Correction of in-situ portable X-ray fluorescence (PXRF) data of soil heavy metal for enhancing spatial prediction

Heavy metal data measured by portable X-ray fluorescence (PXRF), especially by in-situ PXRF, are usually affected by multiple soil factors, such as soil moisture (SM), soil organic matter (SOM), and soil particle size (SPZ). Thus, a correction may be needed. However, traditionally-used correction methods, such as non-spatial linear regression (LR), cannot effectively correct the spatially non-stationary influences of the related soil factors on PXRF analysis. Moreover, these correction methods are not robust to outliers. In this study, robust geographically weighted regression (RGWR) was used to correct in-situ and ex-situ PXRF data of soil Pb in a peri-urban agricultural area of Wuhan City, China. The accuracy of the corrected PXRF data by RGWR was compared with those by non-spatial and spatial but non-robust methods (i.e., LR and GWR). In addition, to find an appropriate method of using the corrected PXRF data for more accurate spatial prediction, we compared robust ordinary kriging with the corrected PXRF data as part of hard data (ROK-CPXRF) and robust ordinary cokriging with the corrected PXRF data as auxiliary soft data (RCoK-CPXRF). Results showed that (i) RGWR obtained higher correction accuracy than LR and GWR on both the in-situ and ex-situ PXRF data; (ii) the accuracy of the RGWR-corrected in-situ PXRF data was increased nearly to that of the RGWR-corrected ex-situ PXRF data; (iii) given the same amount of sample data, ROK-CPXRF obtained higher prediction accuracy than RCoK-CPXRF. It is concluded that the methods suggested in this study may largely promote the application of in-situ PXRF technique for rapid and accurate soil heavy metal investigation in large-scale areas.