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.

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 innercore boundary layers are presented, and the reasons for the differences are discussed.

This is the second of a two-part study of the representation of the planetary boundary layer (PBL) in highresolution 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 lowlevel 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 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.

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, timedependent, 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.Corresponding author address: Daniel P. Stern, RSMAS/MPO, 1 Although he then confuses his own terminology in the following sentence, writing that ''Shea and Gray also showed that the slope of the radius of maximum winds decrease for stronger storms''; by his convention, the slope actually increases for stronger storms.