Identifying causal pathways and risk-decision rules for nitrous oxide emission hot moments in wastewater treatment plants using probabilistic causal machine learning.

Nitrous oxide (N_2O) emissions from biological wastewater treatment represent a significant challenge for climate-responsible operation due to their intermittency and occurrence as short-lived emission hot moments. Effective mitigation therefore requires accurate prediction and systematic identification of causal pathways and operational risk conditions. This study develops a probabilistic causal machine learning framework based on long-term online monitoring data from a full-scale wastewater treatment plant for low-emission process control and operational management. An optimal predictive model is first established to characterize N_2O dynamics under varying operational regimes. Building upon this foundation, cohort-based SHapley Additive exPlanations are used to identify regime-dependent nonlinear effects of key operational variables, including dissolved oxygen, ammonium, nitrate, and temperature. Linear Non-Gaussian Acyclic Model-based causal discovery is then used to characterize causal pathways associated with N_2O emission hot moments under different operational regimes. Copula-based joint probability analysis is conducted to quantify the likelihood of N_2O emission hot moments under interacting process conditions. Results demonstrate that N_2O emission hot moments are not triggered by single-factor thresholds but emerge from specific combinations of operational states, revealing interaction-dominated and regime-sensitive causal pathways. By converting interpretable machine learning outputs into probabilistic risk-decision rules, the proposed framework provides actionable guidance for adaptive aeration control, substrate load regulation, and proactive emission mitigation. This study establishes a data-driven framework for interpreting and managing N_2O emissions in biological wastewater treatment. Overall, the proposed framework provides practical support for proactive N_2O emission mitigation while maintaining process stability in full-scale wastewater treatment plants.