Tropical Cyclone Boundary Layer Research Articles

Supergradient Winds in Simulated Tropical Cyclones

Abstract In a previous paper a formula was derived for the maximum potential intensity of the tangential wind in a tropical cyclone called PI+. The formula, PI+2 = EPI2 + αrmwmηm, where EPI is the maximum potential intensity of the gradient wind and αrmwmηm represents the supergradient winds. The latter term is the product of the radius rm, the vertical velocity wm, the azimuthal vorticity ηm at the radius and height of the maximum tangential wind (rm, zm), and the (nearly constant) α. Examination of a series of simulations of idealized tropical cyclones indicate an increasing contribution from the supergradient-wind term to PI+ as the radius of maximum wind increases. In the present paper, the physical content of the supergradient-wind term is developed showing how it is directly related to tropical cyclone boundary layer dynamics. It is found that , where −umin is the maximum boundary layer radial inflow velocity and lυ(z) is the vertical mixing length.

Wind Gusts Associated with Tornado-Scale Vortices in the Tropical Cyclone Boundary Layer: A Numerical Simulation

It has been demonstrated that the tornado-scale vortex (TSV) is one of the fine-scale structures associated with extreme updrafts in the tropical cyclone boundary layer (TCBL), but the relationship between surface wind gusts and TSVs is still unclear. In this study, the one-second model output simulated in the Weather Research and Forecast (WRF) model with the large eddy simulation (WRF-LES) is used to investigate the relationships between TSVs and surface wind gusts. Results show that surface wind gust factors in the regions where TSVs are prevalent are significantly larger than those in other regions. 88% of the maximum gust factors associated with TSVs (vertical velocity larger than 20 m s−1) are larger than 1.25 (gust factors larger than 1.25 account for only 1% of the 1-min gust factors in the TC inner core), and the mean maximum 1-min gust factor associated with a TSV is larger than 1.3, while the mean 1-min gust factor in the TC inner core is only 1.1. The surface gust factors associated with TSVs in tropical cyclone eyewall can reach about 1.8, which can cause severe surface wind hazards. This study suggests that potential risk will increase in the regions where TSVs are prevalent because of the large wind gusts and gust factors. Finer real-time observations are needed to monitor the evolution of TSVs for improving the operational TC-related surface gust warnings.

Vertical Eddy Diffusivity in the Tropical Cyclone Boundary Layer during Landfall

This study investigated surface layer turbulence characteristics and parameters using 20 Hz eddy covariance data collected from five heights with winds up to 42.27 m s−1 when Super Typhoon Maria (2018) made landfall. The dependence of these parameters including eddy diffusivities for momentum (Km) and heat (Kt), vertical mixing length (Lm), and strain rate (S) on wind speed (un), height, and radii was examined. The results show that momentum fluxes (τ), turbulent kinetic energy (TKE), and Km had a parabolic dependence on un at all five heights outside three times the RMW, the maximum of Km and S increased from the surface to a maximum value at a height of 50 m, and then decreased with greater heights. However, Km and S were nearly constant with wind and height within two to three times the RMW from the TC center before landfall. Our results also found the |τ|, TKE, and Km were larger than over oceanic areas at any given wind, and Km was about one to two orders of magnitude bigger than Kt. The turbulence characteristic and parameters’ change with height and radii from the TC center should be accounted for in sub-grid scale physical processes of momentum fluxes in numerical TC models.

Deep Learning Parameterization of Tropical Cyclone Boundary Layer

Deep Learning Parameterization of Tropical Cyclone Boundary Layer

Idealized simulations of the diurnal variation within the tropical cyclone boundary layer

Idealized simulations of the diurnal variation within the tropical cyclone boundary layer

Sensitivity of the Tropical Cyclone Boundary Layer to Vertical Diffusion in a Turbulent Kinetic Energy‐Based Boundary Layer Parameterization Scheme at Gray‐Zone Resolution

AbstractThe impact of eddy diffusivities in the Mellor–Yamada–Nakanishi–Niino (MYNN) boundary layer parameterization on the fine‐scale turbulence and intensity of tropical cyclone (TC) simulations at gray‐zone resolution was investigated through comparison with large‐eddy simulation (LES) and observations. A series of idealized experiments were performed with varying vertical mixing lengths using the Advanced Research version of the Weather Research and Forecasting model. For enhanced eddy diffusivity cases, the storm intensity was sensitive to the eddy diffusivities and reducing the overestimation of the eddy diffusivities caused a significant increase in intensity. For the reduced eddy diffusivity cases, the TC intensity was marginally influenced by the eddy diffusivities. However, the reduction in eddy diffusivities effectively reproduced the fine‐scale turbulence. The stronger the resolved fine‐scale turbulence that could be established, the more frictional tendencies near the location of maximum wind were provided to the TC, the closer it was to the reference LES and observations. The resolved turbulence also had consequences in terms of preventing the wind gradient from increasing, which was one of the primary reasons for the discrepancies in the nonlinear intensity and fine‐scale features. The results of this study demonstrate that the modification of eddy diffusivities in the MYNN scheme can measure or guide improvements in the simulation of TC boundary layer fine‐scale features and intensity when operating at the gray‐zone resolution.

Assessing the Sensitivity of the Tropical Cyclone Boundary Layer to the Parameterization of Momentum Flux in the Community Earth System Model

Abstract Recent studies have demonstrated that high-resolution (∼25 km) Earth System Models (ESMs) have the potential to skillfully predict tropical cyclone (TC) occurrence and intensity. However, biases in ESM TCs still exist, largely due to the need to parameterize processes such as boundary layer (PBL) turbulence. Building on past studies, we hypothesize that the depiction of the TC PBL in ESMs is sensitive to the configuration of the PBL parameterization scheme, and that the targeted perturbation of tunable parameters can reduce biases. The Morris one-at-a-time (MOAT) method is implemented to assess the sensitivity of the TC PBL to tunable parameters in the PBL scheme in an idealized configuration of the Community Atmosphere Model, version 6 (CAM6). The MOAT method objectively identifies several parameters in an experimental version of the Cloud Layers Unified by Binormals (CLUBB) scheme that appreciably influence the structure of the TC PBL. We then perturb the parameters identified by the MOAT method within a suite of CAM6 ensemble simulations and find a reduction in model biases compared to observations and a high-resolution, cloud-resolving model. We demonstrate that the high-sensitivity parameters are tied to PBL processes that reduce turbulent mixing and effective eddy diffusivity, and that in CAM6 these parameters alter the TC PBL in a manner consistent with past modeling studies. In this way, we provide an initial identification of process-based input parameters that, when altered, have the potential to improve TC predictions by ESMs.

The Evolution of Asymmetries in the Tropical Cyclone Boundary Layer Wind Field during Landfall

Abstract The evolution of the tropical cyclone boundary layer (TCBL) wind field before landfall is examined in this study. As noted in previous studies, a typical TCBL wind structure over the ocean features a supergradient boundary layer jet to the left of motion and Earth-relative maximum winds to the right. However, the detailed response of the wind field to frictional convergence at the coastline is less well known. Here, idealized numerical simulations reveal an increase in the offshore radial and vertical velocities beginning once the TC is roughly 200 km offshore. This increase in the radial velocity is attributed to the sudden decrease in frictional stress once the highly agradient flow crosses the offshore coastline. Enhanced advection of angular momentum by the secondary circulation forces a strengthening of the supergradient jet near the top of the TCBL. Sensitivity experiments reveal that the coastal roughness discontinuity dominates the friction asymmetry due to motion. Additionally, increasing the inland roughness through increasing the aerodynamic roughness length enhances the observed asymmetries. Last, a brief analysis of in situ surface wind data collected during the landfall of three Gulf of Mexico hurricanes is provided and compared to the idealized simulations. Despite the limited in situ data, the observations generally support the simulations. The results here imply that assumptions about the TCBL wind field based on observations from over horizontally homogeneous surface types—which have been well documented by previous studies—are inappropriate for use near strong frictional heterogeneity.

The Effects of Environmental Wind Shear Direction on Tropical Cyclone Boundary Layer Thermodynamics and Intensity Change from Multiple Observational Datasets

Abstract The relationship between deep-layer environmental wind shear direction and tropical cyclone (TC) boundary layer thermodynamic structures is explored in multiple independent databases. Analyses derived from the tropical cyclone buoy database (TCBD) show that when TCs experience northerly component shear, the 10-m equivalent potential temperature θe tends to be more symmetric than when shear has a southerly component. The primary asymmetry in θe in TCs experiencing southerly component shear is radially outward from 2 times the radius of maximum wind speed, with the left-of-shear quadrants having lower θe by 4–6 K than the right-of-shear quadrants. As with the TCBD, an asymmetric distribution of 10-m θe for TCs experiencing southerly component shear and a symmetric distribution of 10-m θe for TCs experiencing northerly component shear was found using composite observations from dropsondes. These analyses show that differences in the degree of symmetry near the sea surface extend through the depth of the boundary layer. Additionally, mean dropsonde profiles illustrate that TCs experiencing northerly component shear are more potentially unstable between 500- and 1000-m altitude, signaling a more favorable environment for the development of surface-based convection in rainband regions. Analyses from the Statistical Hurricane Intensity Prediction Scheme (SHIPS) database show that subsequent strengthening for TCs in the Atlantic Ocean basin preferentially occurs in northerly component deep-layer environmental wind shear environments whereas subsequent weakening preferentially occurs in southerly component wind shear environments, which further illustrates that the asymmetric distribution of boundary layer thermodynamics is unfavorable for TC intensification. These differences emphasize the impact of deep-layer wind shear direction on TC intensity changes that likely result from the superposition of large-scale advection with the shear-relative asymmetries in TC structure. Significance Statement This research investigates how the direction of the winds surrounding the storm impacts the strength of a tropical cyclone. Analyses from this study illustrate that when the winds come from the south the atmospheric boundary layer has a cool and dry side along with a warm and moist side. When the large-scale winds come from the north, temperature and moisture conditions are more uniform throughout the boundary layer. Consequently, results from tropical cyclone climatology show that winds observed to come from the north favor subsequent intensification. These relationships illustrate that tropical cyclone structure and intensity are directly influenced by their surrounding environments and that knowledge of the wind environment could help to improve future forecasts of tropical cyclone intensity change.

An Investigation of the Impact of Different Turbulence Schemes on the Tropical Cyclone Boundary Layer at Turbulent Gray‐Zone Resolution

AbstractAccurately resolving turbulence in the tropical‐cyclone boundary layer (TCBL) is crucial for realistic simulations of tropical cyclones (TCs), but how well the fine‐scale structure of the simulated TCBL can be reproduced at gray‐zone resolutions by state‐of‐the‐art planetary boundary layer (PBL) parameterization schemes, and why the simulated fine‐scale structure is so sensitive to the PBL scheme, are yet to be evaluated and understood. To address these issues, a series of numerical experiments under idealized conditions were conducted using the advanced research weather research and forecasting (WRF‐ARW) model at 500 and 166 m grid spacing. An 18‐hr WRF‐ARW large‐eddy simulation (LES) with a 55‐m grid spacing based on the nonlinear backscatter and anisotropy subfilter‐scale (NBA‐SFS) stress scheme was used as reference (RLES). Results from experiments using five different PBL schemes, that is, two conventional schemes—the Yonsei University (YSU) and the original MYNN (termed MYNN1)—two scale‐aware schemes—the Shin‐Hong (S‐H) and the revised MYNN (termed MYNN2)—and the coarse‐resolution LES (CLES), were subsequently compared with the RLES. The YSU and S‐H not only produced better simulations of TC intensity and structure than the other three PBL schemes, but also produced a fine‐scale turbulent structure reasonably well compared with the RLES. Discrepancies in the simulated fine‐scale structure among the PBL schemes result primarily from the different strength of vertical mixing, which could be reduced by the scale‐aware option. Results from a series of sensitivity experiments with a 166‐m grid spacing demonstrate that the scale‐aware S‐H can significantly improve the finer resolution simulations than the conventional YSU at relatively finer grid spacing at gray zone.

Storm‐Scale and Fine‐Scale Boundary Layer Structures of Tropical Cyclones Simulated With the WRF‐LES Framework

AbstractPrevious studies demonstrated that the tropical cyclone (TC) boundary layer (TCBL) contains small‐scale coherent structures, such as roll vortices and tornado‐scale vortices (TSVs), and they play important roles in energy transport and intensity changes in TCs. However, little is known about how horizontal resolutions can affect storm‐scale and fine‐scale structures in the TCBL with the grid spacing decreasing from the turbulent gray zone (100 m–1 km) to the large‐eddy scale (<100 m). In this study, numerical experiments with the large eddy simulation technique are used to investigate the effect of the model horizontal resolution on the simulated TC‐scale and fine‐scale structures in the TCBL. The simulated TC tends to have a shallower BL, a lower BL jet associated with stronger near‐surface vertical wind shear in the TCBL when the grid spacing decreases from 333 to 111 m or 37 m. When the grid spacing decreases to 111 m or 37 m, the fine‐scale coherent structures and near‐surface wind streaks associated with roll vortices and TSVs can be simulated, and the characteristics of the simulated turbulent kinetic energy in the TCBL are in good agreement with observational studies. With the grid spacing of 111 and 37 m, no significant differences in TC intensity are found in terms of instantaneous maximum and azimuthal‐mean maximum wind speeds. This study suggests that simulations with the horizontal grid spacing of 100 m or less can simulate the small coherent structures in the TCBL and their effect on TC intensity.

Observations of wind and turbulence structures of Super Typhoons Hato and Mangkhut over land from a 356 m high meteorological tower

Knowledge of tropical cyclone (TC, or typhoon, hurricane) boundary layer over land is of vital importance to a variety of applications such as track and intensity forecasts of TCs and design of civil structures and infrastructures. On the basis of the 356-m-high Shenzhen Meteorological Gradient Tower which is the tallest of its kind in Asia, this paper presents an observational study of wind and turbulence structure of two Super Typhoons, namely Hato in 2017 and Mangkhut in 2018. First, the mean wind speed profiles, momentum flux, and drag coefficient are analyzed, and their correlations with upwind terrain and wind speed are discussed. Then, the characteristics of wind spectra are investigated and compared with existing spectral models. Subsequently, wind speed variances and turbulent kinetic energy (TKE) are inspected, and their variations with height are examined. Last, the characteristics and vertical profiles of TKE budget are explored. The outcome of this study is expected to enhance the understanding of TC boundary layer over land, provide useful information for the design of civil structures and infrastructures, benefit the numerical simulation of landfalling TCs, and facilitate the TC hazard prevention in coastal regions.

A direct aircraft observation of helical rolls in the tropical cyclone boundary layer

Helical rolls are known to play a significant role in modulating both the mean and turbulence structure of the atmospheric boundary layer in tropical cyclones. However, in-situ measurements of these rolls have been limited due to safety restrictions. This study presents analyses of data collected by an aircraft operated by the Hong Kong Observatory in Typhoon Kalmaegi (1415) and Typhoon Nida (1604). Examination of the flight-level data at ~ 600 m altitude confirmed the existence of sub-kilometer-scale rolls. These rolls were mostly observed in the outer-core region. Turbulent momentum fluxes were computed using the eddy correlation method. The averaged momentum flux of flight legs with rolls was found to be ~ 2.5 times that of legs without rolls at a similar wind speed range. This result suggests that rolls could significantly modulate turbulent transfer in the tropical cyclone boundary layer. This roll effect on turbulent fluxes should be considered in the planetary boundary layer parameterization schemes of numerical models simulating and forecasting tropical cyclones.

Tropical Cyclone Intensification Simulated in the Ooyama-type Three-layer Model with a Multilevel Boundary Layer

AbstractThe first successful simulation of tropical cyclone (TC) intensification was achieved with a three-layer model, often named the Ooyama-type three-layer model, which consists of a slab boundary layer and two shallow water layers above. Later studies showed that the use of a slab boundary layer would produce unrealistic boundary layer wind structure and too strong eyewall updraft at the top of TC boundary layer and thus simulate unrealistically rapid intensification compared to the use of a height-parameterized boundary layer. To fully consider the highly height-dependent boundary layer dynamics in the Ooyama-type three-layer model, this study replaced the slab boundary layer with a multilevel boundary layer in the Ooyama-type model and used it to conduct simulations of TC intensification and also compared the simulation with that from the model version with a slab boundary layer. Results show that compared with the simulation with a slab boundary layer, the use of a multilevel boundary layer can greatly improve simulations of the boundary-layer wind structure and the strength and radial location of eyewall updraft, and thus more realistic intensification rate due to better treatments of the surface layer processes and the nonlinear advection terms in the boundary layer. Sensitivity of the simulated TCs to the model configuration and to both horizontal and vertical mixing lengths, sea surface temperature, the Coriolis parameter, and the initial TC vortex structure are also examined. The results demonstrate that this new model can reproduce various sensitivities comparable to those found in previous studies using fully physics models.

A Framework for Simulating the Tropical-Cyclone Boundary Layer Using Large-Eddy Simulation and Its Use in Evaluating PBL Parameterizations

AbstractBoundary layer turbulent processes affect tropical cyclone (TC) structure and intensity change. However, uncertainties in the parameterization of the planetary boundary layer (PBL) under high-wind conditions remain challenging, mostly due to limited observations. This study presents and evaluates a framework of numerical simulation that can be used for a small-domain [O(5 km)] large-eddy simulation (LES) and single-column modeling (SCM) to study the TC boundary layer. The framework builds upon a previous study that uses a few input parameters to represent the TC vortex and adds a simple nudging term for temperature and moisture to account for the complex thermodynamic processes in TCs. The reference thermodynamic profiles at different wind speeds are retrieved from a composite analysis of dropsonde observations of mature hurricanes. Results from LES show that most of the turbulence kinetic energy and vertical momentum flux is associated with resolved processes when horizontal grid spacing is O(10 m). Comparison to observations of turbulence variables such as momentum flux, effective eddy viscosity, and turbulence length scale show that LES produces reasonable results but highlight areas where further observations are necessary. LES results also demonstrate that compared to a classic Ekman-type boundary layer, the TC boundary layer is shallower, develops steady conditions much quicker, and exhibits stronger wind speed near the surface. The utility of this framework is further highlighted by evaluating a first-order PBL parameterization, suggesting that an asymptotic turbulence length scale of 40 m produces a good match to LES results.

Investigating Axisymmetric and Asymmetric Signals of Secondary Eyewall Formation Using Observations‐Based Modeling of the Tropical Cyclone Boundary Layer

AbstractThis study examines axisymmetric and asymmetric aspects of secondary eyewall formation (SEF) in tropical cyclones (TCs) by applying a nonlinear boundary layer model to tangential wind composites of observed TCs with and without SEF. SEF storms were further analyzed at times prior to and after SEF, as defined by the emergence of a secondary maximum in axisymmetric tangential wind. The model is used to investigate the steady‐state boundary layer response to the free‐tropospheric pressure forcing derived from observed tangential wind fields. The axisymmetric response to the Post‐SEF wind field displayed a secondary updraft maximum associated with a mature secondary eyewall; the model correctly produced no secondary updraft for non‐SEF storms. The Pre‐SEF response also exhibited a secondary updraft associated with an incipient secondary eyewall largely due to the broadened outer tangential wind field that commonly precedes SEF events. The asymmetric wind fields and model response were analyzed relative to the 850–200 hPa environmental wind shear vector. In Pre‐SEF storms, the tangential wind field displayed a broadened tangential wind structure in the downshear quadrants. The boundary layer response shows a downwind shift toward the left‐of‐shear quadrants, exhibiting the clearest secondary maxima in updrafts, tangential wind, and radial inflow. This left‐of‐shear response was the leading contributor to the secondary eyewall signals in the Pre‐SEF axisymmetric response. Sensitivity analyses confirmed the robustness of these asymmetric signals. These findings suggest that enhanced tangential wind and boundary layer updrafts in the left‐of‐shear sectors may be early indicators and critical features of SEF in sheared TCs.

Potential for New Constraints on Tropical Cyclone Surface-Exchange Coefficients through Simultaneous Ensemble-Based State and Parameter Estimation

AbstractThe tropical cyclone (TC) surface-exchange coefficients of enthalpy (Ck) and momentum (Cd) at high wind speeds have been notoriously challenging to estimate. This difficulty arises from many factors, including the difficulties in collecting observations within the turbulent TC boundary layer, and the complex coupled physical interactions between the TC boundary layer and ocean surface, which are challenging to accurately model. Motivated by recent studies highlighting the limited practical predictability of TC intensity as a result of uncertainty in the physical representation of the air–sea fluxes of momentum and enthalpy at high wind speeds, we investigate the potential to estimate the surface enthalpy and momentum exchange coefficients through ensemble data assimilation. Significant ensemble correlations between tangential wind, radial wind, and simulated infrared brightness temperatures with parameters controlling the enthalpy and momentum exchange coefficients suggest potential to use all-sky satellite and/or airborne radial velocity observations to estimate these unknown parameters. Using a series of observing system simulation experiments (OSSEs), simulated infrared brightness temperature observations, and a known truth, we demonstrate some potential for simultaneous state and parameter estimation with an ensemble-based data assimilation system to converge toward the correct known parameter values. In all OSSEs with either one or multiple unknown parameters, the initial parameter errors are reduced through simultaneous model state and parameter estimation. However, challenges still exist in converging to the precise true parameter values, as state errors during rapid intensification can project onto the parameter estimates.

Sensitivity of Fine-Scale Structure in Tropical Cyclone Boundary Layer to Model Horizontal Resolution at Sub-Kilometer Grid Spacing

In view of the increasing interest in the explicit simulation of fine-scale features in the tropical cyclone (TC) boundary layer (TCBL), the effects of horizontal grid spacing on a 7–10 h simulation of an idealized TC are examined using the Weather Research and Forecast (ARW-WRF) mesoscale model with one-way moving nests and the nonlinear backscatter with anisotropy (NBA) sub-grid-scale (SGS) scheme. In general, reducing the horizontal grid spacing from 2 km to 500 m tends to produce a stronger TC with lower minimum sea level pressure (MSLP), stronger surface winds, and smaller TC inner core size. However, large eddies cannot be resolved at these grid spacings. In contrast, reducing the horizontal grid spacing from 500 to 166 m and further to 55 m leads to a decrease in TC intensity and an increase in the inner-core TC size. Moreover, although the 166-m grid spacing starts to resolve large eddies in terms of TCBL horizontal rolls and tornado-scale vortex, the use of the finest grid spacing of 55 m tends to produce shorter wavelengths in the turbulent motion and stronger multi-scale turbulence interaction. It is concluded that a grid spacing of sub-100-meters is desirable to produce more detailed and fine-scale structure of TCBL horizontal rolls and tornado-scale vortices, while the relatively coarse sub-kilometer grid spacing (e.g., 500 m) is more cost-effective and feasible for research that is not interested in the turbulence processes and for real-time operational TC forecasting in the near future.

A high-fidelity parametric model for tropical cyclone boundary layer wind field by considering effects of land cover and terrain

The proper simulation of the tropical cyclone (TC) boundary layer wind field is essential to predict the maximum wind speed, the imposed wind loading on civil structures, and the related potential disasters. A high-fidelity parametric model is developed to produce the wind field and to study the wind characteristics of TCs in the boundary layer. This model adopts a widely used boundary layer turbulence closure scheme and is built on a terrain-following coordinate system, which can consider various land cover and terrain effects. To improve the computational efficiency, a nested grid system is adopted. The developed model is implemented to reproduce the wind fields of Hurricane Isabel (2003), Hurricane Katrina (2005), Hurricane Irene (2011), Typhoon Hagupit (2008), Typhoon Hato (2017), and Typhoon Mangkhut (2018). Different types of observation datasets are used to validate the developed model, including the Hurricane Research Division's H*Wind snapshots, the National Data Buoy Center's wind records, and several meteorological sounding stations' observations. The spatial wind fields and the wind speed time series are presented. The influence of land cover and terrain on the behavior of TC is investigated. The simulation results demonstrate the high-fidelity and computational efficiency of the developed model, implying its potential applications for TC hazard modeling.

Negative Pressure Perturbations Associated With Tornado‐Scale Vortices in the Tropical Cyclone Boundary Layer

AbstractDangerous turbulences were observed in the eyewall of category 5 Hurricane Hugo (1989) and the surface pressure associated with the turbulence was 8 hPa lower than the mean pressure in the eye. In this study, it is demonstrated that small scale, negative pressure perturbations in the tropical cyclone eyewall are associated with the tornado‐scale vortex (TSV) simulated with the large‐eddy simulation technique in a semi‐idealized numerical experiment. The negative pressure perturbation associated with TSVs is nonhydrostatic, dynamically resulting from the shearing effect. As a result, the negative pressure perturbation is linearly correlated with the vertical component of relative vorticity and maximum wind perturbation. Since the TSV is prevalent near the inner edge of the tropical cyclone eyewall, it is suggested that caution should be taken to estimate the central pressure of tropical cyclones with the extremely low pressure observed in the eyewall.