Spatial extrapolation of cadmium concentration in terrestrial mosses using multiple linear regression model predictions across French biogeographical regions

The French Moss Survey employs forest mosses as indicators to monitor the deposition of atmospheric substances, notably focusing on cadmium (Cd), a known carcinogenic and contributor to respiratory illnesses. This comprehensive study encompasses 55 variables to understand Cd accumulation in terrestrial mosses in France. These variables include moss species, tree cover, biogeographical markers, land use area, proximity to road and rail networks, soil concentration of Cd and atmospheric concentration and deposition of Cd using a physical model. The response variable undergoes a complementary log-log transformation to constrain prediction values within the maximum Cd content in mosses. We have built a regression model to improve predictions, considering the impacts of covariates in France. This model retains biogeographical effects, leading to data segmentation into four distinct biogeographical zones: Atlantic, Continental, Mediterranean and Alpine. Subsequently, zone-specific regression models are explored to refine predictions and consider the impacts of covariates specific to each region, such as those related to railways and roads of the Mediterranean zone. Our biogeographical models effectively mitigate spatial correlation issues and yield accurate predictions, as evidenced by the leave-one-out cross-validation assessment. Compared to ordinary kriging map, the regression prediction maps highlight the contributions of certain covariates, such as the EMEP atmospheric transport model, to areas with high Cd concentrations. Furthermore, these maps exhibit new areas with high (resp. low) Cd concentrations due to high (resp. low) values of the covariates.