Distributional Bias Correction for Madden--Julian Oscillation Forecasts

Subseasonal-to-seasonal weather forecasts are important for anticipating weather-related impacts and risks, and the Madden--Julian Oscillation (MJO) is a major source of predictability on these timescales, influencing tropical rainfall and large-scale atmospheric circulation. Operational dynamical MJO forecasts exhibit lead-time-dependent systematic trajectory errors, while their ensemble uncertainty can be imperfectly represented. Existing machine-learning MJO post-processing has mainly focused on deterministic bias correction, producing a single corrected trajectory without quantifying forecast uncertainty. Here, we develop Distributional Bias Correction (DBC), a trajectory-conditioned post-processor that uses simultaneous quantile regression to estimate component-wise marginal conditional quantiles of the verifying RMM1 and RMM2 values without assuming a fixed parametric marginal distribution. These results show that trajectory-conditioned quantile post-processing can improve the central MJO forecast while providing forecast-dependent uncertainty, supporting more reliable subseasonal MJO guidance.