Adjoint sensitivity study on idealized explosive cyclogenesis

The adjoint sensitivity related to explosive cyclogenesis in a conditionally unstable atmosphere is investigated in this study.The PSU/NCAR limited-area,nonhydrostatic primitive equation numerical model MM5 and its adjoint system are employed for numerical simulation and adjoint computation,respectively.To ensure the explosive development of a baroclinic wave,the forecast model is initialized with an idealized condition including an idealized two-dimensional baroclinic jet with a balanced three-dimensional moderateamplitude disturbance,derived from a potential vorticity inversion technique.Firstly,the validity period of the tangent linear model for this idealized baroclinic wave case is discussed,considering different initial moisture distributions and a dry condition.Secondly,the 48-h forecast surface pressure center and the vertical component of the relative vorticity of the cyclone are selected as the response functions for adjoint computation in a dry and moist environment,respectively.The preliminary results show that the validity of the tangent linear assumption for this idealized baroclinic wave case can extend to 48 h with intense moist convection,and the validity period can last even longer in the dry adjoint integration.Adjoint sensitivity analysis indicates that the rapid development of the idealized baroclinic wave is sensitive to the initial wind and temperature perturbations around the steering level in the upstream.Moreover,the moist adjoint sensitivity can capture a secondary high sensitivity center in the upper troposphere,which cannot be depicted in the dry adjoint run.     

LINEAR AND NONLINEAR BAROTROPIC INSTABILITY

Based on a non-frictional and non-divergent nonlinear barotropic vorticity equation and its solutions oftravelling waves,the criteria for linear and nonlinear barotropic instability are gained respectively at an equilibriumpoint of the equation on a phase plane.The linear and nonlinear analytical solutions to instability waves arealso found.The computational results show that if their amplitudes are equal at the initial time,the amplitudeincrements of nonlinear instable barotropic wave are always less than those of linear instable barotropic wave.The nonlinear effects can slow down the exponential growth of linear instability.The time needed for makingthe amplitude double that of initial time by instabilities,is about 6h for linear instability and about 18h fornonlinear instability,the latter is in agreement with the observations in the real atmosphere.     

A NUMERICAL METHOD FOR SOLVING THE EVOLUTION EQUATION OF SOLITARY ROSSBY WAVES ON A WEAK SHEAR

In this paper an evoluion equation in integral-differential form for finite amplitude Rossby waves on a weak shear is presented and an efficient method for its numerical solution is set up. It is shown that a propagation of solitary wave is possible whenever a proper weak shear in basic flows acts with the nonlinear effects and dispersion of the media, both in the atmosphere and in the ocean. To test the numerical method for solving the evolution equation, a series of experiments are carried out. The results indicate that the solitary solutions, do exist and interact with each other in quite a succinct, manner. Therefore the method is successful and efficient for solving initial value problems of the above equation. The time decoupling problem arising in the numerical scheme and the related filtering technique are discussed. A variety of interesting phenomena such as the interaction of solitary Rossby waves, damping, dispersion and the development of nonlinear wave train are numerically studied.     

APPLICATION OF ADVECTIVE VORTICITY EQUATION TO TYPHOON FUNG-WONG

The momentum advection vorticity equation in the form of cross multiplication is introduced, in which the divergence term in the classic vorticity equation does not appear explicitly. This equation includes the rotation effect of the horizontal wind advection, which are not explicitly included in the classic vorticity equation. The vorticity and its tendency of Typhoon Fung-Wong (0808) that occurred in July 2008 are analyzed. The computed results show that the rotation effect of the advection of the horizontal wind is a leading factor in determining the change of vertical vorticity for Fung-Wong during its life cycle, especially in the period leading up to landfall. The advection term represents the tendency variation of the vertical vorticity, and the positive-value region of the vertical vorticity tendency is almost in accord with the track of Fung-Wong, which may be taken as a factor to locate the key observational region of Fung-Wong. The equation provides a supplementary diagnostic tool for the systems related with strong advection of horizontal wind.     

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 completeset of primitive equations.It was shown that motion in a saturated atmosphere without diabatic heat-ing and friction conserves moist potential vorticity.This property was then used to investigate the de-velopment of vertical vorticity in moist baroclinic processes.Results show that in the framework ofmoist isentropic coordinate,vorticity development can result from reduction of convective stability,orconvergence,or latent heat release at isentropic surfaces.However,the application of the usual analy-sis 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 tothis theory,whether the atmosphere is moist-symmetrically stable or unstable,or convective stable orunstable,the reduction of convective stability,the increase of the vertical shear of horizontal wind ormoist baroclinity may result in the increase of vertical vorticity,so long as the moist isentropic surfaceis slantwise.The larger the declination of the moist isentropic surface,the more vigorous the develop-ment of vertical vorticity.In a region with a monsoon front to the north and the warm and moist airto the south,or by the north of the front,the moist isentropes are very steep.The is the region mostfavorable for development of vorticities and formation of torrential rain.For a case of persistent torrential rain occurring in the middle and lower reaches of theChangjiang and Huaihe Rivers in June 11-15,1991,moist potential vorticity analysis,especially theisobaric analysis of its vertical and horizontal components,i.e.MPV1 and MPV2,respectively,iseffective for identifying synoptic systems not only in middle and high latitudes,but also in low lati-tudes and in the lower troposphere.It can serve as a powerful tool for the diagnosis and prediction oftorrential rain.     

Effect of Baroclinicity on Vortex Axisymmetrization.Part Ⅰ：Barotropic Basic Vortex

The barotropic and baroclinic disturbances axisymmetrized by the barotropic basic vortex are examined in an idealized modeling framework consisting of two layers.Using a Wentzel-Kramers-Brillouin approach,the radial propagation of a baroclinic disturbance is shown to be slower than a barotropic disturbance,resulting in a slower linear axisymmetrization for baroclinic disturbances.The slower-propagating baroclinic waves also cause more baroclinic asymmetric kinetic energy to be transferred directly to the barotropic symmetric vortex than from barotropic disturbances,resulting in a faster axisymmetrization process in the nonlinear baroclinic wave case than in the nonlinear barotropic wave case.     

Analyses and calculation facts of the baroclinic term in synoptic-scale motion over tropics

Analyses are made of all terms in the vorticity equation for the atmosphere at low latitudes by using the scale analysis theory, with the result that for synotic-scale motion the baroclinic term, i. e. the twisting term and the vorticity vertical-transport term, approximates in order to the relative-vorticity advection, divergence and β term. With intensified atmospheric disturbance ratios of the β term to others become smaller while the others stay in more or less fixed proportions between them. This statement has been confirmed by the results of 22 typhoons calculated covering a large area in low latitudes. Besides, the baroclinic term for the genesis and development of 6 typhoons over 1979－1980 is calculated and the results ob-tained show that it has significant effect. Finally, the baroclinicity is shown not to be ignored in dealing with synoptics and dynamics of synoptic-scale systems such as typhoons and easterly waves.     

Dynamical and Thermal Problems in Vortex Development and Movement. Part II: Generalized Slantwise Vorticity Development

The development of vertical vorticity under adiabatic condition is investigated by virtue of the view of potential vorticity and potential temperature (PV-θ) and from a Lagrangian perspective. A new concept of generalized slantwise vorticity development (GSVD) is introduced for adiabatic condition. The GSVD is a coordinate independent framework of vorticity development (VD), which includes slantwise vorticity development (SVD) when a particle is sliding down the concave slope or up the convex slope of a sharply tilting isentropic surface under stable or unstable condition. The SVD is a special VD for studying the severe weather systems with rapid development of vertical vorticity. In addition, the GSVD clarifies VD and SVD. The criteria for VD and SVD demonstrate that the demand for SVD is much more restricted than the demand for VD. When an air parcel is moving down the concave slope or up the convex slope of a sharply tilting isentropic surface in a stable stratified atmosphere with its stability decreasing, or in an unstable atmosphere with its stability increasing, i.e., its stability θ z approaches zero, its vertical vorticity can develop rapidly if its C D is decreasing. The theoretical results are employed to analyze a Tibetan Plateau (TP) vortex (TPV), which appeared over the TP, then slid down and moved eastward in late July 2008, resulting in heavy rainfall in Sichuan Province and along the middle and lower reaches of the Yangtze River. The change of PV 2 contributed to the intensification of the TPV from 0000 to 0600 UTC 22 July 2008 when it slid upward on the upslope of the northeastern edge of the Sichuan basin, since the changes in both horizontal vorticity η s and baroclinity θ s have positive effects on the development of vertical vorticity. At 0600 UTC 22 July 2008, the criterion for SVD at 300 K isentropic surface is satisfied, meaning that SVD occurred and contributed significantly to the development of vertical vorticity. The appearance of the stronger signals concerning the VD and SVD surrounding the vortex indicates that the GSVD concept can serve as a useful tool for diagnosing the development of weather systems.     

MESOSCALE NONLINEAR GRAVITATIONAL WAVES AND THEIR INTERACTION IN VERTICAL SHEAR FLOW*

Interaction equations of two nonlinear gravitational waves in baroclinic atmosphere are presented via multi-scale perturbation method,which can be classified into coupling nonlinear Schrodinger equations.In particular,the interaction course of two nonlinear gravitational waves of basic flow in vertical linear and quadratic shear is illustrated.Numerical calculation displays that wave amplitude enlarges and wave width narrows when two solitary gravitational waves meet and chase;that basic flow with single shear is more beneficial than that with quadratic shear to the interaction of two nonlinear wave packets;and that the interaction of two wave packets makes wave shape change more greatly and energy more dispersive,which contributes to the occurrence of changeable weather.Therefore,one of the probable mechanisms for the appearance of strong convection weather is the interaction between mesoscale nonlinear gravitational waves.     

湿大气中低涡暴雨系统发展东移的初步分析

七十年代,谢义炳教授指出:湿大气动力学和干大气动力学特征有明显差异。结合我们的天气实践,注意到经常造成鄂北强降水的西南低涡处于对流层低层,在这一层次内不仅流场辐合明显,而且水汽丰沛,空气为强烈的对流性不稳定,这些因子对低涡的生消移动必然有较大的影响。本文的目的是,引入水汽因子后,通过简化涡度方程在湿斜压大气中的应用,并考虑湿静力稳定度σ_m既为P的函     

Baroclinic solitary waves with radial symmetry

A model for the structure and motion of baroclinic solitary waves in the atmosphere or ocean is presented. Like gravity wave solitons, these planetary wave solutions are both weakly nonlinear and weakly dispersive. The dispersion effects, induced by β, are small because the scale of the wave is large compared to the deformation radius. The steepening effects are provided by the interaction of the wave with exterior mean shear flow, which may be either barotropic or baroclinic. The solutions have two properties which suggest that such theories may be useful in modelling solitary disturbances in the atmosphere or ocean: radial symmetry and fluid speeds which exceed the phase speed of the wave itself. As an example, we apply the model to Gulf Stream Rings.     

Midlatitude unstable air-sea interaction with atmospheric transient eddy dynamical forcing in an analytical coupled model

While recent observational studies have shown the critical role of atmospheric transient eddy (TE) activities in midlatitude unstable air-sea interaction, there is still a lack of a theoretical framework characterizing such an interaction. In this study, an analytical coupled air-sea model with inclusion of the TE dynamical forcing is developed to investigate the role of such a forcing in midlatitude unstable air-sea interaction. In this model, the atmosphere is governed by a barotropic quasi-geostrophic potential vorticity equation forced by surface diabatic heating and TE vorticity forcing. The ocean is governed by a baroclinic Rossby wave equation driven by wind stress. Sea surface temperature (SST) is determined by mixing layer physics. Based on detailed observational analyses, a parameterized linear relationship between TE vorticity forcing and meridional second-order derivative of SST is proposed to close the equations. Analytical solutions of the coupled model show that the midlatitude air-sea interaction with atmospheric TE dynamical forcing can destabilize the oceanic Rossby wave within a wide range of wavelengths. For the most unstable growing mode, characteristic atmospheric streamfunction anomalies are nearly in phase with their oceanic counterparts and both have a northeastward phase shift relative to SST anomalies, as the observed. Although both surface diabatic heating and TE vorticity forcing can lead to unstable air-sea interaction, the latter has a dominant contribution to the unstable growth. Sensitivity analyses further show that the growth rate of the unstable coupled mode is also influenced by the background zonal wind and the air–sea coupling strength. Such an unstable air-sea interaction provides a key positive feedback mechanism for midlatitude coupled climate variabilities.

     

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。     

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.     

Finite-amplitude, neutral baroclinic eddies and mean flows in an internally heated rotating fluid: 1. Numerical simulations and quasi-geostrophic ‘free modes’

A series of numerical simulations of steady wave flows in a rotating fluid annulus, subject to internal heating and various thermal boundary conditions, is examined to characterise their structures, energetics and potential vorticity transport properties. The last of these characteristics, together with more conventional scaling considerations, indicate the possibility of applying quasi-geostrophic theory to the interior flow in a formulation similar to the inviscid, adiabatic models of Kuo and White.The analytical model of White, describing finite amplitude, neutral baroclinic eddies and mean flows as illustrations of the Charney-Drazin non-acceleration theorem, is then extended to include uniform diabatic heating and the effects of different forms of lateral shear in the background mean zonal flow. Like the solutions discussed by White, those obtained in the present paper consist of steady, internal jet, mean zonal flows, and baroclinic and barotropic Rossby wave components, all having the same three-dimensional wavenumber. Provided the diabatic heating is proportional to the stratification of the background flow, measured by the square of the Brunt-Vaisälä frequency N, the potential vorticity equation remains homogeneous. All the solutions are then characterised by zero net transfer of potential vorticity despite the possibility of non-zero eddy fluxes of heat or momentum and non-trivial Lorenz energy cycles.A series of particular three-component solutions (which, like some of the solutions discussed by White, do not obey conventional lateral boundary conditions) is examined as possible theoretical analogues of the steady waves observed in the numerical simulations of the laboratory flows, and is found to agree encouragingly well in the spatial variations of their mean flows, eddy stream function (pressure) and eddy fluxes of heat and momentum. Potential vorticity fluxes in the numerical simulations are relatively small (though crucially non-zero), supporting the possible analogy with the analytical model and exposing some limitations of the latter in not accounting for weak dissipation and forcing processes present in the laboratory flows.Further implications of the results are discussed, including possible analogies between the laboratory experiments and certain features in planetary atmospheres and oceans.     

Effect of static stability on the pattern of three-dimensional baroclinic lee wave across a meso scale elliptical barrier

Summary In this paper, an attempt has been made to examine the effect of static stability on the pattern of three dimensional (3-D) baroclinic lee wave across a meso-scale elliptical barrier. For this purpose first a 3-D meso scale lee wave model has been developed. Then the model is applied to the Western Ghats (WG) using real time radio sonde data of Santacruz (19°7′N, 72°51′E) (here after SCZ), a station on the windward side of WG, on the days when dynamic and thermodynamic conditions of the atmosphere were favourable to generate lee waves. It is found that the pattern of 3-D baroclinic lee wave is very much sensitive to the value of the static stability parameter N². It is found that during southwest monsoon season trapped lee waves are convergent type (contours of perturbation vertical velocity w′ are crescent shaped convex down wind) and during winter they are divergent type (contours of w′ are crescent shaped concave down wind). The study shows that for a given profile of wind, the value of N² must exceed certain threshold value to obtain divergent type lee wave, otherwise convergent type lee waves are found. It is also found that in the southwest monsoon season, when atmosphere is neutrally stratified, a single divergent lee wave corresponds to a single transverse lee wave, whereas in the winter season, when atmosphere is strongly stratified, a single divergent lee wave corresponds to a number of transverse lee wave. Furthermore, in the former case long (or short) divergent lee wave corresponds to short (or long) transverse lee wave, whereas in the later case long (or short) divergent lee wave, in general, corresponds to long (or short) transverse lee wave. This revised version was published online in November 2004 with corrected captions of Figs. 1 and 2.     

SPATIAL AND TEMPORAL VARIATIONS OF THE KINEMATIC CHARACTERISTICS IN THE PROPAGATION OF ATMOSPHERIC STATIONARY WAVES

Time-mean global general circulation data are employed to analyze the temporal and spatial variations ofthe meridional gradient of zonal mean potential vorticity,the critical wavenumber n_s for horizontal wave-propagation,and the critical wavenumber K_c for vertical wave-propagation.Thereby the kinematic charac-teristics in the propagation of atmospheric stationary waves and their annual variations are studied.Resultsshow that in the troposphere n_s and K_c usually decrease with the increase of either latitude or altitude.Synoptic and near-resonant Rossby waves could be trapped during their upward and meridional propagations.These characteristics possess prominent annual variations,especially in the Northern Hemisphere.It is foundthat the spatial and temporal variations of these kinematic characteristics are in good agreement with those ofthe atmospheric wave patterns.