The structure and propagation of stationary planetary wave packet in the barotropic atmosphere

Monthly or seasonally mean anomalies of large-scale atmospheric circulation are better represented by wave packets or their combination. Both qualitative and quantitative analyses of equations of wave packet dynamics, which are obtained by the use of WKB approximation, are very helpful for the understanding of structure, formation and propagation of stationary and quasi-stationary planetary wave packet patterns in the atmosphere. Indeed, these equations of wave packet dynamics can be directly solved by the method of characteristic lines, and the results can be simply and clearly interpreted by physical laws. In this paper, a quasi-geostrophic barotropic model is taken for simplicity, and the wave packets superimposed on several ideal profiles of the basic current and excited by some ideal forcings are investigated in order to make comparison of the accuracy of calculation with the analytical solution. It is revealed that (a) the rays of stationary planetary wave packet do not coincide with but go away from the great circle with significant difference if the shear of the basic zonal flow is not too small; (b) being superimposed on a westerly jet flow with positive shear (Uλ/y>0), the stationary wave packets excited by low-latitudinal forcing are first intensified during their northeastward propagation in the Northern Hemisphere, then reach their maximum of amplitude at some critical latitude, and after that weaken again; (c) the connected line of extremes (the positive and negative centres) of wave packet does not coincide with but crosses the ray by an angle, the larger the scale of external forcing, the larger the angle; and (d) the whole pattern of a trapped stationary wave packet is complicated by the interference between the incident and reflected waves.     

两层正压准平衡海洋模型的中纬度自由涡旋波动解

建立了具有瑞利摩擦且仅考虑大洋西海岸或同时考虑大洋东、西海岸的两层正压准平衡海洋模型,并做了解析求解,用以研究中纬度的自由涡旋波。得到的主要结论有:模型中该波动的解为波包。在仅考虑大洋西海岸时该波包的载频频率是连续谱;而同时考虑大洋东、西海岸时其为离散谱;且均有载频频率越高(周期越短)水平尺度越大的特点,对过分低频的波动,则会使准平衡的假定不再适用。模型中该波动波包载频的周期约在26天至24年。因考虑了摩擦,该波包的振幅随时间呈指数衰减,但摩擦系数的大小仅影响其衰减程度而不改变其空间结构,最终该波包振幅趋于0,故该两层正压海洋模型的解就趋于大气风场的强迫特解。模型中该波包的载频都是西传的;频率较高则西传较快,波包的特性和变形都很明显;频率低,则西传慢,其波形接近平面简谐波。在该两层正压模型中,该波动上层流场与正压模型中的流动类似,而下层海洋流动则其流速与上层海洋相同,而流向相反。该模型中该波动的性质是准平衡(准无辐散)的涡旋波,当摩擦不太大且其水平尺度在10km以上时,其性质则为准地转的Rossby波。     

Spatial reorganization of SST anomalies by stationary atmospheric waves

The dynamics of sea surface temperature (SST) anomalies that force stationary atmospheric waves, which in turn, feed back on the SST field is addressed. The phenomena is isolated by analyzing the dynamics of a slab ocean that is thermally coupled to an atmospheric model. Particular emphasis is put on identifying SST structures that are weakly damped by the joint effect of air–sea heat transfer and atmospheric wave dynamics.A frame work is presented that singles out long-lived SST features in a slab ocean coupled to an arbitrary linear atmospheric model. It is demonstrated that an SST anomaly eventually disintegrates into a number of propagating wave packets. The wave packets are confined in a Gaussian envelope, and each packet is tied to a stationary wave of a particular wavelength. These structures are a manifestation of coupled SST-atmosphere mode, for which the atmosphere and the ocean nearly are in thermal equilibrium. However, a small disequilibrium causes the wave packet to propagate and to broaden in an apparent diffusive manner.Central ideas pertaining to the mid-latitude SST dynamics are illustrated by analyzing the thermal feedback between a two-level atmospheric model (on a β-plane) and a dynamically passive slab ocean. The relevance of the present idealized coupled-modes to the SST variability in the mid-latitudes and in atmospheric GCMs coupled to slab oceans is discussed.     

季节内尺度热带-中纬相互作用机制初探

本文使用一个简单的全球二层大气环流模式作了强迫响应数值试验。模式中引入了代表热带低频偶极型对流的异常强迫.结果表明这一强迫不仅能激发显著的局地大气响应,也能引起北半球中纬显著的低频异常波列,中纬波列的发展与热带强迫变化之间存在四分之一位相差关系.这些结果与观测研究的结果一致.进一步的分析表明,大气响应的位相滞后与强迫产生的能量从内模向外模的非线性转换过程有关.最后提出了季节内尺度热带-中纬相互作用的可能机制.     

Atlantic Meridional Overturning Circulation response to idealized external forcing

The response of the Atlantic Meridional Overturning Circulation (AMOC) to idealized external (solar) forcing is studied in terms of the internal (unforced) AMOC modes with the Kiel Climate Model (KCM), a coupled atmosphere-ocean-sea ice general circulation model. The statistical investigation of KCM’s internal AMOC variability obtained from a multi-millennial control run yields three distinct modes: a multi-decadal mode with a period of about 60?years, a quasi-centennial mode with a period of about 100?years and a multi-centennial mode with a period of about 300–400?years. Most variance is explained by the multi-centennial mode, and the least by the quasi-centennial mode. The solar constant varies sinusoidally with two different periods (100 and 60?years) in forced runs with KCM. The AMOC response to the external forcing is rather complex and nonlinear. It involves strong changes in the frequency structure of the variability. While the control run depicts multi-timescale behavior, the AMOC variability in the experiment with 100?year forcing period is channeled into a relatively narrow band centered near the forcing period. It is the quasi-centennial AMOC mode with a period of just under 100?years which is excited, although it is heavily damped in the control run. Thus, the quasi-centennial mode retains its period which does not correspond exactly to the forcing period. Surprisingly, the quasi-centennial mode is also most strongly excited when the forcing period is set to 60?years, the period of the multi-decadal mode which is rather prominent in the control run. It is largely the spatial structure of the forcing rather than its period that determines which of the three internal AMOC modes is excited. The results suggest that we need to understand the full modal structure of the internal AMOC variability in order to understand the circulation’s response to external forcing. This could be a challenge for climate models: we cannot necessarily expect that the response to external forcing is realistically captured by a model, even if only strongly damped modes are not well represented that do not account for much variance under present-day conditions.     

2007年夏季江淮强降水过程中10~30d低频变化及其与对流层上层波包活动的联系

利用NCEP/NCAR再分析和全国740站逐日降水资料,运用一点滞后相关等方法,对2007年夏季江淮流域强降水期间低频振荡的波动活动特征及其与降水低频变化的联系进行了分析。结果表明,在2007年夏季降水中,降水低频分量起着重要作用。降水的低频振荡主周期为10~30d,降水距平时间序列与10~30d低频分量具有较好的对应关系。低频扰动在对流层上层和低层都呈现波列状分布,且在降水活跃位相时,低频环流在高、低层具有斜压结构。在对流层上层,低频扰动有缓慢的东移倾向,相速度为每天2~3个经度。西风带中存在多次移动性波列向下游的传播,且在120°E以西以每天14经度的群速度向下游频散能量,表明10~30d低频波动具有明显的下游发展特征。在强降水开始5d前,低频波动与能量可起源于高纬的乌拉尔山附近,沿着西北-东南向的路径向下游传播。下游发展的低频波动为江淮流域带来了能量,为强降水的发生提供了条件。这些结果加深了人们对低频波动在江淮流域强降水过程中所起作用的认识,可为寻找江淮流域强降水过程预报线索提供科学依据。     

Forced Rossby wave packets in barotropic shear flows with critical layers

In this paper, we investigate the meridional propagation of a forced Rossby wave packet towards a critical layer in a zonal shear flow by solving the linearized barotropic vorticity equation. The forcing is applied north of the critical layer. Two approaches are employed for solving this problem. First, an analytic solution valid for large time is derived, using Fourier and Laplace transform techniques and asymptotic approximations. This solution exhibits the modification due to the wave packet of the solution obtained by Warn and Warn (1976) [Warn, T., Warn H., 1976. On the development of a Rossby wave critical level. J. Atmos. Sci., 33, 2021–2024.] in the monochromatic case. A numerical investigation is then carried out using a finite difference scheme and a time-dependent radiation condition. It is found that the forced wave packet is absorbed at the critical layer and the total momentum transferred to the mean flow as a result of the absorption is observed to be proportional to the length scale of the wave packet. We also consider the case of a north–south mean flow with a longitudinally propagating wave packet forced to the east or west of the critical layer. The monochromatic version of this problem has been used before (Geisler, J.E., Dickinson, R.E., 1975. Critical level absorption of barotropic Rossby waves in a north–south flow. J. Geophys. Res., 80, 3805–3811.) to examine the interaction of western boundary currents and oceanic Rossby waves.     

Wind forcing of internal waves in a long narrow stratified lake

A vertically integrated approach to the analysis of thermistor chain and wind data from a long, narrow, stratified lake indicates that forcing events are short relative to the response time. Correlations between forcing and isotherm tilts clearly indicate stratification response times dependent on internal wave speed. In addition, it is possible to infer basin-scale internal wave damping where over 80% of the potential energy in the internal wave setup is lost in one internal wave period.     

Two Types of Arctic Oscillation and Their Associated Dynamic Features

In this paper,the dynamical evolutions of two types of Arctic Oscillation (AO),the stratospheric (S) and tropospheric (T) types,have been investigated on an intermediate time scale in terms of transient eddy feedback forcing and three-dimensional Rossby wave propagation.S-Type (T-type) events are characterized by an anomalous stratospheric polar vortex that is in phase (out of phase) with its tropospheric counterpart.Approximately onethird of AO events,both positive and negative,are T-type events.For the positive phase of a T-type event,the formation and maintenance of stratospheric positive anomalies over the polar cap are associated with an upward propagation of Rossby wave packets originating from the near-tropopause altitude over northeastern Asia.However,such upward propagating features are not found for S-type events.In the troposphere,transient eddy feedback forcing is primarily responsible for the meridional seesaw structure of both the S-and T-type events,with an additional contribution from Rossby wave propagation.     

低空急流和非均匀层结条件下重力惯性波的传播与发展

本文从基流背景下线性化Boussinesq方程组出发,采用WKBJ方法,首先求得重力惯性波的广义波作用量变化方程及波参数随波包的变化方程,讨论了基流切变对重力惯性波传播和发展的影响;然后用Runge-Kutta方法讨论了不同层结(含降水影响)下重力惯性波的传播路径。得到了降水强度大、静力稳定度小的区域对重力惯性波有“吸引”作用,因而引起重力惯性波能量的集中,进而触发和强化对流天气的结论。      

Midlatitude unstable air-sea interaction with atmospheric transient eddy dynamical forcing in an analytical coupled model

While recent observational studies have shown the critical role of atmospheric transient eddy (TE) activities in midlatitude unstable air-sea interaction, there is still a lack of a theoretical framework characterizing such an interaction. In this study, an analytical coupled air-sea model with inclusion of the TE dynamical forcing is developed to investigate the role of such a forcing in midlatitude unstable air-sea interaction. In this model, the atmosphere is governed by a barotropic quasi-geostrophic potential vorticity equation forced by surface diabatic heating and TE vorticity forcing. The ocean is governed by a baroclinic Rossby wave equation driven by wind stress. Sea surface temperature (SST) is determined by mixing layer physics. Based on detailed observational analyses, a parameterized linear relationship between TE vorticity forcing and meridional second-order derivative of SST is proposed to close the equations. Analytical solutions of the coupled model show that the midlatitude air-sea interaction with atmospheric TE dynamical forcing can destabilize the oceanic Rossby wave within a wide range of wavelengths. For the most unstable growing mode, characteristic atmospheric streamfunction anomalies are nearly in phase with their oceanic counterparts and both have a northeastward phase shift relative to SST anomalies, as the observed. Although both surface diabatic heating and TE vorticity forcing can lead to unstable air-sea interaction, the latter has a dominant contribution to the unstable growth. Sensitivity analyses further show that the growth rate of the unstable coupled mode is also influenced by the background zonal wind and the air–sea coupling strength. Such an unstable air-sea interaction provides a key positive feedback mechanism for midlatitude coupled climate variabilities.

     

The Dynamics of ENSO Anomaly as Revealed in Ensemble Climate Simulations-Impact of Mean Stationary Wave

A series of climate ensemble experiments using the climate model from National Centers for Environmental Prediction (NCEP) were performed to exam impact of sea surface temperature (SST) on dynamics of El-Nino/South-crn Oscillation (ENSO).A specific question addressed in this paper is how important the mean stationary wave influences anomalous Rossby wave trains or teleconnection patterns as often observed during ENSO events.Evidences from those ensemble simulations argue that ENSO anomalies,especially over Pacific-North America (PNA) region,appear to be a result of modification for climatological mean stationary wave forced by persistent tropical SST anomalies Therefore,the role of SST forcing in maintaining climate basic state is emphasized.In this argument,the interaction between atmospheric internal dynamics and external forcing,such as SST is a key element to understand and ultimately predict ENSO.     

Diagnosis of the forcing of inertial-gravity waves in a severe convection system

The non-hydrostatic wave equation set in Cartesian coordinates is rearranged to gain insight into wave generation in a mesoscale severe convection system. The wave equation is characterized by a wave operator on the lhs, and forcing involving three terms—linear and nonlinear terms, and diabatic heating—on the rhs. The equation was applied to a case of severe convection that occurred in East China. The calculation with simulation data showed that the diabatic forcing and linear and nonlinear forcing presented large magnitude at different altitudes in the severe convection region. Further analysis revealed the diabatic forcing due to condensational latent heating had an important influence on the generation of gravity waves in the middle and lower levels. The linear forcing resulting from the Laplacian of potential-temperature linear forcing was dominant in the middle and upper levels. The nonlinear forcing was determined by the Laplacian of potential-temperature nonlinear forcing. Therefore, the forcing of gravity waves was closely associated with the thermodynamic processes in the severe convection case. The reason may be that, besides the vertical component of pressure gradient force, the vertical oscillation of atmospheric particles was dominated by the buoyancy for inertial gravity waves. The latent heating and potential-temperature linear and nonlinear forcing played an important role in the buoyancy tendency. Consequently, these thermodynamic elements influenced the evolution of inertial-gravity waves.     

QBO-like Oscillations Induced by Local Thermal Forcing

A zonal-vertical two-dimensional equatorial model is used to study the possibility that the long period oscillation of the zonal mean flow occurring in the lower equatorial stratosphere (QBO) is caused by local thermal ac-tivities at the tropical tropopause. The model successfully reproduces QBO-like oscillations of the zonal mean flow, suggesting that the local heating or cooling at the tropical tropopause is probably the main reason of QBO’s genera-tion. The analysis of the dependence of the oscillation on the wave fencing indicates that the oscillation is not sensible to the forcing scale. The model can reproduce QBO-like oscillations with any forcing scale if the fencing period and amplitude take appropriate values, proving that the internal gravity waves generated by local thermal source take much important roles in QBO.     

热带平流层Kelvin波的能量、动量铅直输送特征的理论分析

本文利用赤道β平面近似下的线性化扰动方程组,假定无外源强迫和基本大气为等温大气的情况下求解,对于v’=0的Kelvin波的特解,得到了波动的能量和动量的铅直输送的结果。在波动位相下传的情况下,波动向上输送能量和西风角动量。这从理论上印证了Kelvin波在铅直方向的能量和动量输送特征,也提示了Kelvin波对准两年振荡(QBO)中西风位相的建立和下传的作用。      

A note on free and forced Rossby wave solutions: The case of a straight coast and a channel

The free Rossby wave (RW) solutions in an ocean with a straight coast when the offshore wavenumber of incident (l₁) and reflected (l₂) wave are equal or complex are discussed. If l₁ = l₂ the energy streams along the coast and a uniformly valid solution cannot be found; if l_1,2 are complex it yields the sum of an exponentially decaying and growing (away from the coast) Rossby wave. The channel does not admit these solutions as free modes.If the wavenumber vectors of the RWs are perpendicular to the coast, the boundary condition of no normal flow is trivially satisfied and the value of the streamfunction does not need to vanish at the coast. A solution that satisfies Kelvin's theorem of time-independent circulation at the coast is proposed.The forced RW solutions when the ocean's forcing is a single Fourier component are studied. If the forcing is resonant, i.e. a free Rossby wave (RW), the linear response will depend critically on whether the wave carries energy perpendicular to the channel or not. In the first case, the amplitude of the response is linear in the direction normal to the channel, y, and in the second it has a parabolic profile in y. Examples of these solutions are shown for channels with parameters resembling the Mozambique Channel, the Tasman Sea, the Denmark Strait and the English Channel. The solutions for the single coast are unbounded, except when the forcing is a RW trapped against the coast. If the forcing is non-resonant, exponentially decaying or trapped RWs could be excited in the coast and both the exponentially “decaying” and exponentially “growing” RW could be excited in the channel.     

The Relationship Between Abnormal Meiyu and Medium-Term Scale Wave Perturbation Energy Propagation Along the East Asian Subtropical Westerly Jet

The East Asian subtropical westerly jet(EASWJ) is one of the most important factors modulating the Meiyu rainfall in the Yangtze-Huaihe River Basin, China. This article analyzed periods of the medium-term EASWJ variation,wave packet distribution and energy propagation of Rossby waves along the EASWJ during Meiyu season, and investigated their possible influence on abnormal Meiyu rain. The results showed that during the medium-term scale atmospheric dynamic process, the evolution of the EASWJ in Meiyu season was mainly characterized by the changes of3-8 d synoptic-scale and 10-15 d low-frequency Rossby waves. The strong perturbation wave packet and energy propagation of the 3-8 d synoptic-scale and 10-15 d low-frequency Rossby waves are mostly concentrated in the East Asian region of 90°-150°E, where the two wave trains of perturbation wave packets and wave-activity flux divergence coexist in zonal and meridional directions, and converge on the EASWJ. Besides, the wave trains of perturbation wave packet and wave-activity flux divergence in wet Meiyu years are more systematically westward than those in dry Meiyu years, and they are shown in the inverse phases between each other. In wet(dry) Meiyu year, the perturbation wave packet high-value area of the 10-15 d low-frequency variability is located between the Aral Sea and the Lake Balkhash(in the northeastern part of China), while over eastern China the wave-activity flux is convergent and strong(divergent and weak), and the high-level jets are strong and southward(weak and northward). Because of the coupling of high and low level atmosphere and high-level strong(weak) divergence on the south side of the jet over the Yangtze-Huaihe River Basin, the low-level southwest wind and vertically ascending motion are strengthened(weakened), which is(is not)conducive to precipitation increase in the Yangtze-Huaihe River Basin. These findings would help to better understand the impact mechanisms of the EASWJ activities on abnormal Meiyu from the perspective of medium-term scale Rossby wave energy propagation.     

对流层上层斜压波包活动与2003年江淮流域梅雨的关系

利用NCEP/NCAR再分析和中国740站逐日降水资料, 研究了2003年淮河流域梅雨期间对流层上层斜压波动的传播情况。结果发现, 斜压波组织成波包向下游传播且具有明显的下游频散效应。波动起源于巴尔喀什湖西北侧, 沿着西北－东南向的路径向东南传播, 传至江淮流域大约需要3天。斜压波包所带来的扰动能量为江淮流域暴雨的发生发展提供了必要的能量积聚。通过与1998和1997年这两个梅雨年份的比较, 发现1998年异常强梅雨年的斜压波包的活动特征与2003年的相似, 但在梅雨降水非常偏少的1997年, 未发现有明显的斜压波包向下游的传播。     

斜压气流中波包的演变及其对外压不稳定波的激发

把斜压气流中的短波槽看成波包，并把波包作为准地转模式的初值进行研究，发现波包的结构对其演变有重要影响，初始阶段急流轴下面向西倾斜的波包能够获得较快的发展，而向东倾斜的波包则是衰减的，这与ＷＫＢＪ方法得出的结论［１］是一致的，但是无论西倾还是东倾的波包，除了其自身随时间的演变外，还会激发出斜压不稳定波动，而且随着扰动的发展，不稳定斜压波会逐步在扰动中占主导地位。由此可以解释某些中纬度气旋的发生发展问题。     

Evolution of large scale disturbances and their interaction with mean flow in a rotating barotropic atmosphere—Part II

In part I of this paper, we have discussed two problems: the general properties of two-dimensional baro-tropic motion and the evolution and structure of both Rossby wave packet and inertio-gravity wave packet. In this part, we shall continue our discussion. Third, normal modes and continuous spectra of both quasi-geostrophic and non-geostrophic models, their different behaviour, and the comparison of normal mode approach to the wave packet approach. Fourth, weakly nonlinear theory of interaction based on the analysis of eddy transports. A nonzonal basic flow as well as non-geostroptaic model is also included in the consideration. The last, the fully nonlinear theory, making emphasis on the conditions for the maintenance of nonzonal disturbances and the conditions for their continuous and complete absorption by the zonal flow. A comparison of Rossby wave absorption to energy cascade in the two-dimensional turbulence is also given.