[Comparison on the methods for spatial interpolation of the annual average precipitation in the Loess Plateau region]

Based on 57 years (1957-2013) daily precipitation datasets of the 85 meteorological stations in the Loess Plateau region, different spatial interpolation methods, including ordinary kriging (OK), inverse distance weighting (IDW) and radial-based function (RBF), were conducted to analyze the spatial variation of annual average precipitation regionally. Meanwhile, the mean absolute error (MAE), the root mean square error (RMSE), the accuracy (AC) and the Pearson correlation coefficient (R) were compared among the interpolation results in order to quantify the effects of different interpolation methods on spatial variation of the annual average precipitation. The results showed that the Moran's I index was 0.67 for the 57 years annual average precipitation in the Loess Plateau region. Meteorological stations exhibited strong spatial correlation. The validation results of the 63 training stations and 22 test stations indicated that there were significant correlations between the training and test values among different interpolation methods. However, the RMSE (IDW = 51.49, RBF = 43.79) and MAE (IDW = 38.98, RBF = 34.61) of the IDW and the RBF showed higher values than the OK. In addition, the comparison of the four semi-variagram models (Circular, Spherical, Exponential and Gaussian) for the OK indicated that the circular model had the lowest MAE (32.34) and the highest accuracy (0.976), while the MAE of the exponential model was the highest (33.24). In conclusion, comparing the validation between the training data and test results of the different spatial interpolation methods, the circular model of the OK method was the best one for obtaining accurate spatial interpolation of annual average precipitation in the Loess Plateau region.