Vertical vorticity development owing to down-sliding at slantwise isentropic surface

Based upon the conservation of Ertel potential vorticity and moist potential vorticity, a ‘parcel dynamic’ approach is used to investigate the development of vertical vorticity of a parcel which is sliding down a slantwise isentropic surface. An accurate form of the tendency equation of vertical vorticity is deduced to interpret such slantwise vorticity development (SVD). In addition to those dynamic terms in the traditional vertical vorticity equation, the newly developed accurate form includes several thermal terms associated with the changes in stability, vertical wind shear and baroclinity. It is proved that the combinative impacts of these thermal terms on the development of vertical vorticity can be expressed by a succinct theory of SVD. According to this theory, when the horizontal component of potential vorticity and stability possess opposite signs, and the slantwise isentropic surfaces are very steep, the vorticity development of the down-sliding flow at such isentropes can be dramatic. It is also shown that in a convectively unstable and saturated atmosphere, such vorticity development must be accompanied by the development of a low-level jet. Study of a torrential rain process shows that moist potential vorticity analysis is a powerful tool in the study of torrential rain occurrence. Results from the present study are in agreement with the contentions of earlier workers that moist symmetric instability is the cause of some heavy rainbands.     

等熵面和湿等熵面倾斜发展的诊断分析

利用等压坐标系中的热力学方程和水汽方程推导出可以诊断分析等熵面（等位温面）和湿等熵面（等相当位温面） 倾斜变化的倾角方程。等熵面倾角的局地变化由倾角平流输送项、风速切变项和非绝热加热项共同决定，而影响湿等熵面倾角局地变化的强迫项除倾角平流输送项、风速切变项和非绝热加热项之外，还包括垂直热量通量切变项。NCEP/NCAR实时分析资料的分析结果表明，大气斜压性、相对垂直涡度与等熵面和湿等熵面的倾角密切相关，它们的正高值区互相重叠；垂直风速切变项，特别是垂直速度的经向切变项是影响等熵面倾斜发展的主要强迫项，而纬向和经向风速的垂直切变项对湿等熵面倾角演变的贡献最大。     

CONSERVATION OF MOIST POTENTIAL VORTICITY AND DOWN-SLIDING SLANTWISE VORTICITY DEVELOPMENT*

An accurate form of the moist potential vorticity(MPV) equation was deduced from a complete set of primitive equations.It was shown that motion in a saturated atmosphere without diabatic heating and friction conserves moist potential vorticity.This property was then used to investigate the development of vertical vorticity in moist baroclinic processes.Results show that in the framework of moist isentropic coordinate,vorticity development can result from reduction of convective stability,or convergence,or latent heat release at isentropic surfaces.However,the application of the usual analysis of moist isentropic potential vorticity is limited due to the declination of moist isentropic surfaces.and a theory of development based on z-coordinate and p-coordinate was then proposed.According to this theory,whether the atmosphere is moist-symmetrically stable or unstable,on convective stable or unstable,the reduction of convective stability,the increase of the vertical shear of horizontal wind or moist baroclinity may result in the increase of vertical vorticity,so long as the moist isentropic surface is slantwise.The larger the declination of the moist isentropic surface,the more vigorous the development of vertical vorticity.In a region with a monsoon front to the north and the warm and moist air to the south,or by the north of the front,the moist isentropes are very steep.The is the region most favorable for development of vorticities and formation of torrential rain.For a case of persistent torrential rain occurring in the middle and lower reaches of the Changjiang and Huaihe Rivers in June 11-15,1991,moist potential vorticity analysis,especially the isobaric analysis of its vertical and horizontal components,i.e.MPV1 and MPV2,respectively,is effective for identifying synoptic systems not only in middle and high latitudes,but also in low latitudes and in the lower troposphere.It can serve as a powerful tool for the diagnosis and prediction of torrential rain.     

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.     

Up-sliding Slantwise Vorticity Development and the complete vorticity equation with mass forcing

The moist potential vorticity (MPV) equation is derived from complete atmospheric equations including the effect of mass forcing, with which the theory of Up-sliding Slantwise Vorticity Development (USVD) is proposed based on the theory of Slantwise Vorticity Development (SVD). When an air parcel slides up along a slantwise isentropic surface, its vertical component of relative vorticity will develop, and the steeper the isentropic surface is, the more violent the development will be. From the definition of MPV and the MPV equation produced here in, a complete vorticity equation is then put forward with mass forcing, which explicitly includes the effects of both internal forcings, such as variations of stability, baroclinicity, and vertical shear of horizontal wind, and external forcings, such as diabatic heating, friction, and mass forcing.When isentropic surfaces are flat, the complete vorticity equation matches its traditional counterpart. The physical interpretations of some of the items which are included in the complete vorticity equation but not in the traditional one are studied with a simplified model of the ChangjiangoHuaihe Meiyu front. A 60-h simulation is then performed to reproduce a torrential rain event in the ChangjiangoHuaihe region and the output of the model is studied qualitatively based on the theory of USVD. The result shows that the conditions of the theory of USVD are easily satisfied immediately in front of mesoscale rainstorms in the downwind direction, that is, the theory of USVD is important to the development and movement of these kinds of systems.     

一次暴雨中尺度涡旋发展机制诊断分析研究

中尺度涡旋可以持续激发新对流,是造成局地持续性降水的重要系统。基于经典涡度方程的诊断无法描述热力信息对于涡旋发展的贡献。本文采用Boussinesq近似对涡度方程进行整理,将方程唯一强迫项定义为垂直速度位涡,其形式与位涡类似,利用垂直速度替换位温。进一步在垂直速度位涡倾向方程中,以气压水平梯度的形式引入热力过程的间接作用,定量描述动热力配置的贡献。以2021年6月15日发生在南疆的一次极端暴雨为例,利用高分辨率数值模拟资料,初步分析了低层动热力强迫作用向垂直涡度的传递。结果表明,垂直速度位涡的局地变化主要来自热力强迫项中低层垂直风切变与低层冷池的耦合作用,两者在降水区前侧产生大范围的正值区。该区域与垂直速度位涡的正值区重叠,促进垂直速度位涡的增长,进而维持降水前缘的正涡度,有利于产生较强的上升运动,触发新对流并造成持续性降水。     

热带气旋Haiyan(2013)快速增强过程内核涡度变化机制的数值模拟研究

选取西北太平洋热带气旋Haiyan(2013)为研究对象,利用中尺度数值模式WRF对其快速增强(RI)过程进行了高时空分辨率的数值模拟,推导出一个包含不同尺度系统相互作用的垂直涡度诊断方程来探究TC内核区域相对涡度的变化特征及其与RI的联系。诊断结果表明:涡旋尺度散度项(stre2)、倾斜项(tilt2)和垂直平流项(advv2)对涡度收支的影响最为重要。RI开始前,stre2在边界层内对涡度收支为正贡献,边界层之上则为负贡献;tilt2在低层促进涡度增加;advv2分布与stre2相反,在低层为负值,高层为正值。RI开始后,stre2在低层(高层)对涡度的正(负)贡献显著增强;tilt2在低层(高层)对涡度的促进(抑制)作用明显增强,但在中层出现正负贡献相互交替的情况;advv2在低层对涡度的正贡献也有所增强。     

湿位涡和倾斜涡度发展

从完整的原始方程出发，在导出精确形式的湿位涡方程的基础上，证得绝热无摩擦的饱和湿空气具有湿位涡守恒的特性。并由此去研究湿斜压过程中涡旋垂直涡度的发展。结果表明，在湿等熵坐标中，涡旋的发展与对流稳定度的减少，等熵面上的辐合和潜热的释放有关。由于等熵位涡分析的应用受等熵面倾斜的限制，又进而发展了Ｚ坐标及Ｐ坐标中的倾斜涡度发展理论。指出无论是湿对称不稳定或对流不稳定大气，还是湿对称稳定或对流稳定大气，除对流稳定度的影响外，风的垂直切变的增加或水平湿斜压的增加均能因湿等熵面的倾斜而引起垂直涡度的增长。湿等熵面的倾斜越大，这种由干湿斜压性加强所引起的涡旋发展更激烈。在梅雨锋附近及其南侧暖湿区的北端，湿等熵面十分陡立，是涡旋发展及暴雨发生的重要地区。对１９９１年６月１２—１５日江淮流域暴雨过程的湿位涡分析表明，湿位涡分析，尤其是等压面上湿位涡量ＭＰＶ１和ＭＰＶ２的分析不仅在中高纬有效，在低纬度及低对流层也十分有效，是暴雨诊断和预报的有力工具。     

Potential vorticity and eddy potential enstrophy in the North Atlantic Ocean simulated by a global eddy-resolving model

Eight-year daily mean output of a quasi-global eddy-resolving model is examined with a focus on the large-scale dynamical characteristics of the North Atlantic Ocean in a framework of potential vorticity (PV) and its derivatives. The model has reproduced some of the observed features of the mean potential vorticity field well. The three-dimensional structure of the mean potential vorticity supports baroclinic instability in most of the basin. Eddies are found to play important roles in the formation and maintenance of the mean potential vorticity fields. The contribution of relative vorticity to the mean potential vorticity field is found to be negligible for the most part. However, relative vorticity contribution to the source/sink of potential vorticity and eddy potential enstrophy is not negligible. We also find that eddies are not necessarily diffusive even on a basin-scale.     

一次西南涡暴雨的等熵位涡特征分析

应用常规资料和0.5°×0.5°的GFS再分析资料,对2010年7月19日发生在河北山东的一次西南涡暴雨过程产生的条件及其等熵位涡演变特征进行了分析。结果表明：西南涡、高、低空急流、地面低压是这次暴雨过程的主要影响系统;等熵位涡的演变和形态对冷空气活动有很好的示踪作用;等熵位涡中心两侧气流辐合,利于地面低压发展;高位涡下传,导致了大暴雨产生;等熵位涡大值区及移动方向与降水落区有很好的对应关系。     

2018年一次非典型梅雨锋暴雨过程诊断分析

利用常规地面气象观测资料、NCEP/NCAR FNL 1°×1°网格点逐6 h再分析资料,对2018年6月20日浙江省一次暴雨过程的主要环流系统、等熵位涡、垂直螺旋度等进行了天气动力学诊断分析。结果表明：850 hPa低涡切变、对流层中层冷空气、200 hPa南亚高压、副热带高压是此次暴雨过程发生的主要影响系统;700 hPa上的正垂直螺旋度中心对暴雨的发生有良好的指示意义;等熵位涡的演变和形态对冷空气活动有较好的视踪作用,等熵位涡中心两侧气流辐合,有利于低压系统发展,高层等熵位涡与冷空气活动有较好的对应关系,等熵位涡大值区偏南侧的移动与强降水落区有较好的对应关系。     

Streamwise vorticity equation

l.IntroductionTheverticalcomPOnentofthevorticityisthedominantpartinthelarge-scalesystems,therefore,itisgoodenoughtoonlyconsidertheverticalcomPOnentofthevorticityinthevorticityequationforstudyinglarge-scalesystems.Withtheapproximationthatstreamlinesaremainlyquasi-horizontalincontrasttotheirverticalcomponents,hence,thecomPOnentofabsolutevorticityalongthestreamline,so-calledsecondaryvorticity,isverysmallandnearlyomitted.ButinthemesoscaleandsmaIl-scalesystems,especiallyinsmall-scalesys-tems,ver…     

THE RELATIONSHIP BETWEEN HORIZONTAL VORTICITY INDUCED BY VERTICAL SHEAR AND VERTICAL MOTION DURING A SQUALL LINE PROCESS

The horizontal vorticity equation used in this study was obtained using the equations of motion in the pressure coordinate system without considering friction, to reveal its relationship with vertical shear. By diagnostically analyzing each term in the horizontal vorticity equation during a squall line process that occurred on 19 June 2010, we found that the non-thermal wind term had a negative contribution to the local change of upward movement in the low-level atmosphere, and that its impact changed gradually from negative to positive with altitude, which could influence upward movement in the mid- and upper-level atmosphere greatly. The contribution of upward vertical transport to vertical movement was the largest in the low-level atmosphere, but had negative contribution to the upper-level atmosphere. These features were most evident in the development stage of the squall line. Based on analysis of convection cells along a squall line, we found that in the process of cell development diabatic heating caused the subsidence of constant potential temperature surface and non- geostrophic motion, which then triggered strong convergence of horizontal acceleration in the mid-level atmosphere and divergence of horizontal acceleration in the upper-level atmosphere. These changes of horizontal wind field could cause a counterclockwise increment of the horizontal vorticity around the warm cell, which then generated an increase of upward movement. This was the main reason why the non-thermal wind term had the largest contribution to the strengthening of upward movement in the mid- and upper-level atmosphere. The vertical transport of large value of horizontal vorticity was the key to trigger convection in this squall line process.     

Mid-latitude atmospheric responses to heat and vorticity forcing using a linear baroclinic model

Based on diagnostic analysis of reanalysis data for 58-year, the distribution characteristics of decadal variability in diabatic heating, transient eddy heating and transient eddy vorticity forcing related to the sea surface temperature (SST) anomalies over the North Pacific, as well as their relationship with anomalous atmospheric circulation have been investigated in this paper. A linear baroclinic model(LBM) was used to investigate atmospheric responses to idealized and realistic heat and vorticity forcing anomalies, and then to compare relative roles of different kinds of forcing in terms of geopotential height responses. The results illustrate that the responses of atmospheric height fields to the mid-latitude heating can be either baroclinic or barotropic. The response structure is sensitive to the relative horizontal location of heating with respect to the background jet flow, as well as to the vertical profile of heating. The response to the idealized deep heating over the eastern North Pacific, mimicking the observed heating anomaly, is baroclinic. The atmospheric response to the mid-latitude vorticity forcing is always barotropic, resulting in a geopotential low that is in phase with the forcing. The atmospheric responses to the realistic heat and vorticity forcing show the similar results, suggesting that diabatic heating, transient eddy heating and transient eddy vorticity forcing can all cause atmospheric anomalies and that the vorticity forcing plays a relatively more important role in maintaining the equivalent-barotropic structure of geopotential height anomalies.     

水平涡度与夏季风环流变化

在斜压涡度发展理论的基础上，讨论了大尺度大气运动中水平涡度向垂直涡度转化的情况，并用以刻划夏季风变动。将声坐标中涡度方程的有关项在2坐标中分离出水平涡度向垂直涡度转化的主要项，经尺度分析得出，在对流层中、高层，这些转化项中的水平分量是大尺度大气斜压性涡度发展的主要因子。通过对1998年4—8月的GAME(GEWEX Asian Monsoon Experiment，全球能量和水分循环试验(GEWEX)的子试验：亚洲季风试验，简称GAME)再分析资料进行实际计算发现，转化项在东亚夏季风上升支的600 hPa及以上层次对P坐标垂直涡度的局地变化贡献很大，不能忽略。同时发现水平涡度向垂直涡度的转化对南海季风爆发和江淮梅雨入梅及其发展过程均有指示性意义。南海季风爆发以后，在中国东南部地区，转化项的大小与夏季风的活跃和中断等活动吻合，转化项的变化反映了西太平洋副高在中国大陆的活动规律。     

北京“7.21”暴雨过程中变形场引起的锋生与倾斜涡度发展诊断分析

从变形场驱动锋生及通过锋生引起倾斜涡度发展的角度对变形场在北京“7.21”暴雨发生、发展过程中的可能作用机制进行了初步探讨。诊断结果发现：北京地区降水产生时,变形向量与等位温线走向一致或有较小夹角,北京地区有较强的变形场局地锋生过程。锋生函数分析发现,变形项对引发暴雨的低层锋生有重要贡献。锋生能够引发大气动力、热力结构的调整,伴随大气锋生过程的高空急流加强和转竖使得北京地区处于高空急流入口区右侧的辐散区中,其带动低层空气辐合,有助于暴雨的加强维持。分析还发现,“7.21”暴雨过程中,垂直涡度存在爆发性发展,尤其是锋面降水阶段,而大气斜压度的增长趋势与垂直涡度增长趋势十分一致。分析全型涡度方程中与变形场有关的斜压度个别变化项发现,与变形场相关的垂直涡度驱动项异常正值区与垂直涡度爆发性增长区相对应,表明变形场在北京“7.21”暴雨过程中对垂直涡度发展有重要贡献。基于变形场沿其压缩轴方向气流汇合的特点,进一步分析了加入水汽作用的水汽通量变形场与暴雨发生、发展的关系。分析结果发现,低层水汽通量变形场的正值区与暴雨具有很强的相关,且水汽通量变形场包含两部分,一部分为比湿平流,其对未来暴雨区位置有很好的指示意义;一部分为变形场项,其对水汽通量变形场分布起主要贡献。     

Sensitivity of Cyclone Tracks to the Initial Moisture Distribution： A Moist Potential Vorticity Perspective

In this study, the characteristics of moist potential vorticity （MPV） in the vicinity of a surface cyclone center and their physical processes axe investigated. A prognostic equation of surface absolute vorticity is then used to examine the relationship between the cyclone tracks and negative MPV （NMPV） using numerical simulations of the life cycle of an extratropical cyclone. It is shown that the MPV approach developed herein, i.e., by tracing the peak NMPV, can be used to help trace surface cyclones during their development and mature stages. Sensitivity experiments are conducted to investigate the impact of different initial moisture fields on the effectiveness of the MPV approach. It is found that the lifetime of NMPV depends mainly on the initial moisture field, the magnitude of condensational heating, and the advection of NMPV. When NMPV moves into a saturated environment at or near a cyclone center, it can trace better the evolution of the surface cyclone due to the conservative property of MPV. It is also shown that the NMPV generation is closely associated with the coupling of large potential temperature and moisture gradients as a result of frontogenesis processes. Analyses indicate that condensation, confluence and tilting play important but different roles in determining the NMPV generation. NMPV is generated mainly through the changes in the strength of baroclinicity and in the direction of the moisture gradient due to moist and/or dry air mass intrusion into the baroclinic zone.     

Sources of CAM3 vorticity bias during northern winter from diagnostic study of the vorticity equation

CAM3 (Community Atmosphere Model version 3) simulation bias is diagnosed using the vorticity equation. The study compares CAM3 output with ECMWF (European Centre for Medium-Range Weather Forecasts) 40?year reanalysis (ERA-40) data. A time mean vorticity bias equation is also formulated and the terms are grouped into categories: linear terms, nonlinear terms, transient contributions, and friction (calculated as a residual). Frontal cyclone storms have much weaker band passed kinetic energy and enstrophy in CAM3. The downstream end of the North Atlantic storm track (NAST) has large location error. While the vorticity equation terms have similar amplitude ranking in CAM3 and ERA-40 at upper levels, the ranking differs notably in the lower troposphere. The linear and friction terms dominate the vorticity bias equation. The transient terms contribute along the storm track, but the nonlinear terms are generally much smaller, with the primary exception being over the Iberian peninsula. Friction is much stronger in CAM3. As evidence, nearly all wavelengths (including the longest planetary waves) have smaller amplitude in CAM3 than in ERA-40 vorticity data. Negative near surface vorticity tendency bias on the European side of the Arctic is linked to the NAST track error (evident in the divergence term). CAM3 misses the Beaufort high in sea level pressure (SLP) due to low level warm temperature bias, too little vortex compression, and to too little horizontal advection of negative vorticity compared with ERA-40. Generally lower SLP values in CAM3 over the entire Arctic follow from lower level warm bias in CAM3.     

能量位涡在雷雨大风天气诊断分析中的应用

从大气基本运动方程及大气总能量概念出发,提出将大气动力学与能量天气学相结合的物理量——干能量位涡与湿能量位涡,并确定其守恒性.通过分析发现,以静力温度表达的能量位涡数学计算更方便,物理意义更明确.以2007年湖北的一次典型雷雨大风天气为例,对雷雨大风天气用能量位涡进行诊断分析.结果表明:本文提出的干能量位涡与湿能量位涡可以较好地预示雷雨大风天气,高空干能量位涡的增强与向下发展使对流层中下层不稳定能量增大,有利于雷雨大风天气发生;低层湿能量位涡的不稳定能量高值区与斜压系统耦合时预示该区域将有雷雨大风发生.     

Potential vorticity and the PV perspective

This paper highlights some theoretical aspects of potential vorticity(PV) and discusses some of the insights the PV perspective has given us. The topics covered include the nature of PV, its controlling role in the symmetric stability of the atmosphere, its inversion to give the flow field, Rossby waves and their coupling to give baroclinic instability, PV and midlatitude weather systems and, finally, insights into tropical motions.