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 growth rate of instable waves depends on the peak radial gradient of the mean vorticity and the tangential wavenumber （WN）. The vortex-semicircle theorem is also derived to provide bounds on the growth rates and phase speeds of VRWs. The typical basic states and different WN perturbations in a tropical cyclone （TC） are obtained from a high resolution simulation. It is shown that the first necessary condition for vortex barotropic instability can be easily met at the radius of maximum vorticity （RMV）. The wave energy tends to decay （grow） inside （outside） the RMV due mainly to the negative （positive） sign of the radial gradient of the mean absolute vorticity. This finding appears to help explain the developemnt of strong vortices in the eyewall of TCs.

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.

GOES-16 ABI Brightness Temperature Observations Capturing Vortex Rossby Wave Signals during Rapid Intensification of Hurricane Irma(2017)

Geostationary Operational Environmental Satellite-16(GOES-16) Advanced Baseline Imager(ABI) observations of brightness temperature(TB) are used to examine the temporal evolutions of convection-affected structures of Hurricane Irma(2017) during its rapid intensification(RI) period from 0600 to 1800 UTC 4 September 2017.The ABI observations reveal that both an elliptical eye and a spiral rainband that originated from Irma's eyewall obviously exhibit wavenumber-2 TB asymmetries.The elliptical eye underwent a counterclockwise rotation at a mean speed of a wavenumber-2 vortex Rossby edge wave from 0815 to 1005 UTC 4 September.In the following about 2 hours(1025–1255 UTC 4 September),an inner spiral rainband originated from the eyewall and propagated at a phase speed that approximates the vortex Rossby wave(VRW) phase speed calculated from the aircraft reconnaissance data.During the RI period of Irma,ABI TB observations show an on–off occurrence of low TB intrusions into the eye,accompanying a phase lock of eyewall TB asymmetries of wavenumbers 1 and 2 and an outward propagation of VRW-like inner spiral rainbands from the eyewall.The phase lock leads to an energy growth of Irma's eyewall asymmetries.Although the eye remained clear from 1415 to 1725 UTC 4 September,an inner spiral rainband that originated from a large convective area also had a VRW-like outward propagation,which is probably due to a vertical tilt of Irma.This study suggests a potential link between convection sensitive GOES imager observations and hurricane dynamics.

Interaction of Typhoon and Mesoscale Vortex

Under two types of initial tropical cyclone structures that are characterized by high and low vorticity zones, four sets of numerical experiments have been performed to investigate the interaction of a tropical cyclone with an adjacent mesoscale vortex (MSV) and its impact on the tropical cyclone intensity change, using a quasi-geostrophic barotropic vorticity equation model with a horizontal resolution of 0.5 km. The results suggest that the interaction of a tropical cyclone characterized by a high vorticity zonal structure and an MSV would result in an intensification of the cyclone. Its central pressure decreases by more than 14 hPa. In the process of the interaction, the west and middle segments of the high vorticity zone evolve into two peripheral spiral bands of the tropical cyclone, and the merging of the east segment and the inward propagating MSV forms a new vorticity accumulation area, wherein the maximum vorticity is remarkably greater than that in the center of the initial tropical cyclone circulation. It is this process of merging and strengthening that causes a greater pressure decrease in the center of the tropical cyclone. This process is also more complicated than those that have been studied in the past, which indicated that only the inward transfer of vorticity of the MSV can result in the strengthening of the tropical cyclone.

GENERALIZED ENERGY CONSERVATION AND UNSTABLE PERTURBATION PROPERTY IN BAROTROPIC VORTEX

Based on a barotropic vortex model, generalized energy-conserving equation was derived and twonecessary conditions of basic flow destabilization are gained. These conditions correspond to generalizedbarotropic instability and super speed instability. They are instabilities of vortex and gravity inertial waverespectively. In order to relate to practical situation, a barotropic vortex was analyzed, the basic flow of which issimilar to lower level basic wind field of tropical cyclones and the maximum wind radius of which is 500 km.The results show that generalized barotropic instability depending upon the radial gradient of relative vorticitycan appear in this vortex. It can be concluded that unstable vortex Rossby wave may appear in barotropic vortex.

The Roles of Barotropic Instability and the Beta Effect in the Eyewall Evolution of Tropical Cyclones

Diabatic heating by convection in the eyewall often produces an annular region of high potential vorticity(PV)around the relatively low PV eye in a strong tropical cyclone(TC).Such a PV ring is barotropically unstable and can encourage the exponential growth of PV waves.In this study,such instability and the subsequent nonlinear evolution of three TC-like vortices having PV rings with different degrees of hollowness on an f-plane are first examined using an unforced,inviscid shallow-water-equation model.Results show that the simulated eyewalls evolve similarly to those in the nondivergent barotropic model.It is also found that the polygonal eyewall structure can be decomposed into vortex Rossby waves(VRWs)of different wavenumbers with different amplitudes,allowing for wave-wave interactions to produce complicated behaviors of mesovortices in the TC eyewall.The same set of PV rings has been examined on a beta-plane.Although the beta effect has been rendered unimportant to the eyewall evolution due to the relatively small scale of the inner-core circulation,this study shows that the beta effect may erode the coherent structure of mesovortices in the eyewall of an initially hollow PV-ring vortex.Mesovortices modeled on the beta-plane with a greater beta parameter tend to experience an earlier breakdown and enhanced radial gradients of the basic-state(azimuthally mean)angular velocity,followed by wave-wave,wave-flow interactions,leading to earlier merger and axisymmetrization processes.This result implies that the beta effect could be one of the forcings that shorten the lifetime of quasi-steady mesovortices in the eyewall of real TCs.

THE TOPOGRAPHIC PARAMETER SENSITIVITY TO VORTICITY PROPAGATION AND TYPHOON TANGENTIAL VELOCITY CHANGES

A high resolution shallow-water model is designed to study the roles which the topographical parameter and latitudinal basic flow play in the propagation of vortex Rossby waves and typhoon tangential velocity changes. With no latitudinal flow, the horizontal scale effects of island terrain on the vortex Rossby waves propagation show that the disturbance vorticity follows a clockwise island-circulating path more significantly, the local maximum wind speed amplitude reduces more sharply, the maximum mean azimuthally tangential wind spins down more substantially, when the topographic horizontal scale augments. With the latitudinal basic flow, the evolution of local wind and mean velocity are affected by the distance changes between TC and the terrain and the time length of topographic action: the local wind amplitude intensifies and the mean velocity diminishes while the distance is shortening; the opposite is true while TC is away from the terrain gradually.

The Dynamical Characteristics and Wave Structure of Typhoon Rananim (2004)

Typhoon Rananim （2004） was one of the severest typhoons landfalling the Chinese mainland from 1996 to 2004. It brought serious damage and induced prodigious economical loss. Using a new generation of mesoscale model, named the Weather Research and Forecasting （WRF） modeling system, with 1.667 km grid horizontal spacing on the finest nested mesh, Rananim was successfully simulated in terms of track, intensity, eye, eyewall, and spiral rainbands. We compared the structures of Rananim to those of hurricanes in previous studies and observations to assess the validity of simulation. The three-dimensional （3D） dynamic and thermal structures of eye and eyewall were studied based on the simulated results. The focus was investigation of the characteristics of the vortex Rossby waves in the inner-core region. We found that the Rossby vortex waves propagate azimuthally upwind against the azimuthal mean tangential flow around the eyewall, and their period was longer than that of an air parcel moving within the azimuthal mean tangential flow. They also propagated outward against the boundary layer inflow of the azimuthal mean vortex. Puthermore, we studied the connection between the spiral potential vorticity （PV） bands and spiral rainbands, and found that the vortex Rossby waves played an important role in the formation process of spiral rainbands.

Properties and Stability of a Meso-Scale Line-Form Disturbance

By using the 3D dynamic equations for small- and meso-scale disturbances, an investigation is performed on the heterotropic instability （including symmetric instability and traversal-type instability） of a zonal line-like disturbance moving at any angle with respect to basic flow, arriving at the following results： （1） with linear shear available, the heterotropic instability of the disturbance will occur only when flow shearing happens in the direction of the line-like disturbance movement or in the direction perpendicular to the disturbance movement, with the heterotropic instability showing the instability of the internal inertial gravity wave; （2） in the presence of second-order non-linear shear, the disturbance of the heterotropic instability includes internal inertial gravity and vortex Rossby waves. For the zonal line-form disturbance under study, the vortex Rossby wave has its source in the second-order shear of meridional basic wind speed in the flow and propagates unidirectionally with respect to the meridional basic flow. As a mesoscale heterotropic instable disturbance, the vortex Rossby wave has its origin from the second shear of the flow in the direction perpendicular to the line-form disturbance and is independent of the condition in the direction parallel to the flow; （3） for general zonal line-like disturbances, if the second-order shear happens in the meridional wind speed, i.e., the second shear of the flow in the direction perpendicular to the line-form disturbance, then the heterotropic instability of the disturbance is likely to be the instability of a mixed Rossby-internal inertial gravity wave; （4） the symmetric instability is actually the instability of the internal inertial gravity wave. The second-order shear in the flow represents an instable factor for a symmetric-type disturbance; （5） the instability of a traversal-type disturbance is the instability of the internal inertial gravity wave when the basic flow is constant or only linearly sheared. With a second or nonlinear vertical shear of the basic flow taken into account, the instability of a traversal-type disturbance may be the instability of a mixed vortex Rossby - gravity wave.

Two Types of Arctic Oscillation and Their Associated Dynamic Features

In this paper,the dynamical evolutions of two types of Arctic Oscillation (AO),the stratospheric (S) and tropospheric (T) types,have been investigated on an intermediate time scale in terms of transient eddy feedback forcing and three-dimensional Rossby wave propagation.S-Type (T-type) events are characterized by an anomalous stratospheric polar vortex that is in phase (out of phase) with its tropospheric counterpart.Approximately onethird of AO events,both positive and negative,are T-type events.For the positive phase of a T-type event,the formation and maintenance of stratospheric positive anomalies over the polar cap are associated with an upward propagation of Rossby wave packets originating from the near-tropopause altitude over northeastern Asia.However,such upward propagating features are not found for S-type events.In the troposphere,transient eddy feedback forcing is primarily responsible for the meridional seesaw structure of both the S-and T-type events,with an additional contribution from Rossby wave propagation.

Contribution of vortex Rossby wave to spiral rainband formation in tropical cyclones

The contribution of the vortex Rossby wave （VRW） to framework of a barotropic non-divergent TC-like vortex model. the spiral rainband in the tropical cyclones （TCs） is studied in the The spectral function expanding method is used to analyze the disturbance evolution of a defined basic state vortex. The results show that the numerical solution of the model is a superposition of the continuous spectrum component （non-normal modes） and the discrete spectrum component （normal modes）. Only the eyewall and the rainbands in the inner core-region in a TC are related to the VRW normal modes, whereas the continuous spectrum wave components play an important role in the formation of secondary-, principal-, and distant- rainbands, especially the outer rainband, through an indirect way. The continuous spectrum can promote the development of the TC circulation for the occurrence of a mesoscale instability. The convection under a favorable moisture condition will trigger the inertial-gravitational wave to cause the formation of unstable spiral bandliked-disturbances outside of the eyewall. The complicated interaction between the basic state-vortex and the VRW disturbances will cause a positive feedback between the TC circulation and the rainband.

COMPARISON OF ON-LINE COUPLED AND CONSTANT TRANSFER SIMULATION METHODS FOR DIRECT RADIATIVE FORCING OF ANTHROPOGENIC SULFATE

1 INTRODUCTION Of three main methods for studying the radiative forcing of anthropogenic sulfate and climatic response on the regional scale, the first is, with given rates for transforming SO2 to sulfate, converting actually released SO2 into sulfate and acquiring the distribution of sulfate by computing transfer equations in the climate model. The second is obtaining the sulfate distribution through chemical reaction and transfer of matters in regional climate models online coupled with an atmospheric chemistry model that includes full chemical reactions for sulfides. The third is to put sulfate distribution data from GCM and its coupled atmospheric chemistry model to regional climate model, which is so called off-line coupled method. As shown in comparisons between the online and offline modeling on the regional scale, the radiative climate effect of sulfate shows large uncertainty due to significant influence from various methods.

A NUMERICAL STUDY ON VORTICITY PROPAGATION AND CHANGES IN TYPHOON INTENSITY

An f-plane quasi-geostrophic barotropic vorticity equation model of high resolution is designed in this paper in order to investigate the characters of vorticity propagation and the effect of nonlinearity on the propagation within a typhoon circulation,wherein two mesoscale vortices coexist at different radial positions.The results of 10 sets of experiments suggest that in comparison with only one vortex,the intensity of the inward propagations of vorticity strengthens distinctly,vorticity detains in the inner region of typhoon circulation for a longer time,and the local maximum wind speed in the inner region increases clearly.The introduction of nonlinear advection into the model weakens the intensity of both inward and outward propagations of vorticity,but makes the inward propagation up to a position closer to the center of typhoon.