Hierarchical Spatial Modeling and Prediction of Multiple Soil Nutrients and Carbon Concentrations

Abstract

Modeling the multivariate spatial distribution of soil carbon and nutrients has been a challenge for ecosystem ecologists. There is a need for explanatory models, which give insight into socio-economic and biophysical controls on soil spatial variability. We propose a hierarchical Bayesian modeling specification, an approach that takes into account the spatial covariates as well as the inter-dependent nature of soil nutrients and carbon pools. We develop the model to explain variability in soil nutrient and carbon pools in the Central Arizona Phoenix Metropolitan region where soil-composition has changed considerably over the years due to socio-economic factors. A fully Bayesian statistical analysis of how these changes have affected soil nutrients provides insight as to how socio-economics influence changes in ecology. Our model included five geomorphic, ecological, and socio-economic independent variables that were used to predict soil total N, organic C, inorganic C, and extractable . Using six levels of hierarchy, we fit a suitable spatial hierarhical model. Using a Bayesian co-kriging strategy, we generate appropriate values used for predictions at new locations where covariate information is unavailable. We compare prediction results from standard models and show that our model is richer and so is the interpretation. To the best of our knowledge, this is the first work that applies hierarchical Bayesian modeling techniques and kriging strategies to study multivarate soil nutrient and carbon concentrations. We conclude a discussion of our findings and the broader ecological applicability of our modeling style.