Beyond point predictions: Probabilistic algal biomass forecasting for risk-based management via Bayesian additive regression trees

Reliable algal biomass forecasting is critical for harmful algal bloom early warning in eutrophic lakes, yet current machine learning applications predominantly deliver deterministic point predictions without quantifying predictive uncertainty. To address this critical issue, we introduced Bayesian additive regression trees (BART) to enable probabilistic forecasting of algal biomass. Adapting to the distributional output of BART, we proposed an exhaustive-subset CRPS-based feature importance algorithm to interpret variable contributions to the full predictive distribution. Taking 1- to 5-day-ahead forecasts of chlorophyll- a (as a proxy for algal biomass) in a typical eutrophic lake (Lake Dianchi, China) as a case study, we found that BART achieved competitive point accuracy (R 2 ranging from 0.79 to 0.59): its 1-day performance was comparable to the strongest benchmark, whereas clearer advantages emerged at longer lead times. Moreover, we showed that the distributional output of BART facilitated uncertainty communication through intervals and probabilities for risk-based algal biomass assessment. Current chlorophyll- a and water temperature were identified as key drivers of future chlorophyll- a , which is broadly consistent with mechanistic understanding. We also characterized probabilistic driver-response relationships, enabling decision-makers to assess both expected responses and their uncertainty. Therefore, BART may serve as a promising and trustworthy tool for algal biomass forecasting and uncertainty-aware water-quality management in real lake ecosystems.