the vorticity budget of developing typhoon nuri (2008) · 2020. 7. 31. · d. j. raymond and c....

Atmos. Chem. Phys., 11, 147–163, 2011www.atmos-chem-phys.net/11/147/2011/doi:10.5194/acp-11-147-2011© Author(s) 2011. CC Attribution 3.0 License.

AtmosphericChemistry

and Physics

The vorticity budget of developing typhoon Nuri (2008)

D. J. Raymond and C. Lopez Carrillo

New Mexico Tech, Socorro, New Mexico, USA

Received: 20 April 2010 – Published in Atmos. Chem. Phys. Discuss.: 2 July 2010Revised: 23 November 2010 – Accepted: 10 December 2010 – Published: 10 January 2011

Abstract. The formation of west Pacific tropical cycloneNuri (2008) was observed over four days from easterly waveto typhoon stage by aircraft using scanning Doppler radarand dropsonde data. This disturbance developed rapidly in asignificantly sheared environment. In spite of the shear, over-lapping closed circulations existed in the frame of referenceof the storm in the planetary boundary layer and at 5 km ele-vation, providing a deep region protected from environmen-tal influences. The rapid spinup of Nuri can be attributed tothe strong increase with height at low levels of the verticalmass flux during and after the tropical depression stage, andthe correspondingly strong vorticity convergence in the plan-etary boundary layer. As Nuri developed, convective regionsof boundary layer vortex stretching became fewer but moreintense, culminating in a single nascent eyewall at the trop-ical storm stage. A non-developing tropical wave case wasalso analyzed. This system started with much weaker circu-lations in the boundary layer and aloft, leaving it unprotectedagainst environmental intrusion. This may explain its failureto develop.

1 Introduction

A detailed accounting of the vorticity budget of a developingtropical cyclone is necessary to understand how the stormspins up. A variety of different mechanisms have been ad-vanced to explain this process.

Developing tropical systems often first exhibit signifi-cant cyclonic vorticity at middle levels in the troposphere(Ritchie and Holland, 1997; Simpson et al.(1997); Bisterand Emanuel, 1997; Raymond et al., 1998). However, thedevelopment of strong near-surface vorticity and the associ-

Correspondence to:D. J. Raymond([email protected])

ated warm core is a key element of tropical cyclone spinup.An important problem is then to understand how the surfacevortex develops.

Ritchie and Holland(1997) andSimpson et al.(1997) as-sert that mid-level vortex merger leads to downward vortexdevelopment, but do not explain how this might occur. Po-tential vorticity anomalies with larger horizontal scale exhibitgreater vertical penetration. Quasi-geostrophic calculationsof this effect for the vortices described in their paper sug-gest that the increased penetration is minimal, but asDavis(1992) has shown, stronger vortices in the nonlinear bal-ance regime exhibit greater vertical penetration than quasi-geostrophic calculations would suggest.

Bister and Emanuel(1997) argue that the development of acool, moist environment resulting from stratiform rain servesas the incubation region for the formation of a low-level,warm-core vortex. Cloud resolving model calculations byRaymond and Sessions(2007) support this assertion. En-vironments cooler at low levels and warmer at upper lev-els by of order 1 K lower the elevation of maximum verti-cal mass flux from≈10 km to≈5 km in their calculations,and by virtue of mass continuity, intensify the low-level in-flow into the convection. In the presence of ambient vortic-ity, low-level convergence would contribute to the spinup ofthe system. This effect may explain why tropical-wave-scalemid-level vorticity fosters tropical storm formation. The bal-anced response to a mid-level vortex is a cold core belowthe vortex and a warm core above, as assumed byRaymondand Sessions(2007). Mapes and Houze(1995) may havedetected this phenomenon in the outer rainbands of a southPacific tropical cyclone, a region far removed from the cy-clone’s warm core.

Dunkerton et al.(2009) emphasize the importance of acontinuing protected region or “pouch” consisting of a quasi-closed circulation in the low to middle troposphere. Thispouch occurs where the critical latitude for a tropical wave(latitude at which the wave propagation speed equals the

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148 D. J. Raymond and C. Lopez Carrillo: Vorticity budget in typhoon Nuri

wind speed) intersects the wave trough axis. Near thispoint the system-relative circulation is approximately closed,which means that dry air from the surrounding environ-ment cannot easily enter and vorticity cannot easily escape.Dunkerton et al.(2009) also emphasized that strong defor-mation flow impedes the organization of vorticity into a co-herent, axially symmetric structure.

Assuming that convergence of low-level vorticity is themost important mechanism for spinning up a tropical cy-clone, how much of this convergence is the result ofwidespread, ordinary convection and how much of it oc-curs in strong but isolated convective systems? The overallcirculation tendency around the cyclone doesn’t depend onhow vorticity convergence is distributed within the circula-tion loop, but the internal structure of the system does.

Hendricks et al.(2004) and Montgomery et al.(2006)present evidence that strong, isolated convection prevails,and denote these convective systems vortical hot towers(VHTs). The updrafts of VHTs are rotating rapidly andHen-dricks et al.(2004) suggest that this rotation may be rapidenough to suppress entrainment and thus alter the verticalmass flux profile of VHTs compared to more mundane formsof deep tropical convection. Furthermore, the core of the de-veloping tropical cyclone appears to form from the merger ofthe residual vortices left by VHTs.

Measurements from a recent field program are used hereto clarify the vorticity budget during the formation and in-tensification of typhoon Nuri (2008) and in a non-developingtropical wave. The THORPEX Pacific Asian Regional Cam-paign (TPARC) and the associated Tropical Cyclone Struc-ture experiment (TCS08) (Elsberry and Harr, 2008) studiedvarious aspects of western Pacific typhoons in August andSeptember of 2008. Numerous observational tools were fo-cused on the formation and development of typhoons and ontheir extratropical transitions during this period.

Typhoon Nuri (2008) intensified from a tropical wave toa typhoon in three days.Montgomery et al.(2010) presentthe synoptic conditions in which the precursor tropical wavedeveloped into a tropical cyclone. They show that the coreof the cyclone formed at the critical latitude, i.e., the lati-tude at which the low-level wind equaled the wave propaga-tion speed. This supports the hypothesis ofDunkerton et al.(2009) that the region of the wave at the critical latitude is fa-vored for development due to the weak wave-relative windsand the lack of import of dry environmental air at this lati-tude. A measure of shear versus curvature vorticity showedthat the latter dominated in the favored region during the pe-riod of development as well, thus avoiding severe deforma-tion of the vorticity anomaly.

We were able to observe tropical cyclone Nuri on four suc-cessive days, later denoted “Nuri 1” through “Nuri 4”, withvarying combinations of dropsondes and airborne Dopplerradar. On these four days the system was successively a trop-ical wave (TW), a tropical depression (TD), a tropical storm(TS), and a typhoon (TY). The data are sufficient to analyze

all terms in the vorticity equation through the full depth ofthe system on the first three days and in the lowest 3 km onthe fourth day. The absence of Doppler radar data limits theanalysis at higher levels on day four. We captured an un-usually complete picture of Nuri’s intensification from theseobservations, shedding significant light on the vorticity dy-namics of tropical storm formation. We also observed in asingle mission a non-developing tropical wave, designatedTCS030. The contrast between this system and the earliestobserved stage of Nuri is enlightening.

Section2 covers the theoretical underpinnings of our ob-servational analysis. Section3 discusses the data sources andanalysis methods used in this case study. The vorticity bud-gets of tropical cyclone Nuri at its various stages and of trop-ical wave TCS030 are described in Sect.4. The implicationsof these results are discussed in Sect.5 and conclusions arepresented in Sect.6.

2 Theoretical considerations

Our analysis of Doppler radar and dropsonde observations isenhanced by an understanding of certain aspects of the vor-ticity and divergence equations discussed below.

2.1 Governing equations

Using the identityv ·∇v = ∇(v2/2)−v ×ζ r wherev is thewind field, v = |v|, andζ r = ∇ ×v is the relative vorticity,the horizontal momentum equation may be written

∂vh

∂t+∇h(v

2/2)+ k×Z+θ∇h5 = 0 (1)

where the subscriptedh indicates the horizontal part of avector, a subscriptedz indicates the vertical component, andwhere

Z = Z1+Z2+Zf = vhζz −ζ hvz + k×F . (2)

The quantity(ζ h,ζz) is the absolute vorticity vector,θ isthe potential temperature,5 = Cp(p/pref)

κ= CpT/θ is the

Exner function,p is the pressure,pref = 1000 hPa is a con-stant reference pressure,Cp is the specific heat of air at con-stant pressure,κ = R/Cp, R is the gas constant for air, andT is the temperature.

The vorticity equation in flux form (Haynes and McIntyre,1987) is obtained by applyingk ·∇h× to (Eq.1),

∂ζz

∂t+∇h ·Z+ k ·∇hθ ×∇h5 = 0, (3)

from which it is clear thatZ is the horizontal flux of the verti-cal component of absolute vorticity, consisting of three parts,Z1 the advective flux,Z2 the vorticity flux associated withvortex tilting, andZf the flux of vorticity due to the horizon-tal force per unit massF associated with the divergence ofthe Reynolds stress. This force is generally thought to be due

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D. J. Raymond and C. Lopez Carrillo: Vorticity budget in typhoon Nuri 149

primarily to surface friction. The termsZ2 andZf are to-gether called the non-advective flux of vorticity. The verticalcomponent of the baroclinic generation termk ·∇hθ ×∇h5

is generally neglected except in highly baroclinic environ-ments such as the hurricane eyewall or mid-latitude fronts.

The divergence equation comes from applying∇h· to(Eq.1):

∂δ

∂t+∇h · [∇h(v

2/2)+ k×Z+θ∇h5] = 0 (4)

whereδ = ∇h ·vh is the divergence. The hydrostatic equationin terms of the Exner function is

θ∂5

∂z+g = 0. (5)

The anelastic mass continuity equation relates the verticalmass fluxM = ρ0vz to the horizontal mass divergenceρ0δ

∂M

∂z= −ρ0δ (6)

where the densityρ0(z) is approximated as depending onlyon height.

The divergence of the advective flux of vorticityZ1 can besplit into two pieces,

−∇h ·Z1 = −vh ·∇hζz −ζzδ, (7)

the first of which simply advects vertical vorticity in the hor-izontal plane and the second of which modifies vorticity viavertical stretching. The advection does not change the mag-nitude of vorticity in a parcel in the flux form of the equa-tions; this role is reserved for the second term, commonlycalled the stretching term, which can increase or decrease themagnitude of vorticity (but not change the sign). This split issometimes useful in distinguishing the stretching part of thevorticity flux from the horizontal advection part.

2.2 Vorticity balance

We introduce a balance condition which is obtained by drop-ping the partial time derivative from the vorticity (Eq.3)equation:

∇h ·Z+ k ·∇hθ ×∇h5 = 0. (8)

As noted above, we can often ignore the vertical componentof the baroclinic generation of vorticity, leaving us with thesimplified form of vorticity balance,

∇h ·Z = 0. (9)

Aside from the neglect of vertical baroclinic generation, thisis an exact equation in the steady state.

Vorticity balance is of interest because vorticity imbalancein the sense defined here is an indicator of evolution of thevorticity field. We demonstrate in Sect.4 that all terms in thevorticity balance equation can be estimated from the data athand, thus allowing vorticity tendencies to be calculated.

An additional balance condition is obtained by setting thetime tendency of divergence to zero in (Eq.4):

∇h · [∇h(v2/2)+ k×Z+θ∇h5] = 0. (10)

If the irrotational part of the horizontal velocity as well as thevertical velocity in (Eq.10) are neglected, then this equationbecomes the nonlinear balance equation (Raymond, 1992).Given the velocity and friction fields, this equation can beused in conjunction with the hydrostatic Eq. (5) to diagnosethe potential temperature and pressure perturbation fields, orat least that part of those fields not associated with large timetendencies in the divergence. We will not use Eq. (10), but itis included for completeness.

Equations (8–10) are not Galilean-invariant, as the dis-carded partial time derivative is different in different ref-erence frames. For instance, imagine a disturbance whichmoves rapidly at constant speed but other than that evolvesonly slowly with time. In the reference frame moving withthe disturbance, the partial derivative of vorticity with time issmall. However, this is not true in the stationary frame, sincethe vorticity at a fixed point in this frame changes rapidlywith time as the disturbance passes by. In order to eliminatetime tendencies due to system motion, we do all calculationsin the co-moving reference frame of the disturbance beingstudied.

2.3 Effects of shear on tropical cyclogenesis

Vertical shear of the horizontal wind has long been consid-ered to be detrimental to both developing and mature tropi-cal cyclones (Gray, 1968, McBride and Zehr, 1981). Con-siderable attention has been given to the dynamical effectsof shear on a strong, isolated vortex (Jones, 1995, 2000a,2000b;Reasor et al., 2004). In this case one frequently findsa precession of the vortex tilt relative to the shear vector, cul-minating in some situations in a tilt of the vortex down andto the left of the shear (in the Northern Hemisphere).

In the formation stage of a tropical cyclone the pattern ofvorticity is quite different from that seen in a mature cyclone.Most commonly one finds an evolving, chaotic distributionof mesoscale vorticity perturbations produced by convectionand other processes, the ensemble of which constitutes thelarger pattern of vorticity associated with the parent distur-bance, be it a monsoon trough, a tropical wave, or other sys-tem. This situation generally has lower Rossby number thanthe strong vortex case, possibly allowing the use of quasi-geostrophic dynamics.Reasor and Montgomery(2001) finda vortex tilt to the left of the shear vector in certain circum-stances under these conditions, particularly when a strongnegative gradient in potential vorticity exists beyond someradius. However, it is unclear whether the Nuri 1 case fallsin this category, and the neglect of the generation of vorticityby convection in that paper may limit its applicability.

We consider here an alternative idealization in which theparent disturbance is assumed to be a vertically aligned

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2 1 0 1 22

1

0

1

2

U

2 1 0 1 22

1

0

1

2

Fig. 1. Schematic illustration of the flow produced by a circu-lar region of constant relative vorticity bounded by the circle (leftpanel) and the same flow with a superimposed constant wind to-ward the right (right panel). The constant windU in the right panelis half that of the induced tangential wind at the radius of the disk ofvorticity. This component is graphically represented by the arrowbetween the plots. The thick line represents the dividing streamlinebetween an interior closed circulation and the exterior flow.

cylinder of enhanced relative vorticity. This vorticity is as-sumed constant at each level within the cylinder and zero out-side. The resulting induced flow is solid body rotation aboutthe cylinder axis within the cylinder and a tangential windinversely proportional to the distance from the axis outside.We thus neglect the fine-scale structure of the vorticity field.The magnitude of the vorticity and the induced flow can varywith height.

The total flow is the superposition of the flow induced bythe vorticity pattern plus the ambient wind. The left panelin Fig. 1 shows schematically the flow induced by the vor-ticity pattern, which has non-zero vorticity within the con-fines of the circle. As expected, zero wind is found at thecenter of the circle. A constant wind toward the right super-imposed on this flow produces the flow pattern shown in theright panel of Fig.1. The point with zero resultant wind hasmoved away from the center of the disk of vorticity towardthe upper boundary, or 90◦ to the left of the constant wind.If the constant wind is too strong, then the resultant wind isnon-zero everywhere in the flow. This occurs in our simplemodel when the constant wind exceeds the speed of the in-duced flow at the edge of the disk of vorticity.

The point of zero wind can be viewed as the center of aclosed circulation. In the case of no superimposed constantwind, the radius of the closed circulation is infinite. How-ever, with the superimposed constant flow, the closed circu-lation occupies a limited area delimited by the thick line inthe right panel. The size, shape, and existence of this closedcirculation depend on the area and magnitude of the region ofnon-zero vorticity and on the strength of the constant wind.

For a vertically aligned cylinder of vorticity in shear, thelocation and extent of the closed region will vary with heightand the displacement of the center of the circulation at eachlevel will be normal to the direction of the relative wind atthat level. These arguments will be used later to explain

the relative locations of circulation centers (in the referenceframe of the moving disturbance) at the various stages of de-veloping tropical cyclones. The overlap of closed circula-tions through a deep layer will be identified as a conditionfavoring the intensification of a tropical wave or depression.

A vertical cylinder of constant vorticity would of coursebe subject to disruption by environmental shear, but giventhe dimensions of a typical wave, the time for this disruptionwould be long compared to the time scale of the embryoniccyclone embedded in the parent disturbance. Furthermore,the parent disturbance would exhibit its own mechanismsfor survival in the face of shear, which would likely includequasi-geostrophic and convective processes. Shear might tiltthe cylinder to a certain degree, but if this tilt were weak itwould result in only minor complication in the determinationof the regions of closed circulation at each level.

If in addition to a solenoidal component to the flow (asrepresented by the stream function) there were an irrotationalcomponent, there would be flow across the streamlines, andparcels could spiral in or out across the boundary betweenthe closed and the external flow. However, if the irrotationalpart were small compared to the solenoidal part, this wouldconstitute minor leakage between the regions. Time depen-dence of the flow could also reduce the isolation of the closedregion, as noted byDunkerton et al.(2009).

2.4 Questions to be addressed

An analysis of observational data in the light of the vorticityand divergence equations can yield significant insight intothe process of tropical cyclogenesis. Among the issues con-sidered here are the following:

1. How does the vertical mass flux profile of convection af-fect the development of a cyclone? The vorticity Eq. (3)together with Eq. (7) indicate that the strongest spinupexists at levels with the largest values of the product ofabsolute vorticity and convergence−ζzδ. The strongestconvergence (strictly, the mass convergence−ρ0δ) oc-curs where the vertical mass flux increases most rapidlywith height.

2. What are the effects of shear on the early stages of thedevelopment of a cyclone embedded in an extensive re-gion of pre-existing vorticity, such as that provided bya tropical wave? This is a very different situation fromthat of an isolated vortex in shear, as discussed above.

3. What is the horizontal distribution of vertical stretch-ing responsible for cyclone spinup? Is it concentratedin a few intense VHTs as proposed byHendricks etal. (2004) andMontgomery et al.(2006), or is it morewidely distributed in numerous but less intense convec-tive systems?

4. How close does the pre-cyclone system come to vortic-ity balance in the boundary layer?



Table 1. Information about the four flights into Nuri (15–19 August) and one into TCS030 (1–2 September). The second and third columnsgive the operation altitude of the two aircraft. The fourth column specifies the reference time to which all observations are reduced, given inunits of kiloseconds since the UTC beginning of the first date listed in column one. Thus, reference times exceeding 86.4 ks actually occuron the following UTC day. The fifth and sixth columns give the location of the low-level circulation center of the system at the referencetime and the eastward and northward components of the observed propagation speed of the system.

Date P3 WC130J Ref time Ref location Storm velocity

15–16 August 2.4 km 9.4 km 93.0 ks (145.5◦ E, 15.5◦ N) (−4.9, 0.0) m s−1

16–17 August 2.4 km 9.4 km 86.0 ks (140.0◦ E, 16.7◦ N) (−8.7, 0.0) m s−1

17–18 August 3.6 km – 90.0 ks (132.7◦ E, 16.5◦ N) (−8.7, 0.6) m s−1

18–19 August – 3.0 km 83.0 ks (127.1◦ E, 17.1◦ N) (−6.8, 1.9) m s−1

1–2 September 2.4 km 9.4 km 76.0 ks (145.0◦ E, 14.5◦ N) (−6.3, 0.6) m s−1

3 Data and methods

3.1 TPARC/TCS08

The TPARC/TCS08 field program took place from 1 Augustthrough 3 October 2008. Though the main operations centerwas located at the US Naval Postgraduate School in Mon-terey, California, aircraft bases were located in Guam, Tai-wan, and Japan. Okinawa was sometimes used as an aux-iliary aircraft base. Driftsonde balloons capable of deploy-ing dropsondes from stratospheric elevations, were launchedfrom the Island of Hawaii.

The aircraft available to the project were two WC-130Jturboprops from the US Air Force Reserve 53rd Weather Re-connaissance Squadron, the US Naval Research Laboratory(NRL) P-3 aircraft (all based in Guam), the Taiwanese DOT-STAR aircraft, a modified Astra business jet operated by theNational Taiwan University (Taipei), and the German Das-sault Falcon 20-E5 jet operated by the Deutsches Zentrum furLuft- und Raumfahrt (DLR; Atsugi, Japan). All aircraft werecapable of deploying dropsondes. In addition, the DLR Fal-con carried downward-looking wind, temperature, and watervapor lidars, while the NRL P-3 carried the National Centerfor Atmospheric Research’s ELDORA radar and a Dopplerwind lidar.

3.2 Observations

Table 1 gives information about the four aircraft missionsinto developing tropical cyclone Nuri and the single missioninto TCS030. The aircraft involved in the observations ofNuri were the two WC-130Js and the NRL P-3, all operatingout of Guam. Though the P-3 generally operated betweenelevations of 2.4 km and 3.6 km, it climbed for a short timeto 7.3 km during the first mission in order to deploy drop-sondes from a higher altitude. The WC130J deployed a fewdropsondes in Nuri from 9.4 km during the third mission, buthad to return to Guam due to mechanical problems. The pre-ferred altitude of operation for the WC130J was 9.4 km, but

it descended to 3.0 km when icing or turbulence became aproblem at the higher altitude.

Times are given in UTC in this paper. Local time in Guamis UTC + 10 hr. All on-station times for Nuri and TCS030flights by the P-3 were in daylight. The Nuri flights departedGuam around 08:00 LT and returned around 15:00 LT. TheTCS030 flight of the P-3 departed at 05:00 LT and returnednear 12:00 LT. The WC-130J generally took off a few hoursbefore the P-3.

The mission of the WC-130Js was to deploy a grid of drop-sondes over the disturbance in question from as high an al-titude as feasible given the conditions. The main mission ofthe P-3 was to make Doppler radar measurements of convec-tion using the ELDORA radar. In most cases the strategy wasto obtain snapshots of as many convective systems as possi-ble within the cyclone; repeated measurements on convectivesystems were generally not made, as obtaining a large statis-tical sample of convection was considered to be more valu-able than following the life cycles of a few systems. In addi-tion, the P-3 deployed dropsondes along the flight path andmade Doppler wind lidar measurements of the atmosphericboundary layer beneath the aircraft.

The ELDORA radar was configured as shown in Table2.The unambiguous range of 75 km means that Doppler radarmeasurements in a 150 km swath were made, centered on theP-3 track, albeit with reduced spatial resolution and sensitiv-ity at the outer limits. Since ELDORA is an X-band radar,attenuation is a significant issue. However, the large unam-biguous velocity of 62 m s−1 means that unfolding of radialvelocities is not a significant problem with the systems ob-served in this case study.

The Doppler radar measurements from the P-3 aircraftand dropsondes from the P-3 and the WC130J were usedfor the first three Nuri missions to produce gridded hori-zontal and vertical winds satisfying mass continuity usinga three-dimensional variational analysis scheme (3D-VAR).This scheme is described in detail byLopez Carrillo and Ray-mond(2010). Only dropsondes deployed during the 4–6 hrin which the P-3 was flying in the system were used. The



Table 2. Characteristics of the ELDORA radar during TPARC/TCS08.

Radar characteristic Value

Wavelength 3.2 cmBeamwidth (H x V) 1.8◦ ×2.0◦

Antenna gain 39.2 dBBeam tilt angle +15.6◦ fore;−16.5◦ aftAntenna rotation rate ≈ 78◦ s−1

Peak transmitted power 40 kWPulse repetition frequency 1600/2000 HzMinimum detectable signal at 10 km −12 dBZUnambiguous range 75 kmUnambiguous velocity (dual PRT) ± 62 m s−1

Number of frequencies 3Total cell length 150 mAlong track sweep spacing ≈500 m

fourth Nuri mission produced only dropsonde data from theWC-130J, and these soundings (deployed from 3 km for op-erational reasons) were used to produce an analysis with the3D-VAR system.

For the first three Nuri missions for which radar data areavailable and for the single TCS030 mission, the grid sizeis 0.125◦ in both latitude and longitude (roughly 14 km) and0.625 km in the vertical. The gridded domain is 5◦

×5◦×

20 km or 40×40×32 cells for Nuri missions 2 and 3 and 7◦×

7◦×20 km or 56×56×32 cells for Nuri mission 1 and the

TCS030 mission. For the fourth Nuri mission in which onlydropsonde data are available, the horizontal grid resolutionis also 0.125◦ with a 4◦

× 4◦ domain size, for a grid with32×32×32 cells.

Though the 3D-VAR scheme produces results in the en-tire domain analyzed, these results are not reliable outside ofthe region where data exist. The results are therefore maskedto include only regions which contain either radar or drop-sonde data (or both). At higher altitudes radar data cover lessarea. Furthermore, the deepest dropsonde soundings beginnear roughly 9 km. For this reason, the regions above 12 kmare ignored and most results come from observations at 5 kmand below. The 3D-VAR scheme is capable of incorporatinghigh elevation angle radar data. However, radar rays with el-evation angles exceeding± 30◦ were not used in the analysisin order to avoid contaminating our results with uncertain-ties in the estimation of particle terminal velocities. Resultsobtained with and without this limitation are quite similar,but the high elevation angle data introduce some “cosmetic”artifacts in vertical velocities which we prefer to avoid. Aminimum of 200 radar radial velocity samples are requiredin each grid cell and the conditiona2 ≥ 0.03 (a measure ofthe quality of the geometry for dual Doppler analysis) is im-posed in order to ensure that only valid dual Doppler resultsare included (see Lopez and Raymond 2010). These condi-

tions largely eliminate random outliers in the radar synthesiswithout significantly limiting radar coverage.

Before applying the 3D-VAR scheme, radar and drop-sonde observations are adjusted to their corresponding po-sitions at a specified reference time using the observed prop-agation velocity of the disturbance over the measurement pe-riod. System positions were estimated from vorticity fields inNational Centers for Environmental Prediction Final Analy-sis (NCEP FNL) data. Both propagation velocities and ref-erence times are listed in Table1. The low-level circulationcenters at the reference time for each mission are also givenin this table.

Different ways of estimating system propagation speedscan yield somewhat different answers early in a system’s de-velopment. In particular,Montgomery et al.(2010) estimatethat Nuri was moving to the west approximately 2 m s−1

faster than we estimated for the first observational period.Tests indicate that our results are not overly sensitive to suchdifferences.

3.3 Vorticity analysis

Once the velocity grid is obtained, all components of the vor-ticity are computed using centered differences. The first twoterms on the right side of (Eq.3) are then computed fromthe vorticity and the velocity. The advection and stretchingcomponents of the first term are also computed separately asindicated in (Eq.7).

In order to compute the third term, the surface wind stressneeds to be calculated and an assumption has to be madeabout the depth over which the stress is distributed. The sur-face stressτ is computed from a bulk flux formula

τ = −ρBLCD|UBL |UBL (11)

where a subscript BL indicates a boundary layer value, withρ indicating air density andU indicating the horizontal windin the earth’s reference frame. Since Doppler radar observa-tions close to the surface are problematic due to sea clutter,UBL is derived primarily from radar (and dropsonde) windsat the first analyzed level above the surface atz = 0.625 km.

Results from the CBLAST (Coupled Boundary LayerAir–Sea Transfer) experiment (figure 5 ofBlack et al., 2007)suggest an estimate for the drag coefficient

CD ≈ (1+0.028|UBL |)×10−3 (12)

thought to be valid up to approximately 30 m s−1. SinceCBLAST results are for 10 m winds, our use of winds near625 m results in a slight overestimate for the surface stress.

The specific frictional forceF is postulated to take theform

ρF ≈ τ exp(−z/zs)/zs (13)

where a scale height ofzs = 1.25 km is chosen to representthe average depth of the planetary boundary layer (PBL) in



120 125 130 135 140 145 150 155 160longitude (deg E)

0

5

10

15

20

25

30

lati

tude (

deg N

)

TWTDTSTY

Nuri track, sea surface temperature (C)

26

27

28

29

30

31

Fig. 2. Sea surface temperature and the observed low-level cir-culation centers of Nuri (white stars) during tropical wave (TW),tropical depression (TD), tropical storm (TS), and typhoon (TY)missions. The blue line indicates the track of the vorticity center in850 hPa FNL data, with the blue dots spaced at 6 hr intervals. Thelarger magenta dots indicate the 00:00 UTC FNL positions nearestto the reference times shown in Table1 for the observational mis-sions.

tropical regions. The postulated scale height is consistentwith the idea that surface friction is mixed through the fullPBL, i.e., the layer containing boundary layer clouds as wellas the sub-cloud layer, via turbulent eddies. Unfortunately,not enough is known about boundary layers topped by con-vective clouds in developing tropical storms to justify a morerefined estimate of the vertical distribution of the drag forceresulting from the surface stress. Given these uncertainties,F is probably known to within only a factor of two. How-ever, this accuracy is sufficient to draw some significant con-clusions, as noted below.

With F roughly known, the third term on the right sideof (Eq.2) is estimated. Substituting this equation in (Eq.3),dropping the vertical baroclinic term, integrating over a hor-izontal areaA, and applying Gauss’s law, we obtain the ten-dency of the absolute circulation around the areaA,

d0

dt= −

∮vnζzdl+

∮ζnvzdl+

∮Ftdl, (14)

where the line integrals are taken to be in the counterclock-wise direction over the periphery ofA, vn and ζn are thehorizontal outward normal components of the velocity andvorticity, andFt is the component ofF tangential to the pe-riphery of A in the direction of the integration. Thus, thecirculation around the areaA depends only on what is hap-pening on the periphery ofA and not in the interior. The firstterm on the right is the spinup tendency due to the conver-gence of absolute vorticity, the second expresses the effectof vortex tilting on the periphery ofA, and the third is thespindown tendency due to friction.

15 16 17 18 19 20day (August, UTC)

300

280

260

240

220

200

180

bri

ghtn

ess

tem

pera

ture

(K

)

M1 M2 M3 M4

WAVE TD TS TY0

40

80

120

160

200

Fig. 3. Histogram of satellite infrared brightness temperatures ofpixels in a 5◦ ×5◦ square as a function of time, centered on trop-ical cyclone Nuri as it intensified. The stages of the storm (wave,tropical depression, tropical storm, typhoon) are shown, as well asthe approximate times of the four aircraft missions, M1-M4 (see Ta-ble1). The color scale indicates the number of pixels with the giventemperature at the given time.

120 125 130 135 140 145 150 155 160longitude (deg E)

0

5

10

15

20

25

30

lati

tude (

deg N

)

TW

TCS030 track, sea surface temperature (C)

26

27

28

29

30

31

Fig. 4. As in Fig.1 except for tropical wave TCS030.

The terms on the right side of (Eq.14) may be computeddirectly, or by area integrating the right side of (Eq.3). Wechoose the latter approach as it is computationally simpler.In addition, by expressing the horizontal velocityvh as rel-ative to the motion of a propagating system, the circulationtendency around the moving system can be computed using(Eq.14).



4 Results

In this section we document the overall development of Nuriand of the tropical wave TCS030. We then examine the vor-ticity structure of these systems and finally analyze the vor-ticity dynamics of intensification.

4.1 Overview of development

Figure 2 shows the locations of tropical cyclone Nuri de-termined from FNL 850 hPa vorticity patterns as well aslow-level circulation centers from our observational analy-sis, along with the Reynolds (Reynolds and Marsico, 1993)sea surface temperature (SST) distribution for the period ofNuri’s intensification. Previous to the typhoon stage, Nuripassed over SSTs of approximately 30◦C. It later encoun-tered decreasing SSTs. The FNL positions are obtained fromsubjective estimates of the vorticity center. As the scatterin successive position estimates shows, this procedure is notvery precise in the tropical wave stage. It also appears to leadto a systematic southward displacement of the estimated po-sition of Nuri during this phase, compared to our observa-tions of the low-level circulation center.

Figure3 shows a time series of the distribution in satelliteinfrared brightness temperature in a 5◦

×5◦ square centeredon Nuri as it intensified and moved to the west. The input forthis figure is a series of Japanese MTSAT geosynchronoussatellite infrared images interpolated to a longitude-latitudegrid with a resolution of 0.2◦

× 0.2◦. A pronounced diur-nal cycle is seen, with coldest cloud tops occurring near18:00 UTC. This diurnal cycle diminishes in amplitude asthe storm intensifies and produces a more extensive region ofhigh overcast. Note that the aircraft missions took place dur-ing periods of warming cloud tops. Operational constraintsprevented us from exploring the diurnal cycle with the air-craft.

Figure4 shows the SST at the time TCS030 was observedand its location at this time. SSTs were in excess of 30◦Cand the system was moving toward even warmer water. Inspite of these favorable conditions, TCS030 did not develop.Instead it fluctuated in intensity and finally made landfall inthe southern Philippines as a tropical wave. The white star inFig. 4 is located near the most intense convection observedin TCS030 since no low-level circulation center was obvious.This estimate is displaced well to the northeast of the positionestimate based on FNL 850 hPa vorticity.

4.2 Vorticity structure

Figures5–7 show the storm-relative winds and absolute vor-ticity at 1.2 km and 5 km for the first three missions into trop-ical cyclone Nuri. The track of the P-3 aircraft and locationsof usable dropsondes are shown in the left-hand panels. Re-flectivities greater than 25 dBZ at 5 km are shown as gray-scale insets in the right-hand panels.

As storm-relative winds are used, the circulation centersin both panels are physically significant since the associatedstreamlines are close to being parcel trajectories. These cir-culation centers are also important thermodynamically, asthey are protected from the injection of dry air from outsidethe system (Dunkerton et al., 2009). The 1.2 km circulationcenters are listed in Table1 and shown in Fig.5.

The low-level circulation center is somewhat ill-defined inthe case of Nuri 1 (first Nuri flight), though it is plausiblylocated at the white star in Fig.5. The low-level vorticityin Nuri 1 shows a northwest-southeast band to the northeastof the assumed center (Fig.5) and an otherwise random pat-tern of vorticity fluctuations. The band bounds the southernlimit of the strong cyclonic flow on the north side of the sys-tem. At 5 km, the pattern is quite different, with the strongestvorticity on the east and southeast sides of the disturbance,encompassing the 5 km circulation center. Visual observa-tion from the P-3 indicated that this region of vorticity aloftcoincided with a large stratiform rain area. This is in con-trast with the western part of the disturbance, which exhib-ited a much more convective structure. The elongated centerof the system-relative circulation at 5 km is in the form ofa northeast-southwest band displaced≈3◦ to the southeastof the low-level center. The southwestern end of this bandis close to the position inferred from FNL 850 hPa vorticity.Maximum relative winds are near 10 m s−1 at both levels.

Given the uncertainty in the Nuri 1 propagation velocity,Fig. 5 was replotted (not shown) with an assumed propaga-tion velocity of (−7,0) m s−1, which is about 2 m s−1 fasterto the west than indicated in Table1 and closer to the ob-served propagation speed for Nuri 2 and Nuri 3. This changein the propagation velocity moves the circulation centers atboth levels to the north-northeast by about 0.6◦, but does notchange the character of the overall storm-relative flow or anyof the conclusions drawn from this plot.

The strength of vorticity perturbations has intensified atboth 1.2 km and 5 km in Nuri 2 (second Nuri flight; seeFig.6), though there is still little system-wide organization at1.2 km. The 1.2 km circulation center is located at the north-west corner of the observed region in this case and the circu-lation center at 5 km is displaced≈ 2◦ to the south-southeastof the low-level center. At 5 km there is a rather strongnorth-south band of vorticity located roughly between thelow and mid-level circulation centers. The overall circulationis slightly stronger than that seen in Nuri 1. Maximum rela-tive winds are near 15 m s−1, with somewhat stronger windsoccurring at 5 km.

Figure 7 shows that the circulation pattern has changeddrastically for Nuri 3 (third Nuri flight), with a strong centralvorticity maximum at 1.2 km and a spiral band of vorticitylinked to the central maximum. A nearly co-located maxi-mum in vorticity exists at 5 km. The maximum winds areabout 20 m s−1 at both levels, with the largest values occur-ring near the central vorticity maximum.



10 m/s

143 144 145 146 147 148 149 150longitude (deg E)

11

12

13

14

15

16

17

18

lati

tude (

deg N

)

z = 1.2 km

0.3

0.2

0.1

0.0

0.1

0.2

0.3

143 144 145 146 147 148 149 150longitude (deg E)

11

12

13

14

15

16

17

18

lati

tude (

deg N

)

z = 5.0 km

0.3

0.2

0.1

0.0

0.1

0.2

0.3

Nuri 1: relative winds, absolute vorticity (ks−1 )

Fig. 5. Absolute vorticity (color levels) and storm-relative winds for Nuri mission 1 at 1.2 km (left panel) and 5 km (right panel). The blackline and black dots in the left panel indicate the P-3 aircraft track and the locations of P-3 and WC-130J dropsondes. The gray scale insets inthe right panel show regions of radar reflectivity exceeding 25 dBZ at 5 km. The white star and the white circle indicate the system-relativecirculation centers in the PBL and at 5 km respectively. The white areas reflect the geometry of the mask chosen for this mission.

10 m/s

138 139 140 141 142 143longitude (deg E)

13

14

15

16

17

18

lati

tude (

deg N

)

z = 1.2 km

0.3

0.2

0.1

0.0

0.1

0.2

0.3

0.4

138 139 140 141 142 143longitude (deg E)

13

14

15

16

17

18

lati

tude (

deg N

)

z = 5.0 km

0.3

0.2

0.1

0.0

0.1

0.2

0.3

0.4


Fig. 6. As in Fig.5 except second Nuri mission.

20 m/s

131 132 133 134 135 136longitude (deg E)

14

15

16

17

18

19

lati

tude (

deg N

)

z = 1.2 km

0.6

0.4

0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

131 132 133 134 135 136longitude (deg E)

14

15

16

17

18

19

lati

tude (

deg N

)

z = 5.0 km

0.6

0.4

0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2


Fig. 7. As in Fig.5 except third Nuri mission. The large red box indicates the central core region and the two smaller red boxes on oppositesides of the core are averaging regions for the wind profile calculation.



40 m/s

125 126 127 128 129lon (deg)

15

16

17

18

19

lat

(deg)

Nuri 4: 2.5 km abs vort (ks−1 ), rel winds

0.4

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

Fig. 8. Vorticity and storm relative winds at 2.5 km for the fourthNuri mission (WC-130J dropsondes only). The black dots indicatedropsondes of sufficient quality to be used. The red box indicatesthe central core region.

Figure8 shows the vorticity and storm-relative winds formission 4. No radar reflectivities are available due to the ab-sence of the P-3 in this mission. The circulation center isclearly defined at this stage. Due to the lack of observationsbetween the legs of the “X” pattern flown by the WC-130J,the analyzed winds and vorticity in the outer regions are dis-torted. However, with the concentration of observations nearthe circulation center, the winds are likely to be more reliablethere. Maximum winds are near 40 m s−1 and the near-corecirculation is highly symmetric.

The circulation in the case of TCS030 (Fig.9) isvery weak, with maximum system-relative winds less than10 m s−1. To the extent that a circulation can be inferred at1.2 km, it is centered at the far northeast corner of the ob-served region. The system-relative flow through the systemat low levels is from the west. Though there is a region ofmoderately strong 5 km vorticity near the northeast corner,the flow at this level does not suggest a closed circulationeven in storm-relative coordinates. In general, vorticities areless than they are in Nuri 1.

Figure10 shows histograms of the relative frequency ofoccurrence of vorticity values at 1.2 km elevation seen inFigs.5–7 and9. (Results from Fig.8 are not included, as fineresolution radar data were not available in this case.) As Nuriintensified, larger values of vorticity developed as expected.However, the overall distribution broadened as well, withmore negative values also occurring. Negative absolute vor-ticity values are likely produced by the tilting term in the vor-ticity equation; the only other possible mechanism would beconvergence of pre-existing negative vorticity, which couldin principle occur, but seems less likely. Increased convec-

tive activity in shear, which promotes tilting, is probably howthis happens. The strong vorticities in the central maximumseen in Fig.7 are highly limited in areal coverage and ap-pear in the extreme tail of the Nuri 3 vorticity distribution.The distribution of vorticity in the tropical wave TCS030 issomewhat similar to that in the tropical wave stage of Nuri,but with more negative and fewer positive values of absolutevorticity.

Figure11shows vertical profiles of wind for the Nuri mis-sions and the TCS030 mission. All but the Nuri 3 profileswere obtained from averaging analyzed winds from the 3D-VAR scheme over the full domains of Figs.5, 6, 8, and9.There is likely to be some contamination of the environmen-tal flow with storm generated winds, but by averaging overthe entire domain, which is at least somewhat centered on thedisturbance, much of this contamination should average out.For Nuri 3, one-degree-square regions on opposite sides ofthe central core (see Fig.7) rather than the entire domain areaveraged in order to cancel out axisymmetric storm pertur-bations to the flow. This seems preferable to averaging overthe full observed domain, since the concentration of obser-vations on the north side of the core of Nuri 3 is likely toincrease greatly the contamination of the environmental flowwith cyclone-generated winds.

Figure 11 shows moderately strong shears of≈7 m s−1

between the surface and 6 km in Nuri 1 and Nuri 2. TheNuri 3 shear is considerably stronger, of order 15 m s−1.The shear was strong enough in the real time forecast forTPARC/TCS-08 forecasters to discount the possibility thatNuri would intensify. The initial mission was therefore un-dertaken as a probable “null” case. The relative wind pro-file in TCS030 differed little in essential characteristics fromthat seen in Nuri 1 with the exception that strong northerlysystem-relative flow existed at middle and upper levels.

4.3 Circulation dynamics

As noted in Sect.3, the advective (Z1 in (Eq. 3)) and non-advective fluxes (Z2+Zf ) of the vertical component of ab-solute vorticity are estimated from the velocity and vorticityfields. Figures12–15 show the total vorticity flux and thevorticity tendency due to vertical stretching for Nuri 1-3 andTCS030 in the PBL and at 5 km. Note that the scales forthe vorticity flux and the stretching tendency differ betweenfigures. The stretching tendency−ζz∇h ·vh is shown ratherthan the total tendency because stretching is the main mech-anism by which parcel values of vorticity are increased, atleast in regions of small tilting tendency. The vorticity advec-tive tendency−vh ·∇hζz exhibits complex patterns which areirrelevant to the parcel increase in vorticity since advectionsimply moves parcels around without changing their vortic-ity. Of course the advective contributions are needed to com-pute the overall circulation tendency given by (Eq.14) sincethey can move parcels in and out of the circulation domain.



10 m/s

140 141 142 143 144 145 146 147longitude (deg E)

10

11

12

13

14

15

16

17

lati

tude (

deg N

)

z = 1.2 km

0.3

0.2

0.1

0.0

0.1

0.2

0.3

140 141 142 143 144 145 146 147longitude (deg E)

10

11

12

13

14

15

16

17

lati

tude (

deg N

)

z = 5.0 km

0.3

0.2

0.1

0.0

0.1

0.2

0.3

TCS030: relative winds, absolute vorticity (ks−1 )

Fig. 9. As in Fig.5 except the TCS030 mission. No circulation centers are indicated.

0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4vorticity (ks−1 )

0

2

4

6

8

10

12

14

rela

tive f

requency

nuri 1

nuri 2

nuri 3

tcs030

Fig. 10. Relative frequency of absolute vorticity values at 1.2 kmin Figs.5–7 and9.

Also shown is the total vorticity flux. The vorticity flux(but not the stretching tendency) has been low-pass filteredwith a filter length of 0.5◦ to improve the clarity of the overallvorticity flow patterns. Mostly the vorticity flux reflects thehorizontal velocity field, demonstrating the large magnitudeof the advective part of the vorticity flux relative to the non-advective part.

The stretching tendency of vorticity indicates regions ofmass convergence, so maxima in this quantity indicate re-gions of convection with significant convergence in theboundary layer. Comparison of stretching maxima in thePBL with regions of strong 5 km reflectivity in the right pan-els of Figs.5–7 and9 shows moderately good, but not per-fect agreement in this respect. Notable examples exhibitingstrong correlations in this regard include the convection near(145.8◦ E, 14.2◦ N) in Nuri 1, (140.2◦ E, 14.4◦ N) in Nuri 2,and (133.0◦ E, 16.0◦ N) in Nuri 3. The strongest stretchingtendencies at 5 km are greater than PBL tendencies in Nuri1, Nuri 2, and in TCS030.

10 5 0 5 10u-relative (m/s)

0

5

10

15

heig

ht

(km

)

10 5 0 5 10v-relative (m/s)

0

5

10

15

heig

ht

(km

)

nuri 1

nuri 2

nuri 3

nuri 4

tcs030

Fig. 11. Storm-relative westerly (left panel) and southerly (rightpanel) wind components for the four Nuri missions and TCS030.

As Nuri intensifies, the regions of stretching become fewerand more intense, culminating in a single strong central vor-tex in Nuri 3. This suggests a transformation from scatteredordinary convection to a more limited number of strong con-vective systems reminiscent of VHTs, which in turn give wayto the cyclone eyewall. Such behavior is seen in the three-dimensional numerical simulations ofNguyen et al.(2008).

Circulations of vorticity flux in the PBL in Nuri 1 and 2,as seen in Figs.12–14 appear to be closed, but the observedregions are too restricted to say with absolute certainty. At5 km the Nuri 1 circulation also suggests closure. For Nuri 2at 5 km and Nuri 3 at both altitudes the vorticity flux circu-lation is clearly closed. These results suggest that regions ofstrong vorticity created by stretching are not exported fromNuri during its growing stage. The pattern of vorticity flux inTCS030 in the PBL may be closed, but observations do notextend far enough to the north to verify this. At 5 km there isno hint of a closed circulation in TCS030, allowing export ofgenerated vorticity at this altitude.

The centers of vorticity circulations are near, but notnecessarily colocated with the centers of mass circulations.This difference in location is due to a combination of



20 km ks−1 day−1

143 144 145 146 147 148 149 150longitude (deg E)

11

12

13

14

15

16

17

18

lati

tude (

deg N

)

Nuri 1: PBL

1.5

1.0

0.5

0.0

0.5

1.0

1.5

143 144 145 146 147 148 149 150longitude (deg E)

11

12

13

14

15

16

17

18

lati

tude (

deg N

)

Nuri 1: 5 km

4.5

3.0

1.5

0.0

1.5

3.0

4.5

Fig. 12. Stretching tendency (filled contours) for vorticity and total vorticity flux (arrows) in the PBL (0< z < 1.2 km; left panel) and at 5 km(right panel) as calculated from the analyzed wind fields for Nuri 1. The white stars (PBL) and circles (5 km) indicate the PBL storm-relativecirculation center and the black contours indicate zero stretching tendency. The vorticity flux has been low-pass filtered with a filter lengthof 0.5◦ for clarity of the overall pattern, but the stretching tendency has not.


138 139 140 141 142 143longitude (deg E)

13

14

15

16

17

18

lati

tude (

deg N

)

Nuri 2: PBL

4.5

3.0

1.5

0.0

1.5

3.0

4.5

138 139 140 141 142 143longitude (deg E)

13

14

15

16

17

18la

titu

de (

deg N

)Nuri 2: 5 km

3.3

2.2

1.1

0.0

1.1

2.2

3.3

Fig. 13. As in Fig.12except for Nuri 2. Note the change in scales.

non-advective fluxes, i.e., tilting and frictional fluxes rep-resented by the second and third terms on the right side of(Eq.3).

Figures16–22 show vertical profiles of planetary and ab-solute circulation0 around the observed regions in Figs.5–8 and9 as well as the integrated vertical mass fluxM. Inaddition, the vertical profiles of the various components ofcirculation tendency are shown. By hypothesis, the frictiontendency is concentrated primarily in the PBL. The domainsizes are different for each case. However, the magnitudeof the integrated planetary circulation, which is roughly theCoriolis parameter times the area, gives a visual estimate ofthe relative domain sizes between plots since the Coriolis pa-rameter is very similar in all cases.

Figure16 shows profiles for Nuri 1. The maximum circu-lation in this tropical wave case occurs in a nearly uniformlayer from the surface up to 4 km with a value of roughlytwice the planetary circulation. The circulation decreasesmonotonically above this level. The vertical mass flux max-imizes at high levels, near 10 km elevation and is actually

negative at low levels, suggesting that downdrafts are strongthere. The vertical derivative of mass flux is very small ornegative in the PBL. Thus, boundary layer convergence as-sociated with convection is small and the circulation ten-dency due to vorticity convergence near the surface is corre-spondingly small. The frictional spindown tendency exceedsvorticity convergence below 1 km. Vorticity convergence in-creases up to the mid-troposphere and then decreases. Abovethis level, tilting makes a significant positive contribution tothe circulation tendency.

Nuri 2 (Fig. 17) exhibits a very different pattern, with thevorticity convergence term greatly exceeding frictional spin-down in the PBL. This is related to the rapid increase in ver-tical mass flux with height and the associated strong massconvergence in the PBL. The vertical mass flux maximizesnear an elevation of 5 km, which is significantly lower thanin Nuri 1. The contribution of tilting is comparatively weakat all levels. The surface circulation is still only about twicethe planetary circulation, but the maximum circulation hasincreased to three times the planetary circulation near 5 km.




131 132 133 134 135 136longitude (deg E)

14

15

16

17

18

19

lati

tude (

deg N

)

Nuri 3: PBL

30

20

10

0

10

20

30

131 132 133 134 135 136longitude (deg E)

14

15

16

17

18

19

lati

tude (

deg N

)

Nuri 3: 5 km

12

8

4

0

4

8

12

Fig. 14. As in Fig.12except for Nuri 3. Note the change in scales.


140 141 142 143 144 145 146 147longitude (deg E)

10

11

12

13

14

15

16

17

lati

tude (

deg N

)

TCS030: PBL

1.5

1.0

0.5

0.0

0.5

1.0

1.5

140 141 142 143 144 145 146 147longitude (deg E)

10

11

12

13

14

15

16

17

lati

tude (

deg N

)

TCS030: 5 km

4.5

3.0

1.5

0.0

1.5

3.0

4.5

Fig. 15. As in Fig.12except for TCS030. No circulation centers are shown in this case.

Figure18 shows that for Nuri 3 the circulation measuredrelative to the planetary circulation has increased at all levelsin comparison to Nuri 2. The elevation of maximum verti-cal mass flux has increased to near 6 km and the mass con-vergence in the PBL is less than for Nuri 2. Tilting con-tributes negatively to the circulation tendency in the lowertroposphere and positively in the upper troposphere.

The circulation tendency due to vorticity convergence isactually negative in the PBL. This is due to the apparent sup-pression of stretching away from the central vorticity maxi-mum. The circulation tendency in the PBL for a 2◦-squarebox centered on the core (Fig.19) is slightly positive, but isindistinguishable from zero given the potential errors in thecalculation of surface friction. Comparison of Fig.18and19also shows that the region within the 2◦ box is responsiblefor 2/3 of the mass flux and circulation and nearly 100% ofthe circulation at the surface.

Figures20 and 21 show the corresponding patterns forNuri 4 except that the region over which the integration isdone for21 is the 1.5◦ box illustrated in Fig.8. As for Nuri3, the circulation tendency due to convergence over the fulldomain is small, with a net spindown tendency in the PBL,while a net spinup tendency exists over the central region.

The spindown tendency over the full domain in Nuri 3 mustbe a transient effect, as the overall circulation over the fulldomain increased between Nuri 3 and Nuri 4 in spite of thespindown tendency at the time of observation.

In the TCS030 case (Fig.22) the circulation is almost non-existent and the vertical mass flux is very weak. Curiously,the mass flux profile has a double maximum, with peak fluxesnear 2 km and 8 km, suggesting two different convective pop-ulations. Even though the entrained mass flux in a thin layernear the surface is quite large in spite of the weak overall pro-file, the vorticity convergence tendency in the PBL (and at alllevels) is negative due to the export of vorticity. This exportis related to the lack of a closed vorticity flux circulation inthe PBL, as shown in Fig.15. The circulation tendency dueto tilting is positive in the upper troposphere.

5 Discussion

The formation of typhoon Nuri over a three day period wasdocumented by aircraft missions on four successive days.During this period the cyclone evolved from a tropical waveto a tropical depression, a tropical storm, and finally to a



0 5 10 15 20 25circulation (km2 /s)

0

4

8

12

16

heig

ht

(km

)

30 15 0 15 30circ tend (km2 /s/day)

0

4

8

12

16convergence

tilting

friction

net

5 0 5 10 15mass flux (109 kg/s)

0

4

8

12

16

Nuri 1

Fig. 16. Nuri 1 vertical profiles integrated over the analyzed regionshown in Fig.5. Left panel: Planetary (red) and absolute (blue)circulations. Center panel: Contributions to the total circulationtendency (red) due to vorticity convergence (blue), vortex tilting(green), and surface friction (magenta). Right panel: Vertical massflux profile.


0

4

8

12

16

heig

ht

(km

)


0

4

8

12

16convergence

tilting

friction

net

0 5 10 15mass flux (109 kg/s)

0

4

8

12

16

Nuri 2

Fig. 17. As in Fig.16except Nuri 2 (Fig.6).

full-fledged typhoon. This rapid intensification occurred inan environment of significant easterly and northeasterly shear(Fig. 11). Intensification began near the island of Guam. Thestorm followed a track toward the west during this periodand Nuri was just to the east of the Philippines during thelast mission (see Fig.1).

As it evolved, Nuri’s convection exhibited a variety of ver-tical mass flux profiles. In the tropical wave stage (Nuri 1)the average mass flux peaked at a high elevation, resulting ina deep inflow which peaks at middle levels. As a result, thecirculation was decaying in the PBL, but increasing in thefree troposphere. This is reflected in the greatly increasedmid-level circulation seen in Nuri 2. While a tropical depres-sion (Nuri 2), the vertical mass flux increased rapidly withheight below 4 km, resulting in an intense inflow in the PBL.This inflow was responsible for the strong positive circula-tion tendency associated with vorticity convergence at theselevels. In the tropical storm stage (Nuri 3), the PBL inflowwas less strong overall, resulting in a net spindown tendencyin the PBL (see Fig.18). However, as Fig.19 shows, the


0

4

8

12

16

heig

ht

(km

)


0

4

8

12

16convergence

tilting

friction

net

0 5 10 15mass flux (109 kg/s)

0

4

8

12

16

Nuri 3

Fig. 18. As in Fig. 16 except Nuri 3 (Fig.7). Note the change inscales.


0

4

8

12

16

heig

ht

(km

)


0

4

8

12

16convergence

tilting

friction

net

0 5 10 15mass flux (109 kg/s)

0

4

8

12

16

Nuri 3 core

Fig. 19. As in Fig.18except for integration over the 2◦-square boxillustrated in Fig.7. Note the change in scales.

spinup tendency around a small box centered on the circula-tion center remained intense. Figures20and21 indicate thatNuri continued this trend as it developed into a typhoon.

In Nuri 1 and Nuri 2, the circulation centers in the PBL andat 5 km are displaced from each other by 2◦–3◦. Comparisonof Figs.5 and6 with the shears shown in Fig.11 shows thatthe displacement of the 5 km circulation center relative to thePBL center is approximately 90◦ to the left of the shear vec-tor between the PBL and 5 km. Thus, in the case of Nuri 1,the shear is from the north-northeast in the lowest 5 km andthe 5 km circulation is southeast of the PBL circulation. ForNuri 2 the shear is east-northeasterly and the correspondingcirculation center displacement is to the south-southeast.

Figure23gives a possible explanation for why the system-relative circulation centers are displaced from each other. Ateach level the total wind is assumed to be the vector sum ofthe system-relative ambient wind and the induced circulationassociated with the wave-scale region of positive relative vor-ticity, which in the idealization of Sect.2.3 is approximatedas an upright cylinder of vorticity which varies in magni-tude only with height. The circulation center at each leveloccurs where the vector sum of these winds is zero. The



0 10 20 30 40 50 60circulation (km2 /s)

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Fig. 20. As in Fig. 16 except Nuri 3 (Fig.8). Note the change inscales.

0 10 20 30 40 50 60circulation (km2 /s)

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Fig. 21. As in Fig. 20 except for integration over the 1.5◦-squarebox illustrated in Fig.8. Note the change in scales.

displacement between the circulation centers is due to thedifference in the ambient wind between the two levels, withthe displacement being normal to this difference.

Around these circulation centers are closed regions of cy-clonic flow as illustrated in Sect.2.3. Air (and vorticity)at each level inside the bounding closed streamline remainswithin the system and is protected from entrainment of envi-ronmental air as postulated byDunkerton et al.(2009) andMontgomery et al.(2010). The area where these regionsoverlap is protected from environmental incursions throughthe full column depth between the PBL and 5 km. It is thuslikely to be the area in which the core of the developing trop-ical cyclone spins up. In Nuri 1 this region contained thestrongest deep convection. In Nuri 2 the most significantvorticity at 5 km was also found in this region, suggestinga history of strong convection there.

As discussed in Sect.2.3, the above explanation forthe displacement of the circulation center with height dif-fers from explanations based on adiabatic vortex dynamics,which consider the interaction between potential vorticitypatterns at different elevations. Our explanation depends ondiabatic processes to maintain the form of the wave-scalevorticity pattern in the face of shear.


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Fig. 22. As in Fig.16except TCS030 (Fig.9).

The high resolution simulation of the development of At-lantic hurricane Felix (2007) byWang et al.(2010a) andWang et al.(2010b) shows many features similar to thoseseen in the formation of Nuri. In particular, the low-levelspinup due to vorticity convergence driven by convection ina protected core and the spinup at upper levels by the tiltingterm are reproduced.

Nuri transformed from a pattern of scattered mesoscalevortices to a highly organized system with a strong centralconcentration of vorticity between mission 2 and mission 3.However, this transformation was not sudden; examinationof Figs. 12–14 shows that the number of regions of vortexstretching decreased as Nuri evolved and the strength of thestretching increased. This suggests the development of fewerbut stronger rotating convective systems as Nuri intensified,culminating in a single core system which developed into theeyewall.

An interesting aspect of Nuri’s evolution is that vorticitybalance in the PBL was far from satisfied. In Nuri 1 and Nuri3 (full observed region) the frictional spindown tendenciesslightly exceeded the spinup tendencies due to vorticity con-vergence. In Nuri 2 spinup due to vorticity convergence farexceeded frictional spindown. Only in the restricted regionencompassing the core of Nuri 3 was approximate vorticitybalance observed (see Fig.19). Uncertainties in the verticaldistribution of surface stress are insufficient to explain thisdiscrepancy, particularly for Nuri 2. We note that significantimbalance was found in the boundary layer of a simulated,intensifying tropical storm (Bui et al., 2009) in agreementwith our observations. The effects of tilting are generally in-sufficient to change these qualitative results, at least at lowlevels.

Superficially, the pre-Nuri tropical wave observed duringNuri 1 was similar to the wave seen in TCS030. Both casesappeared as tropical waves in large-scale analyses and bothhad similar values of shear. However, TCS030 did not ex-hibit a closed circulation at 5 km in our data and the existenceof one in the PBL was doubtful, even in system-relative co-ordinates. Thus, Nuri was able to retain its moist core and



shear

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circ5 km

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centerPBL circ

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Fig. 23. Interaction of shear (thick black vector) with a broad re-gion of positive relative vorticity (large green circle). The circula-tion centers in the PBL and at 5 km are located where the system-relative ambient winds at the respective levels (black arrows) justbalance the induced circulation from the vorticity pattern (green ar-rows). The blue and red “teardrops” represent the limits of closedcirculation streamlines in the PBL and at 5 km. The magenta-colored region of overlap between these areas of closed circulationrepresents the region where the entire column between the PBL and5 km is protected from incursions of environmental air.

vorticity over an extended period while TCS030 could not.The lack of a strong vertical mass flux profile in TCS030most likely results from the lack of a protected core.

6 Conclusions

Our analyses of typhoon Nuri and tropical wave TCS030support the following conclusions:

1. Nuri spun up rapidly from a tropical wave to a typhoonin spite of significant environmental shear. TCS030 wassubject to similar vertical shear but did not spin up. AsNuri intensified, regions of convective vortex stretchingbecame fewer and more intense, culminating in the for-mation of a strong central vortex.

2. The rapid intensification of Nuri appears to be relatedto the development of vertical mass flux profiles show-ing a strong increase with height below 4 km elevation.Mass continuity implies intense inflow at low levels inthis case and correspondingly strong vorticity conver-gence. For Nuri 2, this vorticity convergence domi-nated all other circulation tendency terms in the plan-etary boundary layer, resulting in the development ofNuri into a tropical storm by the following day. Thevertical mass flux in the non-developing TCS030 casewas much weaker.

3. The displacement of the center of the Nuri circulationwith height is explained as the result of the interactionwith shear of a large, wave-associated column of posi-tive relative vorticity. This displacement, though of or-der 2◦–3◦ between the surface and 5 km in the wave andtropical depression stages, was still small enough for acolumn protected from environmental incursions to ex-ist through this elevation range. Such a protected col-umn did not exist for TCS030.

4. The planetary boundary layer was far from vorticity bal-ance during Nuri’s spinup.

This work complements the larger-scale view of Nuri pre-sented byMontgomery et al.(2010).

Acknowledgements.We thank Mike Herman and Jorge Cisnerosfor the FNL and preliminary radar results; Chris Velden and DaveStettner of SSEC for the MTSAT data; crews of the NRL P-3 andthe Air Force Reserve WC-130Js for their excellent work; NCAREOL crew for their dedication, especially in rebuilding ELDORAin the two weeks before the project and in dealing with severedropsonde problems; and Pat Harr for his exemplary leadership.Quality control of dropsondes by EOL contributed to the fidelity ofour analysis. We also thank Kerry Emanuel and Sharon Sessionsfor useful discussions on this manuscript. Roger Smith, MichaelMontgomery, Kevin Tory, Zhuo Wang, and Michael Riemermade many penetrating and useful comments during the reviewprocess. This work was supported by grants N000140810241from the Office of Naval Research and ATM0638801 from the USNational Science Foundation. C. Lopez was partially supportedby Inter-American Institute for Global Change Research grantCRN-2048.

Edited by: T. J. Dunkerton

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