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Daniel P. Stern and Fuqing Zhang

Abstract

In Part II of this study, idealized simulations of tropical cyclones are used to investigate the influence of vertical wind shear on the structure of warming and descent in the eye; results are compared with the no-shear simulation that was analyzed in Part I. During intensification of a tropical cyclone in a quiescent environment, time-averaged eye descent is maximized at 12–13-km height. Warming is not generally maximized at these levels, however, because the static stability is at a minimum. Consequently, the perturbation temperature is maximized at midlevels. Each of the above results remains valid for sheared tropical cyclones, and therefore shear does not systematically alter the height of the warm core.

An analysis of over 90 000 parcel trajectories yields further insight into the mechanisms of eye warming and addresses several outstanding questions regarding the character of eye descent. The rate at which parcels are stirred from the eye into the eyewall is a strong function of intensity. While stirring is large at the beginning of rapid intensification (RI), once a sufficient intensity is achieved, most parcels originating near the storm center can remain inside the eye for at least several days. Many parcels in the upper troposphere are able to descend within the eye by 5–10 km. The above results are relatively insensitive to the presence of up to 10 m s−1 of shear. In contrast, stirring in the eye–eyewall interface region is substantially enhanced by shear.

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Daniel P. Stern and Fuqing Zhang

Abstract

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.

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Daniel P. Stern and Fuqing Zhang

Abstract

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.

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Daniel P. Stern and David S. Nolan

Abstract

In this study, it is shown that the maximum tangential winds within tropical cyclones decrease with height at a percentage rate that is nearly independent of both the maximum wind speed and the radius of maximum winds (RMW). This can be seen by normalizing the profiles of maximum tangential winds V max by their respective values at 2-km height. From Doppler radar analyses, profiles of maximum normalized tangential wind V maxnorm are found to share a common shape, despite spanning a great range of intensities. There is a systematic dependence of V maxnorm on intensity and size, but it is shown to be small, and the mean profile of V maxnorm can be used to accurately “predict” the individual profiles of V max. Using Emanuel’s steady-state analytical vortex model, it is shown that V maxnorm is essentially independent of the size of the RMW. It is shown mathematically that the near independence of V maxnorm from size is due to the facts that the RMW is nearly a surface of constant absolute angular momentum M and that its outward slope increases linearly with radius. As the slope of the RMW is not a function of intensity, V maxnorm is also nearly independent of intensity in theory, and this is confirmed using Emanuel’s simple time-dependent model. In contrast to intensity, it is shown that V maxnorm increases with potential intensity. A suite of idealized simulations using the Weather Research and Forecasting model (WRF) are used to further examine the manner in which the maximum winds change with height. Above 2-km height, vertical profiles of V maxnorm are nearly independent of both intensity and size. Occasional deviations from this near-universal profile in these simulations are due to unbalanced winds, and it is proposed that this is the cause of occasional observations of maximum winds that are nearly constant with height through the midtroposphere, as in Hurricane Gloria (1985) and Hurricane Dennis (2005).

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Daniel P. Stern and David S. Nolan

Abstract

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.

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Daniel P. Stern and David S. Nolan

Abstract

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.

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Daniel P. Stern and George H. Bryan

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Extreme updrafts (≥10 m s−1) and wind gusts (≥90 m s−1) are ubiquitous within the low-level eyewall of intense tropical cyclones (TCs). Previous studies suggest that both of these features are associated with coherent subkilometer-scale vortices. Here, over 100 000 “virtual” dropsonde trajectories are examined within a large-eddy simulation (31.25-m horizontal grid spacing) of a category 5 hurricane in order to gain insight into the nature of these features and to better understand and interpret dropsonde observations. At such a high resolution, profiles of wind speed and vertical velocity from the virtual sondes are difficult to distinguish from those of real dropsondes. PDFs of the strength of updrafts and wind gusts compare well between the simulated and observed dropsondes, as do the respective range of heights over which these features are found. Individual simulated updrafts can be tracked for periods of up to several minutes, revealing structures that are both coherent and rapidly evolving. It appears that the updrafts are closely associated with vortices and wind speed maxima, consistent with previous studies. The peak instantaneous wind gusts in the simulations (up to 150 m s−1) are substantially stronger than have ever been observed. Using the virtual sondes, it is demonstrated that the probability of sampling such extremes is vanishingly small, and it is argued that actual intense TCs might also be characterized by gusts of these magnitudes.

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Daniel P. Stern, George H. Bryan, and Sim D. Aberson

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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.

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Erin B. Munsell, Fuqing Zhang, and Daniel P. Stern

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In this study, the predictability of Tropical Storm Erika (2009) is evaluated by analyzing a 60-member convection-permitting ensemble initialized with perturbations from a real-time ensemble Kalman filter (EnKF) system. Erika was forecast to intensify into a hurricane by most operational numerical models, but in reality it never exceeded 50 kt (1 kt = 0.51 m s−1). There is a fairly large spread in the final intensities of the 60 ensemble members indicating large uncertainty in the deterministic prediction of Erika's intensity at 36–48-h lead times. An investigation into which factors prevented intensification of the weaker ensemble members provides insight that may aid in the forecasting of the intensity of future tropical cyclones under similar conditions.

A variety of environmental and storm-related factors are examined, and the parameters that have the greatest relation to future intensity are determined based on ensemble sensitivity and correlation analysis. It appears that midlevel relative humidity, absolute vorticity, and the distribution of convection relative to the storm center all play a role in determining whether a given ensemble member intensifies or not. In addition, although differences in deep-layer shear among ensemble members are difficult to discern, many of the ensemble members that do not intensify fail to do so because of apparent dry air intrusions that wrap around the centers of the storms, particularly in the 700–500-hPa layer. In the presence of moderate shear, this dry air is able to penetrate the cores of the cyclones, thereby preventing further development.

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David S. Nolan, Daniel P. Stern, and Jun A. Zhang

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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 . 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 and II is provided.

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