Gated recurrent unit model for forecasting greenhouse gas concentrations with uncertainty quantification

Reliable and accurate farm-level forecasting of greenhouse gas concentrations from dairy cattle is important to the formulation of climate change mitigation strategies and policy planning in livestock systems. This study proposed an uncertainty-aware deep learning model that integrated data from multiple sources, including remote sensing and ground-based sensors, to forecast hourly concentrations of nitrous oxide, methane, and carbon dioxide in a controlled zero-grazing dairy system. The forecasting was implemented by formulating a causal multivariate time series using a 24-h lookback window with direct one-step-ahead prediction. A two-stage model evaluation protocol, model hyperparameter tuning via rolling cross-validation, and holdout Test Evaluation were implemented during model development. The model was evaluated using the coefficient of determination, root-mean-square error, and mean squared error. To evaluate model reliability, the study employed a dual-output gated recurrent unit to estimate the conditional mean and heteroscedastic variance, and Monte Carlo dropout and Gaussian Negative Log-Likelihood to quantify epistemic and aleatoric uncertainty. Results indicate stable generalisation across temporal folds and strong probabilistic calibration, with empirical 95% coverage ranging from 93.6 to 94.8% on the holdout test set. Feature selection indicates that rainfall, normalised difference vegetation index, humidity, temperature, trend, and season influence the prediction of concentration. The study shows that incorporating exogenous variables improves model performance. The proposed framework demonstrates proof of concept for controlled zero-grazing systems, with potential for broader application following multi-site validation.