A Diagnostic Study of the Intensity of Three Tropical Cyclones in the Australian Region
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22 MONTHLY WEATHER REVIEW VOLUME 138 A Diagnostic Study of the Intensity of Three Tropical Cyclones in the Australian Region. Part II: An Analytic Method for Determining the Time Variation of the Intensity of a Tropical Cyclone* FRANCE LAJOIE AND KEVIN WALSH School of Earth Sciences, University of Melbourne, Parkville, Australia (Manuscript received 20 November 2008, in final form 14 May 2009) ABSTRACT The observed features discussed in Part I of this paper, regarding the intensification and dissipation of Tropical Cyclone Kathy, have been integrated in a simple mathematical model that can produce a reliable 15– 30-h forecast of (i) the central surface pressure of a tropical cyclone, (ii) the sustained maximum surface wind and gust around the cyclone, (iii) the radial distribution of the sustained mean surface wind along different directions, and (iv) the time variation of the three intensity parameters previously mentioned. For three tropical cyclones in the Australian region that have some reliable ground truth data, the computed central surface pressure, the predicted maximum mean surface wind, and maximum gust were, respectively, within 63 hPa and 62ms21 of the observations. Since the model is only based on the circulation in the boundary layer and on the variation of the cloud structure in and around the cyclone, its accuracy strongly suggests that (i) the maximum wind is partly dependent on the large-scale environmental circulation within the boundary layer and partly on the size of the radius of maximum wind and (ii) that all factors that contribute one way or another to the intensity of a tropical cyclone act together to control the size of the eye radius and the central surface pressure. 1. Introduction intensity and radial wind profile. The model uses input parameters that are readily available and simple to use. The problem of forecasting tropical cyclone intensity The principles upon which the new model is based are and wind field remains an important issue in tropical further described here and then expanded in the en- meteorology. A review of recent work is contained in suing sections. Lajoie and Walsh (2010, hereafter Part I). Based on the Because different atmospheric processes are involved sequence of observed characteristic features during in different parts of a tropical cyclone, and also because intensification and dissipation of Tropical Cyclone the radial wind profiles in different regions have distinct Kathy in Part I, we have developed a mathematical physical features (Shea and Gray 1973), analysis of the model for forecasting all aspects of tropical cyclone circulation is considered in four distinct regions, as shown intensity. As discussed in Part I, it was suggested that in Fig. 1. Region 1 is the circular area of radius r , the eye the inflow of a band of moist, near-equatorial air into e radius. Region 2 is the annular area between r and r . the cyclone center was responsible for bursts of in- e m Region 3 is the area bounded between radii r and r , tensification of the storm. In addition, it was proposed m c the radius of the inner core of the cyclone or of the that the inflow angle of the band was related to the rate central dense overcast (CDO) region, which on average of intensification. The concepts are used here to de- is 18 latitude, as it was for Kathy. The two last regions velop an accurate numerical model of tropical cyclone contain the eyewall cloud, the maximum wind, most of the destructive winds, and very heavy precipitation. * Supplemental information related to this paper is available at the Region 4 is between rc and a radius of 48 latitude. Journals Online Web site: http://dx.doi.org/10.1175/2010MWR2876.s1. To start the analysis, an initial radial wind profile in region 4 a few hours before the start of intensification, or Corresponding author address: Kevin Walsh, School of Earth at t 5 0, is obtained from a streamline and isotach anal- Sciences, University of Melbourne, Parkville VIC, 3010 Australia. ysis. The initial radial surface pressure profile is then cal- E-mail: [email protected] culated to balance the wind profile. Because (i) the feeder DOI: 10.1175/2009MWR2876.1 Ó 2010 American Meteorological Society Unauthenticated | Downloaded 09/29/21 04:37 AM UTC JANUARY 2010 L A J O I E A N D W A L S H 23 In region 2, the wind is assumed to decrease linearly from Vrm to zero at the cyclone center and the cyclo- strophic wind equation is used to obtain pre, the surface pressure at re. Since surface pressure does not vary ap- preciably with radius in the eye of a cyclone (see rele- vant barograms on 285–286 in Riehl (1954)), pre 5 pc, the central surface pressure. Parameters rm and re are determined from the Trop- ical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI; Simpson et al. 1988; Lonfat et al. 2004), TRMM Precipitation Radar (PR) data (Iguchi et al. 2000), or digitized high-resolution IR satellite cloud data (see Lajoie 2007; Lajoie and Walsh 2008). Finally, by using a reduction factor to convert gradient-level mean wind to mean surface winds, and the mean asymmetric FIG. 1. The inner and outer regions of a tropical cyclone. The wind distribution around a tropical cyclone, the hori- former is subdivided into the following: region 1, the eye where 0 # zontal distribution of the sustained mean surface wind as r # re; region 2 where re , r , rm (rm being the radius of maximum well as the maximum gust around the cyclone can be wind); region 3 where rm # r # rc (rc being the external radius of the estimated. CDO); and region 4, the outer region where r , r # 48 latitude. c Section 2 of this paper details the mathematical for- mulation of the prediction model. Section 3 gives results band originates at about 440 km from the cyclone center, of hindcast predictions of intensity changes for Tropical (ii) only moist near-equatorial air spirals through the Cyclone Kathy using the model. Section 4 shows calcu- feeder band into the cyclone core and no cool dry trade air lations of the estimated radial wind profile in Kathy. participates in the cyclonic circulation during intensifica- Section 5 gives hindcast intensity predictions for two tion, and (iii) the convective cloud suppression around the other cyclones, section 6 discusses issues associated with cyclone during the period of intense convection in the the intensification rate of cyclones, and section 7 pro- CDO is observed to extend to about that distance, it is vides concluding remarks. assumed that all physical processes that influence the cy- clone intensity take place within 440 km of the cyclone 2. Model formulation center and that only the cyclonic circulation starting from 440 km to the north and northeast of the cyclone center a. Region 4 (rc # r # r4) needs to be taken into consideration to determine the 1) CIRCULATION ANALYSIS IN REGION 4 change in its intensity or in its intensification rate. An energy equation is then applied to the circulation Streamlines around stationary axisymmetric tropical in region 4. It is shown that because of the sudden cyclones are logarithmic spirals (see Abdullah 1966; change of a4, the angle of inflow at a radius of 48 latitude, Lahiri 1981; Wong et al. 2007). According to Senn and to the north and east of the cyclone at t 5 0, gradient- Hiser (1957, 1959), the trajectories of air parcels are level winds subsequently increase at all radii in region 4 equiangular logarithmic spirals far from the cyclone (48 latitude . r $ 18 latitude). On assuming that air center, while close to the center the angle of inflow de- trajectories are logarithmic spirals, the distances trav- creases with decreasing radius. A similar assumption is eled by air parcels between selected radii can be de- used here. In region 4, the angle of inflow a (see Fig. 2), termined, and from the radial wind profile, Vrc the wind in the northerly airstream to the north and northeast of at r 5 rc or 18 latitude and the time at which air parcels the cyclone, which is assumed to be constant between leaving r 5 48 latitude reaches rc can also be determined. radii 48 and 28 latitude and varies as shown in Fig. 2 for In region 3, a theoretically determined gradient-level smaller radii. The maximum angle of inflow is 208 before wind profile, particularly developed for that region by intensification, 42.58 and later 338 during intensification, Riehl (1954, 1963) and empirically documented by Shea and 208 during dissipation as observed in Fig. 5 of Part I. and Gray (1973), is then used to determine the gradient- The angle of inflow a is assumed to decrease linearly to level winds at different selected radii and the maximum 208 for 28 latitude $ r $ 18 latitude and to decrease to 108 wind Vrm at rm. The gradient wind equation is then used for 18 latitude . r $ 08 latitude. The last assumption is to obtain the surface pressure gradient and the surface made to simplify the computations of pc without greatly pressure at selected radii and at rm. affecting the results. Unauthenticated | Downloaded 09/29/21 04:37 AM UTC 24 MONTHLY WEATHER REVIEW VOLUME 138 The solid curves ending with an arrow represent the streamlines. AB is an arc of a circle of radius r. The quantity P is the location of an air parcel moving along the s direction with a speed V. Vector n is normal to the s direction, u is the angle POX, and O is the cyclone center.