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  • View in gallery

    The model domains and the best track of Typhoon Winnie (∘; every 12 h) from 0000 UTC 6 Aug to 0000 UTC 22 Aug 1997 (JTWC 1997) and the model-simulated track from 0000 UTC 15 Aug to 0000 UTC 19 Aug 1997 (•; every 12 h).

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    NOAA satellite IR images at (a) 2138 UTC 14, (b) 0506 UTC 15, (c) 0456 UTC 16, (d) 1728 UTC 16, (e) 2212 UTC 17, and (f) 0924 UTC 18 Aug 1997.

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    (a) Horizontally polarized 85-GHz microwave Defense Meteorological Satellite Program (DMSP) imagery at 1311 UTC 16 Aug 1997 (from JTWC 1997), and (b) the GMS cloud brightness temperature (Tb; in °C) at 1320 UTC 16 Aug 1997 show Winnie’s large outer eyewall.

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    Model initial conditions in the inner domain D03 (0000 UTC 15 Aug 1997). (a) Sea level pressure (every 2 hPa). The black dot (•) is the position of Winnie estimated by JTWC (1997). (b) Streamlines (solid lines) and wind speed (dashed lines; every 2 m s−1) at 900 hPa. (c) Relative vorticity at 900 hPa (ζ; every 2 × 10−5 s−1). (d) Equivalent potential temperature (θe; every 2 K) at 500 hPa.

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    (a) Observed wind reports from Kadena Air Force Base (AFB), Okinawa (from Lander 1999), are plotted with respect to Winnie’s cloud system (shaded regions), and (b) simulated wind at a point 80 km south of Okinawa. The small black dots along the indicated track are at 5-h intervals. Wind speeds are in m s−1.

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    Time series of the sea level pressure (solid line) recorded at Kadena AFB as Winnie’s outer wall cloud (hatched region) passed (Lander 1999). Sea level pressure (dashed line) simulated at 80 km south of Okinawa. Arrows indicate the wind peaks (m s−1).

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    Model simulated at t = 37 h: (a) sea level pressure (every 2 hPa) and (b) streamlines and wind speed at 900 hPa. A, B, C, and D are the final positions of the parcels associated with the backward trajectories shown in Fig. 13a. (c) TOGA objective analysis for the sea level pressure (every 2 hPa) at 1200 UTC 16 Aug, and (d) same as (c), but for streamlines and wind speed (dashed lines, every 4 m s−1 at 900 hPa). The black dot (•) in (a) and (c) is the position of Winnie estimated by JTWC (1997), and the triangle (▴) in (a) is the location of Okinawa.

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    Model simulated at t = 37 h: (a) 3-h precipitation (with contour of 10, 25, 50, and 100 mm) from t = 34 h to t = 37 h, where shading inside outer eyewall is the area with rainfall greater than 1 mm; (b) the radar reflectivity (every 10 dBZ) at 2-km altitude and sea level pressure (every 2 hPa). Line AB is the position of the vertical cross sections shown in Figs. 11 and 12. (c) Equivalent potential temperature (θe, in K) at 500 hPa.

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    Results of model simulation at h = 37 h (1300 UTC 16 Aug). (a) Relative vorticity (ζ; every 30 × 10−5 s−1) at 900 hPa. (b) Same as (a), but for divergence (D; every 30 × 10−5 s−1), and (c) relative vorticity at 300 hPa (ζ; every 30 × 10−5 s−1).

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    Model-simulated divergence fields (D; every 10 × 10−5 s−1) fields at 900 hPa: (a) t = 1 h, (c) t = 2 h, (e) t = 3 h, and (g) t = 6 h; (b), (d), (f), and (h) same as (a), (c), (e), and (g), but for the relative vorticity (z; every 5 × 10−5 s−1). Rainfall areas greater than 5 mm h−1 are shaded.

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    Model-simulated vertical cross sections at t = 37 h along line AB shown in Fig. 8b. (a) Radar reflectivity (every 10 dBZ), (b) equivalent potential temperature (θe; every 2 K), (c) potential temperature (θ; every 2 K), and (d) relative humidity (RH; every 10%). Shaded areas in (b), (c), and (d) are the radar reflectivity greater than 20 dBZ.

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    Model-simulated vertical cross sections at t = 37 h along line AB shown in Fig. 8b. (a) Wind speeds perpendicular to the cross section represent the tangential wind Vt (every 4 m s−1), (b) wind speed along the cross section (Vr; every 4 m s−1), (c) vertical velocity (W; every 20 cm s−1 for W greater than zero, 10 cm s−1 for W smaller than zero), and (d) relative vorticity (ζ; every 20 × 10−5 s−1). Shaded areas are the radar reflectivity greater than 20 dBZ.

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    (a) Relative backward trajectories of parcels A, B, C, and D from t = 08 h to t = 37 h. Parcels A, B, C, and D are located in the maximum winds near the center at t = 37 h, 900 hPa (Fig. 7b). (b) The temporal variation of the radius, tangential wind speed, and absolute angular momentum of parcel D from t = 08 h to t = 37 h.

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Numerical Study of a Typhoon with a Large Eye: Model Simulation and Verification

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  • 1 National Center for Atmospheric Research,* Boulder, Colorado, and Department of Atmospheric Sciences, Peking University, Beijing, China
  • | 2 Department of Atmospheric Sciences, Peking University, Beijing, China
  • | 3 National Center for Atmospheric Research,* Boulder, Colorado
  • | 4 Center for Coastal and Atmospheric Research, Hong Kong University of Science and Technology, Kowloon, Hong Kong, China
  • | 5 University Corporation for Atmospheric Research, Boulder, Colorado
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Abstract

Typhoon Winnie (1997) was the fourth supertyphoon in the western North Pacific in 1997. In its mature stage, an outer eyewall, consisting of deep convection with a diameter of 370 km, was observed by satellite and radar. Within this unusually large outer eyewall existed an inner eyewall, which consisted of a ring of shallow clouds with a diameter of ∼50 km. In this study, Typhoon Winnie is simulated using a nested-grid version of the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) with an inner grid length of 9 km. The model reproduces an outer cloud eyewall with a diameter of ∼350 km. The simulated radar reflectivity and hourly precipitation are verified with satellite microwave, infrared, and cloud brightness temperature images.

Analysis of the model results indicates that the large outer eyewall in many ways possesses the structure of a typical hurricane eyewall. This includes strong tangential winds and radial inflow outside the eyewall as well as an extremely large horizontal wind shear right at the eyewall. The outer eyewall is characterized with a ring of high vorticity (RHV). This RHV is closely related to a ring of high convergence (RHC). This RHC is caused by organized convective systems along the eyewall. The eye simulated by Winnie is characterized by a broad region of warm, dry slowly sinking air.

The factors determining the diameter of eyes in tropical cyclones are discussed by considering the scale of the environmental angular momentum and the maximum kinetic energy achieved by parcels of air originating in the environment and reaching the radius of maximum wind. It is hypothesized that the formation of a large eye is favored by large circulations in which parcels of air are drawn in toward the center of the storm from great distances, and trajectories of air in Winnie that support this hypothesis are shown.

Corresponding author address: Dr. Ying-Hwa Kuo, MMM, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000. Email: kuo@ucar.edu

Abstract

Typhoon Winnie (1997) was the fourth supertyphoon in the western North Pacific in 1997. In its mature stage, an outer eyewall, consisting of deep convection with a diameter of 370 km, was observed by satellite and radar. Within this unusually large outer eyewall existed an inner eyewall, which consisted of a ring of shallow clouds with a diameter of ∼50 km. In this study, Typhoon Winnie is simulated using a nested-grid version of the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) with an inner grid length of 9 km. The model reproduces an outer cloud eyewall with a diameter of ∼350 km. The simulated radar reflectivity and hourly precipitation are verified with satellite microwave, infrared, and cloud brightness temperature images.

Analysis of the model results indicates that the large outer eyewall in many ways possesses the structure of a typical hurricane eyewall. This includes strong tangential winds and radial inflow outside the eyewall as well as an extremely large horizontal wind shear right at the eyewall. The outer eyewall is characterized with a ring of high vorticity (RHV). This RHV is closely related to a ring of high convergence (RHC). This RHC is caused by organized convective systems along the eyewall. The eye simulated by Winnie is characterized by a broad region of warm, dry slowly sinking air.

The factors determining the diameter of eyes in tropical cyclones are discussed by considering the scale of the environmental angular momentum and the maximum kinetic energy achieved by parcels of air originating in the environment and reaching the radius of maximum wind. It is hypothesized that the formation of a large eye is favored by large circulations in which parcels of air are drawn in toward the center of the storm from great distances, and trajectories of air in Winnie that support this hypothesis are shown.

Corresponding author address: Dr. Ying-Hwa Kuo, MMM, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000. Email: kuo@ucar.edu

1. Introduction

Numerical simulation of tropical cyclones, including hurricanes and typhoons, started in the late 1960s with axisymmetric models (e.g., Ooyama 1969; Yamasaki 1968a,b). The first three-dimensional simulation was achieved by Anthes et al. (1971) and Anthes (1972), using a three-level hydrostatic model with 30-km horizontal grid resolution. This simulation captured many features of a hurricane, including the asymmetric outflow and the spiral rainbands. By using a triply nested model, Jones (1977) simulated an asymmetric ring of maximum winds and a spiral convergence flow. A review of the early numerical simulations of hurricanes can be found in Anthes (1982).

Over the past two decades, considerable progress has been made in the simulation and prediction of typhoons and hurricanes. Kurihara and Bender (1982) simulated the detailed eye structure of intense hurricanes using a nested-grid model with an inner resolution of 5 km. Tripoli (1992) carried out a nonhydrostatic simulation and obtained more realistic structures of hurricane rainbands. Krishnamurti et al. (1989) demonstrated that the Florida State University high-resolution global model could forecast the deepening process and the development of spiral rainbands of a hurricane over the North Atlantic a few days in advance. Reed et al. (1988) showed that the European Centre for Medium-Range Weather Forecasts (ECMWF) model could predict hurricane genesis several days in advance. Recently, Liu et al. (1997, 1999) reported a successful simulation of Hurricane Andrew (1992) using the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (Penn State–NCAR) Mesoscale Model (MM5) with a horizontal grid size of 6 km. They simulated an echo-free eye with a diameter of 18–24 km and analyzed the kinematics and dynamics of this eye.

A well-defined eye is one of the most remarkable features of a mature tropical cyclone. In general, the diameter of a hurricane eye over the Atlantic observed by satellite varies from 55 to 85 km (Weatherford 1984). Eyes with diameters less than 55 km are considered to be small, while those with diameters greater than 85 km are considered to be large. There are some cases with extremely small eyes; for instance, supertyphoon Tip (1979) had a small eye with a diameter of 15 km and a record central pressure of 870 hPa (Dunnavan and Diercks 1980). In contrast, the Joint Typhoon Warning Center (JTWC 1960) reported a 200-mile (370 km) diameter eyewall observed by radar in Typhoon Carmen, 20 August 1960. (The JTWC reports may be found online at http://metoc.npmoc.navy.mil/jtwc/atcr/atcr_archive.html.) Both of these two extreme cases occurred over the western North Pacific and both had unusually large circulations.

Typhoon Winnie (1997) is another typhoon with an extremely large (370-km diameter) eyewall, tying Typhoon Carmen for the largest eye ever recorded (Lander 1999). This is an interesting case because it is possible that the dynamics and structure of this large eyewall may differ from those associated with normal-sized eyes. In this paper, we study the evolution and structure of Winnie’s large-diameter outer eyewall as simulated by a numerical model and verified with satellite and surface observations. Section 2 gives an overview of Typhoon Winnie. The MM5 model and initial fields are discussed in section 3. Section 4 presents the model simulation and verification. The vertical structure of the outer eyewall is analyzed in section 5. A discussion of the factors determining the diameter of eyes is provided in section 6. Finally, a summary is given in section 7.

2. Overview of Typhoon Winnie

Typhoon Winnie originated from a tropical disturbance with organized deep convection near 6°N, 167°E. It was labeled as a tropical depression by JTWC (1997) at 0600 UTC 8 August (Fig. 1). The depression moved west-northwestward and became Tropical Storm Winnie by 0600 UTC 9 August. Winnie intensified rapidly and reached typhoon intensity by 0000 UTC 10 August. It attained its peak intensity at 0600 UTC 12 August with a minimum central pressure of 898 hPa and a maximum wind speed of 72 m s−1 (JTWC 1997). A well-defined small eye was observed on the satellite image with a diameter of about 30 km at 2133 UTC 11 August (not shown) when Winnie reached its peak intensity and approached the northern Mariana Islands. Winnie maintained its intensity for the next 24 h and then weakened slowly. It moved west-northwestward, passing through Mariana Islands; Guam Island; Okinawa, Japan; Taiwan; finally landing in Zhejiang Province on the east coast of China at 1200 UTC 18 August. After landfall, Winnie recurved to the northeast, interacted with a cold front, and dissipated over northeastern China. Winnie caused significant damage along its path; China alone suffered more than several hundred million U.S. dollars in damages.

A series of National Oceanic and Atmospheric Administration (NOAA) polar-orbiting satellite infrared images with a resolution of 5 km shows the evolution of Winnie’s eyewall (Fig. 2). At 2138 UTC 14 August, Winnie was located at 22.8°N, 135.7°E. Convective cloud bands spiraled toward the center. Winnie had a typically sized eye with a diameter of about 30 km (Fig. 2a). We note that at this time there were two large convective rainbands, one located on the northwestern quarter, and the other in the southeastern quarter. Both rainbands appeared to be connected with the inner eyewall. In the next 7 h (Fig. 2b), the spiral cloud bands rotated cyclonically around the center and began to take the shape of an outer eyewall. The outer cloud band became more circular at 0456 UTC 16 August (Fig. 2c). A cloud-free zone formed over about three-quarters of the area between the outer cloud band and the eye, but the cloud band was still connected with the inner cloud eyewall. By 1728 UTC 16 August (Fig. 2d), the outer cloud bands had become detached from the inner cloud eyewall and had formed a large-diameter outer eyewall.1 A nearly cloud-free moat was created between the inner and outer eyewalls.

Observations show that many typhoons that develop a larger-than-average eye do so by the process of concentric eyewall formation with the outer ring becoming the large-diameter eyewall. Examples include Kirk (1996), Jelawat (2000), and Paka (1997). Concentric eyewalls were first reported by Fortner (1958) and were studied by Holliday (1977), Willoughby et al. (1982), and Willoughby (1990). Concentric eyewalls are relatively common features of tropical cyclones, and they frequently result in the outer eyewall contracting and weakening or destroying the inner eyewall. However, the Winnie case is unusual because of the exceptionally large diameter outer eyewall and the vast relatively echo-free region between a weak inner cloud ring and the strong outer eyewall.

Knaff et al. (2003) discuss a class of symmetric hurricanes in the Atlantic and eastern Pacific called annular hurricanes. Annular hurricanes have somewhat larger eyes than the Atlantic average of 23-km radius, but their diameters are much smaller than Winnie’s.

Careful examination of hourly satellite images showed that Winnie’s outer eyewall formed by a linking of the typhoon spiral cloud bands, and this process (approximately from 0400 to 1200 UTC 16 August) took about 8 h. The outer eyewall was quite stable. It persisted through 2212 UTC 17 August (Fig. 2e) when Winnie moved into the East China Sea. At this time, the inner eyewall became more distinct. After landing on the east coast of eastern China by 0924 UTC 18 August, the outer eyewall dissipated quickly (Fig. 2f). The total lifetime of the large-diameter eyewall was about 36 h.

The horizontally polarized 85-GHz microwave imagery at 1311 UTC 16 August (Fig. 3a; from JTWC 1997) and Geostationary Meteorological Satellite-5 GMS-5 cloud-top brightness temperature (Tb) at 1320 UTC 16 August (Fig. 3b) show this large eyewall clearly. The microwave imagery is sensitive to deep convection containing precipitation-sized hydrometeors (especially large ice particles). Mohr and Zipser (1996) used 85-GHz images to study the size and intensity of mesoscale convective systems. The clouds surrounding the eye show that the outer eyewall had a mean diameter of approximately 370 km. The cloud brightness temperature imagery (Fig. 3b) also depicts this large eye clearly. The cirrus layer that formed over the deep convection is dark gray to the infrared sensor, resulting in a wider eyewall in the infrared image.

Within the outer eyewall, there was an inner cloud wall with a diameter of about 50 km. This inner eyewall was weak and indistinct in the microwave imagery and the Tb imagery. It is likely that the development of the outer eyewall suppressed the inner eyewall by cutting off the inflow and convergence of warm moist air, as discussed by Willoughby et al. (1982) and Willoughby (1990).

Because there are no in situ data in the vicinity of the storm, we cannot study the structure of the outer eyewall and its evolution using observations alone. In the ensuing sections, we examine the structure of its extraordinary outer eyewall using the results from a numerical simulation.

3. Model description and initial condition

The MM5 is a nonhydrostatic primitive equation model with a terrain-following sigma (σ) vertical coordinate. The precipitation physics used in this study include both explicit precipitation and cumulus parameterization. The Betts–Miller (Betts and Miller 1986) parameterization scheme is used to represent subgrid-scale convection. The mixed-phase microphysics scheme of Reisner and Bruintjes (1998), which includes five prognostic equations for water vapor, cloud water, cloud ice, snow, and graupel, respectively, is used to represent moist processes on the resolvable scale. Blackadar’s high-resolution planetary boundary layer (PBL) scheme (Blackadar 1979; Zhang and Anthes 1982) is used to calculate the vertical fluxes of sensible heat, moisture, and momentum. Grell et al. (1995) provide a more detailed description of the model.

The computational domains (Fig. 1) consist of an 81-km grid with a mesh size of 112 × 132 (D01), a 27-km grid with a mesh size of 211 × 241 (D02), and a 9-km grid with a mesh size of 262 × 319 (D03). The top of the model is 50 hPa, and all the grids have 31 levels in the vertical. Domains D02 and D03 are nested within domains D01 and D02 using a two-way interaction method (Grell et al. 1995). All grids are initialized at 0000 UTC 15 August 1997 and integrated for 96 h.

The first-guess field is based on the ECMWF Tropical Ocean Global Analysis (TOGA) and is interpolated to the 81-, 27-, and 9-km grids, respectively. The initial conditions are then obtained by objectively analyzing the observational data available from the Global Telecommunication System (GTS). The GTS data include conventional surface and upper-level observations, as well as satellite-derived wind and temperatures. The objective analysis based on the TOGA analysis and GTS data are referred to as the TOGA objective analysis. The daily 1.0° resolution Reynolds sea surface temperature analysis (Reynolds and Smith 1994) from the National Centers for Environmental Prediction (NCEP) is also incorporated into the model’s initial fields. The analyses at 12-h intervals are used as the lateral boundary conditions for the 81-km grid. In order to see if the model can simulate Winnie and its outer eyewall based on the large-scale analysis alone, we did not implant an artificial vortex at the model’s initial time.

Figure 4 shows the initial field (0000 UTC 15 August) of Typhoon Winnie in D03. The central sea level pressure of Winnie is 982 hPa (Fig. 4a), compared with 950 hPa estimated by the Chinese National Meteorological Center (CNMC 1997). The streamlines at 900 hPa show cyclonic confluence of air toward the center. The maximum wind speed at 900 hPa is 29.3 m s−1 (Fig. 4b), compared with 42 m s−1 observed by Doppler radar in a layer from 0.9 to 1.8 km above sea level (JTWC 1997). Thus in the model’s initial field, Winnie is considerably weaker than observed. Since the TOGA analysis has a resolution of 2.5° latitude–longitude, it is not surprising that a weaker vortex is represented in the initial field. The initial position of Winnie (defined as the low pressure center) is located at 22.1°N, 135.8°E, while the position analyzed by JTWC (1997) is 22.8°N, 135.7°E (black dot in Fig. 4a). The position error of Winnie in the initial conditions is around 80 km.

As shown by the surface isobars and low-level wind field (Figs. 4a,b), the circulation associated with Winnie is quite large, with a diameter of approximately 20° latitude (∼2200 km). A broad ring of maximum winds is present with a radius of approximately 500 km. Positive relative vorticity (ζ) occupies a circular area with a maximum of 19.9 × 10−5 s−1 in the center (Fig. 4c). This large cyclonic circulation in the initial conditions is favorable for the formation of a large-diameter eyewall, as is discussed in section 6.

The equivalent potential temperature (θe) at 500 hPa is higher than 350 K over a large area (Fig. 4d). The equivalent potential temperature in the far environment is considerably lower, with values lower than 336 K. There are virtually no mesoscale structures associated with the TOGA objective analysis. In particular, we see no evidence of an inner or an outer eyewall of Winnie in the initial conditions.

4. Results of numerical simulation

The model results on the 9-km grid are presented in this section. Figure 1 depicts the 12-h best track obtained from JTWC (1997) and the track simulated by the model from 0000 UTC 15 August to 0000 UTC 19 August. Both tracks show a west-northwestward movement and are very similar, except that the simulated storm is located slightly south of the observed storm initially and the model storm moves slower than the observed storm. As a result, the model storm passes by Okinawa 12 h later than that of the observed storm.

As the center of Winnie passed south of Okinawa from 16 to 17 August, two wind peaks of 37 m s−1 at 2200 UTC 16 August and 42 m s−1 at 1500 UTC 17 August were recorded (Fig. 5a). These wind speed peaks were associated with the outer cloud eyewall. Since the simulated Winnie’s track was about 80 km south of that observed, the model wind vectors are plotted at a grid point about 80 km south of Okinawa (Fig. 5b). The first wind peak is simulated at 0200 UTC 17 August with a speed of 31 m s−1 and about 4-h delay than the observed peak. The second wind peak occurred at 0300 UTC 18 August with a speed of 32 m s−1, which is 10 m s−1 weaker and about 12 h later than the observed peak. This indicates that the simulated storm is weaker than the observed, particularly during the period from 48 to 72 h, when the movement of Winnie in the model was slower than that observed (Fig. 1).

The sea level pressure (SLP) time trace at Okinawa possesses a typical funnel shape with a minimum of 963 hPa (Fig. 6), with the exception of an approximately 6-h period of near “flat” pressure trace at the “bottom” of the funnel. In the model, the SLP at 80 km south of Okinawa reaches 962 hPa and is associated with two local minima. These local minima are associated with mesoscale lows within the outer eyewall. There is a larger-scale “flat” minimum that lasts for about 12 h with pressure slightly lower than 965 hPa. Although there are differences in the details, both observed and modeled storms exhibit a “flat” minimum of about 12 h in their pressure trace, suggesting a relatively constant pressure field within the outer eyewall.

Since Winnie’s outer eyewall was well established by 1300 UTC 16 August (Fig. 3; equivalent to the model simulation time t = 37 h), we compare the model results at that time against the TOGA objective analyses at 1200 UTC 16 August. Although the TOGA analysis has much coarser resolution than the 9-km grid of the model and so cannot resolve the mesoscale features found in the model, it is still useful in verifying the large-scale aspects of the model simulation. At t = 37 h, the simulated sea level pressure shows a broad region with values less than 970 hPa (Fig. 7a). Within this general area of low pressure, several mesoscale low pressure centers can be identified. The stronger one is located on the northeastern quarter of this large-scale low, with a central pressure of 961 hPa (Fig. 7a). This is only slightly higher than the value of 960 hPa estimated by CNMC (1997) at 1200 UTC 16 August. At 900 hPa, the streamlines show a large confluent circulation with a mean radius of maximum wind (RMW) of ∼250 km (Fig. 7b). A maximum wind speed of 54.8 m s−1 is simulated in the south quadrant of the storm. The Doppler radar in Okinawa indicated a maximum wind speed of 51 m s−1 in the outer eyewall in a layer from 0.9 to 1.8 km above sea level (Lander 1999).

The central pressure analyzed by TOGA objective analysis is 969 hPa (Fig. 7c), which is higher than that simulated by the model. The radius of the ring of maximum winds in the TOGA objective analysis is about 500 km, which is much larger than the simulated RMW. The mesoscale structures of the pressure, wind, and vorticity fields found in the 9-km simulation are absent in the TOGA objective analysis. Most importantly, the ring with strong cyclonic wind shear, which identifies the large outer eyewall, is not present in the analysis. We also notice that the TOGA objective analysis indicates a continuous decrease in surface pressure toward the center. The nearly flat pressure distribution in the inner region, shown in the MM5 simulation, is absent from the low-resolution TOGA analysis.

The precipitation simulated between t = 34 h and t = 37 h (Fig. 8a) shows a close heavy rainfall ring associated with the outer eyewall, with several convective centers of heavier rainfall amount, similar to that in the real storm (Fig. 3a). Two areas of light rainfall occur near the center of the storm, which are associated with the weak inner eye. Figure 8b depicts the simulated radar reflectivity at 2-km altitude calculated using the Read–Interpolate–Plot (RIP) program developed by NCAR and the University of Washington (appendix). The simulated radar reflectivity also shows several high reflectivity bands (>40 dBZ) along the eyewall.

Figure 8c depicts the model’s equivalent potential temperature (θe) at 500 hPa at 37 h. The inner boundary of the outer eyewall is characterized by a ring of high θe gradient (up to 0.25 K km−1), with an average diameter of near 350 km. The outer eyewall is characterized by a ring of θe greater than 354 K. This high θe ring is caused by upward motion and the associated upward transport of high θe air from the boundary layer. Several maxima of θe > 360 K can be identified within the cloud eyewall.

The simulation develops a ring of high relative vorticity (RHV) with a mean diameter of ∼350 km at 900 hPa (Fig. 9a). This RHV lies just inside the ring of strong precipitation (Fig. 8a), which also has a mean diameter of about 350 km and can be regarded as the model eyewall. The structure of the vorticity field is very different from that in the initial condition (Fig. 4c). The formation of this RHV is closely related to the divergence field, as the simulated divergence field at 900 hPa also shows a “ring of high convergence” (RHC) with the same diameter (Fig. 9b). The maximum convergence centers (up to −132 × 10−5 s−1) in the strong convergence belt are collocated with the relative vorticity maxima.

There are several maximum vorticity centers distributed within the RHV, which are similar to the mesoscale structures discussed by Schubert et al. (1999). At 300 hPa, the RHV remains robust with a diameter of near 350 km (Fig. 9c). This suggests that the outer eyewall extends to the upper troposphere and its shape does not change very much with height.

To help explain the rapid development of the outer eyewall and its associated vorticity field, we estimate the amount of time required for vorticity spinup. The time scale (T) needed for the generation of vorticity can be written as (Anthes 1982)
i1520-0493-133-4-725-e1

Here (ζ + f )0 is the absolute vorticity at the initial time, and D = − · v is the divergence. At the initial time (Fig. 4c), the average absolute vorticity over a circular area of radius 350 km from the center of Winnie is ∼17 × 10−5 s−1. If we take D = 10 × 10−5 s−1, the time needed for the vorticity to reach 60 × 10−5 s−1 is only ∼4 h. We note that the vorticity generation through convergence is a nonlinear process, with the convergence increasing along with the vorticity during the spinup process. Convective effects and surface friction can also be important. Therefore, this can only be regarded as a rough estimate, but it does show that the time needed to create a RHV is quite short.

There are two weak vorticity centers associated with the two precipitation areas inside the outer eyewall (Fig. 9a), representing the inner eyewall. Thus, the model simulates both the outer eyewall and the inner eyewall, although the 9-km model resolution is not able to describe this inner eyewall in detail.

We next consider the formation of the outer eyewall, specifically the transformation from the large circular region of vorticity (Fig. 4c) into a ring of strong vorticity (Fig. 9a). Figure 10 shows the evolution of the vorticity and divergence fields at 900 hPa from 1 to 6 h in the 9-km simulation. Areas with hourly rainfall greater than 5 mm are shaded to indicate the heavier convection. At hour 1, two rainfall areas, associated with two convergence centers, develop about 200 km south of the center (Fig. 10a). The vorticity at the center of Winnie does not change much from its initial value (Fig. 10b), while vorticity is locally strengthened over the region of two rainbands. At hour 2, rainfall area has expanded to a ring with a diameter of ∼350 km (Fig. 10c). Several mesoscale vorticity centers greater than 20 × 10−5 s−1 appear between the circular area enclosed by the 10 × 10−5 s−1 and 15 × 10−5 s−1 contours along the convective ring (Fig. 10d). The rings of convection and divergence continue to develop (Fig. 10e), and mesoscale vorticity centers continue to intensify at t = 3 h (Fig. 10f). The vorticity ring with intensity greater than 20 × 10−5 s−1 finally forms at t = 06 h (Fig. 10h). Vorticity at the center of Winnie has decreased to a value lower than 10 × 10−5 from 19.9 × 10−5 s−1 at the initial time (Fig. 4c). These analyses indicate that the 9-km model reproduces the outer eyewall within 6 h of the simulation. With convection triggered at a large distance away from the center, a ring of convergence forms, which transforms the structure of the vorticity field from a large circular area into a ring of strong vorticity, which then becomes the outer eyewall.

5. Vertical structure of the outer eyewall

We focus our analysis on the structure of the outer eyewall at t = 37 h (i.e., at 1300 UTC 16 August) in this section. A series of cross sections along line AB (shown in Fig. 8b), which cuts across the outer eyewall, are constructed. Figure 11a shows the simulated radar reflectivity. High radar reflectivity is concentrated in a narrow band with a width of 100 km and extends upward to 150 hPa, coincident with the outer eyewall clouds observed from satellite (Figs. 3a,b). The diameter of the eyewall remains the same throughout the troposphere; it does not expand with height as found in a typical hurricane eyewall [an example of eyewall expanding with height can be found in the simulation of Andrew by Liu et al. (1997)].

The equivalent potential temperature (θe) cross section shows the thermal structure of the eye (Fig. 11b). The outer eyewall is associated with a column of high θe. The inner boundary of the outer eyewall is characterized by a sharp gradient of θe. The θe within the outer eyewall is relatively high (372 K) at the surface. This warm moist air is caused by the addition of sensible and latent heat from the ocean as air flows into the eye (Rotunno and Emanuel 1987).

The vertical cross section of θe suggests that the potentially unstable air within the PBL, with θe greater than 368 K at the surface, is being transported toward the eye and rises in the eyewall. In the area between inner and outer eyewalls, the boundary layer is potentially unstable, with θe ≈ 370 K at the sea surface, decreasing rapidly to 360 K at 950 hPa. Air with lower θe (<350 K) is located in the middle troposphere both inside and outside the outer eyewalls. Such lower θe air at the center has been observed in Hurricane Inez (1966) (Hawkins and Imbembo 1976). There is not a well-defined warm temperature anomaly at the center of Winnie (Fig. 11c), in contrast to that of a storm with a small intense eye like Hurricane Inez (1996) (Hawkins and Imbembo 1976) or Andrew (1992) (Liu et al. 1997). The mixing ratio at 700 hPa is less than 8 g kg−1 at the center of Winnie, compared with 14 g kg−1 in the outer eyewall (figure not shown). The relative humidity is below 70% in the middle troposphere (Fig. 11d) between the inner and outer eyewall, suggesting subsidence-induced drying.

Figure 12a shows the wind speeds perpendicular to the cross section AB shown in Fig. 8b. A maximum wind speed of 42.9 m s−1 occurs near 850 hPa. The wind speed drops off sharply at the inner boundary of the outer eyewall. The air stops spiraling inward at a large distance from the center of Winnie to rise upward and form the outer eyewall. Strong cyclonic shear [up to 40 m s−1 (50 km−1)] occurs just inside the outer eyewall. The ring of cyclonic wind shear extends up to 250 hPa with very little tilt. In the lowest 100 hPa, the radial inflow reaches 18 m s−1 (Fig. 12b) and decreases rapidly to near zero at the outer eyewall. Moderate outflow occurs between 800 and 400 hPa in the southeast quadrant of the eyewall (right side of the cross section), just above the inflow layer. Outflow extends from 500 to 300 hPa in the northwest quadrant (left side of the cross section).

Strong upward motion occurs at the eyewall (Fig. 12c), with a maximum updraft of ∼201 cm s−1 at 550 hPa. Because of the large area enclosed by the outer eyewall, the compensating downward motion in the eye is rather weak (less than 10 cm s−1). This adiabatic downward motion dries and warms the air.

The relative vorticity is closely related to the horizontal shear of the tangential winds. The maximum cyclonic vorticity in the outer eyewall reaches 1.1 × 10−3 s−1 at the top of the PBL (which is about 20 times greater than the local Coriolis parameter) (Fig. 12d). The two weak cyclonic vorticity centers around 850 hPa near the center of Winnie are associated with the simulated inner eye.

In summary, the model shows that Winnie’s large-diameter eyewall is characterized by an RHV. The mean vertical circulation consists of inflow below 900 hPa and outflow between 850 and 400 hPa. A strong updraft occurs in the RHV, which is also the region of convective cloud and precipitation. The θe in the eyewall is relatively high; this is due to convection, which transports high θe in the boundary layer upward. There is no strong warm, dry downdraft on the inside of eyewall, as occurs in intense hurricanes with small eyes. Since the eye of Winnie is large, the sinking motion covers a broad area and is weak. In the layer 500–700 hPa in the broad eye, the θe is lower than 350 K, and the relative humidity is below 70%.

6. Factors affecting the diameter of eyewalls in tropical cyclones

The successful simulation of Winnie’s large-diameter eyewall, from only large-scale initial conditions, suggests that large-scale environmental factors play a significant role in determining the radius of the eye and the RMW. We hypothesize that the diameter of eyewalls in tropical cyclones is determined to a significant degree by the distribution and horizontal scale of angular momentum in the tropical cyclone environment and the maximum kinetic energy achieved by parcels of air that originate in this environment. For a given maximum wind speed, the greater the initial absolute angular momentum of parcels reaching the RMW, the larger that radius is likely to be. Thus, for large storms like Winnie in which parcels of air arrive at the RMW from a large distance, the RMW will tend to be large.

To show how kinetic energy and angular momentum constraints affect the size of the eye, we consider an axisymmetric vortex on an f plane and neglect friction. In cylindrical coordinates, the absolute angular momentum (M) is
i1520-0493-133-4-725-e2
where V is the tangential velocity, R is the radius from the center of the storm, and f is the Coriolis parameter. At the RMW the specific kinetic energy K is a maximum, Kmax:
i1520-0493-133-4-725-e3
where Vmax is the maximum wind speed achieved by a parcel of air originating in the environment and reaching the RMW, denoted as Rmax.
Under the assumption of no friction, the angular momentum of each parcel is conserved, including the parcels that reach Rmax. The angular momentum of such parcels when they achieve Vmax at the Rmax is the same as their initial angular momentum Mi. Thus we can relate the initial angular momentum Mi to Vmax, and Rmax as
i1520-0493-133-4-725-e4
or
i1520-0493-133-4-725-e5

Thus, Rmax is dependent on Vmax and Mi. For a given Vmax, Rmax increases with increasing angular momentum of parcels originating in the environment and reaching the eyewall. The effect of friction will be to reduce the angular momentum of parcels as they spiral in toward the center of the storm, and hence they can reach smaller distances from the center before they reach Vmax. Thus, the value of Rmax given by (5) is an upper estimate.

In summary, tropical cyclones with large circulations that draw air inward from great distances (where the absolute angular momentum is large) will tend to have large eyewalls. Typhoon Winnie had a large cyclonic circulation; the Mi of parcels drawn in toward the center of the storm was high, and thus a large eyewall was formed. Typhoon Carmen (1960), which is tied with Winnie for the largest eye ever observed, also had an extremely large circulation, about 1500 km in diameter (JTWC 1960).

We illustrate (5) for some parameters representative of the Winnie case. At 0000 UTC 15 August, Winnie was located at 32°N. If we set the maximum wind speed (Vmax) to 50 m s−1 (approximately the maximum wind speed in the simulated eyewall), the Rmax values calculated with different Ri and Mi are shown in Table 1. For these calculations the Coriolis parameter was taken to be 7.73 × 10−5 s−1 (φ = 32°N). For a small circulation, indicated by an Ri = 100 km, the Rmax is only 16 km, while if the initial Ri is taken to be 400 km, the Rmax increases to 262 km, which is nearly the same as the radius of maximum wind in the Winnie simulation. As noted above, friction allows parcels of air to arrive at a smaller Rmax than given by the values of Rmax in Table 1.

Although the absolute angular momentum in tropical cyclones is not conserved because of friction, this calculation shows that a large eye is favored by a large circulation in which air parcels with high angular momentum far from the storm center are drawn inward toward the center. We investigate this hypothesis further by considering several low-level trajectories in the model simulation.

Figure 13a depicts backward trajectories of four parcels (A, B, C, and D) relative to the storm center from 8 to 37 h. At 37 h, all four parcels arrive at 900 hPa in the RMW, with tangential wind speeds ∼40 m s−1. The final locations of the parcels are shown in Fig. 7b. All four parcels originate at lower levels (in the boundary layer) more than 700 km from the center and spiral in toward the center. The temporal variations of the radius, tangential wind speed, and absolute angular momentum of trajectory D are shown in Fig. 13b. In the first 24 h, the tangential wind speed of parcel D remains nearly constant while the radius decreases. The absolute angular momentum also decreases steadily as a result of friction. After 24 h parcel D begins to accelerate in toward the center and the tangential wind speed increases, reaching 41 m s−1 at 37 h, even though the angular momentum decreases significantly due to friction. Without friction, the velocity would have reached 41 m s−1 at a larger radius. These trajectories and the temporal variation of tangential velocity and absolute angular momentum along the trajectories qualitatively support the hypothesis that large eyes are favored by storms in which low-level parcels of air, with initially high values of angular momentum, are drawn inward toward the center of the storm from large distances.

Although the simulation of Winnie and the trajectories of the low-level air approaching the center from large distances in the environment support the hypothesis that large eyes are favored by large circulations, not all typhoons with large circulations have large eyes. For example, Supertyphoon Tip, the most intense typhoon on record, had one of the largest circulations ever observed (∼2200 km diameter) and yet Tip had an eye diameter only about 15 km (JTWC 1979). Thus large circulations do not uniquely determine a large eye; other factors are important, including kinetic energy production, frictional loss of angular momentum along the trajectory of inward-moving air, and likely other related factors such as static stability and vertical mixing of momentum. As discussed above, for a given size of circulation, the diameter of the eyewall will be smaller for higher maximum kinetic energy (V2 max), which is consistent with intense Typhoon Tip’s small eye. Furthermore, if friction is considered as the parcels of air spiral inward toward the center, angular momentum will be lost along the way (as shown in Fig. 13) and the air can reach smaller radii. For storms of a given circulation size, smaller eyes will be favored for situations in which the parcels of air take a long time to reach the center, losing angular momentum along the way, and then gain kinetic energy rapidly near the center of the storm.

Thus the size of the tropical cyclone circulation alone does not determine the radius of maximum wind and the size of the eye. The details of the generation of kinetic energy and the loss of angular momentum by friction must be considered in a complete explanation of what determines the size of the eye and the maximum wind speed. Numerical models with appropriate physics and initialized with a good description of the large-scale environmental flow may be able to correctly forecast the size and intensity of the tropical cyclone inner region.

7. Summary

Typhoon Winnie (1997), with an extremely large-diameter outer eyewall, is studied using the MM5 with a horizontal resolution of 9 km. The main findings are as follows:

  1. The model reproduces an outer eyewall with a mean diameter of ∼350 km. The outer eyewall, though very large in size, in many ways resembles a typical hurricane eyewall, with strong upward motion and precipitation, strong tangential winds and strong radial inflow immediately outside the eyewall. Strong horizontal wind shear exists inside the outer eyewall.

  2. The outer eyewall is characterized by high θe and a large θe gradient at the inner boundary of the eyewall. Because the diameter of the eyewall is extremely large, the subsidence of warm, dry air in the eye is weak and covers a broad area.

  3. The eyewall is also characterized by a ring of high vorticity (RHV) and a ring of high convergence (RHC). The RHC is caused by organized convection, which in turn supports the development of the RHV.

  4. We hypothesize that the size of the eye in a tropical cyclone is determined to a significant degree by the distribution of angular momentum in the tropical cyclone environment, the degree to which angular momentum is conserved as the low-level air spirals inward toward the eye, and the maximum kinetic energy achieved by the parcels of air reaching the eyewall. Very large eyes are favored by large circulations in which air far from the storm center is drawn in toward the center. This hypothesis is supported in the Winnie simulation by trajectories of low-level air that originate far from the storm center and spiral in to reach the radius of maximum wind.

Acknowledgments

The authors would like to thank Drs. C. A. Davis and C.-C. Wu for their valuable comments. This work is supported by NCAR’s Advanced Study Program; the Taiwan Civil Aeronautics Administration’s Advanced Operational Aviation Weather System (AOAWS) Project; the Mesoscale and Microscale Meteorology Division of NCAR; the Chinese Natural Science Foundation under Grants 40233036 and 40375017; and the Chinese National Key Project 2004CB418301.

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APPENDIX

Calculating Scheme of Radar Reflectivity

Radar reflectivity (RF) is calculated using the RIP program developed by NCAR and the University of Washington. It is derived from the model output of pressure, temperature, moisture, rainwater, snow, and graupel mixing ratio:
i1520-0493-133-4-725-eqa1
where ρ is the density of atmosphere
i1520-0493-133-4-725-eqa2
Here P is pressure, Rd = 287.04 n m K−1 kg−1, Tv is virtual temperature, and qr, qs, qp are rainwater, snow, and graupel mixing ratio, respectively.

Fig. 1.
Fig. 1.

The model domains and the best track of Typhoon Winnie (∘; every 12 h) from 0000 UTC 6 Aug to 0000 UTC 22 Aug 1997 (JTWC 1997) and the model-simulated track from 0000 UTC 15 Aug to 0000 UTC 19 Aug 1997 (•; every 12 h).

Citation: Monthly Weather Review 133, 4; 10.1175/MWR2867.1

Fig. 2.
Fig. 2.

NOAA satellite IR images at (a) 2138 UTC 14, (b) 0506 UTC 15, (c) 0456 UTC 16, (d) 1728 UTC 16, (e) 2212 UTC 17, and (f) 0924 UTC 18 Aug 1997.

Citation: Monthly Weather Review 133, 4; 10.1175/MWR2867.1

Fig. 3.
Fig. 3.

(a) Horizontally polarized 85-GHz microwave Defense Meteorological Satellite Program (DMSP) imagery at 1311 UTC 16 Aug 1997 (from JTWC 1997), and (b) the GMS cloud brightness temperature (Tb; in °C) at 1320 UTC 16 Aug 1997 show Winnie’s large outer eyewall.

Citation: Monthly Weather Review 133, 4; 10.1175/MWR2867.1

Fig. 4.
Fig. 4.

Model initial conditions in the inner domain D03 (0000 UTC 15 Aug 1997). (a) Sea level pressure (every 2 hPa). The black dot (•) is the position of Winnie estimated by JTWC (1997). (b) Streamlines (solid lines) and wind speed (dashed lines; every 2 m s−1) at 900 hPa. (c) Relative vorticity at 900 hPa (ζ; every 2 × 10−5 s−1). (d) Equivalent potential temperature (θe; every 2 K) at 500 hPa.

Citation: Monthly Weather Review 133, 4; 10.1175/MWR2867.1

Fig. 5.
Fig. 5.

(a) Observed wind reports from Kadena Air Force Base (AFB), Okinawa (from Lander 1999), are plotted with respect to Winnie’s cloud system (shaded regions), and (b) simulated wind at a point 80 km south of Okinawa. The small black dots along the indicated track are at 5-h intervals. Wind speeds are in m s−1.

Citation: Monthly Weather Review 133, 4; 10.1175/MWR2867.1

Fig. 6.
Fig. 6.

Time series of the sea level pressure (solid line) recorded at Kadena AFB as Winnie’s outer wall cloud (hatched region) passed (Lander 1999). Sea level pressure (dashed line) simulated at 80 km south of Okinawa. Arrows indicate the wind peaks (m s−1).

Citation: Monthly Weather Review 133, 4; 10.1175/MWR2867.1

Fig. 7.
Fig. 7.

Model simulated at t = 37 h: (a) sea level pressure (every 2 hPa) and (b) streamlines and wind speed at 900 hPa. A, B, C, and D are the final positions of the parcels associated with the backward trajectories shown in Fig. 13a. (c) TOGA objective analysis for the sea level pressure (every 2 hPa) at 1200 UTC 16 Aug, and (d) same as (c), but for streamlines and wind speed (dashed lines, every 4 m s−1 at 900 hPa). The black dot (•) in (a) and (c) is the position of Winnie estimated by JTWC (1997), and the triangle (▴) in (a) is the location of Okinawa.

Citation: Monthly Weather Review 133, 4; 10.1175/MWR2867.1

Fig. 8.
Fig. 8.

Model simulated at t = 37 h: (a) 3-h precipitation (with contour of 10, 25, 50, and 100 mm) from t = 34 h to t = 37 h, where shading inside outer eyewall is the area with rainfall greater than 1 mm; (b) the radar reflectivity (every 10 dBZ) at 2-km altitude and sea level pressure (every 2 hPa). Line AB is the position of the vertical cross sections shown in Figs. 11 and 12. (c) Equivalent potential temperature (θe, in K) at 500 hPa.

Citation: Monthly Weather Review 133, 4; 10.1175/MWR2867.1

Fig. 9.
Fig. 9.

Results of model simulation at h = 37 h (1300 UTC 16 Aug). (a) Relative vorticity (ζ; every 30 × 10−5 s−1) at 900 hPa. (b) Same as (a), but for divergence (D; every 30 × 10−5 s−1), and (c) relative vorticity at 300 hPa (ζ; every 30 × 10−5 s−1).

Citation: Monthly Weather Review 133, 4; 10.1175/MWR2867.1

Fig. 10.
Fig. 10.

Model-simulated divergence fields (D; every 10 × 10−5 s−1) fields at 900 hPa: (a) t = 1 h, (c) t = 2 h, (e) t = 3 h, and (g) t = 6 h; (b), (d), (f), and (h) same as (a), (c), (e), and (g), but for the relative vorticity (z; every 5 × 10−5 s−1). Rainfall areas greater than 5 mm h−1 are shaded.

Citation: Monthly Weather Review 133, 4; 10.1175/MWR2867.1

Fig. 11.
Fig. 11.

Model-simulated vertical cross sections at t = 37 h along line AB shown in Fig. 8b. (a) Radar reflectivity (every 10 dBZ), (b) equivalent potential temperature (θe; every 2 K), (c) potential temperature (θ; every 2 K), and (d) relative humidity (RH; every 10%). Shaded areas in (b), (c), and (d) are the radar reflectivity greater than 20 dBZ.

Citation: Monthly Weather Review 133, 4; 10.1175/MWR2867.1

Fig. 12.
Fig. 12.

Model-simulated vertical cross sections at t = 37 h along line AB shown in Fig. 8b. (a) Wind speeds perpendicular to the cross section represent the tangential wind Vt (every 4 m s−1), (b) wind speed along the cross section (Vr; every 4 m s−1), (c) vertical velocity (W; every 20 cm s−1 for W greater than zero, 10 cm s−1 for W smaller than zero), and (d) relative vorticity (ζ; every 20 × 10−5 s−1). Shaded areas are the radar reflectivity greater than 20 dBZ.

Citation: Monthly Weather Review 133, 4; 10.1175/MWR2867.1

Fig. 13.
Fig. 13.

(a) Relative backward trajectories of parcels A, B, C, and D from t = 08 h to t = 37 h. Parcels A, B, C, and D are located in the maximum winds near the center at t = 37 h, 900 hPa (Fig. 7b). (b) The temporal variation of the radius, tangential wind speed, and absolute angular momentum of parcel D from t = 08 h to t = 37 h.

Citation: Monthly Weather Review 133, 4; 10.1175/MWR2867.1

Table 1.

The Rmax of a parcel calculated for different Ri and Mi in Winnie’s initial condition (0000 UTC 15 Aug).

Table 1.

* The National Center for Atmospheric Research is sponsored by the National Science Foundation.

1

 This large-diameter eyewall formed around 1311 UTC 16 August (see Fig. 3a).

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