Downloaded 10/01/21 04:34 PM UTC JANUARY 2015 P O T T E R E T a L

104 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 72

In situ Measurements of Momentum Fluxes in Typhoons

1 HENRY POTTER,* HANS C. GRABER,NEIL J. WILLIAMS,CLARENCE O. COLLINS III, # RAFAEL J. RAMOS, AND WILLIAM M. DRENNAN Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

(Manuscript received 7 February 2014, in ﬁnal form 8 September 2014)

ABSTRACT

One of the scientific objectives of the U.S. Office of Naval Research–sponsored Impact of Typhoons on the Ocean in the Pacific (ITOP) campaign was improved understanding of air–sea fluxes at high wind speeds. Here the authors present the first-ever direct measurements of momentum fluxes recorded in typhoons near the surface. Data were collected from a moored buoy over 3 months during the 2010 Pacific typhoon season. During this period, three typhoons and a tropical storm were encountered. Maximum 30-min sustained wind 2 speeds above 26 m s 1 were recorded. Data are presented for 1245 h of direct flux measurements. The drag 2 coefficient shows evidence of a rolloff at wind speeds greater than 22 m s 1, which occurred during the passage of a single typhoon. This result is in agreement with other studies but occurs at a lower wind speed than previously measured. The authors conclude that this rolloff was caused by a reduction in the turbulent momentum flux at the frequency of the peak waves during strongly forced conditions.

1. Introduction terms of nondimensional bulk transfer coefficients for drag C and enthalpy C . Ooyama (1969) and Emanuel The marine boundary layer is a dynamic region of D K (1986) both indicated the importance of C and C , and Earth in which the ocean constantly interacts with the D K the latter theorized that the intensity of a tropical cy- atmosphere. This interaction facilitates the exchange of clone is proportional to the ratio of these bulk transfer momentum, mass, and heat between these fluids through coefficients, C /C . Comparing observations to results turbulent processes. Tropical cyclones gain their energy K D obtained from a simple axisymmetric model with ide- from this interaction by extracting heat from the un- alized environmental conditions led Emanuel (1995) to derlying ocean through enthalpy fluxes (Riehl 1950) hypothesize that the most likely range of C /C during and lose energy from wind stress on the surface of the K D a tropical cyclone is 1.2–1.5, with a lower bound of 0.75. water (Chen et al. 2007). Consequently, at high wind Few campaigns have set out to directly measure fluxes speeds, turbulent momentum and enthalpy fluxes are in tropical cyclone conditions; thus, the data available to responsible for the genesis, conservation, and dissipa- determine the value of these bulk transfer coefficients is tion of tropical cyclones (Malkus and Riehl 1960; limited. For wind speeds between approximately 5 and Emanuel 1986). The fluxes of momentum and enthalpy 2 20 m s 1, there is general agreement as to the behavior across the air–sea interface are typically represented in of CK and CD. However, at high wind speeds, where measurements are made increasingly difficult because of harsh environmental conditions, data are scarce and * Current affiliation: Remote Sensing Division, Naval Research have a large amount of scatter. Laboratory, Washington, DC. 1 The dedicated campaigns that have investigated en- Current affiliation: Oceanography Division, Naval Research thalpy fluxes [e.g., Humidity Exchange Over the Sea Laboratory, Stennis Space Center, Mississippi. # Current affiliation: Woods Hole Group–Houston, Stafford, (HEXOS; DeCosmo et al. 1996), GasEx (McGillis et al. Texas. 2004), and Surface Wave Dynamics Experiment (SWADE;

Katsaros et al. 1993)] have general agreement that CK has 21 Corresponding author address: Henry Potter, Naval Research no dependence on wind speeds between 5 and 20 m s . 21 Laboratory, 4555 Overlook Ave. SW, Washington, DC 20375. This result was extended to 30 m s by the Coupled E-mail: [email protected] Boundary Layer Air–Sea Transfer (CBLAST) ﬁeld

DOI: 10.1175/JAS-D-14-0025.1

Ó 2015 American Meteorological Society Unauthenticated | Downloaded 10/01/21 04:34 PM UTC JANUARY 2015 P O T T E R E T A L . 105

2 program, during which the ﬁrst direct measurements of about 30 m s 1 wind speeds, but because of uncertainties enthalpy ﬂuxes in the hurricane boundary layer were in the estimate, could not rule out entirely the possibility recorded using measurements from aircraft (Zhang et al. of some continued increase. Wada and Kohno (2012)

2008a). Laboratory experiments reported by Haus et al. also reported a leveling of CD when applying the (2010) and Jeong et al. (2012) extend the ﬁndings to roughness length scheme of Taylor and Yelland (2001) 2 40 m s 1. Using a total energy budget approach, to their numerical simulation of Typhoon Fanapi.

CBLAST data were also used to deduce CK for wind Evidence is mounting that shows CD plateaus or de- 2 speeds between 52 and 72 m s 1. These results suggest creases at high wind speeds. Even beyond the rolloff that it is probable that the magnitude of CK is not de- limits of Donelan et al. (2004) and Powell et al. (2003), pendent on wind speed in major hurricane conditions CK/CD remains around 0.5, much lower than the 0.75 (Bell et al. 2012). threshold suggested by Emanuel (1995). Zhang et al. 2 For wind speeds between 5 and 20 m s 1, it has been (2008a), combining their results with French et al. shown by multiple campaigns that CD increases linearly (2007), found the mean value of CK/CD 5 0.63. Bell with wind speed [e.g., Adverse Weather Experiment et al. (2012), using a budget analysis, found CK/CD likely (AWE; Drennan and Shay 2006), HEXOS (Smith et al. to be less than 1.0 and perhaps as low as 0.4 for wind 2 1992), SWADE (Donelan et al. 1997), Large and Pond speeds to 72 m s 1. The significant variability of this ratio (1981), Smith (1980)]. Outputs from the Coupled highlights the uncertainty in our understanding of the Ocean–Atmosphere Response Experiment (COARE) drag coefficient at high wind speeds. Much of this un- 3.5 algorithm (Edson et al. 2013) have a roughly linear certainty is due to the lack of direct flux measurements wind speed dependence on CD under neutral conditions made at the air–sea interface during tropical cyclones. 21 for wind speeds up to 25 m s . To ascertain the behavior of CD in tropical cyclones, The few measurements of momentum fluxes at or there remains an imperative need for the direct mea- approaching tropical cyclone force winds indicate that surement of momentum fluxes at the air–sea interface.

CD may reach saturation or even decrease at higher One of the objectives of the Impact of Typhoons on wind speeds. Powell et al. (2003) used GPS dropsonde the Ocean in the Pacific (ITOP) campaign was to make profiles of wind speeds extrapolated to the surface to flux measurements in typhoon conditions to understand determine CD. This study was the first to report a level- the behavior of bulk exchange coefficients at high wind ing off, or possible decrease, of CD at wind speeds above speeds. This was achieved using moored surface buoys 2 hurricane force (33 m s 1). Further evidence was put deployed for approximately 3 months during the 2010 forth by Donelan et al. (2004), who, from measurements Pacific typhoon season. The work presented in this pa- made in a wind wave tank, also supported a saturation of per focuses on momentum fluxes collected at the air–sea 21 CD at wind speeds above 33 m s . As part of the interface during the ITOP campaign. In section 2,we CBLAST campaign, French et al. (2007) reported the present the measurement theory. Section 3 is a discus- first open-ocean eddy covariance measurements in sion of the experiment, instruments, and data process- hurricanes. This study determined the drag coefficient ing. Results are shown in section 4, and section 5 is using a Rosemount 858Y probe and a Best Aircraft a discussion. Conclusions are reserved for section 6. Turbulence gust probe mounted on a boom on an aircraft that obtained high-frequency measurements of 2. Theory pressure distribution and temperature. These measurements were used to determine three-dimensional wind In stationary and homogeneous conditions, the mo- velocities during a series of stepped descents within the mentum flux t is assumed to be constant within the boundary layer that were extrapolated to the surface. surface flux layer. Using the eddy covariance method, 2 They found that, for wind speeds greater than 22 m s 1 the momentum flux is calculated above the viscous 21 up to 30 m s , CD begins to level off or decrease. sublayer from high-frequency measurements of the However, because of the highly variable nature of the wind velocity components: measurements and the limited number of individual flux estimates, they were not able to provide a definitive t 5 r[(2u0w0)i 1 (2y0w0)j]. (1) description of the behavior of CD at tropical storm–force winds. CBLAST data were also used by Bell et al. Here, r is the air density, i and j are unit vectors along (2012), who deduced the momentum exchange for wind and perpendicular to the mean wind direction; and u, y, 2 speeds between 52 and 72 m s 1 using the conservation and w correspond to horizontal-downwind, horizontal- of azimuthally averaged angular momentum. They es- crosswind, and vertical components of wind velocity, timated that CD does not continue to increase beyond respectively. The overbar represents a time average

Unauthenticated | Downloaded 10/01/21 04:34 PM UTC 106 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 72

[O(30) min] and primes denote fluctuating components Because of the isolation and harsh environmental such that u0 5 y0 5 w0 5 0. The momentum flux can also be conditions encountered, measuring fluxes at sea is very 5 jt rj1/2 represented in terms of the friction velocity: u* / . challenging and expensive, especially at high wind The friction velocity was introduced by Monin and speeds. As such, it is common for the momentum flux to Obukhov (1954) as a turbulent scaling parameter. be determined instead by using the nondimensional drag Monin–Obukhov similarity theory states that the mean coefficient and the mean wind speed. The drag co- gradient of wind speed is related to the friction velocity efficient is typically expressed in terms of 10-m neutral through a universal dimensionless gradient function uu equivalent conditions U10N and formulated as

›U u qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 5 * u (z), (2) 2 2 ›z kz u (2u0w0) 1 (2y0w0) u2 C 5 5 * . (6) D10N U2 U2 where U is the mean wind speed; z is height; k is the von 10N 10N Kármán constant (’0.4); and z 5 z/L, where L is the Obukhov length (Obukhov 1946). The variable L ac- 3. Experiment overview counts for the effects of buoyancy on the wind profile The ITOP campaign took place between August and and is given by December 2010. During this time, two pairs of fully 3 instrumented buoys were deployed in the Philippine Sea u uy L 52 * . (3) at 19.638N, 127.258E and 21.238N, 126.968E, referred to k 0u0 g(w y) as ‘‘South’’ and ‘‘North,’’ respectively. The buoys were approximately 180 km apart and 750 km east of Taiwan. 5 22 u Here g 9.8 m s is acceleration due to gravity, y is the Each pair consisted of an Extreme Air–Sea Interaction 0u0 mean virtual temperature, and w y is the virtual tem- (EASI) buoy (Drennan et al. 2014) and an Air–Sea perature flux. In magnitude, L represents the height Interaction Spar (ASIS) buoy, (Graber et al. 2000). The near the surface at which shear and buoyancy turbulence buoys were deployed in about 5500 m of water with are equal. The value of L is positive for stable conditions EASI anchored to the seabed by an approximately and negative for unstable conditions. 3100-kg cast iron anchor attached to about 7000 m of line. Integrating Eq. (2), the velocity profile becomes This allowed each EASI to move relatively unhindered on the surface but remain restricted to a circular region u z U 2 U 5 * ln 2 c (z) . (4) of about 5-km radius. ASIS was attached to EASI z 0 k u z0 by a floating 12-mm wire rope tether with a horizontal separation of about 60 m. Here Uz refers to mean wind speed at height z, U0 is The buoys were deployed from the Research Ves- mean wind speed at the surface (typically set equal to sel (R/V) Roger Revelle in early August 2010. On 17 zero), and z0 is the surface roughness length for mo- September [day of year (DOY) 260], during Typhoon mentum. Physically, z0 is a measure of the upwind ter- Fanapi, the northernmost ASIS broke free from its tether rain roughness experienced by the surface wind and is and had to be recovered. Likewise, on 22 October (DOY 2 the height where, theoretically, U U0 goes to zero. 295), during Typhoon Megi, the southernmost ASIS c z u z Also u( ) is the integrated form of u( ): broke free of its tether and also had to be recovered. ð Because of inclement environmental conditions, neither z 1 2 u (z) c z 5 u z of the EASI buoys was able to be recovered in November u( ) d . (5) z z 2010, as planned. They were subsequently retrieved by the 0 R/V Roger Revelle during a return cruise in March 2011. In neutral conditions where buoyant forcing becomes By the time of recovery, the EASI buoys’ data acquisition negligible, jz/Lj goes to zero, whereby the last term in systems had exhausted their power and memory. Eq. (4) becomes zero, yielding the classic logarithmic Because of the harsh conditions encountered during mean wind profile. ITOP, multiple instruments failed or were damaged dur- Although Monin and Obukhov (1954) predicted the ing the campaign. Following a rigorous quality-control existence of the gradient functions, they did not offer procedure, the high-frequency wind speed measurements any suggestions as to their form, believing that they must collected on EASI-South were deemed unreliable. As be determined experimentally. For this study, we have such, they are not considered in the following analysis, and applied the terms for stability correction provided by all further discussion is only related to data collected on Donelan (1990). EASI-North.

Unauthenticated | Downloaded 10/01/21 04:34 PM UTC JANUARY 2015 P O T T E R E T A L . 107 a. Instruments EASI is an adaptation of the Navy Oceanographic Meteorological Automatic Device (NOMAD) buoy. The NOMAD 6-m hull was originally designed in the 1940s for the U.S. Navy’s offshore data collection program but has since been used by the National Data Buoy Center (NDBC), among others. Figure 1 shows EASI deployed during ITOP. EASI was equipped to measure air–sea fluxes of momentum, heat, and mass, as well as mean meteorological and oceanographic parameters. A complete list of the instruments attached to EASI during ITOP is shown in Table 1, and an exhaustive description of EASI buoy and mooring design can be found at Drennan et al. (2014). The momentum flux package mounted on EASI consisted of two Gill R2A sonic an- emometers and a K-Gill (e.g., Katsaros et al. 1993). Each sonic anemometer was installed on a separate mast, one fore and one aft, and was connected to one of the dual, redundant data acquisition systems. The fore mast sonic anemometer was positioned 5 m above mean sea level and recorded at 5 Hz; the aft mast anemometer FIG. 1. EASI deployed in the Philippine Sea during the 2010 ITOP was stationed at 5.45 m above sea mean level and re- campaign. The bow is at the left. corded at 20 Hz. Both were positioned to minimize the effects of flow distortion. Because of the harsh conditions encountered, the fore mast R2A failed during the wave buoy. All 6 degrees of freedom were recorded in experiment, likely because of spray or rain penetration local buoy reference frame, along with compass heading. damaging the electronics. The K-Gill failed when it lost The heave was tilt corrected following Anctil et al. a blade. The rear-mast R2A operated successfully for (1994) and double integrated to produce sea surface over 4 months. elevation. Significant wave height Hs was calculated as 4 Two full-motion packages, each consisting of three times the square root of the integral of surface elevation orthogonally mounted rate gyros (Systron Donner models spectrum. The compass was used to transform pitch and QRS11 and SDG1000), a triaxis linear accelerometer roll to an Earth-fixed coordinate frame and integrated to (Columbia Research Laboratory model SA-307HPTX), produce north–south and east–west sea surface slopes and a compass (Precision Navigation TCM-2), were in- and hence wave directional information. More installed in EASI’s fore and aft hulls. Recording the mo- formation about the performance of EASI as a wave tion of EASI served two purposes. First, it enabled buoy can be found in Collins et al. (2014a,b). Second, the EASI to operate as a single-point triplet surface follower motion of the buoy was used to correct the wind velocity

TABLE 1. Meteorological and oceanographic instruments installed on EASI during the ITOP campaign. Additional thermistors were afﬁxed to EASI’s mooring line.

Instrument Quantity Parameter Gill R2A sonic anemometer 2 u, y, w wind speed, virtual temperature K-Gill anemometer 1 u, w wind speed RM Young anemometer 1 u, y wind speed

LI-COR LI-7500 infrared gas analyzer 2 CO2,H2O gas (one open, one close path) Rotronic humidity–temperature probe MP101A-T7 2 Relative humidity, air temperature Setra 278 barometer 2 Atmospheric pressure Compact Lightweight Aerosol Spectrometer Probe 1 Marine aerosol Eppley precision spectral pyranometer 2 Solar radiation Eppley precision infrared radiometer 2 Infrared radiation Campbell 107-L thermistor 1 Buoy hull temperature WaDaR temperature logger TL-HA 2 Air temperature RBR TR1000 and TR1050 2 Air (one) and ocean (one) temperature

Unauthenticated | Downloaded 10/01/21 04:34 PM UTC 108 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 72

spectra, the magnitude of which is a unique function of the wave energy in this frequency range. Following motion correction, the wind vector was rotated so that u points into the mean wind direction and y 5 w 5 0. b. Data processing Data were collected and stored in blocks, or runs, of 60 min on a custom PC-based data acquisition system. A roughly 5-min pause in acquisition occurred approximately every 3 h while summary meteorological data and buoy location were transmitted to shore via the Advanced Research and Global Observation Satellite (ARGOS). Subsequent analysis was carried out in 30-min blocks. Following Eq. (4), mean winds were raised from their 5.45-m measured speeds to 10-m neutral equivalent values. Drennan et al. (2014) investigated the effect of EASI’s motion on wind speed due to changes in anemometer height caused by platform tilt. They found that, despite the high instantaneous pitch and roll angles, reduction in mean anemometer height was at most 1%, which had a negligible effect on measured wind speed. Another potential error discussed by Drennan et al. (2014) relates to the small-tilt-angle assumption used by FIG. 2. Wind spectra for (top) u, (middle) y, and (bottom) w before (black) and after (blue) motion correction. Environmental motion correction algorithms such as Anctil et al. (1994). 21 8 conditions are (left) developing seas (U10N 5 14.8 m s , HS 5 At the highest tilt angle measured during ITOP, 28 ,the 3.6 m, U10N/Cp 5 1.0) and (right) well-developed seas (U10N 5 instantaneous error in the rotation matrix was under 6%, 21 5 5 10.8 m s , HS 6.3 m, and U10N/Cp 0.46). Black line shows the and typically much less. inertial subrange. The low-frequency peaks visible in the u spectra Sea surface temperature (SST), measured at a 1-m depth coincide with the peak wave frequency. Peaks centered at around 0.45 Hz are due to wave-induced resonance that was inherent in all with an RBR Inc. temperature and depth series 1000 logger precorrected power spectra. They have a magnitude that is (TDR1000), was only recorded until the originally sched- a unique function of the wave energy at this frequency. uled recovery date. Because SST is required for converting

to U10N, the conversion could only be made for the ﬁrst by subtracting the measured platform motion from the 87 days of deployment. As such, only data from DOYs anemometer signal, also following Anctil et al. (1994).In 218–305 are considered here. This amounts to 4097 runs of

Fig. 2, the u, y, and w velocity spectra Suu, Syy, and Sww, 30 min each. before and after motion correction, are plotted against The time series of each run was analyzed for spikes in u, frequency for two typical runs. Each plot represents y,andw. Isolated spikes in the data, with values greater the velocity spectra for a 30-min period, and the solid than four standard deviations from their respective black lines correspond to the inertial subrange. The left means, were interpolated through. Any runs for which 21 column is taken from a time when U10N 5 14.8 m s , more than 0.5% of values fulﬁlled this criterion were HS 5 3.6 m, and inverse wave age U10N/Cp 5 1.0, where discarded, accounting for the removal of 17 runs. Overall, Cp is the phase speed of the peak of the wave spectrum. spikes proved rare, with the highest wind speed runs av- Plots in the right column represent a run when U10N 5 eraging about 20 isolated spikes. Because of our interest 21 10.8 m s , HS 5 6.3 m, and U10N/Cp 5 0.46. These pe- in high-wind-speed ﬂuxes, runs for which U10N is less than 2 riods, representing developing sea and swell-dominated 5ms 1 were also removed from analysis, accounting for conditions, respectively, were chosen to illustrate the the removal of 1025 runs. Data quality of individual runs motion correction during two distinct sea states. The low- was assured by inspecting both the linear cumulative frequency peaks visible in the u spectra coincide with the summations of the covariance and the cumulative in- peak wave frequency fp in their respective runs. The tegrals of cospectrum (ogives) for downwind and cross- higher energy levels in the non-motion-corrected spectra wind stress (French et al. 2007). A total of 572 runs were approximately between 0.3 and 0.6 Hz are due to wave- removed in this manner, accounting for 19% of the runs induced resonance in the motion of EASI (Drennan et al. not already eliminated. Of those removed, 13% had U10N 21 21 2014). These were present in all precorrected power . 10 m s and none had U10N . 15 m s . Many of the

Unauthenticated | Downloaded 10/01/21 04:34 PM UTC JANUARY 2015 P O T T E R E T A L . 109

c. Environmental conditions during ITOP According to the Joint Typhoon Warning Center (JTWC; Angrove and Falvey 2010), 19 storms of various intensities formed in the western North Pacific during the 2010 season. Of these, 14 occurred during the ITOP experimental period and four tracked favorably for EASI to record boundary layer characteristics under high wind speeds. These storms included the three most intense typhoons of the season—Typhoon Fanapi, Su- per Typhoon Megi, and Typhoon Chaba—as well as the second most intense tropical storm of the season, Tropical Storm Dianmu. JTWC estimated maximum sustained (1-min average) wind speeds for these storms 2 2 ranged from 28 m s 1 for Dianmu to 82 m s 1 for Megi. FIG. 3. Data from two (top) accepted and (bottom) discarded Dianmu formed as a tropical depression during de- runs. (left) Cumulative summations for the downwind covariance ployment operations approximately 200 km south of plotted against percentage of total run flux. It is normalized by the 21 total covariance. (right) The downwind ogive for the same runs. EASI and propagated at about 3.5 m s along a clock- wise path roughly equidistant from the buoy over the following 2 days before departing to the north. Dianmu discarded runs were measured at times when the EASI passed closest to EASI on DOY 220, at which time buoy heading changed significantly with respect to the maximum wind speeds were estimated by JTWC to be mean wind. 2 13 m s 1. Roughly 1 month following Dianmu, Fanapi Figure 3 shows a comparison between accepted (top approached EASI from the southeast, propagating at row) and discarded (bottom row) runs for downwind 2 about 9.5 m s 1. On DOY 258, EASI had its closest portions of cumulative summations and ogives. For the encounter with a tropical storm of the season when accepted runs, the cumulative summations increase with a Fanapi’s radius of maximum winds (RMW) passed 12 km near-constant slope for the entire run reflecting stationary to EASI’s east. Fanapi had slowed to an estimated conditions, thereby satisfying this assumption of eddy 2 2ms 1 propagation speed and was supporting JTWC- correlation theory. Here negative values reflect transfer of 2 estimated 23 m s 1 winds as it passed. It then turned momentum downward to the ocean. The normalized abruptly and departed toward the northeast. The ogives for these runs show good agreement and reveal that strongest storm of the season, Super Typhoon Megi, the majority of the energy in the momentum fluxes occurs 2 propagated east to west at 6 m s 1 and passed closest to between 0.01 and 1.0 Hz, as expected by the universal EASI on DOY 290. At that time, EASI was 284 km from curves (e.g., Miyake et al. 1970). The plateau at the high- Megi’s very narrow 20-km RMW, which had JTWC- frequency end of the spectrum at around 2 Hz shows that 2 estimated wind speeds of 82 m s 1. Megi was closely measurements made at 20 Hz are sufficient to include the followed by Chaba, which approached EASI from the energy from all turbulent scales present. Likewise, the southeast on a very similar trajectory to Fanapi. While plateau at around 0.015 Hz shows largest-scale eddies still to EASI’s east, Chaba turned north on DOY 300, its having periods of about 11 min, whereby a 30-min sam- RMW 48 km from EASI at its closest pass. At that time pling interval is adequate to capture all the turbulent Chaba had JTWC-estimated maximum wind speeds of length scales present. The cumulative summations of the 2 2 49 m s 1, which increased to 59 m s 1 over the following rejected runs appear to be nonstationary, as much of the 24 h as it dawdled northward, moving at an average pace energy is contained in abrupt bursts over short periods. 2 of 3 m s 1. Environmental conditions for each of these There is also significant variability in the direction of storms according to the JWTC are summarized in Table 2, turbulent transfer among the rejected runs. The in- and best-track estimates can be seen in Fig. 4. consistencies of these runs are reflected in the ogives, which do not mimic the accepted runs’ smooth slopes and concentration of energy in the middle frequency range. 4. Results Zhang et al. (2008b) showed that atmospheric rolls in hurricanes can manifest themselves through cospectral Figure 5 shows U10N for the entire experiment (30-min irregularities such as these. Atmospheric rolls may be at mean). The four major storms encountered are easily play here, but further investigation is required before this identifiable from their wind speed peaks; their names claim can be substantiated. are shown at the top of the figure. For all three typhoons,

Unauthenticated | Downloaded 10/01/21 04:34 PM UTC 110 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 72

TABLE 2. JTWC-estimated maximum wind speeds, minimum sea level pressure, radius of maximum winds, and speed of propagation for the four storms encountered during ITOP. Also shown is the DOY and distance between EASI and RMW at each storm’s closest pass.

Storm Max wind speed Min sea level Radius of max Speed of propagation DOY (min distance [km]) 2 2 name (1-min avg; m s 1) pressure (hPa) winds (km) (km h 1) from EASI to RMW Dianmu 28 982 28–93 6–63 220 (201) Fanapi 54 944 28–56 5–34 258 (12) Megi 82 903 19–56 5–28 290 (284) Chaba 59 937 28–111 6–53 300 (49)

2 30-min-average wind speeds above 15 m s 1 were re- However, its onset and magnitude were also found to be corded at EASI. Maximum wind speeds for the entire sensitive to both the bin size and run averaging period of experiment were recorded during Chaba on DOY 299. the data. For comparison, processing the data in runs of 21 A 30-min-mean U10N of 26.44 m s , 1-min sustained max- 15 rather than 30 min extended the maximum U10N to 21 21 21 imum U10N of 31.5 m s , and maximum instantaneous 27.22 m s . When fit into 2 m s bins, as before, the 2 wind speed reaching 40.64 m s 1 were recorded during results (not shown) indicate a rolloff at slightly lower that time. wind speed, followed by plateauing of the CD10N,in- 21 Figure 6 shows CD10N as a function of U10N for the dicating no wind speed dependence greater than 24 m s . entirety of the experiment (save the rejected runs) to- Variability was also found when altering bin sizes. gether with a histogram of data distribution. The drag In Fig. 7 the drag coefficient is plotted alongside re- coefficient is seen to increase with increasing wind speed sults from Powell et al. (2003), French et al. (2007), and 21 21 up to about 22 m s , at which point CD10N rolls off and Donelan et al. (2004) up to wind speed of 42 m s . The 2 decreases slightly. This negative slope was found to be Smith (1980) bulk relation, extended to 40 m s 1, well significantly different from zero (.99% confidence). beyond the wind speed range of Smith’s initial data,

FIG. 4. Best-track estimate according to the JTWC (Angrove and Falvey 2010) for the storms of interest during ITOP. EASI-North is represented by a large black dot about 750 km east of Taiwan. The port of Kaohsiung is indicated by a red star. Text color represents individual storms: Dianmu (purple), Fanapi (green), Megi (pink), and Chaba (brown). Daily storm locations at 0000 UTC are represented by black dots on storm tracks. Accompanying numbers refer to DOY and distance from EASI to storm’s RMW (in parentheses).

Unauthenticated | Downloaded 10/01/21 04:34 PM UTC JANUARY 2015 P O T T E R E T A L . 111

FIG. 5. The 30–min-average 10-m neutral wind speeds recorded during ITOP. Peaks in wind speed occur during storms, the names of which are provided at the top. is also included for reference. Both Powell et al. and dependence. The French et al. (2007) results, presented 2 Donelan et al. determined that the drag coefficient’s here in 2.5 m s 1 bins, support the leveling off or de- dependence on wind speed goes through a transition creasing drag coefficient claims of Powell et al. (2003) and 2 at about 33 m s 1. Powell et al. (2003) observed a drag Donelan et al. (2004), although at much lower wind coefficient decrease beyond this transition (measure- speed. CBLAST and ITOP values of CD10N both termi- 2 ments were made in wind speeds above 50 m s 1 but nate their ascents at approximately equal wind speeds. not shown here), whereas Donelan et al. (2004) deter- In Fig. 8 each storm track is shown with their re- mined that it plateaus, no longer exhibiting wind speed spective U10N, HS, and CD10N. Estimated CD10N from the

FIG. 6. (top) CD10N as a function of U10N for the 2490 runs analyzed. Green dots represent 2 average values for bins that are 2 m s 1 wide, and red crosses show one standard deviation on

either side of U10N and CD10N. Bins are joined by solid black line. (bottom) Histogram of data 2 distribution in 1 m s 1 bins.

Unauthenticated | Downloaded 10/01/21 04:34 PM UTC 112 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 72

FIG.7.CD10N as a function of U10N from this study (black), French et al. (2007; green, 2 2.5 m s 1 bins), Smith (1980; red solid, measured; red dashed, extended beyond original measurements), Donelan et al. (2004; blue), and Powell et al. (2003; purple). Error bars denote 95% conﬁdence intervals of the means.

21 Smith (1980) bulk relation is also plotted for compari- speed VP was approximately 2.1 m s .Onthestrong son. Peak U10N was recorded on DOY 299.6, roughly 9 h side, the propagation direction and wind direction are prior to when Chaba passed closest to EASI. The period aligned, whereby the storm’s relative wind speed is in- extending approximately 4 h on either side of this wind creased by VP. On the weak side, the opposite is true; the speed maximum is when the high-wind-speed-CD10N propagation speed counters the wind speed, thereby re- rolloffs occurred. This is one of several episodes when ducing the speed by VP. As such, Chaba’s VP and di- 2 the drag coefficient decreased significantly from Smith’s rection change contributed to an approximately 4.2 m s 1 bulk values (e.g., see DOY 260.2, 290.5, and 301.3). difference in U10N and effectively accounts for the sudden Holthuijsen et al. (2012) showed that storm sector reduction observed. wave state can influence the drag coefficient and may In Fig. 9, boundary layer characteristics recorded on be at play here. The effect of storm sector wave state EASI during Chaba are shown: U10N and HS (top); u* on CD10N during ITOP will be discussed extensively (second row); recorded and Smith (1980) bulk CD10N elsewhere. (third row); wind and wave direction at peak frequency

When Chaba’s highest U10N were recorded, JTWC (fourth row); and inverse wave age U10N/CP, where CP is 21 estimated maximum wind speeds Vmax were 46 m s . wave speed at peak frequency (bottom). The figure is Over the following 6 h, peak storm winds intensified and divided into six panels by vertical black lines. The solid 21 Vmax reached 49 m s . Despite this, U10N at EASI de- line indicates the time when Chaba passed closest to creased over this period, with a rapid drop from 25.5 to EASI. Column I is a period of 18 h, during which Chaba 2 20 m s 1 during a single hour around DOY 299.8. As approached EASI. Columns II and III are periods of 6 h seen in Fig. 8, this abrupt U10N decrease coincided with each, during which the typhoon was still approaching. Of a sudden change in Chaba’s propagation direction as it these, column III represents the period when maximum encountered steering flows from the continent. During sustained winds speeds were reached and the drag co- this time, the storm, which was approaching from the efficient rolloff is observed (see Fig. 6). Column IV is a southeast, swung around and headed north. As a conse- 4-h period immediately prior to Chaba’s closest approach quence of this direction change, EASI’s location relative to EASI. During this time, a rapid reduction in wind to the storm track moved from the right side to the left speed occurred, as discussed above. Columns V and VI side, repositioning EASI from Chaba’s strong to its weak are both periods of 6 h when Chaba began to move away side. Using JWTC estimates, it was found that on DOY from EASI; U10N is approximately constant during pe- 299.8, when Chaba changed direction, its propagation riod V and decreases during VI.

Unauthenticated | Downloaded 10/01/21 04:34 PM UTC JANUARY 2015 P O T T E R E T A L . 113

FIG. 8. (top) Storm paths, (middle) U10N and HS, and (bottom) CD10N for the four named storms of interest in this study: (from left to right) Dianmu, Fanapi, Megi, and Chaba. Storm paths show JTWC-estimated wind speeds (Angrove and Falvey 2010). (top) Axes are degrees of longitude (y axis) and latitude (x axis). Dots on storm track show positions every 6 h and numbers refer to DOY. Large black dot shows location of EASI. (middle) Recorded U10N (black) and HS (blue). (bottom) CD10N plots show recorded values in black and theoretical values from the Smith (1980) bulk relation in red. Solid vertical lines denote the time when each storm was closest to EASI.

At the start of period I, the peak waves were aligned while U10N and HS continued to increase. During these with the wind: both approached from the north- periods, CD10N reached a plateau, causing it to diverge northeast and within about 108 of each other. During from the Smith (1980) bulk values, which continued to this period, the inverse wave age shows that conditions increase following the wind speed. This was especially were nearing full development, although a swell peak is true during period III, when the maximum U10N was also visible in the wave spectra (not shown). Over 12 h recorded and the CD10N rolloff was observed. from DOY 298.75 to DOY 299.25 (still period I), this During the 4 h immediately prior to EASI’s closest swell peak became the dominant frequency, but the encounter with Chaba (period IV in Fig. 9), both U10N wind sea peak was still evident in the wave spectra. This and u* decreased abruptly. However, CD10N remained swell approached from the southeast directly ahead of consistent with those recorded during period III and Chaba, traveling about 908 from the wind direction with lingered below the Smith (1980) bulk values, which 21 cp ; 17 m s . During this time, CD10N is in general dropped because of decreased wind speed. This period agreement with the Smith (1980) bulk value. On DOY also exhibited a rapid reduction in inverse wave age, 21 299.25, with U10N at 17.5 m s and HS above 6 m, the with the winds beginning to turn as Chaba moved to wind waves became dominant. Over the following within 49 km of EASI. When Chaba began to move roughly 12 h (periods II and III), the waves continued to away from EASI (period V in Fig. 9), U10N stayed at 21 be strongly forced, and inverse wave age reached 1.5 around 20 m s , while u* increased (discussed below).

Unauthenticated | Downloaded 10/01/21 04:34 PM UTC 114 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 72

FIG. 9. Boundary layer characteristics recorded during typhoon Chaba: (from top to bottom) U H u C 10N and S; *; recorded and Smith (1980)-estimated D10N; wind direction and wave direction at the peak frequency; and inverse wave age U10N/CP, with level of full development indicated by the horizontal dashed line. Plots are divided into six columns by vertical lines; the solid line in each panel shows the time when Chaba passed closest to EASI. Each column is referred to in the discussion section.

This caused CD10N to increase and align with the Smith mean angle between the wind and stress directions (1980) bulk values. During this period, the wind con- during these 46 h were 12.18 for periods I, V, and VI and tinued to turn and began approaching from the north- 5.68 for periods II, III, and IV, and they were signifi- northwest while the waves also began to turn, lagging cantly different at greater than the 95% confidence behind the wind. During this period, the angle between level. While there does appear to be a clear turning of the wind and waves increased to about 458. As Chaba the wind stress due to the swell (cf. Grachev et al. 2003; continued to move away from EASI (period VI), wind Zhang et al. 2009), the effect is small, perhaps because of and waves continued to turn, U10N and u* both continued the lack of frequency separation between the wind sea to drop, and CD10N remained approximately equal to the and swell systems. This will be the subject of a future Smith (1980) bulk values. publication. During the 46 h examined in Fig. 9, turbulent stress In Fig. 10, the u–w cospectra for selected periods are was supported largely by the downwind component of plotted in the dimensionless scaling of Miyake et al. the flux. During periods I, V, and VI, when the wind was (1970). The cospectra and frequency f were normalized not aligned with the peak waves, the crosswind flux using mean wind speed U, measurement height z 5 2 contributed a mean of 22% to the total. During periods 5.45 m, and the friction velocity squared u* and then II, III, and IV, when the wind was acutely aligned with averaged in equally spaced logarithmic frequency bins. the peak waves, the crosswind flux contributed an av- The blue lines are mean values for each period, black erage of just 10% to the total. These values were found lines are plus or minus one standard error, and green to be significantly different (99% confidence level). The lines are the curves of Miyake et al. (1970). Also shown

Unauthenticated | Downloaded 10/01/21 04:34 PM UTC JANUARY 2015 P O T T E R E T A L . 115

FIG. 10. Mean u–w cospectra plotted in the scaling of Miyake et al. (1970). U is mean wind speed, f is frequency (Hz), and z is measurement height (5.45 m). Plots II, III, IV, and V refer to periods displayed in Fig. 9 and show the evolution of the spectra recorded during Chaba. Blue lines are mean values, black lines are 61 standard error, and green lines are the Miyake et al. (1970) universal curve. The red lines are 1D wave frequency spectra nondimensionalized using z and U as above. The wave spectra are normalized to a maximum of 0.3. Note that panels I and VI (from Fig. 9) are not shown.

are the 1D wave frequency spectra plotted in dimen- inverse wave age dropped by 30%, HS reduced from over sionless frequency, with their magnitude normalized to 10 m to less than 9 m, the waves were becoming mis- a maximum of 0.3. Figure 10 is divided according to aligned from the wind, and the spectral dip was curbed periods II, III, IV, and V as previously defined, repre- significantly. During period V, the angle between the senting the immediate approach and departure of Chaba wind and waves continued to open, the cospectral dip was in relation to EASI. These periods are explored in order gone, and CD10N fell on top of the Smith (1980) values. to understand the reason behind the drag coefficient A cospectral analysis of the y–w flux (not shown) rolloff recorded during period III. found that for periods II, III, and IV the crosswind While generally adhering to the universal curve, the component of the flux did not resemble the universal cospectra at II, III, and IV have dips at the peak wave curve of Miyake et al. (1970). During these times, the frequency. This is most prevalent during period III, when crosswind energy was concentrated in minor peaks aligned the drag coefficient rolloff was observed. During period with the wave frequency. During period V, the crosswind V, as Chaba moved away from EASI, this dip is gone. flux was spread across all measured frequencies.

These cospectral dips occurred when HS was between 8 Save the wave frequency dips, the u–w cospectra in and 11 m and peak wave direction was essentially aligned Fig. 10 resemble the universal curve of Miyake et al. with the wind. As U10N and HS grew between periods II (1970). However, they have the appearance of being and III, the dip became more pronounced and CD10N blueshifted to higher frequencies. This shift increases in increasingly deviated from the Smith (1980) bulk curve. prevalence from period II to period III and then de- 2 During period IV, the winds decreased by 8 m s 1, the creases during period IV. After the storm has passed, the

Unauthenticated | Downloaded 10/01/21 04:34 PM UTC 116 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 72 blueshift has effectively gone (period V). Zhang (2010) used to provide boundary layer wind profiles in previous used CBLAST data recorded in the boundary layer campaigns (e.g., Drennan et al. 2007; Zhang et al. 2011). 2 between outer rainbands at wind speeds above 20 m s 1 However, dropsondes do not provide the reliable near- to examine cospectra of momentum fluxes. He also surface profile measurements that are required here. found that cospectra fell into blueshifted universal The possibility that the wave-coherent dips are spuri- curves, though to a greater extent than seen here. ous, somehow related to the motion of the platform on As seen in Fig. 10, the appearance of a blueshift is the extreme waves, can be discounted. The wave field was supported in the inertial subrange more so than a shift in very similar in both period and height during periods II– peak frequency. A similar comparison to the universal IV (when the dip was present) and period V (when it was curves of Kaimal et al. (1972; not shown) revealed not). Hence, motion-related errors seem unlikely. greater agreement in the inertial subrange and provided Finally, we consider the idea that the wave-coherent no indication of a blueshift. No relationship was found dips are due to flow separation. Donelan et al. (2004) between shift extent and typhoon location, or U10N;as suggested that flow over breaking waves separates from such, it is not evident that the blueshift is a consequence of the surface and reattaches near the crest of the pre- typhoon dynamics or intensity. It is likely that the apparent ceding wave. They went on to propose that the sepa- shiftisaneffectoftheu* nondimensionalization term. rated flow does not ‘‘see’’ the wave troughs, thereby Because of the presence of the wave-coherent spectral dip, limiting the aerodynamic roughness of the surface and u* is reduced, causing the nondimensionalized spectrum to hence the drag. Here we would expect a higher degree of shift toward higher energy. This idea is supported by the flow separation when the peak waves are aligned with variation in the spectral shift in Fig. 10 from period III to the wind (as during II–IV when the dip was prominent) period IV, which is seen to diminish with the reduction of than when they are not (as during V). This is consistent the cospectral dip. with the observations. Although Donelan’s work was completed in a tank where waves are long crested, the 5. Discussion same mechanism may be at play here where the waves are short crested [see, e.g., Fig. 9 of Drennan (2005)]. The presence of these wave-coherent dips reduced the magnitude of the friction velocity and therefore the drag 6. Conclusion coefficient. It is clear that this feature is related to the surface wave field. One possibility is that the EASI Direct measurements of momentum fluxes taken measurements are made within the wave boundary layer from a floating platform during typhoons were pre- (WBL). The WBL is the layer above the surface where sented. Measurements were made over 87 days in the wave-coherent components of the wind field are signif- Philippine Sea during the 2010 Pacific typhoon season. icant. EASI measurements, made 5.45 m above the wa- Over 1200 h of momentum fluxes were calculated using ter level, were indeed well below the crests of the largest the eddy covariance method for wind speeds from 5 to 2 2 waves observed during typhoons. However, modeled 26.44 m s 1. For wind speeds up to 20 m s 1, the drag results of Janssen (1989) and Makin and Mastenbroek coefficient was found to agree well with previous studies. 2 (1996) indicate that the expected height of the WBL is At wind speeds above about 22 m s 1, there is evidence well under 1 m at the friction velocities measured during that the drag coefficient decreases or plateaus. This pro- the typhoons in this study. While the results of Janssen vides support to the previous studies of French et al. (1989) and Makin and Mastenbroek (1996) are strictly (2007), Donelan et al. (2004),andPowell et al. (2003), true for pure wind sea conditions, typhoon measure- who also found a limit to the surface drag. We found that ments here were during mixed wind sea-swell condi- the drag coefficient rolloff is due to a reduction in the tions. However, Drennan et al. (2005) demonstrated turbulent momentum flux at the frequency of the peak that WBL effects are expected to be negligible as long as waves during strongly forced conditions when the wind the overall wave energy is dominated by wind sea (i.e., and waves were closely aligned. This feature is consistent contribution of the total wave energy from wind sea is with some form of flow separation at the wave frequency. more than 50%), as was the case here. The plateau (or decrease) in drag coefficient at high While evidence suggests that the EASI wind speed wind speeds presented in this study is of critical importance measurements were made above the WBL during the for the understanding and modeling of tropical cyclones typhoons, this could only be confirmed with near-surface and other intense storms. Modifying tropical cyclone wind profile measurements, which were not recorded on models to represent a reduced CD in wind speeds 21 EASI. Dropsondes, which were deployed from aircraft above about 22 m s will lead to higher values of CK/ during the ITOP experiment, have been successfully CD and more intense storms. Consequently, surface

Unauthenticated | Downloaded 10/01/21 04:34 PM UTC JANUARY 2015 P O T T E R E T A L . 117 layer parameterization used to predict tropical cy- models: Results from CBLAST-Hurricane. J. Atmos. Sci., 70, clone tracks, ocean mixing, and waves may be invalid, 3198–3215, doi:10.1175/JAS-D-12-0157.1. which will have crucial implications for risk assess- Collins, C. O., III, B. Lund, R. Ramos, W. M. Drennan, and H. C. Graber, 2014a: Wave measurement intercomparison and ment of landfalling storms. platform evaluation during the ITOP (2010) experiment. It has been shown that tropical storm–induced surface J. Atmos. Oceanic Technol., 31, 2309–2329, doi:10.1175/ waves can have marked impact on surface stress. These JTECH-D-13-00149.1. results exemplify the need to couple waves into tropical ——, ——, R. T. Waseda, and H. C. Graber, 2014b: On record- storm prediction models, such as the work of Chen et al. ing sea surface elevation with accelerometer buoys: lessons from ITOP (2010). Ocean Dyn., 64, 895–904, doi:10.1007/ (2013), who have shown that fully coupled wind–wave s10236-014-0732-7. parameterization improves model-simulated surface DeCosmo, J., K. B. Katsaros, S. D. Smith, R. J. Anderson, W. A. wind speed and inflow angle, which are important to Oost, K. Bumke, and H. Chadwick, 1996: Air-sea exchange of storm evolution and structure. Alongside modeling ef- water vapor and sensible heat: The Humidity Exchange Over 101, forts, our work also highlights an inherent need for more the Sea (HEXOS) results. J. Geophys. Res., 12 001– 12 012, doi:10.1029/95JC03796. concurrent measurements of momentum fluxes and Donelan, M. A., 1990: Air-sea interaction. Ocean Engineering waves during tropical cyclones. Our results substantiate Science, B. Le Méhauté and D. M. Hanes, Eds., The Sea— previous claims of a limit in surface drag but stem from a Ideas and Observations on Progress in the Study of the Seas, single event during Typhoon Chaba. Additional mea- Vol. 9A, John Wiley and Sons, 239–292. surements in tropical cyclones are needed in wind speeds ——, W. M. Drennan, and K. B. Katsaros, 1997: The air–sea 2 momentum flux in conditions of wind sea and swell. J. Phys. above 20 m s 1 to better understand the relationship be- Oceanogr., 27, 2087–2099, doi:10.1175/1520-0485(1997)027,2087: tween the drag coefficient and the wave field in typhoons. TASMFI.2.0.CO;2. ——, B. K. Haus, N. Reul, W. J. Plant, M. Stiassnie, H. C. Graber, Acknowledgments. ITOP was funded by ONR under O. B. Brown, and E. S. Saltzman, 2004: On the limiting Grant N0014-09-1-0392. We thank this agency for their aerodynamic roughness of the ocean in very strong winds. Geophys. Res. Lett., 31, L18306, doi:10.1029/2004GL019460. support. We also acknowledge the contributions of Mike Drennan, W. M., 2005: On parameterisations of air-sea fluxes. Rebozo at RSMAS, Joe Gabriele and Cary Smith of Atmosphere-Ocean Interactions, Vol. 2, W. Perrie, Ed., Ad- Environment Canada, and the WHOI mooring group vances in Fluid Mechanics, Vol. 33, WIT Press, 1–33. led by John Kemp. We are also grateful for support and ——, and L. K. Shay, 2006: On the variability of the fluxes of 119, assistance provided by the captains and crew of the R/V momentum and sensible heat. Bound.-Layer Meteor., 81– 107, doi:10.1007/s10546-005-9010-z. Roger Revelle. We acknowledge additional support ——, P. K. Taylor, and M. J. Yelland, 2005: Parameterizing the sea from NSF (Grant OCE-0526442) for the development of surface roughness. Phys. Oceanogr., 35, 835–848, doi:10.1175/ the EASI buoy and ONR (Grant DURIP N00014-09- JPO2704.1. 0818) for funding construction of the second EASI buoy. ——, J. A. Zhang, J. R. French, C. McCormick, and P. G. Black, We also thank the three anonymous reviewers and the 2007: Turbulent fluxes in the hurricane boundary layer. Part II: 64, editor. Latent heat flux. J. Atmos. Sci., 1103–1115, doi:10.1175/ JAS3889.1. ——, H. C. Graber, C. O. Collins III, A. Herrera, H. Potter, R. J. Ramos, and N. J. Williams, 2014: EASI: An air–sea interaction REFERENCES buoy for high winds. J. Atmos. Oceanic Technol., 31, 1397– Anctil, F., M. A. Donelan, W. M. Drennan, and H. C. Graber, 1994: 1409, doi:10.1175/JTECH-D-13-00201.1. Eddy-correlation measurements of air-sea fluxes from a discus Edson, J. B., and Coauthors, 2013: On the exchange of momentum buoy. J. Atmos. Oceanic Technol., 11, 1144–1150, doi:10.1175/ over the open ocean. J. Phys. Oceanogr., 43, 1589–1610, 1520-0426(1994)011,1144:ECMOAS.2.0.CO;2. doi:10.1175/JPO-D-12-0173.1. Angrove, M. D., and R. J. Falvey, 2010: Annual tropical cyclone Emanuel, K. A., 1986: An air–sea interaction theory for tropical cy- report 2010. U.S. Naval Maritime Forecast Center/Joint Ty- clones. Part I: Steady-state maintenance. J. Atmos. Sci., 43, 585– phoon Warning Center, Pearl Harbor, HI, 109 pp. [Available 605, doi:10.1175/1520-0469(1986)043,0585:AASITF.2.0.CO;2. online at www.dtic.mil/dtic/tr/fulltext/u2/a561986.pdf.] ——, 1995: Sensitivity of tropical cyclones to surface exchange Bell, M. M., M. T. Montgomery, and K. A. Emanuel, 2012: Air–sea coefficients and a revised steady-state model incorporating enthalpy and momentum exchange at major hurricane wind eye dynamics. J. Atmos. Sci., 52, 3969–3976, doi:10.1175/ speeds observed during CBLAST. J. Atmos. Sci., 69, 3197– 1520-0469(1995)052,3969:SOTCTS.2.0.CO;2. 3222, doi:10.1175/JAS-D-11-0276.1. French, J. R., W. M. Drennan, J. A. Zhang, and P. G. Black, 2007: Chen, S. S., J. F. Price, W. Zhao, M. A. Donelan, and E. J. Walsh, Turbulent fluxes in the hurricane boundary layer. Part I: Mo- 2007: The CBLAST-Hurricane program and the next- mentum flux. J. Atmos. Sci., 64, 1089–1102, doi:10.1175/JAS3887.1. generation fully coupled atmosphere–wave–ocean models Graber, H. C., E. A. Terray, M. A. Donelan, W. M. Drennan, J. C. for hurricane research and prediction. Bull. Amer. Meteor. Van Leer, and D. B. Peters, 2000: ASIS—A new air-sea Soc., 88, 311–317, doi:10.1175/BAMS-88-3-311. interaction spar buoy: Design and performance at sea. ——, W. Zhao, M. A. Donelan, and H. L. Tolman, 2013: Directional J. Atmos. Oceanic Technol., 17, 708–720, doi:10.1175/ wind–wave coupling in fully coupled atmosphere–wave–ocean 1520-0426(2000)017,0708:AANASI.2.0.CO;2.

Unauthenticated | Downloaded 10/01/21 04:34 PM UTC 118 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 72

Grachev, A. A., C. W. Fairall, J. E. Hare, J. B. Edson, and S. D. temperature). Tr. Akad. Nauk. SSSR Inst. Teorel. Geofiz., 1, Miller, 2003: Wind stress vector over ocean waves. J. Phys. 95–115. Oceanogr., 33, 2408–2429, doi:10.1175/1520-0485(2003)033,2408: Ooyama, K., 1969: Numerical simulation of the life cycle of WSVOOW.2.0.CO;2. tropical cyclones. J. Atmos. Sci., 26, 3–40, doi:10.1175/ Haus, B. K., D. Jeong, M. A. Donelan, J. A. Zhang, and I. Savelyev, 1520-0469(1969)026,0003:NSOTLC.2.0.CO;2. 2010: Relative rates of sea-air heat transfer and frictional Powell, M. D., P. J. Vickery, and T. A. Reinhold, 2003: Reduced drag in very high winds. Geophys. Res. Lett., 37, L07802, drag coefficient for high wind speeds in tropical cyclones. doi:10.1029/2009GL042206. Nature, 422, 279–283, doi:10.1038/nature01481. Holthuijsen, L. H., M. D. Powell, and J. D. Pietrzak, 2012: Wind Riehl, H., 1950: A model of hurricane formation. J. Appl. Phys., 21, and waves in extreme hurricanes. J. Geophys. Res., 117, 917–925, doi:10.1063/1.1699784. C09003, doi:10.1029/2012JC007983. Smith, S. D., 1980: Wind stress and heat flux over the ocean in gale Janssen, P. A. E. M., 1989: Wave-induced stress and the drag of air force winds. J. Phys. Oceanogr., 10, 709–726, doi:10.1175/ flow over sea waves. J. Phys. Oceanogr., 19, 745–754, 1520-0485(1980)010,0709:WSAHFO.2.0.CO;2. doi:10.1175/1520-0485(1989)019,0745:WISATD.2.0.CO;2. ——, and Coauthors, 1992: Sea surface wind stress and drag co- Jeong, D., B. K. Haus, and M. A. Donelan, 2012: Enthalpy transfer efficients: The HEXOS results. Bound.-Layer Meteor., 60, across the air–water interface in high winds including spray. 109–142, doi:10.1007/BF00122064. J. Atmos. Sci., 69, 2733–2748, doi:10.1175/JAS-D-11-0260.1. Taylor, P. K., and M. J. Yelland, 2001: The dependence of sea surface Kaimal, J. C., J. Wyngaard, Y. Izumi, and O. R. Coté, 1972: roughness on the height and steepness of the waves. J. Phys. Spectral characteristics of surface-layer turbulence. Quart. Oceanogr., 31, 572–590, doi:10.1175/1520-0485(2001)031,0572: J. Roy. Meteor. Soc., 98, 563–589, doi:10.1002/qj.49709841707. TDOSSR.2.0.CO;2. Katsaros, K. B., M. A. Donelan, and W. M. Drennan, 1993: Flux Wada, A., and N. Kohno, 2012: Impact of surface roughness length measurements from a SWATH ship in SWADE. J. Mar. Syst., on typhoon simulations. 30th Conf. on Hurricane and Tropical 4, 117–132, doi:10.1016/0924-7963(93)90003-5. Meteorology, Ponte Vedra Beach, FL, Amer. Meteor. Soc., P2.22. Large, W. G., and S. Pond, 1981: Open ocean momentum [Available online at https://ams.confex.com/ams/30Hurricane/ flux measurements in moderate to strong winds. J. Phys. webprogram/Paper204931.html.] Oceanogr., 11, 324–336, doi:10.1175/1520-0485(1981)011,0324: Zhang, F. W., W. M. Drennan, B. K. Haus, and H. C. Graber, OOMFMI.2.0.CO;2. 2009: On wind-wave-current interactions during the Shoaling Makin, V. K., and C. Mastenbroek, 1996: Impact of waves on air- Waves Experiment. J. Geophys. Res., 114, C01018, doi:10.1029/ sea exchange of sensible heat and momentum. Bound.-Layer 2008JC004998. Meteor., 79, 279–300, doi:10.1007/BF00119442. Zhang, J. A., 2010: Spectral characteristics of turbulence in the Malkus, J. S., and H. Riehl, 1960: On the dynamics and energy hurricane boundary layer over the ocean between the outer transformations in steady-state hurricanes. Tellus, 12A, 1–20, rain bands. Quart. J. Roy. Meteor. Soc., 136, 918–926, doi:10.1111/j.2153-3490.1960.tb01279.x. doi:10.1002/qj.610.

McGillis, W. R., and Coauthors, 2004: Air-sea CO2 exchange in the ——, P. G. Black, J. R. French, and W. M. Drennan, 2008a: First equatorial Pacific. J. Geophys. Res., 109, C08S02, doi:10.1029/ direct measurements of enthalpy flux in the hurricane 2003JC002256. boundary layer: The CBLAST results. Geophys. Res. Lett., 35, Miyake, M., R. Stewart, and R. W. Burling, 1970: Spectra and co- L14813, doi:10.1029/2008GL034374. spectra of turbulence over water. Quart. J. Roy. Meteor. Soc., ——, K. B. Katsaros, P. G. Black, S. Lehner, J. R. French, and 96, 138–143, doi:10.1002/qj.49709640714. W. M. Drennan, 2008b: Effects of roll vortices on turbulent Monin, A. S., and A. M. Obukhov, 1954: Basic laws of turbulent fluxes in the hurricane boundary layer. Bound.-Layer Meteor., mixing in the surface layer of the atmosphere. Tr. Geofiz. Inst., 128, 173–189, doi:10.1007/s10546-008-9281-2. Akad. Nauk SSSR, 151, 163–187. ——, R. F. Rogers, D. S. Nolan, and F. D. Marks, 2011: On the Obukhov, A. M., 1946: ‘Turbulentnost’ v temperaturnoj–neodnorodnoj characteristic height scales of the hurricane boundary layer. Mon. atmosfere (Turbulence in an atmosphere with a non-uniform Wea. Rev., 139, 2523–2535, doi:10.1175/MWR-D-10-05017.1.

Unauthenticated | Downloaded 10/01/21 04:34 PM UTC