TR-183 TECHNICAL REPORT WAVE HINDCAST PROJECT NORTH ATLANTIC OCEAN DONALD C. BUNTING Evaluation Branch Oceanographic Analysis Division JANUARY 1966 U. S. NAVAL OCEANOGRAPHIC OFFICE WASHINGTON, D. C. 20390 Price 75 cents A BS Tuk A Cit, A computerized system has been developed for the produc- tion of ocean wave spectra over the North Atlantic Ocean. The spectra results are fairly close to observed conditions. By means of this system a 15-month series of wave spectra has been obtained at 519 gridpoints over the North Atlantic. Each spectrum is described in terms of the spectral energy in 12 directions for 15 different frequencies. QUANTA UNL FOREWORD In early 1960 during discussions at David Taylor Model Basin a need was cited for a world-wide climatological hindcast of ocean wave spectra. Previous experience from manual computations of wave spectra at a single point for one year had shown that this project on an ocean-wide basis and for several years would be a formidable task and probably not feasible except by some electronic computer method. Following several more con- ferences during the year the U. S. Naval Oceanographic Office was assigned the task in early February 1961 of hindcasting by machine methods the ocean wave spectra for the North Atlantic Ocean for various seasons of the year. The climatological wave spectra obtained were to be recorded by some computer processing system so that the spectra could be used in other computer programs. The basic purpose of this study, as initiated by the Bureau of Naval Weapons, was to provide a wave climatology from which carrier-deck motion spectra could be generated as a function of carrier class, speed, and heading for different geographical locations and seasons of the year. The carrier motion data in combination with separate studies to deter- mine airplane response to command signals from the AN/STN-10 Landing Control Central would then define a landing environment and the basis for the structural design of carrier-based airplanes for fully auto- matic landings. This final report gives a resume of the various phases of the task, the problems encountered with their solutions, and a summary of the final results. These results represent the culmination of about four years of determined effort by a large number of people in overcoming the many problems of a complex research project. e ODALE D. WATERS Rear Admiral, U. S. Navy Commander U. S. Naval Oceanographic Office 0 0301 O0b41lbe ec alatat Table of Contents IOI esl 6 6 oO 0 6-0 00.6 OF ONG OO GO 68a 6 List of figures and tables ......+... © Symbols and abbreviations ........ .» AtratiepeorohbVenralor, Go 9G 6 O 0 0 6 6 6 0.0006 0 60 Travelers Research Center Contract... . New York University Contract . ... . 6 « « « « Problems encountered - Travelers .... . Problems encountered - New York University . RSEUNEB 0 6 6 0 0 0 0 0 0 ba 0 6 6.0 g 6 Conclusions and Recommendations ... . jeillolsloyaceysny 9 5.06 66000006605 06 6 Appendix List of wave hindcast project manuscripts, and related papers .... . . .o © e» « reports, 32 10. ll. List of Figures and Tables The regression-wind field for 00%, 18 Dec. 1959: (Pravediers:)!- 1) so u4e: ke ee eee valneyne’ Narre xe les nae : The unsmoothed objective-analysis-wind field for O0g- 1omDec.. 1959s (Travellers). cmeu cn ahien meric imme ie LO Tables and histograms of wave spectra computed from weather ship records of a shipborne wave recorder. 12Z and 152, 22 Dec. 1959 (New York University) .... 14 Graphs of synoptically chosen wave spectra (New York University.)i %) 0% re) tepetemnemnsin onien Pomel stile: weyers M15 Comparison of proposed spectrum with original data for 20-knot winds (New York University) ........ 16 Comparison of proposed spectrum with original data for 25-knot winds (New York University) ........ 17 Comparison of proposed spectrum with original data for 30-knot winds (New York University) ........ 18 Comparison of proposed spectrum with original data for 35-knot winds (New York University) ........ 19 Comparison of proposed spectrum with original data for 40-knot winds (New York University) ........ 20 Significant wave height as a function of wind speed at various elevations from equation 7 and the drag coefficients proposed by Sheppard (New York University). 22 Wind comparisons at Ocean Station Delta (WotSe Weather Bureau) ijsiccnt 1 entre Caco ment on inh OOD Tables All-ship wind-specification equations with developmental- data-sample verification statistics (Travelers) ..... 4 Variables used for input to the screening-regression technique (Travelers). - - + + + + e+ + 2 e+ 2 e+ eee os 5 Final err table (Shows) for new spectra model ( Lockheed) . e e ° eo e e e eo e e ° e e e e e ° e e e 29 vi Symbols and abbreviations JNWP 6a exp ~~ Joint Numerical Weather Prediction gridpoints on the JNWP grid root mean square knots meters the component of the wind, east-west the component of the wind, north-south the 1000-mb geostrophic wind component, east-west the 1000-mb gradient wind component, north-south the 700-mb geostrophic relative vorticity the 1000-mb geostrophic relative vorticity millibar (pressure) the indraft angle (angle of rotation from geostrophic direction-counterclockwise rotation is positive) ocean weather ship feet significant wave height in feet wind speed in kts at elevation of 19.5 m the component spectral energy incremental angular frequency a constant with value of 8.10 x 1073 the acceleration due to gravity the component angular wave frequency in radians per second exponent e a constant with the value of 0.74 the ratio of & to Vi9.5 vii the component frequency energy in (ft )° the incremental component wave frequency the component wave frequency in cps. eyeles per second the wind speed at elevation zo the wind speed at elevation 27 the drag coefficient von Karman constant with value of 0.4 natural logarithm elevation at which Vo is determined elevation at which Vy is determined wind speed at any elevation Stereo Wave Observation Project the component frequency directional energy in (ft )* equivalent to 32.16/2WfVi9 5 incremental frequency incremental direction the direction attached to the spectral component cosine direction from the wind direction total wave spectral energy in (£t)© equal to twice the variance the spectral energy of the component after (with) dissipation the spectral energy of the component before (without) dissipation constants viil WAVE HINDCAST PROJECT-NORTH ATLANTIC OCEAN (PROGRAM 501) Introduction The idea of numerical weather prediction dates back to the year 1922 but it remained impractical until electronic data processing computers became a reality. Even then there were staggering problems that had to be solved before the computer results could compare favor- ably with older, human interpretation methods and then only for the upper levels of the atmosphere. Ocean wave forecasting on a serious basis began back in the 1940's after certain relationships among wind speeds, wind durations, and the lengths of the fetches had been empirically determined. During the 1950's prognostic wave charts giving wave heights over the oceans were being manually produced at a few weather centers for use ae ship operations and routing. The next forward step by the early 1960's was the elimination of the subjectivity of the manual wave forecasting methods by the use of electronic computers. Raw weather data from land and ship obser- vations were fed into computers and the computers produced hemispheric charts of surface pressure and winds. With the winds as the input the computers then produced prognestic charts of wave heights and directions for periods up to 48 hours in advance. However, these forecasts had a limited application because the technique described only the signifi- cant wave height and period rather than the distribution or spectrum of heights and periods (or frequencies) - a more difficult but also a much more realistic means of describing the sea surface. At about this stage in 1961 the U. S. Naval Oceanographic Office was given the task of producing a wave-spectra climatology for the North Atlantic Ocean. v) The first objectives of the program consisted of two major parts: 1. To develop a machine method for obtaining the surface wind field over the North Atlantic Ocean from grid point pressure data. 2. fo develop a machine method for providing wave spectra from the wind field as a function of geography and seasonal periods of the year. Due to the highly specialized nature of the objectives of this program it was immediately recognized that outside private research groups that had already done corresponding work in these areas would be required. The two organizations immediately considered and with whom contracts were later negotiated were Travelers Research Center to make studies of the specification of surface winds over the ocean by machine methods and New York University to perform analytical work and prepare a program for machine computations of wave spectra from the wind field data. Accordingly, technical specifications for the contractual work were prepared and these two organizations were invited to make contract proposals. Proposals from other organizations were also given consider- ation. While the two contracts were being negotiated several studies on various topics related to both winds and waves were completed by the Oceanographic Office. These reports were later sent to the two con- tractors for their information and possible use in fulfilling their contracts. Continuing studies and evaluations of contractual results were also made by the Oceanographic Office throughout the period. Publications reporting these investigations are listed in the Bibliography on page 31 of this report. Although the complete list of personnel who worked on this project would be rather lengthy, credit for the major accomplishments should go to the following: Travelers Research Center Mr. Albert Thomasell, Jr., Research Scientist Mr. James G. Welsh, Research Associate New York University Dr. Willard J. Pierson, Jr., Professor of Oceanography Dr. Leo J. Tick, Senior Research Scientist Mr. Lionel I. Moskowitz, Graduate Assistant Lockheed-California Company (N.Y.U. Subcontract) Dr. Ledolph Baer, Principal Investigator Travelers Research Center Contract A contract was executed with Travelers in February 1962 to make a feasibility study for determining by machine methods a surface wind field over the North Atlantic Ocean. The input data for the work done on this contract consisted of the following: 1. Digitized sea-level pressure grid data on magnetic tape for the North Atlantic Ocean within the time period April 1955 through March 1960 obtained from the U. S. Air Force Project 433L. 2. Digitized surface to 700-mb mean temperature grid data on magnetic tape for the same period, also from Project 433L. 3. Ocean Station Vessel surface synoptic weather data on punched cards for the same period for ship locations B, C, D, and E. 4. Seasonal charts of air-sea temperature difference distribution for the North Atlantic Ocean. 5. Monthly charts of mean sea-surface temperatures for the North Atlantic Ocean. 6. North Atlantic surface-weather ship reports for 15 December through 2/7 December 1959. The U. S. Air Force Project 433L data consist of manually-read sea-level pressure values and pressure height and temperature data for the 700-mb level on a diamond grid network at the JNWP gridpoints for which points i and j are both odd or both even. The data were ex- tracted from subjective synoptic weather map analyses by the U. S. Weather Bureau. Travelers checked all the data for errors, made corrections, and, by interpolation from the diamond grid, computed values for all the standard JNWP gridpoints. The data in corrected form are on IBM 7090 magnetic tapes for the period April 1955 through March 1960. Two methods were investigated by Travelers for the development of a wind-specification technique. The first method used the screening- regression technique to generate wind-specification equations of which six equations (Table 1) using 49 different variables (Table 2) were generated and tested. Winds from these equations are regression winds in this report. The second method, which was much more difficult to obtain, was undertaken to try for improvement of the regression winds. It consisted of an objective analysis of winds using the regression winds as an initial guess and then actual ship wind observations (assuming them to be correct) for correcting the initial guess. These wind estimates are called objectiveeanalysis winds in this report. In addition, geostrophic and gradient winds were computed and evaluated for comparison with the regression winds. TABLE. 1 Alleship windespecification equations with developnent-data-sample verification statistics* (Travelers) Wind-specification equation : Accumulative % — - ; explained: var tance Residual error Wind element Coefficient — Variable | +1.24052 x 10! +6.38537 x 1071 +1.42367 x 102 7.4 knots 42.80490 x 104 +2.66762 x 107! +7298937 x 10-1 é 8.5 knots -3.46355 x 107! +9.30208 x 104 -3.45584 +7.82943 x 107! +2.41837 x 10-1 - 8.6 knots +1.23438 x 109 +1.96295 ; -3. 79605 x 10-2 +3.05386 x 10-4 +3.49295 x 10? -2.79597 x 1079 +1.93047 +6.53799 x - 3.53884 x 42.8763 x -2.81406 x +1.54270 -1.56979 x 1010 #17 cases, no weak rs no measured airs sea, or poo paaannae var lables. 12 = 15-555 0, = 54a = eS ae Variables used for the input eee oe il SOO a technique (Travelers) _ ; ; : ‘| Sea-surface temperature ‘Derived from hour: OOZ = 0; 12Z = 1 Variable a eo a n ° n sin (6-'n month) Derived from month: Jan. = 1; Feb. = 2; etc. cos (67!2 month) Derived from month: Jan. = 1; Feb. = 2; etc. A sin (6-'9 month) 2 cos (67! month) @ sin (6-'m month) @ cos (67'm month) FER R | iil c 2A o n mn Ox Ta = Ts s Ge me Tee (FP T7-10 Mean virtual temperature of the 700-1000-mb layer: T7-10 = 1-8 [0.029197 (Z700 - Z1000) - 255-41 512 T-10 ; 12-1 Clr hr-1 ue eee £700 700-mb geostrophic relative vorticity*t: C700 = af"! B Z700 *f = Coriolis parameter = 22 sin 6. TAI! space derivatives are computed by centered finite-difference approximations over 2 grid intervals. °F 25: 12-hr_ 700-1000-mb mean virtual temperature change: 812 T7210 = 09525546 (8)2 2700 - 812 21000) 1000-mb geostrophic relative vorticity*t: b1000 = af! % 24600 A 2 9 TABLE 2 (continued) © eee Components of monthly mean sea-surface deg ft-1 i deg ft-1 | f+ sec-1 Vg ft sec-1 thee ft sec-1 Vor ft sec-1 Kyf-! Ve, + Vgr - Vg = 0 UAZ ft sec-1 1000-mb isallobaric-wind components* t+ on ft sec Waz = -9f-2 Yp (021 000/8t) Ver Gradient wind speed f Gradient of mean virtual temperature in the 700-1000-mb layer ¢ temperature gradient f Components of mean virtual 700-1 000-mb temperature gradient t¢ 1000=mb geostrophic-wind components*ft: Vg= gf-1 kk x Vp 21000 - 1000-mb gradient-wind components*tt: ‘ ; 1000-mb advection of vorticity by geostrophic wind*tt 700-mb advection of vorticity by geostrophic wind¥tt ‘Advection of monthly mean sea-surface temperature by 1000-mb geostrophic wind*ft Advection of mean (00-1000-mb temperature by the mean 100-1000-mb geostrophic wind* ++ Curvature of the 1000-mb height contourst¢: eZ au , &2 (er eZ OZ ¥Z _ Be By aye \x) 7 & OY Sy : eee: H Ky Vo. ¢71 ft sec7! Cyclostrophic term of gradient-wind equation* +t H "gr Ik. (WT. x VpT7-10)| (°F )Ee Ft-2 A stability parameter tit ; *f = Coriolis parameter = 2Q sin Oe TAI| space derivatives are computed by centered finite-diftference approximations over 2 grid intervals. ee ‘ TAII vector components are referred to the earth's geographical coordinate system; x is positive eastward and y is positive northward. : 6) nw |. To obtain the regression winds three screening-regression runs were made resulting in three sets of six wind specification equations. The first run used ship B data only and was used primarily as a test of machine programs. The second run used data from all four weather ships and provided the equations subsequently used for specifying the North Atlantic wind field. The third run was made to test the usefulness of the measured air- and sea-temperature functions. From the results of all three runs it appeared that the best wind estimate had a rms error of about 8.5 kts. for each wind component. The wind speed was deter- mined mainly by the geostrophic wind speed modified slightly for curvature effects. The wind direction was given by the geostrophic- wind direction, rotated counterclockwise 15555 It was found from the third run that the measured air-sea temperature difference did not demonstrably show itself as any aid in specifying the indraft angle. Hence, further studies with computed variables that are merely approxi- mations of this measured quantity were considered unnecessary. Based on all the results of the three runs it was decided by Travelers to use the following u- and v- wind component equations com- puted from 4,417 samples for specifying the North Atlantic wind field: (1) u = 0.266762+ 0.798937 Uz -0.346355 V,.+ 9.30208 X 1G cag (2) = -3-45088 + 0.782943 Vv, + 0.241837 U, +1.23438 X HOP pei (3) @ = 15.5490° These three equations then specify the regression winds. A test sample wind field was computed with these equations for 17-18 December 1959. The results (Fig. 1) show two large extratropical cyclones moving northeastward across the Atlantic Ocean at approximately 20 kts. In the five separate fields computed, the continuity of the cyclones was ex- cellent, the wind pattern well organized, and the wind speeds reasonable. The large grid mesh, however, causes small scale features, such as multiple centers, to disappear and frontal shear lines have been quite blurred for the same reason. In view Of the rms error of 8.5 kts. for each of the components of the regression winds it was decided to test the possibility that a better wind specification could be obtained from the direct use of ship wind observations. Objective-analysis winds were prepared for the period 15-27 December 1959 from North Atlantic surface-weather ship reports which had been manually checked for errors. In a large-scale effort a program would have to be developed whereby this could be handled by computer. The initial-guess wind field for the objective- analysis winds was the regression wind. The ship observations were integrated with the regression winds by a conditional relaxation anal- ysis method and then verified by the areal-mean-error method. The grid- point values were determined by extrapolating from or interpolating between locations at which observations of the winds were available. The procedure required that the gridpoint values satisfied Poisson's equation subject to the constraints imposed by the observations and an jog Bee eee Tn a Figure 1, The regression-wind field for 00Z, 18 Dec. 1959 (Travelers) | arbitrarily defined set of boundary values consisting of the regression winds along the grid perimeter. The ship observation locations usually lie randomly within the gridblocks. The difference between the observed wind and the regression wind (initial guess) was translated to the nearest gridpoint and used to correct the initial guess there, which then became an internal boundary point. The Poisson's equation was solved by a relaxation procedure throughout which the boundary values remained unchanged. In general the windfield which satisfied the Poisson's equation con- tained unreal data and required a certain amount of smoothing to elim- inate small-scale wiggles from the analysis. The degree of smoothing can be variable and several values of the smoothing operator were tested. The goal of the objective-wind-analysis tests was to determine the proper smoothing factors that resulted in minimum error. Twenty-six separate wind fields were analyzed by the conditional relaxation analysis method with the regression winds serving as the initial guess and the Laplacian of the initial guess serving as a forcing function. Each analysis was smoothed and verified several times. The minimum analysis error occurred in the totally unsmoothed analysis (Fig. 2) as would be expected but the field was quite erratic. A comparison of the regression wind errors with the objective-analysis wind errors showed that the direct use of wind observations does reduce the wind specifi- cation errors but only near the location of the wind observations. There is but slight or no improvement elsewhere. Three objective-analysis wind fields were obtained corresponding to the same times as the regression wind fields. The main discernible difference between them was that the regression winds specified larger areas of strong winds in the vicinity of the cyclone centers than did the objective-analysis winds. Otherwise they were quite similar. The simplest method for specifying wind over the ocean is to compute the geostrophic or the gradient wind. As a third approach to see if these might be better than either the regression or the objective- analysis winds, geostrophic and gradient winds were computed from the sea-level pressure gridpoint data at Ships B, C, D, and E and compared with the ship observations. The winds were computed from centered finite-difference approximations over two JNWP grid intervals at each of the four gridpoints surrounding the ships. By curvilinear inter- polation a value was then computed at the ships' locations. The results of this showed that the geostrophic and gradient wind errors were about 2 kts. higher in all categories than the regression winds. Thus, they were judged inferior to the regression winds. To evaluate the relative quality of regression winds with objective- analysis winds one should consider not only the verification scores from tests but also the gridpoint wind fields. Since strong winds are con- sidered more significant for ocean wave forecasting although they usually cover only a small area of the map, care must be taken in interpreting the verification scores. The scores are space averages Figure 2. The unsmoothed objective-analysis-wind field for 00Z, 18 Dec. 1959 (travelers) aslo). of all the wind errors both strong and weak, so they reflect chiefly the errors of the less important and more abundant weaker winds. For a given wind field it would certainly be possible that a minimum error score wind would not specify the strong winds as well as a larger error score wind of some other type. For the objective-analysis winds, the strongest winds were given by the unsmoothed analyses. The effect of smoothing, while showing improve- ment in the error scores up to a certain point, was to attenuate the strong winds, the greater the smoothing the greater the attenuation. The regression wind fields specified winds at least as strong as and often stronger than those of the unsmoothed objective analysis winds. Travelers recommended that the regression winds, the unsmoothed objec- tive-analysis winds, and the smoothed-objective analysis winds all be subjected to a wave spectra test to see which one most exactly pro- duced the observed spectra. New York University Contract In April 1962 a contract was executed with New York University with a subcontract to Lockheed-California to perform research in two phases: 1. To develop and verify techniques for forecasting directional wave spectra by means of computers and based on synoptic reports over the North Atlantic Ocean. 2, To produce a wave-spectrum climatology based on 12-hourly sea- level pressure data for the North Atlantic Ocean during a 5-year period beginning April 1955 and ending March 1960. The data used in performing the work under this contract consisted of the following: 1. Approximately 800 shipborne wave-recorder records from OWS Weather Explorer and OWS Weather Reporter provided by the National Institute of Oceanography, Great Britain. 2. Digitized sea-level pressure and surface to 700-mb mean temper- ature grid data on magnetic tapes for the North Atlantic Ocean from April 1955 through March 1960 obtained from the U. S. Air Force Project 433L, error checked and corrected by Travelers Research Center. 3. Ship surface weather reports over the North Atlantic Ocean in Card Decks 116, 117, and British reports for the 15-month period January through December 1959, December 1958, November 1956, and December 1955 On magnetic tapes obtained from the National Weather Records Center, Asheville. The subcontract between New York University and Lockheed-California Company was executed in mid-1962 for the purpose of providing technical support to the total project leading to an ocean wave=spectra climatology 11 for the North Atlantic Ocean. The original objectives of the subcontract were to: 1. Compare the results obtained using the Neuman spectrum with those using the Bretschneider and Darbyshire spectra. 2. Optimize the grid size and time-step length. 3. Consider the effects of sea-air temperature differences and other stability and atmospheric turbulence criteria on the effectiveness of the wind in generating waves. 4, Build in an automatic correction capability so that any available wave observations will continually correct hindcasts used as initial conditions in the forecast. After the project had started several problems previously unfore- seen became evident so that a modification of the objectives was necessary. Priority was then given to improving the spectrum model, preparing a new wave growth function, and adding the effects of dis- sipation to the program. The point of departure for starting the subcontract was the previous research on machine comp Seton of wave spectra over the North Atlantic Ocean performed by Baer for a doctoral degree at New York University. The data used for preparing a new growth function were the spectra com- puted at New York University from the British shipborne wave records. Various changes in machine programming to produce a better fit of spectral shapes did not require additional data. A complete spectral analysis was made for a selected 460 out of the approximately S00 shipborne wave records and the results were published in both tabular and graphical form. The raw spectra of all 460 records have been placed on magnetic tape and are available for any further research. The four main locations in the North Atlantic where the data were taken are as follows: Position A (62°N, 33°W) Position I (59°N, 19°W) Position J (52.5°N, 20°w) Position K (45°N, 16°w) These are the on-station positions for the weather ships in the eastern North Atlantic Ocean. Except for a few records, each was of 15 minutes duration and was reduced to a time series of 600 points. This series was analyzed by an electronic computer so that the energy spectrum was estimated at 60 points over the frequency range from zero to 0 37° eycles per second using procedures given by Blackman and Tukey( 9 Final corrections and smoothing were then made on these estimates to give the corrected spectrum in units of (ft)©. These values were tabu- lated for each wave record and the corrected spectrum plotted as a histogram or a regular graph (Fig. 3). The dates of the various wave records ranged from April 1955 to September 1961. Extensive use of these wave record spectra has been made for deter- mining estimates of the power spectra for fully-developed seas at various wind speeds and also to develop a new wave-model equation. A group of synoptically chosen spectra was analyzed to determine the mean spectra for speeds of 20, 25, 30, 35, and 40 knots. Each situation used was chosen so that both fetch and wind duration would have produced a fully- developed sea condition according to various theories. A nested family of wave spectra was obtained for these five wind speeds (Fig. 4) whereby the frequency of the maximum energy was inversely proportional to the wind speed. Also the significant height relationship to the wind speed was found to be (4) Hyg 0.0182 Vise From statistical tests it was further found that wind speed alone at the location and time ot the wave condition did not specify the correct sea state. Rather the spectrum was e function of wind duration and fetch as well as wind speed. Using the data for the spectra of fully-developed seas at wind speeds from 20 to 0 knots a new non-directional waveespectrum model was devel- oped. Over the most important range of frequencies that define the total variance of a wave spectrum, the proposed spectral model produced a better fit for the range of wind speeds from 20 to LO knots than some previous models (pips, 5, O, Fo Ss 9). It was noted, however, that the proposed new spectral model was highly sensitive to wind speed, since only slight variations of speed had large effects on the shape and position of the spectral curve. This spectral model is a compromise among various other proposed spectra and has similar features to many of them. The equation for the proposed spectral form is given by a, 4 d. 2 = eat, (5) S( W )dw = Be. ex [- eC) o where Q, ie OS Since A and é are dimensionless any consistent set of units can be used in the equation. If wind speed is in knots, frequency in cycles er second and component energy in (ft)¢, the equation reduces to (GAG (a)ar E O.CLOTOGe a fi63.e1 | Hae : °V19.5 This form of the spectral model will undoubtedly need further refinements when additional accurate data become available. 13 SMOOTHED HINDLASTING SPECTRA COMPUTED MAKCH 1963 10.8 RECORD 36.1 UPPER HGT. Ble4 LOWER HGT. +0230 WIND SPEED CORR-FI42 UPPER 21350 +2469 +1430 22636 +2500 +4608 +3250 «5991 +2010 3705 +1140 «2102 +5850 1.0783 2.2549 4.1560 4.2804 7.8893 T1574 13.1922 11.7723 21.6981 13.0457 24.0451 8.6476 15.9368 4.5546 6.3949 4.1046 7.5654 4.4007 6.1111 303218 6.1225 1.86749 3.4558 1.2026 2.2162 1.4869 2.7368 1.6874 3.1102 1.2779 2.3553 26618 1.2199 3950 ©7280 23406 96277 29lh ©5365 +2970 35474 +3388 +6265 23273 +6033 3358 +6190 23126 +5TOL 2053 +3784 22392 +4408 23344 ~6163 = 3066 +5652 «3267 +6021 23386 +6241 «1898 +3498 +0898 +1655 1417 +2612 +1760 +3245 1652 «3044 =1415 «2607 +1528 +2815 +1936 35608 42237 34126 +2165 «3990 2465 4542 +3706 .6830 34355 +8026 «5720 +2067 -O3LL ~1398 +1548 +2853 20973 «1794 +0000 +0000 +0000 «0000 +0000 .0000 +0000 .0000 +0000 +0000 9.7 RECOKD 38.6 UPPER HGT. 93.0 LOWER HGI. -O717 WIND SPEED CORR.FT.2 UPPER +1103 «2033 +3263 6016 +5763 1.0622 +6033 1.1120 +5503 1.0143 +3543 6530 +3313 .6107 34343 2.7268 8.2962 11.0832 9.5225, 8.3266 7.0454 5.1365 4.7106 3.8719 421336 3.6501 2.0167 29373 1.0510 1.2462 1.0486 «8862 28909 1.0533 1.2261 1.1678 29231 4673 -2479 +4840 ~5037 +2809 +1963 +2942 =3782 +3058 +2397 +5295 +8665 +8907 +5920 1.0911 =3512 © 6585 +1576 «2906 +0000 .0000 +0000 0000 +0000 0000 +0000 0000 20472 0870 21672 42713 22691 «4959 24319 «7961 =4132 «7616 20180 = 0331 +0000 .0000 +0000 0000 +0000 0000 = .0000 .n000 DATE = 22/12/59 AV. To HOUR = 12 SIGeHGT. = TOTAL OF =122 CORK. VAR. = NOISE LEVEL = Ho FRE. UNIT#rT.2 FILTERED -NUISE 0 .00v «1580 +1580 «1350 1.006 +1660 +1660 «1430 2.011 +2730 +2730 © «2500 3 O17 #3480 «3480 «3250 4 022 22240 +2240 +2010 5S .028 «1370 21370 «1140 6 .033 23983 23963-63713 7 .039 1.7213 1.7213 1.6983 8 049 306175 3.6175 3.5965 9 .050 Oe47L7T (624717 6.4487 10.056 11.0976 11.0976 11.0746 LL 061 12.5971 12.5971 12.5741 12 .067 8.4539 8.4539 6.4309 13.072 424622 444622 4.6392 le .078 3.9088 3.9650 15.083 4.2085 4.1855 le .089 3.1470 3.1240 L7 094 1.7222) 1.6992 18.100 1.0792 1.0792 1.0562 19.106 1.2806 1.2808 1.2578 gO sill 1.3971 1.3971 1.3741 2. oLLT 1.0200 1.0200 ©9970 22.122 +5160 +3160 4930 23) 2128 «3030 «2800 24 «2133 2520 «2290 25° 2134 +2080 1850 26 2146 +2010 «1780 27 «150 «2140 +2140 1910 28 «156 +1960 +1960 «1730 29 .16L +1890 +1890 =. 1660 30 2167 = 1670 +1670 «1440 3L 172 «1Llo +11L0 .0880 32. 178 «1180 +1180 0950 33.183 +1460 +1460 21230 34 189 +1270 +1270 ©. 1040 35 2194 +1250 =1250 .1020 36-200 +1200 +1200 .0970 37.206 «0728 +0728 0498 36.211 20465 +0445 -.0215 39° 217 +0539 +0539 .0309 40.222 +0627 +0579 0349 41.228 «0523 =0527 © .0297 42.233 0434 +0460 0230 43.239 +0448 +0454 0224 4& +244 ~0405 +0485 0255 45.250 +0522 +0494 40265 46.256 +0449 +0459 = 60229 47 «261 +0416 +0463 = 0233 48.267 -0570 +0542 0312 49.272 -O6LL +0555 0326 50 278 +0430 +0435 .0206 5L 2283 +0271 '.0295 .0066 52.289 =0210 +0238 .0009 53.294 +0263 +0264 0034 54 .300 +0321 =0291 0062 55 306 +0261 +0264 00346 56 .31L 0212 -0214 0000 57 317 +0173 ~0179 0000 58 2322 +0159 -0170 .0000 59.328 -OL9L +0185 .0000 60 .333 +0199 -0195 0000 SMOOTHED HINUCASTING SPECTRA COMPUTED MARCH 1963 DATE = 22/12/59 AV. T= HOUR = 15 SIG.HGT. = TOTAL DF =163 CORK. VAR. = NOISE LEVEL = HH FRee UNIT=FI.2 FILTERED -NOISE 0 .000 +1820 «1820-1103 1.008 3980 +3263 2.0L +6480 =5763 3.017 +6750 +6750 6033 4 022 +6220 +6220 © 5503 5 +4260 +4260 © «3543 6 +2820 +2820 «2103 7 =3988 =3988 3271 8 2.3616 2.3616 2.2899 9 725464 725464 7.4747 10 10.4980 10.4980 10.4263 lt 9.2500 9.2500 9.1783 12 8.1897 8.1697 8.1 LO 13 6.9386 6.9386 6.8669 14 5.6142 5.6142 5.5425 15 4.5520 445520 4.4403 16 3.7131 367131 7 3.8179 3.8179 18 3.2780 3.27A0 19 1./4800 1.7800 20 +8350 +8350 2. «BOLT «BOLT 22 1.0000 1.0000 23 +8150 +8150 24 26690 +6690 25 26380 +6380 26 +7030 +7030 27 +7630 +7630 28 +6890 +6890 29 «5280 «5280 30 +2670 +2870 3h -1780 +1780 32 +2640 +2640 33 =?570 +2570 34 +1670 +1670 35 +1330 +1330 36 +1560 = 1960 37 +1710 +1710 36 +1450 = 1650 19 +1240 -1240 40 -1640 «1767 a 2550 +2275 42 +2360 +2165 43 = 1340 +1585 44 +1200 +1188 45 -0962 -0903 40 +0490 +0602 47 +0466 =0512 46 +0626 +0600 64 +0684 +0685 50 20747 +0748 oL +0615 -0803 52 -0636 +0456 53 -0937 -0913 54 «0443 «ObR2 55 +0704 +0123 46 +0542 -058T oT +0954 +0573 56 +0634 20613 oy) 20626 20616 60 20579 0602 - Figure 3. Tables and histograms of wave spectra computed from weather ship < records of a shipborne wave recorder, 12% and 15Z, 22 Dec. 1959 (New York University) +0060 .0000 «1691 +2157 +2004 +2129 +1953 =2080 «2156 1208 +0572 +0902 eLL2L +1052 «0901 «0973 1233 21425 1378 +1569 22300 22773 =1976 0714 +0108 20483 0986 +0620 «0000 -=0000 +0000 +0000 -0000 22712459 js 3 22/12/59 4 JHB SMOOTHED HINUCASTING SPECTRA COMPUTED M4RCH 1963 SMOOTHED HINDCASTING SPECTRA COMPUTED MAKCH 1963 AVERAGE = -0000E+00 HOUR 12 AVERAGE = ~0000E+00 HOUR#LS 1-46¢0L 1.68€°0R LevZECOR 2.hGteOk 2.43t¢31 1.20E¢0L 7Te21E+00 9.62E*00 2-09E-O7 2.4000 4.81E+00 Le23E°OL L.43E¢0 1.63E°0L 1.8601 2.06E¢01 1.02€¢01 6.-OLE-08 2.06E*00 %.U9E#00 6.13£+00 8.17E¢00 D0) O00) Gee) 0.0) Ch 0) Oss 0108 DUC Us UsCnO Cs 0'O) OV Os Ons DsOnCuOstathecnQnp Ou0U0e0 Utd Oue0 UO dnd. 0100-0 1h rivet CEACOCTLECC ACE Mt Ilte Wit itt TLLOEE AELteouts Iitett LUUTQniie mt TRCUELALTAULECUUROLELCREELCEEUEEE CULLLELLUCLELeEt CUULECLGTOLULIEE TUCCEROCCUEELEL — UIiteit - Ulfelt ee ° ee . —-See- tee~me reruns CO “ ° = e ° ° NON oOOoDN0 0000 000 « 4 2.16€¢DL 2.60te01 BoG@ECOR 1.92€°01 8 c oo. t LZ Gc T.21E+00 9.62t#U0 1.20E°OL 1.466E°08 2.40€+00 4.816400 a 2.09E-uT o € F I J « L-OZE*OL 1.23E*OL 1.43E+01 1.63E40L 1-86E+01 2.06001 c 6-O1E-08 2.04£400 4%.09&+00 6.13£+00 6.17E+00 o (AqTSieatun YI0Z MeN) erzoeds ozo col ie) eee ee OACM uesoyo ATT eOTydouks go sydeip °H -eanaty o1o soo ers fo}] (0) SLONY O02 SLON™ SZ SLON O€ SLON GE SLON Ob gf!) 15 (AqTSiteatun x0 non) Spuya 7OUN-OZ AOF SYep TeUTSTIO yYTM umzzOeds pesodord yo uostreduog °¢ eae O8I/H = 3} H 9€ ve ce o¢ 82 92 ve oe O02 8! 91 5 a a eS ee oh O) a e pv: Le — ON i" oot 8 —~e el 91° Oc “SJTFUTT eouepTjuoe 446 pue ¢ juasaeider sautT peyseq bz: felt) jo SE ULI. NI St GNV O81 /(7 *H)=3 OL 08 1/(=- H)= } WOYS WNYLIIZdS JHL 40 8c" TWHYOSLNI FHL SI G3LL01d 3JNIWA) SLYO2 I3INIWA 1VYLIIdS — He G3SO0d0YUd -SL» S‘'6| O—O G3SOd0Y¥d - SLY O2 *—>" gjouy ut paeds pulm Equivalent Beaufort number a Figure 11, Wind comparisons at ocean station Delta (U.S. Weather Bureau) hindeasts. In this way the poor initial conditions improved as time duration became a part of the output and as the swell was gradually introduced into the computations. In addition to this problem, results obtained from the original machine program indicated that there were the following problems needing solution: 1. A better spectral model 2. A better growth function for 3-hourly intervals 3. A proper assumption for the nature of the high-frequency end of the spectrum 4, A proper dissipation function for the spectrum, Taken together these four problems would make a formidable task for any individual effort but by a team assault they were all finally solved so that the end product gave acceptable though not perfect results. After having tried several different spectral models, the new non- directional spectrum developed at New York University was programmed and showed very good results for the Eastern North Atlantic Ocean when com- pared to the wave observations taken by shipborne recorders on weather ships. Also later tests with weather ships wave observations in the Western Atlantic and with wave staff observations at Argus Island gave similarly good results. To determine the proper growth function it was first necessary to use an equation for the maximum spectrum that could be generated, assuming an infinite fetch, eae duration, and certain directional effects found in other studies.\/) The form of the equation used was (9) A°(f, 6) = ; ch exp -Co0" J Azad.o+ 0.5+0.82 exp (-0.50"')] eos(0.0349065 B,)+0.32 exp (O,50-") cos (0.069813 Pa for 90° =| 6,| and zero otherwise and where D = 19.08 - direction from the wind direction LS Af = incremental frequency A@ = incremental direction f = frequency in cycles per second Vio.5 = wind speed in knots at 19.5 m height C] and Co = constants To compute the growth function, a curve fitting program was designed for the computer so that the end product was a 3-hourly final growth table showing wind speeds at 2-knot intervals from 40 to 60 knots versus the E-values (Table 3). Here E is in units of (ft)© and represents a number twice the variance of the spectral density. The new growth assumes that a partially developed spectrum has the same shape as the fully-developed spectrum for the lower wind speed that would produce the same significant height waves. This assumption yields a much more reason- able spectrum during periods of wave growth and propagation than do other assumptions. Another study at New York University led to the conclusion that the high-frequency end of the wave spectrum could be simply represented within the limits of forecast accuracy as a function of wind speed alone. Thus, the machine program could be modified to assume full development for all waves with periods less than 7 seconds. A further consequence of this idea was the assumption that all waves with periods below 7 seconds dissipated immediately if the wind decreased. With these assump- tions the machine programming was considerably simplified. In a test of the original machine program it was found that the waves at a point did not dissipate as fast as they should because the pro- grammed dispersion was too low. To remedy this an empirical dissipation function was developed and tested. The form of the dissipation function (10) as (2, @ ) = ae (z, @) exe [es | C,) where AS(f, @ ) = spectral energy of component after (with) dissipation AG(E, @ ) = spectral energy of component before (without) dis- sipation f = center frequency of spectral component 6 = center direction of spectral component C3 = 345.0, a constant total energy in spectrum le - wind direction/ E “Sf Aa(f, 6 atae and K(/6) < 75°) K(75 < J@,|$105°) = 1.5 K(105& j@] $135°) = 3.0 K(1350< 181 € 165°) = 4.5 K(165 <(B/ $180°) = 6 By using this empirical dissipation factor a solution was found for the problem of shifting wind directions and decreasing wind speeds. Thus, when the original program had been modified by using a new spectral model, a new growth function, a new dissipation factor, and a specification only for the long period end of the spectrum, then the results compared favorably with wave observations in most of the situations. ots Results Since the project began in 1961 a total of 27 reports, papers, and manuscripts have been written as a result of the hindcast project, all except one by project or contract personnel. These are listed by authors in chronological order at the end of this report. The major purpose of the project - to produce by machine methods a wave spectrum climatology over the North Atlantic Ocean - has in general been realized. A series of magnetic tapes containing four times daily wind directions and speeds and wave spectra hindcasts for each of 519 gridpoints over the North Atlantic Ocean for 15 months, including the entire year 1959, has been made available. A new spectral form for fully-developed seas at wind speeds from 20 to 40 knots has been developed. This spectral form appears to be an improvement over pre- viously proposed spectral forms. New machine programs have been devel- oped for the production of wind fields from pressure gridpoint data and ships weather reports. A better understanding of wind speed profiles and drag coefficients has been indicated from the studies made. A new, improved machine program for producing hindcasts or forecasts of wave spectra at gridpoints over the North Atlantic Ocean has been made avail- able. A study of the representativeness of the weather over the North Atlantic for the year 1959 compared with seven other years from 1957 to 1964 indicates that the 1959 weather was generally normal except for the month of December which was above normal but not anomalous. Conclusions and Recommendations 1. The most serious problem in the present production of accurate machine hindcasts or forecasts of wave spectra appears to be the inability to produce adequate wind fields. Over large expanses of the oceans there is a complete lack of weather observations and even in the shipping lanes, the ships may often be poorly spaced. Discontinuities of the winds, such as along fronts, present a special problem since computer analysis techniques tend to smooth out the discontinuities. 2. The procedures for the observation of winds and waves should be im- proved and standardized. The winds should be automatically recorded at perhaps several different elevations on weather ships. Anemometers should be located so that the effect of the ship on the wind is elimin- ated. For various types of ships a standard level above the sea surface should be used for the height of the anemometer, such as 10 m or 19.5 m depending on the ship size and superstructure. Shipborne wave recorders should be installed at least on the U. S. weather ships and possibly on some of the Navy ships so that more adequate wave data can be obtained in the Western North Atlantic. The winds should be recorded and averaged for the same length of time as used for the wave observations, say 15 or 20 minutes. A measurement of gustiness, if any, should also be included in the observation. The length of the wave records should depend on the wind speed. For example, when the wind speed is over 35 knots at an elevation of 19.5 m, it would be advisable to take continuous recordings of the waves. . ry TABLE 3 Final growth table (3-hour) for new spectra model (Lockheed) WIND SPEED (KNOTS) EZERO 10 12 14 16 18 20 22 «24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54. 56 58 60 64 68 72 80 0 0.5 Wy eS 1.7 Weed 735) ty fH) 5.3 6, 6.5" 7 8 ) °) ") Y 9 7, 9 10 1 ee! 162224525 rn} 0.5 lA) teZ/ he? 250 Oe Se/, 4.5 5.3 6) 6.5) 7 8 9 9 9) 9 oe ) 9 10 1 12 SIA G22 2A eS 2 We alas) iNeed Wace 7215) Or ecele eae. 5.3 Cy es) 7/ 8 9 ") 9 ") 9 9 9 10 1] 122 SE AS Ges 22) 2A 2S 4 eo he sy? 2.5 SEL © ola) 5.3 @) (iq8) 7/ 8 9 9 9 9 9 9 9 10 1 U2 AN Eke EX) 8 1.7 eh 725) 4} Gh a7/ 4.5 5.3 Ge G0) 7, 8 9 9 y 9 9 ”) 9 10 1] 12 1S 4 S22 2A 25 12 3c 3.5 5.0 is 8 9 O59) Poe) P55) 110) 1 11 12 14 Sen zi) k0) ee sh) 18 3.5 4.0 8 10 9 il 1] 12 Is 14 18 819 20 202) 2 22 OS 2S 25 4.0 Cy —1K0) 10 12 13! 15 16 Ir Ail 28) 23 24 24 25) 25) 28) 34) 386) 87, 32 6 6 8 10 13 15 WW IL A 2) 26 27 40 6 6 eli 15 WP 7X5 PKs) 7K? 3] 32 50 6 6 10 14 20) 24529) 31 32 34 34 60 6 8 1h 19 2455 0 34585 36 37 75 8 10 [Stn 22527 CO SS 40 42 95 0 } Ko) 45 47 110 0 10 16 22 30 41 48 50 130 10 14 «21 38 50 54 150 10 12 [Bi 32 42 52 180 12 14 25 36 49 210 14 +20 29 40 240 15 22 31 270 16 26 300 16 20 330 20 360 20 390 420 450 500 550 600 650 700 750 800 900 K ? “All units are (£t)~ 29 . Sips q 36 Evaluations of the newly developed spectral form, the various new machine programs for integrating ship observations with an initial guess regression wind, for handling wave growth and decay, for specifying the wave spectrum at high frequencies, and for interpolating between 12- hourly observations all show that the results agree with observed wave spectra within the expected accuracy in view of the many variables in- volved. This is not to say that further improvement is impossible because there is still much work remaining to be done. It is believed that the 15 months of wave spectra which have been obtained for 519 points over the North Atlantic Ocean represent a definite step forward and the machine techniques used in obtaining these data are a break- through in this field of endeavor. Bibliography (a) (2) (3) (4) BAER, LEDOLPH - An experiment in numerical forecasting of deep water ocean waves. IMSC-801296, Contract NOnr 285(03), Office of Naval Research. Lockheed Missile and Space Company, California. 1962. BLACKMAN, R. B. and J. W. Tukey - The measurements of power spectra from the point of view of communications engineering. Dover Publi- cations, New York. 1958. BUNTING, DONALD C. - Errors in significant heights and E-values of ocean waves from incorrect wind speeds. Informal Manuscript Report ‘No. 0-54-62, U. S. Naval Oceanographic Office. September 1962. (Unpublished Manuscript) MOSKOWITZ, LIONEL I. - A further evaluation and comparison of errors in significant wave heights and E-values for fully developed seas based on errors in wind speed. Informal Manuscript Report No. 0-60-63, U. S. Naval Oceanographic Office. October 1963. (Unpub- lished Manuscript ) SHINNERS, WILLARD - Comparison of measured and estimated wind speeds at sea. U. S. Weather Bureau, Washington. 1963. BUNTING, DONALD C. - Studies on the variability of surface winds. Informal Manuscript Report No. 0-52-63, U. S. Naval Oceanographic Office. October 1963. (Unpublished Manuscript) PIERSON, WILLARD J., JR. - The directional spectrum of a wind generated sea as determined from data obtained by the stereo wave observation project. Meteorological Papers Vol. 2, No. 6. New York University, New York. 1960. Appendix - List of wave hindcast project manuscripts, reports, and related papers in chronological order. All are unclassified. BUNTING, DONALD C. 1961. Comparisons of wind generated wave spectra and their parameters. Informal Oceanographic Manuscript No. 2-62 Use Naval Oceanographic Office, Washington, D. C. (Unpublished) 1961.