Investigating the inter-annual precipitation changes of Iran

Precipitation is an important factor in the management of a variety of agricultural and industrial projects. This study investigated the temporal-spatial change of inter-annual precipitation of Iran from 1977 to 2007 by using the APHRODITE precipitation database. Statistical methods were applied, such as spatial auto-correlation, Global Moran’s index, Local Moran’s I index, and hotspots to acquire the variations in precipitation. The highest spatial anomalies belong to September (75.26) and October (45.02), based on the Dispersion index. Also, the size of the largest cluster of Iran’s precipitation clusters is developed during winter, cited by the index’s outputs, which indicates the relative regularity of Iran’s precipitation. The results of the spatial statistics showed that inter-annual precipitation changes in Iran have an upward cluster model. The results of the Global Moran statistics showed that September, with the lowest number (0.712114), has the highest spatial precipitation anomalies throughout the year in Iran. Meanwhile, precipitation has a positive spatial autocorrelation on the Caspian Sea shores and western and south-western parts of the country (mainly Zagros highlands) and a negative spatial autocorrelation in parts of the central and south-eastern areas based on the Local Moran index and hotspots.


INTRODUCTION
Precipitation is the most important climate element and is usually investigated from the two perspectives of time and place. Emphasizing the perspective of time determines temporal change and emphasizing the perspective of place determines spatial change. In climatological studies, these two aspects are always interdependent (Alijani et al. ), because climate is an element with both spatial and temporal aspects. Therefore, understanding temporal and spatial variability is very important in environmental planning. Knowledge of the spatial and temporal distribution of precipitation is necessary for making precipitation forecasts and monitoring weather conditions (Chappell et al.  The geostatistic method has been confirmed as an appropriate way to assess precipitation data (Delhomme ; Goovaerts ; Asakreh ). Geostatistics can be used specifically for precipitation variability (Barancourt et al. ; Berne et al. ). In this study, the spatial structure of Iran's spatio-temporal precipitation variability has been investigated using geostatistical techniques. An accurate estimation of the spatial precipitation distribution requires a dense and regular cellular network (Goovaerts ). A static spatial model must have a fixed mean, variance and direction across the study area (Fortin & Dale ). introduced the best pattern of this function. As temporalspatial changes are among the most important issues of applied climatology, the main purpose of this study was to monitor spatio-temporal changes in Iran's precipitation at a monthly scale.

METHODOLOGY
Iran is a rugged land, which emphasizes the variability of precipitation in the country. The need for studies on precipitation and its behaviour is strongly felt, due to the climatic characteristics of Iran and the importance of precipitation in water resource management. Therefore, a precipitation data investigation study would be useful, in which longterm precipitation data are available to the researchers.
Accessing long-term precipitation data is not possible in Iran. There are currently more than 380 synoptic stations but only 50 or 60 of them have long-term (30 years or more) statistics of meteorological variables which is not sufficient to investigate the spatial autocorrelation precipitation with high spatial and temporal fluctuations given Iran's large area. In addition to the long-term data accessing problems, desert areas and internal deserts and areas with an altitude of over 2,600 m (country's pond centres) lack precipitation measurement stations. Further adjacent areas with high climate variability, such as the north-south slopes of Alborz and eastern and western slopes of Zagros, lack stations (Asakreh ). The data obtained from all available precipitation databases such as Global Precipitation Climatology Project (GPCP), Global Precipitation Climatology Centre (GPCC) and Asian Precipitation -

Highly-Resolved Observational Data Integration Towards
Evaluation of Water Resources (APHRODITE) were reviewed. On GPCP and GPCC databases, the rainfall data were available on a monthly scale, thus not showing extremes of rainfall events. In addition, the high spatial resolution of the APHRODITE database (0.25 by 0.25 degree spatial resolution) was compared to the GPCP database (2.5 by 2.5 degree spatial resolution). Finally its allocation was compared to that of Asia. Therefore, the outputs obtained from the APHRODITE database evaluated the temporalspatial changes of Iran's seasonal precipitation. Figure 1 shows synoptic stations in the country and APHRODITE precipitation database with a spatial resolution of 0.25 × 0.25 . In the present research, the data available in the Middle East (APHRO_ME) were taken from the latest product of the APHRODITE database entitled v1101 with spatial resolution 0.25 × 0.25 and degree of arc 0.5 × 0.5 with the NETCDF obtained from the above website. Then, the programming capabilities of Grads and Matlab software packages were used to elicit the data from all existing data in the database (APHRO ME). The cells pertaining to the area of Iran were extracted using the capabilities of ArcGIS software. As the mentioned data exist at a spatial resolution 0.25 × 0.25, for the next stage, using geostatistical techniques and Kriging interpolation methods, the cells to the dimensions of 15 × 15 km 2 were spanned on the study region. The Kriging interpolation method refers to an optimal technique that provides regional observations in the regions without any value (Asakreh & Razmi ). Also, Phillips et al.
() showed that the Kriging geostatistical model is the best method to predict rainfall for areas without data. Instead of fulfilment of the analysis process on a matrix with data representing the spatial resolution 0.25 × 0.25 and acquisition of the results from the study area, the micro scale data were used to the dimensions 15 × 15 km. From this, boundaries of climate regions and spatial patterns were revealed. In the present study, the spatial statistics have been evaluated in order to investigate Iran's cellular spatial precipitation structure. Statistics used are: index of dispersion (ID): this index investigates the variance to mean ratio. If the studied data follow random distribution, ID is expected to equal 1. This statistic fits the data following an X 2 test with degrees of freedom of n-1: relation (1) Index of cluster frequency (ICF) (Douglas ), a criterion for cluster measurement based on K function from a negative binomial distribution; relation (4); Index of mean crowding (IMC) (Lloyd ), the average number of points in the study area which is evaluated from one single point randomly; relation (5).
Also, skewness coefficient (G 1 ), and peaking factor coefficient (G 2 ) are calculated separately for each month: To examine the prevailing pattern in precipitation in Moran precipitation spatial auto-correlation examines spatial auto-correlation based on dispersion areas of two amounts and analyses, the considered characteristics of the geographical state in that area (Griffith ). To calculate the Moran index, first the Z-value and P-value are calculated, and the next stage is to consider the evaluation and significance of the index. To calculate spatial auto-correlation, the Global Moran index is used from the following equation: where z i is the deviation of an attribute for feature I from its Moran's I can be calculated based on: where x i represents the characteristic of i, x represents the mean of the given characteristic, and w i,j represents the spatial weight between features i and j. The value of s i is calculated based on Equation (11): where n equals the number of all features; z Ii is calculated using the equation below: To calculate V [I i ], Equation (13) is used: The analysis of hotspots uses the Getis-Ord Gi*statistics for all events in the data (Rogerson  Getis-Ord Gi*statistics is calculated as follows: In the above relationship, x j is the feature value for event j and w i,j is the spatial weight between i and j, and n events. In order to calculate S, relation (16) is used: Considering that it is itself a kind of a Z score, Z's re-calculation has been avoided. September. The distribution coefficient of skewness (G1) of all months' precipitation has been positive. A positive skewness indicates that the frequency of precipitation events is higher than the mean, and is higher than the frequency of precipitation events lower than the mean. In other words, the frequency of the data greater than the mean value is higher than the ones with a value lower than the mean. Rain-bearing systems, due to their dynamic and thermodynamic conditions and depending on their geographic locations, can cause different areas of rain when dealing with local conditions (Ghayour et al. ). Therefore, the amount of precipitation will have different indices. For every month of the year, the difference between the median, mean and standard deviation of the mean indicates that the data do not follow a normal distribution. As also specified in the difference in precipitation is less, due to rainfall in most parts of Iran. In some places, a small amount of rainfall will cause a relative regularity of precipitation rate in Iran and, to some extent, the low value of the peak coefficient.

Preparation of data
Geostatistical methods will be optimal in cases where data are normally distributed, thus before performing these methods, examination of the histograms of the data is required to check the normality and identification of outlier data. In this research, data were obtained from the theory. Therefore the normality of the data has been confirmed as well.
To If samples are taken as grids in this case, the distance between grids will be a suitable measure for the size of steps.
Yet if the data are taken at random, the determination of step size is not simple; in this case the size of data must be con- techniques are used (Moreno & Bravo ). In this study, the two statistics of R 2 and RMSE have been used.
where N represents the number of stations used in estimation and modelling, O represents the extent of a measured variable at each station and P represents the estimated amount for each station. For evaluation through the aforementioned statistics, it is taken that the closer RMSE is to 0 and R 2 is closer to 1, then greater values of R 2 represent higher accuracy of the used method. Among the used methods, the Kriging method employing the auxiliary variable of height indicated the least amount of RMSE (1.654658) and the highest amount of R 2 (0.914); hence, this method was recognized as the most accurate among those used in the region.

1977-2007)
Outputs of Global Moran's precipitation spatial autocorrelation are listed in Table 3 and Figure 3. In general, if the Moran index is close to þ1, data will have spatial auto-correlation and a clustering pattern, and if the Moran index is close to À1, data will be discrete.
Graphical output represents scattering or clustering data. According to the Global Moran index, the null hypothesis is based on the assumption that there is no spatial clustering between values of the element associated with geographical features. Yet when the P-value is so small and the calculated Z-value is so large, the null hypothesis can be rejected.
If the Moran index is greater than 0, the data will represent a type of spatial clustering. If the Moran index is less than 0, the geographical features under study will have a scattered pattern. As shown in can be deduced that inter-annual changes of precipitation over the country follow a high clustering pattern. Hence, with regard to high Z-value and low P-value, the null hypothesis can be rejected based on the lack of spatial auto-correlation between data for all 12 months. If spreading the precipitation in a normal way during various months over Iran was assumed, the Global Moran index will be equal to À0.000139. imply that the considered condition has been dominated by similar features. Hence, the considered feature is a part of that cluster. If the I-value is negative, this will imply that the feature has been enclosed by dissimilar features.
These are called outliers. The value of these statistics has been calculated in the framework with the standard score, and P-value can be analysed. In these statistics, HH represents clusters with positive spatial auto-correlation at 99% confidence level, LL represents clusters with negative spatial auto-correlation at 99% confidence level, HL represents outliers in which a high value has been enclosed via low values, and LH represents single cells in which the condition enjoys a low value, enclosed via high values. In  (Table 4). Low cluster models (negative spatial respectively, and areas with no spatial autocorrelation have been allocated 49.61% of the country's total area (see Table 4). As can be seen, top clusters (HH) cover the north coast (especially Babolsar to Anzali), with the centre and northwest of the Zagros as islands. In just one month

CONCLUSION
Iran has special precipitation circumstances due to its wide range of latitude and longitude, the existence of ripples' patterns and exposure to the prevailing air mass. The general structure of precipitation in Iran is influenced by latitude, longitude and air masses in a way that with the change of each of these factors precipitation will change as well. In other words, the general conditions of precipitation are a function of latitude and altitude, and other factors such as water and surface characteristics which are referred to as local factors, are involved in the formation of Iran's precipitation. Spatio-temporal analysis has been performed in the present study using modern methods of spatial statistics.
In this context, Global and Local Moran, hotspots and cluster and non-cluster analysis methods have been used. The present study has concentrated on the assumption that Iran's precipitation is a function of the cluster model and the pattern of precipitation itself is also a function of the internal and external conditions. To achieve this goal, the APHRODITE precipitation database of monthly mean for  Gulf breeze (to a limited extent) impact the warm season precipitation that is to be expected in the Fars province; (2) seasonal weather which creates Iran's southern and south-eastern precipitation systems through low thermal stress which is created in Pakistan and India in summer.
However, it should be emphasized that the impact of this system is discovered when the uplift factor is also available.
To sum up, spatial analysis has shown that Iran's precipitation models are classified into two forms of rainfall patterns in the south region (LL, low precipitation pattern), northern region (the Caspian Sea shores) and west and northwest (HH, high precipitation pattern). The investigation indicated that in the study period, low precipitation models (negative spatial autocorrelation) have had a much higher frequency compared to high precipitation models.
To sum up, given that Iran is a rugged land, the variability of rainfall is very high and the management of water resources is strongly felt. The main problem in managing water resources is changes in rainfall, which were difficult to detect due to the lack of sufficient rain gauges and synoptic stations over the country. Therefore, in this study, by using the APHRODITE database, high and low precipitation patterns and clusters were identified within the country. This can be used in water resources management such as supplying agricultural water resources, dam construction, etc. Therefore, in future research, different regions of Iran can be examined in terms of the cultivation of various agricultural products (such as the cultivation of drought-tolerant plants in low-rainfall areas and vice versa), location of dam construction and so on.