Empirical nitrogen and sulfur critical loads of U.S. tree species and their uncertainties with machine learning
Critical loads (CLs) of atmospheric deposition for nitrogen and sulfur are used to support decision making related to air regulation and land management. Frequently CLs are calculated CLs using empirical methods, and the certainty of the results from these methods depends on their accurate representation of underlying ecological processes. Many methods fail to incorporate important aspects of these relationships, including non-linearities and interactions with environmental variables. Moreover, CLs are often defined without an explicit quantification of uncertainty. Machine learning models perform well in empirical modeling of processes with non-linear characteristics and significant variable interactions and can be used to assess uncertainty in results. We used bootstrap ensemble machine learning 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 machine learning models to predict tree growth and survival and used partial dependence to characterize the relationship between deposition and tree species response. Using four statistical methods, we quantified the uncertainty of CLs in 95% confidence intervals (CI) and compared these results to previously reported CL values. Our analysis shows that bootstrap machine learning ensembles can be effectively used to quantify critical loads and their uncertainties. We show that the CLs for just over half of tree species are uncertain with our methods (CI = ± >10 kg N ha-1 yr-1 or ± 5 kg S ha-1 yr-1). At the lower bound of the CL uncertainty estimate, 80% or more of tree species have been impacted by N 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). CL uncertainty from techniques such as bootstrap ensemble machine learning can be used to support decision-making with respect to atmospheric deposition.