Tropical Cyclone Kinematic Structure Retrieved from Single-Doppler Radar Observations

3982 MONTHLY WEATHER REVIEW VOLUME 128

Tropical Cyclone Kinematic Structure Retrieved from Single-Doppler Radar Observations. Part III: Evolution and Structures of Typhoon Alex (1987)

WEN-CHAU LEE National Center for Atmospheric Research,* Boulder, Colorado

BEN J.-D. JOU AND PAO-LIANG CHANGϩ Department of Atmospheric Sciences, National Taiwan University, Taipei, Taiwan, Republic of China

FRANK D. MARKS JR. NOAA/AOML/Hurricane Research Division, Miami, Florida

(Manuscript received 22 October 1999, in ®nal form 16 May 2000)

ABSTRACT This paper is the third of a series that focuses on the applications of the ground-based velocity track display (GBVTD) technique and the GBVTD-simplex center ®nding algorithm developed in the previous two papers to a real tropical cyclone (TC). The evolution and structure of Typhoon Alex (1987), including full tangential winds, mean radial winds, one component of the mean ¯ow, and their derived axisymmetric angular momentum and perturbation pressure ®elds are reconstructed from 16 volume scans (6.5 h of data with a 2-h gap) from the Civil Aeronautic Administration (CAA) Doppler radar while Typhoon Alex moved across the mountainous area in northern Taiwan. This analysis retrieves a plausible and physically consistent three-dimensional primary circulation of a landfalling TC using a single ground-based Doppler radar. Highly asymmetric wind structures were resolved by the GBVTD technique where the maximum relative tangential wind at z ϭ 2 km evolved from 52 m sϪ1 (before landfall), to less than 40 m sϪ1 (after landfall), to less than 35 m sϪ1 (entering the East China Sea). Alex's eye began to ®ll with precipitation while its intensity decreased rapidly after landfall, a characteristic of circulations disrupted by terrain. The mean radial wind ®eld revealed a layer of low-level in¯ow in agreement with past TC observations. The outward slope of the eyewall re¯ectivity maximum was consistent with the constant angular momentum contours within the eyewall. After Alex entered the East China Sea, its circulation became more axisymmetric. The axisymmetric perturbation pressure ®eld was retrieved using the gradient wind approximation, which, when used in conjunction with one or more surface pressure measurements within the analysis domain, can estimate the central pressure. The retrieved perturbation pressure ®elds at two time periods were compared with surface pressures reported in northern Taiwan. Considering the assumptions involved and the in¯uence of terrain, good agreement (only 1±2-mb deviation) was found between them. This agreement indicates the relative quality of the GBVTD-retrieved axisymmetric circulation and suggests GBVTD-retrieved quantities can be useful in operational and research applications.

1. Introduction Research Program by the Fifth Prospectus Development Hurricane forecasts near landfall has been identi®ed Team (PDT-5) (Marks et al. 1998). In order to improve as one of the three research focuses in the U.S. Weather the understanding of the physical processes and provide the initial conditions for realistic numerical predictions, PDT-5 recognized the need to collect comprehensive three-dimensional (3D) datasets over the storm scale * The National Center for Atmospheric Research is sponsored by the National Science Foundation. from all available observing platforms (e.g., Doppler ϩ Current af®liation: Wu-Fen-Shan Radar Station, Central Weather radar, satellite, aircraft, etc.). Several of the research Bureau, Taipei, Taiwan, Republic of China. objectives identi®ed by PDT-5 require detail descrip- tions of the tropical cyclone (TC) circulation near landfall. The recently completed coastal Weather Surveil- Corresponding author address: Dr. Wen-Chau Lee, National Cen- ter for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307- lance Radar-1988 Doppler (WSR-88D) network in the 3000. United States provides a unique opportunity to contin- E-mail: [email protected] uously monitor the precipitation intensity (via radar re-

᭧ 2000 American Meteorological Society

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¯ectivity factor) and Doppler velocity of landfalling II). It is demonstrated in Part II that a nominal 1±2-km TCs. error in the estimated TC center is required to keep the Although the 3D kinematic structures of TCs have error in the GBVTD-derived asymmetric circulation be- been deduced from single- and/or dual-airborne Doppler low 20%. In order to achieve this goal, the GBVTD- radar analysis (e.g., Marks and Houze 1987; Marks et simplex TC center ®nding algorithm was developed to al. 1992; Lee et al. 1994; Roux and Viltard 1995; Roux objectively identify the TC center2 from single-Doppler and Marks 1996), past ground-based dual-Doppler radar radar data. When tested on analytical TCs with a known analyses on a few TCs revealed primarily TC rainband circulation center, Part II showed that the mean errors structures, not the storm-scale circulation (e.g., Blue- of the GBVTD-simplex determined TC centers were less stein and Hazen 1989; Ishihara et al. 1986; Jou et al. than 500 m computed on a 1-km horizontal grid reso- 1997, 1999; Wang and Tseng 1999). This disparity re- lution. When the GBVTD-simplex algorithm was ap- sults from the fact that the dual-Doppler analysis domain plied to Typhoon Alex (1987), the estimated uncertainty is usually limited only to a portion of the TC. Single- of the objectively determined center3 were between 1 Doppler radar analysis techniques (e.g., Wood and and 2 km while the uncertainty can be as high as 3±4 Brown 1992) can estimate intensity and location of an km in some conditions discussed in Part II. axisymmetric TC from the Doppler velocity dipole sig- The purpose of this paper is twofold: 1) demonstrate nature. These Doppler velocity signatures (e.g., zero that the GBVTD technique produced reasonable TC Doppler velocity line, Doppler velocity maxima, and structures on a real TC, and 2) document the evolution the Doppler velocity gradient across the zero Doppler and structure of Typhoon Alex under the in¯uence of velocity line) are valuable information to infer TC cir- topography. Emphasis is placed on the structure and culations in operational forecast. However, Lee et al. intensity change before, during, and after Alex's landfall (1999) illustrated that structures of asymmetric TCs may on northern Taiwan where terrain played a major role not be properly inferred via these basic Doppler velocity in modifying the storm structure. Although there were signatures due to the close proximity in these velocity no aircraft in situ measurements to verify the retrieved patterns. This series of papers [including Lee et al. kinematic quantities, the retrieved axisymmetric per- (1999, hereafter Part I) and Lee and Marks (2000, here- turbation pressure is compared with the surface pressure after Part II)] attempts to bridge this gap by proposing reported at ®ve stations in northern Taiwan to test the and demonstrating a TC wind retrieval technique, the consistency of the wind retrieval. ground-based velocity track display (GBVTD) present- Section 2 presents a synopsis of Typhoon Alex. Sec- ed in Part I, that can be used to derive a plausible and tion 3 discusses the GBVTD analysis procedures and consistent TC primary circulation (i.e., tangential derived quantities. The evolution and asymmetric struc- winds) from the velocity data collected by a single ture of Alex are presented in section 4. Section 5 illus- ground-based Doppler radar. trates the axisymmetric structure of Alex using the The mathematical formulation of the GBVTD tech- GBVTD-retrieved axisymmetric winds, angular mo- nique and its intrinsic assumptions and limitations were mentum, and perturbation pressure. The perturbation presented in Part I. Assuming a circular wind model and pressures at two time periods are compared with surface ignoring asymmetric radial winds,1 the GBVTD tech- pressure reports in section 6. Summary and conclusions nique retrieves the axisymmetric tangential wind and are presented in section 7. Practical limitations of ap- radial wind, wavenumbers 1±3 of tangential wind, and plying GBVTD technique to real data are discussed in the mean cross-TC ¯ow, via a least squares ®t of the the appendix. observed radial velocities on each radius and altitude on a cylindrical coordinate centered at the TC. Part I 2. Typhoon Alex showed that the GBVTD technique retrieved robust two- dimensional asymmetric TC primary circulations from Typhoon Alex formed in the western Paci®c, east of the simulated single-Doppler radar observations of sev- the Philippines on 23 July 1987. It moved northwest eral analytic TCs, especially for the three lowest wave- steadily along the southwestern edge of the subtropical numbers. high. Alex then moved NNW along the east coast of It is noted in Part I and other studies (e.g., Lee et al. Taiwan. Alex's intensity (maximum wind speed and cen- 1994; Roux and Marks 1996) that accurately knowing the TC center critically determines the quality of the GBVTD-retrieved TC circulation. Here, the TC center 2 In a circular ¯ow model, the most dynamically consistent TC is de®ned as the circulation center or the vorticity center circulation center is a point that maximizes the axisymmetric tan- of a TC (consistent with de®nition used in Parts I and gential wind at the radius of maximum wind (Part II).

3 The center is de®ned as the average position among all possible 1 The three components of the TC circulation in the TC cylindrical centers (within one standard deviation) computed from various initial coordinates are termed tangential wind, radial wind, and vertical guesses. The uncertainty is estimated from the standard deviation wind, while the single-Doppler velocity is termed Doppler velocity. among all runs.

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FIG. 1. The minimum central pressure (P), the maximum wind speed (W), and the storm motion (Vs) of Typhoon Alex (1987). Here TS represents tropical storm [adapted from Wang (1987)]. tral pressure) and storm speed from 1400 LST (LST ϭ UTC ϩ 8; hereafter, all times are LST) 24 July to 0800 28 July 1987 estimated from satellite images are illustrated in Fig. 1 [adapted from Wang (1987)]. Alex reached hurricane strength (maximum wind exceeding 34 m sϪ1) about 1400 25 July 1987, and weakened to a tropical storm about 1100 27 July 1987. During this 3-day period, it moved generally NNW between 5 and 7msϪ1. The Civil Aeronautic Administration (CAA) Doppler radar is a C-band operational radar located at Chiang- Kai-Shek International Airport in northwestern Taiwan (marked by the radar symbol in Fig. 2). The characteristics of the CAA Doppler radar are summarized in Table FIG. 2. The circulation centers (indicated by hurricane symbol) of 6 of Part II. The CAA Doppler radar has a maximum Typhoon Alex determined from the GBVTD-simplex algorithm from range of 120 km in the Doppler mode and completes a 0417 to 1047 LST on 27 Jul 1987. Gray shades are the topography 10 elevation angle volume scan every 15 min. Alex's of northern Taiwan. center entered CAA's Doppler range around 0400 27 July 1987 and left CAA's Doppler range about 1100 27 July 1987. There were no observations between 0700 There were 1±2-km variations in Alex's computed and 0917 due to a power outage at the CAA radar site. centers from 1- to 3-km altitude. Our results suggest A total of 16 volume scans (0432±0647 and 0917±1032) that radius of maximum wind (RMW) may vary with were available for analysis. height, which is supported by the vertical tilt of the The topography in northern Taiwan within 120 km axisymmetric tangential winds and re¯ectivity factors of the CAA radar is quite variable (Fig. 2). The altitude with altitude. No subjective adjustments to the GBVTD- simplex derived TC centers were made in this study. of the central mountain range decreases from ഠ3000 m We chose to use the GBVTD-simplex determined TC south of CAA to ഠ500 m east of CAA. As a result, circulations below 1-km altitude were partially blocked centers at 2-km altitude (above the terrain in northern by the central mountain range east to southeast of the Taiwan) (Table 1 and Fig. 2) and realized there were CAA radar. CAA Doppler radar data were edited to potential errors in the retrieved asymmetric components remove noise and ground contaminated data. The dual- resulting from this assumption. Unfortunately, we can- pulse repetition frequency capability of the CAA radar not assess the impact of using a ®xed TC center without independent information such as concurrent aircraft in extended the maximum unambiguous velocity to Ϯ48 situ data. msϪ1. Hence, the velocity was easily dealiased because the Doppler velocities are between Ϯ55 m sϪ1. Alex's circulation center in each radar volume was 3. The GBVTD analysis and products objectively determined using the GBVTD-simplex TC a. The GBVTD analysis center ®nding algorithm (Part II) and was computed in a 1-km grid in all three directions from 1 to z ϭ 10 km The GBVTD analysis provides one component of the altitude. However, in this case the center computation mean ¯ow, axisymmetric tangential and radial winds, is unusable above 4 km because of missing data at higher and the asymmetric tangential winds from single-Dopp- altitudes. Please refer to Part II for computational details ler radar data, as outlined in Part I. The Doppler radar and limitations of the GBVTD-simplex algorithm. data collected in a constant elevation angle mode are

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TABLE 1. The GBVTD-simplex derived center locations, radius of TABLE 2. The single largest data gap allowed to determine the maximum wind, direction and speed of Typhoon Alex, and domain maximum wavenumber used in the least squares ®t. for the GBVTD analysis at 2-km altitude and different time. Wavenumber Gap (Њ) Central x Central y RMW Spd Domain 0 Յ180 Time (km) (km) (km) Dir (Њ) (m sϪ1) (km) 1 Յ90 417 95.50 Ϫ50.00 31.0 303.94 13.93 5±60 2 Յ60 432 85.10 Ϫ43.00 30.0 300.67 13.18 5±60 3 Յ30 447 75.10 Ϫ37.90 21.0 314.44 8.01 5±60 502 74.80 Ϫ32.90 23.0 326.82 8.63 5±60 517 66.60 Ϫ24.90 25.0 311.69 9.86 5±60 533 61.10 Ϫ20.70 25.0 319.21 9.10 5±60 dinates are always positioned near 90Њ and 270Њ in all 547 55.90 Ϫ12.50 24.0 320.19 7.63 5±51 radii while those peaks in ␪ coordinates move toward 602 52.60 Ϫ10.50 16.0 316.11 6.09 5±48 180Њ as the radius increases. These characteristics re¯ect 617 48.30 Ϫ4.60 19.0 335.74 8.65 5±43 632 46.20 3.70 23.0 336.42 10.97 5±41 the distortion of the GBVTD geometric relationship 917 9.80 60.00 28.0 347.56 7.74 5±60 where differences between ␪ and ␺ increase with in- 932 8.30 66.80 30.0 342.62 6.69 5±60 creasing R. The least square curves ®t the observed 947 6.20 71.50 30.0 333.89 5.92 5±60 Doppler velocities quite well with standard deviations 1004 3.30 77.00 30.0 338.93 6.28 5±60 of 0.8, 0.9, and 1.2 m sϪ1 on each radius. These small 1018 2.00 82.40 29.0 336.73 6.48 5±60 1032 Ϫ1.00 87.00 26.0 323.71 5.63 5±60 rms errors between the data and the least square curves 1047 Ϫ3.80 90.30 27.0 319.69 4.81 5±60 indicate that resolving TC wavenumbers 0±3 accounts Mean 325.6 8.7 for the majority of the variance. The ®t in Fig. 3 is better than those shown in Lee et al. (1994) using data from an airborne Doppler radar. This result is not surprising interpolated into constant-altitude plan position indi- because the airborne Doppler radar data are inherently cators (CAPPIs) in Cartesian coordinates with a 1-km more noisy due to the uncertainties associated with a grid spacing on all three axes. Instead of linearly in- mobile platform. Wavenumber 14 (i.e., primary the TC terpolating data onto an evenly spaced azimuthal grid mean tangential wind) contains the majority of the var- at a constant radius from the TC center as illustrated in iance in agreement with the ®ndings in more intense Part I, we allowed all data points that fall into a 4-km- storms such as Hurricane Gloria (1985) (Lee et al. 1994) wide annulus to be included in the least squares ®t. This and Hurricane Norbert (1984) (Marks et al. 1992). modi®cation not only ties results on adjacent radii to- The second largest component is wavenumber 0 (i.e., gether, reducing the variations on adjacent radii seen in component of the TC mean ¯ow along the radar±TC Lee et al. (1994), but also reduces the in¯uence of out- centerline), which contributes to the apparent asym- liers in the least squares ®t in data-sparse regions. In metry in the observed Doppler velocities. Examining this study, we allowed up to wavenumber 3 asymmetry Eq. (13) in Part I, the amplitude of wavenumber 0 on in the GBVTD-retrieved tangential winds (i.e., a max- each radius contains not only the TC mean ¯ow (should imum of nine coef®cients in the least squares ®t). The be a constant across all radii), but also wavenumber 1 actual truncation of the Fourier series on each radius of the TC tangential and radial winds (could be different depends on the largest single data gap (Table 2) on a on each radii). Therefore, the variation of the wave- given radius and the geometric factor (sin␣max, de®ned number 0 amplitude between radii is expected (Fig. 3). as the ratio of radius to the TC center, R, and the distance All other wavenumbers have amplitudes on the order Ϫ1 between radar and TC, RT) described in Part I. These of 2±3 m s . Note that the relative importance of the criteria reduce the potentially incoherent behavior of different wavenumbers varies with time. For example, higher wavenumbers (especially wavenumbers 2 and 3) before Alex's landfall, wavenumbers 2 or 3 (TC wave- over large data gaps (inherent in real data) and ensure numbers 1 or 2) are the second largest components (not that the errors due to the geometric distortion are smaller shown). than 20%. However, discontinuities of the retrieved There are two factors that may result in deviations of wind ®elds occur when the truncation of the Fourier the Doppler velocities from the least squares ®t in Fig. series differs on adjacent radii. 3: 1) the natural variability of TC structures among dif- The GBVTD analysis is computed on a distorted co- ferent radii due to the use of a 4-km-wide annulus in ordinate system ␺, while its relationship with the math- collecting data for the least squares ®t, and 2) small- ematic coordinates, ␪, is derived in Part I. Deviation scale circulations shown as systematic deviations of data between ␺ and ␪ increases as sin␣max increases (i.e., as from the curve (e.g., ␪ ഠ 270Њ at R ϭ 35 km and ␪ ഠ R increases for a ®xed RT). Examples of the curve ®t in the distorted GBVTD coordinates, ␺ (left column), and the mathematic coordinates, ␪ (right column), and 4 The wavenumber n in the least squares curve ®t represents pri- the decomposed Fourier series (middle column) at radii marily the wavenumber n Ϫ 1 in TC circulation due to the projection 20, 35, and 50 km and altitude 2 km, are shown in Fig. of the TC circulation on to the radar beam direction. See Part I for 3. Notice that the peak Doppler velocities in ␺ coor- details.

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FIG. 3. The least squares curve ®t of the Doppler radar data (0932 LST and z ϭ 2 km) at (top) R ϭ 20 km, (middle) R ϭ 35 km, and (bottom) R ϭ 50 km, on ␺ and ␪ coordinates. The amplitudes of each Fourier component are plotted in the middle column.

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The high standard deviation of individual least squares ®ts during the landfall stage is consistent with the in¯uence of the terrain on the TC circulation. Or- ganized TC circulations tend to break down (i.e., higher wavenumbers were generated) under the in¯uence of terrain. These small-scale circulations are evident from the ragged zero Doppler velocity lines and decoupling between high re¯ectivity (convection) and the high Doppler velocity (primary circulation) over land (shown in the next section). In general, ␴ increases at outer radii primarily due to truncation of the Fourier series as a result of larger data gaps. Although the high wavenumber behavior of the TC circulation may not be properly represented by the truncated Fourier series, there is little effect on the quality of the retrieved mean tangential winds.

b. Quantities derived from GBVTD-retrieved axisymmetric winds Among the GBVTD-derived quantities, the axisymmetric tangential and radial winds have less ambiguity than their asymmetric counterparts. Between these two axisymmetric components, the tangential wind is the most robust due to its relatively large magnitude compared with the other wind components. One focus of this paper is kinematic properties of quantities derived from the axisymmetric tangential (angular momentum and perturbation pressure) and radial winds (divergence and vertical velocity). Since the axisymmetric radial winds are more sensitive to the errors in estimating TC center, only qualitative interpretation of the axisymmetric divergence and vertical velocity are justi®ed, par- FIG. 4. Time±height plot of (a) the mean of the standard deviations of all radii at one altitude (mean std), and (b) same as (a) but for ticularly during the landfall stage where terrain in¯u- standard deviation (std-std). ences were at a maximum. ١H ´ V) can) The axisymmetric horizontal divergence be calculated from the axisymmetric radial winds (V ): 30Њ at R ϭ 50 km in Fig. 3). Both of these factors are R VVץ more pronounced due to terrain in¯uences after Alex's (V ϭϩRR, (1 ´ ١ RRץ landfall. These systematic deviations could be signa- H tures of mesocyclones or convective-scale convergence and divergence that will be addressed in a future paper. where R is the TC radius and variables with an overbar The standard deviations (␴), representing the scatter represent the axisymmetric quantities (averaged around of Doppler velocities along a least squares curve, can a radius). These axisymmetric quantities are functions be used to assess the closeness of ®t of the truncated of radius and altitude (z) only as de®ned in Part I. Ver- Fourier series on the actual data. Standard deviations tically integrating the anelastic mass continuity equation on each radius are computed and their mean value on using the axisymmetric divergence ®eld results in the each altitude (mean-std) is presented in Fig. 4a. The axisymmetric vertical velocity (w): standard deviation of these ␴'s on each altitude (std- VVץ std), representing the spreads of ␴'s with respect to the zϭ10km ␳w ϭϪ ␳ RRϩ dz, (2) RRץ ͵ mean-std, is presented in Fig. 4b. The mean-std is highly correlated with the in¯uence of the Taiwan terrain. As zϭ0 ΂΃ Alex approached Taiwan (Fig. 2), mean-std increased where ␳ is the environmental density. In addition, w ϭ and maintained a similar value after its landfall at 0517. 0 is applied on both the top (z ϭ 10 km) and bottom The std-std shows a similar trend but peaks at 0517 and (z ϭ 0 km) boundaries and the O'Brien (1970) adjust- 4-km altitude. After Alex entered the East China Sea ment on the divergence pro®le is applied. The unob- and moved away from Taiwan (after 0917), both mean- served divergence in the lowest 1 km is assumed to be std and std-std decreased signi®cantly. the same as the divergence at 1-km altitude. This as-

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sumption tends to underestimate the vertical velocity at be larger than RT. This criterion effectively shrinks the low levels. analysis domain as a TC moves toward a Doppler radar. The unit mass axisymmetric angular momentum (M) When applying the GBVTD technique to real TCs, in a frictionless environment with a constant Coriolis both the radar characteristics (e.g., beamwidth, pulse parameter ( f) can be computed from the axisymmetric repetition frequency, etc.) and the storm characteristics tangential velocity (V T) as follows (e.g., Hawkins and (e.g., vertical extent, RMW, etc.) determine the maxi- Imbembo 1976): mum range that GBVTD technique can be applied. De- tailed discussions of these factors are provided in the 1 M ϭ VRϩ fR2. (3) appendix for interested readers. The best range for the T 2 GBVTD technique to resolve the storm-scale circulation (with an average beam resolution of 2 km) is when the The TC axisymmetric tangential winds are governed TC is located between 60 and 150 km from a WSR- approximately by the gradient wind balance (e.g., Yanai 88D. The average separation of the current WSR-88D 1964; Hawkins and Rubsam 1968; Willoughby 1979) network is ഠ250 km. Hence, a TC moving out of the as follows: best range for one WSR-88D will likely enter the best 2 range of a nearby WSR-88D, making continuous mon- pЈץ VT 1 ϩ fVT ϭ , (4) itoring of a TC circulation using the GBVTD technique -R feasible. However, gaps in GBVTD coverage are unץ R ␳ avoidable when a WSR-88D radar is inside the RMW where pЈ represents the axisymmetric perturbation pres- of a TC. sure. Hence, the axisymmetric angular momentum and perturbation pressure of a TC can be computed from the GBVTD-retrieved axisymmetric tangential winds. 4. Storm evolution and asymmetric structure Since the axisymmetric tangential wind cannot be rea- The evolution of Alex's vortex is illustrated using sonably retrieved inside R ϭ 5 km because few scat- 2-km altitude CAPPI re¯ectivity and Doppler velocity terers are found near the TC center, the tangential winds and the GBVTD-derived relative tangential winds. The inside R ϭ 5 km are obtained by assuming the wind relative tangential wind is de®ned as the sum of all speeds decrease linearly from the ®rst available winds wavenumbers except for the mean ¯ow, whereas the beyond 7-km radius to the center of the typhoon. The total tangential wind is de®ned as the sum of the relative deviation of the wind pro®le inside the eye from the tangential wind plus the mean ¯ow. Note that the mean assumed linear pro®le may create some minor errors in ¯ow deduced by the GBVTD analysis is the component the retrieved pressure gradient near the center. The de- of the mean ¯ow along the radar±TC center direction, rived axisymmetric perturbation pressure gradient is de- de®ned in Part I. Hence, the total tangential wind is an termined at each altitude using (4). The central pressure approximation of the ``full tangential wind'' when the can then be calculated if the pressure values at the data from only one radar are available. In this study, boundary of the analysis domain at each altitude are the relative tangential wind is used in the discussion known. This calculation assumes that the vortex-scale unless otherwise speci®ed. For the convenience of dis- pressure ®eld is primarily due to the axisymmetric tan- cussion, the 16 time periods of data are divided into gential wind while the asymmetric circulations produce three stages: prelandfall stage (0432±0502), landfall minor perturbation upon it. Based on this assumption, stage (0517±0647), and postlandfall stage (0917±1032). the central pressure can be determined from any point Landfall is de®ned as the time when the TC center cross- in the environment provided that the edge of the analysis es the coastline. domain is close to the ``environment.'' Since the exact pressure on the boundary is usually unknown, we cannot retrieve the absolute pressure but the pressure gradient a. Prelandfall stage at each altitude (Gal-Chen 1978). At 0432, Alex's entire eyewall was within CAA's radar range (Fig. 5a). The maximum inbound Doppler c. Operation limits of the GBVTD technique velocity exceeded 45 m sϪ1 in the northern portion of the eyewall while the maximum outbound velocity ex- Theoretically, the GBVTD technique is limited only ceeded 20 m sϪ1 just onshore the southwestern eyewall by the geometric distortion, which is measured by ഠ(60 km, Ϫ60 km) (hereafter, all coordinates are in sin␣max. It has been shown in Part I that the tolerable units of km). The eyewall at 0432 was composed of upper limit on sin␣max is wavenumber dependent (i.e., two distinct re¯ectivity bands (labeled A and B in Fig. inversely proportional to the wavenumber).For example, 5a), which are typical in weaker TCs (Willoughby et al. the upper limit of sin␣max varies from 1 for resolving 1982). Bands A and B also denote two separate regions TC wavenumber 0 to 0.33 when TC wavenumber 3 is of Doppler velocity maximum exceeding 45 m sϪ1 SE included. Since sin␣max is always Ͻ1.0, this implies that of the center (not shown in Fig. 5a due to contour in- the largest radius suitable for GBVTD analysis cannot terval selection). Another rainband labeled C extended

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FIG. 5. (left panels) The 2-km CAPPI and (right panels) the GBVTD-derived tangential winds of Alex from 0432 to 0503 LST. Re¯ectivity is in gray shades. Solid (dashed) lines are positive (negative) Doppler velocities in CAPPI and the contour interval is 10 m sϪ1. Thick solid line is zero Doppler velocity. The CAA radar is indicated by the radar symbol. Thicker solid line is the coastline of northern Taiwan. The contour interval of the relative tangential wind is 5msϪ1. Alex's circulation center at each time is labeled by the typhoon symbol.

Unauthenticated | Downloaded 09/30/21 11:47 AM UTC 3990 MONTHLY WEATHER REVIEW VOLUME 128 over the western portion of the eyewall and was prom- northeastern Taiwan around 0503 where the maximum inent at 5-km altitude (not shown). These bands con- wind in the eyewall (NW of the eye) dropped below 50 solidated between 0432 and 0447, where the upwind msϪ1. The 50 m sϪ1 wind maximum ഠ10 km south of edge of band B merged with band A, and were related the center seemed questionable. In fact, this wind max- to a single inbound velocity maximum Ͼ50 m sϪ1 [at imum is caused by a large (ഠ18 m sϪ1) wavenumber 1 (80, Ϫ21) in Fig. 5c]. The eyewall was comma shaped maximum inside the RMW superimposed on a ഠ30 m with rainbands spiraling out to the east. These rainbands sϪ1 axisymmetric tangential wind. This unusually large rotated counterclockwise around the circulation center wavenumber 1 component in the eye can be a result of and the upwind ends of band A, B, and C could still be multiple vortices forming inside RMW when the eye- identi®ed in Fig. 5c at 0447. The radar re¯ectivity pat- wall impinges on the terrain. When the GBVTD-simplex tern suggested that other spiral bands existed on the east derived TC circulation center is optimized for the pri- and southeast quadrants of the eyewall. By 0503, rain- mary eyewall around R ϭ 23 km, this center may not bands A and B had merged into rainband C and formed be the center for the small-scale vortices near the TC a large spiral band. center. The zigzag of the centers at 0447 and 0502 with The low-level tangential winds at 0432 (Fig. 5b) in- respect to the mean track may re¯ect the uncertainty in dicated two maxima in the southeast and northeast quad- center locations due to multiple vortices. More evidence rants of the TC. In general, the eyewall re¯ectivity max- of these multiple vortices will be discussed in the next imum was associated with high winds. There were some subsection. discontinuities in the tangential wind ®eld near R ϭ 30 km owing to the data void beyond the unambiguous b. Landfall stage range of the radar, an obvious limitation of the GBVTD analysis when only part of the storm was within the Alex's center crossed the Taiwan coastline around effective Doppler range. As Alex moved closer to the 0517 (not shown). This stage is characterized by slow radar, the GBVTD-retrieved wind ®elds became more disintegration of the organized eyewall circulation due coherent. The tangential winds at 0447 (Fig. 5d) showed to the in¯uence of terrain. After 0517, the eye began to a comma-shaped pattern, in good agreement with the ®ll with small, shallow convective cells (echo top Յ6 eyewall re¯ectivity with the upwind portion wrapping km, not shown) similar to those documented in Mura- around east of the center. Maximum tangential winds at matsu (1986). At 0533 (Fig. 6a), a small ring of high 0447 were located north-northwest of the typhoon center re¯ectivity [ഠ18 km diameter centered at (67, Ϫ27), with 51 m sϪ1 maxima at 2-km altitude (Fig. 5d). This referred to as the inner eyewall] formed within and at- 51msϪ1 maximum (located at Rϭ 20 km and 338Њ tached to the southern part of the original eyewall. A azimuth) was the sum of a mean tangential wind at 38.9 similar but weaker re¯ectivity structure was visible at msϪ1, a wavenumber 1 of 9.1 m sϪ1, a wavenumber 2 0517 connected to the western part of the original eye- of Ϫ2.0msϪ1, and a wavenumber 3 of 4.9 m sϪ1.At wall (not shown). Assuming this feature moved with the this location, the angle between the radar beam and the mean tangential wind of ഠ35msϪ1 at 23-km radius, it tangential velocity vector was 50Њ because the tangential would rotate a quarter circle in ഠ17 min, consistent with wind was along 248Њ while the radar viewed along 300Њ/ the location of the feature at 0533. Unfortunately, the 120Њ. Hence, the 51 m sϪ1 tangential wind produced a 15-min period between volume scans does not allow us 33msϪ1 Doppler radial velocity toward the radar, to trace the origin of this inner eyewall before 0517. which, when added to the 8 m sϪ1 mean ¯ow toward Vertical cross sections (at 0533) through the center the radar, yeilds the observed 41 m sϪ1 Doppler velocity of the inner eyewall are shown in Fig. 7. The east±west toward the radar in Fig. 5c. While the retreived wind cross section (Fig. 7a) indicated that the re¯ectivity on is subject to aliasing errors from the unresolved asym- the west side (x ഠ 60 km) is higher than that on the metric radial ¯ow (a limitation/assumption of the east side (x ഠ 73 km). The pattern of Doppler velocities GBVTD technique), the major strength of the GBVTD indicated that there is convergence (divergence) near technique is the ability to use the gradient of the Doppler the west (east) side of the inner eyewall, a feature that velocity along a constant radius from the TC center to can be inferred from the curvature of the zero Doppler retreive the winds without observing the actual maxi- velocity line through the inner eyewall (Fig. 6a) illus- mum and minimum. trated in Fig. 4 in Part I. Note that the Doppler velocities Typhoon Alex reached its peak intensity at 0447 in Fig. 7b are in and out of the page; therefore, they shortly before it made landfall, as de®ned by the oc- show a counterclockwise rotation. The original and in- currence of the peak inbound Doppler velocity and the ner eyewalls did not share the same circulation center tightest Doppler velocity gradient north of the center in (Fig. 6a) as evidenced by the offset of the typhoon sym- Fig. 5c. Achieving this level of detail in the GBVTD- bol and the center of the inner eyewall. In fact, the retrieved tangential winds represents a big step forward GBVTD-simplex algorithm did identify a center at compared with the structures inferred from the single- (61.5, Ϫ32.3) and 2-km altitude with an RMW of 9 km Doppler velocity patterns. Alex's intensity weakened and a maximum axisymmetric tangential wind of 18 m after the eyewall re¯ectivity impinged on the terrain in sϪ1. This offset demonstrates how the single vortex cen-

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FIG. 6. Same as Fig. 5 but from 0532 to 0632 LST. In order to keep the distance scale consistent, there are white strips in (d) and (f) beyond the GBVTD analysis domain. ter assumption used by the GBVTD analysis can break creased rapidly as indicated by the diminishing inbound down in complex ¯ow. Doppler velocities with time. Tracing the motion of the The ®lling of Alex's eye accelerated after 0533 and minimum radar re¯ectivity from 0517 to 0632 (left pan- the inner eyewall cannot be identi®ed at 0547 (not els in Fig. 6) suggests it moved around the terrain par- shown). As Alex moved farther inland, its intensity de- alleling Taiwan's northeastern coast. Comparison of the

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the eyewall possessed numerous wind maxima but in general the highest wind speed was on the east side of the storm between 0532 and 0617. This portion of the TC was mostly over the ocean and least affected by the terrain. A secondary maximum, on the west side of the TC, was associated with enhanced re¯ectivity over land.

c. Postlandfall stage After the CAA site regained power at 0917, Alex was located 60 km north of the radar and tracked NNW for the next few hours. The zero Doppler velocity line curved westward beyond the typhoon center and the centers were located east of the zero Doppler velocity line (e.g., 0932 and 1004; Figs. 8a and 8c). From these two signatures we can infer that the mean ¯ow was southerly (see Part I), in good agreement with the 6±7 Ϫ1 ms GBVTD-retrieved southerly mean ¯ow VM cos(␪T Ϫ ␪M) (Table 1). Since the typhoon motion and the radar viewing angle are almost parallel to each other, ␪T ഠ ␪M and VM cos(␪T Ϫ ␪M) ഠ VM. At 0932 (Fig. 8a), most of the high re¯ectivity was located in the southeast quadrant and connected to precipitation over northern Taiwan. Another rainband was FIG. 7. Vertical cross sections through the center of the inner located north of the center. Scattered re¯ectivity max- eyewall at 0533 LST: (a) east±west, and (b) north±south. Re¯ec- ima can be seen surrounding the TC center indicating tivity is in gray shades. Solid (dashed) lines are positive (negative) Doppler velocities. Thick solid line represent zero Doppler velocity. residual re¯ectivity inside the eyewall from Alex's landfall. A ring of high re¯ectivity began to form out- side the RMW at 1004 (Fig. 8c) and can be seen until 1047 (not shown). The peak outbound and inbound location of the re¯ectivity minimum and the circulation Doppler velocities remained ഠ35 and ഠϪ25msϪ1 center deduced from the GBVTD-simplex algorithm, or from 0917 to 1047 with similar patterns throughout inferred from the zero Doppler velocity line, suggested this period. This trend suggests that Alex attempted to that this re¯ectivity minimum was displaced ഠ20 km redevelop after leaving the terrain in¯uence of Taiwan. to the north of the circulation center. From 0602 to 0632, The GBVTD-derived relative tangential winds are il- the inbound maximum Doppler velocities were collo- lustrated in the right panels of Fig. 8. The relative tan- cated with the re¯ectivity minimum while the circula- gential wind is characterized by a wavenumber 1 com- tion center was associated with high re¯ectivity. This ponent located on the north (front) side of the storm. re¯ectivity±velocity decoupling is not commonly ob- From 0917 to 1032, the relative tangential winds at 1 served in mature TCs over the ocean and is likely a km are generally stronger on the west side of the center sign of terrain in¯uence. The magnitude of the inbound (not shown). These characteristics agree with simula- Doppler velocity maximum decreased with time while tions of axisymmetric and slow-moving hurricanes the outbound velocity maximum associated with con- (Shapiro 1983) where the enhanced in¯ow and conver- vection over land increased with time. Stationary re- gence in front of the hurricane are caused by friction ¯ectivity features on the western slopes of the central in the boundary layer. The re¯ectivity maximum and mountain range [e.g., radar re¯ectivity maximum at the Doppler velocity on the north and northwest quad- (25.0, Ϫ20.0)] were also observed during this period. rants of the TC intensi®ed and broadened, re¯ected as The GBVTD-derived relative tangential winds from the widening of the 32 m sϪ1 contour northwest of the 0532 to 0632 are shown in the right panels of Fig. 6. center at 1004 and 1032. As Alex approached the CAA radar, the effective ra- When adding mean ¯ow to the relative tangential wind dius of the GBVTD analysis reduced from 60 km at ®eld, the tangential winds have a maximum on the north- 0532 to 48 km at 0602 and ®nally to 40 km at 0632. east quadrant of the storm (not shown), which is consistent This shrinking analysis domain results from limiting with the Doppler velocity pattern (Fig. 8) and in agreement sin␣max Ͻ 0.9 to minimize the geometric distortion with previous observations (e.g., Gray and Shea 1973). discussed in Part I. During this time, the peak relative Therefore, the apparent asymmetry in the Doppler velocity tangential wind speed dropped from 45 m sϪ1 at 0517 pattern is primarily due to the mean ¯ow instead of the to 37 m sϪ1 at 0632. The overall wind pattern within wavenumber 1 asymmetry, consistent with the orientation

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FIG. 8. Same as Fig. 5 but from 0917 to 1032 LST. The contour interval for the CAPPI Doppler velocity is5msϪ1.

of the zero Doppler velocity contour illustrated in Part I. 5. Axisymmetric circulation More importantly, the GBVTD analysis revealed a wavenumber 1 asymmetry north of the center that cannot be In this section, Typhoon Alex's circulation is dis- inferred from the Doppler velocity pattern. cussed using the axisymmetric tangential winds, radial

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FIG. 9. Axisymmetric structure of (a) tangential winds, (b) radial winds, (c) angular momentum, and (d) perturbation pressure, at 0447 LST. Solid (dashed) lines represent positive (negative) values. Thick solid line is zero contour. Axisymmetric re¯ectivity is in gray shades. Vectors in (b) represent axisymmetric radial wind and vertical velocity. The vectors represent the symmetric radial wind and vertical velocity.

winds, and their derived divergence, vertical velocity, layer of in¯ow5 at low levels (Fig. 9b), a layer of out¯ow angular momentum, and perturbation pressure. These in the midlevel, and in¯ow at the upper level sloping quantities were computed on a 1-km grid in both radius down along the inner edge of the eyewall toward the and height, representing the axisymmetric mean ®elds. center. The low-level in¯ow (ഠϪ7msϪ1) peaked at R ϭ 27 km and z ϭ 1 km, and the convergence zone extended inward to the inner edge of the eyewall at R a. The prelandfall stage ϭ 15 km. The primary updraft (ഠ1.5msϪ1) coincided with the maximum tangential wind. When the updraft The axisymmetric vortex of Typhoon Alex at 0447 encountered the downdraft at high levels (e.g., R ϭ 25 is illustrated in Fig. 9 where the three components of km, z ϭ 7.5 km), part of the updraft entered the eye the velocity ®eld are shown in panels (a) and (b) and and the rest merged with the downdraft and ¯owed out- the angular momentum and perturbation pressure ®elds ward at midlevels. Downdrafts were resolved inside the are shown in panels (c) and (d). At 0447, the axisymmetric tangential wind maximum reached ഠ39msϪ1 and the RMW was 22 km. Alex's maximum axisym- 5 metric tangential wind was about 14 m sϪ1 weaker than Note the data below z ϭ 1 km are not observed by CAA radar. However, it is reasonable to assume in¯ow exists below z ϭ 1km that of Hurricane Norbert, the weakest of the three hur- by extrapolating the coherent ¯ow structure downward and the mag- ricanes studied previously. There was a deep (ഠ2 km) nitude of the in¯ow may even be stronger near the surface.

Unauthenticated | Downloaded 09/30/21 11:47 AM UTC DECEMBER 2000 LEE ET AL. 3995 sloping eyewall re¯ectivity. Again, although the patterns b. Landfall stage and magnitudes look plausible, some unrealistically large vertical velocities were generated by questionable The axisymmetric structure at 0533, illustrated in Fig. radial wind gradients inside the eye above z ϭ 6 km, 10, changed signi®cantly during the 45 min since 0447. which is a problem when few scatters are available. The eye was ®lled with high re¯ectivity and the low- The angular momentum (Fig. 9c) shows a similar level in¯ow penetrated all the way to the typhoon center pro®le to that in Hurricane Norbert (Marks et al. 1992) (Fig. 10b). The outward tilting eyewall re¯ectivity at where the contours are nearly vertical inside the eyewall 0447 was replaced by a widespread re¯ectivity pattern, (R ϭ 15 km) and slope outward with height. If an air stratiform in appearance. The axisymmetric tangential parcel conserves angular momentum in a frictionless winds at 1-km altitude (Fig. 10a) decreased rapidly at environment ignoring the Coriolis effect, the slope of all radii indicative of increasing surface friction as Alex constant angular momentum surface is a function of the moved over land. The unrealistically large in¯ow above maximum axisymmetric tangential wind, the RMW, and z ϭ 7 km and beyond R ϭ 30 km corresponds to poor the vertical shear of the axisymmetric tangential wind data coverage at high altitude and large radii. As Alex at the RMW [eq. (4) in Jorgensen (1984)]. The estimated moved farther inland, the height of the maximum tan- slope of the constant angular momentum surface in the gential winds rose from 1- to 3-km altitude after 0602 eyewall at 0447 is 28Њ from the horizontal. This constant and increased radially outward (not shown), consistent angular momentum slope is consistent with a 25Њ slope with the increasing terrain in¯uence at low levels. computed from the eyewall radar re¯ectivity (e.g., 25- In response to the evolution of the axisymmetric tan- dBZ contour), but not as steep as the 60Њ reported in gential wind, the low-level angular momentum (Fig. other hurricanes over the ocean (e.g., Marks and Houze 10c) decreased beyond the RMW (R ϭ 30 km) while 1987; Marks et al. 1992; Lee et al. 1994). However, a the angular momentum at midlevel increased. This similar slope of eyewall re¯ectivity was reported in the change in structure is consistent with decaying low-level much stronger Hurricane Allen (1980) by Jorgensen storm intensity after Alex's landfall while the midlevel (1984). These results suggest that the eyewall slope is wind speed actually increased slightly after Alex's land- not entirely determined by the storm intensity. fall. The perturbation pressure pattern (Fig. 10d) showed Generally, the angular momentum increases with ra- that the pressure de®cit at z ϭ 1 km decreased from dius because the mean tangential wind decreases more Ϫ20 mb at 0502, to Ϫ16 mb at 0533, and ®nally to slowly than the radius increases. The maximum angular Ϫ11 mb at 0632. momentum of 16 ϫ 105 m 2 sϪ1 was located at R ϭ 60 km and z ϭ 6 km due to the upward and outward slope c. Postlandfall stage of the peak axisymmetric tangential wind. In a layer below z ϭ 2 km and beyond R ϭ 20 km, the angular After Alex left Taiwan, its circulation became nearly momentum contours slope radially outward with height, axisymmetric with the RMW located at ഠ30 km. High which is an indication of angular momentum loss at the re¯ectivity ®lled the eye and the maximum re¯ectivity bottom of the in¯ow layer due to friction (e.g., Marks was stronger than that during the landfall stage. An et al. 1992). This angular momentum loss may be par- example of axisymmetric structure at 1032 is shown in tially compensated by the boundary layer in¯ow, which Fig. 11. Enhanced eyewall re¯ectivity coincided with crosses the constant angular momentum contours, trans- the peak tangential wind around R ϭ 30 km. The area porting higher angular momentum inward. of strong tangential wind (e.g., 25 m sϪ1 contour) is The perturbation pressure ®eld is shown in Fig. 9d. shallow and spread horizontally through a broad radial This bell-shaped pressure de®cit pattern is similar to band that does not resemble the upright structure shown that in a simulated axisymmetric hurricane (Fig. 5b in in mature tropical cyclones (e.g., Marks and Houze Rotunno and Emanuel 1987). The nearly vertical pres- 1987; Marks et al. 1992; Lee et al. 1994). sure contours (e.g., Ϫ3- and Ϫ6-mb contour lines) be- The radial ¯ow (Fig. 11b) showed an in¯ow at 1-km low 5 km are due to the outward and upward slope of altitude beyond 44-km radius and suggested in¯ow be- the tangential wind maximum. The horizontal pressure low 1 km penetrated to the RMW. There was mid- to gradient maximum is located at z ϭ 1 km and decreases upper-level out¯ow beyond R ϭ 35 km. A re¯ectivity with height. There is less than 3-mb horizontal pressure maximum at R ϭ 40 km intensi®ed with time, consistent drop at z ϭ 10 km compared with a 21-mb pressure with the convergence at R ϭ 44 km and 1-km altitude, drop at z ϭ 1 km across the 60-km domain. The vertical and the updraft above the convergence. The very weak perturbation pressure gradient is strongest at the TC updraft associated with the primary eyewall (R ϭ 28 center and decreases as the radius increases. The down- km) is probably due to the underestimated convergence draft inside the eye is downgradient, but the low-level below 1-km altitude. The existence of the outer sec- out¯ow from the typhoon center is countergradient. The ondary circulation may reduce the supply of the high existence and maintenance of this out¯ow from the TC angular momentum air reaching the inner re¯ectivity center requires downward motion inside the eyewall, maximum. The double re¯ectivity and wind maxima which is consistent with the ¯ow pattern resolved here. structure resembled many aspects of an eyewall replace-

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FIG. 10. Same as Fig. 9 but for 0533 LST. ment cycle discussed in Shapiro and Willoughby (1982) (Fig. 12a). As a further check of the GBVTD-derived and Willoughby et al. (1982). Some indication of the winds, we compare the surface pressure gradient com- double-eyewall structure can also be found at 1032 (Fig. puted from these surface pressure reports with the re- 8e). trieved surface perturbation pressure gradient. The angular momentum and perturbation pressure in- The GBVTD-retrieved surface perturbation pressure creased slightly compared with those in the landfall gradient at different radii from the typhoon center was stage suggesting that Alex reintensi®ed after it left the estimated by extrapolating the pressure ®elds retrieved in¯uence of Taiwan's terrain. Although the maximum at 0502 and 0602 downward from z ϭ 1 km. Addi- tangential wind decreased slightly after 1004 (not tionally, we computed the likely uncertainty of the re- shown), the widening of the tangential wind maximum trieved pressure ®eld by imposing a Ϯ2msϪ1 bias (rms produced an additional 2-mb pressure de®cit at 1047 of the Doppler velocity about the GBVTD curve pre- (not shown). sented in Fig. 4 at 1-km altitude for 0502 and 0602) to the axisymmetric tangential winds across all radii. The 6. Comparison of the retrieved perturbation envelope of the uncertainty expands toward the TC cen- pressure with surface pressure observations ter where a Ϯ3 mb accumulated uncertainty is found at There was no aircraft reconnaissance in Typhoon the TC center. The size of the envelope depends on the Alex. The surface wind, highly affected by the terrain, uncertainty in the GBVTD-retrieved axisymmetric tan- did not provide a good direct comparison with the re- gential winds. With a smaller uncertainty in the post- trieved wind ®eld at z ϭ 1 km. However, there were landfall stage, the retrieved pressure gradient will be ®ve surface stations reporting pressure at 0500 and 0600 more accurate than the example shown here. In addition, in northeast Taiwan within 70 km of the typhoon center the uncertainty in the pressure estimates will be much

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FIG. 11. Same as Fig. 9 but for 1032 LST. smaller if the errors in the axisymmetric tangential trieved axisymmetric circulation in Typhoon Alex, but winds are random rather than a bias. also suggests that our technique has the potential to The surface pressure observed at each station was retrieve the central pressure of a TC within 2±3 mb. subtracted from the pressure at the station farthest from Therefore, it may be feasible to estimate central pressure the typhoon center (690 at 0500 and 706 at 0600) to of a landfalling TC from the GBVTD-retrieved axisym- obtain the ``observed'' axisymmetric surface pressure metric tangential winds in conjunction with one or two gradient (Fig. 12b). In this example, the central pressure surface pressure measurements within the GBVTD- of Alex, ഠ969.5 mb (973.8 mb) at 0502 (0602), can be analysis domain. More case studies will be performed estimated by adding the pressure de®cit, ഠϪ23 mb and compared with surface and aircraft dropsonde data (Ϫ16 mb) from R ϭ 60 km (48 km), to the measured in the future. surface pressure of 992.5 mb (989.8 mb) at station 690 (706). Although there were no surface pressure obser- 7. Summary and conclusions vations within 20 km of Alex's center, the ``GBVTD- retrieved''pressure gradient beyond 20-km radius was This paper completes a three-part study of a ground- consistent with the observed surface pressure gradient. based single-Doppler radar TC wind retrieval technique, Considering all the assumptions (e.g., axisymmetry, gra- GBVTD, by presenting applications of the GBVTD dient wind approximation, uncertainty in TC center, etc.) technique on landfalling Typhoon Alex. Under different involved in retrieving the perturbation pressure, and the storm intensity and degrees of terrain in¯uence, we dem- in¯uence of the terrain on each station, the 1±2-mb de- onstrate that plausible and physically consistent primary viations between the retrieved and the observed surface circulations of a TC can be retrieved from ground-based pressure gradient is remarkably small. This agreement single-Doppler radar data using this technique and the not only indicates the consistency of the GBVTD-re- GBVTD-simplex center ®nding algorithm. In addition,

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gular momentum surface within the eyewall re¯ectivity. Alex reached its minimum surface pressure, ഠ969 mb (a 23-mb pressure de®cit from R ϭ 60 km), at 0447. A deep layer of low-level in¯ow collided with out¯ow from the eye at the bottom of the eyewall and produced a broad region of updraft. This in¯ow also brought in higher angular momentum air from outer radius into the eyewall region. Alex's circulation weakened after landfall and the eye began to ®ll. The low-level axisymmetric wind maximum gradually elevated from 1- to 3-km altitude and expanded outward. The re¯ectivity center (minimum re- ¯ectivity) and circulation center (maximum vorticity) were decoupled as Alex moved farther inland. The circulation center moved across the terrain while the re- ¯ectivity center moved around the terrain following the coastline. Within 90 min after landfall, the retrieved central pressure ®lled ഠ10 mb. Upon leaving Taiwan's northern coast, Alex attempted to reintensify as the central pressure deepened 3±4 mb in the next 2 h. The maximum axisymmetric winds reappeared at 1-km altitude and broadened horizontally with the eyewall re- ¯ectivity maximum. The retrieved perturbation pressure ®elds at 0502 and 0602 were compared with the surface pressure reported over northern Taiwan. The observed and GBVTD-retrieved pressure gradient was within only 1±2 mb beyond 20-km radius. The agreement seems very good considering the assumptions involved and the in¯uence of terrain. This agreement suggests that the GBVTD- retrieved quantities can be used for operational and research purposes. The simple circular vortex and single circulation center assumptions in the GBVTD technique and GBVTD- simplex algorithm caused some problems in Typhoon Alex when multiple vortices formed as the primary circulation impinged on the terrain. Nevertheless, while the break down of these assumptions has some impact FIG. 12. (a) The surface stations report hourly data in northern on the asymmetric circulation, it has little effect on the Taiwan. Typhoon locations at 0502 and 0602 LST are indicated by the typhoon symbols. Terrain is in gray shades. (b) The thick line is axisymmetric tangential wind. the GBVTD-derived axisymmetric perturbation pressure (PЈ)atthe In conclusion, the GBVTD technique provides a new surface. Solid (hollow) circles are the perturbation pressure of ®ve way to examine TC circulations from single ground- surface stations in northern Taiwan at 0502 (0602). The gray areas based Doppler radar. The ability to resolve realistic 3D represent the uncertainties in the retrieved pressure gradients bounded axisymmetric and asymmetric structures of a TC near bya2msϪ1 bias on the GBVTD-retrieved axisymmetric winds. landfall in real time not only expands the capability of using ground-based Doppler radar data in TC forecasts the derived axisymmetric dynamical parameters (an- but provides researchers an opportunity to examine TC gular momentum and perturbation pressure) are inter- kinematic and some derived dynamic structures. There nally consistent with the radar re¯ectivity structures. is no doubt that the GBVTD technique needs to be tested A total of 16 volumes (6.5 h data with a 2-h gap) on a wider spectrum of TCs in conjunction with other were collected while Typhoon Alex moved across the independent measurements so a more complete com- mountainous terrain of northern Taiwan. Before landfall, parison of the results can be performed. A version of Alex was characterized by a highly asymmetric circu- the GBVTD analysis package that uses coarser-resolu- lation with a maximum axisymmetric tangential wind tion WSR-88D level IV data has been implemented in of 39 m sϪ1 and a maximum total tangential wind of near±real time at the National Hurricane Center in Mi- ഠ52 m sϪ1 at z ϭ 2 km, north-northwest of the center. ami to provide low-level wind structure in landfalling Also, the eyewall re¯ectivity was tilted ഠ25Њ from hor- TCs to forecasters. We plan to perform GBVTD analysis izontal in agreement with the slope of the constant an- on Hurricane Danny (1997) and Georges (1998) where

Unauthenticated | Downloaded 09/30/21 11:47 AM UTC DECEMBER 2000 LEE ET AL. 3999 a more rigors comparison can be performed with aircraft A1 to obtain the true beam altitude. The altitude of the in situ measurements, dropsonde data, and dual-Doppler lowest elevation angle and the vertical extent of the TC's analysis. eyewall determine the maximum distance a TC center can be detected by a radar. The center of the 0.5Њ beam Acknowledgments. The authors thank the CAA for exceeds 1-km altitude beyond 80 km from the radar. As providing the Doppler radar data. The authors are grate- a result, it is possible to resolve a limited portion of ful to Drs. Peter Hildebrand, Tammy Weckwerth, Mr. circulation beneath 1-km altitude when the TC center Peter Dodge, Mr. Vincent Wood, Mr. Scott Ellis, and is within 60 km of the radar. For a typical TC with the two anonymous reviewers for their valuable comments eyewall convection reaching 10-km altitude, the TC that greatly improved this paper. Ms. Susan Stringer center can be detected by a ground-based radar (at 0.5Њ helped prepare ®gures and Ms. Jennifer Delaurant proof- elevation angle scan) up to R ϭ 340 km. However, the read the manuscript. This research is supported by the maximum effective range of the GBVTD technique is National Science Foundation, the National Oceano- further restricted by other factors discussed in this ap- graphic and Atmospheric Administration, the National pendix. Science Council of Taiwan, Republic of China (ROC), and the Technology Advisors Of®ce, Ministry of Trans- b. Scanning strategy portation and Communication of Taiwan, ROC, under Grant NSC89-2111-M002-019-Ap6. For a given TC, the solid angle required for a radar to sample the same region of the storm (for a given diameter and altitude) increases as the storm approaches APPENDIX the radar. This effect results in the need for a larger Practical Considerations of the GBVTD Technique azimuth angle and elevation angle sector to be scanned by a radar. The effect of a larger azimuth angle sector The operational limits and accuracy of the GBVTD- (equivalent to increasing ␣max) increases the contribu- derived TC circulations are constrained by the earth's tion from the unknown cross-beam component of the curvature, radar characteristics, beam geometry, scan- mean ¯ow into the mean tangential winds and limits the ning strategy, and the uncertainties in vertical velocity ability to recover the higher wavenumber wind com- and precipitation terminal velocity. Here, these factors ponents due to distorted geometry (see Part I). are discussed to better understand and interpret the For a TC with the top of the eyewall convection at GBVTD-derived winds in real TCs. Each factor pro- 10 km and a 30-km-radius eyewall, a Doppler radar vides its own limits to the GBVTD technique. needs to scan up to 9Њ elevation when the center of the storm is located at 150 km from the radar in order to a. Earth curvature cover the eyewall at 120 km (see Fig. A1). A radar needs to scan up to the 20Њ elevation when the TC center The propagation path of a radar beam is affected by is 100 km from the radar. As a result, the errors in the refractive index and the altitude of a horizontally particle terminal fall speed (␷ t estimation and unknown pointing beam, which increases with distance from the vertical velocity, w) could contaminate the results at radar due to the curvature of the earth (Rinehart 1991, closer range (discussed later in this appendix). As the chapter 3, Fig. 3.2). The mean sea level altitude at the elevation angle increases, an operational Doppler radar center of a radar beam at various distances are shown has to scan in larger elevation angle steps (i.e., sacri- in Fig. A1. The radar altitude needs to be added to Fig. ®cing vertical resolution) to complete a volume scan within a preset time interval.

c. Beam spreading The beamwidth of a Doppler weather radar is usually between 0.5Њ and 1Њ. A typical 1Њ beam is ഠ7.5 km wide at 400-km range from the radar accounting for two- thirds of the depth of a typical TC. To sample a TC with less than a 3-km-average beamwidth, the storm center must be within 180 km of a Doppler radar with a 1Њ beam. At larger ranges, the magnitude of TC tangential wind maximum will be smoothed by the beam.

d. Range and velocity ambiguity The maximum unambiguous range and velocity of a FIG. A1. Altitude of elevation angles as a function of slant range. pulsed Doppler radar transmitting at a single pulse rep-

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TABLE A1. The maximum unambiguous range and velocity for Beard (1985) where H is the altitude (km). At 5-km different PRFs for 5- and 10-cm wavelength Doppler radars. Ϫ1 altitude, Z ϭ 50 dBZ gives ␷ t ϭ 10ms . The projection Wavelength (␭) (cm) of the ␷ T on Doppler velocity (Vd) at an elevation angle Ϫ1 10 5 of 15Њ is Յ2ms . Even with a 50% uncertainty in estimating particle terminal velocity, the error in the PRF (sϪ1)R(km) V (m sϪ1) V (m sϪ1) N N N Doppler velocity from the terminal velocity uncertainty 350 428 Ϯ8.75 Ϯ4.375 is Յ1msϪ1. 750 200 Ϯ18.75 Ϯ9.375 Intense vertical velocities (Ն10msϪ1) within a TC 1000 150 Ϯ25.0 Ϯ12.5 1500 100 Ϯ37.5 Ϯ18.75 are usually located in the eyewall and outer rainbands 2000 75 Ϯ50.0 Ϯ25.0 (Black et al. 1996). As discussed in Lee et al. (1994), ignoring w in Eq. (2) in Part I produces Յ2msϪ1

uncertainty in Vd even in the eyewall region. Hence, the etition frequency (PRF) are governed by the following errors due to uncertainties in w and ␷ t are small (usually equations (Doviak and Zrnic 1993): Յ10% because they tend to partly cancel each other) compared with V (Ն34 m sϪ1) of a TC at hurricane 1 C T R ϭ and (A1) strength. max 2 PRF ␭ ϫ PRF V ϭϮ , (A2) REFERENCES N 4 where ,C,PRF are the wavelength of the radar (m), Atlas, D., R. C. Srivastava, and R. S. Sekhon, 1973: Doppler radar ␭ characteristics of precipitation at vertical incidence. Rev. Geo- 8 Ϫ1 speed of electromagnetic wave (3 ϫ 10 ms ), and phys. Space Phys., 11, 1±35. pulse repetition frequency (sϪ1), respectively. It is clear Beard, K. V., 1985: Simple altitude adjustments to raindrop velocities

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