Abstract

In many numerical simulation studies there is a need to obtain the balanced initial fields in numerical models with σ as the vertical coordinate. By employing an equation that establishes the balance between the mass and wind fields directly on σ surface, we can obtain mass fields from wind fields, or vice versa. Since the balance equation is generally nonlinear, numerical methods must be used to obtain approximate solutions. However, the term corresponding to the divergence of the pressure gradient in the σ system is more complicated compared to that in pressure or height coordinates. As a result previous studies have made various approximations for this term. In this paper, a relatively accurate and consistent numerical scheme is proposed to solve the inverse balance equation in a coordinates. Several numerical calculations show that the proposed scheme is more accurate and more consistent than that used by Kurihara and Bender and Kurihara et al.

Abstract

In Part I, the author analyzed the asymmetric structure in the inner core of a numerically simulated tropical cyclone and found that the asymmetry near the eyewall in the mid–lower troposphere is dominated by wavenumber-1 and -2 vortex Rossby waves. These waves are found to be well coupled with asymmetries in eyewall convection and thus may play an important role in the life cycle of a tropical cyclone. In this paper, analyses are extended to include the role of these vortex Rossby waves in tropical cyclone structure and intensity changes. The waves are found to transport angular momentum from the eyewall to the eye, accelerating tangential winds in the eye at the expense of decelerating the tangential wind in the eyewall, and thus they play an important role in the inner core dynamics of the tropical cyclone.

Convection in the eyewall is enhanced between the downstream trough and upstream ridge in the vortex Rossby waves but suppressed between the downstream ridge and upstream trough. This close relationship stems from inflow (outflow) associated with the waves in the former (latter) region. Propagation of these waves around the eyewall can produce changes in eyewall shape and polygonal eyewalls with cyclonic rotation. The waves also propagate radially outward and stagnate at radii of 70–90 km, where the radial potential vorticity gradient disappears or reverses its sign. It is at these radii where strong outer spiral rainbands most frequently occur. These outer rainbands spiral cyclonically inward and occasionally perturb the eyewall. In many cases, outward-propagating inner spiral rainbands can be initiated and emanated from the eyewall, especially when the eyewall is perturbed by an outer spiral rainband. When such a perturbation is strong and in phase with strong vortex Rossby waves in the eyewall, the eyewall may experience a breakdown and then be recovered through the axisymmetrization process. The eyewall breakdown (recovery) is accompanied by a weakening (intensifying) cycle of the tropical cyclone.

Abstract

A long-standing issue on how outer spiral rainbands affect the structure and intensity of tropical cyclones is studied through a series of numerical experiments using the cloud-resolving tropical cyclone model TCM4. Because diabatic heating due to phase changes is the main driving force of outer spiral rainbands, their effect on the tropical cyclone structure and intensity is evaluated by artificially modifying the heating and cooling rate due to cloud microphysical processes in the model. The view proposed here is that the effect of diabatic heating in outer spiral rainbands on the storm structure and intensity results mainly from hydrostatic adjustment; that is, heating (cooling) of an atmospheric column decreases (increases) the surface pressure underneath the column. The change in surface pressure due to heating in the outer spiral rainbands is significant on the inward side of the rainbands where the inertial stability is generally high. Outside the rainbands in the far field, where the inertial stability is low and internal atmospheric heating is mostly lost to gravity wave radiation and little is left to warm the atmospheric column and lower the local surface pressure, the change in surface pressure is relatively small. This strong radially dependent response reduces the horizontal pressure gradient across the radius of maximum wind and thus the storm intensity in terms of the maximum low-level tangential wind while increasing the inner-core size of the storm.

The numerical results show that cooling in the outer spiral rainbands maintains both the intensity of a tropical cyclone and the compactness of its inner core, whereas heating in the outer spiral rainbands decreases the intensity but increases the size of a tropical cyclone. Overall, the presence of strong outer spiral rainbands limits the intensity of a tropical cyclone. Because heating or cooling in the outer spiral rainbands depends strongly on the relative humidity in the near-core environment, the results have implications for the formation of the annular hurricane structure, the development of concentric eyewalls, and the size change in tropical cyclones.

Abstract

It has been long known that cloud microphysics can have a significant impact on the simulations of precipitation; however, there have been few studies so far that have investigated the effect of cloud microphysics on tropical cyclones. In the most advanced simulation of tropical cyclones by numerical models, the use of explicit cloud microphysics becomes more and more attractive with cumulus parameterization bypassed at very high resolutions. In this study, the sensitivity of the simulated tropical cyclone structure and intensity to the choice and details of cloud microphysics parameterization is investigated using the triply nested movable mesh tropical cyclone model TCM3 described in Part I but with several refinements. Three different cloud microphysics parameterization schemes are tested, including the warm-rain-only cloud microphysics scheme (WMRN) and two mixed-ice-phase cloud microphysics schemes, one of which has three ice species (cloud ice–snow–graupel; CTRL) while the other has hail instead of graupel (HAIL).

It is shown that, although the cloud structures of the simulated tropical cyclone can be quite different with different cloud microphysics schemes, intensification rate and final intensity are not very sensitive to the details of the cloud microphysics parameterizations. This occurs because all of the schemes produce similar vertical heating profiles and similar levels of rainbands, stratiform clouds, and downdrafts. The latter are found to be prohibitive factors to tropical cyclone intensification and intensity. Both evaporation of rain and melting of snow and graupel are responsible for the generation of downdrafts and rainbands. This is demonstrated using two extra experiments in which the evaporation of rain and melting of snow and graupel are removed from WMRN or CTRL experiments. In these two extreme cases, neither significant rainbands nor downdrafts were generated. As a result, the storm developed much more rapidly and reached an intensity that was much stronger than those in the experiments with both evaporation of rain and melting of ice species.

In comparison with the substantial sensitivity of simulated tropical cyclones to different cumulus parameterization schemes found in previous studies, the weak sensitivity of the simulated tropical cyclone intensity to cloud microphysics parameterizations from this study indicates the potential advantage in using explicit cloud microphysics in tropical cyclone models to improve the intensity forecasting.

Abstract

Results from an explicit simulation of tropical cyclones are presented in this study. The numerical model used in the study is the triply nested movable mesh primitive equation model newly developed by the author. It uses the hydrostatic primitive equations with explicit treatment of cloud microphysics. The integration domain is triply nested by a two-way nesting strategy with the two interior meshes being movable following the model tropical cyclone. The model physics are chosen based on the up-to-date developments, including an E-ϵ closure scheme for subgrid-scale vertical turbulent mixing [with E being the turbulent kinetic energy (TKE), and ϵ the TKE dissipation rate]; a modified Monin–Obukhov scheme for the surface flux calculation, with an option to include the effect of sea spray evaporation; an explicit treatment of mixed-ice phase cloud microphysics; and dissipative heating, which has been found to be important in tropical cyclones.

New developments include a new iteration scheme to solve the nonlinear balance equation in σ coordinates in the nested-mesh grids, which is used for model initialization; an initialization scheme for both TKE and its dissipation rate fields based on a level-2 turbulence closure scheme deduced from the TKE and its dissipation rate equations; and a modified formula for the timescale that determines the rate at which cloud ice converts to snow via the Bergeron process.

The success of the multiply nested movable mesh approach and the conservative property of the numerical model is first tested with an experiment in which the model was initialized with an axisymmetric cyclonic vortex embedded in a uniform easterly flow of 5 ms⁻¹ on an f plane, but with no model physics. Results from a control experiment with the full model physics are then discussed in detail to demonstrate the capability of the model in simulating many aspects of the tropical cyclone, especially the inner core structure and both the inner and outer spiral rainbands in the cyclone circulation. The vortex Rossby waves in the simulated tropical cyclone core region are also identified and analyzed. Sensitivity of the model results to various model physics and major physical parameters will be given in a companion paper.

Abstract

The structure and formation of an annular hurricane simulated in a fully compressible, nonhydrostatic tropical cyclone model—TCM4—are analyzed. The model is initialized with an axisymmetric vortex on an f plane in a quiescent environment, and thus the transition from the nonannular hurricane to the annular hurricane is attributed to the internal dynamics. The simulated annular hurricane has all characteristics of those recently documented by Knaff et al. from satellite observations: quasi-axisymmetric structure, large eye and wide eyewall, high intensity, and suppressed major spiral rainbands. A striking feature of the simulated annular hurricane is its large outward tilt of the wide eyewall, which is critical to the quasi-steady high intensity and is responsible for the maintenance of the large size of the eye and eyewall of the storm. Although the annular hurricane has a quasi-axisymmetric structure, marked low-wavenumber asymmetries exist in the eyewall region.

The formation of the simulated annular hurricane is found to be closely related to the interaction between the inner spiral rainbands and the eyewall convection. As the inner rainbands spiral cyclonically inward, they experience axisymmetrization due to strong shear deformation and filamentation outside the eyewall and evolve into a quasi-symmetric convective ring, which intensifies as it contracts while the eyewall breaks down and weakens. Eventually, the convective ring replaces the original eyewall. The new eyewall formed in such a way is wider and tilts more outward with height than the original eyewall. Several such eyewall cycles in our simulation produce an annular hurricane with large eyewall slope, large eye, and wide eyewall. The response of low-level winds to the tilted convective heating in the eyewall is an increase outside and a decrease inside the radius of maximum wind, prohibiting further contraction of the new eyewall. Strong convective mass flux in the eyewall updraft corresponds to strong convective overturning subsidence outside the eyewall, greatly suppressing the development of any major rainbands outside the eyewall. Although the eyewall cycle documented in this study contributes to the formation of annular hurricanes, it could be a general process causing the increase in eye size of real tropical cyclones as well.

Abstract

The asymmetric structure in the inner core of a numerically simulated tropical cyclone is analyzed in this study. The simulated tropical cyclone is found to be highly asymmetric in the inner core. In the mid–lower troposphere, the asymmetry in the core is dominated by azimuthal wavenumber-1 and wavenumber-2 vortex Rossby waves. These waves propagate azimuthally upwind against the azimuthal mean cyclonic tangential flow around the eyewall, and thus have a much longer cyclonic rotation period (by a factor of 2) than the period of a parcel moving with the cyclonic mean tangential flow around the circumference. They also propagate outward against the boundary layer inflow of the azimuthal mean cyclone. The waves are only visible within a radius of about 60 km from the cyclone center. Beyond this distance, the radial gradient of potential vorticity (PV) of the azimuthal mean cyclone is too weak to support the vortex Rossby waves. Although the divergent motion remains strong, the geopotential height and wind fields of the vortex Rossby waves are quasi-balanced, with confluent cyclonic (divergent anticyclonic) flow collocated with low (high) perturbation geopotential height. The waves spiral cyclonically inward with maximum amplitudes near the radius of maximum wind (RMW) in the horizontal and tilt radially outward with height. The upward motion of the waves leads cyclonic vorticity in both azimuthal and radial directions by about one-quarter wavelength, implying that convective heating, which is coupled with low-level convergence and upward motion, is the driving force for the vortex Rossby waves.

A PV budget shows that diabatic heating contributes greatly to both the azimuthal mean PV and perturbation PV budgets. The PV tendency associated with diabatic heating is largely balanced by the advective (both horizontal and vertical) flux divergence of the symmetric PV, respectively, due to the asymmetric flow (vortex beta term, similar to the planetary beta term in the large-scale vorticity equation) for the vortex Rossby waves, and due to the symmetric flow for the symmetric cyclone. The vortex Rossby waves transport cyclonic PV from the eyewall to the eye, thus mixing the PV between the eyewall and the eye and spinning up the tangential wind in the eye at the expense of weakening the tangential wind near the RMW. Moreover, the PV tendency due to nonlinear processes associated with the wavenumber-1 vortex Rossby waves is a significant PV source for the wavenumber-2 vortex Rossby waves, indicating a strong wave–wave interaction in the eyewall. An eddy kinetic energy budget indicates that within the RMW, the vortex Rossby waves receive their kinetic energy from the azimuthal mean cyclone through baroclinic conversion and flux divergence of eddy kinetic energy due to the azimuthal mean vortex. Under the eyewall and just outside the RMW in the mid–lower troposphere, the main source for eddy kinetic energy is the eddy potential energy conversion, which is related to the asymmetric diabatic heating associated with moist convection in the eyewall. An interesting finding is that, in both the barotropic and baroclinic conversions, terms related to the radial flow of the azimuthal mean vortex are dominant and contribute to the kinetic energy of the vortex Rossby waves. The horizontal shear of the azimuthal flow of the mean vortex damps eddy kinetic energy, stabilizing the vortex Rossby waves in the mid–lower troposphere. However, both barotropic and baroclinic conversions related to the tangential flow of the azimuthal mean vortex, together with the eddy potential energy conversion, are responsible for the development of asymmetry in the outflow layer.

Abstract

In a recent study, Rozoff et al. proposed a possible mechanism to explain the formation and maintenance of the weak-echo annulus (or moat) outside of the primary eyewall of a tropical cyclone observed in radar images. By this mechanism, the moat is determined to be a region of the strain-dominated flow outside of the radius of maximum wind in which essentially all fields are filamented and deep convection is hypothesized to be highly distorted and even suppressed. This strain-dominated region is defined as the rapid filamentation zone wherein the filamentation time is shorter than the overturning time of deep convection. An attempt has been made in this study to test the hypothesis in a full-physics tropical cyclone model under idealized conditions and to extend the concept to the study of the inner-core dynamics of tropical cyclones. The foci of this paper are the evolution of the rapid filamentation zone during the storm intensification, the potential roles of rapid filamentation in the organization of inner spiral rainbands, and the damping of high azimuthal wavenumber asymmetries in the tropical cyclone inner core.

The presented results show that instead of suppressing deep convection, the strain flow in the rapid filamentation zone outside the elevated potential vorticity core provides a favorable environment for the organized inner spiral rainbands, which generally have time scales of several hours, much longer than the typical overturning time scale of individual convective clouds. Although the moat in the simulated tropical cyclone is located in the rapid filamentation zone, it is mainly controlled by the subsidence associated with the overturning flow from eyewall convection and downdrafts from the anvil stratiform precipitation outside of the eyewall. It is thus suggested that rapid filamentation is likely to play a secondary role in the formation of the moat in tropical cyclones. Although the deformation field is determined primarily by the structure of the tropical cyclone, it can have a considerable effect on the evolution of the storm. Because of strong straining deformation, asymmetries with azimuthal wavenumber >4 are found to be damped effectively in the rapid filamentation zone. The filamentation time thus provides a quantitative measure of the stabilization and axisymmetrization of high-wavenumber asymmetries in the inner core by shearing deformation and filamentation.

Abstract

A coupled atmosphere–ocean–coastline model driven by solar radiation is advanced to understand the essential physics determining the annual cycle of the intertropical convergence zone (ITCZ)–equatorial cold tongue (ECT) complex and associated latitudinal climate asymmetry. With a thermocline depth similar to that of the western Pacific, the aquaplanet climate is latitudinal symmetric and stable. The presence of an oceanic eastern boundary supports an east–west asymmetric climate and an ECT due to unstable air–sea interaction and counter stabilization provided by zonal differential surface buoyancy flux. Formation of latitudinal climate asymmetry requires the presence of the ECT.

The antisymmetric solar forcing due to annual variation of the solar declination angle can convert a stable latitudinal symmetric climate into a bistable-state latitudinal asymmetric climate by changing trade winds, which in turn control annual variations of the ECT. The ECT then interacts with ITCZ, providing a self-maintenance mechanism for ITCZ to linger in one hemisphere, either the northern or southern, depending on initial conditions. The establishment of the bistable-state asymmetry requires a delicate balance between counter effects of the antisymmetric solar forcing and self-maintenance. Two factors are critical for the latter: (i) The annual variation of ECT follows the SST of the ITCZ-free hemisphere and the meridional SST gradients between the ECT and ITCZ sustain moisture convergence, which prolongs residence of the ITCZ in summer hemisphere. (ii) The latent heat released in the ITCZ produces remarkable asymmetry in Hadley circulation and trades between the two hemispheres, and the stronger evaporation cooling in the ITCZ-free hemisphere delays and weakens the warming and convection development in that hemisphere.

The annual cycle of insolation due to the earth–sun distance variation may convert the bistable-state asymmetry into a preferred latitudinal asymmetric climate. The earth’s present orbit (with a minimum distance in December solstices) favors ITCZ staying north of the equator by compelling the ECT into a delayed in-phase variation with the Southern Hemisphere SST. With annual-mean solar forcing a tilted eastern boundary can support a weak preferred latitudinal asymmetry. Inclusion of the annual variation of insolation can dramatically amplify the asymmetry in the mean climate through the self-maintenance mechanism.

Abstract

Typhoon Megi (15W) was the most powerful and longest-lived tropical cyclone (TC) over the western North Pacific during 2010. While it shared many common features of TCs that crossed Luzon Island in the northern Philippines, Megi experienced unique intensity and structural changes, which were reproduced reasonably well in a simulation using the Advanced Research Weather Research and Forecasting Model (ARW-WRF) with both dynamical initialization and large-scale spectral nudging. In this paper processes responsible for the rapid intensification (RI) of the modeled Megi before it made landfall over Luzon Island were analyzed. The results show that Megi experienced RI over the warm ocean with high ocean heat content and decreasing environmental vertical shear. The onset of RI was triggered by convective bursts (CBs), which penetrate into the upper troposphere, leading to the upper-tropospheric warming and the formation of the upper-level warm core. In turn, CBs with their roots inside of the eyewall in the boundary layer were buoyantly triggered/supported by slantwise convective available potential energy (SCAPE) accumulated in the eye region. During RI, convective area coverage in the inner-core region was increasing while the updraft velocity in the upper troposphere and the number of CBs were both decreasing. Different from the majority of TCs that experience RI with a significant eyewall contraction, the simulated Megi, as the observed, rapidly intensified without an eyewall contraction. This is attributed to diabatic heating in active spiral rainbands, a process previously proposed to explain the inner-core size increase, enhanced by the interaction of the typhoon vortex with a low-level synoptic depression in which Megi was embedded.