3D spatial distribution of soil pollutants based on geo-shadowing anisotropic RBF-PCA

Abstract

Research on soil contamination has become increasingly important, but there is limited information about where to sample for pollutants. Thus, the use of three-dimensional (3D) spatial interpolation techniques has been promoted in this area of study. However, the application of traditional interpolation methods is limited in geography, especially in the expression of anisotropy, and it is not associated with geographical properties. To address this issue, we used a test site (a factory in Nanjing) to develop a new research method based on the geographical shading radial basis function (RBF) interpolation method, which considers 3D anisotropy and geographical attribute expression. Drilling and uniform sampling were used to sample the contaminated area at this test site. This approach included two steps: i) An ellipsoid with anisotropic properties was constructed. Thus, the first step was to determine the shape of the ellipsoid using principal component analysis (PCA) to determine the main orientations and construct a rotational and stretched matrix. The second step was determining the ellipsoid size by computing the range using the variogram method for orientations. ii) During field measurement, the geospatial direction influences soil attribute values, so a shadowing calculation method was derived for quadratic weight determination. Then, the weight of the attribute value of known points can be assigned to meet the field conditions. Lastly, the model was evaluated using the root mean square error (RMSE). For the 2D space, the RMSE values of Kriging, RBF, and the proposed method are 6.09, 7.12, and 5.02, respectively. The R2 values of Kriging, RBF, and the proposed method are 0.871, 0.832, and 0.946, respectively. For the 3D space, the RMSE values of Kriging, RBF, and the proposed method are 2.65, 2.23, and 2.58, respectively. The R2 values of Kriging, RBF, and the proposed method are 0.934, 0.912, and 0.953, respectively. The resulting fitted model was relatively smooth and met experimental needs. Thus, we believe that the interpolation method can be applied as a new method to predict the distribution of soil pollutants.