Emissions of nitrogen oxides (NO_x) and ammonia (NH₃) result in atmospheric deposition of nitrogen compounds onto the land, surface, which can lead to acidification and eutrophication (nitrogen enrichment) of terrestrial and aquatic ecosystems. The cumulative impacts of atmospheric deposition on ecosystems affect timber production, carbon sequestration, soil fertility, biodiversity, habitat preservation, commercial and recreational fishing, and tourism.

Critical loads (CLs) are estimates of a quantitative threshold for levels of deposition above which significant harmful ecological effects occur. Typically, this threshold is reported as a single value, often with an uncertainty estimate, for a specific class of an impacted endpoint. For example, a single CL may be reported for a particular species of plant. However, environmental factors such as climate and soil conditions may influence the sensitivity of individuals of a species to harmful effects from nitrogen deposition. As a result, the CL value for individuals of the same species may vary over space and time due to variations in environmental conditions. These variations are not adequately represented in the reported CL values that are most commonly used.

We recently developed machine learning techniques to estimate nitrogen-CLs for 108 tree species. The machine learning methods use environmental factors to support the CL values. In this work, we extend these methods to calculate the variation in sensitivity to atmospheric deposition across individuals of a particular tree species due to differences in environmental factors. Using variable interactions represented within the machine learning models, we apply a new assessment approach to estimate CLs for atmospheric deposition of nitrogen at individual sites across the U.S. Variability is estimated by accounting for the effect that variables, including soil characteristics and climate, have on tree sensitivity to deposition. In future work, these results can be used to investigate the implications of future climate scenarios for these CLs.