风速和风向的变分同化及其观测算子线性化的作用研究

A new methodology for assimilating wind observations in their observed form of speed (spd) and direction (dir) was developed in WRFDA (asm_sd). The asm_sd is to consider dir observation error as an independent source from spd observation error, thus, the weight of spd or dir observation into analysis is affected exclusively by the corresponding spd or dir observation error, which changes with observation types. As a comparison, the standard WRFDA assimilates u and v (asm_uv), transformed from dir and spd, In WRFDA, u and v components are separated into the background check in asm_uv, thus, could be rejected or assimilated separately. However, it seems unreasonable to assimilate the other one when u or v is rejected, in the consideration that u and v components are calculated by single observation pair of spd and dir when the quality of spd or dir can affect both u and v. Generally, three key factors will build the theoretical and practical benefits of the new methodology: (i) spd (dir) observation errors, corresponding to the types or heights of observations, will independently affect the weight of spd (dir) observations into analysis in asm_sd; whereas, the weight of observations in asm_uv is decided by spd observation errors, which are inversely proportional to dir observation errors. (ii) in the aspect of quality control, asm_sd is superior to asm_uv in screening observations. The former could reject spd or dir observations based on observation quality, however, the latter one can’t attribute the errors in u or v to spd or dir. (iii) the wind vector analysis in asm_sd locates between background and observation in the terms of spd and dir in the scalar nature, and as a comparison, asm_uv could produce spd in analysis smaller than both background and observation, and even zero spd, when u or v components in the vector nature of background and observation point to the opposite directions. However, these improvements were only supported partly in the idealised experiments, where most of assumptions and conditions are not valid for any experiment using real data. Therefore, the asm_sd will be performed using real data in this proposal. The study will give a new direction to understand wind assimilation and provide improvements on the standard wind assimilation.

目前，风资料同化研究将风观测的纬向和经向分量作为同化变量。该方法风变量的观测算子是单位矩阵，更新向量计算准确，但同时也存在明显的不足，如由于观测变量和同化变量不同，质量控制无法分辨观测误差的源变量，风速（风向）观测能够影响与其非相关的风向（风速）分析等，极大地降低了风观测的利用效率和同化准确性。项目拟将风速和风向作为同化变量，研究风速和风向同化对常规同化方法的实际改进作用。项目将考虑风观测误差和观测风速的相关性，研究多资料匹配法计算以观测风速为变量的风速和风向观测误差（作为同化权重），同时，研究质量控制系数与观测风速的函数关系，优化质量控制，这将提高观测筛选、同化的准确性和观测的利用效率；通过研究非线性观测算子线性化对分析增量的影响，提高线性化精度并改进增量形式的代价函数。该研究将提高准确、合理地利用风观测资料的能力，改进分析和预报，为未来风观测的同化研究和应用提供创新性思路和有价值的参考

项目针对目前观测资料的偏差订正、观测误差估计、观测质量控制和风观测同化研究中存在的问题，发展了基于变分法的观测资料系统偏差校正、以三类资料匹配为核心算法的观测误差估计、满足正态分布函数的观测质量控制和风观测直接同化等方法。. 在资料同化前的观测质量控制部分，项目首先发展了基于变分法的系统偏差校正方法。该方法通过扩展模式状态变量，将影响系统性偏差的主要因素作为参数，随代价函数极小化过程迭代估计。待代价函数达到全局极小值时，该参数被用来计算观测资料的系统性偏差，并进行偏差校正。该方法利用其他所有同化的观测资料和背景预报作为约束条件，相对于普遍应用的“参考值方法”，有效地降低了校正值包含参考值系统性偏差的风险，解决了“参考值”方法无法正确地校正系统性偏差随时间变化的观测。在观测误差计算部分，基于三类资料匹配的观测误差统计方法通过三类资料两两匹配的方程组把真值项销项，计算得到了不包含任何其他误差源的观测误差，一方面解决了传统方法潜在的包含参考值中的系统性偏差和随机误差的问题，另一方面计算了风速和风向的观测误差，为风速风向直接同化研究奠定了基础。在观测质量控制部分，基于高斯分布函数的质量控制方程有效地剔除了错误观测，并为每个观测分配一个0-10的质量值，有助于了解单体或总体观测质量。在风速和风向直接同化部分，项目通过理想模型实验和实际观测实验，定性和定量地评估了新方法对传统风水平分量同化方法的改进作用。结果表明，风矢量直接同化方法有效地解决了传统方法风速分析不连续和零风速分析值问题；确定了风向观测误差对风矢量分析的直接影响；改进了受下垫面和湍流影响显著的低层风向观测的质量控制。. 上述一系列质量控制方法为资料同化提供了更“合理”、更“准确”的观测场；风观测直接同化方法提高了合理地利用风观测资料的能力；两者共同为我国风资料同化的研究和应用提供了创新性的思路，具有参考价值；项目完成了既定目标。