The inverse cascade range of quasi-geostrophic turbulence

Summary The homogeneous form of the quasi-geostrophic equations are examined from the perspective of the statistical theory of turbulence, utilizing the eddy-damped, Markovian quasinormal EDMQN approximation. After describing the historical origin of this procedure, together with some of its qualitative physics, we focus on an application to the large scales of the mesoscale. The specific problem investigated is an inverse cascade in which the energy source is at the small, thunderstorm-scale range, and the scales considered are all those larger than the forcing scale. We examine in particular the issue of the degree of anisotropy (in stretched coordinates) of the flow, the dependence of the flow on forcing and dissipation, and the applicability of the concept of negative eddy viscosity for the quasi-geostrophic equations.With 3 FiguresThe National Center for Atmospheric Research is sponsored by the National Science Foundation.     

On nonlinear stability theorems of 3D quasi-geostrophic flow

Nonlinear stability criteria for quasi-geostrophic zonally symmetric flow are improved by establishing an optimal Poincar′e inequality. The inequality is derived by a variational calculation considering the additional invariant of zonal momentum. When applied to the Eady model in a periodic channel with finite zonal length, the improved nonlinear stability criterion is identical to the linear normal-mode stability criterion provided the channel meridional width is no greater than 0.8605· · · times its channel length (which is the geophysically relevant case).     

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     

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.     

再论不等距差分格式的计算紊乱问题

不等距差分格式中存在的计算紊乱问题在文章[1]中已有较好的研究,那里比较了三种构造不等距差分格式的方法,给出了“超高频”条件的表达式,并指明:当出现“超高频”条件时,波不能穿透“界面”,由细网格一侧传到粗网格一侧,而在细网格一侧产生完全的伪反射.但该文没有分析所有可能的情况,本文再用物理分析和数值试验的方法对该文未曾分析的情况进行了详细研究,主要结果有:1.在特殊情况下,即在频率等于临界值时,理论和数值试验结果都表明,不仅在细网格一侧有伪反射,而且在粗网格一侧还有放大的透射波.2.当区域中布多种网格时,不     

高原热力作用下的非绝热Rossby波

从含非绝热项的准地转运动方程组出发，分析了青藏高原大尺度热力作用下非绝热Rossby波的一些性质。从理论上证明当背景西风气流为正压时，冬季高原冷却作用有利于Roosby波的经向传播。又由非绝热Rossby波的频率方程说明冬季高原的热力作用是中高纬季节内振荡的重要激发机制。此外，当背景西风气流为斜压时，求解了高原热力作用下非绝热Rossby波的频率，并由频率方程说明冬季高原冷却作用有利于波动向不稳定方向发展，而夏季高原的大尺度热力作用对波动稳定性的影响存在临界值。     

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。     

Solitary waves of two-layer quasi-geostrophic flow and analytical solutions with scalar nonlinearity

In this paper we investigate the instability of two-layer quasi-geostrophic model with scalar nonlinearity, which is a geophysical fluid dynamics model, and give a nonlinear stability criterion. Furthermore, the analytical solutions of the two-layer quasi-geostrophic model are obtained via the Jacobi elliptic periodic function transform method and symbolic computation. It is efficient in solving a range classes of nonlinear partial differential equations for this method. The result shows that the structure of Rossby waves is influenced by many factors such as base flow and scalar nonlinearity.     

The solitary waves of the barotropic quasi-geostrophic model with the large-scale orography

Starting from a modified barotropic quasi-geostrophic model equation, considering the actual situation of the large-orography of the Tibetan Plateau, neglecting its slope in x direction, and using the reductive perturbation method, then the solitary waves are obtained. The results show that the orography is essential factor exciting solitary Rossby waves in a flow without shear.     

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.     

Propagation of the Rossby waves on two dimensional rectangular grids

Summary A simple two-dimensional quasi-geostrophic linearized model of the atmosphere is used to investigate the behaviour of the quasi-geostrophic modes for five horizontal rectangular grids. Numerical expressions for frequencies of Rossby waves for all grids are evaluated. It was found that the B and C grids produce only negative frequencies as well as the continuous case. The D grid has negative and zero frequencies. Finally, it was found that the A and E grids produce positive frequencies and eastward moving Rossby waves.With 2 Figures     

Variable resolution on quasi-uniform grids: linear advection experiments

Summary A couple of different techniques for implementing the variable resolution within numerical models of the atmosphere that use quasi-uniform grids are estimated and compared based on their merit in the simple linear advection experiments. These techniques are: grid stretching, Schmidt transforming and grid overlapping. The quasi-uniform grids are: a conformal cubic and an octagonal grid. The techniques for the variable resolution are evaluated from the perspective of their effects on numerical solution and the practicality of their application. Our analysis suggests that the grid stretching is for now the most optimal choice. However, a special form of grid overlapping is presented that has potential to become a viable alternative in the future.     

Calculation on the light scattering function of hexagonal ice crystals

Hexagonal ice crystal is a basic form of the particles in cirrus. The emphasis in this paper is on discussing the computational results of scattering phase matrices for infrared absorptive band by making use of the model developed by the authors. Comparisons have been made between infrared and visible light as well as between hexagonal columns and plates and equivalent spheriods and spheres. It is found that the effects of light absorption on phase function may cause the decreases of scattering energy in side direction and the directions near backscattering, and weaken halo and rainbow peaks which are induced by the refractions and internal reflections. There is a general agreement in the phase functions for ice crystals with different shapes. However, the scattering intensity in side direction for spheres and in backward and backside directions for spheroids is weaker as compared with hexagons. It is believed that these features would, doubtless, have influences on the detection of cirrus by laser and radiation transfer in the atmosphere.     

副热带天气尺度系统短期演变的泛准地转机理

在 Rossbs数λ《1的情况下,如果在大范围降水区域中潜热增温率大于温度平流,或者因热力对流引起的动量铅直传递大于动量平流,都能使运动偏离准地转状态。散度场和垂直速度场都比准地转情况下强。但除少数极端情况外,涡度场仍是准地转的。基于这一点,关于西风带天气系统准地转演变的一些基本原理也适用于一般副热带场合。本文论证了上述观点,提出泛准地转演变的概念。并给出一种能够清晰、简洁地表述泛准地转演变中各种扰源制约场变化的一般规律近似解析解。特别讨论了水汽潜热和涡度的对流铅直传递在其中的地位。     

An accurate multimoment constrained finite volume transport model on Yin-Yang grids

A global transport model is proposed in which a multimoment constrained finite volume (MCV) scheme is applied to a Yin-Yang overset grid. The MCV scheme defines 16 degrees of freedom (DOFs) within each element to build a 2D cubic reconstruction polynomial. The time evolution equations for DOFs are derived from constraint conditions on moments of line-integrated averages (LIA), point values (PV), and values of first-order derivatives (DV). The Yin-Yang grid eliminates polar singularities and results in a quasi-uniform mesh. A limiting projection is designed to remove nonphysical oscillations around discontinuities. Our model was tested against widely used benchmarks; the competitive results reveal that the model is accurate and promising for developing general circulation models.     

不规则格点上的车贝雪夫多项式展开问题

以往国内外关于车贝雪夫多项式应用的研究,都只限于等距格点。本文将车贝雪夫多项式推广到不规则格点上。推广后的车贝雪夫多项式兼有三角函数、球函数、自然正交函数的优点,因而在气象学上有着更加广泛的用途。     

放射性核素大气弥散模式研究综述

放射性核素大气弥散模式可以模拟正常工况和事故工况下,放射性核素在不同尺度下的大气输送与扩散,为核电站选址、辐射环境监测和核事故应急提供科学依据。归纳了目前广泛用于模拟核素大气弥散的各种模式,介绍了这些模式的研究进展和适用范围。结果表明：对于区域范围小于2 km的弥散,一般可采用CFD（Computational fluid dynamics）湍流模式;对于20 km范围内的局地扩散,一般可采用高斯模式;而对于中尺度（20—200 km）和大尺度（200 km以上）弥散,则采用拉格朗日模式或欧拉模式。为了避免各种模式本身的局限性,采用嵌套模式将是较好的选择。最后,对放射性核素大气弥散模式发展前景进行了讨论。     

Large-scale modes impact on Iraq climate variability

The impact of large-scale modes on Iraq climate is investigated here based on winter and spring fields of temperature and precipitation. The temperature data (1971–2010) was recorded at 8 stations whereas the precipitation fields (1981–2010) were recorded at 18 locations. Empirical orthogonal function analyses were performed in order to characterize the spatial variability of the Iraq climatological parameters. The relationships between the global sea surface temperature, sea level pressure, and geopotential height fields with the dominant modes of Iraq temperature and precipitation were also investigated. Correlation and regression maps emphasize links between Iraq climate and large-scale modes, like the Atlantic Multidecadal Oscillation and the El Niño Southern Oscillation phenomenon.     

放射性核素大气弥散模式研究综述

放射性核素大气弥散模式可以模拟正常工况和事故工况下,放射性核素在不同尺度下的大气输送与扩散,为核电站选址、辐射环境监测和核事故应急提供科学依据。归纳了目前广泛用于模拟核素大气弥散的各种模式,介绍了这些模式的研究进展和适用范围。结果表明：对于区域范围小于2 km的弥散,一般可采用CFD（Computational flu...