A Method of Forecasting Development of Tropical Cyclones

Home , Thermal low, Typhoon Louise (1945)

WILLIAM KRASNER and JULIUS LONDON *

ABSTRACT

A method is devised (based on the theory of Bjerknes and Holmboe on the deepening of cyclones), for the forecasting of the deepening of tropical cyclones. It is shown that the distribution of divergence around an easterlies trough ("easterly wave"), as revealed through consideration of the vorticity equation agrees with this application to the deepening of tropical cyclones. The conclusion is reached that an estward tilt of the pressure, or streamline, axis of a trough or developing tropical disturbance is most favorable for deepening; whereas, in deep easterlies, a westward tilt of the axis would result in filling and dissipation. A technique is also suggested for a quick qualitative evaluation of the direction of slope of the axis of such a pressure or streamline system.

HE FOLLOWING is an attempt to arrive at ing cyclonic curvature."* The second, the a qualitative method by which the factor of latitude, is a result of the change of T development of tropical storms may be velocity with latitude, so that . . . "diver- forecasted using data available at any first- gence [occurs] in currents with a component order station in the tropics. There has long towards the equator and convergence in cur- been a need for such a method, especially in rents with a component towards the pole."f the central and western North Pacific Ocean In westerlies troughs, these factors are op- areas, where there are great open stretches posite in sign and effect. That is, west of the with few or no reporting stations—stretches trough line increasing cyclonic curvature (con- which, many of them criss-crossed by heavily vergence) is associated with equatorward dis- traveled air and water routes, are the areas of placement (divergence); and east of the trough incubation of many of our most destructive line the reverse occurs. storms. The net effect is chiefly dependent on the This paper originated as a project of the velocity of the wind with changing curvature Research Section, Tropical Weather School, effects dominating above certain critical wind AAF Weather Service, Pacific Ocean Areas. speeds, changing latitude effects below them. Army Weather Central at Guam has since re- The vertical picture then, with increasing examined its typhoon data in the light of these westerlies aloft, often shows the low-level ideas and its comments are appended at the pattern of divergence becoming reversed end of this report. above a "level of non-divergence." If we assume balanced gradient flow as a Since surface tendencies are the result of first approximation to stream-line flow in the mass divergence* within a vertical column of tropics, this technique may be considered as air from the surface to infinity, that is being based essentially on the ideas described dp foo by Bjerknes and Holmboe in their article, — = — g I div (pv)dz, "On the Theory of Cyclones", in the Journal dt of Meteorology, September 1944 (Vol. I, Nos. the total effect, as it affects these surface 1 and 2). Their conclusions are reviewed tendencies, depends for the most part on the briefly in the following. height of the level of non-divergence. The distribution of convergence and diver- The pressure tendency at the center of a gence around a sinusoidal streamline wave— wave and therefore the rate of deepening or disregarding acceleration effects—is the result filling becomes a function of the degree and of primarily two factors. In the first, the direction of vertical tilt of the associated factor of changing curvature, . . . "diver- trough, which determines whether the divergence prevails where particles go along their gence pattern in the eastern or western half trajectory toward decreasing cyclonic or in- of the trough will dominate the center. "... creasing anticyclonic curvature. Convergence A baroclinic westerly current is dynamically prevails where particles along their trajectory * Bjerknes, J., East Asian Circulation (Winter), go toward decreasing anticyclonic or increas- AAF Wea. Serv. Bull., July-Aug. '45, p. 6, "Tool of Reasoning No. 2". * Department of Weather, Chanute Field, 111. t Ibid., "Tool of Reasoning No. 3".

Unauthenticated | Downloaded 10/01/21 03:39 AM UTC unstable for waves whose level of non-diver- state, common in the tropics, there is little or gence is sufficiently low and tends to make no temperature gradient, and therefore no tilt these waves grow strong, however weak they to the pressure axis. In the baroclinic state may be at the start."** the pressure axis tilts toward colder air, which If we apply these principles to the easterlies, the picture is even more simple: the two factors (effects of changing curvature, and changing latitude) act in the same direction, reinforcing each other, and all waves have the distribution of divergence and convergence shown belown (FIG. 1).

FIG. 3

with east-west isotherms, would be to north or south. Isotherms in the tropics, however, like streamlines, are seldom straight east- west; perturbations form and move along

FIG. 1. Easterlies Trough ("Easterly Wave") them, accompanying northerly or southerly transport of air. Where, for example, the In a closed center, the effect of changing easterly component of the wind in an easterlies curvature is no longer operative, but the same trough is greater than the trough speed, a net distribution of divergence exists (FIG. 2). wind moving toward the south will make itself felt on the west side of the trough, and a northbound wind on the east,* and the isotherms will be bent correspondingly, causing temperature ridges and troughs.** There will be, therefore, a certain amount of east or west tilt in each easterlies trough depending on the thermal distribution, and it is these tilts which are the most important.

FIG. 2. Distribution of Convergence in a Closed Low.

Thus due to latitudinal displacement alone, divergence is present west of the closed center and convergence to the east. It follows therefore, that the rate of deepening or filling in a trough in the easterlies depends on the tilt of the streamline axis even more obviously than in the case of trough in FIG. 4. Baroclinic State, Case I. the westerlies. A tilt forward (to the west) In the baroclinic state, there are two major must result in filling; a tilt backward (to the cases: CASE I—warm air originally to the east) must result in deepening (FIG. 3). south; east wind decreasing with height, often The tilt of the axis of a pressure system is reversing to westerlies (FIG. 4). Only shallow the result of horizontal thermal asymmetry stable waves will result from such a distribu- across the system, and . . . "the magnitude tion, with forward tilt and therefore a tend- of the slope varies inversely as the horizontal ency to fill almost as soon as formed. This temperature gradient."J In the barotropic case is more common in winter.

** Bjerknes and Holmboe, op. ext., p. 18. * Riehl, H., "Waves in the Easterlies and the Polar t Panofsky, H. A., The Slope of Axes of Pressure Front in the Tropics", Univ. of Chicago Press, Misc. Systems, Bull. Amer. Met. Soc., April '45 (Vol. 26, Report No. 17, p. 14. No. 4) pp. 101-2. ** Bjerknes and Holmboe, op. cit., p. 18.

Unauthenticated | Downloaded 10/01/21 03:39 AM UTC CASE II—warmer air originally to the after the storm has recurved and resembles north, east wind increasing with height the pattern discussed by Bjerknes and Holm- (FIG. 5). With this distribution—more com- boe.* The storm will continue to deepen only mon during the summer when the heat equator if the axis of its center tilts to the west or northwest. Special reference is made to just such a case in the comments appended to this report. The simplified picture of balanced gradient flow, on which the foregoing development was based, is not, however, completely applicable to the tropics. Consideration of changes in vorticity gives a fuller analysis of tropical

FIG. 5. Baroclinic State, Case II. stream flow, since these changes are concerned with the actual wind patterns. In the tropics is in the northern hemisphere—the tilt of the the density gradient is normally so small that axis is toward the east, or southeast; and mass divergence as used in the tendency equa- troughs tend to deepen and move slowly west- tion can correctly be considered from the ward. High-level divergence is present, in- viewpoint of divergence of stream flow neglect- tensified by the high velocities aloft—an effect ing lateral changes in density. which will continue even after a closed low The broad easterly stream is held in its has formed in the lower levels. This, then, is sinusoidal path by the effect of the constantly the ideal case for deepening of tropical cy- changing vorticity relative to the rotation of clones. the earth. This is accompanied by shrinking or stretching of a significant depth of the column of air and hence is an application of the vorticity theorem developed by Rossby, which states that /+ $ P = constant,

where / is the angular rotation of the earth, £ is the relative vorticity of the air particles relative to the earth's rotation (measured positive for cyclonic rotation), and D is the depth of the significant portion of the column

FIG. 6. Closed LowlwithSOpenJWave Aloft of air considered. Getting the change of vorticity along the An interesting development is the case trajectory of the air parcels we have in an where the closed low moves into higher lati- easterlies wave (FIG. 8), tudes and is surmounted by an open westerlies d trough (FIG. 7). This will be the development ( l\ \ dt JT \dtST \dt/r

FIG. S.

FIG. 7. Closed Low with Westerlies Trough Aloft. * Op. cit., p. 19.

Unauthenticated | Downloaded 10/01/21 03:39 AM UTC Since at 10°-15°, / and df/dt are larger than d£/dt in all but fully developed typhoons, there must be corresponding changes in the depth of the layer to compensate. In the case of poleward flow where the trajectory changes from an anticyclonic to a cyclonic pattern d£/dt is positive and dD/dt would have to be relatively large to balance the increase in the Coriolis parameter. Hence, increased convergence is associated with poleward flow. The reverse is true for the case FIG. 10. Shift of Wind with Height in a Trough of equatorward flow and there is a corre- with Tilting Axis. sponding decrease in the values of D and hence decreased convergence. Qualitatively, the results will be the same Thus convergence to the east (vertical in both cases. A tilt anywhere in the east or stretching), and divergence to the west (verti- southeast quadrant should show divergence cal shrinking), agrees with both the observed aloft and conditions favorable for deepening. distribution of weather around a developed It must be emphasized that clear-cut cases easterlies trough, as well as the picture ob- of steadily changing winds do not always tained by using the assumption of balanced occur, and for this reason, as well as possible gradient flow, and upper level divergence over observational or transmission inaccuracies, the axis of stream flow, resulting from a good several rawins should be examined from each eastward tilt of the axis, should be reflected in station. Often the wind will remain steady negative pressure tendencies and consequent in the lower levels and change in velocity deepening of the system. above 10-12 thousand feet. In such a case, In practice, the tilt of the axis is easily the axis will not tilt in the lower levels. determined. Several rawin reports from the There will be, nevertheless, a net pressure rise area affected by the disturbance, especially or fall at the center (or along the trough line) near the center of the trough line, are usually of the system, due to the upper level tilt, and, enough. With balanced gradient-flow and a however slight, a resultant deepening or filling. baroclinic distribution, often all that is neces- Such a system tends to deepen or fill very sary is to examine the wind field to determine slowly, and will seldom depart from this trend the thermal gradient, and the actual tilt may unless the tilt should change. be found by drawing a shear vector diagram Change in degree or direction of tilt will (FIG. 9) of representative winds. foreshadow a change in the intensity of the storm. Generally speaking, the closer the rawin to the center of the cyclone, except perhaps in the eye itself, the more representative the tilt diagram. Some allowance should be made, in small storms at least, for the large horizontal movement of the balloon causing an apparent degree of tilt. Any sizeable deepening will tend to be followed soon after by strong low-level con- vergent flow and it has been suggested that FIG. 9. Using Shear Vectors to Determine Axis Tilt. the isallobaric component of the wind would If no assumptions as to thermal gradient be large enough in the tropics to provide for are made, the degree and direction of tilt can this low-level convergence. easily be determined by fixing the changing To summarize briefly, therefore, the situa- wind report relative to the axis of the sinus- tion will be favorable for the development oidal streamline (FIG. 10). and maintenance of deep tropical cyclones if

Unauthenticated | Downloaded 10/01/21 03:39 AM UTC the following conditions are obtained in the During the latter part of April, 1945 a trade flow of the northern hemisphere: storm appeared in the Marshall Island area 1. Axis tilt to the east. which gave a good deal of weather at Eniwetok, 2. North-south thermal gradient (if any and caused some apprehension at Guam. Re- gradient at all is present). peated storm warnings were sent out; how- 3. Deep easterlies, with increasing veloci- ever, when it finally appeared in the Marianas ties aloft. area, it was found to be not nearly so intense 4. Easterly wind speed greater than trough as expected. Following are two representa- speed. tive rawins taken in the storm area: the first for Eniwetok for April 220200Z, the second Of thirteen storms examined at the typhoon for Saipan for April 260800Z. The tilts are research section of Army Weather Central Guam, eight were found to be "good examples obviously to the west; and the decrease of of deepening with eastward tilt of the axis easterlies aloft and the low occurrence of and/or filling with westward tilt"; four were westerlies marks this definitely as a Case-I "fair or neutral examples (little or no tilt)"; type storm. (See Fleet Weather Central Paper and only one, a storm which was not detected No. 11, entitled "A Condensed Report of a until already out of the tropics, developed Tropical Disturbance Affecting the Kwajalein- contrary to these ideas. These do not include Guam Airway Between 18 April and 25 April, those disturbances examined by the authors 1945".) and one or more other forecasters in the Marshall-Gilbert area, all of which—those CASE II, EXAMPLE I: "Louise" (FIGURE 12) whose history could be traced—deepened or filled as described here. While these numbers are not in themselves impressive, they repre- sent almost all of the tropical cyclones for which sufficient rawin data and histories were available in the Central Pacific at that time.* Three examples follow.

EXAMPLE OF CASE I (FIGURE 11)

FIGURE 12

On 9 October the typhoon "Louise", called by the newspapers "The most destructive in 20 years", passed over Okinawa, causing ex- tensive damage and loss. Her history and movement were well known and had been closely followed, so it was possible to correlate FIGURE 11 such wind data as were forthcoming with her * See articles by Kidd and Reed, Bull. Amer. Met. Soc., May and June 1946. recorded development.

Unauthenticated | Downloaded 10/01/21 03:39 AM UTC The first three upper winds plotted (Guam shortly after this one—18 December, 1944— 041600Z, Saipan 050400Z and 061000Z) rep- caught elements of the United States Navy resent the vertical structure of the cyclone in off the NE tip of Luzon, causing considerable the formative stage, while she was still in the damage. Since these cyclones occurred so Marianas area. The tilt is obviously toward close together, it is probable that the thermal the southeast quadrant, showing "Louise" to distribution characteristics of Class II, dem- have been definitely a Case II type cyclone, onstrated by the following winds aloft data, and foreshadowing the great deepening which was still then in existence. was to follow. The upper winds at Angaur for December The last diagram, that of ship #114 for 071230Z, although not yet directly influenced 090400Z, represents the vertical wind distri- by the vorticity of the cyclone, show great bution through "Louise" at the beginning of increase aloft of the easterly component. her decline. The tilt had shifted to the north- The upper wind reports for Ulithi December west; and though still very active and capable 071800Z and Angaur December 080600Z show of giving severe weather for some time yet, the backward tilt of the cyclone itself. she was definitely past her peak. This was borne out by the acceleration which she REFERENCES shortly underwent. She moved almost twice [1] Bjerknes, J. East Asian Circulation (Winter), AAF Wea. as far in the period 091200Z-100000Z as she Serv. Bull., July-Aug. '45. had in the preceding 12 hours, and somewhat [2] Bjerknes, J. and Holmboe, J. On the Theory of Cyclones, Journal of Meteorol- more than twice that in the 12 hour period ogy, Sept. '44, Vol. 1, Nos. 1 and 2. which followed. In the typhoon advisory for [3] Dunn, G. E. Analysis and Forecasting of Tropical Cyclones 110000Z her intensity was described as "de- with Special Reference to the Atlantic Ocean. Institute of Tropical Meteorology of the creasing". Univ. of Chicago, reprinted by AAF Weather Wing, Asheville, N. C., 1944. [41 "A Condensed Report of a Tropical Disturbance CASE II, EXAMPLE II (FIGURE 13) Affecting the Kwajalein-Guam Airway Between 18 April and 25 April 1945", Oahu, T. H.: Fleet Weather Central Paper, No. 11. [51 Kindle, E. C. An Application of Kinematic Analysis to Tropical Forecasting, May 1945, AAF Weather Wing Regional Control Office, 9th Wea. Region. [6] Kidd, K. P. and Reed, C. K. Typhoons in the Southwest Pacific—1945, Bull. Amer. Met. Soc., 27 (6): 288-305. 1946. [71 Panofsky, H. A. The Slope of Axes of Pressure Systems, Bull. Amer. Met. Soc., 26 (4): 101-103. 1945. [8] Riehl, H. Waves in the Easterlies and the Polar Front in the Tropics, Chicago, Department of Mete- orology, Univ. of Chicago, Misc. Reports No. 17. [9] Riehl, H. and Shaefer, R. J. The Recurvature of Tropical Storms, Journal of Meteorology, Sept. '44, Vol. 1, Nos. 1 and 2. [10] Rossby, C. G. Planetary Flow Patterns in the Atmosphere, Quarterly Journal, Royal Meteorological Society, Vol. LXVI, Supplement, 1940. [11] Tannehill, I. R. Hurricanes, Princeton University Press, 1944. [12] Tropical Meteorology, AAF Manual 105-0-2. 1945. 100 pp.

FIGURE 13 COMMENTS OF THE AAF TYPHOON OFFICER This storm occurred in the early part of AT GUAM December, 1944. Rawins were not then in very general use, and reliable wind data were Thirteen tropical disturbances, a complete hard to come by. It was difficult, therefore, or partial record of which is on file at this to follow the further history of this particular station, were re-examined in the light of the storm. However, a storm which moved in ideas of this research paper. No attempt

Unauthenticated | Downloaded 10/01/21 03:39 AM UTC has been made to do more than analyze avail- to the circulation center the better, as far as able winds aloft runs for tilt and/or thermal true evaluation of tilt is concerned. gradient, and trace observed storm histories B. The one example of strong development with the results in mind. Many storms could in the face of continued northwest tilt leads not be included in the study, or are included to the conclusion that the theories of the paper only in part, because of the lack of upper-air are not applicable in northerly latitudes—nor data. Ships, for instance, rarely are able to were they meant to be. Aside from all other make pibal runs when in a tropical storm's considerations, the occurrence of westerly circulation, for obvious reasons. A conscious winds at low elevations would result in west- effort has been made not to "force" data to fit east shear with north or northwest thermal preconceived theories, although in many cases gradient and subsequent storm filling indi- this is easy to do, especially in retrospect. cated. Actually the storm's history of deep- Of the thirteen storms examined, eight are ening and filling probably would depend on considered good examples of deepening with many other factors in a case of this type. eastward axis tilt and/or filling with westward C. In analyzing rawin runs it is felt that a tilt, four are fair or neutral examples (little practical height limit must be set, above which or no tilt), and one storm developed steadily winds will not be considered in determining to full typhoon strength with consistent north- tilt. 20,000' was used in the evaluation of west tilt in the circulation axis. The ideas in the runs in this study because any divergence the paper would have been, for the most part, above that level involves so little actual mass valuable forecasting tools in the tropical of air its effect in aiding lower-level conver- storms considered, although the interpreta- gence is negligible. tion of the scanty data available at the outset D. A rather obvious thing to watch, if of any storm is at best highly subjective. successive rawins are available throughout Some ideas accumulated from the study of the storm's history, is the trend of tilt indi- the storms are summarized briefly here. In cated. In that way, perhaps, if tilt changes no case may they be considered conclusive, from west to east or becomes more pronounced one way or the other, future changes in storm because of the limited scope of the investiga- intensity may be anticipated. tion, but some may merit further study: A. In winds aloft observations the position E. The problem of timing a forecast of of the reporting station with reference to the deepening or filling of a tropical storm is an almost insoluble one at present, but very storm center seems to have an effect on the important in a practical sense. As brought degree of the tilt indicated; it might affect the out by the histories under consideration, direction of tilt in extreme cases. Assuming strong deepening took place from 12 hours a station is to the south of a storm center and to 6 days after eastward tilt became evident a closed thermal low exists somewhere near on the rawins. The best that can be done the dynamic low aloft, to take a hypothetical under the circumstances is to make a qualita- case, any thermal gradient indicated by winds tive estimate of the speed of intensification aloft at the station would be to the north. from the degree of tilt. A forecaster in this case would expect filling The paper offers a very practical hypothesis of the system on the basis of northward tilt, for solving one of the field problems in tropical whereas the actual tilt may be in any direction storm forecasting which should certainly be and the rawin run completely misleading. In investigated further.—Harry T. Magill, 2nd any case, it is obvious that the closer the run Lt., Air Corps.

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