Spatial methods to analyze the relationship between Spanish soil properties and cadmium content

In this study, concentrations of cadmium using 3778 samples encompassing the total size of Spain (about 505 km²) were investgated. Two novel spatial methods namely Moran eigenvector spatially varying coefficient (MESVC) and spatially filtered unconditional quantile regression (SF-UQR) were employed with the aim of avoiding the problem of local collinearity which is prevalent in regression models. Additionally, the spatially varying coefficients methods were applied to assess the influence of soil properties together with soil texture on the spatial variations of cadmium. It was indicated that the overall level of cadmium is low compared to the concentrations found around the world. In particular, the values of Cd varied between 0.01 and 2.00 mgkg^-1, with the median of 0.23 mgkg^-1. The residual standard error and adjusted R² produced by MESVC were 0.16 and 0.69, respectively which are better than 0.21 and 0.39 yielded by the SF-UQR model. Both of these models outperformed compared to the geographically weighted regression (GWR) and the performance of MESVC was also better than the traditional method of kriging. For instance, in terms of willmott index (d) and root mean squared relative error (RMSRE), the MESVC had superior performance with values equal to 0.612 and 0.275 compared to 0.399 and 0.379 obtained for the ordinary kriging. The MESVC and GWR demonstrated that CaCO₃, sand, silt and clay had a negligible influence on spatial variations of cadmium whereas, EC had the largest contribution followed by SOM and pH.