隐式等权重粒子滤波及其在海洋资料同化中的应用研究

As the spatial and temporary resolutions of the numerical models are increasing, the nonlinearity of the numerical models are becoming stronger and stronger. The contemporary data assimilation methods, such as 3DVAR, 4DVAR and EnKFs, are doing data assimilation process through searching for the specific variables of the posterior pdf of the model states, e.g. mean, covariance, modes, etc. But these variables or methods cannot describe the posterior pdf of the model states accurately. Particle filters could solve the problem of precisely description of the posterior by using Monte-Carlo method, and the theory of Implicit Equal-Weights Particle Filter (IEWPF) proposed by the member of the author's group and Professor Peter Jan van Leeuwen has solve the “curse of dimensionality” which has plagued the particle filter community for decades. Through doing the research of the not fully-understanding and unsolved scientific problems of Implicit Equal-Weights Particle Filter, we want to solve that the parameter selection problem, the bias problem in low-dimensional systems, the modelling of model error covariance matrix problems. Through the implementation of IEWPF in high-nonlinear high-dimensional geo-physical systems, we could check the performance and characteristics of the new method. At the same time, we choose the ocean general circulation model ROMS as the operational model that we use to implement the IEWPF, we should solve the scientific and technical problems of implementing IEWPF in real operational system, and we could realize the first implementation of the particle filters in operational models.

数值天气预报模式的时间和空间分辨率越来越高，其非线性程度也随之不断增强。现在的资料同化方法，比如变分同化方法和集合卡尔曼滤波方法，通过搜索模式状态的后验概率分布的特定统计量进行资料同化，并不能准确描述模式状态的后验概率密度分布。粒子滤波通过蒙特卡洛方法可以准确描述模式状态的后验概率密度分布，申请人团队成员与英国雷丁大学Peter Jan van Leeuwen教授最近合作提出的隐式等权重粒子滤波方法解决了粒子滤波中难以解决的“维数灾难”问题。通过对隐式等权重粒子滤波中若干未解决的科学问题的研究，解决隐式等权重粒子滤波中参数选择、模式误差协方差建模以及该方法在低维系统中的偏差问题。利用在高维非线性地球物理系统中实现隐式等权重粒子滤波资料同化，研究隐式等权重粒子滤波的表现和特性。同时，在海洋数值模式ROMS中率先实现隐式等权重粒子滤波资料同化方法，解决粒子滤波方法在实际业务应用中需要解决的科学和技术问题，实现粒子滤波的业务应用。

地球物理系统是一个非线性、非高斯系统，资料同化技术能够提高模式初始值的质量，但目前广泛应用的业务资料同化方法——变分方法或集合卡尔曼滤波方法通过搜索模式状态的后验概率分布的特定统计量进行资料同化，并不能准确描述模式状态的后验概率密度分布，只能提供概率密度函数的一阶矩或二阶矩信息，无法满足真实地球物理系统的需求。本项目基于非线性模式以及实际海洋环流模式 ROMS ，研究和探索隐式等权重粒子滤波的参数选择方案，资料同化系统偏差，粒子滤波系统模式误差协方差建模方法等一系列的科学问题，并将隐式等权重粒子滤波应用到海洋业务模式 ROMS 中，完善海洋预报模式的集合资料同化和集合预报体系，并针对我国南海区域进行了初步的应用，为粒子滤波的业务化应用提供了理论基础和试验数据支撑。