Daniel P. Stern

Tropical cyclone intensification from asymmetric convection : Energetics and efficiency

Abstract 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 sour...

Evaluation of Planetary Boundary Layer Parameterizations in Tropical Cyclones by Comparison of In Situ Observations and High-Resolution Simulations of Hurricane Isabel (2003). Part I: Initialization, Maximum Winds, and the Outer-Core Boundary Layer

In this study, thefirst of two parts, the planetary boundarylayer (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‐Janjic´ (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 describedforavarietyofparameterchoicesandforthetwoparameterizations.Theeffectsontrackandintensity 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 maximaon the innermost grid with 1.33-kmresolutionare shown to be an accurate representation of the simulated 1-min sustained winds. Thesimulatedboundarylayersareevaluatedby directcomparison ofthePBLassimulatedandasobserved by in situ data from the CBLAST experiment in the ‘‘outer core’’ region of the storm. The two PBL schemes and their modifiedcounterparts reproduce the observed PBL remarkably well. Comparisonsare 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.

Evaluation of Planetary Boundary Layer Parameterizations in Tropical Cyclones by Comparison of In Situ Observations and High-Resolution Simulations of Hurricane Isabel (2003). Part II: Inner-Core Boundary Layer and Eyewall Structure

This is the second of a two-part study of the representation of the planetary boundary layer (PBL) in highresolutionWeatherResearchandForecastModel(WRF) simulationsofHurricaneIsabel(2003).TheYonsei University (YSU) PBL parameterization and the Mellor‐Yamada‐Janjic´ (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.

Reexamining the Vertical Structure of Tangential Winds in Tropical Cyclones: Observations and Theory

A few commonly held beliefs regarding the vertical structure of tropical cyclones drawn from prior studies, bothobservationalandtheoretical,areexaminedinthisstudy.Oneofthesebeliefsisthattheoutwardslopeof the radius of maximumwinds (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,andtheslopesoftheRMWandMsurfacesareobjectivelydetermined.TheoutwardslopeoftheRMW 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 essentiallyno dependence of slope on intensity.An exactly analogous equationcan be derivedin 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 assumptionsthat requirethe slope of the RMW to be a functionof its size but not of the intensityof 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.

On the Height of the Warm Core in Tropical Cyclones

AbstractThe 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 ...

Revisiting the Relationship between Eyewall Contraction and Intensification

AbstractIn 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 ...

How Does the Eye Warm? Part I: A Potential Temperature Budget Analysis of an Idealized Tropical Cyclone

AbstractIn 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 adve...

On the Vertical Decay Rate of the Maximum Tangential Winds in Tropical Cyclones

In this study, it is shown that the maximumtangential winds within tropicalcyclones 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 Vmax by their respective values at 2-km height. From Doppler radar analyses, profiles of maximum normalized tangential wind Vmaxnorm are found to share a common shape, despite spanning a great range of intensities. There is a systematic dependence of Vmaxnorm on intensity and size, but it is shown to be small, and the mean profile of Vmaxnorm can be used to accurately ‘‘predict’’ the individual profiles of Vmax. Using Emanuel’s steady-state analytical vortex model, it is shown that Vmaxnorm is essentially independent of the size of the RMW. It is shown mathematically that the near independence of Vmaxnorm 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,Vmaxnormis 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 Vmaxnorm 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 Vmaxnorm 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).

Predictability and Dynamics of a Nonintensifying Tropical Storm: Erika (2009)

AbstractIn 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 Erikas 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 hu...

An Expanded Dataset of Hurricane Eyewall Sizes and Slopes

AbstractUsing airborne Doppler radar data from 39 flights into hurricanes from 2004 to 2010, the authors examine the outward slope of the eyewall, revisiting the recent studies of Stern and Nolan. The slope of the radius of maximum winds (RMW) is found to increase nearly linearly with size and is uncorrelated with intensity. The slope of the eyewall absolute angular momentum surface M increases with increasing size (strong correlation) and decreases with increasing intensity (weak to moderate correlation). Two other measures of eyewall slope are also investigated: the 20-dBZ reflectivity isosurface (dBZ20) and the radius of maximum azimuthal-mean updraft (RWMAX). The slopes of both dBZ20 and RWMAX increase with their size. The slope of dBZ20 decreases with intensity, though the correlation is weak, while the slope of RWMAX is uncorrelated with intensity. The absolute angular momentum decreases on average along the RMW by 9% from 2- to 8-km heights. With this larger dataset, the previous results are genera...