一种求解条件非线性最优扰动的快速算法及其在台风目标观测中的初步检验  

A fast algorithm to obtain CNOP and its preliminary tests in a target observation experiment of typhoon

作　　者：王斌[1] 谭晓伟[1] 

机构地区：[1]中国科学院大气物理研究所,LASG,北京100029

出　　处：《气象学报》2009年第2期175-188,共14页Acta Meteorologica Sinica

基　　金：国家973项目(2004CB418304);公益性行业(气象)科研专项(GYHY(QX)2007-6-15)。

摘　　要：条件非线性最优扰动(CNOP)是Mu等2003年提出的一个新的理论方法,它是线性奇异向量在非线性情形的推广,克服了线性奇异向量不能代表非线性系统最快发展扰动的缺陷,成为非线性系统可预报性和敏感性等研究新的有效工具。然而,由于以往CNOP的求解需要采用伴随技术,计算量相当巨大,限制了该方法的推广应用。为了克服这一困难,本文基于经验正交分解(EOF),提出了一种求解CNOP的快速算法,利用GRAPES区域业务预报模式实现了 CNOP快速计算,并在台风"麦莎"的目标观测研究中得到初步检验,通过观测系统模拟实验(OSSE)检验了该方法确定敏感性区域(瞄准区)的有效性和可行性。试验结果表明,用快速算法求解的CNOP,其净能量随时间快速地发展,而且发展呈非线性。在台风"麦莎"个例的目标观测试验中,用快速算法得到的预报时间为24 h的CNOP可以有效地识别瞄准区,并通过瞄准区内初值的改善,可明显减少目标区域(检验区)内24 h累计降水预报误差。尤其,累计降水预报的这种改进效果能够延伸到更长时间(如72 h),尽管检验时间是设在第24小时。进一步分析发现,24 h累计降水预报误差的减少是通过利用瞄准区内改善的初值改进初始时刻台风暖心结构、高空相对涡度以及水汽条件等而得以实现的。Conditional nonlinear optimal perturbation （CNOP） is a new method proposed by Mu et al. in 2003, which generalizes linear singular vector （LSV） to include nonlinearity. It has become a powerful tool for studying predictability and sensitivity, among other issues in nonlinear systems. This is because the CNOP is able to represent, while the LSV is unable to deal with, the fastest-de- veloping perturbation in a nonlinear system. The wide application of this new method, however, has been limited due to its large computational cost related to the use of an adjoint technique. In order to greatly reduce the computational cost, we hereby propose a fast algorithm for solving the CNOP based on the empirical orthogonal function （EOF）. The algorithm is tested in target observation experiments of Typhoon Matsa using the Global/Regional Assimilation and PrEdiction System （GRAPES）, an operational regional forecast model. The effectivity and feasibility of the algorithm to determine the sensitivity （target） area is evaluated through two observing system simulation experiments （OSSEs）. The results show that the energy of the CNOP solved by the new algorithm develops quickly and nonlinearly. In the OSSEs of Typhoon Matsa, the sensitivity area is effectively identified with the CNOP solved by the new method using 24 h as the prediction time window, and the 24-h accumulated rainfall prediction errors （ARPEs） in the verification region are reduced significantly compared with the ＂true state＂ when the initial conditions （ICs） in the sensitivity area are replaced with the ＂observations＂. The decrease of the ARPEs can be achieved for even longer prediction time （e. g. , 72 h）, although the verification is done 24 h after the initial time. Further analyses reveal that the decrease of the 24-h ARPEs in the verification region is attributable to improved simulations of the initial structure of the typhoon＇s warm core, upper-layer relative vorticity, water vapor conditions etc. as a result of t

关 键 词：快速算法 条件非线性最优扰动 目标观测 观测系统模拟实验 

分 类 号：P435[天文地球—大气科学及气象学]