Uncertainty decomposition and quantification of seasonal precipitation forecasting based on Bayesian neural networks

Seasonal climate forecasts are inherently uncertain due to the chaotic nature of the climate system and the limitations of predictive models. Quantifying and decomposing this uncertainty are essential for reliable forecasts. In this study, we investigate machine learning-based seasonal forecasting (MLSF) using a Bayesian adaptation of TelNet, a neural network model for precipitation prediction. We reformulate TelNet as a Bayesian Neural Network trained via variational inference, with alternative implementations based on Monte Carlo (MC) dropout. Both continuous (ensemble-based) and categorical (tercile-based) prediction strategies are assessed. Training is conducted with ERA5 reanalysis and historical simulations from 18 CMIP6 models, followed by validation and testing with ERA5 data over South America. We decompose predictive uncertainty into ML-aleatoric (data-related) and ML-epistemic (model-related) components. Results show that ML-aleatoric uncertainty dominates, being on average two orders of magnitude larger than ML-epistemic uncertainty. ERA5-trained models exhibit lower aleatoric uncertainty but are often overconfident and not well-calibrated, whereas CMIP6-trained models show higher aleatoric uncertainty but improved calibration. Models trained with continuous targets achieve lower uncertainty than categorical models, which lose information through discretization. Probabilistic accuracy, evaluated via Ranked Probability Score (RPS), indicates that CMIP6-based models trained with continuous targets and Continuous Ranked Probability Score (CRPS) loss perform best overall. Seasonal analysis reveals better calibration in austral summer (DJF) compared to winter (JJA), consistent with stronger teleconnection signals during summer. Finally, case studies of El Niño, La Niña, and neutral years demonstrate that forecast confidence and uncertainty strongly depend on the training dataset and target representation.