on the results of autocorrelation and partial autocorrelation diagrams, the best model fitted to the data was the model Arima(2,1,1). Finally, due to randomness and time delay outside the range of zero based on partial autocorrelation residual and residual autocorrelation in the data prediction model is less than 0.05. The model was then estimated to be reliable. And according to the fitted model, precipitation will have a decreasing trend of 0.2.
Conclusion:
The analysis of random phenomena in the realm of statistics and probability is a subset of hydrology and meteorology. Due to the fact that meteorological processes are random, so the basis for the analysis of these phenomena is meteorology, statistics and probability. Accordingly, time series are used. It is natural that the existence of appropriate statistical data in the study area as input to models in processing problems and receiving reliable outputs is very important and effective. In the present studies, using 32-year data (1986-2018) of Kermanshah, Islamabad, Kangavar and Sarpole-Zahab stations as well as time series models, precipitation was modeled and predicted in the software minitab18.Based on the results obtained from the autocorrelation and partial autocorrelation diagrams, the best fit model on the data was the model Arima(2,1,1). Finally, due to randomness and time delay (Lag-time) outside the range of zero based on the residual of the partial autocorrelation function (PACF ) and the residual of the autocorrelation function (ACF ) in the data prediction model is less than 0.05, so the model Reliable forecast was estimated and according to the fitted model, precipitation will decrease by 0.2.