HURRICANES - Judith Curryhurricane or typhoon. Once a tropical cyclone has sustainedwindsZ50ms 1...
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HURRICANES F D Marks, Hurricane Research Division, Miami, FL, USA Copyright 2003 Elsevier Science Ltd. All Rights Reserved. Introduction ‘Hurricane’ is the term used in the Western Hemi- sphere for one of the general class of strong tropical cyclones, including western Pacific typhoons and similar systems, that are known simply as cyclones in the Indian and southern Pacific Oceans. A tropical cyclone is a low-pressure system which derives its energy primarily from evaporation from the sea in the presence of 1-minute sustained surface wind speeds 417 m s 1 and the associated condensation in con- vective clouds concentrated near its center. In contrast, midlatitude storms (low-pressure systems with associated fronts) get their energy primarily from the horizontal temperature gradients that exist in the atmosphere. Structurally, the strongest winds in tropical cyclones are near the Earth’s surface (a consequence of being ‘warm-core’ in the tropo- sphere), while the strongest winds in midlatitude storms are near the tropopause (a consequence of being ‘warm-core’ in the stratosphere and ‘cold-core’ in the troposphere). ‘Warm-core’ refers to being warmer than the environment at the same pressure surface. A tropical cyclone with the highest sustained wind speeds between 17 and 32 m s 1 is referred to as a tropical storm, whereas a tropical cyclone with sustained wind speeds Z33 m s 1 is referred to as a hurricane or typhoon. Once a tropical cyclone has sustained winds Z50 m s 1 it is referred to as a major hurricane or super typhoon. In the Atlantic and eastern Pacific Oceans hurricanes are also classified by the damage they can cause using the Saffir–Simpson scale (Table 1). The Saffir–Simpson scale categorizes hurricanes on a scale from 1 to 5, with 1 the weakest and 5 the most intense. Major hurricanes correspond to categories 3 and higher. The reasons that some disturbances intensify to a hurricane, while others do not, are not well understood. Neither is it clear why some tropical cyclones become major hurricanes, while others do not. Major hurricanes produce 80–90% of the United States hurricane-caused damage despite accounting for only one-fifth of all landfalling tropical cyclones. Only two category 5 hurricanes made landfall on the mainland United States (Florida Keys 1935 and Camille 1969). Recent major hurricanes to make landfall on the United States were Hurricanes Bonnie and Georges in 1998, and Bret and Floyd in 1999. As with large-scale extratropical weather systems, the structure and evolution of a tropical cyclone is dominated by the fundamental contradiction that while the airflow within a tropical cyclone represents an approximate balance among forces affecting each air parcel, slight departures from balance are essential for vertical motions and resulting clouds and precip- itation, as well as changes in tropical cyclone intensity. As in extratropical weather systems, the basic vertical balance of forces in a tropical cyclone is hydrostatic except in the eyewall, where convection is superim- posed on the hydrostatic motions. However, unlike in extratropical weather systems, the basic horizontal balance in a tropical cyclone above the boundary layer is between the sum of the Coriolis ‘acceleration’ and the centripetal ‘acceleration’, balanced by the hori- zontal pressure gradient force. This balance is referred to as gradient balance, where the Coriolis ‘accelera- tion’ is defined as the horizontal velocity of an air parcel, v, times the Coriolis parameter, f .(f is the Coriolis parameter (f ¼ 2O sin f), where O is the angular velocity of the Earth (7.292 10 5 s 1 ) and f is latitude. The Coriolis parameter is zero at the equator and 2O at the pole.) Centripetal ‘force’ is defined as the acceleration on a parcel of air moving in a curved path, directed toward the center of curvature of the path, with magnitude v 2 =r, where v is the horizontal velocity of the parcel and r the radius of curvature of the path. The centripetal force alters the original two-force geostrophic balance and creates a nongeostrophic gradient wind. Table 1 Saffir–Simpson scale of hurricane intensity Category Pressure (hPa) Wind (m s 1 ) Storm surge (m) Damage 1 4980 33–42 1.0–1.7 Minimal 2 979–965 43–49 1.8–2.6 Moderate 3 964–945 50–58 2.7–3.8 Extensive 4 944–920 59–69 3.9–5.6 Extreme 5 o920 Z70 Z5.7 Catastrophic 942 HURRICANES
Transcript of HURRICANES - Judith Curryhurricane or typhoon. Once a tropical cyclone has sustainedwindsZ50ms 1...
HURRICANES
F DMarks, Hurricane Research Division, Miami, FL,USA
Copyright 2003 Elsevier Science Ltd. All Rights Reserved.
Introduction
‘Hurricane’ is the term used in the Western Hemi-sphere for one of the general class of strong tropicalcyclones, including western Pacific typhoons andsimilar systems, that are known simply as cyclones inthe Indian and southern Pacific Oceans. A tropicalcyclone is a low-pressure system which derives itsenergy primarily from evaporation from the sea in thepresence of 1-minute sustained surface wind speeds417m s� 1 and the associated condensation in con-vective clouds concentrated near its center. In contrast,midlatitude storms (low-pressure systems withassociated fronts) get their energy primarily fromthe horizontal temperature gradients that exist inthe atmosphere. Structurally, the strongest windsin tropical cyclones are near the Earth’s surface(a consequence of being ‘warm-core’ in the tropo-sphere), while the strongest winds in midlatitudestorms are near the tropopause (a consequence ofbeing ‘warm-core’ in the stratosphere and ‘cold-core’in the troposphere). ‘Warm-core’ refers to beingwarmer than the environment at the same pressuresurface.
A tropical cyclone with the highest sustained windspeeds between 17 and 32m s�1 is referred to as atropical storm, whereas a tropical cyclone withsustained wind speeds Z33m s� 1 is referred to as ahurricane or typhoon. Once a tropical cyclone hassustained windsZ50m s�1 it is referred to as a majorhurricane or super typhoon. In the Atlantic andeastern Pacific Oceans hurricanes are also classifiedby the damage they can cause using the Saffir–Simpsonscale (Table 1).
The Saffir–Simpson scale categorizes hurricanes ona scale from 1 to 5, with 1 the weakest and 5 the mostintense. Major hurricanes correspond to categories 3and higher. The reasons that some disturbances
intensify to a hurricane, while others do not, are notwell understood. Neither is it clear why some tropicalcyclones become major hurricanes, while others donot. Major hurricanes produce 80–90% of the UnitedStates hurricane-caused damage despite accountingfor only one-fifth of all landfalling tropical cyclones.Only two category 5 hurricanes made landfall on themainland United States (Florida Keys 1935 andCamille 1969). Recent major hurricanes to makelandfall on the United States were Hurricanes Bonnieand Georges in 1998, and Bret and Floyd in 1999.
As with large-scale extratropical weather systems,the structure and evolution of a tropical cyclone isdominated by the fundamental contradiction thatwhile the airflow within a tropical cyclone representsan approximate balance among forces affecting eachair parcel, slight departures from balance are essentialfor vertical motions and resulting clouds and precip-itation, as well as changes in tropical cyclone intensity.As in extratropical weather systems, the basic verticalbalance of forces in a tropical cyclone is hydrostaticexcept in the eyewall, where convection is superim-posed on the hydrostatic motions. However, unlike inextratropical weather systems, the basic horizontalbalance in a tropical cyclone above the boundary layeris between the sum of the Coriolis ‘acceleration’ andthe centripetal ‘acceleration’, balanced by the hori-zontal pressure gradient force. This balance is referredto as gradient balance, where the Coriolis ‘accelera-tion’ is defined as the horizontal velocity of an airparcel, v, times the Coriolis parameter, f . (f is theCoriolis parameter (f ¼ 2O sinf), where O is theangular velocity of the Earth (7.292� 10� 5 s� 1) andf is latitude. The Coriolis parameter is zero at theequator and 2O at the pole.) Centripetal ‘force’ isdefined as the acceleration on a parcel of air moving ina curved path, directed toward the center of curvatureof the path, with magnitude v2=r, where v is thehorizontal velocity of the parcel and r the radius ofcurvature of the path. The centripetal force alters theoriginal two-force geostrophic balance and creates anongeostrophic gradient wind.
Table 1 Saffir–Simpson scale of hurricane intensity
Category Pressure (hPa) Wind (ms� 1) Storm surge (m) Damage
1 4980 33–42 1.0–1.7 Minimal
2 979–965 43–49 1.8–2.6 Moderate
3 964–945 50–58 2.7–3.8 Extensive
4 944–920 59–69 3.9–5.6 Extreme
5 o920 Z70 Z5.7 Catastrophic
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The inner region of the tropical storm, termed thecyclone ‘core’, contains the spiral bands of precipita-tion, the eyewall, and the eye that characterize tropicalcyclones in radar and satellite imagery (Figure 1). Theprimary circulation – the tangential or swirling wind –in the core becomes strongly axisymmetric as thecyclone matures. The strong winds in the core, whichoccupies only 1–4% of the cyclone’s area, threatenhuman activities and make the cyclone’s dynamicsunique. In the core, the local Rossby number is always41 and may be as high as 100. The Rossby numberindicates the relative magnitude of centrifugal (v=r)and Coriolis (f ) accelerations, Ro ¼ V=fr, where V is
the axial wind velocity, f the Coriolis parameter, and rthe radius from the storm center. An approximatebreakdown of regimes is: Roo1, geostrophic flow;Ro > 1, gradient flow; and Ro > 50, cyclostrophicflow. When the Rossby number significantly exceedsunity, the balance in the core becomes more cyclo-strophic, where the pressure gradient force is almostcompletely balanced by the centrifugal ‘force’. Thetime scales are such that air swirling around the centercompletes an orbit in much less than a pendulum day(defined as 1=f ).
When the atmosphere is in approximate horizontaland vertical balance, the wind and mass fields are
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Figure 1 NOAA-14 AVHRRmultispectral false color image of Hurricane Floyd at 2041 UTC, 13 September 1999 about 800 km east of
southern Florida. (Photo courtesy of NOAA Operationally Significant Event Imagery website: http://www.osei.noaa.gov/.)
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tightly interconnected. The distribution of a singlemass or momentum variable may be used as a startingpoint to infer the distribution of all other suchvariables. One such variable is potential vorticity(PV), approximately equal to the vorticity timesthe thermal stratification, which is related to thethree-dimensional mass and momentum fieldsthrough an inverse second-order Laplacian-like oper-ator. The benefit of such a relationship is that PVvariations in a single location are diagnosticallyrelated to variations in mass and wind fields at adistance. Areas of high PV correspond locally to lowmass, or cyclones, while areas of lowPV correspond toanticyclones.
Typical extratropical weather systems containhigh PV values around 0.5� 10� 6m 2 s� 1K kg�1
(0.5 PVU) to 5 PVU, whereas typical values in thetropical cyclone core areZ10PVU.Figure 2 shows thewind and mass fields associated with an idealizedaxially symmetric tropical cyclone PV anomaly withthe PV concentrated near the surface rather than in avertical column. The cyclonic anomaly (positive in theNorthern Hemisphere) is associated with a cycloniccirculation that is strongest at the level of the PVanomaly near the surface, and decreases upward.Temperatures are anomalously warm above the PVanomaly (isentropic surfaces are deflected down-
ward). While consistent with the simple PV distribu-tion, the wind and mass fields are also in horizontaland vertical balance. The tropical cyclone being awarm-core vortex, the PV inversion dictates that thewinds that swirl about the center decrease withincreasing height, but they typically fill the depth ofthe troposphere. If the PV reaches values Z10 PVU,the inner region winds can become intense, as inHurricane Gloria (Figure 3). Gloria had PV valuesexceeding 500 PVU just inside the radius of maximumwinds of 15 km where the axisymmetric mean tan-gential winds exceeded 65m s�1.
Many features in the core, however, persist withlittle change for (pendulum) days (mean life span of atropical cyclone is about 5–10 days). Because theselong lifetimes represent tens or hundreds of orbitalperiods (B1h), the flow is nearly balanced.Moreover,at winds 435m s� 1, the local Rossby radius ofdeformation is reduced from its normal B103 km toa value comparable with the eye radius. The Rossbyradius of deformation is the ratio of the speed of therelevant gravity wave mode and the local vorticity, or,equivalently, the ratios of the Brunt–Vaisala andinertial frequencies. This scale indicates the amountof energy that goes into gravity waves compared withinertial acceleration of the wind. In very intensetropical cyclones, the eye radius may approach the
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Figure 2 v (gradient wind) ðms�1Þ and y0 (perturbation potential temperature) (K, top panel); and h 0 (geopotential height perturbation)(dm)and z=f (bottompanel) for awarmcore, lower cyclone. The tropopause location is denotedby the bold solid line, and the label 0 on the
horizontal axis indicates the core (and axis of symmetry) of the disturbance. The equivalent pressure deviation at the surface in the center
of the vortex is �31 hPa. (Reproduced with permission from Thorpe AJ (1986) Synoptic scale disturbances with circular symmetry.
Monthly Weather Review 114: 1384–1389; r American Meteorological Society.)
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depth of the troposphere (15 km), making the aspectratio unity. Thus, the dynamics near the center of atropical cyclone are so exotic that conditions in thecore differ from the Earth’s day-to-day weather asmuch as the atmosphere of another planet does.
Climatology
There are 80–90 tropical cyclones worldwide per year,with the Northern Hemisphere having more tropicalcyclones than the Southern Hemisphere. Table 2shows that of the 80–90 tropical cyclones, 45–50reach hurricane or typhoon strength and 20 reachmajor hurricane or super typhoon strength. Thewestern North Pacific (27 tropical cyclones), easternNorth Pacific (17 tropical cyclones), south-west Indi-an Ocean (10 tropical cyclones), Australia/south-westPacific (10 tropical cyclones), and North Atlantic (10tropical cyclones) are the major tropical cycloneregions. There are also regional differences in thetropical cyclone activity bymonthwith themajority ofthe activity in the summer season for each basin.Hence, in the Pacific, Atlantic, and North Indian
Ocean the maximum numbers of tropical cyclonesoccur in August through October, while in the SouthPacific and Australia regions the maxima are inFebruary and March. In the South Indian Ocean, thepeak activity occurs in June. In the western NorthPacific, BayofBengal, and South IndianOcean regionstropical cyclones may occur in any month, while theother regions at least one tropical cyclone-free monthoccurs per year. For example, in the North Atlantic,there has never been tropical cyclone activity inJanuary.
Some general conclusions can be drawn from theglobal distribution of tropical cyclone locations(Figure 4A). Tropical cyclone formation is confinedto a region approximately 301N and 301 S, with87% of them located within 201 of the Equator. Thereis a lack of tropical cyclones near the Equator, as wellas in the eastern South Pacific and South Atlanticbasins. From these observations there appear to be atleast five necessary conditions for tropical cyclonedevelopment.
� Warm sea surface temperature (SST) and largemixed-layer depth (i.e., the thickness of the mixed
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Figure 3 Radial-height cross-section of symmetric potential vorticity for Hurricane Gloria, 24 September 1985. Contours are 0.1PVU.
Values in the data-sparse region, within 13 km of vortex center, are not displayed. (Reproduced with permission from Shapiro LJ and
Franklin JL (1995)Potential vorticity inHurricaneGloria.MonthlyWeatherReview123: 1465–1475;rAmericanMeteorological Society.)
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layer, defined as the depth of the sharp temperatureinversion (also referred to as the thermocline)between the cooler bottom water and the warmernear surface water). Numerous studies suggest aminimum SST criterion of 261C for development.The warm water must also have sufficient depth(i.e., 50m). Comparison of Figures 4A and 4B, theannual mean global SST, shows the strong correla-tion between regions where the SST is 4261C andannual tropical cyclone activity. An SSTof4261C issufficient but not necessary for tropical cycloneactivity, as is evidenced by the regions with tropicalcyclone activity when the SST o261C. Some of thediscrepancy exists because storms that form overregions where the SST is 4261C are advectedpoleward during their life cycle. However, tropicalcyclones are observed to originate over regionswhere the SST o261C. These occurrences are notmany, but the fact that they exist suggests that otherfactors are important.
� Background Earth vorticity. Tropical cyclones donot form within 31 of the Equator. The Coriolisparameter vanishes at the Equator and increases toextremes at the poles. Hence, a threshold value ofEarth vorticity (f ) must exist for a tropical cycloneto form. However, the likelihood of formation doesnot increase with increasing f . Thus, nonzero Earthvorticity is necessary, but not sufficient to producetropical cyclones.
� Low vertical shear of the horizontal wind. In orderfor tropical cyclones to develop, the latent heatgenerated by the convection must be kept near thecenter of the storm. Historically, shear was thoughtto ‘ventilate’ the core of the cyclone by advecting thewarm anomaly away. The ventilation argumentsuggests that if the storm travels at nearly the same
speed as the environmental flow in which it isembedded then its heating remains over the distur-bance center. However, if it is moving slower thanthemeanwind at upper levels then the heating in theupper troposphere is carried away by themean flow.Recent analysis suggests that the effect of shear is toforce the convection into an asymmetric patternsuch that the convective latent heat release forcesflow asymmetry and irregular motion rather thanintensification of the symmetric vortex. Thus, if thevertical shear is too strong (416m s�1) then exist-ing tropical cyclones are ripped apart and new onescannot form.
� Low atmospheric static stability. Static stability isthe ability of a fluid to become turbulent (unstable)or laminar (stable) due to the effects of buoyancyneglecting all other inertial effects of motion. Thetroposphere must be potentially unstable to sustainconvection for an extended period. Typically meas-ured as the difference between the equivalent po-tential temperature, ye, at the surface and 500 hPa,instability must typically be 410K for convectionto occur. This value is usually satisfied over tropicaloceans.
� Tropospheric humidity. The higher the midlevelhumidity, the longer a parcel of air can remainsaturated as it entrains the surrounding air during itsascent. Vigorous convection occurs if the parcelremains saturated throughout its ascent. A relativehumidity of 50–60% at lower to midlevels(700–500 hPa) is often sufficient to keep a parcelsaturated during ascent. This condition is regularlyevident over tropical oceans.
These conditions are usually satisfied in the summerand fall seasons for each tropical cyclone basin.
Table 2 Mean annual frequency, standard deviation (s) and percentage of global total of the number of tropical storms (winds
Z17ms� 1), hurricane-force tropical cyclone (windsZ33ms�1), and major hurricane-force tropical cyclone (windsZ50ms� 1). Dates
in parentheses provide the nominal years for which accurate records are currently available
Tropical cyclone basin Tropical storm
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% of
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Hurricane annual
frequency (s)% of
total
Major hurricane
annual
frequency (s)
% of total
Atlantic (1944–00) 9.8 (3.0) 11.4 5.7 (2.2) 12.1 2.2 (1.5) 10.9
NE Pacific (1970–00) 17.0 (4.4) 19.7 9.8 (3.1) 20.7 4.6 (2.5) 22.9
NW Pacific (1970–00) 26.9 (4.1) 32.1 16.8 (3.6) 35.5 8.3 (3.2) 41.3
N Indian (1970–00) 5.4 (2.2) 6.3 2.2 (1.8) 4.6 0.3 (0.5) 1.5
SW Indian (30–1001E)(1969–00)
10.3 (2.9) 12.0 4.9 (2.4) 10.4 1.8 (1.9) 9.0
Australian/SE Indian
(100–1421E) (1969–00)6.5 (2.6) 7.5 3.3 (1.9) 7.0 1.2 (1.4) 6.0
Australian/SW Pacific
(1421E) (1969–00)10.2 (3.1) 11.8 4.6 (2.4) 9.7 1.7 (1.9) 8.5
Global (1970–00) 86.1 (8.0) 47.3 (6.5) 20.1 (5.7)
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However, even when all of the above conditions arefavorable, tropical cyclones don’t necessarily form. Infact, there is growing evidence for significant inter-annual variability in tropical cyclone activity, wherenumerous tropical cyclones form in a given basin overaweek to 10 days, followed by 2–3weekswith little orno tropical cyclone activity. Figure 5 shows just suchanactive period in theAtlantic basin inmid-September1999, where two hurricanes (Floyd and Gert), bothmajor, and an unnamed tropical depression formedwithin a few days of each other. During these activephases almost every disturbance makes at least trop-
ical storm strength, whereas in the inactive phasepractically none of the disturbances intensify. The twohurricanes and unnamed depression in Figure 5represented the second 10-day active period duringthe summer of 1999. An earlier period in mid-Augustalso resulted in the development of three hurricanes(Brett, Cindy, and Dennis), two of which were major,aswell as a tropical storm (Emily). There is speculationthat the variability is related to the propagation of aglobal wave. Because the SST, static stability, andEarth vorticity don’t vary thatmuch during the season,the interannual variability is most likely related
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Figure 4 (A) Frequency of tropical cyclones per 100 years within 140 km of any point. Solid triangles indicate maxima, with values
shown. Period of record is shown in boxes for each basin. (B) Annual sea surface temperature distribution (1C).
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to variations in tropospheric relative humidity andvertical wind shear.
It has long been recognized that the number oftropical cyclones in a given region varies from year toyear. The exact causes of this remain largely specula-tive. The large-scale global variations in atmosphericphenomena such as the El Nino Southern Oscillation(ENSO) and the Quasi-Biennial Oscillation (QBO)appear to be related to annual changes in the frequencyof tropical cyclone formation, particularly in theAtlantic Ocean. The ENSO phenomenon is charac-terized by warmer SSTs in the eastern South Pacificand anomalous winds over much of the equatorialPacific. It influences tropical cyclone formation in thewestern North Pacific, South Pacific, and even theNorth Atlantic.
During the peak phase of the ENSO, often referredto as El Nino (which usually occurs during themonthsJuly–October), anomalous westerly winds near theEquator extend to the dateline in the western NorthPacific acting to enhance the intertropical convergencezone (ITCZ) in this area, making it more favorable for
formation of tropical cyclones. Another effect ofthe El Nino circulation is warmer SST in the easternSouth Pacific. During such years, tropical cyclonesform closer to the Equator and farther east. Regionssuch as French Polynesia, which are typicallyunfavorable for tropical cyclones owing to a strongupper-level trough, experience numerous tropicalcyclones. The eastern North Pacific is also affectedby the El Nino through a displacement of the ITCZsouth to near 51N. Additionally, the warm oceananomaly of El Nino extends to near 201N, whichenhances the possibility of tropical cyclone formation.The result is an average increase of two tropicalcyclones during El Nino years. Cyclones also developcloser to the Equator and farther west than during anormal year.
The QBO is a roughly 2-year oscillation of theequatorial stratosphere (30–50 hPa) winds from east-erly towesterly and back. The phase andmagnitude ofQBO are associated with the frequency of tropicalcyclones in the Atlantic. Hurricane activity is morefrequent when the 30-hPa stratospheric winds are
Figure 5 GOES multispectral false color image of Hurricanes Floyd and Gert and an unnamed tropical depression at 1935 UTC, 13
September 1999. (Photo courtesy of NOAA Operationally Significant Event Imagery website: http://www.osei.noaa.gov/.)
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westerly. The exact mechanism by which the QBOaffects tropical cyclones in the troposphere is not clear;however, there are more North Atlantic tropicalcyclones when the QBO is in the westerly phase thanwhen it is in the easterly.
Tropical Cyclogenesis
Enthalpy is a thermodynamic state function definedfor an ideal gas as the temperature times the specificheat at constant pressure plus a constant. For a systemlike the atmosphere which consists of a mixture ofcomponents the total enthalpy is the mass-weightedsum of the enthalpies of each component. Thus, thetotal enthalpy for a system consisting of a mixture ofdry air, water vapor, and liquid water is defined as aconstant plus the temperature times the sum of thespecific heats at constant pressure for each componenttimes the masses of each component, respectively. Inan adiabatic, reversible process, the total enthalpy isconserved, although the component enthalpies maynot be due to the exchange of enthalpy betweencomponents in phase changes. Most of the energyneeded for tropical cyclones to form and maintainthemselves is realized through the difference in en-thalpy between the warm near-surface waters of thetropical ocean and the tropospheric column. Theprocess of bringing the late-summer tropical tropo-sphere into thermodynamic equilibrium with the seasurface at 28–301C, mainly through the irreversibleenergy transfer from the ocean to the air by evapora-tion, can produce hydrostatic pressures as low as theminimum sea-level pressures of the most intensetropical cyclones. Thus, much of the tropical oceanscontain enough moist enthalpy to support a majorhurricane.
Throughout most of the Trade Wind regions,gradual subsidence causes an inversion that trapswater vapor in the lowest kilometer. Sporadic convec-tion (often in squall lines) that breaks through theinversion exhausts the moist enthalpy stored in thenear-surface boundary layer quickly, leaving awake ofcool, relatively dry air. This air comes from just abovethe inversion and is brought to the surface by down-drafts driven by the weight of hydrometeors andcooling due to their evaporation. If the squall line doesnot keepmoving it quickly runs out of energy.Aday, oreven several days, may pass before normal fair-weather evaporation can restore the preexistent moistenthalpy behind the squall. The reasons why squallline convection generally fails to produce hurricaneslie in the limited amount of enthalpy that can be storedin the sub-inversion layer and the slow rate ofevaporation under normal wind speeds in the trades.
For a tropical cyclone to occur, evaporation mustspeed up and the equilibrium enthalpy at the seasurface temperature must rise through a lowering ofthe surface pressure. Tropical cyclones are thus finite-amplitude phenomena. They do not grow by somelinear process from infinitesimal amplitude. Thenormal paradigm of searching for the most rapidlygrowing unstable linear mode used to study midlati-tude cyclogenesis through baroclinic instability failshere. The surfacewind has to exceed roughly 20m s� 1
before evaporation can prevail against downdraftcooling.
How then do tropical cyclones reach the requiredfinite amplitude? The answer seems to lie in thestructure of tropical convection. As explained previ-ously, behind a squall line the lower troposphere(below the 01C isotherm at B5 km) is dominated byprecipitation-driven downdrafts which lie under the‘anvil’ of nimbostratus and cirrostratus that spreadsbehind the active convection. Above 5 km, a combi-nation of differential radiative fluxes at the top andbottom of the anvil and residual condensationalheating from the main updraft maintains weak risingmotion. This updrafts-over-downdrafts arrangementrequires horizontal convergence centered near 5 kmaltitude to maintain mass continuity. The importantkinematic consequence is formation of patchy shallowvortices near the altitude of the 01C isotherm. Thetypical horizontal scales of these ‘mesovortices’ aretens to hundreds of kilometers. If they were at thesurface or if their influence could be extended down-ward to the surface then they would be the means toget the system to the required finite amplitude.
The foregoing reasoning defines the importantunanswered questions: (1) how do the midlevelmesovortices extend their influence to the surface,and (2) what are the detailed thermodynamics at theair–sea interface during this process? Leading hypoth-eses for (1) are related to processes that can increasethe surface vorticity through changes in static stabilityand momentum mixing, both horizontally and verti-cally. However, the answers to these questions awaitnew measurements that are just becoming availablethrough improved observational tools.
Basic Structure
Primary and Secondary Circulations
Inner core dynamics have received a lot of attentionover the last 40 years through aircraft observations ofthe inner core structure. These observations show thatthe tropical cyclone inner core dynamics are dominat-ed by interactions between ‘primary’ (horizontalaxisymmetric), ‘secondary’ (radial and vertical)
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circulations, and a wavenumber one asymmetrycaused by the storm motion. The primary circulationis so strong in the cyclone core that it is possible toconsider axisymmetric motions separately, if accountis taken of forcing by the asymmetric motions. Theprimary circulation is in near-gradient balance, andevolves when heat and angular momentum sources(often due to asymmetric motions) force secondarycirculations, which in turn redistribute heat andangular momentum.
Figure 6 shows that the primary circulation issustained by the secondary circulation that consists offrictional inflow that loses angular momentum to thesea as it gains moist enthalpy. (Angular momentumM ¼ Vrþ fr2=2, where V is the tangential windvelocity, f the Coriolis parameter, and r the radiusfrom the storm center.) The inflow picks up latent heatthrough evaporation, and exchanges sensible heatwith the underlying ocean, as it spirals into lowerlevels of the storm under influence of friction. Theevaporationof sea spray addsmoisture to the air,whileat the same time cooling it. This process is important indetermining the intensity of a tropical cyclone. Nearthe vortex center, the inflow turns upward and bringsthe latent heat it acquires in the boundary layer intothe free atmosphere. Across the top of the boundarylayer, turbulent eddies cause significant downwardflux of sensible heat from the free atmosphere to theboundary layer. The energy source for the turbulenteddies is mechanical mixing caused by the strongwinds. The eddies are also responsible for downwardmixing of angular momentum. Hence, these turbulenteddy fluxes fuel the storm.
As the air converges towards the eye and is lifted inconvective clouds that surround the clear eye, itascends to the tropopause (the top of troposphere,where temperature stops decreasing with height). Asshown in Figure 6, the convective updrafts in theeyewall turn the latent heat into sensible heat throughthe latent heat of condensation to provide the buoy-ancy needed to loft air from the surface to tropopauselevel. The updraft entrains midlevel air, promotingmass and angular momentum convergence into thecore. It is the midlevel inflow that supplies the excessangular momentum needed to spin up the vortex. Thethermodynamics of a storm can be modeled as anidealized heat engine, running between a warm heatreservoir, the sea, at around 300K, and a coldreservoir, 15–18 km up in the tropical troposphere,at about 200K. The net energy realized in the wholeprocess is proportional to the difference in tempera-ture between the ocean and the upper troposphere.Storm-induced upwelling of cooler water reducesocean SST by a few degrees, which has a considerableeffect on the storm’s intensity.
As shown in Figure 7, the secondary circulation alsocontrols the distribution of hydrometeors and radarreflectivity. It is much weaker than the primarycirculation except in the anticyclonic outflow, wherethe vortex is also much more asymmetric. Precipita-tion-driven convective updrafts form as hydrometeorsfall from the outward sloping updraft. Condensationin the anvil causes a mesoscale updraft above the 01Cisotherm and precipitation loading by snow fallingfrom the overhanging anvil causes a mesoscale down-draft below 01C isotherm. The melting level itself
Sat
urat
edad
iabatic
expansion
Figure6 Schematic of the secondary circulation thermodynamics. (Reproducedwith permission fromWilloughbyHE (1999)Hurricane
heat engines. Nature 401: 649–650; rMacmillan Magazines Ltd.)
950 HURRICANES
marks the height of maximum mass convergence.Inside the eye, dynamically driven descent and mo-mentum mixing leads to substantial pressure falls.
In order for the primary circulation to intensify, theflow cannot be in exact balance. Vertical gradients ofangular momentum due to vertical shears of the
primary circulation cause updrafts to pass through theconvective heat sources, because the path of leastresistance for the warmed air lies along constantangular momentum surfaces. Similarly, horizontaltemperature gradients due to vertical shears causethe horizontal flow to pass through momentumsources, because the path of least resistance lies alongisentropes (potential temperature or y surfaces).Although the flow lies generally along the angularmomentum or isentropic surfaces, it has a smallcomponent across them. The advection by this com-ponent, not the direct forcing, is the mechanism bywhich the primary circulation evolves.
Some of the most intense tropical cyclones exhibit‘concentric’ eyewalls, i.e., two or more eyewall struc-tures centered at the circulation center of the storm. Inmuch the same way as the inner eyewall forms,convection surrounding the eyewall can becomeorganized into distinct rings. Eventually, the innereye begins to feel the effects of the subsidence resultingfrom the outer eyewall, and the inner eyewall weak-ens, to be replaced by the outer eyewall. The pressurerises due to the destruction of the inner eyewall areusually more rapid than the pressure falls, due to theintensification of the outer eyewall, and the cycloneitself weakens for a short period of time. Thismechanism, referred to as the eyewall replacementcycle, often accompanies dramatic changes in stormintensity. The intensity changes are often associatedwith the development of secondary wind maximaoutside the storm core.
A good example of contracting rings of convectioneffecting the intensification of a hurricane is shown inFigure 8 for Hurricane Gilbert on 14 September 1988.Two convective rings, denoted by intense radarreflectivity, are evident in Figure 8A. The outer ringis located near 80–90 km radius and the inner one at10–12 km radius. Figure 8B shows that both areassociated with maxima in tangential wind andvorticity. Figure 9 shows that in the ensuing 12–24 hthe storm filled dramatically. However, it is not clearhow much of the filling was caused by the stormmoving over land and how much by the contractingouter ring and decaying inner ring of convectiveactivity.
A process has been proposedwhereby: (1) nonlinearbalanced adjustment of the vortex to eddy heat andangular momentum sources generated by some envi-ronmental interaction in the storm’s periphery pro-duces an enhanced secondary circulation; (2) asecondary wind maximum develops in response; and(3) the wind maximum contracts as a result ofdifferential adiabatic warming associated with theconvective diabatic heating in the presence of a inwardradial gradient of inertial stability. Under these
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Figure 7 (A) Schematic of the radius–height circulation of the
inner core of Hurricane Alicia (1983). Shading depicts the reflec-
tivity field, with contours of 5, 30, and 35dBZ. The primary
circulation (ms�1) is depicted by dashed lines and the secondary
circulation by the wide hatched streamlines. The convective
downdrafts are denoted by the thick solid arrows, while the
mesoscale up- and downdrafts are shown by the broad arrows. (B)
Schematic plan view of the low-level reflectivity field in the inner
core of Hurricane Alicia superimposed with the middle of the three
hydrometeor trajectories in (A). Reflectivity contours in (b) are 20
and 35dBZ. The storm center and direction are also shown. In (A)
and (B) the hydrometeor trajectories are denoted by dashed and
solid lines labeled 0-1-2-3-4 and 00-10-20. (Reproduced with
permission from Marks FD and Houze RA (1987) Inner core
structure of Hurricane Alicia from airborne Doppler radar observa-
tions. Journal of the Atmospheric Sciences 44: 1296–1317;
rAmerican Meteorological Society.)
HURRICANES 951
circumstances, understanding the intensification ofthe tropical cyclone reduces to determining whatmechanisms can produce an enhanced secondarywindmaximum.
Inner core – eyewall and eye The most recognizablefeature foundwithin a hurricane is the eye (Figure 10).It is found at the center and is typically between20–50 km in diameter. The eye is the focus of thehurricane, the point about which the primary circu-lation rotates and where the lowest surface pressuresare found in the storm. The eye is a roughly circulararea of comparatively light winds and fair weatherfound at the center of strong tropical cyclones.Although the winds are calm at the axis of rotation,strong winds may extend well into the eye. As seen inFigure 10, there is little or no precipitation andsometimes blue sky or stars can be seen. The eye isthe region of warmest temperatures aloft – the eyetemperature may be Z101C warmer at an altitudeof 12 km than the surrounding environment, but only0–21C warmer at the surface.
The eye is surrounded by the eyewall, the roughlycircular area of deep convection associated with theup-branch of the secondary circulation and the highestsurfacewinds. The eye is composed of air that is slowlysinking and the eyewall has a net upward flow becauseofmanymoderate – occasionally strong –updrafts anddowndrafts. The eye’s warm temperatures are due towarming by compression of the subsiding air. Mostsoundings taken within the eye are similar to that forHurricane Hugo in Figure 11. They show a low-levellayer which is relatively moist, with an inversionabove, suggesting that the sinking in the eye typicallydoes not reach the ocean surface, but instead gets onlywithin 1–3 km of the surface. An eye is usually presentonly in hurricane-strength tropical cyclones.
The general mechanisms by which the eye andeyewall are formed are not fully understood, althoughobservations shed some light on the problem. Thecalm eye of the tropical cyclone shares many qualita-tive characteristics with other vortical systems such astornadoes, waterspouts, dust devils, and whirlpools.Given that many of these lack a change of phase ofwater (i.e., no clouds and diabatic heating areinvolved), it may be that the eye feature is a funda-mental component to all rotating fluids. It has beenhypothesized that supergradient wind flow (i.e.,swirling winds generating stronger centrifugal ‘force’than the local pressure gradient can support) presentnear the radius of maximum winds causes air to becentrifuged out of the eye into the eyewall, thusaccounting for the subsidence in the eye. However,others found that the swirling winds within severaltropical cyclones were within 1–4% of gradient
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Figure 8 (A) Composite horizontal radar reflectivity of Hurricane
Gilbert for 0959–1025 UTC, 14 September 1988; the domain is
360 km�360 km,marked every 36 km. The line through the center
is the WP-3D aircraft flight track. (B) Profiles of flight-level angular
velocity (o, solid) tangential wind (short dash), and smoothed
relative vorticity (z, long dash) along the southern leg of the flight
track shown in (A). (Reproduced with permission from Kossin JP,
Schubert WH, and Montgomery MT (2000) Unstable interactions
between a hurricane’s primary eyewall and a secondary ring of
enhancedvorticity. Journal of theAtmospheric Sciences57: 3893–
3917;r American Meteorological Society.)
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Figure 9 Hurricane Gilbert’s minimum sea-level pressure
(MSLP) and radii of the inner and outer eyewalls as a function of
time, September 1988. Solid blocks at bottom indicate times over
land. (Reproduced with permission from Black ML andWilloughby
HE (1999) The concentric eyewall cycle of Hurricane Gilbert.
Monthly Weather Review 120: 947–957; r American Meteoro-
logical Society.)
952 HURRICANES
balance. It may be thought that the amount ofsupergradient flow needed to cause such centrifugingof air is only on the order of a couple of percent andthus difficult to measure.
Another feature of tropical cyclones that probablyplays a role in forming and maintaining the eye is theeyewall convection. As shown in Figure 12, convec-tion in developing tropical cyclones is organized into
Figure 10 Eyewall of Hurricane Georges, 1945 UTC, 19 September 1998. (Photo courtesy of M. Black, NOAA/OAR/AOML Hurricane
Research Division.)
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Figure 11 (A) Skew T lgp diagram of the eye sounding in Hurricane Hugo at 1839 UTC, 15 September 1989, 17.41N, 54.81W.
Isotherms slope upward to the right; dry adiabats slope upward to the left; moist adiabats are nearly vertical curving to the left. Solid and
dashed curves denote temperature and dew point, respectively. The smaller dots denote saturation points computed for the dry air above
the inversion, and the two larger dots temperature observed at the innermost saturated point as the aircraft passed through the eyewall.
(B) ye, water vapor mixing ratio, and saturation pressure difference, P-PSAT, as functions of pressure at 2123 UTC. (Reproduced with
permission from Willoughby HE (1998) Tropical cyclone eye thermodynamics.Monthly Weather Review 126: 3189–3211;r American
Meteorological Society.)
HURRICANES 953
long, narrow rainbands that are oriented in the samedirection as the horizontal wind. Because these bandsseem to spiral into the center of a tropical cyclone, theyare sometimes called spiral bands. The earliest radarobservations of tropical cyclones detected these bands,which are typically 5–50 km wide and 100–300kmlong. Along these bands, low-level convergence is amaximum, and therefore upper-level divergence ismost pronounced. A direct circulation develops inwhich warm, moist air converges at the surface,ascends through these bands, diverges aloft, anddescends on both sides of the bands. Subsidence isdistributed over a wide area outside of the rainband,but is concentrated in the small inside area. As the airsubsides, adiabatic warming takes place, and the airdries. Because subsidence is often concentrated on theinside of the band, the adiabatic warming is strongerinward from the band, causing a sharp contrast in
pressure falls across the band since warm air is lighterthan cold air. Because of the pressure falls on theinside, the tangential winds around the tropicalcyclone increase, owing to an increased pressuregradient. Eventually, the band moves toward thecenter and encircles it and the eye and eyewall form.
The circulation in the eye is comparatively weakand, at least in the mature stage, thermally indirect(warm air descending), so it cannot play a direct role inthe storm energy production. On the other hand, thetemperature in the eye ofmanyhurricanes exceeds thatwhich can be attained by any conceivable moistadiabatic ascent from the sea surface, even accountingfor the additional entropy (positive potential temper-ature, y, anomaly) owing to the low surface pressure inthe eye (the lower the pressure, the higher the y at agiven altitude and temperature). Thus, the observedlow central pressure of the storm is not consistent withthat calculated hydrostatically from the temperaturedistribution createdwhen a sample of air is lifted froma state of saturation at sea surface temperature andpressure. The thermal wind balance restricts theamount of warming that can take place. In essence,the rotation of the eye at each level is imparted by theeyewall, and the pressure drop from the outer to theinner edge of the eye is simply that required by gradientbalance.
Because the eyewall azimuthal velocity decreaseswith height, the radial pressure drop decreases withaltitude, requiring, through the hydrostatic equation,a temperature maximum at the storm center. Thus,given the swirling velocity of the eyewall, the steady-state eye structure is largely determined. The centralpressure, which is estimated by integrating the gradi-ent balance equation inward from the radius ofmaximum winds, depends on the assumed radialprofile of azimuthal wind in the eye.
In contrast, the eyewall is a region of rapid variationof thermodynamic variables. As shown in Figure 13,the transition from the eyewall cloud to the nearlycloud-free eye is often so abrupt that it has beendescribed as a form of atmospheric front. Early studieswere the first to recognize that the flow under theeyewall cloud is inherently frontogenetic. The eyewallis the upward branch of the secondary circulation anda region of rapid ascent that, together with slantwiseconvection, leads to the congruence of angular mo-mentum and moist entropy (ye) surfaces. Hence, thethree-dimensional vorticity vectors lie on ye surfaces,so that the moist PV vanishes. As the air is saturated,this in turn implies, through the invertibility principleapplied to flow in gradient and hydrostatic balance,that the entire primary circulation may be deducedfrom the radial distribution of ye in the boundary layerand the distribution of vorticity at the tropopause.
North
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Figure 12 (A) Schematic of the rainband in radius–height
coordinates. Reflectivity, ye, mesoscale (arrows), and convective
scalemotionsare shown. (B)Plan view.Aircraft track, reflectivities,
cells, stratiform precipitation, 150m flow, and ye values are shown
(Reproduced with permission from Barnes GM, Zipser EJ,
Jorgensen DP, and Marks FD (1983) Mesoscale and convective
structure of a hurricane rainband. Journal of the Atmospheric
Sciences 40: 2125–2137; r American Meteorological Society.)
954 HURRICANES
In the classic semigeostrophic theory of deforma-tion-induced frontogenesis, the background geo-strophic deformation flow provides the advection oftemperature across surfaces of absolute momentumthat drives the frontogenesis, whereas in the hurricaneeyewall, surface friction provides the radial advectionof entropy across angular momentum surfaces. Alsonote that the hurricane eyewall is not necessarily afront in surface temperature, but instead involves theye distribution, which is related directly to density insaturated air.
There is likely a two-stage process in eye formation.The amplification of the primary circulation is strong-ly frontogenetic and results, in a comparatively shorttime, in frontal collapse at the inner edge of theeyewall. (Frontal collapse is an increase in thehorizontal gradient of an airmass property, principallydensity, and the development of the accompanyingfeatures of the wind field through the secondarycirculation that typify a front.) The frontal collapseleads to a dramatic transition in the storm dynamics.While the tropical cyclone inner core is dominated byaxisymmetric motions, hydrodynamic instabilities arepotential sources of asymmetric motions within thecore. In intense tropical cyclones the wind profileinside the eye is often U-shaped, in the sense that thewind increases outwards more rapidly than linearlywith radius (Figure 13). The strong cyclonic shear justinside the eyewall may result in a local maximum ofabsolute vorticity or angular momentum, so that theprofile may actually become barotropically unstable.(This refers to the hydrodynamic instability arisingfrom certain distributions of vorticity in a two-dimensional nondivergent flow. It is an inertial insta-bility in that kinetic energy is the only form of energytransferred between the current and perturbation. Awell-known necessary condition for barotropic insta-
bility is that the basic state vorticity gradientmust haveboth signs in the domain of interest.) This instabilityleads to frontal collapse as a result of radial diffusionof momentum into the eye, and also may explain the‘polygonal eyewalls’ where the eyewall appear onradar to be made up of a series of line segments ratherthan as a circle. It may also explain intense mesoscalevortices observed in the eyewalls of Hurricanes Hugoof 1989 and Andrew of 1992.
Once the radial turbulent diffusion of momentumdriven by the instability of the primary circulationbecomes important, it results in a mechanicallyinduced, thermally indirect (warm air sinking) com-ponent of the secondary circulation in the eye andeyewall. Such a circulation raises the vertically aver-aged temperature of the eye beyond its value in theeyewall and allows for an amplification of the entropydistribution. Feedbacks with the surface fluxes thenallow the boundary layer entropy to increase andresult in a more rapid intensification of the swirlingwind. Thus, the frontal collapse of the eyewall is anessential process in the evolution of tropical cyclones.Without it, amplification of the temperature distribu-tion relies on external influences, and intensification ofthe wind field is slow. Once it has taken place, themechanical spinup of the eye allows the temperaturedistribution to amplify without external influencesand, through positive feedback with surface fluxes,allows the entropy field to amplify and the swirlingvelocity to increase somewhat more rapidly.
Outer structure and rainbands The axisymmetriccore is characteristically surrounded by a less sym-metric outer vortex that diminishes into the synoptic‘environment’. In the lower troposphere, the cycloniccirculation may extend more than 1000 km from thecenter. As evident in Figure 14 the boundary between
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Figure 13 Time series plots of tangential wind (Vy), radial wind (Vr), vertical velocity (w ), and ye in Hurricane Hugo at 1721–1730UTC,
15September 1989. The aircraft flight trackwas at 450m. Thick dashed vertical lines denote thewidth of the eyewall reflectivitymaximum
at low levels.
HURRICANES 955
cyclonic and anticyclonic circulation slopes inwardwith increasing height, so that the circulation in theupper troposphere is primarily anticyclonic, exceptnear the core. In the outer vortex, there are no scaleseparations between the primary and the secondarycirculations, the asymmetric motions, or the vortextranslation, as they are roughly all of the samemagnitude. The asymmetric flows in this regioncontrol the vortex motion and sustain an eddyconvergence of angular momentum and moisturetoward the center. Interactions between the symmetricmotions of the inner core with the more asymmetricmotions in the outer portion of the storm are the key toimproved forecasts of tropical cyclone track andintensity.
Spiral bands of precipitation characterize radar andsatellite images in this region of the storm (Figures 1and 15). As seen in Figures 8, 12 and 15, radarreflectivity patterns in tropical cyclones provide agood means for flow visualization, although theyrepresent precipitation, not winds. Descending mo-tion occupies precipitation-free areas, such as the eye.The axis of the cyclone’s rotation lies near the center ofthe eye. The eyewall surrounds the eye. In intensehurricanes, it may contain reflectivities as high as50 dBZ equivalent to rainfall rates of 74mmh� 1.(1 dBz 10 lg Z, where Z is equivalent radar reflecti-vity factor (mm 6m�3).) Less extreme reflectivities,40 dBZ (13mmh� 1), characterize most convective
rainfall in the eyewall and spiral bands. The verticalvelocities (bothupanddowndrafts) in convectionwithhighest reflectivity may reach 25m s� 1, but typicalvertical velocities areo5m s�1. Such intense convec-tion occupies less than 10% of the tropical cyclone’sarea.Outside convection, reflectivities are still weaker,30 dBZ, equivalent to a 2.4mmh� 1 rain rate. This‘stratiform rain’, denoted by a distinct reflectivitymaximum or ‘bright band’ at the altitude of the 01Cisotherm, falls out of the anvil cloud that grows fromthe convection. The spiral bands tend to lie along thefriction-layer wind that spirals inward toward theeyewall (Figure 12).
Many aspects of rainband formation, dynamics,and interaction with the symmetric vortex are stillunresolved. The trailing spiral shape of bands andlanes arises because the angular velocity of the vortexincreases inward and deforms them into equiangularspirals. In the vortex core, air remains in the circula-tion for many orbits of the center, while outside thecore, the air passes through the circulation in less thanthe time required for a single orbit. As the tropicalcyclone becomes more intense, the inward ends of thebands approach the center less steeply approximatingarcs of circles. Some bands appear to move outward,while others maintain a fixed location relative to thetranslating center.
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Figure 14 Vertical cross-section of the azimuthal mean tangen-
tial wind for Hurricane Gloria on 24 September 1985. Anticyclonic
contours are dashed. (Reproduced with permission from Franklin
JL, Lord SJ, Feuer SE, and Marks FD (1993) The kinematic
structure of Hurricane Gloria (1985) determined from nested
analyses of dropwindsonde and Doppler radar data. Monthly
Weather Review 121: 2433–2451; r American Meteorological
Society.)
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Figure 15 Schematic representation of the stationary band
complex, the entities that compose it, and the flow in which it is
embedded. (Reproduced with permission from Willoughby HE,
Marks FD, and Feinberg RJ (1984) Stationary and moving
convective bands in hurricanes. Journal of the Atmospheric
Sciences 41: 3189–3211;r American Meteorological Society.)
956 HURRICANES
As shown inFigure 15,motionof the vortex throughits surroundingsmay cause one stationary band, calledthe principal band, to lay along a convergent stream-line asymptote that spirals into the core. A tropicalcyclone advected by midlevel steering with westerlyshear moves eastward through surrounding air at lowlevels. Thus, the principal band may be like a bowwave, caused by the displacement of the environmen-tal air on the eastern side of the vortex. Its predom-inant azimuthal wavenumber is one.
Moving bands, and other convective features, arefrequently associated with cycloidal motion of thetropical cyclone center, and intense asymmetric out-bursts of convection are observed to displace thetropical cyclone center by tens of kilometers. Thebands observed by radar are often considered mani-festations of internal gravity waves, but these wavescan exist only in a band of Doppler-shifted frequenciesbetween the local inertia frequency (defined as the sumof the vertical component of the earth’s inertialfrequency, f , and the local angular velocity of thecirculation, V=r) and the Brunt–Vaisala frequency(i.e., the natural gravity wave frequency, the squareroot of the static stability defined as ðg=yÞ qy=qz). Onlytwo classes of trailing-spiral, gravitywave solutions liewithin this frequency band: (1) waves with anytangential wavenumber that move faster than theswirling wind, and (2) waves with tangential wave-numberZ2 that move slower than the swirling wind.
Bands moving faster than the swirling wind withoutward phase propagation are observed by radar.They are more like squall lines than linear gravitywaves. Waves moving slower than the swirling windpropagate wave energy and anticyclonic angularmomentum inward, grow at the expense of themean-flow kinetic energy, and reach appreciableamplitude if they are excited at the periphery of thetropical cyclone. Alternate explanations for theseinward-propagating bands involve filamentation ofvorticity from the tropical cyclone environment,asymmetries in the radially shearing flow of thevortex, and high-order vortex Rossby waves. Detailedobservations of the vortex-scale rainband structureand windfield are necessary to determine whichmechanisms play a role in rainband developmentand maintenance.
While the evolution of the inner core is dominatedby interactions between the primary, secondary, andtrack-induced wavenumber-one circulation, there issome indication that the local convective circulationsin the rainbands may impact on intensity change.Although precipitation in some bands is largelystratiform, condensation in most bands tends to beconcentrated in convective cells rather than spreadover wide mesoscale areas. As shown in Figure 12,
convective elements form, move through the bands,and dissipate as they move downwind. Doppler radarobservations indicate that the roots of the updrafts liein convergence between the low-level radial inflowand gust fronts produced by convective downdrafts.This convergencemay occur on either side of the band.A 20K decrease in low-level ye was observed in arainband downdraft, suggesting that the draft acts as abarrier to inflow. This reduction in boundary layerenergy may be advected near the center, inhibitconvection, and thereby alter storm intensity.
Motion
Tropical cyclone motion is the result of a complexinteraction between a number of internal and externalinfluences. Environmental steering is typically themost prominent external influence on a tropicalcyclone, accounting for as much as 70–90% of themotion. Theoretical studies show that in the absenceof environmental steering, tropical cyclones movepoleward and westward owing to internal influences.
Accurate determination of tropical cyclone motionrequires accurate representation of interactions thatoccur throughout the depth of the troposphere on avariety of scales. Observations spurred improvedunderstanding of how tropical cyclones move usingsimple barotropic and more complex baroclinic mod-els. To first order, the storm moves with some layeraverage of the lower-tropospheric environmentalflow: the translation of the vortex is roughly equal tothe speed and direction of the basic ‘steering’ current.However, the observations show that tropical cyclonetracks deviate from this simple steering flowconcept ina subtle and important manner. Several physicalprocesses may cause such deviations. The approachin theoretical and modeling of tropical cyclones hasbeen to isolate each process in a systematic manner tounderstand the magnitude and direction of the trackdeviation caused by each effect. The b effect opposesthe advection of relative vorticity through the differ-ential advection of the Earth’s vorticity, f , that slowsthe advection of the disturbance. (The b effect is theasymmetric vorticity advection around the vortexcaused by the latitudinal gradient of f ; b ¼ 2O cosf. bhas a maximum value at the Equator (i.e.,2.289� 10� 11 s�1) and becomes zero at the pole.)Models that are more complete describe not only themovement of the vortex but also the accompanyingwavenumber-one asymmetries that develop owing tothe differential advection of f on the east andwest sideof the vortex. It was also discovered that the role ofmeridional and zonal gradients of the environmentalflow could add greatly to the complexity even in thebarotropic evolution of a vortex. Hence, the evolution
HURRICANES 957
of the movement depends on not only the relativevorticity gradient and on shear of the environment butalso the structure of the vortex itself.
Generally, the propagation vector of these modelbaroclinic vortices is very close to that expected from abarotropic model initialized with the vertically inte-grated environmental wind. An essential feature inbaroclinic systems is the relative vorticity advectionthrough the storm center, where the vertical structureof the tropical cyclone produces a tendency for thelow-level vortex to move slower than the simplepropagation of the vortex due tob. Vertical shear playsan important factor in determining what the relativeflow is, though there is no unique relation between theshear and storm motion. Diabatic heating effects alsoalter this flow and change the propagation velocity.Thus, tropical cyclone motion is primarily governedby the dynamics of the low-level cyclonic circulation;however, the addition of observations of the upper-level structure may alter this finding.
Interaction with the Atmospheric Environment
A consensus exists that small vertical shear of theenvironmental wind and lateral eddy imports ofangular momentum are favorable to tropical cycloneintensification. The inhibiting effect of vertical shear inthe environment on tropical cyclone intensification iswell known from climatology and forecasting experi-ence. Exposure of the low-level circulation fromunderthe tropical cyclones large area of cirrus (central denseovercast) in satellite imagery is universally recognizedas a symptom of shear, and as an indication of anonintensification or weakening. Nevertheless, thedetailed dynamics of a vortex in shear has been thetopic of surprisingly little study, probably becausewhile the effect is a reliable basis for practicalforecasting, it is difficult to measure and model.
In contrast, the positive effect of eddy momentumimports at upper levels has received extensive study.Modeling studies with composite initial conditionsshow that eddy momentum fluxes can intensify atropical cyclone even when other conditions areneutral or unfavorable. It has been shown theoreticallythatmomentum imports can forma tropical cyclone inan atmosphere with no buoyancy. Statistical analysisof tropical cyclones reveals a clear relationshipbetween angular momentum convergence and inten-sification, but only after the effects of shear and SSTvariations are accounted for. Such interactions occurfrequently (35% of the time, defined by eddy angularmomentum flux convergence exceeding 10m s�1
day� 1), and likely represent the more commonupper-boundary interaction for tropical cyclones.
Frequently they are accompanied by eyewall cyclesand dramatic intensity changes.
The environmental flows that favor intensification,and presumably inward eddy momentum fluxes,usually involve interaction with a synoptic-scalecyclonic feature, such as a midlatitude upper-leveltrough or PV anomaly. Given the interaction of anupper-level trough and the tropical cyclone, the exactmechanism for intensification is still uncertain. Thesecondary circulation response to momentum andheat sources is very different. Upper-troposphericmomentum sources can influence the core directly.As can be seen in Figure 16, large inertial stability inthe lower troposphere protects the mature tropicalcyclone core from direct influence by momentumsources (inertial stability is a measure of the resistanceto horizontal displacements, based on the conserva-tion of angular momentum for a vortex in gradientbalance, and is defined as ðf þ zÞðf þ V2=rÞ, where z isthe relative vorticity, V the axial wind velocity, f theCoriolis parameter, and r the radius from the stormcenter); however, the inertial stability in the uppertroposphere is smaller and a momentum source caninduce an outflow jet with large radial extent justbelow the tropopause. If the eyewall updraft links tothe direct circulation at the entrance region of the jet,as shown in Figures 17C and 17D, the exhaust outflowis unrestricted. The important difference between heatand momentum sources is that the roots of thediabatically induced updraft must be in the inertially
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Figure 16 Axisymmetric mean inertial stability for Hurricane
Gloria on 24 September 1985. Contours are shown as multiples of
f 2 at the latitude of Gloria’s center. (Reproduced with permission
from Franklin JL, Lord SJ, Feuer SE, and Marks FD (1993) The
kinematic structure of Hurricane Gloria (1985) determined from
nested analyses of dropwindsonde and Doppler radar data.
Monthly Weather Review 121: 2433–2451; r American Meteor-
ological Society.)
958 HURRICANES
stiff lower troposphere, but the outflow jet due to amomentum–flux convergence can be confined to theinertially stable upper troposphere. Momentum forc-ing does not spin the vortex up directly. It makes theexhaust flow stronger and reduces local compensatingsubsidence in the core, thus cooling the upper tropo-sphere and destabilizing the sounding. The coolerupper troposphere leads to less thermal-wind shearand a weaker upper anticyclone.
A two-dimensional balanced approach providesreasonable insight into the nature of the tropical
cyclone intensification as a trough approaches. Isen-tropic PV analysis (Figure 17), which express theproblem in termsof a quasi-conserved variable in threedimensions, are used to describe various processes inidealized tropical cyclones with considerable success.The eddy heat and angular momentum fluxes arerelated to changes in the isentropic PV through theircontribution to the eddy flux of PV.
It has been suggested that outflow-layer asymme-tries, as in Figure 17, and their associated circulationscould create a mid- or lower-tropospheric PV
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Figure17 Wind vectors and potential vorticity on the 345K isentropic surface at (A) 1200UTC30August; (B) 0000UTC 31August; (C)
1200UTC 31August; and (D) 0000UTC 1September 1985. PV increments are 1PVUand values41PVUare shaded.Wind vectors are
plotted at 2.251 intervals. The 345K surface is approximately 200 hPa in the hurricane environment and ranges from240 to 280hPa at the
storm center. The hurricane symbol denotes the location of Hurricane Elena. (Reproduced with permission from Molinari J, Skubis S,
and Vollaro D (1995) External influences on hurricane intensity. 3. Potential vorticity structure. Journal of the Atmospheric Sciences 52:
3593–3606; r American Meteorological Society.)
HURRICANES 959
maximum outside the storm core, either by creatingbreaking PV waves on the mid-tropospheric radial PVgradient (Figure 3) or by diabatic heating. It has beenshown that filamentation of any such PVmaximum inthe ‘surf zone’ outside the tropical cyclone core (thesharp radial PV gradient near 100 km radius) producesa feature much like a secondary wind maximum,which was apparent in the PV fields of HurricaneGloria in Figure 3. These studies thus provide mech-anisms by which outflow-layer asymmetries couldbring about a secondary wind maximum.
An alternative argument has been proposed forstorm reintensification as a ‘constructive interferencewithout phase locking’, as shown in Figure 18. As thePV anomalies come within the Rossby radius ofdeformation, the pressure and wind perturbationsassociated with the combined anomalies are greaterthan when the anomalies are apart, even though thePV magnitudes are unchanged. The perturbationenergy comes from the basic-state shear that broughtthe anomalies together. However, constructive inter-ference without some additional diabatic componentcannot account for intensification. It is possible thatintensification represents a baroclinic initiation of awind-induced surface heat exchange. By this mecha-nism, the constructive interference induces strongersurface wind anomalies, which produce larger surfacemoisture fluxes and thus higher surface moist en-thalpy. This feeds back through the associated con-vective heating to produce a stronger secondarycirculation and thus stronger surface winds. The smalleffective static stability in the saturated, nearly moistneutral storm core ensures a deep response, so thateven a rather narrow upper trough can initiate thisfeedback process. The key to this mechanism is thedirect influence of the constructive interference on thesurface wind field, as that controls the surface flux ofmoist enthalpy.
Interaction with the Ocean
As pointed out in the climatology section, preexistingSSTs4261C are a necessary but insufficient conditionfor tropical cyclogenesis. Once the tropical cyclonedevelops and translates over the tropical oceans,statistical models suggest that warm SSTs describe alarge fraction of the variance (40–70%) associatedwith the intensification phase of the storm. However,these predictive models do not account either for theoceanic mixed layers having temperatures of 0.5–11Ccooler than the relatively thin SSTover the uppermeterof the ocean or horizontal advective tendencies bybasic-state ocean currents such as the Gulf Stream andwarm core eddies. Thin layers of warm SST are wellmixed with the underlying cooler mixed layer water
well in advance of the storm where winds are a fewmeters per second, reducing SST as the storm ap-proaches. However, strong oceanic baroclinic featuresadvecting deep, warm oceanic mixed layers representmoving reservoirs of high-heat-content water availa-ble for the continued development and intensificationphases of the tropical cyclone. Beyond a first-orderdescription of the lower boundary providing the heatand moisture fluxes derived from low-level conver-gence, little is known about the complex boundarylayer interactions between the two geophysical fluids.
One of the more apparent aspects of the atmos-pheric–oceanic interactions during tropical cyclonepassage is the upper-ocean cooling asmanifested in theSST (and mixed-layer temperature) decrease startingjust in back of the eye. As seen in Figure 19, oceanmixed-layer temperature profiles acquired during thepassage of several tropical cyclones revealed a cres-cent-shaped pattern of upper-ocean cooling andmixed-layer depth changes, which indicated a right-ward bias in the mixed-layer temperature responsewith cooling by 1–51C extending from the right rearquadrant of the storm into thewake regime. These SSTdecreases are observed through satellite-derived SSTimages, such as that of the post-Hurricane BonnieSST (Figure 20), which are indicative of mixed-layerdepth changes due to stress-induced turbulent mixingin the front of the storm and shear-induced mixingbetween the layer and thermocline in the rear half ofthe storm. The mixed-layer cooling represents thethermodynamic and dynamic response to the strongwind that typically accounts for 75–85% of the oceanheat loss, compared with the 15–25% caused bysurface latent and sensible heat fluxes from theocean tothe atmosphere. Thus, the upper ocean’s heat contentfor tropical cyclones is governed not solely by SST;rather, it is the mixed-layer depths and temperaturesthat are significantly affected along the lower bound-ary by the basic state and transient currents.
Recent observational data have shown that thehorizontal advection of temperature gradients bybasic state currents in a warm core ring affected themixed-layer heat and mass balance, suggesting theimportance of these warm oceanic baroclinic features.In addition to enhanced air–sea fluxes, warm temper-atures (4261C)may extend to 80–100m inwarmcorerings, significantly impacting themixed-layer heat andmomentum balance. That is, strong current regimes(1–2m s�1) advecting deep, warm upper-ocean layersnot only represent deep reservoirs of high-heat-content water with an upward heat flux, but transportheat from the tropics to the subtropical and polarregions as part of the annual cycle. Thus, the basicstate of the mixed layer and the subsequent responserepresent an evolving three-dimensional process with
960 HURRICANES
NW _12 _ 8 _ 4 0 4 8 12 SE
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Figure18 Cross-sectionsof potential vorticity fromnorth-west (left) to south-east (right) through theobservedcenter ofHurricaneElenaat the same timesas inFigure17, plus (A)at 0000UTC
30August and (F) 1200UTC1September. Increment is 0.5PVUand shading above 1PVU. (Reproducedwith permission fromMolinari J, Skubis S, andVollaro D (1995) External influences on
hurricane intensity. 3. Potential vorticity structure. Journal of the Atmospheric Sciences 52: 3593–3606;r American Meteorological Society.)
HURRIC
ANES
961
surface fluxes, vertical shear across the entrainmentzone, and horizontal advection. Simultaneous obser-vations in both fluids are lacking over these baroclinicfeatures prior, during, and subsequent to tropicalcyclone passage, and are crucially needed to improveour understanding of the role of lower boundary inintensity and structural changes to intensity change.
In addition, wave height measurements and currentprofiles revealed the highest waves and largest fetchesto the right side of the storm where the maximummixed-layer changes occurred. Mean wave-inducedcurrents were in the same direction as the steadymixed-layer currents, modulating vertical currentshears and mixed-layer turbulence. These processesfeed back to the atmospheric boundary layer byaltering the surface roughness and hence the dragcoefficient. However, little is known about the role ofstrong surface waves on the mixed-layer dynamics,and their feedback to the atmospheric boundary layerunder tropical cyclone forcewinds by altering the dragcoefficient.
A Bonnie
Danielle
TMI
31292725SST (°C)
Figure 20 Cold wake produced by Hurricane Bonnie for 24–26 August 1998, as seen by the NASA TRMM satellite Microwave Imager
(TMI). Small white patches are areas of persistent rain over the 3-day period.White dots showHurricaneBonnie’s daily position from24 to
26August.Gray dots show the later passage of HurricaneDanielle from27August to 1September. Danielle crossedBonnie’swake on 29
August and its intensity dropped. (Reproduced with permission from Wentz FJ, Gentemann C, Smith D, and Chelton D (2000) Satellite
measurements of sea surface temperature through clouds. Science 288: 847–850;r owned by the American Geophysical Union (http:/
www.sciencemag.org).)
53
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Figure 19 Schematic SST change (1C) induced by a hurricane.
The distance scale is indicated in multiples of the radius of
maximum wind. Storm motion is to the left. The horizontal dashed
line is at 1.5 times the radius of maximum wind. (Reproduced with
permission from Black PG, Elsberry RL, and Shay LK, (1988)
Airborne surveys of ocean current and temperature perturbations
induced by hurricanes. Advances in Underwater Technology,
OceanScienceandOffshoreEngineering16: 51–58;rSociety for
Underwater Technology (Graham & Trotman).)
962 HURRICANES
Tropical Cyclone Rainfall
Precipitation in tropical cyclones can be separated intoeither convective or stratiform regimes. Convectiveprecipitation occurs primarily in the eyewall andrainbands, producing rains 425mmh� 1 over smallareas. However, observations suggest that only 10%of the total rain area is comprised of these convectiverain cores. The average core is 4 km in radius (area of50 km2), and has a relatively short lifetime, with only10% lasting longer than 8min (roughly the time a1mm diameter raindrop takes to fall from the meanheight of the 01C isotherm at terminal velocity). Theshort life cycle of the cores and the strong horizontaladvection produce a well-mixed and less asymmetricprecipitation pattern in time and space. Thus, over24 h the inner core of a tropical cyclone as a wholeproduces 1–2 cm of precipitation over a relativelylarge area, and 10–20 cm in the core. After landfall,orographic forcing can anchor heavy precipitation to alocal area for an extended time. Additionally, midlat-itude interactionwith a front or upper-level trough canenhance precipitation, producing a distortion of thetypical azimuthally uniform precipitation distribu-tion.
Energetics
Energetically, a tropical cyclone can be thought of, to afirst approximation, as a heat engine; obtaining itsheat input from the warm, humid air over the tropicalocean, and releasing this heat through the condensa-tion of water vapor into water droplets in deepthunderstorms of the eyewall and rainbands, thengiving off a cold exhaust in the upper levels ofthe troposphere (B12km up). One can look at theenergetics of a tropical cyclone in two ways: (1) thetotal amount of energy released by the condensation ofwater droplets or (2) the amount of kinetic energygenerated to maintain the strong swirling winds of thehurricane. It turns out that the vastmajority of the heatreleased in the condensation process is used to causerising motions in the convection, and only a smallportion drives the storm’s horizontal winds.
Using the first approach, we assume an averagetropical cyclone produces 1.5 cm day� 1 of rain insidea circle of radius 665 km. Converting this to a volumeof rain gives 2.1� 1016 cm3 day� 1 (1 cm3 of rainweighs 1 g). The energy released through the latentheat of condensation to produce this amount of rain is5.2� 1019 J day�1 or 6.0� 1014W, which is equiva-lent to 200 times the worldwide electrical generatingcapacity.
Under the second approach we assume that for amature hurricane, the amount of kinetic energygenerated is equal to that being dissipated due to
friction. The dissipation rate per unit area is air densitytimes the drag coefficient times the wind speed cubed.Assuming an average wind speed for the inner core ofthe hurricane of 40m s� 1 winds over a 60-km radius,thewind dissipation rate (wind generation rate)wouldbe 1.5� 1012W. This is equivalent to about half theworldwide electrical generating capacity.
Either method suggests hurricanes generate anenormous amount of energy.However, they also implythat only about 2.5% of the energy released in ahurricane by latent heat released in clouds actuallygoes to maintaining the hurricane’s spiraling winds.
Tropical Cyclone-Related Hazards
In the coastal zone, extensive damage and loss of lifeare caused by the storm surge (a rapid, local rise in sealevel associated with storm landfall), heavy rains,strong winds, and tropical cyclone-spawned severeweather (e.g. , tornadoes). The continental UnitedStates currently averages nearly $5 billion (in 1998dollars) annually in tropical-cyclone-caused damage,and this is increasing, owing to growing populationand wealth in the vulnerable coastal zones.
Before 1970, large loss of life stemmed mostly fromstorm surges. The height of storm surges varies from 1to 2m in weak systems to more than 6m in majorhurricanes that strike coastlines with shallow wateroffshore. The storm surge associated with HurricaneAndrew (1992) reached a height of about 5m, thehighest level recorded in south-east Florida.HurricaneHugo’s (1989) surge reached a peak height of nearly6m about 20miles north-east of Charleston, SouthCarolina, and exceeded 3m over a length of nearly180 kmof coastline. In recent decades, large loss of lifedue to storm surges in the United States has becomeless frequent because of improved forecasts, fast andreliable communications, timely evacuations, a better-educated public, and a close working relationshipbetween the National Hurricane Center (NHC), localweather forecast offices, emergencymanagers, and themedia. Luck has also played a role, as there have beencomparatively few landfalls of intense storms inpopulous regions in the last few decades. The rapidgrowth of coastal populations and the complexity ofevacuation raises concerns that another large stormsurge disaster might occur along the eastern or GulfCoast shores of the United States.
In regions with effectively enforced building codesdesigned for hurricane conditions, wind damage istypically not so lethal as the storm surge, but it affects amuch larger area and can lead to large economic loss.For instance, Hurricane Andrew’s winds producedover $25 billion in damage over southern Florida andLouisiana. Tornadoes, although they occur in many
HURRICANES 963
hurricanes that strike the United States, generallyaccount for only a small part of the total stormdamage.
While tropical cyclones are most hazardous incoastal regions, the weakening, moisture-laden circu-lation can produce extensive, damaging floods hun-dreds of miles inland long after the winds havesubsided below hurricane strength. In recent decades,many more fatalities in North America have occurredfrom tropical-cyclone-induced inland flash floodingthan from the combination of storm surge and wind.For example, although in 1972 the deaths from stormsurge and wind along the Florida coast from Hurri-caneAgneswereminimal, inland flash flooding causedmore than 100 deaths over the north-eastern UnitedStates. More recently, rains from Hurricane Mitch in1998 killed at least 10 000 people in Central America,the majority after the storm had weakened to tropicalstorm strength. An essential difference in the threatfrom flooding rains, compared with that from windand surge, is that the rain amount is not tied to thestrength of the storm’s winds. Hence, any tropicaldisturbance, from depression to major hurricane, is amajor rain threat.
Over each ocean basin that experiences tropicalcyclones, the poleward movement of a tropicalcyclone into the midlatitudes is normally associatedwith the decay stage of its life cycle. However, thesesystems can develop into fast-moving and rapidlydeveloping extratropical cyclones that contain tropi-cal cyclone-force winds. These transforming tropicalcyclones may accelerate from forward speeds of5m s� 1 in the tropics to 420m s�1 in the midlati-tudes. They pose a serious threat and forecast problemto maritime activities and shore locations over widegeographic regions that do not normally experiencesuch conditions. A common problem in all theseregions is the difficult challenge of predicting accu-rately the track, intensity, and impacts of these rapidlychanging systems after advisories have been discon-tinued by the tropical cyclone forecast center. Fore-casters responsible for producing warnings andadvisories during extratropical transition are facedwith the potential for large amounts of precipitation,continued high wind speed, and generation of largeocean waves and swell common in tropical cyclones.However, the increased translation speed decreases thewarning time.Over land, the impacts are related to theintensity of surface winds and precipitation as inHurricane Hazel in 1954, which resulted in a rapidintensification and precipitation amounts 4200mm,leading to 83 deaths in the Toronto area of southernOntario. Over the open ocean the increased stormmotion combinedwith the continuedhighwind speedsproduces extremely large surface waves, as in Hurri-
cane Luis in 1995, which produced waves 430m,causing extensive damage to the luxury liner QueenElizabeth II.
Tropical Cyclone Forecasting
When a tropical cyclone threatens there are fourquestions that must be answered: (1) where will it hit,(2) when will it hit, (3) how strong will it be, and (4)what type of threat should be expected (i.e., wind,storm surge, heavy rain, severe weather). The answersto these four questions are the goal of tropical cycloneforecasters. Track is the most important forecast, as itdetermines the answers to the first two questions.Operational tropical cyclone track forecasting is asemiobjective process that combines conventional,satellite, and reconnaissance observations with inputfrom objective predictionmodels. At 12–24-h forecastintervals, persistence of storm motion is a majorcomponent of the forecast. However, an error in theinitial motion of 1m s� 1 will yield an 84.6 km error inthe 24 h forecast position. Since the tropical cyclonemotion processes are complex and nonlinear, trackuncertainty increases with time. For example, in theUnited States, where track errors are the lowestglobally, the mean 24-h track error over the last 10years is 170 km.However, 5% of the 24-h track errorsover the last 10 years are 4370 km. To minimize thepossibility that a coastal area may be struck withouttime to prepare, much larger areas are warned thanwill actually experience damaging winds. While spe-cific track models have indicated up to 15% improve-ment over the past 2–3 years, the average length ofcoastline warned, 730 km (roughly a 4:1 ratio to thetrack error) has not decreased over the past decade. Infact, it has increased over the 30-year mean of 556 kmin response to the emergency manger’s desire forlonger lead time.
In the United States, emergency managers requirecommunities with limited escape routes to completepreparation and evacuation before 17m s�1 windsarrive on the coast. Hence, the length of coastlinewarned is a combination of the forecast uncertainty inthe track forecast and the uncertainty in the forecast ofthe radius of the 17m s�1 winds. Themean 24-h errorof the forecast 17m s�1 wind radii is 71 km, which isabout 30–35%of the actual radii, and represents a 4-herror in lead time for a typical storm motion of5m s�1. However, 5% of the 17m s� 1 wind radiiforecasts exceed 255 km. The warning of 730 km ofthe coastline is justified as the sum of the 370 kmuncertainty in the track forecast plus the 255 kmuncertainty in the 17m s� 1 wind radii forecast to bemore than 95%confident that a coastal regionwill notbe struck without warning. Such overwarning is
964 HURRICANES
costly!Our best estimates of average preparation costsfor the warned coastline have increased roughlysixfold from $50million in 1989 to $300million in1996 ($410 000 km� 1 warned).
Another factor in the warning equation is stormintensity, which addresses the third question. Prepa-rations differ considerably for a major hurricane orsuper typhoon than for a lesser storm (e.g., storm surgeinundation varies greatly with storm intensity). In theUnited States the mean 24-h intensity forecast errorover the last 10 years is 5m s� 1 (half a category on theSaffir–Simpson scale;Table 1), and 5%of the intensityerrors are412.5m s�1 (over 1 category on the Saffir–Simpson scale). At 48 h, the mean intensity error is8m s� 1, and 5% are 420m s�1 (two categories onthe Saffir–Simpson scale). Because the forecast inten-sity of the storm at landfall is a key factor in whoevacuates, greater accuracy can lead to increasedpublic safety and reduced costs, although these savingshave yet to be quantified.
Understanding and predicting intensity change ismore complex than that for track as it requiresknowledge of interactions throughout the depth ofthe troposphere over a broad spectrum of scales.Observations are sparse in upper troposphere, atmos-pheric boundary layer, and upper ocean, limitingknowledge of environmental interactions, angularmomentum imports, boundary layer stress, and air–sea interactions. Moreover, sea surface temperatureremains an important but incomplete measure of theocean’s influence on tropical cyclone intensity change.Crucial unanswered questions concerning tropicalcyclone intensity change lie in the relative impactand interactions of three major components: (1) thestructure of the upper-ocean circulations that controlthe oceanic mixed-layer heat content, (2) the storm’sinner core dynamics, and (3) the structure of thesynoptic-scale upper-tropospheric environment. Asuccessful intensity forecast requires knowledgeof the mechanisms that modulate tropical cycloneintensity within the envelope defined by these threecomponents.
Once the 17m s� 1 wind radius crosses the coast theimportant forecast issues relate to determining howmuch damage is likely fromwind, ensuing surge, rain,and severe weather, the answer to the fourth question.These factors will determine the type and level ofemergency management response, and dictate wherethe most resources for recovery are needed. To a firstorder, the areas impacted bywind, ensuing surge, rain,and severe weather are determined by the horizontaland vertical wind distribution in the boundary layerand the interaction of the wind field with coast andinland topography. Currently, only a little informationis known about the wind structure and its distribution
with height and radial distance near landfall becauseof the paucity of observations (research quality orotherwise). Hence, a concerted effort is needed tobetter understand what determines the distribution ofwind with height and radial distance in a high-windboundary layer. Aswith the intensity forecasts, greateraccuracy in the specification of the three-dimensionalwind structure at landfall should lead to increasedpublic safety and reduced costs, although these savingshave yet to be quantified.
Summary
‘The eye of the storm’ is a metaphor for calm withinchaos. The core of a tropical cyclone, encompassingthe eye and the inner 100–200 km of the cyclone’s1000–1500 km radial extent, is hardly tranquil. How-ever, the rotational inertia of the swirling wind makesit a region of orderly, but intense, motion. It isdominated by a cyclonic primary circulation inbalance with a nearly axisymmetric, warm-core,low-pressure anomaly. Superimposed on the primarycirculation are weaker asymmetric motions and anaxisymmetric secondary circulation. The asymmetriesmodulate precipitation and cloud into trailing spirals.Because of their semibalanced dynamics, the primaryand secondary circulations are relatively simple andwell understood. These dynamics are not valid in theupper troposphere, where the outflow is comparableto the swirling flow, nor do they apply to theasymmetric motions. Since the synoptic-scale envi-ronment appears to interact with the vortex core in theupper troposphere by means of the asymmetricmotions, future research should emphasize this aspectof the tropical cyclone dynamics and their influence onthe track and intensity of the storm.
Improved track forecasts, particularly the locationand timewhen a tropical cyclone crosses the coast, areachievable with more accurate specification of theinitial conditions of the large-scale environment andthe tropical cyclone wind fields. Unfortunately, obser-vations are sparse in the upper troposphere, atmos-pheric boundary layer, and upper ocean, limitingknowledge of environmental interactions, angularmomentum imports, boundary layer stress, and air–sea interactions. In addition to the track, an accurateforecast of the storm intensity is needed because it isthe primary determinant of localized wind damage,severe weather, storm surge, ocean wave runup, andeven precipitation during landfall. A successful inten-sity forecast requires knowledge of the mechanismsthat modulate tropical cyclone intensity through therelative impact and interactions of three major com-ponents: (1) the structure of the upper ocean circula-tions that control themixed-layer heat content, (2) the
HURRICANES 965
storm’s inner core dynamics, and (3) the structure ofthe synoptic-scale upper-tropospheric environment.Even if we could make a good forecast of the landfallposition and intensity, our knowledge of how atropical cyclone’s structure changes as it makeslandfall is in its infancy, because few hard data survivethe harsh condition. To improve forecasts, develop-ments to improve our understanding through obser-vations, theory, and modeling need to be advancedtogether.
See also
Convective Storms: Overview. Cyclogenesis. Dyna-mic Meteorology: Balanced Flows; Overview; Potential
Vorticity. El Nino and the Southern Oscillation:Obser-vation; Theory. Middle Atmosphere: Quasi-BiennialOscillation. Severe Storms. Tropical Meteorology:Inter Tropical Convergence Zones (ITCZ).
Further Reading
Elsberry R (ed.) (1995) Global Perspectives of TropicalCyclones. World Meteorological Organization ReportNo. TCP-38. Geneva: WMO.
Emanuel KA (1986) An air–sea interaction theory fortropical cyclones. 1. Steady-state maintenance. Journalof the Atmospheric Sciences 43: 585–604.
Ooyama KV (1982) Conceptual evolution of the theory andmodeling of the tropical cyclone. Journal of the Meteor-ological Society of Japan 60: 369–380.
HYDRAULIC FLOW
RB Smith, Yale University, New Haven, CT, USA
Copyright 2003 Elsevier Science Ltd. All Rights Reserved.
The study of hydraulic flow is one branch of a broaderfield of fluid mechanics dealing with the dynamics ofdensity stratified flow under the influence of a gravityfield. It has a natural application to the stratifiedatmosphere and ocean. The field of hydraulics isdistinguishable from other studies of stratified flow byits emphasis on layered flow and the use of thehydrostatic or longwave approximation. Typically, inhydraulic flow formulations, the fluid system is com-posed of one or more homogeneous fluid layers,separated by sharp interfaces with density discontinu-ities. This formulation, together with the hydrostaticassumption, insures that the velocity is nearly uniformwith heightwithin each layer. In thisway, a continuousproblem is reduced to a problem with one or morediscrete layers; this results in a vast reduction in thenumber of degrees of freedom. The possibilities formathematical analysis, numerical computation, andphysical conceptualization are greatly enhanced by thesimple formulation of hydraulic theory.
Historically, the field of hydraulics arose out of, andis still largely involved in, the study of natural riverflowand engineering problems related towater flow inchannels. Its application to atmosphere and oceandynamics is more recent. Beginning in the 1950s, agrowing number of atmospheric applications havebeen suggested. On large scales, C. G. Rossby, G.Benton, and N. A. Phillips developed two-layer
mathematical models of the midlatitude atmosphereincluding the Coriolis force. On smaller scales,following the pioneering work of R. R. Long and M.Tepper, a variety of atmospheric phenomena havebeen treated with hydraulic models. Cool outflowingair from thunderstorms, sea breeze fronts, and theleading edges of cold fronts all behave like gravitycurrents. Existing cool layers beneath marine inver-sions and frontal layers behave hydraulically inmountainous areas, causing barrier jets, gap jets,hydraulic jumps, severe downslope winds, and wakeeddies. Cold high terrain can generate layered cold airavalanches and katabatic winds.
In oceanography too, hydraulic theory has foundwide application. Basin to basin exchange of watermasses is limited by hydraulic control at sills andstraits. The propagation of tidal currents and tsunamisis controlled by the long-wave speed. Turbiditycurrents slump into the deep ocean according togravity current dynamics. Coastally trapped currentsobey amodified set of hydraulic equations. Even large-scale wind-driven ocean currents are often modeled astwo layers, defined by the thermocline, with windstress and the Coriolis force playing dominant roles.
The theory of hydraulic flow is based on a fewfundamental definitions and concepts. These are:reduced gravity, the long-wave speed, Froude number,hydraulic control, conjugate states, the hydraulicjump, and gravity or density current. Reduced gravity(g0) is a measure of the effective magnitude of gravityacting on layers of different density. It definedas the product of the acceleration of gravity
966 HYDRAULIC FLOW
