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Article Understanding the Role of Mean and Eddy Momentum Transport in the Rapid Intensification of (2017) and Hurricane Michael (2018)

Alrick Green 1, Sundararaman G. Gopalakrishnan 2, Ghassan J. Alaka, Jr. 2 and Sen Chiao 3,*

1 Atmospheric Physics, University of Maryland, Baltimore County, Baltimore, MD 21250, USA; [email protected] 2 Hurricane Research Division, NOAA/AOML, Miami, FL 33149, USA; [email protected] (S.G.G.); [email protected] (G.J.A.) 3 Department of Meteorology and Climate Science, San Jose State University, San Jose, CA 95192, USA * Correspondence: [email protected]; Tel.: +1-408-924-5204

Abstract: The prediction of rapid intensification (RI) in tropical cyclones (TCs) is a challenging problem. In this study, the RI process and factors contributing to it are compared for two TCs: an axis-symmetric case (Hurricane Irma, 2017) and an asymmetric case (Hurricane Michael, 2018). Both Irma and Michael became major hurricanes that made significant impacts in the United States. The Hurricane Weather Research and Forecasting (HWRF) Model was used to examine the connection between RI with forcing from the large-scale environment and the subsequent evolution of TC structure and . The observed large-scale environment was reasonably reproduced by   HWRF forecasts. Hurricane Irma rapidly intensified in an environment with weak-to-moderate vertical wind shear (VWS), typically favorable for RI, leading to the symmetric development of Citation: Green, A.; Gopalakrishnan, vortical convective clouds in the cyclonic, vorticity-rich environment. Conversely, Hurricane Michael S.G.; Alaka, G.J., Jr.; Chiao, S. rapidly intensified in an environment of strong VWS, typically unfavorable for RI, leading to major Understanding the Role of Mean and Eddy Momentum Transport in the asymmetries in the development of vortical convective clouds. The tangential wind momentum Rapid Intensification of Hurricane budget was analyzed for these two hurricanes to identify similarities and differences in the pathways Irma (2017) and Hurricane Michael to RI. Results suggest that eddy transport terms associated with convective processes positively (2018). Atmosphere 2021, 12, 492. contributed to vortex spin up in the early stages of RI and inhibited spin up in the later stages of RI https://doi.org/10.3390/ in both TCs. In the early stages of RI, the mean transport terms exhibited notable differences in these atmos12040492 TCs; they dominated the spin-up process in Irma and were of secondary importance to the spin-up process in Michael. Favorable aspects of the environment surrounding Michael appeared to aid in Academic Editor: Da-Lin Zhang the RI process despite hostile VWS.

Received: 10 February 2021 Keywords: eddy vorticity fluxes; momentum budget; hurricanes rapid intensification; HWRF Accepted: 6 April 2021 Published: 14 April 2021

Publisher’s Note: MDPI stays neutral 1. Introduction with regard to jurisdictional claims in published maps and institutional affil- A (TC) is one of the most dangerous forms of natural disaster to iations. impact society and coastal communities annually. To offer as much preparation time as pos- sible, it is essential to accurately predict the track and changes in intensity associated with these weather systems. Although the prediction of TC intensity change has generally im- proved [1], TC rapid intensification (RI), defined when the maximum wind speed increases by at least 30 kt (15 m s−1) in a 24 h period [2], remains a great forecast challenge [1,2]. Prior Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. studies have shown that TC intensity variability involves multiscale nonlinear interaction This article is an open access article of different variables including vertical wind shear (VWS), mid-level moisture, upper distributed under the terms and ocean temperatures and heat content, cloud microphysics, air–sea interaction, and inner conditions of the Creative Commons core dynamics and thermodynamics. All these factors are well known to influence TC RI Attribution (CC BY) license (https:// (e.g., [3–9]). creativecommons.org/licenses/by/ Environmental VWS interactions with the TC vortex have been investigated by using 4.0/). both in situ observations and numerical simulations (e.g., [10–14]). VWS is widely recog-

Atmosphere 2021, 12, 492. https://doi.org/10.3390/atmos12040492 https://www.mdpi.com/journal/atmosphere Atmosphere 2021, 12, 492 2 of 22

nized to be anticorrelated with RI (e.g., [2,8]). Several mechanisms have been proposed to explain why TCs usually weaken in the presence of strong VWS, including TC vortex tilting [11], mid-tropospheric ventilation of the TC inner core [12,13], dilution of the upper- tropospheric TC warm core by divergent fluxes [14], and downdrafts that reduce moist entropy in the boundary layer in the TC inner core region [13]. However, the relationship between VWS and TC intensity is complex, and some TCs have been observed to intensify rapidly in the presence of hostile environmental shear (i.e., >15 m s−1)[14–18]. Chen and Gopalakrishnan [7] investigated the RI of Hurricane Earl (2010) in an environment of strong VWS using the operational Hurricane Weather Research and Forecasting (HWRF) system. A great number of aircraft observations in the inner core were used to verify the forecast of Earl, an asymmetric TC that rapidly intensified in a hostile environment. They concluded that the triggering mechanism for RI was the development of an upper-level warm core over the TC surface center. The upper-level warm core developed due to deep convection and subsidence-induced warm air advection in the upshear left region of the TC. This warm air was transported radially inwards from the upshear left region until it was coincident with the TC surface center position [7]. Another TC that experienced RI in hostile shear was Tropical Storm Gabrielle (2001). Gabrielle was impacted by environmental shear of 13 m s−1) when it underwent RI, with the central pressure dropping by 22 hPa within 3 h [15,16]. Despite hostile VWS, the key factor behind Gabrielle’s RI was an intense convective cell. This intense convective cell developed in the downshear left quadrant of the TC and moved cyclonically inward to a radius of 17 km within the radius of maximum winds. Consequently, this convective cell amplified the efficiency for kinetic energy produc- tion to spin up the vortex. Rios-Berrios et al. [17] examined the RI of Hurricane Katia (2011) in a sheared environment using the Advanced Hurricane Weather Research and Forecasting (HWRF) model. Despite the presence of strong environmental shear, they found that Katia rapidly intensified due to moistening of the low to middle troposphere to the right of the shear vector. Leighton et al. [18] used an experimental ensemble of HWRF forecasts to investigate the RI associated with (2014). Although both intensifying and non- intensifying ensemble members had deep convection in the downshear right quadrant of the TC, convection propagated into the upshear region only in intensifying members. A budget analysis of tangential momentum showed that the radial eddy vorticity flux contributed positively to the spin-up process of tangential winds in the middle to upper troposphere and reduced vortex tilt in the RI members. As for the non-intensifying mem- bers, negative eddy vorticity flux spun down the tangential winds in the midddle to upper troposphere, and Edouard’s vortex never became vertically aligned. Gopalakrishnan et al. [19] used a high-resolution version of HWRF to understand the role of shear-induced asymmetries on the intensification of Hurricane Earl (2010). Results from their study revealed that eddy radial vorticity fluxes play a significant role in controlling TC intensity changes in sheared storms. In the case of Earl, despite persistent environmental shear and a lack of symmetric convection, a positive eddy vorticity flux in the middle to upper troposphere created by mesoscale convective complexes had a profound influence in accelerating the TC spin-up process. Clearly, while in one case of sheared storm, eddy vorticity fluxes aided spin-up of the TC vortex, in another case, eddy vorticity fluxes have a negative role. In this study, two hurricanes that underwent RI were investigated to understand better how TCs spin up in different environments. Hurricane Irma (2017) was embedded in an environment of weak VWS and developed as a nearly symmetric storm. Hurricane Michael (2018), on the other hand, developed in an environment of strong VWS with persistent convection initially only in the northern sector. The following questions are addressed in this study: What are the differences between the modeled large-scale environmental conditions between the two TCs and how do they verify with reality? How does a hurricane intensify in the presence of environmental shear? Atmosphere 2021, 12, 492 3 of 22

What will be the contributions from the mean and eddy terms in the two different storms? We used the HWRF system and Global Forecast System (GFS) analysis to answer these questions. Section2 provides case descriptions. Section3 entails a detailed description of the experimental design and methods behind the research along with modeling and postprocessing tools used. The results from observations and HWRF simulations on each tropical cyclone are presented in Section4. A summary of the key findings and future research are discussed in Section5.

2. Case Descriptions Detailed TC reports on Hurricanes Irma (2017) and Michael (2018) were prepared by the National Hurricane Center [20,21]. Nevertheless, a summary of the large-scale perspectives relevant to the current study is provided here.

2.1. Hurricane Irma (2017) Irma, a long-lived TC, originated from a with widespread deep con- vection that departed off the west coast of Africa on 27 August 2017. The wave organized into Tropical Depression 11 roughly 200 km west–southwest of the Cabo Verde Islands at 0000 UTC on 30 August 2017. Six hours later, the cyclone strengthened to Tropical Storm Irma and maintained a westward trajectory south of a mid-level ridge over the Atlantic Ocean (for reference, the model simulation was started the same day at 1200 UTC when Irma was still a tropical storm). Irma rapidly intensified into a hurricane by 0600 UTC on 31 August. Favorable conditions, including weak VWS, promoted further development of deep convection and intensification. As a result, Irma continued its RI, reaching major hurricane status (i.e., Category 3 on the Saffir–Simpson scale) at 0000 UTC on 01 September. For the next 72 h, the intensification process halted due to dry air intrusion and eyewall replacement cycles, which disrupted the intensification process and caused minor fluctuations in intensity. Irma turned to the west–southwest after the mid-level ridge to its north strengthened and, consequently, moved over high sea surface temperatures [20]. Irma reached a maximum intensity of 155 kt (~80 m s−1) at 1800 UTC 05 September after the completion of an eyewall replacement cycle, registering as a Category 5 hurricane. By this point, the TC had become extremely organized with a well-developed and symmetric deep convection in the eyewall. Irma made its first on the island of at roughly 0600 UTC on 06 September and later in the at 1600 UTC. Irma continued as a Category 5 hurricane for more than 48 h before making another landfall in as a Category 4 hurricane on 08 September. On 09 September, Irma weakened to a Category 2 hurricane after prolonged interaction with Cuba. Irma then turned to the northwest in response to a low-pressure system, which brought the TC over the Straits of where high sea surface temperatures (SSTs) supported re- intensification into a Category 4 hurricane. Irma continued to turn to the north, making two final on Cudjoe Key and Marco Island, Florida on 10 September. Irma rapidly decayed as it moved over the Florida Peninsula and ultimately dissipated over the continental United States [20].

2.2. Hurricane Michael (2018) Michael, a powerful and short-lived TC, originated from a low-pressure system that became embedded in a large cyclonic gyre over the northwestern Caribbean Sea on 6 October 2018 (for reference, the model simulation was started at 1800 UTC on the same day). At 0600 UTC on 7 October 2018, Michael became a tropical depression located 130 nautical miles south of Cozumel, Mexico with a northward trajectory towards the Gulf of Mexico. Michael began an RI period despite hostile atmospheric conditions, including strong VWS. Michael soon became a tropical storm and later a hurricane at 1200 UTC on 8 October despite persistent southwesterly wind shear. Michael encountered an abrupt hiatus in intensification as it passed west of Cuba, possibly due to dry air intrusion, a cold ocean eddy, and strong VWS. By 9 October, Michael Atmosphere 2021, 12, 492 4 of 22

resumed its RI process and was steered generally northward toward the continental United States by a mid-level ridge and a mid-level shortwave over the northwest Gulf of Mexico. Michael rapidly intensified to a Category 5 hurricane just before it made landfall near Mexico Beach, Florida, with maximum winds of 140 kt (72 m s−1) at 1730 UTC on 10 October. After landfall, Michael rapidly decayed as it moved deeper into the continental United States. By 11 October, Michael transitioned into an over [21].

3. Experimental Design and Methods 3.1. Model Description The HWRF system was developed jointly by the National Centers for Environmental Prediction (NCEP) in the National Oceanographic and Atmospheric Administration’s (NOAA) (NWS) and the Hurricane Research Division in NOAA’s Atlantic Oceanographic and Meteorological Laboratory (AOML) as a part of the Hurricane Forecast Improvement Project (HFIP) [22–27]. HWRF utilizes the WRF Nonhydrostatic Mesoscale Model (WRF–NMM) dynamical core to solve governing equations of dynamics and thermodynamics [28]. Hurricanes Irma (2017) and Michael (2018) were simulated using version 4.0 of the operational HWRF system, an ocean-coupled regional model that utilizes moving nested domains to achieve cloud-resolving scales [29]. The atmospheric component of HWRF is coupled to the Message Passing Interface Princeton Ocean Model-Tropical Cyclone (MPIPOM–TC) via the NCEP coupler. The three nested domains in this version of HWRF have horizontal grid spacings of 13.5 km for the outermost domain, 4.5 km for the intermediate domain, and 1.5 km for the innermost domain [29]. The intermediate and innermost domains are moving nests that follow the TC center anywhere within the outermost domain. Conversely, the outermost domain does not move throughout the forecast period and is roughly centered on the initial TC position (e.g., Figure1). HWRF is Atmosphere 2021, 12, x FOR PEER REVIEW 5 of 23 configured with 75 hybrid pressure-sigma vertical levels and a model top of 10 hPa for the North Atlantic basin.

FigureFigure 1. TheThe outermost domain forfor aa HurricaneHurricane Weather Weathe Researchr Research and and Forecasting Forecasting (HWRF) (HWRF) forecast fore- castof Hurricane of Hurricane Michael Michael initialized initialized at 1800 at 1800 UTC UTC on 06 on October 06 October 2018. 2018. (courtesy (courtesy of EMC). of EMC).

HWRFHWRF is is configured configured with an advanced advanced phys physicsics suite that has been extensively tested forfor TC TC forecasts forecasts [29]. [29]. HWRF HWRF physics physics options options include include the the scale-aware scale-aware simplified simplified Arakawa– Arakawa– Schubert (SASAS) cumulus parameterization for deep and shallow convection, the Fer- rier–Aligo cloud microphysical parameterization for explicit moist physics, the Geophys- ical Fluid Dynamics Laboratory (GFDL) surface-layer parameterization to account for air– sea interaction over warm water and under high-wind conditions, the Noah land surface model, the rapid radiative transfer model for global circulation models (RRTMG) shortwave and longwave radiation scheme, and the hybrid eddy-diffusivity mass-flux (Hybrid EDMF) planetary boundary layer scheme [29].

3.2. Model Simulations, Verification, and Analysis The initial conditions and lateral boundary conditions are from the GFS forecast. The forecasts for hurricanes Irma and Michael were initialized at 1200 UTC on 30 August 2017 and 1800 UTC on 06 October 2018, respectively. The forecast periods for each TC were carefully chosen to include the respective RI events and subsequent evolution. The HWRF large-scale environment was compared with the NCEP Global Data Assimilation Sys- tem/Final 0.25 Degree Global Tropospheric Analyses and Forecast Grids (FNL) to evaluate environmental shear, sea surface temperatures, and mid-level moisture [30]. The ad- vanced diagnostic postprocessing, analysis, and display system (DIAPOST) were used to perform two coordinate transformations, i.e., (1) to convert the model output from the native HWRF E-grid to an A-grid and (2) to interpolate the model output to cylindrical polar coordinates with height and radius in units of km. The transformed variables were used for analyzing the momentum budgets.

3.3. Tangential Wind Momentum Budget Terms To understand the impact of VWS on the evolution of a TC vortex better, the tangen- tial wind momentum budget is computed, an approach similar to that described in [18,19,31–33]. Equation (1) shows the azimuthally averaged tangential wind momentum budget as follows:

Atmosphere 2021, 12, 492 5 of 22

Schubert (SASAS) cumulus parameterization for deep and shallow convection, the Ferrier– Aligo cloud microphysical parameterization for explicit moist physics, the Geophysical Fluid Dynamics Laboratory (GFDL) surface-layer parameterization to account for air–sea interaction over warm water and under high-wind conditions, the Noah land surface model, the rapid radiative transfer model for global circulation models (RRTMG) shortwave and longwave radiation scheme, and the hybrid eddy-diffusivity mass-flux (Hybrid EDMF) planetary boundary layer scheme [29].

3.2. Model Simulations, Verification, and Analysis The initial conditions and lateral boundary conditions are from the GFS forecast. The forecasts for hurricanes Irma and Michael were initialized at 1200 UTC on 30 August 2017 and 1800 UTC on 06 October 2018, respectively. The forecast periods for each TC were carefully chosen to include the respective RI events and subsequent evolution. The HWRF large-scale environment was compared with the NCEP Global Data Assimilation System/Final 0.25 Degree Global Tropospheric Analyses and Forecast Grids (FNL) to evaluate environmental shear, sea surface temperatures, and mid-level moisture [30]. The advanced diagnostic postprocessing, analysis, and display system (DIAPOST) were used to perform two coordinate transformations, i.e., (1) to convert the model output from the native HWRF E-grid to an A-grid and (2) to interpolate the model output to cylindrical polar coordinates with height and radius in units of km. The transformed variables were used for analyzing the momentum budgets.

3.3. Tangential Wind Momentum Budget Terms To understand the impact of VWS on the evolution of a TC vortex better, the tan- gential wind momentum budget is computed, an approach similar to that described Atmosphere 2021, 12, x FOR PEER REVIEW 6 of 23 Atmosphere 2021, 12, x FOR PEER REVIEW 6 of 23 in [18,19,31–33]. Equation (1) shows the azimuthally averaged tangential wind momentum budget as follows:

⟨⟩ ⟨⟩ (1) ⟨⟩ = −< 𝑢 >< 𝑓 + 𝜁 > − < 𝑤 ⟨> ⟩ − < u ′ 𝜁 ′ > − < 𝑤′ > + < 𝐷 > +< 𝐷 > = −< 𝑢 >< 𝑓 + 𝜁 > − < 𝑤 > − < u ′ 𝜁 ′ > − < 𝑤′ > + < 𝐷 > +< 𝐷 > (1)

The budget terms are color coded to simplify the identification of each term. In cylin- TheThedrical budget budget coordinates, terms terms areuare, v, colorand w coded codedrepresent to to simplifythe simplify radial, the tangential, the identification identification and vertical of ofeach components each term. term. In cylin-of In cylindricaldricalvelocity, coordinates, coordinates, respectively. u, vu,, andv ,The and w ve representwrticalrepresent component the the radial, radial, of relative tangential, tangential, vorticity and and is verticaldenoted vertical componentsby components 𝜁 and f is of velocity,the Coriolisrespectively. parameter. The veThertical azimuthal component mean isof denoted relative by vorticity < > and iseddy denoted (e.g., departureby 𝜁 and f is of velocity,from respectively. the azimuthal The mean) vertical is denoted component by ‘ (prime). of relative The highlighted vorticity is denotedterms on bythe right-and f the Coriolis parameter. The azimuthal mean is denoted by < > and eddy (e.g., departure is the Coriolishand side parameter. of the (1) Theare the azimuthal mean radial mean influx is denoted of absolute by < vertical > and eddyvorticity (e.g., (first departure term, 0 fromfrom the yellow),the azimuthal azimuthal the mean mean) mean) vertical is denoted is advectiondenoted by ofby(prime). mean ‘ (prime). tangential The highlightedThe momentum highlighted terms (second terms on the term, on right-hand the blue), right- sidehand of theside (1)eddy of are theradial the (1) mean vorticity are radialthe fluxmean influx (third radial of term, absolute influx red), verticaltheof absolute eddy vorticity vertical vertical advection (first vorticity term, of yellow), eddy (first tan- term, the meanyellow), verticalgential the advectionmomentummean vertical of (fourth mean advection term, tangential green), of mean momentum and thtangentiale mean (second tendency momentum term, terms blue), due(second theto vertical eddy term, radialand blue), vorticitythe eddyhorizontal flux radial (third diffusion vorticity term, red),(f ifthflux term, the (third eddy purple). term, vertical red), advection the eddy of vertical eddy tangential advection momentum of eddy tan- (fourthgential term, momentumThe green), residual and (fourth term, the whichmeanterm, tendencyincludesgreen), andnumerical terms the mean due errors to tendency vertical and the and pressureterms horizontal due gradient, to vertical diffusion is ne- and (fifthhorizontal term,glected. purple). diffusion The residual (fifth may term, originate purple). from interpolation between the model coordinate sys- TheThetem residual residualto the polar term, term, cylindrical which which includesincludes coordinates. numerical This approximation errors errors and and theis the especially pressure pressure validgradient, gradient, for this isis ne- study because the diffusion tendency terms were explicitly computed within the model neglected.glected. The The residual residual may may originate originate from from interpolation interpolation between between the the model model coordinate coordinate sys- and are not included in the residual. We used the outputs from the innermost (1.5 km) systemtem to to the the polar polar cylindrical cylindrical coordinates. This approximationapproximation isis especially especially valid valid for for this this domain for our analysis of the vortex spin-up mechanism in terms of (1) in the following studystudy becausesection. because For the the both diffusion diffusion cases, the tendency tendency mean TC terms motionterms were waswere explicitlyremoved explicitly to computed calculate computed the within tangentialwithin the the modelwind model andand are aremomentum not not included included budget. in in the the residual. residual. We We used used the the outputs outputs from from the the innermost innermost (1.5 (1.5 km) km) domaindomain for for our our analysis analysis of of the the vortex vortex spin-up spin-up mechanism mechanism in in terms terms of of (1) (1) in in the the following following section.section.4. For Results For both both cases, cases, the the mean mean TC TC motion motion was was removed removed to to calculate calculate the the tangential tangential wind wind momentummomentum4.1. Model budget. budget. Verification: Track and Intensity Simulated track and intensity produced by HWRF for both TCs are compared with 4. Resultsthe National Hurricane Center (NHC) best track [34]. Irma’s simulated track followed 4.1. Modelgenerally Verification: close to theTrack best and track, Intensity except with a slower translation speed (Figure 2a). Mi- chael’s simulated track was also quite close to the best track, except for a slight west bias Simulated track and intensity produced by HWRF for both TCs are compared with (Figure 2b). The differences between simulated and best tracks in both cases could be due the Nationalto minor discrepanciesHurricane Center in the synoptic-scale(NHC) best trackenvironment [34]. Irma’s and will simulated be investigated track in followed later generallysections. close The to intensitythe best predictions, track, except as depictedwith a slower by the evolutiontranslation of speedminimum (Figure mean 2a). sea- Mi- chael’slevel simulated pressure track(MSLP) was and also maximum quite close 10 m towind thes, best are also track, reasonably except forreproduced a slight westby the bias (Figuremodel 2b). (FigureThe differences 3a–d). An betweenRI phase wassimulated clearly andcaptured best bytracks the simulationin both cases of each could TC. be In due to minorthe casediscrepancies of Irma (Figure in the 3a,b), synoptic-scale the RI phase environmentis followed by aand steady-state will be investigated phase and then in alater sections.slow The intensification intensity predictions,phase. The stages as depicted of intensity by change the evolution are consistent of minimum with the descrip-mean sea- level tionspressure provided (MSLP) in Figure and maximum 2a. Hurricane 10 Michaelm wind intensifieds, are also untilreasonably landfall reproduced(Figure 2b). Alt- by the modelhough (Figure predicted 3a–d). values An RI of phase minimum was MSLP clearly were captured too high byan dthe maximum simulation 10 m ofwinds each were TC. In too weak in the Michael simulation (Figure 3c,d), the hurricane correctly intensified until the case of Irma (Figure 3a,b), the RI phase is followed by a steady-state phase and then a landfall. slow intensification phase. The stages of intensity change are consistent with the descrip- tions provided in Figure 2a. Hurricane Michael intensified until landfall (Figure 2b). Alt- hough predicted values of minimum MSLP were too high and maximum 10 m winds were too weak in the Michael simulation (Figure 3c,d), the hurricane correctly intensified until landfall.

Atmosphere 2021, 12, 492 6 of 22

4. Results 4.1. Model Verification: Track and Intensity Simulated track and intensity produced by HWRF for both TCs are compared with the National Hurricane Center (NHC) best track [34]. Irma’s simulated track followed generally close to the best track, except with a slower translation speed (Figure2a). Michael’s simu- lated track was also quite close to the best track, except for a slight west bias (Figure2b ). The differences between simulated and best tracks in both cases could be due to minor discrepancies in the synoptic-scale environment and will be investigated in later sections. The intensity predictions, as depicted by the evolution of minimum mean sea-level pres- sure (MSLP) and maximum 10 m winds, are also reasonably reproduced by the model (Figure3a–d ). An RI phase was clearly captured by the simulation of each TC. In the case of Irma (Figure3a,b), the RI phase is followed by a steady-state phase and then a slow intensi- fication phase. The stages of intensity change are consistent with the descriptions provided

Atmosphere 2021, 12, x FOR PEER REVIEWin Figure2a. Hurricane Michael intensified until landfall (Figure2b). Although7 of predicted23 values of minimum MSLP were too high and maximum 10 m winds were too weak in the Michael simulation (Figure3c,d), the hurricane correctly intensified until landfall.

(a)

(b) Figure 2. The 126 h HWRF forecast tracks (red) and corresponding observed National Hurricane Figure 2. The 126 h HWRF forecast tracks (red) and corresponding observed National Hurricane Center (NHC) best track (black) for (a) Hurricane Irma initialized at 1200 UTC on 30 August 2017 andCenter (b) Hurricane (NHC) Michael best track initialized (black) at for 1800 (a) HurricaneUTC on 06 October Irma initialized 2018. Markers at 1200 represent UTC on the 30 trop- August 2017 icaland cyclone (b) Hurricane (TC) position Michael every initialized6 h. at 1800 UTC on 06 October 2018. Markers represent the tropical cyclone (TC) position every 6 h.

Atmosphere 2021, 12, 492 7 of 22 Atmosphere 2021, 12, x FOR PEER REVIEW 8 of 23

FigureFigure 3.3. HWRF forecasts (red) are comparedcompared with thethe NHCNHC bestbest tracktrack (black)(black) forfor HurricaneHurricane IrmaIrma ((aa,,bb)) andand HurricaneHurricane Michael ((cc,d,d).). TheThe presented presented features features include include (a ,c(a), minimumc) minimum mean mean sea levelsea level pressure pressure (hPa) (hPa) and ( band,d) maximum(b,d) maximum 10 m winds 10 m winds (m s−1). The forecasts for Hurricane Irma and Hurricane Michael were initialized at 1200 UTC on 30 August 2017 (m s−1). The forecasts for Hurricane Irma and Hurricane Michael were initialized at 1200 UTC on 30 August 2017 and and 1800 UTC on 06 October 2018, respectively. 1800 UTC on 06 October 2018, respectively. 4.2. Large-Scale Environment 4.2. Large-Scale Environment An evaluation of the large-scale (i.e., synoptic-scale) environment is performed for An evaluation of the large-scale (i.e., synoptic-scale) environment is performed for Hurricanes Irma and Michael to assess the fidelity of the HWRF simulations with respect Hurricanes Irma and Michael to assess the fidelity of the HWRF simulations with respect to to the GFS analysis (FNL) and to understand environmental forcing on the TC vortices, the GFS analysis (FNL) and to understand environmental forcing on the TC vortices, includ- including the evolution of the tangential wind momentum budget (see Section 4.4). Spe- ing the evolution of the tangential wind momentum budget (see Section 4.4). Specifically, cifically, this evaluation focuses on the large-scale momentum (e.g., VWS), moisture, this evaluation focuses on the large-scale momentum (e.g., VWS), moisture, MSLP, and MSLP, and sea surface temperatures (SSTs) to identify key differences in the environmen- sea surface temperatures (SSTs) to identify key differences in the environmental forcing on tal forcing on Hurricane Irma and Hurricane Michael. Irma was embedded in an environ- Hurricane Irma and Hurricane Michael. Irma was embedded in an environment conducive ment conducive for RI with weak VWS, a moist middle troposphere, and warm SSTs. On for RI with weak VWS, a moist middle troposphere, and warm SSTs. On the other hand, the other hand, the environment around Michael was more hostile and generally unsup- the environment around Michael was more hostile and generally unsupportive of RI due portive of RI due to strong VWS, although the middle troposphere was moist and SSTs to strong VWS, although the middle troposphere was moist and SSTs were warm. wereDeep-layer warm. VWS is calculated as the 200 hPa wind minus the 850 hPa wind and is typicallyDeep-layer inversely VWS related is calculated to TC intensity as the 200 change. hPa wind In other minus words, the 850 TC intensityhPa wind change and is tendstypically to be inversely positive related (negative) to TC when intensity VWS is ch weakange. (strong). In other Deep-layer words, TC VWS intensity and 200change hPa streamlinestends to be positive revealed (negative) an environment when VWS around is Hurricaneweak (strong). Irma Deep-layer that was conducive VWS and for 200 RI, hPa as shownstreamlines in HWRF revealed and FNLan environment (Figure4). In around fact, the Hurricane HWRF and Irma FNL that fields was are conducive nearly identical for RI, atas 0000shown UTC in HWRF on 31 August and FNL 2017, (Figure which 4). isIn notfact, surprising the HWRF given and FNL that fields the valid are nearly time is iden- only 12tical h intoat 0000 the UTC HWRF on simulation.31 August 2017, Irma which was embedded is not surprising in a zonal given strip that of the VWS valid less time than is 15only m 12 s− 1hthat into extended the HWRF from simulation. the west coastIrma ofwas Africa embedded to the Lesserin a zonal Antilles. strip Higherof VWS VWS less magnitudesthan 15 m s−1 to that the extended north and from south the of west Irma coast in conjunction of Africa to with the theLesser 200 Antilles. hPa streamline Higher patternVWS magnitudes indicate well-established to the north and upper-tropospheric south of Irma in conjunction outflow associated with the with 200 hPa the TC.stream- The outflowline pattern to the indicate north ofwell-established Irma was aided upper- by antropospheric upper-tropospheric outflow trough associated centered with at the 35 ◦TC.N, 25The◦ W.outflow That troughto the north was not of Irma close was enough aided to by Irma an toupper-tropospheric force higher VWS trough values centered in its inner at core.35° N, As 25° expected, W. That Irma trough experienced was not close RI in enough this low-shear to Irma environment to force higher as it VWS moved values generally in its

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inner core. As expected, Irma experienced RI in this low-shear environment as it moved westwardgenerally westward (see Figures (see2a Figures and3b), 2a with and the 3b), onset with of the the onset RI period of the occurringRI period atoccurring the time at shownthe time in shown Figure in4. Figure The RI 4. period The RI halted period at ha 1200lted at UTC 1200 on UTC 31 August on 31 August 2017 (forecast 2017 (forecast hour 24) as Irma approached a different upper-tropospheric trough to its northwest with VWS hour 24) as Irma approached−1 a different upper-tropospheric trough to its northwest with greaterVWS greater than 25than m s25 m. As s−1 shown. As shown in Figure in Figure2a, Irma 2a, actuallyIrma actually turned turned to the to northwest the northwest as it approachedas it approached the trough, the trough, which which likely likely contributed contributed to steady-state to steady-state intensity intensity for the for next the 36next h after the RI period concluded. 36 h after the RI period concluded.

FigureFigure 4.4. Deep-layer (200–850 hPa) vertical wind shear (VWS, shaded),shaded), 200 hPa streamlines, and mean sea level pressure (MSLP)(MSLP) centerscenters in in the the environment environment near near Hurricane Hurricane Irma Irma (2017) (2017) from from (a) 12(a) h12 into h into an HWRF an HWRF forecast forecast initialized initialized at 1200 at UTC1200 onUTC 30 on August 30 August 2017 2017 and (andb) Final (b) Final Analysis Analysis (FNL) (FNL) valid valid at 0000 at 0000 UTC UTC on on 31 31 August August 2017. 2017. The The center center position position ofof IrmaIrma isis −1 identifiedidentified by a a black black circle. circle. VWS VWS has has units units of ofm ms , s and−1, andMSLP MSLP has units has units of hPa. of The hPa. trou Thegh trough axes relevant axes relevant to these to discus- these sions are marked by blue lines. discussions are marked by blue lines.

Mid-tropospheric moisture moisture is is calculated calculated as as the the mass-weighted mass-weighted average average of relative of relative hu- humiditymidity (RH) (RH) in inthe the 700–400-hPa 700–400-hPa layer layer and and is is typi typicallycally directly directly proportional proportional to to TC intensity change [[35–38].35–38]. Moist Moist environments support support deep deep convection and thus intensification.intensification. HWRF andand FNLFNL were, were, once once again, again, nearly nearly identical, identical, providing providing more confidencemore confidence that HWRF that reasonablyHWRF reasonably reproduced reproduced the large-scale the large-scale environment environment near Irma near (Figure Irma (Figure5). During 5). During the RI period,the RI period, Irma was Irma associated was associated with a verywith moista very middle moist middle troposphere troposphere that had that RH had greater RH thangreater 80% than (Figure 80% 5(Figure). In particular, 5). In particular, high RH high values RH werevalues noticeable were noticeable to the north to the and north south and ofsouth Irma of inIrma both in HWRFboth HWRF and FNL. and FNL. A large A larg areae ofarea dry ofair dry was air observedwas observed to the to northwestthe north- ofwest Irma of Irma in association in association with with the Saharan the Sahara airn layer, air layer, which which generally generally acts acts to suppress to suppress TC intensification.TC intensification. When When dry dry air isair entrained is entrained into into a TC’s a TC’s inner inner core, core, it often it often interrupts interrupts the the RI processRI process by by limiting limiting the the amount amount of moistureof moistu necessaryre necessary to supportto support deep deep convection convection [35 –[35–38]. Although38]. Although this this dry dry air didair did not not prevent prevent Irma’s Irma’s RI, itRI, likely it likely played played a role a role in haltingin halting the the RI processRI process as RHas RH less less than than 50% 50% began began to wrapto wrap into into the the western western side side of theof the TC. TC. Historically, SST has been long known to limit or enhance TC formation and intensifi- cation [2,8,11,38]. TCs typically do not develop or intensify over regions with SSTs cooler than 26 ◦C. As SSTs increase above 26 ◦C, they drive a larger disequilibrium between the ocean and the atmosphere. As a result, enthalpy fluxes increase to fuel stronger TCs, which, in turn, drive even higher enthalpy fluxes related to increased surface winds. While details of the coupled HWRF simulation on the ocean response to the hurricanes are out of the scope of the current study, a large-scale analysis is carried out in this section to understand the differences between the oceanic environment in the two cases of Hurricanes Irma and Michael. The HWRF and FNL fields were quite similar, with only minor differences up to 0.5 ◦C in the environment near Irma (Figure6). Irma was centered over SSTs near 28 ◦C, which is warm enough to support deep convection and RI. The MSLP field revealed a weakness in the subtropical ridge to the north of Irma due to a pair of mid-latitude cyclones over the Figure 5. Mid-troposphericnorthern (400–700 hPa North average) Atlantic relative (Figures humidity5 and (RH,6). The shaded TC) had and beenmean steered sea level generally pressure (MSLP, westward contours and centers) in theup enviro to thisnment point near byHurricane the subtropical Irma from ridge(a) 12 h (Figures into an HWRF5 and6 forecast). However, initialized the at erosion 1200 UTC of the subtropical ridge allowed Irma to turn to the northwest, and the TC moved over cooler

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inner core. As expected, Irma experienced RI in this low-shear environment as it moved generally westward (see Figures 2a and 3b), with the onset of the RI period occurring at the time shown in Figure 4. The RI period halted at 1200 UTC on 31 August 2017 (forecast hour 24) as Irma approached a different upper-tropospheric trough to its northwest with VWS greater than 25 m s−1. As shown in Figure 2a, Irma actually turned to the northwest as it approached the trough, which likely contributed to steady-state intensity for the next 36 h after the RI period concluded.

Figure 4. Deep-layer (200–850 hPa) vertical wind shear (VWS, shaded), 200 hPa streamlines, and mean sea level pressure (MSLP) centers in the environment near Hurricane Irma (2017) from (a) 12 h into an HWRF forecast initialized at 1200 UTC on 30 August 2017 and (b) Final Analysis (FNL) valid at 0000 UTC on 31 August 2017. The center position of Irma is identified by a black circle. VWS has units of m s−1, and MSLP has units of hPa. The trough axes relevant to these discus- sions are marked by blue lines.

Mid-tropospheric moisture is calculated as the mass-weighted average of relative hu- midity (RH) in the 700–400-hPa layer and is typically directly proportional to TC intensity change [35–38]. Moist environments support deep convection and thus intensification. HWRF and FNL were, once again, nearly identical, providing more confidence that HWRF reasonably reproduced the large-scale environment near Irma (Figure 5). During the RI period, Irma was associated with a very moist middle troposphere that had RH greater than 80% (Figure 5). In particular, high RH values were noticeable to the north and Atmosphere 2021, 12, x FOR PEER REVIEW 10 of 23 Atmosphere 2021, 12, 492 south of Irma in both HWRF and FNL. A large area of dry air was observed to the north-9 of 22 west of Irma in association with the Saharan air layer, which generally acts to suppress TC intensification. When dry air is entrained into a TC’s inner core, it often interrupts the

on 30 August 2017 and (b) FNLRI process valid at by 0000 limiting UTC on the 31 amountAugust◦ 2017. of moistu The centre ernecessary position ofto Irmasupport is identified deep convection by a black [35– circle. RH is measured as a 38].percentage,waters Although with and SSTs thisMSLP lessdry has thanair units did 27 of not hPa.C. prevent Cooler SSTsIrma’s combined RI, it likely with played dry mid-tropospheric a role in halting the air played a significant role in halting the RI process by 1200 UTC on 31 August 2017. RI process as RH less than 50% began to wrap into the western side of the TC. Historically, SST has been long known to limit or enhance TC formation and intensification [2,8,11,38]. TCs typically do not develop or intensify over regions with SSTs cooler than 26 °C. As SSTs increase above 26 °C, they drive a larger disequilibrium between the ocean and the atmosphere. As a result, enthalpy fluxes increase to fuel stronger TCs, which, in turn, drive even higher enthalpy fluxes related to increased surface winds. While details of the coupled HWRF simulation on the ocean response to the hurricanes are out of the scope of the current study, a large-scale analysis is carried out in this section to understand the differences between the oceanic environment in the two cases of Hurricanes Irma and Michael. The HWRF and FNL fields were quite similar, with only minor differences up to 0.5 °C in the environment near Irma (Figure 6). Irma was centered over SSTs near 28 °C, which is warm enough to support deep convection and RI. The MSLP field revealed a weakness in the subtropical ridge to the north of Irma due to a pair of mid-latitude cyclones over Figure 5. Mid-tropospheric the(400–700 (400–700 northern hPa hPa avNorth average)erage) Atlantic relative relative (Figureshumidity humidity 5(RH, (RH, and shaded shaded)6). The) and andTC mean meanhad beensea sea level level steered pressure pressure generally (MSLP, (MSLP, west- contours and centers) in the wardenviro environment upnment to this near point Hurricane by the Irma subtropical from (a) 12 ridg h into e (Figuresan an HWRF HWRF 5 forecast forecast and 6). initialized However, at 1200the erosion UTC UTC of on 30 August 2017 and (b) FNLthe subtropical valid at 0000 ridge UTC onallowed 31 August Irma 2017. to turn The to center the northwest, position of Irmaand the is identified TC moved by aover black cooler circle. RH is measured as a percentage,waters with and SSTs MSLP less has than units 27 of °C. hPa. Cooler SSTs combined with dry mid-tropospheric air played a significant role in halting the RI process by 1200 UTC on 31 August 2017.

Figure 6. SeaSea surface surface temperatures temperatures (SSTs, (SSTs, shaded) shaded) and and mean mean sea sealeve levell pressure pressure (MSLP, (MSLP, contours contours and centers) and centers) in the in envi- the environmentronment near nearHurricane Hurricane Irma Irma from from (a) 12 (a h) 12into h an into HWRF an HWRF forecast forecast initiali initializedzed at 1200 at 1200UTC UTCon 30 on August 30 August 2017 and 2017 (b and) FNL (b) valid at 0000 UTC on 31 August 2017. The center position of Irma is identified by a black circle. SST has units of °C, and FNL valid at 0000 UTC on 31 August 2017. The center position of Irma is identified by a black circle. SST has units of ◦C, MSLP has units of hPa. and MSLP has units of hPa.

Contrary toto thethe Irma Irma case, case, deep-layer deep-layer VWS VWS and and 200 hPa200 streamlineshPa streamlines indicated indicated a hostile a hostileenvironment environment around around Hurricane Hurricane Michael Michael that was that unconducive was unconducive for RI (Figure for RI7). (Figure Neverthe- 7). Nevertheless,less, Michael experiencedMichael experienced RI for much RI offor its much life cycle of its prior life cycle to landfall. prior to Overall, landfall. the Overall, HWRF theand HWRF FNL fields and FNL were fields similar were at 1800 similar UTC at on1800 08 UTC October on 08 2018 October (forecast 2018 hour (forecast 48),with hour only 48), withminor only differences minor differences near Michael. near AsMichael. Michael As moved Michael northward moved northward (see Figure (see2b ),Figure it moved 2b), −1 itinto moved a region into of a strongregion VWS of strong (>20 mVWS s−1 )(>20 that m was s enhanced) that was by enhanced an upper-tropospheric by an upper- tropospherictrough positioned trough over positioned the northern over Gulfthe nort of Mexicohern Gulf and of the Mexico United and States. the United An additional States. Anupper-tropospheric additional upper-tropospheric trough centered trough to the east centered of Florida to the enhanced east of theFlorida outflow enhanced on the east-the outflowern side on of Michael’sthe eastern circulation. side of Michael’s The 200 circul hPa streamlinesation. The 200 revealed hPa streamlines that upper-tropospheric revealed that upper-troposphericoutflow was well-established outflow was to thewell-established east of Michael to andthe east was of virtually Michael non-existent and was virtually to the non-existentwest of Michael. to the This west enhanced of Michael. outflow, This enhanced albeit asymmetric, outflow, albeit became asymmetric, a critical became driver of a criticalstrong deepdriver convection of strong deep by evacuating convection mass by evacuating from the TC mass circulation from the in TC spite circulation of the un- in spitefavorable of the VWS. unfavorable In essence, VWS. the twoIn essence, upper-tropospheric the two upper-tropospheric troughs had opposing troughs positive had opposingand negative positive impacts and onnegative Michael. impacts As the on troughMichael. over As the trough United over States the weakened United States and weakenedmoved northward, and moved outflow northward, became outflow more became pronounced more on pronounced the northern on the and northern eastern sideand easternof Michael’s side of circulation, Michael’s includingcirculation, a clearincluding northerly a clear outflow northerly channel outflow in the channel 200 hPa in flow the 200to the hPa east flow of theto the TC. east These of outflowthe TC. channelsThese outflow are known channels to foster are TCknown intensification to foster TC by intensificationventilating outflow by ventilating in a single, outflow narrow in pathway a single,[ narrow35]. pathway [35].

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Figure 7. Deep-layer (200–850 hPa) vertical wind shear (VWS, shaded), 200 hPa streamlines, and mean sea level pressure Figure 7. Deep-layer (200–850 hPa) vertical wind shear (VWS, shaded),shaded), 200 hPa streamlines, and mean sea level pressure (MSLP) centers in the environment near Hurricane Michael from (a) 48 h into an HWRF forecast initialized at 1800 UTC (MSLP) centers in the environment near Hurricane Michael from (a) 48 h into an HWRF forecast initialized at 1800 UTC on on 06 October 2018 and (b) FNL valid at 1800 UTC on 08 October 2018. The center position of Michael is identified by a 06 October 2018 and (b) FNL valid at 1800 UTC on 08 October 2018. The center position of Michael is identified by a black black circle. VWS has units of m s−1, and MSLP has units of hPa. The trough axes relevant to these discussions are marked −1 circle.by blue VWS lines. has units of m s , and MSLP has units of hPa. The trough axes relevant to these discussions are marked by blue lines. Mid-tropospheric moisture was asymmetric around Hurricane Michael, with RH Mid-tropospheric moisture was asymmetric around Hurricane Michael, with RH greater than 80% to the north and east of the TC and a region of drier air (RH < 50%) to greater than 80% to the north and east of the TC and a region of drier air (RH < 50%) to the the south of the TC (Figure 8). The dry air had clearly intruded into the TC circulation by south of the TC (Figure8). The dry air had clearly intruded into the TC circulation by this this time, and dry air near a TC center has the potential to inhibit deep convection, time, and dry air near a TC center has the potential to inhibit deep convection, especially especially when VWS is strong. Overall, the moisture pattern was simulated realistically when VWS is strong. Overall, the moisture pattern was simulated realistically by HWRF. by HWRF.

Figure 8.8. Mid-tropospheric (400–700 hPa av average)erage) relative relative humidity humidity (RH, (RH, shaded shaded)) and and mean mean sea sea level level pressure pressure (MSLP, (MSLP, contours and centers) in the environment near Hurricane Michael from (a) 48 h into an HWRF forecast initialized at 1800 contours and centers) in the environment near Hurricane Michael from (a) 48 h into an HWRF forecast initialized at UTC on 06 October 2018 and (b) FNL valid at 1800 UTC on 08 October 2018. The center position of Michael is identified 1800 UTC on 06 October 2018 and (b) FNL valid at 1800 UTC on 08 October 2018. The center position of Michael is identified by a black circle. RH is measured as a percentage, and MSLP has units of hPa. by a black circle. RH is measured as a percentage, and MSLP has units of hPa. Unlike the VWS and moisture fields, very warm SSTs (>29 °C) were supportive of Unlike the VWS and moisture fields, very warm SSTs (>29 ◦C) were supportive of deep convection and RI (Figure 9). While strong VWS likely acted to ventilate Michael’s deep convection and RI (Figure 99).). WhileWhile strongstrong VWSVWS likelylikely actedacted toto ventilateventilate Michael’sMichael’s inner core, allowing drier mid-tropospheric air to reach the center of the TC, SSTs may inner core, allowing drier drier mid-tropospheric mid-tropospheric ai airr to to reach reach the the center center of of the TC, SSTs may have played a significant role in the intensification process by supplying warm, humid air have played played a a significant significant role role in in the the intensification intensification process process by by supplying supplying warm, warm, humid humid air toair the to thetroposphere troposphere that that could could counteract counteract th thee hostile hostile dry dry air air and and shear. shear. It It should be mentioned that that SSTs SSTs in in the the HWRF HWRF simulation simulation (F (Figureigure 9a)9a) were were 0.5–2 0.5–2 °C ◦coolerC cooler than than in the in analysisthe analysis (FNL) (FNL) near nearHurricane Hurricane Michael Michael (Figure (Figure 9b). 9Despiteb). Despite cooler cooler SSTs SSTsin HWRF, in HWRF, they werethey wereadequately adequately warm warm to support to support deep deep convection convection and and RI RI (>28 (>28 °C).◦C). However, However, these

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reduced SSTs in HWRF may have limited the predicted intensification rate, compared to reduced SSTs in HWRF may have limited the predicted intensification rate, compared to reducedthe best trackSSTs (seein HWRF Figure may3c,d). have limited the predicted intensification rate, compared to the best track (see Figure 3c,d).

Figure 9 9... SeaSea surface surface temperatures temperatures (SSTs, (SSTs, shaded) shaded) and and mean mean sea sealeve levelll pressurepressure pressure (MSLP,(MSLP, (MSLP, contourscontours contours andand centers)centers) and centers) inin thethe in envi-envi- the ronmentenvironment near nearHurricane Hurricane Irma Irmafrom from(a) 12 (ha )into 12 han into HWRF an HWRF forecast forecast initialized initialized at 1800 atUTC 1800 on UTC 06 October on 06 October 2018 and 2018 (b) FNL and valid at 1800 UTC on 08 October 2018. The center position of Michael is identified by a black circle. SST has units of °C, (validb) FNL at 1800 valid UTC at 1800 on UTC08 October on 08 October 2018. The 2018. center The centerposition position of Mich ofael Michael is identified is identified by a black by a black circle. circle. SST SSThas units has units of °C, of and MSLP has units of hPa. and◦C, andMSLP MSLP has hasunits units of hPa. of hPa.

4.3.4.3. TC TC Inner Inner Core Core LatentLatent heating heating due due to to convection convection in in the the eyewall eyewall region region of of a a TC TC drives drives the the intensifica- intensifica- tiontion and and maintenance maintenance of the the system. system. The The organization organization of of convection convection both in the the azimuthal azimuthal andand radial radial directions directions and and eddy eddy processes, processes, es especiallypecially those those associat associateded with with the thesegregation segrega- andtion andmerging merging of vortical of vortical hot hotconvective convective clouds, clouds, are are known known to to influence influence TC TC intensity changeschanges [14,18,19,31,32,39–45]. [14,18,19,31,32,39–45]. Therefore, Therefore, it it is is criticalcritical to to understand the the organization of convectionconvection in in order order to to examine examine the the vortex vortex spin-up spin-up mechanism mechanism in both in both TCs. TCs. The Theorganiza- orga- tionnization of convection of convection and associated and associated asymmetries asymmetries are explored are explored in vertical in vertical velocity velocity and rela- and tiverelative vorticity vorticity fields fields in the in upper the upper troposphere troposphere (10 km) (10 during km) during RI periods RI periods of both of TCs both (Fig- TCs –1−1 ures(Figures 10 and 10 and 11). 11 It). is It noted is noted that that vorticity vorticity is isscaled scaled by by h h–1 forforfor thethe the convenienceconvenience convenience ofof of budgetbudget calculationscalculations (Section 4.4).4.4).

–1 –1 Figure 10. Azimuthal structure of vertical velocity (units of m s–1,, shaded)shaded) andand relativerelative vorticityvorticity (units(units ofof hh–1,, contours)contours) atat Figure 10. Azimuthal structure of vertical velocity (units of m s−1, shaded) and relative vorticity (units of h−1, contours) 10 km height during the RI of Hurricane Irma.Irma. InIn allall panels,panels, redred contours/shadecontours/shades denote positive values, and blue con- at 10 km height during the RI of Hurricane Irma. In all panels, red–1 contours/shades denote positive values, and blue tours/shades denote negative values. The contour interval is 1.0 h–1.. TheThe blackblack ringring indicatesindicates thethe approximateapproximate radiusradius ofof contours/shades denote negative values. The contour interval is 1.0 h−1. The black ring indicates the approximate radius of maximum surface wind. Each box is 200 km × 200 km, with dashed gray range rings every 50 km. maximum surface wind. Each box is 200 km × 200 km, with dashed gray range rings every 50 km.

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–1 –1 Figure 11. Azimuthal structurestructure ofof verticalvertical velocityvelocity (units (units of of m m s −s 1,, shaded)shaded) andand relativerelative vorticityvorticity (units (units of of h h−1, contours) atat 10 km height during the (a) early and (b) late RI period of Hurricane Michael. In all panels, red contours/shades denote 10 km height during the (a) early and (b) late RI period of Hurricane Michael. In all panels, red contours/shades denote positive values, and blue contours/shades denote negative values. The contour interval is 1.0 h–1. The black ring indicates positive values, and blue contours/shades denote negative values. The contour interval is 1.0 h−1. The black ring indicates the approximate radius of maximum surface wind. Each box is 200 km × 200 km, with dashed gray range rings every 50 × thekm. approximateThe arrow shows radius the of approximate maximum surface directio wind.n of deep-layer Each box vertical is 200 km wind200 shear. km, with dashed gray range rings every 50 km. The arrow shows the approximate direction of deep-layer vertical wind shear. Figure 10 shows the presence of localized, rotating, deep-convective plumes, so- Figure 10 shows the presence of localized, rotating, deep-convective plumes, so-called called vortical hot towers [39,40,44,45], aggregating into mesoscale convective complexes vortical hot towers [39,40,44,45], aggregating into mesoscale convective complexes in the in the horizontal direction (red contours) at a height of 10 km during the RI period of Irma horizontal direction (red contours) at a height of 10 km during the RI period of Irma (centered around 12 h). These complexes grew almost symmetrically in both axial and (centered around 12 h). These complexes grew almost symmetrically in both axial and radial directions in the cyclonic, vorticity-rich environment around Irma. On average, the radial directions in the cyclonic, vorticity-rich environment around Irma. On average, plumes enhance the mean vorticity of the environment (note the abundance of red con- the plumes enhance the mean vorticity of the environment (note the abundance of red tourscontours in Figure in Figure 10). 10 At). At9 h, 9 h,positive positive (red (red contours) contours) and and negative negative (blue (blue contours) contours) vorticity couplets are are clearly clearly visible visible rotating rotating around around th thee TC TC center. center. In the In theTC inner TC inner core, core, these these cou- pletscouplets usually usually develop develop early early in the in intensificatio the intensificationn stage stage and straddle and straddle either either side of side the of local the windlocal windmaxima maxima in the in mesoscale the mesoscale circulation. circulation. The negative The negative part partof the of couplet the couplet is usually is usually ex- pelledexpelled from from the the incipient incipient vortex vortex or mixed or mixed with with an environment an environment of abundant of abundant positive positive vor- −1 ticity.vorticity. Additionally, Additionally, the negative the negative relative relative vorticity vorticity regions regions are less are than less or than equal or to equal −1.0 h to −1 and−1.0 coincident h−1 and coincident with planetary with planetaryvorticity that vorticity is on thatthe order is on theof 0.2 order h , ofindicating 0.2 h−1, indicatingthat abso- lutethat vorticity absolute vorticityis negative is negativein these regions in these and regions that and inertial that instability inertial instability also accounts also accounts for the breakupfor the breakup of negative of negative relative vorticity. relative vorticity.On the other On hand, the other the positive hand, the part positive of the couplet part of increasesthe couplet the increases ambient the lower-tropospheric ambient lower-tropospheric relative vorticity relative in vorticity the region inthe and region therefore and servestherefore to servesprecondition to precondition a strong mean a strong spin mean up [39]. spin upIt should [39]. It be should noted be that noted mixing that mixingof neg- ativeof negative vorticity vorticity in a region in a regionrich with rich positive with positive vorticity vorticity may cause may some cause spin some down, spin but down, fre- quentbut frequent convective convective bursts typically bursts typically offset thos offsete minor those negative minor negative effects. Indeed, effects. by Indeed, 12 h and by 12within h and the within TC inner the core TC inner(i.e., radius core (i.e., < 50 radius km), the < 50 initially km), the dipolar initially structure dipolar of structurevorticity (redof vorticity and blue (red contours) and blue had contours) reorganized had reorganized into a monopolar, into a monopolar, positive vorticity positive structure vorticity (mostlystructure red (mostly contours red within contours the within black thering) black that ring)is accompanied that is accompanied by segregation, by segregation, merging

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merging and axisymmetrization, as described in [19]. By 15 h, the axisymmetrization process was completed, as indicated by stronger positive vertical velocity (red shade) in the eyewall region with a pronounced monopolar structure. The subsiding motion was observed within the developing eye (blue shade), providing more evidence that Irma had become extremely well organized in the upper troposphere. In the case of Michael, strong VWS had a significant impact on the organization of convection (Figure 11). Figure 11a shows the vertical motion and vorticity early in the RI period of Michael. Although the vortical convective plumes were organized in the form of mesoscale convective complexes [19] at 34 h, as seen in Irma, merging and segregating of these plumes were restricted mostly downshear and to the left of the shear vector (e.g., northern region). There is also evidence of vorticity couplets, including a long filament of negative vorticity that extended over the TC surface center at this time. As was the case with Irma, negative relative vorticity is of the opposite sign and larger magnitude than the planetary vorticity, indicating that inertial instability is present to assist in the expulsion of these negative vorticity regions. Nevertheless, even at 10 km height, weak upward motion (shaded in yellow) is present in most of the domain at this time (Figure 11a), perhaps an indication of the larger cyclonic gyre (vorticity-rich environment) that encompassed the circulation of Michael (Section2b ). Later in the early RI stage (37 h), positive vorticity increased in coverage within 50 km of the TC center, consistent with deep convection near or inside of the radius of maximum surface wind, and was prominent in the northern and eastern quadrants of the TC circulation, consistent with a downshear vortex tilt (Figure 11a). However, deep convection and positive vorticity were still weak or absent in the southern and western quadrants of the TC (Figure 11a). Positive vorticity and upward motion continued to increase in coverage to the west and south of the TC center by 40 h (Figure 11a). Despite continued segregation, merging, and mixing in the eyewall region (blue and red contours), the vortical plumes (red contours) contributed to an increase in the mean vorticity of the environment accompanied by stronger upward motion (red shading). The vortical plumes, drawn into long mesoscale convective structures (red contours), were observed to wrap around the vortex later in the RI period (Figure 11b). These structures, also known as mesocyclones, were reported to have formed in the eyewall region of Hurricane Michael and led to an increase of positive vorticity in all quadrants of the storm (Figure 11b). These mesocyclones could rapidly contribute to the increase in the mean vorticity of the environment and could have helped to sustain the RI of Michael. Furthermore, strong updrafts were also observed on the upshear side of the TC near and within the radius of maximum wind, an ingredient for RI (e.g., [46]). By 59 h, upward motion and positive vorticity had increased in the hurricane’s organization, although the structure was not quite monopolar, as in Irma. In fact, vertical velocity exhibited a wavenumber one pattern around the TC center. Downward motion (e.g., subsidence, downdrafts) was visible at this time within the northern semicircle of the eyewall, as Michael’s maximum wind speed at the surface was greater than 45 m s−1 (see Figure3d). This downward motion was also observed in previous studies [47–49], although the positioning of these downdrafts was typically upshear at lower levels. Additionally, negative vorticity (blue contours) was not efficiently mixed out of the circulation, even with the aid of inertial instability, likely due to persistent VWS, indicating eddy spin down that was competing with strong mean spin-up of the vortex throughout the RI period (Figure 11). Interestingly and similar to Irma (Figure 10), other studies [22,41,45], including our earlier ones [7,18,19], have generally observed the near disappearance of negative vorticity near the eyewall region at the end of the merging and axisymmetrization phase. Despite the complicated structure at 10 km height and persistent VWS, localized, rotating, deep-convective plumes [39–45] had propagated to the upshear side of Michael’s circulation (i.e., western and southern quadrants), which is an indication that mesoscale convective complexes were growing asymmetrically in the Atmosphere 2021, 12, 492 14 of 22

cyclonic, vorticity-rich environment as the TC intensified (e.g., [19]). Clearly, counteracting processes caused by eddy motions resulting from asymmetric convection cannot be ignored.

4.4. Tangential Wind Momentum Budgets To understand the influence of asymmetries on the evolution of the mean vortex of Hurricanes Irma and Michael further, we analyzed the tangential momentum budget described in Section 3.3. It should be noted that such a generalized framework may be very useful for understanding both the evolution of symmetric and asymmetric TCs that develop in an environment of high VWS. Our earlier studies [7,18,19] on two other hurricanes, Earl (2010) and Edouard (2014), which developed in environments of significant VWS, indicated that eddy processes had a profound influence on the RI of these storms. Contributions from positive eddy vorticity flux alone were the dominant spin-up mechanism in the case of Earl [18]. An ensemble of forecasts of Edouard showed that eddy terms aided (indicated by red and green in Equation (1)) spin-up in the RI members and impeded intensification of non-intensifying members. The azimuthally averaged radial wind, tangential wind, and vertical velocity (e.g., Figure 12a–c) is provided to evaluate the TC structure in concert with the budget analysis (e.g., Figure 12d–f). To simplify the following evaluation, the budget terms were combined into mean transport and eddy transport terms. Mean transport terms (e.g., Figure 12d) include the mean radial vorticity flux and the mean vertical advection of mean tangential momentum (i.e., the first two terms on the right-hand side in Equation (1)). Eddy transport terms (e.g., Figure 12e) include the eddy radial vorticity flux, the eddy vertical advection of eddy tangential momentum, and diffusion (i.e., the last four terms on the right-hand side of Equation (1)). It should be noted that the contribution from diffusion (i.e., so-called frictional terms) is restricted to the boundary layer, suggesting that momentum tendencies above 1 km height solely reflect contributions from the eddy terms. Finally, the net tendency of tangential wind momentum is also shown (e.g., Figure 12f) to provide a complete picture of how the budget relates to changes in the TC structure. At the onset of RI in Hurricane Irma (i.e., 12 h into the HWRF forecast), the radial circulation was represented by a shallow layer of strong inflow roughly 1 km deep in the lower troposphere (Figure 12a). A weak inflow layer developed in the mid-levels (5–9 km) above the primary inflow near the surface. Above the weak second inflow in the upper troposphere was the presence of a moderate outflow of 5 m s−1. At this time, Irma was still a tropical storm with a well-developed deep vortex and maximum winds greater than 25 m s−1 within the boundary layer (Figure 12b). The mean vertical motions revealed an updraft core within the eyewall (>1 m s−1), along with some subsidence within the forming eye (Figure 12c). The corresponding tangential wind momentum budget indicated a net spin-up of the vortex at all heights up to 12 km (Figure 12f). The budget is dominated by the mean transport terms (Figure 12d). These mean terms acted to spin up the vortex throughout the entire depth of the eyewall (compare with Figure 12e) and were strikingly similar to the net tangential wind tendency (compare with Figure 12f). The eddy terms aided spin-up in the lower-to-middle troposphere (up to ~8 km) and spun down the vortex above that (Figure 12e). Eddy-induced spin-down (negative contribution), prominent in the mid-to-upper levels of the TC, was evidence of subsidence within the developing eye that transported lower momentum air downward (Figure 12c). It is also possible that eddy-induced spin-down at these levels was associated with the radially outward eddy vorticity flux. However, the spin-down induced by the eddy terms aloft was not enough to counteract the net spin-up of the vortex. Below 8 km, the eddy vertical advection of eddy tangential wind contributed to vortex spin-up, an indication that rotating, localized updrafts were transporting momentum upward in the eyewall. In the boundary layer, the diffusion terms (Figure 12e) offset the spin-up due to the radial absolute vorticity influx at a distance of 25–60 km from the TC center. The evolution of tangential wind in Atmosphere 2021, 12, 492 15 of 22

Atmosphere 2021, 12, x FOR PEER REVIEWHurricane Irma during its RI period is parallel to findings in previous studies that spin-up16 of 23

of a symmetric TC occurs within the boundary layer and eyewall ([18,50]).

Figure 12. Radius-height momentum (a–c) and momentum tendency (d–f) from a 12 h HWRF forecast of Hurricane Irma. Figure 12. Radius-height momentum (a–c) and momentum tendency (d–f) from a 12 h HWRF forecast of Hurricane Shown: (a) radial velocity (contour interval of 2 m s−1); (b) tangential velocity (contour interval of 5 m s−1); (c) vertical Irma. Shown: (a) radial velocity (contour interval of 2 m s−1); (b) tangential velocity (contour interval of 5 m s−1); velocity (red contour interval of 0.4 m s−1 for positive velocities and blue contour interval of 0.01 m s−1 for negative veloci- (c) vertical velocity (red contour interval of 0.4 m s−1 for positive velocities and blue contour interval of 0.01 m s−1 for ties) and maximum vertical velocity (green contour interval of 2 m s−1); (d) sum of the mean radial influx of absolute −1 d verticalnegative vorticity velocities) and the and mean maximum vertical vertical advection velocity of (greenthe mean contour tangential interval momentum of 2 m s ); (contour ( ) sum ofinterval the mean of 2 radial m s−1 influx h−1); (e) sumof of absolute the eddy vertical radial vorticity vorticity and flux, the the mean eddy vertical vertical advection advection of theof eddy mean tangential tangential mo momentummentum, (contourthe vertical interval diffusion, of −1 −1 and2 the m s horizontalh ); (e) diffusion sum of the (contour eddy radial interval vorticity of 2 m flux, s−1 h the−1); and eddy (f vertical) net tangential advection wind of eddy tendency tangential (contour momentum, interval of the 2 m −1 −1 s−1 hvertical−1). All diffusion,red/blue contours and the horizontalrepresent positive/negative diffusion (contour azimuthally interval of 2 aver m s agedh fields.); and Green (f) net contours tangential in wind (c) represent tendency the − − maximum(contour vertical interval velocity of 2 m s over1 h all1). azimuths. All red/blue All contours fields are represent temporally positive/negative averaged over azimuthallya 1 h period averaged centered fields.on the Green forecast hour.contours The y-axis in (c )represents represent theheight maximum from 0–15 vertical km, velocityand the overx-axis all shows azimuths. radius All from fields 0–120 are temporally km. averaged over a 1 h period centered on the forecast hour. The y-axis represents height from 0–15 km, and the x-axis shows radius from 0–120 km. At the onset of RI in Hurricane Irma (i.e., 12 h into the HWRF forecast), the radial circulationLater was in the represented RI period (20 by h),a shallow Irma had layer a strong of strong primary inflow inflow roughly roughly 1 km 1 km deep deep in in the the lower troposphere with weaker inflow above that up to a height of 10 km (Figure 13a). lower troposphere (Figure 12a). A weak inflow layer developed in the mid-levels (5–9 km) Outflow greater than 7 m s−1 was observed above 10 km, indicating a healthy secondary above the primary inflow near the surface. Above the weak second inflow in the upper circulation. The mean tangential wind revealed a much stronger TC with maximum surface −1 tropospherewinds near 40was m the s−1 presenceand a deep of vortexa moderate that extended outflow above of 5 m 16 s km. At (Figure this time, 13b). Irma Figure was 13 stillc a tropicalshows a strongstorm with updraft a well-developed core on the order deep of 1 vortex m s−1 within and maximum the eyewall winds along greater with strong than 25 msubsidence s−1 within the within boundary the eye thatlayer extended (Figure 12b). down The 6 km mean height. vertical motions revealed an up- draft coreThe within tangential the windeyewall momentum (>1 m s−1 budget), along revealed with some a net subsidence spin-up of within the vortex the informing the eyeeyewall (Figure up 12c). to ~10 km (Figure 13f), albeit weaker than the spin-up earlier in the RI period (seeThe Figure corresponding 12f). The reduced tangential spin-up wind supports momentum the fact budget that Irma indicated was close a net to the spin-up end of of its the vortexRI period. at all Furthermore, heights up to weak 12 km spin-down (Figure on 12f). the The inside budget edge ofis thedominated eyewall representedby the mean transporta broadening terms of (Figure the eye, 12d). another These indicator mean term thats the acted end to of spin the RIup period the vortex was near.throughout The themean entire transport depth of terms the eyewall dominated (compare the net with tangential Figure wind 12e) tendencyand were within strikingly the eyewallsimilar to theand net hurricane tangential boundary wind tendency layer (Figure (compare 13d). Aswith expected, Figure 12f). frictional The termseddy terms offset theaided radial spin- up in the lower-to-middle troposphere (up to ~8 km) and spun down the vortex above that (Figure 12e). Eddy-induced spin-down (negative contribution), prominent in the mid- to-upper levels of the TC, was evidence of subsidence within the developing eye that transported lower momentum air downward (Figure 12c). It is also possible that eddy-

Atmosphere 2021, 12, x FOR PEER REVIEW 17 of 23

induced spin-down at these levels was associated with the radially outward eddy vorti- city flux. However, the spin-down induced by the eddy terms aloft was not enough to counteract the net spin-up of the vortex. Below 8 km, the eddy vertical advection of eddy tangential wind contributed to vortex spin-up, an indication that rotating, localized up- drafts were transporting momentum upward in the eyewall. In the boundary layer, the diffusion terms (Figure 12e) offset the spin-up due to the radial absolute vorticity influx Atmosphere 2021 12 , , 492 at a distance of 25–60 km from the TC center. The evolution of tangential wind in16 Hurri- of 22 cane Irma during its RI period is parallel to findings in previous studies that spin-up of a symmetric TC occurs within the boundary layer and eyewall ([18,50]). fluxLater of absolute in the RI vorticity period in (20 the h), lowest Irma levelhad a of strong the hurricane primary boundary inflow roughly layer (Figure 1 km deep 13e). in theAbove lower the troposphere boundary layer, with theweaker eddy inflow terms contributed above that toup spin-down to a height in of the 10 eyewallkm (Figure region, 13a). Outflowwith strong greater spin-down than 7 m in s the−1 was mid-to-upper observed levelsabove of 10 the km, TC indicating (6–12 km height).a healthy This secondary eddy- circulation.induced spin-down The mean was tangential supported wind by revealed the transport a much of lower stronger tangential TC with wind maximum anomalies sur- faceinto winds regions near of higher40 m s− anomalies,1 and a deep e.g., vortex vertical that motions extended associated above 16 with km the (Figure symmetrization 13b). Figure 13cof shows the vortex a strong throughout updraft the core eyewall. on the These order same of 1 eddy m s− terms1 within had the previously eyewall along shown with a positive contribution to spin-up in the lower troposphere (see Figure 12e). strong subsidence within the eye that extended down 6 km height.

FigureFigure 13. 13. AsAs in in Figure Figure 12, 12 ,except except that that it it shows shows a 20 hh HWRFHWRF forecastforecast of of Hurricane Hurricane Irma. Irma.

TheThe tangential mean structural wind momentum evolution of budget Hurricane reve Michaelaled a net during spin-up its RI of period the vortex had simi- in the eyewalllarities up and to differences ~10 km (Figure with Irma’s 13f), albeit evolution. weaker Early than in the the spin-up RI period earlier (37 h), in Michael the RI period was (seea tropical Figure storm12f). The (20–25 reduced m s− 1spin-up) with weak, supports deep the inflow fact andthat asymmetricIrma was close distribution to the end of of − itsvertical RI period. velocity Furthermore, (Figure 14 weaka–c). Azimuthally spin-down on averaged the inside outflow edge wasof the greater eyewall than represented 7 m s 1 a aloftbroadening and indicated of the aneye, environment another indicator of upper-level that the divergence end of the despite RI period strong was VWS. near. At The meanthis time,transport Michael terms was dominated not as well the organized net tangential as Irma. wind Although tendency mean within vertical the eyewall motions and hurricaneindicated boundary a weak, unorganized layer (Figure core 13d). updraft As expected, within the frictional eyewall terms (Figure offset 14c), the maximum radial flux vertical velocities (yellow contours in Figure 14c) provided evidence that strong updrafts of absolute vorticity in the lowest level of the hurricane boundary layer (Figure 13e). within deep convection were occurring within Michael, likely on the downshear (northeast) Above the boundary layer, the eddy terms contributed to spin-down in the eyewall side of the TC (see Figure 11a). region,The with tangential strong spin-down wind momentum in the mid-to-upper budget showed levels a net of spin-up the TC of (6–12 the vortex km height). through- This out the troposphere and extending out to 120 km in radius (Figure 14f). Conversely, Irma’s spin-up occurred at smaller radii (< 40 km). The eddy transport terms were very important to the net tangential wind tendency, especially below 6 km height and above 11 km height within 30 km of the TC center (Figure 14e). These terms also dominated the net spin

up from 6–11 km height at radii larger than 30 km. The mean transport terms weakly contributed to vortex spin-up in the boundary layer and from 6–13 km height (Figure 14d). At lower levels, the vertical advection of mean tangential momentum was near zero due to Atmosphere 2021, 12, x FOR PEER REVIEW 18 of 23

eddy-induced spin-down was supported by the transport of lower tangential wind anomalies into regions of higher anomalies, e.g., vertical motions associated with the symmetrization of the vortex throughout the eyewall. These same eddy terms had previously shown a positive contribution to spin-up in the lower troposphere (see Figure 12e). The mean structural evolution of Hurricane Michael during its RI period had similarities and differences with Irma’s evolution. Early in the RI period (37 h), Michael was a tropical storm (20–25 m s−1) with weak, deep inflow and asymmetric distribution of −1 Atmosphere 2021, 12, 492 vertical velocity (Figure 14a–c). Azimuthally averaged outflow was greater than17 7 of m 22 s aloft and indicated an environment of upper-level divergence despite strong VWS. At this time, Michael was not as well organized as Irma. Although mean vertical motions indicated a weak, unorganized core updraft within the eyewall (Figure 14c), maximum verticalweak mean velocities vertical (yellow velocity. contours As expected, in Figure the vertical14c) provided and lateral evidence diffusive that terms strong (frictional updrafts withinterms) deep negatively convection contributed were to theoccurring spin-up wi processthin inMichael, the hurricane likely boundary on the layerdownshear and (northeast)offset spin-up sidecaused of the TC by the(see radial Figure influx 11a). of absolute momentum (Figure 14d,e).

FigureFigure 14. 14. AsAs in inFigure Figure 12, 12 except, except that that it it shows shows a a 37 37 h h HWRF forecast ofof HurricaneHurricane Michael. Michael. The Thex-axis x-axis shows shows the the radius radius from 0–150 km. from 0–150 km.

TheLater tangential in the RI wind period momentum (56 h), Michael’s budget structure showed hada net improved spin-up considerably,of the vortex through- with a outstrong the troposphere secondary circulation, and extending a deep out vortex to 120 with km in maximum radius (Figure surface 14f). winds Conversely, near 45 m Irma’s s−1, spin-upand a well-organizedoccurred at smaller updraft radii core (< 40 (~1 km). m s −The1) that eddy sloped transport radially terms outward were very with important height to(Figure the net 15 tangentiala–c). The wind secondary tendency, circulation especially consisted below of 6 strong km height inflow and near above the surface 11 km andheight − withinstrong 30 outflow km of aloft,the TC both center greater (Figure than 14e). 7 m sThese1 (Figure terms 15 alsoa). Subsidencedominated wasthe observednet spin up fromwithin 6–11 the km eye height at radii at radii less thanlarger 20 than km (Figure30 km. The15c). mean In the transport tangential terms wind weakly momentum contrib- utedbudget, to vortex the net spin-up tangential in the wind boundary tendency laye revealedr and thatfrom vortex 6–13 spin-upkm height was (Figure concentrated 14d). At lowercloser levels, to the nowthe vertical well-defined advection eyewall of (Figuremean tangential15f). At this momentum time, the budget was wasnear dominated zero due to by the mean transport terms within the eyewall and hurricane boundary layer (Figure 15d), consistent with Irma later in its RI period. Furthermore, the eddy transport and diffusive terms partially offset the net vortex spin-up at most levels (Figure 15e), again consistent with Irma later in its RI period (see Figure 13e). Interestingly, the eddy vertical advection of eddy tangential momentum positively contributed to vortex spin-up in some regions, including radially inward of ~10 km and at radii of 20–50 km in a layer from 4–7 km (Figure 15e). Although Michael had symmetrized greatly by this time, the spotty pattern of the eddy transport terms indicates that the TC still had asymmetry because it continued to battle a hostile shear environment, and eddy convective structures were still positively contributing to the spin-up in some regions. Regardless, the tangential wind momentum budget provides evidence that Michael’s vortex continued to spin up despite unfavorable VWS. Atmosphere 2021, 12, x FOR PEER REVIEW 19 of 23

weak mean vertical velocity. As expected, the vertical and lateral diffusive terms (fric- tional terms) negatively contributed to the spin-up process in the hurricane boundary layer and offset spin-up caused by the radial influx of absolute momentum (Figure 14d,e). Later in the RI period (56 h), Michael’s structure had improved considerably, with a strong secondary circulation, a deep vortex with maximum surface winds near 45 m s−1, and a well-organized updraft core (~1 m s−1) that sloped radially outward with height (Figure 15a–c). The secondary circulation consisted of strong inflow near the surface and strong outflow aloft, both greater than 7 m s−1 (Figure 15a). Subsidence was observed within the eye at radii less than 20 km (Figure 15c). In the tangential wind momentum budget, the net tangential wind tendency revealed that vortex spin-up was concentrated closer to the now well-defined eyewall (Figure 15f). At this time, the budget was domi- nated by the mean transport terms within the eyewall and hurricane boundary layer (Fig- ure 15d), consistent with Irma later in its RI period. Furthermore, the eddy transport and diffusive terms partially offset the net vortex spin-up at most levels (Figure 15e), again consistent with Irma later in its RI period (see Figure 13e). Interestingly, the eddy vertical advection of eddy tangential momentum positively contributed to vortex spin-up in some regions, including radially inward of ~10 km and at radii of 20–50 km in a layer from 4–7 km (Figure 15e). Although Michael had symmetrized greatly by this time, the spotty pat- tern of the eddy transport terms indicates that the TC still had asymmetry because it con- tinued to battle a hostile shear environment, and eddy convective structures were still Atmosphere 2021, 12, 492 positively contributing to the spin-up in some regions. Regardless, the tangential18 wind of 22 momentum budget provides evidence that Michael’s vortex continued to spin up despite unfavorable VWS.

Figure 15. As in Figure 1212,, except that it shows a 56 h HWRF forecast of Hurricane Michael. The x-axis shows the radius from 0–150 km. from 0–150 km.

5. Discussions and Conclusions In this study, rapid intensification (RI) was explored in a near axisymmetric TC (Hurricane Irma, 2017) and an asymmetric TC (Hurricane Michael, 2018). Forecasts of Irma and Michael from the HWRF model were analyzed to study how differences in both inner core structure and the large-scale environment were linked to RI. For each TC, the model realistically reproduced the large-scale environment, and its track and intensity. The study

aimed to answer the following questions: (1) How did the environments surrounding Hurricanes Irma and Michael modulate the evolution of TC structure in each case, especially the inner core? (2) How and why did Hurricane Michael rapidly intensify into a major hurricane despite hostile environmental conditions? (3) What was the role of eddy and mean transport terms in the intensification processes for Hurricanes Irma and Michael? Differences in the evolution of environmental VWS were critical to the RI pathways in Irma and Michael. Irma was embedded in an environment of weak VWS (<10 m s−1) that was favorable for RI, while Michael was located in an environment of strong VWS (>10 m s−1), typically unfavorable for RI. Despite these differences in VWS, both TCs expe- rienced RI and became major hurricanes. In Irma, weak VWS allowed for the development of a vertically aligned vortex with deep rotating convective plumes that coalesced into mesoscale clusters in an environment of abundant vorticity (Figure 10). This is consistent with previous studies [19,44], which found that vertical plumes merge and stretch low-level vorticity near the boundary layer to create a stronger inflow that supports intensification. Unlike Irma, strong environmental VWS created a highly asymmetric structure in Michael, with convection primarily located in the downshear left quadrant. Strengthening of the vorticity as it propagated into the upshear left region was observed early in the RI period (Figure 11a). Later in the RI period, an abundance of vorticity near the radius of maximum Atmosphere 2021, 12, 492 19 of 22

winds indicated the merging of the lower- and upper-tropospheric vortices, resulting in a more symmetric structure (Figure 11b). The initially symmetric structure of Irma and the asymmetric structure of Michael led to key differences in the tangential wind momentum budget. Both early and later in Irma’s RI period, the spin-up of tangential winds was dominated by the mean radial transport of absolute vorticity, especially in the boundary layer, and the vertical advection of the mean tangential momentum within the eyewall region (Figures 12d–f and 13d–f). The eddy transport terms (Figure 12e) contributed to the vortex spin-up above the boundary layer up to the middle troposphere. In particular, the eddy vertical advection of eddy tangential wind was responsible for transporting momentum vertically in localized updrafts. At higher altitudes (7–15 km), eddy-induced spin-down represented the development of the eye, where lower tangential wind anomalies were transported downward via subsidence. As expected, diffusion terms counteracted and offset spin-up in the hurricane boundary layer. The overall spin-up process occurred solely in the eyewall. These results are parallel to findings in previous studies that the spin-up of a symmetric TC occurs within the eyewall boundary region [18,19]. Later in the RI period, the mean transport terms continued to dominate the tangential wind tendency in Irma, and the eddy transport terms became negative in the eyewall region, indicating a counteracting of the spin-up induced by the mean terms (Figure 13d–f). The eddy transport terms become negative due to the vertical advection of lower tan- gential wind anomalies into regions of higher tangential wind anomalies, thus contributing to a reduction of momentum and a spin-down of the vortex. However, more analysis is required to determine the exact eddy processes that cause vortex spin-down, which will be the topic of future research. This eddy-induced spin-down could be accomplished through anomalous downdrafts (e.g., weaker updrafts), acting upon tangential wind anomalies that increase downward, or through anomalous updrafts (e.g., stronger updrafts), acting upon tangential wind anomalies that increase upward. Early in Michael’s RI period, eddy transport terms contributed more to the net tangen- tial wind spin-up than the mean transport terms, especially from 1–7 km (Figure 14e). Weak spin-up induced by the mean transport terms is explained by the highly asymmetric nature of Michael at this time. For example, although maximum vertical velocity values were greater than 4 m s−1, azimuthal averages of vertical velocity were near zero (Figure 14c). The mean transport terms were much weaker in Michael than in Irma early in their respec- tive RI periods, consistent with previous evaluations of asymmetric TCs [7,18,19]. A novel result is the notion that the eddy transport terms contributed to vortex spin-up at low levels rather than upper levels, which provides evidence that these terms can help initiate RI at low levels within a developing eyewall. These eddy transport terms allowed Michael to overcome unfavorable VWS by transporting higher tangential wind anomalies into regions of lower tangential wind anomalies, presumably through localized convective updrafts that distributed momentum upward in the eyewall. As Michael rapidly intensified, the TC became more symmetric. Consequently, the mean transport terms dominated the net tangential wind spin-up later in the RI period. As in Irma, the eddy transport terms mostly counteracted the vortex spin-up, presumably through similar mechanisms. We conclude that the pathway to vortex spin-up through positive tangential wind tendency differs for asymmetric (i.e., sheared) and axisymmetric TCs. The former relies on eddy transport terms, especially the eddy vertical advection of eddy tangential momentum, early in the RI period when mean transport is weak. The latter is dominated by mean transport terms, both radial and vertical, with secondary contributions from the eddy transport terms. As an asymmetric TC rapidly intensifies, it typically becomes more symmetric, leading to similar contributions from budget terms later in the RI period, as seen in axisymmetric cases. Future research will focus on a closer inspection of eddy terms to diagnose precisely how symmetrization of the vortex and vertical motions are connected to tangential wind tendency in rapidly intensifying TCs. In particular, we will concentrate Atmosphere 2021, 12, 492 20 of 22

on how eddy transport terms redistribute momentum to enhance vortex spin-up early in RI periods and to counteract vortex spin-up later in RI periods.

Author Contributions: Conceptualization, S.G.G., G.J.A.J., and A.G.; methodology, S.G.G. and G.J.A.J.; software, S.G.G., G.J.A.J., and A.G.; validation, A.G., G.J.A.J., S.G.G., and S.C.; formal analysis, A.G.; investigation, A.G., S.G.G., G.J.A.J., and S.C.; resources, S.G.G. and S.C.; data curation, G.J.A.J. and S.G.G.; writing—original draft preparation, A.G.; writing—review and editing, S.G.G., G.J.A.J., and S.C.; visualization, A.G.; supervision, S.G.G., G.J.A.J., and S.C.; project administration, S.C.; funding acquisition, S.C. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by NCAS-M, NOAA/EPP Cooperative Agreement #NA16SEC4810006, and the Center for Applied Atmospheric Research and Education (CAARE) at San Jose State University. Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available due to their large size. Acknowledgments: We acknowledge the suppliers of datasets utilized in this research. Computa- tions were performed at the National Center for Atmospheric Research (NCAR). We wish to express our appreciation to Kyle Ahren and Andy Hazelton for the discussions and valuable suggestions. Comments and suggestions by three anonymous reviewers were much appreciated. The authors also thank all the AOML’s Hurricane Research Division team for their support. Conflicts of Interest: The authors declare no conflict of interest.

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