تحلیل فضایی بارش ماهانة شمال غرب ایران با استفاده از آمارۀ خودهمبستگی فضایی

Introduction
Precipitation is a vital component in the hydrological cycle. Its spatio-temporal variations have great environmental and socioeconomic impacts. The spatial variation of rainfall depends upon many factors. Some of these variations are due to synaptic systems and some others formed by local physiographical characteristics of stations such as elevation from sea level, slope, windward and leeward slopes, land cover and land use and etc. If the rainfall is formed by widespread and pervasive synoptic system, it can show a significant spatial similarity and homogeneity in the amount of a given rainfall in all over the region. This is affected by synoptic system. But if the rainfall is dominated by local factors the higher heterogeneity of given amount of the rainfall can be expected.
Methodology
In this study, we used 20-years monthly average precipitation (1990-2010) for 42 synoptic stations, in the west and north western portion of Iran. These include 6 provinces namely: the East and West Azerbaijan, Kurdistan, Ilam, Kermanshah, Hamadan and Zanjan. We prepared these data as long term average of monthly precipitation for each station and then import them into GIS by metric projected coordinate system (PCS). We used Moran,s Index as an spatial statistic approach to investigate the spatial relations of monthly precipitation. This tool measures spatial autocorrelation (feature similarity) based on both feature locations and feature values simultaneously. Given a set of features and an associated attribute, it evaluates whether the pattern expressed is clustered, dispersed, or random. The tool calculates the Moran's I Index value and both a Z score and p-value evaluating the significance of that index. In general, a Moran's Index value near +1.0 indicates clustering while an index value near -1.0 indicates dispersion. However, without looking at statistical significance you have no basis for knowing if the observed pattern is just one of many, many possible versions of random. In the case of the Spatial Autocorrelation tool, the null hypothesis states that "there is no spatial clustering of the values associated with the geographic features in the study area". When the p-value is small and the absolute value of the Z score is large enough that it falls outside the desired confidence level, the null hypothesis can be rejected. If the index value is greater than 0, the set of features exhibits a clustered pattern. If the value is less than 0, the set of features exhibits a dispersed pattern.
The Morans I Statisic for spatial autocorrelation is given as
 

Moran index  
 

 
where, Zi is the deviation of an attribute for feature I from its mean, wij is the spatial weight between feature i and j, n is total number of object and S0 is aggregate of spatial weight.
 
Results and Discussion
We found that the amount of monthly rainfall in the study region in cool season (November to February) has a significant positive autocorrelation. On the other hand, the spatial variation coefficient of rainfall in these months is smaller than other remaining month. The revealed Moran’s I indicated the 4 mentioned months so strong significance that this spatial homogeneity cannot be considered by chance and randomness. In the cool season, the study area located in west and northwestern Iran is dominated by westerlies and following them the atmospheric synoptic systems entrance to country affect all of the country area. Then, the rainfall formed by widespread and pervasive synoptic systems has significantly spatial similarity and homogeneity in all over the region and the strong positive autocorrelation is revealed in these months. In the warm season (July, September, August, October, and May) we find inverse condition. The Moran’s index in these months was very small and near to zero. We couldn’t detect any significant spatial autocorrelation in these months. In our study region the warm season especially summer season (July to September) is the dry period of year. The occurred rainfall in these months is usually sporadic and non-comprehensive. These rainfalls are usually characterized by being showery. This is formed by local atmospheric convective cells. In this type of rainfall the different local physiographical characteristics such as elevation from sea level, slope, windward and leeward slopes, land cover and land use and etc. have a substantial roll in formation and spatial distribution of this rainfall. 
Conclusion
The difference in physiographical characteristics of each region of this local formed precipitation is not very similar.  In the warm season, one can see the absence of westerlies in this region, the local physiographical characteristics of the occurred rainfall due to this physiographical dissimilarity in the region, and heterogeneity of given amount rainfall. The spatial variation coefficient of rainfall in warm season is very higher than cool season. The revealed Moran’s I was not significant in 0.95 confident levels and there are no spatial pattern. The findings of this research indicated that only the cool season months reveal a significant spatial autocorrelation in 0.95 and 0.91 confident levels.