Introduction
Due to the increasing significance of water supply in Iran, the management of water resources is of a particular importance. Precipitation is regarded as the most considerable source of water that is faced with great temporal (daily, monthly, seasonal and yearly) and spatial changes among other climatic factors. Therefore, the studies, focusing extensively on this issue are really useful, for they would provide the ways for optimal use and water management in the temporal and spatial scales.
Generally, there are a lot of predictive methods trying to determine the relationship between dependent and independent variables. Moreover, different statistical models have been applied to predict climatic variables. In recent years, the analysis of time series has been extensively used in scientific issues.
As a matter of fact, the analysis of a time series provides the ways to determine its possible structure, recognize its components to analyze and predict the process and future values. Therefore, the investigation and prediction of precipitation in different temporal dimension (daily, monthly, seasonal, and yearly) for each region and watershed are considered as the most important climatic parameters for optimal use of water resources affecting temporal and spatial distribution of other climatic factors. Accordingly, it is necessary to recognize the seasonal pattern of precipitation, and spatial similarities and differences of this time pattern, especially when they are not the same for different regions of Iran. The present research aims at studying the seasonal precipitation of Iran. It turns out that the precipitation does not follow a distinct unique pattern in each part of Iran, so the recognition of seasonal precipitation, separating different region, would help the authorities for environmental planning and management. Moreover, it even can lead to more successful predictions.
Materials and methods
In the present study, seasonal precipitation time series of synoptic stations (during the statistical period of 1985- 2014) is modeled applying SARIMA model. The accuracy of the fitted models to the data series for each station is evaluated by the standardized residuals graph, autocorrelation graph of residuals models and Ljung-Box test (in the significance level of 0.05). Then, the appropriate model for seasonal precipitations is presented for each station (Table. 1) according to Akaik Information Criterion (AIC). Furthermore, seasonal and inter-seasonal autoregressive rate (P, p) and moving average rate (Q, q), which were found by fitted models, are studied to investigate the seasonal and interseasonal precipitation relationship in each station. At the end, the relationship of seasonal precipitation patterns is mapped by applying ArcGIS.
Moreover, all statistical tests and temporal series computations are conducted in the environment of R software. 
Results and discussion
Evaluating the adequacy of the fitted models has revealed that the model of correlation structure is able to describe the data for all stations in this study (except for Booshehr, Shahr-e-Kurd, Birjand, Omidiye Aghajari, and Rasht). This can analyze seasonal precipitations for the stations correctly. Therefore, it is adequate enough. Seasonal and interseasonal autoregressive rate (P. p) and moving average (Q, q) from the fitted models have been used to determine the relationship of seasonal and interseasonal precipitation for each station. Except for Kashan, Abali, Doushantape, Semnan and Shahroud stations, the other 62 studying stations (93%) follow the seasonal pattern showing seasonal behavior. Furthermore, the rate of seasonal part of the model (P) shows that there is a direct relationship between the precipitation of each season and the precipitations of that season in the previous years (1 to 2). The (Q) rate has revealed that random oscillation of seasonal precipitations of 1 to 2 years before is also indirectly effective for some stations. The rates of interseasonal difference (d) have been investigated to analyze the process of time series of precipitation for the studying stations. It has demonstrated that the stations of Maraghe, Sanandaj, Hamedan-Nouzhe, and Ferdos have a decreasing process in their data, while, in the other stations, seasonal precipitation does not follow a decreasing or increasing process. In fact, it follows a constant process having no static process.
Conclusion
Applying SARIMA model, the relationship of seasonal and interseasonal precipitations of Iran has been recognized.  Hence, first, the adequacy of SARIMA model has been evaluated. The findings prove that the aforesaid model can describe the correlation structure of the data for the studying stations (except for Booshehr, Shahr-e-Kurd, Birjand, Omidiye Aghajari and Rasht) well and it is adequate enough. This fact is in accordance with the findings of Alijani and Ramezani (2002), Golabi et al (2013), Chang et al (2012), Bari et al (2015) who used SARIMA model to predict drought and temporal series of precipitation to prove its adequacy.
The investigation of seasonal and interseasonal precipitation dependency and the analysis of temporal series process of seasonal precipitation in each station show that, according to seasonal autoregressive rate (P) in all studying stations (except for Kashan, Abali, Doushantape, Semnan and Shahroud), the precipitations of each season is directly dependent upon the precipitations of that seasons in the previous years (1 to 2). Besides, the random oscillation of seasonal precipitation of the previous years (1 to 2) also affects the seasonal precipitations on some stations. Therefore, it can be concluded that the precipitations of the stations (93%) follow the seasonal patterns showing seasonal behavior. Furthermore, the findings of interseasonal autoregressive rate (p) for all stations prove that the precipitations of each season have a direct relationship with the precipitations of the previous season for 19 stations (28%).
Analyzing the process of seasonal precipitations has indicated that, except for Maraghe, Sanandaj, Hamedan-Nouzhe and Ferdos stations,  time series of seasonal precipitation has no process (random or non-random) in the stations. This process has a decreasing process for these 4 stations, while it is static in the other stations.