Analysis of the accuracy of the various interpolation methods in estimating the rainfall distribution in order to select the most optimal algorithm (Case Study: Kurdistan Province)

  Environmental management requires continuous spatial information of the environmental variables. However, many of these data are taken discretely and point by point. Therefore, the methods to convert point data to continuous data have become indispensable tools (Lee et al., 2014: 173). The spatial interpolation makes able the conversion of point data to area data (Chang, 2004: 275) by predicting the values of a main point variable in the sample area (Barov and Daniel, 1998: 244). There are different algorithms for spatial interpolation (Faraji Sabokbar and Azizi, 2006: 1), which generally fall into two deterministic and geo-statistics categories (Mir Mousavi et al., 2009: 107). In deterministic methods (Inverse Distance Weighting (IDW), Radial Basis Function (RBF), and so on), interpolation is done according to the level of the sampling points and similarities. However, geo-statistical methods (Kriging) of spatial correlation quantity consider sampling points, and estimates based on the location of the non-measured samples (Taze et al., 2008: 8). In this study, in order to assess the accuracy of the various interpolation methods to estimate the rainfall distribution of Kurdistan Province, pluviometry stations, synoptic, and climatology data were used. After reviewing the statistical situation of the stations, statistical period of 2001-2013 has been selected, and among all stations in the basin, stations, which had had 12 years of full or recyclable statistics until 2013 were selected for the study. It must be noted that the selection of the stations was according to their statistics rebuilt, by the application of the highest correlation with the adjacent stations method. Finally, data quality and data sets normality were recorded, and were evaluated by using Komogorov-Smirnov and Chi square X2 statistical tests. In addition, the digital elevation model data, collected by the SRTM satellite sensors with spatial resolution of 30 m, as well as analytic functions of the ArcGIS 10.2.2, Surfer 11, and IBM SPSS Statistics 22 software were used. After reviewing the data of the available stations (77 pluviometry stations, 22 synoptic and climatology stations of the Meteorology Organization, and 76 pluviometry and evaporation stations of the Department of Energy), according to the statistical course of the stations, and with regard to the missing rainfall data in the reconstruction, the least common period of it should not be less than 10 years (Sun and Patterson, 2006: 1990). The normality of the test data was done, and 145 stations were selected for analyzing of the interpolation methods, and choosing the best method. The methods used in this study were Inverse Distance Weighting, Spline (with Tension, Thin Plate and Completely Regular functions), Ordinary Kriging (with Circular, Spherical, Exponential, and Gussian functions), and Universal Kriging (with Rational Quadratic and Liner functions) are. Figure2 shows the steps of the study to select data and the most optimal method. After depicting the spatial rainfall data, the normal distribution of them was investigated by Komogorov - Smirnov and Chi square X2. The results showed that the data distribution at the level of 95% has no significant difference with a normal distribution. In order to analyze the accuracy of the various interpolation methods, the models were implemented using the GIS Arc Software. By applying each of these models on rainfall data, the maps were obtained (Figure 5). In order to evaluate and determine the most optimal model, the validity and the accuracy of the maps were evaluated. As it mentioned in the previous section, the more the Mean Absolute Error (MAE) and the closer Mean Bias Error (MBE) to zero, the accuracy of the model is higher. On the other hand, the less the Root Mean Square Error (RMSE), and the higher the correlation coefficient (R2), the model error is less. Table1 shows the error rate of implementation of the interpolation methods. Based on the findings of the study, the lowest error observed belongs to the Ordinary Kriging Method of interpolation with the circular function. After that, it belongs to the General Kriging Method with the Quadratic Variogram. In general, the Kriging method provides a higher accuracy than the other methods. In this study, the accuracy of the various algorithms was compared in the interpolation of rainfall distribution in Kurdistan Province. To compare the actual results, the same conditions were used to assess the accuracy. Then the most important methods of the validity were extracted and identified: Mean Absolute Error (MAE), Mean Bias Error (MBE), Root Mean Square Error (RMSE), and correlation coefficient (R2). Ordinary Kriging Method of interpolation with the circular function had the highest accuracy compared to the other methods (Table 1). One of the most important factors to achieve high accuracy in this method is its ability to depict the non-bias linear estimation. Of course, other methods, especially the Universal Kriging with Quadratic function, due to the use of local procedures offers an acceptable accuracy