^'^ lA 93943 NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS AN EVALUATION OF 700 M3 RECONNAISSANCE DATA FOR NORTHWEST PACIFIC TROPK AIR SEL :al CRAFT ECTED CYCLONES by George Mi It on Dunnavan The sis Advisor : R. L. Elsberr ^y Approved for public release; distribution unlimited T 21^53 SECURITY CLASSIFICATION Of THIS PACE (Whmn Dmta Entmrad) REPORT DOCUMENTATION PAGE 1. REPORT NUMBEM READ INSTRUCTIONS BEFORE COMPLETING FORM 2. GOVT ACCESSION NO 3. RECIPIENT'S CATALOG NUMBER 4. TITLE (and Subtilla) An Evaluation of 700 mb Aircraft Reconnaissance Data for Selected Northwest Pacific Tropical Cyclones 5. TYPE OF REPORT & PERIOD COVERED Master's Thesis; SeDtember 1983 6. PERFORMING ORG. REPORT NUMBER 7. AUTHOMr«> Georse Milton Dunnavan 8. CONTRACT OR GRANT NUMBERr»J I. ^eHFORWINO OROANIZATION NAME ANO AOORESS Naval Postgraduate School Monterey, California 939U3 10. PROGRAM ELEMENT. PROJECT. TASK AREA i WORK UNIT NUMBERS II. CONTROLLINO OFFICE NAME ANO AOORESS Naval Postgraduate School Monterey, California 939^-3 12. REPORT DATE September 1983 13. NUMBER OF PAGES 92 14. MONITORING AGENCY NAME A ADOHESSfll dUturant tnm Controttlna Otilcm) 15. SECURITY CLASS, (ol this report) UNCLASSIFIED 15«. DECLASSIFICATION/ DOWNGRADING SCHEDULE l«. OISTRISUTION STATEMENT (et ihia Kap»ri) Approved for public release; distribution unlimited 17. OISTRIBUTION STATEMENT (ot tha abatraet antarad In Block 30, It dlHaranl Irom Raport) IS. SUPPLEMENTARY NOTES It. KEY WOROS (Canllnua on rararaa alda II naeaaaaiy i*d Idanllty by black rtumbar) Tropical cyclones Typhoons Hurricanes Aircraft reconnaissance Tropical cyclone intensity Equivalant potential temperature Moist static energy 20. ABSTRACT (Canlinua en ravaraa alda II naeaaa^rr and Idanttty by block numbar) The 700 mb aircraft reconnaissance data for 25 selected north- west Pacific tropical cyclones were analyzed and compared with similar data for Atlantic tropical cyclones. Correlations of observed winds and winds calculated from the height gradient indicated that the cyclostrophic equation provided a very good approximation of the observed winds, although the root mean square and bias errors suggested that a gradient wind DD .l FORM AM 7S 1473 EDITION OF 1 NOV «8 IS OBSOLETE S/N 0102- LF- 014- 6601 SECURITY CLASSIFICATION OF THIS PAGE (Whan Data Enlarac SECURITY CLASSIFICATION OF THIS PAGE (TWi«n Dmtm Enfnd) expression was a slightly better estimate. A wind-radius relationship evaluated by Shea and Gray (1972) for Atlantic cyclones was shown to apply very well for this data set also. Based on the surface pressure-equivalant potential teiriDerature relationship noted by Malkus and Riehl (1960), it is proposed that periods of rapid/explosive deepening are related to the inward transport to the eyewall of "pulses" of high equivalent potential temperature air. The evaluation of the aircraft reconnaissance data from four super typhoons suggests, but does not provide conclusive proof, that such pulses do exist. S-N 0102- LF- 014-6601 SECURITY CLASSIFICATION OF THIS PAGEfWh«fi Dmtm Bntmrmd) Approved for public release; distr ibation unlijiited An Evaluation of 700 mb Aircraft Reconnaissance Data for Selected Northwest Pacific Tropical Cyclones by George n, Dunnavan Lieutenant, Qnirsd States Navv 3.S., aniversity of Washington, T975 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN METEOROLOGY AND OCEANOGRAPHY from the NAVAL POSTGRADUATE SCH3DL September 1983 7^V fr- ever, inferences concerning the structure close to the cen- ter of the system, e.g. within 100 NM (nautical miles), become tenuous because of the smaller data base available. Upper-air soundings near the center of tropical cyclones are rare for two reasons. Tropical cyclones form over tropical oceans away from rawinsonde sites, and it is very difficult *o launch rawinscndes during the adverss weather conditions associated with mature tropical cyclones. On the other hand, reconnaissance aircraft have provided routine observa~ions of the tropical cyclone circulation during various stages of its development. The major draw- back to aircraft observations is that they are taken at only a small number of pressure levels (usually only one) , and thus do not provide the vertical structure information which a rawinsonde does. Still, much infor:nation concerning the central structure can be gleaned from the large amount of aircraft data which is available from many cyclones. 13 This -thssis prssents analyses of 733 mb aircraft reccn- naissance data for 25 selected -ropical cyclonas which occurred in the r.Drthwsst Pacific b9ti#9en 1978 and 1981. The first goal of this study was to de-^rmine if -h= meteo- rological observations obtained by operational reconnais- sance aircraft (whose primary mission is forecast support) are of sufficiently high quality to provide tropical cyclone structure information which is consistent with the informa- tion provided by the more sophisticated research aircraft. Second, an attempt was made to determiie, from the 700 mb aircraft data, if a relationship exists between ihe arrival of high equivalent potential temperature air near the eyewall and a subsequent drop in central surface pressure. 1«* II. RECONNAISSANCE AIRCRAFT TROPICAL CYCLONE ui^rs A. BACKGROUND Early aircraft reconnaissance (T & WA, Inc, 1945; Wexler and Wood, 1945) was conducted primarily to determine whether it was possible for an aircraft to penetrate safely through the center of a mature tropical cyclone. Observations dur- ing these flights were mainly ^risual, but they did provide new information concerning the large-scale dynamic and thermodynamic processes which take place near the center of a tropical cyclone. For example, aarly reconnaissance flights discovered the existence of a narrow band of ascend- ing air near the cyclone center, "the eyewall", with gener- ally descending air (except in the vicinity of the rainbands) outside of this area (Wexler and Wood, 1945). Prior to these obeservat ions, it was -hDught -hat ascending air should exist Dver the entire area encompassed by the cyclone, with descending air only within the eye. By the late 1940*3, aircraft reconnaissance to support tropical cyclone forecast centers was being routinely con- ducted by the U.S. Navy and Air Force in the Atlantic and 15 th9 northwest Pacific Oceans. Although these flights were operational in nature, it was often possible to gather research data. Simpson (1952, 1954) and Simpson and Star- rett (1955) performed the first extensive evaluation, of air- craft reconnaissance data from operational and research flights into both Atlantic and northwest Pacific tropical cyclones. Information provide! by these studies expanded and, in some cases, altered the existing theories of the horizontal and vertical structure of the tropical cyclone temperature and wind fields, pressure gradients and associ- ated cloud features. With the advent of specially equipped tropical cyclone research aircraft in 1955, it was possible to increase both the quantity and quality of the data col- lected. This advancement was crucial for the detailed study of the near-eye structure as well as the wind, pressure, temperature and dewpoint fields (La Seur and Hawkins, 1963). The most complete study to date of the tropical cyclone's inner core region was accomplished by Shea and 3ray (1973), who composited 13 years of research aircraft reconnaissance data for tropical cyclones in the west Atlan- tic Ocean. The composite of this large amount of data allowed the documentation of subtle wind and temoerature 16 asymmetries. The variabili-y among th9 individual cycicnrs was also demonstrated. Studies of aircraft reconnaissance data from opsrational and research flights have also provided the operational forecaster with some useful tools. Thesa include: a -ech- nigue for estimating central sea level pressure from air- craft observations (Jordan, 1958); a proposed method for the determination of tropical cylone intensity through upper- tropospheric aircraft reconnaissance (Gray, 1979b); and a technique for forecasting intense tropical cyclones using aircraft-provided temperature and dew point data (Dunnavan, 1931) . B. NORTHWEST PACIFIC AIRCRAFT DATA COLLECTION Tropical cyclone aircraft reconnaissance in rhe nort-h- wsst Pacific is conducted by the 5Uth Weather Reconnaissance squadron of the United Stages Air Forc= using WC-130 air- craft. Since 1978, the Aircraf- Reconnaissance Weather Officer (ARHO) on each reconnaissance mission has prepared "peripheral data" messages which are relayed to the fore- casters at the Joint Typhoon Warning Center (JTWC) in Guam via teletype. The peripheral data asssage contains the position of the tropical cyclone's 700 mb cen-er, the 700 mb 17 height, temperature and dew point at tiit center; =nd the 700 mb height, temperature, dew point aad flight level wind at 30, 60, 90 and 120 NM from the cyclone center for both an inbound and an outbound flight leg. Except in areas of restricted airspace, the inbound and outbound Isgs are in different (usually opposite) quadrants of the cyclone. It has been the policy of the JTWC to request aircraft recon- naissance to support at least two of ths four daily tropical cylcone warnings, when logistically possible. Thus,. 700 mb peripheral data, observed at intervals of 12 h (hours) or less, has been collected for many northwest Pacific tropical cyclones from 1978 to the present. The 700 mb height data were obtained using an AN/APN-42A Radar Altimeter (or as a baclcup, either an SCR-718 or APN-133 Radio Altiaeter), together with a 3arrett Airsearch Digital Pressure Encoder (or as a backup, an AIMS Counter- drum pointer Aneroid Pressure Altimeter) . The radar or radio altimeter provided the absolute altitude of the air- craft and the pressure encoder (or altiaeter) provided the pressure altitude. A series of calculations and corrections was employed to reduce these two measurements to a 700 mb height value (Henderson, 1980). The accuracy of a 700 mb 18 haighr det'srmined this way is about 23 di (Der. U , Air Wsather Service, 1980, Typhoon Dury Officer Brief). The 700 mb temperatures ware measurei by a Roseaour.t AN/AMQ-28 Total Temperature System. This device employs a resistance element in an external probe which is positioned to reduce fricticnal effects. It is accurate to within 1°C (Henderson, 1980) . The 700 mb dew point temperatures ware measured by a Cambridge Systems AN/AMQ-34 Aircraft Hygrometer. This instrument essentially measures the temperature of a mirror which has been cooled to the poinx where condensation forms. The device is accurate to within 1^ C for temperatures above 0^ C (Henderson, 1980). The flight level winds ( i. a . 700 mb) were determined using a one-minute average from a Dopplar radar. Measured wind directions are accurate to within 5 degrees and speeds -0 within 5 kt (knots) . It should be no-cad that Doppler attenuation in heavy precipitation could produce spuriously low wind speed values (Det 4, Air Weather Servica, 1980, Typhoon Duty Officer Brief). 5Jind speeds were not reported if it was obvious to the observer thax extreme attenuation had occurred. However, small reductions in wind speed due 19 to attsauation wsrs generally not detectable, and tl-iersfore ware a source of error in the data base. C. TROPICAL CYCLONES USED FOR THIS STUDY It was decided that only those tropical cyclones which -ransi-ed the Philippine Sea east of tha Philippine Islands, wast of -he Island of 3uam and south of Japan would be con- sidered for this study for the following reasons. By ana- lyzing tropical cyclones which existed in the same general area, but. reached different intensities, it was hoped that any geographic dependence on intensification would be reduced. Climatology indicates that the overwhelming major- ity of northwest Pacific tropical cyclo.ias pass through this area (Joint Typhooi Warning Csnter, 1979-1932). Also, most tropical cyclones which reach super-typhoon strength, or undergo a period of rapid intensification, do so in this region (PJclliday aid Thompson, 1979). Rawinsonde sites are sparse in this part of the Pacific, so it was necessary for the JTWC to request extensive aircraft reconnaissance for cyclones in this area. This region is also equidistant from the reconnaissance aircraft launch and recovery sites at Clarke Air Base in the Philippine Islands, Yckota Air Base in Japan, Andersen Air Force Base on 3uam, and Kadena Air 20 Biss on Okinawa. Thus, *he aircraft have long on-s-ation times which permit the ccllecticn of large amoun-s of da- a in the vicinity of cyclones in this area. Reconnaissance aircraft observations for storms outside of the region were excluded from this study. TABLE I List of Tropical Cyclones With Peripheral Data # ST = super typhoon, TY = typhoon, TS = tropical s-oria Year Month Cyclone Maximum Wind Min Name (kt) 1981 Aug TY# Thad 85 1981 Seo ST Elsie 150 1981 Nov TY Hazen 100 1981 Nov ST Irma 135 1981 Nov TS Jeff 35 1981 Dec TY Kit 115 1930 :iav TY Dom 90 1930 May TY Ellen 110 1980 Jul TS Ida 60 1980 Jul TY Joe 105 1980 Jul ST Kim 130 1930 Oc- TY Betty 120 1979 Jan TY Alice 110 1979 Mar TY Bess 90 1979 Jul TS Faye UO 19 79 Jul ST Hope 130 1979 Aug TY Irving 90 1979 Aug ST Judy 135 1979 Seo TY Owen 110 1979 Oct ST Tip 165 1979 Nov ST Vera lao 1979 Dec TY Abby 110 1978 Jul TY Trix 70 1978 Oct ST Rita 155 1978 Nov TY Viola 125 TOTAL RADIAL LEGS = 1002 The geographic constraints established above allowed the selection of 25 tropical cyclones which developed between 1979 and 1981. Ml of the peripheral data for these 25 Pressure No. Of (mb) Radial Legs 965 34 893 38 956 32 902 32 999 6 924 60 956 14 931 60 980 18 9ao 22 908 40 928 4a 930 76 958 30 998 10 898 6 954 34 887 52 918 58 870 102 915 28 951 64 967 44 878 58 911 40 21 cyclones were obtained from ^he archives of the National Climate Center (Table I) . This set included Bight super typhoons (maximum sustained winds of 133 kt or greater), nine average typhoons (maximum sustained winds between 100 kt and 130 kt) and eight weaker tropical cyclones ( maximum winds less than 100 kt) . D. DATA PREPARATION Copies of the peripheral data messages prepared by the ARWOs were obtained from the National Climate Center. The message format was sufficiently consistent from year to year to allow compiling of the data into a master file of all of the aircraft observations frDra the 25 tropical cyclones. The master file contained 4008 observations, each of which contained: the year, month, date and time of the observa- tion, the cyclone name and numoer; the 700 mb height, temperature and dew point at th5 cyclona center; the 700 mb height, temperature, dew point and flight level winl speed and direction at the location; the location of the cyclone center (latitude and longitude); ths location of the observation with respect to the cyclone center by quadrant and radial distance from the center (30, 60, 90, or 120 NM) ; a designation which indicated whether ths cyclone ultimately 22 became a weak, typical or saper typhoon; and an ir.dica-.ion if the observation was made before tie cyclone reached maximum intensity. Eight consecutive lines represen-ed one peripheral data message. That is, four inbound observations ( at 120, 90, 60, and 30 NM) in one quadrant, and four ouzbound observa- tions ( at 30, 60, 90 and 120 NM) in another quadrant. To reduce the effects of cyclone movement and asymmetries in the dynamic and thermodynamic fields, i second data set was generated. This data set was composed of 2004 observations which represented the meteorological variables at 30, 60, 90 and 120 NM as determined by averaging rhe values obtained on the inbound leg and outbound leg at each radial distance for each penetration of the tropical cyclone. 23 III. THE HORIZONTAL WIND STRUCTURE OF THE CTCTL^fT-ES — After the aircraft data had been averaged as described in Chapter II and scanned for obvious errors, they were ana- lyzed to determine if the wind observations sa-isfiei gradi- ent and/or cyclostrophic mass-wind balance. Also, a wind speed-radius relaxionship was evaluated and compared to a relationship noted by Hughes (1952), Malkus and Riehl (1960) and Shea and Gray (1972). The evaluation of the observed winds involved three basic assump-icns. First, it was assuaed -hat che average of the wind speeds for the inbound and outbound legs at a radius was somewhat representative of the wind speed for the entire t,ropical cylcone at that radius and time. This assump-ion would have been stronger if it had been possible to average more than just -wo radial legs at a time. Secondly, i- was assumed that the magnitude of the tangen- tial wind could be approximated by the magnitude of the observed wind. This assumption is supported by the findings of Shea and Gray (1973), who determined that there was very weak azimuthally-averaged inflow or outflow at the 24 mid- levels (750, 650, 525 mb) from th^ radias of maxiir.uin winds (RMW) -c at Least HO NM. This implies that the radial wind was either very small, or that the inward radial veloc- ities occurred as often as the outward velocities. I- was assumed that Shea and Gray's results could be applied to the 700 mb level and cut to 120 NM. Wi-h a Large data set, such as the one used in this study, the azimathal averaging would tend to eliminate the radial wind component so that the observed wind would be a good approximation of the tangen- tial wind. Finally, the mass-wind balance equations which were used in this study are valid for steady state situ- ations only (i.e. the wind speed is not changing with time). Although the data represent tropical cyclones at all stages of development, it was believed that the large size of the data set would allow for an assumption of steady state con- ditions. This same assumption was also made by Shea and Gray (1973). A. THE MASS-WIND BALANCE The gradient wind balance equation (Holton, 1979) rake the form: can ^ or where, V = tangential wind speed (1) 25 r = radial distance from th5 center f = Coriolis parame-er X - geopotential height Solving for V with the positive root yialis: v=-i'-V^ iLL'^r r^ (2) Because 700 tnb height da^ a * ere available at 0, 30, 60, 90 and 120 NM from the cyclone center, r- could be esti- mated at 30, 60, and 90 NM using a centered finiie differ- ence scheme. By using this approximation -o the derivative, it was possible to calculate gradient wind speeds based on the latitude of tha cyclone, the distance from the cyclone center and the 700 mb gecpctential heigit gradient. These gradient wind speeds were th«=n compared to the observed wind speeds (Table II) . The Coriolis parameter in the tropics is small, and the wind speeds associated with tropical cyclones can be high. As a consequence, a scaling of the individual terms in the gradient wind equation indicates that to a good approximation, this equation can be reduced to a cyclcstrophic balance equation: (3) 26 or V = ^/ '' ^ (4) Intuitivaly, this balance shDuli be mos- applicable near rhs cyclone center where r is small and/or in the lower lati- tudes where the Coriolis parameter is saall. These cyclo- strophic winds were also compared to the observed winds at 30, 60 and 90 NM (Table II). TABLE II Correlation of Cyclostrophic/Gra dient Wind and Observed Wind Balance Radius Obs. Used 3orr. Regression equation % (NM) Coeff. (winds in m/s) "Ideal Case" 1.000 y = 1.000 x + 0.0 Gradient 30 ALL . 782 y = 1.075 x + 2. 5 Lat LT 20 N # .798 y = 1.116 x + 2.3 Lat GT 20 N * .736 y = .922 x + 4.4 60 ALL . 812 y = 1.011 x + 2. 1 Lat LT 20 N .809 y = 1.021 x + 1.7 Lat GT 20 N .805 y = .960 x + 3.9 90 ALL . 800 y = .947 x + 2.5 Lat LT 20 N .824 y = .988 x + 1.4 Lat GT 20 N .685 y = .796 x + 7.0 Cyclcstrophic '30 ALL .785 y = 1.081 x + 3.5 Lat LT 20 N .799 y = 1.127 x + 2.9 Lat GT 20 N .738 y = .922 x + 6.0 60 ALL .814 y = 1.035 x + 3.8 Lat LT 20 N .809 y = 1.038 x + 3.1 Lat GT 20 N .808 y = .969 x + 6.8 90 ALL . 803 y = 1.011 x + 4.3 Lat LT 20 N .825 y = 1.031 x + 3.1 Lat GT 20 N .684 y = .810 x +11.2 % X refers to observed wind, y refers to calculated wind # observations south of 20 North latitude * observations north of 20 North latitude 27 Wh9n all latitudes and all radii W£r9 included, tha correlations of rhs calculated wind speeds with the observed wind speeds ranged from aboux 0.78 to 0.81 for both the gra- dient and the cycLostrophic winds. The linear regression equations are also listed in Table II. The coefficient mult plying the observed wind in the linear regression equa- tion is near 1.0 ia most cases. The y intercept is generally between 2 and 5 m/s , which suggests that the observed winds are, on the average, 2 to 5 m/s lower than the calculated gradient or cyclost rophic winds. This is reasonable, because the observed winds contained random errors due to inaccuracies in the radius determination, and systematic instrument errors. Also, fricticnal effects were not con- sidered. Errors are likewise introduced due to the wind averaging process. Anthes (193 2) has saown that if tangen- tial wind profiles which are in perfect gradient balance are averaged, the resjltant set of averaged winds will actually be subgradient. This may provide an explanation for at least part of the discrepancy between the calculated and observed winds noted previously. The Large number of cor- related pairs (an average of 450 per case), together with the linear regression equations, support the contention that 28 the calculated winds are a gDDd estiraats of tha observed winds. Significant diffarsnc=£ between the correlation of observed winds with gradient winds, iad -hat of observed winds with cyclost rophic winds, were not evident. An attempt was made to discern the effects of the Coriolis parameter by evaluating the cycl ostrophic and gradient winds for cyclones north and south of 20 N . Again, there was no significant difference, although the correlation coefficient was smaller for the 90 NM winds of cyclones north of 20 N. This was probably because many of the cyclones were weaken- ing and/or undergoing extratropical transition north of 20 N. As a result, the wind and mass fields were becoming deformed to such an extent that the symmetry assumptions previously stated were no longer applicable. The largest correlation coefficients were associated with the 60 NM winds (Fig. 1 and 2) and the lowest with the 39 NH winds (Fig. 3 and U) . It was suspected that the lower correlations at 30 NM were due to a combination of the effects of the proximity of the 30 N?l observation to the eyewall, which could differ significantly from cyclone to cyclone, and the Doppler attenuation problems which can 29 occur in the heavy precipitation near the cyclone center. Also, since the slope of the 700 mb surface begins zo change very rapidly across the region from -he eyewall to the cyclone center, the centered finite difference approxima- tion to the derivative of geopotential haigh- with respect to radial distance may become less accurate. This is criti- cal, since the height at the canter and the height at 60 NM were used tc estimate the derivative at the 30 NM radius. These computational inaccuracies could contribute to the larger amount of scatter about the linsar regression "best fit" lines at wind speeds greater than 20 m/s. Since the scatter below 20 m/s is significantly lass than the scatter above 20 m/s (Figs. 3 and H) , a wind spaai of 20 m/s (40 kt) may indicate a thrashold for accurate estimates of the inner geopotential gradient. Below 20 m/s, the finite difference approximation appears to be valid, but as the 700 mb heights fall near the cyclone center, and wind speeds increase to above 20 m/s (tropical storm intensity), tha accuracy of the approximation decreases. This threshold is possibly associ- ated with the development of the eyewall, which is a crucial stage necessary for the continued intensification of the cyclone. 30 It was also tested whether the error statis-ics =t 30 N.I could be improved by changing the finite differencing technique to reduce the inaccuracy in estimating the 700 mb slope across the eyewall. Therefore, the 30 NM data were also analyzed using gradient and cyclos trophic equations which evaluated the 700 mb slope at 30 NM using -he height values at 30 and 60 NJ1, vice 0 and 60 NM. In both cases the correlation coefficients were slightly sialler (0.779 versus 0.782 for the gradient case; 0.777 vsrsus 0.785 for the cyclostrophic case> . Significant improvement was evident in the RMS errors, however (as compared to the RMS values for the centered differencing scheme listed in Table III). For the gradient case, the RMS error dropped from 11.2 m/s -o 8.8 m/s. For the cyclostrophic case, the RMS error dropped from 11.69 m/s to 3.6 m/s. The decreases were probably due to the eliminaricn of the erroneously high gradien- approxi- mations associated with the small, compact cylones. The very large reductiDn in the RMS error which occurred in the cyclostrophic case was probably due to the fact that the magnitude of the cyclostrophic wind is dependent entirely upon the height gradient, whereas the gradient wind magni- tude is also dependent upon the Coriolis parameter. The 31 bias errors were of similar magnitudes, bat diffsren-. signs. For th«^ gradient case, the bias changed from ^4 . 5 ca/s •c -a.6 ni/s. The cyclostr ophic bias changed from 5.6 m/s to -3.5 ai/3. This implies Tihat the centered differencing scheme overestimated the slope and the non-ceitered differencing scheme underesrimat ed it. The bigges:: discrepancies were evident in the comparison of the regression equations. For both the gradient and cyclos-rophic cases the slop? of the regression line was reduced from near 1.0 to less -han 0.63. This also emphasized the overall undsrestimation of the height gradient by the non-centered differencing technique. Thus, no particular advantage was gainsd by using the non- centered differencing technique at 30 NP1. Although errone- ously high gradisnts were eliminated, erroneously low gradients were introduced. It appears mat 30 NM is a crit- i::al distance where finite differencing approximations become tenuous. Some knowledge of eye radius would be necessary to choose the proper scheme foe a givan situation. The primary conclusion which can be drawn from Table II is that for most purposes the mass-wind balance within 90 NM can be approximated by a cyclost rophic balance equation. An examination of the root mean sgiare error (RMS) and the bias 32 values (Tabl-r III), however, indicates that a graiirr.- oal- afiCe equation may be slightly more accurate -har. the cyclstrophic balance equation for this iata sei wh=-r. a cen- tered differencing approximation to the height deriv=tiv= is used. Both the 30 NH and the 60 NM RMS error and bias values are lower for the gradient equation case. TABLE III RMS Error and Bias Values for Sradient/Cyclostrcphic winds Gradient Wind Case: RMS (m/s) 30 NM radius 1 1 . 2J 60 NM radius 7. 04 Cyclostrophic Wind Case: 30 NM radius 11.69 60 NM radius 3. 18 Bias (m/s) 4.50 2.40 5.61 4.62 Figure 1. O LJ cn O-i o- o « o- U~) Q a _j o o o- o- oo o OH o o. • • J: * • • 'Ia.*^ ca wi CU Icul nd ( rve 0.0 10. Q 20.0 30.0 40.0 50.0 60.0 70.0 OBSERVED NINE (M/SECJ ated gradient wind (y-axis) vs observed X-axis) at 60 NM radius. Winds in m/s. is least squares best fit to the data. 33 CJ ° LiJ o- CO ^ Z O- I— I ^ CD <=•■ cIj ^ E— o _J o- cn '^ o ° o Figure 2. 0.0 10.0 20.0 30.0 40.0 50.0 60. G 70.0 OBSERVED NIND [M/SECJ similar to Fig. 1, except cyclostrophic vs observed wind. LiJ a- (Jl '^ QO 2. o- I—I ■^ Q °- LJ " E-H o _j o- cn ^ o. • «... •. .y /- • y • • • ".: •; 1 \ I 1 I I I 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 OBSERVED NIND (M/SEC] Figure 3. Similar to Fig. 1, except at 33 NM radius. 34 o O ° LJ o cn ^ \ o in ^ o- CiJ ^ . « • ••• • •> .*- ^* -• • 0.0 10. 0 20.0 30.0 40.0 50.0 60. G 70. 0 OBSERVED WIND [fl/SEC] Figur<5 4. Similar to Fig. 2, except at 30 HM radius, B. THE WIND SPEED-RADIUS RELATIONSHIP It has been observad (Hugh=s, 1952; Malkus an i Eiahl, 1960; Riehl, 1953; and Shea and Gray, 1972) that tha horizontal wind structure of a tropioal cyclone can be represented by an equation of the form: V r^ = C (5) whers, 7 = tangential wind speed r = radial distance of observation from the cyclone center X = constant c = constant 35 Rirhl (1963) assunad conservation of pot'?ntial vortici-y for a steady state hurricane. This assamption iaiplies -hat the C'irl of -he tangential frict ional drag is equal to zero. This further implies that the partial derivative of the sur- face tangential stress with respect to height multiplied by the radius is equal to a constant (since the partial deriva- tive is proportional to the frictional drag) . Integrating this partial derivative from the surface to the level at which the surface stress equals zero yields the relation- ship: rx = constant, where r is the radial distance from the cyclone center and t is the surface tangential stress. If the drag coefficient is assumed to be constant, rhe sur- face tangential stress is directly proportional to the square of the tangential velocity: z - constant X v^ Combining this equation with rx = constint produces vr = CO nstant . Shea and Gray (1972) calculated a value for x, in (5), of -1.05 (♦/-0.6) inside the R MW (radius of maximum wind) and 0.U7 (+/-0.3) outside the RMW, for profiles of flight levels between 903 to 500 mb. The latter value is very close to the value of 0.5, determined by Riehl (1963). 36 To calculate a value for x in (5) from the wind obs tions associated wirh the 25 tropical cyclones of study, (5) was expressed as: er va- where, x = - x' (6) In V = x' In r + C or (7) For each radial leg, a least squares besr fiz line was determined for the set of four pairs of (la V, In r) points at 30, 60, 90, and 120 NM. By evaluating the slope of the (In V,ln r) lines for many radial legs, it was possible -o obtain an average x». The data set used for this thesis did no-: contain suffi- cient information to determine the RMW accurately . There- fore, to eliminate those situations in which the 30 NM wind observation was definitely within the r:iw, only those radial legs which displayed an increase in wind speed with decreas- ing radius were considered. With this restriction, an aver- age x of 0.U7 (+/-0.2) was obtained for the data set. This value is exceptionally close to Shea and Sray's value, which indicates that the quality of the operational reconnaissance 37 data is or. a par with the quality of zhB data collec-ed by research aircraft. Using the exponent value of 0.U7, iiquat-ion (5) transformed to calculate the 700 mb tangan-ial wind at greater than the RMW, given the wind speed at 120 NM . was raai; . .47 120 (8) V(r) = V(120) where, V (r) = wind speed a:: radius r r = radius greater than RMW V(120) = wind speed at 120 Nil Correlations between the winds calculated using (8) and the observed winds are shown in Table IV. TA3LE IV Correlation of Winds Calculated from Eg. (8) with Actual Winds Radius (NM) "Ideal case" 30 60 90 Corr. Coeff. 1-000 .735 .861 .9 20 Regression Eguation (Winds in m/s) y = 1 .000 X + 0.0 y = 1 .071 X - 1.6 y = 1.066 X - 2.9 y = 1.039 X - 1.9 y refers to calculated wind, x refers to observed wind 38 For all "three radii the cDrrelation coefficients were high and the calculated regression equation was very close to the "ideal" equation. This is another demonstration iihat the wind observations of this data set adhere to the rela- tionship which has been noted in previous research. This contention is further supported by the small RMS error and bias values (Table V). TABLE V RMS and Bias for the Wind-Radius Rela-ionship of Sq. (8) Radius (NM) RMS (m/s) Bias (i/s) 30 8,90 .85 60 4.96 -1.17 90 3.24 -1.37 Figs. 5, 6 and 7 are plots of measured wind vs wind cal- culated from (8) for radii of 30, 60, and 90 NM , respec- tively. The scatter about the best fit curves decreases with increasing radius, which implies that the accuracy of the wind- radius relationship of (8) is reduced as the radius decreases from 120 NM, Specifically, the large scatter about the best fit curve at 30 NM is probably due to the proximity of the observations to the radius of maximum wind (which is not known) , where the coefficient in (8) changes values. Doppler attenution problems in that region, as previously mentioned, can also produce spurious wind data. 39 Rishl (1963) r.oted that (5| , with x = 0.5, d?p?arer! to hold fcr the tropical cyclones evaluated for his s-.udy. The tangential velocities he considered, howevBr, were gener- ally obtained at altitudes of several thousand feet. There- fore, it may not be proper to conclude that (5), with x = 0.5, is validated by these data. Riehl's relationship was developed from other relationships which involved surface tangential stress, but these 70 0 mb observations are some- what above the surface frictional layer. Also, the assump- tion that the drag coefficient is constant throughout the tropical cyclone may be questioned. It may be more correct to refer to (5), with x = 0.47, as simply an empirically derived equation, without attempting to give a physical interpretation to the relationship between wind and radius. 40 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 OBSERVED NIND [M/SEO figure 5. Wind from Eg. (8) (y-axis) vs Dbsarvad wind (x- axis) at 30 NM. Curve is leas- sjuares bes^ -^-'t to data. 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 OBSERVED WIND [M/SEC] Figure 6. Similar ro Fig. 5, except for 50 NM radius U1 1 1 1 1 1 1 1 O.QIO.O 20.0 30.0 40.0 50.0 60.0 70.0 OBSERVED NINE (M/SECJ Figure 7. Similar to Fig. 5, =xecpt for 90 NM radius 42 IV. THE MDIST STATIC EN ERG Y/I NTSNSI FIC ATI ON ^TUDT A. BSVIEW OF TROPICAL CYCLONE INTENSIFICATION THEORIES For the purposes of this stady, tropical cyclon9 inten- sity and change in intensity were arbitrarily defined in -erms of central surface pressure. Sheets (1969) showed -hat the 100 mb surface in the vicinity of a hurricane is not altered by the presence of the tropical cyclone. Thus, the central surface pressure is directly proportional to the aean temperature of the colunin of air Dver the csnter (by the hypsometric equation) . An analysis of the relationship between central surface pressure (as detsrniinsd by extrapo- lation from 700 mb) and 700 mb center t r mperatur e (a crude estimats of the mean temperature of thr air column) , pro- duced a correlation coefficient of -0.68 for the data of this study. Givea the large number of t=mperatur e/pressure pairs evaluated (U76) , a coefficient of this size implies that the two paramsters are related, as was expected (Fig. 8) . The temperature/pressure relationship described above is a cornerstone of most tropical cyclone development theories. 43 5= S^ Q::: o => o* en u3- CD CD LJ ct: a. o LJ 2- CJ (D a: §° CO CD. ID CO _i cn o ^ CO. LJ o 0.0 5.0 Figure 8 30.0 35.0 10.0 15.0 20.0 25.0 700 MB CENTER TEMP(C] 700 mb tsmperaturs vs central pressure for a cyclones. Curve is least squirss best _i- z data. for all 0 A prsvailing theory of tropical cyclone in- ansif ica-ion (3.g. Anthes, 1982) involves a ra-her complex sarins of f^edbaclc mechanisms dealing with tha release cf latent hea* and the associated vertical ad justmen-cs, which are no* ye^ fully understood. A simplified explanation cf this theory is as follows. As low-level air spirals toward -he center of a developing tropical cyclone, the temperature and mois- ture content are increased due to fluxes of heat and water vapor from the sea surface and downward transfer of heat from above due to entrainment mixing and sabsidence. When nn this low-level air reaches -he eyewall ii: begins to rise rapidly. Cooling due to expansion eventually induces conden- sation and the resultant release of rreraendcus anoun-s of latent heat. Rather than increasing tne ambient temperature within the eyewall, the latent heat instead is -ransformei into potential energy by increasing the buoyancy of the air. Once the air reaches the top of the eyewall some of i- is eventually entrained into the eye where it is forced to sub- side. The physical process responsible for this subsidence is one of the phenomena which is net fully understood. The subsiding air within the eye warms by compression and pro- duces a decrease ia the surface pressure. Thus, the sensi- ble and latent heat which the air acquired as it passed over the ocean surface eventually is manifest as an ambient temperature increase and, therefore, pressure drop, within the eye. The drop in surface pressure increases the inflow near the surface which in turn enables the inflowing air to absorb still larger amounts of sensible and latent heat energy and the vertical circulation is enhanced. Some of this energy continues to find its way into the eye where it causes still further temperature increases and associated pressure drops, and the feedback cycle continues. The 45 tangential wind near the center increases, as th? vertical circulation intensifies, due to conssrvation Df angular momentua. Once a tropical cyclone is deprived of its source of latent and sensible heat, as is the case when it mov=3 over land, for example, dramatic wealcening can occur. As emphasized by Holland (1983), clouds are a crucial factor in the intensification process. Besides providing the latent heat which controls the strength of the vertical circulation, the clouds also provide for a local recycling of mass. This recycling produces warming necessary to main- tain a balance between the mass field and the developing wind field under ths vertical circulation. Also, Gray (1979b) suggests that the recycling induces a local enhance- ment of the evaporation from the sea surface which helps balance the export of moist static energy by th^ vertical circulation (Holland, 1983). The simplified description of tropical cyclon 9 develop- ment presented above, known as the CISK (conditional insta- bility of the second kind) thsory, was proposed by Charney and Eliassen (196U). Other research (as summarized by Holland, 1983, for example) has indicated that the CISK theory does not adequately explain all aspects of tropical 46 cyclone development. Ramage (1959) hypothesized tha* posi- tive vorticity advection downstream of an upper-level trough ia the westerlies could induce upper-le/al divergence over an incipient tropical cyclone. The iDw-level convergence associated with the upper-level divergence could then lead to intensification. Riehl (1975) has proposed that a tropi- cal cyclone may intensify if a nearby cold upper-level tro- po spheric low collapses. A secondary circulation is set up by the subsiding air in the cold low and the rising air in the cyclone. Intensification occurs a= angular momentum is transported inward at low levels. Sadl=r (1973) has noted the relationship between tropical cyclone development ana the position of the Tropical Upper-Tropospher ic Trough (TUTT) relative to the cyclone. He suggests that the establishment of easterly and westerly outflow channels by the TUTT increases the ventilation of heat away from the cyclone. This process appears to result in intensification, although a complete explanation of how upper-level outflow patterns affect intensity change is lacking. In addition to the intensification mechanisms described above, which rely to a great exent on thermodynamic processes, a purely dynamic intensification mechanism has ilso been proposed. 47 Conservation of angular momenta m produces regions of neg- ative vorticity at upper levels near the center of a tropi- cal cyclone. The outflow air can become inertially unstable if this negative vorticity exceeds the planetary vorticity. In this situation, outward acceleration at upper levels would develop. Mass continuity would require surface con- vergence, pressure falls and, therefore, cyclone intensifi- cation. Although inertial instability is evident in tropical cyclone models, it has not bee.i directly observed (Black and Anthes, 1971, for example). From the discussion above, it seems probable that tropi- cal cyclone intensification is controllei by the interaction between the cyclone and the synoptic scales of motion, as well as the interaction between the moist convection and the cyclone scales of motion (CISK) , as suggested by Holland (1983). The role of the synoptic scale environment may be to assist in organizing the moist convection fields to per- mit optimum exploitation by the cyclone scale environment. Although tropical cyclone intensification is controlled by the dynamic interaction between the cyclone and synoptic scale environment, it is ultimately dependent upon the moist convection (Holland, 1983). 48 Claarly, thera is a direct relationship betwssn th^ strength of the vertical circula-wion aad -he intensity of the tropical cycloae. The more vigorous the vertical circu- lation, the lower the central surfac= pressure and the greater the tangential wind speed near the central region. Since the vertical circulation is controlled -o a great extent by the clouds near the circulation center, it is plausible to assuae that a relationship may exis- between changes in the near-center cloud energetics and subsequent changes in cyclone intensification. It would noz be neces- sary to know the exact cause of the change in cloud ener- getics (which may involve complex interactions) in order -o evalua-e the effects of such changes. B. AN EQUIVALENT POTENTIAL TEMPERATURE STUDY One parameter that can be used to estimate the energy of a parcel of air (the non-kinetic portioni is the equivalent potential temperature, since it takes into account the energy due to both sensible and latent heat. Malkus and Riehl (1960) attempted to determine the relationship between a change in equivalent potential temperature and a cor- responding change in surface pressure. They began with the assumption that the conditions within the eyewall of a 49 tropical cyclone ars vary nearly mois- aiiabatic. This was later verified by Riehl (1970). The hydros-atic aquation was then integratsd to determine the surface pressure under the eyewall assuming that the 100 mb level was undisturbed. Because the air was assumed to be saturated, the equivalent potential temperature within the coluna was constant with height and the temperature at any level could be determined from a moist adiabat. Using this technique, and solving for different values of equivalent potential temperature, Malkus and Riehl (1960) developed the following relationship: AP = -2.5/^9^1 (9) where, ^P = surface pressure change under eyewall ^Qq - equivalent potential temperature change Using aircraft reconnaissance data for Atlantic tropical cyclones and a linear regression metnod, Riehl (1963) determined the following empirical relationship: fp-1005J= -2.56 |9g - 350) (10) where, P = surface pressure under eyewall Ue = equivalvent potential temperature (1005 and 3 50 are reference values) 50 Bell and Tsui (1973) found similar results froni a set cf northwest Pacific tropical cyclones, except the coefficient was determined to be -2.25 vice -2.56. The results of the above studies give a strong indica- tion that a change in equivalent potential temperature is a necessary, though probably not sufficient, condition for tropical cyclone intensification. It is further implied that those processes which govern the transfer of sensible and latent heat to the lower atmosphere ( sea surface temperature and wiad speed, for example) also have a signif- icant influence on the intensification pattern of a tropical cyclone. Tropical cyclones typically deepen at rates cf less than 1 mb/hour, but occasionally a cyclone will undergo a period of rapid, or even explosive, deepening. Holliday and Thompson (1979) defined rapid deepening as a pressure drop of 30 mb in 2U hours (-1.25 mb/hour) and explosive deepening as a drop cf 30 mb in 12 hours (-2.5 mb/hour) . The majority of tropical cyclones in the northwest Pacific which reach super-typhoon strength (maximum sustained surface wind speeds of at least 130 kt, or a raininum central surface pressure less than about 91 1 mb) attain that intensity 51 following a period of explosive intensif ica -ion (Holliday and Thompson, 1979). Two attempts have been made to develop techniques which could be used to forecast explosive deepening based on 700 nb equivalent potential temperature. Silcora (1976) analyzed dropsonde and upper air sounding data associated with tropi- cal cyclones in the northwest Pacific. \n evaluation of the available data indicated that the potential for explosive deepening increased when the 700 mb equivalent potential temperature exceeded 370 K. Sikora was quick to point cut, however, that his results were based on a small data set and therefore may not be conclusive. Dunnavan (1981) developed an intensity forecasting technique foe northwest Pacific tropical cyclones which involves monitoring the relationship between the minimum sea level pressure at the cyclone center and the central 700 mb equivalent potential temperature as determined by aircraft. Simultaneous pressure and temper- ature values are plotted verses time on the same graph. The vertical pressure and temperature axes are oriented, based on an empirically derived relationship, so that explosive deepening is anticipated if the pressure and temperature traces intersect. This technique has shown some skill and is currently used operationally by forecasters at the JTWC. 52 C. A PROPOSED INTENSITY CHANGE RELATIONSHIP Thera is significant evidence to support the con-en-ion fnaT: ar least some of the change in tropical cyclone inten- sity can be directly related to changes in equivalent poten- tial temperature. If this is indeed the ^ase, it can be assumed that a steady, constant increase in equivalent potential temperature would be associate! with a steady, constant decrease in central surface pressure, and there- fore, an increase in intensity. Likewise, a sudden increase in the equivalent potential temperature of the air moving into the eyewall light be expected to produce a subsequent sudden decrease in surface pressure, and thereby initiate a period of explosive deepening. Rapid or explosive deepening may often be due to the arrival, at the base of the eyewall, of a "pulse" of air of significantly higher equivalent potential temperature. These pulses could be the result of an increase in the strength of the northeast trade winds, a surge in the southwest monsoonal flow or areas of anoma- lously high sea surface temperatures, for example. In each case the low- level moisture content, and therefore equivalent potential temperature, could be increased significantly. 53 If such pulses do exist, it may be possible -o de-ec- their presence from the reconnaissance aircraft data before they reach -he base of the eyewall. The detec-iicn of a palse before it reaches the eyewall might provide a fore- caster with advance nDtice that conditions favorable for a rapid change in intensity were developing. Significant lead time may be possible because a period Df time is required for the latent and sensible heat in the low-level air to be transported from the ocean surface to the interior of xhe eye, where it can produce the surface pressure drop, D. ASSUMPTIONS NECESSARY TO EVALUATE INTENSITY CHAN3S By compositing rawinscnde data for lany Atlan-^ic tropi- cal cyclones. Gray (1979a) was able to show that the strong- est inflow exists below 800 rab within 120 Nil of the tropical cyclone center (Fig. 9) . Thus, the high equivalent poten- tial temperature air flows toward the eyewall in a region which is generally below the flight level (700 mb) flown by the reconnaissance aircraft in the northwest Pacific. Fran)c (1977) has determined that the maximum vertical motion associated with a tropical cyclone also occurs within 120 NM of the cyclone center. Since at least some of the near-surface air is advected upward through the 700 mb 54 6 8 10 12 14 r Clot) Figure 9. Composite cross section of -lis radial wind component (m/s)_ , azimu-hally averaged, for wes-ern Atlantic Ocean tropical cyclones (Gray, 1979a). level, it is assumed that any fluctuations in the near-sur- face equivalent potential temperature would be reflected at the 700 mb level where it could be detec-ad by a reconnais- sance aircraft. A detailed analysis of Hurricane Inez by Hawkins and Imbembo (1976) showed that subs-antial variation existed in the horizontal equivalent potential -: etnperatur e field. Vert-ical variations, however, appeared -o follow a pattern (Fig. 10). Areas of lower (or higher) equivalent po-ential temperature at 700 mb appeared to extend vertically into the regions below 700 mb, as indicated by 55 the vertical orientation of the contours. Based on th=: Hurricane Inez study, the assuoipticn is made that -ha equiv- alent potential temperature at 700 mb is related to the equivalent potential temperature in zhs radial inflow layer below. HURRICANE INEZ EQUIVALENT POTENTIAL TEMPERATURE CK) 1000 50 40 30 20 10 0 10 20 30 RADIAL DISTANCE IN NAUTICAL MILES FROM GEOMETRICAL CENTER Figure 10. Vertical cross section of equivalent potential temperature (K) for Hurricane Inez on 28 September, 1966 (Hawkins and Imbembo, 1976). 56 Another assumption must be caade concerning the averaging of the data for the 25 tropical cyclones of this s-udy. Ideally, the tropical cyclones would exhibit axi-sy maeiry with respect to the temperature and dew point fields (and, therefore, the equivalent potential teaperature field) in the horizontal. If this were the case, then it would be possible to assume that an average of the inbound and out- bound flight leg temperature and dew point values, at a given radius, would be representative of the entire cyclone for that radius. Clearly, complete symmetry is not often observed (e. g. the field in Fig. 10 for Hurricane Inez, 1966) . It is assumed that the change in central pressure will be due to the net change in equivalent potential temperature of the low-level air which is arriving at the eyewall from all directions. Thus, if high equivalent potential temper- ature air from one semicircle of the cyclone arrives at the eyewall at the same time that low equivalent potential temperature air arrives from the opposite semicircle, they may tend to offset, so that no significant change in the intensification trend would occur. An average of the equiv- alent potential teaperatures for the two semicircles in the 57 above example would likely result in an squivalen- pDt=n-ial t.3inperature which would be consistent with a szeaay develop- ment trend. However, if high eguivaleat. potential temper- ature air arrives from both semicircles, the average of the two potential temperatures would be large and significant intensification would be anticipated. Because rhe aircraft reconnaissance data of -his study ware used to analyze the equivalent poten-ial temperature/ intensity change relationship, it was aecessary to assume that the data cbtained for a radial leg were representative of the semicircle that they were centered on. This is prob- ably a good assumption for developing cyclones (which are the main focus of -his study) . The assumption begins to break down, however, as the cyclones begin to fill and become extratropical . Equivalent potential temperature values are extremely sensitive to the amount of water vapor present in the air Therefore, tc minimize the effects of extreme fluctuations in moisture associated with random encounters with rain- bands, the emphasis of the study is on the 30 NM observa- tions. It was hoped that the relative humidity would be more consistent in that area since clouds and precipitation tend to concentrate more uniformly near the cyclone center. 58 Moist static energy is a msasure of tha "total 5ff=c-ive energy", since it takes into account boch the sensible and latent heat contained in an air parcel (Hawkins and Rabsam, 1968). The equatiDn which defines moist static ensrgy can take the form; H = CpT + gz + Lq (11) where, H = moist static energy per unit mass "p = specific heat of dry air at constant pressure T = air temperature g = acceleration of gravity z = height of pressure surface L = latent heat of condensation q = mixing ratio of parcel It can be shown (Holtcn, 1979) that loist static energy is approximately conserved when equivalent potential temper- ature is conserved. Therefore, moist static energy was cal- culated rather thai equivalent potential temperature, since H is more easily evaluated. 59 E. EVALUATION OF THE INTENSITY CHANGE RELATIONSHIP Fourteen of tha 25 tropical cyclones of this s-udy had data records of sufficient length and detail to describe their evolution. Four of these 14 cycloaes attained surface central pressures of 911 mb or below following a period of rapid intensification. The average pressure drop was approximately -1.7 mb/h ( -80.0 mb/48.0 h ), which lies between the rapid and explosive deepening rates defined in Chapter IV. Graphs of central surface pressure versus time and averaged 700 ub moist static energy (at 30 NH) versus time were prepared for each tropical cyclone. The four rap- idly deepening cyclones were evaluated because their rapid intensification periods were similar. The remaining 10 cyclones could not be compared because tieir intensification and moist static energy trends had very little in common. However, the graphs of two of these: typhoon Owen and super typhoon Judy are contrasted with the four rapid deepening cyclones in subsection 2. '' • Four Rapidly Deepening l£2£i:^§i sl£i211i§ An examination of the graphs Df the four rapidly deepening tropical cyclones (Figs. 11-14) indicates that the moist static energy reached a peak at or just prior to the 60 period of rapid despening, and decrsassd during th= subse- quent 43 hours, Th? notsable exception is super typhoon Irma (Fig. 14) whose 30 NM moist static energy continued to increase during the 48-h deepening phase. Irma may have been an atypical cyclone, however, since her 700 tnb eye temperature never exceeded 20 C. This is very low compared to the typical values of 25 Z or higher which have been observed for tropical cyclones of her intensity (JTWC, 1980 and 1982, for example). 48.0 96.0 144.0 192.0 240.0 288.0 336.0 TIME FROM FIRST OB [HOURS] Figure 11. Pressure and moist static energy vs time curves for ST Tip. Solid curve is surface pressure and dashed curve is 700 mb moist static energy at 30 NM. Vertical dashed lines indicate 48-h period of most rapid deepening. 61 o o CD Q^ o, — ) in CO ^ CO LJ Q:: Q_ -J °t LJ O o in CD ! to CO X O ^. CD CO N^ CO ^-^ m " tiJ CO 2Z to CO I i I 1 I 96.0 144.0 192.0 240.0 288.0 336.0 Fi 0.0 48.0 TIME FROM FIRST OB [HOURS] gure 12. Similar to Fig. 11, except for TY Viola I CO CO -■5 CO X O ". CD CO \^ to ^-^ CO oa to .to 0.0 48.0 \ 1 \ 1 96.0 144.0 192.0 240.0 288.0 336.0 TIME FROM FIRST OB (HOURS) Figure 13. Similar to Fig. 11, except for ST Kim 62 0.0 48.-0 96.0 144.0 192.0 240.0 288.0 336.0 ■ TIME FROM FIRST OB [HOURS] Figure 14. Similar tD Fig. 11, except for 3T Irma The pressure and moist static energy correlations indicated in Figs. 11-14 are consistant with the moist static =nergy/intensity change relationship discussed in Chapter IV, The peaks in moist static energy prior to the rapid deepening phase may indicate the arrival, at the 30 NM point, of pulses of high equivalant potential temperature air. The response to these pulses (i. e. rapid surface pressure drop) occurs during the subsequent 48 h. The decrease in racist static energy during the 48 h intensifica- tion period implies that air with lower sguivalent potential 63 tsmperature had replaced the high potential temperature air at 30 NM, outside the eyewall. The response to -he lower equivalent potential temperature air (i.e. a pressure rise) is not manifest until after -che rapid intensification period ends. A sharp pressure rise after the ainimum central sur- face pressure was reached, was observed in all four cases. It should be noticed that super typhoon Tip (Fig. 11) ulti- mately continued to deepen (to a record 873 mb) after the initial rapid deepening phase. Immediately after the U8-h deepening period, however, aircraft reconnaissance revealed a short-lived period of pressure increase (Fig. 11) which may correspond to the previous decrease in moist static energy. The moist, static energy /intensity change relation- ship presented in Section C suggests that a sudden increase in eguivalent potential temperature is associated with a subsequent decrease in central surface pressure. This implies that the magnitude of the moist static energy change, and the period over which it occurs, may be cf greater importance than the magnitude Df the peak value. The moist static eaergy curves of three of the four rapidly deepening tropical cyclones indicated a rapid increase (to a 6U psak) prior to the U8-h deepening perioi. It can be specu- lated rhat the decrease in the moist static energy of super typhoon Tip prior to the final rise {Fig. 11) may be due to smaller scale fluctuations, which wera encountered by the aircraft at 30 NM by chance. Also, it should be noted that the fourth rapidly deepening typhoon, Irma (Fig. 14) , did not display a sharp jump in moist stitic energy prior to rapid intensification, but instead followed a steady increasing trend. 2. Examples C? n t ra r y to the Relationship Two other tropical cyclones, typhoon Owen (Fig, 15) and super typhoon Judy (Fig. 16), also experienced abrupt increases in moist static energy, but these increases occur- red during, rather than prior to, the dispening phase. The peak moist static energy values were attained about 24 h prior to the time Df minimum central pressure. Unlike the four rapidly deepening cyclones above, thesa two did not develop to maximum intensity during a singla rapid deepening period, but instead, intensified in spurts. This made it more difficult to svaluate the relationship of moist static energy change and pressure change. Also, the significant pressure decreases prior to the rapid increase in moist 65 static anergy, can r.ot be sxplainad solely by tha mois- static energy/intensity relationship proposed in Srcticn C. gure 15. 48.0 96.0 144. 0 192.0 240.0 288.0 336.0 TIME FROM FIRST OB [HOURS] Similar to Fig. 11, except for TY Owen, Peak, values, or periods of rapii increase of moist static energy were not confined to the tropical cyclone developing phase only, as is indicated oy Figs. 11-16. In fact, the highest values and most extreme fluctuations often occurred during the filling stage (Figs. 11 and 16, for example). This may be due to the expansion of the inner-core region (as the tropical cyclone weakens) which could place the 3D NM observations in the high equivalent 66 CD CO to X O . CD CO \^ CO — CO 2Z CM CO CO 48.0 96.0 144.0 192.0. 240.0 288.0 TIME FROM FIRST OB [HOURS] Figure 16. Similar -co Fig. 11, except for ST Judy 336.0 potential temperature air within the eya. Also, a general breakdown in the tropical cyclDn-^ structure due to extra- tropical transition could cause the avsraging assumption to become questionabls, especially if tha cyclone developes large asymmetries in the horizontal teapsrature and height fields. Large differences between successive moist static energy observations (which ars especially ncticable during the weakening stages) probably arise because each observation provided the thermodynamic properties for only one section of the cyclone. Any one observation may define thermodynamic values which are radically different from the 67 values obtained for o-.her sections of zh= cyclone which wer = observed on previous or subsequent aircraf- reconnaissance jiissions. In this situarion, no one temperature or dew point observation can be thoughr of as rspresenta- ive of the cyclone as a whole. As previously s-a-ed, it was hoped that this problem could be reduced by consiiering moist static energy changes a- 30 NM, but Figs. 11-15 indicate that this procedure was not antirely successful. Another way to mini- mize this problem would be to examine rhe moist static energy changes in specific quadrants. This technique was not used for the northwest Pacific data of this study, how- ever, because the time period between successive observa- tions in any particular quadrant was coo long to permit a meaningful evaluation of the rapid intensity change relationship. 3« R "rjxaininat ion of the Intensity Change Relationship Given the central pressure and aoist static energy fluctuations above, it is virtually impossible to correlate a specific moist static energy change with the subsequent pressure change. This problem may be compounded by the variability in the time period between observations and the differences in the intensification trends of the individual 68 cyclones. rYPhoon Alice (Fig. 17) aii sup=r typhoon 5i-= (Fig. 18) illustrate this problem. A good correlation may exist, but the time and space resolution of the northwest Pacific aircraft reconnaissance data may not be high enough to permit an evaluation of the cause and effect relation- ship. It is, however, possible to compare the four rapidly deepening tropical cyclones, because they have scm=thing in common: a U3-h period when they were de=pening at a similar rate. It is assumed that the processes responsible for the deepening were the same for each cyclone. 0.0 48.0 96.0 144.0 192.0 240.0 288.0 TIME FROM FIRST OB (HOURS] Figure 17. Similar to Fig. 11, except for lY Alice. 336.0 69 48.0 96.0 144. 0 192.0 240.0 288.0 TIME FROM FIRST OB [HOURS] Figure 18. Similar to Fig. 11, except for ST Rita 336.0 During the tropical cyclor.9 devsloping st3.t = , the assump-ion of horizontal symmetry in rhs low-level temper- ature and height fields is probably reasonable. However, horizontal moisture fluctuations appear to be substantial. Fluctuations in moist static energy are due almost entirely to the latent h^^at term in (11)^ as illustrated by the curves of H and dry static energy (Cpr ■♦• gz) for super typhoon Tip (Fig. 19). Sines the difference between the curves is the latent heat term (Lq) , it is apparent that the fluctuations in H must be due primarily to the moistare con- tent of the air. Therefore, the quality of a moist static 70 energy estimate is dependent upon how represen'a-ci ve -.he dew point observations are at a particular radius, A representative moisture vaius for a particular radius is the most difficult parameter to determine from the aircraft data. It had been hoped that non-r epresenta-^. ive dew point observations could b= minimized by examining moist static energy close to the center (30 N'l) , However, the dew point values are highly dependent upon the location of the aircraft relative to the convective elements near the cen- ter. The rapid fluctuations evident in the moist static energy curve for super typhoon Tip's noist static en<=rgy curve (Fig. 19) during the filling stage are also probably due to this effect. The areal extent of a pulse of high equivalent potential temperature air may also be as important as the raagnituds cf the moist static energy, A narrow pulse of high energy air nay have little effect on changing the intensification trend of the entire tropical cyclone. To determine whether i sudden increase in moist static energy at 30 NM was associated with a puls5 of significant horizon- tal extent, curves of moist static energy versus time for radii from 0 to 120 NM were constructed. If peaks in the 71 LD X in X ro O ^ — 1 \ CD ^ \ — ) ' — ' o QJ ro CO in CpT + gz T 1 I 1 I \ 1 0.0 48.0 96.0 144.0 192.0 240.0 288.0 336.0 TIME (HOURS] Figure 19. Mcist static energy (H) and dry static snergy (CpT+gz) versus time for ST rip. moist static energy curves at. 30 NM coiaciied with peaks iz 60 NM or 90 NM, it would give an indicacioa of the width of the approaching pulse. The increase in the moist static energy of typhoon Viola (Fig. 20) at 30 NM, prior to the period of most rapid deepening, is refisctad at 60 NM, and possibly at 90 NM. In the case of super typhoon Tip (Fig. 21), however, it is questionable whether the smaller peaks at 60 and 90 NM are actually a reflection of the peak at 30 NM. The peak in the 30 NM moist static energy of super typhoon Kim (Fig. 22) prior to rapid deepening appears to be 72 rafl9C-ad out. to 120 NM, However, the amplitude of th.9 p-^a'c becomes quite small at the larger radii. Although typhcor. Irma did not reach a definite peak, prior to rapid deepening, her rapid deepening is probably keyed to the steady increase in moist static energy at 30 NM daring that period. But this steady increase is only weakly (if at all) reflected in the curves for greater radii (Fig. 23) . Typhoon Ali::e (Fig. 24) IS an ex ample of a tropical cyclone which did not undergo a significant period of rapid deepening. The moist static energy curves do not correlate well with the excep- tion of a brief period when she had reached maximum inten- sity (centered near 1 U4 h). The implication of Figs. 20-24 is that a pulse of high equivalent potantial air which is large enough tc induce a period of rapid deepening .must not only be evident at 30 NM, but must be reflected at the 60 MM or greater radii as well. There is a problem whioh arises, however, when air- craft data from cyclones of different sizes are analyzed. For example, super typhoon Tip (Fig. 21| and super typhoon Rita (Fig. 25) attained similar mininiim central surface pressures (876 mb for Rita; 870 mb for Tip) , but they dif- fered significantly in size. Rita was an extremely compact 73 120 NM CO to" in ro' ro i90NM 60 NM 30 NM ONM 0.0 48.0 I 1 96.0 144.0 I I I I 192.0 240.0 288.0 336.0 TIME [HOURS Figure 20. Hoist static energy versus -ime for tyDhoo?. Viola at radii from 0 to 120 N.I. 74 to' ro to" in to' ro to' in to' LO X '*: O ro' in \ to CO 120NIVI /lAr^ 90 NM 60 NM 3QNIV1 ONM 1 1 — 0.0 48.0 — 1 1 i \ 1 1 96.0 144.0 192.0 240.0 288.0 336.0 TIME (HOURS) ?iaur<= 2 1 . Similar to Fia. 20, excspt for sup Tip. 9r tvDhoon 75 in to' ID X • to ^-^ LJ ■^ cn to i_ to to tv to Y^ 120NM 90NIVI ONM 30 NM 0.0 48.0 96.0 H4.0 192.0 240.0 288.0 336.0 TIME [HOURS] Figure 25. Sitnilar to Fig. 20, axcapt f^r sucsr typhoon Rita. 80 30.0 Fiaure 26 60.0 90.0 RflDIflL DISTnNCE: (NMl 120, Corr 3 n — z valu corr maxi corr corr -he elation of ST Tip's 30 N^! moisr static gy with corresponding moist static enrray es at 30, 60, 90 and 120 JJ M . Cur/e (a) 'is e lit ion of observations obtained af-er mui intensity was reached; curve (b) is elation of all observations; curve (c) is elation of observations obtained prior to time of maximum intensity. (0.60 to 0.4 6) indicate that the influence of the center region decreases rapidly with distance from the center. These two cases illustrate a significant problem which can not be resolved with the available aircraft recon- naissance data. It is impossible to determine the dimen- sions of a high potential temperature pulse if the data are 81 30.0 Figure 27. 60.0 90.0 RnOIflL'DISTnNCE: [NM] similar to Fig. 26, axcep- for 3T Rita 120, always r^stric-ed to Dbserva-ion points at 30 NM intervals from the 120 NM point to th° r^nrer, withou- regard to the variability in size of the cyclones. In ihe case of extremsly large tropical cyclones (a.g. rip), the influence of the cyclone's c=nrer may extend to beyond 120 NM, making it difficult to determine the size of a pulse which is mov- ing into the cyclone from the environment. Likewise, 30 NM rssolution may be too coarse to permit the detection of 82 sab^le changes in the moist static energy in 'he vicir.i-y of an extremely compact cyclone (e. g. Rita) . U • Summary Clearly, a change in the equivalent potential temperature is not the only mechanism which is related to tropical cyclone development. Upper-level divergence and changes in angular momentum, for example, may also be impor- tant. Periods of rapid deepening which aight be expected to occur due to changes in equivalent potential temperature may not develop because of an unfavorable upper-level divergence pattern. It was not possible to determine when th-^ fluctua- tions of moist static energy at a particular radius reflected a genuine increase. The non-representativeness of the moist static energy values could be reduced, but not eliminated, by analyzing 30 n:i data. It is thus concluded that it is not possible to fully evaluate the moist static energy/intensity change relationship using the limited northwest Pacific tropical cyclone data. 83 V. CONCLUSIONS An analysis of the reconnaissance aircraft data of 25 northwest Pacific tropical cyclones produced results which are consistent with empirical relationships obtained by ear- lier researchers with Atlantic tropical cyclones. The mass-wind fields of the cyclones determined from -hese air- craft data were found tc satisfy a cy^los-crophic balance relationship. However, an examination of RMS and bias errors of observed winds versus winds calculated from the mass field revealed that a gradien- balance realtionship was slightly more accurate, as was anticipated (Holton, 1979). The aircraft reconnaissance data were also used to eval- uate a long established wind-radius relationship: Shea and Gray (1972) obtained a value for x, using Atlantic tropical cyclone data, of 0.47 (•♦•/-0. 3) for radii outside the radius of maximum wind (RMW) . For the 25 northwest Pacific tropical cyclones of this study, an x value of 0.47 (+/-0.2) was calculated. Eiehl (1963) also justified a value of x of 0.5 by assuming a surface tangential stress-wind speed 84 relationship and that the curl of the tangantial fric-.icr.al drag was equal to zero. The value of 0.47 calculated by rhis study, ard by Shea and Gray (1972), does not necessarily verify Riehl's theoretical results, since his relationship involves surface tangential s-ress which aay nor apply in regions above the boundary layer. Malleus and Riehl (1960) have shown that a change in the equivalent potential temperature at the base of the eyewall is directly proportional to the associated change in surface pressure. 3ased on this finding, a relationship was sought between suddan increases in equivalent potential temperatura (a "pulse") at the base of the eyswall and subsequent dacreases in central surface pressure. An evaluation of the surface pressure changes associated with four rapidly deep- ening tropical cyclones indicated that i build-up in moist static energy (directly related to equivalent potential temperature) occurred just prior to a U8-h period of rapid deepening. Likewise, a subsequent irop in moist static energy during the 48-h deepening phase appeared to correlate with a later pressure rise in three of the four cases. How- ever, the results of only four cases are not sufficient to establish a causality relationship. 85 The conclusive evidence needed to vsrify a rela-.ic?.ship between moist s-atic energy change and intensity change light be obtained through more ax-^ensive aircraft reconnais- sance. It would be necessary to obtain complete low-level moist static energy data around the outside of the eyewall at closely spaced intervals. This would reduce the problem of having to determine an average low-level moist static energy value for the entire tropical cyclone based on only one or two observations at 700 mb. Also, if the observa- tions were obtained at closely small time intervals, it would be less likely that a significant "pulse" would pass undetected. In summary, a large amount of aircraft reconnaissance data from the vicinity of northwest Pacific tropical cyclones has been collected over the past 20 years by air- craft of the 5Uth Weather Reconnaissance Squadron. i\lt hough the observations are usually restricted to the 700 mb level, they can still provide useful information on the structure of tropical cyclones. The quality, but not quantity, of this data is en a par with the high density data collected by research aircraft in the Atlantic region. Also, there is some indication that significant changes in the 86 intensification trsnd of tropical cyclDnes are related -o changes in the moist static snsrgy of zlia low-lsvsl air. It may be possible to correlate the relationship during pcst- analysis, but ths significant fluctuations that can occur are often too ambiguous to allow a foracastar to usa moist static energy as an operational intensity forecast tool. 87 LIST OF REFERENCES Anthes, R. A., 1982: rropical c^clon^s: Their evolution, s-tructur? and effects . XmericirT He tecroiDglcal ^ocie~y, Fost"cn, 20B'~pp. Bell, G. J., and Tsui, Kar-Sing, 1973: Some typhoon soundings and their comparison wi-h soundings in hurricanes. 1' A£Dlied Meteor., 9, 32 9-34 2. Black, P. G. , and R. A, Anthes, 1971: On the asymmetric structure of the tropical cyclone outflow layer." J. Atmos. Sci. , 28, 13U8-1366. ~ Charney, J. G. , and A. Eliassen, 1964: Dn the growth of hurricane depressions. J. Atmos. Sci,, 2 1_ , 68-/5. Dunnavan, G. M., 1981: Forecasting intense tropical cyclones using vOO-mb equivalent potential temperature and central sea-level pressure. NAVOCSANCOMCEN/JTWC Tech Note 81-1 , 12 pp. Dunnavan, G. H.^ and J. W. Dierclcs, 1983: An analysis of super tyohoon Tip (October 1979) . Mon. Hea. Rev., 138, 19T5-1923. — Frank, W. M., 1977: The structure and energetics of the tropical cyclone I. storm structure. Mon. Wea. R=v. , 105, 119-1145. Gray, W. M.^ 1965: Calculations of .cumulus vertical draft velocities m hurricanes from aircraft ooservations. J. Ad El- ilil^21- » 4, 463-4 74. Gray, W. M., 1979a: Hurricanes: Their formation, structure, and likely role in the tropical circulation. Meteorolo^v Over the Trooical Dceans, D. B. Shaw, Ed., Roy ."TTeteor , "* ^oc7.7"T55-2TB: Gray, w. M., 1979b: Tropical cyclone intensity determination through upper-tropospheric aircraft reconnaissance. Bull. Amer. Meteor. Soc. , 50, 1069-1074, Hawkins, H. F., and D. T. Rubsaa, 1968: Hurricane Hilda, 1964- II. Structure and budgets of the Hurricane on October 1, 1964. jlcn. Wea. Rev., 96, 617-6 36. Hawkins^ H. F., and S. M. Imbembo, 1976: The structure of a small, intense hurricane, Inez 1966. Mon. Wea. Rev., 104, 4 18-442. Henderson, R. S. ^ 1980: WC-130 meteorological system and its utilization m operational weather rsconnaissance. Air Weather Service Technical Report 80/02, 79 pp. 88 HDlland, G. J., 1933: Tropical cyclones in the Australia/soutnwest Pacific region. Dept. of Atmos. Sci. P=per No. 363, CoId. State Univ. , Ft. Collins CO, 25U pp. Holliday, C. R., and A. H. Thompson, 1979: Climatological characteristics of raoidly intensifying typhoons. Mon. Wea, 111- > lQ.lf 1022-1034.^ I ^ If Holton, J. R. , 1979: An introduction to ixnamic lil§.2I2l25Z* Acadeiic Fress,~!rew Yorlt, T9T pp7 ~ Hughes, L. A., 1952: On the low-level wind structure of tropical storms. J. Meteor., 9, U22-U28. Guam, Mariana Islands Jordan, C. L. , 1953: Estimation of surface central pressures in tropical cyclones from aircraft reconnaissance. Bull. Aaer. Meteor. Soc. , 39, 345-352. Jordan, E. S., 1952: An cbserva ticnal study of the upper wind circulation around tropical s-orms. J. Meteor., 9, 340-3U6. " " La Seur, N. H., and H. F. Hawkins, 1963: An analysis of hurricane Cleo (1958) based on data from reconnaissance aircraft. Men. Wea. Rev., 91., 6 94-709. Malkus, J. S., and H. Riehl, 1950: On ttis dynamics and energy transformation in steady-state hurricanes. Trllus, 12, 1-20. Ramage, C. S., 1959: Hurricane development. J. M5t=or., 15, 22 7-237. ~ Riehl, H., 1963: Some relationships between wind and thermal structure of steady state hurricanes. J. Atmos. Sci. 20, 276-287. ~ Riehl, H., 1970: Some aspects of cumulonimbus convection in ralation to tropical weather disturbances Bull. Am. Meteor. SoC' f 20.* 587-595. Riehl, H. , 1975: Further studies on the origin of hurricanes. Dept. of Atmos. Sci. Paper No. 235, Colo. State Univ., Ft. Collins, Co., 22 pp. Sadler, J. C, 1978: A role of the tropical upper tropospheric trough in early season typhoon development. fl2Il- W^a- lev., m, 1266-1278, 89 Shea, D. J., and W. M. Gray, 1972: The structure and dynamics of the hurr ica nes' s inoer core rsgion. A-:nDspheric Sciences Paper No. 182, Colorado State University, 134 pp. Shea, D. J., and W. t5 . Gray, 1973: The hurricane's inner core rsgion. I. symmetric and asymmetric structure. J. Amnios. Sci. , 30, 1544-1564. Sheets, R. C, 1969: Some mean hurricane soundinas. J. 4E£l- ilil££I- # §.t 134-146. Sikora^ C. R. , 1976: An investigation of equivalent potential temceraturs as a measure of tropical cylcone intensity. fLs WEAZEN TECH NOTE: JTWC 75 ;3, 12 pp. Simpson, R. H. , 1952: Exploring the eye of typhoon ":iarg6", 1951. 3ull. Amez. Heteor,. Soc. , 7, 286-298. Simoson, R. H., 1954: Structure of an imaature hurricane. Bull. Amer. Meteor. Soc., 35, 33 5-350. SimDson, R. H. , and L. G. Starrett, 1955: Further studies of Hurricane s+ructure by aircraft reconnaissance. Bull. Altl' ^^1±22- Soc., 36, 459-468. TSWA, Inc., 1945: Weather conditions on a flight tropical storm of October 19, 1944 while in northe Florida, Bull. Ames:« Jl^teor. Soc., 26, 199-203. Lcross the :n Wexler, F. 3., and H. Hood: Flight into the September 1944 hurricane off Cape Henry, Virginia. Bull. Amer. Meteor. 32£- » 26 , 153-159. 90 INITIAL DISTRIBUTION LIST No. CODi