{"Bibliographic":{"Title":"A procedure to reduce northward drift of tropical storms in a numerical model","Authors":"","Publication date":"1992","Publisher":""},"Administrative":{"Date created":"08-20-2023","Language":"English","Rights":"CC 0","Size":"0000053606"},"Pages":["QC\n996\nDEPARTMENT\nOF\nCOMMUNITY\n.T33\nno.71\nAMERICA\nA Technical Memorandum NWS NMC 71\nSTATES OF\nA PROCEDURE TO REDUCE NORTHWARD DRIFT OF TROPICAL STORMS IN A NUMERICAL MODEL\nNational Meteorological Center\nWashington, D. C.\nJuly 1992\nU.S. DEPARTMENT OF\nNational Oceanic and\n/\nNational Weather\nCOMMERCE\nAtmospheric Administration\nService","NOAA TECHNICAL MEMORANDUMS\nNational Meteorological Center\nNational Weather Service, National Meteorological Center Series\nThe National Meteorological Center (NMC) of the National Weather Service (NWS) produces weather\nanalyses and forecasts for the Northern Hemisphere. Areal coverage is being expanded to include the\nentire globe. The Center conducts research and development to improve the accuracy of forecasts, to\nprovide information in the most useful form, and to present data as automatically as practicable.\nNOAA Technical Memorandums in the NWS NMC series facilitate rapid dissemination of material of\ngeneral interest which may be preliminary in nature and which may be published formally elsewhere at a\nlater date. Publications 34 through 37 are in the former series, Weather Bureau Technical Notes (TN),\nNational Meteorological Center Technical Memoranada; publications 38 through 48 are in the former series\nESSA Technical Memoranda, Weather Bureau Technical Memoranada (WBTM). Beginining with 49, publications\nare now part of the series, NOAA Technical Memoranadums NWS.\nPublications listed below are available from the National Technical Information Service (NTIS),\nU.S. Department of Commerce, Sills Bldg., 5285 Port Royal Road, Springfield, VA 22161. Prices on\nrequest. Order by accession number, (given in parentheses).\nWeather Bureau Technical Notes\nTN 22 NMC 34\nTropospheric Heating and Cooling for Selected Days and Locations over the United States\nDuring Winter 1960 and Spring 1962. Philip F. Clapp and Francis J. Winninghoff, 1965, 18\npp. (PB-170-584)\nTN 30 NMC 35\nSaturation Thickness Tables for the Dry Adiabatic, Pseudo-adiabatic, and Standard Atmos-\npheres. Jerrold A. LaRue and Russell J. Younkin, January 1966, 18 pp. (PB-169-382)\nTN 37 NMC 36\nSummary of Verification of Numerical Operational Tropical Cyclone Forecast Tracks for\n1965. March 1966, 6 pp. (PB-170-410)\nTN 40 NMC 3\"\nCatalog of 5-Day Mean 700-mb. Height Anomaly Centers 1947-1963 and Suggested Applica-\ntions. J. F. O'Conner, April 1966, 63 pp. (PB-170-376)\nESSA Technical Memoranda\nWBTM NMC 38\nA Summary of the First-Guess Fields Used for Operational Analyses. J. E. McDonell,\nFebruary 1967, 17 pp. (AD-810-279)\nWBTM NMC 39\nObjective Numerical Prediction Out to Six Days Using the Primitive Equation Model-A\nTest Case. A. J. Wagner, May 1967, 19 pp. (PB-174-920)\nWBTM NMC 40\nA Snow Index. R. J. Younkin, June 1967, 7 pp. (PB-175-641)\nWBTM NMC 41\nDetailed Sounding Analysis and Computer Forecasts of the Lifted Index. John D. Stackpole,\nAugust 1967, pp. (PB-175-928)\nWBTM NMC 42\nOn Analysis and Initialization for the Primitive Forecast Equations. Takashi Nitta and\nJohn B. Hovermale, October 1967, 24 pp. (PB-176-510)\nWBTM NMC 43\nThe Air Pollution Potential Forecast Program. John D. Stackpole, November 1967, 8 pp.\n(PB-176-949)\nWBTM NMC 44\nNorthern Hemisphere Cloud Cover for Selected Late Fall Seasons Using TIROS Nephanalyses.\nPhilip F. Clapp, December 1968, 11 pp. (PB-186-392)\nWBTM NMC 45\nOn a Certain Type of Integration Error in Numerical Weather Prediction Models. Hans\nOkland, September 1969, 23 pp. (PB-187-795)\nWBTM NMC 46\nNoise Analysis of a Limited-Area Fine-Mesh Prediction Model. Joseph P. Gerrity, Jr.\nand Ronald D. McPherson, February 1970, 81 pp. (PB-191-188)\nWBTM NMC 47\nThe National Air Pollution Potential Forecast Program. Edward Gross, May 1970, 28 pp.\n(PB-192-324)\nWBTM NMC 48\nRecent Studies of Computational Stability. Joseph P. Gerrity, Jr., and Ronald D. McPherson\nMay 1970, 24 pp. (PB-192-979)\nNOAA Technical Memorandums\nNWS NMC 49\nA Study of Non-Linear Computational Instability for a Two-Dimensional Model. Paul D.\nPolger, February 1971, 22 pp. (COM-71-00246)\nNWS NMC 50\nRecent Research in Numerical Methods at the National Meteorological Center. Ronald D.\nMcPherson, April 1971, 35 pp. (COM-71-00595)\nNWS NMC 51\nUpdating Asynoptic Data for Use in Objective Analysis. Armand J. Desmarais, December\n1972, 19 pp. (COM-73-10078)\nNWS NMC 52\nToward Developing a Quality Control System for Rawinsonde Reports. Frederick G. Finger\nand Arthur R. Thomas, February 1973, 28 pp. (COM-73-10673)\n(continued on inside back cover)\nNOAA\ncomments\nDEPARTMENT\nOF","QC\n996\n,T33\nno.71\nNOAA Technical Memorandum NWS NMC 71\nA Procedure to Reduce Northward Drift of Tropical Storms\nin a Numerical Model\nLIBRARY\nSEP 1 4 1992\nUS Dept of Commerce\nMakut B. Mathur and Alan M. Shapiro\nWashington, D.C.\nJuly 1992\nATMOSPHERN\nAND\nUNITED STATES\nNational Oceanic and\nNational Weather\nNOAA\nDEPARTMENT OF COMMERCE Atmospheric Administration\nService\nBarbara Hackman Franklin\nJohn A. Knauss\nElbert W. Friday, Jr.\nSECURITY\nSecretary\nUnder Secretary\nAssistant Administrator\nOF","A procedure to reduce northward drift of tropical storms\nin a numerical model\nMukut B. Mathur\n(National Meteorological Center, Washington D.C.)\nand\n1\nAlan M. Shapiro\n(UCAR Visiting Scientist, National Meteorological Center, Washington D.C)\n1\nPresent Affiliation : CAPS, University of Oklahoma, Norman, OK","ABSTRACT\nOperational primitive equation models often predict hurricane tracks that lie to the right of the\nobserved motion. Such a bias in the National Meteorological Center's Quasi-Lagrangian Model\n(QLM) is most pronounced for the storms that moved westward. It is shown that a westward\ndisplacement of the storm's circulation in the initial analysis significantly contributes to this\nerroneous motion to the right of the observed track in the QLM.\nA procedure to reduce this bias for westward moving storms is presented. It consists of\nimposing a secondary circulation (a dipole) over the initial storm area. The cyclonic (anticy-\nclonic) lobe of the dipole is centered to the south (north) of the observed track. The use of this\ndipole procedure resulted in a substantial improvement in the forecast track throughout the 72\nhour period in several cases.","1 Background\nThe Quasi-Lagrangian Model (QLM) of the National Meteorological Center (NMC) provides\nnumerical track forecast guidance for tropical storms in the Atlantic Ocean, the Gulf of Mexico,\nand the eastern Pacific Ocean. The QLM is integrated in the cases of rapidly developing\ndepressions, tropical storms and hurricanes. We are not concerned here with the forecast of a\ntropical cyclone's intensity. A storm in this paper refers to a disturbance in any of the above\nstages of a tropical cyclone.\nThe QLM employs a set of primitive equations with o (= pressure / surface pressure) as a\nvertical coordinate, a horizontal grid of 111 X 111 points with a 40 km spacing, and 16 vertical\nlayers. The center of the grid coincides with the initial position of the observed storm. Because of\nlack of observations near a storm's center, a storm's circulation is often not well analyzed\noperationally. Therefore, an idealized symmetric vortex whose structure depends on five\nparameters (the central pressure Pc, pressure of the outermost closed isobar Pb (reckoned with a\nprecision of 1 mb), mean distance r max (which is also referred to below as the size or radius of a\nstorm) of the outermost closed isobar from the center, storm center latitude Clas and longitude\nClon is merged into the NMC's Global Aviation (AVN) analysis to simulate a storm in the\nQLM's initial state. These parameters are derived by the National Hurricane Center (NHC) from\ntheir analysis and are transmitted to the NMC. The idealized vortex has a warm core and nearly\nthe same size and intensity as the observed storm (except that the central pressure is set to 970\nmb whenever Pc is less than this value because large gradients can not be prescribed well with\nthe use of a 40 km grid spacing). The winds are cyclonic in the lower and middle troposphere\nand anticyclonic in the upper troposphere. The vortex and the AVN analysis are first projected\nseparately on the QLM grid and then merged using the relation:\nX = wx,+(1-w)X\nwhere, X is one of the variable (a horizontal component of the wind, the virtual potential\ntemperature, the mixing ratio, or the surface pressure). The subscripts m, V and a denote a field in\nthe merged data, vortex and analysis, respectively. The vortex is projected SO that the vortex\ncenter coincides with the center of the QLM grid. The weight function W is given by:\n1","w=\nr\nw=0 otherwise.\nHere r is the distance from the observed center. The lateral boundary conditions for the QLM are\nderived from the AVN model's forecast on the o surfaces. A description of the QLM is given in\nMathur (1983, 1991) and the specification of the initial vortex including the merging procedure\nis provided in Mathur 1988.\nDuring the 1988 hurricane season, no systematic bias in the QLM forecast storm tracks was\nnoticed for the storms that moved northward or northeastward. However, the predicted track was\nlocated to the north of the observed track in many cases where the observed motion of a storm\nwas towards the west (between angles 210° and 310° reckoned clockwise from the north). The\nerroneous northward drift generally occurred in the first 24 hours of a forecast. It should be noted\nthat the operational position of the storm center that was provided by the NHC for the QLM\nforecast is referred to as the observed storm center throughout this paper.\nAs an example, we show (Fig. 1.) the observed and predicted track of hurricane Gilbert for\nthe initial time 12 GMT 10 September 1988. The QLM uses the maximum relative vorticity at\n850 mb as the locus of the storm's center. The storm in the model forecast moved north-north-\nwestward in the first 24 h, then, at later times, nearly paralleled the observed track. The\nnorthward drift of storms has also been noted in other tropical cyclone models (e.g., see Hodur\n1989, and Iwasaki et al. 1987.)\nThe northward drift of storms due to the variation in the Coriolis parameter has been\ninvestigated in several studies. Rossby (1948) suggested that an initially symmetric cyclonic\nvortex would accelerate to the north on a - plane due to the differential strength of the Coriolis\nparameter. As a refinement of this conception, the barotropic studies of Chan and Williams\n(1987) and Fiorino and Elsberry (1989) suggested that an initially symmetric vortex is first\ndistorted by differential advection of earth's vorticity which sets up a pair of counter-rotating\n- gyres, a cyclonic gyre is developed to the west and an anticyclonic gyre to the east of the\n2","vortex center. The vortex is then advected by the flow associated with the gyres. The net effect\nis for an initially symmetric vortex to move north-westward in the northern hemisphere. This SO\ncalled - drift (where B = af/dy) increases with the size of the storms.\nMathur (1986,1987) conducted several experiments to further study the motion of storms\nutilizing a 10 layer version of the QLM. A grid spacing of 40 km, and idealized initial vortices of\ndifferent size and intensity with or without a zonal basic current were used. The initial vortex\nintensified into a hurricane in all cases. (The integration were carried out to 120 h for no basic\ncurrent cases and to 72 h for uniform basic current cases). The northward displacement when\naveraged over the entire forecast period was greater for a larger (and/or stronger) initial vortex\nthan for a smaller (and/or weaker) initial vortex. Thus, the northward drift depended on both the\nsize and the intensity of the initial vortex.\nOn the other hand in the operational QLM forecasts, a larger and stronger storm (Hurricane\nGilbert, Fig. 2), drifted less northward than a smaller storm (Tropical storm Joan, Fig. 3). In view\nof the experimental studies cited above, this difference in the northward drift can not be\nexplained solely by the variation in the Coriolis parameter.\nWe therefore examined the AVN analysis (interpolated to the QLM grid) as a possible cause\nof the spurious northward drift. The center of the storm circulation in both cases considered\nabove is located to the west of the observed center (Fig. 4). Recall that the QLM's initial state is\ndesigned so that the center of a storm coincides with the observed center. When a storm's center\nis displaced in the analysis, a part of the symmetric component of the analyzed circulation will\nappear as an asymmetric circulation over the central vortex area in the merged state. This\nasymmetric circulation may steer the storm model vortex. The displacement is larger and the\nanalyzed southerly winds over and near the observed center area are stronger in Joan than in\nGilbert (Fig. 4). Therefore a greater northward displacement is anticipated in the Joan case than\nin the Gilbert case. The QLM predicted storm tracks depicted in Figs. 2 and 3 demonstrate that\nthis was the case.\nOther case studies also suggest that the erroneous northward drift of the storms in the QLM is\nlargely due to a systematic westward displacement of the cyclonic circulation in the analysis\nrelative to the observed storm center. As a consequence of this displacement, a southerly flow is\n3","analyzed over the observed storm location. Such a westward displacement of tropical distur-\nbances in the NMC operational analyses has been noted by C.J. Neumann and S. Lord (personal\ncommunications).\nOne may therefore anticipate that the erroneous northward drift in the QLM for westward\nmoving storms should be reduced by decreasing a storm's location error in the AVN analysis.\nAndersson and Hollingsworth (1988), and M. Ueno (personal communication) have attempted to\nimprove the structure and location of storms in a global analysis by introducing bogus soundings\nin the region of storms. The bogus data are derived from an empirical symmetric vortex\nrepresenting the structure of a mean hurricane that has been adjusted based on a few observed\nparameters. Different specifications of the vortex and levels for inserting bogus data are used in\nthe two studies. In the Andersson and Hollingsworth study, the first guess-fields (six hour\nforecast from the previous cycle) truncated at T20 are added to the bogus vortex to represent the\nlarge-scale circulation. Because of the coarse global analysis grid spacing (of the order of a few\nhundred kilometers), storm location errors can be more than 100 km even with the use of bogus\ndata.\nProcedures to reduce the storm location error to a tolerably small value (ideally zero) in the\nAVN analysis have not yet been developed. We have therefore considered techniques to\ncompensate for the location error and thus reduce the northward drift in the model track\npredictions. Use of a method in which a dipole was imposed on the idealized vortex led to a\nsubstantial improvement in forecast tracks. The dipole is described in section 2, and results\nshowing improved track forecasts are presented in section 3. In contrast to some earlier reports\n(e.g., Pike 1972) where a uniform steering current is imposed, our procedure is more general, the\ncurrent varies in the horizontal and the variation is controlled by a few parameters.\n2 Specification of a dipole\nWe superpose a secondary circulation resembling a dipole over the primary symmetric vortex.\nThe free parameters appearing in this description will be related to analyzed storm parameters in\nthe next section. The dipole is specified in a Cartesian coordinate system (X,Y) with the origin\nat the storm's center. The negative X axis is directed along an angle Y measured clockwise from\nthe axis Y', where (X' , Y' are the coordinate axes on the QLM grid (see Fig. 5). The\n4","maximum dipole wind speed, \"max is at the observed vortex center and is directed along the\nnegative X axis. The anticyclonic (cyclonic) circulation center of the dipole is located along the\npositive (negative) Y axis.\nThe streamfunction that describes the dipole perturbation is:\n4=Aexp{-(ax+bly)} sin(y/) =\n(1)\nwhere a, b, I, and A are disposable parameters. X and y are the distances along the coordinate axis\nX and Y respectively. Differentiating Eq. (1) with respect to y and X gives, respectively, the\nvelocity components directed along and perpendicular to the dipole axis.\nu = - A exp{-(ax/+by)}{-by/y) sin(y/l) + cos(y/l)/1}\n(2)\n= -Aexp{-(ax/+bly)} ax/xsin(y/) -\n(3)\nV\nSince the maximum u-component of the dipole velocity is at the storm center, (x=0, y=0),\nUmax = -A/l .\n(4)\nSince the dipole streamfunction is constant (zero) along the coordinate values y=nrl (for\ninteger n), the y-component of wind vanishes along these coordinate lines. For n=1, ly| and\nthe u-component takes the value at x=0\n= .\nThis equation may be rewritten as an expression for b\nb -\n(5)\nThe parameter L is defined such that at x=0 and y=L (or -L) both u and V are zero, i.e., the\n5","coordinates (0,L) and (0,-L) define the centers of the dipole lobes. Evaluating (2) at the dipole\nlobe centers gives the formula\ntan(L/l) = 1/bl\n(6)\nA simple expression for b results from inserting (4) into (5)\nb = - In\n(7)\nSubstituting (7) into (6) provides a simple expression for 1\n/ = - L / tan-1 {r/In/Uedge/Umax1}\n(8)\nThe adjustment in the height field (z) required by the insertion of the dipole streamfunction is\nspecified as a simple geostrophic increment to the primary vortex height field\nZ =fulg ,\nwhere g is the acceleration due to gravity.\nIn summary, the analytic perturbation dipole has five free parameters: a, b, A, 1 and Y. It was\nconvenient to specify a, Y, L, , \"max and uedges and compute 1 from (8), A from (4), and the\nattenuation factor, b, from (7).\nThe original purpose of the present work was to use a dipole to impose steering winds based\non observed motion (persistence) over the idealized vortex on the QLM model grid. A dipole\nwas selected for two reasons: (1) to study the impact of nonuniform steering current on the\nmotion of storms. We envisioned that a current (having nearly the same direction as the observed\nstorm motion) in a narrow zone (zonal width of the order of max) with the maximum wind at the\nstorm's center may give most improvement in track forecasts. Note that the horizontal variation,\nthe strength, and the width of the current can be adjusted by a suitable choice of all or some of\nthe five parameters. The variation in the vertical can be taken into account by using vertical\nweighting functions. (2) The use of a dipole may reduce the northward motion of westward\n6","moving storms because the relative vorticity in the dipole is negative to the north and positive to\nthe south of the storm center in these cases. The change in relative vorticity due to the advection\nof the dipole relative vorticity by the symmetric storm winds is thus of an opposite sense to the\nchange due to the advection of planetary vorticity.\nBecause only limited computer resources were available, it was not possible to study the\nimpact on the forecast track of varying each free parameter while keeping the remaining\nparameters fixed. Instead, a narrow steering current zone was specified by setting a and \"edge as a\nfraction of b and \"max respectively, and specifying L as a value smaller than max Various values\nof \"max between 2 and 25 m/s and of Y within 40° of the observed storm motion were used. Only\nthe three cases of Figs. (1)-(3) were considered. In an experiment Y was set to the observed\ndirection of a storm, and \"max was evaluated SO that the mean wind over a circular area of radius L\nmatched the observed storm speed. Although this general procedure did improve the forecast, a\ncomparison of experimental results showed that a fixed value of Y of 270° and \"max specified by\nEq. (9) yielded the best forecasts for the westward moving storms (observed motion between\n210° - 310°). Attempts are currently underway to optimally tune the parameters for the general\ndipole case. The remainder of this paper is concerned with the experimental design and\nnumerical results corresponding to Y fixed at 270°.\na. Dipole parameters\nThe above experiments also showed that the reduction in the northward drift of a storm with\nthe use of a dipole depends on the strength and the width of the easterlies (case Y = 270°)\nbetween the dipole lobes. This dependence may be expected as the advection of the vortex\nwould depend on the width and strength of the steering current (see also section 3b). The\nnorthward drift in the 1988 operational QLM forecast cases was large for storms that were small\nin size and for those that were located at low latitudes. The empirical relations for \"max in\n(9),\nand L in (10) were formulated taking the above dependence of drift on the latitude and size of a\nstorm. The numerical coefficients were determined as optimal values for reducing the drift in\nthree cases in Figs. 1-3.\n\"max , \" edge's a and L were defined by the following relations.\n7","\"max = C/(Clas RR)\n(9)\nUedge = =.8 Umax\na=0.6b\n.\nL =\n(10)\nHere C = - 136000 km m/s, RR = MAX ( max 500). Here Imax is expressed in kilometers.\nNoise developed in a few 72 h forecasts where a value of \"max less than - 20 m/s was used.\nTherefore, 14max is set to -20 m/s, if it is less than this value.\nUse of a value of L greater than 600 km for a storm with max larger than 650 km (e.g.,\nGilbert) resulted in excessive southward displacement of the forecast center, an upper limit of\n600 km is therefore assigned to L.\nWith the above specifications, the wind over the storm center is from the east. The easterlies\ndecrease in all directions from the center, and eventually change to westerlies to the north (south)\nof the anticyclonic (cyclonic) lobe centers. The velocity and height fields of the dipole in the\nidealized vortex area (i.e., within a radius max of the observed storm center) were added to the\nQLM initial state in all vertical layers. It is shown in section 3a that the predicted storm direction\nin the QLM has nearly zero correlation with the direction of asymmetric winds above 500 mb.\nNote that the initial asymmetric wind consist of a vector sum of the dipole wind and the\nasymmetric component that is derived from the analysis as a result of merging of vortex into the\nanalysis. In a very few cases, the QLM was also integrated using a weighted dipole, where the\nweight was set to 1 up to level 10 (o = .472), and then linearly reduced upward with a value of\n0.2 at the top most layer. The forecast using the weighted dipole was not significantly different\nfrom the case when weights are set to unity at all levels.\nAn example of a dipole structure is provided in Fig. 6. The dipole streamfunction (1) for\nGilbert on 12 GMT 14 September ( max = 740 km) is shown in Fig. 6a. The winds at 850 mb\nwithout a dipole (Fig. 6b) are nearly axisymmetric. The imposition of the dipole (Fig. 6c) results\nin stronger winds to the north and weaker winds to the south compared with the case without a\ndipole.\n8","3 Numerical results\nResults from 72 h integrations of the QLM with a dipole for nine cases in which a northward\ndrift was predicted in the operational QLM are now considered. It is shown that a significant\nimprovement in forecast mean track errors is obtained with the use of a dipole (section 3a).\nPredictions for three representative cases are also presented (section 3b-3d). Operational\nimplementation of the dipole procedure is discussed in section 3e.\na. Mean track forecast errors\nThe QLM was integrated using a dipole for the cases in which the observed storm motion was\ntowards the west (between 210° and 310° ) and the AVN forecasts that are required for the QLM\nlateral boundary conditions were available. A list of these cases with the observed and predicted\n(without a dipole) motion of storms during the first 12 h are presented in Table 1. The analyzed\nwinds averaged over square areas inscribing circles of radii of [max 2 r max , and 3 max for the\ninitial time are also shown. The vertical averaging was carried out using only the data for layers\n1 (o = 1) to 10 (o = .472), because we have noticed that the motion of storms in the QLM has\nnearly zero correlation with winds above the 500 mb level. For example, we have examined the\npredicted asymmetric part of the wind over the central storm area (of radius 2 - 3° latitude) in a\nfew cases at different forecast hours. The direction of asymmetric winds below 500 mb is often\nwithin 20 - 30° of the predicted direction of storm motion, while the wind direction above 500 mb\ndiffered by nearly 180° from the predicted storm motion.\nInspection of Table 1 reveals two points of interest. First, note that the direction of QLM\nvortex motion is correlated more with the 1 max average analyzed wind direction than with the 2\nImax or 3 r max averages. This is consistent with the non-divergent barotropic model results of\nSmith et al. (1990) in which the environmental wind averaged over the innermost of the\n1°, 1 - 3°, 3 5°, -7°, latitude annular regions (centered on the vortex vorticity center)\nyielded the best agreement with the motion of the vorticity center. Secondly, the observed\nmotion is in closer agreement with the 3 max average analyzed wind direction except in the\ncases when the difference between the observed and predicted direction of motion is small. In\nthe latter cases, both directions are close to the 1 max\nThe\ndifference\nbetween\nthe\naverage.\nvortex speed in the QLM and the average analyzed 1 max speed is generally 2 m/s or less.\nThis\n9","implies that the QLM vortex may be steered by its immediate model environment, at least in the\nfirst 12 hours, whether or not it is a correct representation of the real atmosphere. When the\nobserved direction of storm motion does not agree with the 1 max average then one can\nanticipate that the model vortex will drift significantly from the observed storm track.\nThe mean QLM forecast track error is significantly reduced by including a dipole perturbation\nto the wind and pressure fields (Table 2). The greatest improvement in the storm track occurs at\n72 hours where the mean error was reduced by 228 km. The mean error is reduced with the use\nof the dipole in the three representative cases by 228 km at 24 h, 128 km at 48h, and 194 km at\n72 h. The reduction in mean error is also large in the rest of the six cases (independent sample), it\nis 148 km at 24 h (6 cases), 156 km at 48 h (5 cases), and 261 km at 72h (3 cases). Since some of\nthe storms dissipated before 72 hours, the number of cases considered decreased with time.\nAn improvement in the forecast track with the use of a dipole occurred in all cases when the\nentire forecast period (721 is considered. However, the improvement differed considerably\nfrom one case to another. The largest improvement resulted for the case of Gilbert 12 GMT 10\nSeptember (Fig. 1), and the smallest improvement in the case of Joan 12 GMT 12 October (Fig.\n3). A discussion of three track predictions including these latter two cases is now presented.\nb. Case 1 : Gilbert 12 GMT 10 September 1988\nAs noted above, the storm's center in the operational QLM forecast (a case without the use of\na dipole) for 12 GMT 10 September drifted northward in the first 24 hours (Fig. 1). Thereafter\nthe center paralleled the observed track so that the track forecast errors were nearly constant at\nabout 250 km during the 12 to 72 h period. The predicted track was located much closer to the\nobserved track during the first 48 h when a dipole was used. Although the storm moved more\nrapidly towards the northwest in the forecast than indicated by the observations after 48 h, the\nlocation errors still remained smaller. Notice that the time and location of landfall over Jamaica\nare predicted well when the dipole is included.\nC. Case 2 : Gilbert 12 GMT 14 September\nThe forecast speeds of the storm both without and with the dipole included were slower than\nobserved during the first 12 hours (Fig. 2). The center was located very close to the observed\n10","center at 24 and 36 h in the forecast including the dipole, whereas the storm center is about 200\nkm to the east of the observed center at these hours in the forecast without the dipole. Gilbert\nwas observed to drift towards the northwest after 36 h; this drift began after 24 h in forecast\nwithout the dipole and only after 48 h with the dipole. Consequently, the storm center at 48 h in\nwith (without) the dipole is located to the south (north) of the observed center. The time and the\nlocation of landfall over Mexico are better predicted with the dipole compared to without the\ndipole.\nFurther insight into the behaviour of storm with and without a dipole can be gained by\ncomparing the terms in the vorticity equation in the two cases. Neglecting the diffusive terms\nthe tendency equation for relative vorticity (pressure cordinates) may be written as:\n-\nHere is is the vertical component of relative vorticity, f is the Coriolis parameter, w is the\nvertical p-velocity, and u' and v' are horizontal components of wind in the QLM coordinate\nsystem. The total tendency is the sum of five terms on the right hand side; these terms are the\nhorizontal and vertical advection of vorticity, divergence, twisting and B- - term respectively.\nHere\nB - dr\nIn an observational study Chan (1984) showed that tropical cyclones nearly move along the\naxis connecting the vorticity tendency minimum behind the storm to the vorticity tendency\nmaximum ahead of the storm. The total tendency at 6h in the dipole and no dipole cases at 850\n11","mb (Figs. 7a and 7c) shows that the minimum to maximum value axis is oriented east-west in the\ndipole case, and southeast-northwest in the no dipole case. The orientation of this axis in the\nhorizontal advection term (the location of maximum and minimum centers are shown in the\nabove figures) is nearly the same in both forecasts. Note that in both cases the two minimum\ncenters (total and horizontal terms) nearly coincide, but the maximum center in the total\ntendency field is displaced to the south of the corresponding center in the horizontal advection\nfield. This displacement of the maximum center is related to the location of the maximum in the\nstretching term to the southwest of the storm center (Figs. 7b and 7d). The maximum value in\nthe horizontal advection field is 213 (units: 10-10 s-2 in the dipole case and 232 in the no dipole\ncase. The stretching term is of nearly the same magnitude as the horizontal advection term in the\ndipole case but is smaller in the no dipole case. The contribution from other terms to the total\ntendency is relatively small except that for the vertical advection term. The maximum in\nvertical advection term (not shown) in both cases has nearly the same magnitude as the minimum\nof the stretching term and the two centers nearly coincide. The location of the minimum in the\ntotal tendency is therefore not much displaced from the corresponding location of the minimum\nin the horizontal advection field in both predictions, and the maximum center in total is located\ncloser to maximum center of the stretching term in the dipole case than in the no dipole case.\nThe distribution and magnitude of the various terms are not the same in the two cases, and the\nstretching and the vertical advection term contribute more to the motion of the storm in the\ndipole than in the no dipole case.\nd. Case 3 Joan 12 GMT 12 October 1988\nThe operational QLM forecasts for Joan from the initial times 00 and 12 GMT between 12\nOctober and 23 October showed that an excessive northward drift occurred in many forecasts\nbetween the 12th and 17th. AVN forecasts needed for QLM boundary conditions were available\nin only two of these cases. The two cases are included in the mean forecast error comparison\n(Table. 1), and one (12th October) is discussed below.\nThis storm drifted northwestward in the QLM integrations (Fig. 3) without and with a dipole.\nThe forecast track errors are ,however, reduced throughout the 72 h period with the use of the\ndipole. The predicted tracks are parallel after 24 h, which suggests that the inclusion of a dipole\nimpacted the forecast only during the first 24 h.\n12","Joan also drifted northwestward in the AVN model's 36 h forecast (Fig. 8a) and at 72 h (Fig.\n8b). The centers of the storm at these hours in the AVN and the QLM are close to each other. We\nconclude from this comparison that the extended northward drift in this case is due to errors in\nthe analysis over a very large area surrounding this storm.\ne. Operational implementation\nThe inclusion of the dipole procedure operationally is likely to provide an improved forecast\ntrack guidance in cases where a storm circulation is displaced in the analysis. Since there is\ncurrently a systematic westward bias in the analysis, we have restricted our attention in this\npaper to compensating for this particular problem. However, recent experiments performed with\nthe QLM indicate that a significant improvement in storm track prediction can be attained in\nmost cases with the application of a generalized dipole (Mathur 1991).\nIt should be noted that the analyzed circulation sometimes appears only as a trough. The\ndisplaced circulation often has a vertical tilt, and the maximum displacement often occurs at a\nhigher level (usually 700 or 500 mb level). Because the structure of the displaced circulation\n(closed circulation or a trough, orientation of the trough axis associated with the circulation, and\nvertical tilt), and the distance of its center (or trough axis) from the observed center vary greatly\nfrom case to case, a satisfactory numerical procedure could not be developed to diagnose\nwhether a storm is displaced in the analysis.\nDuring the 1988 hurricane season, a westward moving storm drifted northward in the QLM\nforecast in a very large number (about 90%) of cases. The dipole procedure (section 2a) was\ntherefore implemented for the 1989 season, since its inclusion is likely to improve the forecast\ntrack in a majority of westward moving storm cases. The NHC provided the expected direction\nof motion and speed of a storm in addition to the five parameters listed in section 1. A dipole was\nused if the direction was between 210° - 310° and the speed was greater than 1 m/s (It was\nanticipated that the latter requirement would exclude nearly stationary storms that are likely to\nrecurve). The QLM without a dipole was run in parallel to the operational QLM (with dipole) in\nmany 1989 westward moving storm cases. The forecast with the use of a dipole were superior to\nthose without a dipole in a majority of cases. In a few cases where a northward drift did not\n13","occur in the QLM without a dipole, the track forecast errors without a dipole were similar to\nthose with a dipole. Cases of operational forecasts with the use of a dipole are presented in a\nseparate report where 1989 season QLM forecast tracks are discussed (Mathur, 1991).\n4 Discussion\nCurrent operational primitive equation models often predict tropical storm tracks that are\nlocated to the right of the observed tracks. The largest such forecast errors in the QLM occurred\nfor the westward moving storms. Three factors are thought to contribute to this erroneous\nnorthward motion in the model forecasts. First, a part of the drift could be due to the latitudinal\nvariation in the Coriolis parameter. In previous QLM studies utilizing idealized symmetric\nstorms with and without a uniform steering current, Mathur (1986, 1987) showed that the\nnorthward drift due to the - effect was smaller in the first 24 hours than in the periods 24 - 48\nand 48 - 72 h. This is because the gyres induced by the B - effect take some time to develop.\nAdditionally Mathur found that larger (stronger) storms drifted further north than smaller\n(weaker) storms. On the other hand, the drift in many operational 1988 cases was larger in the\nfirst 24 h than in the later 24 h periods (e.g., Figs. 1 and 3). Also, a smaller and weaker storm\n(Joan , Fig. 3) moved further north than a larger and stronger storm (Gilbert , Fig. 2). Although\nthe B - effect may have contributed to the northward drift, some other processes were undoubtedly\nalso operating.\nA second source of error is associated with a systematic displacement of the storm center in\nthe analysis to the west of the observed center. In this case, the winds in the analysis have a\nsignificant southerly component over the observed storm area. Forecasts from several cases\nsuggest that if the erroneous southerly flow is strong or its area is large compared to the model\nstorm, then the storm in the QLM forecast is likely to be advected significantly northward during\nthe first 24 hour. For instance, the analyzed southerly winds were stronger over the small storm\n(Joan) than over the large storm Gilbert. As a result, the smaller storm Joan drifted much farther\nto north than the stronger storm Gilbert in the first 24 h QLM forecasts.\nObviously, poorly analyzed fields over very large areas of the domain can also degrade the\nQLM forecast. This third source of error has not been fully investigated. However one may\nanticipate that when the large scale analysis is incorrect an erroneous \"drift\" from the observed\n14","track may be large and may operate during all time periods. The continual northward drift of\nJoan in both the QLM and AVN forecasts for all time periods (section 3d) may have been due to\nimproperly analyzed large scale features (a displaced vortex probably contributed to the 0-24 h\ntrack errors as well). If the analysis provides a good representation of large-scale atmospheric\nfeatures but is deficient in the vicinity of the storm, one may expect good predictions of storm\nspeeds and directions after an initial period of model storm drift. For instance, the track errors for\nthe two Gilbert cases considered in section 3 level off at 24-36 h. Since the horizontal resolution\nof the analysis is of the order of a few hundred kilometers and the mean error during this period\nin the two cases is smaller (of the order of 200 km) than the resolution of the analysis, it may be\nassumed that the analyses in these two cases were good. This suggests that the so-called\n\"steering\" current over the observed storm area in the real atmosphere and over the predicted\nstorm area in the QLM were in good agreement during the 24-72 h period.\nSince the dipole wind and height fields are imposed only within the area occupied by the\nobserved storm, it is unlikely that its inclusion would lead to a reduction in track forecast errors\narising from large-scale analysis errors. The numerical results (section 3) suggest that the\ninclusion of a dipole reduces the northward drift arising from the erroneous southerly steering\ncurrent that appears over the storm area in the QLM initial state (associated with a westward\ndisplacement of the observed vortex in the analysis). Recall that the dipole of section 2\nintroduces an easterly steering current over the storm area between the lobes (see Eq. 10 for the\nlocation of lobe centers) and that storm motion in the QLM is correlated well with the vertically\naveraged winds over a 1 max area (see section 3 and Table 1). The inclusion of the dipole\neasterlies therefore leads to a more westward motion of a vortex.\nThe contribution of various terms in the propagation of the vorticity maximum at 850 mb (this\nmaximum defines the storm center in the QLM) was also investigated in a case (section 3). The\nmaximum in relative vorticity tendency is located to the south and to the west of the storm center\nin the dipole case compared to the no dipole case. The two terms which contribute the most in\nthis displacement of the maximum tendency are the horizontal advection term and the stretching\nterm. The maximum in the horizontal advection term in the dipole case is located to the south of\nthe maximum in the no dipole case (Fig. 7). The stretching term is of the same order as the\nhorizontal advection term in the dipole case and the maximum in this term is located to the\nsouthwest of the center. The stretching term is weaker in the no dipole case.\n15","Smith et al. (1990) used a barotropic model on both f and - plane and studied the motion of a\nsymmetric vortex embedded initially in a southerly current that was prescribed using a west-east\ndipole. They varied the dipole scale to shift the asymmetric vorticity centers from the storm\ncenter. In the case the asymmetric vorticity was initially concentrated in the region of large\nshear in the tangential wind of the symmetric storm, the asymmetric vorticity underwent large\ndistortion (wrapped around the storm center) and the storm initially stalled. This distortion\nbecame weaker as the asymmetric vorticity centers were displaced farther away from the region\nof the large tangential wind shear. We have not noticed any wrapping around of vorticity in our\nexperiments, this may be due to the fact that the dipole lobes are initially located in the weak\ntangential wind shear near the storm boundary.\n16","5\nREFERENCES\nAndersson, E., and A. Hollingsworth, 1988: Typhoon bogus observations in the ECMWF data\nassimilation system. ECMWF Technical Memorandum No. 148, 25pp. [ECMWF, Shinfield\nPark, Reading, Berkshire RG2 9AX, England.]\nChan, J. C. L., 1984: An observational study of physical processes responsible for tropical\ncyclone motion. J. Atmos. Sci, 41,1036-1048\nChan, J. C. L., and R. T. Williams, 1987: Analytical and numerical studies of the - effect in\ntropical cyclone motion. Part I: Zero mean flow. J. Atmos. Sci., 44, 1257-1265.\nFiorino, M., and R. L. Elsberry, 1989: Some aspects of vortex structure related to tropical\ncyclone motion. J. Atmos. Sci., 46, 975-990.\nHodur, R. M., 1989: Tropical cyclone track prediction in a regional model. Extended Abstracts.\n18th Conf. on Hurricanes and Tropical Meteorology, San Diego, Amer. Meteor. Soc., 174-175.\nIwasaki, T., H. Nakano, and M. Sugi, 1987: The performance of a typhoon track prediction\nmodel with cumulus parameterization. J. Meteor. Soc. Japan, 65, 555-57.\nMathur, M. B. , 1983: A quasi-Lagrangian regional model designed for operational weather\nprediction. Mon. Wea. Rev., 111, 2087 - 2098.\n, 1986: Application of quasi-Lagrangian model to hurricane prediction. Extended\nAbstracts. WMO/IUGG International Symposium on Short and Medium Range Numerical\nWeather Prediction. WMO/TD NO. 114, 461 - 464.\n, 1987: Development of the NMC's high resolution hurricane model. Extended\nAbstracts, 17th Conf. on Hurricanes and Tropical Meteorology, Miami, Amer. Meteor. Soc., 60\n-63.\n17","1988: The NMC Quasi-Lagrangian Hurricane Model. Technical Procedure Bulletin\n,\n377, National Weather Service, Silver Spring, Maryland. 10pp. [NOAA/NWS/NMC, Develop-\nment Division, W/NMC2, WWB Room 204, Washington D.C. 20233.]\n, 1991: The National Meteorological Center's Quasi-Lagrangian Model for Hurri-\ncane prediction. Mon. Wea. Rev., 119, 1419-1447.\nPike, A. C. , 1972: Improved barotropic hurricane track prediction by adjustment of the initial\nwind field. NOAA Technical Memorandum NWS SR-66, National Weather Service, Silver\nSpring, Maryland. 17pp. [National Hurricane Center, 1320 S. Dixie Highway, Coral Gables, Fla.\n33146.]\nRossby, C.G., 1948: On displacement and intensity changes of atmospheric vortices. J. Mar.\nRes., 7, 175-187.\nSmith, R. K., W. Ulrich, and G. Dietachmayer, 1990: A numerical study of tropical cyclone\nmotion using a barotropic model. I: The role of vortex asymmetries. Quart. J. Roy. Meteor. Soc.,\n116, 337-362.\n18","Table 1. Observed and QLM predicted storm motion for the first 12 hours. Analyzed wind\nspeed and direction averaged vertically over the model's first 10 sigma levels and horizontally\nover a square of sides Irman 2rm. and 3rmax max are also presented. Direction is given in degrees\nreckoned clockwise from the north. Speed is given in m/s.\nStorm\nObserved\nQLM vortex\nRMAX\nAveraged analysis wind\nname/date speed and speed and\n(km)\nspeed and direction\ndirection direction\n1r\n3r\n2r\nGilbert\n12Z 9/10/88 283/6.8\n332/7.2\n370\n308/8.4\n295/6.9\n284/5.6\n00Z 9/12/88 284/8.3\n329/7.1\n555\n317/5.7\n293/4.8\n282/3.5\n12Z 9/14/88 288/7.5\n277/4.3\n740\n300/5.8\n316/3.1\n12/1.3\n12Z 9/15/88 287/5.2\n281/2.7\n740\n300/4.1\n319/2.6\n42/0.8\nJoan\n12Z 10/12/88 277/6.3\n313/7.8\n170\n324/8.0\n308/7.3\n297/6.9\n12Z 10/16/88 266/3.7\n331/5.2\n280\n306/5.0\n289/5.6\n283/5.1\nFabio\n12Z 8/2/88\n284/5.1\n355/5.6\n465\n308/3.5\n281/5.1\n269/5.1\n12Z 8/3/88\n303/6.5\n320/9.3\n465\n304/7.1\n282/7.5\n273/6.5\nUleki\n00Z 8/30/88 284/5.1\n329/2.4\n170\n328/4.7\n303/4.7\n291/4.7\n19","Table 2. Mean QLM forecast track errors (km) with and without a dipole.\nHour\nNo Dipole\nDipole\nCases\n9\n0\n-\n-\n9\n12\n183\n106\n24\n317\n143\n9\n211\n9\n36\n363\n246\n8\n48\n391\n337\n7\n60\n502\n352\n6\n72\n580\n20","30N\n80W\nGILBERT\n12 GMT 10 SEPTEMBER 88\nA - OBSERVED\nE\n- NO DIPOLE\nF\n- DIPOLE\nE\nF\nE\n2ON\nE\n-\nF\nE\nE\nA\nA\nE\nA\nF\nA\nF\nF\nA\nFIG. 1. Observed (A) and QLM predicted storm tracks (without (E) and with (F) a dipole) for\nGilbert. Initial time is 12 GMT 10 Sept. 1988. Subsequent locations are shown at 12 hour\nintervals.","3ON\nGILBERT\n12 GMT 14 SEPTEMBER 88\nA\nOBSERVED\n-\nE\nNO DIPOLE\n-\nE\nF\nDIPOLE\nF\n-\nA\nF\nE\nE\nA\nE\nF\nAF\nF\nA\n2ON\n80W\n90W\nFIG. 2. Observed (A) and QLM predicted storm tracks (without (E) and with (F) a dipole) for\nGilbert. Initial time is 12 GMT 14 Sept. 1988. Subsequent locations are shown at 12 hour\nintervals. max = 740 km, Clas = 20.3N (operational position).","JOAN\nE\n12 GMT 12 OCTOBER 88\n-20N\nA\nOBSERVED\n-\nE\nE\nNO DIPOLE\n-\nF\n- DIPOLE\nE\nE\nE\nF\nF\nA\nA\nA\nA\nA\nA\n1ON\n70W\n60W\nFIG. 3. Observed (A) and QLM predicted storm tracks (without (E) and with (F) a dipole) for\nJoan. Initial time is 12 GMT 12 Oct. 1988. Subsequent locations are shown at 12 hour intervals.\nmax = 170km, Clas = 12.3N (operational position).","80W\n24N\nZON\n16N\n16N\n40\n52W\n48W\n2DN\n16N\n18R\nIGN\n12M\n1ON\nFIG. 4. Wind analysis (AVN) at 700 mb for (a) Gilbert at 12 GMT 14 Sept. 1988, and (b) Joan\nat 12 GMT 12 Oct. 1988. Observed location of the storm is shown by a heavy dot.","ANTS\nQLM X' AXIS\nY\nDIPOLE\n+\nAXIS\nFIG. 5. Relative orientation of dipole and QLM\naxes.","2RMAX\n0\n-2RMAX\n1.00\n1.00\n2.00\n2.00\n3.00\n3.00\n3.00\n3.00\n2.00\n2.00\n1.00\n1.00\n0.0\n0.0\n1.00\n1.00\n2.00\n2.00\n3.00\n3.00\n3.00\n-3.00\n2.00\n2.00\na\n1.00\n-1.00\n80W\n90W\n90W\n80W\n16.\n20\n25N\n20\n25N\n40\n40\n42\n15N\n4.8\n15N\nC\nFIG. 6. Dipole structure for Gilbert at 12 GMT 14 Sept. 1988: (a) dipole streamfunction.\nWinds at 850 mb without (b) and with (c) a dipole. max\n= 740 km.","84W\n92W\n92W\n84W\n0.0\n24N\nH\n26.\n24N\n50\nL\n50\n-18.\nL\n26.\n0\n-7.3\nH\n30.\n0\nH\n228\n-14.\nH\n20N\n20N\nL\n-15.\n-26.\nH\nR\n14.\n60\nL\n-17.\n11.\na\nC\n0.0\n92W\n92W\n84W\n84W\nH\n4.5\nL\nH\n-.32\n4.\n24N\n0\nH\n5.3\nH\n5.2\n10\nzad\n20N\n50\n30.\n819.\n4\n108\n20N\n50\n0\nL\n-11.\n0.0\n16N\nb\nd\nFig. 7. 850 mb vorticity tendency terms: (a) total, and (b) stretching term in dipole case. (c)\nTotal and (d) stretching term in no dipole case. Units: 10-10 5-2. The location of maximum and\nminimum in horizontal advection term are shown by a heavy dot and a cross respectively in (a)\nand (c).","Z 1000MB 1968 12. OCT. 12Z FT= 36\n40N\n35N\n30N\n25N\n20N\n15N\n90\n10N\n60.\n5N\nEQ\n80W\n75W\n70W\n65W\n60W\n55W\n50W\n45W\nCONTOUR INTERVAL\n30.00\nZ\n1000MB\n1988\n12\nOCT,\n127\nET5\n40N\n35N\n30N\n180\n25N\n20N\n120\n15N\n90\n10N\n5N\nbe\nEQ\n80W\n75W\n70W\n65W\n60W\n55W\n50W\n45W\nCONTOUR INTERVAL =\n30.00\nFIG. 8. AVN 1000 mb wind forecast for Joan, initial time 12 GMT 12 Oct.: (a) 36 h (b) 72 h.\nObserved location of the storm is shown by a heavy dot.","(continued from inside front cover)\nNOAA Technical Memorandums\nNWS NMC 53\nA Semi-Implicit Version of the Shuman-Hovermale Model. Joseph P. Gerrity, Jr., Ronald D.\nMcPherson, and Stephen Scolnik, July 1973, 44 pp. (COM-73-11323)\nNWS NMC 54\nStatus Report on a Semi-Implicit Version of the Shuman-Hovermale Model. Kenneth Campana,\nMarch 1974, 22 pp. (COM-74-11096/AS)\nNWS NMC 55\nAn Evaluation of the National Meteorological Center's Experimental Boundary Layer Model.\nPaul D. Polger, December 1974, 16 pp. (COM-75-10267/AS)\nNWS NMC 56\nTheoretical and Experimental Comparison of Selected Time Integration Methods Applied to\nFour-Dimensional Data Assimilation. Ronald D. McPherson and Robert E. Kistler, April\n1975, 62 pp. (COM-75-10882/AS)\nNWS NMC 57\nA Test of the Impact of NOAA-2 VTPR Soundings on Operational Analyses and Forecasts.\nWilliam D. Bonner, Paul L. Lemar, Robert J. Van Haaren, Armand J. Desmarais, and Hugh M.\nO'Neil, February 1976, 43 pp. (PB-256-075)\nNWS NMC 58\nOperational-Type Analyses Derived Without Radiosonde Data from NIMBUS 5 and NOAA 2 Tem-\nperature Soundings. William D. Bonner, Robert Van Haaren, and Christopher M. Hayden,\nMarch 1976, 17 pp. (PB-256-099)\nNWS NMC 59\nDecomposition of a Wind Field on the Sphere. Clifford H. Dey and John A. Brown, Jr.\nApril 1976, 13 pp. (PB-265-422)\nNWS NMC 60\nThe LFM Model 1976: A Documentation. Joseph P. Gerrity, Jr., December 1977, 68 pp. (PB-\n279-419)\nNWS NMC 61\nSemi-Implicit Higher Order Version of the Shuman-Hovermale Model. Kenneth A. Campana,\nApril 1978, 55 pp. (PB-286-012)\nNWS NMC 62\nAddition of Orography to the Semi-Implicit Version of the Shuman-Hovermale Model.\nKenneth A. Campana, April 1978, 17 pp. (PB-286-009)\nNWS NMC 63\nDay-Night Differences in Radiosonde Observations in the Stratosphere and Troposhere.\nRaymond M. McInturff, Frederick G. Finger, Keith W. Johnson, and James D. Laver,\nSeptember 1979, 54 pp. (PB80 117989)\nNWS NMC 64\nThe Use of Drifting Buoy Data at NMC. David Wright, June 1980, 23 pp. (PB80 220791)\nNWS NMC 65\nEvaluation of TIROS-N Data, January-June 1979. David Wright, June 1980, 21 pp.\n(PB80 220494)\nNWS NMC 66\nThe LFM II Model--1980. John E. Newell and Dennis G. Deaven, August 1981, 20 pp.\n(PB82 156845)\nNWS NMC 67\nGulf Stream System Landward Surface Edge Statistics. Stephen J. Auer, October 1983,\n20 pp. (PB84 104314)\nNWS NMC 68\nCompendium of Marine Meteorological and Oceanographic Products of the Ocean Products\n(REVISION 1)\nCenter. David M. Feit, September 1986, 93 pp. (PB87 101812/AS)\nNWS NMC 69\nAn Evaluation of NESDIS TOVS Physical Retrievals Using Data Impact Studies. Clifford, H. Dey,\nRalph A. Petersen, Bradley A. Ballish, Peter M. Caplan, Lauren L. Morone, H. Jean Thiebaux and\nGlenn H. White (NMC); Henry E. Fleming, Anthony L. Reale, and Donbald G. Gray (Office of Res.\nand Applications, NESDIS); Mitchell D. Goldberg and Jamie M. Daniels (ST Systems Corp);\nJune 1989, 54 pp.\nNWS NMC 70\nThe Beta and Advection Model for Hurricane Track Forecasting. Donald G. Marks, January 1992,\n89 pp.","NOAA SCIENTIFIC AND TECHNICAL PUBLICATIONS\nThe National Oceunic and Atmospheric Administration was established as part of the Department of\nCommerce on October 3. 1970. 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S. DEPARTMENT OF COMMERCE\n5285 PORT ROYAL ROAD\nSPRINGFIELD, VA 22161\nE/AI22\nLibrary & Information\nServices Division, NOAA\n6009 Executive Blvd.\nRockville, MD 20852"]}