Numerical Simulations of the Genesis of Hurricane Diana (1984). Part I: Control Simulation

AUGUST 2001 DAVIS AND BOSART 1859

CHRISTOPHER A. DAVIS National Center for Atmospheric Research,* Boulder, Colorado

LANCE F. B OSART Department of Earth and Atmospheric Sciences, University at Albany, State University of New York, Albany, New York

(Manuscript received 25 July 2000, in ®nal form 23 January 2001)

ABSTRACT The complete transformation of a weak baroclinic disturbance into Hurricane Diana is reproduced by numerical simulations using the ®fth generation Pennsylvania State University±National Center for Atmospheric Research Mesoscale Model. Three distinct phases of the evolution are evident. First, baroclinic and barotropic development, strongly modi®ed by the effects of latent heating, occurs. During the latter part of this phase, the low-level circulation is strengthened through the axisymmetrization of remote potential vorticity anomalies that are generated by condensational heating and then advected toward the incipient storm. The axisymmetrization process evinces properties of both nonlinear, discrete vortex merger and vortex Rossby wave dynamics. The transformation from cold-core to warm-core vortex occurs in this development stage. In the second phase, lasting 10±12 h, little deepening occurs. Spiral bands of convection begin to form and the core of the storm moistens, eventually reaching 95% humidity averaged between the top of the boundary layer and 600 hPa at the radius of maximum wind. The third stage ensues, driven mainly by the positive feedback between ¯uxes of latent heat and the increase of the tangential wind. In this stage, the storm readily develops a clear eye. The transition to the hurricane stage occurs 12±24 h sooner in the model than in nature. The maximum intensity was also underestimated, with peak winds in the model being about 42 m s Ϫ1 (at 40 m above ground level) whereas sustained winds of nearly 60 m s Ϫ1 were observed.

1. Introduction cursors in many cases of tropical cyclone development, especially near and poleward of 20ЊN latitude. The pro- a. Tropical cyclone genesis cess by which such an incipient mesoscale or synoptic- The general conditions favoring tropical cyclone for- scale disturbance becomes a coherent mesoscale cir- mation have been known for some time (e.g., Gray culation capable of self-ampli®cation has remained par- 1968; McBride and Zehr 1981). These consist of a series ticularly elusive and may not be a single mechanism of practically necessary, but by no means suf®cient, but, rather, any process that concentrates mesoscale vor- constraints on sea surface temperature (SST), environ- ticity. mental shear (weak), presence of ambient cyclonic vor- Observations to date have generally been inadequate ticity, and large-scale divergence aloft. Tropical cyclone to capture mesoscale aspects of the genesis stage of formation also requires a preexisting disturbance of suf- tropical cyclones except for brief glimpses during the ®cient amplitude such that air±sea interaction can occur process. Experiments such as the Tropical Experiment (Riehl 1948; Rotunno and Emanuel 1987). Recent ev- in Mexico (Bister and Emanuel 1997) and Tropical Cy- idence from studies by Hess et al. (1995), Lehmiller et clone Motion experiments TCM-92 (Ritchie and Hol- al. (1997), Molinari et al. (1998), and Bracken and Bos- land 1997) and TCM-93 (Harr et al. 1996a,b) over the art (2000) points to the importance of upper-level pre- western Paci®c Ocean are some recent examples. All of these studies suggest the importance of a preexisting large-scale disturbance that organizes convection and * The National Center for Atmospheric Research is sponsored by an importance of lower-tropospheric cyclonic potential the National Science Foundation. vorticity (PV) anomalies that form within the organized convection. One such vortex appears to make a trans- Corresponding author address: Christopher A. Davis, National formation to warm core and form the seed of the tropical Center for Atmospheric Research, P.O.Box 3000, Boulder, CO 80307. cyclone. However, there does not exist a dataset that E-mail: [email protected] temporally resolves this transformation.

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A fairly comprehensive review of tropical cyclone simulations is found in Liu et al. (1997). Simulations of the genesis phase, fully in three dimensions with domains large enough to capture both the evolving meso- and synoptic scales and the inner core dynamics, do not exist. Zhang and Bao (1996a) produced a marginal tropical storm in a 90-h integration, but their resolution (25-km grid spacing) was too coarse to capture the inner structure of the storm. Even Liu et al. did not simulate tropical storm genesis because their study of Tropical Cyclone Andrew began after the disturbance had reached tropical storm strength. All high-resolution (less than 20-km grid spacing) studies have had to em- ploy a bogusing scheme to initialize a vortex, and in simulations of observed cases, the initial vortex is usu- ally of tropical storm strength. Thus, the imposed initial disturbance is capable of self-ampli®cation, so the question of how this disturbance originates is not addressed.

Several recent papers have dealt with the topic of the FIG. 1. Track and intensity of observed and simulated storms. formation of tropical depressions and tropical storms as Heavy solid line indicates the observed track, with the storm positions an amalgamation of diabatically produced potential vor- marked by L's. This line is the simulated track, with 3-hourly position ticity (PV) maxima in the lower and middle troposphere. marked by ϩ's. Heavy ϩ's denote time-matching observations. Small Observational evidence that a merger process is im- integers (1±9) refer to times listed at lower left. Inset ®gure depicts minimum SLP (hPa) as a function of time with observations indicated portant comes from Harr et al. (1996a,b) and Ritchie by ®lled circles. Shaded ®eld is SST (ЊC) obtained from manual and Holland (1997), who examined western Paci®c sys- analysis, interpolated to the 9-km domain. tems. Organized latent heating and the generation of multiple PV anomalies on the mesoscale appears to involve background synoptic-scale upward motion (Simp- rare class of tropical cyclones with origins as an extra- son et al. 1997), but the mechanisms producing wide- tropical, baroclinic cyclogenesis. Diana formed to the spread weak ascent are varied. Easterly waves (Reed east of Florida, and slightly poleward of a decaying 1979), the monsoon trough in the western Paci®c Ocean stationary front that had moved unusually far south for (e.g., Simpson et al. 1997), and extratropical troughs in early September. A large anticyclone dominated the east the upper troposphere (Riehl 1954; Molinari and Vollaro coast of the United States. To the south of this anti- 1989; DeMaria et al. 1993; Montgomery and Farrell cyclone and poleward of the surface front, strong east- 1993; Molinari et al. 1998) are all thought to provide erly ¯ow drove large latent heat ¯uxes over a mesoscale favorable environments for producing multiple cloud region, with observed values approaching 1000 W mϪ2. clusters and associated PV anomalies, which can merge The incipient development as seen in water vapor and intensify into a nascent tropical cyclone. imagery was highly reminiscent of frontal cyclogenesis The view espoused by Ritchie and Holland is that the (Fig. 7 of BB). Tropical storm Diana formed on the merger process in the real atmosphere is a strong analog western edge of a baroclinic zone that was anomalously of two-dimensional barotropic dynamics, where the en- strong given its latitude and season. This incipient cy- ergy cascade is entirely upscale. Montgomery and En- clone itself was diagnosed by BB to grow in response agonio (1998) have viewed the vortex intensi®cation to mesoscale ascent and vortex stretching caused by a process in terms of Rossby waves propagating on the cold-core upper-tropospheric trough centered over Flor- PV gradient outside the radius of maximum wind. Vor- ida at 1200 UTC September. The upper-tropospheric ticity transport into the core is accomplished by wave trough had become increasingly cut off from the main ¯uxes. It is possible that these two views of axisym- westerlies farther north. The process of trough fracture metrization are complementary, but not necessarily so. could also be viewed as a large-scale anticyclonic wave- In the idealizations presented by Ritchie and Holland, breaking episode in the upper troposphere with attendant Rankine vortices are assumed and the vortices are large- ®lamentation of vorticity and PV (Thorncroft et al. amplitude, coherent structures. In Montgomery and En- 1993). agonio, disturbances are more wavelike, propagating on Figure 1 shows the track and intensity of Diana and a radially distributed vorticity gradient. It is not cur- the pre-Diana disturbance. Diana initially moved west- rently known which perspective more accurately re¯ects ward and featured a highly asymmetric distribution of nature. wind and precipitation (as judged from satellite). The storm was named around 1500 UTC 8 September b. Tropical Cyclone Diana (1984) (Lawrence and Clark 1985) even though it still resembled As discussed in detail by Bosart and Bartlo (1991, a baroclinic cyclone (Fig. 8c of BB). By 0000 UTC 9 hereafter BB), Hurricane Diana was one of a relatively September, the storm had deepened to moderate tropical

Unauthenticated | Downloaded 09/26/21 04:27 AM UTC AUGUST 2001 DAVIS AND BOSART 1861 storm, had lost most of its baroclinic character, and began neously resolve the core of the storm, including the to exhibit a more axially symmetric pressure and wind eyewall development, and the synoptic scales, including ®eld at the surface. During this period of deepening, the preexisting upper-level trough and low-level baro- Diana drifted slowly northwestward to within 100 km of clinic zone. These questions also require relatively long the Florida coast. The observed storm tracked northward simulations in order that the different stages of devel- within a relatively strong gradient of SST between 1200 opment can be simulated. In this regard, this particular UTC 9 September and 0000 UTC 1 September.1 The case is well chosen since the total development occurred upper-tropospheric cutoff low essentially disappeared, in about 3 days, which is fairly rapid for tropical cy- presumably because of latent heating, either directly clones. It is interesting to note that some of the cases through diabatic growth of anticyclonic vorticity and PV presented in the literature are chosen speci®cally be- anomalies aloft, or indirectly from deformation at the cause of their long gestation times in order to maximize tropopause induced by the storm out¯ow. the observational sampling of the genesis process. Following this time, Diana moved steadily north and Despite the fairly obvious differences between this northeastward, and, after a roughly 12-h period of weak case and other cases studied, particularly in the ampli- development, once again deepening rapidly, achieving tude of the precursor baroclinic disturbance, our results maximum intensity around 0000 UTC 12 September will show a common theme regarding the importance 1984 with peak sustained winds near 60 m sϪ1. Bluestein of pooling vorticity anomalies2 in the lower troposphere and Marks (1987) studied the inner core structure of the into a sustainable central vortex capable of self-ampli- storm near its peak intensity using airborne radar and ®cation. By choosing a case with a substantial upper- satellite images. The mature hurricane became infamous tropospheric trough and low-level baroclinity, we sur- for its erratic track, executing a full loop near Cape Fear, mise that we can augment the predictability of the event North Carolina, before ®nally making landfall on 13 insofar as we have con®dence in the ability of mesoscale September (Lawrence and Clark 1985). models to predict marine cyclogenesis (Kuo and Low- There are many questions about the Diana life cycle Nam 1990) and some attendant mesoscale features (Kuo that the observations alone have been unable to answer. et al. 1996). The rapid evolution through the genesis The present paper (and a companion article) utilizes phase is also well suited to numerical prediction because numerical simulations with the ®fth generation Penn- of the relatively smaller risk of prediction errors on the sylvania State University±National Center for Atmo- large scales over a short time interval. This highlights spheric Research (PSU±NCAR) mesoscale model in or- the inherent difference one encounters in choosing a der to examine the dynamics of the storm intensi®cation case for numerical versus observational investigation. in more detail and document the critical physical pro- In the remainder of the paper, we ®rst present details cesses and sensitivities for the development of the storm, of our simulation approach (section 2). We then discuss particularly the early stages when the transformation the control simulation in section 3. Sensitivity simula- from cold to warm core took place. An overarching goal tions will be discussed primarily in a companion article. for this study is to quantify the roles of internal dynam- In section 4, a breakdown of the simulated development ics and external processes in the development of Diana. of Diana into three stages is postulated, and the gov- By the former, we mean processes that depend on the erning dynamics of each stage discussed with particular existence of the storm itself. By the latter, we mean emphasis on the intensi®cation to tropical storm processes that determine the environment in which the strength. Finally, we discuss the similarity of our ®nd- storm develops. In the present case, the external in¯u- ings in the broader context of marine cyclones, both ences are represented by a large-amplitude cold trough tropical and extratropical. in the upper troposphere and baroclinity throughout the troposphere. The internal in¯uence is primarily growth 2. Methodology: Numerical simulations through air±sea interaction as the storm matures. Particular questions we address in the context of this As emphasized by Liu et al. (1997), there are few case are the following: numerical simulations of tropical cyclone genesis with 1) How can we understand the process by which Diana enough resolution to resolve the inner core and a large formed from a weak, synoptic-scale baroclinic dis- enough domain to capture the evolving synoptic-scale turbance? What is the role played by preexisting syn- ¯ow and its effect on the cyclogenesis. Thus, the present optic-scale features? study appears unique among simulation studies of trop- 2) How does the incipient development differ from the ical cyclones because we achieve three objectives: 1) eventual transformation into a full-¯edged hurri- high resolution to study the inner core [mostly presented cane? in Part II (unpublished manuscript)], 2) domains large Both questions require simulations that can simulta- 2 Unless otherwise speci®ed, vorticity anomalies refer to mesoscale maxima in the vertical component of vorticity. Once a well-de®ned 1 The SST analysis was digitized from a hand analysis of all the center of circulation is established, vorticity anomalies are de®ned ship and buoy reports obtained for the period 7±8 September. with respect to the azimuthal mean vorticity.

Unauthenticated | Downloaded 09/26/21 04:27 AM UTC 1862 MONTHLY WEATHER REVIEW VOLUME 129 enough to study large-scale motions, and 3) no bogusing of the initial tropical cyclone vortex. The modeling system used here is the PSU±NCAR Mesoscale Model 5 version 2 (MM5) (Grell et al. 1994). The model is nonhydrostatic, compressible, and it in- tegrates the primitive equations with a leapfrog time- stepping scheme combined with an Asselin ®lter. The modeling system offers numerous choices of ``physics,'' that is, distinct representations of various atmospheric physical processes. The control simulation discussed in this article uses the medium-range forecast model plan- etary boundary layer (PBL) scheme (Hong and Pan 1996), the numerical weather prediction explicit microphysics scheme (NEM; Schultz 1995), the Dudhia (1989) radiation scheme, and the Kain±Fritsch cumulus FIG. 2. Domain con®guration for MM5 simulations. Dimensions of scheme (Kain and Fritsch 1993). each domain (north±south by east±west) are shown. The PBL scheme is a ®rst-order closure scheme with vertical mixing dependent on stability and shear. In the Fritsch cumulus scheme on the 9-km domain. We found unstable regime, instantaneous upward transfer of con- that the simulation was signi®cantly improved (relative served variables occurs, attempting to mimic the effects to observations) by including the Kain±Fritsch scheme of strong, large eddies. The NEM scheme is a three- at 9 km. In general, the use of a cumulus scheme at category ice microphysics scheme (rainwater, snow, and horizontal grid spacings of 10 km or less is inappropriate graupel) designed to run ef®ciently. The Dudhia radi- for continental, extratropical convection. However, for ation scheme interacts with clouds but does no spectral the maritime, tropical environment studied herein, it is decomposition beyond long- and shortwave radiation. possible that cumulus towers have a suf®ciently small As mentioned in the introduction, the study of this scale compared to the model grid that the use of a cu- case is partly motivated by the assumption that by hav- mulus scheme is more appropriate. The addition of a ing a baroclinic precursor that is reasonably resolved by fourth domain of 3-km grid spacing, within which no the upper-air network over the Florida peninsula, the implicit cloud scheme is used, will be discussed in Part event may offer greater predictability than is typically II. The primary bene®t of higher resolution is to better seen in tropical cyclone simulations. This will prove to treat convection near the eyewall and produce a more be the case. Nonetheless, there is considerable sensitiv- realistic deepening rate during the intensi®cation to hur- ity of our simulation to the choice of representation of ricane strength. However, the use of ®ner resolution does physical processes such as moist convection and treat- not signi®cantly affect the earlier storm development or ment of the attendant air±ocean interface. We will ex- storm track. plore the causes of this sensitivity in Part II. The choice The control simulation studied herein is initialized at of physics and computation of initial conditions used 1200 UTC 7 September by a method detailed below. here yields a control simulation whose performance rel- Additional simulations show that this is the earliest time ative to the observations is representative of the results that adequate simulations may be initialized, so this time obtained with other choices, but we have not made an is chosen as it covers the entire spinup process. The earnest attempt to optimize the agreement with data. In National Center for Atmospheric Research±National our view, the totality of model behavior must be un- Centers for Environmental Prediction (NCAR±NCEP) derstood and the choice of a control simulation is some- reanalysis data are used as a ®rst guess and for lateral what arbitrary so long as it is useful for understanding boundary conditions on the outermost domain, modi®ed the permutated simulations. by available upper-air and surface observations. As We adopt an interactive grid nesting approach as has shown in Fig. 3, the data over Florida are crucial for been done in most other studies of tropical cyclones. properly analyzing the maximum in PV that de®nes the Here, we use three domains (Fig. 2) with a grid spacing upper-level trough. of 81, 27, and 9 km with domain sizes of 60 ϫ 80, 97 Motivated by a desire to perturb the initial conditions ϫ 97, and 151 ϫ 133 grid points, respectively. Each (Part II) and by a desire to remove any serious imbal- nest is free to feed back information to the next coarser ances in the initial state that may lead to arti®cially large domain (i.e, the domains are ``two-way interactive''). (or small) precipitation early in the simulation, we em- A total of 37 terrain following coordinate surfaces are ploy dynamically balanced initial conditions. These con- used as the vertical discretization. The top of the model ditions derive from the inversion of Rossby±Ertel PV is at about 90 hPa. A time step of 240 s is used on the (Davis and Emanuel 1991) and require simultaneous coarsest grid (domain 1), reduced by a factor of three solution of a relation between PV, geopotential height, within each successive nest. The physical processes are and nondivergent streamfunction, and a balance con- the same on each domain, including use of the Kain± dition, relating geopotential height and streamfunction.

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FIG. 3. Potential vorticity on the 340-K isentropic surface (in PV units, 1 PVU ϭ 10Ϫ6 m2 KkgϪ1 sϪ1), wind on the 340-K surface, and SLP (contour interval is 2 hPa) for 1200 UTC 7 Sep, the start time of the model (t ϭ 0).

The advantage of having an initial state that is balanced in this way is that it is straightforward to perform sensitivity simulations with speci®ed initial PV anomalies and their associated balanced wind, temperature, and pressure perturbations removed (see Part II), similar to a strategy adopted by Huo et al. (1999). Given an analysis obtained from the ®rst guess enhanced with surface and raob data using a simple Cress- man analysis scheme, PV is calculated and inverted sub- ject to the constraints of nonlinear balance (similar to gradient balance), hydrostatic balance, and the de®nition of Rossby±Ertel PV (hereafter simply PV) in terms of the geopotential and nondivergent streamfunction (Da- vis et al. 1996). Balanced vertical motions and divergent FIG. 4. Temperature and wind at 500 hPa for (a) the balanced initial wind were diagnosed, but because of their small mag- state and (b) the initial state obtained after objective analysis. nitudes (typically only about 1±2 cm sϪ1 and 1±3 m sϪ1, respectively) their addition to the initial conditions did not make a noticeable difference in the model in- averaged turning and speed reduction relative to the 1- tegration over the ®rst few hours. Apparently, the model km MSL winds in the standard analysis. In general, the was able to spin up these weak motions quickly. surface winds were turned by an angle of about 15Њ with The effect of balancing the initial condition is to re- a speed reduction of about 20%. In the sea level pressure duce the amount of adjustment in the model, particularly (SLP), there was a difference of about 2 hPa between above the boundary layer where the condition of non- the standard and balanced states, distributed over a large linear balance is more accurate. Figure 4 shows the bal- scale. Despite this, local gradients of SLP were similar anced and standard initial states at 1200 UTC 7 Sep- overall. However, there were some smaller-scale dis- tember. Disagreement between the two is signi®cant, crepancies between standard and balanced SLP distri- particularly in the vicinity of the Nassau sounding where butions. In particular, the effects of an apparently er- the 500-hPa temperature of Ϫ7Њ is not represented in roneous SLP observation over the Gulf of Mexico in the balanced state. Large temperature advections im- the standard analysis are removed by using a balanced plied by the standard analysis are signi®cantly reduced initial condition (not shown). in the balanced state, implying a slower, more gradual Only simulations initiated from the balanced initial evolution. state will be shown. In general, the important differences In order to help preserve the frictional balance within occurred in the ®rst 6 h. Thereafter, both simulations the boundary layer, the winds below about 1 km mean developed storms that were quantitatively similar, mean- sea level (MSL) were adjusted according to the domain- ing that the difference in storm track and intensity is

Unauthenticated | Downloaded 09/26/21 04:27 AM UTC 1864 MONTHLY WEATHER REVIEW VOLUME 129 considerably smaller than differences caused by varying investigating the dynamics of storm genesis, the primary model physics or SST analyses (see Part II). The control focus of this paper. simulation is integrated for 60 h (1200 UTC 7 Septem- ber±0000 UTC 10 September). This is the time required b. System structure for the simulated storm to reach hurricane intensity, although we primarily analyze the ®rst 48 h of the sim- Herein we present an overview of the structural evo- ulation, before the time at which inner core dynamics lution of the storm and the environment as represented associated with eyewall convection become important. by the evolving synoptic-scale disturbances. Maps of mean SLP and hourly accumulated precipitation show that a surface low of modest intensity develops between 3. Description of control simulation 24 and 36 h (Figs. 5a and 5b). Evident at 24 h are numerous localized maxima of precipitation. These re- a. Track and intensity sult from the explicit precipitation scheme in the model, A comparison of the predicted and observed storm which activates over a broad region due to synoptic- track and intensity (Fig. 1) reveals a reasonably accurate scale and mesoscale ascent. Throughout this 12-h pe- prediction, especially considering that there was no bo- riod, there are numerous asymmetries in the pressure gusing of the storm into the initial conditions in this and wind ®elds near the surface. By 36 h, although the case and that there was no continuous data assimilation disturbance has attained tropical storm strength, there as the simulation progressed. The track of the simulated is a relative absence of deep convection near the storm storm appears to agree less well with observations early center. This relative minimum in convective activity per- in the development. Part of this error is due to the fact sists for the next 10 h. that the low-level cyclonic circulation was broad and By 48 h, an intense band of convection erupts on the weak. Bosart and Bartlo (1991) show a well-de®ned low east side of the storm (Fig. 5c). The largest pressure center at 0000 UTC 8 September, but given the distri- gradient, coincident with the strongest winds (not bution of observations and the elongated nature of the shown) is now also located on the east side of the storm, pressure trough, there is some uncertainty as to the lo- marking a major change in structure from 12 to 24 h cation and intensity of the incipient cyclone. More to earlier when the strongest winds were on the northwest side of the storm, augmented by the larger-scale north- the point, the position of the cyclone along the frontal easterlies in the region. Rapid deepening is occurring zone is probably sensitive to mesoscale details that are at 48 h and the storm achieves hurricane strength around not resolved in our initial conditions. However, to cor- 54 h (see Fig. 12), reaching a central pressure of 979 rect this initial error through methods such as inserting hPa by 0000 UTC 10 September, the 60-h prediction an arti®cial vortex would undermine the study of storm (Fig. 5d). formation. As the simulated and observed circulations During the ®rst 24 h of the simulation (through 1200 intensi®ed, the position error became small, less than UTC 8 September), the lower-tropospheric baroclinity 40 km at 0000 UTC 9 September. At this time the central gradually intensi®es due to frontogenesis, depicted in pressures differed by about 1 hPa. Figs. 6a and 6b as the time rate of change of the hor- Errors grew rapidly later in the simulation. Following izontal gradient of potential temperature caused by shear 0000 UTC 9 September, the observed storm tracked and stretching deformation. By 18 h into the simulation, nearly westward before turning northward after 1200 a southwest±northeast elongated band of frontogenesis UTC 9 September, during which time the deepening was is evident at 900 hPa. As is apparent in Fig. 6, the modest. The simulated storm turned northward about western portion of this frontal zone, where Diana de- 12 h earlier and began deepening rapidly by 0900 UTC velops 12±18 h later, lifts northward and intensi®es. 9 September. This deepening preceded a similar deep- At 850 hPa (Fig. 7), the 24-h prediction characterizes ening in the observations by about 18 h, but being pre- the cyclone as a still cold-core disturbance on the south- mature, led to a central pressure error of about 13 hPa western edge of the baroclinic zone. Frontogenesis is after 60 h of integration (0000 UTC 10 September). The still actively occurring near and to the northeast of the track of the simulated storm nearly followed the axis of cyclonic circulation center (not shown) along with an maximum SST during the 60-h simulation whereas the intense thermally direct vertical circulation. A vertical observed storm tracked along the contrast of SST to the cross section oriented normal to the front (and averaged west of the maximum. Note that observed storm posi- over a distance of 180 km perpendicular to the cross tions are shown after the end of the simulation at 1200 section indicated in Fig. 7a) shows a sloping updraft UTC 10 September and 0000 UTC 11 September. The within and above the frontal zone (Fig. 8). The sloping errors in track and intensity late in the simulation would updraft, containing vertical velocities of nearly 1 m sϪ1, limit its practical utility were this an operational fore- produces large precipitation rates (Fig. 5a), implying cast. Despite these errors, the fact that the simulation strong diabatic heating. accurately predicts the timing and intensity of the for- By 36-h a warm-core structure is evident (Fig. 7b) mation of an incipient tropical storm makes it ideal for and the storm has reached tropical storm intensity. Two

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FIG. 5. SLP and hourly precipitation (shading) for (a) 24 h, (b) 36 h, (c) 48 h, and (d) 60 h. Numbers on the ordinate and abscissa refer to grid points within the 9-km resolution domain. The distance between each tick mark corresponds to 9 km. Scale for gray shading is below plot. factors contribute to the warm-core structure. The more in the core, making the overall radial temperature con- important is the formation of localized warm anomalies trast greater than it would be otherwise. By 60 h (Fig. coincident with localized PV anomalies in the lower 7d), in the mature storm, the core temperature has risen troposphere (see Fig. 9), which are, in turn, a result of another 2Њ with the surrounding temperature about the strong condensational heating. A secondary effect is the same as before. Maximum winds at this level are about advection of cooler air around the storm center in a 45msϪ1. manner that resembles an occlusion process. We believe The PV evolution at both lower and upper levels is that this is made possible by the synoptic-scale baro- most interesting early in the development. To summarize clinity present initially. By 48 h (Fig. 7c), air with T Ͻ the evolution of PV in the lower troposphere, we choose 17ЊC completely encircles the storm at a radius of about PV at the 900-hPa level. In the tropical environment 100 km, while the core temperature is almost 20ЊC. This studied here, this level is near or slightly above cloud entwining of cooler air effectively enhances the warmth base and evinces the largest PV perturbations of any

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PV anomalies is consistent with the relatively low altitude at which the vertical gradient of heating occurs within frontal circulations in general. Alternatively, one can see from Fig. 8 that the vertical velocity within the frontal circulation increases markedly between 500 m and 3 km above ground level (AGL) implying a con- centration of cyclonic vorticity in this layer due to vortex stretching. A series of PV anomalies form in the east-northeasterly ¯ow poleward of the frontogenesis evident in Fig. 6 and are advected westward toward the PV anomaly coincident with the circulation center (Fig. 9a). These vorticity anomalies often coincide with areas of explicit precipitation predicted by the model; they are not directly produced by the implicit precipitation scheme. Close in- spection of Figs. 9b and 5a, both valid 1200 UTC 8 September, reveals that many heavy precipitation areas are coincident with positive PV anomalies at 900 hPa. The advection of low-level diabatically produced PV anomalies toward the developing cyclone center was seen in simulations by Zhang and Bao (1996b). Near t ϭ 26 h (Fig. 9d), a merger of PV anomalies occurs as a portion of the elongated strip becomes in- tertwined with an especially strong PV maximum approaching from the east-northeast. This merger marks the transition from southwest±northeast elongated anomalies in PV and vorticity and an associated trough- like circulation in the wind ®eld to a nearly circular, localized distribution of PV and more of an axisymmetric wind ®eld. The merger is probably not adequately described as a barotropic process due to the continuing condensational heating and intensi®cation of the anomaly during the period of 24±30 h. However, the behavior is qualitatively similar to the upscale growth of vorticity well known in two-dimensional turbulence and featured in Ritchie and Holland (1997). The PV anomaly at t ϭ 30 h, following the merger, is coincident with a warm-core structure, with a pronounced warm anomaly at 850 hPa (exceeding 2ЊC). FIG. 6. Temperature, wind, and frontogenesis at 900 hPa on domain This structure is consistent with ¯ow nearly in gradient 2 (27-km resolution) for (a) 1800 UTC 7 Sep, a 6-h forecast; and (b) and hydrostatic balance. To verify the gradient nature 0600 UTC 8 Sep, an 18-h forecast. Temperature is contoured in in- crements of 1ЊC, long barb represents 5 m sϪ1 and frontogenesis is of the balance, we solved the nonlinear balance equation 2 ١␺ ϩ 2Jxy(␺x, ␺y) for a geopotential ␾b ´ f ١ shaded lightly for positive values greater than 10 Ϫ5ЊCmϪ1 dayϪ1 and ٌ ␾b ϭ shaded heavily for values greater than 4 ϫ 10Ϫ5ЊCmϪ1 dayϪ1. Dashed given the streamfunction for the nondivergent wind. box in (b) represents area depicted in Fig. 7. Here all derivatives are taken at constant pressure. For curved ¯ows, this equation closely approximates the gradient wind condition, but is more general. The lateral lower-tropospheric level. At 900 hPa, a strip of PV boundary conditions for ␺ are as de®ned in Davis and forms between about 15 and 19 h, we believe mainly Emanuel (1991). We ®nd that the temperature derived in response to organized latent heating within the frontal from ␾ exhibits a warm core that is about 1ЊC warmer circulation. Such large values (several PV units3)ofPV b than the 3Њ±4ЊC central temperature anomaly at 850 hPa are known to form in frontal circulations (e.g., Emanuel shown in Fig. 7b. 1985). Following this time, from 21 to 24 h, there occurs Because the PV and vorticity anomalies were pro- the burst of convective activity noted in Fig. 5a, which duced at low levels within the frontal circulation, the generates more vorticity and PV anomalies within the balanced ¯ow associated with these anomalies is warm lower troposphere. The seemingly low altitude of the core from the outset. No downward development of a midlevel PV anomaly is needed to achieve a warm-core 3 1 PVU ϭ 10Ϫ6 m2 KkgϪ1 sϪ1. structure in this case. After the merger, the PV in the

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FIG. 7. Wind and temperature at 850 hPa for (a) 24 h, (b) 36 h, (c) 48 h, and (d) 60 h. Winds are plotted at alternate grid points. core of the cyclone is suf®ciently large that subsequent ing of 8 September, the storm rapidly lost its frontal PV anomalies tend to be swept around the cyclone and cyclone structure and the wind and pressure ®elds be- either dissipate or merge with the central PV anomaly came more axisymmetric. During this period, the storm (Figs. 9d and 9e). One will note banded structure in the was named, suggesting that at least modest intensi®- PV ®eld surrounding the core at these times. Only the cation occurred to increase the winds past tropical storm band to the north of the storm center is collocated with strength. Furthermore, satellite imagery supports the no- a precipitation band. tion of strong and widespread convection erupting be- While it is not possible to directly verify the evolution tween 0900 and 1500 UTC 8 September very close to of the low-level PV described above, some important where the model predicts it (see Figs. 11a and 11b). consistencies between the simulation and observations This convection subsides by 0000 UTC 9 September, can be pointed out. First, BB show that during the morn- as it does in our simulation.

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it through deformation in the process of axisymmetrization (Fig. 10d). While the data offshore are insuf®cient to verify much of the upper-level structure, indirect veri®cation is possible through satellite imagery. To facilitate comparison, the cloud-top temperature is deduced from MM5 output (Stoelinga and Warner 1999) and shaded according to the National Environmental Satellite Data and Informa- tion Service operational gray-scale enhancement algo- rithm. In Fig. 11, the enhanced infrared satellite image is also shown. At 1200 UTC 8 September, a large area of cold cloud tops (less than Ϫ58ЊC, shown as black) is evident near the nascent storm center, indicating an erup- tion of deep convection. Although the model-derived cloud-top temperatures show a broader distribution of deep cloud with somewhat greater minimum temperatures, the timing of an outbreak of deep convection appears consistent in both model and observations. The basic cloud structure, with a dry slot and a southwest± FIG. 8. Vertical cross section (see Fig. 7a for orientation) of relative northeast-oriented primary cloud band, is similar in both humidity (Ͼ90% shaded), normal wind component (contour interval 5 msϪ1, potential temperature (contour interval 3 K), and air¯ow in the model and observation. The observed clouds are more plane of the section (vectors) at 1200 UTC 8 Sep, the 24-h prediction. extensive, especially poleward of the storm. By 0000 UTC 9 September, the extent of the deep convection has diminished in both observations and in It appears that the transition from baroclinic cyclone the model (see also Fig. 5b). The dry slot is readily to nearly axisymmetric tropical storm coincides with a visible in both, suggesting an accurate placement of the burst of convection in the real atmosphere and in the rising and sinking motions and probably a fairly ac- model, favoring a local intensi®cation of the cyclonic curate depiction of the upper-level trough and down- circulation. Although we cannot verify the details of the stream ridge. Areas of discrepancy include the spurious merger of PV features seen in our simulation, the pro- convection noted over west-central Florida and a smaller pensity of positive PV anomalies to merge is well known northward extent of the cirrus shield near the southeast and probably occurs during the tropical storm formation U.S. coastline. However, these areas are not important stage in the real atmosphere. to the storm development. Now turning to upper-level PV, we focus on the 340- K surface (about 250 hPa). As noted, the PV initially 4. Three stages of deepening exhibits a north±south elongated maximum over Flor- ida, with low-PV air to the east (Fig. 3). Between 12 Evidence for three distinct stages of deepening of and 24 h the dramatic in¯uence of latent heating is seen Diana is presented in Fig. 12. Here we show the natural as the highly divergent and dif¯uent out¯ow pattern acts log of the maximum vorticity at the lowest model level to thin the PV strip over northern Florida (Figs. 10a and (about 40 m AGL) versus time. To select a scale rep- 10b). There is also a clear importance of direct diabatic resentative of the core of the cyclone, the vorticity is redistribution of PV owing to the rapid appearance of averaged over a 9 ϫ 9 gridpoint box (81 km ϫ 81 km). negative PV values within the otherwise positive upper- Prior to about t ϭ 34 h, there is consistent growth of tropospheric anomaly (Fig. 10a). Both diabatic and ad- the vorticity perturbation, with an e-folding time of vective redistribution of PV lead to a localization of the about 12±18 h. For the subsequent 10 h, there is little PV on the southern end of the trough (Fig. 10b). This intensi®cation of the circulation, although the central cutoff low feature then moves slowly eastward, shed- pressure during this period did fall about 3 hPa. Fol- ding a fragment of PV, which is subsequently advected lowing this period, rapid deepening ensued, at a rate over the cyclogenesis area between 24 and 36 h (Figs. that was comparable to the earlier growth of vorticity. 10b and 10c). The burst of deep convection noted in By 57 h, much of the deepening was over as the storm Fig. 5 coincides with the shedding of this PV feature. continued to move northeastward. Once the warm-core disturbance is established and It is unclear whether the same three-stage behavior deepening toward hurricane intensity commences there was present in the observations. However, Fig. 9 from is a marked growth of a diabatically generated anomaly Lawrence and Clark (1985) does depict a nonmonotonic on the 340-K surface. This cyclonic anomaly quickly deepening of the storm. In particular, between 1600 overwhelms the surrounding remnants of the preexisting UTC 9 September and 0600 UTC 10 September, the upper trough. The cyclonic circulation above the storm central pressure of the storm did not fall. While this core acts to shred the upper low to the south and destroy period of nondeepening lags the analogous period in the

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FIG. 9. Ertel PV (PVU, note grayscale) and wind at 900 hPa. control simulation by 18 h, the length of this period and through 0000 UTC 10 September, its maximum intensity the geographical region in which it occurs are similar. (occurring just after 0000 UTC 10 September) was se- One might argue that the simulated deepening of Diana riously de®cient. This is speculation, and it may be that all occurred on a compressed timescale relative to the there is not a one-to-one mapping of the details in the observations, perhaps related to the fact that its trans- deepening time series between the observed and sim- lation was too rapid and its northward turn occurred too ulated storms. Regardless, the similar degree of non- soon. This is consistent with the fact that, while the monotonicity in the observed and simulated deepening simulated storm was deeper than the observed storm time series is suggestive of distinct periods of differing

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FIG. 10. Wind and PV on the 340-K isentropic surface for (a) 12 h, (b) 24 h, (c) 36 h, and (d) 48 h. Plotting convention for winds is as in Fig. 7. The tropical storm symbol indicates storm center in (c) and (d). Lightly shaded areas denote negative PV. dynamics. We now investigate these three stages of the azimuthally, we instead display the maximum hourly simulated storm evolution in more detail. rainfall with each 9-km-range ring. To improve temporal Further evidence that distinct processes were occur- continuity, we average the precipitation over a 3 ϫ 3 ring in each of the three stages is brought out through gridpoint box before ®nding the maximum. Between 20 the use of time±radius representations of various pa- and 35 h (Fig. 13), there is a clear signal of precipitation rameters. In what follows, the ®xed MM5 domain was features moving inward toward the center of the incip- remapped into a coordinate system moving with the ient storm. Another, notably weaker precipitation max- point of maximum vorticity averaged over a 9 ϫ 9 grid. imum appears to move inward between 38 and 42 h, For some purposes it was necessary to perform azi- but generally the period from 35±44 h exhibits a gradual muthal averages and this was done for range rings of decrease in the intensity of precipitation. The transition 9-km width (25 km width for 200-hPa ®elds) by simply to hurricane intensity, beginning at about 45 h, shows averaging the parameter in question over all grid points a clear preference for precipitation extrema between 30- that lay within a given ring (r1 Ͻ r Ͻ r2). and 60-km radius. This is essentially the eyewall, al- We ®rst examine precipitation evolution in time±ra- though, as noted earlier, the storm does not possess a dius space. Rather than simply average the precipitation symmetric eyewall for most of its life cycle.

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FIG. 11. Comparison of simulated cloud-top temperatures deduced from MM5 cloud ice, water, and hydrometer, and enhanced IR satellite photographs: (a) enhanced IR at 1200 UTC 7 Sep, (b) model at 1200 UTC 8 Sep, (c) enhanced IR at 0000 UTC 9 Sep, (d) model at 0000 UTC 9 Sep.

The precipitation anomalies featured in Fig. 13 are gests a profound importance of asymmetries in the early mainly produced by the model's explicit microphysics stages of development. In order to investigate the rel- scheme. The large region in Fig. 13 devoid of shading, ative importance of asymmetries to the mean radial cir- primarily for r Ͼ 100 km and t Ͼ 35 h is dominated culation, we ®rst appeal to the vorticity equation: by the implicit scheme. The lack of features in this region suggests a nearly statistically steady distribution vץ ␨ץ .of parameterized convection (ϫ F. (1 ١ ´ ˆv␩ ϩ wkˆ ϫϩk ´ ϭϪ١ zץt ΂΃ץ a. Low-level vorticity Here, ␨ is the vertical component of relative vorticity, We note that a depiction of vorticity extrema in the ␩ is the absolute vorticity, w is the vertical velocity, F time±radius domain exhibits some similarity to the pat- is the sum of frictional and dissipational forces, and the tern seen in Fig. 13, with positive anomalies moving vector wind and gradient operators are two-dimensional inward until about t ϭ 34 h (not shown). Figure 9 sug- (horizontal plane). We have neglected the baroclinic

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FIG. 12. Time series of the natural log of maximum relative vorticity, averaged over a 9 ϫ 9 gridpoint box, maximum tangential wind, and minimum SLP. The vorticity has been scaled by 104 before computing the natural log.

١p) because its vertical component tends the eyewall. The term F t is the azimuthally averaged ١␳ ϫ) term to be quite small.4 tangential frictional force. In cylindrical coordinates, (1) becomes Given that the mean vorticity can be expressed

( r␷)ץ u 1ץץ ␷ 1ץץ ␨ 1ץ ϭϪ ru␩ ϩ rw Ϫ r␷␩ Ϫ w ␨ ϭ , (4) rץ z rץ ␣ץzrץr ΂΃΂΃ץtrץ ϫ F. (2) we can directly integrate (3) for the tendency of the ١ ´ ˆϩ k tangential wind. At r ϭ 0, ␷ ϭ 0, u ϭ 0, and all per- We have used u and ␷ to denote the radial and tan- turbation quantities vanish, hence the acceleration at any gential wind components, respectively, and ␣ is the az- given radius is determined solely by the local ¯uxes imuthal angle and r is the radius. We then may rewrite (3) as De®ning an azimuthal mean by overbars, (2) can be ␷ץ␷Јץ ␷ץ -written as an equation for the rate of change of sym ϭϪuЈ␩ЈϪu␩ Ϫ wЈϩw Ϫ F . (5) z tץ zץ tץ :metric vorticity ␷ We average the implied acceleration from the groundץ␷Јץץ ␨ 1ץ ϭϪ ruЈ␩Јϩru␩ ϩ rwЈϩrw ϩ rFt . to about 2-km MSL (the lowest 10 model levels) and zץ zץ rץtrץ ΂΃depict the results in time±radius format in Fig. 14. Rath- (3) er than simply show all terms individually, it is more The ®rst two terms on the right-hand side are, re- instructive to combineu␩ with F t. This is because a spectively, the eddy ¯ux term and the mean radial con- portion of the low-level convergence occurs in response vergence term. The eddy ¯ux term contains the effects to dissipation, primarily surface friction, within the of asymmetries such as described above. The last two boundary layer. By grouping those two terms we see terms arise partly from tilting effects and represent ver- the net contribution toward intensi®cation. In addition, tical ¯uxes of horizontal momentum. In particular, the the horizontal diffusion will become important once a momentum transport by the azimuthal mean circulation pronounced tangential wind maximum forms, acting to can be a signi®cant term in a mature hurricane within broaden the tangential wind pro®le. At the top of Fig. 14c, we note that initially, there is little intensi®cation between 19 and 24 h. This is con- 4 As we will be considering the azimuthal mean vorticity budget, sistent with Fig. 9. After this time, acceleration of the only the deviations from the azimuthal mean will contribute. For a tangential velocities is apparent within a radius of about scaling estimate, given a length scale of 100 km, a typical variation in density (due to temperature only; the pressure contribution to den- 250 km, corresponding to the eddy ¯ux term (Fig. 14a). sity variations does not contribute to the baroclinic term) is perhaps As suggested by Fig. 9, the eddy ¯ux comes about due 1% and a typical pressure variation is 1 hPa, giving a vorticity ten- to the diabatic generation of vorticity and PV anomalies dency of the order of 10Ϫ10 sϪ2. This is about an order of magnitude and their subsequent transport and propagation inward. smaller than the other terms considered. Note that even within frontal zones this scaling holds because the principle gradients of density The vortex merger process noted in Fig. 9 at about t ϭ and pressure are parallel and do not contribute to the generation of 25 h is seen in Figs. 14a and 14b as a contribution due vertical vorticity. to both the mean and eddy terms. Once the radius of

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1997). The two perspectives can be contrasted by the extent to which each depends on mean, radial gradients of vorticity (or more generally, PV). In the former, no gradients are necessary and the dynamics can be en- capsulated by a model in which vortex patches merge. In such a model, all vorticity gradients exist on an in- ®nitesimal ring at the edge of each patch. In the vortex Rossby wave view, a distributed gradient of symmetric vorticity is crucial for radial propagation of vortex Ross- by waves and radial transport of vorticity into the core of the storm. By examining radial pro®les of mean absolute vorticity and the standard deviation of eddy vorticity about this mean (for each radius interval), we can deduce ®rst whether wave propagation is possible (excluding the edge waves that could exist on a concentrated vorticity gradient; these are ineffective transporters of vorticity) and second if a vorticity gradient exists, whether the behavior of the asymmetries is characterized by linear or nonlinear waves. Figure 16 shows radius±height pro®les of the mean absolute vorticity and the standard deviation of the eddy vorticity with respect to the azimuthal mean, averaged FIG. 13. HovmoÈller depiction (time vs radius) of the maximum precipitation within each radius ring averaged over a 3 ϫ 3 gridpoint within each range ring and averaged between 23 and 34 box. Each radius ring is 9 km wide. h. If we assume a characteristic eddy scale of about 50 km (crudely estimated from Fig. 9), the region just outside the radius of maximum wind assumes a local Beta± maximum wind has been established at about 45 km, Rossby number R␤ ϭ ␨ˆ/⌬␩␨of less than unity. Here, ˆ the eddy term becomes negative within and positive is the characteristic eddy vorticity (obtained from the outside it during the times when the storm intensi®es standard deviation of vorticity) and ⌬␩ is the variation (up to 35 h and again after 44 h). This acts to concentrate of radial mean vorticity over a radius L. A local estimate vorticity near the radius of maximum wind. Throughout of R␤ is obtained by dividing the standard deviation of the remainder of the ®rst deepening stage, the mean ¯ux vorticity by the variation of␩ over 50 km (L). At all term dominates the intensi®cation and shifts the radius radii greater than about 70±80 km, R␤ Ͼ 1 and the of maximum wind in farther while the eddy term slowly disturbances are inherently nonlinear. Thus, over much accelerates the tangential wind farther out. It is clear of the region where the eddy term contributes to cy- from Figs. 14 and 9 that the ®rst important stage in the clonic spinup, the dynamics appears nonlinear, with intensi®cation to a tropical storm is the amalgamation large-amplitude vorticity anomalies, de®ned as depar- of vorticity anomalies into a coherent, more circular tures from an azimuthal mean, superposed on a rela- central vorticity and PV maximum. tively weak azimuthal mean vorticity gradient. The net effect over the ®rst deepening stage can be The foregoing discussion is important as it suggests summarized by accumulating all terms and comparing that the dynamics in the present case would not be ad- them to the total acceleration over this time period (23± equately described by a linear wave-mean ¯ow model. 34 h, Fig. 15). Figure 15 shows all the same terms in However, it is equally clear that the radial distribution the tangential momentum budget as in Fig. 14, again of symmetric vorticity cannot be adequately modeled as grouping dissipative terms with the mean ¯ux term. a simple Rankine vortex. There is an appreciable non- Good agreement is seen between the total velocity zero vorticity gradient out to at least 150-km radius. change and the sum of all terms (the estimated change) Some aspects of the low-level vorticity behavior, par- except at the radius of maximum wind in spite of using ticularly the merger near 25 h, resemble the conceptual model output with only hourly resolution to estimate model of Ritchie and Holland (1997), where vortex the acceleration. The results indicate that the mean ¯ux merger dominates. Some aspects represent the vortex term dominates within 75-km radius and the eddy term Rossby wave paradigm of Montgomery and Kallenbach dominates between 75- and 175-km radius. (1997) and Montgomery and Enagonio (1998), in which Having shown the importance of the eddy vorticity waves propagating on a nonzero vorticity gradient ¯ux ¯ux, a remaining question is whether the physical mech- cyclonic vorticity into the core. The relatively rapid anism producing the ¯ux is the merger of coherent struc- growth of the vorticity in this case (e-folding in about tures (Ritchie and Holland 1997) or ¯uxes induced by 12 h) may result partly from a complementary operation vortex Rossby waves (Montgomery and Kallenbach of vortex merger and Rossby wave mechanisms. How-

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FIG. 14. HovmoÈller depiction of (a) tangential momentum tendency due to eddy ¯ux term and (b) tangential momentum ¯ux tendency due to mean convergence term. The contour interval in (a) and (b) is 0.5 m s Ϫ1 hϪ1. (c) The tangential wind with a contour interval of1msϪ1. Labeled contours in (c) are reproduced as gray solid lines in (a) and (b) for reference. In (a) and (b) negative values are denoted by dashed lines and the zero contour is a heavy solid black contour. All quantities represent averages over the lowest 10 model levels (1.8 km). A single pass of a 2-⌬x smoother has been applied to the ®elds in (a) and (b). ever, an element of the above theories that is neglected the maximum radial out¯ow is located near r ϭ 150 but probably important here is that condensational heat- km and is only about 3 m sϪ1. ing seems to accompany at least some of the vortex The overall minimum in the symmetric out¯ow is mergers. Thus the strength of the merged PV or vorticity found around t ϭ 45 h, the start of the rapid deepening anomalies appears greater than the sum of the anomalies to hurricane intensity. Following this time, the sym- prior to the merger. metric out¯ow increases markedly. Cyclonic vorticity becomes pronounced within the core of the storm sur- rounded by anticyclonic relative vorticity and only b. Upper-level vorticity weakly positive absolute vorticity. Between 45 and 60 A HovmoÈller depiction of vorticity and mean radial h, there is also the suggestion of outward moving fea- velocity at about 200 hPa indicates a large-scale diver- tures in the absolute vorticity ®eld. The translation speed gence above the developing tropical storm until t ϭ 34 of these is estimated to be about 9 m sϪ1, considerably h, after which the divergence shifts inward and weakens faster than the mean radial motion. Assuming this mo- (Fig. 17). This divergence is clearly visible in Fig. 10. tion represents the translation of material entities, the The period of weak divergence aloft coincides well with fact that the speed is uniformly greater than that of the the period of minimal intensi®cation. During this period symmetric out¯ow implies that asymmetries are im-

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FIG. 15. Radial pro®le of eddy (thin solid), mean (heavy solid), and total momentum (thin dashed) tendencies integrated from 23 to 34 h (1100 UTC 8 Sep to 2200 UTC 8 Sep). The heavy dashed line represents the total simulated tangential wind change during the period. Flux quantities are de®ned as in Fig. 14. portant in the expulsion of low vorticity air within the FIG. 16. Height±radius depiction of azimuthal mean absolute vorticity (thin lines) and the standard deviation of absolute vorticity with storm out¯ow. respect to the azimuthal mean (heavy lines). Both quantities are av- An analogous diagnostic of the vorticity ¯ux terms eraged from 23 to 34 h and are expressed in units of 10 Ϫ4 sϪ1. as presented in Figs. 14 and 15 reveals that the mean term contributes to a large-scale anticyclonic vorticity tendency, as expected. The perturbation ¯ux term be- tation of the well-known observation that in cases of haves similarly at upper levels as at low levels in that notable in¯uence of upper-tropospheric troughs, the sign there is a net ¯ux convergence of vorticity and a ten- of the convergence of eddy angular momentum ¯ux is dency to increase vorticity due to the eddy term in (3), consistent with whether one expects deepening of the although at high levels this term is dominated by the surface cyclone (¯ux convergence) or ®lling (¯ux di- mean term. However, the nature of the correlation between radial wind and vorticity anomalies is different at high levels versus low levels. The main effect of the asymmetries is to transport low-vorticity air outward at high levels as opposed to the inward transport of high- vorticity air at low levels. As was evident from Fig. 10, especially early in the development (up to about 33 h), the out¯ow aloft is itself highly asymmetric, being almost entirely northward directed. There are different ways to view the cause of this asymmetry. One is that there is a synoptic- scale asymmetry in upper-level PV imposed by the presence of the weak baroclinic disturbance and the trough fracture process, which leads to high PV to the south of the developing disturbance and low PV (and weak inertial stability) to the north, on the anticyclonic shear side of the polar jet. Studies of convection in such in- homogeneous environments (e.g., Blanchard et al. 1998) indicate that such asymmetries in the environment pro- foundly affect the out¯ow characteristics of organized convection. In this case, all the low PV air will be trans- ported northward in the convective out¯ow, while high PV air is advected toward the storm from the south. The result is a negative (cyclonic) eddy ¯ux of vorticity and PV aloft, which will tend to increase vorticity over the FIG. 17. HovmoÈller depiction of radial wind and absolute vorticity center of the storm. at 200 hPa. Here, 25-km radius bins are used for azimuthal averaging. There are implications here regarding the interpre- The contour interval for the radial wind is 1 m s Ϫ1.

Unauthenticated | Downloaded 09/26/21 04:27 AM UTC 1876 MONTHLY WEATHER REVIEW VOLUME 129 vergence) (Molinari and Vollaro 1989; DeMaria et al. 1993). However, the physical link between upper-tropospheric eddy angular momentum ¯uxes and low-level development has remained elusive. In the present case, the link would seem to be more associative than causal. There is a basic asymmetry in the upper-level PV, vorticity, and storm out¯ow that is provided by the weak baroclinic disturbance present initially and by the ridg- ing to the north of that disturbance. This asymmetry is also precisely the asymmetry needed for mesoscale vertical motion, which acts to focus the convection, which, in turn, produces the low-level PV anomalies that are deemed critical to the early development. One could argue that it is the widespread upward motion that is key for organizing the latent heating, not so much the increase of vorticity or angular momentum aloft, though both tend to occur simultaneously. The interpretation is clear in terms of a vorticity ¯ux or a nonadvective ¯ux of PV. From this perspective, the notion of direct downward transport does not exist FIG. 18. Balanced horizontal wind and vertical motion at 700 hPa (Haynes and McIntyre 1987). Because of the divergence for 1200 UTC 8 Sep (t ϭ 24 h). Vertical motion (cm sϪ1) is shaded, form of (3), vorticity can only be ¯uxed laterally. Thus, with negative values outlined with solid lines as well. Also shown the effect of an eddy ¯ux of vorticity aloft can only be are black circles indicating approximate locations of regions of pre- Ϫ1 indirect and must, at a minimum, involve a redistribu- cipitation greater than 12 mm h (see Fig. 5a). tion of vorticity and PV through diabatic processes. These processes are functions of the mesoscale and syn- recent guess for omega. The resulting vertical motion optic-scale vertical motions. This redistribution can be is converted to vertical velocity (cm sϪ1) for display. realized as both enhancement of a core region of high We use a balanced equation system for computing ver- vorticity through axially symmetric convergence acting tical motion rather than a spatial or temporal average on local absolute vorticity and through axisymmetri- of the model vertical motion because the latter will zation of vorticity and PV anomalies produced at con- strongly alias the convective motion that is occurring. siderable distances (up to 200 km or more) from the By using the PV and omega equations, we better isolate cyclone center. In the present case, both are crucial. the larger scales because convective motions and fast- It is possible to link the formation of the PV and timescale buoyancy oscillations project weakly onto the vorticity anomalies at low levels with ascending motion PV and hence the computed vertical motion. on the meso- and synoptic scales. To demonstrate this, The technique does not always converge to a solution, we ®rst consider the quasi-balanced vertical motion ob- though in the present case convergence was obtained tained by inverting the balanced omega equation. The for all attempts on domain 1. Attempts to invert PV on details of the calculation are outlined in Davis and domain 2 proved largely unsuccessful, primarily due to Emanuel (1991). We perform the calculations on domain the extremely large area of negative PV in the upper 1 (81-km grid spacing), using the PV, potential tem- troposphere that grew as the storm developed. The ome- perature, and relative humidity de®ned on that domain. ga equation solver also does not converge uniformly in The procedure for inverting the PV is identical to that all cases, particularly if the variations in the moist static used to de®ne the initial condition of the model simu- stability from one iteration to the next are too great. lations. Using the balanced ®eld resulting from this in- Again, however, convergence (maximum change of ver- version, we solve the omega equation and the tendency tical motion less than 0.01 cm sϪ1 from one iteration to equations for the nondivergent streamfunction and geo- the next) was obtained on domain 1 for all times of potential as well as the mass continuity equation. The interest. effects of condensational heating are incorporated as a From Fig. 18, it is apparent that the area of balanced reduced static stability where the air is ascending and ascent at 24 h is coincident, or slightly downshear from the relative humidity (adjusted for ice saturation below the areas of heavy precipitation (see, e.g., Fig. 5) noted 0ЊC) is greater than 96%.5 Because the location of as- on the 9-km domain (domain 3). The area is also slightly cending motion is not known a priori, the solution tech- upstream relative to the convective elements, consistent nique allows the effective moist static stability to vary with their westward movement. The area of ascent at from one iteration to the next according to the most 700 hPa (and at 500 hPa, not shown) coincides with lower-tropospheric warm advection, which is, in turn, 5 As long as the value chosen is greater than about 95%, the answer part of the weak baroclinic cyclone developing in the is not sensitive to the exact choice. area. It should be noted that the full vertical motion

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FIG. 20. Four trajectories ending at 50 m AGL at 0800 UTC 9 Sep (44 h). Selected times along trajectory 12 are labeled. Dots at 32-h and 44-h indicated locations for soundings shown in Fig. 22. Relative humidity at 44 h at 50 m MSL is shaded for values exceeding 70%.

ifestation of a Lagrangian increase for most of the par- FIG. 19. HovmoÈller depiction of water vapor mixing ratio at the lowest model level (about 40 m AGL). The contour interval is 0.25 cels. This Lagrangian increase is evident from the en- gkgϪ1. semble of trajectories depicted in Fig. 21. The increase is particularly rapid between about 38 and 44 h, in ac- cord with the Eulerian perspective in Fig. 19. Note that ®eld, which contains the imprint of convection on the nearly all of these trajectories are con®ned to the lowest inner domains, is substantially more widespread and 200 m MSL during their history. more intense than the part diagnosed through the omega To examine the evolution of the thermodynamic pro- equation. Nonetheless, the balanced portion of vertical ®le near the storm center, we show soundings following Ϫ1 motion, despite being only 1±3 cm s , is strong enough the path of parcel 12 (Fig. 22). The ®rst sounding (30 to cause important changes in the low-level sounding h) is initially characteristic of a frontal environment, structure as air is lifted within the frontal zone on time- with relatively cold and dry air at low levels beneath a scales of several hours. weak inversion, above which the air is moist and neutral or slightly conditionally unstable. This pro®le warms c. Boundary layer water vapor and midtropospheric and moistens notably during the ensuing 14 h. The in- moistening version disappears and the ®nal state is one in which boundary layer parcels exhibit small convective inhi- Following the initial deepening phase during which bition and small convective available potential energy. the storm attained marginal tropical storm strength in the model, there was a period of about 10 h when vorticity increased little and pressure fell by only 3 hPa. This period is nonetheless important for the eventual deepening into a hurricane as the so-called internal processes begin to dominate the evolution of the storm. By this we mean that ¯uxes of water vapor from the ocean are now more driven by the storm itself than by the synoptic-scale environment. A HovmoÈller depiction of water vapor at the lowest model level is shown in Fig. 19. An increase from about 16.5 to nearly 18 g kgϪ1 is apparent between t ϭ 34 h and t ϭ 44 h within about 100 km of the storm center. This is consistent with an elevation of near-surface relative humidity within a ring of 40±80-km radius by 44 h (0800 UTC 9 September; Fig. 20). Trajectories ending on the east side of the storm's circulation at 44 h, a FIG. 21. Lagrangian time series of water vapor mixing ratio fol- subset of which are shown in Fig. 20, reveal that the lowing 19 boundary layer parcels ending at or slightly east of the local increase in water vapor mixing ratio is the man- storm center at 44 h.

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FIG. 23. Trajectories ending at 2 km MSL at 0800 UTC 9 Sep. The altitude of parcels is graphed based on hourly values along the trajectory to quantify signi®cant altitude changes. FIG. 22. Skew T±log p depiction of temperature and dewpoint temperature pro®les along trajectory 12 at 32 and 44 h (see Fig. 20 for locations). dependent on the elevated SSTs within the path of the storm. We note that the adjustment process depends on the action of convection over the trajectory of the parcel. In particular, some of the adjustment is done with the d. Hurricane formation Kain±Fritsch scheme. This effectively prevents the The predicted storm deepens about 22 hPa in the time boundary layer from building up conditional instability. between 45 and 60 h, with peak deepening exceeding Removal of the frontal inversion also indicates meso- 2 hPa hϪ1. By 57 h, the maximum wind at the lowest scale lifting of air in the lower troposphere. model level exceeds 40 m sϪ1 while the mean tangential Parcel trajectories ending at 2 km AGL near and to wind is about 39 m sϪ1 at this time. By about 54 h, a the east of the surface low position reveal that mesoscale well-de®ned eye is visible (Fig. 24) and the eye tends lifting occurs and is fairly vigorous (Fig. 23). Ascent to grow in size with time. The grid spacing of 9 km is rates during the period are typically 10 cm sϪ1 in un- arguably not adequate to study the eye dynamics. Sim- saturated air. Hence, parcels originating near the top of ulations performed at 3-km resolution (Part II) will be the boundary layer can reach saturation in as little as 2 examined extensively to reveal details about the eye and h. While this mesoscale lifting is present since the start eyewall formation. of the simulation, only during the period preceding the As has been mentioned, the primary deepening mech- hurricane genesis is this lifting focused near the radius anism during the last 16 h of the simulation is the release of maximum wind and coupled with the boundary layer of latent heat by the condensation of water vapor ex- warming and moistening in the absence of a frontal tracted from the ocean by the tangential circulation of inversion. Deep convective overturning begins around the storm itself. A sensitivity simulation was performed, 44 h. The nearly saturated conditions (note humidity detailed further in Part II, in which the maximum wind around the storm center at 44 h in Fig. 23) would lead velocity allowed in the computation of surface rough- to a relative absence of unsaturated downdrafts, imply- ness was 15 m sϪ1, effectively eliminating the feedback ing an ef®cient development of the classical vertical mechanism between ¯uxes and storm intensity for wind circulation within a warm-core vortex that is a signature speeds greater than this threshold. Not surprisingly, the of the developing hurricane. This signature was noted simulation with reduced ¯uxes revealed a storm that was earlier in terms of the rapid acceleration of the radial 17 hPa weaker by 60 h, though only 2 hPa weaker by out¯ow aloft and in¯ow at low levels within 200 km 45 h. of the storm center. Although air±sea interaction accounts for much of the Our results are consistent with earlier work espousing total deepening during this phase, the storm structure the importance of elevated humidity in the lower- and and details of the temporal variation of the deepening midtroposphere tropical cyclogenesis (McBride and appear rather complex. The high-resolution simulation Zehr 1981; Bister and Emanuel 1997). In Part II, we discussed in Part II reveals numerous asymmetries near will show how the onset of rapid deepening is strongly or slightly inside the radius of maximum wind during

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maxima of low-level PV, which are advected toward and merge with the PV at the center of the nascent low. This merger process transforms a distributed set of PV anomalies into a coherent, nearly circular PV maximum at the core of Tropical Storm Diana. The vortex produced in the ®rst stage of development is strong enough to produce locally enhanced ¯uxes of latent heat from the ocean surface. This increases the water vapor in the boundary layer near and inside the radius of maximum wind over a period of about 10 h. There is a concomitant increase of water vapor (and relative humidity) above the boundary layer over the same area. Despite focusing on a single case, we believe that the present study supports a more general viewpoint of mesoscale cyclogenesis, regardless of the label of tropical or extratropical. We believe that the distinction between these systems is not so clear. There is the obvious fact that numerous extratropical cyclones develop tropical- cyclone-like structures in their mature stages (Bosart 1981; Gyakum 1983; Neiman et al. 1993). There is the more subtle point that none of the dynamics discussed about the initial development of Diana (at least through about 36 h) is peculiar to tropical cyclogenesis. The vorticity dynamics that appear so crucial herein may be FIG. 24. Model-derived cloud-top temperature for 1800 UTC 9 Sep representative of the development of mesoscale cy- (t ϭ 54 h). Color scale as in Fig. 11. clones within larger cyclones. Indeed, even idealized simulations of baroclinic cyclogenesis in moist environments (Montgomery and Farrell 1993) reveal be- this phase of evolution, and these appear to strongly havior reminiscent of the development of Diana.6 It ap- modulate the storm deepening on timescales of a few pears that the fundamental issue is the ability of syn- hours (approximately the angular frequency of the optic-scale cyclones to develop mesoscale rotational storm). features within their circulations, which may intensify by processes other than baroclinic conversion of avail- 5. Conclusions able potential energy. Typically, this occurs in marine cyclones where mesoscale vortices are able to tap the The present study has described the transformation latent energy reservoir contained in the ocean. of a synoptic-scale baroclinic disturbance into Hurricane While the transformation to warm core is a critical Diana as occurring through three distinct development issue in terms of subsequent ampli®cation by air±sea stages. The ®rst is the baroclinic development on the interaction, it appears almost as a by-product of the synoptic scale. The second is the scale contraction of vortex merger described herein and the adjustment of the synoptic-scale disturbance and spin up of a meso- the merged vortex to a balance state. A localized PV scale vortex to marginal tropical storm strength. The maximum at 900 hPa will have a warm-core structure third is the warm-core vortex ampli®cation to the fully if balanced. An important aspect of this case is that the developed hurricane through air±sea interaction. diabatic heating occurs within a frontal circulation, Our results are based on a simulation with the PSU± hence the PV anomalies produced are located at low NCAR MM5, initialized using the NCEP±NCAR re- levels (e.g., Emanuel 1985). This contrasts to the pro- analysis data and conventional surface and upper-air duction of midlevel PV anomalies in mesoscale con- observations at 1200 UTC 7 September 1984. Tropical vective systems, which must ``grow downward'' to be- storm formation occurs within about 36 h after initial- come warm core. ization, and hurricane formation about 18 h after that. A related, important factor in this case is that the low- The ®rst development period is characterized by the level PV anomaly following the merger must be suf®- appearance of mesoscale features within the synoptic- ciently strong so as to dominate other PV anomalies and scale cyclone. First an east±west maximum of PV forms that its warm temperature anomaly must be larger than in response to condensational heating. Then a strong the background baroclinity in order for the secondary, burst of convection over a mesoscale region, triggered by an increase in low-level frontogenesis and the ap- 6 Montgomery and Farrell used the case of Diana as partial mo- proach of a mobile trough aloft, produces numerous tivation for their own idealized modeling study.

Unauthenticated | Downloaded 09/26/21 04:27 AM UTC 1880 MONTHLY WEATHER REVIEW VOLUME 129 radial circulation to emerge. The vortex merger event Emanuel, K. A., 1985: Frontal circulations in the presence of small near 26 h results in a 2Њ±3ЊC warm anomaly near the moist symmetric stability. J. Atmos. Sci., 42, 1062±1071. Gray, W. M., 1968: Global view of the origin of tropical disturbances core, commensurate with the strength of the baroclinic and storms. Mon. Wea. Rev., 96, 669±700. zone. Following this time, the baroclinic zone weakens Grell, G. A., J. Dudhia, and D. R. Stauffer, 1994: A description of and moves northeastward relative to the center of the the ®fth-generation Penn State/NCAR Mesoscale Model (MM5). incipient tropical storm by 36 h (Fig. 7b), a process seen NCAR Tech. Note 398, 121 pp. in other marine cyclones (e.g., Neiman et al. 1993). As Gyakum, J. R., 1983: On the evolution of the QE II storm: Part II: Dynamic and thermodynamic structure. Mon. Wea. Rev., 111, is a well-known aspect of extratropical cyclones, the 1156±1173. reduction in baroclinity can be attributed mainly to the Harr, P. A., R. L. Elsberry, and J. C. L. Chan, 1996a: Transformation nonlinear equilibration of baroclinic cyclogenesis. In the of a large monsoon depression to a tropical storm during TCM- present case, this effectively separates the warm-core 93. Mon. Wea. Rev., 124, 2625±2643. ÐÐ, M. S. Kalafsky, and R. L. Elsberry, 1996b: Environmental vortex from the baroclinicity and yields a disturbance conditions prior to the formation of a midget tropical cyclone with considerable axial symmetry. This disturbance then during TCM-93. Mon. Wea. Rev., 124, 1693±1710. undergoes the moistening phase due to storm-induced Haynes, P.H., and M. E. McIntyre, 1987: On the evolution of vorticity latent heat ¯uxes from the ocean and, ®nally, a renewed and potential vorticity in the presence of diabatic heating or other deepening to hurricane intensity. forces. J. Atmos. Sci., 44, 828±841. Hess, J. C., J. B. Elsner, and N. E. LaSeur, 1995: Improving seasonal Sensitivity of numerical simulations of tropical cy- hurricane predictions for the Atlantic Basin. Wea. Forecasting, clogenesis to physical parameterizations in models is a 10, 425±432. major issue and we will address this in Part II. Our Hong, S.-Y., and H.-L. Pan, 1996: Nocturnal boundary layer vertical conclusion is that the dynamics of the transformation diffusion in a medium-range forecast model. Mon. Wea. Rev., of Diana to tropical storm strength are much less de- 124, 2322±2339. Huo, Z., D.-L. Zhang, and J. R. Gyakum, 1999: Interaction of po- pendent on model physics than is the intensi®cation to tential vorticity anomalies in extratropical cyclogenesis. Part II: hurricane strength. Thus, the warm-core transformation Sensitivity to initial perturbations. Mon. Wea. Rev., 127, 2563± appears as a robust process, in this case strongly mod- 2575. ulated by preexisting synoptic-scale features. 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