Discrete Spectra and Continuous Spectrum of the Barotropic Quasi-Geostrophic Model-A Calculation of Meteorological Data

l.Intr0ducti0nMaintenance,developmentanddecay0fmiddlelatitudeatmosphericdisturbancesarecentraltotheunderstandingofsynopticweatherprocessesandshort-termclimatevariability.FrontogenesisandsurgeofcoldwavesaretypicallyassociatedwithrapiddevelopmentoffavorablyconfiguredsmalldisturbancesintheuppertroPOsphere.Thesedisturbancesfurtheractasinteractivetransientforcingtocauselowfrequencyvariabilities.Theyalsoaffectthein-tensityofwesterliesandtheequator-to-P0letemPeraturegradientoftheatmosphere.Studieso…     

Wave-Mean Flow Interaction: the Role of Continuous-Spectrum Disturbances

Traditionally, “eddy feeds zonal flow” in the atmosphere is considered as a result of decaying unstable waves. We show that disturbances made of non-modal solutions-the continuous-spectrum disturbances-can also effectively transport zonal angular momentum and interact with the zonal basic flow. These disturbances, though stable, eventually decay, losing their energy to strengthen the westerly jets in the atmosphere.Calculations with observational data illustrate that the atmospheric zonal flow is maintained primarily by continuous-spectrum disturbances rather than by unstable waves. Angular momentum transport by continuous-spectrum disturbances is one order of magnitude larger than that by all kinds of normal modes (referred as discrete-spectrum disturbances) including unstable waves.     

Duplex equilibria of Ural circulation anomalies

Atmospheric circulation anomalies over the Ural Mountains are crucial indicators of the anomalous downstream weather and climate over East Asia. Here, we provide a new perspective on the mechanism of Ural circulation anomalies. We use a simple theoretical model to determine that the relationship between the solar forcing and three Ural circulation patterns, namely, neutral type, trough anomaly and ridge anomaly, is a nonlinear relationship following the supercritical pitchfork bifurcation theory. The theory predicts that when the total solar irradiance (TSI) is below a critical value, trough and ridge anomalies represent duplex equilibria and are equally likely to occur at the same TSI. Based on 180 winter months record, we have estimated the bidimensional probability density of TSI and the monthly mean geopotential height at 500 hPa or zonal wind at 850 hPa over the Ural Mountains. Results show that Sc = 1360.9 W m−2 is a critical value of TSI, the neutral type pattern is the single circulation regime when TSI > Sc, whereas trough and ridge anomaly patterns are duplex circulation regimes when TSI < Sc. Besides, when TSI < Sc, during the same TSI range, trough and ridge anomaly events occur at nearly the same frequencies. These results generally agree with the theoretical model. We demonstrate that trough and ridge anomalies, as duplex equilibria, result from the large-scale zonal flow interacting with the Ural Mountains. Low TSI tends to strengthen the large-scale zonal flow over the Ural Mountains, hence inducing either a trough anomaly or ridge anomaly.     

Normal mode theory of lee cyclogenesis and the initial value problem

Summary An initial value problem is proposed to study the influence of mountains upon atmospheric flows. The normal mode, quasigeostrophic theory of lee cyclogenesis is revisited; in order to model Alpine cyclogenesis, the flow, upon which the mountain acts, should represent a cyclone wave propagating eastward in a sheared zonal current. Two different models are considered in order to describe cyclone waves: an unstable Eady normal mode and a finite amplitude, neutral Rossby mode in the two layer model. It is shown that the topographic modifications proper of normal modes emerge very rapidly from the integration of the initial value problem. It is also shown that an enhanced deepening of the upper level trough can occur when finite amplitude effects are taken into account.With 8 Figures     

Comparative energetics analysis of CCM2 with different horizontal resolutions

 Comprehensive global energetics analysis is carried out for the NCAR CCM2 with different horizontal resolutions of R15, T42, T63, and T106 to assess the effect of various model truncations on the global energetics characteristics in climate models. Both the energy levels and energy transformations are examined over the zonal wave number domain during a northern winter and summer. In addition to the simulated atmosphere, the ECMWF global analysis during 1986 to 1990 is analyzed for comparison using the same diagnostic scheme. Previous studies have revealed that zonal kinetic energy is supplied by synoptic disturbances in terms of the zonal-wave interactions of kinetic energy. According to our result, however, such an energy flow from eddies to zonal motions is valid only for zonal wave numbers up to about 30. We find that the zonal-wave interactions of kinetic energy change sign beyond wave number 30 where the energy is transformed from zonal to eddies for both the ECMWF and CCM2-T106. The large-scale zonal motions are diffusive against the short waves beyond wave number 30, which may well be parameterized by various forms of the diffusion schemes. We suggest from this result that the atmospheric disturbances with wave numbers lower than 30 are necessary to represent accurately the two-way interactions between zonal and eddy motions, because these waves can actively influence the behavior of the zonal motions. Based on this finding, we suggest that the model resolution of R15 is inadequate for climate studies from the energetics point of view, and that resolution of T42 is the minimum requirement to represent the general circulation adequately. Some other discrepancies are discussed in detail for the coarse resolution climate models. Received: 15 July 1996/Accepted: 3 January 1997     

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.     

热带平流层多尺度波动分离方案的研究：多站点高分辨率无线电探空联合分析

利用太平洋地区台风过境期间6个热带气象站的高分辨率无线电探空资料,结合扩展经验正交函数（EEOF）展开,对热带下平流层行星波和重力波扰动进行了分离,给出了一种热带地区提取重力波扰动的新方案。对观测数据做EEOF展开后,选择表征行星尺度波动模态的特征向量和相应权重进行气象要素场的重建。结果显示,在不同的台风过程期间,温度、纬向风和经向风的重建扰动量显示出不同的动力学偏振关系:在准两年振荡（QBO）东风位相时与赤道开尔文波的偏振关系一致,而在准两年振荡西风位相时与混合罗斯贝-重力波（MRG）的偏振关系一致。把行星尺度波动模态从原始观测中剔除,得到新的扰动廓线,对其进行重力波垂直波数谱的谱型拟合。结果发现,与以往方法提取的重力波扰动相比,新方法所得谱型参数中特征垂直波长λ*在不同时期不同站点变化很小,稳定在1.7 km左右,且低频波数段谱斜率s的数值与理论假设1十分接近。综合其研究结果可以推测,用新方法提取的热带重力波扰动更加符合当前的理论垂直波数谱模型。      

Signature of quasi–biennial oscillation and long-period equatorial disturbances in the lower atmosphere over Thiruvananthapuram

Summary An attempt has been made in this paper to examine different modes of oscillation in the wind field during different seasons over Thiruvananthapuram (lat. 8.29° N, long. 76.59° E, located at the extreme southwest coast of India) based on daily upper air observations for the period from January 1997 to December 1999. A power spectral analysis is carried out with the upper air data of the station. The study shows that one and half cycle of Quasi–Biennial Oscillation (QBO) and the power spectra of the meridional wind component exhibit peaks between the period of four days and seven days (corresponding frequency range between 0.25 day⁻¹ and 0.15 day⁻¹) during all seasons. The seasonal variation of these large-scale oscillations over the station depends upon the background mean zonal flow, which in turn closely related to the QBO structure. The time sequence of power spectra shows that the disturbances with periods between four days and seven days dominantly prevail in the upper troposphere and lower stratosphere throughout the year. The regimes of high power spectral intensity in this period range are maintained in the levels where the mean zonal flow (westerly or easterly) weakens and changes with height. The study establishes the fact that disturbances (mixed Rossby-gravity waves) acquire maximum power in the winter season whereas the south-west monsoon exhibits minimum spectral intensity when spreading of energy over a frequency range takes place.     

Three－dimensional Global Scale Permanent－wave Solutions of the Nonlinear Quasigeostrophic Potential Vorticity Equation and Energy Dispersion

The three-dimensional nonlinear quasi-geostrophic potential vorticity equation is reduced to a linear form in the stream function in spherical coordinates for the permanent wave solutions consisting of zonal wavenumbers from 0 to n and rn vertical components with a given degree n. This equation is solved by treating the coefficient of the Coriolis parameter square in the equation as the eigenvalue both for sinusoidal and hyperbolic variations in vertical direction. It is found that these solutions can represent the observed long term flow patterns at the surface and aloft over the globe closely. In addition, the sinusoidal vertical solutions with large eigenvalue G are trapped in low latitude, and the scales of these trapped modes are longer than 10 deg. lat. even for the top layer of the ocean and hence they are much larger than that given by the equatorial β-plane solutions. Therefore such baroclinic disturb-ances in the ocean can easily interact with those in the atmosphere.Solutions of the shallow water potential vorticity equation are treated in a similar manner but with the effective depth H = RT / g taken as limited within a small range for the atmosphere.The propagation of the flow energy of the wave packet consisting of more than one degree is found to be along the great circle around the globe both for barotropic and for baroclinic flows in the atmosphere.