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Jeffrey D. Kepert

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Jeffrey D. Kepert

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Spiral bands are ubiquitous features in tropical cyclones and significantly affect boundary layer thermodynamics, yet knowledge of their boundary layer dynamics is lacking. Prompted by recent work that has shown that relatively weak axisymmetric vorticity perturbations outside of the radius of maximum winds in tropical cyclones can produce remarkably strong frictional convergence, and by the observation that most secondary eyewalls appear to form by the “wrapping up” of a spiral rainband, the effect of asymmetric vorticity features that mimic spiral bands is studied. The mass field corresponding to an axisymmetric vortex with added spiral vorticity band is constructed using the nonlinear balance equation, and supplied to a three-dimensional boundary layer model. The resulting flow has strong low-level convergence and a marked updraft extending along the vorticity band and some distance downwind. There is a marked along-band wind maximum in the upper boundary layer, similar to observations, which is up to about 20% stronger than the balanced flow. A marked gradient in the inflow-layer depth exists across the band and there is an increase in the surface wind factor (the ratio of surface wind speed to nonlinear-balanced wind speed) near the band. The boundary layer dynamics near a rainband therefore form a continuum with the flow near a secondary eyewall. None of these features are due to convective momentum transports, which are absent from the model. The sensitivities of the flow to band length, width, location, crossing angle, and amplitude are examined, and the possible contribution of boundary layer dynamics to the formation of the tropical cyclone rainbands discussed.

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Jeffrey D. Kepert

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The GPS dropsonde allows observations at unprecedentedly high horizontal and vertical resolution, and of very high accuracy, within the tropical cyclone boundary layer. These data are used to document the boundary layer wind field of the core of Hurricane Georges (1998) when it was close to its maximum intensity. The spatial variability of the boundary layer wind structure is found to agree very well with the theoretical predictions in the works of Kepert and Wang. In particular, the ratio of the near-surface wind speed to that above the boundary layer is found to increase inward toward the radius of maximum winds and to be larger to the left of the track than to the right, while the low-level wind maximum is both more marked and at lower altitude on the left of the storm track than on the right. However, the expected supergradient flow in the upper boundary layer is not found, with the winds being diagnosed as close to gradient balance.

The tropical cyclone boundary layer model of Kepert and Wang is used to simulate the boundary layer flow in Hurricane Georges. The simulated wind profiles are in good agreement with the observations, and the asymmetries are well captured. In addition, it is found that the modeled flow in the upper boundary layer at the eyewall is barely supergradient, in contrast to previously studied cases. It is argued that this lack of supergradient flow is a consequence of the particular radial structure in Georges, which had a comparatively slow decrease of wind speed with radius outside the eyewall. This radial profile leads to a relatively weak gradient of inertial stability near the eyewall and a strong gradient at larger radii, and hence the tropical cyclone boundary layer dynamics described by Kepert and Wang can produce only marginally supergradient flow near the radius of maximum winds. The lack of supergradient flow, diagnosed from the observational analysis, is thus attributed to the large-scale structure of this particular storm. A companion paper presents a similar analysis for Hurricane Mitch (1998), with contrasting results.

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Jeffrey D. Kepert

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Three diagnostic models of the axisymmetric tropical cyclone boundary layer, with different levels of approximation, are applied to the problem of tropical cyclones with concentric eyewalls. The outer eyewall is shown to have an inherently stronger frictional updraft than the inner because it is in an environment of lower vorticity. Similarly, a relatively weak local enhancement of the radial vorticity gradient outside the primary radius of maximum winds can produce a significant frictional updraft, even if there is no outer wind maximum. Based on these results, it is proposed that the boundary layer contributes to the formation of outer eyewalls through a positive feedback among the local enhancement of the radial vorticity gradient, the frictional updraft, and convection. The friction-induced secondary circulation associated with the inner eyewall is shown to weaken as the outer wind maximum strengthens and/or contracts, so boundary layer processes will contribute, along with the heating-induced secondary circulation, to the weakening of the inner eyewall during an eyewall replacement cycle. An integral mass constraint on the friction-induced secondary circulation is derived and used to examine the oft-stated proposition that “the outer eyewall uses up the inflowing energy-rich boundary layer air.” Using the integral constraint, the author argues that formation of a secondary eyewall will tend to increase the total friction-induced secondary circulation and that, if the moat between the two eyewalls has a local vorticity minimum, then sufficient subsidence may occur there to maintain the primary eyewall's updraft. It is noted, however, that the enthalpy of the updraft is important as well as its mass.

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Jeffrey D. Kepert

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A new technique for objectively locating the pressure center of a hurricane from high-density observations is presented. It was designed particularly for use with global positioning system (GPS) dropsonde observations of pressure within the cyclone core, but is also useful for aircraft data. Unlike previously documented techniques, it uses pressure data rather than wind, and is therefore useable in the boundary layer. A further advantage is that it can utilize data taken over a period of several hours, while previous techniques required the use of nearly instantaneous data. It is shown that, for data coverage typical of research aircraft missions, the technique can locate the cyclone center with a root-mean-square error of a few kilometers, and the cyclone motion with a root-mean-square error of a few tenths of a meter per second. The application of an automated objective quality control procedure to the method is also discussed.

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Jeffrey D. Kepert

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The transient response of the tropical cyclone boundary layer is studied using linearized and nonlinear models, with particular focus on the frictionally forced vertical motion. The impulsively started, linearized tropical cyclone boundary layer is shown to adjust to its equilibrium solution via a series of decaying oscillations with the inertial period . In the nonlinear case, the oscillation period is slightly lengthened by inward advection of the slower-evolving flow from larger radii, but the oscillations decay more quickly. In an idealized cyclone with small sinusoidal oscillations superimposed on the gradient wind, the equilibrium nonlinear boundary layer acts as a low-pass filter with pass length scaling as , where is the 10-m frictional inflow. This filter is absent from the linearized boundary layer. The eyewall frictional updraft is similarly displaced inward of the radius of maximum winds (RMW) by a distance that scales with , owing to nonlinear overshoot of the inflowing air as it crosses the relatively sharp increase in I near the eyewall. This displacement is smaller (other things being equal) when the RMW is small, and greater when it is large, including in secondary eyewalls. The dependence of this distance on may explain, at least partially, why observed RMW are seldom less than 20 km, why storms with relatively peaked radial profiles of wind speed can intensify more rapidly, and why some secondary eyewalls initially contract rapidly with little intensification, then contract more slowly while intensifying.

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Jeffrey D. Kepert

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Part I of this paper presented a detailed analysis of the boundary layer of Hurricane Georges (1998), based mainly on the newly available high-resolution GPS dropsonde data. Here, similar techniques and data are used to study Hurricane Mitch (1998). In contrast to Hurricane Georges, the flow in the middle to upper boundary layer near the eyewall is found to be strongly supergradient, with the imbalance being statistically significant. The reason for the difference is shown to be the different radial structure of the storms, in that outside of the radius of maximum winds, the wind decreases much more quickly in Mitch than in Georges. Hurricane Mitch was close to inertially neutral at large radius, with a strong angular momentum gradient near the radius of maximum winds. Kepert and Wang predict strongly supergradient flow in the upper boundary layer near the radius of maximum winds in this situation; the observational analysis is thus in good agreement with their theory. The wind reduction factor (i.e., ratio of a near-surface wind speed to that at some level further aloft) is found to increase inward toward the radius of maximum winds, in accordance with theoretical predictions and the analysis by Franklin et al. Marked asymmetries in the boundary layer wind field and in the eyewall convection are shown to be consistent with asymmetric surface friction due to the storm’s proximity to land, rather than to motion. The boundary layer flow was simulated using Kepert and Wang’s model, forced by the observed storm motion, radial profile of gradient wind, and coastline position; and good agreement with the observations was obtained.

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Jeffrey D. Kepert

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The boundary layer in a tropical cyclone is in some respects unlike that elsewhere in the atmosphere. It is therefore necessary to evaluate boundary layer parameterizations for their suitability for use in tropical cyclone simulation. Previous work has shown substantial sensitivity to the choice of scheme and identified specific shortcomings in some schemes, but without recommending which schemes are most suitable. Here, several schemes, representative of those available in popular modeling systems, are reviewed and applied in a simplified modeling framework. Based on a comparison with observations and on theoretical grounds, one popular class of schemes is shown to be badly flawed in that it incorrectly predicts the near-surface wind profile, and therefore should not be used. Another is shown to be sensitive to diagnosis of the boundary layer depth, a difficult problem in the core of the tropical cyclone, and caution is advised. The Louis boundary layer scheme and a higher-order closure scheme are, so far as can be discerned, without major problems, and are recommended. The recommendations and discussion herein should help users make a more informed choice of boundary layer parameterization, and to better understand the results that they obtain.

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Juliane Schwendike and Jeffrey D. Kepert

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This paper describes the boundary layer wind structure and dynamics of Hurricanes Danielle (1998) and Isabel (2003), based on the analysis of high-resolution global positioning system dropwindsonde data and simulation of the flow by a three-dimensional boundary layer model produced by Kepert and Wang. The observations show that the hurricane boundary layer has a complex three-dimensional structure with large variability over small distances. The analysis emphasizes three aspects: the degree of gradient-wind balance, the radially varying depth of the boundary layer, and the strength of the near-surface wind speed relative to that at a higher level. Each aspect is compared both with results obtained in a simulation of the individual storm by Kepert and Wang’s model and with theoretical predictions. The observations show that the boundary layer depth decreases toward the center of the storm, consistent with theoretical arguments. The strongest azimuthal winds occur near the top of, but still within, the frictional inflow layer. These strong azimuthal winds are marginally supergradient in Hurricane Danielle but strongly so in Hurricane Isabel, where the imbalance amounts to approximately 10 m s−1 near the radius of maximum winds and is statistically significantly nonzero. This layer of supergradient flow is surmounted by a layer of outflow, in which the flow returns to gradient balance. The maximum storm-relative azimuthal wind occurs in the left front of Hurricane Danielle, and the strongest inflow is located in the right front. These asymmetries rotate anticyclonically with height, but there is also a clear wavenumber-2 asymmetry superimposed, which shows less rotation with height and is possibly forced by environmental factors associated with the storm’s impending recurvature. In Hurricane Isabel, the azimuthal wind maximum is located in the left rear and the inflow maximum in the left front, with neither showing much tendency to vary in azimuth with height. The ratio of the near-surface wind speed to that farther aloft increases toward the storm center for both storms. The largest values are located near the radius of maximum wind, and in general higher values are found on the left of the storm’s track than on the right. Simulations of the two storms with the boundary layer model are able to explain several of these factors; they also show some ability to reproduce individual dropsonde wind observed profiles. Important is that the model predicts weakly supergradient flow in Danielle and strongly supergradient flow in Isabel, in excellent agreement with the observational analysis. Based on these simulations, physical arguments, and earlier studies, the authors conclude that the differences between these storms in this respect result from their differing radial profiles of gradient wind and argue that the occurrence of supergradient flow in the upper boundary layer of individual hurricanes should be readily predictable.

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Jeffrey D. Kepert, Juliane Schwendike, and Hamish Ramsay

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Plausible diagnostics for the top of the tropical cyclone boundary layer include (i) the top of the layer of strong frictional inflow and (ii) the top of the “well mixed” layer, that is, the layer over which potential temperature θ is approximately constant. Observations show that these two candidate definitions give markedly different results in practice, with the inflow layer being roughly twice the depth of the layer of nearly constant θ. Here, the authors will present an analysis of the thermodynamics of the tropical cyclone boundary layer derived from an axisymmetric model. The authors show that the marked dry static stability in the upper part of the inflow layer is due largely to diabatic effects. The radial wind varies strongly with height and, therefore, so does radial advection of θ. This process also stabilizes the boundary layer but to a lesser degree than diabatic effects. The authors also show that this differential radial advection contributes to the observed superadiabatic layer adjacent to the ocean surface, where the vertical gradient of the radial wind is reversed, but that the main cause of this unstable layer is heating from turbulent dissipation. The top of the well-mixed layer is thus distinct from the top of the boundary layer in tropical cyclones. The top of the inflow layer is a better proxy for the top of the boundary layer but is not without limitations. These results may have implications for boundary layer parameterizations that diagnose the boundary layer depth from thermodynamic, or partly thermodynamic, criteria.

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