条件非线性最优扰动在可预报性问题研究中的应用

本文总结了近年来条件非线性最优扰动方法的应用研究的主要进展.主要包括四个方面:(1)将条件非线性最优扰动(CNOP)方法拓展到既考虑初始扰动又考虑模式参数扰动,形成了拓展的CNOP方法.拓展的CNOP方法不仅能够应用于研究分别由初始误差和模式参数误差导致的可预报性问题,而且能够用于探讨初始误差和模式参数误差同时存在的情形;(2)将拓展的CNOP方法分别应用于ENSO和黑潮可预报性研究,考察了初始误差和模式参数误差对其可预报性的影响,揭示了初始误差在导致ENSO和黑潮大弯曲路径预报不确定性中的重要作用;(3)考察了阻塞事件发生的最优前期征兆(OPR)以及导致其预报不确定性的最优增长初始误差(OGR),揭示了OPR和OGR空间模态及其演变机制的相似性及其局地性特征;(4)研究了台风预报的目标观测问题,用CNOP方法确定了台风预报的目标观测敏感区,通过观测系统模拟试验(OSSEs)和/或观测系统试验(OSEs),表明了CNOP敏感区在改进台风预报中的有效性.具体地,台风OGR的主要误差分布在某一特定区域,空间分布具有明显的局地性特征,在台风OGR的局地性区域增加观测,有效改进了台风的预报技巧,该区域代表了台风预报的初值敏感区.事实上,上述El Ni(n)o事件、黑潮路径变异以及阻塞事件的OGR的空间分布也具有明显的局地性特征,这些事件的OGR刻画的局地性区域可能也代表了初值敏感区.     

Partial Reduction in the N-Body Planetary Problem using the Angular Momentum Integral

We present a new set of variables for the reduction of the planetary n-body problem, associated to the angular momentum integral, which can be of any use for perturbation theory. The construction of these variables is performed in two steps. A first reduction, called partial is based only on the fixed direction of the angular momentum. The reduction can then be completed using the norm of the angular momentum. In fact, the partial reduction presents many advantages. In particular, we keep some symmetries in the equations of motion (d'Alembert relations). Moreover, in the reduced secular system, we can construct a Birkhoff normal form at any order. Finally, the topology of this problem remains the same as for the non-reduced system, contrarily to Jacobi's reduction where a singularity is present for zero inclinations. For three bodies, these reductions can be done in a very simple way in Poincaré's rectangular variables. In the general n-body case, the reduction can be performed up to a fixed degree in eccentricities and inclinations, using computer algebra expansions. As an example, we provide the truncated expressions for the change of variable in the 4-body case, obtained using the computer algebra system TRIP.     

SECOND-ORDER SOLUTION FOR THE ZONAL PROBLEM OF SATELLITE THEORY

The analytical solution for the perturbations of an artificial satellite due to the zonal part of the geopotential is presented. The Hamiltonian is fully normalized up to the second order by a single averaging transformation and the generating function is given explicitly. The formulas allow an arbitrarily high degree of geopotential harmonics to be included. The transformation from mean to osculating variables or vice versa is performed by means of a numerical method proposed by the author in a previous paper (Breiter,1997): periodic perturbations are computed by means of a Runge-Kutta method of order 2 instead of being explicitly derived from a generator. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Roles of Spatial Locations and Patterns of Initial Errors in the Uncertainties of Tropical Cyclone Forecasts

In this study,a series of sensitivity experiments were performed for two tropical cyclones (TCs),TC Longwang (2005) and TC Sinlaku (2008),to explore the roles of locations and patterns of initial errors in uncertainties of TC forecasts.Specifically,three types of initial errors were generated and three types of sensitive areas were determined using conditional nonlinear optimal perturbation (CNOP),first singular vector (FSV),and composite singular vector (CSV) methods.Additionally,random initial errors in randomly selected areas were considered.Based on these four types of initial errors and areas,we designed and performed 16 experiments to investigate the impacts of locations and patterns of initial errors on the nonlinear developments of the errors,and to determine which type of initial errors and areas has the greatest impact on TC forecasts.Overall,results from the experiments indicate the following:(1) The impact of random errors introduced into the sensitive areas was greater than that of errors themselves fixed in the randomly selected areas.From the perspective of statistical analysis,and by comparison,the impact of random errors introduced into the CNOP target area was greatest.(2) The initial errors with CNOP,CSV,or FSV patterns were likely to grow faster than random errors.(3) The initial errors with CNOP patterns in the CNOP target areas had the greatest impacts on the final verification forecasts.     

西藏地区强降雪过程的波包分布及传播特征

利用NCEP/NCAR高度场的再分析资料,通过波包传播诊断方法(WPD),对2005年10月19～23日西藏地区中东部及南部边缘地区一次大范围强降雪天气过程进行波包分布与波能传播特征分析。结果表明:500hPa高度场的波包分布和传播特征很好地反映此次过程;强降雪天气发生在波包大值区域内而且反映了过程的爆发和消亡;波包的分布特征与强对流天气的发生状况是一致的;波包的移动路径很好地反映了扰动能量的传播。此次过程是"积累-释放"的三次循环。     

Sensitivity of the DRP-4DVar Performance to Perturbation Samples Obtained by Two Different Methods

The dimension-reduced projection four-dimensional variational data assimilation (DRP-4DVar) approach utilizes the ensemble of historical forecasts to estimate the background error covariance (BEC) and directly obtains the analysis in the ensemble space.As a result,the quality of ensemble members significantly affects the DRP-4DVar performance.The historical-forecast-based initial perturbation samples are flow-dependent and can describe the error-growth pattern of the atmospheric model and the balanced relat...     

Algorithm Studies on How to Obtain a Conditional Nonlinear Optimal Perturbation (CNOP)

The conditional nonlinear optimal perturbation (CNOP), which is a nonlinear generalization of the linear singular vector (LSV), is applied in important problems of atmospheric and oceanic sciences, including ENSO predictability, targeted observations, and ensemble forecast. In this study, we investigate the computational cost of obtaining the CNOP by several methods. Differences and similarities, in terms of the computational error and cost in obtaining the CNOP, are compared among the sequential quadratic programming (SQP) algorithm, the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, and the spectral projected gradients (SPG2) algorithm. A theoretical grassland ecosystem model and the classical Lorenz model are used as examples. Numerical results demonstrate that the computational error is acceptable with all three algorithms. The computational cost to obtain the CNOP is reduced by using the SQP algorithm. The experimental results also reveal that the L-BFGS algorithm is the most effective algorithm among the three optimization algorithms for obtaining the CNOP. The numerical results suggest a new approach and algorithm for obtaining the CNOP for a large-scale optimization problem.     

What Kind of Initial Errors Cause the Severest Prediction Uncertainty of El Nino in Zebiak-Cane Model

With the Zebiak-Cane(ZC)model,the initial error that has the largest effect on ENSO prediction is explored by conditional nonlinear optimal perturbation(CNOP).The results demonstrate that CNOP-type errors cause the largest prediction error of ENSO in the ZC model.By analyzing the behavior of CNOP- type errors,we find that for the normal states and the relatively weak El Nino events in the ZC model,the predictions tend to yield false alarms due to the uncertainties caused by CNOP.For the relatively strong El Nino events,the ZC model largely underestimates their intensities.Also,our results suggest that the error growth of El Nino in the ZC model depends on the phases of both the annual cycle and ENSO.The condition during northern spring and summer is most favorable for the error growth.The ENSO prediction bestriding these two seasons may be the most diffcult.A linear singular vector(LSV)approach is also used to estimate the error growth of ENSO,but it underestimates the prediction uncertainties of ENSO in the ZC model.This result indicates that the different initial errors cause different amplitudes of prediction errors though they have same magnitudes.CNOP yields the severest prediction uncertainty.That is to say,the prediction skill of ENSO is closely related to the types of initial error.This finding illustrates a theoretical basis of data assimilation.It is expected that a data assimilation method can filter the initial errors related to CNOP and improve the ENSO forecast skill.     

集合预报风场扰动的物理结构及演变特征

初始扰动结构和振幅的合理性直接影响到集合预报的质量和整体性能,合理的初始扰动结构是确保集合预报扰动质量的关键.本文基于欧洲中期天气预报中心数据、我国T639全球集合预报系统以及GRAPES区域集合预报系统的预报场,针对模式初值不确定性,主要研究了风场初始扰动结构及其集合离散度、扰动能量等结构和演变特征,分析了集合预报风...