Bayesian spatial regression for digital mapping of soil herbicide dynamic

Abstract

Retention and dissipation processes lead the environmental dynamics of herbicides in soils. Landscape mapping of herbicide dynamic parameters related to sorption to soil (Kd) and degradation (half-life) is useful in environmental risk assessments. However, analytical quantification of herbicides in the soil matrix is too costly for being applied in extensive soil surveys. We developed and illustrated spatial regression models that use site-specific covariates of sampled soils as predictors of herbicide Kd and half-life at unsampled sites and allow us for digital soil mapping (DSM) of herbicide dynamics. First, we selected from a large set of potential environmental (edaphoclimatic and agricultural management) variables the explanatory site-covariates by coupling through machine learning techniques and predictive criteria. Second, we fitted a hierarchical Bayesian regression model (BR) using site-covariates and a random site effect to explain Kd and half-life variability observed in a sample of n=90 soils and n=60 soils fortified with Glyphosate and Atrazine herbicide molecules in lab conditions. Integrated Nested Laplace Approximation (INLA) with SPDE was used to estimate model parameters, hyperparameters and predict the dynamic parameters from the posterior distribution of predicted values at each site of the prediction grid. Thus, Kd and half-life were mapped at a regional grid through the predicted means and the projection of the spatial random effect. The target spatial domain was the Córdoba Province in central Argentina. Results from BR were compared with site-specific predicted values derived from Regression Kriging and Random Forest with kriged residuals models. The predictive performance was evaluated according to a design that varies the number of explanatory variables and the sample site used for model fitting. BR fitted with the selected environmental variables was similar against other methods on quantitative criteria of statistical performance (i.e., prediction errors, correlation between observed and predicted values, average explained variance) with the advantage of providing a direct quantification of the uncertainty of predicted values. In conclusion, the spatial Bayesian INLA-SPDE model strategy is suitable for mapping complex edaphic processes, such as herbicide sorption to soils and dissipation. BR models provide regression coefficients which enhance environmental interpretations and are easier to obtain site-specific prediction uncertainty measures.