<TEXT N="Bab5800"> <BODY> <DIV1> <P><PB REF="00000001.tif" SEQ="00000001" RES="600dpi" FMT="TIFF6.0" FTR="TPG" CNF="842" N=""> THE UN I VE RS I TY OF MI C H I GAN COLLEGE OF ENGINEERING Department of Meteorology and Oceanography Final Report WAVE HINDCASTS VS. RECORDED WAVES Supplement No. 1 (1965 Data) A.lP/ian L. QCle Associate i Researc Kieteorolog i st John C. Ayer s Proj ect Director ORA Project 06768 under contract with. U.S. ARMY ENGINEER DISTRICT, LAKE SURVEY CONTRACT DA-20-064-CIVENG-65-6 DETROIT, MICHIGAN administered through: OFFICE OF RESEARCH ADMINISTRATION, ANN ARBOR May 1967 </P> <P><PB REF="00000002.tif" SEQ="00000002" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="432" N=""> I ( t CCH </P> <P><PB REF="00000003.tif" SEQ="00000003" RES="600dpi" FMT="TIFF6.0" FTR="TOC" CNF="871" N="III"> TABLE OF CONTENTS Page LIST OF TABLES LIST OF FIGURES ABSTRACT 1. INTRODUCTION 1 2. GENERAL CONSIDERATIONS 3 3. WIND ANALYSES 9 4. HINDCAST AND OBSERVED WAVES 15 5. STRONG WIND CONDITIONS 20 6. SUMMARY AND CONCLUSIONS 23 APPENDIX A. 1965 WIND DATA AND SCATTER DIAGRAMS FOR MUSKEGON, MICHIGAN 28 B. 1965 WAVE DATA AND SCATTER DIAGRAMS FOR MUSKEGON, MICHIGAN 37 C. 1965 WAVE DATA FOR POINT BETSIE AND PORT HURON, MICHIGAN 63 D. COMPARISON OF 1964 WAVE DATA AT MUSKEGON, MICHIGAN 66 E o SUCCESSIVE APPROXIMATION TECHNIQUE FOR ANALYSIS OF PRESSURE AND WIND FIELDS 70 Fo DERIVATION OF THE SIGNIFICANT WAVE HEIGHT AS A FUNCTION OF THE STANDARD DEVIATION 83 BIBLIOGRAPHY 86 </P> <P><PB REF="00000004.tif" SEQ="00000004" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="100" N="IV"> </P> <P><PB REF="00000005.tif" SEQ="00000005" RES="600dpi" FMT="TIFF6.0" FTR="LOT" CNF="890" N="V"> LIST OF TABLES Table Page 3-1 Fetches and upwind land stations used in 12 the calculation of Richards winds at the Muskegon tower. 4-1 Summary of wind data used with each wave 17 hindcast method. 5-1 Summary of wind and wave conditions, 0100E, 20 29 November 1966. USCGC ACACIA. (44-29.5N 82-53W) 6-1 Wind analysis correlation summary. 23 6-2 Significant wave height correlation summary. 24 6-3 Wave period correlation summary. 25 A-1 Surface wind for 1965 wave hindcast 29 period. B-1 Significant wave heights during 1965 hind- 38 cast periods. B-2 Significant period or period of maximum 43 energy for 1965 wave hindcast times. B-3 Period band and maximum wave height for 1965 48 wave hindcast times. C-1 Significant wave heights and periods for 64 1965 wave hindcast times. Point Betsie, Michigan. C-2 Significant wave heights and periods for 65 1965 wave hindcast times. Port Huron, Michigan. D-1 Comparison of SMB, PNJ, PM and OBS wave data 67 for 1964 hindcast periods. Muskegon Research Tower. v </P> <P><PB REF="00000006.tif" SEQ="00000006" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="395" N="VI"> I </P> <P><PB REF="00000007.tif" SEQ="00000007" RES="600dpi" FMT="TIFF6.0" FTR="LOI" CNF="893" N="VII"> LIST OF FIGURES Figure Page 1-1. Flow chart of wind and wave analyses. 2 4-1. Typical wave spectra at Muskegon research 19 tower as produced by the U.S. Army Coastal Engineering Research Center. 5-1. Wind conditions measured by the U.S.C.G.C. 21 ACACIA on 28 November 1966. The base of the arrow indicates the location of the ship while the arrow shows wind direction and speed. The numbers by each arrow are the E.S.T. of the observation. A-1. Scatter diagram of Bretschneider winds 34 vs. surface (10 meters) measured winds. A-2. Scatter diagram of the Jacobs 7.5 meter winds 34 vs. surface (7.5 meters) measured winds. A-3. Scatter diagram of the Jacobs 19.5 meter winds 35 vs. surface (16 meters) measured winds. A-4. Scatter diagram of the Richards winds vs. 35 surface (16 meters) measured winds. A-5. Scatter diagram of the Richards winds vs. 36 surface (10 meters) measured winds. B-1. Scatter diagram of CERC observed significant 52 wave heights vs. those calculated from the standard deviation of the staff gage data. B-2. Scatter diagram of hindcast significant 52 wave heights calculated by the SMB (Bretschneider winds) method vs. the observed significant wave heights. B-3. Scatter diagram of hindcast significant 53 wave heights calculated by the PNJ (Jacobs 7.5 meter winds) method vs. the observed significant wave heights. vii </P> <P><PB REF="00000008.tif" SEQ="00000008" RES="600dpi" FMT="TIFF6.0" FTR="LOI" CNF="855" N="VIII"> Figure Page B-4. Scatter diagram of hindcast significant 53 wave heights calculated by the PM (Jacobs 19o5 meter winds) method vs. the observed significant wave heights, B-5. Scatter diagram of hindcast significant 54 wave heights calculated by the SMB (Richards winds) method vs. the observed significant wave heights. B-6. Scatter diagram of hindcast significant 54 wave heights calculated by the PNJ (Richards winds) method vs. the observed significant wave heights. B-7. Scatter diagram of hindcast significant 55 wave heights calculated by the PM (Richards winds) method vs. the observed significant wave heights0 B-8~ Scatter diagram of hindcast significant 55 wave heights calculated by the SMB (measured winds) method vs. the observed significant wave heights. 3E-9. Scatter diagram of hindcast significant 56 wave heights calculated by the PNJ (measured winds) method vs. the observed significant wave heights, B-10 Scatter diagram of hindcast significant 56 wave heights calculated by the PM (measured winds) method vs. the observed significant wave heights, B-1llo Scatter diagram of hindcast significant 57 period calculated by the SMB (Bretschneider winds) method vs. the observed period of maximum energy. B-12. Scatter diagram of hindcast period of 57 maximum energy calculated by the PNJ (Jacobs' 7,5 meter winds) method vs, the observed period of maximum energy. Oi 5, </P> <P><PB REF="00000009.tif" SEQ="00000009" RES="600dpi" FMT="TIFF6.0" FTR="LOI" CNF="888" N="IX"> Figure Page B-13. Scatter diagram of hindcast period of 58 maximum energy calculated by the PM (Jacobs' 19.5 meter winds) method vs. the observed period of maximum energy. B-14o Scatter diagram of hindcast significant 58 period calculated by the SMB (Richards' winds) method vs. the observed periods of maximum energy. B-15. Scatter diagram of hindcast of period 59 of maximum energy calculated by the PNJ (Richards winds) method vs. the observed period of maximum energy. B-16. Scatter diagram of hindcast of period 59 of maximum energy calculated by the PM (Richards winds) method vs. the observed period of maximum energy. B-17. Scatter diagram of hindcast significant 60 wave period calculated by the SMB (measured winds) method vs. the observed period of maximum energy. B-18. Scatter diagram of hindcast wave period 60 of maximum energy calculated by the PNJ (measured winds) method vs. the observed period of maximum energy. B-19. Scatter diagram of hindcast wave period 61 of maximum energy calculated by the PM (measured winds) method vs. the observed period of maximum energy. B-20. Frequency distribution of significant 62 wave heights as calculated by the SMBBretschneider wind method and the PNJJacobs 7.5 meter wind method and as observed by the staff wave gage. ix </P> <P><PB REF="00000010.tif" SEQ="00000010" RES="600dpi" FMT="TIFF6.0" FTR="LOI" CNF="891" N="X"> Figure Page E-1. The analysis grid and the locations of 72 data sources for the Successive Approximation Technique. E-2. A portion of the Successive Approximation 78 Technique map output. E-3. Computer listing of input pressures for the 79 Successive Approximation Technique analysis. E-4. Gridpoint pressures as calculated by the 80 Successive Approximation Technique. E-5. Contours of the calculated pressure field. 81 </P> <P><PB REF="00000011.tif" SEQ="00000011" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="896" N="XI"> ABSTRACT This study was conducted to evaluate existing methods of wind analysis and wave hindcasting for utilization in the determination of wave climatology for Lakes Huron and Superior. Various calculated and measured winds were used as inputs to the Sverdrup, Munk and Bretschneider (SMB), the Pierson, Newmann and James (PNJ) and the Pierson Moskowitz (PM) wave hindcasting schemes. Of these techniques, the wind analysis of Bretschneider and the SMB wave hindcast method showed better correlations with observed wind and wave data. The predominant finding of this investigation is that all aspects of wave hindcasting for the Great Lakes are subject to question. Further investigation and development are needed to improve the final product. Despite the preceeding statement, the determination of a wave climatology by hindcast methods is feasible at this time. xi </P> <P><PB REF="00000012.tif" SEQ="00000012" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="893" N="1"> 1 INTRODUCTION This report is a supplement to the final report of the research program "Wave Hindcasts vs. Recorded Waves", Contract DA20-064-CIVENG-65-6. The aim of this investigation has been to evaluate wind analyses and wave hindcasting techniques in order to specify the best methods for use in the development of a wave climatology for Lakes Huron and Superior. The original research compared wave hindcasts with measured wave parameters for the intervals from August 1 through August 10 and September 13 through September 23, 1964. The Pierson, Neumann and James, (PNJ) and Pierson and Moskowitz, (PM) wave spectral methods were used to calculate significant wave heights and periods from 1964 data. This supplemental report presents the results of research carried out on 1965 data using the Sverdrup, Munk and Bretschneider (SMB) significant wave height method as well as the PNJ and PM wave spectral techniques. For the 1965 data, the wave hindcasting was split into three phases. The first phase was a determination of a mesoscale wind field over the lakes while the second phase was the calculation of the surface wind field, Thirdly, with a surface or'"anemometer height" wind established, the wave statistics were determined. Figure 1-1 illustrates the combinations of wind analyses and wave hindcast methods that were utilized. The general considerations of the wave hindcast problem are treated in Chapter 2. The wind analyses are discussed in Chapter 3 and the wave hindcasts in Chapter 4. Comparisons made between calculated and observed values of wind and wave parameters are reported in Chapter 6. The availability of wind and wave measurements from the research tower in Lake Michigan near Muskegon operated by the Great Lakes Division of the University of Michigan determined the dates and times for wave hindcasts during September, October, and November, 1965o In general, these time periods represented growing or fully developed seas. In addition to the analyses of 1965 data, the SMB method was applied to the 1964 data and results compared with the earlier findings. In late November, 1966 an intense storm passed over Lake Huron with winds reported to 44 knots and waves to 20 feet. Wind analyses and wave hindcasts were made for the high wind conditions of this storm~ </P> <P><PB REF="00000013.tif" SEQ="00000013" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="861" N="2"> Pressure Analysis Geostrophic f Wind Upwind Land Bretschneider Gradient,, Wind Station Wind (1951) Jacobs Richards Dragert and (1965) Mc I ntyre (1966) Anemometer Height Wind Richards Wind Observed Wind 10 m 16m 7.5 m SMB PM PNJ SMB PM PNJ SM PM PNJ WAVE FIELD WAVE SPECTRA Figure 1-1. Flow chart of wind and wave analyses. </P> <P><PB REF="00000014.tif" SEQ="00000014" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="889" N="3"> 2. GENERAL CONS IDERATI ONS Introduct ion The Great Lakes are bodies of water with a maximum dimension of the order of 300 nautical miles embedded in a large continental land mass. Weather and climate of the surrounding land areas are continental with maritime modifications that decrease with distance from the lakes. A true maritime weather or climate does not exist anywhere in the area; however the maritime modification of the continental climate can be very pronounced at times while being minimal at other times. Over the lakes, the atmospheric conditions are normally in a state of transition from the continental character shown over the upwind land areas toward a maritime character over the water. This transition was clearly shown by Richards, Dragert and McIntyre (1966) in their discussion of the variation of the surface wind from a land station to a downwind ship location. They showed that length of overwater fetch and air-sea temperature differences may cause the overwater wind to be as much as three times the land wind. Likewise, Strong and Bellaire (1965) have shown that the reduction of geostrophic winds to surface winds and the heights of Great Lakes waves depend strongly on the stability of the lowest levels of the atmosphere over the lakes. The atmospheric stability has been shown by Bellaire (1965) and Lansing (1965) to have a decided seasonal variation over the lakes. The atmosphere is generally rather stable during the spring and early summer while during the fall and winter it becomes quite unstable. As an unstable atmosphere will transport more momemtum downward, the waves should be more energetic in fall and winter. That this is true is easily observed. Likewise, different stability regimes would be expected to produce different wave spectra. No experimental data have been published to show the extent of these variations. Wave Hindcasts The direct approach to the problem of determining wave statistics at any location would be to record the wave heights and periods and apply well known statistical methods to the resulting data, However, adequate wave records do not exist and an indirect method of wave hindcasting must be usedo By use of wave hindcasting techniques, meteorological records of pressure, wind, temperature, humidity, etco were analysed to produce a wind field over the bodies of water for which wave statistics were required. From - 3 </P> <P><PB REF="00000015.tif" SEQ="00000015" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="891" N="4"> this field the resultant wave field was determined and the wave statistics calculated. This technique has at least three advantages. First, meteorological records have been kept for many years and many stations in the Great Lakes area as compared with wave records at a few locationsand only for limited times. Second, the wave hindcast technique can be applied anywhere on the lakes and especially at locations where the installation of a wave sensor and recorder would be impossible or very costly. Indeed, after the wind field for the Great Lakes area has been calculated, wave statistics can be produced rather rapidly and relatively inexpensively at any new location. Third, with an input of current meteorological data plus a weather forecast the wave hindcast becomes a wave forecast which may be of considerable value to anyone using the lakes for commerce or recreation. The disadvantages of the wave hindcast method is that it is an indirect method requiring the use of analyses that were developed from ocean data that may not be applicable to the Great Lakes. Indeed the purpose of this investigation was to evaluate these oceanic analytical methods and determine the best one for use on the Great Lakes. Theoretically, the process of wave hindcasting consists of the following steps: 1. The determination by meteorological methods of a wind field over the water area under consideration. 20 The reduction of the wind field to a wind stress field at the height or heights which are responsible for transferring energy to the wave field. 3. The calculation of the energy transfer from wind field to wave field and the resulting wave lengths, heights and periods as a function of time and location. 4. The computation of the statistics of the wave field, Of the above four steps, only the first and last have been achieved with any certainty at the present time, and then only with simplifying assumptions, i.e. a geostrophic or gradient wind field can be calculated from the surface pressure field as reduced to sea level. Also, according to Longuet-Higgens (1952), wave height statistics can be calculated if, over a limited frequency range, a Rayleigh distribution can be assumed. 4 - </P> <P><PB REF="00000016.tif" SEQ="00000016" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="883" N="5"> The reduction of the gradient wind field to a wind stress field and its effect on wave generation are areas of micrometeorology and air-sea interaction that are extremely complicated. Much research effort has been expended on these fields and much more will be required before they become amenable to routine calculationso In practice, steps 2, 3, and 4 have been combined into semiempirical relations which generate wave statistics when the wind speed, fetch and duration are known at some prescribed anemometer height. The SMB and PNJ wave hindcasting techniques are examples of these relations. The investigations conducted for this project were divided into the following three phases1o The determination of a meso-scale wind field over the Great Lakes area. 2. The reduction of this wind field to'"anemometer height" or "surface winds" over the lakes. 3. The determination of the wave statistics from the speed, fetch and duration of the surface winds. Phase 1 The Determination of the Meso-Scale Wind Field A direct determination of the meso-scale wind field by an analysis of streamlines (lines everywhere tangent to the wind vector) and isogons (lines of constant wind speed) from a chart of plotted wind reports often leads to erroneous results, especially for low wind speeds. An anemometer and a wind vane sample the wind only at one point which may be quite non-representative of the actual wind field due to the exposure of the instruments to the wind, ie, a wind vane located near a river flowing between sand dunes into Lake Michigan will most likely be biased by the channeling effect of the valley. Likewise, the data from anemometers mounted on Great Lakes vessels may well be biased due to the proximity of smoke stacks, wheel houses, and other parts of the superstructure. Unlike the wind field, the pressure field is a scalar quantity and lends itself to accurate measurement. By use of the geostrophic and/or gradient wind assumptions, a wind field can be computed in a straightforward manner. If there is no change of pressure gradient in the lower atmosphere, an actual wind equal to the gradient wind may be found above the friction layer~ However, a vertical change -5 </P> <P><PB REF="00000017.tif" SEQ="00000017" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="893" N="6"> of horizontal pressure gradient usually exists and the gradient wind is generally a fictious wind, however, it is one that is reproducible for any given pressure distribution, well known to all meteorologists, and constitutes a convenient and reliable entry into analysis problems such as wave hindcasting. A program for the IBM 7090 computer has been developed to analyze the pressure field, compute the geostrophic wind, curvature of the isobars, and the gradient wind at grid points spaced 75 km apart over the western Great Lakes area. This objective analysis for the meso-scale wind constitutes a step towards the complete computer program for wave hindcasts that must be perfected eventually. Phase 2 The Reduction of the Geostrophic or Gradient Wind Field to a Surface Wind. The geostrophic wind field is calculated from the pressure field under the assumptions that the isobars are straight and parallel, there are no friction forces, and the pressure pattern is invariant with time. The geostrophic wind is thus a result of the balance between pressure gradient and Coriolis forces. The gradient wind is similar except the isobars are assumed to be circular and the wind is the resultant motion due to a balance of pressure gradient, Coriolis and centrifugal forces. In the boundary layer near the surface of the Earth these assumptions are never fully satisfied and rarely approached. Indeed, the exact detailed solution of the problem with friction, randomly curved and spaced isobars, energy and humidity exchanges, time dependence of all variables and parameters, etc. is an extremely difficult if not impossible task. The lack of requisite data is a prime reason for relatively little progress in this field. Therefore, the common practice is to calculate the geostrophic or gradient wind and determine, empirically, the deviations of speed and direction at or near the surface. These deviations have been studied as functions of atmospheric stability, isobaric curvature, overwater fetch, etc. Bretschneider (1952) published a surface wind chart showing the ratio between the surface wind (defined as 10 meters above the mean sea surface) and the geostrophic wind vso the difference in seaair temperature (T - T ) for various radii of cyclonic and anticyclonic curvature. The chart was based on oceanic data originally obtained by Arthur (1947). Richards, Dragert and McIntyre (1966) have reported on the influence of atmospheric stability and length of overwater fetch on - 6 - </P> <P><PB REF="00000018.tif" SEQ="00000018" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="890" N="7"> the ratio U /U where U is the wind as measured on a vessel on Lake Erie or Lake Ontario and U is the wind speed at an upwind land station. This report showed the lake winds to be greater than the land winds except under very stable conditions. They also showed that under unstable over-lake conditions the wind increased with fetch up to a fetch of about 25 nautical miles, but no further increase occurred with additional fetch. They did not consider geostrophic or gradient winds and did not display equations for calculating surface lake winds. This method of calculating winds has been tested with the SMB, PNJ, and PM wave hindcasting methods. Strong and Bellaire (1965) published data on the effect of air stability, as measured by the air-lake temperature difference, on wind and waves for Lake Michigan. This report included regression equations for the computation of surface winds from geostrophic winds. These findings were based on ship observations of wave height, which are estimates only and on ship reports of winds, which are sometimes biased by the location of the wind sensors. However, these data and the equations derived from them by Jacobs (1965) constitute an available technique for reducing gradient wind speed to surface wind speed for the Great Lakes and they were used for computing winds for the PNJ wave hindcasting method. Phase 3 The Determination of the Wave Statistics From Surface Winds. The term wave statistics is used in a broad sense and includes any result of statistical manipulations of wave height data. Under this definition, wave spectra are wave statistics as are such obvious quantities as mean wave height, significant wave height, etc. The wave statistics produced by this investigation are the significant wave height and the significant wave period. The field of ocean wave spectra and wave statistics is an active research area in which the theories of Bretschneider and associates and Pierson-Neumann and associates predominate with Darbyshire, Longuet-Higgens, Wilson and others making significant contributions. There has been no agreement as to which of the wave spectra forms advocated by these leaders in the field will best describe ocean-wave fields. However, recent, Pierson (1965), publications indicate their results may be approaching each other as they better define such quantities as "the anemometer height wind". The SMB, PNJ and PM methods were evaluated in this study and the SMB found to correlate best with measured wave data. - 7 - </P> <P><PB REF="00000019.tif" SEQ="00000019" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="894" N="8"> Observed Winds and Waves Wind and wave values, for comparison with those calculated from the various schemes, were obtained from the data taken at the research tower in Lake Michigan near Muskegon, Michigan. This tower, operated by the Great Lakes Division of the Institute of Science and Technology of the University of Michigan extended 16 meters above the water and was located approximately one mile from the shore. An Aerovane wind speed and direction sensor was mounted at the top and Climet 3-cup anemometers and resistance thermometers were installed on the tower to provide wind profile and lapse rate data. Thermometers in the water measured water temperature and a staff gage on the tower gave wave data. Humidity measurements were also taken. When these instruments and their recorders were operational, they provided the data for comparison and evaluation with the calculated parameters. However, failures did occur and all desired data were not available at all times. </P> <P><PB REF="00000020.tif" SEQ="00000020" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="889" N="9"> 3. WIND ANALYSES Introduction One of the major factors in any wave hindcasting method and often one of the greatest causes of error is the calculation of the wind field responsible for the wave development. The problems of wind field analysis may be conveniently divided into two categories. First, there is no agreement among authorities in the field as to what wind should be determined and secondly, the methods of obtaining the desired wind or wind profile or wind spectra are not well understood. This report will not treat the first problem as the input wind requirements for each wave hindcasting scheme have been accepted as published. Methods of obtaining mean winds at various specified heights of the atmosphere have been evaluated by comparing calculated winds with measured winds at the Muskegon research tower. Bretschneider Wind The name "Bretschneider Wind" has been applied to the wind input for the SMB wave hindcasting method as outlined by the U.S. Army Corps of Engineers (1961). A surface wind scale, Bretschneider (1951), relates the sea-air temperature difference to the ratio of surface wind vso geostrophic wind for a family of curves of varying cyclonic and anticyclonic curvature. From the surface wind vso geostrophic wind ratio and the geostrophic wind the surface wind was easily calculated. The data used to determine the sea-air temperature difference came from a number of sources. Lake temperatures were obtained from the water temperature measurements at the Muskegon research tower and the instrumented ships on the Great Lakeso Air temperatures came from the above sources and from U.S. Weather Bureau reports at land stations near the lake. Continuity and extrapolation were widely employed to arrive at a best estimate of the temperatures in the wave generating area, The lake-air temperature data are poor but probably contain no greater error than other aspects of the wave hindcast procedures. There is no account taken of the spatial variability of surface temperature and none can be expected in the near future due to a serious lack of measurements. - 9 - </P> <P><PB REF="00000021.tif" SEQ="00000021" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="886" N="10"> The geostrophic wind speeds and the radii of curvature of the streamlines were obtained from weather maps using a geostrophic wind scale and a curvature scale. The weather maps, obtained from the Chicago forecast center of the U.S.W.B., were reanalyzed for 1 mb isobars in the vicinity of Lake Michigan prior to the calculation of geostrophic wind speed and curvature. The calculated wind direction was taken to be the direction of the isobar located nearest to Muskegon, Michigan. The calculated Bretschneider winds for the 1965 data are listed in Table A-1 of Appendix A and should be compared with the 10 meter observed winds at the Muskegon tower listed in the same table. Figure A-1 is a scatter diagram of the Bretschneider winds vs. the observed 10 meter winds. The correlation coefficient of 0,63 between the Bretschneider winds and the observed winds was the best obtained for any calculated wind. Jacobs 7.5 meter winds For the PNJ wave hindcast scheme, Jacobs (1965) presented the following empirical equations for the calculation of the surface (7.5 meters) wind from the gradient wind. V = wind speed at 7.5 meters in knots = 7.9 +.28 V AT < -50F Stable (3-1) g = 9.5 +.27 V -50F I AT < 5~F Neutral (3-2) = 13.1 +.31 V AT > 50F Unstable (3-3) where V is the gradient wind calculated from surface pressure data and A Tg is the water-air temperature difference, ioeo a stability factor. The gradient wind, V, was calculated by the standard meteorological equations: - 10 - </P> <P><PB REF="00000022.tif" SEQ="00000022" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="871" N="11"> V 2 4- - f pV for anticyclonic geo curvature V-= -Q + + fpV for cyclonic g 2 4 geo curvature where V = the geostrophic wind in knots, geo p = radius of curvature of isobar lines in nautical miles f = Coriolis parameter The results of these calculations are shown in Table A-lo The corresponding measured winds, for comparison, are listed under the heading of Muskegon Tower 7.5 meter winds. Figure A-2, a scatter diagram of the Jacobs 7.5 meter winds vs. the measured 7.5 meter winds shows the calculated winds to be generally larger than the measured winds. The linear correlation coefficient between these winds was 0.56. Jacobs 19.5 meter winds Wave statistics as determined from the Pierson-Moskowitz spectrum require a mean wind input for 19.5 meters. Jacobs (1965) developed ratios between the 7.5 and 19.5 meter winds as measured in 1963 and 1964 on the Muskegon tower (Elder, 1965) V wind speed at 7.5 m U wind speed at 19.5 m.85 AT < -50F (3-6) 95 -5~F < AT < + 5 F (3-7) = 1.00 AT > 50F (3-8) - 11 - </P> <P><PB REF="00000023.tif" SEQ="00000023" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="884" N="12"> These ratios were used with the Jacobs 7.5 meter winds to obtain the Jacobs 19.5 meter winds which are listed in Table A-i. The Muskegon tower was 16 meters high with an Aerovane wind speed and direction sensor on top. The data from the Aerovane system was used to compare with the Jacobs 19.5 meter wind as illustrated by the scatter diagram, Figure A-3. The wide scatter of these data is obvious and is confirmed by the low correlation coefficient of 027. Richards Winds In the Monthly Weather Review, Richards, Dragert and McIntyre (1965) reported ratios of overwater wind to overland wind as functions of the atmospheric stability and the fetch from land to the overwater wind observation location. They used ship winds and water temperatures with upwind land station winds and air temperatures to calculate the ratios of overwater wind to overland windo These ratios were then tabulated according to fetch and the stability parameter, Ta - Tw These ratios were used to calculate an overwater wind at the Muskegon tower using the Muskegon tower water temperature and an upwind land-station air temperature and wind speed. The up-wind landstations were chosen on the basis of the wind direction at the Muskegon tower or the Muskegon UoS.W.B. The wind directions considered, their fetches and the upwind land stations used are listed in Table 3-1 below: Table 3-1 Fetches and upwind land stations used in the calculation of Richards winds at the Muskegon tower. Overwater fetch Wind Direction n mi. Upwind Land Station 1800 50 5/3 St. Joseph, Micho 1900 80 SBN South Bend, Indo 2000 98 SBN 2100 102 ORD O'Hare Airport Chicago, Ill. 220~ 91 ORD 2300 86 ORD 2400 77 MKE, 53/ Milwaukee, Wiso 250~ 68 MKE, 53/ - 12 - </P> <P><PB REF="00000024.tif" SEQ="00000024" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="890" N="13"> Overwater fetch Wind Direction n mi. Upwind Land Station 2600 69 MKE, 53/ Milwaukee, Wiso 2700 70 MKE, 53/ 2800 69 MKE, 53/ 2900 68 MKE, 53/ 300 71 GRB, MTW, Green Bay or Manitowac, Wis. 3100 79 GRB, MTW 3200 84 GRB, MTW 330 100 GRB, MTW The Richards winds data are tabulated in Table A-1 and compared with the Aerovane winds from the Muskegon tower on the scatter diagram, Figure A-4. These data show the calculated winds to be generally lower than the corresponding Aerovane measured winds. When compared with the 10 meter Muskegon tower winds, Figure A-5, the Richards winds are seen to scatter rather widely but have no particular trend with respect to the observed winds. The concept of determining the overwater wind by the technique used above seems very sound from a conceptual view; however, practical considerations appear to make it not acceptable. The major sources of error probably are due to the strong dependence of the method on the value of the upwind land station winds and the stability factor over the lake. The latter are not measured with any regularity and the former suffer from being non-representative short time averages at single locations. Jacobs (1965) showed that the Muskegon UoSoW.B. wind speed data correlated poorly with either Muskegon tower winds or with ship winds. Wind Direction The only calculated wind directions were obtained by assuming that the geostrophic and gradient winds have the same direction as the isobars from which they were derived. These wind direction data are listed in Table A-1 with the corresponding wind directions as measured by the Aerovane instrument on the Muskegon tower. As predicted by the theory and observations, the measured wind shows a tendency to flow across the isobars toward lower pressure. A mean deviation 13 - </P> <P><PB REF="00000025.tif" SEQ="00000025" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="890" N="14"> of 290 from the isobaric direction was calculated from the data. There is nothing new or unusual about these findings. They merely verify accepted data and hypotheses. Successive Approximation Technique The successive approximation technique of Cressman (1959) has been applied to a pressure analysis of the Great Lakes area. From the pressure analysis, geostrophic and gradient wind can be computed. While the technique is described in detail in Appendix E, it is pertinent at this point to mention that it is a computer analysis technique that produces a smoothed pressure and geostrophic wind analysis. The smoothing built into this program should make the results more representative of the wind over an area the size of Lake Michigan and therefore better wave hindcasts should result. Discussion and Recommendations The Bretschneider winds correlated with the observed wind better than any other wind analysis technique. However, a correlation coefficient of 0.63 for 36 pairs of data is not a high correlation. It is apparent that additional knowledge of the lower level wind systems must be obtained before improved accuracy in wave hindcasting can be achieved. The successive approximation technique should be the first step in an improved analysis method. From the calculated pressure field, geostrophic wind field, or gradient wind field, a surface wind must be calculated taking into account the overwater stability, the upper air stability, fetch, wind speed, etc. Indeed, according to Pierson (1964) and Harris, (1967) the measurement of a mean wind at one level provides insufficient data for the determination of surface stress and wave spectra. Thus the more difficult problem of calculating the surface stress or wind profiles from the synoptically observed data has been posed0 Progress along these lines will not be quick and it appears the best procedure at this time is to compute the geostrophic wind which can be reduced to a lake level (10 meters) wind by Bretschneider's surface wind speed curves~ Research should continue to upgrade these procedures. - 14 </P> <P><PB REF="00000026.tif" SEQ="00000026" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="892" N="15"> 4. HINDCAST AND OBSERVED WAVES Introduction Two wave hindcasting methods have achieved prominence in the United States. These are the Sverdrup, Munk and Bretschneider, (SMB) method and the Pierson, Neumann and James (PNJ) method. Both methods are applicable to fetch and duration limited seas as well as fully developed seas and both are semi-empirical as experimental data was used in some phase of their derivations. The SMB method predicts two statistics of the wave field: the significant wave height and the significant wave period. From these two statistics wave spectra and other statistics can be calculated using the wave distribution of Longuet-Higgins (1952). The PNJ method predicts the wave spectra, from which wave statistics can be computed by use of the wave distribution of Longuet-Higgins (1952). In recent years the wave spectra and wave statistics derived from both methods have become more nearly equal. A third hindcast method, the PM method, due to Pierson and Moskowitz (1964) is very similar to the PNJ method except that a different spectra is calculated from the input data. However, no procedure has been published for wave spectra calculations when fetch and duration are limited. This limitation seriously curtails the usefulness of the method for Great Lakes wave hindcasting. The SMB Wave Hindcast Method The SMB method originated with Sverdrup and Munk's (1947) consideration of the transfer of energy from the wind field to the wave by both normal and tangential stresses. They assumed the energy of the wave field would increase until an equilibrium condition was reached where the rate of energy transfer from the wind to the waves equalled the rate of energy dissipation from the waves. This condition was called the fully developed sea and was characterized by a condition of maximum wave heights, periods, and speeds for a given wind speed. The fully developed sea is also independent of fetch and wind duration, The theoretical work of Sverdrup and Munk required knowledge of coefficients and constants that could be determined only from empirical data, which at the time were rather meager. With additional data, Bretschneider (1951 and 1958) revised the forecasting relations of Sverdrup and Munk (1947) into the SMB method~ - 15 - </P> <P><PB REF="00000027.tif" SEQ="00000027" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="892" N="16"> From these relations a series of deep water wave forecasting curves were developed which now appear in many reports and books; Uo.S Army Corps of Engineers (1961) and Bretschneider (1965). The SMB wave forecasting (hindcasting) method requires the following input parameters: a. The surface (10 meters) wind speed. b. The duration of the wind from the given direction. c. The overwater fetch. With these wind parameters and the SMB wave hindcasting curves, the wave parameters of significant wave height and significant wave period can be obtained. The significant wave height is defined as the average of the highest 1/3 of the wave heights of a given wave train of at least 100 consecutive waves, while the significant wave period is the average period of these same waves. Bretschneider (1965) pointed out that the significant wave period is also a period around which is concentrated the maximum wave energy. This latter concept allows the SMB significant wave period to be compared with the period of maximum energy as determined from measured wave data. Longuet-Higgins' (1952) presentation of the Rayleigh distribution for wave height variability based on a narrow spectrum and its subsequent verification by Bretschneider (1957 and 1959) and others permits many statistical parameters to be determined from the significant wave height. Bretschneider (1965) has reviewed the state of the art of wave generation in general and the SMB method in particular; therefore, the method will be discussed no further except as it relates directly to the problem of Great Lakes wave hindcasting. The PNJ Wave Hindcast Method The PNJ wave hindcasting method is attributed to Pierson, Neumann and James (1955) and is a development of Neumann's (1952) theoretical wave spectrum of energy. The PNJ method predicts an E-value, where E is related to the generated wave energy; from which, by use of the theoretical wave distribution of Longuet-Higgins (1952), wave statistics can be calculated. In particular, the significant wave height, the period of maximum energy, the average wave height, and the upper period and lower period for significant wave energy were calculatedo Jacobs (1965) has discussed the PNJ method in considerable detail, as have other authors, hence it will not be reviewed further except when pertinent to Great Lakes wave hindcasting - 16 - </P> <P><PB REF="00000028.tif" SEQ="00000028" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="882" N="17"> The input data for the PNJ method are listed below: a. Average surface (7.5 meter) wind speed, b. Duration of surface wind from given direction. c. Fetch of surface wind. It will be noted that these parameters are the same as those for the SMB method except the surface wind is specified to be at 7.5 meters rather than 10 meters. The Pierson-Moskowitz Spectrum For a fully developed sea, Pierson and Moskowitz (1964) proposed a wave spectrum based on the similarity theory of Kitaigorodski (1961) Jacobs (1965) has reviewed this spectrum and tabulated the equations used to calculate appropriate wave statistics. However, the requirement of a fully developed sea severely restricts the application of this spectrum to the wave hindcasting problem. The Calculated Wave Statistics Wave statistics were determined using the SMB, PNJ, and PM methods with calculated and measured wind inputs. Table 4-1 summarizes the input wind data used with each wave hindcast method. Table 4-1 Summary of wind data used with each wave hindcast method. Wave Hindcast Method Input Wind Data 1. Bretschneider Wind SMB 2. Richards Wind 3. 10 meter Measured Wind 1. Jacobs 7.5 meter Wind PNJ 2. Richards Wind 3. 7.5 meter Measured Wind 1. Jacobs 19,5 meter Wind PM 2o Richards Wind 3. 16 meter Measured Wind - 17 - </P> <P><PB REF="00000029.tif" SEQ="00000029" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="885" N="18"> The significant wave height and the significant wave period or period of maximum energy were calculated for each of these cases and compared with measured significant wave heights and periods of maximum energy. In addition, the period band, within which resides 92% of the wave energy, was calculated from the PNJ method using the Jacobs 7.5 meter wind. Observed Wave Statistics The U.S. Lake Survey operated a staff wave-gage on the Muskegon tower during the 1965 wave hindcast periods. Data from this gage were used to calculate the observed significant wave height and period of maximum energy during the hindcast periods. These calculated heights and periods were used as the standard or "correct" value for comparison with hindcast heights and periods. Staff-gage data for the selected wave hindcast periods of 1965 were analyzed by the U.S. Army Coastal Engineering Research Center using their wave spectrum analyzer, Caldwell and Williams (1961). The wave analyzer output, Figure 4-1, is a spectral curve of the frequency distribution of the linear average and square average wave heights taken over a twenty minute time interval with a filter band width of 0.027 cycles per second. In addition, the cumulative peak wave height is displayed. The period of maximum energy is read directly from the spectrum as the abscissa of the maximum value of the square average wave height curve. The significant wave height for a spectrum is readily obtained from the relation: Significant Wave Height =Maximum Linear Average Value Significant Wave Height = 0e45 0.45 due to Caldwell (1963). The significant wave height can also be obtained by calculating the standard deviation of the staff-gage data and multiplying by four. This relation is derived in Appendix F. The standard deviation was computed as a running mean of the preceeding twenty minutes of real-time staff-gage record using the hybrid analog/digital computer of the Department of Meteorology and Oceanography, University of Michigan. The significant wave heights as computed by the standard deviation method and the periods of maximum energy as read from the spectral curves constituted the check data for evaluation of the wave hindcasts, -18 - </P> <P><PB REF="00000030.tif" SEQ="00000030" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="320" N="19"> Wave Frequency (Cycles Per Second) 0.04.06.08 0.10.12.14.16.18 0.20.22.24.26.28 0.30.32 STATION-'1' O^OE~~~., -' -F; B'. -71 GAGE3-S IU TAP ~ -'T~l DATE -~ 8tgG~ TIME /,OQ. ANALYSIS-STANDARD — ISPECIA LREMARKS /O,,r,-v - ANALYZED BY-QZ4_DAT i: Ma~ 19F 9 — 5- FILTER O1PENING FOR STANDARD ANALYSIS IS 0.027 Cy/Sec. - —! _' 2 I,, eL I II!26 ml - 128' 13OI.3'IIl 25 ~~20' II —- I~1 —-~o -JI J II i I - -L -'' 4L III II1I1I 1 - II ~1 1; il,,~ F-... I I I'r II I II 11 II II I I 0 i' u,~~~~~~~~~~~~~~~~~~~~~~~~;. I - -- i 5 -I I1]~ % — ~ m --..c i i.~~5 -':~:~;l c-t~,' k ~ -:~'Ji I' L -' Period(Sec Figure 4-1~~~~~~~~~~~~. Typica wave spcr2tMseo eerhtwra rdcdb At ResearchC:enter. tl~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~l~~~~~~~~~~~~~. I,, _.. O O~, 30520115 1 1 8 76... ~'i': Wav!eiod ( ~.,:. Figure 4-1. Typical wave spectra at Muskegon research tower as produced by the~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~' U.S. Army Coastal Engineering Research Center~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,, </P> <P><PB REF="00000031.tif" SEQ="00000031" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="884" N="20"> 5. STRONG WIND CONDITIONS A sizeable fraction of the wave hindcasts of this study were made for wind speeds, in knots, ranging from the low teens to the high twenties. Indeed, 28 knots was the highest observed wind speed of all the 1965 data. However, wave destruction on the Great Lakes is usually caused by winds that exceed 28 knots. One opportunity for study of a strong wind situation occurred during late November, 1966 when a low pressure system deepened over northern Lake Huron and produced abnormally high winds and waves. On the 28th. of November the U.S.C.G.C. ACACIA ventured into southern Lake Huron and recorded winds to 44 knots and waves estimated to 20 feet. Figure 5-1 shows her location and the measured wind at various times. Wind analyses and wave hindcasts were made for 0100E on 29 November 1966 when the ACACIA was well into Lake Huron and the wind and waves were near their maximum values. The results of these analyses are listed below: Table 5-1 SUMMARY OF WIND AND WAVE CONDITIONS 0100E 29 NOVEMBER 1966 U.S.C.G.C. ACACIA (44-29.5 N 82-53 W) S ignificant Winds Wave Height Wave (kts.) (ft.) Period SMB- Bretschneider Winds 68 PNJ- Jacobs 7.5 meter Winds 25 Richards Winds 28-46 Bretschneider- Jacobs Average Winds 47 SMB- Bretschne ider-Jacobs Average Winds 19 1003 PNJ- Bretschne ider-Jacobs Average Winds 14 8.1 USCGC ACACIA 42 20 - 20 </P> <P><PB REF="00000032.tif" SEQ="00000032" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="764" N="21"> '"'""/ )2 ICE A P~o LAKE HURON FNSCT 1928 Nov 1966 FNT 10 I. MTC ACACIA Figure 5-1. ind conditions measured by the U.S.C.G. C. Acacia on 28 November 1966. The base of the arrow indicates the location of the ship while the arrow shows wind direction and speed. The numbers by each arrow are the E.S.T. of the observation. - 21 </P> <P><PB REF="00000033.tif" SEQ="00000033" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="890" N="22"> After calculating the Bretschneider wind to be 68 knots and the Jacobs 7.5 meter wind to be 25 knots it became apparent that both schemes were badly in error. With a strong wind and extremely unstable atmosphere conditions, TLake - Tair = +80 to + 180F, there should be very little difference between a 10 meter wind speed and a 7.5 meter wind speed. Therefore, averages of the Bretschneider winds and Jacobs 7.5 meter winds were calculated and used for wave hindcasting. This average of 47 knots for 0100E on 29 November 1966 compares favorably with the ACACIA's measured wind of 42 knots. The Richards wind of 38 to 46 knots very nicely bracketed the 42 knot observed wind. Using the average winds with the SMB and PNJ wave hindcast methods, significant wave heights of 19 and 14 feet, respectively, were obtained. The estimate of 20 foot wave heights from the ACACIA compares well with the SMB significant wave height of 19 feet. This exercise in wave hindcasting for strong wind conditions points out inadequacies in the wind analysis schemes. Possibly these techniques were developed from data biased toward lower wind conditions and do not extrapolate well to stronger winds. It appears that investigations into high wind conditions are required in order to accomplish further improvements in the wind analyses and wave hindcast procedures. - 22 - </P> <P><PB REF="00000034.tif" SEQ="00000034" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="887" N="23"> 6. SUMMARY AND CONCLUSIONS Summary of results Tables A-1i B-l, and B-2 of Appendices A and B tabulate all observed and hindcast values of the surface wind, the significant wave heights and the significant wave periods, respectively for the 1965 data at the Muskegon research tower. Figures A-1 through A-5 of Appendix A and Figures B-1 through B-19 of Appendix B are scatter diagrams of calculated vs. observed values of winds, significant wave heights, and significant wave geriods. On each scatter diagram, the line of perfect correlation (45 line) has been drawn as well as the least-squares regression line. The regression equation for the plotted data and the correlation coefficient are also displayed on each scatter diagram. Figure B-20 is a frequency distribution of significant wave heights for the SMB-Bretschneider wind method, the PNJ-Jacobs 7.5 meter wind method and the observed values. These curves show a similar gross behavior. However, a chi square test indicated that the hypothesis that the SMB and PNJ data were drawn from the same set of random variables as the observed data must be rejected at the 99.5% significance level. Table 6-1, a summary of the correlation coefficients between calculated and measured wind speeds, shows how the Bretschneider winds correlated better with measured winds than did the other analyzed winds. The 10 meter, 7.5 meter and 16 meter winds used for comparison were those measured on the Muskegon research tower. Table 6-1 WIND ANALYSES CORRELATI ON SUMMARY n r Bretschneider Winds vs. 10 meter winds 36.63 Jacobs 7.5 meter winds vs. 7.5 meter winds 43.55 Jacobs 19.5 meter winds vs. 16 meter winds 49.37 Richards winds vs. 16 meter winds 44.36 Richards winds vs. 10 meter winds 36.24 n = number of data pairs r = correlation coefficient - 23 - </P> <P><PB REF="00000035.tif" SEQ="00000035" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="885" N="24"> Table 6-2 summarizes the significant wave height results of this research and clearly shows how the SMB wave hindcast values correlate better than either the PNJ or the PM. It should be noted that the SMB method correlates best with measured wind input as well as with the calculated Bretschneider wind input. In all cases, the significant wave height listed was correlated with that obtained from the standard deviation calculation, Appendix F. The CERC observed significant wave heights were calculated from the CERC wave spectra. Table 6-2 SIGNIFICANT WAVE HEIGHT CORRELATION SUMMARY n r CERC observed significant wave heights 85.89 SMB-Bretschneider Wind 69.60 PNJ-Jacobs 7.5 meter wind 73.35 PM-Jacobs 19.5 meter wind 30.32 SMB-Richards wind 59.36 PNJ-Richards wind 74.46 PM -Richards wind 36.15 SMB-Measured wind 53.62 PNJ-Measured wind 37.47 PM-Measured wind 16.34 n = number of data pairs r = correlation coefficient Table 6-3 summarizes the wave-period correlation coefficients obtained by comparing hindcast values with those measured by the CERC spectrum analysis. With the Richards wind input and with the measured wind input, the SMB method showed a higher correlation of wave periods than did PNJ or PM. However, PM with Jacobs 19,5 meter wind input correlated better than SMB with Bretschneider wind input or PNJ with Jacobs 7.5 meter wind input. The latter three correlation coefficients are all so small that none of these techniques can be designated as a reliable method. - 24 </P> <P><PB REF="00000036.tif" SEQ="00000036" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="887" N="25"> Table 6-3 WAVE PERIOD CORRELATION SUMMARY n r SMB-Bretschneider Winds 68.20 PNJ-Jacobs 7.5 meter winds 72.11 PM-Jacobs 19.5 meter winds 31.31 SMB-Richards winds 50.40 PNJ-Richards winds 54 o37 PM -Richards winds 32.17 SMB-Measured 10 meter winds 51.67 PNJ-Measured 7.5 meter winds 31.51 PM-Measured 16 meter winds 13.64 n = number of data pairs r = correlation coefficient Table C-1 of Appendix C lists significant wave heights and periods calculated for Point Betsie, Michigan during some of the time intervals studied at Muskegon. As comparative observed values were not readily available these data do not contribute to the evaluation of wind analysis and wave hindcasting techniques for the Great Lakes. Table C-2 lists significant wave heights and periods for Port Huron, Michigan during the same times. As the Muskegon data were selected for onshore winds on the eastern shore of Lake Michigan, most days considered showed offshore winds at Port Huron and drastically short fetches. Therefore, these data are very limited and of no value in the evaluation. Table D-1 of Appendix D compares significant wave heights and periods for the days in 1964 that were previously considered by Jacobs, The PNJ, PM, and OBS values are repeated from Jacobs (1965) report while the SMB values are new. The wind speed and fetches were too low for an SMB analysis in many cases, so the points that can be compared are rather limited. Perusal of these data does not point out any marked superiority of any technique. - 25 - </P> <P><PB REF="00000037.tif" SEQ="00000037" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="889" N="26"> Conclusion The results of this investigation show the Bretschneider wind analysis method produced the best surface mean winds and the SMB wave hindcast method calculated the best significant wave heights. The latter result is undoubtedly due in part to the better fit of the Bretschneider winds to the measured winds. However, the SMB method also produced better wave hindcasts when measured winds were used as input to the hindcast schemes, thus the combination of Bretschneider winds and SMB wave hindcasts appears to be the best method to be utilized, at this time, for wave statistics studies on the Great Lakes. Despite being the best method available, neither the Bretschneider wind correlation coefficient of 0.63 nor the SMB Bretschneider significant-wave correlation coefficient of 0.60 are outstanding. The SMB-Bretschneider wave-period correlation coefficient of.20 is an indication that wave periods on the Great Lakes can not be hindcast with any accuracy. Indeed, a coefficient of.20 indicates almost a lack of correlation; a fact that is born out by the scatter diagram, Figure B-ll. Both the wind analysis and the wave hindcasting methods are not totally adequate and research in both fields must continue in order to improve the existing methods or develop new ones. However, more data will be necessary before significant advances can be expected. The results of the investigation of the November, 1966 storm indicate the wind analysis schemes are biased toward low wind speed data. Indeed, the Jacobs wind equations were derived with data containing very few wind speeds greater than 30 knots. While the results of one study of one storm compared with the observations from one ship can not refute existing wind analysis and wave hindcast techniques, these results do raise questions as to the applicability of these techniques to high wind conditions. As the high wind conditions are the most important for any user of a wave climatology, it is imperative that they be studied in greater detail. Wave Climatology for Lakes Huron and Superior The production of a wave climatology for the Great Lakes should proceed at this time using the following procedure. 26 - </P> <P><PB REF="00000038.tif" SEQ="00000038" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="892" N="27"> 1. With synoptic weather data (0000, 0600, 1200, 1800 GCT), use the successive approximation technique machineanalysis to calculate a surface pressure field and a geostrophic wind field. All output data should be stored on computer tape for future input to newly developed programs. 2. Determine a stability factor, Twater - Tair from a subjective analysis of water temperature climatology, ship records, etc. Continuity, smoothing, interpolation and extrapolation must be judiciously applied to this process. Measure isobaric curvature on a weather chart. 3a. Use the Bretschneider surface wind chart with the stability factor and the isobaric curvature to determine the ratio of surface-wind to geostrophic-wind. Calculate the surface (10 meter) wind field upwind of each wave hindcast location. 3b. If the calculated surface wind exceeds 30 knots, Jacobs empirical wind equations and the Richards, Dragert and McIntyre computations should be utilized to obtain additional wind estimates. These must be considered, along with ship and land wind reports, in the final determination of surface wind speed. 4. Use the SMB wave hindcast charts to determine the significant wave height and significant wave period. 5. For high wind or fast moving storm conditions, reduce the time between analyses from 6 hours to 3 hours. The wind analysis and wave hindcast schemes discussed in this report and proposed above for the development of a wave climatology should be considered to be the best available now but improvements in the future are vitally needed and must be anticipated. The program of wave climatology production must remain flexible so that any new developments can be rapidly exploited. - 27 - </P> <P><PB REF="00000039.tif" SEQ="00000039" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="853" N="28"> APPENDIX A 1965 WIND DATA AND SCATTER DIAGRAMS FOR MUSKEGON, MICHIGAN - 28 </P> <P><PB REF="00000040.tif" SEQ="00000040" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="863" N="29"> TABLE A - 1 SURFACE WIND FOR 1965 WAVE HINDCAST PERIOD Muskegon Research Tower V = Geostrophic Wind g V = Gradient Wind gr VR = Richards Wind V = Jacobs Wind (19.5 meters ) VB = Bretschneider Wind (10 meters ) V = Jacobs Wind (7.5 meters ) J1 Wind Speed (kts) Observed Calculated Wind Direction QD (degrees) Date:Time(C.S.T.)16m 10m 7.5m V g Vg VR J VB VJ1 Observed Gradient September, 1965 23:0000 15 16 14.6 25 25 15 17 16 17 240 260 23:0600 12 17 33 31 11 19 22 19 230 260 23:1200 24 22 24 28 28 16 22 20 22 210 250 23:1800 20 19 20 30 30 19 22 19 22 260 310 24:0000 14 12 13 25 25 16 21 17 21 290 290 24:0600 16 14 15 23 18 13 19 16 19 290 310 24:1200 17 14 15 25 28 15 22 21 22 280 310 24:1800 18 16 16 28 35 11 24 25 24 260 290 25:0000 20 18 18 35 35 13 24 26 24 260 270 25:0600 22 20 20 48 39 17 25 33 25 240 270 25:1200 24 21 20 35 61 18 32 29 32 210 250 25:1800 22 18 18 16 17 19 15 10 15 200 240 26:0000 11 11 11 0 0 22 0 0 0 26:0600 20 13 12 35 26 21 23 21 cont'd cont'd </P> <P><PB REF="00000041.tif" SEQ="00000041" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="805" N="30"> Wind Speed (kts) Ob s er ved Calculated Wind Direction (degrees) Date:Time(C.S.T4) 16m 1Cm 7.5m V VV V B Observed Gradient 28:0000 12 20 19 19 16 19 140 180 28:0600 19 19 19 14 19 140 050 28:1200 24 24 21 16 21 130 200 28:1800 12 12 13 6 13 160 190 29:0000 19 12 17 11 17 160 170 29:0600 6 11 3 200 170 29:1200 6 6 10 15 4 15 180 190 30:0600 40 40 21 25 21 140 190 30:1200 40 40 21 24 21 170 200 30:1800 32 25 12 17 16 17 180 240 0 October 1965 01:0000' 24 38 44 19 23 26 23 240 290 01:0600 25 48 31 10 23 30 23 280 320 01:1200 23 37 52 15 29 32 29 320 340 02:0600 17 40 40 16 21 26 21 220 260 02:1200 25 60 60 23 27 38 27 200 250 02:1800 23 48 39 13 22 22 22 220 280 03:0000 30 50 42 16 23 27 23 310 340 03:0600 30 45 39 26 21 26 21 330 360 03:1200 28 34 24 24 24 340 360 05:1200 16 20 19 14 19 150 190 05:1800 13 10 19 17 13 15 12 15 180 200 06:0000 18 18 28 26 21 19 21 160 220 06:0600 20 52 35 15 20 28 20 210 230 06:1200 23 19 33 33 15 19 22 19 190 220 06:1800 13 17 15 14 8 14 170 230 Cont'd </P> <P><PB REF="00000042.tif" SEQ="00000042" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="856" N="31"> Wind Speed (kts) Observed Calculated Wind Direction (degrees ) Date:Time(C.S.T.) 16m lom 7.5m V Vgr V VJ VB V Observed g r V V,. Observed Gradient 2 1 07:0000 12 21 22 17 17 13 17 190 210 07:0600 19 48 36 20 27 20 160 220 07:1200 24 35 26 17 17 18 17 180 240 07:1800 18 23 21 15 16 14 16 230 230 08:0000 22 50 43 19 24 26 24 280 300 08:0600 27 65 44 21 22 38 22 280 310 08:1200 27 45 31 19 19 26 19 290 310 08:1800 28 62 41 18 22 35 22 280 300 09:0000 21 50 36 13 20 29 20 310 320 09:0600 25 48 31 21 23 29 23 320 340 11:0600 9 15 21 13 16 10 16 310 340 11:1200 17 23 23 18 20 16 20 290 330 11:1800 19 26 24 12 17 16 17 300 300 12:0000 25 45 26 19 17 26 17 290 310 12:0600 28 43 39 13 25 29 25 300 320 22:1800 11 8 12 28 43 12 22 22 22 300 310 23:0000 20 18 19 11 23:0600 19 17 14 23:1200 22 20 25 42 63 33 37 33 350 350 23:1800 20 30 28 22 20 22 350 350 24:0000 16 52 44 27 40 27 350 360 24:0600 16 13 52 52 29 40 29 010 060 24:1200 11 11 14 19 19 13 19 14 19 330 350 24:1800 6 5 7 19 19 12 19 15 19 260 260 25-0000 20 18 18 34 31 15 23 26 23 240 360 25:0600 27 24 24 30 30 9 22 22 22 200 260 cont'd </P> <P><PB REF="00000043.tif" SEQ="00000043" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="865" N="32"> Wind Speed (kts) Observed Calculated Wind Direction (degrees) Date:Time(C.S.T.) 16m 10m 7.5m Vg Vgr VR V VB V Observed Gradient 2 1 25:1200 19 19 27 22 15 20 17 20 25: 1800 23 18 10 19 14 19 29:0600 18 17 28 28 15 22 20 22 29:1200 21 21 55 89 16 41 48 41 29: 1800 23 21 80 80 10 38 56 38 30:0000 22 22 60 60 16 27 40 27 30:0600 17 16 30 30 15 19 19 19 30:1200 12 11 50 20 14 24 20 24 30:1800 8 27 16 16 18 16 18 31:0.000 22 22 62 54 19 27 32 27 270 31:0600, 27 28 80 80 18 33 47 33 350 31:1200 21 22 53 53 18 27 31 27 330 31:1800 18 18 32 37 13 20 24 20 330 November 1965 01:0000 18 18 19 15 16 14 10 14 330 01:0600 12 13 37 23 16 16 20 16 310 01:1200 16 18 25 24 18 17 14 17 310 01:1800 7 7 19 19 11 15 13 15 280 03:0600 17 19 37 37 21 22 21 230 03:1200 19 20 48 43 24 22 28 22 230 03:1800 16 04:0000 17 04:0600 16 04:1200 16 04:1800 10 8 6 cont'd </P> <P><PB REF="00000044.tif" SEQ="00000044" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="834" N="33"> Wind Speed (kts) Observed Calculated Wind Direction (degrees) Date:Time(C.S.T.) 16m 10m 7.5m Vg Vgr VR VJ VB VJ1 Observed Gradient 05:0000 9 8 5 05:0600 18 13 14 10 14 190 05:1200 25 16 13 21 13 21 230 05:1800 33 21 8 16 15 16 250 06:0000 23 19 16 12 16 270 06:0600 13 15 14 9 14 270 IA. </P> <P><PB REF="00000045.tif" SEQ="00000045" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="834" N="34"> 30 Y 10.4+.27X 20 MKG Tower + + +/ Winds IOm. kts. 15 + / / | Wind Comparison Muskegon Tower 10 m. vs 10 Bretschneider Correlation r. 63' 5 4 5 10 15 20 25 30 35 40 Bretschneider Winds kts. Figure A-1. Scatter diagram of Bretschneider winds vs. surface (10 meters) measured winds. 30 + 20 x / + / MKG + + Tower 7. 5 m. kts. 15 + 1o0 / +Muskegon Tower 7.5m. Winds vs Jacobs 7. 5 m. Winds /+ + Correlation r. 55 5 5 10 15 20 25 30 35 7. 5m. Jacobs Winds kts. Figure A-2. Scatter diagram of the Jacobs 7.5 meter winds vs. surface (7.5 meters) measured winds. - 34 - </P> <P><PB REF="00000046.tif" SEQ="00000046" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="715" N="35"> 30 + t + /Y=x 25 4 + 4/ + + + 16m.20 Y 9.99+.45X 16m. 20 MKG + Tower + + Winds + * kt. 15 /,/ t Wind Comparison / / + t' Muskegon Tower Aerovane vs / + + Jacobs 19. 5 m. 10' + Correlation r =.37 0 5 10 15 20 25 30 35 19.5 m. Jacobs Winds kts. A-3. Scatter diagram of the Jacobs 19.5 meter winds vs. surface (16 meters) measured winds. 30 + + + + 1m.2+ + MKG + + 25 i + + Aerovane + /+ Wind Comparison 16 m. ns I / + + /Muskegon Tower vs Richards 5t S. 1t Correlation r =.3 7 + / + ~~10 + + + M KG + 5 ++ 5 10 15 20 25 30 Richards Winds kts. Figure A -4.Muskegon Tower vsdiagram of the Richards winds vs. surfacigure A-4. Scatmeter diagram of the Richardsmeasured winds vs. sur- 35 </P> <P><PB REF="00000047.tif" SEQ="00000047" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="841" N="36"> 25 + /Y -= 11.0 +.37X 20 MKG + Tower + + 10 m. + Winds +1+ + Wind Comparison kts. 15 Muskegon Tower 10 m. wind vs Richards Wind. Correlation r =. 24 10 _ 5 5 10 15 20 25 30 Richards Winds kts. Figure A-5. Scatter diagram of the Richards winds vs. surface (10 meters) measured winds. - 36 - </P> <P><PB REF="00000048.tif" SEQ="00000048" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="878" N="37"> APPENDIX B 196 5 WAVE DATA AND SCATTER DIAGRAMS FOR MUSKEGON, MICHIGAN - 37 </P> <P><PB REF="00000049.tif" SEQ="00000049" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="874" N="38"> TABLE B - 1 SIGNIFICANT WAVE HEIGHTS DURING 1965 HINDCAST PERIODS Muskegon Research Tower SK = SMB Wave Hindcasts with Bretschneider winds. B = SMB Wave Hindcasts with Richards winds. R = SMB Wave Hindcasts 10 meter measured winds. M PNJ = PNJ Wave Hindcasts with Jacobs 7.5 measured winds. J PNJ= PNJ Wave Hindcasts with Richards winds. R PNJ PNJ= PNJ Wave Hindcasts with 7.5 meter measured winds. M = PM Wave Hindcasts with Jacobs 19,5 meter winds. J2 = PM Wave Hindcasts with Richards, winds. PM = PM Wave Hindcasts with 16 meter measured winds. OBS = Significant wave heights as calculated from the standard deviation of the wave record. OBS CERC= Significant wave heights as calculated from the CERC spectra of the wave record. Abbreviations for sea state: FD=fully developed, FL = fetch limited, DL = duration limited and Sw = swell. All significant wave heights are in feet. cont d </P> <P><PB REF="00000050.tif" SEQ="00000050" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="866" N="39"> Date Time Sea SMB SMB SMB PNJ PNJ PNJ PM PM PM OBS OBS C.S.T. State B R M J R M J2 R M CERC September 1965 23:0000 DL 2.4 2.7 2.5 2.2 2.1 2.2 2.3 3.1 23:0600 FD 5.3 2.6 4.7 6.1 1.8 4.9 6.3 2.2 2.6 3.7 3.6 23:1200 FL 5.9 3.9 6.4 5.9 4.2 7.7 5.5 5.4 23:1800 DL 4.5 5.3 5.5 2.9 6.9 7.3 7.0 6.1 24:0000 FL 4.8 4.4 2.8 7.4 4.5 2.7 4.7 3.6 6.1 5.3 24:0600 FD 4.5 3.3 3.5 6.7 2.7 3.5 6.5 3.1 4.7 3.7 4.5 24:1200 FL 6.5 4.0 3.7 8.7 3.8 4.0 4.1 5.3 4.6 4.1 24:1800 FL 7.7 2.5 4.4 7.8 1.8 4.6 2.2 5.9 4.2 4.1 25:0000 FL 8.2 3.0 5.2 7.8 2.7 5.9 4.7 7.3 5.1 5.1 25:0600 FL 11.0 4.4 6.1 8.0 5.1 7.7 8.8 4.9 5.4 25:1200 FL 9.4 5.6 7.0 8.7 6.1 8.3 5.9 10.5 7.6 7.0 25:1800 FD 2.4 5.3 3.2 6.9 5.9 4.0 6.6 8.0 7.6 7.0 26:0000 5.1 1.9 2.2 4.6 4.6 26:0600 FL 3.1 2.0 28:0000 FL 2.5 2.2 2.4 2.1 28:0600 DL 3.6 7.1 2.9 2.3 28:1200 FD 4.7 8.4 7.7 2.9 2.4 28:1800 FD 2.5 3.3 2.7 2.4 29:0000 FL 8.2 1.7 1.1 29:0600 FL 1.5 1.0.9 29:1200 FD 2.0 3.7 1.4 4.1 1.8.9 30:0600 DL 8.0 7.5 1.6 1.3 30:120U FD 8.3 8.2 8.3 4.2 3.3 30:1800 FD 4.6 4.7 2.0 5.4 4.4 4.4 cont'd </P> <P><PB REF="00000051.tif" SEQ="00000051" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="810" N="40"> Date: Time Sea SMB SMB SMB PNJ PNJ PNJ PM PM PM PM OBS OBS C.S.T. State B R M J R M J2 R M CERC October 1965 01:0000 DL 5.1 3.4 4.2 2.3 5.1 5,0 5.5 01:0600 FL. 8.7 2.2 7.0 9.7 1.4 1.8 7.3 7.3 01:1200 FL 1,9 3.2 7,6 8.9 3.6 5.8 1.2 02:0600 FL 8.3 2.5 2.5 7.5 2.2 2.4 2,5 02:1200 FL 13.2 5.6 5.9 8.2 7.6 2.0 5.8 5.8 02:1800 FD 7.7 3,5 6.3 6.8 2.7 4.7 9.0 3.1 6,9 5,1 03:0000 FL 4.5 8.2 4.5 4.7 5.6 4.6 03:0600 FL 7.3 10.3 7.3 7.1 6.2 03:1200 FL 3.6 2.9 05:1200 DL 3.4 7.2.8 0 05:1800 FD 2.8 3.3 2.1 2.1 4.0 2,0 2,3 06:0000 FD 4.5 9.1.6 8.2 5.9 3.3 4.0 06:0600 DL 8.0 2.2 2.9 6.9 2.2 5.0 5,8 5.3 06:1200 FD 7.4 3.7 5.2 6.4 3.8 8.9 6.9 4.1 7.6 6.0 06:1800 FD 2.2 3.7 4,4 3.0 07:0000 FD 3.5 2.8 2.7 2.2 5.1 2.2 2.0 07:0600 DL 7.1 5.7 2.1 3,7 3.5 07:1200 FD 5.4 2.8 4.2 4.8 2.2.8 5.5 10.5 5.2 4. 1 07:1800 FD 3.9 4.0 5.1 3,9 3.8 1.2 4.6 4.1 5.9 6,3 6.0 08-:000 DL 7.0 5.2 5.5 3.3 6.5 4.2 3.4 08:0600 DL 13.0 7.4 6.8 8.5 7.9 2.2 8.2 8.6 08:1200 FD 8.5 5,5 8.2 6.1 6.9 7.5 6.4 6,6 8.3 8.1 08:1800 FD 12.0 5.1 8,6 8.4 6.1 9.0 8.5 5.9 14.3 7.2 7,0 09: 0000 FD 10, 0 3 3 6 1 7.0 2.7 9.7 7.4 3.1 8.0 6.5 4.5 0900600 FL 5.3 7.8 10.7 5.5 4.8 11.4 5.8 2.7 11:0600 FL 2.1 2.2 1.7 cont d </P> <P><PB REF="00000052.tif" SEQ="00000052" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="777" N="41"> Date:oTime 9vate SMD SMB SMB PNJ PNJ PNJ PM PM PM OBS OB C.S T a B R M J R M J R M CR 11:-1200 FD 4.7 4.0 2.7 8.1 4.9 7.4 2.4 2. 11:1800 FD 4.5 2.9 4.5 4.5 2.2 5.2 2.6 4.5 3. 12:0000 FD 8.6 4,5 7.0 4.9 5.1 5.5 5.2 5.5 12:00600 DL 10.0 3.2 7.8 7.5 2.7 3,1 9.1 6. 22:1800 DL 3.9 2.2 2.0 1.8 23:0000 2.4 3.2 1.8 2.2 3.6 3E 23:0600 4.1 2. 23:1200 FL 2,3 3.4 25 23:1800 FL 4.8. 24:0000 FL 2.6 4.0. 24:0600 FL 2.6 2. 3 24:1200 FL 2.1 2.5. H 24:1800 DL 2.1 2.7 1.6 2.2 2.6 1C.9. 25:0000 FL 3.7 3.3 3.8 4.1 3.8 5. 25: 0600 DL 3.8 4.6 2.2 1.1 1.5 7.3. 25:1200 DL,,FL 4.6 3.2 5.9 7.5 3.1 3.3 25:1800 FD 3.6 2.4 6.7 1.4 6.5 1.8 C5 29:0600 FL 4.8 2.3 2.9 8.5 2.1 59 3. 29:1200 FL 14.8 3.9 5.5 12.3 4.5 4.7 7. 6. 29:1800 FL 21.5 2.4 7.7 10.3 1.4 1.8 8.4 8. 30:00000 FL 14.2 3.6 7.6 8.0 4,5 8.4 6. 30:0600 FD 5.4 4.3 5.0 5.7 2.7 4.1 76 6.0 30:1200 FL 6.0 3.9 3.1 7. 3.2 3.6 5.5 4. 30:-1800 FD 4,4 4.2 4.5 6.0 4.7 3.1 25 31.0000 DL 9.0 4,5 4.0 6.3 2.1 3.1 4.3 3 1:-0600 FL 3,1 5,5 6.7 4,9 8.0 5.9 7.53 31:01200 DL 6.3 3.5 4.2 2.3 2.2 3.8 7.6E. 31:1800 FD 8.4 3.5 4.5- 7,3 5,1 6.0 7.6 3.1 4.5 4.2 </P> <P><PB REF="00000053.tif" SEQ="00000053" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="829" N="42"> Date: Time Sea SMB SMB SMB PNJ PNJ PNJ PM PM PM OBS OBS C.S.T. State B R M J R M J2 R M CERC November 1965 01:0000 FD 4.4 5.4 3.0 2.0 4.2 3.7 4.7 3.3 2.7 01:0600 FD 4.2 4.4 2.8 4.2 1.8 2.8 4.9 4.7 3.0 2.2 01:1200 FD 3.8 5.2 3.6 4.4 5.0 5.1 5.9 3.6 2.7 01:1800 FD 3.2 2.5 3.6 6.1 4.3 2.2 2.5 1.8 03:0600 FD 7.0 2.7 7.4.7 7.7 4.5 4.2 03:1200 FL 9.2 4.5 5.0 7.7 7.5 6.3 7.1 03:1800 4.4 2.1 4.7 5.5 4.7 04:0000 5.0 2.2 5.3 5.0 5.2 w 04:0600 4.7 3.8 4.7 3.5 2.7 -P, 04:1200 4.5 1.1 4.7.9 04:1800 FL 3.1.8 2.2 05:0000 1.4 1,0 05:0600 FD 2.7 3.4 3.7 05:1200 DL 2.7 5.5 2.1 3.6 05:1800 FD 3.8 3.1 5.3 4.8 1.2 2.9 06:0000 FD 2.7 3.6 4.4 2.9 2.7 06:0600 FD 3.0 2.1 3.8 2,8 2.6 06:1200 4.5 1.7 06:1800 1.4 o7 </P> <P><PB REF="00000054.tif" SEQ="00000054" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="831" N="43"> TABLE B-2 SIGNIFICANT PERIOD OR PERIOD OF MAXIMUM ENERGY FOR 1965 WAVE HINDCAST TIMES Muskegon Research Tower SMB = SMB Period hindcasts with Bretschneider winds. B SMB = SMB Period hindcasts with Richards winds. R SMB SMB Period hindcasts with measured 10 meter winds. PNJ PNJ Period hindcasts with Jacobs 7.5 meter winds. Ji PNJ = PNJ Period hindcasts with Richards winds. R P - PNJ Period hindcasts with measured 7.5 meter winds. PM = PM Period hindcasts with Jacobs 19.5 meter winds. PM PM Period hindcasts with Richards winds. R PM PM Period hindcasts with measured 16 meter winds. M Period of Maximum Energy as determined from the CERC spectra of the wave CERC record. Abbreviations for sea state: FD= Fully developed, FL= Fetch limited, DL= Duration Limited, and Sw= Swell. All periods are in seconds. </P> <P><PB REF="00000055.tif" SEQ="00000055" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="835" N="44"> Date: Time Sea SMB SMB SMB PNJ PNJ PNJ PM PM PM OBS C. S.T. State B R M J1 R M J2 R M CERC September 1965 23:0000 DL 3.8 4.0 3.8 4.8 4.3 4.5 4.1 23:0600 FD 5.8 4.9 5.6 7.1 4.4 6.2 7.0 4.1 4.5 4.9 23:1200 FL 6.4 5.2 6.8 9.3 7.6 7.4 5.8 23:1800 DL 5.3 6.1 6.2 6.9 9.9 8.9 6.6 24:0000 FL 5.9 5.7 4.8 8.4 6.5 4.9 7.0 6.0 5.3 5.8 24:0600 FD 5.8 5.2 5.2 7.6 5.3 5.5 4.9 6.0 5.0 24:1200 FL 6.7 5.5 5.3 9.7 6.1 5.7 5.6 6.4 5.0 24:1800 FL 7.2 4.7 5.7 8.7 4.4 6.0 4.1 6.8 5.0 25:0000 FL 7.3 4.8 6.1 8.7 5.3 6.7 4.9 7.5 5.4 25:0600 FL 8.2 5.4 6.5 8.5 7.8 7.4 8.3 5.5 25:1200 FL 7.2 6.5 7.1 8.1 7.3 7.7 6.8 9.0 6.7 25:1800 FD 4.7 6.2 5.7 7.7 6.7 5.5 7.1 7.9 6.5 26:0000 9.4 6.9 4.1 26:0600 FL 28:0000 FL 3.8 4.7 4.6 28:0600 DL 5.4 10.9 5.1 28:1200 FD 5.9 8.3 7.7 5.0 28:1800 FD 5.1 5.0 4.7 29:0000 FL 29:0600 FL 3.0 4.7 29:1200 FD 4.5 4.0 3.8 30:0600 DL 7.3 3.3 30:1200 FD 7.6 9.9 8.1 5.4 30:1800 FD 5.8 6.1 5.2 6.5 4.9 cont'd </P> <P><PB REF="00000056.tif" SEQ="00000056" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="787" N="45"> Date: Time Sea SMB SMB SMB PNJ PNJ PNJ PM PM PM OBS C.S.T. State B R M i R M J2 R M CERC October 1965 01:0000 DL 5.2 4.3 4.8 4.7 6.3 5.6 01:0600 FL 7.6 4.5 6.8 13.0 4.0 3.8 6.6 01:1200 FL 2.7 4.7 6.8 8.3 7.2 6.5 02:0600 FL 7.5 3.8 3.8 9.3 4.3 3.9 02:1200 FL 8.7 5.9 6.0 8.6 7.9 5.7 02:1800 FD 6.7 5.4 6.8 7.7 5.3 8.4 4.9 6.8 03:0000 FL 2.4 5,7 7.4 6.5 6.0 5.3 03:0600 FL 2.4 6.7 8.3 6.8 7.3 03:1200 FL 2.3 4.5 05:1200 DL 5.0 10.9 5.5 3.1 U, 05:1800 FD 5.0 3.3 2.8 5.7 5.1 8.0 3.9 06:0000 FD 5.4 8.6 4.7 06:0600 DL 6.9 3.7 4.2 10.6 4.3 7.3 6.2 06:1200 FD 7.2 5.2 6.0 7.9 6.1 5.4 5.6 6.7 06:1800 FD 5.3 6.2 5.9 07:0000 FD 5.6 4.0 3.0 6.1 4.1 4.0 07:0600 DL 6.5 8.9 6.5 4.5 07:1200 FD 6.3 4.0 4.8 7.1 4.1 6.0 5.6 07:1800 FD 5.7 5.5 6.2 6.1 6.1 5.6 6.0 08:0000 DL 6.5 6,0 6.2 5.8 5.3 5.0 08:0600 DL 8.6 6.6 6.8 10,0 9.1 7.1 6.7 08:1200 FD 7.4 6.3 7.2 7.3 7.7 8.1 7.1 6.7 08:1800 FD 8.3 6.1 7.4 8.3 7.3 7.5 6.8 6.4 09:0000 FD 8.0 5.2 6.6 8.1 5.3 4.9 5.9 09:0600 FL 5.9 7.2 6.3 11:0600 FL 3,3 2.4 5.1 11:1200 FD 6.1 5.1 4.2 8.2 6.8 7.6 3.7 cont'd </P> <P><PB REF="00000057.tif" SEQ="00000057" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="831" N="46"> Date:Time Sea SMB SMB SMB PNJ PNJ PNJ PM PM PM OBS C.S.T. State B R M J1 R M J2 R M CERC 11:1800 FD 5.7 4.9 5.5 6.5 4.8 6.3 4.5 5.0 12:0000 FD 7.5 5.4 6.7 6.7 6.5 6.6 5.6 12:0600 DL 8.0 5.2 7.2 8.3 5.3 4.9 6.9 22:1800 DL 3.2 2.4 5.1 5.1 23:0000 4.5 4.4 4.4 6.2 4.1 23:0600 23:1200 FL 23:1800 FL 24:0000 FL 24:0600 FL 24:1200 FL 3.3 2.9 5.2 4.4 24:1800 DL 3.6 5.7 4.7 4.8 2.6 4.5 6.8 25:0000 FL 2.4 5.2 4.4 6.1 6.8 5.6 4.8 25:0600 DL 4.7 4.6 5.0 4.7 3.6 8.4 3.4 6.7 25:1200 DL, FL 5.8 4.7 6.6 10.0 5.7 7.9 25:1800 FD 5.3 4.8 7.6 4.0 3.8 4.3 5.2 3.0 9.0 5.2 6.3 3.9 4.5 29:0600 FL 5.6 3.7 4.2 9.2 4.3 4.0 4.4 29:1200 FL 8.7 5.2 6.0 8.9 6.5 8.8 6.0 6.7 29:1800 FL 10.5 4.8 7.3 8.6 4.0 8.0 3.8 10.5 6.7 30:0000 FL 9.0 4.8 7.3 8.6 8.0 8.2 7.9 7.1 30:0600 FD 6.2 5.8 6.2 7.1 6.1 6.1 5.6 9.4 6.9 30:1200 FL 6.5 5.7 5.2 10.3 5.7 4.5 5.3 6.5 30:1800 FD 5.7 6.3 6.5 3.0 6.8 6.0 5.7 31:0000 DL 7 ol 6.2 4.8 7.6 9.4 4.5 31:0600 FL 3.1 6.4 6.8 7.3 6.7 6.8 6.2 cont'd </P> <P><PB REF="00000058.tif" SEQ="00000058" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="788" N="47"> Date: Time Sea SMB SMB SMB PNJ PNJ PNJ PM PM PM OBS C.S.T State B R M Ji R M J2 R M CERC 31:1200 DL 5.8 4.7 5.0 4.6 5.3 5.1 7.8 31:1800 FD 7.6 5,5 5.5 7.9 5.3 8.8 7.7 4.9 5.7 November 1965 01:0000 FD 5,7 6.3 5.5 6.5 5.8 5.4 6.0 4.6 01:0600 FD 5.0 5.7 4,9 6.3 6.5 5.0 6.2 6.0 4.7 01:1200 FD 5.5 6.1 4.9 6.1 7.3 6.8 6.2 6.8 4.9 01:1800 FD 5.1 4.7 5.9 4.4 2.8 5.8 4.1 4.3 03:0600 FD- 7.0 4.0 7.9 4.0 7.7 5.4 03:1200 FL 7.6 5,0 5.8 10.1 8.1 9.2 6.6 03:1800 5.7 6.5 6.0 04:0000 6.2 6.9 6.4 04:0600 6.0 6.5 6.0 04:1200 5,8 6.5 6.0 04:1800 FL 05:0000 05:0600 FD 3.4 5.3 5.2 05:1200 DL 4,4 3.6 7.8 5.1 05:1800 FD 5.3 5.6 3.2 6.1 3.0 50 06:0000 FD 4.8 5.9 5.8 4.1 06:1200 06: 1800 6.-3 </P> <P><PB REF="00000059.tif" SEQ="00000059" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="843" N="48"> TABLE B-3 PERIOD BAND AND MAXIMUM WAVE HEIGHT FOR 1965 WAVE HINDCAST TIMES PNJ = Period band and maximum wave height in preceding 20 minutes as calculated from PNJ wave hindcasting method, using Jacobs' 7.5 meter wind. PM = Period band as calculated from wave hindcasts based on PM spectra. OBS = Maximum wave height as determined from wave spectra of wave gauge record. Period Band (sec) Maximum Wave Height (ft) Date:Time PNJ PM PNJ OBS 00 September 1965 23:0000 1.0- 4.8 3.8 3.7 23:0600 2.4- 9.8 2.8-7.0 10.6 4.5 23:1200 2.9- 9.3 10.2 7.5 23:1800 2.5- 6.9 5.0 7.4 24:0000 3.1- 8.4 12.8 7.3 24:0600 2.8-10.4 2.8-7.0 11.6 5.7 24:1200 3.3- 9.7 15.1 4.8 24:1800 3.1- 8.7 13.5 5.2 25:0000 3.1- 8.7 13.5 6.2 25:0600 3.1- 8.5 13.9 7.4 25:1200 3.1- 8.1 15.1 9.9 25:1800 1.5- 7.8 2.2-5.5 5.5 9.3 28:0000 1.0- 4.7 3.8 2.8 28:0600 3.0-10.9 12.3 3.8 28:1200 3.1-11.4 3.1-7.7 14.6 2.9 28:1800 1.1- 7.2 1.8-4.6 4.3 3.1 29:0000 14.2 1.4 cont'd </P> <P><PB REF="00000060.tif" SEQ="00000060" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="868" N="49"> Period Band (sec) Maximum Wave Height (ft) Date: Time PNJ PM PNJ OBS 29:1200 1.8- 8.3 2.2-5.6 6.4 - 30:0600 3.0- 9.9 13.0 1.7 30:1200 1.8- 8.3 3.2-8.1 14.2 3.9 30:1800 2.1- 9.0 2.5-6.5 8.1 4.6 October 1965 01:0000 1.3- 4.7 4.0 6.6 01:0600 3.5-13.0 16.8 9.6 01:1200 3.2- 8.3 15.4 5.6 02:0600 3.0- 9.3 13.0 3.8 02:1200 3.1- 8.6 3.3-8.4 14.2 8.7 02:1800 2.8-10.5 11.8 6.7 05:1200 3.0-10.9 2.2-5.6 12.5 - 05:1800 1.5- 7.8 3.1-8.0 5.7 2.9 06:0000 3.2- 7.5 15.8 7.5 06:0600 3.0-10.6 2.9-7.3 12.0 7.5 06:1200 2.4-10.2 2.1-5.4 11.1 9.0 06:1800 1.0- 7.0 2.5-6.2 3.8 3.7 07:0000 1.5- 8.3 4.7 3.0 07:0600 2.8- 8.9 2.6-6.5 9.9 4.6 07:1200 2.1- 9.1 2.4-6.0 8.3 5.0 07:1800 1.8- 8.3 6.7 7.0 08:0000 1.4- 5.8 5.7 4.7 08:0600 3.1-10.0 2.8-7.1 14.7 11.1 08:1200 2.5-10.0 3.2-8.1 10.6 10.8 cont'd </P> <P><PB REF="00000061.tif" SEQ="00000061" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="861" N="50"> Period Band (sec) Maximum Wave Height (ft) Date: Time PNJ PM PNJ OBS 08:1800 3.1-11.4 3.0-7.5 14.6 9.6 09:0000 2.8-10.5 12.1 6.0 09:0600 3.6 18.5 7.2 11:1200 3.0-11.2 3.0-7.5 14.0 3.1 11:1800 2.0- 8.8 2.5-6.3 7.8 4.5 12:0000 2.2- 9.1 2.6-6.6 8.5 6.9 12:0600 3.0- 8.3 13.0 10.3 12:1800 0.9- 4.7 3.8 cn 25:0600 0.9- 9.1 3.8 10.1 25:1200 3.1-10.0 13.0 25:1800 2.8-10.4 2.8-7.1 11.6 29:0600 3.2- 9.2 14.7 4.1 29:1200 3.7- 8.9 21.2 7.0 29:1800 3.5- 8.6 17.8 9.9 30:0000 3.1- 8.6 13.8 8.7 30:0600 2.4- 9.7 9.9 9.0 30:1200 3.1-10.3 13.5 5.4 30:1800 1.9- 8.5 2.7-6.8 7.3 9.5 31:0000 2.9- 7.6 10.9 31:1200 0.9- 4.6 4.0 6.4 31:1800 2.9-10.8 3.0-7.7 12.6 4.5 cont'd </P> <P><PB REF="00000062.tif" SEQ="00000062" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="826" N="51"> Period Band (sec) Maximum Wave Height (ft) Date:Time PNJ PM PNJ OBS November 1965 01:0000 1.4- 7.6 2.1-5.3 5.2 3.1 01:0600 1.9- 8.5 2.4-6.2 7.3 2.7 01: 1200 1.8- 8.1 2.5-6.2 7.6 6.2 01:1800 1.7- 8.1 2.3-5.8 6.2 2.3 03:0600 2.9-10.8 3.0-7.7 12.8 5.0 03 1200 3.1-10.1 13.3 8.8 05:0600 1.2- 7.4 2.0-5.1 4.7 05:1200 2.7- 7.8 9.5 05:1800 1.5- 7.7 2.4-6.1 5.4 2.8 06:0000 1.7- 8.1 2.3-5.8 6.2 3.1 06:0600 1.4- 7.6 2.1-5.4 5.2 3.1 </P> <P><PB REF="00000063.tif" SEQ="00000063" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="768" N="52"> 8 Y =. 84 +. 94X - 4 = 7 + + 6 4H1/3 + 5 + / OBS 5 4 ft. 4 +.4./ Significant Wave Heights 4+' Observed vs CERC Observed + + Correlation Coeffecient r =.89.,-+ 3 40 I I I I I I I I l I I 2 3 4 5 6 7 8 9 10 Observed - CERC H113 ft. Figure B-1. Scatter diagram of CERC observed significant wave heights vs. those calculated from the standard deviation of the staff gage data. 12 ~~~~10 ~~Y=x 8f 6 + / + + / v *+ + Observed vs +MB - Bretschneider Winds H +/ + + + 1 /3 +1 Y I 2.55+. 35X OBS + 0 21. 6 8 12 14 16 18 20+ 4 + + ++ +++ H Olserved vs SMB - Bretschneider Winds 2 +X4~C++ + Correlation Coeffecient r-,60 2 4 6 8 I0 12 14 16 18 20 H/3 SMB - Bretschneider Winds ft. Figure B-2. Scatter diagram of hindcast significant wave heights calculated by the SMB (Bretschneider winds) method vs. the observed significant wave heights. - 52 - </P> <P><PB REF="00000064.tif" SEQ="00000064" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="817" N="53"> 12 10 -/, Y=X 8 4. + H + + + + 1/3 + + + //|++ + Y= 2,90-.29X OBS _ / + ft. Significant Wave Heights 4 __ + _ + +'++ Observed vs PNJ - Jacobs Winds' +++ + t + Correlation Coefficient, r=.35 2 + + + 0 2 4 6 8 10 12 14 16 18 20 H 1/3 PNJ - Jacobs Winds ft. Figure B-3. Scatter diagram of hindcast significant wave heights calculated by the PM (Jacobs 7.5 meter winds) method vs. the observed significant wave heights. 8 + + Y=x — _ / Y=X 446 + H113 OBS 5 Y=2.03+. 32X ft. 3 + Significant Wave Heights 2 / + a Observed vs PM - Jacobs 19. 5 m. Winds 2/ Correlation r =. 32 1 2 3 4 5 6 7 8 9 H113 PM - Jacobs 19. 5 m. Winds ft. Figure B-4. Scatter diagram of hindcast significant wave heights calculated by the PM (Jacobs 19.5 meter winds) method vs. the observed significant wave heights. - 53 </P> <P><PB REF="00000065.tif" SEQ="00000065" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="814" N="54"> 4 + t Y=2.7+.63X 7/+ + 46 + +, 1/3 5 OBS Significant Wave Heights ft. 4. + Observed vs SMB - Richards Winds 4 / Correlation Coeffecient r =.36 + + I 2 3 4 5 6 7 8 9 10 H1/3 SMB- Richards Winds ft. Figure B-5. Scatter diagram of hindcast significant wave heights calculated by the SMB (Richards winds) method vs. the observed significant wave heights. +' 8 -- + + + 7 / Y = 2-73 +.57X _ + / + O 5 + 4 4 4 4 ++ I 2 3 4 5 6 7 8 9 10 H1/3 PNJ - Richards Winds ft. Figure B-6. Scatter diagram of hindcast significant wave heights calculated by the PNJ (Richards winds) method vs. the observed significant wave heights. - 54 - </P> <P><PB REF="00000066.tif" SEQ="00000066" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="806" N="55"> t 8 4/- Y:2. 32+. 68X 7 __ + + H 113 5L _ /+ Significant Wave Heights OBS Observed vs PM - Richards Winds ft. 4 < / + Correlation r. 55 4t. + 3/ / I I 2 3 4 5 6 7 8 H /3 PM - Richards Winds Figure B-7. Scatter diagram of hindcast significant wave heights calculated by the PM (Richards winds) method vs. the observed significant wave heights. 9 tt e -Y=X 8 / + t 7 + i + + +6:~, e Y =2.55 +.59X,t H 113 5 + OBS ft 4 3 / + Significant Wave Heights $/x + Observed vs SMB - Measured Winds 2 Correlation Coeffecient r =. 62 0 1 2 3 4 5 6 7 8 9 10 11 H 113 SMB- Measured Winds ft. Figure B-8. Scatter diagram of hindcast significant wave heights calculated by the SMB (measured winds) method vs. the observed significant wave heights. - 55 - </P> <P><PB REF="00000067.tif" SEQ="00000067" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="830" N="56"> 8 + 7 + + / ~-+ + 6 + H 1/ + + OBS + Significant Wave Heights OBS 4 Observed vs PNJ - Measured Winds ft. + +. Correlation r =.47 0 1 2 3 4 5 6 7 8 9 10 H1/3 PNJ - Measured Winds Figure B-9. Scatter diagram of hindcast significant wave heights calculated by the PNJ (measured winds) method vs. the observed significant wave heights. Y =X 6 1 Y=4. 02+. 13X 5 4 + H 11 /Significant fVave Heights H1I3 t / t Observed vs PM - Measured /inds OBS 3 + Correlation r=. 34 ft. 1 2 3 4 5 6 7 8 9 10 H,,: PM - Measured Winds ft. Figure B-10. Scatter diagram of hindcast significant wave heights calculated by the PM (measured winds) method vs. the observed significant wave heights. - 56 </P> <P><PB REF="00000068.tif" SEQ="00000068" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="813" N="57"> 8 / = O*+_t+Y = 4. 90+.11 X OBS + + Sec. + ++ 4 X i+ ++ Wave Periods Observed VS SMB- Bretschneider 2 _/Correlation r =.20 1 2 3 4 5 6 7 8 9 10 11 12 Tsig. SMB - Bretschneider Sec. Figure B-ll. Scatter diagram of hindcast significant period calculated by the SMB (Bretschneider winds) method vs. the observed period of maximum energy. 8 Y=X ~~~7 4+~ 6 L+ 1 t+* t-t + +~ /+ 4 T+ ~ + +e + Tm Y = 5.02 +.05X OBS ++ + + + + + Sec. / + + 4 /++ t 3 * Wave Periods CERC - Observed vs PNJ - Jacobs Winds 2 Correlation r =. 11 0 I I I I I I I I I I I 1 1 2 3 4 5 6 7 8 9 10 11 12 T PNJ - Jacobs Winds Sec. m Figure B-12. Scatter diagram of hindcast period of maximum energy calculated by the PNJ (Jacobs' 7.5 meter winds) method vs. the observed period of maximum energy. - 57 </P> <P><PB REF="00000069.tif" SEQ="00000069" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="795" N="58"> Y =X 8 T + 3. 15/ + 31 OBS 5 4 * + I / Wave Periods Observed VS PM - jacobs 19 5 n. Winds 2 Correlation r =, 31 I 2 3 4 5 6 7 8 9 10 I 1 12 T1 PM -Jacobs 19. 5 vn. Ninds Sec. Figure B-13. Scatter diagram of hindcast period of maximum energy calculated by the PM (Jacobs' 19.5 meter winds) method vs. the observed period of maximum energy. Y =X 7 /+ = 0 08+.51X 7s it t t~+ + + + 6 Sec. + - / ~~+ / Observed vs SMB - Richards Winds / + Correlation r =.40 1 2 3 4 5 6 7 3 9 10 11 12 T SVIB - Richards Vinds Sec. Figure B-14. Scatter diagram of hindcast significant period calculated by the SMB (Richards' winds) method vs. the observed periods of maximum energy. 58 - </P> <P><PB REF="00000070.tif" SEQ="00000070" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="808" N="59"> ~~m~~~~~~~ t t+ + 6 +: 4, 18 +25 x OBS -, sec 4t+ Wave Periods Observed vs PNJ - Richards Winds 2 / Correlation r= 37.1 2 3 4 5 6 7 8 9 10 II 12 Tm PNJ - Richards Ninds sec Figure B-15. Scatter diagram of hindcast of period of maximum energy calculated by the PNJ (Richards winds) method vs. the observed period of maximum energy. 8, Y = X 7 T + Tm 5 + 1 + $/+ + 6 Iss. 1 OBS, / sec. 4, -Wave Periods 3 / Observed vs PM - Richards Winds Correlation r.17 2 O 2 3 4 5 6 7 8 9 10 11 12 Tn PA - Richards Winds sec Figure B-16. Scatter diagram of hindcast of period of maximum energy calculated by the PM (Richards winds) method vs. the observed period of maximum energy. - 59 </P> <P><PB REF="00000071.tif" SEQ="00000071" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="814" N="60"> 8 ~~~7 -~~~~~~~~ 2 64 t.54X 6 + + Tm t, 4.+ + OBS 5 _ + sec 4 Nave Periods Observed vs SMB - Measured Winds 3 Correlation r =.67 2 I 2 3 4 5 6 7 8 9 i I 1 12 T SMB - Measured Winds sec m Figure B-17. Scatter diagram of hindcast significant wave period calculated by the SMB (measured winds) method vs. the observed period of maximum energy. 6 + Y+ = 4. / — 4.o08 +.26 X i' ++ OBS sec / Vave Periods Observed vs PNJ - MVeasured Winds 3 _ / Correlation r =.51 I 2 3 4 5 6 7 8 9 10 11 12 Tm PNJ - Measured Winds sec Figure B-18. Scatter diagram of hindcast wave period of maximum energy calculated by the PNJ (measured winds) method vs. the observed period of maximum energy. - 60 - </P> <P><PB REF="00000072.tif" SEQ="00000072" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="828" N="61"> 8 /Y =X 7 + 6 o + /Y /3 3.47 +.31 X T 5 + OBS sec 4 Wave Periods Observed vs PM - Measured Winds 3 / Correlation r I.64 1 2 3 4 X 5 6- 7 8 9 10 11 12 T PM - Measured Winds sec. Figure B-19. Scatter diagram of hindcast wave period of maximum energy calculated by the PM (measured winds) method vs. the observed period of maximum energy. - 61 </P> <P><PB REF="00000073.tif" SEQ="00000073" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="813" N="62"> 12 OBS PNJ Frequency of Occurrence 10 iA 8 |\ Significant Wave Heights \ Frequency of Occurrence I il\ OBS, SMB, PNJ | | I \ /\ ~ \'/ | \ Selected Dates Sept- Nov, 1965 6 Muskegon Tower oL I I I I I I I I IA\ SM B 2 0 I I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 H 1 3 Classes Figure B-20. Frequency distribution of significant wave heights as calculated by the SMB-Bretschneider wind method and the PNJ-Jacobs 7.5 meter wind method and as observed by the staff wave gage. </P> <P><PB REF="00000074.tif" SEQ="00000074" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="870" N="63"> APPENDIX C 1965 WAVE DATA FOR POINT BETSIE AND PORT HURON, MICHIGAN - 63 - </P> <P><PB REF="00000075.tif" SEQ="00000075" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="832" N="64"> TABLE C - 1 SIGNIFICANT WAVE HEIGHTS AND PERIODS FOR 1965 WAVE HINDCAST TIMES Point Betsie, Michigan SMB Wave Hindcasts Date: Time Significant Significant C.S.T. Wave Height (ft) Wave Period (sec) 28:0600 3.4 4.5 28:1200 5.3 6 o 2 October, 1965 23:1200 6.2 5 o8 23:1800 19.0 9,9 24:0000 6.2 6.7 24:0600 8.4 7 2 24:1200 3.1 5 o 0 24:1800 4.1 5 o 4 25:0000 7.0 6.5 25:1200 4.7 5 5 November, 1965 01: 0000 40 4.80 4 01:0600 6.4 6.4 01:1800 1o9 4,2 05:0600 5.3 5 c5 05:1200 8.0 7.0 05:1800 5.0 507 06. 0000 2.8 4 o5 - 64 - </P> <P><PB REF="00000076.tif" SEQ="00000076" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="876" N="65"> TABLE C - 2 SIGNIFICANT WAVE HEIGHTS AND PERIODS FOR 1965 WAVE HINDCAST TIMES Port Huron, Michigan SMB Wave Hindcasts Date: Time Significant Significant Wave Heights (ft) Wave Periods (sec) October, 1965 23:1200 4.2 4.8 28:1800 6.0 6.2 24:0000 7.5 7.0 24:1200 13.5 9.3 - 65 - </P> <P><PB REF="00000077.tif" SEQ="00000077" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="879" N="66"> APPENDIX D COMPARISON OF 1964 WAVE DATA AT MUSKEGON, MICHIGAN - 66 - </P> <P><PB REF="00000078.tif" SEQ="00000078" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="870" N="67"> TABLE D-1 COMPARISON OF SMB, PNJ, PM AND OBS WAVE DATA FOR 1964 HINDCAST PERIODS Muskegon Research Tower SMB = SMB Wave Hindcasts with Bretschneider Winds PNJC PM and OBS are taken from Jacobs (1965) Significant Wave Height Period of Maximum Energy Date:Time Sea SMB PNJ PM OBS SMB PNJ PM OBS C.S.T. August, 1964 01:0600 FD 5.2 3.8 4.7 5.3 6.1 6.0 01:1200 FD 5.5 4.5 5.3 6.4 6.5 6.4 01:1800 FD 4.9 3.2 4.1 6.2 5.7 5.6 02:0600 FD 3.2 2.7 4.1 5.1 5.3 5.6 02:1200 FD 4.5 3.2 4.7 5.5 5.7 6.0 02:1800 5.6 6.3 02:1926 Sw 3.2 4.7 1.6 5.7 6.0 4.2 07:0600 4.1 5.0 07:0726 Sw 3.2 4.1 2.2 5.7 5.6 4.6 07:1200 FD 4.7 3.8 4.7 5.8 6.1 6.0 07:1736 FD 3.8 4.7 1.7 6.1 6.0 4.6 07:1800 2.6 4.8 10:1200 3.2 4.4 </P> <P><PB REF="00000079.tif" SEQ="00000079" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="823" N="68"> Significant Wave Height Period of Maximum Energy Date:Time Sea SMB PNJ PM OBS SMB PNJ PM OBS C.S.T. 10:1330 Sw 3o2 4.1 1.9 5.7 5.6 3.8 10:1530 Sw 3.2 4.1 2.0 5.7 5.6 4.2 10:1800 5.1 5.9 10:1950 Sw 3.0 4.0 1.7 5.7 5.6 5.0 11:0000 7.4 7.0 September, 1964 13:0000 0 0 0 0 13:0600 FD 2.5 1.2 1.6 0 3.8 3.8 3.5 13:1200 FD 3.7 2.2 3.1 1.8 5.3 4.8 4.9 00 13: 1800 FD 1.8 3.1 1.6 4.4 4.9 14:0000 FD 2.7 3.2 4.1 2.7 4.3 5.3 5.6 14:0600 FD 4~5 4.5 5.3 3.2 5.4 6.5 6.4 20:1200 FL 3.4 2.8 0.6 4.4 5.5 20:1800 FL 4.3 2.8 0.8 5.4 5.9 21:0000 FL 2.6 3.0 2.0 4.8 5.0 21:0100 4.8 21:0300 3.8 21:0500 5.6 21:0600 FD 2.9 3.8 4.7 4.4 6.1 6.0 21:0900 1.4 4.8 23:0000 FL 6.6 0.9 0.6 5.9 2.5 23:0300 0.9 23:0600 DL 7 7 2.8 2.8 6.3 4.0 23:0700 5.7 23:0900 6.6 23:1100 7.0 </P> <P><PB REF="00000080.tif" SEQ="00000080" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="841" N="69"> Significant Wave Height Period Of Maximum Energy Date: Time Sea SMB PNJ PM OBS SMB PNJ PM OBS C o ST o 23: 1200 DL 4.8 5 7 6.3 5.2 7.0 23:1500 6.5 7.8 23:1800 FL 9,0 9.0 7.5 7.5 6.0 23:1900 6.4 8.2 23:2000 6.8 8.3 23:2100 8.7 7.3 8.6 23:2200 7.7 8.7 23:2300 8.1 8.9 24:0000 FL 4.7 9.0 5.8 8.5 8.9 i </P> <P><PB REF="00000081.tif" SEQ="00000081" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="885" N="70"> APPENDIX E SUCCESSIVE APPROXIMATION TECHNIQUE FOR ANALYSIS OF PRESSURE AND WIND FIELDS - 70 </P> <P><PB REF="00000082.tif" SEQ="00000082" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="887" N="71"> APPENDIX E Successive Approximation Technique for Pressure and Geostrophic Wind Analysis Introduction The successive approximateion technique, hereafter called SAT, is an objective analysis method of computing data at the points of a regularly arranged grid from measurements taken at irregularly spaced locations. Figure E-1 illustrates the grid and the location of weather stations used in the analysis. The gridpoint array is 18 x 17 (306 gridpoints) with a 75 km ( ^ 40 n. mi.) spacing. For geostrophic wind calculations, the grid system reduces to 16 x 15 (240 gridpoints) while the gradient wind calculations further reduce it to 14 x 13 (182 gridpoints). The grid array has been made large enough so that truncation does not affect the Great Lakes region. Reliable sealevel pressure analyses and geostrophic wind analyses have been made while curvature analyses and gradient wind analyses have been produced that show discrepancies when compared with hand analyses or measured values. The Analysis Method For purposes of explanation, consider the pressure analysis for the area shown in Figure E-lo The SAT consists essentially of a method of successively correcting grid-point pressures using reported data. Smoothing is accomplished by the calculation of a mean correction for each scan as well as by the introduction of smoothing operationso The First Guess Pressure Field The SAT starts with a first guess grid-point pressure analysis, The first guess used for this analysis was obtained by advection of the pressure analysis of 6 hours earlier by 50% of the 500 mb wind. For the area under consideration, the Green Bay, Wisconsin, 500 mb wind was used in most cases. If no previous computer analysis existed, a hand analysis of the previous map was produced and advected for use as the first guess - 71 </P> <P><PB REF="00000083.tif" SEQ="00000083" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="357" N="72"> XL/ OQ QN yU~~~~~~5 83, vi~~~~~~~~~~~~~~~~~~~~~~~~~ ~. o~.... ~i,,, -.,f \ I, _ WR TS I Ir l~~~~~~'~'i~"a;~'"~.~:.00,~~~cC 74 *'' 9B Y GI G PKF 0l- 7 30( 7~31 741 RHI IT E EjU~J -AZ_ Q... 646 G6396 t ~ ~ ~ ~ I ~~~~~~~I I II ~~~~~~~~~OSTE ost 64 \IS osH 64 GANN ~""' ~ i ~~~. 34 TAX MKH OAS FODLNR 641 GRR T G K)D 9 ~~~~~~~~~641 Aft e 65 0 52 — ~~~~~~3 539 AZIO BTI 5 7t s DSA I~~~~~~~ ORD - 0 NFB T1 1Y~2 B F" ~~ Li JC)Tn 5 W 5SH ~ ~ ~ ~ \\ 544 ~~~~~~~~~~~~~~~~~~~~~~~~~~.5!~~~~~~~~ 10 IT I MFD M 43P HUF 0 z~~`~~ Figure E-1. The analysis grid and the locations of data sources for the Successv Approximation Technique. </P> <P><PB REF="00000084.tif" SEQ="00000084" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="884" N="73"> The First Scan For the first scan or iterative correction process, all pressure measurements within 4.75 grid lengths of each grid point were used to correct the grid point pressure. The amount of correction contributed by any measured station pressure is weighted inversely to its distance from the grid point. Specifically, the following procedures were followed for the first scan. a. All weather stations within a radius of 4.75 grid lengths of the grid point being considered were identified. b. For each of these stations the interpolated station pressure was calculated by bilinear interpolation from the first guess pressure field. The difference between the interpolated and measured station pressure is the error of the first guess field at the station location. ER P - P measured interpolated c. A weight function for each weather station within the 4.75 grid length radius of the grid point in question was calculated. 2 _ d2 WT 2 2 N + d where N = scanning radius d = distance from grid point to station. Note that the WT is unity for a station on a grid point and is zero for a station one scanning radius from the grid point. The weight was zero for all stations outside of the scanning radius. do The correction applied to the grid point wasWT * ER correction = ER Z stations - 73 - </P> <P><PB REF="00000085.tif" SEQ="00000085" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="874" N="74"> where Z stations = the total number of stations contributing to the correction. Thus the correction was a mean value of weighted errors. Scans Two and Three Scans two and three followed the same procedure as scan one except the scanning radius, N, was decreased to 3.60 and 2.25 grid lengths respectively. The results of each previous scan were used as the input pressure fields. By reducing the radius of influence, the measured data closer to each grid point more strongly influenced the correction for the grid point. The First Smoothing To suppress calculation instabilities, the grid point pressures were smoothed between scans three and four and after scan four. Interior grid points were smoothed by the following five point smoother. Where +P1 +P2 +P +P4 +P3 1 2 Smoothed p0 = p0 + P1 0 0 8 0 4 * P0 + P1+ P2 + P3 + P4 8 For perimeter grid points, the following smoothing was used: +P1 P P P2 or +P2 + + + +P2 - 74 </P> <P><PB REF="00000086.tif" SEQ="00000086" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="864" N="75"> 2 * p0 + P1 + P2 Smoothed p0 = The corner grid points were not smoothed. The Fourth Scan The technique of scan one was used for scan four with the scanning radius = 1.5 grid lengths and the correction given by: Z WT * ER correction = - Z WT The Second Smoothinq The second smoothing was done the same as the first and the resultant smoothed pressure values constituted the pressure analysis according to the successive approximation technique. The Geostrophic Wind Field The u and v components of the geostrophic wind at each grid point were calculated from standard meteorological equations in centered finite difference form. I Pl - P3 0 p f Y - Y3 1 P4 P2 p f x4 - x2 where f = the Coriolis parameter p = the density +Pl +P2 +P0 +P4 +P3 - 75 </P> <P><PB REF="00000087.tif" SEQ="00000087" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="859" N="76"> The magnitude and direction of the geostrophic wind relative to the grid were calculated from the following equation: 2 2 I:Vgeol =/ u + v Direction = 3 = arctan u/v where 3 = the meteorological definition of wind direction, i.e. the direction from which the wind is blowing. The Radius of Curvature of the Wind Field The curvature of the wind field is required in order to compute the gradient wind or the Bretschneider wind. The radius of curvature, R, was computed directly from the geostrophic wind direction by considering the change of wind direction between grid points. a+2 0 4s Ax K- 1~ da dx Ha dy R ds ax ds ay ds K ~ ) * cos a + ) s in a o AX o o AY o 0 a4 2 * cos ac + 1 * sin a 2L o 2L o where: K = the curvature of the streamlines, which is a good approximation to the trajectory curvature R = radius of curvature a = angle of the wind vector, measured clockwise from the positive x axis </P> <P><PB REF="00000088.tif" SEQ="00000088" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="876" N="77"> = 37T/2 - f radians s = distance along a steamline L = grid spacing The Gradient Wind Field With the geostrophic wind and the radius of curvature computed for the grid points, the gradient wind was computed from standard meteorological equations. V fR f for cyclonic V2 +J V+ fRV g 2 A 4 geo curvature / 22 fR -. f R - fRV for anticyclonic geo g 2 / 4 curvature The SAT pressure analysis described above and the geostrophic and gradient wind calculations were made from input pressure values at 114 weather stations, Bilinear interpolation provided pressure and wind at any location in the region. For evaluation of the technique, 47 winds at shoreline locations plus pressure and wind data from five ships per lake were entered into the computer but withheld from the analysis. The program compared these reports with the computed values and listed input values, computed values and the errors between them. The output can be varied depending on use. One map output, a portion of which is shown in Figure E-2 lists the pressure, geostrophic wind, curvature and gradient wind at each interior grid point. In addition, it lists the input station pressures, the shoreline station winds, the ship weather reports, computed values of all parameters and errors, The overlake atmospheric stability, Tlake Tair is listed and averaged for each lake, The input pressure can be listed as shown in Figure E-3 and the calculated gridpoint pressures as in Figure E-4. Contouring of the pressure field as shown by Figure E-5 is also possible but rather costly in time. - 77 - </P> <P><PB REF="00000089.tif" SEQ="00000089" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="493" N="78"> *+**********************************************************+******+***~****+********** * I I I I * * I I I * * (88) (87) (86) (85) * * * * ***** i,* * ******* (46) —* *r~~~ ~ (88) (87) (86) * ********(851(46-* * —4461 * ** * * ** *8** * * * * 8** * *8* 8* * 4 **8 *8 *8 * *88 - * 8 ** * ( * * 8 * *8 8++* * *, 150 129 8106 * * 093 080 * * * + + ESC —X* +* * * - + ** * 35/47 00/60 (MMM)* 03/56* * 00/36 01/33 ** PLN * 8 (MM/MM) ** * * X * * * * * (070) * *4 ~~~~~~~ * * (26/20) i * * * * * MICH * ** * / )4(CH*.* * * w/S 8. *** **** * * (* *** * * * 048 126 * 099 090 077 * * * + + * *, + *+ * ~ * 00/58 35/66 * * 35/49 33/34 31/28 * 4 HNH~~~~MN ------ X* *++ * NM *8* *8.* 8* * 4 * + * * * * 1~~~~~~~~~~~~~~~~~~~~~~45)-*+ *. * 8 8 * * * *4** *-(453 * * * * * * * * 8 * *.* 888* * * * *8 8$ 8* * * *8 - * 8 8 t* *,* * ** 148 * 130 *8 113 105*** 095 * * * *0 + + X —---— PTB + 8 8 35/54 8 34/54 30/53 29/55 27/62 * * * *8 * * X —— TVC 8 8 08* * 888* * * (096) * * 0 8*8 8 * (25/15) * 7!I42( * * * * (27/9( * * * *.... ~~~~~~~~~~~~~~~~~~~~~44-* 4~~~~~ * r 8 88 8+* + * 159 151 143 142 137UIVRIT F IHIA + * + * + X......PT * 34/46 30/42*8 28/47 0 28/52 27/58 * * --- ------- * - * 8R * 044- * * * 8 (85) * P * *CT U 0 * 8 8 (1:: * * 8 ***8888*****~**~* 8 9 * 3 2 8 159 151 143 8 142 137 * UN(E*SNTY OP C(L8(0*E 8,* +-.~+ + ~ X-+ * —- +P EFE ENTC F ++ * 32/30 30/34 29/34 28/29 27/30 *9ETEOROLOOV *80 4 CEANON RAPGYW 3/2* * 28/5 * 8 8 8 WAVE...0..X*(80 * *-(43)~~~~ ~~ 143I —*. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~DT —-034 ~OV1*6 * * * * PROJECT NUMBER06768 8 3* 8r, 8 -* * x * * * _**8***8************************ 8 8 8 * OEOST*0P8(C 8(80 880 8 8 8 * 8 PRESSURE CALCULATWIN 8 * 175 * 159 1 153 48 144 * GRI=30 NAUTCAL MILES * 8 + 8 + *. —----..G + * REFERMENCE 1016 85 (0 8. 3/25 30/25 29/ 298/3 29/26 (149) 30/27 * PORDT4EG.N 870EA.G 8 * 8 (27/15) HDAN * *-(43) 8 8 (43( —* 8 8 * 8 8 OATE —-03 808,0965 8 8 MKI 8 1*8 8 T(ME —-18010(2400Z9 2 8 08 M —G —1 —-9 0 * 8 * (165) 8 (149) * STA PRESS W(ND 8 8 (26/20) 8 (26/20) 888888*8888888*8,******8*8***8 RAC 8~* ** ESTC -1.8N MNM/M 8 072 3 165 162 159* 0 154 * GR0 1014.2 27/15 * * + * + ~ + *...MKEL 1016.5 26/20 * * 31/27 * 29/28 28/31 28/36 28/36 8 8*0 1018.2 26/18 8 8 * * 6 088 1018.7 25/15 1 81 8(5 * * 08* 1014.9 26/20 8 8 8 —---— * 8 6 MEG 1014.9 27/15 1 1* I 77* 8* / TVC 1009.6 2515 * 8 8 * * PIN 1007.0 26/20 8 4 r * ~~~~~~~~~~~~~~~~~~~~~~****************+************** * _* 8 8 (4 1012.8 8; * 8 8 PEP 1019.1 * 8 _180 8 177 175 *j74 169. * 068 1021.8 8 8 + 8 * 8 8 K: G R * 1017.9 8 * 29/33 28/33 27/43 * 28/41 28/42 * LNR 1018.9 888~~* 6 —---- MXN 1017.9 8 0*0. 8 8 8 * DB 1020.5 *-(42) * (42) —* RFD 1018.6 8 84~~ ~(182) 8 1 8 P(A 1021.5 N 8*~~ ~(26/10) * RA * *8 1021.7 8 8 8 8 8 LAF 1022.8 * * 8A 8 -8HL 1022.3 * 8 7 1GX0 —-— 1X * CH * FWA 1020.6 8 8 888 —------— ~ * TOL 1019.1 * * 195 189 (8 194***8 NO 0 188 184 * JXN 1016.3 8 8 + ( I * *+ / + 8 FNT 0014.2 * * 27/63 27/36 *8 *27/76 / 28/43 28/42 * HTL 1011.4 * 84 ~I *****G S*N / * 1009.8 / 8 I 0 (187) — * APG 1007.2 * * ILL I IND (25/15) * SSM 1008.5 * I~~~~~~~ * I * 10286 4~~~~~~~~~~~~~~~ * PK — ~ * (88).17 1 *. (8) * 8 ~ ~~~ ( ( * T8 UW11. * OR D, * * OBO 1020.5 * *8t******++** *88*888***8*8888**8888***8**88*8*88888*** 8*888***88*8*8*8 Figure E-2. A portion of the Successive Approximation Technique map output. - 78 </P> <P><PB REF="00000090.tif" SEQ="00000090" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="713" N="79"> 21 SEP,1965 1800C(2400Z) LH*500 50C MB WIND= 24"/55 PLO*500 MO0123 + + 4- + 4- + + 4- + + + + 4- 4- + + WG4*051 YW*078 QK*C66 XL*070 QN*081 4- + + + + + + + + + + 4- + 4 + JB*094 + + + 4 + VJ*046 + + + + + + +YU*101 + + + + I NL*C 32 GFK* 54 4 + + + + + + + + + WR*077 + + +TS'096 + + QT*036 V0O085 6JI*C27 + + + + + + + + + + + + + + + + HIB*008 XR*081 FAR*C66 + + + + + +CMX*034 + 4 + + + + + + + + DLH*014 MW*1~4 + + 4 + + + + ++MQT*049 + + + + + SB*103 YB*107 + AXN*344 SSM*088 PKF*010 +STC*-029 + + + + + + ESC*057 + + + +ZE*094 + + + + XI*111 PLN*087 + MSP*044 + + + + + + + + + -+ + + + + +'.., Kw~~lc:~R.F* 65 EAU*051 AUW*043 APN*095 QA*121 to ~~~~5) ~~~~~~~~~~~~~~~~~TVC*090 VV*12" + + + + + + + GRB*068 + + + +OSC*.117 + + + + RST.076 HTL*107 TR*149 LSE*078 MN*5CO 4 + + + + + + + + +4 + + + +YZ*144 + SPC*?78 MCW*C94 LNR.066 MBS*500 CE*142 ROC*175 + + + + + MSN*O075 + +MKG*107 + + + + XU* 150+ +4BUF*163 MKE*095 GRR*120 FNT*131 OC.158 ALO*095 + + + + 0BQ*092 + + + + + + + DET*138+ + + + + RFD*088 JXN*127 CID*106 ORD*112 ERI*171 DSM*112 + + + + + + + + + + 4- + + + + + MLI*094 SBN*131 TOL*146 YNG OTM*118 CLE*166. 188 OUJ*209 4+ + + + + 4 + + + + + + + + + + + + + PSB*22C LMN*111 FWA*152 FDY*161 CAK*185 PIA*119 BHL PIT*20C + IRK*114 + + + + + LAF*152 4153 + + + + + + + +A00'212 RAN*1l27 ZZV UIN*IC? CMH*178 *194 MKC*118+ + + + +SPI*125 + + +IND*167 + DAY*170 + + 4 + + MGW*2n7 + MRB*202 CBI1115 HUF*158 PKB*191 VLA*141 CVG*174 STL*133 EKN*225 Figure E-3. Computer listing of input pressures for the Successive Approximation Technique analysis. </P> <P><PB REF="00000091.tif" SEQ="00000091" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="739" N="80"> 21 SEP,1965 1800C(24001) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 17* * + + + + + + + + + + 4 4 + + + + + + *417 58 68 13 75 78 80 82 83 86 92 101 108 112 114 115 117 116 110 16* * + + 4 + 4 + + 4 + 4 4 4 + + + 4 4 4 4*16 61 64 63 62 63 63 68 75 77 82 92 100 106 107 105 104 105 101 15*4- + + + + + + 4 + + + 4 + + + + + + + * 415 58 53 44 41 45 46 52 62 68 75 84 92 99 102 100 96 96 93 144- + + + 4 + 4 4 + 4 4 4 4 4 4 4 4 + 4 4 * 414 48 39 30 28 34 34 39 49 62 71 78 84 91 96 95 89 88 87 13*4 4 4 + 4 4 4 4 4 + 4 + 4 4 + 4 4 + *4*13 35 23 15 17 26 27 33 43 56 67 74 79 83 87 86 83 84 86 12* * + + + + + + + + + + + + + + + + + + * *12 32 17 11 11 17 20 27 38 52 64 74 81 80 84 91 91 92 93 11*4- + + + + + + + + + + + + + + + + + + 36 25 19 15 9 9 21 36 52 68 81 86 87 90 100 105 106 103 10*4 *+ + + + + + + + + + + + + + + + + 4 *4-10 42 31 29 27 18 16 25 42 56 71 84 89 91 96 107 112 112'111 09*4- 4 4 + + 4 + 4 4 4 + 4 4 4 4 4 + 4+ + *409 57 44 43 44 42 38 43 56 66 78 89 95 98 104 113 116 119 124 08* * + + + + + + + + + + + + + + + + + + * *08 73 69 67 66 63 54 57 69 78 87 98 107 112 117 123 126 130 138 0 07*4- + + + + + + + + + + + + + + + + + 4+ *-07 81 88 87 83 74 63 67 79 89 97 107 116 122 127 134 138 143 151 06*4- + + + + + + + + + - + + + + + + + + + *4-06 90 95 93 89 80 73 78 90 100 109 117 123 129 135 145 152 158 164 054-4 + + + + + + + + 4 4 4 4 4 4 4 4 + + *05 103 102 100 97 90 85 89 102 112 119 124 129 136 144 156 164 171 181 04* + + + + + + + + + + + + + + + + + + 4-4-04 110 110 109 105 96 92 99 113 123 130 134 138 146 155 165 177 188 199 03*4- + + + + + + + + + + + + * + + + + + *4-03 112 115 115 111 108 107 112 123 135 143 148 152 158 165 176 189 200 209 024-4 + + + + + + + + + + + + + + + + + + 4-402 112 118 112 10'8 117 119 121 132- 147 156 160 164 169 178 188 196 204 210 0144 + + + + + + + + + + + + + + + + + 401 108 111 114 113 120 126 131 143 157 166 167 169 176 185 192 199 206 209 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 Figure E-4. Gridpoint pressures as calculated by the Successive Approximation Technique. </P> <P><PB REF="00000092.tif" SEQ="00000092" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="862" N="81"> 21 SEP, 1965 1800C(24002Z) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 5 * * * * * * * 11 17* * 666666 8888888888888888888 00000000 * -*17 6666666666 88888888888 00000000 000 666666666666666666666666 8888888 0000000000000000000000000000000 16* * 66666666666666666666666666666666 8888888 0000000000000000000000000000000 * *16 666666 6666666 88888 0000000000000000000000000 444444 6666666 88888 00000000000000 15* * 4444444444444444444444 6666666 888888 00000000 * *15 444444 444444444444 666666 8888888 4444444 4444444 66666 88888888 8888 14* * 44444 2222222 44444 66666 88888888 88888888888 * *14 44 22222222222 44444 66666 888888888 88888888888888 22222 22222222222222 4444 666666 8888888888 8888888888888888888 13* * 2222 22222222222 4444 666666 88888888888888888888888888888 * *13 2222 222222222222 4444 66666 888888888888888888888888888888 222 22222222222 444 66666 8888888888888888888888888888 12* * 222 222222 4444 6666 888888888888888 * *12 222 2222 4444 6666 888888888888888 22222 2222 444 6666 8888888888888888 0000000000 11* * 2222222 0000000 222 444 666 888888888888888 0000000000000000 * *11 2222222222 2222 444 666 8888888888888 00000000000000000 4 222222222222 222 444 666 888888888888 000000000000000000 10* * 44 2222222222 2222 444 666 888888888 000000 * *10 4444 2222222222222 4444 666 8888888 000000 4444 444 6666 888888 000000 09* * 44444444444444444444 44444 66666 88888 0000000 2222 * *09 66 4444444444444 66666 88888 0000000000 2222222222 66666666 4444 6666 88888 000000000 222222222222 O0 08* * 66666666666666666 6666 888888 0000000 222222222222 * *08 H1 6666666 66666 88888 000000 22222222222 44 888888888 66666 6666666 88888 00000 22222222 44444 07* * 88888888888888888 6666666666 88888 00000 222222222 44444444 * *07 88888 88888888888 666666 88888 00000 222222222 444444444 888 8888888 6 8888 000000 222222222 44444444 06* * 888888 8888 000000 222222222 444444 6666 * *06 888888 88888 00000 222222222 44444 6666666 88888888888888 00000 222222222 4444 6666666 05* * G000000OOOO 8888888888 00000 2222222222 44444 6666666 8 * *05 000000000000000 88888 00000 2222222222 444444 666666 8888 OOOOCOOOOOOOOOO000000 8 0000 222222222 444444 66666 88888 04* * 000C00000C0000000 0000 2222222 444444 66666 8888 * *04 00000000 00000 22222 444444444 66666 8888 0 0OOOOOOOOOOOOO 2222 44444444444 66666 8888 000 03* * 0000000000 2222 444444444 666666 8888 000000 * *03 2222 4444444 6666666 8888 000000 0 22222 44444 6666666 88888 0000000 02* * 000 2222222 4444 66666666666 88888 0000000 * *02 0 222222222 444 666666666666 888888 00000000 0 222222222 444 66666666666666 888888 000000000 01* * 00 222222222 4444 66666666666666 888888 000000000 *. *01 10 20 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 Figure E-5. Contours of the calculated pressure field. </P> <P><PB REF="00000093.tif" SEQ="00000093" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="898" N="82"> Evaluation of the Successive Approximation Technique Comparisons between measured ship pressures and computed ship pressures show the SAT does indeed analyze the pressure field. The geostrophic wind field appears to be smooth and regular and compares well with the measured winds. The radius of curvature field shows irregularities and inconsistencies that point out a need for further development. The gradient wind field is not a smooth field with reasonable values but is quite irregular and not an acceptable analysis. The poorness of this analysis is undoubtedly due to the poor radius of curvature input. It must be concluded, at this time, that the SAT produces good pressure and geostrophic wind analyses but the radius of curvature and gradient wind analyses are unreliable. For the development of a wave climatology, the SAT is feasible for the determination of geostrophic wind. Curvature, however, should be determined from measurements on hand analyzed charts until more consistent machine results can be obtained. - 82 - </P> <P><PB REF="00000094.tif" SEQ="00000094" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="853" N="83"> APPEND IX F DERIVATION OF THE SIGNIFICANT WAVE HEIGHT AS A FUNCTION OF THE STANDARD DEVIATION - 83 - </P> <P><PB REF="00000095.tif" SEQ="00000095" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="832" N="84"> APPENDIX F Derivation of the Significant Wave Height as a Function of the Standard Deviation The height of the lake surface, h(t), is a classical random variable and must be analyzed by the techniques of random data analysis. Bendat and Piersol (196t) define the mean square value, 2 of random data to be: h' 2 1 T 2 = lim - h (t) dt (F-l) h ToT T-*oo 0 and the variance to be: 2 1 T 2 h = lim [h(t) h dt (F-2) Th lim~ h T-oo where dh is the mean value of the lake level. 1 T Wth = Jim T- x(t) dt (F-3) T-ooT By a change of coordinates such that h(t) is measured from the mean lake level, ~h can be made zero over the time period 0 to T and 2 2 1 T 2 =f z =lim ( h(t) dt (F-4) T I h T->oT This should be compared with Jacobs' (1965) equation (4) chapter 2. 1 0T 2 E = 2 1im p h (t) dt (F-5) where E is the PNJ energy parameter. From (F-4) and (F-5), we obtain: E T (F-6) h 2 - 84 - </P> <P><PB REF="00000096.tif" SEQ="00000096" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="855" N="85"> 2. and the root mean square wave height (the positive square root of the variance) E /2 h ( and E 1.414 Th (F-7) Pierson, Neumann and James (1955) have stated that the significant wave height, H1/3, can be determined from the E value of a sea state by: H1/3 = 2.83 E.83* 1.44 Th (F-8) or 1H/3 = 4 Th (F-9) The analog computer analysis used to compute Xh removes the mean value h from the data, so equation (F-9) can be used to determine H /3" - 85 </P> <P><PB REF="00000097.tif" SEQ="00000097" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="884" N="86"> BIBLIOGRAPHY Arthur, R. S., 1947: Revised wave forecasting graphs and procedures. Wave Report No. 73, Scripps Institute of Oceanography, 14 pp. Bendat, J. S. and A. G. Piersol, 1966: Measurement and Analysis of Random Data. John Wiley and Sons, Inc., New York. Bellaire, F. R., 1965: The modification of warm air moving over cold water. Proceedings of the Eight Conference on Great Lakes Research, March 29-30, 1965, Ann Arbor, Michigan, pp. 249-256. Bretschneider, C. L., 1951: Revised wave forecasting curves and procedures. Technical Report No. HE-155047, Institute of Engineering Research, University of California, Berkeley, 28 pp. (Unpublished)., 1957: Revisions in wave forecasting: deep and shallow water. Proceedings VI th. Conference on Coastal Engineering, Chapter 3, pp. 30-67, e 1959: Wave variability and wave spectra for wind generated gravity vanes. Beach Erosion Board, UoS. Army Corps of Engineers, Technical Memo. No. 118, pp. 192. 1965: Generation of waves by wind. State of the Art, Report by National Engineering Science Company, Washington, D.C., 20036. Caldwell, J. M., 1963: Rapid spectrum of ocean wave trains. Proceedings of the International Association of Hydraulic Research Congress, Volo 1, ppo 205, London., and L. C. Williams, 1963: The Beach Erosion Board's Wave Spectrum Analyzer and its Purpose, Ocean Wave Spectra, Prentice Hall, pp. 259-266. Cressman, G. P., 1959: An operational objective analysis system. Monthly Weather Review, Vol. 87, No. 10, pp. 367-374, - 86 - </P> <P><PB REF="00000098.tif" SEQ="00000098" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="879" N="87"> Elder, Fo C., 1965: An investigation of atmospheric turbulent processes over water, report number two: data, 1963 and 1964. Contract Cwb-10714, University of Michigan Report 05982-1-f. pp. 71. Harris, D. L., 1967: The air-sea boundary layer. Paper presented at the Conference of the American Meteorological Society on Physical Processes in the Lower Atmosphere, March 20-22, 1967, Ann Arbor, Michigan. Jacobs, S. J., 1965: Wave hindcasts vs. recorded waves. Final Report 06768-1-f. Office of Research Administration, University of Michigan, Ann Arbor, Michigan. Kitaigorodski, S. A., 1961: Application of the theory of similarity to the analysis of wind-generated wave motion as a stochastic process. IZV, Geophys. Ser., pp. 105-117. Lansing, L., 1965: Air mass modification by Lake Ontario during the April-November period. Proceedings of the Eighth Conference on Great Lakes Research, March 29-30, 1965, Ann Arbor, Michigan, pp. 257-261. Lonquet-Higgins, M. S., 1952. On the standard distribution of the heights of sea waves. Journal of Marine Research, Vol. XI, No. 3, pp. 345-366. Newmann, G., 1952: On ocean wave spectra and a new method of forecasting wind-generated seae Beach Erosion Board, U.S. Army Corps of Engineers, Tech. Memo. No. 43, pp. 42 Pierson, W. J. Jr., 1964: The interpretation of wave spectrums in terms of the wind profile instead of the wind measured at a constant height. Journal of Geophysical Research, Volo 69, No. 24, pp. 5191-5203., G. Newmann, and R. James, 1955. Practical methods for observing and forecasting ocean waves. H.O. Publ, 603, U.S. Navy Hydrographic Office. _ and L. Moskowitz,1964: A proposed spectral form for fully developed seas based on the similarity theory of S.A. Kitaigoradskii. Journal of Geophysical Research, Vol. 69, pp. 5181-5190. - 87 - </P> <P><PB REF="00000099.tif" SEQ="00000099" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="875" N="88"> Richards, T. Lo, H. Dragert and D. R. MacIntyre, 1966: Influence of atmospheric stability and over-water fetch on winds over the lower Great Lakes. Monthly Weather Review, Vol. 94, No. 1, pp. 448-453. Strong, A. E., and F. R. Bellaire, 1965: The effect of air stability on wind and waves. Proceedings of the Eight Conference on Great Lakes Research, March 29-30, 1965, Ann Arbor, Michigan, pp. 283-289. Sverdrup, H. U. and W. H, Munk, 1947: Wind, sea and swell: theory of relations for forecasting. Hydrographic Office Publ, No. 601. U.S. Department of the Navy, pp. 44. U.So Army Corps of Engineers, 1961: Shore protection, planning and design. Beach Erosion Board Technical Report No. 4 (BEB T.R. 4), Rev. - 88 - </P> <P><PB REF="00000100.tif" SEQ="00000100" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="843" N="89"> UNIVERSITY OF MICHIGAN 3I 9015 02082 7609 THE UNIVERSITY OF MICHIGAN DATE DUE </P> </DIV1> </BODY> </TEXT>