Effective Hamiltonian for the D'Alembert Planetary Model Near a Spin/Orbit Resonance

The D'Alembert model for the spin/orbit problem in celestial mechanics is considered. Using a Hamiltonian formalism, it is shown that in a small neighborhood of a p:q spin/orbit resonance with (p,q) different from (1,1) and (2,1) the 'effective' D'Alembert Hamiltonian is a completely integrable system with phase space foliated by maximal invariant curves; instead, in a small neighborhood of a p:q spin/orbit resonance with (p,q) equal to (1,1) or (2,1) the 'effective' D'Alembert Hamiltonian has a phase portrait similar to that of the standard pendulum (elliptic and hyperbolic equilibria, separatrices, invariant curves of different homotopy). A fast averaging with respect to the 'mean anomaly' is also performed (by means of Nekhoroshev techniques) showing that, up to exponentially small terms, the resonant D'Alembert Hamiltonian is described by a two-degrees-of-freedom, properly degenerate Hamiltonian having the lowest order terms corresponding to the 'effective' Hamiltonian mentioned above.     

非保守弹性动力系统两类变量的广义拟变分原理及其应用

按照广义力和广义位移之间的对应关系,将弹性动力学的各基本方程分别乘上相应的虚量,然后在相应的体积域和面积域上积分,将积分式代数相加,再将代数和在时间域上积分,代入本构关系,并考虑到体积力和面积力均为伴生力,进而建立了非保守弹性动力系统的第1类两类变量的广义拟变分原理;再应用类似的方法,通过代入另一类本构关系,建立了非保守弹性动力系统的第2类两类变量广义拟变分原理.应用第1类两类变量广义拟余能原理给出同时求解1个典型的非保守弹性动力系统的固有频率、变形和内力的计算方法.最后,讨论了有关问题.     

IMPACT OF DIABATIC PROCESSES IN AGCM ON 4-DIMENSIONAL VARIATIONAL DATA ASSIMILATION*

The impact of diabatic processes on 4-dimensional variational data assimilation (4D-Var) was studied using the 1995 version of NCEP's global spectral model with and without full physics.The adjoint was coded manually.A cost function measuring spectral errors of 6-hour forecasts to "observation" (the NCEP reanalysis data) was minimized using the L-BFGS (the limited memory quasi-Newton algorithm developed by Broyden,Fletcher,Goldfard and Shanno) for optimizing parameters and initial conditions.Minimization of the cost function constrained by an adiabatic version of the NCEP global model converged to a minimum with a significant amount of decrease in the value of the cost function.Minimization of the cost function using the diabatic model, however,failed after a few iterations due to discontinuities introduced by physical parameterizations.Examination of the convergence of the cost function in different spectral domains reveals that the large-scale flow is adjusted during the first 10 iterations,in which discontinuous diabatic parameterizations play very little role.The adjustment produced by the minimization gradually moves to relatively smaller scales between 10-20th iterations.During this transition period,discontinuities in the cost function produced by "on-off" switches in the physical parameterizations caused the cost function to stay in a shallow local minimum instead of continuously decreasing toward a deeper minimum. Next,a mixed 4D-Var scheme is tested in which large-scale flows are first adiabatically adjusted to a sufficient level,followed by a diabatic adjustment introduced after 10 to 20 iterations. The mixed 4D-Var produced a closer fit of analysis to observations,with 38% and 41% more decrease in the values of the cost function and the norm of gradient,respectively,than the standard diabatic 4D-Var,while the CPU time is reduced by 21%.The resulting optimal initial conditions improve the short-range forecast skills of 48-hour statistics.The detrimental effect of parameterization discontinuities on minimization was also reduced.     

On ensemble representation of the observation-error covariance in the Ensemble Kalman Filter

Evensen (2003) presents a modification of the Ensemble Kalman Filter (EnKF), in which the observation-error and background-error covariance matrices are both represented by ensembles, in contrast to the usual practice, where only the background error is so represented. It is shown that this modification can cause the ensemble to collapse to a single member, in the common situation where the number of observations is more than twice the number of ensemble members, and to be rank-deficient when the number of observations is greater than or equal to the ensemble size. It is also shown that some further modifications to the scheme, presented by Evensen as offering numerical efficiencies, can prevent this collapse. However, these latter modifications are shown in some simple numerical examples to require tuning to produce acceptable results, which are nevertheless inferior to those of the standard EnKF.Acknowledgements The author acknowledges useful discussions with Peter Steinle, and other participants at the EnKF workshop held in BMRC in November, 2003.     

Global Bifurcations of Periodic Solutions of the Restricted Three Body Problem

We describe global bifurcations from the libration points of non-stationary periodic solutions of the restricted three body problem. We show that the only admissible continua of non-stationary periodic solutions of the planar restricted three body problem, bifurcating from the libration points, can be the short-period families bifurcating from the Lagrange equilibria L ₄, L ₅. We classify admissible continua and show that there are possible exactly six admissible continua of non-stationary periodic solutions of the planar restricted three body problem. We also characterize admissible continua of non-stationary periodic solutions of the spatial restricted three body problem. Moreover, we combine our results with the Déprit and Henrard conjectures (see [8]), concerning families of periodic solutions of the planar restricted three body problem, and show that they can be formulated in a stronger way. As the main tool we use degree theory for SO(2)-equivariant gradient maps defined by the second author in [25].This revised version was published online in October 2005 with corrections to the Cover Date.     

Validation of the effects of temperature simulated by multi-model ensemble and prediction of mean temperature changes for the next three decades in China

Using series of daily average temperature observations over the period of 1961–1999 of 701 meteorological stations in China, and simulated results of 20 global climate models (such as BCCR_BCM2.0, CGCM3T47) during the same period as the observation, we validate and analyze the simulated results of the models by using three factor statistical method, achieve the results of multi- model ensemble, test and verify the results of multi-model ensemble by using the observation data during the period of 1991–1999. Finally, we analyze changes of the annual mean temperature result of multi-mode ensemble prediction for the period of 2011–2040 under the emission scenarios A2, A1B and B1. Analyzed results show that: (1) Global climate models can reproduce Chinese regional spatial distribution of annual mean temperature, especially in low latitudes and eastern China. (2) With the factor of the trend of annual mean temperature changes in reference period, there is an obvious bias between the model and the observation. (3) Testing the result of multi-model ensemble during the period of 1991–1999, we can simulate the trend of temperature increase. Compared to observation, the result of different weighing multi-model ensemble prediction is better than the same weighing ensemble. (4) For the period of 2011–2040, the growth of the annual mean temperature in China, which results from multi-mode ensemble prediction, is above 1 °C. In the spatial distribution of annual mean temperature, under the emission scenarios of A2, A1B and B1, the trend of growth in South China region is the smallest, the increment is less than or equals to 0.8 °C; the trends in the northwestern region and south of the Qinghai-Tibet Plateau are the largest, the increment is more than 1 °C.     

LAPS分析场在一次强对流天气过程尺度分析中的应用

利用LAPS（local analysis and prediction system）同化系统融合多种观测资料,对2010年8月25日发生在上海的一次强对流天气过程进行中尺度分析。结果表明,这次强对流天气主要是由中、低空中尺度辐合系统直接触发形成的。强对流形成阶段,地面有分散辐合形成并逐渐加强,成为触发中尺度垂直环流的主要机制,垂直结构上出现低层辐合高层辐散的有利配置,风暴中心附近出现明显的上升气流区,中高层相对湿度显著增加。成熟阶段,强对流云体中心附近的对流层底层开始出现下沉气流,上升气流在其拖曳作用下明显倾斜。衰减阶段,下沉气流加强使中尺度环流动力结构和水汽供应受到破坏,垂直结构上转为底层辐散高层辐合。因此,与天气尺度分析相比,基于LAPS的中尺度分析能更深刻地揭示中小尺度系统的三维结构和时空演变特征。     

区域集合预报系统2 m温度预报的校准技术

采用非齐次高斯回归 (NGR) 技术对国家气象中心区域集合预报系统的2 m温度预报结果开展了一阶偏差和二阶离散度的校准研究。对预报结果比较详尽的检验分析表明:校准后的2 m温度预报可靠性和预报技巧均显著提高,表现为校准后集合预报成员的均方根误差与离散度更为接近;原Talagrand直方图中的“L”形分布现象得到有效改善;Brier评分、最小连续分级概率评分 (CRPS) 明显减小,相对作用特征 (ROC) 面积增大,说明校准后的2 m温度预报表现出更好的预报技能。此外,NGR技术与自适应误差订正技术的对比试验表明,NGR在消除集合平均偏差和提高集合离散度两个方面均有优势。     

散射计和下投式探空仪资料对台风模拟的影响

为了评估同化QuikSCAT海平面气压场资料和Dropsonde资料对台风"Bilis"和"Kat-rina"模拟的影响,通过WRF-3DVAR变分同化系统将QuikSCAT海平面气压场资料和Dropsonde资料同化到WRF模式中,并以未同化任何资料和同化了QuikSCAT海平面气压场以及同化了Drop-sonde资料的数据为初始场,应用WRF模式进行模拟预报,并对得到的初始分析场和模拟预报得到的结果与台风实况报文进行了对比,得到的结论是:对台风初始时刻海平面气压场分布、初始台风中心定位、台风初始暖心结构的改善、台风路径、海平面最低气压场、海面最大风速和雷达回波的模拟方面,同化QuikSCAT海平面气压场的效果比同化Dropsonde资料明显,其中二者对海平面最低气压场的改进效果比海面最大风速的要好。但是两种资料的同化对初始相对湿度和台风强度细节变化方面都没有产生明显改善作用。同化QuikSCAT海平面气压场试验虽然仅仅同化了单层海平面气压场,但是在三维变分同化系统的动力约束作用下,也可以影响到中高层的各个要素场。