高效计算的集合卡尔曼滤波近似算法研究

To implement Bayes’ Theorem for data assimilation, an ensemble Kalman filter (EnKF) uses a set of model integrations to simulate the temporally-varying background probability distribution function (PDF). Due to the merit of the derived data assimilation solution completely combining information from model background and observations, EnKF has risen as a widely-promising data assimilation algorithm in weather and climate studies. However, its huge computational resource demanding for ensemble model integrations sets a significant limitation on the applications. In addition, the statistics based on a finite ensemble cannot well represent the character of slow-varying oscillations. Given that the model background PDF could be partitioned by a stationary and slow-varying part that reflects periodic and slow-varying signals such as stationary wave, ENSO and decadal variations, and a fast-varying part, a high efficiency approximate EnKF (HEA-EnKF) is designed to dramatically enhance the computational efficiency. The HEA-EnKF consists of an optimal interpolation and a filtering process that is implemented by sampling fast-varying information from a single model integration. The preliminary validation results with a low-order model show that compared to the standard EnKF, the HEA-EnKF enhances the assimilation quality by 30% due to its better representation to the statistics on stationary and slow-varying oscillations, and reduces computational expenses by 95%. The proposed project will use the low-order model and a primary equation coupled model throughout the study to validate the algorithm. Once validated by the realistic model, the new algorithm will be very useful for high-resolution models and complex earth system models.

集合卡尔曼滤波是贝叶斯定理所阐述资料同化问题的一个直接求解。它用一组模式集合成员模拟动力背景可能性分布函数来抽取观测信息。推导的同化解理论上包含了全部的动力背境和观测信息，已成为地球流体领域最受关注的同化算法。但集合模式积分对巨大计算资源需求严重阻碍其应用，有限集合成员的统计也不能正确代表背景流中的慢变振荡特征。项目首先研究背景统计信息可分为缓变和瞬变的物理特性，研发一个高效计算的近似算法，缓变部分用历史分析资料统计，瞬变部分用单一模式积分的高频信息近似模拟。项目拟用低阶模式和耦合全球环流模式对其进行系统研究和验证。低阶模式对算法的初步设计和测试表明，由于对缓变信息统计比有限集合的传统算法更具代表性，新算法提高同化质量超过30%，提高计算效率达95%。新算法保留传统算法理论优势的同时，克服了对巨大计算资源依赖，具有广阔应用前景，尤其对推动高分辨率多圈层耦合模式同化和预报发展具有重大意义。

集合卡尔曼滤波算法直接解贝叶斯理论阐述的资料同化问题，但在实践应用中存在2个挑战性问题：1）对集合成员数有较大依赖性，从而对计算资源有巨大需求，当模式本身变得很昂贵时（如高分辨率地球系统模式），它基本上就不适用了；2）有限集合在有限时间内的模式积分很难代表背景流的低频统计信息。本项目同样基于贝叶斯理论，研发一个高效计算的集合卡尔曼滤波近似算法，将背景场可能性分布函数分为3类统计信息用历史资料来评估计算：1）反映驻型不变或超低频的背景信息，比如与扩散过程和定常波相关信息；2）反映缓慢变化的背景信息，比如与ENSO和年代际振荡相关信息；3）反映高频快速变化部分的背景信息，比如与瞬变天气过程和海洋涡等相关信息，由于不用模式的集合积分从而缓解集合卡尔曼滤波存在的上述问题。之后在低阶耦合模式和耦合大气海洋环流模式进行验证，结果证实新算法在改进同化质量的同时也大幅度减小了计算资源需求。本项目提出的紧扣贝叶斯理论的集合卡尔曼滤波近似算法，在计算效率和同化质量上都有所突破，增加滤波算法对高精度模式的适用性，可将我国在高分辨率模式资料同化算法方面的研究向前推进一步，同时可以提高大气海洋模式预报预测初始化水平，更好地减灾防灾，为国家经济建设和国防建设服务。