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Chanh Kieu and Quan Wang

Abstract

A low-order dynamical model that demonstrates the stable property of the tropical cyclone (TC) maximum potential intensity (MPI) equilibrium under the wind-induced surface heat exchange feedback was recently presented by Kieu. In this study, an alternative TC-scale model that allows for the gradient wind imbalance in the planetary boundary layer is proposed to further examine the stability of the MPI equilibrium. Despite different balanced assumptions, it is shown that the new TC-scale model possesses a similar MPI equilibrium with the same asymptotic stability. The structurally stable property of the MPI equilibrium is held for a range of the model parameters, regardless of the model initial conditions or numerical configurations. In addition, an explicit dependence of the MPI on the environmental lapse rate is obtained from the new TC-scale model, which reveals subtle impacts of the tropospheric stratification on TC intensity beyond the traditional MPI framework. The existence and interpretation of two distinct time scales during TC development will be also discussed.

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Alexandria Downs and Chanh Kieu

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Various modeling and observational studies have suggested that tropical cyclone (TC) intensity tends to increase in the future due to projected warmer sea surface temperature (SST). This study examines the effects of the tropospheric stratification that could potentially offset the direct increase of TC intensity associated with the warmer SST. Using reanalysis datasets and TC records in the northwestern Pacific and the North Atlantic basins, it is shown that there exists a consistently negative correlation between the annually averaged TC intensity and the basinwide average of the tropospheric static stability. This negative correlation is more robust in the northwestern Pacific basin when using the TC lifetime maximum intensity but is somewhat less significant in the North Atlantic basin. Further separation of the troposphere into a lower (1000–500 hPa) and an upper layer (500–200 hPa) reveals that it is the upper-tropospheric static stability that plays a more dominant role in governing the TC intensity variability. The negating effects of a stable troposphere on TC intensity as found in this study suggest a partial offset of the projected increase in the TC potential intensity due to the future warmer SST. Thus, the tropospheric static stability is one of the key large-scale factors that need to be properly taken into account in studies of long-term TC intensity change.

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Chanh Q. Kieu and Zachary Moon

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Weather has long been projected to possess limited predictability due to the inherent chaotic nature of the atmosphere; small changes in initial conditions could lead to an entirely different state of the atmosphere after some period of time. Given such a limited range of predictability of atmospheric flows, a natural question is, how far in advance can we predict a hurricane’s intensity? In this study, it is shown first that the predictability of a hurricane’s intensity at the 4–5-day lead times is generally determined more by the large-scale environment than by a hurricane’s initial conditions. This result suggests that future improvement in hurricane longer-range intensity forecasts by numerical models will be most realized as a result of improvement in the large-scale environment rather than in the storm’s initial state. At the mature stage of a hurricane, direct estimation of the leading Lyapunov exponent using an axisymmetric model reveals, nevertheless, the existence of a chaotic attractor in the phase space of the hurricane scales. This finding of a chaotic maximum potential intensity (MPI) attractor provides direct information about the saturation of a hurricane’s intensity errors around 8 m s−1, which prevents the absolute intensity errors at the mature stage from being reduced below this threshold. The implication of such intensity error saturation to the limited range of hurricane intensity forecasts will be also discussed.

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Chanh Q. Kieu and Da-Lin Zhang

Abstract

This comment presents some concerns with the study of Stern et al. and their misinterpretation of the contraction of the radius of the maximum wind (RMW) in tropical cyclones. It is shown that their geometrical RMW contraction model provides little dynamical understanding of the RMW contraction during tropical cyclone intensification, and it differs fundamentally from the RMW contraction model of Willoughby et al. that was derived from the directional derivative concept. Moreover, it is demonstrated that Stern et al. were mistaken in commenting on the derivation of the governing equation for the RMW contraction in Kieu.

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Chanh Q. Kieu and Da-Lin Zhang

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In this study, the roles of merging midlevel mesoscale convective vortices (MCVs) and convectively generated potential vorticity (PV) patches embedded in the intertropical convergence zone (ITCZ) in determining tropical cyclogenesis are examined by calculating PV and absolute vorticity budgets with a cloud-resolving simulation of Tropical Storm Eugene (2005). Results show that the vortex merger occurs as the gradual capture of small-scale PV patches within a slow-drifting MCV by another fast-moving MCV, thus concentrating high PV near the merger’s circulation center, with its peak amplitude located slightly above the melting level. The merging phase is characterized by sharp increases in surface heat fluxes, low-level convergence, latent heat release (and upward motion), lower tropospheric PV, surface pressure falls, and growth of cyclonic vorticity from the bottom upward. Melting and freezing appear to affect markedly the vertical structures of diabatic heating, convergence, absolute vorticity, and PV, as well the production of PV during the life cycle of Eugene. Results also show significant contributions of the horizontal vorticity to the magnitude of PV and its production within the storm.

The storm-scale PV budgets show that the above-mentioned amplification of PV results partly from the net internal dynamical forcing between the PV condensing and diabatic production and partly from the continuous lateral PV fluxes from the ITCZ. Without the latter, Eugene would likely be shorter lived after the merger under the influence of intense vertical shear and colder sea surface temperatures. The vorticity budget reveals that the storm-scale rotational growth occurs in the deep troposphere as a result of the increased flux convergence of absolute vorticity during the merging phase. Unlike the previously hypothesized downward growth associated with merging MCVs, the most rapid growth rate is found in the bottom layers of the merger because of the frictional convergence. It is concluded that tropical cyclogenesis from merging MCVs occurs from the bottom upward.

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Da-Lin Zhang and Chanh Q. Kieu

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Although the forced secondary circulations (FSCs) associated with hurricane-like vortices have been previously examined, understanding is still limited to idealized, axisymmetric flows and forcing functions. In this study, the individual contributions of latent heating, frictional, and dry dynamical processes to the FSCs of a hurricane vortex are separated in order to examine how a hurricane can intensify against the destructive action of vertical shear and how a warm-cored eye forms. This is achieved by applying a potential vorticity (PV) inversion and quasi-balanced omega equations system to a cloud-resolving simulation of Hurricane Andrew (1992) during its mature stage with the finest grid size of 6 km.

It is shown that the latent heating FSC, tilting outward with height, acts to oppose the shear-forced vertical tilt of the storm, and part of the upward mass fluxes near the top of the eyewall is detrained inward, causing the convergence aloft and subsidence warming in the hurricane eye. The friction FSC is similar to that of the Ekman pumping with its peak upward motion occurring near the top of the planetary boundary layer (PBL) in the eye. About 40% of the PBL convergence is related to surface friction and the rest to latent heating in the eyewall.

In contrast, the dry dynamical forcing is determined by vertical shear and system-relative flow. When an axisymmetric balanced vortex is subjected to westerly shear, a deep countershear FSC appears across the inner-core region with the rising (sinking) motion downshear (upshear) and easterly sheared horizontal flows in the vertical. The shear FSC is shown to reduce the destructive roles of the large-scale shear imposed, as much as 40%, including its forced vertical tilt. Moreover, the shear FSC intensity is near-linearly proportional to the shear magnitude, and the wavenumber-1 vertical motion asymmetry can be considered as the integrated effects of the shear FSCs from all the tropospheric layers. The shear FSC can be attributed to the Laplacian of thermal advection and the temporal and spatial variations of centrifugal force in the quasi-balanced omega equation, and confirms the previous finding of the development of wavenumber-1 cloud asymmetries in hurricanes.

Hurricane eye dynamics are presented by synthesizing the latent heating FSC with previous studies. The authors propose to separate the eye formation from maintenance processes. The upper-level inward mass detrainment forces the subsidence warming (and the formation of an eye), the surface pressure fall, and increased rotation in the eyewall. This increased rotation will induce an additional vertical pressure gradient force to balance the net buoyancy generated by the subsidence warming for the maintenance of the hurricane eye. In this sense, the negative vertical shear in tangential wind in the eyewall should be considered as being forced by the subsidence warming, and maintained by the rotation in the eyewall.

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Chanh Q. Kieu and Da-Lin Zhang

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In this study, a piecewise potential vorticity (PV) inversion algorithm for an arbitrary number of PV pieces is developed by extending Wang and Zhang’s PV inversion scheme, and then the nonlinear responses to various types and magnitudes of axisymmetric PV anomalies (PVAs) in hurricane vortices are investigated. Results show that the upper- and lower-level PVAs in the eye help enhance cyclonic flows in the eyewall, but with weak vertical interactions between them. The balanced flows corresponding to the PVAs in the eyewall appear to account for a substantial portion of the warm core and the minimum pressure in the eye. However, the lower-level PVA in the eye inversion layer is more effective in contributing to the hurricane intensity than that at the upper levels. Results also show that the radius of the balanced response of PVAs is more sensitive to the mean vortex intensity than the vertical penetration; the weaker the mean vortex intensity, the larger the radius of the influence will be. Similar behaviors are also observed for the quasi-balanced secondary circulations. That is, given a diabatic heating profile in the eyewall, the weaker the background vortex or the PVAs, the stronger the secondary circulations will be.

It is found that the development of an outer eyewall (or spiral rainbands) could be inimical to the inner eyewall in several ways, such as by 1) adding an anticyclonic flow inside to offset the cyclonic rotation of the inner eyewall, 2) enhancing a ring of a lower pressure zone underneath to broaden the inner-core lower pressure region, 3) inducing an inward (outward) radial flow outside (inside) in the PBL (upper level) to block the energy supply to (outflow of) the inner eyewall, and 4) generating subsidence between the two eyewalls to suppress the development of deep convection in the inner eyewall.

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Chanh Q. Kieu and Da-Lin Zhang

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Although tropical cyclogenesis occurs over all tropical warm ocean basins, the eastern Pacific appears to have the highest frequency of tropical cyclogenesis events per unit area. In this study, tropical cyclogenesis from merging mesoscale convective vortices (MCVs) associated with breakdowns of the intertropical convergence zone (ITCZ) is examined. This is achieved through a case study of the processes leading to the genesis of Tropical Storm Eugene (2005) over the eastern Pacific using the National Centers for Environmental Prediction reanalysis, satellite data, and 4-day multinested cloud-resolving simulations with the Weather Research and Forecast (WRF) model at the finest grid size of 1.33 km.

Observational analyses reveal the initiations of two MCVs on the eastern ends of the ITCZ breakdowns that occurred more than 2 days and 1000 km apart. The WRF model reproduces their different movements, intensity and size changes, and vortex–vortex interaction at nearly the right timing and location at 39 h into the integration as well as the subsequent track and intensity of the merger in association with the poleward rollup of the ITCZ. Model results show that the two MCVs are merged in a coalescence and capture mode due to their different larger-scale steering flows and sizes. As the two MCVs are being merged, the low- to midlevel potential vorticity and tangential flows increase substantially; the latter occurs more rapidly in the lower troposphere, helping initiate the wind-induced surface heat exchange process leading to the genesis of Eugene with a diameter of 400 km. Subsequently, the merger moves poleward with characters of both MCVs. The simulated tropical storm exhibits many features that are similar to a hurricane, including the warm-cored “eye” and the rotating “eyewall.” It is also shown that vertical shear associated with a midlevel easterly jet leads to the downshear tilt and the wavenumber-1 rainfall structures during the genesis stage, and the upshear generation of moist downdrafts in the vicinity of the eyewall in the minimum equivalent potential temperature layer. Based on the above results, it is concluded that the ITCZ provides a favorable environment with dynamical instability, high humidity, and background vorticity, but it is the merger of the two MCVs that is critical for the genesis of Eugene. The storm decays as it moves northwestward into an environment with increasing vertical shear, dry intrusion, and colder sea surface temperatures. The results appear to have important implications for the high frequency of development of tropical cyclones in the eastern Pacific.

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Chanh Kieu, Richard Rotunno, and Quan Wang

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This study examines the role of frictional feedback in the atmospheric boundary layer during tropical cyclone (TC) development. Using a reduced model of TC dynamics, it is shown that a feedback between frictional convergence and convective heating in the absence of slantwise moist neutrality is capable of producing a stable maximum-intensity limit, even without surface fluxes. However, the efficiency of this frictional-convergence feedback depends crucially on how effectively boundary layer moisture convergence is converted into convective heating, which decreases rapidly as the TC inner core approaches a state of moist neutrality. This decreasing efficiency during TC intensification explains why the effect of the frictional-convergence feedback is generally small compared to that of the wind-induced surface heat exchange (WISHE) feedback under the strict conditions of slantwise moist neutrality. Examination of the reduced TC model with a constant-heating source reveals that TC intensification is not peculiar to any specific feedback mechanism but, rather, is a direct consequence of the inward advection of absolute angular momentum, regardless of feedback mechanism.

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Chanh Q. Kieu and Da-Lin Zhang

Abstract

In this study, a series of sensitivity simulations is performed to examine the processes leading to the genesis of Tropical Storm Eugene (2005) from merging vortices associated with the breakdowns of the intertropical convergence zone (ITCZ) over the eastern Pacific. This is achieved by removing or modifying one of the two vortices in the model initial conditions or one physical process during the model integration using the results presented in and as a control run. Results reveal that while the ITCZ breakdowns and subsequent poleward rollup (through a continuous potential vorticity supply) provide favorable conditions for the genesis of Eugene, the vortex merger is the most effective process in transforming weak tropical disturbances into a tropical storm. The sensitivity experiments confirm the authors’ previous conclusions that Eugene would not reach its observed tropical storm intensity in the absence of the merger and would become much shorter lived without the potential vorticity supply from the ITCZ.

It is found that the merging process is sensitive not only to larger-scale steering flows but also to the intensity of their associated cyclonic circulations and frictional convergence. When one of the vortices is initialized at a weaker intensity, the two vortices bifurcate in track and fail to merge. The frictional convergence in the boundary layer appears to play an important role in accelerating the mutual attraction of the two vortices leading to their final merger. It is also found from simulations with different storm realizations that the storm-scale cyclonic vorticity grows at the fastest rate in the lowest layers, regardless of the merger, because of the important contribution of the convergence associated with the boundary layer friction and latent heating.

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