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September 1968 Harry F. Hawkins and Da ry l T. Rubsam 617

HURRICANE HILDA, 1964II. STRUCTURE AND BUDGETS OF THE HURRICANE ON OCTOBER 1, 1964

HARRY F. HAWKINS and DARYL T. RUBSAMNa tion al H urricane Research Laboratory, Research Laboratories, ESSA, M i a m i , Fla.

ABSTRACTAircraft data from five levels (900 to 180 mb.) are used to depict the structure of a mature hurricane. Horizontal

analyses, vertical cross sections, and various budgets, which have been prepared from the research flight data only,are presented. New estimates of the drag coefficient under hurricane conditions are derived from a different formula-tion-utilizing the momentum budget int he inflow layer.

1. INTRODUCTIONOn Oct. 1, 1964, as hurricane Hilda was still deepen-

ing and already an intense hurricane [6], the ResearchFlight Facility in support of the National HurricaneResearch Laboratory launched a special data-gatheringeffort. The plan was t o gather meteorological da ta through-out the intense core of the storm at five levels. Each ofthe two DC-6's was responsible for data sampling attwo levels at or below 500 mb. The fist DC-6 tookobservations along the flight pattern shown in figure laat 900 mb. (3,240 f t . PA) . When this pattern was com-pleted, the plane climbed to 750 mb. (8,090 ft. PA )and executed a pattern similar t o that shown in figure lb.The other DC-6 flew a pattern similar to that in figurel a a t 650 mb. (11,780 f t . PA) , then climbed to 500 mb.(18,280 f t . PA) , and followed the pattern shown infigure lb . The high altitude je t at 180 mb. (40,870 ft.PA) flew the pattern shown in figure ICand then had tohead for its staging base because of its extremely shortrange. This five-level collection of data is unique in theNHRL-RFF files. It presented the best vertical resolu-tion that had become available up to that date, and forthis and other reasons it seemed appropriate that thedata should be analyzed exhaustively and that budgetstudies for various parameters be prepared where thedata permitted.2. DATA COMPOSITING AND DATA LIMITATIONS

The primary tool used in compositing the data aboutthe moving storm is the time-lapse radar film record. Atfrequent intervals, when the radar eye of the storm isdiscernible on the film, the relative range and bearing ofthe plane to the geometric center of the radar eye wall istabulated. These relative fixes of the plane to the stormare fed into the computer, which interpolates betweenfixes using the known motion of the storm and the Dopplernavigation information of the motion of the plane (carriedon the magnetic tape together with the meteorological

observations). For some purposes, this compositing tech-nique and its accuracy are quite satisfactory. For otherpurposes, the present equipment permits only marginallyacceptable compositing. For instance, if the plane islocated 60 n.mi. from the eye center and is misplacedazimuthally by a distance of 1n.mi., i.e., lo , hen an errorin the radial wind component equal to sin 1 multiplied bythe wind speed will result. Thus, i f the wind speed is 60kt., the error in radial' wind speed will be 1 kt. Mostmeteorological parameters have very small tangential orazimuthal gradients, however, and such errors may bequite unimportant for many of the uses that may be madeof these data.

The winds were Doppler winds, which are measuredrelative to the surface over which the plane is flying. If thesurface interrogated by the radar beam has a mean motionin a given direction, the wind computed by the Dopplersystem will be in error by an amount equal and oppositeto the motion of the reference plane. Most of the windspeeds with which we are concerned are large, while mostestimates of the net water motion (particularly the radialmotion) are quite small. O'Brien and Reid [17] used anumerical model in arriving a t an estimate of the maximumradial water motion of around 1 kt. and a maximumtangential motion of 2 to 3 kt. These velocities, however,were means fo r the water motion over depths of the orderof 60 m. In the present study all winds were calibrated(post-flight) for errors in true air speed and drift.

Temperatures were measured by vortex thermometersrequiring no dynamic correction. Many researchers whohave used vortex temperatures are of the opinion thatduring flights through cloud and falling rain, particularlyheavy rain, the values obtained may be to o low by asmuch as 1.5Oc. to 2.OoC. Having examined the data,we found no satisfactory systematic manner in which toapply this knowledge. In some situations, use of suchcorrections apparently improved the thermal structure,but in others where the correction apparently should alsobe applied, it made the thermal structure less acceptable.

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618 MONTHLY WEATHER REVIEW Vol. 96, o.

80:TAILED FL IGHT PAT TER N FL IGHT NO. 641001-8?ESSURE ALTITUDE 3.240 FT. 900 MB.

AIRCRA FT TRACK PA. 40.870 FT (180MEH U R R I C A N E " H I L D A " F L I G H T NO, 641001 -C O CTO BER 1. 19631Z./bk9. I ' I ' I I I ' I ' J ',

ITIME G M T

60

IIRCRAFT TRACK PA. 18.280 FT. (500 ME.)I U R R I C A N E " H I L D A " F L I G H T NO. 6 4 1 0 0 1 - A O C T O B E R 1.1964

-C. . . IC TRACUAIC TIMES 16 4 0 0 0 t - 17 36 002

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Consequently, the temperatures were not corrected for['in'' or "out" of falling rain, nor were any systematiccorrections deemed applicable to the DC-6 vortex ther-mometer readings as a result of the temperature checksmade with the radiosonde runs at Key West and Miami.The high altitude aircraft temperatures were finally

40i....

FIGURE.-Flight pattern, relative to the moving hurricane cen(at 0 n.mi. radius), at (a) low level, (b) 500 mb., and (c) 180 mb

judged to be 3OC. too high after extensive checkingother flights that season, und consistency tests of the daand the soundings on the day of the flight.

3. HORIZONTAL ANALYSESThe data coverage made detailed horizontal analys

possible out to a radial distance of 70 to 80 n.mi. In tinterests of brevity, and because intermediate changwere relatively small, we present the analyses at onthree levels: 900 mb., 500 mb., and 180mb.

The streamline analyses for these levels are presentein figure 2. Figure 2a shows that the air motion relatito the moving storm at 900 mb. was a nearly circulafairly symmetric, spiral indraft. Similar flows with progresively decreasing indrafts were analyzed at the 750- an650-mb. levels. At 500 mb. (fig. 2b) the inner 40 n.mshowed little indraft or outdraft although at greater rada shght outdraft was evident. Hence the "low leveinflow layer terminated somewhere between the 650- an500-mb. levels. A t 180 mb. (fig. 2c) the inner cycloncirculation was preserved. Strong diffluence, beginnisome 25 to 30 n.mi. out, was observed mainly east ansoutheast of the storm center. To the northwest and the southeast, the wind turned anticyclonically.

Maximum wind speeds (relative to the moving centewere recorded between 100 and 110 kt. at both the 900-m(fig. 3a) and 750-mb. levels, where the radius of maximu

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September 1968 Harry F. Hawkins and Daryl T. Rubsam 619

STREAMLINES (REL.WINDS) PA . 18.280 FT (500MB.)tiU R R CA NE "HI L DA " FLIGHT NO 641001-A O C T O B E R 1. 1964

60 40 20 20 40 60 8001 ' I ' I ' I ' 1 I ' I ' I ' IW E S T D I S T A N C E ( N A U T I C A L M I L E S ) E A S T, -

winds was about 12 n.mi. Note that these two levels wereinvestigated by the same aircraft so that there was aneffective time difference of about 3 hr. between the datasamples. At 900 mh. the isotach analysis showed a rela-tively simple pattern with fairly strong radial gradients

- .60 40 20 20 40 60 BO01 ' I ' I ' I ' 1 ' ' I ' I ' J

W E S T D I S T A N C E I N A U T I C A L M I L E S ) E A S T

FIGURE.-Streamline pat tern at (a) low level, showing the na tureof the spiral inflow relative to th e moving cente r; (b) 500 mb.,showing practically no significant inflow or outflow; (c) 180 mb.,showing outflow from the storm a nd stron g diffluence to thesoutheast.

but weak tangential gradients. The pattern appeared tobecome more complex with elevation at least to around500 mb. (fig. 3b), where numerous small centers of maxi-mum and minimum wind speed appeared. The 180-mb.wind speeds (fig. 3c) were surprisingly well sustained withheight. Some 18 n.mi. from the center 50-kt. winds wereassociated with the cyclonic core of the hurricane. Some30 n.mi. southwest from the center, another, larger windspeed maximum of 50 kt . appeared to be more closelyrelated to the larger scale circulation in which the vortexwas embedded.

Even at the low level of 900 mb. the warm-core structureof hurricane Hilda was manifest (fig. 4a). Temperatures inthe eye reached 23C. a t this level. Some 40 to 50 n.mi.out, on the other hand, temperatures averaged between18 and 19C. It is not impossible that this fairly strongtemperature difference was enhanced because of the vortexthermometer deficiency previously discussed. At 500 mb.(fig. 4b) the strongest gradients were in or near the eyewall. Temperatures were above 3.0"C.in the center of theeye and decreased sharply with distance just outsidethe eye. This first annulus of cool air outside the eye wassucceeded by warmer air at greater radii until a secondcool pool was met some 70 n.mi. to southwest of the center.All in all the 500-mb. temperature pattern seemed more

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620 MONTHLY WEATHER REVIEW Vol. 96, No.

J80 ~ ~ " ' i ~ ; l ~ f i " '0 40 20 20 40 60 80D I S T A N C E ( N A U T I C A L MILES) E A S TW E S T

complex than one might have anticipated a priori. At180 mb. (fig. 4c) the pattern was mainly one of circularsymmetry about the eye with temperatures rising (as theeye was approached) to the highest value (-48"C.),which was encountered in the eye.

W E S T D I S T A N C E ( N A U T I C A L M IL E S ) E A S

FIGURE.-Isotachs at (a)900 mb.; (b) 500 mb. (Not e the increain complexity of the pattern, presumably a reflection of thturbulent structure of the storm.) ; and (c) 180 mb.

The 900-mb. D-values presented in figure 5a show structure of nearly concentric circles. Figure 5b shows very similar structure for 500 mb., except for reducegradients. There were usable D-values from the jet aicraft at 180 mb. and these were merged with valuecomputed hydrostatically using figure 5b as a base anemploying the temperature data from 500 and 180 mband the humidity data from 500 mb. Figure 5c shows thfurther weakening of the cyclonic vortex with height thaone would expect in a warm-core vortex.

The final horizontal analyses are for the specific humidities for 900 and 500 mb., shown in figures 6a and respectively. No humidity measurements were taken fromthe jet aircraft. For the most part specific humidities increased with decreasing radius until the eye was reachedIn the eye, they remained at or near the maximum. Afirst glance their high values may seem somewhat surprising but, as pointed out by LaSeur and Hawkins [12the temperatures rise so rapidly as the eye is approachethat within the eye the relative humidities are less thathey are in the surrounding wall cloud and in the adjacenregions beyond.

4. VERTICAL CROSS SECTIONSThe similarities in the patterns flown by the variou

planes were designed for specific purposes. The firstraverses (see fig. 7) were planned from northeast tsouthwest through the storm center, but because th

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September 1968 Harry F. Hawkins and Daryl T. Rubsam 621

80

A D J U S T E D T E M P E R A T U R E ("C3 P A . 3 . 2 4 0 F T ( 9 00 M B . )H U R R I C A N E " H I L D A " F L I G H T NO, 641001-6 O C T O B E R 1 , 1 9 6 4

3f2'/6kt8 0 , I , , , I I I I I '

ADJUSTED TEMPERATURE ("C.) PA. 18.280 FT (500 MB.)H U R R I C A N E "H IL D A" F L I G H T NO. 6 4 1 0 0 1 A O C T O B E R 1 , 1 9 6 431T/6k/ I ' I, I ' ) I I ' I I I '

WEST D I S T A N C E ( N A U T I CA L M I L E S ) E A S T

60 40 20 20 40 6001 ' I ' I ' 1 " I ' I ' I '' W E S T D I S T A N C E ( N A UT IC A L M I L E S ) EA $

ADJUSTED TEMPERATURES ("C.) PA . 40.870 FT (180MB.IH U R R I C A N E " H I L D A " F L I G H T NO 6 4 1 0 0 1 - C O C T O B E R 1. 19641 ' 5 5 080 , I I I I5 4 5 54 5. l I T / 6 k l . I ' I

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. . . /C4 Ic TIMES i6*40QOZ- 1748002TRACK60 40 20 2 0 40 60 800 ' I I I I ' I I ' I ' I 'WEST D I S T A N C E ( N A U T I C A L M IL E S ) EAST

FIQURE.-Temperature at (a) 900 mb., showing a marked tend-ency 'towards a warm-core structure; (b) 500 mb., showing atotal temperature rise only slightly larger than at 900 mb.; and(c) 180 mb., showing a smooth, relatively simple temperaturepattern. Al l temperatures are negative in c.

Rather than being "stacked" vertically the planes hadtangential separations ranging up to around 40 mi. Thedata were composited, however, as f synoptic in time an dsuperposed in space for the purpose of constructingvertical cross sections. When necessary, the data weresubjectively smoothed and reasonable allowances weremade for the method of compositing.

TEMPERATURESBased on the data from the five levels (800, 750, 650,

500, and 180 mb.) soundings were constructed a t 10-n.mi.intervals on either side of the storm out to 60 n.mi. onthe east and 70 n.mi. on the'west side (fig. 8). The lowestportions of the soundings; i.e., below 900 mb., wereconstructed under the assumptions that: 1) the cloudceiling lowered from 1,500 ft. a t 70 n.mi. to 800 ft. at theeye wall, which seemed reasonable in the light of ourexperience in low level hurricane penetrations; 2) thesounding was saturated, or very nearly so, from the900-mb. observation down to the lifting condensationlevel at the cloud base; and 3) from cloud base to ocean

storm was a little farther north than anticipated, the firstpenetration ran more from east-northeast to west-south-west at 900 and 650 mb. These planes were subsequentlyjoined by the jet for a three-plane traverse at 750, 500,and 180 mb. The total time spread was about 5 hr.

surface the sounding was essentially dry adiabatic. Theterminal sea level pressures were estimated from calcu-lations that extrapolated the 900-mb. D-values to equiva-lent sea level pressures and from preliminary analysis ofthe D-value profile (to be discussed later). For the most

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622AD J U ST ED "D " VALUES (FT.) PA . 40.870 FT (180 MEHURRICANE "HILDA" FLIGH T NO. OCTOBER I , 19 6B o , l , l , l , I I I I I IJI2' /6k1

MONTHLY WEATHER REVIEW Vol. 96,N o .A D J U S T E D "D " VALUES ( F T ) PA. 3,240 F T (900ME.)HURRICANE "HILDA" FLIGH T NO 641001-8 OCTOBER 1 , 1 9 6 4BO ,

bIT/6kI I

60 40 20 20 40 60 BOW E S T D I S T A N C E ( N A U T I C A L M I L E S ) E A S T

part no abrupt discontinuities of lapse rate were intro-duced or necessary at the 900-mb. level because of theseassumptions.

The lapse rates appeared to be consistently stable,particularly on the east side of the storm in the layerbetween 650 and 500 mb. Since the two temperatures

.. . . AlC TRACK 'D ' VALUES I U E I N ANNUAL T R O P I C I L IA/C T l M E S L 6 4 0 0 0 L - I 7 1 8 O O Zfin 10 7 0 2 0 40 60- ._ EASTI S T ~ N C EN A U T I C A L M I L E S )W E S T

FIGURE.-D-values at (a) 900 mb., (b) 500 mb., and (c) 18mb., the latter were partially constructed hydrostatically fromthe 5O&mb. brsse.

defining this stability were measured from the samaircraft, no single correction applied consistently to thiparameter would change the relative lapse rate.

It seems possible that the vortex thermometer"wetting effect" might have contributed to exaggeratinthe stability since the 500-mb. pass was mainly abovewhile much of the 650-mb. pass was in the active precipitation. However, even if one raised the 650-mtemperatures 2C. on the eastern side of the stormlayer of marked stability would still remain. Moreovethe correction is presumably not applicable 60 mi. easof the center where the stability was quite well markedThe west side of the storm did not . show the curiouwarmth at 500 mb. although on this side, too, the flighwas not through any extensive areas of precipitation.

The dashed curves in figure 8 offer an appropriatmoist adiabat for comparison with each sounding. Igeneral, the closer the soundings with reference to thstorm center, the warmer they were (particularly ahigher levels). A t most radii the lapse rate was close tmoist (and also dry) adiabatic at the uppermost datpoint, 180 mb.

The composite eye sounding deserves mention. It showthat a stable layer existed from the "cloud base" tabout the 750-mb. level, above which the lapse rate wabriefly greater than moist adiabatic but in general verclose to it. The structure was not unlike that in the ey

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September 1968 H a r r y F. H a w k i n s a n d D a r y l T. Rubsam 623

W E S T D I S T A N C E ( N A U TI C A L M I L E S ) E A S T

'4.060 40 20 20 40 60I ' I I I ' ' ' I I ' "D I S T A N C E ( N A U T IC A L M I L E S 180FIGURE.-Specific humidity at (a) 900 mb., showing again the

maintenance of high specific humidity values through the eyeof the storm; and (b) 500 mb., showing some tendency for lowereyevalues.

of hurricane Arlene, as documented by Stear [21]. Inthat instance, the raob showed a very stable layer up toabout 750 mb., a slightly greater than moist adiabatic

lapse rate above this level to near 450 mb., above whichthe sounding was close to moist adiabatic. Thus, despitethe hazards inherent in the time-space compositingtechnique, we felt that the eye-sounding was reasonablyrealistic. The upper level stability of the outer soundingsmay, of course, be attributed to the outflow of warm airafter ascent in the core of the storm.

The vertical cross section of temperature anomaly(fig. 9) was prepared from the soundings shown in figure 8using Jordan's [8] mean tropical sounding as normal.From 30 mi. outward below the 650-mb. level the anoma-lies were relatively insignificant. The strongest horizontaltemperature gradients occurred in the eye wall at levelsbelow 550 mb. Although the center of warm anomalies(+l6"C.) was located a t 250 mb., the horizontal gradientsabove 500 mb. in the outflow layer were much weakerthan through the wall cloud at lower levels. The magnitude(+12"C.) of the anomaly that still persisted at 180 mb.was somewhat surprising. The tropopause may havebeen not only higher but also (probably) colder thannormal, resulting in a rather strong vertical temperaturegradient between 180 mb. and the tropopause level(Koteswaram [lo]).

This anomaly pattern may be compared with that ofhurricane Cleo, 1958 (LaSeur and Hawkins [12]). Theupper flight level in that, much weaker, storm was at239 mb. and the maximum recorded anomaly was +11C.Although in the case of Hilda the maximum anomaly(+ 6C.) was interpolated from the composited eyesounding, we felt that, barring marked upper level stablelayers, there was not too much choice in drawing the eyesounding between 500 and 180 mb. I n addition, thesoundings were used to make hydrostatic computationsthat appeared to meet all consistency requirements. Wefeel, therefore, that although minor errors may haveexisted in the thermometry it was highly unlikely that'any correction would be large enough to affect the majorfeatures of the patte rn.

One further point of interest may be found in the sealevel temperature gradient (heavy dashes at bottom offig. 9). Since the temperatures were derived from thelow level aircraft data extrapolated downward as alreadydescribed, an interesting point arises as t o whether ornot the anomaly increase with decreasing surface pressurecorresponds to that which would accompany the isother-mal expansion proposed by Byers [2] as characteristicof the low level circulation of a hurricane. Inspection ofthe sea level "terminal" temperatures (fig. 8) shows thatthey all terminated at the same temperature within aquite acceptable tolerance of fO.2"C. In view of theassumptions involved in processing the aircraft data andin the extrapolation t o sea level this seems to be anacceptable independent confirmation that the in-spirallingair did indeed undergo an approximate isothermal ex-pansion. I t does not, however, prove that temperaturesrecorded in the low level pass itself were not too lowbecause of extended flight through falling rain. Presumably

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624 MONTHLY WEATHER REVIEW V o l . 96, oI 1 I I I I I I I I I I I I I I I II-ALL HEIGHTS (MEA N ANNUAL TROPICAL ATMOSPHERE)

AL L T I M E S G . M . T .

' G 1 7 ' 0 3 : O OH U R R I C A N E " H I LD A " O C T O B E R 1, 1964A I R C R A F T T R A C K S U S E D FO R

FIGURE .-The elevations, times, and relative horizontal tracks of the aircraft traverses used in constructing east-west vertical crosections of hurricane Hilda.

a uniform positive correction applied t o those temperatureswould lead to a similar result but at a somewhat greatertemperature. D-VALUES

The D-value cross section (fig. 10) is, in part at least,a mirror image of the cross section of temperature anomaly.We may note that the D-value equals the radar or truealtitude minus the pressure altitude (in the mean tropicalatmosphere). Thus as one scans the cross section horixon-tally, the D-value variations indicate the change in al-titude which that constant pressure surface underwentin hurricane Hilda. The five data levels were analyzedusing the aircraft data plus hydrostatic computations t oensure vertical consistency. Only very minor adjustmentsof the aircraft D-value profiles were necessary after theprofile had been positioned at the correct mean level.Gradient winds calculated from the derived field of valueswere found to be in general agreement with the observedwinds. R4aximum D-value horizontal gradients occurredin the lower levels in the eye wall near the radius ofmaximum winds.

As expected, the largest negative anomalies occurrein the eye at sea level. The magnitude of the negativanomalies decreased outward and upward, becomingenerally positive above 200 mb. at just about all radiThe negative D-values, i.e., low pressures, are obviousattributable t o the mass of warm light air above angiven point. The air picks up sensible heat from the oceain its isothermal expansion while spiraaling in at lolevels and also (as will be demonstrated) acquires evemore energy in the form of latent heat. Much of thheated air rises in the wall cloud and spiral bands neathe wall and then flows outward. The sea level pressugradient is, in a sense, the integrated result of thesprocesses. However, since the sea level pressure patteritself is a significant factor in one of these processes therare manifest possibilities for the existence of a feedbacmechanism.

WIND SPEEDSThe ,wind speeds (relative to the moving storm) ar

presented in a vertical cross section of hurricane Hild

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625eptember 1968 Harry F. Hawkins and Daryl T. Rubsam

1 COMPOSITEWEST70 N.Mi._,,'

OF ZMPERATURE'1o1 "HILD,E A S T40 N.Mi..," \\>-;.\'*z.

' OCTOBER 1 ,1 9 6 4

FIGURE.-Temperature soundings (solid line) a t 10-n.mi. intervals across hurricane Hilda. The dashed line is an appropriate pseudoadiabat.in figure 11. Maximum winds of 100 to 110 kt. were ob-served some 11 to 12 n.mi. east of the storm center. Thepattern has been subjectively smoothed because timeand space differences in cornpositing did not permit perfectcoincidence of values. Maintenance of wind speeds withheight (Hawkins [5]) was best demonstrated near and inthe eye wall, where maximum winds of around 105 kt . onthe east side at low levels gave way to a maximum of 48kt . a t 180 mb. On the west side of the storm the windshear was even less, with low level values of around 95kt. diminishing to around 55 kt. a t 180 mb.A careful check on the consistency of the wind andtemperature field and on the balance and/or imbalanceof these fields composited in the manner described (andsmoothed subjectively) was made as follows :If one considers the thermal wind equation in cylindricalcoordinates and assumes steady state, frictionless motion,one can write: +) aT,_ _vo p ar p .aPStrictly speaking one should more properly consider,a) the total wind, b) the radius of trajectory curvature,and c) the shear of the curvature with pressure. However,the total winds are very similar to the actual tangentialwinds and one may for the nionient assume that thecurvature does not change with height in the inflow layer.With these reservations in mind computations were madethrough the inflow layer using the given equation forevaluating the shear over 5-n.mi. radial intervals and100-mb. vertical increments.

Table 1 shows the results of these calculations for the800-, 700-, 600-, and 500-mb. levels. The observed windsfor 900 mb. are shown in the top row. The 800-mb.observed winds, the computed winds for this level, andthe differences between the two occupy the next threerows. The differences are recorded as positive where theobserved wind exceeds the computed and as negativeotherwise. Differences are underlined once where theyexceed 10 percent of the observed wind speed and areunderlined twice where the differences exceed 20 percent.The computed winds are based on the observed 900-mb.winds (and the radial virtual temperature gradient), sothat in effect all shears are cumulative from this level.Only six of the 96 values differ by 20 percent or moreand 16 of the 96 differ by from 10 to 20 percent (of theobserved wind speed). For the most part the differencesbetween observed and computed speeds are small ornegligible. Further, as the table shows, pluses predominateon the left (left side of the storm), negatives on the right(right side of the storm). If one considers the radius oftrajectory curvature, it must be larger on the right ofthe direction of motion of the vortex and smaller on theleft, an effect that would tend to diminish the magnitudeof the positives on the left and the negatives on theright. The oiily coiiclusion possible from this array isthat no coiisistent and strong deviations from the thermalwind relationship appear in the inflow layer.

Gray [4] has pointed out that the cumulus activity ina hurricane may play an ambiguous role in that the pene-trative cumulonimbus towers which carry up and releasethe heat (making the storm warm core and weakeningwith height) also carry up higher momentum from thelower levels, tending to extend the strong lower level

3 1 5 - 5 2 1 0 - 66 - 6

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626 MONTHLYO C T O B E R 1 , 1 9 6 4

( F R O M M E A N A N N U A L T R O P IC A L A T M O S P H E R E )I I J J I ~ I ' I ' I ' I ' I ' I

WEATHER REVIEW Vo l . 96, o.HuR R IcA N E "H ILDA" O C T O B E R i . 1964

V E R T I C A L C R O S S - S E C T IO N

FIGURE0.-Vertical cross section of D-values (from the meatropical atmosphere).

G E O M E T R I C A L C E N T E R OF H U R R I C A N E E Y E

FIGURE.-Vertical cross section of temperature anomaly preparedfrom the soundings presented in figure 8.

circulation to higher elevations. While momentary ex-cesses of wind over gradient may well exist in such gustsor bubbles, it seems unlikely that over any appreciabletime period or any exteiisive area excessive imbalancescan be maintained. Nevertheless, the dual opposing rolesthat the cumulus plays have been well posed by Gray.

RADAR ECHOESThe radar cross section (fig. 12) has been prepared by

scanning the RDR-1D (3.2 cm.) vertical cross-sectionradar on each of the four, lo\\-er level flights. The flighttrack was stippled when the plane appeared to be in anactive echo. Because of the extremely short ranges ( 5 to10 mi. 011 the average) and the small antenna, spuriousechoes from side lobes and general clutter made interpre-tation of the scope exceedingly dimcult. The major por-tion of the area under surveillance was characterized byprecipitation falling from the bright band which was, forthe most part, quite well defined. Thus the radar echotops were generally even and stratiform. The major ex-

ception to this condition was in the mall cloud. On theastern (right hand) side of the storm echoes rose tabout 200 mb., i.e., around 40,000 f t . This was the onarea of the storm in which really deep, vigorous asceappeared to mount well into the upper troposphere. Thpercentage area covered by active cumulus or cumulonimbus towers was certainly not greater than the generalsmall figure usually allotted to this activity. The visibcloud, of course, surmounted the echoes in all areas, fothe jet aircraft at 180 mb. was in cirrus throughout moof its transit of the storm.

On a lower level of the diagram we have depicted ithick lines the areas where the APS-20 (10 cm.) radasuggested the more prevalent major rain bands were lcated. These were cornposited over some period of timfrom the two APS-20 films available. In view of the diferences in the radars and in the method of cornpositinit is not surprising tha t there are differences in the twcomposite presentations. Since only the stronger bandare distinguishable on the APS-20 (10 cm.) one shoulexpect the echo area to be smaller than the precipitatioarea derived using the 3-cm. set. The most unusual feature of the figure is the length of flight through rain athe lowest level. Presumably the hardest rain occurrein the limited areas of the 10-cm. radar echoes.

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September 1968 H a r r y F. H a w k i n s and Daryl T. Rubsarn 627

72707007067+368624-66755-12--7.5595860-25657-15256-44755-8-

H U R R I C A N E " H IL D A" O C T O B E R I , 1 9 6 4V E R T I C A L C R O S S S E C T I O N

O F R E L A T I V E W I N D S P E E D S ( KN OT S)

79777707775+27569+67262+1062.5575658-25557-25056-64556-5 1-

GEOMETRI CAL CENTER OF HURRI CANE EYEFIQURE1.-Vertical cross section of wind speeds relative to the

moving hurricane eye.

Radial DistanceLevel (mb.)Boo - - - ---. .- - --.- - - - -800......................

600......................

500--. ..................

Radial DistanceLevel (mb.)goo-.. ...................800- .....................

500. .....................

5. FEATURES OF THE MASS FLOW FIELD-RADIAL MASS FLOW

We have already mentioned the hazards involved incompositing observations around the moving storm. Oneof the parameters most sensitive to thes,e uncertaintiesis the radial velocity. Nevertheless, if we wish to investi-gate certain classes of problems, we have to estimateradial velocities as best we can. The various budgetstudies demand reasonable values of the radial velocity(v,) and several techniques have been devised for dealingwith the problem.

This most important single item in the budget studies,the distribution of radial velocities with height and radius,is shown in figure 13. Mean values of v, (relative to themoving storm) were acquired a t each flight level for every10-n.mi. radial interval by reading wind direction andspeed along radials constructed at 30' intervals from eachof the horizontal field analyses and then computing theradial components. These values were plotted on a dia-gram (fig. 13) fo r purposes of analysis. Since no data wereavailable below 900 mb. some decision had to be madeas to the general shape of the curve a t low levels.

We have assumed that the low level inflow increaseswith decreasing elevation through most of the frictionlayer, an assumption similar to those made by otherresearchers (Miller [14], [15], [16]; Riehl and Malkus [19];Rosenthal [20]). The inflow layer itself was fairly welldefined by these means and was shown to extend fromthe surface to about 650 mb. ; there was a slight suggestion,but no conclusive evidence, that the inflow layer de-

TABLE .-Wind speeds (kt .) , observed and computed ( j r o m the radial thermal gradient)(n.mi. left)..............Ob s.....................0bs.. - - - - - - - - - --.--..Comp...................Diff..-.._-._._ _ - - - - -Obs.....................Comp...................Diff-. ...................Obs.....................Comp...................Diff.. ...................Obs.....................Comp...................Diff .....................

67.424140

+14140+l4037+33932+2

(n.mi. right). ...........Ohs.....................Obs.....................Comp...................Diff.....................Obs.....................Comp...................Diff.....................Obs.....................Comp...................Diff.....................0bs.. ...................Comp...................Diff.....................

12. 5107105104+195100-58593-87787-10-

-2.5454442+24443+14344-14241+I17. 591Bo9008787838307580-5

0 .

57.5474745

+24641+54640+64440t-4

-

22.5828279+38077+3757506572-7-

-52.!494947+24843+548404736

f11

--8--27.7775757372

+16870-26069-9-

47.5515149

+25146+550434935--14e-32. 5727068

+26865+3636305861-3

-2.5545450+45346+75241+Q5138

+13

---37. 568676706463+16158+355550-

37. 5585754

+35651f 55548+75344+9

--42.56564640626205855

+35348+5

-32.5626160+16058+25855+35652+4-7. 563626206061-15759-25256-4-

27. 5676666065646360+36055f 5

+I

52.5616059

+I5857

+I5453+15051-1

23.5 I 17.! 12.5878784+38578+78572

4-138565f20

---___67.5565456-25156-54756-94353-10

--

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62 8 MONTHLY WEATHER REVIEW Vol . 96, o . 91

HUR R CA NE I' HILDA " R A D A R C R O S S S E C T I O N O CT OB ER 1. 1964IO0 I I I I I I - ( I l l I I I ~ I ~ I ~ I

FIGURE2.-Vertical cross sect ion of radar echoes. Each flight level is stippled where th e plane appeared to be in a n active 3-cm. radar echoThe bright band is indicated where observed by th e RDR-ID vertical height-finding radar. Th e lower, thick lines labeled "radar echoes"are the more stable and well-marked bands composited from the 10-cm. APS-20 film as representative of the band structure over themajor portion of the period of flight. Darker stippling has been used to represent the major wall cloud and its more active cumuluscharacter .

100 M B -200MB - HURRICANE "HILDA" OCT. 1,1964VERTICAL PROF ILES OF R ADIAL WINDS300 M B - R / l O V.S. PRESSURE4 0 0 H B - -

WT2 5 0 0 M B - -v)WmQ1 6oo - -

700 M B - -

S O O M B - -

900M E - -1000 M B - -

1 1 1 1 1 1 1 1 1 1 1 1 1 1 I I I I I I I I I I I I I I I I I I I I I I I I I- 44 -40 - 3 6 - 3 2 -28 - 2 4 - 2 0 -16 - 1 2 - 8 - 4 0 4 8 12 16 2 0 2 4 2 8 32- K N O T S X N A U TI C A L MI LE S

FIGURE3.-curves of radial velocity (in the form of rv,/l0) against pressure for various radii. Mass balance is required a t every radius

scended with decreasing radius. In the layer from 650 to500 mb., radial motion was weak or nonexistent, and at500 mb. the I OWT extremes of the outflow layer werebarely visible.

The curves in the outflow layer were drawn under theassumptions that 1) the radial f l o ~oes to zero a t 100mb. and 2 ) the mass outflow across any given radius just

balances the mass inflow across the radius. Althoughthe values of the inflow at 180 mb. obtained from theflight data were most helpful, they were above the maxi-mum (in elevation) and allowed considerable flexibilityin the shape of the curve. We have also assumed tha tgradations in the radial flow from one radius to anotherwould be in the form of gradual transit ions ra ther

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I I I 1 I I I I10 20 30 40 50 60 70 ED 90._ --DISTANCE (NAUTICAL MILES 1-FIGURE4.-Vertical cross section of absolute angular momentum

for tangential winds that have been averaged azimuthally aboutthe moving storm.

than in the form of alternate annular rings representingconvergence, divergence, etc. All these criteria could bemet if one assumed tha t the computed mean radialvelocities were accurate to f l kt., Le., that the curvesas drawn did not depart from the appropriate data pointsby more than the equivalent difference of 1 kt . in the meanradial flow. Any more explicit reliance on the meanobserved radial velocities would be unrealistic.

The radial wind profiles are the most importan t singlefactor in all budget computations. The curves have beendrawn with the greatest possible care and the equal areaswere measured by means of a planimeter. Some furtherdocumentation was available at 900 mb. Figure l a showsthat a closed hexagonal figure was flown about the stormat this level. The mean radial velocity of the 5,500 ob-servations gathered around this closed path at 900 mb.was plotted on the radial wind profiles at the mean radialdistance and has been drawn to exactly. Note that inboth the inflow and outflow layers these radial velocitieswere rather small compared with those used by otherinvestigators and in general were about half the normallyassumed values.

MEAN TANGENTIAL FLOWIn a manner similar to that employed in computing the

mean (relative) radial velocities, the mean (relative tothe moving storm) tangential velocities (ve) were also

H U R R I C A N E H I L D A O C T O B E R 1, 1964V E R T I C A L C R OS S - S E C T I O N OF ABSOLUTE V O R T I C I T YSa ( lo- sec:)

I I I I I I I 1

2OOM8.-

300MB.-

40 0 M8.-Wa2 500M8.-anW

60 0 ME.-

70 0 MR-i

80 0 MB.-

900MR-

i000MB.-I I I I I I Ii0 20 30 40 50 60 70 80DISTANCE (NAUTICAL MILES)

FIGURE5.-Vertical cross section of absolute vortic ity forthe meantangential relative winds.

computed. From these winds we constructed cross sectionsof absolute angular momentum (fig. 14) and of absolutevorticity (fig. 15).

The absolute angular momentum,M = v s r f fr 2/2,

of a parcel of air in the inflow layer obviously decreasedas the parcel spiraled inward. This decrease, directly attr ib-utable to the drag exerted on the sea surface by the movingair, was imparted to the ocean. At upper levels in the out-flow layer, the absolute angular momentum of the parcelswas more likely to be conserved. Here the isopleths becomealmost horizontal, particularly at the higher levels. Figure14 suggests that the air which penetrated farthest inwardlost more of its momentum than other parcels and mayhave risen quite high before significant outward motiontook place. It seems doubtful, however, that the parcelsfollowed exactly along the isopleths; turbulent exchangewith adjacent parcels of different value would tend toalter the absolute angular momentum value with whichthe parcel traveled along on its outward trajectory.

The mean cross section of absolute vorticity,

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Vol. 96, o.30 MONTHLY WEATHER REVIEWO C T O B E R 1 , 1 9 6 4

) x ioi4 grn. cm/sec.A B S O L U T E V O R T I C I T YI I I I

100

200

300

4 0 0

W5 500lnlnWUI oo

700

800

900

10001 I I I I I I

10 20 30 4 0 50 6 0 7 0 80DISTANCE (NAUTICAL MILES)FIGURE6.-Solid lines are Stokes str eam function superimposed

on (dashed) lines of absolute vorticity. Selected streamtub es areindicated by 1, 2, etc.

TABLE.-Conseruation of potential vorticity1 - Streamtube

is presented in figure 15. Most of the values were greaterthan 10-~et.-' and near the eye wall values of the orderof set.-' were encountered. Riehl and Malkus [19]have pointed out that while frictional influences un-doubtedly affect the vorticity field, the major configura-tion of the vorticity field (and the absolute angularmomentum field) is presumably still linked to the distri-bution of convergence and divergence so that, in thefirst approximation, the theorem of potential vorticitymay hold. If so,

l a 2- p2,la , AP1

where Ap is the pressure depth of the column considered.

We have computed Stokes stream function for the radiaand vertical motions that follow from the radial winprofiles. If the equation of continuity is employed,

from which

and

The stream function was computed from the latter expression and the streamtubes are shown as continuoulines in figure 16. A number of the streamtubes were useto evaluate the conservation of potential vorticitTable 2 shows that within the inflow layer there \vastendency to conservation. In the very lowest layer wherfrictional effects were strongest there was little conservtion. In the layers of streamtubes from about 950 mb. 850 mb., however, potential vorticity was conserved asprobably also was above this level, although uncertaintin evaluating the terminal pressure depths cast somdoubt on the numerical evaluations.As figure 16 shows, in the upper portions of the outflo

layer the streamtubes are very nearly parallel to the lineof constant angular momentum. There seems every reasoto expect that absolute angular momentum is conserveat these levels and that some turbulent mixing is the onmodifying process.

6. BUDGET OF ABSOLUTE ANGULAR MOMENTUAND EVALUATION OF THE SURFACE STRESS

The mean flux of absolute angular momentum ( M )wcomputed for t.he mean symmetrical hurricane. Figu17 presents the results of these calculations, which abasically similar to the computations of Riehl and Malku[19] and Miller [14]. The horizontal fluxes in figure 1were calculated a t 10-n.mi. intervals radially and 1OO-mintervals vertically, i.e., flux=2?~rMv,Aplg , where and E are the appropriate mea n values of absolute angulamomentum and radial velocity.

The momentum extracted by the ocean was computein two ways and the results are tabulated immediatebelow 1000 mb. in figure 17. Values in parentheses wederived using the net horizontal fluxes into and outthe annular volumes from sea level up to the 100-mlevel. In each volume there was a net excess representinthe momentum lost to the ocean. The weakness in thprocedure lies in the fact that the outflow layer data wervery sparse and the maximum outflow occurred below

-

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~~ ~


I I I I I I I10 2 0 30 40 50 60 70 80D I S T A N C E ( N A U T I C A L - M I L E S 1FIGURE7.-Flux of angular momentum for the mean symmetric

hurricane Hilda. In the lower boxes, numbers in parentheses aremomentum losses to the sea computed to the top of the atmos-phere (100 mb.). Immediately below ar e the same losses computedon t he basis of the bet ter defined inflow layer data . Enclosed inthe boxes are momentum losses per unit area in units of 108 gm.set.+

the upper observational level, in the very region wherethe vertical gradient of absolute angular momentum wasquite strong. This meant that horizontal fluxes in theoutflow layer could be materially altered by relativelyminor shifts in the rvr profile aloft. For these reasons, analternate method was used based only on data from thebetter defined inflow layer. The resulting values are givenimmediately below the estimates in parentheses. Thedifferences in most cases were of the order of 10 percentor less.

As one might expect, the total angular momentum lostto the ocean was greater in the outer volumes and de-creased inward. This is attributable to the greater oceansurface area in the outer volumes, which apparently morethan compensates for the increasing wind speeds andgreater drags in the inner volumes. The enclosed figuresgiven at the bottom of figure 17 are the momentum lossesper square centimeter (X l o s gm. sec.-l) in each of theannular rings. These show that the rate at which angularmomentum was extracted per unit area increased as the

radial distance decreased, resulting in greater loss perunit area at higher wind speeds.With the data at hand, estimates were then made of

the surface stresses by means of which the angularmomentum was transferred to the ocean. In the moreconventional approach, the tangential equation of motionin cylindrical coordinates may be written:

where lateral frictional effects have been ignored and thesymbols are conventional, with T O , defined as the shearingstress in the 8-2 plane. If we assume a steady staterelative to the moving system and symmetry, i.e., in effectthat the tangential gradients of p and vg are negligible, wemay write:

or

where p o is the surface pressure, p , is the pressure at thetop of the inflow layer (where V, is zero and 7 8 , is usuallyassumed negligible). The second term on the right hasbeen variously estimated at around 10 percent of the firstterm and is usually neglected.

An equivalent expression can be derived, which involvesthe absolute angular momentum, M , in the place of theabsolute vorticity:

also,

areJp: -rg$ d p =J H r1 r v , M ) +$( M r ) ] d p;and,

where use has been made of the appropriate expression forthe equation of continuity. In this latter form of the equa-tion fo r the stress, we can make ready use of the rv , curves(fig. 13) and of the angular momentum profile (fig. 14).The vertical velocities were calculated from the rv, curves.If instead of integrating only over the inflow layer, oneintegrates to the top of the atmosphere, re, becomesnegligible. However, uncertainties arise because of thelack of data at upper levels.

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632 MONTHLY WEATHER REVIEW Vol. 96, o

3 5

1 9 . 3 .

18.0

15.3

17.7

8 .410.7119.1-

TABLE .-The tangential shearing stress computed in four differen tways for 10-n.mi. annular rings centered on 16, 26, etc. n.mi.

4 5

15.0

43.9

15.9

(24) (19)17.8

10.3

(7.9)iB.2

TABLE .-Drag coejicients computed from the indicated stress valu

RADIUS (N.Mi .1 io-20 20-30 30-40 40-50 50-60 60-70 70-

Eo D y n e s I C m c ) 52.44 26.98 19.30 15.00 11.00 8.04 5.6

H U R R I C A N E ' H I L D A ' STRESS UN ITS DYNES /CM. 'R A D I U S N A U T IC A L M I LE SI

8. 7

52 .4 27.0.-2 2 . 7

.11.0-10.7

Cd x l b I 3.56 2.17 I 1.99 I 1.84 1.58 1.42 I 1.2r drd p , r M $ 57 .2 I II I I I I I I36.3

(7.2143.5,- 4. 3(3.0)

27.3

9. 7

11.2)10.9-

I URRICANE .HELENE"A HURRICANE "DONNA.

HURRICANE " HILDA"15.452.5167.9- .8115.0)

23.8-

~ " ' " " " " " ' " " " " " 'SO 40WI ND SPEED IM,/SEC,I Uo10

FIGURE8.-Drag coefficients for hurricane Hilda plotted againa background of other hurricane and lower speed determinatio(after Miller [17]).

We evaluated the surface stress, re,, (assuming re#negligible) in four "different" ways. That is, we-inte-grated each of the expressions through the inflow layerand also from the surface to the top of the atmosphere(assumed to be 100 mb.). The results of these numericalintegrations are presented in table 3. The top line repre-sents the most convenient expression to evaluate com-puted through the inflow layer where the data were best.The second line evaluated these same expressions fromthe surface to 100 mb. In general the agreement appearsto be fairly good. The data were of such quality that wedo not feel the differences in the Too values reflect thevalue of TOH in any significant way.

The lower two lines of table 3 present analogous cal-culations for reo using the expression involving the abso-lute vorticity and including the frequently neglectedshear term. In the inflow layer the shear term was about10 percent of the vorticity advection term except in thesmallest annulus. When evaluation was made to the topof the atmosphere the shear term became, in general,the dominant term. With the exception of the innermostannular ring, the final values are reasonably similar. Forreasons already stated, the evaluation through the well-documented inflow layer (top line) was selected as "best"and these values were used in determining the momentumexchange coefficient. These calculations involved themean transport terms only.

The stress averaged around 6 dynes/cm.2 in the outerring where winds were about 24 m./sec., rising to some52 dynes/cm.2 in the innermost ring where winds averagedabout 41 m./sec. Through use of the empirical formula

~ O o = p c d z ) @ v =p c d v O 2

ated for the various annular rings and correspondinwind speeds. The dimensionless drag coefficients rangein value from 0.0012 to 0.0036 and have been plotteagainst wind speed (large solid circles) in figure 18. Thdrag coefficients for higher wind speeds from hurricaneHelene and Donna were obtained by Miller [16], whalso presented estimates for lower wind speeds takefrom a summary by Deacon and Webb [3]. The valufor hurricane Hilda appear overall to be somewhat loa t intermediate speeds but agree with Miller's estimatat maximum speed. They suggest a curvilinear dependence of drag coefficient on wind speed rather than thlinear relation (dashed line, fig. 18) suggested by MillePalmen and Riehl [18] used the composited mean hurrcane data of Hughes [7] and E. Jordan [9] to estimadrag coefficients. Their values ranged from 1 .1X2.1X 1 0 - ~ or winds that varied from 6 to 26 m./sec. Thtechnique they used also employed an angular momentum budget.In working with the data of hurricane Daisy, Rieand Malkus [19] used an assumed constant drag coefficieof 2.5 X 1 0 - ~ nside the 80-n.mi. radius to estimate thtransfer of angular momentum into the ocean. Thefound that while the disturbance was in the tropicstorm stage the angular momentum balance was reasonably satisfied without transfer by lateral stresses. Whethe hurricane reached maximum intensity, howevebalance was achieved only through sizable exports bmeans of lateral stresses.

The computations just cited also included estimateof the lateral transports by eddies. The day when hurri

where V is the total wind (as contrasted to the tangentialsurface wind) the drag coefficients (table 4) were evalu-

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~~ ~ ~

Harry F. Hawkins and Daryl T. Rubsam 633TABLEi.-For the indicated radial intervals the following quantitiesare listed i n order: the air-sea temperature difference, the air-sea(saturation at sea temperature) specijic humidity difference, meanwind speed, exchange coeflcients, sensible heat transfer, latent heattransfer, the Bowen ratio, and outgoing radiant heat energy.

cane Daisy was at maximum strength the eddy transportof angular momentum was outward and was approxi-mately 10 percent of the total import a t the given radialdistance. In the case of hurricane Hilda we had availablethe circumnavigation d ata a t 900 mb. a t a mean radialdistance of about 50 n.mi. The inward angular momentumtransport by the mean mass flow for the 950- to 850-mb.layer at this distance was 3.6 x 1022 gm. cm.2 sec.-2;the eddy transport corresponding to this mean was1.4 X lo2' gm. cm.2 sec.-2, directed outward. Thus, theeddy transport was about 5 percent of the mean andin a direction opposite t o that of the mean transport.

7. B U D G E T O F T O T A L E F FE CT IV E E N E R G YThe phrase "total effective energy," H , is used hereto indicate the total energy of the parcel less the kinetic

energy. Since even in a hurricane the kinetic energy isbut a small fraction of the total energy, H is a usefulconcept although a misnomer in the sense that for somepurposes the energy of the wind is the effeche portionof the kinetic energy.

Computations of the exchanges of sensible and latentheat a t the ocean surface involved the following assump-tions and procedures :

1) The exchange coefficients for sensible heat, C,,, andmoisture, Ce , were assumed identical with that formomentum, C,.

2) The sea surface temperature, To,was assumed tobe a uniform 30" C. This warmth before the passage ofHilda has been well documented by Leipper [13]. Whetherone is justified in assuming a uniform t.emperature thatapplies equally to the front and rear of the storm appearsdubious in the light of Leipper's findings. (The recentadvent of reliable infrared thermometers will provide ahandy tool for further research in this area.)

3) The air temperature, Tal at the various radii wasderived from the soundings shown in figure 8 by extrapo-lation from the 900-mb. flight temperatures, as pre-viously described.

4) With the ocean temperature and pressure given,the saturation mixing ratios at the sea surface, qo , was

computed using a tephigram. The actual mixing ratioof the air, qa, was similarly obtained by tephigram onthe basis of the 900-mb. da ta level under the assumptionsprevious listed.

5) The vertical transports of sensible and latent heatwere computed using the usual expressions

where - ndicates areal averaging, V is the total windspeed, and A is area.I n addition to the foregoing, the Bowen ratio, T b , wascalculated using the relationship

A rough order of magnitude calculation was made of theinfrared radiation from the top of an idealized inner cirrusshield. Using the equation E=aT4, where a=8.22X1011cal. om.+ min.-l, the Stefan-Boltzman constant, assumingT=220A., which equates to an effective radiating cloudtemperature of -53C. located between the 150- and180-mb. levels, one obtains the radiation in joules/dayfrom an annular ring as

Ra=Er ( b2 - a2 ) 440,4.186where a and b are the pertinent radii.

The results of these calculations are presented in table5, which shows that the air-sea temperature differenceswere close t o 5.0"C.or about twice as large as those usedby Miller [14] for hurricane Helene and by Riehl andMalkus [19] for hurricane Daisy. The air-sea humiditydifferences were also about twice those used by theseinvestigators. Because of these similar proportions, theBowen ratio was also quite similar, and varied from 0.15to 0.21. Thus the latent heat added from the ocean sur-face was about five times the sensible heat given up bythe water.

The bottom line of table 5 suggests that long waveradiation under the high cirrus shield was a minor factorat the inner radii, but one cannot conclude from this thatradiation effects in hurricanes are unimportan't. In a veryinteresting paper, Anthes and Johnson [l ] recently com-puted the infrared radiation from the area outside thecirrus shield (from 500 to 1000 km.), using radiation ratesfrom the Tropics as measured by Kuhn and Johnson [l11.Anthes and Johnson found that in hurricane Hilda onthe same day, Oct. 1, 1956, the radiant loss of energyin the outer ring was equivalent to a cooling of the airmass at 1.5"C./day. This cooling in turn helped to con-tribute to the baroclinicity and to the production of avail-able potential energy in quantities that were not insignifi-cant when compared with that engendered by the releaseof latent heat at shorter radii. Th e effect of the increasedalbedo of the cloud shield in diminishing these baroclinictendencies has apparently no t been considered.

The budget for the total effective energy,H=c ,T+gz+Lq

including the fluxes of sensible and la tent heat, is shown

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I 1 I 1 1 "I4 10 2 257 51 8 4 3 5 53 7 4 14

- - e 9 -.47 - -1438 - -2053 - -2 5 0 5 - -286r --3i32 - -3396

MONTHLY WEATHER REVIEW

5 0 0 .-6 0 0 .I

Vol. 96, o

" 1 1 1 1 1300.6 209.0 221. 3 214. 2 212. 1 223. 3 r7.3201.5 . 2.4---4 - - - - -+--

230.6 2 0 6 . 6

1oc

800

900

I A A A A A 1262.0 168. 6 184. 2 184.7 181.1 182.8 175.1

.-8.S .-04.6 --169.0 c- 40.6 --311.1 --373.3 - -434.3 .-494.8.165. 9 104.2 112.6 114.2 118.9 LdL. 8 114. 6

7-10.6 .-164.2 T- 217.4 - -357 .2 --457.6 .-59,s .-65.4 .-763.2

200

300

40 0

1000. 4 " t " . 4 " ! " ? " : A : AQS QS Qs 0. QS 9 5 Q *2.11 1.82 2.06 2.15 2.24 2.35 2.4810.17 9.23 10.74 11.56 14.77. 13.47 14.34

Qe Qa

700

I 1

R A D I A L I N T E R V A L ( N . Y U 10-20 2 0 - 3 0 30- 40 40-50

-+- -+- -+-212.1 230. 6 206.62 9 18.4 25 .0 28.4

5 0 - 6 0 60-70 70-80 10-8

RAI NFALL I LNCHES/ DAY) 17.7 7.i 5 . 4 4 . 5 3.8 2. 9 2 .5 4 . 5

FIGURE9.-Budget of H=c.T+Ly+gz, the total effective energy,including the flux of sensible and latent heat from the ocean.Lowest numbers (enclosed) are the l aten t heat losses per unitarea an d time in units of joules om.? see.-'

T O T A L R A I N F A L L .DURING PASSAGE OFINDICATED ANNULARR I N G S I I N C H E S I (6K1

in figure 19. Mean horizontal fluxes of H were computedfrom the TU , curves using mean temperatures, mixingratios, and heights fo r the appropriate pressure intervals.At the top of the diagram, a net excessldeficit for eachannulus is indicated by an upward/downward arrow.An upward arrow indicates that energy in the amountcited was available for loss through radiative processes.Five of the rings show excesses bu t the amounts are oftoo large an order of magnitude to be accounted for bythe expected radiative cooling a t these radii. I t seemsmore likely that the net annular amounts simply reveallimitations in data and procedures. At the one radialdistance (about 50 n.mi.) a t which the 900-mb. circum-navigation was made, a computation of the net eddy trans-port revealed that the transport was inward (in the samedirection as the mean) but was only about 1 percent ofthe mean in magnitude.

The bottom row in figure 19 shows that the flux oflatent heat from the sea surface diminished from 14.3units in the outermost ring to 10.2 units in the innermost,or by a factor of )5, and that the flux per unit area ofsea surface went from 0.09 units to 0.31 units over the

2 . 4 3 0.98 0.74 0.62 0.52 0.40 0.34 6.

FIGURE0.-Budget of moisture showing the horizontal metransport a nd evaporation from the ocean surface.

TABLE -Rainfall rates for indicated annular rings assuming thall the convergent water vapor falls as precipitat ion

same interval. Thus, over the innermost ring, despithe lower air-sea humidity difference, the ocean gaup to the atmosphere about three times as much lateheat per unit area as at the outer limits. The most efficiearea in which to inhibit this transfer would be in the innemost rings where, however, the winds are strongest anthe seas are the roughest. These latter factors havargued against experiments using monomolecular filmt o inhibit the transfer of water vapor and thus try diminish the energy available to the storm. On the othhand, over the much larger mea of the outermost rinmore total latent heat was supplied the storm under mucless turbulent conditions, and under such conditions

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September 1968

~

H a r r y F. H a w k i n s a n d Daryl T. Rubsam 635film would have a much bet ter chance of remaining intactand effective.

8. BUDGET OF MOISTURE AND RAINFALLFigure 20 presents the water vapor budget in units of

log gm./sec. For comparative purposes one can convertthese into joules/sec. (X used in figure 19, bymultiplying the entries in figure 20 by 2.5. I n the layerfrom 900 to 1000 mb., about 12 to 13 percent of the totaleffective energy was in the form of latent heat. I n thelayer from 800 to 900 mb., the latent heat representedabout 10 percent of the total effective energy, while inthe layer from 700 to 800 mb. i t represented 7 to 8 percentof the total. Note that at the 50-n.mi. radius at 900 mb.(i.e., from 850 to 950 mb.) the eddy transport of watervapor was about 10 percent of the mean and in the samedirection.

In table 6 the net convergence of water vapor in theannular volumes is indicated, together with the rainfallthat might be expected if the excess vapor were con-densed out. We see that the rainfall rate increased ratherslowly with decreasing radius until the last two rings arereached, where the precipitation rate increased mostabruptly. The lower line of the table gives the totalrainfall t ha t could be expected with the passage of thestorm directly overhead, moving at its observed speedof 6 kt. The values include rainfall for both sides of thegiven annular ring. A total fall of 6.0 in. would be ex-pected to occur during the passage of this inner portionof the storm (i.e., inner 80 n.mi.). Precipitation wouldalso be expected outside this inner area so that thefinal total would probably fall in the range of 8 to 10 in.Since an average hurricane is hormally expected toproduce about 10 in. in passing, this total is not at oddswith the usually accepted averages. Riehl and Malkus [19]calculated some 12 in. of precipitation for the passage ofthe inner 100 n.mi. of hurricane Daisy 1958 (on the 27th)and Miller [14] calculated some 7 .3 in. for the passageof the inner 60 n.mi. of hurricane Helene.

9. BUDGET OF KINETIC ENERGYAn expression for the ra te of change of kinetic energy

in an annular volume may be derived from the horizontalequation of motion

-=- f kXV - v++Fd tby taking the dot product with V, assuming circularV2symmetry and setting K=--, the kinetic energy per2unit mass. ak ak ak- - -= -vr - -~ - -V* V++V* Fat ar a pIf we introduce the equation of continuity in its appro-priate form (%++-)=, 0,

aPand integrate over the mass of air in the annular volume

TABLE.-Kinetic energy budget f o r the mean motion in hurrican_. HildaH U RR C A N EK I N E T I C E N E RG Y BUD1

H IL DA R A D I A L I N T E R V A L 1N.M;)

M E A N A D V E C T I O N

M E A N P R O D U C T I O N

ADVECTION PLUSPRODUCTION

OISSIPATIDN DUE TOSURFACE FRICTIONLEFT OVER FORI N T E R N A L F R I C T I O NR A T I O O F I N T E R N A LFRICTION TO GROUNDOISSIPATION

O C T O B E R i , 4 9 6 4T u n i t s o f io K j . l d a y

0 .08 0 . 2 8 0 . 4 6 0 . 6 5 0.74 D . 8 L 0.91 0 . 48

(between 1000 and 100 mb.), we obtain

n-h-k dM=-2rJH PO (vr,bkb--vrUaku) P- r ( b z - - a z ) ~ ~at 9 ar 9

The first term on the right is the differential horizontaladvection across radii a and b integrated over the verticalimits of the storm. It was evaluated over 100-mbintervals from 1000 to 100 mb. The second term is theproduction of kinetic energy by pressure forces as the airparcels move across the isobars where the bar term isthe mean from radius a to radius b. The third term, whereF is friction, represents loss of kinetic energy due tofrictional effects.

Th e results of these computations are presented in table7 , which shows that mean advection decreased steadilyinward with decreasing radius. (Eddy transport acrossthe 50-n.mi. radius at 900 mb. was slightly more than10 percent of the mean advection and in the same direction, namely inwards.) The production of kinetic energyon the other hand, increased with decreasing radiusreaching its maximum in the innermost annular ringOverall, production contributed less that did advectionto the increase of kinetic energy within the radii studiedhere. This is in contrast to the relative importance ofthese terms as determined by Riehl and Malkus [19and by Miller [14].

The dissipation of kinetic energy due to friction can besubdivided into 1) losses caused by surface or groundfriction and 2) losses resulting from internal friction. The

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[ R e c e i v e d D e c e m b e r 12, 1967; r e v i s e d M a r c h 27, 19681

first may be approximated by the expressionn

which means that any estimate of internal friction mustbe determined through the use of residuals. Although thismethod leaves much to be desired, table 7 indicates that,despite the decreasing ground area of the smaller annularrings, surface frictional losses of kinetic energy increasedas the radius decreased. This is not too surprising whenone considers that the losses are proportional to the cubeof the wind speed, which increases at smaller radii.However, the amounts left over fo r internal friction appearto be inadequate, particularly a t smaller radii, a fact bestreflected in the ratio of internal friction to tha t dissipatedat the ground. It seems unlikely, though not impossible,that this ra te should decrease as the radius decreases, i.e.,as the winds and turbulence increase. In contrast to theinvestigators cited above, who found this ratio to increasewith decreasing radius, we found by experiment that bydoubling the production of kinetic energy in each annulusthe ratio of internal to ground friction is maintained justabout constant. We therefore concluded that while ourbudget may be deficient in certain respects it is probablycorrect to better than just the order of magnitude.

10. SUMMARYThe horizontal and vertical structures of the inner core

of hurricane Hilda were examined in the detail permittedby the flights of Oct. 1 , 1964. Greater vertical resolu-tion and data from higher altitudes have permitted moredetailed analyses and higher vertical coverage thanprevious data collections. Various budgets were prepared,which fo r the first time were drawn exclusively from air-craft data. The budgets compare rather favorably withthose of previous investigators, who used a combinationof conventional and aircraft data, but must be acceptedwith some reservations. Perhaps the major point withregard to the budgets is that they appear to be almost butnot quite definitive. They suggest that fo r a storm offeringbetter radar definition and hence more accurate compos-iting of the data, a similar collection of da ta would permitmore definitive conclusions to be reached.

REFERENCES1 . R. A. Anthes and D. R . Johnson, G eneration of Available

Potential Energy in Hurricane Hilda (1964), M o n t h l yWeather Review, Vol. 96, No. 5, Ma y 1968, pp . 291-302.2. H. R. Byers, General Meteorology, McGraw-Hill. Book Co.,

Inc., New York, 1944, pp . 578-581.3. E. L. Deacon and E. K. Webb, Interchange of Prope rties

Between Sea and Air, T h e S e a , Interscience Publishers,New York, 501. 1, 1962, pp. 43-87.

4. W. M. Gray, Th e Mutu al Variation of Wind, Shear, andBaroclinicity in the Cumulus Convective Atmosphere othe Hurricane, Monthly Weather Rev iew, Vol. 95, No. 2Feb. 1967, pp . 55-73.

5. H. F. Hawkins, Vertical Wind Profiles in Hurricanes,National Hurricane Research Project Report No. 55, U.SWeather Bureau, Washington, D.C., June 1962, 16 pp.

6. H. F. Hawkins and D. T. Rubsam, Hurricane Hilda, 1964I. Genesis, as Revealed by Satellite Photographs, Conventional and Aircraft Data, Monthly Weather Rev iew, Vol

7. L. A. Hughes, On th e Low-Level Wind Struct ure of Tro picaStorms, J o u r n a l of Meteorology, Vol. 9, No. 6, Dec. 1952

8. C. L. Jordan, Mean Soundings for the West Indies Area,J o u r n a l of Meteorology, Vol. 15, No. 1, Feb. 1968, pp . 91-979. E. S. Jordan, An Observational Study of the Upper Wind

Circulation Around Tropical Storms, J o u r n a l of Meteorology10. P. Koteswaram, On the Structure of Hurricanes in the Uppe

Troposphere and Lower Stratosphere, M o n t h l y W e a t h eReview, Vol. 95, No. 8, Aug. 1967, pp . 541-564.11. P. M. Kuhn and D. R. Johnson, Improved Radiometersond

Observations of Atmospheric Infrared Irradian ce, J o u r n aof Geophysical Research, Vol. 71, No. 2, Jan. 1966, pp. 367-37312. N. E. LaSeur and H. F. Hawkins, An Analysis of Hurrican

Cleo (1958) Based on D at a From Reasearch ReconnaissancAircraft, Monthly Weather Rev iew, Vol. 91, No. 10-120ct.-Dec. 1963, pp . 694-709.

13. D. F. Leipper, Observed Ocean Conditions and HurricanHilda, 1964, J o u r n a l of the Atmospheric Sciences, Vol. 24No. 2, Mar. 1967, pp. 182-196.

14. B. I. Miller, On the Momentum and Energy Balance oHurricane Helene (1958), Nat ional Hurr icane ResearcProject Report No. 53, U.S. Weather Bureau, WashingtonD.C., Apr. 1962, 19 pp .

15. B. I. Miller, A Study of the Filling of Hurricane Donn(1960) Over Land, Monthly Weather Rev iew, Vol. 92, No. 9Sept. 1964, pp . 389-406.

16. B. I. Miller, Energy Exchanges Between the Atmosphere andthe Oceans, American Soc ie ty for Oceanography Publ icat ioN o . 1, Hurr icane Sympos ium, October 10-11, 1966, HoustonT e x a s , pp. 134-157.

17. J. J. OBrien and R. 0. Reid, The Non-Linear Responsof a Two Layer, Baroclinic Ocean to a Stationary, AxiallSymmetric Hurricane: Part I. Upwelling Induced by Momentum Transfer, J o u r n a l of the Atmospher ic Sc iencesVol. 24, No. 2, Mar. 1967, pp. 197-207.

18. E. H. Palmen and H. Riehl, Budget of Angular Momentumand Energy in Tropical Cyclones, J o u r n a l of MeteorologyVol. 14, No. 2, Apr. 1957, pp . 150-159.

19. H . Riehl and J. Malkus, Some Aspects of H urricane Daisy1958, Te l l u s , Vol. 13, No. 2, May 1961, pp. 181-213.

20. S. L. Rosenthal, Concerning the Mechanics and Thermodynamics of the Inflow Layer of t he Ma ture Hur ricaneNational Research Project Report No. 47, U.S. WeatheBureau, Washington, D.C., Sept. 1961, 31 pp.

21. J. R. Stear, Sounding in the Eye of Hurri cane Arlene to108,760 Feet, Monthly Weather Rev iew, Vol. 93, No. 6June 1965, pp . 380-382.

96, NO. 7, July 1968, pp. 428-452.

pp. 422-428.

V O ~ ., NO. 5, Oct. 1952, pp . 340-346.

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