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A Technique to Determine the Radius of Maximum Wind of a Tropical Cyclone

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A Technique to Determine the Radius of Maximum Wind of a Tropical Cyclone OCTOBER 2008 LAJOIEANDWALSH 1007 A Technique to Determine the Radius of Maximum Wind of a Tropical Cyclone FRANCE LAJOIE AND KEVIN WALSH School of Earth Sciences, University of Melbourne, Parkville, Victoria, Australia (Manuscript received 2 October 2007, in final form 22 January 2008) ABSTRACT A simple technique is developed that enables the radius of maximum wind of a tropical cyclone to be estimated from satellite cloud data. It is based on the characteristic cloud and wind structure of the eyewall of a tropical cyclone, after the method developed by Jorgensen more than two decades ago. The radius of maximum wind is shown to be partly dependent on the radius of the eye and partly on the distance from the center to the top of the most developed cumulonimbus nearest to the cyclone center. The technique proposed here involves the analysis of high-resolution IR and microwave satellite imagery to determine these two parameters. To test the technique, the derived radius of maximum wind was compared with high-resolution wind analyses compiled by the U.S. National Hurricane Center and the Atlantic Oceano- graphic and Meteorological Laboratory. The mean difference between the calculated radius of maximum wind and that determined from observations is 2.8 km. Of the 45 cases considered, the difference in 50% of the cases was Յ2 km, for 33% it was between 3 and 4 km, and for 17% it was Ն5 km, with only two large differences of 8.7 and 10 km. 1. Introduction Another sensor on board a polar-orbiting satellite that can produce high-resolution surface wind fields r To determine m, the radius of maximum wind for a over the ocean is the Wind Field Synthetic Aperture tropical cyclone, one needs to analyze the strong sur- Radar (WiSAR). It measures the small-scale ocean sur- face winds in its inner core and in its eyewall. There are face roughness from which can be determined the di- a number of methods that have been developed to rection and the speed of the surface wind (Lehner et al. measure or estimate surface winds from satellite sen- 2006). WiSAR waves can penetrate cloud layers and sors but they are not reliable in the inner core of a rain and can operate day and night in all weather con- tropical cyclone. The Special Sensor Microwave Imager ditions and are therefore well suited to determining the (SSM/I) can only be used in cloudless sky and cannot radius of maximum wind in a tropical cyclone. The only therefore be used within the central dense overcast problem with WiSAR is that the data are only available (CDO) or in the eyewall of a tropical cyclone (Good- when the tropical cyclone is along the satellite track and berlet et al. 1989). Satellite-based microwave scatter- are therefore available only twice a day. ometers can only produce a reasonably good estimate Surface winds inside the CDO are also obtainable of light to moderate surface winds in areas of no or from reconnaissance planes that fly at an altitude of slight precipitation (Weissman et al. 2002; Yueh et al. about 3 km. The measured 3-km winds are reduced to 2003). They are therefore not reliable for estimating the the surface by using an empirically derived relationship strong winds associated with tropical cyclones. Surface (Franklin et al. 2003). Using these flight data, the U.S. winds can also be estimated from satellite cloud track National Hurricane Center can determine the maxi- winds deduced from geostationary satellites (Dunion mum surface wind and the radius of maximum wind. and Velden 2002; Velden et al. 2005), but these also are But these flight wind data are now only available in the only useful outside the CDO. North Atlantic when a hurricane is within the flight range of the reconnaissance aircraft. In the central North Atlantic and in other tropical cyclone basins Corresponding author address: Dr. Kevin Walsh, School of Earth Sciences, University of Melbourne, Parkville, VIC 3010, there is no method to directly measure the maximum Australia. winds or the radius of maximum wind. E-mail: [email protected] Recently, Kossin et al. (2007) used reconnaissance DOI: 10.1175/2008WAF2007077.1 © 2008 American Meteorological Society Unauthenticated | Downloaded 09/27/21 06:36 PM UTC WAF2007077 1008 WEATHER AND FORECASTING VOLUME 23 flight data to investigate the relationship that exists be- tween the eye size (re) and rm. They assumed re to be the mean radius of the Ϫ45°C isotherm in the cloud-top brightness temperature analysis. Their mean absolute error in determining rm was 4.7 km. Hsu and Babin (2005) have suggested that the radius of maximum winds in a tropical cyclone is the distance between the coldest cloud-top temperature surround- ing the eye and the warmest temperature in the eye. They evaluated their hypothesis on only one cyclone, however. Here, we describe below a simple and easy- to-use technique for estimating rm from the color- enhanced imagery of high-resolution IR satellite cloud data, from microwave Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI; Simpson et al. 1988; Lonfat et al. 2004) and TRMM Precipitation Radar (PR) data (Iguchi et al. 2000). 2. A technique for determining rm from satellite cloud data Jorgensen (1984a,b) has studied the eyewall structure of tropical cyclones, using a comprehensive set of sat- ellite cloud pictures, photographs of eyewall clouds, and radar and reconnaissance flight data along 146 flight legs across the eye and eyewall of five hurricanes. His schematic representation of a cross section of the eyewall of North Atlantic Hurricane Allen on 5 August 1980 is shown in Fig. 1a. More recent studies (e.g., Marks and Houze 1987; Marks et al. 1992; Corbosiero et al. 2005) have found rather similar structures in their analyses, although unlike in Fig. 1a downdrafts are also typically observed in regions close to the main updraft. In Fig. 1a a few letters have been added to help in the following discussion. We use “A” as the inner edge of the eyewall at the surface and “T” as the top of the most developed cumulonimbus nearest to the cyclone center. Let the coordinates of “A” and “T” be denoted, respectively, by (re, 0) and (rt, ht) (see also Fig. 1b). The line AT is inclined to the horizontal by an angle ␸ that may be as large as 45°–75° for intense storms with small eye radius (re) and rm, and as small as 25° for weaker storms or for storms with large re and rm (Jorgensen 1984a). Let the straight line AT be inclined to the hori- ␸ zontal by an angle . The maximum updraft wm within this cumulonimbus is along BC, which represents the FIG. 1. (a) A schematic cross section of eyewall features, after Jorgensen (1984b). The schematic depicts the locations of the variation of wm with height in the low and middle levels, clouds and precipitation, observed RMW, and the radial–vertical B being the maximum wm at the base of the cloud at airflow through the eyewall of Hurricane Allen on 5 Aug 1980. radius rb. Here, DE represents the variation with height The slope of the cloudy region on the inside edge of the eyewall is based on radar minimum detectable signal analysis (10 dBZ), of the radius of maximum tangential wind (V␪)m and is inclined at an angle to the horizontal equal to or slightly aircraft altimeter readings, handheld photography, and observer ␸ ␺ notes. Here, A is the inner edge of the eyewall at the surface and different from , denoted by . It is assumed that the T is the top of the most developed cumulonimbus nearest to the radius of maximum wind varies linearly with height: cyclone center. Darker regions along BC denote the location of although fine-resolution model simulations indicate the largest radial and vertical velocities. The variation of the maxi- mum tangential velocity is along DE, with maximum low-level wind at D. (b) Schematic diagram illustrating the main features of (a) but with the addition of line EDЈ and angle ␺Ј. Unauthenticated | Downloaded 09/27/21 06:36 PM UTC OCTOBER 2008 LAJOIEANDWALSH 1009 | Ј Ϫ | ␣ ϭ some departure from linearity of this feature (e.g., TABLE 1. Minimum and maximum rm rm for 10° and ␾ ϭ Zhang and Kieu, 2006); since we are only taking the 20° and for 75° and 60°. The range of h␷ is assumed to vary two end points in our calculation, this will not affect our between 5 and 7 km. final results. Max ␣ Min Max ␾ | Ј Ϫ | | Ј Ϫ | In Fig. 1a, the vertical line TEF passes through E, the (°) (°) rm rm (km) rm rm (km) maximum tangential wind (V␪)m at level E. Let the co- 75 10 1.0 1.4 ordinates of E and F be (rt, hV) and (rt, 0), respectively. 75 20 2.2 3.0 Because D is the maximum wind at the surface, the 60 10 1.1 1.8 60 20 2.0 4.3 coordinates of D are (rm, 0). Note also that rr, the ra- 45 10 2.1 3.0 dius of maximum precipitation rate in the lowest 2–3 45 20 3.7 8.0 km of the troposphere, measured from radar observa- tions, is on average greater by 3 km than rm but less of the CDO represents very warm temperature or part than rt (Jorgensen 1984b). According to Jorgensen of the eye, while the nearby green patch represents the (1984a,b), re, rm, and rr have all preferred locations rela- tive to each other and always occur in the same order, top of the middle-level stratiform cloud.
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