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.     

2008年1月中国南方低温雨雪期间异常阻塞高压事件的多尺度动力过程分析

2008年1月,中国南方发生了罕见的低温雨雪灾害,造成这次灾害的关键系统之一是乌拉尔山以东地区的异常阻塞高压（阻高）。基于NCEP再分析资料,利用新发展的多尺度子空间变换和重构分析了这一期间阻高的多尺度特征,发现其源头来自欧洲地区,强度减弱后东移,在乌拉尔山—贝加尔湖地区重新增强并得以维持相当长的时间。结果表明,两次阻高过程本质上是同一过程在不同阶段的表现。为探讨上述过程的动力学机制,利用基于多尺度子空间变换的局地多尺度能量分析方法以及正则传输理论对其进行了分析,发现此次异常阻高过程源自32 d以下尺度系统的动能强迫,具体地说,能量来自32 d以下尺度系统向32—128 d低频尺度系统的正压正则传输,而且这种正则传输在阻高环流的东、西两侧不对称,西侧在强度上远大于东侧。分析表明,上述非对称的强迫作用由动能空间输运来平衡,平流将西侧获得的32—128 d低频尺度动能向东侧输运,以此来维持阻高环流的整体稳定和均一。上述两种内部的物理过程是高压环流在东移的过程中得以重新增强并长时间维持的机制。      

一次自上向下发展的高原涡的多尺度动力学分析

高原涡作为经常给我国带来暴雨等灾害的天气系统,其形成一般认为是通过感热和潜热自下而上激发的,然而,2013年5月下旬发生的一次引发其下游灾害性强降水的高原涡却是由对流层高层天气尺度低涡诱发的.为此,基于新发展的多尺度子空间变换和多尺度能量涡度方法以及ERA5再分析资料对其动力学过程进行了详尽的探讨,先将原始场重构到三个...     

一次典型的平流层爆发性增温中的局地多尺度洛伦兹循环

利用一种新的工具,多尺度子空间变换(MWT),以及基于MWT的局地多尺度能量与涡度分析(MS-EVA)与Lorenz循环诊断方法,对2009年1月中下旬平流层发生的一次强爆发性增温(SSW)事件的内在动力学过程进行了研究。首先用MWT将各个场重构于三个尺度子空间,即平均尺度、爆发性增温尺度(或SSW尺度)和天气尺度子空间上。结果表明,极地迅速增长的温度主要是由于SSW尺度子空间上极区内的斜压不稳定引起的正则传输(有效位能从平均尺度子空间传输到SSW尺度子空间)造成的,显著增加的有效位能(APE)转换到了SSW尺度子空间的动能(KE)中,加之快速增温前极区内正压不稳定引起的正则传输(动能从平均尺度子空间传输到SSW尺度子空间)的作用,共同导致了极夜急流的反转。     

一次闽南暖区暴雨的多尺度动力过程

作为气象研究中的一个难点问题,暖区暴雨的动力学一直为学界所关注。基于多尺度子空间变换(MWT)以及基于MWT的局地多尺度能量学分析和正则传输理论,对2018年5月7日的一次闽南暖区暴雨进行研究以了解其多尺度动力过程。首先将原始物理量场重建到三个尺度子空间:背景流子空间、天气尺度子空间和暴雨子空间。重构场上可以很好地看出背景环流尺度的高低空急流,以及暴雨尺度上的垂直环流。以往的研究普遍认为暖区暴雨的动力过程具有弱斜压性这一特征,而就此次事件而言,正压失稳和斜压失稳都起着很关键的作用,暴雨主要落区内既发生了正压失稳,也发生了斜压失稳。研究表明,对流层不同高度上的动力学存在差异,低层主要表现为正压失稳,天气尺度子空间与背景流子空间向暴雨子空间传输的动能相当; 中层主要是混合失稳,除正压失稳外,斜压正则传输也将有效位能从背景流子空间传输到了暴雨子空间,再通过浮力转换将有效位能转为动能,从而维持暴雨在中层的动力过程; 高层则与低层相似,但只存在背景流子空间向暴雨子空间的能量传输。      

大西洋阻塞高压上层冷中心的成因

基于ERA-40再分析资料以及多尺度子空间变换和多尺度能量分析方法,探讨了大西洋阻塞高压平流层底部冷中心的形成机制,发现该冷中心形成的根本原因为16 d以下(高频尺度)和64 d以上过程(基本气流)向阻高尺度有效位能的正则传输,所获得有效位能在阻高尺度内被输运到西北和东南侧,并转换成动能,起到使阻高强度增加或者维持的作用。这种过程在西北侧表现得尤为明显,这可能是阻高形态不断向西北侧扩展的原因。在传统的认知中,大气有效位能从大尺度向小尺度传输,但本研究发现,阻高发生时,有效位能在平流层底部的传输方向表现为从高频尺度和基本气流尺度同时向阻高尺度传输。此外,前人的研究表明,阻高发展加强之后对流层中阻高动能向有效位能转化使得阻高消亡,而本文的分析表明两种能量的转换方向在平流层底部完全相反——由有效位能向动能转换,起到了使阻高加强或维持的作用。最近的研究表明对流层顶附近的动力学对于阻高的发展和维持非常重要,上述发现增进了对这些动力学深层的了解。     

The global energy cycle of stationary and transient atmospheric waves: Results from ECMWF analyses

Summary The role of stationary (monthly mean) and transient (departure from monthly mean) waves within the atmospheric energy cycle is examined using global analyses from the European Centre for Medium Range Weather Forecasts (ECMWF) for the period 1980–1987. Only January and July averages are considered.It is confirmed that planetary stationary waves are basically baroclinic. Their contribution to the globally averaged energy cycle of the atmosphere is comparable to that of the transient waves. In January they contribute about 40% to the baroclinic conversion (CA) from zonal mean to eddy available potential energy. Local values for the northern hemisphere even show a predominant role of the stationary wave conversions over those originating from transient waves. Part of the available potential energy of stationary waves (A _SE) is converted to kinetic energy by warm air rising and cold air sinking. Nonlinear energy conversion, which can be interpreted as destruction of stationary temperature waves by transients, is the second sink forA _SE. The order of magnitude of these two processes is similar.Barotropic nonlinear conversions, though negligible in the global average, reveal large conversion rates between the mean positions of the polar and the subtropical jets. Their orientation is suggestive of a tendency to increase stationary wave kinetic energyK _SE at its local minimum between the jets at the expense of the synoptic scale transients.While all terms of the energy cycle related to stationary waves reveal a predominance of the planetary scale (zonal wave numbers 1–3) transient waves are governed by synoptic scale waves (zonal wave numbers 4–9) only with respect to the baroclinic and barotropic conversions: a significant amount of transient wave energy (50% for the global average ofA _TE) is due to planetary scale waves.With 15 Figures     

Charney's Model—the Renowned Prototype of Baroclinic Instability—Is Barotropically Unstable As Well

The Charney model is reexamined using a new mathematical tool, the multiscale window transform(MWT), and the MWT-based localized multiscale energetics analysis developed by Liang and Robinson to deal with realistic geophysical fluid flow processes. Traditionally, though this model has been taken as a prototype of baroclinic instability, it actually undergoes a mixed one. While baroclinic instability explains the bottom-trapped feature of the perturbation, the second extreme center in the perturbation field can only be explained by a new barotropic instability when the Charney–Green number γ 1, which takes place throughout the fluid column, and is maximized at a height where its baroclinic counterpart stops functioning.The giving way of the baroclinic instability to a barotropic one at this height corresponds well to the rectification of the tilting found on the maps of perturbation velocity and pressure. Also established in this study is the relative importance of barotropic instability to baroclinic instability in terms of γ. When γ 1, barotropic instability is negligible and hence the system can be viewed as purely baroclinic; when γ 1, however, barotropic and baroclinic instabilities are of the same order;in fact, barotropic instability can be even stronger. The implication of these results has been discussed in linking them to real atmospheric processes.     

冬季北半球风暴轴的多尺度能量变化特征及其可能机制

基于1971—2016年NCEP/NCAR(美国环境预报中心和国家大气研究中心)的逐日再分析资料及NCPC(美国国家海洋和大气管理局气候预报中心)的海温、大气环流及海洋指数等资料通过多尺度能量分析(MS-EVA)等方法,把冬季北半球风暴轴看做一整体,分析了风暴轴区域多尺度的能量变化特征及其可能机制。主要结论概括如下:(1)多年气候平均状态下,风暴轴的动能来源主要表现为在风暴轴中上游先由低频尺度向天气尺度输送有效位能,随后在风暴轴主体区再由天气尺度有效位能转换为天气尺度动能,其中风暴轴西端可直接由低频尺度向天气尺度输送动能。(2)北半球三大风暴轴联合EOF结果表明:第一模态下,主要体现了北西伯利亚风暴轴与北太平洋风暴轴强度的减弱(增强),同时伴随着北大西洋风暴轴位置北抬(南压);第二模态下,主要体现了北西伯利亚风暴轴强度减弱(增强),同时北太平洋风暴轴位置北抬(南压)中东部强度增强(减弱),而北大西洋风暴轴位置南压(北抬)。(3)回归分析表明:北半球风暴轴异常在不同模态下与低频尺度环流联系密切。低频尺度波动可通过海温及西风急流等异常变化先影响风暴轴区域多尺度间的能量转换,进而影响风暴轴整体的异常变化。     

Numerical convergence of the dynamics of a GCM

 Atmospheric general circulation models (GCMs) are characterized by many features but especially by: (1) the manner of discretizing the governing equations and of representing the variables involved at a given resolution, and (2) the manner of parameterizing unresolved physical processes in terms of those resolved variables. These two aspects of model formulation are not independent and it is difficult to untangle their intertwined effects when assessing model performance. The attempt here is to separate these aspects of GCM behaviour and to ask, “Given a perfect parameterization of the physical processes in a model, what resolution is needed to capture the dominant dynamical aspects of the atmospheric climate?” Alternatively, “At what resolution do the dynamics of a GCM converge”? The perfect parameterization approach assumes that the calculation of the physical terms returns the “correct” result at all resolutions. In the idealized case, a time-independent forcing is one of the simplest that satisfies this condition. However, experiments show that it is difficult for the dynamics of a GCM to balance a time-independent forcing with atmosphere-like flows and structures. The model requires, and the atmosphere presumably includes, physical feedback mechanisms which act so as to maintain the kinds of flows and structures that are observed. Resolution experiments are performed with a simplified forcing function for the thermodynamic equation which combines a dominant time-independent specified forcing with a weak linear relaxation feedback. These experiments show that the dynamics of the GCM have essentially converged at T32 and certainly by T63 which is the next resolution considered. This is shown by the constancy of structures, variances, covariances, transports and energy budgets with increasing resolution. Experiments with an alternative forcing proposed by Held and Suarez, which has the form of a linear relaxation, show somewhat less evidence of convergence at these resolutions. In both cases the “physics” are known by assumption. However, the form and nature of the forcing is different, as is the behaviour with resolution. The implication for the real system is that the resolution required for simulating the dynamical aspects of climate is rather modest. The simulated climate does, however, apparently depend on the ability to correctly and consistently parameterize the physical processes in a GCM, involving both forcing and feedback mechanisms, as a function of resolution. Received 19 January 1996/Accepted 22 August 1996     

Energy analysis of open regions of turbulent flows — mean eddy energetics of a numerical ocean circulation experiment

The concepts involved in the interpretation of energy budgets in subregions of a turbulent flow are examined in order to determine the processes responsible for the production, transport, and dissipation of energy throughout a dynamically inhomogeneous circulation. An interpretation of the effects of Reynolds stress—mean flow interaction work for open regions is presented in terms of the change in the total mean kinetic energy. In an arbitrary volume of fluid the changes in kinetic energy of the mean flow and the mean kinetic energy of the eddy flow are not generally equal and opposite, so this process is not generally responsible for a conversion of energy between the two forms. These ideas are then applied to a regional kinetic energy analysis of the mesoscale resolution general ocean circulation numerical experiment of Robinson et al. (1977). The spatial structure of the various terms in the equation for the mean eddy kinetic energy is examined. The issues involved in selection of a set of analysis regions are discussed and explored via examination of budgets over different subregions of this flow. Thereby a relatively simple picture of the regional energetics emerges. Mean eddy kinetic energy is produced by conversion of kinetic energy of the mean flow in the net over the recirculation and near field of the northern boundary current system and roughly half of this energy is lost to each of mean eddy pressure work transport and diffusion work. Budgets over subregions of this net source region are much more complex. The interior eddy field is driven by pressure work influx, while the southwestern region has eddy buoyancy work conversion of mean potential energy as its energy source. At every depth level the eddy field draws its kinetic energy from the mean flow, when averaged over the horizontal extent of the basin or over the recirculation and near field.     

A Case Study on MJO Energy Transport Path in a Local Multi-scale Interaction Framework

A new local kinetic energy (KE) budget for the Madden-Julian Oscillation (MJO) is constructed in a multi-scale framework. This energy budget framework allows us to analyze the local energy conversion processes of the MJO with the high-frequency disturbances and the low-frequency background state. The KE budget analysis is applied to a pronounced MJO event during the DYNAMO field campaign to investigate the KE transport path of the MJO. The work done by the pressure gradient force and the conversion of available potential energy at the MJO scale are the two dominant processes that affect the MJO KE tendency. The MJO winds transport MJO KE into the MJO convection region in the lower troposphere while it is transported away from the MJO convection region in the upper troposphere. The energy cascade process is relatively weak, but the interaction between high-frequency disturbances and the MJO plays an important role in maintaining the high-frequency disturbances within the MJO convection. The MJO KE mainly converts to interaction KE between MJO and high-frequency disturbances over the area where the MJO zonal wind is strong. This interaction KE over the MJO convection region is enhanced through its flux convergence and further transport KE to the high-frequency disturbances. This process is conducive to maintaining the MJO convection. This study highlights the importance of KE interaction between the MJO and the high-frequency disturbances in maintaining the MJO convection.     

On the conversion between mean and eddy components of potential and kinetic energy in isentropic and isopycnic coordinates

Equations for the mean and eddy kinetic energy and for the mean and eddy potential energy in isopycnic and isentropic coordinates are derived, and conversion terms between the four energy forms are identified. Contrary to Lorenz' isobaric formulae, a conversion term between mean kinetic and eddy potential energy is found in the isopycnic/isentropic framework; furthermore, no term governing direct conversion between eddy and mean potential energy exists in isopycnic coordinates. The option of “re-routing” some energy conversion processes to eliminate the formal difference between the isopycnic/isentropic and the isobaric viewpoint is discussed. A numerical simulation of baroclinic instability in an isentropic coordinate model is used to illustrate the energy conversion processes.     

Diagnostic Study of Global Energy Cycle of the GRAPES Global Model in the Mixed Space-Time Domain

Some important diagnostic characteristics for a model’s physical background are reflected in the model’s energy transport, conversion, and cycle. Diagnosing the atmospheric energy cycle is a suitable way towards understanding and improving numerical models. In this study, formulations of the “Mixed Space-Time Domain”energy cycle are calculated and the roles of stationary and transient waves within the atmospheric energy cycle of the Global-Regional Assimilation and Prediction System （GRAPES） model are diagnosed and compared with the NCEP analysis data for July 2011. Contributions of the zonal-mean components of the energy cycle are investigated to explain the performance of numerical models. The results show that the GRAPES model has the capability to reproduce the main features of the global energy cycle as compared with the NCEP analysis. Zonal available potential energy （AZ） is converted into stationary eddy available potential energy （ASE） and transient eddy available potential energy （ATE）, and ASE and ATE have similar values. The nonlinear conversion between the two eddy energy terms is directed from the stationary to the transient. AZ becomes larger with increased forecast lead time, reflecting an enhancement of the meridional temperature gradient, which strengthens the zonal baroclinic processes and makes the conversion from AZ to eddy potential energy larger, especially for CAT （conversion from AZ to ATE）. The zonal kinetic energy （KZ） has a similar value to the sum of the stationary and transient eddy kinetic energy. Barotropic conversions are directed from eddy to zonal kinetic energy. The zonal conversion from AZ to KZ in GRAPES is around 1.5 times larger than in the NCEP analysis. The contributions of zonal energy cycle components show that transient eddy kinetic energy （KTE） is associated with the Southern Hemisphere subtropical jet and the conversion from KZ to KTE reduces in the upper tropopause near 30？S. The nonlinear barotropic conversion between stationary     

Barotropic processes associated with the development of the Mei-yu precipitation system

The barotropic processes associated with the development of a precipitation system are investigated through analysis of cloud-resolving model simulations of Mei-yu torrential rainfall events over eastern China in mid-June 2011. During the model integration period, there were three major heavy rainfall events: 9–12, 13–16 and 16–20 June. The kinetic energy is converted from perturbation to mean circulations in the first and second period, whereas it is converted from mean to perturbation circulations in the third period. Further analysis shows that kinetic energy conversion is determined by vertical transport of zonal momentum. Thus, the prognostic equation of vertical transport of zonal momentum is derived, in which its tendency is associated with dynamic, pressure gradient and buoyancy processes. The kinetic energy conversion from perturbation to mean circulations in the first period is mainly associated with the dynamic processes. The kinetic energy conversion from mean to perturbation circulations in the third period is generally related to the pressure gradient processes.     

Maintenance and oscillation mechanisms of summer tropical upper-tropospheric easterlies

The mechanisms of the maintenance and oscillation of 1982 summer tropical 200-hPa mean easterly flow and extra-long waves are investigated in terms of the energy equations in wavenumber-frequency space. Calculation results show that the difference in heating between land and sea and the boundary effect serve as the main source of energy; frictional dissipation as the sink; the conversion of available potential energy into kinetic takes place dominantly in the waves of number 1–2 such transformation is accomplished in just a small amount in zonal mean flow and therefore can be ignored because of the value. In the interaction between wave and zonal mean flow, the latter loses its available potential and gains kinetic energy. The tropical easterly belt over 20°N-5°S is found barotropically stable and that over 10°-5°S, unstable. The waves of number 2 and 1 manifest themselves a primary source and sink of kinetic energy, respectively, in the interplay between waves and between zonal mean flow and wave. It is found that zonal mean flow and the waves of number 1-2 have a roughly 40-and 20-day oscillational period of kinetic energy, respectively, whose primary mechanism is the transfer of barotropic energy, the conversion of baroclinic energy, and the boundary effect.     

云南暴雨涡散场动能转换函数的动态分析

对1996年云南主汛期（6－8月）逐日散度风动能和旋转风动能之间的转换函数C（KD,KR）特征进行深入研究,同时分析了C（KD,KR）各项Af、Az、B、C在动能转换函数中所起的作用。研究结果表明,对流层内C（KD,KR）＞0,同时对流层低层的C（K,KR）＞中高层的C（KD,KR）之和．极易出现暴雨过程;Af项在整个动能转换中起主要作用,71％的Af与C（KD,KR）具有相同的符号,Az项和B项在动能转换中起振荡作用,Az＋B控制着29％的动能转换方向。     

THE EFFECTS OF TOPOGRAPHY ON THE SUMMER ATMOS-PHERIC ENERGETICS OF THE NORTHERN HEMISPHERE IN A LOW-RESOLUTION GLOBAL SPECTRAL MODEL

An analysis is made of the effects of topography on the summer atmospheric energetics of the Northern Hemisphere in a low-resolution global spectral model. The numerical model is a global, spectral, primitive equation model with five equally spaced sigma levels in the vertical and triangular truncation at wavenumber 10 in the horizontal. The model includes comparatively full physical processes.Each term of the energy budget equations is calculated in four specific latitudinal belts (81.11°S-11.53°S; 11.53°S-11.53°N; 11.53°N-46.24°N; 46.24°N-81.11°N) from a five-year simulation with mountains and a one-year simulation without mountains, respectively. Differences between them are compared and statistically tested. The results show that synoptical scale waves transport available potential energy and kinetic energy to long waves and increase conversion from available potential energy of the zonal flow to eddy’s and from the eddy kinetic energy to the zonal kinetic energy in region 3 (11.53°N-46.24°N) due to mountains; topography intensifies the atmospheric baroclinity in region 3, consequently the baroclinic conversion of atmosphere energy is increased. The seasonal characteristics associated with the summer atmospheric energy source in region 3 are caused by seasonal variation of the solar radiation and the land-ocean contrasts and independent of topographic effects. The mechanism of topographic effects on the increase of long wave kinetic energy is also discussed.     

MAINTENANCE AND OSCILLATION MECHANISMS OF SUM-MER TROPICAL UPPER-TROPOSPHERIC EASTERLIES

The mechanisms of the maintenance and oscillation of 1982 summer tropical 200-hPa mean easterly flow and extra-long waves are investigated in terms of the energy equations in wavenumber-frequency space. Calculation results show that the difference in heating between land and sea and the boundary effect serve as the main source of energy; frictional dissipation as the sink; the conversion of available potential energy into kinetic takes place dominantly in the waves of number 1-2; such transformation is accomplished in just a small amount in zonal mean flow and therefore can be ignored because of the value.In the interaction between wave and zonal mean flow, the latter loses its available potential and gains kinetic energy. The tropical easterly belt over 20oN-5oS is found barotropically stable and that over 10oN-5oS, unstable. The waves of number 2 and 1 manifest themselves a primary source and sink of kinetic energy, respectively, in the interplay between waves and between zonal mean flow and wave.It is found that zonal mean flow and the waves of number 1-2 have a roughly 40-and 20-day oscillational period of kinetic energy, respectively, whose primary mechanism is the transfer of barotropic energy, the conversion of baroclinic energy, and the boundary effect.