Nonlinearity and Finite-Time Instability in a T21L3 Quasigeostrophic Model

In this paper,a nonlinear optimization method is used to explore the finite-time instability of the atmospheric circulation with a three-level quasigeostrophic model under the framework of the conditional nonlinear optimal perturbation (CNOP).As a natural generalization of linear singular vector (SV),CNOP is defined as an initial perturbation that makes the cost function the maximum at a prescribed forecast time under certain physical constraint conditions.Special attentions are paid to the different structures and energy evolutions of the optimal perturbations.The results show that the most instable region of the global atmospheric circulation lies in the midlatitude Eurasian continent.More specially,SV and CNOP in the total energy norm with an optimization time of 2 days both present localness:they are mainly located in the midlatitude Asian continent and its east coast.With extension of the optimization time,SVs are more upstream and less localized in the zonal direction,and CNOPs differ essentially from SVs with broader zonal and meridional coverages; as a result,CNOPs acquire larger kinetic and available potential energy amplifications than SVs in the nonlinear model at the corresponding optimization time.For the climatological wintertime flow,it is seen that the baroclinic terms remain small over the entire time evolution,and the energy production comes essentially from the eddy kinetic energy,which is induced by the horizontal shear of the basic flow.In addition,the effects of SVs and CNOPs on the Eurasian atmospheric circulation are explored.The results show that the weather systems over the Eurasian continent in the perturbed fields by CNOPs are stronger than those by SVs at the optimization time.This reveals that the CNOP method is better in evaluating the instability of the atmospheric circulation while the SV method underestimates the possibility of extreme weather events.     

A further investigation of the decadal variation of ENSO characteristics with instability analysis

Based on instability theory and some former studies, the Simple Ocean Data Assimilation （SODA） data are analyzed to further study the difference between the propagation of the ENSO-related oceanic anomaly in the off-equatorial North Pacific Ocean before and after 1976. The investigation shows that after 1976 in the off-equatorial North Pacific Ocean, there is a larger area where the necessary conditions for baroclinic and/or barotropic instability are satisfied, which may help oceanic anomaly signals propagating in the form of Rossby waves to absorb energy from the mean currents so that they can grow and intensify. The baroclinic energy conversion rate in the North Pacific after 1976 is much higher than before 1976, which indicates that the baroclinic instability has intensified since 1976. Prom another perspective, the instability analysis gives an explanation of the phenomena that the ENSO-related oceanic anomaly signal in the North Pacific has intensified since 1976.     

Phillips模式的斜压不稳定的非线性饱和问题:能量情形

A conservation law for the Phillips model is derived. Using this law, the nonlinear saturation of purely baroclinic instability caused by the vertical velocity shear of the basic flow in the Phillips model-the case of energy-is studied within the context of Arnold's second stability theorem. Analytic upper bounds on the energy of wavy disturbances are obtained. For one unstable region in the parameter plane, the result here is a second-order correction in ε to Shepherd's; For another unstable region, the analytic upper bound on the energy of wavy disturbances offers an effective constraint on wavy (nonzonal) disturbances φ'i at any time.     

远距离台风暴雨过程的正/斜压不稳定

利用正／斜压联合不稳定计算方法，分析了由9711号台风引起的远距离台风暴雨(实况及MM4模拟结果)过程中不同时段、不同位置的正／斜压项。结果表明：台风暴雨初始时段的降水主要由台风系统本身正压不稳定扰动引起，随着台风与西风带系统的结合，其南北部出现了2个雨区，均是正／斜压联合不稳定的产物；北部雨区的斜压不稳定较明显，且有随高空急流的非纬向性增强而增强的趋势。     

正斜压模演变所揭示的武汉暴雨过程

对1998年7月21—22日发生在武汉附近的大暴雨过程的大气正、斜压分量演变过程进行了研究，结果表明：大气流场正压分量的演变与此次大暴雨的酝酿、发展和消亡具有内在的联系；正压分量在暴雨区的演变在一定程度上反映高、低空急流耦合形势；正、斜压平均相对模的演变与暴雨生命史相吻合。     

The generalized energy equation and instability in the two-layer barotropic vortex

The linear two-layer barotropic primitive equations in cylindrical coordinates are used to derive a gen- eralized energy equation, which is subsequently applied to explain the instability of the spiral wave in the model. In the two-layer model, there are not only the generalized barotropic instability and the super high- speed instability, but also some other new instabilities, which fall into the range of the Kelvin-Helmholtz instability and the generalized baroclinic instability, when the upper and lower basic flows are different. They are perhaps the mechanisms of the generation of spiral cloud bands in tropical cyclones as well.     

Localized multi-scale energy and vorticity analysis: II. Finite-amplitude instability theory and validation

A novel localized finite-amplitude hydrodynamic stability analysis is established in a unified treatment for the study of real oceanic and atmospheric processes, which are in general highly nonlinear, and intermittent in space and time. We first re-state the classical definition using the multi-scale energy and vorticity analysis (MS-EVA) developed in Liang and Robinson [Liang, X.S., Robinson, A.R., 2005. Localized multiscale energy and vorticity analysis. I. Fundamentals. Dyn. Atmos. Oceans 38, 195–230], and then manipulate certain global operators to achieve the temporal and spatial localization. The key of the spatial localization is transfer-transport separation, which is made precise with the concept of perfect transfer, while relaxation of marginalization leads to the localization of time. In doing so the information of transfer lost in the averages is retrieved and an easy-to-use instability metric is obtained. The resulting metric is field-like (Eulerian), conceptually generalizing the classical formalism, a bulk notion over the whole system. In this framework, an instability has a structure, which is of particular use for open flow processes. We check the structure of baroclinic instability with the benchmark Eady model solution, and the Iceland–Faeroe Frontal (IFF) intrusion, a highly localized and nonlinear process occurring frequently in the region between Iceland and Faeroe Islands. A clear isolated baroclinic instability is identified around the intrusion, which is further found to be characterized by the transition from a spatially growing mode to a temporally growing mode. We also check the consistency of the MS-EVA dynamics with the barotropic Kuo model. An observation is that a local perturbation burst does not necessarily imply an instability: the perturbation energy could be transported from other processes occurring elsewhere. We find that our analysis yields a Kuo theorem-consistent mean–eddy interaction, which is not seen in a conventional Reynolds stress framework. Using the techniques of marginalization and localization, this work sets up an example for the generalization of certain geophysical fluid dynamics theories for more generic purposes.     

阻塞过程中正斜压涡度拟能相互转换机制的重要性

使用正斜压涡度拟能方程对一次乌拉尔山阻塞过程的研究表明，虽然正、斜压涡度拟能向阻塞区内的净输送、阻塞区域内正斜压涡度拟能的净生成以及β效应是阻塞环流建立、维持和崩溃的基本能源，但正斜压涡度拟能相互转换机制则是阻塞过程得以形成的根本原因。如果没有正斜压涡度拟能相互转化机制，则阻塞环流不但不能形成，反而使大气的斜压性不断增强，正压性不断减弱。     

一次强降水过程中尺度系统发生发展动力机制的诊断分析

利用1°×1°经纬度NCEP/NCAR再分析资料、地面1h观测降水资料和TRMM卫星产品资料,分析了2009年6月8~9日引发贵州南部的强降水天气过程的中尺度对流系统活动,并进一步研究了大气正压非平衡强迫、湿斜压热动力耦合强迫在强降水天气发生发展与维持过程中的作用。结果表明:8~9日贵州南部的强降水主要是由中尺度系统的发生发展引起的。南海季风不仅给贵州南部强降水区带来充足的水汽,同时也带来足够的能量。正压非平衡强迫在降水的开始阶段与降水落区有较好的对应关系,是强降水的启动机制。斜压热动力耦合强迫在降水的维持阶段,特别是当大气层结转为弱湿中性时,其分布和强度与中尺度对流系统和降水的强度与落区有较好的对应关系,可能是强降水的维持机制。     

一次强降水过程中尺度系统发生发展动力机制的诊断分析

利用1°×1°经纬度NCEP/NCAR再分析资料、地面1h观测降水资料和TRMM卫星产品资料,分析了2009年6月8～9日引发贵州南部的强降水天气过程的中尺度对流系统活动,并进一步研究了大气正压非平衡强迫、湿斜压热动力耦合强迫在强降水天气发生发展与维持过程中的作用。结果表明：8～9日贵州南部的强降水主要是由中尺度系统的发生发展引起的。南海季风不仅给贵州南部强降水区带来充足的水汽,同时也带来足够的能量。正压非平衡强迫在降水的开始阶段与降水落区有较好的对应关系,是强降水的启动机制。斜压热动力耦合强迫在降水的维持阶段,特别是当大气层结转为弱湿中性时,其分布和强度与中尺度对流系统和降水的强度与落区有较好的对应关系,可能是强降水的维持机制。     

Evolution of instability before and during a torrential rainstorm in North China

NCEP-NCAR reanalysis data were used to analyze the characteristics and evolution mechanism of convective and symmetric instability before and during a heavy rainfall event that occurred in Beijing on 21 July 2012.Approximately twelve hours before the rainstorm,the atmosphere was mainly dominated by convective instability in the lower level of 900-800 hPa.The strong southwesterly low-level jet conveyed the moist and warm airflow continuously to the area of torrential rain,maintaining and enhancing the unstable energy.When the precipitation occurred,unstable energy was released and the convective instability weakened.Meanwhile,due to the baroclinicity enhancement in the atmosphere,the symmetric instability strengthened,maintaining and promoting the subsequent torrential rain.Deriving the convective instability tendency equation demonstrated that the barotropic component of potential divergence and the advection term played a major role in enhancing the convective instability before the rainstorm.Analysis of the tendency equation of moist potential vorticity showed that the coupled term of vertical vorticity and the baroclinic component of potential divergence was the primary factor influencing the development of symmetric instability during the precipitation.Comparing the effects of these factors on convective instability and symmetric instability showed some correlation.     

Sensitivity of Nonlinearity on the ENSO Cycle in a Simple Air-sea Coupled Model

In this paper,the influence of the El NioSouthern Oscillation (ENSO) cycle on the sensitivity of nonlinear factors in the numerical simulation is investigated by conducting numerical experiments in a simple air-sea coupled model for ENSO prediction.Two sets of experiments are conducted in which zonal nonlinear factors,meridional nonlinear factors,or both are incorporated into the governing equations for the atmosphere or ocean.The results suggest that the ENSO cycle is very sensitive to the nonlinear factor of the governing equation for the atmosphere or ocean.Thus,incorporating nonlinearity into air-sea coupled models is of exclusive importance for improving ENSO simulation.     

The Roles of Barotropic Instability and the Beta Effect in the Eyewall Evolution of Tropical Cyclones

Diabatic heating by convection in the eyewall often produces an annular region of high potential vorticity(PV) around the relatively low PV eye in a strong tropical cyclone(TC). Such a PV ring is barotropically unstable and can encourage the exponential growth of PV waves. In this study, such instability and the subsequent nonlinear evolution of three TC-like vortices having PV rings with different degrees of hollowness on an f-plane are first examined using an unforced, inviscid shallow-water-e...     

Simulating tropical instability waves in the equatorial eastern Pacific with a coupled general circulation model

Satellite observations of SSTs have revealed the existence of unstable waves in the equatorial eastern Pacific and Atlantic oceans. These waves have a 20-40-day periodicity with westward phase speeds of 0.4-0.6 m s-1 and wavelengths of 1000-2000 km during boreal summer and fall. They are generally called tropical instability waves (TIWs). This study investigates TIWs simulated by a high-resolution coupled atmosphere-ocean general circulation model (AOGCM). The horizontal resolution of the model is 120 km in...     

一次梅雨期苏北大暴雨的时空结构及其非线性亚临界对称不稳定

利用WRF V2.2模式对2006年6月30日00时—7月1日12时（世界时）江苏宝应地区的大暴雨过程进行数值模拟,并利用从模拟结果提取出的环境风场和中尺度扰动风场对此次大暴雨过程的时空结构,尤其是风场的垂直切变和非线性亚临界对称稳定性进行分析,结果表明：整层大气平均风垂直切变矢量转为西南偏西风后其南风分量随时间增大到最大值,对暴雨的发生有提前5-4 h的指示意义,相应时刻绝对水平螺旋度亦达到极值;暴雨发生前3 h首次出现强烈的整层垂直上升气流,预示大暴雨发生;在暴雨发生前9 h,高层200 hPa涡度、散度两波呈π/2位相差,对应强烈地转不平衡重力波,随时间向下传播,至暴雨发生前3 h下传到800 hPa;中尺度扰动风场的加强与降水的加强关系密切,在暴雨发生前3 h,出现中尺度非线性亚临界对称不稳定,激发暴雨发生,并对大暴雨的发生有重要的指示意义。     

The impact of nonlinear stability and instability on the validity of the tangent linear model

l.Intr0ducti0nTheequationsgoverningthemotionsoftheatmosphereandoceanaren0nlinear0nes.Itisdiffcultandcomplicatedtodealwiththenonlinearproblem.Sothetangentlinearmodel(TLM),whichisobtainedbylinearizingthenonlinearmodelinthevicinityofthebasicflow.iswidelyutilizedinthetheoreticalresearchandpracticalimplementationintheatmosphericandoceanicsciences.First-TLMcanbeusedtoestimatetheev0luti0nofsmallPerturbati0nsinaf0recastmodel.Second,itisadoptedinextendedKalmanfilterinthedataassimilation(Evensen,l99…     

东亚地区南北两个风暴源地中风暴的结构和动力学差异

基于欧洲中心中期天气预报再分析资料(ERA-40),使用涡旋追踪和合成技术、多尺度子空间变换以及局地多尺度能量分析方法研究了东亚地区南北两个风暴源地中风暴的差异。结果发现,南、北两个源地风暴在结构上和内部动力过程上均存在着显著不同。南支源地(40°N以南)风暴底层比高层强,与线性斜压模式中的最不稳定模态结构相似;而北支源地(40°N以北)风暴则正好相反,与下游发展理论所描述的斜压波结构相似。并且发现,南支源地风暴的非地转风场比北支源地风暴的强。能量学诊断结果显示,南支源地风暴的能量源除了斜压不稳定外,有很大一部分来自正压不稳定,而北支源地风暴中则是存在弱的动能逆尺度传输。此外,南支源地风暴的浮力转换和非绝热做功均比北支源地风暴的强,其主要原因是南支源地风暴的垂直运动更强,风暴中的水汽更加充足。      

Mid-latitude atmospheric responses to heat and vorticity forcing using a linear baroclinic model

Based on diagnostic analysis of reanalysis data for 58-year, the distribution characteristics of decadal variability in diabatic heating, transient eddy heating and transient eddy vorticity forcing related to the sea surface temperature (SST) anomalies over the North Pacific, as well as their relationship with anomalous atmospheric circulation have been investigated in this paper. A linear baroclinic model(LBM) was used to investigate atmospheric responses to idealized and realistic heat and vorticity forcing anomalies, and then to compare relative roles of different kinds of forcing in terms of geopotential height responses. The results illustrate that the responses of atmospheric height fields to the mid-latitude heating can be either baroclinic or barotropic. The response structure is sensitive to the relative horizontal location of heating with respect to the background jet flow, as well as to the vertical profile of heating. The response to the idealized deep heating over the eastern North Pacific, mimicking the observed heating anomaly, is baroclinic. The atmospheric response to the mid-latitude vorticity forcing is always barotropic, resulting in a geopotential low that is in phase with the forcing. The atmospheric responses to the realistic heat and vorticity forcing show the similar results, suggesting that diabatic heating, transient eddy heating and transient eddy vorticity forcing can all cause atmospheric anomalies and that the vorticity forcing plays a relatively more important role in maintaining the equivalent-barotropic structure of geopotential height anomalies.     

Study on moist potential vorticity and symmetric instability during a heavy rain event occurred in the Jiang-Huai valleys

In the light of the theory on moist potential vorticity (MPV) investigation was undertaken of the 700 hPa vertical (horizontal) component MP1 (MPV2) for the heavy rain event occurring in Ju-ly 5-6,1991. Results show that the distribution features of the two components were closely related to the development of a mesoscale cyclone as a rainstorm-causing weather system in the lower troposphere in such a way that the ambient atmosphere of which MPV1>0 and MPV2<0 with |MPVl|≥|MPV2| favored the genesis of conditional symmetric instability (CSI) and that, as in-dicated by calculations, a CSI sector was really existent in the lower troposphere during the heavy rain happening and contributed greatly to its development.     

线性准地转模型中基本流和辐射冷却对感热加热强迫的副热带高压形态的影响

通过求取定常线性准地转位涡模式的数值解,研究了感热型垂直非均匀分布的冷、热源强迫所激发的副热带环流的结构特征,讨论了副热带背景风场和洋面辐射冷却对洋面副热带高压"三角形偏心"结构形成的重要作用。结果表明,基本流对感热加热强迫的副热带环流有重要影响,当基本流为常数时,感热加热强迫的气旋和反气旋主要集中在对流层中下层,且地面系统远强于中高层。当基本流为非常数时,其经向切变能改变气旋和反气旋中心的经向位置,使它移至0风速所在纬度附近;其垂直变化加强了中高层气旋和反气旋,中心位于对流层上层,与南亚高压的位置基本一致。研究结果还表明,在大洋东部洋面辐射冷却与副热带地区背景风场的共同作用下,形成了洋面副热带高压特有的"三角形偏心"结构。副热带高纬度的西风使感热强迫的洋面副热带高压东移,低纬度的东风使其西移,形成东北—西南走向的"平行四边形"结构,且中心位于大洋西部。大洋东部强洋面辐射冷却激发的洋面反气旋加强了大洋东部的副热带高压,使其中心东移至大洋东部,从而表现出东北—西南走向的"三角形偏心"结构。