Assessment the spatial correlation of precipitation in Iran

Introduction
As the stations measuring precipitation continuously are not regularly available, the best solution should be to investigate the points without statistics using optimal methods. Among these methods, we can mention geostatistical methods. Geostatistical methods have been approved as appropriate ways for studying precipitation data and estimating precipitation regions. Results of many studies have shown that geostatistical techniques are more accurate than conventional interpolation methods. Statistical context can also be used for precipitation variability. Accurate estimation of the spatial distribution of precipitation requires a dense and regular cell network. The spatio-temporal variation of precipitation is one of the most important issues of applied climatology, so the main purpose of this study is to monitor the spatio-temporal variation of precipitation in Iran in seasonal context by the application of the mentioned techniques.
 
Data and Methods
In this study, the common statistics of 125 synoptic stations in the country with the statistical period of 30 years (1980-2010) have been used. Also, the station data were generalized to the 15 km cell spaces using the Kriging interpolation method in ArcGIS 10.2.2 software. To speed up the computational process, the capabilities of GS + software were used to fit the variogram, and ArcGIS software was used to map the precipitation regions of the country. In order to study the pattern of precipitation, spatial autocorrelation techniques (local Moran and global Moran) were used. Also, the skewness coefficient (G1) and the peak degree coefficient (G2) were calculated separately for each of the months studied.
Cluster and non-cluster analyses and hot spot method were used to study the patterns and spatio-temporal variations of precipitation. Cluster and non-cluster analysis, also known as Moran local Anselin index is an optimal model for showing the statistical distribution of phenomena in space (Anselin et al, 2009: 74). For cluster and non-cluster analyses for each complication in the layer, the value of the local Moran index score, which represents the significance of the calculated index, was also calculated.
 
Results and Discussion
The value of the global Moran index for all 4 studied seasons and the annual total is above 0.95, which indicates the pattern of high clusters of precipitation in the country at the level of 95 and 99%. However, the highest Moran index in the world with a value of 0.970356 is related to the winter. Statistics for each of the five decades studied are high, between 255 and 261. Therefore, based on global trends, it can be inferred that the annual changes in precipitation in the country follow a very high cluster pattern. Consequently, due to the high value and low value, the hypothesis of no spatial autocorrelation between data in each of the five decades can be rejected. If precipitation were to be normally distributed in space for different seasons in the country, the global Moran index would be -0.000139.
Moran's spatial autocorrelation only determines the type of pattern. For this reason, to show the spatial distribution of the pattern governing the distribution of precipitation in Iran, local Moran has been used during the studied periods. In winter (36.56%) there was no pattern or in other words it lacked spatial autocorrelation. This amount increased by 1.14% for spring and reached 37.70. This amount has increased significantly in summer, so that it has increased by 47.04% compared to spring. It has reached areas with no spatial autocorrelation in autumn (41.92) and winter (36.56). LL precipitation patterns have been distributed in the five studied periods with values of 36.53, 0, 34.64, 35.31 and 38.29% in the country, respectively, and in the form of nationwide spots in the eastern, southeastern and central regions. Precipitation values with negative spatial correlation in summer had the highest value (84.74%) and the lowest annual average (35.06%). However, values with high rate or positive spatial autocorrelation in all five studied periods were limited to the northern regions of the country, the highlands of Alborz, Zagros and had significant fluctuations in some parts of the country. Local Moran Anselin statistics have been able to well determine the process of precipitation (Masoudian, 1390: 97) and the era of windbreak slopes as well as adjacent areas with climatic contrasts such as north-south slopes of Alborz and slopes of east-west Zagros. Due to the complexity of precipitation patterns in the country, spatial statistics can well explain precipitation patterns. The general results of this statistic (local Anselin Moran) indicate that the amount of rainy areas in the country has been reduced during five study periods. It should be noted that most of these reductions were related to the Zagros region, the southeast of the country and the northern regions of Khorasan.
 
Conclusions
Iran has special conditions in terms of precipitation due to its vastness with respect to latitude and longitude, the configuration of unevenness and exposure to air masses. The general structure of precipitation in Iran is affected by latitude, altitude and air masses, so that with the change of any of these factors, precipitation will also change. In other words, the general conditions of precipitation are a function of latitude and altitude, and other factors such as water areas and land cover, which are referred to as local factors, play a role in the formation of Iranian precipitation. In the present study, spatio-temporal analysis of Iranian precipitation has been done using a new method of spatial statistics. For this purpose, high and low clustering methods, local and global Moran, hot spots and cluster and non-cluster analyses have been used. The present study focuses on the assumption that precipitation in Iran follows a cluster pattern and the pattern of precipitation distribution is itself a function of internal and external conditions. To achieve this goal, the average seasonal and annual precipitation statistics of 125 synoptic stations in the country during the statistical period of 1980-2010 were used. Then, to apply the methods used in this research, the capabilities of GIS were used. The results of the global Moran method and the K-function of some distances showed that the annual changes in precipitation in Iran follow the pattern of high clusters. According to spatial autocorrelation analyses, the areas with negative spatial autocorrelation in all studied periods are related to the southeast, the coasts of the Oman Sea to Abadan and parts of the northeast of the country. Areas with positive spatial autocorrelation were often located on the southern shores of the Caspian Sea and the Zagros strip. In all the studied periods, less than one quarter of the country's area lacked a significant spatial autocorrelation pattern. Spatial analyses showed that Iran's precipitation patterns are divided into two precipitation spots of southern tabs (low precipitation spot LL), and Caspian coasts west and northwest (precipitation spot HH). The results also indicated that during the period under study, low precipitation spots (negative spatial autocorrelation) had much more frequency than precipitation spots.