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## The method of decomposing wind field in a limited area and its application to typhoon SAOMEI

Zhou Yu-Shu, Cao Jie, Gao Shou-Ting
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• #### 摘要

介绍了有限区域水平风场分解的调和-余弦计算方法，该方法把函数分成两部分之和.第一部分是Laplace方程在给定边界条件下的解，由于Laplace方程的解是调和函数，这个部分可称为调和部分，又因为其与区域内部值无关，也称外部部分.第二部分是原始函数与调和部分之差，这个函数是齐次边条件下Poisson方程的解，只与区域内部的涡度或散度有关，故称为内部部分，可以展开成双傅氏的余旋函数系列.调和-余弦计算方法的求导都是用谱系数进行，计算精度比常用的差分方法高两阶以上.而且，由于外部部分对应的边界条件物理意义清楚，边界光滑，成功克服了有限区域流函数和速度势迭代求解出现的计算不稳定、原始风场无法还原、边界上的系统缺失等问题，可以准确分解和重建有限区域的风场.利用NCEP/NCAR 1°×1°的实时分析资料和日本气象厅区域谱模式(RSM)20km分辨率的再分析资料，利用调和-余弦算法得到的无辐散风分量和无旋风分量，对2006年的8号超强台风“桑美"(SAOMEI)进行风场结构的比较分析.结果发现，低层无辐散风比原始风场与台风中心的对应关系更好；同时，无旋风分量能更好地显示原始风场上并不明显的低层辐合高层辐散的特征，大尺度无辐散风分量可以更清晰地显示出台风的水汽输送通道.从与台风中心的对应关系看，台风在海上发展阶段，SAOMEI台风的旋转中心与辐合中心并不是时时重合，这个特点只能通过风场分解才能得到.此外，SAOMEI登陆以后，南部洋面上发展起来的对流活动从水汽和能量补充方面都不利于SAOMEI的维持.可见，分解后的无辐散风场和无旋风场能更清楚地体现出SAOMEI的风场结构，在台风结构分析中有重要的推广应用价值.

#### Abstract

The harmonic-cosine series expansion method (H-C method) for horizontal wind is introduced. It divides a function, such as horizontal wind, stream function and velocity potential, into two parts. One is a harmonic function which is the solution of a Laplace equation with nonzero boundary condition, and thus can be called the harmonic part. It is also been called the external part since it is independent of any values inside the limited area. The other is the difference of the original wind and the harmonic part, which is the solution of Poisson equation with homogeneous boundary condition and can be expanded into double Fourierism cosine series. It only depends on vorticity or divergence inside the limited area, so it is also called the inner part. The H-C method uses a spectrum approach in calculating derivatives, so it is more precise than the differential ones. The boundary condition given to solve the harmonic part has definite physical meaning and it is well handled in solving stream function and velocity potential in a limited area. Therefore, problems such as the instability in the calculation, the original wind field not being able to be reversed accurately, and the system deficiencies on the boundary occurring in previous methods, are successfully overcome. Using the NCEP/NCAR 1°×1° analysis data with a time resolution of 6 h, the Regional Spectrum Model (RSM) reanalysis data from Japan Meteorological Agency with a horizontal resolution of 20km and a time interval of 6 h, we decompose the horizontal wind of super-intensity Typhoo SAOMEI (0608) based on the H-C method. The two parts are called the nondivergent and the irrotational components, respectively. Analyses of the two parts indicate that the typhoon center marked by the nondivergent component at lower levels approaches more closely the observed center than the original wind did. In addition, the nondivergent wind can clearly manifest the water transporting passageway. The phenomenon that horizontal winds converge at lower levels and diverge at upper levels is more obvious in irrotational wind field than that in the original one. Convective activities at the South China Sea and in the west of Philippines confront the development of SAOMEI by blocking off its water transport after it landed. It may be a reasonable explanation for the fact that SAOMEI weakened so rapidly despite of its landing as a super-intensity typhoon. Before it landed, the nondivengent and irrotational centers in wind component fields are not always in the same location. It can only be seen by using the decomposing method for horizontal winds. The two components derived from the H-C method may provide more detailed characteristics than the original wind does. Therefore, this approach would be important in understanding the characteristics of typhoon and can be used widely in the future.

#### 作者及机构信息

###### (1)中国科学院大气物理研究所，北京 100029; (2)中国科学院大气物理研究所，北京 100029；中国科学院研究生院，北京 100049
• 基金项目: 国家重点基础研究发展规划(批准号：2009CB421505)，中国科学院知识创新方向性项目(批准号：KZCX2-YW-206-4)，国家自然科学基金(批准号：40505009)和中国科学院海外杰出学者基金(批准号：2005-2-16)资助的课题.

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##### 出版历程
• 收稿日期:  2007-07-19
• 修回日期:  2008-03-20
• 刊出日期:  2008-05-05

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