Empirical nitrogen and sulfur critical loads of US tree species and their uncertainties with machine learning

Critical loads (CLs) of atmospheric deposition for nitrogen (N) and sulfur (S) are used to support decision making related to air regulation and land management. Frequently, CLs are calculated using empirical methods, and the certainty of the results depends on accurate representation of underlying ecological processes. Machine learning (ML) models perform well in empirical modeling of processes with non-linear characteristics and significant variable interactions. We used bootstrap ensemble ML methods to develop CL estimates and assess uncertainties of CLs for the growth and survival of 108 tree species in the conterminous United States. We trained ML models to predict tree growth and survival and characterize the relationship between deposition and tree species response. Using four statistical methods, we quantified the uncertainty of CLs in 95 % confidence intervals (CI). At the lower bound of the CL uncertainty estimate, 80 % or more of tree species have been impacted by nitrogen deposition exceeding a CL for tree survival over >50 % of the species range, while at the upper bound the percentage is much lower (<20 % of tree species impacted across >60 % of the species range). Our analysis shows that bootstrap ensemble ML can be effectively used to quantify critical loads and their uncertainties. The range of the uncertainty we calculated is sufficiently large to warrant consideration in management and regulatory decision making with respect to atmospheric deposition.