Intensity fluctuations in Hurricane Irma (2017) during a period of rapid intensification

. Intensity fluctuations observed during a period of rapid intensification of Hurricane Irma (2017) between 04 September and 06 September were investigated in a detailed modelling study using an ensemble of Met Office Unified Model (MetUM) convection permitting forecasts. These intensity fluctuations consisted of alternating weakening and strengthening phases. During weakening phases the tropical cyclone temporarily paused its intensification. It was found that weakening phases were associated with a change in the potential vorticity structure, with a tendency for it to become more monopolar. Convection 5 during strengthening phases was associated with isolated local regions of high relative vorticity and vertical velocity in the eyewall, while during weakening phases the storm became more azimuthally symmetric with weaker convection spread more evenly. The boundary layer was found to play an important role in the cause of the intensity fluctuations with an increase in the agradient wind within the boundary layer causing a spin–down just above the boundary layer during the weakening phases whereas during the strengthening phases the agradient wind reduces. This study offers new explanations for why these 10 fluctuations occur and what causes them.


Introduction
One of the biggest challenges in weather forecasting is predicting when a tropical cyclone (TC) will rapidly intensify.Rapid intensification is defined as a rate of surface wind increase of at least 15.4 m s -1 per 24 hours (Kaplan et al., 2010).Most strong tropical cyclones undergo a period of rapid intensification (Kaplan and DeMaria, 2003).Although convection-permitting numerical weather prediction models are capable of producing rapidly intensifying TCs, models still perform poorly when it comes to the timing of rapid intensification events (e.g.Short and Petch, 2018;DeMaria et al., 2021), indicating that the current understanding and representation of intensification processes prior to and during rapid intensification is likely incomplete.
Being able to accurately predict rapid intensification events can influence mitigation strategies as the wind speed strongly influences the potential damage the tropical cyclone may cause.
The simplest paradigm for tropical cyclone intensification can be understood by considering the case of a stationary vortex in gradient wind balance.Eliassen (1951) derived the Sawyer-Eliassen equation, that describes the response of the secondary circulation to angular momentum and heat sources.A point heating source located just within the :::::::::::::: height-dependent : radius of maximum windspeed (RMW) will result in an axisymmetrical response of the secondary circulation, in accordance with the dipolar solutions of the Sawyer-Eliassen equation, with most of the streamlines outside the RMW aligning in the radial direction and most of the streamlines inside the RMW in the vertical direction.The result is a drawing in of absolute angular momentum (AAM) surfaces which, in turn, causes an increase in the tangential velocity, and forms a more intense tropical cyclone (Vigh and Schubert, 2009).
The boundary layer spin-up mechanism, as described by Montgomery and Smith (2018), has extended the understanding of intensification mechanisms by examining the role of the highly unbalanced boundary layer.If air parcels spiral inwards towards a tropical cyclone centre fast enough to compensate for frictional AAM loss, then an initially subgradient tangential wind in the boundary layer inflow may become supergradient, allowing the tangential wind within the boundary layer to be higher than the tangential wind above it.The unbalanced mechanism can also spin up the free vortex above the boundary layer through vertical transport of the high AAM air at the top of the boundary layer.
The axisymmetric theory does not fully explain the development of a TC, particularly during rapid intensification, due to the presence of asymmetric processes.These include the role of vortical hot towers (VHTs), which are local small, regions of high relative vorticity and high vertical velocity regions within the eyewall.VHTs and their associated downdrafts can act to transport heat and angular momentum inwards to the eye prior to rapid intensification (Guimond et al., 2010) causing the storm to intensify by warming the eye and increasing the relative vorticity in the region of the VHTs.One other phenomenon not accounted for in the balanced, symmetric paradigm is vortex Rossby waves (VRWs) which are waves that propagate on the radial potential vorticity (PV) gradients in tropical cyclones in a similar way to Rossby waves on planetary scale meridional PV gradients (Montgomery and Kallenbach, 1997).Vortex Rossby waves are capable of inducing barotropic instability within the eyewall which can affect the annular heating distribution and therefore impact on the intensity of the storm (Schubert et al., 1999).
Many of these unbalanced and asymmetric processes have been examined in studies of intensity fluctuations that occur during the intensification of TCs, which are not easily explained by an axisymmetric balanced dynamical theory.One example is vacillation cycles, a form of intensity fluctuations that sometimes occurs during rapid intensification.Nguyen et al. (2011) showed that, during rapid intensification, Hurricane Katrina (2005) exhibited structural changes that caused it to 'vacillate' between monopolar and ring-like states, which also led to short-term intensity changes with the more monopolar states associated with acceleration of the tangential wind well inside the RMW and little intensification near the eyewall.The monopolar and the ring-like states were termed 'symmetric' and 'asymmetric' respectively because the former was associated with a smaller azimuthal standard deviation of PV and the latter a higher azimuthal standard deviation of PV.It should be noted that monopolar vs. ring-like and symmetric vs. asymmetric are independent metrics but are, in this case, correlated.Hankinson et al. (2014) ::::::::::::::::: Nguyen et al. (2011) showed that the asymmetric states were associated with radially inward moving isolated PV anomalies .The cause of the asymmetric states was further examined by Reif et al. (2014) who ::: and : related asymmetric periods to both convective and barotropic instability.Hardy et al. (2021) showed similar processes occurring during the rapid intensification of Typhoon Nepartak (2016) with monopolar states associated with near stagnant tangential wind tendency and weaker eyewall updrafts than in the ring-like phase.Similar changes in structure have been identified in observational data, notably in Kossin and Eastin (2001) who identified two regimes with a monopolar and ring-like angular velocity distribution, which also have concomitant monopolar and ring-like equivalent potential temperature distributions.
Another form of intensity fluctuation that can occur in strong TCs are eyewall replacement cycles, where convection associated with outer rainbands develop into a second outer eyewall that gradually moves inwards and replaces the original inner eyewall (Willoughby et al., 1982).Eyewall replacement cycles are known to cause large intensity changes in TCs; however, the RI does not typically resume immediately after the formation of the secondary eyewall, although they are often the cause of cessation of a rapid intensification period, for instance in Hurricane Earl (2010) (Montgomery et al., 2014).Diurnal cycles have also been known to induce intensity fluctuations in TC structure during rapid intensification (Lee et al., 2020;Dunion et al., 2014) although these fluctuations can be explicitly linked to the external environment and have an imposed period of 24 hours.
Hurricane Irma (2017) underwent RI twice (Fig. 1b).During the latter RI event intensity fluctuations have been observed by Fischer et al. (2020) who used observational data to identify two periods of weakening during rapid intensification where the RMW suddenly increased.The two periods of weakening were hypothesised to have different causes but were both linked to lower tropospheric convergence and VRW activity.The intensity fluctuations in Fischer et al. (2020) were subtle (relatively small intensity changes compared to most eyewall replacement cycles), but did involve an expansion of the RMW which, as in the case of a full eyewall replacement cycle, can increase the radius of gale force winds and increase the probability of storm surge, hence motivating a need to understand and be able to predict these forms of fluctuations.
In this paper we analyse the intensity fluctuations of Hurricane Irma using both observations and convection-permitting ensemble simulations to help to understand whether or not the inner core intensity fluctuations are a previously unknown phenomenon or exist on a spectrum that may include vacillation cycles, eyewall replacement cycles or other structural changes that occur during rapid intensification.This will involve investigating the cause of the intensity fluctuations and understanding the structural and dynamical changes of the TC in the transition between a strengthening and weakening phase.
The paper will be organised in the following way: Section 2 will describe the evolution of Hurricane Irma during the relevant rapid intensification period and highlight the structural and intensity changes as well as the track.Section 3 will describe the data used in the analysis, including observations, and the setup of the model simulations.The results are presented in section 4 with discussion in section 4.5.Section 5 generalizes the results across more ensemble forecasts and concluding remarks are given in Section 6.
2 Synoptic overview of Hurricane Irma (2017) Hurricane Irma was the first major hurricane of the 2017 North Atlantic hurricane season.Irma peaked at an intensity of 80 m s −1 (1-minute sustained surface wind speeds) with a central surface pressure estimate of 914 hPa early on 06 September before making landfall in Barbuda.A summary of the track of Irma is shown in Fig. 1 along with the best track surface wind speed.
afternoon of 05 September.Mean sea level pressure data is preferable to tangential wind data as an intensity proxy, because the latter is strongly dependent on the direction of the flight into the eyewall and the height of the aircraft.
The dropsonde data is available in a quality-controlled post processed format (in some cases raw data was used instead due to lack of availability).In addition some of the NOAA aircrafts are equipped with C-band and doppler radars on the nose, lower fuselage and tail.The processed lower fuselage and tail radar data is used in the analysis and shows precipitation in dBZ reflectivity.All the processed dropsonde and flight-level data used in this analysis is available from the Hurricane Research division.1 .

Intensity fluctuations in observations
The focus of the analysis is on the second period of rapid intensification which starts on 04 September at around 00 UTC and finishes around 00 UTC on 06 September (Fig. 1b, Fig. 2).During the period of rapid intensification the MSLP decreases from around 970 hPa to its minimum value of 914 hPa.This rapid deepening is interrupted by two periods of stagnation or slight weakening where the MSLP does not continue to decrease.These periods of weakening are marked by blue bands in Fig. 2. The first weakening period starts around 13 UTC on 04 September and lasts for about 12 hours and is followed by a strengthening period from 01 UTC on 05 September until 11 UTC on 05 September.The second weakening period starts around 11 UTC on 05 September and lasts for about 4 hours.
Figure 3 shows observations, from in-flight radar and satellite imagery, of the structural changes just before and after the start of the second weakening period.The convection during the weakening period appears more azimuthally symmetric and continuous as shown in Fig. 3b compared to Fig. 3a where two regions in the north-west and south-east eyewall have relatively high rainrates.The convection is shallower in the weakening period as indicated by warming cloud tops shown in Fig. 3d compared to Fig. 3c.The shallower nature of the convection is also evident in the microwave imagery in Fig. 3e and Fig. 3f.A similar structural change occurs during the first weakening period (not shown) with banded features within the eyewall giving way to broader but shallower convection compared to prior to the weakening period.

Numerical model
An 18-member ensemble of convection-permitting forecasts for Hurricane Irma has been produced using a limited-area configuration of the Met Office Unified Model (MetUM; Cullen, 1993), coupled to the Joint UK Land Environment Simulator (JULES) model for the land surface (Best, 2011;Clark et al., 2011).The ensemble forecast was initialised at 00 UTC 03 September 2017 and run out to four days.
The MetUM solves the fully compressible, deep-atmosphere, non-hydrostatic equations of motion using a semi-implicit, semi-Lagrangian scheme (see Wood et al. (2014) for details).Model prognostic variables are defined on a grid with Arakawa-C grid staggering (Arakawa and Lamb, 1977) in the horizontal and Charney-Phillips grid staggering (Charney and Phillips, 1953) in the vertical, with a terrain-following vertical coordinate.
Both the MetUM and JULES include a comprehensive set of parametrisation schemes for key physical processes, and the way in which these are configured defines a model science configuration.Here we use the tropical version of the Regional Atmosphere and Land -Version 1 (RAL1-T) configuration presented in Bush et al. (2020), designed for use in km-scale regional models in the tropics.We have made one change to the RAL1-T configuration, which is to reduce the air-sea drag at high wind speeds, as motivated by observational data (Powell et al., 2003;Black et al., 2007).This improves the match to the observed wind-pressure relation of tropical cyclones and has since been included in RAL2-T.
The extent of the regional model domain is shown in Fig. 1, and has been chosen so that Irma is located well away from the boundaries at the forecast initialisation time.The horizontal grid spacing is 0.04 deg (approximately 4.4km) in both directions, and there are 80 vertical levels with a horizontal lid at 38.5 km above sea level (ASL).The model time step is 75 s.
Each member of the convection-permitting ensemble is one-way nested inside a corresponding member of the Met Office global ensemble prediction system, MOGREPS-G (Bowler et al., 2008).The science configuration used in MOGREPS-G is Global Atmosphere 6.1 (GA6.1;Walters et al. (2017)), which was used operationally at the Met Office for global deterministic and ensemble weather forecasting at the time the research was undertaken.The most important difference between GA6.1 and RAL1-T is that convection is parametrised in the former but explicit in the latter.The global model grid spacings are 0.28125°a nd 0.1875°in the zonal and meridional directions (about 31 km × 21 km in the tropics), respectively.In the vertical there are 70 levels up to a fixed model lid 80 km ASL.The model time step is 450 s.Initial conditions for each MOGREPS-G member are formed by adding perturbations to the Met Office global analysis, where the perturbations are generated using an ensemble transform Kalman filter (Bishop et al., 2001).The initial state of each MOGREPS-G member is then interpolated to the finer regional grid to provide initial conditions for the nested convection-permitting ensemble member.There is no data assimilation or vortex specification scheme in the regional model itself, but central pressure estimates from tropical cyclone warning centres are assimilated as part of the global model data assimilation cycle (Heming, 2016).Lateral boundary conditions for each convection-permitting ensemble member are provided by the driving MOGREPS-G member at an hourly frequency.
The initial SSTs, which differ between perturbed members, are held fixed throughout each forecast.
MOGREPS-G includes two stochastic physics schemes to represent the effects of structural and subgrid-scale model uncertainties: the random parameters scheme (Bowler et al., 2008) and the stochastic kinetic energy backscatter scheme (Bowler et al., 2009).These are not included in the convection-permitting ensemble, so that ensemble spread is generated only by differences in the initial and boundary conditions inherited from the driving model.

Diabatic tracers
Incorporated into the MetUM are two sets of tracers (PV and potential temperature, θ) capable of diagnosing diabatic contributions from various parametrisations within the model (Saffin et al., 2016).Examples of this being done previously in extratropical cyclones include, for example, Chagnon et al. (2013).The PV is diagnosed in a semi-Lagrangian way by the tracer such that, The change in PV is given by the sum of increments from all physical processes in the first term represented by the subscript phy (namely radiation, microphysics, gravity wave drag, boundary layer diabatic heating and friction and cloud pressure rebalancing).There are also dynamical processes in the second term represented by the subscript dyn which include the dynamical solver and mass conservation tracers.Ideally these would be zero and preserve the material conservation of PV.
However, approximations in the dynamical core mean that such processes may be non zero.The ε term represents residuals in the PV budget which may come from truncation errors or non linear interaction effects between the physical tracers.PV adv (x, y, z, t + 1) − PV(x, y, z, t). (2)

TC centre finding method
Much of the analysis is done from an axisymmetric perspective in storm relative cylindrical coordinates.Calculations such as this can be highly sensitive to the location of the storm centre.The simplest way to find the TC centre in the model simulation is to find the coordinates that minimize the surface level pressure field.However, meso-vortices within the eyewall often lead to the minimum surface level pressure being displaced from the geometric centre of the eye into the inner eyewall which can cause the tangential flow within the eye to be overestimated and the tangential flow outside the eye to be underestimated.
Several more robust methods have been proposed, each with their own advantages and disadvantages.These include finding PV centroids (e.g.Riemer et al., 2010), geopotential height minima (e.g.Stern and Zhang, 2013) or finding the point that maximises tangential wind speed in cylindrical coordinates at its RMW (e.g.Ryglicki and Hart, 2015).
The method used in this analysis balances the need for a consistent and reliable method for finding the location of the TC centre to an appropriate degree of precision, while considering the computational cost of doing so for 18 ensemble members over a 4 day simulation period.The method used here is similar to the one used by Reasor et al. (2013) for flight-level radar data which can also be applied to model fields and uses a simplex algorithm to find the point that maximises the tangential wind within an annulus with a radius equal to the :::::: surface RMW.The simplex algorithm applies geometric transformations to triangles consisting of three points (the simplex) to find the next set of three points.Each point in each simplex is a prospective TC centre where the tangential wind within the :::::: surface RMW annulus can be evaluated.For each iteration in the simplex algorithm the three points will, progressively, increase the tangential wind within the :::::: surface RMW annulus until it is maximised.
The convergence criteria for the algorithm are: no more than 50 function evaluations, an absolute error between iterations of no more than 0.5 m s −1 for the function evaluation, and an absolute error of no more than 0.5 km between points inside a simplex (well under the grid spacing of the model at 4.4 km).Some studies (e.g.Bell and Lee, 2012) average an ensemble of solutions based on different initial simplexes; however, it was found that changing the location of the initial simplex did not result in a significantly different TC centre and so a single solution method was used.

Results
The fluctuations modelled during rapid intensification in Hurricane Irma have similarities to both vacillation cycles and eyewall replacement cycles but with important differences that will be discussed in detail.

Model simulation of intensity fluctuations
The second period of rapid intensification in Hurricane Irma is broadly captured by the convection-permitting ensemble forecasts (Fig. 1).One of the ensemble members (ensemble member 15) was analysed in detail as it was judged to be most representative in terms of the size of the :::::: surface : RMW, the surface wind speed, mean sea level pressure and track, in comparison to the observations.Fig. 4 shows how the MSLP and surface wind speed change in this ensemble member in addition to the :::::: surface RMW.The modelled MSLP is slightly higher than the NOAA best track values but the rate of deepening is captured well with the rapid intensification occurring at the correct time.Even with the reduced drag at high wind speeds the windpressure relation in the model is too steep (wind speeds too slow for a given central pressure) and consequently the wind-speed is underestimated compared to observations once RI occurs.However, the timing of the rapid intensification and its cessation is accurate.The track of this forecast and the other ensemble members are shown in Fig. 1 and all agree reasonably well with the best track.
The maximum tangential wind, particularly near the top or just above the boundary layer (e.g. at 1532 m) also exhibits these fluctuations but does lag behind compared to higher levels (e.g. at 3002 m) where the maximum tangential wind follows a similar pattern to the surface total wind speed.This is also true of the expansion of the RMW, with the increase in the RMW happening at 1532 m (dark green line) prior to the increase in the surface RMW (aqua line).At the surface, the signal in the tangential wind speed is weaker compared to at higher levels.The role the radial flow plays in modifying the total surface windspeed during the fluctuations, and the reason for the tangential wind spin-down preceding a weakening phase is explored in detail in Section 4.4.
The simulation shows four weakening periods and three strengthening periods which are defined in terms of surface wind speed, surface RMW and MSLP.There is also an uninterrupted period of intensification prior to these fluctuations.During the period of intensity fluctuations from 45 hours to 84 hours Irma is still rapidly intensifying overall, so the brief interruptions in intensification do not stop rapid intensification from happening.The main aim of the analysis is to determine why these intensity fluctuations happen during this period of rapid intensification, the mechanisms behind them and any structural changes with which they are associated.
It should be noted that during the analysed rapid intensification period Hurricane Irma was a fairly symmetric storm under low vertical wind shear with environmental factors playing a minimal role in these fluctuations.Changes in vertical shear, translation speed, sea surface temperature, maximum potential intensity and the diurnal cycle of convection are not correlated with the intensity fluctuations (not shown).helpful :: to ::::::: examine ::: this ::: PV :::::::: structure.: Fig. 5 and Fig. 6 show the PV field from a horizontal (just above the boundary layer where the change is most visible) and azimuthally-averaged perspective with times selected to best illustrate the evolution of the PV from just prior to the start of a weakening phase to the end of the weakening phase and start of the next strengthening phase.
The evolution during the strengthening phases is less dramatic and is not shown.Prior to each weakening phase the PV field is ring-like and elliptical (Fig. 5a, f, k, p).This elliptical PV field becomes more circular at the start of each weakening phase (Fig. 5b,g,l,q).The PV field also becomes more monopolar during a weakening phase with higher PV in the centre of the storm and lower PV in the eyewall.A comparison of Fig. 6a,f,k,p with Fig. 6b,g,l,q shows that the transition from a ring-like to a more monopolar PV structure at the start of the weakening phase occurs primarily just above the boundary layer especially between 1 km and 2 km height.The trend towards a more monopolar distribution continues to the middle of the weakening phases where a 'C' shaped ring of high PV (Fig. 5c,h,m,r) develops near the TC centre above the boundary layer (Fig. 6c,h,m,r).
The PV within the boundary layer also declines but maintains a more ring-like structure.The end of the weakening phase is characterised by the upward movement of the high PV zone at around 2 km height in the eye (Fig. 6d,i,n,s), and re-formation of a weak, circular, PV ring above the boundary layer (Fig. 5d,i,n,s).The start of the strengthening phase roughly coincides with the strengthening of this new PV ring (Fig. 5e,j,o,t) which becomes increasingly elliptical during the strengthening phase.
The elliptical to circular transitions are particularly prominent in W1 and W4 which are more pronounced weakening phases than W2 and W3.
Figure 7a summarises these PV structure changes throughout the simulation with an index that describes how monopolar or ring-like the PV distribution is above the boundary layer (Hardy et al., 2021).Higher values of the ratio PV 0 /PV max , where PV 0 is the layer averaged PV at the centre of the storm and PV max is the maximum layer averaged PV, imply the vorticity structure is more monopole-like while lower values imply the structure is more ring-like.
During the weakening phases there is a trend for the PV structure to become more monopolar.At the end of each weakening phase the trend suddenly reverses and the vorticity structure becomes more ring-like.The change in the tendency of the vorticity structure is very sudden and coincides exactly with the start and end of each phase.However, as indicated by Fig. 6 the PV distribution does not change uniformly at all heights.At lower levels closer to the boundary layer the PV field is more monopolar at the beginning of the weakening phase, while at higher levels it lags behind and is more monopolar at the start of the next strengthening phase.Note how the storm is continually transitioning away from or towards a ring-like structure.This behaviour is different to intensity fluctuations associated with vacillation cycles where the storm can remain in the monopolar state for 10 hours or more (Hardy et al., 2021).It should be noted that the more dramatic weakening phases, W1 and W4 shown in Fig. 5a-e,p-t and Fig. 6a-e,p-t are associated with a more pronounced realignment of PV both in terms of the ring becoming more monopolar and an overall decrease in PV between Fig. 5 c,r and Fig. 5 d,s.Fig. 7a shows a much bigger increase in PV 0 /PV max for W1 and W4 compared to W2 and W3.This is also seen in Hardy et al. (2021) with a greater change in PV 0 /PV max associated with a more dramatic intensity fluctuation.Other metrics that describe the barotropic structure (Fig. 7b-d) also show a more pronounced change during W1 and W4 compared to W2 and W3.It is well understood that annular vorticity rings can only be maintained by constant diabatic forcing and that without this the rings will be unstable and the vorticity will be redistributed into a monopole like structure (e.g.Prieto et al., 2001;Nguyen et al., 2011).
apparent when 10-minute data is averaged over an hour.The PV contribution from diabatic processes other than large scale transport, during the weakening phase, is negative indicating the entire positive PV tendency is linked to movement of PV into the eye.The negative PV tendency regions in Fig. 8 are caused by the loss of PV through the updraft in the eyewall.There is also a gain of PV advected near the surface particularly at T+48 h (Fig. 8b) which can be linked to an increase in the inflow within the eye region and transport of frictionally generated PV from greater radii.
In addition to the radial PV structure the PV also varies azimuthally with the intensity fluctuations.One way of describing the azimuthal PV symmetry is the method of Nguyen et al. (2011) and Reif et al. (2014), where the azimuthal standard deviation of PV is calculated at each radius and the maximum value is taken.A high standard deviation of PV implies a less azimuthally symmetrical storm.It should be emphasised that this is a separate metric not related to the radial distribution of PV (i.e monopolar and ring-like distributions).In the case of Nguyen et al. (2011) for example, the radial and azimuthal measures of PV were used interchangeably to describe 'symmetric' or 'asymmetric' states (the ring-like PV distribution in Nguyen et al. (2011) was correlated to an azimuthally symmetric state which is not the case here).In this study, references to symmetry only refer explicitly to variations in the azimuthal distribution of PV.PV rings become increasingly more elliptical (higher eccentricity) confirming that the start of a weakening phase is associated with a rapid change from an elliptical PV ring to a more circular one (also seen in Fig. 5).
Figure 9 shows perturbation vertical velocity and relative vorticity at different heights at the same times as in Fig. 5.The VHT-like structures are more likely to be present during strengthening phases (particularly towards the end of the strengthening phases) and rarely form during weakening phases although an already existing VHT-like structure may persist for a couple of hours into the weakening phase.These structures typically last on the order of an hour which is a little shorter than the lifespan of convective structures found by Yeung (2013) during the rapid intensification of Typhoon Vicente.The VHT-like structures move anticlockwise, with the flow, near the RMW.Filaments of high pertubation vertical velocity, but relatively low pertubation relative vorticity, associated with inner rain-bands, also commonly emanate outward from these VHT-like structures (see, for example Fig. 9p north of the RMW).It is fairly common, within the strengthening phases, to see two VHT-like structures at once which typically are 180 degrees from each other.In this case one VHT-like structure tends to be much stronger than the other.An example of this is shown in Fig. 9a with the VHT-like structure in the southwest quadrant being more intense and deeper than the one in the northeast quadrant.
During the weakening phases VHT-like structures rarely form such that in the middle of a weakening phase it is unusual to see one of these structures.The T+72.2 h panel (Fig. 9 m) does show a weak, shallow, VHT-like structure in the northwest quadrant though it should be noted that W3 is the weakest weakening phase.Towards the end of a weakening phase VHTlike structures may redevelop and often form outside of the RMW.The T+50.7 h panel (Fig. 9d) shows signs of a VHT-like structure on the eastern side of the TC outside of the RMW that forms before moving inwards.If Fig. 9 is compared to Fig. 5 it can be seen that the VHT-like structures are typically located at the two points on the elliptical PV rings furthest away from the centre (i.e.along the semi-major axis of the PV elliptical ring).The strongest VHT-like structures tend to form just prior to a weakening phase and may last for the first few hours of the weakening phase.The VHT-like structure in Fig. 9a,p are examples of particularly strong VHT-like structure that occur just prior to the W1 and W4 phases respectively but are shown to very quickly dissipate during the start of W1 and W4 respectively (Fig. 9b,q).The regions of locally high vertical velocity and relative vorticity associated with the VHT-like structures becomes increasingly de-localized and distributed over the entire eye-wall region resulting in a more axi-symmetric structure.Any regions of high pertubation vorticity or vertical velocity that form during the weakening phases are much weaker and shallower than the VHT-like structures that form during the strengthening phases (such as the low-level region of high relative vorticity north-west of centre in Fig. 9m) or occur well outside of the RMW (such as the updraught south-east of centre in Fig. 9r).

Tangential wind budget
The spin-up of a TC can be examined in terms of the tangential wind budget which describes contributions to the mean tangential wind tendency from radial and vertical advection of absolute angular momentum, which can be further split up into mean and eddy contributions.A form of the tangential wind budget based on Persing et al. (2013) is: where v is the tangential wind, u is the radial wind, w is the vertical velocity, f is the Coriolis parameter, and ζ is the relative vorticity.Overbars represent azimuthal averages of these terms while primes represent perturbations from the azimuthal average.The terms on the right hand side of the equation from left to right are: mean radial vorticity flux, mean vertical advection of absolute angular momentum, eddy radial vorticity flux and vertical eddy advection of absolute angular momentum.
The final term, F , represents sub-grid frictional contributions to the budget which are negligible outside of the boundary layer.
In order to understand the contribution of the VHT-like structures to the spin-up or spin-down of the TC, the eddy and mean contributions to the tangential wind budget were examined.Fig. 10 shows the contributions to the tangential wind budget through mean and eddy radial vorticity fluxes and vertical advection of AAM.Near the eyewall, the mean term has a positive contribution to the tangential wind in the boundary layer due to the radial inflow and a negative contribution above the boundary layer where the boundary layer outflow jet is (Fig. 10a,c).The larger positive contribution to the tangential wind in the boundary layer, and larger negative contribution above the boundary layer in S1 compared to W1 is attributed to a stronger inflow and outflow in and above the boundary layer respectively.
Just above the boundary layer the eddy term has a positive contribution to the tangential wind budget in both S1 and W1 (Fig. 10 b,d).However, in S1 the magnitude of the positive eddy contribution above the boundary layer (around 1500 m) is larger.This finding is robust across all strengthening and weakening phases and extends generally to other ensembles that show these intensity fluctuations (see Section 5).The greater positive contribution, to the tangential wind, of the eddies just above the boundary layer during the strengthening phases is associated with VHT-like activity.These results are illustrated in Fig.
11 which shows during the 45.5 hour to 57.5 hour period (comprising both W1 and S1 periods) a composite of all times where there is either no VHT activity (Fig. 11 a,b) or strong VHT activity (Fig. 11 c,d).In total there were 12 times where strong VHT activity occurred and 10 times where no VHT activity occurred during this period.This allows the effect of the VHT-like structures to be analysed more directly.As can be seen by comparing Fig. 11 b and d VHT-like structure activity is associated with an increased positive tangential wind tendency from the eddy terms just above the boundary layer compared to times without VHT activity.This is despite the increase in the negative contribution from the mean flow (Fig. 11 a,c).It is harder to say if the association between VHT-like structures and an increased eddy positive wind tendency above the boundary layer is causal and may instead be related to the relative frequency of VHTs during weakening phases compared to strengthening phases.Times during S1 with VHT activity (not shown) were associated with greater eddy tangential wind tendency compared to times during S1 without VHT activity but the effect was small.
This can also be seen in the observations in Fig. 3 a,b which shows the convection in the eyewall appearing to thicken with the moderately high precipitation rates occupying a greater radial extent during a weakening period than just prior to it.The overall heating rates are substantially weaker during the middle of the weakening phases compared to the strengthening phases (e.g. a maximum of around 30 K h −1 in the middle of W1 compared to around 45 K h −1 at the start of S1) with substantial heating occurring outside the RMW.In the strengthening phases the heating is concentrated in a narrow band (of around 10 km width) just inside the RMW, while in the weakening phases the heating maximum is shifted outside of the RMW.Just above the boundary layer there is a heating maximum in both the strengthening and weakening phases, the heating here is stronger in the strengthening phases but is located inside the RMW during both the weakening and strengthening phases.The effect of eddy diabatic heating was also investigated.These results are not shown since the azimuthally averaged eddy heating was small, typically an order of magnitude smaller than the mean heating terms which is similar to the results of, for instance, Montgomery and Smith (2018).The eddy terms had the largest contribution just below the freezing level and had a dipole-like structure with heating below and cooling above.No significant differences in the azimuthally averaged eddy heating distribution were detected between the strengthening and weakening phases with eddy momentum effects from the VHT-like structures playing a much more significant role in causing the intensity fluctuations than their effect on azimuthally averaged eddy diabatic heating.
In terms of how the heating distribution changes just prior to a weakening phase Fig. 12b,c shows a secondary heating maxima at around 55 km radius and 5 km height associated with the inner rainbands.Along these rainbands near their intersection with the eyewall there are regions of enhanced convection which can be seen in Fig. 13a T+44.5 h in the northwest and southeast associated with VHT-like structures which are responsible for most of the heating.The secondary heating maxima associated with the inner rainbands becomes more distinct by T+45.5 h (Fig. 12b) which develops into a secondary updraft by T+46.5 h (Fig. 12c).A single VHT-like structure is still visible at T+46.5 h in the southeast quadrant (Fig. 13c).However, by T+47.5 h (Fig. 13d) an azimuthal symmetrisation has taken place with the inner-rainband convection visible as a second ring outside the eyewall.The heating from VHT-like structures that occur in the inner rainbands near where they intersect with the eyewall becomes less significant between T+44.5 h and T+47.5 h (Fig. 12a-d), but the secondary heating maximum from the inner rainbands becomes more distinct (Fig. 13a-d).
Over the next few hours the secondary convective ring becomes more symmetrical and the VHT-like structures continue to become less visible.Eventually by T+50.5 h the secondary convective ring has replaced the first (Fig. 13g).In the remaining hour of W1 the RMW expands out to coincide with the diabatic heating maximum.Note, the inner rainband activity and the associated VHT-like structures may be necessary conditions for a weakening phase to begin; however, it is not sufficient.For example, prior to W1 a VRW event at T+38 h led to the development of a secondary convective ring, which subsequently weakened and did not replace the primary ring.Another particularly strong single VHT-like event that occurred around T+35, in the eyewall region, also did not lead to an intensity fluctuation.

Unbalanced dynamics and the boundary layer
If the boundary layer plays a significant role in the cause of the intensity fluctuations then it may be necessary to attempt to understand the fluctuations in terms of the boundary layer spin-up mechanism as described by Montgomery and Smith (2018).
Examining the agradient wind in and above the boundary layer allows the importance of the unbalanced spin-up mechanism in the intensity fluctuations to be determined.

Primary and secondary circulation in or just above the boundary layer
The agradient wind is the deviation of the tangential wind from gradient wind balance (as in, for example, Miyamoto et al., 2014).The gradient wind is not output directly from the MetUM but calculated from other diagnostic variables.Details of the form of the agradient wind are available in the Appendix.
Figure 14 shows how the agradient wind, the tangential and radial wind vary throughout the simulation both at the radius of 35 km and at the RMW (such that the agradient wind can be examined both at the eyewall and at a fixed radius as during a weakening phase the RMW increases).A negative agradient wind corresponds to a subgradient flow while a positive agradient wind corresponds to a supergradient flow.The blue curve near the surface is chosen to show the subgradient boundary layer flow.The green curve shows the agradient flow a little higher up but still within the boundary layer (Fig. 14a) this is at a height where during the weakening phases the subgradient flow becomes supergradient indicated by the crossing of the zero line).
During the weakening phase an increase in the agradient wind is seen within the boundary layer (Fig. 14 a and c) which gives rise to a stronger outflow jet just above the boundary layer (Fig. 14d).This enhanced outflow jet continues to increase throughout the weakening phase and reaches a maximum at the start of the next strengthening phase.

Tangential wind budgets
To understand how the boundary layer and outflow jet change and lead to a spin-down above the boundary layer Fig. 15 shows how the primary and secondary circulation change and what drives these changes by using the tangential wind budget.The times shown correspond to the times in Fig. 5a-c.
The increase of the agradient wind at the start of the weakening phase leading to an intensification of the outflow jet can be seen by comparing Fig. 15a with Fig. 15c.The main result of this comparison is a radial advection of low angular momentum (Fig. 15d) which acts to cause a spin-down of the eyewall above the boundary layer (Fig. 15c).The spin-down of the tangential wind just above the boundary layer pushes the RMW outwards and results in the 'kink'-like appearance of the RMW.Above the kink the tangential wind is in approximate gradient balance and the flow runs nearly parallel to the AAM surfaces.Eventually the expansion of the RMW above the boundary layer in combination with the weakening inflow within the boundary layer leads to the vertical advection of angular momentum into the low angular momentum region above the boundary layer which can be seen in the pink area near the RMW (in the highlighted yellow ellipse) in Fig. 15f compared to Fig. 15d where the same region is blue.At the increased radius, the coherent eyewall structure reforms with a spin-up as a result of the vertical advection of absolute angular momentum.The outflow jet, which previously reduced the tangential wind in the eyewall now does so within the eye which brings the TC into a strengthening phase.The PGF increases, the supergradient wind in the boundary layer becomes less supergradient, and the outflow jet weakens.
In summary the intensity fluctuations in Hurricane Irma can be understood in terms of unbalanced boundary layer dynamics.
Firstly the agradient wind in the boundary layer increases as a result of a decline of the PGF (likely due to an inner rainband creating a convergence zone above the boundary layer), the rapid increase in the supergradient wind within the boundary layer leads to an intensification of the outflow jet just above the boundary layer which acts to spin down the primary circulation above the boundary layer by advecting in low angular momentum air from the eye, as well as expanding the RMW above the boundary layer.The eyewall restrengthens above the boundary layer with a higher RMW and a recoupling of the primary circulation at the higher RMW with the boundary layer signals the start of the new strengthening phase.This can be seen explicitly by looking at Fig. 12h; the eye-wall forms at approximately the same radius as the updraft located further from the centre of the storm in Fig. 12d.

Discussion
During the weakening phases the RMW expanded, the wind speed decreased and the MSLP stagnated or rose, while during the strengthening phases the opposite occurred.These phases were found to be associated with different diabatic heating distributions, with weakening phases associated with broad and weak columns of heating outside the RMW and strengthening phases associated with stronger, narrower heating columns just inside the RMW.The changing diabatic heating structure during the weakening and strengthening phases is consistent with a simple balanced interpretation of the results; however, heating in high inertial stability environments as in Schubert and Hack (1982) was not found to be a useful predictor of the fluctuations, although inertial stability in the core region did overall increase throughout rapid intensification.
Some of these VHT-like structures may be related to the vortex Rossby wave activity which occured concurrently in some cases.VHTs often appear in a tropical cyclone's immature phase just prior to rapid intensification, such as in Guimond et al. (2010), where their appearance precedes the rapid strengthening and increased azimuthal symmetry of the storm.Although the VHT-like structures in Hurricane Irma do precede a more azimuthally symmetric state of the storm, this is typically during a weakening phase.This difference, on the storm's intensification, between the impact of VHT-like structures in this study and pre-RI such as in Guimond et al. (2010) suggests that VHT-like structures may have different impacts on a mature storm undergoing rapid intensification compared to a much weaker storm that has not yet undergone rapid intensification.
In a study on vacillation cycles Nguyen et al. (2011) described VHT-like structures that appeared to be the result of barotropic and convective instabilities.The VHT-like structures, in Hurricane Irma here, precede the weakening phaseand thus seem to be a cause of the instability rather than a symptom of it.Additionally, the mixing of PV described in Nguyen et al. (2011) causes a decrease in MSLP.However, the opposite of this occurs in the weakening phases in our simulations with MSLP increasing or stagnating during weakening phases.Another key difference between prior work on vacillation cycles is the association of azimuthal symmetry with the radial structure.In Nguyen et al. (2011) the azimuthal symmetry is positively correlated with the ring-like PV distribution, whereas here we have found it to be anti-correlated.The reasons for this are uncertain and should be investigated in future work but it may indicate the fluctuations modelled here may be different kinds of intensity fluctuations to those found in Nguyen et al. (2011).
In terms of trying to understand what these fluctuations are, there are similarities to vacillation cycles particularly with the simulation conducted in Reif et al. (2014) which exhibits transitions from ring-like to monopolar PV distributions but with a more ring-like state than Nguyen et al. (2011).Although one significant difference compared to the vacillation cycles in Hardy et al. ( 2021) is that the more monopolar state during the weakening phases were transient with PV 0 /PV max peaking at the end of the weakening phase before dropping rapidly.The role of barotropic and convective instability does also seem to play a role.However, the azimuthally asymmetric VHT-dominated periods (for example in Nguyen et al., 2011) are not explicitly linked to strengthening phases as they are in this study.Fischer et al. (2020) did identify these fluctuations in the observational data of Hurricane Irma and described them as two separate eyewall replacement cycles triggered by lower-tropospheric convergence associated with a rainband and lower-tropospheric convergence associated with a super-gradient flow respectively.
5 Composites over multiple ensemble forecasts The prior analysis has been carried out for one ensemble forecast.To demonstrate the robustness of the analysis composites of selected key results will be presented across multiple ensemble members.Five out of 18 ensemble members (including ensemble member 15), initialized on 03 September 00 UTC, showed the intensity fluctuations previously discussed.A further six ensembles also showed similar but weaker fluctuations.An additional model simulation, initialized on 02 September 12 UTC, found seven out of 18 ensemble members with the same kind of fluctuations.The following composites are based on the five ensemble members initialised on the 03 September at 00 UTC that show the strongest fluctuations.The composites are over all weakening and strengthening phases in all of these five ensemble forecasts.These weakening and strengthening phases vary in length from one hour to 10 hours, with 4-5 hours being typical and with the data outputted hourly.There are a total of 45 weakening and strengthening phases averaged over.
One of the key aspects of the analysis is the transition during weakening phases from a ring-like PV distribution at the start of the weakening phase towards a more monopolar PV distribution towards the end of the weakening phase.Figure 17 shows a PV tendency composite plot for all weakening and strengthening phases for the five ensemble members with the strongest intensity fluctuations.During the weakening phases there is a positive PV tendency within the inner eye and a negative tendency within the high PV annulus confirming the results from Section 4.2 for Irma's PV structure to become more monopolar in the weakening phases.The opposite is shown in the strengthening phases with PV decreasing in the inner eye and rising in the high PV annulus.Near the RMW outside the PV ring there are positive PV tendencies at the end of the weakening phases which can also be seen in Fig. 5e,j,o,t to Fig. 5d,i,n,s which show, from left to right, the structural PV changes that occur from the start of the weakening phases to the start of the strengthening phases in ensemble member 15.Near the RMW (dashed black line), PV starts to increase at the end of the weakening phases and at the start of the next strengthening phase.
Figure 18 shows the contributions to the tangential wind budget through mean and eddy advection of angular momentum of the strengthening composite relative to the weakening composite (strengthening phases minus weakening phases).Above the boundary layer at a radial distance of 20 km to 35 km the eddy term plays a beneficial role in both the strengthening and weakening phases; however, in the strengthening phases the effect is distinctly greater.This comparison confirms some of the findings shown in Fig. 10 that the eddy momentum flux acts to cause intensification above the boundary layer particularly during strengthening phases.The effect of the mean momentum fluxes are also similar with greater tangential wind spin-up in the boundary layer in strengthening phases compared to weakening phases but also with greater spin-down above the boundary layer in the outflow jet during the strengthening phases.
The composites demonstrate that similar processes are likely occurring in the other ensemble members.The fluctuations in intensity that occurred during rapid intensification and are not just limited to a single ensemble member.This study focuses on a single case, Hurricane Irma (2017), so it is unclear how common this type of intensity fluctuations is in tropical cyclones.
The ensemble forecasts showed no link between the likelihood of the intensity fluctuations and the environmental conditions so the causes of the fluctuations are likely stochastic in nature (in particular with respect to the radial location of VHT-like convective structures that develop).The fluctuations are shown to occur in around a third of the ensemble forecasts suggesting they may be a common feature in rapid intensification and motivating analysis of more cases.
-During strengthening phases, the diabatic heating distribution had a smaller radial extent ::::: spread : and a stronger heating maximum which is located within the RMW.During weakening phases the heating was outside the RMW and had a greater radial extent ::::: spread : than the diabatic heating during the strengthening phases.In conclusion, the findings from this analysis, as summarized in Fig. 19, show the proposed mechanism for the intensity fluctuations observed in Hurricane Irma, and highlight the importance of both the VHT-like structures that develop on the intersection of inner rainbands with the eye-wall and of the development of the supergradient wind within the boundary layer.
It was found that these intensity fluctuations appear in about 1/3 of the ensemble simulations.No link was found between the environment of the storms and the presence of these intensity fluctuations indicating they are governed by stochastic processes.

Figure 1 .Figure 2 .
Figure 1.(a) Best track of Hurricane Irma (black line) with points corresponding to the position of Irma on each date from 30 August 2017 to 13 September 2017.Orography (m) is shown in shading.The domain of the regional model used in this study is shown by the red rectangle.The 18-ensemble member tracks are displayed in grey with ensemble member 15 shown in orange.Islands where landfall occurred are indicated by white dots and labels.(b) The best track wind speed (black), the maximun surface wind speed of the ensemble members initialised on 03 September 00 UTC (grey contours) with ensemble member 15 highlighted in orange.In both panels periods of RI are highlighted in yellow.

Figure 3 .
Figure 3. NOAA P3 flight-level radar (in dBZ) on (a) 05 September 0943 UTC and (b) 05 September 1232 UTC, colour enhanced infrared (IR) imagery (in °C) on (c) 05 September 0945 UTC and (d) 05 September 1245 UTC, and MIMIC microwave imagery (brightness temperature in K) for (e) 05 September 0945 UTC, (f) 05 September 1245 UTC.The upper and lower rows correspond to times just before and after the start of the period indicated by the second blue bar in Fig 2.

Figure 5 .Figure 7 .
Figure 5. PV (PVU, shaded) at 1532 m height for selected times and vertical velocity (1 m s −1 , black contour).The :::::: 1532-m ::::: height RMW is indicated by the dashed black line.A cross marks the centre of the TC.The data is output in 10-minute intervals, times are given to the nearest 0.1 hours.The data is from ensemble member 15 which was initialised at 03 September 2017 at 00 UTC.

Figure 8 .
Figure 8. Change in PV over the past hour due to advection only (shaded, PVU h −1 ).Black line contours show the PV field in intervals of 5 PVU.Additionally, four sets of trajectories are shown for the following (r,z) points (black scatter points): (5 km, 1532 m), (15 km, 1532 m), (5 km, 782 m), and (15 km, 782 m).Purple lines and scatter points represent the forward trajectory over the next hour while mustard lines and scatter points represent the backward trajectory over the previous hour.Each set of trajectories contains 8 points going back or forward with the same radial distance from the storm centre but with different azimuthal angles around the storm centre: to the east, northeast, north, northwest, west, southwest, south and southeast of the storm centre.The grey contours show vertical velocity (ascent) in 0.25 m s −1 intervals indicating the location of the inner eyewall.Yellow dashed line shows the -1 m s −1 inflow contour.

Figure 10 .
Figure 10.Colour shading shows the (a,c) mean and (b,d) eddy contributions to the tangential wind budget (see equation 4) in m s −1 h −1 .Line contours show the average tangential wind tendency in 2 ms −1 h −1 intervals with dashed contours indicating negative tendencies.The top row shows the composite for W1 (every 10 minute output in the W1 phase averaged over) while the bottom row shows the composite for S1 (every 10 minute output in the S1 phase averaged over).The frictional term (not shown) also contributes a large positive :::::: negative tangential tendency in the boundary layer.

Figure 13 .:Figure 14 .
Figure 13.Diabatic heating (Kh −1 :::: K h −1 : shading) for height 4963 m before and during the first weakening phase W1.Vertical velocity contours in intervals of 2 m s −1 .Yellow crosses indicate the location of the maximun local pertubation vertical velocity at the same level for any VHT-like structures as determined by criteria adapted fromn Smith and Eastin (2010).

Figure 17 .Figure 18 .
Figure 17.Composite PV tendencies (PVUh −1 ::::::: PVU h −1 : shading) at 1532 m across all weakening and strengthening phases in the five ensembles with distinct intensity fluctuations.Green dashed lines show the full range of RMWs at the same level.Hatching indicates regions where the average PV exceeds 30 PVU. Black circles show 25 km radial intervals.