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.

翻译：本文通过采用连续排序概率评分作为损失函数，证明了集合预报中轨迹学习的可行性。以双尺度洛伦兹'96系统为案例，我们开发并训练了加性和乘性随机参数化方案来生成集合预测。结果表明，基于CRPS的轨迹学习能够产生既准确又锐利的参数化方案。所得参数化方案易于校准，且在短期预报中优于基于导数拟合的参数化方法。由于其在短预见期内的准确性，该方法在数据同化应用中具有显著潜力。