State-space analysis of soil data: an approach based on space-varying regression models

The assessment of the relationship among soil properties (such as total nitrogen and organic carbon) taken along lines called transects is a subject of great interest in agricultural experimentation. This question has been usually approached through standard state-space methods by some authors in the soil science literature. Important limitations of the mentioned procedures used in practice are pointed out and discussed in this paper, specially those related to the model parameters, meaning and practical interpretation. In the standard state-space approach, based on an autoregressive structure, it does not present any parameters that express the variables relationship at the same point in space, but only at lagged points. Also, its model parameters (in the transition matrix) have a global meaning and not a local one, not expressing more directly the soil heterogeneity. Therefore, the objective here is to propose an alternative state-space approach, based on dynamic (space-varying parameters) regression models in order to avoid the mentioned drawbacks. Soil total nitrogen and soil organic carbon samples were collected on a Typic Haplustox. Samples were taken along a line (transect) located in the middle of two adjacent contour lines. The transect samples, totaling 97, were collected in the plow layer (0-0.20 m) at points spaced 2 meters appart. Results show the comparative advantages of the proposed method (based on an alternative state-space approach) in relation to the standard state-space analysis. Such advantages are related to a more adequate incorporation of soil heterogeneity along the spatial transect resulting in a better model fitting, and greater flexibility of the model's building process with an easier interpretability of the local model coefficients.