Rainfall erosion is a key factor in soil erosion processes. Determining the quantitative values of the rainfall erosion factor is assumed as a first step in sustainable management of soil and water resources. In terms of quantity, rainfall erosion is one of the characteristics that has the highest correlation with soil losses. Modified Fournier index (MF) is a simple rainfall erosion index which is widely used as a quantitative index in soil erosion projects. In this research, the spatiotemporal variation of the modified Fournier index was determined in west Azerbaijan province for a twenty-year period from 1993 to 2012. A total of 66 rain gauge data were used to determine the MF and precipitation concentration index (PCI). The spatial pattern of the MF and PCI were mapped by Kriging. The findings indicated that there was a wide range for MF, 28.28-116.22 mm, and the highest value of MF was observed in southwest of the region while the smallest values of the MF is located at the northeast of the region. Descriptive statistics of the PCI indicated that the 80 percent of the stations shows a seasonal pattern of rainfall distribution, while 20 percent of the stations have a moderate seasonal rainfall distribution pattern. There was a strong positive relationship between the annual rainfall and MF (r= 0.934, p< 0.001). A significant relationship was not observed between the PCI with annual rainfall and MF. The spatial patterns of the MF and annual rainfall showed a regular decreasing from south to the north of the region.
Extended Abstract
1- Climate change in the current era is one of the most important environmental challenges. Precipitation is one of the most important climate elements directly affecting the availability of water resources. Low amount of precipitation and its extreme fluctuations in the daily, seasonal and annual scales is an inherent characteristic of Iran’s climate. Due to significant impacts of rainfall on water resources such as groundwater, surface water, and snow reservoir, some indices, Standard Precipitation Index (SPI) and Precipitation Concentration Index (PCI), are applied to explain its changes. SPI index includes applicable indices that are used in most studies, while PCI index has been introduced in recent years. Different indices have been used to assess the density of precipitation, inwhich the Precipitation Concentration Index (PCI) is recommended, for it provides information on long-term total variability in the amount of received rainfall. Rain erosion is recognized as a key factor on erosion. Accurate knowledge of the amount of rainfall erosion in a region is considered as a primary step in the sustainable management of soil and water. Early indices (Fournier and modified Fournier) are one of the most important indicators of rainfall erosion, which have widely been used in soil erosion studies due to easy calculation compared with other indices.
2- West Azerbaijan province with an area of 37210 square kilometers (including the Urmia Lake) is the thirstiness province of Iran in extent which is located at a geographic location of 44° 3' to 47° 23' East longitude and 35° 58' to 39° 3344' Northern latitude. In this study, rainfall data from gauge stations of West Azerbaijan (Iran) were used in order to investigate of Precipitation Concentration Index. Referring to Iran water resources management, information, including daily rainfall data, geographical coordinates of the stations and years of statistics, received. After reviewing, the stations with incomplete data were excluded and finally, 66 rain gauge stations were selected. Information on daily rainfall for a period of 20 years (1993-2012) was reviewed in terms of homogeneity and normality using Kolmogorov-Smirnov test and was used for calculating of PCI index. The aim of this research is to establish a regression relationship between the early indices with the EI30 index for studying the spatial and temporal changes in the rainfall erosion index during the period of 1993-2012 in West Azerbaijan province. Therefore, the data of 66 rain gauges and 13 rain-fed stations were used and erosion indices and precipitation concentration index of the region were calculated and spatial changes map was mapped using the Kriging method.
3- Average rainfall in the entire area during a twenty-year period is approximately 325 mm. The mean value of PCI was 16.66 indicating the seasonal distribution of rainfall in the province. The minimum value of PCI for the area was 12.36 demonstrating the fair distribution of rainfall and the maximum value of this index for the entire period as 22.17 that represents the distribution of rainfall is very seasonal. The important note is the few differences in statistics related to Precipitation Concentration Index so that during the period of two decades, mean changes of PCI is less than 2%. The EI30 index has the highest correlation with the overall corrected Fournier index (R2 = 0.9). The EI30 index variation is very high in the province and is located in a range of 62.54 to 230.05 mega Jules millimeter per hectare per hour per year. The maximum erosion was observed in the southwestern part of the province and in the forests of Piranshahr and Sardasht, and at least in the northern and eastern of the province. According to the precipitation concentration index, rainfall pattern in the province was observed as relatively seasonal and seasonal. In terms of statistical period, rainfall amount and erosion indices showed an increase during the second decade compared to the first decade. The results showed that the erosive indices and the amount of annual precipitation decrease regularly by moving to higher geographic latitudes.
4- In general, in lower latitudes, rainfall is higher in parts of the western highlands and in the southwest of the province which is decreasing regularly by moving towards the northern and eastern regions. This is in line with the results of Jalali and Shafi'i (2012) investigations conducted for West Azarbaijan province. ). Examining the annual and seasonal changes of rainfall in different climate zones by Azarakhshi et al (2013), and Ghaderpour (2014) by the assessment of precipitation spatial trend in the watershed of Lake Urmia announced that the province has a rising and declining trend in rainfall on an annual basis and the results are in accordance with this study.

Rainfall variability and its impact on water resources are important climatic issues. Intra-annual variations in rainfall are characterized as precipitation concentration index (PCI). Another feature that directly correlates with the concentration of precipitation is the rain erosivity (Modified Fournier Index MFI). The aim of this study is to investigate the PCI and MFI indices and map their spatial variations. The Modified Fournier and precipitation Concentration indices were calculated using rainfall data from 55 meteorological stations located in Khuzestan province. To produce the spatial variations map, point information is converted to regional using geostatistical and deterministic methods. The results indicated that the ordinary and simple Kriging with Gaussian type have highest accuracy for interpolation of the PCI and MFI indices, respectively. According to the spatial variation map of the PCI, the highest values of that index are seen in the southern region and the lowest values are in the north and northeast of the Khuzestan province. The PCI values ranged between 20 and 31 indicating severe seasonality. The MFI values vary from 49 to 224 in which the highest values are for the northeast region of the province and the lowest ones are for the south and southwest zones. Generally Rainfall limited in a certain months.alues are for the northeast region of the province and the lowest ones are for the south and southwest zones. Generally Rainfall limited in a certain months.

Rainfall erosivity factor is the first noticeable point in soil erosion issues that plays very important role in detachment of soil particle from the origin bed. Hence, investigation of rainfall erosivity factor trend is necessary in decision-making and planning in order to manage soil and water resources. However, studies on various aspects of erosivity like trend and in interaction with precipitation and SPI index have not been attended well. The present study therefore aimed to investigate the rainfall erosivity factor trend based on the Fournier index in 28 stations throughout North-Khorasan Province during the period of 1987 to 2006 by using the Mann-Kendall test. In addition, the SPI and precipitation trend were comprehensively investigated for better characterization of erosivity trend analysis. Results showed that Noushirvan, Faruj, Ayerqayeh and Gholaman stations had decreasing trend and other study stations (71.85%) had increasing trend in the modified Fournier erosivity index. The SPI and precipitation in the study area indicated that most of the stations (89.28%) excluding Khartot, Noushirvan, Faruj and Ayerqayeh had increasing trend. The maximum and the minimum values of modified Fournier erosivity index with 70.97 and 33.44 mm were also assigned to Darkesh and Abiary Bojnourd stations, respectively.

Today, Soil erosion is considered as one of the important issues of watershed management at the national and global levels. Estimating risk of soil reduction and its spatial distribution is one of the key factors for successful assessment of soil erosion. Rain erosivity index is the most important factor affecting soil erosion and is a function of the physical properties of rain. The aim of this study is to evaluate and model rainfall erosivity indices using geostatistical techniques. In the present study, rain erosivity in Golestan province has been modeled and estimated through Fournier, modified Fournier, IAS and Ciccacci models and based on the 20-years statistical period (1999 to 2019) of the Meteorological Organization stations. After calculating the Rain erosivity factor for the desired stations, using inverse distance method (IDW), universal polynomial interpolation (GPI), radial basis function (RBF) and Kriging interpolation, map  of rain erosivity indices of the province were drawn and to select the best interpolation method, the statistical indices of root mean square error (RMSE), mean absolute error (MAE) and mean basis error (MBE) were used. The results showed that the modified Fourier method is the best index (based on RMSE, MAE and MBE less in all four interpolation methods) and the radial basis function method is the best method among the methods used to estimate of rain erosivity. The results also showed that the rate of rain erosivity in the central areas of the province, especially the Gorganrood watershed and also eastern north and north of province with average minimum and maximum annual rainfall (216.1 and 776.9) and several points in the southwest of the province with average minimum and maximum annual rainfall (2/205 and 751) have more than the amount of rain erosion coefficient that such changes are affected by the pattern of rainfall distribution, intensity and topographic characteristics. The study of rain erosivity power of Golestan province shows that the pattern of rain erosivity distribution is significantly affected by the average rainfall of the region. So that the amounts of erosivity and average rainfall in this province are consistent and show almost the same pattern of behavior.

In this research the indices EI30, AIm,ý KE>1ý as well as P/√tý were determined for 16 pluviograph as well as for 3 Namak Lake Basin nearby stations. Regression relationships were established between the dependent variables of EI30, AIm, KE>1ý as well as P/√tý Indices and other easily accessible rainfall indices of: fournier, modified fournier, maximum monthly rainfall, maximum daily rainfall, standard deviation of monthly and annual rainfall as well as pluviometer site elevations. This made the establishment of appropriate relationships between rainfall intensity dependent indices and the dependent variable of rainfall intensity (at stations where intensity was non-existent) possible. In the next step, the indices as well as easily accessible rainfall data from pluviograph stations were exploited to find out EI30 ,AIm ,ý KE>1ý as well as P/√tý indices, while using the previously obtained regression relationships.

Rainfall erosivity is one of the major factors of soil erosion that expressed as some indices. The objective of this study is to determine the appropriate rainfall erosivity index in West Azarbaijan in relation to soil loss at the erosion standard plates. After recording the rainfall amounts in a certain time periods, erosivity indices calculated and appropriate index was selected for the area. Selected index calculated through available indicators such as Modified Fournier, annual rainfall and average maximum daily rainfall in stations without rainfall Intensity statistics and the best index was obtained. To provide the Iso-erosive map, geostatistics based interpolation methods were used by cross validation. Results showed that AWT IMAGE were the best correlated with soil loss than other erosivity indices. The results also showed the modified Fournier index had a significant correlation at 95% with EI30. The error of the co-kriging method when compared to the IDW, Ordinary kriging, Universall kriging and spline methods declined by 10.57%, 0.71%, 4.6% and 0.67% respectively but due to the unstability of the EI30 data, Spline Interpolation method is well fitted for rain erosivity index. The annual value of this index obtained between 200 and 700 MJ mm ha h. Prepared map presence of rain erosion index decreased from West to East of the province.

Rainfall erosivity (RE) energy is an important factor on the soil detachment and transition of them implying an important role on the regional potential region erosion. . In this study SPI index was used in order to determine the climate condition and its consequent effects on RE in Fashand watershed, Elburz province. At first the drought, wet and normal periods were determined for four rain gage station and then, both EI30 and modified Fournier index (MFI) were calculated at each gauge station. The regression analysis was used to investigate the relationship between EI30, MFI and 24-hour rainfall as well as annual rainfall of data-logging rainfall stations. After that through applying the regression equation the EI30 was extrapolated for eleven typical rain gauges over the different climate periods. The best correlation was obtained between EI30 and annual rainfall (R2 = 0.71). The spatial zonation RE maps were extracted through Geostatistical analysis for drought, wet and normal condition . According to the findings the effects of climate variability on the amount of RE are significant. Maximum and minimum RE are related to the wet and dry period respectively. However the RE on the summer season of dry condition is more than the wet condition and such condition together with low vegetation cover related to the drought condition lead to complicated situation. Despite the popular thought that the low RE can be addressed into the drought condition the rainfall pattern affect the erosivity potential and not the amount of precipitation.

Rainfall erosivity as one of the major factors of soil erosion is expressed as indexes. The objective of this study is determining the appropriate rainfall erosivity index in Iran and generalizes it by its estimation from more readily available indexes to stations without rainfall intensity data and to determine the most accurate interpolation method for preparation of its map. For this reason, necessary data were collected from seven soil erosion research plots in Western Azerbyjan, Khorasan Razavi, Zanjan, Semnan, Mazandaran, Markazi, and Yazd provinces, respectively. The rainfall intensities were recorded, as was the sediment yield associated with storm events, and 64 different erosivity indices based on rainfall intensity were computed for these soil erosion research stations. Our founding shows that were the best correlated with sediment than other erosivity index. Further, rainfall erosivity indices, based on the amount of rainfall, were also computed for all soil erosion research plots and synoptic and climatic stations. The results showed that the modified Fournier index had a significant correlation with After normalizing the primary data, semi-variograms were determined and the best model was obtained. Then, different interpolation methods were compared and spline was chosen for drawing the rainfall erosivity map. The output map showed a decreasing trend from west and north to east and south of the country and this trend was correlated with climatic change from humid to semiarid regions.