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The warm-core structure of Hurricane Earl (2010) is examined on four different days, spanning periods of both rapid intensification (RI) and weakening, using high-altitude dropsondes from both the inner core and the environment, as well as a convection-permitting numerical forecast. During RI, strong warming occurred at all heights, while during rapid weakening, little temperature change was observed, implying the likelihood of substantial (unobserved) cooling above flight level (12 km). Using a local environmental reference state yields a perturbation temperature profile with two distinct maxima of approximately equal magnitude: one at 4–6-km and the other at 9–12-km height. However, using a climatological-mean sounding instead results in the upper-level maximum being substantially stronger than the midlevel maximum. This difference results from the fact that the local environment of Earl was warmer than the climatological mean and that this relative warmth increased with height. There is no obvious systematic relationship between the height of the warm core and either intensity or intensity change for either reference state. The structure of the warm core simulated by the convection-permitting forecast compares well with the observations for the periods encompassing RI. Later, an eyewall replacement cycle went unforecast, and increased errors in the warm-core structure are likely related to errors in the forecast wind structure. At most times, the simulated radius of maximum winds (RMW) had too great of an outward slope (the upper-level RMW was too large), and this is likely also associated with structural biases in the warm core.

In the widely accepted convective ring model of tropical cyclone intensification, the intensification of the maximum winds and the contraction of the radius of maximum winds (RMW) occur simultaneously. This study shows that in idealized numerical simulations, contraction and intensification commence at the same time, but that contraction ceases long before peak intensity is achieved. The rate of contraction decreases with increasing initial size, while the rate of intensification does not vary systematically with initial size. Utilizing a diagnostic expression for the rate of contraction, it is shown that contraction is halted in association with a rapid increase in the sharpness of the tangential wind profile near the RMW and is not due to changes in the radial gradient of the tangential wind tendency. It is shown that a number of real storms exhibit a relationship between contraction and intensification that is similar to what is seen in the idealized simulations. In particular, the statistical distribution of intensifying tropical cyclones indicates that, for major hurricanes, most contraction is completed prior to most intensification. By forcing a linearized vortex model with the diabatic heating and frictional tendencies from a simulation, it is possible to qualitatively reproduce the simulated secondary circulation and separately examine the vortex responses to heating and friction. It is shown that heating and friction both contribute substantially to boundary layer inflow. They also both contribute to the contraction of the RMW, as the positive wind tendency from heating-induced inflow is maximized inside of the RMW, while the net negative wind tendency from friction and frictionally induced inflow is maximized outside of the RMW.

The warm-core structure of tropical cyclones is examined in idealized simulations using the Weather Research and Forecasting (WRF) Model. The maximum perturbation temperature in a control simulation occurs in the midtroposphere (5–6 km), in contrast to the upper-tropospheric (>10 km) warm core that is widely believed to be typical. This conventional view is reassessed and found to be largely based on three case studies, and it is argued that the “typical” warm-core structure is actually not well known. In the control simulation, the height of the warm core is nearly constant over a wide range of intensities. From additional simulations in which either the size of the initial vortex or the microphysics parameterization is varied, it is shown that the warm core is generally found at 4–8 km. A secondary maximum often develops near 13–14 km but is almost always weaker than the primary warm core. It is demonstrated that microwave remote sensing instruments are of insufficient resolution to detect this midlevel warm core, and the conclusions of some studies that have utilized these instruments may not be reliable. Using simple arguments based on thermal wind balance, it is shown that the height of the warm core is not necessarily related to either the height where the vertical shear of the tangential winds is maximized or the height where the radial temperature gradient is maximized. In particular, changes in the height of the warm core need not imply changes in either the intensity of the storm or in the manner in which the winds in the eyewall decay with height.

In this first part of a two-part study, the mechanisms that accomplish the warming in the eye of tropical cyclones are investigated through a potential temperature budget analysis of an idealized simulation. The spatial structure of warming varies substantially with time. During rapid intensification (RI), the warming is maximized at midlevels, and as a consequence, the perturbation temperature is always maximized in this region. At the start of RI, total advection of potential temperature is the only significant term contributing to warming the eye. However, for a substantial portion of RI, the region of most rapid warming actually undergoes mean ascent. The net advective warming is shown to be a result of eddy radial advection of potential temperature, dominated by a wavenumber-1 feature that is likely due to a dynamic instability. At a sufficient intensity, mean vertical advective warming becomes concentrated in a narrow zone just inward of the eyewall. In agreement with prior studies, this advective tendency is largely canceled by diabatic cooling. Subgrid-scale horizontal diffusion of potential temperature plays a surprisingly large role in the maintenance of the warm-core structure, and when the storm is intense, yields a negative tendency that can be of the same magnitude as advective warming.

In this study, the first of two parts, the planetary boundary layer (PBL) depicted in high-resolution Weather Research and Forecast Model (WRF) simulations of Hurricane Isabel (2003) is studied and evaluated by direct comparisons with in situ data obtained during the Coupled Boundary Layer and Air–Sea Transfer Experiment (CBLAST). In particular, two boundary layer schemes are evaluated: the Yonsei University (YSU) parameterization and the Mellor–Yamada–Janjić (MYJ) parameterization. Investigation of these schemes is useful since they are available for use with WRF, are both widely used, and are based on entirely different methods for simulating the PBL. In this first part, the model domains and initialization are described. For additional realism of the low-level thermodynamic environment, a simple mixed layer ocean model is used to simulate ocean cooling. The YSU and MYJ schemes are discussed, along with some modifications. Standard measures of the accuracy of the hurricane simulations, such as track, maximum surface wind speed, and minimum surface pressure are described for a variety of parameter choices and for the two parameterizations. The effects on track and intensity of increased horizontal and vertical resolutions are also shown. A modification of the original YSU and MYJ schemes to have ocean roughness lengths more in agreement with recent studies considerably improves the results of both schemes. Instantaneous wind maxima on the innermost grid with 1.33-km resolution are shown to be an accurate representation of the simulated 1-min sustained winds. The simulated boundary layers are evaluated by direct comparison of the PBL as simulated and as observed by in situ data from the CBLAST experiment in the “outer core” region of the storm. The two PBL schemes and their modified counterparts reproduce the observed PBL remarkably well. Comparisons are also made to the observed vertical fluxes of momentum, heat, and moisture. In Part II, the detailed comparisons of the intensities and structures of the simulated and observed inner-core boundary layers are presented, and the reasons for the differences are discussed.

Previous studies have found surprisingly strong vertical motions in low levels of some tropical cyclones. In this study, all available dropsondes (12 000) within tropical cyclones during 1997–2013 are examined, in order to create a dataset of the most extreme updrafts (10 m s−1; 169 sondes) and wind speeds (90 m s−1; 64 sondes). It is shown that extreme low-level (0–3 km) updrafts are ubiquitous within intense (category 4 and 5) tropical cyclones, and that few such updrafts have been observed within weaker storms. These extreme updrafts, which are almost exclusively found within the eyewall just inward of the radius of maximum winds, sometimes occur in close association with extreme horizontal wind speeds. Consistent with previous studies, it is suggested that both the extremes in vertical velocity and wind speed are associated with small-scale (1 km) vortices that exist along the eye–eyewall interface. As a substantial number of updrafts are found within a kilometer of the surface, it can be shown that it is implausible for buoyancy to be the primary mechanism for vertical acceleration. Additionally, the azimuthal distribution of both the extreme updrafts and wind speeds is strongly associated with the orientation of the environmental vertical wind shear.

This is the second of a two-part study of the representation of the planetary boundary layer (PBL) in high-resolution Weather Research and Forecast Model (WRF) simulations of Hurricane Isabel (2003). The Yonsei University (YSU) PBL parameterization and the Mellor–Yamada–Janjić (MYJ) PBL parameterization are evaluated by direct comparison to in situ data obtained by research aircraft. The numerical model, simulation design, details of the PBL schemes, and the representation of the boundary layer in the outer-core were presented in Part I. This part presents a detailed study of the inner-core PBL, including its axisymmetric and asymmetric structures, and comparisons to analyses of dropsonde data from previous studies. Although neither PBL scheme was designed specifically for hurricane conditions, their simulated boundary layers are reasonably good representations of the observed boundary layer. Both schemes reproduce certain unique features of the hurricane boundary layer, such as the separate depths of the well-mixed layer and the inflow layer, and the pronounced wind speed maxima near the top of the inflow layer. Modification of the original YSU and MYJ schemes to have ocean roughness lengths more in agreement with recent studies considerably improves the results of both schemes. Even with these improvements, the MYJ consistently produces larger frictional tendencies in the boundary layer than the YSU scheme, leading to a stronger low-level inflow and a stronger azimuthal wind maximum at the top of the boundary layer. For both schemes, differences in the low-level asymmetries between the simulated and observed wind fields appear to be related to eyewall asymmetries forced by environmental wind shear. The effects of varying horizontal and vertical resolutions are also considered. Increasing the vertical resolution in the PBL results in minor improvements in the inner-core structures. Increasing the horizontal resolution around the eyewall also leads to improved boundary layers, as well as an improvement of the vertical structure of the inner-core wind field. A summary and discussion of the results of both Parts I and II is provided.

In tropical cyclones (TCs), the peak wind speed is typically found near the top of the boundary layer (approximately 0.5–1 km). Recently, it was shown that in a few observed TCs, the wind speed within the eyewall can increase with height within the midtroposphere, resulting in a secondary local maximum at 4–5 km. This study presents additional evidence of such an atypical structure, using dropsonde and Doppler radar observations from Hurricane Patricia (2015). Near peak intensity, Patricia exhibited an absolute wind speed maximum at 5–6-km height, along with a weaker boundary layer maximum. Idealized simulations and a diagnostic boundary layer model are used to investigate the dynamics that result in these atypical wind profiles, which only occur in TCs that are very intense (surface wind speed > 50 m s −1 ) and/or very small (radius of maximum winds < 20 km). The existence of multiple maxima in wind speed is a consequence of an inertial oscillation that is driven ultimately by surface friction. The vertical oscillation in the radial velocity results in a series of unbalanced tangential wind jets, whose magnitude and structure can manifest as a midlevel wind speed maximum. The wavelength of the inertial oscillation increases with vertical mixing length l ∞ in a turbulence parameterization, and no midlevel wind speed maximum occurs when l ∞ is large. Consistent with theory, the wavelength in the simulations scales with (2 K / I ) 1/2 , where K is the (vertical) turbulent diffusivity, and I 2 is the inertial stability. This scaling is used to explain why only small and/or strong TCs exhibit midlevel wind speed maxima.

Prior studies of the linear response to asymmetric heating of a balanced vortex showed that the resulting intensity change could be very closely approximated by computing the purely symmetric response to the azimuthally averaged heating. The symmetric response to the purely asymmetric part of the heating was found to have a very small and most often negative impact on the intensity of the vortex. This result stands in contrast to many previous studies that used asymmetric vorticity perturbations, which suggested that purely asymmetric forcing could lead to vortex intensification. The issue is revisited with an improved model and some new methods of analysis. The model equations have been changed to be more consistent with the anelastic approximation, but valid for a radially varying reference state. Expressions for kinetic and available potential energies are presented for both asymmetric and symmetric motions, and these are used to quantify the flow of energy from localized, asymmetric heat sources to kinetic energy of the wind field of the symmetric vortex. Previous conclusions were based on simulations that used instantaneous temperature perturbations to represent rapid heat release in cumulus updrafts. Purely asymmetric heat sources that evolve over time and move with the local mean wind are shown to also cause vortex weakening. Weakening of the symmetric vortex is due to extraction of energy by the evolving asymmetries that undergo significant transient growth due to downgradient transport of momentum across the radial and vertical shears of the symmetric wind field. While much of this energy is returned during the axisymmetrization of the resulting potential vorticity anomalies, there is typically a net loss of energy for the symmetric vortex. Some variations on the rotation rate and duration of the heat sources can lead to intensification rather than weakening, as does a deeper (more barotropic) vertical structure of the symmetric vortex. However, it is reaffirmed that these asymmetrically forced changes are small compared to the response to the azimuthally averaged heating of an isolated heat source. Following the work of Hack and Schubert, the efficiency of the intensification process, defined as the ratio of injected heat energy to the kinetic energy change of the symmetric vortex, is computed for vortices of different sizes and strengths. In the limit of small perturbations, the efficiency does not depend on the temporal distribution of the heating. The efficiency is shown to increase with the intensity of the vortex and with the Coriolis parameter, with substantial efficiency increases for weak vortices. Potential applications of these results for predicting tropical cyclone formation and rapid development are discussed.

A few commonly held beliefs regarding the vertical structure of tropical cyclones drawn from prior studies, both observational and theoretical, are examined in this study. One of these beliefs is that the outward slope of the radius of maximum winds (RMW) is a function of the size of the RMW. Another belief is that the outward slope of the RMW is also a function of the intensity of the storm. Specifically, Shea and Gray found that the RMW becomes increasingly vertical with increasing intensity and decreasing radius. The third belief evaluated here is that the RMW is a surface of constant absolute angular momentum M. These three conventional wisdoms of vertical structure are revisited with a dataset of three-dimensional Doppler wind analyses, comprising seven hurricanes on 17 different days. Azimuthal mean tangential winds are calculated for each storm, and the slopes of the RMW and M surfaces are objectively determined. The outward slope of the RMW is shown to increase with radius, which supports prior studies. In contrast to prior results, no relationship is found between the slope of the RMW and intensity. It is shown that the RMW is indeed closely approximated by an M surface for the majority of storms. However, there is a small but systematic tendency for M to decrease upward along the RMW. Utilizing Emanuel’s analytical hurricane model, a new equation is derived for the slope of the RMW in radius–pressure space. This predicts a linear increase of slope with radius and essentially no dependence of slope on intensity. An exactly analogous equation can be derived in log-pressure height coordinates, and a numerical solution yields the same conclusions in geometric height coordinates. These conclusions are further supported by the results of simulations utilizing Emanuel’s simple, time-dependent, axisymmetric hurricane model. As both the model and the analytical theory are governed by the dual constraints of thermal wind balance and slantwise moist neutrality, it is demonstrated that it is these two assumptions that require the slope of the RMW to be a function of its size but not of the intensity of the storm. Finally, it is shown that within the context of Emanuel’s theory, the RMW must very closely approximate an M surface through most of the depth of the vortex.