Statistical Calibration of ArchesWeatherGen for Enhanced Sub-Seasonal and Longer Predictions

The capabilities and skill of emerging data-driven weather forecasting and climate models are steadily increasing and significant progress has been made in terms of their quality in the last years. Data-driven weather forecasting models predict the state of the atmosphere for a single step, e.g. 6h. Longer lead times are obtained using time-stepping where predictions are fed back into the model for the next step. Although many models exhibit stable behaviour for long rollouts, the training only considers short trajectories. The trained models are therefore statistically not well calibrated at longer lead times and for phenomena like blocking patterns or teleconnections, which happen on time scales larger than a few days, the predictions are poorly constrained by the training. To address this issue, the training of data-driven models needs to consider information about the atmospheric conditions from several days up to several weeks. 

We approach this problem by using ArchesWeather and ArchesWeatherGen. ArchesWeather provides a deterministic prediction of the next state of the atmosphere. ArchesWeatherGen, a probabilistic flow-matching model, corrects  the deterministic prediction to obtain a probabilistic prediction that matches the ground truth state. We tackle the long lead time calibration problem by applying ArchesWeatherGen after a large number of deterministic forecasting steps, in contrast to the single step used for ArchesWeatherGen for medium-range weather forecasting. We therefore condition ArchesWeatherGen on an entire long forecast trajectory produced by the deterministic model. Through this, ArchesWeatherGen obtains more temporal information about the atmosphere as well as the error development and can explicitly learn longer-time correlation patterns in the atmospheric dynamics. This leads to a better calibrated model at longer lead times. It also reduces the number of diffusion steps, and hence the computational costs, as we only correct the mean prediction after a larger number of deterministic autoregressive forecasting steps. For our study, we examine the influence of the length of the input trajectory and evaluate the improvement of our approach compared to the results obtained with a single step model correction.