Mapping rainfall erosivity in Lorestan province using Kriging geostatistic technique

Rainfall erosivity is defined as the aggregative power of the rain. If other effective features on soil erosion be considered constant then soil loss could be directly connected to rainfall erosivity. Rain erosion term was proposed by Wichmeier and Smith in 1978 to consider the effect of climate on raw erosion. Measurements of meteorological parameters by the traditional methods require a dense rain gauge network. But, due to the topography and cost problems, it is not possible to create such a network in practice. Given the significant change in rainfall in time and space on the one hand and low rain-gauge stations to record rainfall on the other hand, the necessity of using geostatistical methods for rainfall erosivity mapping is inevitable. Geostatistical methods use the spatial correlation between observations in the estimation processes. In these cases the spatial distribution pattern of rainfall erosivity can be produced using different methods of interpolation. Study area Lorestan province is located in southwest of Iran and covers an area of 28249 square kilometers. It is located between the latitudes 32º 37' and 34º 22' N and the longitudes 46˚51ʹ and 50˚30ʹE. The main objective of this research were: (1) analyze the spatial distribution of rainfall erosivity using two different interpolation methods namely ordinary Kriging and simple Kriging; (2) put forward the best interpolation method through cross-validation, construct the high resolution grid data of rainfall erosivity and provide the reliable information for relevant researches
 In the first step, the precipitation data collected from 53 precipitation stations and Modified Fournier Index (MF) calculated based on Eq. (1)
                                                                                                (1)
 Where MF is the modified Fournier index value (mm), pi  is averagemonthly precipitation (mm) and P is average annual precipitation (mm). Then Eq. (2) and Eq. (3) were used to estimate rainfall erosivity or R-factor values (MJ mm ha -1 h -1 year -1).
 
It is suggested that Eq. (2) be applied for locations with MF values less than 55 mm and Eq. (3) be used for locations with MF values greater than 55 mm.
  In this article two interpolation techniques namely simple and ordinary Kriging were compared in GS+5.1.1 and ArcGIS10.3 software’s in order to determine which one describe better the spatial distribution of rainfall erosivity. Kriging methods assume that the spatial variation of a continuous climatic variable is too irregular to be modeled by a continuous mathematical function, and its spatial variation could be better predicted by a probabilistic surface. The predictions of Kriging-based methods are currently a weighted average of the data available at neighboring sampling points (weather stations). The weighting is chosen so that the calculation is not biased and the variance is minimal. A function that relates the spatial variance of the variable is determined using a semi-variogram model which indicates the semi variance between the climatic values at different spatial distances. The resulting maps from interpolation were compared by using a set of validation statistics include Mean error (ME), Mean Standardized Error (MSE) and the root mean square error (RMSE) by Eq. (4), (5) and (6)
  Based on the results, rainfall erosivity values varied from 11.1 to 749.5 MJmmha−1 h−1 y−1. Differences between the simple and ordinary Kriging models regarding the validation statistics were narrow, but allowed for a comparison. The obtained results showed that ordinary Kriging with higher R2 and lower ME, MSE and RMSE had better precision in mapping rainfall erosivity. The spatial distribution of rainfall erosivity showed the areas along north-south of Lorestan province and central regions had higher values while lower rainfall erosivity was seen in the western and eastern areas of the study area. The availability of high-quality environmental maps is a key issue for agricultural and hydrological management in many regions of the world.  Produced rainfall erosivity map in this research can be used for estimation of soil loss by USLE model. Rainfall erosivity maps also can be suitable as guidance for soil conservation practices and identifying areas with the high potential of soil retention as an ecosystem service. Further research may be directed to find reliable erosivity indices which can be computed from daily precipitation data.