1600 MONTHLY WEATHER REVIEW VOLUME 131

In¯ow Layer Energetics of Hurricane Bonnie (1998) near Landfall

DEREK R. WROE AND GARY M. BARNES University of Hawaii at Manoa, Honolulu, Hawaii

(Manuscript received 10 December 2001, in ®nal form 3 January 2003)

ABSTRACT On 26 August 1998, a NOAA WP-3D aircraft executed a curved track that mimics an in¯ow trajectory to the eyewall of Hurricane Bonnie. Global positioning system (GPS) sondes and airborne expendable bathyther- mographs jettisoned along the trajectory provide the observations to conduct an energy budget for the 1600-m- deep in¯ow to the eyewall. Surface ¯uxes are estimated via the bulk aerodynamic equations and the ¯ux at the top of the in¯ow is solved as a residual.

From 170- to 125-km radial distance from the circulation center the mean ␪e of the in¯ow remains constant despite combined sensible and latent surface ¯uxes in excess of 500 W m Ϫ2. Convective cells remove energy from the in¯ow boundary layer at a rate similar to the inputs from the sea. From 125 to 100 km, in the annulus

adjacent to the eyewall, mean ␪e increases 4.5 K in response to higher surface ¯uxes and little loss through the

in¯ow top. Energy balance may be achieved by either entrainment of higher ␪e through the top of the in¯ow layer, or by inclusion of just half the estimated heat from viscous dissipation. The authors infer that the secondary circulation of the eyewall inhibits convective cells from forming in this region and thus facilitates the rapid increase of energy in the in¯ow. The results support hypotheses that hurricane intensity appears to be strongly modulated by energy exchange in a meso-␤ region adjacent to and under the eyewall.

1. Introduction vides an unprecedented, detailed portrayal of the in¯ow layer to the eyewall of Hurricane Bonnie (1998). Where and how does the in¯ow boundary layer to an eyewall acquire the requisite additional energy to create and sustain a ? Impediments to an an- a. Importance of in¯ow energy content swer include the challenging measurement conditions associated with a hurricane. What few observations we Riehl (1954), Malkus and Riehl (1960), Palmen and do have come from either providentially sited buoys Newton (1969), and Emanuel (1986) deduce that a trop- (e.g., Cione et al. 2000) or carefully executed aircraft ical cyclone (TC) cannot be sustained by simply using experiments (e.g., Jorgensen 1984; Black and Holland the ambient convective available potential energy 1995). Since Hurricane Hugo (1989), low-level pene- (CAPE). Additional energy, extracted from the sea, is trations of the eyewall of high-category hurricanes by needed to drive the TC heat engine (e.g., Riehl 1951, manned reconnaissance is not considered prudent. This 1954; Emanuel 1986). This energy enters into the TC has left the meteorological community with an impaired via the in¯ow boundary layer. The importance of this view of the thermodynamics affecting hurricane inten- additional energy is highlighted in the successful inten- sity. si®cation and maintenance of simulated TCs initiated in The global positioning system (GPS) dropwindsonde an environment devoid of CAPE (Rotunno and Emanuel (sonde), developed by the National Center for Atmo- 1987). Observations verify that CAPE is reduced as air spheric Research, the National Oceanic and Atmospher- ¯ows to the eyewall (Bogner et al. 2000); this is partly ic Administration (NOAA), and the German Aerospace due to a cooling of the in¯ow temperature (Korolev et Research Group, has become available for hurricane re- al. 1990; Cione et al. 2000; Barnes and Bogner 2001), search (Hock and Franklin 1999). With a 2-Hz sampling and partly due to warming aloft (Jordan and Jordan rate, the GPS sonde delivers 7-m vertical resolution of 1954; Sheets 1969; Frank 1977). kinematic and state variables from shortly after the The in¯ow layer acquires the additional energy epi- sonde is jettisoned to the sea surface. A novel ¯ight sodically. One may infer this from the height±radius pattern has been used to deploy these sondes and pro- cross sections of equivalent potential temperature (␪e) (Hawkins and Imbembo 1976; Jorgensen 1984). These cross sections show radial swaths with little change in Corresponding author address: G. M. Barnes, Dept. of Meteorol- ogy, University of Hawaii at Manoa, 2525 Correa Rd., Honolulu, HI ␪e, and other swaths, usually adjacent to the eyewall, 96822. where ␪e increases rapidly (Fig. 1). Simulations of an E-mail: [email protected] axisymmetric TC by Rotunno and Emanuel (1987) also

᭧ 2003 American Meteorological Society

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FIG. 1. Radial cross section of ␪e in Hurricane Inez (1966). [From Hawkins and Imbembo (1976).]

show little gain in ␪e in certain radial bands despite high is often not uniform spatially, contrary to what was surface ¯uxes. Entrainment of dry air from above, or assumed in early energy budgets (Hawkins and Rubsam convective exchanges, drain the in¯ow layer of any na- 1968; Hawkins and Imbembo 1976). Cool wakes, iden- scent surplus of energy, countering the surface ¯uxes. ti®ed with airborne expendable bathythermographs Barnes et al. (1983) and Powell (1990a,b) indicate that (AXBTs) may result in little or no sensible energy being convectively active can tap the energy-rich transferred to the in¯ow layer (Black and Holland 1995), in¯ow and replace it with low-␪e downdraft air. Betts while warm eddies may enhance the ¯uxes (Shay et al. and Simpson (1987) concur that losses from convective 2000). transports can overwhelm gains from surface ¯uxes. Bister and Emanuel (1998) discuss the possibility that

They argue that to obtain an increase in the ␪e of the viscous dissipation of turbulent kinetic energy in the in¯ow and develop a more intense hurricane, the evap- surface layer could be an additional heat source for the oration in the subcloud layer and upward ¯uxes at cloud TC. Maximum dissipative heating would tend to occur base need to be minimized. The ®ndings support the in the high wind regime near and under the eyewall, argument that energy ¯ux divergence of the in¯ow layer where rain and spray would be available to evaporate, changes sign over small spatial or correspondingly short perhaps resulting in a latent energy input into the TC. temporal scales. The factors contributing to the episodic A critical point is that the stress expended in wave pro- increases in the ␪e of the in¯ow layer are only partially duction would not be available for dissipative heating. documented. Energy contributions to the in¯ow may come from Much of the uncertainty deals with the air±sea inter- the layer above. Simulations by Anthes and Chang face. Sensible and latent heat ¯uxes through the ocean (1978) and a budget analysis by Frank (1984) show that surface increase markedly near the eyewall in response the entrainment of high potential temperature (␪) can to the escalating wind speeds (Riehl and Malkus 1961; contribute to the maintenance of an isothermal subcloud Hawkins and Rubsam 1968). Spray, which becomes layer. Barnes and Powell (1995) describe conditions ra- ubiquitous in high winds, complicates the situation dially outward of a strong where higher ␪e (Fairall et al. 1994; Andreas and DeCosmo 1999; Wang overlays the in¯ow layer; shear-induced entrainment led et al. 2001; Andreas and Emanuel 2001). Most re- to increases in the energy content. The results support searchers expect a radical change in the magnitude and the hypothesis that rainbands can help as well as hinder distribution of the ¯uxes once the atmospheric surface the stoking-up process needed to drive the TC heat en- layer is ®lled with spray droplets. gine. The sea surface temperature (SST) ®eld under the TC The prior observational work (Malkus and Riehl

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1960; Riehl and Malkus 1961; Miller 1962; Hawkins and Rubsam 1968; Hawkins and Imbembo 1976; Frank 1984; Powell 1990b) established methods to estimate an energy budget, but were often limited by one or more constraints that included single-layer sampling, incom- plete knowledge of the SST ®eld, no radar to assess convective activity, and limited vertical resolution. The preponderance of the evidence supports the argument that energy increases rapidly over a short distance ad- jacent to the eyewall. A wide range of surface ¯uxes have been offered, and ¯uxes at the top of the in¯ow, in the form of convective overturning or entrainment from the adjacent layer, appear to play a vital role in the energy content of the in¯ow, and ultimately hurri- cane intensity. b. Goals GPS sondes deployed in Hurricane Bonnie are used to 1) identify the thermodynamic and kinematic struc- tures of the in¯ow layer, 2) determine changes in the energy content of a column of air along an in¯ow tra- jectory, and 3) estimate the energy ¯uxes necessary to achieve balance. Our focus is on the entire low-level FIG. 2. Portions of the aircraft ¯ight pattern (dotted lines) executed in¯ow layer, not just the mixed layer. Based on the wind to obtain the three sampled trajectories. GPS drops are shown (*), ®elds adjacent to and in the eyewall (Jorgensen 1984; and the resultant SST from AXBTs is displayed in ЊC. The HRD track of the circulation center of Bonnie is the dashed line. Marks et al. 1992) we assume that the entire in¯ow is processed by the eyewall. Turbulence in the eyewall updraft will homogenize the ␪e of this in¯ow. It is the data from seven GPS sondes deployed approximately 90± mean ␪e of the eyewall column that has been related to 170 km from the storm center. TC intensity (Malkus and Riehl 1960; Betts and Simp- son 1987). Our eventual desire is to learn how changes b. The GPS dropwindsonde in the in¯ow energy content affect tropical cyclone in- tensity, particularly near landfall where it has the great- The GPS sonde falls at a rate of 12±14 m sϪ1 in the est impact on society. lower troposphere, retarded by a pyramid-shaped para- chute. The descent time is nearly 4 min to the ocean surface, given the aircraft altitude of 3.7 km. During the 2. Data and methodology descent the GPS sonde transmits measurements of air a. Flight plan and sampling strategy temperature, pressure, humidity, and position at a rate of 2 Hz. NOAA's Hurricane Research Division (HRD) A unique sampling strategy was executed to study the has devised the Hurricane Analysis and Processing Sys- in¯ow layer of Hurricane Bonnie on 26 August 1998 when tem (HAPS), providing real-time quality control. The it was near , . A NOAA WP-3D sonde data are further postprocessed at HRD with great- aircraft ¯ew curved tracks of approximately 200 km from er user interaction. The HAPS identi®es the splash point the outer portions of the storm to the circulation center of the GPS sonde and applies a sequence of automated (Fig. 2), to mimic several different trajectories of low- algorithms to ¯ag erroneous data (Hock and Franklin level in¯ow. The curved tracks were ¯own at 3.7-km al- 1999), and after this process, numerous options are titude with GPS sondes deployed every 20±30 km. available to correct the data. The GPS sonde typical Three trajectories were sampled by the aircraft with 55 measurement errors for pressure, temperature, relative GPS sondes and 16 AXBTs (Fig. 2). First, the northern humidity, and wind speed are 1.0 hPa, 0.2ЊC, Ͻ5%, and trajectory was obtained over the nearly undisturbed Gulf 0.5±2.0 m sϪ1, respectively (Hock and Franklin 1999). Stream and shallow coastal waters off the coast. The sec- The GPS sondes appear to be reporting accurate winds ond trajectory, sampled in the right-rear quadrant, de- based on comparisons with nearby surface marine plat- scribes a region through which the storm has passed, leav- forms (Houston et al. 2000). Maximum error in ␪e could ing cool, upwelled SSTs. The third trajectory describes air reach 3.5 K, if temperature and humidity sensors to- with a probable continental history overlying warm SSTs gether read high or low. The HAPS corrected almost all in the southwestern section of the hurricane. This study suspicious data save for saturated layers that had a dry- focuses on a segment of the northern trajectory, containing adiabatic lapse rate. These layers were subjectively cor-

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rected, assuming that the relative humidity sensor failed (Qr), plus the subgrid ¯uxes in the vertical, minus vis- to dry out upon exiting cloud. Unusual thermodynamic cous dissipation (␧) are equal to zero. We have made structures such as moist absolutely unstable layers the standard assumption that the subgrid-scale ¯uxes in (MAULs; Bryan and Fritsch 2000), and mixed layers the horizontal are much smaller than the subgrid-scale with atypical potential temperature (␪) and ␪e pro®les, vertical ¯uxes and may be neglected. Dissipation is nor- are the subject of a forthcoming paper. mally neglected, but there is the possibility that with HRD's track of Bonnie was used to determine storm very high stress (very strong wind speeds) some heat position and speed, which was about 5 m sϪ1 during the is put into the atmospheric surface layer (Bister and experiment. Subtraction of the TC motion vector from Emanuel 1998). the earth-relative winds, followed by a coordinate trans- Albrecht and Cox (1975) identi®ed the mean cooling formation, provides the tangential (VT, positive is cy- rate from radiation in a clear tropical environment to Ϫ1 clonic) and radial (Vr, positive is away from the center) be 1±2 K day . Over the duration of the trajectory, ¯ows relative to the storm center. this rate would result in cooling of 0.085±0.170 K. Con- sidering that the trajectory environment is dominated c. The WP-3D radars by layers of clouds, the cooling is much less than even this estimate and is considered to be negligible. The aircraft radars, described by Marks (1985), are Fluxes at the interface would be technically contained used to determine if convective cells or stratiform rains in a molecular transport term, but after invoking a con- exist along the trajectory. This information is crucial stant ¯ux in the surface layer, this term is represented for assessing the region sampled by a GPS sonde and by the subgrid-scale ¯uxes since turbulence quickly determining the degree to which an individual sonde dominates molecular transfer just a few centimeters represents the trajectory. The tail Doppler radar provides above the sea surface. data for a pseudo-dual-Doppler analysis, resulting in We assume that the horizontal gradient of ␪e is un- horizontal wind ®eld estimates as low as 600 m above changing during the 2 h that the column takes to reach the sea. Doppler analyses follow the technique devel- the eyewall; this steady-state assumption eliminates the oped by Marks and Houze (1987). storage term. Support for this assumption includes a steady MSLP for Bonnie, a nearly constant radius of d. Budget scheme maximum winds, and a slowly evolving re¯ectivity pat- tern. The GPS data are used to determine the in¯ow depth Finally we assume that the gradients in the azimuthal and its energy content. Differences from sounding to direction are negligible compared to the gradients in the sounding show the apparent increments of energy that radial direction leaving us with are acquired on the column's journey to the eyewall. (wЈ␪Ј)ץ ␪ץ ␪ץ The radial wind (V ) is used to assess the time the in¯ow r V eeϩ w ϭϪ e ϩ␧. (2) zץ zץ rץ column takes to traverse the trajectory. Data obtained r in the surface layer allow for an estimation of the ¯ux at the interface via the bulk aerodynamic equations. Note that w ϭ vertical velocity and z ϭ height, and r Fluxes at the top of the in¯ow layer are a residual. is radial distance. The ®rst term on the lhs of (2) is the

We will use ␪e in our budgets because 1) it is con- product of the radial ¯ow and the radial gradient of ␪e served despite the evaporation of rain or spray and thus estimated along the in¯ow trajectory. If one views simpli®es the situation and 2) the moist enthalpy of the height±radius cross sections of ␪e such as that proffered air is the critical factor that controls the maximum po- by Hawkins and Imbembo (1976), one could get the tential intensity of a TC (e.g., Malkus and Riehl 1960; impression that there is a very large increase near the Andreas and Emanuel 2001). eyewall, and it would naturally appear to be entirely

A budget equation for ␪e, following Anthes (1982), due to diabatic sources. Actually, if the in¯ow has a may be written as vertical gradient of ␪e, and there is convergence, then such an interpretation of this cross section would mis- (wЈ␪Ј e)ץ ␪ץ␪ eeץ ϩ u JrϪ Q ϩϪ␧ϭ0, (1) lead. Much of the apparent increase would simply be ,(z due to redistribution of energy (second term on the lhsץ x Jץ tץ where uJ represents the mean or grid-scale components perhaps from the mixed layer (200±400 m) into the of the three-dimensional velocity vector, xJ represents deeper in¯ow layer (1000±2000 m). This is not the ad- the spatial components of a three-dimensional vector, t ditional energy responsible for the maintenance of the

ϭ time, Qr ϭ radiative divergence, and ␧ϭdissipation. TC (e.g., Malkus and Riehl 1960). Most prior budgets Hereinafter, the mean is represented as the variable (␪e based on observations of one level in the in¯ow would z ϭ 0; this could resultץ/␪eץ ϭ mean quantity) and the prime represents the subgrid- be forced to assume that scale component. Equation (1) states that the change in in an overestimate of the subgrid-scale ¯uxes necessary

.t) plus grid- for energy balanceץ/␪eץ) storage of ␪e in the in¯ow column xJ), minus radiative divergence The ®rst term on the rhs of the equation (2) representsץ/␪eץscale advection (uJ

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FIG. 4. The 30-min lower-fuselage radar re¯ectivity composite (1239:11±1309:21 UTC) with the northern trajectory ¯ight path. The radar image is 360 km ϫ 360 km; the coastline is the thin line pattern. FIG. 3. Location of the relevant portions of the three sampled tra- Re¯ectivity values appear in the table to the lower left. The two boxes jectories (dotted lines) with the GPS drop locations (*). The mean are the approximate locations of the lower-fuselage scans in the fol- winds of the in¯ow layer are shown in vector form. lowing two ®gures.

sampling of the northern trajectory. Based on the lo- the subgrid-scale ¯uxes. These are the surface ¯uxes at cation of re¯ectivity features greater than 35 dBZ, the the air±sea interface, or convective and turbulent ex- eyewall has a radius of approximately 85 km. This - changes at the top of the in¯ow layer. The ®nal term wall is not a complete circle, and there is evidence sug- on the rhs is the viscous dissipation. gesting that another eyewall-like feature is present with- One could also imagine following a column of in¯ow in the eye. A prominent rainband is located in the north- air that receives energy through its top and bottom. In west quadrant and merges with the eyewall. this case horizontal advection terms would become zero, Figure 5a, obtained when the aircraft is at 150-km and the storage term would survive. radial distance, reveals scattered small convective ele- The success of the experiment is dependent on two ments along the aircraft track. The tail radar scan (Fig. factors. First the track of the aircraft must mimic the 5b) shows that the prominent rainband north of the air- in¯ow trajectory. This is done by following the shape craft contains a bright band indicative of stratiform or of the stratiform rainbands, which serve as a tracer to convective cells late in their life. Cell tops reach to 10 the low-level ¯ow. Figure 3 is evidence that the aircraft km. At 105-km radial distance the radars reveal (Fig. ¯ew along the approximate streamline, given that the 6a) that the latter part of the trajectory is dominated by aircraft track is tangent to the mean boundary layer stratiform re¯ectivity of 26±30 dBZ, with the eyewall winds. The second factor is the steadiness of the me- about 10 km south of the aircraft. Near the merger of soscale re¯ectivity pattern (rainbands and eyewall) dur- the rainband and the eyewall, re¯ectivity reaches to 15- ing the in¯ow column's journey to the eyewall. Ex- km altitude (Fig. 6b). amination of the radar shows that the re¯ectivity ®eld evolves slowly. Our assumption of steadiness over 1±2 h is far less demanding than what many successful anal- b. Kinematic structure yses have required (e.g., Willoughby et al. 1984; Black The radius±height cross section of relative tangential and Holland 1995). wind sampled along the trajectory extends from ϳ170 to ϳ90 km radial distance from the circulation center 3. Results (Fig. 7). Wind speeds in excess of 50 m sϪ1 are located about 500±1000 m above the sea and within a radius a. Re¯ectivity structure of nearly 95 km. This location of the radius of maximum Figure 4 shows two complete ¯ight legs displayed winds (RMW) matches the position of the eyewall in- over a 30-min re¯ectivity composite from the lower- dicated by the re¯ectivity data. fuselage radar, including the data obtained during the The radial ¯ow for the same cross section (Fig. 8)

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FIG. 5. Radar re¯ectivity at a radius of approximately 150 km from the circulation center. (a) The lower-fuselage radar (120 km ϫ 120 km) at 1228:07 UTC and (b) the tail radar (20 km ϫ 162 km) at 1227:57 UTC. The tail scan is oriented south to north. Re¯ectivity values are de®ned in the color tables for each frame; the cross marks the aircraft position.

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FIG. 6. Similar to Fig. 5 but at a radius of 105 km. (a) PPI scan is at 1238:10 UTC and (b) tail scan, oriented southeast to northwest, is at 1237:57 UTC. shows that 90% of the in¯ow is located under 1600 m, 90 km, the gradient of the in¯ow speed results in a and this altitude is de®ned as the in¯ow-layer top for signi®cant amount of convergence that is collocated all calculations. The strongest in¯ow is located in the with the eyewall. Along the trajectory the in¯ow av- lowest kilometer of the in¯ow layer. Near a radius of erages over 10 m sϪ1; this makes a sample in¯ow col-

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FIG. 7. Radius±height cross section of relative tangential wind (m FIG. 8. Radius±height cross section of relative radial wind (m s Ϫ1) sϪ1) along the trajectory. along the trajectory. umn traverse the 80 km to the eyewall in about 125 vertical gradient of ␪e. For divergence we use the stan- min. Shear of the radial wind component in the in¯ow dard two-dimensional assumption that has been used averages Ϫ12.0 ϫ 10Ϫ3 sϪ1. successfully in TCs (e.g., Jorgensen 1984; Powell 1990a): w/ z ( V / r V /r). (3) ϩ ץrr ץϭϪ ץ ץ c. Thermodynamic structure The vertical term ( w/ z), is determined by the chang- ץ ץThe gently sloping isentropes (Fig. 9) reveal the warm Ϫ r), and the reductionץ/ Vץ) es in the radial ¯ow with radius core of the hurricane, and the depressed isentropes near r of area with decreasing radius (V /r). The V /r term appears 150-km radius are evidence of subsidence. A mixed- r r as a result of the cylindrical coordinate system. Due to the layer depth of about 400 m (about the height of the 301- consequences of the sampling strategy, the highest con- K contour) is found beyond radii of 140 km, and de- ®dence is placed in the accuracy of V /r, with more un- creases gently to about 250 m near the eyewall. A region r .rץ/ Vץ certainty likely in of lower-␪ air is situated near the surface at radii of r The region outside of approximately 140-km radius 145±105 km. This cooling of ϳ1 K may be the result of convective-scale downdrafts as argued by Cione et is characterized by divergence (Fig. 11), corresponding al. (2000) and Barnes and Bogner (2001), and less likely to an increase in the radial ¯ow in the in¯ow layer. The due to evaporation of spray, given that it is not correlated temperature and dewpoint temperature structures in this with the highest surface winds. area reveal the presence of subsidence or downdrafts, with higher-␪ air being con®ned to the lowest several Examination of the cross section of ␪ (Fig. 10) reveals e e hundred meters (Fig. 10). At radii less than 140 km that the lapse rate and mean value (353 K) of the in¯ow Ϫ4 column are essentially unchanged from 170 to 125 km, convergence is prevalent, and increases to Ϫ4 ϫ 10 despite the presence of warm, underlying SSTs and high surface wind speeds. Inside of 125 km the vertical gradient from 500 to about 1000 m disappears, and the mean ␪e of the lowest 1600 m increases to over 357 K by 100-km radius, just beyond the eyewall outer edge. Surprisingly,

␪e does not change throughout the cross section below 500-m depth. A signi®cant increase does occur relatively close to the eyewall, in the upper two-thirds of the in¯ow layer. This results in a mean increase of ϳ4.5 K through the depth of the 1600-m in¯ow. d. Energy budget

1) DIVERGENCE A solution for the lhs of Eq. (2) is possible given that we have estimates of the radial ¯ow, the radial gradient of ␪e, the divergence necessary to estimate w, and the FIG. 9. Radius±height cross section of ␪ (K) along the trajectory.

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Ϫ4 Ϫ1 FIG. 10. Radius±height cross section of ␪e (K) along the trajectory. FIG. 11. Radius±height cross section of divergence (ϫ10 s )

.r ϩ Vr /r) along the trajectoryץ/ Vrץ) due to sϪ1 near the eyewall. From 125 to 100 km the mean value of divergence in the lowest 900 m is about Ϫ2.0 number (moisture transfer coef®cient, Cq). Both CH and Ϫ4 Ϫ1 ϫ 10 s , leading to a vertical velocity of approxi- Cq can be expressed in terms of the drag coef®cient Ϫ1 mately 18 cm s at the top of the mixed layer. This (CD), height, and stability. The uncertainty for the trans- vertical velocity redistributes the high-␪e air 440 m fer coef®cients remains at least 20%. Measurements deeper into the 1600-m in¯ow layer. from the moored tower or any of the ships do not extend Ϫ1 Ϫ1 Prior studies (e.g., Hawkins and Imbembo 1976; re- beyond 23 m s for CH and cease by 14 m s for Cq produced here as Fig. 1) did not have the GPS sonde (Large and Pond 1982). In the high wind conditions we and were not able to determine the vertical gradient in assume near-neutral stability. The eddy ¯ux and dissi- the low-level structure of ␪e. This naturally would lead pation measurements support a weak dependency of the one to the assumption of a well-mixed in¯ow, and the coef®cients on speed (Large and Pond 1982), which we conclusion that the second term on the lhs of Eq. (2) have adopted here. Both CH and Cq increase much more would have no effect. The ultimate result would be a slowly with wind speed than does CD. The 10-m wind much greater demand of energy from the sea to account speeds from 170- to 125-km range from 20 to 32 m sϪ1. for the apparent increases in ␪e. This is especially true Extrapolation of the coef®cients to winds reaching 42± for studies with only one level of observation in the 46msϪ1, encountered from 125 to 100 km, involves in¯ow. For Hurricane Inez (see Fig. 1) the assumption greater uncertainty. of a 2-km-deep in¯ow of 10 m sϪ1 from 37 to 17 km From 170 to 125 km, the combined ¯uxes through would demand surface ¯uxes in excess of 12 000 W the surface layer are 400±625 W mϪ2. Fluxes of sensible Ϫ2 Ϫ2 m to account for the 12-K increase in ␪e! Such a heat range from 50 to 145 W m , and the transfer magnitude is dif®cult to accept. For Bonnie we see con- coef®cient for sensible heat ¯ux (Ch) varies from 1.37 Ϫ3 vergence in the presence of a vertical gradient of ␪e, to 1.66 ϫ 10 . Sea±air temperature differences range which reduces the ¯uxes needed for balance consider- from about 1 K to in excess of 2.5 K (Fig. 12a). Fluxes ably. of latent heat range from 345 to 505 W mϪ2, and the

The behavior of ␪e in Bonnie invites separation of transfer coef®cient for moisture ¯ux (Cq) varies from the in¯ow into two parts. There is essentially no change 1.45 to 1.76 ϫ 10Ϫ3. The mixing ratio difference shows in the energy content of the in¯ow column in the outer a small variation from 3.6 to 4.8 g kgϪ1 (Fig. 12b). portion of the trajectory, from 170 to 125 km. From The ¯uxes of sensible and latent heat increase with 125 to 100 km, 940 W mϪ2 are needed to account for decreasing radius, and yet, the energy content of the the increase in the in¯ow energy [the lhs of Eq. (2)]. in¯ow column remains essentially constant from 170- to 125-km radius. The implication is that the ¯uxes into the bottom of the column are balanced by the ¯uxes out 2) SURFACE LAYER FLUX of the top. This region contains scattered convective Sea surface ¯uxes are contained in the turbulent ver- elements (Figs. 5a,b) that are capable of transporting

.z) of Eq. (2) and are cal- energy out of the in¯ow layerץ/( wЈ␪Јe)ץ) tical transport term culated via the bulk aerodynamic method. The estimates In the in¯ow trajectory from radii of 125±100 km of SST from the AXBTs, and the observations at 10 m there is a substantial change in structure and mean en- from the GPS sonde supply the necessary inputs. Large ergy content. The combined sea surface ¯uxes increase and Pond (1982) offer recommendations for the Stanton to about 1040 W mϪ2 in the ®nal 10 km of the trajectory, number (heat transfer coef®cient, CH) and the Dalton due to the increase in both the 10-m wind speeds and

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FIG. 13. Combined sea surface ¯uxes determined by the techniques derived from Large and Pond (1982) (solid line), and by Fairall et FIG. 12. (a) Estimated SST (K, dashed line) and 10-m air temper- al. (1994) (dashed line), as a function of wind speed. ature (K) along the trajectory. (b) Estimated saturated mixing ratio Ϫ1 (qs,gKg ) in the in®nitesimally thin layer of air in contact with the sea surface and mixing ratio (q, gKgϪ1) at 10-m altitude along in high wind speeds is encountered once more, but the the trajectory. formulas were again extrapolated beyond their recom- mended range of wind speed to observe the tendencies. the transfer coef®cients. The sensible heat ¯ux increases The net effect of the inclusion of sea spray effects is to more than 200 W mϪ2. The sea±air temperature dif- a lower combined energy ¯ux, as compared to Large ference remains in excess of 2 K (Fig. 12a), and CH ϭ and Pond's recommendations (Fig. 13). The conditions 1.85±1.93 ϫ 10Ϫ3. The mixing ratio difference varies are representative of those in the region of the rapid Ϫ1 between 3.6 and 4.1 g kg , and Cq ϭ 1.96±2.05 ϫ energy increase with an air±sea temperature difference 10Ϫ3; this pushes the latent ¯uxes to nearly 840 W mϪ2 of 2.2ЊC, and a mixing ratio difference of 4.2 g kgϪ1. by r ϭ 100 km. At low wind speeds the small difference in ¯ux between The mean combined ¯ux of heat and moisture from the techniques is mainly due to the use of the lower 125 to 100 km is 830 W mϪ2. The sensible and latent bulk transfer coef®cients offered by Fairall et al. At ¯uxes across the interface provides about 88% of the higher speeds spray is produced, but the evaporation of required energy needed in the in¯ow trajectory, leaving sea spray extracts sensible energy from the air, leading a ¯ux de®cit of about 110 W mϪ2. The many possible to a cooling and moistening of the boundary layer (Fair- causes of the residual are discussed in the next section. all et al. 1994). Therefore, the total ¯uxes are only about 675WmϪ2 at a wind speed of 42 m sϪ1, and the average total ¯uxes over the last 25 km are little more than 565 3) POSSIBLE SOURCES FOR THE RESIDUAL WmϪ2. Some possible solutions to the energy de®cit include Another ¯ux scheme was discussed by Wang et al. 1) the sea surface ¯uxes are larger under high wind (2001), who explored the effects of sea spray evapo- speeds, 2) higher values of convergence in the in¯ow ration in a tropical cyclone model developed by Wang distribute energy through a deeper layer, 3) viscous dis- (1999). Wang et al. implemented the sea spray algorithm sipation contributes some heating, and 4) the ¯ux of described by Andreas and DeCosmo (1999) combined energy at the top of the in¯ow contributes to the energy with the bulk ¯ux algorithm of Fairall et al. (1996) that content of the column. was developed from the Coupled Ocean±Atmosphere Perhaps the inclusion of the effects of sea spray can Response Experiment. Wang et al. compared the model increase the energy ¯uxes to satisfy the energy needs. results using this scheme and the Fairall et al. (1994) Fairall et al. (1994) have attempted to quantify the con- scheme. tribution of sea spray on the sea surface ¯uxes. The bulk With surface wind speeds of 40 m sϪ1 and the Andreas sea surface ¯uxes are estimated through the aerodynam- and DeCosmo (1999) scheme, the model produced a ic equations, using constant transfer coef®cients of CH combined sea surface ¯ux that was approximately 26% Ϫ3 ϭ Cq ϭ 1.3 ϫ 10 , and a parameterized formulation greater than the Fairall et al. (1994) sea surface ¯ux. for the sensible and latent heat ¯uxes of spray is de- The spray scheme of Andreas and DeCosmo (1999) veloped. The authors indicate that the spray formulas, produces more ¯ux due to the treatment of the spray which are dependent on the whitecap function of An- droplets. The droplet airborne residence time is suf®- dreas (1992), are applicable under wind speeds no great- cient for sensible heat transfer to the air, while being er than 30 m sϪ1. Therefore, the problem of usefulness insuf®cient for droplet evaporation. In the region of rap-

Unauthenticated | Downloaded 09/30/21 04:02 AM UTC 1610 MONTHLY WEATHER REVIEW VOLUME 131 id energy increase in Hurricane Bonnie, sea surface ¯ux- es 26% greater than those indicated by the Fairall et al. (1994) technique would be just slightly less than the combined sea surface ¯ux of the Large and Pond (1982) technique. Thus, the Andreas and DeCosmo (1999) technique does not account for the residual. However, either technique is within 15% of the observed require- ments. One can imagine that a small underestimate in the wind speed could account for the shortfall. Enhanced convergence is the second possibility that might account for the residual. In order for convergence to alter the in¯ow layer and account for the remaining 110 WmϪ2 of energy ¯ux input, the mean convergence in the lowest 900 m must increase by little more than 5% to values of about Ϫ2.1 ϫ 10Ϫ4 sϪ1, leading to a vertical velocity of 19 cm sϪ1 in the last 25 km leading to the FIG. 14. The vertical pro®le of ␪ (K) at 125 km from the eyewall. This slight increase results in lowering the energy e circulation center. needs from the surface. It is our view that the ¯ight pattern does not provide the best data for divergence estimates and is the prime cause of the residual. The fourth possibility is the inclusion of viscous dis- The third possibility is ¯ux from above. The vertical sipation (Bister and Emanuel 1998). The heating in- ¯ux of any variable across the layer top is driven by dif- creases as the cube of the wind speed, and could result ferences in the variable across the interface (Stull 1988). in some very large inputs [e.g., 290 W mϪ2 with 40 m In order for the layer to be energized from above, a positive sϪ1 surface winds; Businger and Businger (2001)]. This vertical gradient of ␪e must exist across the top of the is assuming that all the stress goes to generating heat, layer. For ␪e this is an unusual condition, but evidence has and all of it enters the atmosphere. Any stress that is been found in at least one situation, by Barnes and Powell expended in making waves would not be available for (1995), where out¯ow from a hurricane rainband was di- heating; it is also possible that some heat goes into the rectly above the in¯ow. The entrainment velocity, which sea as well. The portion that enters the atmosphere may controls the mixing rate, is enhanced by wind shear and be in latent form if it serves to evaporate spray or rain. is typically estimated as a measure of the turbulence ap- Perhaps a ®rst-order estimate is that half the viscous propriate for the interface type. heating would enter the surface layer.

Is higher ␪e being mixed into the in¯ow layer from From 170 to 125 km the inclusion of 50% of ␧ from above, at the end of the in¯ow trajectory in Hurricane equation (2) has little effect because the magnitude is Ϫ2 Bonnie? First, a positive vertical gradient of ␪e must small (10 W m ) and would simply add to the loss of exist above the in¯ow layer top, which is de®ned at an energy through the top of the in¯ow. Here we have altitude of 1600 m for the trajectory. In the outer portion applied Eq. (7) in Businger and Businger (2001). Mean Ϫ1 of the trajectory no ␪e increase is detected to an altitude conditions are 26 m s , the drag coef®cient is 2.2 ϫ of 3700 m, which is far above the in¯ow layer, and thus 10Ϫ3, roughness length is 0.002 m (Stull 1988), and a no entrainment of high ␪e is possible. However, by 125 surface-layer depth of 20 m is assumed. An increase of km a ␪e minimum of about 345 K exists near the in¯ow the surface layer to 100 m increases the input only 5 Ϫ2 top (Fig. 14) and a steady increase of ␪e occurs above Wm . From 125 to 100 km, where the mean wind (ϩ4 K in the next 1000 m). Therefore, the required speed is 37 m sϪ1, the drag coef®cient increases to 2.90 Ϫ3 vertical gradient of ␪e exists for the ¯ux of higher-␪e ϫ 10 , and 50% of ␧ results in an additional 100±115 air into the in¯ow layer. Based on Fig. 14 the jump of WmϪ2 of heating of the in¯ow. The inclusion of half

␪e across the in¯ow top (␪e,T Ϫ ␪e,B) is about 1.5 K. the dissipative heating would balance the energy budget Following simple parameterizations for the ¯ux across in this second portion of the trajectory where we witness a mixed layer (Stull 1988), the 4.5-K increase of ␪e in the in¯ow. A schematic (Fig. 15) summarizes diagnosed condi- (wЈ␪Ј) ϭϪw (␪ Ϫ ␪ ). (4) eee,Te,B tions for the northern trajectory. Note that surface ¯uxes We can estimate the entrainment velocity necessary to do not reach the very large values of some earlier in- produce 110 W mϪ2 to be about 0.07 m sϪ1. This is vestigations, in part because the GPS sondes provide a within the range estimated for mixed layers that are more complete view of the in¯ow and allow us to better growing primarily through buoyant eddies (e.g., Stull quantify the role that convergence plays in reducing the 1988). In addition, vertical wind shear is present that diabatic energy inputs to the column. In the outer part could also enhance entrainment velocities. Thus, it is of the trajectory the prime issue is the bleeding of energy possible that modest mixing from the layer above could out of the in¯ow, most likely due to convective pro- also account for the residual. cesses, but turbulent mixing is also possible. This is a

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FIG. 15. A height±radius schematic of the in¯ow to Hurricane Bonnie. From 170 to 125 km,

␪e is about constant (ϳ353 K) because convective clouds and entrainment withdraw as much

energy as is put in at the sea surface. From 125 to 100 km, ␪e increases to ϳ357 K. Fluxes (W mϪ2) are the wide arrows, with those at the air±sea interface indicative of combined latent and sensible heat transports. Balance may be achieved in the 125±100-km annulus by either ¯uxes from above or by the inclusion of one-half the viscous dissipation. veri®cation of the simulation results by Rotunno and of the trajectory is easily accounted for with slight in-

Emanuel (1987). In the second stage of the in¯ow the creases of convergence, entrainment of higher ␪e from column energy needs are largely met by the enhanced the layer above, or the inclusion of half the heating due surface ¯uxes. The residual, if not due to measurement to viscous dissipation. error, can be met by either entrainment of energy through the top, which appears possible given the lapse rate of ␪e, or from just half the viscous heating that is b. Speculation available. There are substantial sea to air ¯uxes for the entire trajectory, and probably for a region that extends ra- 4. Conclusions dially beyond our observations. Despite these enhanced a. Summary ¯uxes, the in¯ow energy increases only near the eye- wall. The eyewall circulation suppresses competing con- On 26 August 1998, a NOAA WP-3D aircraft ¯ew vection in the adjacent annulus and, thus, limits the curved tracks to sample in¯ow trajectories to the eye- losses through the top of the in¯ow. Farther away from wall of Hurricane Bonnie as it approached the North the eyewall convection exists, it taps the enriched in- Carolina coast. GPS sondes, AXBTs, and aircraft radar ¯ow, and replaces it with lower-␪ air that inhibits hur- re¯ectivity data are used to describe the evolution of e ricane intensi®cation. Hurricanes that achieve a high the energy content of the northern in¯ow trajectory that overlays the warm coastal seas. category are those that have an eyewall that dominates The behavior of the in¯ow column can be summa- competing convection in the adjacent annulus. If ¯uxes near and under the eyewall, and thus over rized in two stages: from 170- to 125-km radius, ␪e in the 1600-m-deep in¯ow changes little despite combined small spatial and short temporal scales, have the greatest surface ¯uxes that average 520 W mϪ2. Convective impact on eyewall ␪e, then intensity forecasts will be (subgrid scale) processes transport most of the energy dependent on resolving meso-␤ features such as warm obtained via ¯uxes at the sea surface out of the in¯ow ocean anomalies, eyewall structure, and rainband activ- ity close to the hurricane center. Passage of the inner and thus hold the ␪e to a steady 353 K. From 125 to 100 km, adjacent to the eyewall, the core of the hurricane over even a small warm ocean eddy (ϳ100 km length scale) may result in greater sur- mean ␪e of the in¯ow column increases 4.5 K. The ¯uxes Ϫ2 necessary for balance are 940 W m ; interfacial and face ¯uxes, higher ␪e in the in¯ow, and increases in Ϫ2 spray ¯uxes provide as much as 830 W m .Ofthe hurricane intensity, if the higher ␪e reaches the eyewall. three surface ¯ux parameterizations (Large and Pond At least a part of this scenario has been invoked to 1982; Fairall et al. 1994; Andreas and DeCosmo 1999) explain the rapid deepening of Hurricane Opal (Shay et it appears that either Large and Pond's or Andreas and al. 2000). The key to intensi®cation may be the com- DeCosmo's schemes reduced the residual to the smallest bination of enhanced ¯uxes from the sea, and the con- value. The modest residual of 110 W mϪ2 for this part tainment of this energy until it reaches the eyewall.

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Acknowledgments. This work was supported by NSF Structure and budgets of the hurricane on October 1, 1964. Mon. Grant ATM97-14400. The dedication and support from Wea. Rev., 96, 617±636. ÐÐ, and S. M. Imbembo, 1976: The structure of a small, intense NOAA, Aircraft Operations Center, and the Hurricane HurricaneÐInez 1966. Mon. Wea. Rev., 104, 418±442. Research Division were crucial to the success of the Hock, T. F., and J. L. Franklin, 1999: The NCAR GPS dropwindsonde. experiment in Bonnie. The comments by Mark Powell Bull. Amer. Meteor. Soc., 80, 407±420. and an anonymous reviewer resulted in substantial im- Houston, S. H., P.P.Dodge, M. D. Powell, M. L. Black, G. M. Barnes, provements. Garpee Barleszi's sniping led to a leaner and P. S. Chu, 2000: Surface winds in hurricanes from GPS- sondes: Comparisons with observations. Preprints, 24th Conf. introduction. on Hurricanes and Tropical Meteorology, Fort Lauderdale, FL, Amer. Meteor. Soc., 339. Jordan, C. L., and E. S. 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