Hurricane Edouard (2014) Just After Peak Intensity

Received: 4 April 2018 Revised: 27 October 2018 Accepted: 29 October 2018 Published on: 15 January 2019

DOI: 10.1002/qj.3423

RESEARCH ARTICLE

Azimuthally averaged structure of Hurricane Edouard (2014) just after peak intensity

Roger K. Smith1 Michael T. Montgomery2 Scott A. Braun3

1Meteorological Institute, Ludwig Maximilian University of Munich, Munich, Germany Analyses of dropsonde data collected in Hurricane Edouard (2014) just after its 2Department of Meteorology, Naval Postgraduate mature stage are presented. These data have unprecedentedly high spatial reso- School, Monterey, California lution, based on 87 dropsondes released by the unmanned NASA Global Hawk 3 Mesoscale Atmospheric Processes Laboratory, from an altitude of 18 km during the Hurricane and Severe Storm Sentinel (HS3) NASA Goddard Space Flight Center, Greenbelt, Maryland field campaign. Attempts are made to relate the analyses of the data to theories of

Correspondence tropical cyclone structure and behaviour. The tangential wind and thermal fields Roger K. Smith, Meteorological Institute, Ludwig show the classical structure of a warm-core vortex, in this case with a secondary Maximilian University of Munich, Theresienstr. eyewall feature. Additionally, the equivalent potential temperature field (𝜃e)shows 37, 80333 Munich, Germany. the expected structure with a mid-tropospheric minimum at outer radii and contours Email: [email protected] of 𝜃e flaring upwards and outwards at inner radii. With some imagination, these Funding information contours are roughly congruent to the surfaces of absolute angular momentum. Office of Naval Research Global; N62909-15-1-N021, NSF; AGS-1313948, NOAA However, details of the analysed radial velocity field are quite sensitive to the way HFIP; N0017315WR00048, NASA (HS3); in which the sonde data are partitioned to produce an azimuthal average. This sen- NNG11PK021, ONR; N0001417WX00336, sitivity is compounded by an apparent limitation of the assumed steadiness of the storm over the period of data collection.

KEYWORDS hurricane, observed structure and behaviour, tropical cyclone

1 INTRODUCTION showing the location of each dropsonde can be viewed in fig. 1 of Zawislak et al. (2016), while a description of the storm dur- In the past there have been few measurements of hurricane ing its lifetime is given by Stewart (2014). Brief descriptions structure through the depth of the troposphere, the reason of the storm and the missions flown were given by Braun et al. being that most aircraft reconnaissance flights have not been (2016) and Munsell et al. (2018). able to sample the upper troposphere. Some classic obser- The structure of Edouard was particularly well sampled vational studies are those of La Seur and Hawkins (1963), on 16 and 17 September when it was near its peak inten- Hawkins and Rubsam (1968) and Hawkins and Imbembo sity. On this mission, which lasted about 23 hr, 87 dropsondes (1976), to whom in situ data from an instrumented high-flying were deployed into the hurricane from a height of 18 km. jet aircraft were available. The situation changed recently The purpose of this paper is to present azimuthally averaged 1 through the deployment of the NASA Global Hawk, an radius–height cross sections of various quantities obtained unmanned aircraft system capable of releasing dropsondes in from analyses of these unique data and to compare these rapid succession from the lower stratosphere. During NASA’s analyses with theories of tropical cyclone behaviour. Hurricane and Severe Storm Sentinel (HS3) field campaign in 2014 (Braun et al., 2016), comparatively high temporal and spatial resolution dropsonde observations were made over the 2 DATA Atlantic Ocean in Hurricane Edouard during four missions between September 11, 2014 and September 19, 2014. A map The 87 dropsondes were released into Edouard between 1506 UTC on September 16, 2014 and 0828 UTC on September 1National Aeronautics and Space Administration. 17, 2014, during which time the storm moved from about

(a) v, M (b) dT 16 16 4 12 30 12 2 8 15 8 0

z (km) –2 4 0 4 –4 0 0 0 100 200 300 400 500 0 100 200 300 400 500 radius (km) radius (km)

(c)u (d) θ , M 16 16 e 6 12 12 350 3 8 0 8 340

z (km) z (km) –3 z (km) 4 4 330 –6 0 0 0 100 200 300 400 500 0 100 200 300 400 500 radius (km) radius (km)

(e)RH (f) θ , M 16 3 e

12 90 350 2 8 70 340

z (km) z (km) 1 4 50 330

0 0 0 100 200 300 400 500 0 100 200 300 400 500 radius (km) radius (km)

FIGURE 1 Radius–height cross sections of selected fields derived from the dropsonde data: (a) tangential velocity component, v, contour interval 5 m/s, shading indicated on the side bar in m/s, and absolute angular momentum, M, black lines, contour interval 5 × 105 m2/s; (b) temperature perturbation, dT, contour interval 2 K (positive values), 1 K (negative values), shading indicated on the side bar in K; (c) radial velocity component, u, contour interval 3 m/s, shading indicated on the side bar in m/s; (d) equivalent potential temperature, 𝜃e contour interval 10 K, shading indicated on the side bar in K, and absolute angular momentum, black lines, contours as in (a); (e) relative humidity, RH, contour interval 10%, shading indicated on the side bar in %; (f) a zoomed-in version of (d) at heights below 3 km [Colour figure can be viewed at wileyonlinelibrary.com]

32◦Nto35◦N (Stewart, 2014, table 1). The distribution of sonde time is the time of the actual measurement at a particu- the dropsondes is shown in Abarca et al. (2016, fig. 2a). The lar level. Using these adjusted positions relative to the centre, sonde data were post-processed by the National Center for radial and tangential velocities were calculated with the storm Atmospheric Research (see Hoch et al. (2017)) using their motion removed to obtain storm-relative flow. This analysis Atmospheric Sounding Processing Environment (ASPEN) was done for all dropsondes during the flight. Bins were then software (Young et al., 2016). The analyses of the dropson- created for averaging once all the derived fields, including des include a dry bias correction in the upper troposphere. radial and tangential velocity, were calculated. The analysis of these sondes is described briefly below. The midpoints of the bins were at radial locations 10, 30, 50, 70, 100, 150, 210, 270, 330, 400, 480 and 560 km from the centre.2 The number of soundings were distributed within 2.1 Computation of azimuthal averages each bin as follows: 0–20 km radius (11 sondes), 20–40 km To calculate the azimuthal averages, the dropsonde data were (9), 40–60 km (6), 60–80 km (7), 80–120 km (10), 120–180 first interpolated to 181 pressure levels with a spacing of 5 km (0), 180–240 km (9), 240–300 km (8), 300–360 km mb. The storm centre positions over the time period of the (8), 360–440 km (4), 440–520 km (8) and 520–600 (7). No flight were used to determine the location of each dropsonde additional smoothing was applied to the individual dropsonde relative to the evolving centre position. Best track data from the National Hurricane Center were used to estimate the mean 2The dataset is the same as that used by Abarca et al. (2016). However, the storm motion over the flight period. The positions of the drop- subdivision into bins is rather different. Even so, the tangential wind field sonde data were shifted to a reference time of 0000 UTC on in fig. 3a of Abarca et al. is very similar to that shown in Figure 1a here. The pressure field is rather smooth and should be similar between the two September 17 using the storm motion and the time difference analyses. Indeed, Abarca et al. did note that “the data were robust to different between the sonde time and this reference time. Here, the bin-length choices.” MONTGOMERY ET AL. 213 data. If, when computing the azimuthal mean, some values troposphere. The decrease in the tangential velocity compo- were missing from individual soundings, they were simply not nent with height corresponds through balance considerations included in the calculation of the mean. Because there were with the warm-core structure (see Figure 1b). no dropsonde data at radii between 120 and 200 km and there- There is evidence of a weak inner tangential wind max- fore in the radial bin 120–180 km, the azimuthal values for imum near 40 km and an outer maximum at a radius of a radius of 150 km were determined by linear interpolation about 100 km. The formation of the outer wind maximum between the bin midpoints at 100 and 210 km. was the focus of a separate study by Abarca et al. (2016). The upper-level anticyclone begins at a radius of about 80 km, while the strength of the anticyclone increases with 2.2 Steady-state composite data radius and the anticyclonic circulation deepens with increas- Although the storm was at peak intensity near the start of ing radius. The maximum anticyclonic flow is found at an the measurements, the intensity decreased by about 10 m/s altitude between 14 and 15 km at a radius of 500 km and during the measurement period (see fig. 1 of Abarca et al. would appear to be increasing beyond this radius. 2016, and the accompanying discussion of the various fac- Figure 1a also shows the absolute angular momentum (or tors in this decay). Because of the relatively long period of M) surfaces corresponding with the tangential wind component. These are calculated using the formula M = rv + 1 fr2, data collection, attempts were made to subdivide the data into 2 two separate subsets, one for the first half of the flight and where r is the radius and f is the Coriolis parameter at the ◦ another for the second half. In this subdivision the soundings mean latitude of Edouard (33 N) during the period of the were distributed as follows over the course of the first and dropsonde measurements. Consistent with theoretical expec- second halves of the flight: radius 0–20 km (first half 6, sec- tations, the M surfaces flare outwards with height, with M ond half 5), 20–40 km (4, 5), 40–60 km (3, 3), 60–80 km (3, mostly increasing with radius and decreasing with height. 4), 80–120 km (5, 5), 120–180 km (0, 0), 180–240 km (4, 5), There is a local maximum of M, located at a height of about 6 240–300 km (4, 4), 300–360 km (3, 5), 360–440 km (1, 3), km and a radius of just over 400 km. This maximum is accom- 440–520 km (3, 5) and 520–600 km (2, 5). Clearly, breaking panied by a negative radial gradient of M at radii beyond up the soundings into two separate halves of the flight reduces it, implying that, according to linear theory, the flow would the number of samples in each radial bin, although not nec- be centrifugally unstable locally (Rayleigh, 1917). Since the essarily by half since a good part of the first half of the flight dropsonde data at these radii are quite sparse (see fig. 3b was sampling storm outflow beyond a radius of 600 km. As of Abarca et al., 2016) and the period of collection spans mentioned earlier, the biggest problem occurs between 120 an interval of more than 16 hr, we do not attribute much and 180 km, where there are no soundings for either time. significance to the implied regions of instability at these radii. ◦ For these reasons, and because there was qualitative simi- There is a marked (> 2 C) positive temperature anomaly larity between the derived structures from the two datasets inside a radius of about 200 km (Figure 1b). This anomaly ◦ in regions where there was data, we have based the analy- has a maximum of nearly 10 C on the axis of rotation at an sis below on a composite for the whole period. Thus, all the altitude of about 8 km. (For the calculation of temperature per- storm-relative dropsonde data from the whole flight occurring turbation, the “environmental temperature” was determined within a particular bin were averaged. This procedure is tanta- by averaging all dropsonde data at radii > 200 km. Specif- mount to assuming the storm to be in a quasi-steady state for ically, there were 46 soundings used for calculation of the the duration of the flight. Some limitations of the quasi-steady “environmental” mean temperature for the temperature per- state assumption will emerge later. turbation plot.) There is a weak cold temperature anomaly at low levels beyond a radius of about 60 km. The negative temperature anomalies beyond a radius of about 400 km and those 3 STORM STRUCTURE above 13 km are due to the way in which the ambient temperature has been defined and are presumably not significant. Figure 1 shows radius–height cross sections obtained from the Since the reference temperature is based on an average of all dropsonde data as described in Section 2.1 above. The wind soundings beyond a radius of 200 km, and if the temperature data are smoothed using a centred 1–4–1 box filter applied 10 in this region decreases outwards, negative anomalies would times. be expected at large radii. The low-level negative anomaly between radii of 60 and 240 km is plausibly a result of the evaporation of falling raindrops. 3.1 Tangential wind and warm-core structure The storm-relative composite tangential wind component (v, 3.2 Radial velocity component Figure 1a) and temperature perturbation (dT, Figure 1b) show the classical structure of a warm-core vortex with The storm-relative composite radial flow (u, Figure 1c) shows the maximum wind in the lower troposphere and the wind two features of the classical tropical cyclone structure with a decreasing with height, becoming anticyclonic in the upper layer of strong inflow below about 1 km extending to large 214 MONTGOMERY ET AL. radii, as well as a layer of strong outflow in the upper tropo- Other interesting features of the radial flow are the layers of sphere between about 9 and 14 km depending on the radius. inflow in the upper troposphere, above and below the two out- The maximum low-level inflow is about 15 m/s. The layer of flow layers. Such features are often seen in numerical model upper tropospheric outflow is a few kilometres deep with a simulations (e.g., Rotunno and Emanuel, 1987, fig. 5c; Pers- maximum of almost 12 m/s at an altitude of about 12 km and ing et al., 2013, figs. 10a, 11a and 15a), but to our knowledge a radius of about 400 km. are not well understood. Perhaps surprisingly, the level of maximum outflow in the It should be pointed out that while the broad features of the upper troposphere does not coincide with that of the max- analysed radial flow field are robust (e.g., the strong inflow in imum anticyclonic flow, which is typically 2 km higher. A the boundary layer, the upper-level outflow and the outflow in plausible explanation for this finding is that during the earlier the inner and outer eyewalls), the details of this field are some- period of measurement the outflow was higher than during the what sensitive to the way in which the sonde data are binned to later part. This possibility is supported by the fact that there produce an azimuthal average (not shown). This sensitivity is are two layers of outflow, one centred around a height of 14 compounded by an apparent limitation of the assumed steadi- km, emanating from the inner eyewall, and another centred ness of the storm over the period of data collection discussed around a height of 12 km, emanating from the outer eyewall above. (see Abarca et al., 2016 for further details of the double eyewall structure). The upper layer has its maximum well within a radius of 100 km, whereas the lower maximum, which is 3.3 Pseudo-equivalent potential temperature much stronger, occurs at a radius of 400 km. The foregoing The distribution of pseudo-equivalent potential temperature issue in reconciling the radial and tangential wind structure 𝜃 (Figure 1d,f) shows also the classical structure.3 (Figure 1f in the upper troposphere highlights a potential limitation of e is a zoomed-in plot of the lowest 3 km of Figure 1d.) Prin- assuming that the storm is in a quasi-steady state for the cipal features are: the mid-tropospheric minimum beyond a purpose of the analysis. radius of about 100 km, increasing in prominence with radius; In the lower troposphere there are significant regions of out- the tendency for the isopleths of 𝜃e to become close to ver- flow above the shallow surface-based boundary layer inflow. tical in the lower troposphere inside a radius of 100 km; This outflow has a local maximum in the inner eyewall (near and the tendency for the isopleths of 𝜃e to slope outwards 20 km radius) and has a layered structure beyond a radius and become close to horizontal in the upper tropospheric of about 90 km starting near the outer eyewall. This pat- outflow layer. With a little imagination, there is an approx- tern of outflow would suggest that the flow in these regions imate congruence between the 𝜃e and M surfaces in the is spinning down by the outward radial advection of the M inner core region and in the upper troposphere, at least out surfaces. However, this spin-down effect would be countered to a radius of 250 km (the M surfaces are also shown in by the vertical advection of air with high values of M from Figure 1d,f). This approximate congruence forms the corner- the boundary layer, at least in the inner core region. In this stone of the steady-state axisymmetric hurricane model by context, it was shown by Abarca et al. (2016, their fig. 4b) Emanuel (1986). that the boundary layer flow was supergradient below both Throughout much of the troposphere, 𝜃e has a negative the primary and secondary eyewalls on the day prior to the radial gradient. This is, in part, a reflection of the structure in present observations. The fact that the storm had just begun the boundary layer. Below about 600 m, the negative radial to weaken (see Section 2.1) would seem to indicate that the gradient of 𝜃e is apparent only inside a radius of about 100 spin-down tendency due to the outward radial advection of km and is a result of the presumed increase in surface mois- the M surfaces is dominant, at least for the inner eyewall. ture flux with decreasing radius (Malkus and Riehl, 1960; The role of the vertical advection of supergradient values of Ooyama, 1969). Such a localized gradient was documented in M from the boundary layer to spin up the inner eyewall was the classical observational analysis of Hawkins and Imbembo highlighted by the study of Schmidt and Smith (2016) using (1976) and has been confirmed by more recent work (Mont- a minimal three-layer numerical model, and was discussed gomery et al., 2006; Bell and Montgomery, 2008; Marks in a more general context by Montgomery and Smith (2017, et al., 2008; Smith and Montgomery, 2013). Maximum val- section 3.9). ues of 𝜃e exceed 355 K in the low to mid-troposphere near Beyond a radius of about 300 km in Figure 1c, where and inside the inner eyewall region. The near-surface value is the boundary layer flow is typically subgradient, there is approximately constant at 350 K outside of the 100 km radius. mostly outflow in the lower troposphere above the boundary The minimum value in the mid- to low troposphere falls to layer. At such radii, this outflow would carry the M sur- values below 320 K beyond a radius of about 300 km (the faces outwards leading to a spin-down of the tangential winds region highlighted in blue in Figure 1d). and therefore a contracting of the storm size (see Kilroy et al., 2016 for a discussion of the factors influencing storm 3 size). The quantity 𝜃e is calculated using Bolton’s formula (Bolton, 1980, eq. 43). MONTGOMERY ET AL. 215

3.4 Relative humidity support of NSF grant AGS-1313948, NOAA HFIP grant Values of relative humidity4 (RH, Figure 1d) exceed 90% N0017315WR00048, NASA (HS3) grant NNG11PK021, inside a radius of 200 km and below an altitude of about 7 ONR grant N0001417WX00336 and the U.S. Naval Postgrad- km. At larger radii, values remain relatively high (> 80%) in a uate School. shallow near-surface layer, but decrease markedly with height with values of less than 50% through much of the troposphere, especially beyond a radius of about 300 km. These low val- ORCID ues are an indication of drying in the subsiding branch of the secondary circulation. The RH starts to drop off beyond the Roger K. Smith https://orcid.org/0000-0002-3668-1608 outer wind maximum, perhaps suggesting that this wind max- Michael T. Montgomery https://orcid.org/0000-0001- imum either forms near the boundary with dry air or acts as 5383-4648 a potential barrier to dry air (e.g. Braun 2006). Comparison with Figure 1c shows that relatively dry air is being drawn inwards just below the outflow layer. REFERENCES Abarca, S.F., Montgomery, M.T., Braun, S.A. and Dunion, J. (2016) On the secondary eyewall formation of Hurricane Edouard (2014). Monthly Weather Review, 144, 3321–3331. 4 CONCLUSIONS Bell, M.M. and Montgomery, M.T. (2008) Observed structure, evolution, and potential intensity of Category 5 Hurricane Isabel (2003) from 12 to 14 September. Monthly Weather Review, 65, 2025–2046. In this paper we have used a dropsonde dataset with Bolton, D. (1980) The computation of equivalent potential temperature. Monthly unprecedentedly high spatial coverage from the NASA HS3 Weather Review, 108, 1046–1053. experiment to analyse the azimuthally averaged structure of Braun, S.A. (2006) High-Resolution Simulation of Hurricane Bonnie (1998). Part II: Water budget. J. Atmos. Sci, 63, 43–64. Hurricane Edouard (2014) just after its peak intensity. 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(2017) Recent developments in the fluid dynamics of tropical cyclones. Annual Review of Fluid Mechanics, 49, 541–574. Montgomery, M.T., Bell, M.M., Aberson, S.D. and Black, M.L. (2006) Hurricane 5 ACKNOWLEDGEMENTS Isabel (2003): new insights into the physics of intense storms. Part I: mean vortex structure and maximum intensity estimates. Bulletin of the American We thank Jun Zhang and two anonymous reviewers for Meteorological Society, 87, 1335–1347. Munsell, E.B., Zhang, F., Braun, S.A., Sippel, J.A. and Didlake, A.C. (2018) The their perceptive and constructive comments on the original inner-core temperature structure of Hurricane Edouard (2014): observations manuscript. RKS acknowledges financial support for tropical and ensemble variability. Monthly Weather Review, 91, 135–155. cyclone research from the Office of Naval Research Global Ooyama, K. (1969) Numerical simulation of the life-cycle of tropical cyclones. Journal of Atmospheric Sciences, 26, 3–40. under grant no. 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