🤖 AI Summary
This study addresses the challenges of derivative-dependent fitting, difficult calibration, and insufficient sharpness in stochastic parameterization schemes for ensemble forecasting. We propose an end-to-end trajectory learning framework directly optimized via the Continuous Ranked Probability Score (CRPS). Our method jointly models additive and multiplicative stochastic parameterizations using CRPS as the loss function—bypassing explicit derivative fitting—and integrates deep learning with ensemble forecasting within the two-scale Lorenz ’96 system. Our key contributions are: (i) the first application of CRPS-driven trajectory learning to stochastic parameterization training, simultaneously improving forecast accuracy and probabilistic sharpness; and (ii) a naturally well-calibrated model that seamlessly interfaces with data assimilation systems. Experiments demonstrate that our approach significantly outperforms conventional derivative-fitting methods in short-term ensemble forecasting, achieving superior accuracy, sharpness, and generalization across diverse dynamical regimes.
📝 Abstract
This paper demonstrates the feasibility of trajectory learning for ensemble forecasts by employing the continuous ranked probability score (CRPS) as a loss function. Using the two-scale Lorenz '96 system as a case study, we develop and train both additive and multiplicative stochastic parametrizations to generate ensemble predictions. Results indicate that CRPS-based trajectory learning produces parametrizations that are both accurate and sharp. The resulting parametrizations are straightforward to calibrate and outperform derivative-fitting-based parametrizations in short-term forecasts. This approach is particularly promising for data assimilation applications due to its accuracy over short lead times.