Spatio-temporal geochemical data: a novel inferential framework for the analysis

In recent years the increasing need for analysing high-dimensional and complex data structures led to the development of functional data analysis. In this broad framework, the aim of this contribution is to introduce a functional regression framework for modelling space-time geochemical measurements. The motivating data set includes monthly measurements of potassium chloride pH taken from the site near Brno, Czech Republic. Sampling locations were selected with the purpose of testing if the site can be divided in two parts, agricultural and for- est soil, according to its chemical properties. We suggest treating measurements as functions of time distributed in space and propose a function-on-scalar spatial regression model to describe the tempo- ral distribution of the geochemical elements. To test for the possible differences between the two soil types, we propose a non-parametric functional testing procedure. The inference cannot be done directly on the original observations due to their dependency on spatial co- ordinates, instead, the procedure is performed on the residuals of the spatial functional model. Several regression models were fit to the data in order to derive spatially independent and thus permutable residu- als. The proposed methodology will be demonstrated on the available geochemical dataset and geological interpretation of the results will be given.