A Numerical Study on Tropical Cyclone Intensification. Part I: Beta Effect and Mean Flow Effect

Transcription

1 1404 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 56 A Numerical Study on Tropical Cyclone Intensification. Part I: Beta Effect and Mean Flow Effect MELINDA S. PENG Naval Research Laboratory, Monterey, California BAO-FONG JENG AND R. T. WILLIAMS Department of Meteorology, Naval Postgraduate School, Monterey, California (Manuscript received 24 April 1997, in final form 9 June 1998) ABSTRACT The effect of planetary vorticity gradient (beta) and the presence of a uniform mean flow on the intensification of tropical cyclones are studied using a limited-area primitive equation model. The most intense storm evolves on a constant- f plane with zero-mean flow and its structure is symmetric with respect to the vortex center. The presence of an environmental flow induces an asymmetry in a vortex due to surface friction. When f varies the vortex is distorted by the beta gyres. Fourier analysis of the wind field shows that a deepening cyclone is associated with a small asymmetry in the low-level wavenumber-one wind field. A small degree of asymmetry in the wind field allows a more symmetric distribution of the surface fluxes and low-level moisture convergence. On the other hand, a weakening or nonintensifying cyclone is associated with a larger asymmetry in its wavenumber-one wind field. This flow pattern generates asymmetric moisture convergence and surface fluxes and a phase shift may exist between their maxima. The separation of the surface flux maximum and the lateral moisture convergence reduces precipitation and inhibits the development of the tropical cyclone. Since the orientation of the asymmetric circulation induced by beta is in the southeast to northwest direction, the asymmetry induced by a westerly flow partially cancels the beta effect asymmetry while that of an easterly flow enhances it. Therefore, in a variable- f environment, westerly flows are more favorable for tropical cyclone intensification than easterly flows of the same speed. 1. Introduction Intensity prediction for tropical cyclones is a challenging task. Forecasts of tropical cyclone (TC) motion have shown significantly improved skill in past decades, but intensity forecasts have not improved (Elsberry et al. 1992). The lack of skill in intensity forecasts is partially a result of insufficient data and it may also be attributed to less research emphasis. Studies on TC intensity change using analyzed data are focused mainly on the upper levels where satellite and aircraft data are available to compensate for the shortage of conventional data on open tropical oceans. A number of studies have simulated the genesis and the evolution of TCs using numerical models. The advantage of using a numerical model is that many parameters related to storm intensity can be analyzed in detail without the problem of in- Corresponding author address: Dr. Melinda S. Peng, Code 7533, Marine Meteorology Division, Naval Research Laboratory, Monterey, CA peng@nrlmry.navy.mil sufficient data and poor data resolution. We will now review some of the more relevant literature. Some studies have suggested that small vertical shear in the environmental wind and large inward eddy imports of angular momentum into the vortex center are favorable for tropical cyclone intensification. Holland and Merrill (1984) gave a dynamic argument to explain the influence of upper-level angular momentum flux on the intensification of tropical cyclones. In the upper troposphere where the inertial stability is small, the inward displacement of a parcel experiences less resistance. Therefore, the response to external forcing, such as the momentum transport, can penetrate to the vortex center at upper levels. Merrill (1988a,b) distinguished the upper-level environmental pattern, relative to the storm motion, for intensifying hurricanes (IHs) and nonintensifying hurricanes (NIHs) over the Atlantic Ocean by composite analysis. The major difference between these two patterns was that the IHs have unrestricted outflows that organize into jets and decelerate as they diverge from the vortex center. On the other hand, the NIHs have unidirectional flow across the center and closed streamlines that merge back into the vortex. Further, the IHs

2 15 MAY 1999 PENG ET AL have slower speeds associated with the principal outflow streamline and weaker azimuthally averaged anticyclonic flow. A schematic diagram depicting possible contributions to tropical cyclone intensity change and the positive/negative feedbacks by Merrill was given in Elsberry et al. (1992). Ooyama (1987) used a shallow water model with fixed mass and momentum at the cyclone center to study TC development. Without an environmental flow, the outflow was a nearly symmetric anticyclone and there was no development of the vortex. When a sheared zonal flow was included, an outflow jet developed and the eddy momentum fluxes led to development of the TC. Kurihara and Tuleya (1981) simulated the genesis of a tropical storm from an easterly wave in an idealized basic flow constructed from the Global Atmospheric Research Program Atlantic Tropical Experiment (GATE) period III flow field. Tuleya and Kurihara (1981) further investigated the effect of an environmental flow on storm genesis. Their experiments produced storm genesis in an easterly vertical shear flow but not in a westerly shear or a no-shear easterly flow. The genesis mechanism required that the upper-level warming be in phase with the low-level moisture convergence. The inhibiting effect of environmental vertical shear flow on tropical cyclone growth has been a popular concept (i.e., Gray 1968). It has been hypothesized that if the vertical shear is too large, upper-level temperature and moisture anomalies associated with the inner core of the storm will be advected away from the low-level circulation, which will inhibit cyclone intensification (Anthes 1982). Madala and Piacsek s (1975) numerical simulation using a three-layer model confirmed the inhibiting effect of the vertical shear. The effect of the planetary vorticity gradient on TC motion has been studied rigorously on a beta plane (i.e., Madala and Piacsek 1975; Chan and Williams 1987; Fiorino and Elsberry 1989). A wavenumber-one asymmetry, induced by interaction between the symmetric circulation and the planetary vorticity gradient, causes the northwestward motion of the TC in a zero-mean flow environment on a beta plane. The effect of beta on the development of tropical cyclones was addressed by Madala and Piacsek (1975). In their simulations, a vortex on a beta plane intensified at a slower rate than the one on an f plane before the storm stage, but at the same rate thereafter. DeMaria and Schubert (1984) carried out tropical cyclone simulations using a three-layer spectral model and they found that the intensification rates for simulations on an f plane and a beta plane were very similar until 48 h. Afterward, the intensity of the storm on an f plane continued to intensify, while the storm on a beta plane began to level off. They attributed this difference to larger inertial stability in the upper layer and a shearing of the centers in different layers in the beta plane simulation. The beta effect on TC development was also studied by Khain (1988) and his results were similar to those of DeMaria and Schubert (1984). Bender (1997) studied the effect of relative flow on generating the asymmetric structure in the interior of hurricanes. His results also indicated that the presence of the beta effect or an easterly mean flow induced asymmetry in the precipitation and convergence/divergence relative to the storm center. In this paper, we will study the effect of beta and an environmental mean flow on TC development. The dynamics and thermodynamics associated with these effects will be explored in a different manner than in previous studies. The numerical model and initial conditions are described in section 2 along with a description of our experiments. The time evolution of all cases is discussed in section 3. Analysis of parameters that are related to the intensity are given in section 4. The superposition effect of planetary vorticity gradient and a mean flow is examined in section 5. Summary and conclusions are given in section Numerical model and initial conditions The numerical model used for this study is the Naval Research Laboratory limited-area primitive equation model (Madala et al. 1987). The model employs a second-order finite difference scheme in flux form in space and split-explicit leapfrog scheme in time. The physical parameterizations in the model that are important for tropical cyclone simulation include the modified Kuo scheme (Kuo 1965, 1974) for cumulus and a one-anda-half-order closure scheme for the planetary boundary layer (Holt and Raman 1990). The horizontal grid size is 0.5 in the latitude longitude coordinates and the model domain covers an area of centered at 20 N where the vortex is placed initially. A total of 16 layers in the terrain-following vertical coordinate are used with higher resolution concentrated in the lower troposphere. The initial vortex is symmetric with a modified Rankine profile that is blended with the environment using a weighting function so that the tangential wind goes to zero at some radial distance, r out, that is, 2 2 V max(r/r max)(1 r /r out) r rmax b 2 2 V(r) V (r /r) (1 r /r ) r r r 0 r r out, max max out out max (2.1) where r max 1, r out 7.5, b 0.5, and V max 35 m s 1 at r max on the lowest level. The maximum wind of the vortex, V max, decreases gradually with height, reaching zero at 100 hpa. This somewhat large initial wind is used to reduce the spinup time. The initial mass fields are in gradient wind balance with the wind field. The SST is set to a constant of 29.5 to eliminate variations in the thermodynamic forcing as the vortex moves during the integration. The relative humidity is 95% at the first two lowest pressure levels and decreases linearly

3 1406 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 56 TABLE 1. The primary 10 experiments. Mean flow speed U (m s 1 )/Coriolis parameter f Group A (constant f) FCU0 FCW5 FCW10 FCE5 FCE10 Group B (variable f) FYU0 FYW5 FYW10 FYE5 FYE10 to 10% at the top. The thermal and moisture fields are the same for all experiments, and all integrations are carried to 72 h. The beta effect will be studied by comparing integrations with a constant Coriolis parameter ( f ) and integrations with a variable Coriolis parameter. The effect of a uniform environmental flow on TC intensification will be studied with five cases in which the mean flow U equals 10, 5, 0, 5, and 10 m s 1, respectively, both with a constant f and a variable f. The combination of these variations totals 10 experiments in two groups (Table 1). The experiments in group A are integrated on a constant- f plane and those in group B are integrated with f varying with latitude. 3. Time evolution of the vortices Figure 1 contains the time evolution of the minimum sea level pressure (MSLP) for all cases. The vortices weaken slightly during a model adjustment period until 12 h. The evolutions of all vortices are similar, although their intensities and structures vary in the different environments. The case with constant f and zero-mean flow has the highest intensity (lowest MSLP). This is our control case and it will be discussed in more detail in the first subsection before comparing it with other cases. FIG. 1. Time evolution of the MSLP of the vortex for the five cases with U 10, 5, 0, 5, and 10 m s 1 : (a) constant f and (b) variable f. a. Vortex with zero-mean flow and constant f (the control case) The vortex with zero-mean flow and constant f intensifies continuously until 60 h and then it levels to 940 hpa at 72 h. The cyclone remains at the same location and has a fairly symmetric structure with respect to the center with a slight asymmetry shown by the isotachs at 60 h in Fig. 2a. The asymmetry observed here is due to truncation error introduced in the initial divergence field and should not be confused with the asymmetry introduced by other effects that will be discussed later. The upper-level wind field shows predominately anticyclonic divergent flow, which is essential for storm development (Kurihara and Tuleya 1981; Shi et al. 1990). At t 36 h when the vortex is intensifying, the vertical circulation across the center in the east west direction shows two branches of upward motion that correspond to the eyewall and large downward motion at the center. The upper part of the circulation has a layer of outflow between 300 and 100 hpa that corresponds to the upper-level divergent anticyclonic flow. Although the inflow component is largest within the boundary layer, it extends almost to 350 hpa. At 60 h, two branches of upward motion and downward motion in the center remain, but the sinking motion is weaker in comparison with the surrounding upward motion. Also, the upward branch has contracted inward, indicating a smaller eyewall. The downward motion at the center is observed throughout the intensification period. To save space, only a diagram at 60 h is shown in Fig. 2b. The instantaneous rainfall rate, which includes both the convective and the stable parts, also has a symmetric structure (Fig. 2c). The location of the maximum rainfall rate region changes somewhat with time but there are mainly

4 15 MAY 1999 PENG ET AL FIG. 2. The vortex structure at 60 h in a quiescent environment for a constant f [(a) surface wind isotachs (m s 1 ), (b) vertical circulation (unit of u r :ms 1 ; unit of : bar s 1 ), and (c) instantaneous rainfall rate (cm day 1 )] and for a variable f [(d) surface wind isotachs, (e) vertical circulation, and (f) instantaneous rainfall rate].

5 1408 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 56 two rainbands surrounding the center, one to the north and one to the south. b. Effect of planetary vorticity gradient (variable f) Comparing cases in Fig. 1a with cases in Fig. 1b, one can see that including the beta effect inhibits the development of tropical cyclones. The effect of a variable f can best be illustrated with the two zero-mean flow cases without the influence of an environmental flow. Whereas the vortex in a constant- f environment intensifies continuously until 60 h, the vortex in a variable- f environment reaches its maximum intensity by 36 h and then levels off afterward. The wind field at the sea surface is somewhat symmetric before 36 h, which is similar to the control run, but becomes asymmetric afterward (Fig. 2d). Large cross-isobaric winds occur on the east and southeast side of the cyclone. This asymmetry is similar to the analysis of Tropical Cyclone Kerry in 1979 by Black and Holland (1995). The north south circulation has a highly asymmetric distribution with only one dominant branch of upward motion in the southern part (Fig. 2e). Comparing it with the vortex in a constant- f environment shown in Fig. 2b, the eyewall extends farther outward and vertical motion in the center is smaller and mixed. Whereas the size of the eyewall expands when the vortex ceases to intensify in this case, the eyewall constricts in the intensifying vortex with constant f. This conforms with the eyewall mechanism associated with the vortex intensity change (Willoughby et al. 1982). The upper-level flow at 150 hpa is asymmetric as well, with a larger outflow in the southeastern quadrant (not shown). At 36 h, when the vortex is at its maximum strength, the instantaneous rainfall rate remains fairly symmetric with respect to the center. Beyond that time, it becomes highly asymmetric and there is only one rainband located mainly in the southern part (Fig. 2f), corresponding to the upward motion in the vertical circulation. The rainfall amounts are also smaller than those in a constant- f environment. The azimuthal averages of the 850-hPa tangential wind profiles for these two zero-mean flow cases with a constant f and a variable f are depicted in Fig. 3. In the constant- f case (Fig. 3a), both the maximum wind (representing the core intensity) and the strength increase with time. In the variable- f case (Fig. 3b), the core intensity decreases after 36 h while the size continues to increase. This corresponds well with the composite analysis for intensifying and decaying TCs by Merrill (1984). c. Effects of a mean flow on TC intensification Comparing cases in each group with the same Coriolis parameter but different mean flows indicates that including a uniform mean flow reduces vortex intensity. This is best illustrated with cases in group A (Fig. 1a) that include no beta effect. With zero-mean flow, the FIG. 3. Azimuthal average of the 850-hPa tangential wind profile of the zero-mean flow cases with (a) constant f and (b) variable f. storm deepens to 940 hpa by 72 h, the lowest in our experiments. Vortices with U 5 and U 5ms 1 have similar tendencies and their final MSLP are comparable with the zero-mean flow case, but the overall intensities are slightly weaker. Evolution for vortices with U 10 and 10ms 1 are similar; both weaken after 48 h and their final MSLP is around 980 hpa. Therefore, when f is constant, no directional bias of the mean flow is associated with TC intensification. However, the larger the mean wind, the weaker the vortex is. The TCs in group B with a variable f intensify at the same rate as those in group A before 36 h (Fig. 1b). Afterward, four cases cease to develop while the vortex in a westerly flow of 5 m s 1 continues to intensify to

6 15 MAY 1999 PENG ET AL FIG. 4. The 850-hPa wavenumber-one asymmetric wind field for vortex at 48 h; (a) for the case U 0 and a constant f, (b) U 10 and a constant f, (c) U 10 m s 1 and a constant f, and (d) U 0ms 1 and a variable f. 953 hpa at 72 h, which is the lowest in group B. The intensity of the vortex with zero-mean flow has the second lowest MSLP of 972 hpa. The vortex in an easterly flow of 10 m s 1 has the weakest intensity, trailed by the one in a 5 ms 1 easterly flow. Both of these are weaker than their counterparts in the constant- f group (Fig. 1a). The two vortices in westerly flows have higher intensities than their counterparts in the easterly flows when beta effect is included. Therefore, there is a directional bias of the mean flow associated with TC intensification in the presence of the beta effect. The vortexina5ms 1 westerly flow deepens more than the vortex with no mean flow. This time evolution is similar in pattern to those obtained by Tuleya and Kurihara (1981) in their simulations of storm genesis. In particular, they also found a higher intensity for the vortex with a westerly uniform flow of 5 m s 1. We hypothesize that the presence of a westerly flow partially cancels the beta effect while an easterly flow adds to it, so that a westerly flow is more favorable for cyclone develop- FIG. 5. Tracks of the vortices in group A with a constant f.

7 1410 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 56 FIG. 7. Final MSLP vs the space- and time-averaged across-thecenter flow speed. The s represent cases with variable f and the s represent cases with constant f. The evolution of the area average of the upper-level (150 hpa) divergence is also positively correlated with the TC intensity change. This indicates that the development of a vortex is strongly vertically coupled. To understand the dynamics associated with these intensity differences, some relevant properties are examined in the following section. FIG. 6. Time evolution of the area-averaged wavenumber-one asymmetric flow within a 5 of radius for all cases: (a) group A with a constant f and (b) group B with a variable f. ment when the beta effect is included. This issue will be discussed in more detail later. In general, the presence of a large mean flow and the variation of f (beta) are not favorable for TC intensification. The evolutions of the area-averaged 12-h accumulated precipitation are positively correlated with the vortex intensity (figure not shown). Cases in group A with a constant f have larger precipitation amounts than those in group B with a variable f. Within each group, the precipitation amounts associated with vortices in different mean flows are also positively correlated with their intensities. In group A, the largest precipitation is found in the zero-mean flow case corresponding to its highest intensity, while in group B, the vortex in a westerly mean flow of 5 m s 1 has the highest intensity and largest rainfall amount. 4. Analysis a. Wavenumber-one asymmetry One of the main points of the paper is that storm growth is related to the degree of asymmetry of the various storm fields. For example Figs. 2 and 3 show that the vortex with constant f, which is still growing at 60 h, is also more symmetric in horizontal structure. It is well known that interaction between the symmetric circulation of a cyclonic vortex and the planetary vorticity gradient (variable f ) generates a wavenumber-one circulation (the beta gyre). In a quiescent environment, the beta gyre orients toward the northwest, which is also the direction of vortex motion (Fiorino and Elsberry 1989). When a basic flow is present, interaction between a vortex and a mean flow also generates a wavenumberone asymmetry because the wind speed, and therefore wind stress, vary around the vortex. Smith and Montgomery (1995) demonstrated that the wavenumber-one asymmetry dominates in the near-vortex region. To explore the mechanisms associated with these interactions, we will examine the asymmetric wavenumber-one circulation of the vortex. This is done by transforming the wind field to polar coordinates centered at the geopotential minimum at each level. Fourier analysis along

8 15 MAY 1999 PENG ET AL FIG. 8. Time evolution of the orientation of the wavenumber-one wind circulation for a vortex with U 0 and constant f (solid line) and variable f (dotted line), and constant f with U 10 m s 1 (dashed line). The angle increases in a counterclockwise direction. the azimuthal direction is then performed to obtain the wavenumber-one circulation. The motion of the vortex is subtracted from the total wind field at each time frame before Fourier analysis is carried out. Careful examination of the flow patterns shows that they fluctuate considerably in time. Figure 4a gives the wavenumber-one asymmetric wind field at t 48 h for f equals constant and U 0. Note that the wavenumberone wind field always has a component across the vortex center. In this case the circulation is weak. This is expected since if the initial condition were perfectly symmetric, the wavenumber-one asymmetry would remain zero. The circulation for U 10 m s 1 and f equals constant is shown in Fig. 4b for t 48 h. In this case the air enters the vortex from the northeast leaves to the southwest. Figure 5 shows that this vortex moves rapidly to the east with the mean flow with a small displacement to the south. Figure 4c gives the circulation at t 48 h for U 10 m s 1 and f equals constant. This circulation is approximately the reverse of Fig. 4b and the vortex moves in the opposite direction (Fig. 5). These figures suggest that when f is constant the air enters the vortex in the quadrant that is to the left of the mean flow direction. This asymmetry comes from the asymmetry in wind stress around the vortex when there is a mean flow. The circulation pattern is oriented northwest southeast when the variation of f is included as can be seen in Fig. 4d for U 0. The strength of the wavenumber-one asymmetric circulation is measured by taking the area average of the asymmetric wind within a radius of 5 of latitude longitude. This circulation strength, which is shown in Fig. 6, oscillates with time but there are definite trends. The relation between the storm intensity and the asymmetric FIG. 9. Schematic diagram showing where the maximum surface fluxes might be for a vortex with (a) U 0 and a constant f, (b) U 0 and a variable f, (c) a westerly mean flow and a constant f, and (d) an easterly mean flow and a constant f. circulation strength is revealed by comparing Fig. 6 with the intensity change (Fig. 1). In general, cases in group A with a constant f (Fig. 6a) have smaller circulation strengths than cases in group B with a variable f (Fig. 6b), indicating that the circulation strength is enhanced by the beta effect. Within each group, larger mean flows generate larger circulation strengths and thus weaker TC intensity. The vortex with U 5ms 1 in group B has the largest intensity in its group and its circulation strength is the smallest. The circulation strength for the vortices in a westerly flow are smaller than their counterparts in an easterly flow and their intensities are slightly higher. The combined effect of beta and a mean flow will be examined later in section 5. To illustrate the relation between Figs. 1 and 6 more clearly, the time mean circulation strength and the final MSLP of each case is plotted in Fig. 7. There is a linear relation between the MSLP and the circulation strength in the asymmetric circulation. Cases with a constant f (marked with ) have smaller circulation strength and they deepen to lower MSLP than cases with a variable f (marked with ). The time change of the orientation of the wavenumber-one circulation is depicted in Fig. 8 for three representative cases. With no mean flow or beta effect, the orientation of the wavenumber-one asymmetric circulation changes very little with time. The beta effect and the presence of a mean

9 1412 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 56 FIG. 10. Surface momentum flux (N m 2 )att 48 and 72 h for the vortex with U 0: (a) and (b) f equals constant; (c) and (d) f varies with latitude. flow all induce a cyclonic rotation of the wavenumberone circulation. b. Surface fluxes The basic energy source for TC intensification is the sensible and latent heat that the inflowing air draws from the warm sea. This heat source provides energy for the upward motion in the eyewalls and for the condensation heating in the eyewalls that further supports the updraft. The moisture flux, in the meantime, continuously provides moisture to the atmosphere (Emanuel 1994). The sensible heat flux is induced by the differential temperature (T*) and the latent heat flux, induced by evaporation, is due to the moisture differential (q*) between the air and ocean. Both fluxes are proportional to the friction velocity (u*), which is determined by the magnitude of the surface wind (k V ) u*, (4.1) [ln(z/z 0) m] where 5z/L z/l 0 m (z/l){c3 [(z/l)(c2 Cz/L)]} 1 z/l 0 (4.2) and where C , C , C , z/l is Monin Obukhov stability parameter, k is the von Kármán constant, V is the magnitude of the surface wind, z is the height of model s lowest level, and z 0 is the roughness length.

10 15 MAY 1999 PENG ET AL FIG. 11. Same as in Fig. 10 except for vortices with constant f: (a) and (b) U 10ms 1 ; (c) and (d) U 10 m s 1. To investigate the asymmetry associated with storm development, the moisture flux (u*q*), the heat flux (u*t*), and the momentum flux (u*u*) are examined. The moisture flux and the heat fluxes have basically the same pattern as the momentum flux but they contain more small-scale features. We will use the momentum flux to illustrate the degree of asymmetry of a vortex due to beta effect and mean flow effect. Before we examine the surface flux fields from our experiments, a schematic diagram (Fig. 9) is presented to illustrate the region of maximum surface flux in different situations. In the case of zero-mean flow and a constant f, the asymmetric circulation strength is small. The surface frictional wind is determined by the symmetric flow that is cyclonic and convergent so that the surface flux is symmetric with respect to the center, and its maximum is located near the radius of maximum wind (Fig. 9a). When the beta effect is present, a wavenumber-one wind circulation oriented from southeast toward northwest is induced (Fiornio and Elsberry 1989). The asymmetric flow of the beta gyre increases the inward radial wind in the southeast quadrant and increases the tangential wind in the northeastern part of the cyclone. The friction velocity, which is proportional to the magnitude of the wind speed, has its maximum in the eastern and southeastern part. The largest surface fluxes are expected to be located in the same place as sketched in Fig. 9b. In the presence of a westerly flow, the tangential wind on the south side and the inward radial wind on the west side of the cyclone are increased. Therefore, a westerly flow is expected to generate maximum surface flux in the southwest part of the vortex

11 1414 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 56 FIG. 12. Moisture convergence at 850 hpa corresponding to cases shown in Fig. 10. (Fig. 9c). Conversely, an easterly mean flow generates maximum tangential flow on the north side and maximum inward radial flow on the east side of a cyclonic vortex. In this case the maximum surface fluxes would be located on the northeast side of a cyclone (Fig. 9d). The distributions of surface momentum flux for each case in our experiments are similar to each other up to 36 h. After this time the patterns diversify. The control case (Figs. 10a,b) maintains its symmetry with an annulus shape except for a few local maxima within the annulus. The momentum flux for the vortex in a variable- f environment without a mean flow is highly asymmetric (Figs. 10c,d). The maximum is always located in the southeast quadrant of the cyclone as expected from Fig. 9b. The effect of a mean flow on the distribution of momentum flux is illustrated by constant- f cases with opposite, but equal, speeds of 10 m s 1 (Fig. 11). The largest wind stress is located in the south and southwest side for the vortex in a westerly flow, whereas it is located in the north and northeast side in an easterly flow. Both cases exhibit highly asymmetric distributions and the maximum region remains in the same quadrant for each case. All of these cases agree with our schematic diagrams depicted in Fig. 9. Figures 10 and 11 show that both a mean flow and the planetary vorticity gradient can induce an asymmetry in the surface fluxes due to asymmetric distributions of the frictional velocity. The maximum region remains in the same quadrant in each case. This asymmetric distribution of the surface flux is not favorable for TC intensification, as will be explained in the next section.

12 15 MAY 1999 PENG ET AL FIG. 13. Moisture convergence at 850 hpa corresponding to cases shown in Fig. 11. c. Low-level moisture convergence The core intensity of a TC depends directly on the moisture convergence that induces the precipitation (Gray 1968). In the modified Kuo cumulus parameterization scheme, convective precipitation and latent heating are proportional to the moisture convergence within the unit column. Even when the convective precipitation is not triggered, large moisture convergence also induces grid-scale precipitation. To explore the relation between the asymmetric circulation, the distribution of surfaces fluxes, and the intensity change, we compute the moisture convergence [ (Vq)] on the 850-hPa level. For the control vortex (constant f and zero-mean flow), the moisture convergence field has a rather symmetric distribution around the cyclone center (Figs. 12a,b). The two sources for TC development, surface fluxes (Figs. 10a,b) and the low-level moisture convergence (Figs. 12a,b), are symmetric and in phase with each other. On the other hand, the moisture convergence for the vortex in a variable- f environment that does not intensify is highly asymmetric with respect to the center (Figs. 12c,d) and is separated from the maximum momentum flux region (Figs. 10c,d). Similarly, the moisture convergence for vortices in a 10 m s 1 westerly (Figs. 13a,b) and easterly (Figs. 13c,d), respectively, in a constant- f environment exhibit high degrees of asymmetry. The surface moisture flux provides moisture from the ocean that the low-level wind field transports from the surrounding environment into the vortex. Both effects contribute to the three-dimensional moisture convergence in the vortex. Meanwhile, the sensible and latent

13 1416 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 56 FIG. 14. Asymmetric perturbation wind field (streamlines and isotachs, m s 1 ) superimposed on the reflectivity (dbz). The domain of the analysis is 82.5 km on a side centered on the storm (hurricane symbol). Tick marks are 8.25 km. Reflectivity values are depicted by increasing shades of gray at 10, 20, 30, 40, and 44 dbz (from Marks et al. 1992). heat fluxes provide the buoyancy force needed for upward motion. When the maximum moisture convergence and the buoyancy force are in phase, precipitation is enhanced, which can lead to TC intensification. In the situation where these two are asymmetric with respect to the center, the rotation of the wavenumber-one circulation will shift the maximum moisture convergence region away from the maximum surface flux region since the latter stays roughly in the same place. When the horizontal moisture convergence and the surface fluxes (heat and moisture source from sea) are not in place, precipitation is less likely to occur and intensification is inhibited. Figures 11a,b and 13a,b demonstrate this out-of-phase relation. The symmetric distribution in Figs. 10a,b and 12a,b is more favorable for TC development because the surface energy source region overlaps the region of moisture convergence. The area of maximum moisture convergence is generally located in the inflow region of the asymmetric wavenumber-one circulation and the area of moisture divergence is located in the outflow region. This is illustrated by comparing the wavenumber-one wind fields displayed in Fig. 4 with Figs. 12 and 13. Since the precipitation rate has the same pattern as the moisture convergence, the correspondence between the asymmetric inflow/outflow and the convergence/divergence observed here conforms with the analysis of Hurricane Norbert by Marks et al. (1992) (Fig. 14). The time evolution of the maximum moisture convergence is positively correlated with the precipitation amount and the intensity change (Fig. 1), and is negatively correlated with the area-averaged asymmetric wind speed (Fig. 6). Therefore, smaller asymmetric circulation strength leads to larger moisture convergence and higher TC intensity. d. Equivalent potential temperature Figure 15 depicts several vertical profiles of e for the control case with zero-mean flow and a constant f, and its counterpart with a variable f. Before 36 h, both cases show similar patterns where the warm e center originally located near the surface (12 h) is shifted upward due to adiabatic warming in the sinking region so that a warm core is developed at midlevel. At and beyond 48 h, the control vortex continues its intensification so that the warming of the core extends farther upward. During the same period, the weakening cyclone in a variable- f environment confines its warming to a lower altitude so that the 360-K line does not extend above the 300-hPa level (Fig. 15f). Another significant difference between these two cases is the existence of a warm e area at the center within the boundary layer for the intensifying case, indicating a continuing supply of the moisture from the ocean to support intensification. In our 10 primary experiments, there are four cases that intensify beyond 36 h while six cases weaken or level off (Fig. 1). Their e profiles at 72 h are depicted in Fig. 16, grouped into the intensifying group (a) and the nonintensifying group (b), respectively. The cases within each group are strikingly similar. All intensifying vortices extend the warming upward to the upper part

14 15 MAY 1999 PENG ET AL FIG. 15. Vertical profile of the equivalent potential temperature (in K) at (a) 12 h, (b) 36 h, and (c) 60 h for case U 0 and a constant f; and (d) 12 h, (e) 36 h, (f) 60 h for case U 0 and a variable f.

15 1418 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 56 FIG. 16. Vertical profile of the equivalent potential temperature (in K) at 72 h for (a) four intensifying cyclones and (b) six nonintensifying cyclones. of the domain and a small warm center exists within the boundary layer at the center. The nonintensifying vortices, on the other hand, confine the warming of the core to lower levels so that the 360-K contour line never extends above 300 hpa and there is no warm pocket at the center within the boundary layer. The upward extension of the warm e is a result of cyclone intensification rather than the cause. These comparisons between intensifying and nonintensifying cyclones seem to indicate that a TC cannot sustain itself through the original ideal of conditional instability of the second kind (CISK) (Charney and Eliassen 1964; Ooyama 1964) without continued supply of moisture and heat fluxes from the ocean surface (Ooyama 1969; Emanuel 1994). 5. Superposition effect of planetary vorticity gradient and a mean flow In general, the beta effect reduces tropical cyclone intensity, as can be seen by comparing cases in group B with cases in group A (Fig. 1). However, a more careful examination of Fig. 1b indicates that, when the beta effect is included, vortices in a westerly mean flow have greater intensity than vortices in an easterly mean flow of the same speed. Furthermore, the cyclone in a 5ms 1 westerly flow has even higher intensity than the zero-mean flow case. When the beta effect is absent, a westerly and an easterly flow give similar results (Fig. 1a). Considering the gyre orientation induced by the beta

16 15 MAY 1999 PENG ET AL FIG. 16. (Continued)

17 1420 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 56 TABLE 2. The variable mean flow experiments in Group B. Mean flow speed U (m s 1 ) Westerly flow Easterly flow FYU0 FYW3 FYW5 FYW7 FYW10 FYU0 FYE3 FYE5 FYE7 FYE10 effect in a quiescent environment, the asymmetry is in the northwestward direction. The asymmetry of a vortex induced by a westerly mean flow cancels some of the asymmetric wind field induced by the beta effect. On the other hand, the ventilation effect of an easterly flow is in the same direction as the beta effect so that their combination is even less favorable for TC development. To verify this, we carry out additional experiments for both westerly and easterly flows in a variable-f environment where the wind speed is increased by small increments. The additional experiments, combined with old experiments in group B, are listed in Table 2 and the time evolutions of their MSLP are depicted in Fig. 17. As expected, a small westerly mean flow (U 3 ms 1 ) gives the most intense TC, and the westerly cases with U 3ms 1,5ms 1,and7ms 1 develop a more intense cyclone than the U 0 case. When U 10 m s 1, the ventilation flow becomes so large that the TC becomes weaker than the one in the zero-mean flow. For the easterly flow cases, the ventilation effect adds to the beta effect so that even a small wind speed is less favorable for cyclone development than the zero-mean flow case. The larger the wind speed, the weaker the cyclone. The superposition effect of beta and a mean flow can be demonstrated by the displacements of the vortices for the experiments in a variable- f environment listed in Table 2 (Fig. 18). The zonal component of the beta drift is small compared to the meridional component and the vortex with zero-mean flow has more northward movement than westward movement. All vortices in a westerly flow have smaller east west displacement than the vortices in an easterly flow with the same speed, indicating the cancellation (enhancement) effect between the planetary vorticity gradient and westerly (easterly) flows. This effect can also be found by comparing cases in Fig. 5 with those in Fig. 18 that have the same mean flow. The horizontal displacement of a vortex in a westerly flow with beta effect is smaller than the one without. On the contrary, horizontal displacement of a vortex in an easterly flow with beta effect is greater than the one without. The momentum flux at 48 h for the four vortices with nonzero-mean flow in group B are depicted in Fig. 19. Among these four cases, vortices in the westerly flow have larger momentum fluxes than vortices in the easterly flow and the asymmetry increases with the flow FIG. 17. Time evolution of the MSLP of the vortices in Table 2 for (a) westerly flow and (b) easterly flow in a variable- f environment. speed. The vortex in a 5 m s 1 westerly with variable f (Fig. 19a) has an overall larger momentum flux than the one with zero-mean flow (Fig. 10c) and it deepens to a lower MSLP. This also confirms our hypothesis that a weak westerly flow cancels some of the beta effect and reduces the asymmetric circulation strength induced by the beta effect. Therefore, when a weak westerly is present the vortex in a variable- f environment can deepen to lower MSLP than in a quiescent environment. On the other hand, an easterly flow induces a higher degree of asymmetry and weaker momentum fluxes so that it is not as favorable for vortex development. 6. Summary and conclusions A limited-area primitive equation model is used to study the dynamics associated with the intensification of tropical cyclones in different uniform mean flows

18 15 MAY 1999 PENG ET AL FIG. 18. Tracks of the vortices in Table 2 with a variable f. FIG. 19. Surface momentum fluxes (N m 2 ) at 48 h for vortices with a variable f : (a) U 5ms 1, (b) U 10ms 1, (c) U 5m s 1, (d) U 10 m s 1.

19 1422 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 56 with and without the planetary vorticity gradient. Our study focuses on storm intensification beyond the genesis stage. The vortex in a constant- f environment with zeromean flow deepens to the lowest MSLP (highest intensity). Both the presence of the planetary vorticity gradient and a mean flow generate asymmetry that limits the development of the cyclone. An intense storm is associated with large precipitation, large upper-level divergence, and large moisture convergence. The intensity of a storm is inversely proportional to the strength of the wavenumber-one asymmetry. The distinction between an intensifying vortex and a nonintensifying vortex lies in the degree of asymmetry in its horizontal structure. An intensifying cyclone is associated with a small wavenumber-one asymmetry that allows a more symmetric distribution of the surface fluxes and lowlevel moisture convergence around the center. A large wavenumber-one asymmetry generates a large asymmetry in the surface fluxes and moisture convergence. The maximum moisture convergence occurs in the inflow region of the wavenumber-one wind circulation and it rotates with time, but the location of maximum surface flux stays roughly at the same place. When the maxima of the surface fluxes are not in place with the low-level horizontal moisture convergence maximum, the precipitation is less likely to occur and the cyclone is less likely to intensify. The large wind speed associated with tropical cyclones induces large surface fluxes, but if the maximum surface flux is sheared from the region of low-level moisture convergence, the cyclone s intensification is inhibited. The inhibiting effect of asymmetry on tropical cyclone development conforms with the consensus of intensity analysis by Dvorak (1984) using satellite images. Due to the nature of the orientation of the wavenumber-one circulation induced by the beta effect in a quiescent environment, asymmetry induced by a westerly basic flow cancels some part of the asymmetry generated by beta effect while an easterly flow adds to the beta effect. Therefore, a westerly flow is more favorable for tropical cyclone development when the planetary vorticity gradient is present. Sensitivity of our results on the resolution is examined by rerunning some cases using higher horizontal resolution. The results using a grid size of ⅓ generate higher intensity for all cases. The asymmetry induced by the beta effect and/or a mean flow remains, but the degree of asymmetry, measured by the ratio of the asymmetric kinetic energy to the total kinetic energy, is less for more intense vortices. The intensity difference between cases also decreases. This indicates that the effect of asymmetry on tropical cyclone intensification is stronger for weaker cyclone and vice versa for intense cyclones. Raymond and Emanuel (1993) criticized the Kuo cumulus parameterization on various theoretical grounds. The main shortcomings are that the scheme does not use a cloud model or parameterized convective downdrafts. In tropical cyclones the downdrafts tend to reduce overall growth because they bring drier air into the lower levels around the cyclone. Wang and Seaman (1997) carried out a comparative study of four cumulus parameterization schemes in a mesoscale model with a grid size of 36 km. They found that the Kuo scheme was not significantly less accurate in terms of total precipitation than any of the other schemes (two of which included downdrafts). As a result we believe that improvements in our cumulus parameterization scheme would not change the main conclusions of this paper. Even though the cases studied in the present research are in idealized conditions, the difference in characteristics associated with intensifying cyclones and nonintensifying cyclones may provide some guidance in real case studies. The results presented can be useful for bogussing a tropical cyclone into the initial fields for numerical models in the consideration that one may need to insert a stronger vortex in a easterly flow than in a westerly flow. Future studies that examine the effects of vertical and horizontal shear and initial vortex latitude on tropical cyclone development will need to take into account the results from this study. Acknowledgments. This work was supported by the Office of Naval Research Marine Meteorology Program and the National Science Foundation under Grant ATM REFERENCES Anthes, R. A., 1982: Tropical Cyclones: Their Evolution, Structure and Effects. Meteor. Monogr., No. 41, Amer. Meteor. Soc., 208 pp. Bender, M. A., 1997: The effect of relative flow on the asymmetric structure in the interior of hurricanes. J. Atmos. Sci., 54, Black, P. G., and G. J. Holland, 1995: The boundary layer of Tropical Cyclone Kerry (1979). Mon. Wea. Rev., 123, Chan, J. C.-L., and R. T. Williams, 1987: Analytical and numerical studies of the beta-effect in tropical cyclone motion. Part I: Zero mean flow. J. Atmos. Sci., 44, Charney, J. G., and A. Eliassen, 1964: On the growth of the hurricane depression. J. Atmos. Sci., 21, DeMaria., M., and W. Schubert, 1984: Experiments with a spectral tropical cyclone model. J. Atmos. Sci., 41, Dvorak, V., 1984: Tropical cyclone intensity analysis using satellite data. NOAA Tech. Rep. NESDIS 11, 47 pp. [Available from NOAA, Washington, DC ] Elsberry, R. L., G. J. Holland, H. Gerrish, M. DeMaria, C. P. Guard, and K. Emanuel, 1992: Is there any hope for tropical cyclone intensity prediction? A panel discussion. Bull. Amer. Meteor. Soc., 73, Emanuel, K. A., 1994: Atmospheric Convection. Oxford University Press, 580 pp. Fiorino, M., and R. L. Elsberry, 1989: Some aspects of vortex structure related to tropical cyclone motion. J. Atmos. Sci., 46, Gray, W. M., 1968: Global view of the origin of tropical disturbances and storms. Mon. Wea. Rev., 96, Holland, G. J., and R. T. Merrill, 1984: On the dynamics of tropical

20 15 MAY 1999 PENG ET AL cyclone structural changes. Quart. J. Roy. Meteor. Soc., 110, Holt, T., and S. Raman, 1990: Marine boundary layer structure and circulation in the region of offshore redevelopment of a cyclone during GALE. Mon. Wea. Rev., 118, Khain, A. P., 1988: A three-dimensional numerical model of a tropical cyclone with allowance for the beta-effect. Izv. Atmos. Oceanic Phys., 24 (4), Kuo, H. L., 1965: On formation and intensification of tropical cyclones through latent heat release by cumulus convection. J. Atmos. Sci., 22, , 1974: Further studies of the parameterization of the influence of cumulus convection on large-scale flow. J. Atmos. Sci., 31, Kurihara, Y., and R. E. Tuleya, 1981: A numerical simulation study on the genesis of a tropical storm. Mon. Wea. Rev., 109, Madala, R. V., and S. A. Piacsek, 1975: Numerical simulation of asymmetric hurricanes on a beta-plane with vertical shear. Tellus, 27, , S. W. Chang, U. C. Mohanty, S. C. Madan, R. K. Paliwal, V. B Sarin, T. Holt, and S. Raman, 1987: Description of Naval Research Laboratory limited area dynamical weather prediction model. NRL Tech. Rep. 5992, Washington, DC, 131 pp. [Available from Naval Research Laboratory, 4555 Overlook Ave. S.W., Washington, DC ] Marks, F. D., Jr., R. A. Houze Jr., and J. F. Gamache, 1992: Dualaircraft investigation of the inner core of Hurricane Norbert. Part I: Kinematic structure. J. Atmos. Sci., 49, Merrill, R. T., 1984: A comparison of large and small tropical cyclones. Mon. Wea. Rev., 112, , 1988a: Characteristics of upper-tropospheric environmental flow around hurricanes. J. Atmos. Sci., 45, , 1988b: Environmental influences on hurricane intensification. J. Atmos. Sci., 45, Ooyama, K. V., 1964: A dynamical model for the study of tropical cyclone development. Geophys. Int., 4, , 1969: Numerical simulation of the life cycle of tropical cyclones. J. Atmos. Sci., 26, 3 40., 1987: Numerical experiments of steady and transient jets with a simple model of the hurricanes outflow layer. Preprints, 17th Conf. on Hurricanes and Tropical Meteorology, Miami, FL, Amer. Meteor. Soc., Raymond, D., and K. Emanuel, 1993: The Kuo cumulus parameterization. The Representation of Cumulus Convection in Numericial Models, Meteor. Monogr., No. 46, Amer. Meteor. Soc., Shi, J. J., S. W. Chang, and S. Raman, 1990: A numerical study of the outflow layer of tropical cyclones. Mon. Wea. Rev., 118, Smith, G. B., and M. T. Montgomery, 1995: Vortex axisymmetrization: Dependence on azimuthal wave-number or asymmetric radial structure changes. Quart. J. Roy. Meteor. Soc., 121, Tuleya, R. E., and Y. Kurihara, 1981: A numerical study on the effects of environmental flow on tropical storm genesis. Mon. Wea. Rev., 109, Wang, W., and N. Seaman, 1997: A comparison study of convective parameterization schemes in a mesoscale model. Mon. Wea. Rev., 125, Willoughby, H. E., J. A. Clos, and M. G. Shoreibah, 1982: Concentric eye walls, secondary wind maxima, and the evolution of the hurricane vortex. J. Atmos. Sci., 39,