球上最小二乘问题向后误差的估计

A.N.Malyshev给出了球上最小二乘问题计算解的最佳向后扰动量表达式。从该表达式出发计算最佳向后扰动量却是很困难的。本文给出 1种有效的估算方法 ,所得结果对检验计算解的向后稳定性是有用的。并用几个简单的数值例子验证了所给算法的有效性。     

The Optimal Precursors for ENSO Events Depicted Using the Gradientdefinition-based Method in an Intermediate Coupled Model

The predictability of El Ni?o?Southern Oscillation (ENSO) has been an important area of study for years. Searching for the optimal precursor (OPR) of ENSO occurrence is an effective way to understand its predictability. The CNOP (conditional nonlinear optimal perturbation), one of the most effective ways to depict the predictability of ENSO, is adopted to study the optimal sea surface temperature (SST) precursors (SST-OPRs) of ENSO in the IOCAS ICM (intermediate coupled model developed at the Institute of Oceanology, Chinese Academy of Sciences). To seek the SST-OPRs of ENSO in the ICM, non-ENSO events simulated by the ICM are chosen as the basic state. Then, the gradient-definition-based method (GD method) is employed to solve the CNOP for different initial months of the basic years to obtain the SST-OPRs. The experimental results show that the obtained SST-OPRs present a positive anomaly signal in the western-central equatorial Pacific, and obvious differences exist in the patterns between the different seasonal SST-OPRs along the equatorial western-central Pacific, showing seasonal dependence to some extent. Furthermore, the non-El Ni?o events can eventually evolve into El Ni?o events when the SST-OPRs are superimposed on the corresponding seasons; the peaks of the Ni?o3.4 index occur at the ends of the years, which is consistent with the evolution of the real El Ni?o. These results show that the GD method is an effective way to obtain SST-OPRs for ENSO events in the ICM. Moreover, the OPRs for ENSO depicted using the GD method provide useful information for finding the early signal of ENSO in the ICM.     

Ensemble Forecasts of Tropical Cyclone Track with Orthogonal Conditional Nonlinear Optimal Perturbations

This paper preliminarily investigates the application of the orthogonal conditional nonlinear optimal perturbations(CNOPs)–based ensemble forecast technique in MM5(Fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model). The results show that the ensemble forecast members generated by the orthogonal CNOPs present large spreads but tend to be located on the two sides of real tropical cyclone(TC) tracks and have good agreements between ensemble spreads and ensemble-mean forecast errors for TC tracks. Subsequently, these members reflect more reasonable forecast uncertainties and enhance the orthogonal CNOPs–based ensemble-mean forecasts to obtain higher skill for TC tracks than the orthogonal SVs(singular vectors)–, BVs(bred vectors)– and RPs(random perturbations)–based ones. The results indicate that orthogonal CNOPs of smaller magnitudes should be adopted to construct the initial ensemble perturbations for short lead–time forecasts, but those of larger magnitudes should be used for longer lead–time forecasts due to the effects of nonlinearities. The performance of the orthogonal CNOPs–based ensemble-mean forecasts is case-dependent,which encourages evaluating statistically the forecast skill with more TC cases. Finally, the results show that the ensemble forecasts with only initial perturbations in this work do not increase the forecast skill of TC intensity, which may be related with both the coarse model horizontal resolution and the model error.     

东北亚地区Ms5.0以上地震前后空间电场时空演化特征研究

本文利用2005年1月—2009年12月DEMETER电磁卫星观测的极低频/甚低频(ELF/VLF)39 Hz~6 kHz频段电场功率谱密度(PSD)观测量, 将研究频段划分为5个子频段对东北亚地区(38°N~58°N; 105°E~145°E)内发生的8个M_S≥5.0地震前后空间电场时空演化特征进行研究。 研究发现同一地震不同频段异常扰动区域并不完全在同一位置, 且同一地震的不同频段地震前后扰动形态也并不一致; 8个地震40次统计中有25% 的统计数据虽然基本在地震前后所有时间段都超过阈值2σ, 但未见明显扰动规律, 其余75%的统计数据中发现其扰动特征可以归纳为3类: 52%的统计数据在震前扰动幅度增大, 达到最大时发震, 震后持续降低; 7.5%的统计数据在震前扰动幅度达到高值, 而后下降过程中发震; 15%的统计数据在震前扰动幅度一直在增加且绝大部分时间低于2σ, 直至震后超过2σ, 且出现这种类型的异常均为震例的第五频段演化特征。 异常扰动区域主要集中在震中±4°以外的区域。     

火星非球形引力位田谐项联合摄动分析解

火星非球形引力场模型与地球有明显差别,其非球形引力位中的田谐项系数基本都要比地球的相应值大一个量级,尤其是J_2,2项（赤道椭率项）的大小接近它的动力学扁率项J₂.对于低轨探测器,若要使轨道外推1 d弧段的精度达到500 m(相当于标准单位10^-4量级),在构造环火探测器的轨道分析解时,田谐项与J₂项以及田谐项与田谐项之间的联合摄动不容忽视.根据摄动量级分析和构造的摄动分析解证实,上述联合摄动对轨道沿迹方向的影响可超过10^-4,并给出了数值验证.结果表明,与地球低轨卫星不同,在类似的问题中,构造环火卫星摄动分析解时,必须考虑这些联合摄动项的影响.     

圆形涡旋中心非对称扰动的斜压不稳定研究

涡旋中的非对称扰动又是一种较为常见的流体运动现象,如不成熟飓风中出现的中尺度深厚对流云区(又称圆形抽气云CEC),热带风暴发展时的不对称性以及环流中心往往位于浓密云区的边缘等,都是涡旋中存在不对称扰动的表现形式.然而对于涡旋中非对称扰动的稳定性问题的研究,目前还比较少.文中从柱坐标下的斜压模式出发,研究了热带气旋等一类涡旋中心的非对称扰动的不稳定问题,结果表明:(1)与平直的基本流相比,涡旋中更容易出现斜压不稳定,扰动更容易发展;(2)不稳定可以使涡旋中的能量由基本场向扰动场转换,涡旋变得不对称.扰动是一种重力内波,其传播速度远小于基本流角速度,有些甚至逆基本流缓慢倒转;(3)在通常的稳定度参数条件下,发展扰动主要集中在高层,从结构上看,扰动的倾斜度大.当稳定度参数很小时,扰动可扩展到整个对流层,倾斜度较小;(4)高层反气旋也可以激发出不稳定内波,这种扰动在低层表现明显.当稳定度参数较小时,扰动发展较快,并且也以很小的速度倒转.     

热力强迫对局地环流的扰动作用

用积分变换法求解了包含地面加热作用的二维不可压缩流体的Boussinesq方程组,得到一组描述地面加热作用激发的局地扰动流场的解析解,主要有垂直风、水平扰动风、扰动气压、扰动温度。进而用动力学分析的观点结合图形分析,定性讨论了热力强迫作用对局地环流的扰动作用,以及加热影响下各物理扰动场的空间分布及时间演变特征。     

A Preliminary Application of the Differential Evolution Algorithm to Calculate the CNOP

A projected skill is adopted by use of the differential evolution （DE） algorithm to calculate a conditional nonlinear optimal perturbation （CNOP）. The CNOP is the maximal value of a constrained optimization problem with a constraint condition, such as a ball constraint. The success of the DE algorithm lies in its ability to handle a non-differentiable and nonlinear cost function. In this study, the DE algorithm and the traditional optimization algorithms used to obtain the CNOPs are compared by analyzing a theoretical grassland ecosystem model and a dynamic global vegetation model. This study shows that the CNOPs generated by the DE algorithm are similar to those by the sequential quadratic programming （SQP） algorithm and the spectral projected gradients （SPG2） algorithm. If the cost function is non-differentiable, the CNOPs could also be caught with the DE algorithm. The numerical results suggest the DE algorithm can be employed to calculate the CNOP, especially when the cost function is non-differentiable.     

Impact of Different Guidances on Sensitive Areas of Targeting Observations Based on the CNOP Method

The conditional nonlinear optimal perturbations(CNOPs) obtained by a fast algorithm are applied to determining the sensitive area for the targeting observation of Typhoon Matsa in 2005 using an operational regional prediction model-the Global/Regional Assimilation and PrEdiction System(GRAPES).Through a series of sensitivity experiments,several issues on targeting strategy design are discussed,including the effectivity of different guidances to determine the sensitive area(or targeting area) and the impa...     

Evolution of density perturbations in double exponential quintessence models

In this work we investigate the evolution of matter (linear) density perturbations for quintessence models with a self-interaction potential that is a combination of exponentials. One of the models is based on the Einstein theory of gravity, while the other is based on the Brans-Dicke scalar tensor theory. We constrained the parameter space of the models by using the determinations of the growth rate of perturbations derived from data of the 2-degree Field Galaxy Redshift Survey.