642 MONTHLY WEATHER REVIEW VOLUME I08Further Development of a Barotropic Operational Model for Predicting Paths of Tropical StormsFREDERICK SANDERS, ALAN L. ADAMS,1 NORMA J. B. GORDON~ AND WADE D. JENSENsDepartment of Meteorology, Massachusetts Institute of Technology, Cambridge 02139(Manuscript received 6 August 1979, in final form 11 January 1980)ABSTRACT To enable use of aircraft winds and satellite cloud-motion vectors in the SANBAR model for prediction of tropical storm tracks, we have derived regression equations for estimating the troposphericallyaveraged flow from information at one,. two or three levels. Two-level results represent an improvementover climatology and a third level yields substantial further improvement. We find from a study of the 1975'season in the Atlantic Basin that reduction in initial position and track-velocity errors can produce substantial improvement in position-forecast accuracy out to 72 h range. We recommend a new procedurefor evaluating and using wind observations within the region influenced by the storm circulation. The newmethod has the potential for substantial reduction of present forecast error for storms within 24 h of landfall.1. Introduction A barotropic filtered model (SANBAR) wasdeveloped by Sanders et al. (1975) and by others foroperational prediction of the tracks of tropicalstorms at ranges out to 72 h. This model has beenused since 1968 at the National Hurricane Center(NHC), where recent results (see Table 1)4 indicatethat it performs competitively with other objectivemodels which are credited (Dunn et al., 1968) for theimprovement, however slow, in the final subjectivejudgement. We were prompted to try barotropic predictionbecause its basic mechanism, the conservation ofabsolute vorticity, is an explanation of the apparent "steering" of the intense storm vortex by thelarger scale current in which it is embedded, as suggested by Riehl et al. (1956) and by Jordan (1952),among others before and since. On physical grounds,too, it seemed that variation of vorticity advectionacross the storm center was the most likely effect inthe vorticity equation for producing storm motion.We say this because the more intense the vorticitymaximum, the more intense the cross-center gradientof the.mechanism must be to produce a given motion of the center. The cross-center gradient of horizontal advection becomes more intense as more in ~ Air Weather Service, U.S. Air Force. ~ Bureau of Air Quality Control, Maine Department of Environmental Protection, Augusta, ME. a Meteorology Research, Inc., Altadena, CA. 4 From C. J. Neumann, 1979: A guide to Atlantic and EasternPacific Models for the prediction of tropical cyclone motion.NOAA Tech. Memo. NWS NHC-II. [NTIS $$$ $$$]. The othermodels are discussed therein.0027-0644/80/050642-13507.25 1980 American Meteorological Societytense vorticity maxima are considered. It seemsunlikely that non-advective effects, principally convergence and divergence, can produce dominanteffects on storm motion, in view of the typicallysymmetric character of the cloud and precipitationnear the center, unless the large-scale steering isextremely weak. Baroclinic effects, of course, mayplay an important role in the temporal-evolutionof the large-scale motions themselves, which willhave an important effect on storm motion beyondthe shortest ranges, but it seemed desireable to exploit the relatively inexpensive barotropic calculation as a first step. The failure of earlier attempts at barotropic prediction (e,g., Birchfield, 1960; Vanderman, 1962;Kasahara, 1959) to achieve operational acceptancewas regarded as due to the difficulty of establishingan adequate initial large-scale analysis on the basisof rawinsonde-derived pressure data in lower latitudes, where errors are often as large as naturalvariability. Hence the SANBAR model relies on ananalysis of wind observations, averaged throughthe depth of the troposphere, and makes no directreference to the pressure-height data. Difficultieswith the separation of the vortex from the large-scaleflow in the forecasting process (Kasahara, 1959), ledus to utilize a relatively small 150 km mesh lengthand to predict the storm as an integral part of thetotal flow field. Two problems had to be dealt with immediately:I) analysis over the tropical oceans where rawinsonde data are almost completely absent, and 2) assessment of the effect of the storm circulation, asdistinct from the large-scale influence, on soundingsmade in the vicinity of the storm (necessary forMAY 1980 S.ANDERS, ADAMS, GORDON AND JENSEN 643TABLE 1. Homogeneous sample of forecast position errors (n mi) over period 1973-78 in the Atlantic Basin.RangeMo~lel 12 h 24 h 48 h 72 hCLIPER 56 125 276 381NHC 67 56 119 293 428NHC 72 55 120 269 393NHC 73 54 120 244 367SANBAR 60 121 2156 389Number of cases 261 232 161 109realistic construction of the total initial flow). Thefirst was handled by the provision, at first subjectively and later by objective automated rneans (Pike,1975, private communication), of "bogus" winddata at a coarse array of. points covering large portions of the SANBAR forecast area. The secondproblem was first handled by subtracting fromnearby wind observations a vector contributionfrom an idealized axisymmetric vortex specified bythe geographical position of its center, and by itsmaximum wind, eye diameter and radius of influence.All of these parameters except the last are reasonably well known initially in real time. The radius ofinfluence was subjectively determined, with resultsthat often seemed so unsatisfactory that 300 n miwas adopted as an almost ubiquitous nominal value.When this technique continued to provide unreasonable-looking "residual" large-scale winds fromtime to time, it was decided to ignore nearby windsoundings altogether and to substitute, at the affected points of the SANBAR grid, first (Pike, 1972)the vector sum of the storm contribution describedabove and a constant large-scale contribution equalto the recently observed direction and speed of thestorm track, and later (Sanders et al., 1975) a fixedstreamfunction field calculated from these windsand the storm parameters. Aside from purely technical improvements in theSANBAR calculations two avenues seem open forimproving performance. One stems from the improvement in the large-scale oceanic data base overthe past decade, due to increased numbers of betterwind observations from aircraft and especially tolarge numbers of wind estimates now derived fromcloud motions observed by geosynchronous satellites. The other road to improvement,, howeverdifficult it has been in the past, must lie in the effective use of wind observations in the storm-influencedregion. This paper repo.rts principally our effortsalong these two lines.2. Regression estimates of the tropospheric mean wind The current data base over the oceans comprisesrelatively dense coverage in the lowest 2 km, fromsurface observations by ship and from low cloudmotion observations by satellite, and in the layerfrom 9 to 12 km, from wind observations derivedfrom aircraft navigation systems and from high cloudmotions observed by satellite. We must infer thetropospheric mean wind from information in thesetwo layers. Thus, following preliminary work by Pike (1975,private communication), we derived some definitiveregression equations from an extensive sample ofdata in the NHC region of forecast responsibilityduring the period June-October 1971-74. In theseequations rawinsonde wind observations at 850 and250 mb were used to approximate the troposphericmean wind calculated from the winds at the 10 mandatory pressure levels from 1000 to 100 mb in thesame soundings. Our results, obtained from a totalof 11 682 observations in June-October at Bermuda, San Juan, Hatteras, Miami, Tampa, LakeCharles, Brownsville and Merida, are given inTable 2. Note that the root-mean square error, if not reduced by the analysis and initialization processes,would yield 24 h rms displacement errors of 82 and74 n mi in the zonal and meridional directions,respectively. These errors would be larger whenavailable surface, aircraft and satellite observations are used in regression equations.tailored forrawinsonde data. In fact, these errors approachpresent state-of-the-art errors, so that we cannotexpect use of our two-level regression equations toimprove dramatically the statistics of forecasterrors. We might hope, nevertheless, that their usewould reduce the number of very large errors madefar from the reach of rawinsonde data when theinitial analysis relies on less systematic applicationof the few available data. In the anticipation that SANBAR might be usedin other regions of the Northern Hemisphere, weobtained similar equations for the eastern Pacific(from 5594 observations at Vandenberg, AFB, Hilo,Johnston Island and Midway Island), and for thewestern Pacific (from 10 145 observations fromGuam, Wake Island, Truk, Ponape, Kwajalein,Majuro, Yap and Koror).a Equations for these two ~ The former of these sets may not represent the wind structurein the zone of tropica/cyclogenesis, where next to no rawinsondedata exist, but they should be more reliable as the storm approaches these populated locations. TABLE 2. Regression equations for estimated zonal andmeridional components of tropospherically averaged winds, inNHC region of responsibility. Speeds are in knots. Root Redu~- mean tion of square variance error~ooo-~oom~ = +0.4 + 0.53Usso + 0.37u~0 0.92 3.4bxo00-xoom~ = -0.5 + 0.45~8s0 + 0.33V~o 0,85 3.1644 MONTHLY WEATHER REVIEW VOLUME 108TABLE 3, Regression equations for eastern and western Pacific regions. Speeds are in knots. RootReduc- meantion of squarevariance errorEastern Pacifict~tooo-~oo mb= +0.2 + 0.52U85o + 0.36U:5o 0.87 3.9b~0oo-~0omb = +0.1 + 0.46vs50 + 0.36v2~0 0.88 3.3Western Pacific~1000-1~0 mb m -2.2 + 0.43u5~0 + 0.32u2~0 0.77 3.3b~000-~00 mb = --0.4 + 0.40V850 + 0.26V~0 0.70 2.7additional regions are given in Table 3..The resultsindicate no substantial difference between theAtlantic and eastern Pacific areas. In the westernPacific, however, the zonal equation is quite different, and it appears that the vertical structure of thezonal component is noisier. Although the reductionof variance in both components is smaller in thisregion, so is the rms error, indicating that the windis less variable in the Pacific sample, but we cannottell to what extent the reduction is temporal orspatial. Stratification of the above samples into earlyseason (June-August) and late-season (SeptemberOctober) portions showed, only minor differences inthe resulting regression equations, reductions ofvariance and rms errors. The accuracy of estimate of the troposphericmean wind, however, is sensitive to the number oflevels at which information is available. We derivedregression equations appropriate for the unfortunatecircumstances when only low-level or only highlevel data were available, and for the optimistic hopethat wind information for a mid-tropospheric level(say, 500 mb) might somehow become available.These equations are shown in Tables 4 and 5 inwhich the data of Table 1 are included for cornparison. If only one level is available, the meanwind can probably be specified with little or no skillrelative to local climatology, although one is somewhat better off to have data in the upper than in thelower troposphere. If the middle tropospheric datacould be added to observations at the other twolevels, substantial improvement would be felt inspecification of the tropospheric mean wind. Comparing Tables 4 and 5, we see large differences whendata are available at only one level, because of thedifferent vertical structure of wind fields in the tworegions; but when data are available at three levelsthe regression equations and the rms errors arealmost identical. The reductions of variance suggest more skill thanis ~ctually present in the equations, because part ofthe variance doubtless resides in differences in theclimatological average wind from station to stationwithin each region. This is particularly true of thesample from the Atlantic sector. We made no attempt to use zonal components aspredictors for meridional components of the tropospheric mean winds or vice versa. Such an attemptmight yield useful results if trough and ridge tilts, forexample, were consistently northeast-southwest ornorthwest-southeast, but substantial improvementover what we have already obtained seems unlikely. When satellite cloud-motion vectors are used inplace of rawinsonde data. in the two-level equations(as would be done in practice, for example) weestimate a 50% increase in the rms error of specification of the tropospheric-mean wind. The details ofthis estimation, and of the entire regression analysis,are given by Adams and Sanders (1975).3. Sources of error in 1975 operational forecasts We undertook to study the causes of large SANBAR'forecast errors in the 1975 hurricane season,with the aim of applying our regression equationsTABLE 4. Regression equations for one, two and three levels of information for region of NHC forecast responsibility. Speeds are'in knots.Reduction Root-meanof variance square errorOne level fi~ooo-~oo(850) = +4.8 + 0.71u8~o t~ooo_~oo(250) = -2.1 + 0.43uaao b~ooo-~oo(850) = -1.5 + 0.51V8~o b~ooo-~oo(250) = +0.9 + 0.35V~oTwo levels t~ooo-~oo(850, 250) = +0.4 + 0.53U8,o + 0.37U~o b~ooo-~oo(850, 250) = -0.5 + 0.45V85o + 0.33V~5oThree levels fi~oo6-~oo(850, 500,250) = -0.1 + 0.31U8~o + 0.36U~oo + 0.26U:~o bxooo-~oo(850, 500, 250) = -0.3 + 0.30V85o + 0.35V~oo + 0.24V2so0.43 8.80.69 6.50.34 6.60.60 5.20.92 3.40.85 3.20.97 1.90.95 1.8MAY 1980 SANDERS, ADAMS, GORDON AND JENSENTABLE 5. Regression equations for one, two and three levels of information for the western Pacific region. Speeds are in knots.645Reduction Root-meanof variance square errorsOne level ~ooo-~oo(850) = -4.5 + 0.28U85o t~1ooo_~oo(250) = -5.9 + 0.22U2~o b~ooo_~oo(850) = -0.8 + 0.40V85o b~ooo_~oo(250) = +0.2 + 0.26V8~oTwo levels t~ooo_~oo(850, 250) = -2.2 + 0.43U8~o + 0.32U2~o b~ooo-~oo(850, 250) = -0.4 + 0.40Vsso + 0.26V25oThree levels fi~ooo-~oo(850, 500,250) = -0.8 + 0.28u~5o + 0.32Usoo + 0.25U2~o b~ooo-~oo(850, 500, 250) = -0.4 + 0.30v~o + 0.31V~oo + 0.24V~so0.24 6.00.28 5.80.24 4.30.42 3.70.77 3.30.70 2.70.92 1.90.89 1.7in revised predictions. As a preamble to this effort,we made revised forecasts based on post-season"best-track" initial positions and track velocities(Hebert, 1976). As illustrated in Table 6, these revised forecasts presented a substantial improvementover the original operational predictions at rangesout to 48 h. On the other hand, the mean initial errorsin position and track velocity (based on the premisethat the best-track information represents absolutetruth) suggest that it will be extremely difficult toreduce the mean SANBAR position error in the 24 hforecast below 75 n mi, the expected (or hoped for)error cited by Sanders and Burpee (1968), Incidentally, the 1975 tracks were remarkable intwo respects: only one storm failed to recurve towardthe northeast, and no storm executed a loop or otherexotic excursion. There was a slight tendency foroperational positions to lie westward of the besttrack locations and for operational track velocitiesto be insufficiently northeastward, both biases probably due to the forecasters' reluctance to anticipatefully the degree of recurvature and accelerationwhich was actually occurring. In the event of erraticstorm tracks, operational errors in initial positionand track velocity would probably have been larger. Sanders and Gordon (1976) studied a number ofthe 1975 cases in detail, finding the large forecasterrors to stem from a variety of causes. One of thecases analyzed in detail, for Faye starting at 0000GMT 26 September, is illustrated in Figs. 1 and 2.From a comparison of predicted and observed tracksin Fig. 1, it is seen first that the slow predicted speedwas responsible for the large 212 n mi operationalerror at 24 h, which was improved in the best-trackprediction only by a more accurate specification ofthe initial track direction. Second, neither forecastanticipated the dramatic acceleration after 48 h,producing errors of 961 and 772 n mi in the operational and best-track predictions at 72 h. The unusually dense initial observational coverageshown in Fig. 2, comprising mainly wind estimatesfrom satellite-observed cloud-motion vectors, precludes lack of data as an explanation of the forecasterrors. It appears, however, that the numerousobservations within the 300 n mi influence distanceof Faye indicate a large-scale flow toward the northwest at a speed in excess of the specified initial speed.Application of the regression equations in Table 1indicates, in fact, a large-scale speed of about 15 kt,in contrast to the initial 11 kt specified initially inboth the operational and best-track predictions. The12 h observed displacement speed was in fact 17 kt.In the present analysis procedure, of course, thesewind data are discarded in favor of the specifiedinitial speed. Clearly, useful data are being lost. The large error at 72 h arises from another cause.Fig. 3 shows the initial large-scale flow pattern, withits observed and predicted change. The ridge whichTABLE 6. Comparison of operational and best-track forecasts. 00 h 12 h 24 h 36 h 48 h 72 hMean position error, operational forecasts (n mi)Mean position error, best-track forecasts (n mi)Percentage improvement of best-track over operational forecastsMean magnitude of error in operational specification of initial track velocity (kt)Number of forecasts 15 -67 0 50100 252.8 -74 67121 181 261 39399 152 224 37618 16 14 458 51 44 33646MONTHLY WEATHER REVIEW 75-W45-N40~'N35-N30-N70- 65o 6,0-;! '?/!/ ~ ,%0 / ~7Z // / '~'~ 60 ~ ~ ~48 ~ ~ ~ ~, ~ 3~ X~L..X~ '.. 36 X~ '... ~ ~, 'e 2 4 ~ .. ~'. ~1~ '~'~,oo55- 50-I II25~N I I Fro. 1. Tracks of Faye 0000 GMT 26 September. Dashed line indicates observed track, solid line operationalforecast track, and dotted line best-track revised forecast. Dots show forecast positions, labeled in number ofhours after initial time. Corresponding observed positions are shown by hurricane symbols. VOLUME 10845-Winitially extended northwestward of the storm waspredicted to change little during 48 h, whereas, infact, the trough in the central United States advanced northeastward to pick up the acceleratingstorm. The forecast error was evidently not due tofixed boundary conditions in the SANBAR modelbut rather to the presence of important barocliniceffects. This vew is supported by the portions ofthe National Meteorological Center hemispheric500 mb prognostic charts show.n in Fig. 4. Note thatthe barotropic forecast suffers from the same defectas the SANBAR prognosis, while the baroclinic PEforecast has the right idea, as usual, but is a bit slowabout it. Note further from Fig. 2 that the large-scalestructure in the vicinity of the storm was hardlybarotropic. The tropospheric shear in this case wassubstantial av/d well organized, with a probable directeffect on storm behavior. In other instances, large SANBAR forecast errorswere found to be attributable to failure to use satellite-derived pressure-height data poleward of 30-N,to paucity of data of all types, and to fixed values ofvorticity and streamfunction on the northernboundaries of the grid area.4. Interpretation of storm-influenced winds Rawinsonde observations made within the circulation of a tropical storm, often with great difficulty and at substantial hazard to the observers,should be a valuable source of iv/formation concerning the track of the storm. Yet both the SANBARand MFM (Hovermale, 1975) models discard all suchobservations. The reason, in the case of SANBAR,is that we have not been able objectively to evaluatethe contribution of the storm circulation with sufficient accuracy. The idealized radial profile of the tangential stormwind component used operationally in SANBAR,(Sanders et al., 1975) is given byVo = 0.72Vmaxwhere Vmax is understood to be the maximum surface wind (kt) as given in the current advisory, Reyeis the radial distance from the center of the eye to themaximum wind (nearly always taken as 20 n mi),and Rmax is the maximum influence distance of theMAY 198080WSANDERS, ADAMS, GORDON AND JENSEN75W 70~ 65W 60W 55W 50W 45W 40W6~7storm (nearly always taken as 300 n mi). This expression can be written as k-~-6-/ JJ ' (2) We have considered the possibility of allowingthe wind observations within the storm-influencedregion to tell us the "best" values of the stormparameters X~, X2, Xa, rather than using a profileprescribed without examination of the observations,a practice which often yields unrealistic and irregularresidual winds. By best we mean those values of the648 MONTHLY WEATHER REVIEW - W 120 1iS IlO 105 I00 95 90 85 80 65 60 55 50 45 40 WVOLUME 1085C40 N5520W120 115 I10 105 I00 95 90 85 80 7'5 70 65 60 55 50 ,45 40W5C40 N3530252015I0(b) FIG. 3. Large-scale initial flow pattern 0000 GMT 26 September (solid lines) and 48 h streamfunction changes for (a) observed and (b) predicted by SANBAR. Streamfunction lines areat intervals of 3 x 106 ma s-2. Dashed lines indicate streamfunction rises and dotted lines falls,in units of 3 x 106mas-:.parameters that yield the "smoothest" set of residualwinds Vr, given by vr(x,,x2,x3) ---Vo - vo(x,,x2,x3),where Vo is the observed wind. By smoothest wemean a set of residual winds that shows the closestfit to a linear interpolation among the winds at thethree stations surrounding each station in the influence region. Specifically, consider station A surrounded by stations B, C and D, as illustrated inFig. 5. Observed winds are shown for stations B andC. At station D a residual wind is shown becauseit is within the maximum influence distance of thetropical storm. Bilinear interpolation of the zonalMAY 1980 SANDERS, ADAMS, GORDON AND JENSEN 649and meridional components yields a plane-fit windVv at station A. The difference V' ----= Vr -- -v atstation A is a measure of the smoothness of that valueOf Vr(X~,X2,Xs). We chose as the optimum values ofX~, X~, and Xa for a given synoptic case that set,from the possibilities given in Table 7, which minimized the rms magnitude of -' over the stationswithin the maximum influence distance for that case. Finally, of course, the values of Vr should providea good specification of the storm-track velocity at thetime of the observations. We would hope that thisspecification is as accurate as the operational estimate made in real time by NHC for the official40N3C40N4ON30 FIG. 4. NMC prognostic charts: (a) 36 h barotropic forecastvalid at 0000 GMT 27 September; (b) 24 h PE baroclinic forecastvalid at 0000 GMT 27 September; and (c) 72 h PE forecast validat 0000 GMT 29 September. FIG. 5. Illustrating a comparison between the residual wind atstation A and the plane-fit wind, Vp, obtained by interpolationbetween observations at stations B, C and D.advisories. To this end, a value of Vr at the locationof the storm center was determined, for the optimumset of storm parameters, by stepwise screeningregression for both zonal and meridional wind components, given the station values of Vr. We wouldbe satisfied if initial specification of storm-trackvelocity were as accurate as operational estimation,because our proposed procedure yields a variablelarge-scale wind field in the vicinity of the storm,with the possibility of substantial predicted changesin track velocity, whereas the current operationalprocedure yields a displacement in the first 12 hat very nearly the instantaneous initial velocity. Fifty data sets, for nine tropical storms, were TABLE 7. Frequency of values of parameters chosen tominimize V': In0.5 X~ = 0.72Vmax, X2 -- - In(re/300)X, (kt) N r~ (n mi) N Xa N5 0 3 7 0.2 1310 8 6 1 0.4 515 6 9 5 0.6 320 7 12 4 0.8 625 4 15 7 1.0 230 1 18 I 1.2 635 4 21 2 1.4 540 2 24 2 1.6 245 3 27 2 1.8 250 0 30 2 2.0 155 0 33 2 2.2 060 0 36 1 2.4 065 1 39 2 2.6 170 2 42 1 2.8 075 3 45 1 3.0 280 0 48 2 3.2 l85 2 51 I 3.4 090 5 54 1 3.6 095 2 57 1 3.8 0100 0 60 5 4.0 1Total 50 50 50650 MONTHLY WEATHER REVIEW VOLUME 108'TABLE 8. Frequency of errors of specification of initial trackvelocity and of 12 h extrapolation forecast based on it.Error range Error range(kt) (n mi)Initial track ' 12 h forecastvelocity ' Frequency bosition Frequency0-1.7 7 0-20 51.8-3.3 9 21-40 113.4-5.0 14 41-60 165.1-6.7 11 61-80 86.8-8.3 4 81-100 38.4-10 3 101-120 3>10 2 >120 4'Total 50 50chosen for study on the basis of the presence of twoor more simultaneous rawinsonde observationswithin the influence region of the storm. Understandably, these storms lay within 300 n mi or so ofthe United States coast and thus representedespecially important forecast problems for NHC.Selection frequencies for the discrete values of Xx,X2 and Xa are shown in Table 7. We note with surprise that in about half the instances the impliedvalue.of Vmax is no more than 35 kt, and that theshape of the radial profile is very flat, as evidencedby small values of Xa. The current operational SANBAR value of Xa = 1.5 is exceeded less than 20%of the time in the present sample. Study of individualcases shows that the tropical storm is often em 95; 90' 85- 80- 75* 700 65- 60- ~/ ~ ~ I ~ ~. ' ~ x . ~ .r,o~~ -'"-' Z,,.o..i,~ ,~~~~'~'~.....- ,.,o~ / ~,,o~ ~,.,o. ', ,~0,oo. "C,, ) / ~ ,,,.,. ~;.108/07 +~ 083/13 o~x% ,45-o~OO35- - FIG. 6. Initial mean winds for.0000 GMT 9 July 1959. Central position and influence regionof Hurricane Cindy are shown, respectively, by the hurricane symbol and the dashed circle.Positions of the storm 12 h earlier and,later are shown by hurricane symbols southeast andnorthwest, respectively, of the current position. The length and direction of the heavy arrowrepresent a 12 h linear displacement at the specified velocity. Plotted winds represent Vr,also given by numerical notation. Values in the parentheses denote the observed wind V0.I I ~ 7 30o - I85* 80'~ 75o25*30-MAY 1980 SANDERS, ADAMS, GORDON AND JENSEN 65135'30'25-20-~15~' I10- I 0 5 - IOO- 95- 90- 85- 80- 75?a + + 4 ~L~60/23 233/lej V :0 ~ U:O + ~tt ~6~/~1 ~,----.-o + 193/14 + )51/05~ o~ 150/11 +(, + 074/05 'k~ , I 5O ./ '. ~:o~ -~ ,~ ~ F + Or2/19 + + ~ / / / ~ ~ ~ ~ ~ ~ O: 0 + 06~9 , v=O I t , I f I 105" 100- 95- 90 oFIG. 7a. Initi'al mean winds for Hurricane Delia, 1200 GMT 4 September 1973. Notation as in Fig. 6, exceptthat heavy lines represent zero isopleths for zonal and meridional velocity components.~ 35-30-.25-20-bedded in a relatively weak cyclonic circulation ofrelatively large scale, and that really strong windsare rarely sampled by the rawinsonde system, leading to these unexpected results. For each synoptic case, we compared the specifiedinitial track velocity emerging from the regressionanalysis with an estimate of the actual initial velocityobtained from the best-track information. The meanmagnitude of the vector difference was 4.2 kt,slightly worse than the probable discrepancy between operationally specified and best-track initialvelocities, as discussed earlier. The frequency distribution of the differences in Table 8 shows, however, that operational accuracy was probably exceeded about half the time, and that our regressionprocedure occasionally yielded extremely largeerrors. Examination of cases showed that thesetended to be instances in which rawinsonde observations were available in only a single quadrant ofthe storm. There was little bias in specified directionor speed. A deficiency in westward motion might beexpected due to our neglect of the effects of thelatitudinal variation of earth vorticity, but the effectis evidently small enough to be masked by othersources of error. In a few cases in which the storm center was veryclose to a sounding location the regression resultwas extremely sensitive to the position of the centerand large errors were likely. Ten cases of this typewere recalculated with the station less than 85 n miof the center excluded, yielding much improvedresults. Fig. 6 shows such a case, in which the erroris 13 kt, between the specified southeastward andthe observed northwestward motion. If the stormcenter were located 17 n mi to the north-northeast,however, and the storm wind contribution to theCharleston observation were increased from 22 to28 kt, then a perfect specification would have resulted. Modest asymmetry in the storm circulationas well as moderate position error could producethe large specification error.6 Thus, we are still unable to make constructive use of observations veryclose to the storm center. An especially interesting storm is Delia 1973,which performed a loop along the Texas Gulf Coastbefore moving inland. The operational SANBAR24 h forecasts were very poor during this time, forobvious reasons. The numerous observations withinthe influence region were discarded in favor of astraight uniform large-scale flow representing themost recent storm-track vector. Our new procedure, ~ A recalculation with the Charleston observation excludedyielded an error of 3 kt.652 MONTHLY WEATHER REVIEW VOLUME 10835~115' IlO- I0~ !00~ 9~* 9.0e 85~V=O 29Z/10 211/19 - + ~ ~ ~ 311/25+ + 206/14 + "% ~ ~~o o '---~~ ~._~ f' . ~ 183/,0 ,59,15 ~o ~ ' , : ~ / 2?~/la 9u~ ~R ~ , ~ ,,o,,, / ~,,,,o~, ~ ~ ~ ~ / __ ' ~/o~ --'. ~ ~ , ~.' --- .,~ ~ X ~ ~%o~,~, /- ~ ~ , ~ ~"~ ,~o~,,L- ~ -~] i( ) ~ X '~`01 9i ~ ~ ~ 't~5i(, 5 u o ~"-~'~ ~ ' ,/ ~ X X + oo~m x ~3~s / / i~ ~ ~ - ' ~ ~ i ~~o~,~ -- - ~ ~~~ ~~~2 ), + ' ~:/ ,~;o~ 105- IO0* 95~ 90 ~'=080* 75*U:O85-FIG. 7b. Initial mean winds for Hurricane Delia, 0000 GMT 5 September 1973. Notation as in Fig. 6.55*30*25-20-l t5* I[0- 105' I000 95- 90- 85- 80- 75*35'30"25"20' O2 3/30V::O - ? 0~4/34+ U:O ~ -r '-~' "~ -m - ~'~ ~ ~ + ~ 351/33/ /~ ~ ~'..~'~-:~,~, .~o ~,,~ ~ ?~,~o ~ ~,~ ~.~~ ~ + X x ~3::/~- ) X ~ ~*~"" 105' I000U =0 --176123 127/02 ~ 132/05 150/11 \ 169/17 I /+95- 90-FiG. 7c. As in Fig. 7b except for 1200 GMT 5 September.35-30*~_5-20*MAY 1980 SANDERS, ADAMS, GORDON AND JENSEN 65335'115- II0' 105' I00- 95* 90* 85?052/1'313940cl) 9,4/20 ~ +t58/23 ++ 157/24 ~64/25 ,; ,.,o0 ~74/20V:O[v 0v:o95- 90- 85*Fro. 7d. As in Fig. 7b except for 0000 GMT 6 September.35':5*115'-, IIQ* 105-, I0~0- 95-~ 9.0'~ $ V :0 ~ ~ ~ + 078/17 / ~ ~ 116/08 067/25102/27 ~ + ~+//~ ~ ~.. ,~/,4 +'~ / . t Q - ~- ~015/23 / [ t54/~5 X 169/22 , ~,, / ~ ~,~9,~o) ,,~, ~. / ,~*/,9 u'o 3,/~ ~ / ~ '~ ~ ~ , ~ / 276/24~ / + ~ 17) ~+/ +t 166/2065- V:O~6~/08137/08105' + i00- 95- 9o-FIG. 7e. As in Fig. 7b except for 1200 GMT 6 September.30"20- 75* 30- 85- 20-+654 MONTHLY WEATHER REVIEW VOLUM- 108as illustratedin Fig. 7, shows excellent specificationof the track velocity during the loop (probably betterthan the velocity estimated in real time), as Deliaand a larger cyclone, denoted by the heavy blockletter, ci~:cle about each other. The looping motionof Delia seems plainly accountable as a barotropicprocess. The motion of the larger cyclone is a mootquestion. Although the new procedure has not been incorporated in the SANBAR analysis program, we estimated the errors that would have ensued from usingthe specified track velocity as a 12 h extrapolationforecast. The frequency of various ranges of error inthis forecast is given in Table 8. Despite the presence of some large errors in this sample, the primarypotential advantage of the new procedure is that thelarge-scale flow in the storm-influenced region is notconstrained to be uniform.5. Concluding Summary For use of aircraft winds and satellite cloudmotion vectors in the SANBAR prediction model,we have derived some definitive regression formulas,for the zonal and meridional components of the windaveraged over the depth of the tropical troposphere,given 1) data in the lower or upper troposphere alone,2) in both these layers, and 3) in the middle tropo-'sphere as well as in these layers. We find that dataat only one level yield a result little better than useof the climatological mean, while addition of middletropospheric data, difficult with current satellitecapability, would improve substantially upon estimates based on lower- and upper-tropospheric data.We find some benefit in use of separate formulas forthe Atlantic and Pacific areas, but little in stratification into earlier and later portions of the tropicalstorm season. From a study of SANBAR forecast errors, we findthat the present model suffers from inaccurate specifications within the storm-influenced region, fromneglect'of pressure-height data outside the tropics,from fixed boundary conditions in the middle-latitudeportion of the forecast grid, and from neglect ofbaroclinic effects 'in the large-scale flow patternsurrounding the storm. We recommend a new procedure for use when twoor more-rawinsonde observations lie within .the~storm-influenced region. This procedure, in whichthe 'observations determine some parameters of thestorm circulation itself appears capable of specifyingthe initial storm-track velocity about as well aspresent subjective practice, but removes the presentSANBAR assumption of a uniform large-scale flowwithin the storm-influenced region. It should beespecially useful when erratic tracks occur close tolandfall. Acknowledgments. We are grateful to PatriciaStrat, Massachuseits Institute of Technology, for aidin tabulation and analysis of data, to Roy Jenne andPaul Mulder, National Center for Atmospheric Research, for providing data and for preparing revisedSANBAR forecasts, to Isabelle Kole for preparationof the manuscript, and to Air Force GeophysicsLaboratory for support under Contract F1962875-C-0059. REFERENCESAdams, A. L.,. and F. Sanders, 1975: Application of satellite cloud-motion vectors to hurricane track prediction. Sci. Rep. No. 1, Contract F 19628-75-C0059, AFCRL-TR-75-0635.Birchfield, G. E., 1960: Numerical prediction of hurricane move-ment with the use of a fine grid, J. Meteor., 17, 406-414.Dunn, G. E., R. C. Gentry and B. M. Lewis, 1968: An eight-year - experiment in improving forecasts of hurricane motion. Mon. Wea. Rev., 96, 708-713.Hebert, P. J., 1976: Atlantic hurricane season of 1975. Mon. Wea. Rev., 104, 453-465.Hovermale, J. B., 1975: First season storm.movement char acteristics of the NMC objective hurricane forecast model. Paper presented at Twelfth Annual NOAA NWS Warning Service Evaluation Conference, Coral Gables, FL.Jordan, E. S., 1952: An observational study of the upper-wind circulation around tropical storms. J. Meteor., 9, 340-346.Kasahara, A., 1959: A comparison between geostrophic and nongeostrophic numerical forecasts of hurricane movement with the barotropic steering model. J. Meteor., 16, 37~-384.Pike, A. C., 1972: Improved barotropic hurricane track predic tion by adjustment of the initial wind field. NOAA Tech. Memo. NWS SR-66.Riehl, H., W. H. Haggard and R: W. Sanborn, 1956: On the pre diction of 24 h hurricane motion. J. Meteor., 13, 415-420.Sanders, F., and R. W. Burpee, 1968: Experiments in barotropic hurricane track forecasting. J. Appl. Meteor., 7, 313-323.--, A. C. Pike and J. P. Gaertner, 1975: A barotropic model for operational prediction of tracks of tropical storms. J. Appl. Meteor.~, 14, 265-280. , and N. J. B. Gordon, 1976: A study of forecast errors in an operational model for predicting paths of tropical storms. Sci. Rep. No. 2, Contract F19628-75~C-0059, AFGL-~TR 77-0079.Vanderman, L. W., 1962: An improved NWP model for fore casting the paths of tropical cyclones. Mon. Wea. Rev., 90, 19-22.