From fixed to condition-dependent emission factors: probabilistic tabular learning for wastewater N₂O inventories

Reliable estimation of nitrous oxide (N₂O) emissions from wastewater treatment remains a major challenge for greenhouse gas inventories. Current inventory practice typically relies on static, site-invariant emission factors (EFs), despite evidence that episodic N₂O fluxes and heterogeneous monitoring protocols produce nonlinear and highly skewed EF observations across real-world wastewater treatment systems. Here, we present DynEF-PFN, a process-informed and protocol-aware tabular learning framework for estimating process-resolved probabilistic EFs from sparse, partially observed, and non-Gaussian evidence. The framework uses structured prior support to regularize poorly sampled operating regions while retaining real literature observations as the empirical basis for evaluation. Across heterogeneous wastewater treatment processes, DynEF-PFN achieved high predictive fidelity on the original EF scale (MAE = 0.306, RMSE = 0.624, R² = 0.931), outperforming CatBoost and interval-capable probabilistic baselines in accuracy, coverage, and sharpness. By conditioning EF distributions on monitoring context, process configuration, and aeration or mass-transfer descriptors, DynEF-PFN represents reported EFs as condition-dependent estimates shaped by both operating and observational settings. In pathway-level inventory translation, condition-dependent EFs reallocated relative source contributions among treatment routes and revealed process-specific deviations that fixed factors tend to obscure. DynEF-PFN thus provides an Intergovernmental Panel on Climate Change (IPCC) Tier 3-compatible framework for generating process-resolved, condition-dependent EFs for wastewater N₂O inventories, supporting more robust inventory development and mitigation prioritization.