A numerical integration of a two-level quasi-geostrophic model with variable Rossby parameter

Summary Circulation patterns were obtained from a two-level quasi-geostrophic model, in which the Rossby parameter varied with latitude. The initial basic state was characterized by a constant zonal flow at both reference level. The results we re compared with the pattern obtained in a series of experiments with a similar model, in which the Rossby parameter was assumed to be constant. the initial zonal flow in these experiments was assumed in one case to be constant with latitude, in the second casse to have a symmetrical jet centered on the central latitude, and in the thrid case to have its maximum in the southern half of the region. the results of the experiment with a variable Rossby parameter have the closest resemblance to the patterns observed in the real atmospehre. In particular, during the mature stages of the run, the distribution of the zonallyaveraged eddytransport of momentum corresponded quite well to patterns actually observed in the atmosphere.

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Zusammenfassung Aus einem quasi-geostrophischen Modell mit breitenabhängigem rossby-Parameter wurden Zirkulationsformen errechnet. Der Anfangszustand war durc eine konstante zonale Strömung in zwei Niveaus charakteriseirt. Die Resultate wurden mit Zirkulationen verglichen, die in einer Reihe von Experimenten mit einem ähnlichen Modell, in dem aber der Rossby-Parameter konstant angenommen war, erhalten worden waren. In einemk dieser Fälle wurde angenommen, daß die ursprüngliche zonale Strömung breitenunabhängig war, in einem anderen fall wurde angenommen, daß die Strömung in einem symmetrischen Jetstream über eine mittleren Breite konzentriert war, und in einem dritten Fall wurden angenommen, daß die zonale Strömung ihr Maximum in der südlichen Hälfte des Bereiches hatte. Die Resultate des Experiments mit dem veränderlichen Rossby-Parameter haben die meiste Ähnlichkeit mit Zirkulationsformen in der wirklichen Atmosphäre. Insbesondere paßt die Verteilung des zonal gemittelten Momentumtransports in den Reifestadien des Versuchs gut zu den tatsächlich in der Atmosphäre beobachteten Zirkulationsformen.

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Résumé On a calculé les formes de circulation découlant d'un modèle quasigéostrophique dont le paramètres de Rossby dépendaient de la latitude. L'état initial en était caractérisé par un courant zonal constant aux deux niveaux. Lels résultats ont été comparés à ceux d'une série d'essais effectués avec un modèle semblable, mais dans lequel les paramètres de Rossby restaient constants. Dans un de ces cas, on a admis que la circulation zonale initiale ne dépendait pas de la latitude. Dans un deuxième, on a simulé un jet symétriquement à une latitude moyenne. Dans un troisième enfin, on a placè le maximum de la circulation zonale dans la moitié sud de l'espace étudié. Les résultats obtenus en partant des essais basés sur un paramètre de Rossby variable sont les plus semblables aux formes de circulation observées réellement dans l'atmosphère. En particulier, la répartition du transport turbulent de la quantité de mouvement — moyenne zonale calculée au stade de maturité de l'essai — est très voisine des formes de circulation observées réellement dans l'atmosphère.

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With 9 Figures

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The research reported in this document has been sponsored by the Air Force Cambridge Research Laboratories under Grant AF EOAR 63-108 through the European Office of Aerospace Reasearch (OAR), United States Air Force.     

Topography and the non-linear Rossby wave in the zonal shear basic flow

Under semi geostropical approximation, by means or phase angle function the non-linear ordinary differential equation is derived involving topography and zonal shear basic flow. Conditions for the existence of limited amplitude periodical and isolated wave solutions are directly obtained based on the qualitative theory of the ordinary differentical equation. Analysis is thus made of the influence of topography and zonal shear flow on the existence of wave solution. Finally, explicit wave solutions are determined by function approaching with the result that topogra-phy and zonal shear flow affect not only the existence but also the form of waves, indicating the non-linear features of waves and the effect of topography and shear basic flow on undulation.     

Rossby wave propagation in a barotropic atmosphere

The ideas of ray tracing from geometrical optics and wave propagation in a slowly varying medium are applied to Rossby waves propagating in a barotropic atmosphere.The propagation of low-frequency Rossby waves in a zonally symmetric basic state is compared with that for stationary waves presented by Hoskins and Karoly (1981). These ideas are then used to study the propagation of Rossby waves in a basic state with zonally varying middle latitude or low latitude jets. Conditions which allow cross-equatorial wave propagation are presented. For a zonally varying middle latitude jet, there is weak wave convergence in regions of decreasing jet speed, However, this is not sufficient to explain the enhanced wave amplitude found in numerical-model experiments using a zonally varying basic state.     

Vortex Rossby Waves in Asymmetric Basic Flow of Typhoons

Wave ray theory is employed to study features of propagation pathways(rays) of vortex Rossby waves in typhoons with asymmetric basic flow, where the tangential asymmetric basic flow is constructed by superimposing the wavenumber-1 perturbation flow on the symmetric basic flow, and the radial basic flow is derived from the non-divergence equation. Results show that, in a certain distance, the influences of the asymmetry in the basic flow on group velocities and slopes of rays of vortex Rossby waves are mainly concentrated near the radius of maximum wind(RMW), whereas it decreases outside the RMW. The distributions of radial and tangential group velocities of the vortex Rossby waves in the asymmetric basic flow are closely related to the azimuth location of the maximum speed of the asymmetric basic flow, and the importance of radial and tangential basic flow on the group velocities would change with radius. In addition, the stronger asymmetry in the basic flow always corresponds to faster outward energy propagation of vortex Rossby waves. In short, the group velocities, and thereby the wave energy propagation and vortex Rossby wave ray slope in typhoons, would be changed by the asymmetry of the basic flow.     

Patterns of low-frequency variability in a three-level quasi-geostrophic model

 To assess the extent to which atmospheric low-frequency variability can be ascribed to internal dynamical causes, two extended runs (1200 winter seasons) of a three level quasi-geostrophic model have been carried out. In the first experiment the model was forced by an average forcing field computed from nine winter seasons; in the second experiment we used a periodically variable forcing in order to simulate a seasonal cycle. The analysis has been focused on the leading Northern Hemisphere teleconnection patterns, namely the Pacific North American (PNA) and the North Atlantic Oscillation (NAO) patterns, and on blocking, both in the Euro-Atlantic and Pacific sectors. The NAO and PNA patterns are realistically simulated by the model; the main difference with observations is a westward shift of the centres of action of the NAO. Related to this, the region of maximum frequency of Atlantic blocking is shifted from the eastern boundary of the North Atlantic to its central part. Apart from this shift, the statistics of blocking frequency and duration compare favourably with their observed counterparts. In particular, the model exhibits a level of interannual and interdecadal variability in blocking frequency which is (at least) as large as the observed one, despite the absence of any variability in the atmospheric energy sources and boundary conditions on such time scales. Received: 30 January 1997 / Accepted: 17 June 1997     

Rossby wave interactions with Mediterranean and subtropical latitudes

The downstream influence of a Rossby wave on weather conditions in the Mediterranean and North Africa is studied. The objective is to gain a better understanding of the atmospheric processes in these regions and to improve their quantification. The emphasis is placed on high-impact weather events to improve numerical forecasts and warnings about these hazardous weather phenomena. For this purpose, 4 days from 5 to 8 February 1997 are used to investigate both a Mediterranean low and a subtropical African convective situation. Sensitivity studies, using a potential vorticity inversion tool associated with the French atmospheric model ARPEGE, are presented. The Mediterranean surface low under study is shown to be associated with the mid-latitude upper level potential vorticity anomaly, itself associated with a Rossby wave. A subtropical convective cell is shown to be related to upward vertical motions associated with a cut-off low; this cut-off low coming from a mid-latitude Rossby wave.     

The interaction of a mechanically driven three-wave zonal background flow with model mountains in the Northern Hemisphere

Summary Laboratory experiments concerning the interaction of a mechanically driven, uniform shear, zonal, westerly flow superimposed on a three-wave pattern, including cut-off lows, with models of Greenland, the Rocky Mountains and Tibet are conducted. The modeling criteria considered are the matching of the Rossby, Burger and Ekman numbers as well as a number of geometrical parameters. The -effect has not been modeled.The model demonstrates the variation in strength of cut-off lows as they advect over and/or around the model mountains. For example, the low upwind of the Rocky Mountains weakens on approaching the mountains, transforming to a trough in passing over the model and then strengthening again in the lee. The model also shows the influence of the mountains in blocking the lows upstream and then having them accelerate as they advect over the topography.The experiments show how mother cut-off lows approaching the Rocky Mountains can develop daughter troughs/cut-off lows in the lee and further how these mother/daughters coalesce again in the lee. Finally the experiments demonstrate the effects of a cut-off low being advected from west to east past and to the north of the Tibetan Plateau. The process first develops a closed anticyclone in the southeastern region of the Tibetan Plateau. This anticyclone is later replaced by a trough and then a cut-off low. The experiments, generally, demonstrate a number of phenomena observed in the real atmosphere.With 12 Figures     

Mesoscale Barotropic Instability of Vortex Rossby Waves in Tropical Cyclones

In this study, the barotropic stability of vortex Rossby waves (VRWs) in 2D inviscid tropical cyclone (TC)-like vortices is explored in the context of rotational dynamics on an f-plane. Two necessary instable conditions are discovered: (a) there must be at least one zero point of basic vorticity gradient in the radial scope; and (b) the relative propagation velocity of perturbations must be negative to the basic vorticity gradient, which reflects the restriction relationship of instable energy. The maximum ...     

层结流体中具有纬向基本剪切流的Rossby波振幅的mKdV方程

In this paper,modified Korteweg-de Vries (mKdV) equations for the amplitude of solitary Rossby waves in stratified fluids with a zonal shear flow are derived by using a weakly nonlinear method.It is found that the coefficients of mKdV equations depend not only on the β effect and the Visl-Brunt frequency,but also on the basic shear flow.     

隐式等权重粒子滤波在高维准地转模式中的特性研究

粒子滤波自从被引入资料同化领域以来,对于高维系统存在的粒子衰退问题一直困扰着资料同化领域的研究。隐式等权重粒子滤波（Implicit Equal-Weights Particle Filter,IEWPF）通过在高维的状态空间维数的前提下,隐式从每个粒子都具有特殊协方差的提议密度中进行采样,构建等权重的粒子集合,从而解决高维系统的粒子衰退问题。通过在高维准地转模式中应用IEWPF方法,验证了IEWPF的系统一致性和资料同化效果。通过对水平动能谱的检验,验证了IEWPF可以保持系统的原始平衡特性。通过IEWPF与等权重粒子滤波（Equivalent Weights Particle Filter,EWPF）的对比试验发现,两者的资料同化分析场非常接近,但在运行效率上,IEWPF远优于EWPF。同时,IEWPF也为解决一系列的资料同化问题,比如参数估计,提供了新的解决途径。      

Stationary Rossby wave propagation in a shear flow along a reflective boundary

Summary This study investigates the impact of lateral boundary conditions on the propagation and dispersion of locally excited Rossby waves in a zonally periodic, barotropic, quasigeostrophic channel model on the β-plane. We use basic flows with either a linear meridional shear or a jet-like profile. On the southern boundary of the channel we impose either a rigid wall or a radiation condition, whereas the northern sidewall is permeable for Rossby waves. We compare the numerical solutions found for a reflecting southern boundary in a weakly dissipative flow to the solutions obtained from a WKB-analysis for the corresponding unforced nondissipative situation. Furthermore, we compare the generalized Eliassen-Palm flux vectors to the ray paths of Rossby wave packets, obtained from WKB ray tracing. In particular, we focus our investigation on the two-dimensional structure of trapped modal waves and wavetrains in a simple linear numerical model. Summarizing our results, we find that along the reflective wall, trapped modal wave structures as well as reflected wavetrains occur with characteristics (e.g., wavenumbers, turning latitudes) similar to the ones computed using asymptotic methods. In a linear sheared flow wave packets are trapped for all zonal wave numbers in contrast to a jet-like mean flow which has a selective effect on the waves; i.e., a turning latitudes phenomenon between the coast and the flow maximum occurs for short waves, while long waves can propagate freely across the zonal mean flow. This comes out clearly when studying the stream lines of the Eliassen-Palm flux vectors of the numerical model simulations. Furthermore, due to the reflected wave activity, the dispersion of Rossby waves is influenced by the southern boundary condition not only in the vicinity of the border but also in regions away from the boundary. These results appear to be important on the one hand for the existence of trapped Rossby waves in large-scale oceanic shear flows along a zonally oriented coast. And, on the other hand for large-scale boundary waves in conceptional atmospheric channel models which can lead to unwanted resonance effects. Received July 18, 2000/Revised June 9, 2001     

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.     

两层准地转模式里中期天气过程的初步计算和试验

本文用两层准地转模式,初步考虑海陆的差异,不同尺度波动之间的非线性作用,将场用富氏级数展开,得到一组非线性常微分方程组。讨论了中期过程的演变。 得到近于纬向的环流向经向环流转变。极地高压形成等结果。而这类大型过程的转变主要是由于超长波的发展。还讨论了动力、热力因子的作用。     

Assimilation of time-averaged observations in a quasi-geostrophic atmospheric jet model

The problem of reconstructing past climates from a sparse network of noisy time-averaged observations is considered with a novel ensemble Kalman filter approach. Results for a sparse network of 100 idealized observations for a quasi-geostrophic model of a jet interacting with a mountain reveal that, for a wide range of observation averaging times, analysis errors are reduced by about 50% relative to the control case without assimilation. Results are robust to changes to observational error, the number of observations, and an imperfect model. Specifically, analysis errors are reduced relative to the control case for observations having errors up to three times the climatological variance for a fixed 100-station network, and for networks consisting of ten or more stations when observational errors are fixed at one-third the climatological variance. In the limit of small numbers of observations, station location becomes critically important, motivating an optimally determined network. A network of fifteen optimally determined observations reduces analysis errors by 30% relative to the control, as compared to 50% for a randomly chosen network of 100 observations.     

A quasi-geostrophic diagnosis of the zonal flow associated with cut-off lows over South Africa and surrounding oceans

Climate Dynamics - The zonal flow associated with cut-off lows (COLs) comprises two jet streaks of different spatial extents. The smaller scale jet streak, located north of the COLs, forms as a...     

On the direction of Rossby wave breaking in blocking

The direction of Rossby wave breaking at the onset of large-scale atmospheric blocking events is shown to relate closely to its position relative to the location of the climatological storm tracks. Using ERA-Interim reanalysis data from October 1989 to March 2009 and a dynamically-based blocking index, Rossby wave breaking is shown to occur preferentially cyclonically to the north, and anticyclonically to the south of the average storm tracks location. Therefore the results support existing theory on the relation between Rossby wave breaking direction and barotropic shear of the background wind. The further away from the storm tracks the breaking occurs, the stronger this preference in breaking direction. Regional differences can also be explained. For the European region on average 70?% of the detected blocking took place after anticyclonic Rossby wave breaking event that occurred on average 6° south of the climatological storm tracks position. Over Western Pacific wave breaking prior to blocking occurs predominantly cyclonically and on average 6° north of the storm tracks. Differences in blocking duration and intensity are found to be within estimated error margins at most longitudes, except for the Atlantic-Europe sector where the blocking events following anticyclonic blocking are also the strongest.     

线性准地转模型中副热带感热加热强迫的定常波

通过求取定常线性准地转位涡模式的解析解,研究了感热加热强迫所激发的副热带定常波的结构特征,讨论了基本流、牛顿冷却及地面摩擦等对定常波振幅和位相的影响。结果表明,东风时定常波在垂直方向上表现为上、下层反位相的第一斜压结构,且地面系统远强于中高层;西风时定常波呈现出向上的传播特征,在高层,随着风速增大振幅随高度的升高有增大趋势。在近地层,东风时气旋（反气旋）主体位于加热西（东）侧;西风时气旋（反气旋）主体位于加热东（西）侧,近地层以上相反。此外,发现东、西风基本流的作用具有对称特征,这与潜热加热显著不同。研究结果还表明,牛顿冷却对定常波有重要影响,基本流越弱影响越显著。在静止大气中,感热加热强迫下无斯韦尔德鲁普（Sverdrup）解,考虑牛顿冷却时,感热强迫在热源范围内的近地层和中高层分别激发出气旋式和反气旋式环流,气旋中心位于加热中心略偏西的位置。在非静止大气中,牛顿冷却项使地面系统中心向上风方向移动,东风时向东移。牛顿冷却对高、低层系统均有削弱作用。地面摩擦则明显不同,它总会使低层系统减弱,高层系统增强。     

The Rossby wave train patterns forced by shallower and deeper Tibetan Plateau atmospheric heat-source in summer in a linear baroclinic model

观测结果表明,在夏季青藏高原高层大气热源(TPUHS)的发展和衰减阶段(高原热源由浅向深发展),北半球的环流异常表现出不同的Rossby波列型。本研究利用线性斜压模式LBM来探究深浅TPUHS的波列效应。模拟结果表明,深浅TPUHS能强迫出不同的Rossby波列型,而且波列型与观测结果相似。对应浅的TPUHS,Rossby波列型从青藏高原延伸至美国西海岸;而对应深的TPUHS,Rossby波列型从青藏高原延伸至阿拉斯加。