Background Use of the fallout radionuclide ¹³⁷Cs as a tracer recently has been widely employed for the assessment of soil erosion. In the ¹³⁷Cs method, the magnitude of the rate of soil erosion is estimated by comparing the ¹³⁷Cs inventory of the sampling points with the local reference inventory, therefore, it is of extreme importance to determine the ¹³⁷Cs reference inventory obtained from a local stable site neither erosion nor deposition occurred while studying soil erosion using this tracing technique.

Methods Based on the measured data from 147 meteorology stations and the ¹³⁷Cs fallout model derived by Walling & He, a case study on the application of geographically weighted regression Kriging interpolation (GWRK) combined with principal component analysis (PCA) for the assessment of the spatial distribution of the ¹³⁷Cs reference inventories was undertaken at Sichuan province, Southwest China.

Results 1) Using PCA, the transformation process to turn the influence factors of longitude, latitude and precipitation into 2 principal component variables were educed. This measure not only maintained the 90% information of original data, but also decreased the multicollinearity among the variables significantly. It was the basis for the further interpolation of ¹³⁷Cs reference inventory. 2) With the principal components as input variables, the spatial distribution of the ¹³⁷Cs reference inventories at Sichuan province were obtained by 3 different methods:the GWRK method, the ordinary Kriging (OK) method and global regression Kriging method (GRK). In the meantime, some indicators such as Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Mean Absolute Relative Error (MARE) were calculated for evaluating the accuracy of different interpolation results. In terms of the interpolation results, taking into consideration of various influence factors and their spatial non-stationarity, the GWRK method had better accuracy compared with the other methods. Furthermore, this simulation result is in exactly agreement with those of the measurement.

Conclusions This study reveals the regulars of space distribution of ¹³⁷Cs reference inventory and the effect of different factors. Additionally, the results of this study also demonstrate that it is obviously an approach available for obtaining the spatial distribution of ¹³⁷Cs reference inventory with high resolution and accuracy to adopt the GIS interpolation on the basis of the measured data, which is referential for the study of soil erosion using ¹³⁷Cs tracing technique.