Probabilistic assessment of algal nutrient limitation across lakes, leveraging trends with temperature and depth

Abstract Lake eutrophication remains a significant challenge for water‐quality management across the world. Many management strategies focus on reducing nutrient inputs, but other environmental factors can substantially influence the yield of algal biomass for a given level of nutrients. While various large‐scale studies have explored how different lake characteristics impact eutrophication, there remains a need to integrate these factors into a comprehensive model capable of assessing nitrogen vs. phosphorus limitation. In this study, we refine chlorophyll–nutrient relationships across the conterminous United States by considering auxiliary variables (i.e., temperature, lake depth, and nutrient enrichment) within a Bayesian hierarchical framework. We leverage over 4000 sampling events of 2755 different lakes from the National Lakes Assessments (2007–2022) to inform model development. We first consider auxiliary variables independently, exploring how they influence the intercept, slope, and critical nutrient ratio (nitrogen : phosphorus) in a regression to predict chlorophyll based on the limiting nutrient. Next, we integrate significant auxiliary variables into a comprehensive model for chlorophyll prediction. Results indicate that the critical nutrient ratio increases in relation to increased lake depth, and the slope of the nutrient–chlorophyll relationship increases with increasing temperature. We apply the model to map mean summer conditions across US lakes and find that 23% and 16% of lakes are strongly limited by phosphorus and nitrogen, respectively (i.e., at > 90% probability). These proportions, however, vary substantially across different subregions. Overall, the probabilistic modeling approach and results can serve as an effective tool to inform water resources management, especially at large spatial scales.