Geostatistical approach for identifying scale-specific correlations between soil thickness and topographic attributes

Abstract

This paper investigates how the spatial correlations between topographic attributes and a soil thickness can be improved by focusing on the relationships between them at specific spatial scales. In addition, this paper examines the effects of the topographic attribute data sources that are used as explanatory variables for modeling the response variable, and considers the possibility of model extrapolation for mapping beyond the area where the model was established. Here, factorial kriging analysis (FKA) and partial least square regression (PLSR) analysis are used to separate nuggets and small- and large-scale structures in data including four topographic attributes and soil thickness (ST). These analyses were conducted at different scales to analyze the relationships between ST and the selected topographic attributes in the southwest region of the Parisian Basin. The structural correlation coefficients from the FKA show strong correlations between the variables. These correlations, which change as a function of spatial scale, are not revealed by the linear correlation coefficients. The Eigen vectors from the principal component analysis that was performed on the small-scale and large-scale structures of the linear co-regionalization model are used to obtain ST and the topographic attributes at both spatial scales over the study area. The ST models are built as a function of topographic attributes using PLSR. Results have shown that the models built using variables that were assessed at a specific scale are better at predicting the target variable than models that were built using raw data. Regarding the models that were built using raw data, the structural correlations that occur at different spatial scales are merged together and the variance–covariance matrix of the nugget that represents data noise is not filtered out. Measures of model performance that are based on a validation data set have shown that the model based on small-scale structure (Model-S) is better for predicting soil thickness than the model based on large-scale structure (Model-L). The effects of topographic attribute data sources as explanatory variables for modeling ST are less significant than the effects of the two models for mapping. Moreover, extrapolation of the model-S beyond the area where it was generated is appropriate. The decomposition process is associated with a modeling approach, such as the PLSR, which accounts for the collinearity between predictor variables and leads to an efficient prediction model. These results are important for modeling soil properties based on topographic attributes and for spatially generalizing models that have been established over small to large areas. Thus, in the presence of nested variogram models, the correlations between variables of interest and auxiliary information should be improved by filtering out some of the spatial structures by factorial kriging. The information filtered is associated with an appropriate approach for modeling when collinearity occurs between the predictor variables and provides a suitable model for predicting and spatially generalizing a locally established model.