CLIMATOLOGICAL WAVE STATISTICS DERIVED FROM FNWC SYNOPTIC SPECTRAL WAVE ANALYSES Felix Michael Reynolds saval postgraduate schouc •monterey, california 93sm0 ? NPS-58ReTh76061 NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS CLIMATO LOGICAL WAVE STATISTICS DERIVED FROM FNWC SYNOPTIC SPECTRAL by WAVE ANALYSES Felix Michael Reynolc Ls June 19 7 6 Th esis Advisor: W. C. Thompson Approved for public release; distribution unlimited. Prepared for: Department of Navigation and Ocean Development. State of Cal i forni a Sacramento, California 95815 T174977 SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) REPORT DOCUMENTATION PAGE READ INSTRUCTIONS BEFORE COMPLETING FORM 1. REPORT NUMBER NPS-58ReTh76061 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER 4. TITLE (and Subtitle) Climato logical Wave Statistics Derived from FNWC Synoptic Spectra Wave Analyses 5. TYPE OF REPORT & PERIOD COVERED Master's Thesis Final Report (Jan- Jul 1976 6. PERFORMING ORG. REPORT NUMBER 7. AUTHORS Felix Michael Reynolds in conjunction with Warren C. Thompson 8. CONTRACT OR GRANT NUMBERfa; 9. PERFORMING ORGANIZATION NAME AND AOORESS Naval Postgraduate School Monterey, California 93940 10. PROGRAM ELEMENT. PROJECT, TASK AREA 4 WORK UNIT NUMBERS N622716WE00029 II. CONTROLLING OFFICE NAME AND ADDRESS Department of Navigation and Ocean Development, State of California Sacramento, California 95814 12. REPORT DATE June 1976 13. NUMBER OF PAGES 141 14. MONITORING AGENCY NAME 4 AOORESS(il different from Controlling Oftice) Naval Postgraduate School Monterey, California 9 3940 15. SECURITY CLASS, (of thla report) Unclassified 15«. DECLASSIFI CATION/ DOWN GRADING SCHEDULE 16. DISTRIBUTION STATEMENT (o( this Report) Approved for public release; distribution unlimited. 17. DISTRIBUTION STATEMENT (of the abatract entered in Block 20, it different from Report) IS. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue on reverse aide it neceaaary and Identify by block number) Spectral Wave Statistics, Spectral Wave Climatology, Wave Climatology 20. ABSTRACT (Continue on reveraa aide if neceaaary and Identity by block number) A summer and winter month of 12-hourly synoptic spectral wave analyses produced by the Fleet Numerical Weather Central , Monterey , California were used to develop three experimental wave climato- logy formats for a point in the Gulf of Alaska; the analyses were produced by the Spectral Ocean Wave Model at FNWC which computes the wave energy contained in 12 direction bands and 15 frequency bands for a grid point array in the Northern Hemisphere oceans/ DD u AN 73 1473 EDITION OF 1 NOV 65 IS OBSOLETE S/N 0102-014- 6601 | SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) ftCUWTy CLASSIFICATION OF This dOEi^m D«.<« Enfrvd The gross climatology format displays frequency of occurrence of significant wave height by period and direction, but does not differentiate between sea and swell. The two-dimensional spectral climatology format is a tabulation of the frequency of occurrence of spectral energy in various frequency and direction bands. The one-dimensional spectral format displays the distribution of spectral wave energy over various frequency bands but contains no directional information. Both of the spectral formats appear to have their greatest potential application in resonance response of floating and fixed structures. DD Form 1473 ; 1 Jan 73 S/N 0102-014-6601 SECURITY CLASSIFICATION OF THIS PAGEf*»>«n Dmtm Entmrmd) NAVAL POSTGRADUATE SCHOOL Monterey, California Read Admiral Isham Linder Superintendent Jack R. Borsting Provost This thesis was prepared in conjunction with research supported in part by the Department of Navigation and Ocean Development, State of California, 1416 9th Street, Sacramento, California 95814 under standard agreement No. 5-42-96-22. Reproduction of all or part of this report is not authorized with- out permission of the Naval Postgraduate School. Released as a Technical Report by: Climatological Wave Statistics Derived from FNWC Synoptic Spectral Wave Analyses by Felix Michael Reynolds Lieutenant, United^ States Navy B.S., University of Washington, 1966 Submitted in parxial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN OCEANOGRAPHY from the NAVAL POSTGRADUATE SCHOOL June 1976 c/ *AVAL POSTGRADUATE SCnowfi MONTEREY, CALIFORNIA 93940 ABSTRACT A summer and winter month of 12-hourly synoptic spectral wave analyses produced by the Fleet Numerical Weather Central, Monterey, California were used to develop three experimental wave climatology formats for a point in the Gulf of Alaska; the analyses were produced by the Spectral Ocean Wave Model at FNWC which computes the wave energy contained in 12 direc- tion bands and 15 frequency bands for a grid point array in the Northern Hemisphere oceans. The gross climatology format displays frequency of occurrence of significant wave height by period and direction, but does not differentiate between sea and swell. The two-dimensional spectral climatology format is a tabulation of the frequency of occurrence of spectral energy in various frequency and direction bands. The one- dimensional spectral format displays the distribution of spec- tral wave energy over various frequency bands but contains no directional information. Both of the spectral formats appear to have their greatest potential application in resonance res- ponse of floating and fixed structures. TABLE OF CONTENTS I. INTRODUCTION ------------------ H A. OBJECTIVE- --------------- 11 B. SCOPE- --- -- --_--__ _ 11 C. BACKGROUND ------------- -- 12 D. PROCEDURE- ----------------- 13 E. WIND REGIME- ---------------- 14 II. FNWC SPECTRAL OCEAN WAVE MODEL --------- 16 A. INTRODUCTION ---------------- 16 B. WAVE ENERGY GROWTH MODEL ---------- 16 C. WAVE ENERGY PROPAGATION MODEL- ------- 18 D. FNWC SOWM OUTPUT -------------- 20 E. ONE-DIMENSIONAL FREQUENCY SPECTRUM ----- 23 F. ONE-DIMENSIONAL DIRECTIONAL SPECTRUM - - - - 2 5 III. CLIMATOLOGY FORMATS _______ __ 27 A. INTRODUCTION ---------------- 27 B. GROSS CLIMATOLOGY FORMAT ---------- 28 C. TWO-DIMENSIONAL SPECTRAL CLIMATOLOGY FORMAT- 3 3 D. ONE-DIMENSIONAL FREQUENCY SPECTRUM FORMAT- - 3 9 IV. APPLICATIONS _____---- i+i+ LIST OF REFERENCES ------------------ i+8 TABLES I THROUGH XVIII ---------------- 49 FIGURES 1 THROUGH 13----------------- 66 APPENDIX A: CONVERSION FORMULAE FOR COMMONLY USED WAVE HEIGHT PARAMETERS ------- 79 APPENDIX B: SPECTRAL WAVE GROWTH PARAMETERS AND STEEPNESS CRITERIA FOR 20, 30, 40, and 50 KNOT WINDS ---------- 80 APPENDIX C: SPECTRAL ENERGY DISTRIBUTION FOR FULLY ARISEN SEAS FROM WIND SPEEDS OF 20, 30, 40, AND 50 KNOTS FOR A 30° DIRECTION BAND- ----------- 82 APPENDIX D: CLIMATOLOGICAL WAVE TABLES OF THE GROSS STATISTICS FOR FEBRUARY 19 7 5- - - - 87 APPENDIX E: CLIMATOLOGICAL WAVE TABLES OF THE GROSS STATISTICS FOR AUGUST 1974- - - - - 100 APPENDIX F: CLIMATOLOGICAL WAVE TABLES OF THE TWO-DIMENSIONAL WAVE STATISTICS FOR FEBRUARY 19 75------------ 113 APPENDIX G: CLIMATOLOGICAL WAVE TABLES OF THE TWO-DIMENSIONAL WAVE STATISTICS FOR AUGUST 1974 --_------___- 126 INITIAL DISTRIBUTION LIST- -------------- 139 LIST OF TABLES TABLE I. Frequency/Period Parameters for the FNWC/SOWM- - 49 II. Occurrence of Period Peaks for August 19 74 and February 19 7 5---------------- 50 III. Occurrence of Directional Peaks for August 1974 and February 1975- ---------------50 IV. Wave Height Code for the Gross Climatology Formats- -------------------- 51 V. Gross Wave Statistics for All Directions for February 1975- --------------- 52 VI. Gross Wave Statistics for All Directions for August 1974- ---------------- 53 VII. Energy Density Code for the Spectral Climatology Formats- -------------- 54 VIII. Two-Dimensional Wave Climatology for February 19 75 (i/> = 3)-------------- 55 IX. Two-Dimensional Wave Climatology for February 1975 (ip = 3) Adjusted for Equal Frequency" Bandwidths ----------- 55 X. Energy Spectrum of FNWC SOWM Analysis for 19 February 1975, 0000Z for ^=3------ 57 XI. Energy Spectrum for Fully Arisen Sea for 2 0 Knot Wind ---------------- 58 XII. Energy Spectrum for Fully Arisen Sea for 3 0 Knot Wind ---------------- 59 XIII. Energy Spectrum for Fully Arisen Sea for 4 0 Knot Wind ---------------- 60 XIV. Energy Spectrum for Fully Arisen Sea for 5 0 Knot Wind ---------------- 61 XV. Two-Dimensional Wave Climatology for August 1974 (^ = 3)- ------------- - 62 XVI. One-Dimensional Frequency Spectrum for 0.0055 Hz Bandwidths for February 1975 ----- 63 XVII. One-Dimensional Frequency Spectrum for 0.0055 Hz Bandwidths for August 1974 ------ 64 XVIII. National Marine Consultants Sample Wave Climatology -----------_-___ 65 LIST OF FIGURES FIGURE 1. Icosahedral-Gnomonic Projection of the World Oceans ------------------- 66 2. FNWC SOWM Output for 714083100Z ---------- 67 3. One -Dimensional Frequency Spectrum- FNWC Frequency Bandwidths for 74083100Z --------68 4. One-Dimensional Frequency Spectrum-Equal Frequency Bandwidths for 74083100Z --------69 5. Occurrence of Multiple Frequency Peaks- August 1974- -------------------70 6. Occurrence of Multiple Frequency Peaks- February 1975- ------------------71 7. One-Dimensional Directional Spectrum for 74083100Z- ------------------72 8. Event Occurrence by Direction for February 19 7 5 and August 19 7 U- ---------- 73 9. Wave Steepness versus Wind Duration- ------- 74 10. Wave Steepness Criterion Envelope of H1/3/Tx2 (Adjusted) > 0.125- -----------75 11. Comparison of Energy Content for FNWC Frequency Bandwidths and Common Frequency Bandwidths of Af= 0.0055 Hz -----------76 12. One-Dimensional Frequency Spectrum Climatology for February 1975- ----------77 13. One-Dimensional Frequency Spectrum Climatology for August 1974- -----------78 ACKNOWLEDGEMENT The author wishes to express his most sincere apprecia- tion to Professor Warren C. Thompson for the many hours spent in consultation, and his immeasurable assistance to- ward the completion of this thesis. Additionally, the assistance of Sheldon Lazanoff of the Naval Oceanographic Research and Development Activity, and Norman Stevenson and Joe Bottaro of the Development Department of Fleet Numerical Weather Central, is greatly appreciated for the time and effort contributed in producing the spectral wave analyses used in this study. Finally, the author wishes to thank his wife, Margot , without whose periodic inspiration this work might never have been completed. 10 I. INTRODUCTION A. OBJECTIVE The objective of this thesis is two-fold: (1) to examine the properties of the Fleet Numerical Weather Central's (FNWC) Spectral Ocean Wave Model (SOWM) to determine the nature and character of wave information available from this product, and (2) to design and compile three climatological formats using two selected months of SOWM data and to exam- ine their characteristics and potential uses. B. SCOPE The FNWC SOWM output provides wave analyses only for specific deep water sites, or grid points, in the Northern Hemisphere oceans. Therefore this thesis deals only with deep water wave climatology and is restricted in application to the Northern Hemisphere. Shallow water wave climatology and transformation processes, i.e., refraction, shoaling, etc. will not be addressed, except to point out the poten- tial applications of the deep-water climatologies in predict- ing nearshore wave conditions, surf conditions, littoral drift, etc. The SOWM output is a computer product. Lazanoff and Stevenson (1975) evaluated the SOWM product in some detail by comparison with observed wave conditions from data buoys and shipboard observations, and concluded that the spectral 11 model is far superior to the previous FNWC non-spectral model. For the purposes of this thesis the wave data is con- sidered to be accurate, and verification of the data with actual wave conditions will not be addressed. C. BACKGROUND Existing wave climatologies , often compiled in terms of frequency of occurrence of wave height, direction, and per- iod, may be derived from wave hindcasting techniques, in- strument sensors, or visual shipboard observations. These data vary greatly in their time-space sampling, information content, quality, and format. On 19 December 19 7 4 the FNWC put into operational use its SOWM. This approach to analy- sis and forecasting of the sea surface conditions uses an energy density spectral function which represents the dis- tribution of wave energy over the range of frequencies pres- ent in the sea. The two-dimensional spectral analysis routine calculates the total wave energy distribution, or variance, contained in 15 variable frequency bands and 12 direction bands on a twice daily basis (0000Z and 1200Z) for a grid point array covering the Northern Hemisphere oceans , and in the forecast mode can predict wave conditions to 7 2 hours. This spectral approach is considered to be a signi- ficant improvement over previous wave analyses in informa- tion content and quality of data. Wave climatologies, then, compiled from these FNWC spectral analyses should be ex- pected to be a significant improvement over existing wave statistics . 12 D. PROCEDURE Two months of 12-hourly spectral wave analyses were pro- vided by FNWC for grid point 164 in subpro jection 3. The location of this analysis point is shown in Figure 8. One summer month (August 1974) and one winter month (February 1975) were chosen to illustrate the seasonal variability of the wave conditions in the Gulf of Alaska. This point was selected due to its proximity to Ocean Station Papa for pos- sible comparison of the spectral analyses to observed wave conditions . The two months of wave data were extracted from the FNWC historical tapes and printed in the spectral format of which Figure 2 is a sample. A graph of the frequency spectrum showing energy density per equal frequency band- width was also computed and plotted for each synoptic analy- sis by FNWC as shown in Figure 4. From the two month series of analyses, all information potentially useful for the design of the climatology formats was extracted from the SOWM and tabulated in chronological sequence for both months. The design of the wave climatology formats was initially approached by examining currently existing climatologies for display content and format. To this author's knowledge, spectral climatologies have not previously been formulated; accordingly, the formats for the spectral wave data developed and presented herein are considered to be experimental. These formats present frequency of occurrence statistics. Two of the three experimental formats are similar in design to the widely used statistical tabulations for the California 13 coast prepared by National Marine Consultants (1960). The third format presents cumulative occurrence statistics in graphical form. E. WIND REGIME To better understand the climatological wave statistics for February and August developed for grid point 164, it is instructional to briefly discuss the general meteorological situation which generates the wave fields in this area. This discussion affords a better understanding of the synop- tic situations and their associated wind patterns which are responsible for the waves. During the winter season (January through March) the most severe weather transits through the Gulf of Alaska as strong cyclonic lows which follow a fairly typical storm track. The lows generally originate east of Japan and travel northeastward passing south of Shemya and Adak in the Aleutian Islands and then eastward into the Gulf of Alaska where they recurve to the northeast. These lows develop and deepen considerably as they approach Adak Island, and then move into the Gulf of Alaska at 2 0 to 3 0 knots where they stagnate and die out. The low centers generally pass to the northwest of grid point 16 M- , generating a west to southwest wind field at the station. Westerly winds of up to 80 knots are not uncommon during the passage of these storms in the Gulf during the winter months. During the summer months (July through September) the Gulf of Alaska is influenced by two meteorological regimes: 14 (1) high pressure centers or ridges south of grid point 164 which generally transit slowly to the east, and (2) weak low pressure centers which move parallel to but to the north of the wintertime lows. Summer season winds at grid point 164 vary from 20 to 30 knots from the west to southwest, but on occasion severe low pressure centers may generate westerly winds of nearly 60 knots over this area (Gerst, 1971). 15 II. FNWC SPECTRAL OCEAN WAVE MODEL A. INTRODUCTION The Spectral Ocean Wave Model (SOWM) is a hindcasting technique which provides a two-dimensional wave spectrum which is composed of a matrix of 12 30-degree direction bands and 15 frequency bands of varying bandwidth. The general hindcasting approach for wave spectra can be applied to historical or real time synoptic surface pressure analyses and to forecasted synoptic conditions as well. The FNWC , model presently computes twice daily real-time spectral wave analyses and forecasts out to 7 2 hours. The SOWM employs a power spectral density function which represents the dis- tribution of total wave energy (sea and swell) at ocean grid points in the Northern Hemisphere. The total wave energy at any location is composed of the energy which is generated by the local wind at that point (sea) plus the energy pro- pagated from the surrounding area (swell) through that point. The SOWM, therefore, consists of two separate parts; the wave energy or growth model (sea), and the wave energy pro- pagation model (swell). B. WAVE ENERGY GROWTH MODEL The basic approach for the generation of wind wave energy consists sequentially of obtaining the best estimate of the sea-level pressure distribution, calculating the wind 16 fields therefrom, and generating the resultant wave field energy. The growth model employs a modified Miles-Phillips technique. When the sea initially begins to grow from calm conditions, the Phillips resonance mechanism predominates, but as wind velocities increase the Miles instability mech- anism becomes more dominant. The Phillips theory essential- ly states that a resonance between the air-sea system occurs when a component of the surface pressure distribution moves at the same speed as a free surface wave of the same wave number. The Miles instability theory states that the mean rate of energy transferred from the parallel shear flow to the surface wave is proportional to the curvature of the wind profile at the height where the mean wind velocity is the same as the phase speed of the wave component (Lazanoff and Stevenson, 1975). The modification of the Miles-Phillips technique is the result of an alteration of the initial growth portion of the model by Professor Vincent Cardone of New York University. For wind speeds less than or equal to 30 knots, the wave energy will grow at a faster rate during the initial six hours using the Cardone modification than for the unmodified model. The reverse is true for wind speeds greater than 30 knots. After six hours the modified growth rate is always slower than the unmodified one. Energy input from the growth model is limited by the Pierson-Moskowitz fully developed spectrum for any give wind velocity. This imposes a ceiling on energy output, i.e., 17 the fully arisen sea, and precludes unlimited growth of the sea for a given wind speed. Since energy from a wind field is propagated by the wave field in directions other than the mean wind direction, a partitioning of the wave energy by direction is required. This is accomplished in the SOWM by means of an equation de- veloped by the Stereo-Wave Observation Project which is used to distribute energy in the directional spectra. Since direction bands are computed in 30-degree increments the dis- tribution of wave energy is partitioned as follows: 37.5% in the sector containing the mean wind direction, 25% in the two 30-degree sectors on either side of the mean wind, and 6.25% in the two sectors adjacent to the 25% sectors. A treatment of the mathematics of the generation model is beyond the scope of this paper; however, more detail is given by Lazanoff and Stevenson (1975). C. WAVE ENERGY PROPAGATION MODEL The SOWM propagates wave energy at the group speed of each individual frequency component in accordance with linear wave theory. Swell waves travel across the ocean surface by great circle routes, accordingly the gnomonic projection was selected to simplify mathematical calculations because great circles appear as straight lines on this plane projection. Since great areal distortion would result in attempting to display large ocean areas on one gnomonic projection, the globe was projected onto an icosahedron (a 20-sided polygon with equilateral triangles for its faces) to reduce this 18 distortion. Each triangle of the icosahedron is a separate gnomonic projection. The icosahedral-gnomonic projection of the globe is shown in Figure 1. Although some distortion re- mains, it is considered to be within acceptable limits. The projection of the earth's surface onto these planar icosa- hedral faces alters great circle routes to straight lines (geometrical directions). This fact results in so-called meteorological direction bands (the direction from which wave energy propagates) in which the central direction of each band is different for every grid point. To prevent refrac- tion when wave energy is propagated from one subproj ection to another a row of grid points is aligned along each side of the triangle. This scheme precludes discontinuities from existing in the directional propagation of energy. As a result of computer limitations in storage and compu- tational time, the SOWM is only computed for the Northern Hemisphere. All points south of the equator are treated as land points in the Northern Hemisphere model. Accordingly any swell generated in the Southern Hemisphere will not be included in the Northern Hemisphere wave spectra. In both the growth and the propagation model, wave energy is dissipated only when the waves encounter land or when swell destructively interacts with the wind. In the later case wave energy dissipation is calculated if the angle be- tween the mean wind direction and the wave direction exceeds 7 5 degrees. Wave-wave interaction, whitecap generation, and foam streaks are not included in the model as dissipation 19 mechanisms, although it is felt at least some of these fac- tors may be significant. D. FNWC SOWM OUTPUT The SOWM output at a grid point is a two dimensional re- presentation of wave energy. The basic format is shown in Figure 2 and contains the following information: 1. DATE TIME GROUP: DTG 74083100Z 197t+ August 31st 0000Z 2. TAU: The TAU operator denotes the time of computa- tion relative to the DTG. TAU = 0 : real time synoptic analysis TAU = -6 : hindcast mode TAU = 12 to 72: forecast mode from 12 to 7 2 hours 3. SUBPROJECTION: Denotes the number of the icosahed- ral triangle in which the grid point is located; in this example it is number 3 (see Figure 1). 4. GRID POINT: Numbered from 1 to 32 5 in each subpro- jection. The grid point number is the identi- fier for the location at which spectral energy is computed. In the sample a number of 0.0 0 is shown. This is an artifact of the calling rou- tine for the extraction of climatological data. The actual grid point number for this spectral printout is 164. 5. LAT, LONG: The latitude and longitude of the grid point. Latitude is always given in degrees north 20 Longitude is always given in degrees east (from 0° to 360°E) . 6. WIND SPEED: Given to nearest hundredth in knots. 7. WIND DIRECTION: Given in geographical degrees. It is the direction from which the wind blows . 8. USTAR: Frictional wind velocity computed from the analyzed or computed wind speed. USTAR is the actual input to the wave spectral model growth equations . 9. FREQ : The central frequency of each of the 15 fre- quency bands. For these frequencies, the frequen- cy bands, frequency bandwidths , scaling factors, and equivalent period values are given in Table I. Note all frequency bands are not of equal bandwidth. 10. DIR: Each coded entry, 1 through 12, corresponds to the MET DIR's listed in item 11. 11. MET DIR: The central direction, called the meteor- ological direction, is given in geographical degrees in each of the 12 30-degree bands. 12. The matrix of 180 data bits (12 directions times 15 frequencies) will be subsequently referred to as "internal" data. Each entry represents the ener- gy in terms of sea surface variance in dimensions 2 of (feet) , associated with a particular frequen- cy band and a particular direction band. 13. Item 13 represents the summation of all energy con- tained in a given frequency band irrespective of 21 direction, and therefore constitutes a one-dimen- sional frequency spectrum. These entries will be subsequently referred to as "external" data. The entry of maximum energy will be referred to as E-. , with its associated frequency or period, T, . The entry containing the second largest amount of energy is designated E„, with its corresponding period, T~ , etc. The values of E, , E? , etc. may or may not be adjusted to equal bandwidths . This adjustment will be discussed in a later section. 14. Item 14 reflects the summary of energy in a given di- rection band, over all frequencies. These values constitute a one-dimensional direction spectrum, and will also be referred to as "external" data. The entry containing maximum energy from the direc- tion spectrum will be designated as E and the corresponding direction band \p ; secondary values a will be designated E, , ty, , etc. No correction for variable bandwidth need be applied to these data . 15. Item 15 represents the total energy in the frequency spectrum and also in the direction spectrum, and is given by 15 1 E Ef = £ E, = E^ V t r=l ^ = a E is also given by the total of the 180 energy bits in the internal data. E. is total variance; 22 accordingly, the significant wave height is given by: ^-1/3 = L+^E"t • Other wave height para- meters that may be of interest are given in Appendix A; they may be computed in an analogous manner to those listed in H. 0. 603. It should be noted for subsequent reference that the gross characteristics of the sea surface, referred to within FNWC as singular wave data, may be given by H-.,-, ip , and T . These parameters describe the significant height of the wave field, the central direction of the band containing the maxi- mum amount of wave energy, and the central period (inverse of frequency) of the band containing the maximum amount of energy, respectively. E. ONE-DIMENSIONAL FREQUENCY SPECTRUM Although not routinely produced by FNWC, it is instruc- tional to examine a plot of the external one-dimensional fre- quency spectrum. The data can be plotted for the bandwidths generated by the SOWM output or for equal bandwidths . Both types of presentations will be examined in some detail. Figure 3 is a plot of the one-dimensional frequency spec- trum using the FNWC variable bandwidths as displayed on the SOWM output shown in Figure 2 . The total area under the curve, is not equivalent to E . This particular synoptic analysis was selected to illustrate additional information which may be obtained from the SOWM. The lower frequency energy peak of 0.067 Hz clearly represents incoming swell. It may be noted that the swell is fairly narrowly constrained 23 in bandwidth and significantly longer in period than the sea component that is also present. The apparent peak of energy centered about a period of 7.5 seconds represents wind- generated sea at the grid point. It exhibits the general tendency of sea to occupy a broader period spectrum than swell when plotted on a linear frequency scale. An FNWC machine-generated plot of the same one-dimensional frequency spectrum is shown in Figure M- . In this plot the energy component values of each FNWC frequency bandwidth have been multiplied by a scaling factor so as to give the energy density per constant bandwidth. The scaling factors are given in Table I. The standard bandwidth used for this computation is 0.0055 Hz. In contrast to Figure 3, the total area under the curve is proportional to the actual total energy in the wave field. The frequency bands from 0.039 Hz through 0.083 Hz, which are of constant bandwidth, retain the same shape as in Figure 3, although the energy scale is magnified by a factor of 180. For periods greater than 12 seconds , alteration of the curve becomes apparent as a re- sult of the variable scaling factors. In Figure 3 there are three points of peak energy, while in Figure 4 there are four. It may also be noted that the period maximum of the sea present does not agree in the two figures. The correct portrayal of the shape of the frequency spectrum is that of Figure 4 . It is not always possible to distinguish between sea and swell in the frequency spectrum, especially under high wind conditions; nevertheless, multiple energy peaks apparently 24 representing wave energy from different wind areas are fre- quently present. Figures 5 and 6 show the occurrence of multiple peaks for two selected months of FNWC 12-hourly analyses. Both time series graphs were constructed using the equal bandwidth frequency spectrum plots generated by FNWC. It was initially presumed that it frequently would be possible to identify individual wave trains on the basis of their con- tinuity from a time-series analysis of monthly data. How- ever, the highly discontinuous nature of secondary and lower order peaks for both months appear to preclude this as a possibility. From these data, however, a frequency of occur- rence tabulation of period peaks (T, , T„ , etc.) was generated and is presented in Table II. Examination of Figure 5 shows that for the August data, the primary energy peak, T, , is with few exceptions confined to periods of 6.1 seconds to 9.7 seconds. The February data in Figure 6, however, shows the primary energy peaks to be contained within a range of periods from 9.7 seconds to about 16.4 seconds. This result is not unexpected as longer period waves are generated under the higher wind conditions which exist during the winter months in the North Pacific. F. ONE-DIMENSIONAL DIRECTIONAL SPECTRUM The one-dimensional directional spectrum represents the energy propagated in the 12 direction bands, independent of frequency. Figure 7 is a plot of the directional spectrum for the SOWM printout shown in Figure 2 . The energy peak centered about \b - 3 (259.5 degrees true) can be identified a to 25 as the same wave energy which was previously identified as swell. As may be seen in Figure 2, this energy i-s contained in the 3 0-degree direction band centered about MET DIR 3. The secondary band centered about i|;,= 5 corresponds to the energy previously identified as sea which, even though of lesser energy content, occupies a somewhat broader directional distribution than does the swell. For the two selected months of 12-hourly FMWC wave analyses mentioned above, the frequency of occurrence of multiple direction peaks was computed and is contained in Table III. It will be noted that the maximum number of peaks never exceeded two in number. For this reason, a time-series analysis for multiple direction peaks was not considered to be of significant value in describing the directional spectrum. The interpretation of the one-dimensional frequency and direction spectra in the preceding sections is based on some basic principles of wave analysis. First, sea is more broad- banded in both direction and frequency distribution than swell for the same peak energy density, and second, for two or more separate wave trains, the higher frequency energy may be sea or swell, and all other components of lower frequency are swell (Kinsman, 1965). From the application of these principles it may be possible to identify sea arid swell com- ponents of the wave field which could assist the user in the interpretation of synoptic wave data. 26 III. CLIMATOLOGY FORMATS A. INTRODUCTION The SOWM spectral analyses yield two basic types of wave data: the gross data and the spectral data. The so-called gross form derives its name from the fact that a single height, period, and direction value give a gross or overall picture of the wave field conditions. Both of these kinds of data may be compiled in several ways to pro- duce wave climatologies. A most useful form for many wave statistics users is a compilation by frequency of occurrence of wave height (or energy) with an associated period and direction parameter. Three experimental formats were selected to explore and demonstrate several alternatives available for the display of useful wave climatology data: The gross (singular) format, the two-dimensional spectral format, and the one-dimensional spectral format. In all three formats the data entries in the various "cables represent the number of specific occur- rences during the two representative summer/winter months for grid point number 16M-. One occurrence represents the wave conditions or parameters which exist at the time of a single 12-hourly analysis; thus, a 30-day month would have a total of 60 12-hourly analyses, or 60 occurrences. It was decided that event occurrences (i.e., number of events) would be a more preferable parameter in which to express the frequency 27 of occurrence for data display than percentage occurrence or duration of occurrence. This was done because the monthly data are not continuous or complete owing to some missing ob- servations in the FNWC f s historical synoptic files for the two months selected. Conversion from number of occurrences to percentage or duration of occurrence can readily be accom- plished if desired. B. GROSS CLIMATOLOGY FORMAT The data extracted from each 12 -hourly FNWC synoptic analysis which were used to built the gross wave climatology is composed of the total energy, E (which yields significant height via a simple arithmetic operation) , the central direc- tion of the directional bandwidth containing the maximum amount of energy, \p , and the central period (adjusted to the a standard frequency bandwidth of 0.0 05 5 Hz) containing the maximum energy, T-, (adjusted). Using the SOWM printout i n Figure 2 as an example, these data were obtained as follows: 2 E corresponds to item 15, and equals 3.145 ft (accordingly H, /q = 7.09 ft), and ip corresponds to the directional band number 3 or 259.5 degrees. From Figure 4, T-. (adjusted) is a period of 15.0 seconds, or 0.067 Hz. The basis for selec- tion of E and \p as parameters for describing the gross l a character of a wave field is obvious. It is evident, however, from the discussion in Section HE, that the identification of the period of maximum energy density per standard frequency bandwidth is somewhat more complex because of the use of variable frequency bandwidths by FNWC. Since the use of 28 variable frequency bandwidths does not give the energy dis- tribution in equal frequency segments, the energy values composing the frequency spectrum must be adjusted to equal bandwidths by application of the scaling factors listed in Table I in order to allow identification of T, (adjusted). The gross climatology format that has been designed con- tains a linear wave height scale employing two foot incre- ments up to 4-0 feet and keyed to coded values from 01 to 21, as shown in Table IV. The selection of the two-foot height increments was subjective, but it was felt that this scale provides adequate definition of the lower wave heights , and should be retained to preserve the accuracy available from the SOWM in the higher wave heights. The 12 directional bands from the SOWM were used in the interest of preserving as much directional definition as is available, as were the 15 central periods (frequencies). The resultant gross cli- matology format is illustrated in the tables of Appendices D and E. The actual procedure for data entry into the climatology format amounts to the extraction from each 12-hourly analysis of T-, (adjusted), i> , and H, ,«, according to the procedures described above. These constitute one synoptic analysis event which is entered in the appropriate table of the gross climatology. Tables D-l through D-12 of Appendix D contain the gross climatology for the month of February 19 75, and Tables E-l through E-12 of Appendix E is a similar compila- tion for August 1974. These tables are presented in the appendices because of their bulky size. Because of the 29 sparcity of data in these tables and in order to better il- lustrate the nature of the statistical distribution, cumula- tive totals of event occurrence for all directions were compiled for February and August, and are shown in Tables V and VI. The cumulative climatology for February exhibits an envelope limiting the highest wave heights in each period band. As previously discussed, the growth (sea) portion of the SOWM is energy-limited by the Pierson-Moskowitz fully developed spectrum. The envelope for maximum values of H, , ~ , or energy, approximate a fully developed Pierson-Moskowitz spectrum for the stronger winds present during the month. The energy content for a given period may even exceed fully arisen conditions as a result of the superposition of the sea on swell arriving simultaneously at the analysis point. The limitation on wave energy versus period exhibited in the February statistics (Table V) will be addressed in greater detail in Section IIIC. A comparison of the cumulative statistics shown in Tables V and VI for the months of February and August illustrate some seasonal aspects of the wave climatology at the selected station. As would be expected, the summer month contains far less wave energy and significantly shorter wave periods than does the winter month. However, during February, low energy waves of long period (quite evidently swell) were dominant on at least five occasions and clearly reflect instances where the sea was of lesser consequence than the incoming swell. During August only one case of long-period swell dominance is 30 immediately evident. It is thus apparent that even though the winds were relatively light throughout August and pro- duced low seas, the swell energy was of even lesser conse- quence . Figure 8 is a plot of event occurrence by direction for all frequencies. The February statistics show a maximum oc- currence from MET DIR 3, with lesser but significant occur- rences along directions 4 and 5. This fact correlates well with the predominant west to southwest wind patterns previous- ly discussed in the meteorological section. The summer wave statistics show a generally similar directional distribution to winter. This is due also to the predominance of west to southwest winds which occur during the summer months and in- fluence the wave analyses at grid point 164. Wave statistics users may desire to know if sea or swell waves are represented by the statistics in the climatology tables. Wave steepness may be used to distinguish sea from swell and also determine whether swell has had a short propa- gation distance (young swell) or a longer propagation distance (old swell) from the generating area. Wave steepness for monochromatic wave trains is defined as the ratio of wave height to wave length. For deep water waves this may be written as 7- = *• . Since -£- is a constant, the wave L JL t2 2Tr 2tt 2 steepness may be represented by H/T . For a spectrum, steep- 2 ness will be defined here as H, ,3/T, (adjusted). Figure S is a plot of the wave steepness parameter computed using Cardone's program for duration- limited and fully arisen energy spectra generated by wind speeds of 20, 30, 40, and 31 50 knots. The compilations for this figure are given in Ap- pendix 3. It may be seen in the figure that for wind speeds greater than 20 knots, seas in all stages of growth have steepnesses in excess of 0.125. Since swell can be presumed to have lower steepnesses than sea, values less than 0.12 5 may be considered to be swell. Figure 10 is a plot of the wave steepness envelope in the climatology format for values greater than or equal to a steepness criteria of 0.125. It may be concluded that for wind speeds greater than 2 0 knots, climatological entries ly- ing to the left of the curve represent sea. and those to the right of the curve are swell. It is evident that the steep- ness associated with any entry in the gross climatology tables of Appendices D and E can readily be determined. A cursory examination of Figures 4 and 7 reveal two short- comings Inherent in the gross wave climatologies. For the synoptic wave conditions illustrated in Figure 2 , the gross wave statistics indicate a single wave train having an E-. ,~ value of 7.09 feet, a T-, (adjusted) of 15.0 seconds, and a ty of 259.5 degrees (MET DIR 3). However, Figure 4 clearly a shows a secondary energy peak in the shorter period bands and Figure 7 shows the same wave train centered about MET DIR 5. The secondary wave train would not be revealed in the gross climatology. A wave statistics user concerned about secondary wave energy maxima would not find this information available in the gross climatology statistics. 32 C. TWO-DIMENSIONAL SPECTRAL CLIMATOLOGY FORMAT The two-dimensional spectral format is a tabular repre- sentation of the frequency of occurrence by direction and period of the "internal" energy values, or variance compo- nents , obtained from the synoptic analyses covering a given time period. The tabulations for all 12 direction bands for February 1975 and August 1974 are contained in Appendix F (Tables F-l through F-12) and Appendix G (Tables G-l through G-12) respectively. The "internal" section of the FNWC synoptic analysis (item 12 in the printout of Figure 2) con- tains 180 energy bits of both zero and non-zero values, the sum of these 180 bits constituting the total energy, E . Each non-zero energy value has been extracted from the FNWC analyses and entered into the spectral climatology format to build the wave climatology for the given month. The tables for February 1975 are derived from 45 12-hourly analyses, and the tables for August 1974 from 61 12-hourly analyses. As in the gross climatology tables, the energy values in the spectral climatology tables are coded according to the key shown in Table VII. The units of the energy values are 2 (feet ) ^/frequency bandwidth, where the frequency bandwidth may be either the FNWC bandwidths or an adjusted common bandwidth. It may be recognized that while the total energy (E.) in a given spectral analysis may be equated to some wave height parameter (such as H-.,« in the gross statistics), the indi- vidual energy values which comprise E cannot. For this reason an energy scale rather than a height scale is employed in the two-dimensional spectral climatology format. The 2 scale below 2 ft was expanded to provide better definition 33 of the energy distribution in this lower energy range. This expansion is a result of the fact that of the 2951 non-zero entries in the two-dimensional February Statistics only 1.5 2 per cent exceeded values of 2 ft , and none exceeded this value in the August data. This scale expansion results in a discontinuity at the coded value of 09. The maximum inter- nal energy density value occurring during the two months of 2 data was 8.36 ft (00Z analysis on 19 February 1975). Two alternatives were available for expressing the magni- tude of the energy values associated with the period bands, that of energy density per FNWC variable frequency bandwidth or per constant frequency bandwidth. Table VIII is the two- dimensional spectral format for the month of February 197 5 for meteorological direction 3 using the FNWC variable fre- quency bandwidths. Table IX, for the same month and direction band, reflects the same energy values adjusted to equal fre- quency bandwidths . In Table VIII the energy values were obtained directly from the FNWC analyses (e.g., from item 15 of Figure 2) con- verted to the coded values given in Table VIII, and were entered into the climatology format. These energy values are contained in the FNWC unequal frequency bandwidths , and there- 2 fore have units of (feet) /FNWC bandwidth. The table accu- rately represents the total energy for February for \p = 3 but does not give the energy contained in equal frequency band- widths . As shown in Table I, the FNWC frequency bandwidths from 0.083 Hz (12.0 seconds) to 0.039 Hz (25.7 seconds) are equal 34 and have a value of Af = 0.0055 Hz. At periods shorter than 12.0 seconds the FNWC bandwidths vary. In order to compare the energy density in one frequency band of Table VIII with that in another it is necessary to adjust these energy densi- ties to a common frequency bandwidth. This may be accom- plished by multiplication of the energy values coded in Table VIII by the factors listed in Table I, normalized by dividing by 130. Table IX represents the result of this pro- 2 cedure . All values in this table have the units ft /0.0055 Hz bandwidth. In Table IX the wave energy values may be compared directly from one frequency band to another, but the total energy in the table does not represent the total energy in the waves for MET DIR 3 for February. The relationship between Tables VIII and IX can best be understood through the use of a specific example. Table VIII shows one incidence of occurrence in energy level 02 (0.2 5 — 2 O.M-9 ft ) contained m the period bands of 8.6 seconds and 2 0.0 seconds. Assuming an average value for this energy 2 level of 0.37 ft , a bar graph for these FNWC bandwidths would appear as in the upper part of Figure 11. Application of the normalized FNWC scaling factors contained in Table I to convert the energy values to an equal bandwidth basis of 0.00 5 5 Hz is shown in the lower part of Figure 11. Examina- tion of the two sets of data in this figure reveals that although the energy contained in the two FNWC bandwidths is equal, from an equal bandwidth point of view, the energy in the 8.6 second period is reduced by a factor of one third from that of the 2 0.0 second period. This apparent 'reduction 35 in energy content in the 0.117 Hz band (8.6 second band) re- sults from the exclusion of the energy contained in the bands from 0.108 Hz to 0.114 Hz and from 0.120 Hz to 0.125 Hz. A comparison of Table IX with Table VIII reveals that the over- all effect of adjustment to a common frequency bandwidth is a proportional reduction in the energy values for the period bands of 10.9 seconds and lower. Both of the two-dimensional climatologies contained in the tables of Appendices F and G were tabulated using the FNWC variable bandwidths . The reason for this choice is that variable bandwidth tables retain more information about the wave energy distribution than do adjusted bandwidth tables. For example, given the FNWC climatology in Table VIII, it is possible by frequency bandwidth adjustment to produce Table IX. However, given Table IX it is not possible to generate Table VIII. Additionally, the total wave energy for the month is shown in Table VIII, while only part of this energy is reflected in Table IX. In the use of these climatology tables the reader is cautioned that he cannot make direct comparisons of the energy levels across the frequency spectrum. In order to do this he must correct the energy values to an equal (common) frequency bandwidth. To perform this conver- sion the normalized scaling factors listed in Table I would be required. The envelope of maximum energy versus period illustrated in Tables VIII and IX is the result of energy saturation of the sea surface. As the sea progressively builds, the shorter period bands become energy saturated first, followed 36 successively by longer ones. Once a period band is saturated unless the wind velocity increases that band can absorb no additional energy. For a given climatology table the satura- tion trend is established by the highest wave conditions (i.e., heaviest seas plus swell) occurring during the period covered by the data. For example, Table X shows an energy- period plot for the FNWC analysis of 19 February 1975 at 00Z for \p = 3, which contained for this direction band a total 2 energy density of 38.15 ft . By comparison with Table VIII it may be seen that the data in Table X represents the most nearly saturated condition that occurred during the month of February. All energy values for seas generated by weaker winds (plus swell) are contained inside the envelope of these maximum limiting values. It is of interest to examine the frequency spectrum of fully arisen seas when plotted on a spectral climatology for- mat. To accomplish this the energy levels in the fully de- veloped spectrum produced by Cardone were reduced to that energy contained in a 30 degree direction bandwidth centered about the mean wind direction. This was done for seas pro- duced by wind speeds of 20, 30, 4-0, and 50 knots by applying the FNWC 37.5 per cent factor to the energy content of each spectrum. This reduction is shown in Tables C-l through C-4 of Appendix C. Tables XI through XIV show this information tabulated in a climatology format for these four wind speeds. The fully arisen spectra for these wind speeds are presented for both the FNWC variable frequency bandwidths and equal bandwidths adjusted as described above. Although swell 37 commonly occurs simultaneously with seas, and is included in the climatological plots for February and August, no swell energy is contained in Tables XI-XIV. The reduction of the saturated wave energy spectra to a 30-degree direction bandwidth permits direct comparisons with the spectral climatologies of February 197 5 and August 1974, and provides a rough estimate of the peak wind speeds respon- sible for the wave conditions during the month. For example, comparison of the two-dimensional spectral climatology com- piled for meteorological direction 3 for August 1974 shown in Table XV with Table XII (using the energy distribution for the FNWC bandwidths) suggests that the maximum winds at the observation point did not exceed 30 knots. In fact, 2 3.8 knots was the highest analyzed during August. The effect of the additional energy due to swell which is included in the spectral climatologies can be illustrated by a comparison of Table VIII (the spectral climatology for February 19 7 5 for MET DIR 3) with Tables XIII and XIV. For periods shorter than 12.0 seconds it can be seen that fully arisen sea conditions were not attained for wind speeds of 40 knots. However, for periods greater than 12.9 seconds the 40 knot fully arisen conditions are significantly exceeded by the climatology. Comparison of Table VIII with Table XIV shows that in the 2 0.0 second period band of the climatology, the energy values exceed even the fully arisen conditions realized under 5 0 knot winds, even though the maximum winds calculated for February did not exceed 42 knots. Obviously these wind conditions were of insufficient duration to attain 38 fully arisen status . The additional energy resulted from the simultaneous occurrence of swell with sea and increased the total wave energy to a considerable extent, especially in the longer period bands. Swell energy is not as easily identifiable in the spec- tral climatology tables as it is in the gross climatology tables , although in meteorological direction 4 of the August 1974 data (Table G-4 of Appendix G) the event occurrence of 17 in the 16. 4 second period band with an energy level of 01 is undoubtedly swell, as are other high event occurrences in the long period bands of the other tables of Appendices F and G. As in the gross statistics, a comparison of the February and August spectral data (Appendices F and G) reveals that the maximum wave energy in both cases comes from meteorologi- cal direction 3 with lesser, but significant, amounts from adjacent directions. D. ONE-DIMENSIONAL FREQUENCY SPECTRUM FORMAT The one dimensional frequency spectrum climatology is a tabulation of cumulative energy density versus frequency summed over all directions. The energy density values tabu- lated from the SOWM analyses are those contained in the fre- quency spectrum shown in the FNWC printout (item 13 of Figure 2). The tabulations for February 1975 and August 1974 for grid point 164 are shown in Tables XVI and XVII for equal frequency bandwidths (Af = 0.00 5 5 Hz). The construction of this format involved the extraction of the external energy values E, through E, - and their 39 associated period bands from the FNWC SOWM 12-hourly analyses for the month of interest. Subsequent conversion of the FNWC energy density values to an equal frequency bandwidth basis using the normalized scaling factors in Table I was then accomplished. The energy values for the common bandwidths were then coded with the energy scale from Table VII and entered into Tables XVI and XVII. The entries in the tables represent event occurrence vice duration or per cent occur- rence for reasons previously discussed. A total of M-5 12- hourly analyses were entered for February 19 7 5 and 61 for August 19 74. Tables XVI and XVII are similar in construction and appearance to the tables contained in Appendices F and G; however, the energy densities are not directly comparable. In the latter tables the occurrence entries for a given per- iod band refer to energy values for each of the 12 direction bands , while in the former, the entries refer to the cumula- tive energy in all direction bands. The energy values in the former tables, therefore, are larger. The individual occurrence entries in all of the climato- logy tables in this thesis could be cumulated so as to show the cumulative occurrence of wave heights or energy densities in any frequency band equal to or higher (lower) than a given value. This has been done for the data contained in Tables XVI and XVII, and the results are shown in graphical form in Figures 12 and 13. These figures show curves of coded energy density plotted versus period and cumulative frequency of occurrence. The period is the reciprocal of the central 40 wave frequency for a given frequency bandwidth. The coded energy density values may be translated into variance values through the use of Table VII. The 01 energy density category includes zero wave energy. Cumulation through the energy value of 01, therefore, will yield a total number of event occurrences equal to the total number of 12-hourly analyses during the month. This climatology format will yield period/ energy event occurrences for any period from 6 to 2 6 seconds. In constructing the figures , the individual cumulative event occurrence/period entries for the same coded energy level were plotted for both months. All points having the same coded energy level were then connected to form a curve. Interpolation, when required, was accomplished in a manner consistent with the shape of the data points. Although Fig- ures 12 and 13 contain basically the same information as Tables XVI and XVII, graphical presentation of the statistics in cumulative form is easier to visualize and to use. It will be noted that use of the graphs permits determination of the event occurrence for any wave period rather than only for FNWC periods. The statistical distribution for February 19 7 5 in Figure 12 is seen to have a distinctive appearance that is not unlike a series of nested fully arisen sea spectra generated by a range of wind speeds. The maximum occurrence for all energy density curves, shown as a dashed line, is the counterpart of the curve of energy density maxima, T , in nested spec- **J J ' max' v tra. The curves show a surprising uniformity for the small size of the occurrence sample (M-5 total events). The 41 irregularities in the plot for February would be expected to largely disappear if the data base were lengthened to in- clude several years of February spectral statistics. The most striking difference between the February and August climatologies is the energy content of the two months. The maximum energy level observed in August (Figure 13) oc- curred at a coded energy level of 04 in the period band of 15 seconds, while a very much greater energy maximum of 26 occurs at 18 seconds in the February statistics. Addition- ally, the energy in February is contained in longer period bands (greater than 2 6 seconds) than that of August. The remaining comments in this section will be directed to use of Figures 12 and 13. Period (or frequency) and energy levels may be used as entering arguments to obtain an event occurrence for that combination for the given monthly climatology. If, for example, a user desired to operate a spar buoy in February whose resonant period was known to be 15 seconds, and the maximum tolerable energy level could not 2 . exceed 1.50 ft at this period, a determination of frequency of occurrence of these conditions could be established as 2 follows. From Table VII, 1,50 ft is represented by energy code 07. Entry into the February climatology with a 15 sec- ond period and an energy level 07 reveals that energy levels 2 of 1.50 ft or greater occurred 18 times during the clima- tology base period of M-5 total possible occurrences. The same entry arguments in the August data reveal that at no time was the energy content in the 15 second period in excess of energy level 04 (0.75 to 0.99 ft2). 42 To determine the frequency of occurrence of a particular 2 energy level in a given period band, e.g., 2.00 to 2.50 ft at 13.8 seconds for February, enter 13.8 seconds to the 09 energy curve and obtain an occurrence of 2 0 events, then enter the 10 curve for an occurrence of 17. The difference, or 3 , is the occurrence in this energy density band at 13.8 seconds. The frequency of occurrence of energy level 01 is determined in the same manner, but the total number of 12- hourly analyses must be known. For example, for the February data with 4-5 total events the frequency of occurrence of energy state 01 in the 18 second band is 4-5 minus 17 (the frequency of occurrence of energy level 02), or 28. 43 IV. APPLICATIONS It is of interest to compare the experimental gross cli- matology format and data contained in Appendices D and E of this thesis with similar wave climatologies which are cur- rently available to wave statistics users. One such compila- tion was made by National Marine Consultants (NMC) for three deep-water stations along the Oregon-Washington coast (NMC, 1961) and seven deep-water stations along the California coast (NMC, 1960). Table XVIII is a sample wave climatology extrac- ted from the NMC data for February (average of three years) at a station located in deep water off the Washington-Oregon border. The formats of the NMC data and the gross statistics presented herein are similar, but there are some significant differences. The NMC data were derived manually (as is the case with all other wave statistics known to the writer) by the hindcasting methods contained in H. 0. 603, while the gross statistics presented here were derived from computer produced spectral wave analyses. The frequency of occurrence entries in the NMC statistics are presented in per cent whereas those in the tables herein are given in number of synoptic events. Conversion of one to the other may be easily accomplished. The NMC data are presented as separate tables of sea and swell while the gross statistics show the total wave energy. Combining the sea and swell tables of the NMC data to obtain 44 the total wave energy is difficult. One difficulty arises from the fact that while the NMC sea tables always total to 100 per cent (lower portion of Table XVIII) the swell tables (upper portion of Table XVIII) do not. This is a result of the mode of compilation of the NMC swell statistics. The basic problem the user is faced with is how to convert the NMC swell statistics to 100 per cent total occurrence. A second difficulty involves the method by which sea and swell should be combined and is due to the fact that sea and swell may occur simultaneously or separately. These problems do not occur in the gross statistics because the FNWC Spectral Ocean Wave Model generates sea and propagates swell together and does not separate sea from swell. Some resolution between sea and swell is possible in the gross statistics, however, with the use of the steepness criterion discussed in Section IIIB. It was pointed out there that each height-period entry in the climatology format can be converted by the user into a crude measure of wave steepness which will indicate whether the larger waves present approximate steep sea, young swell of moderate steepness, or old swell of low steepness. The gross wave statistics described in this paper would have similar applications by wave statistics users to those climatologies currently available. A major advantage of wave statistics compiled from FNWC spectral analyses is the ability to lengthen the statistical data base beyond the three years used by the NMC and some other similar statistics. From six-hourly surface pressure analyses archived in FNWC it would be possible to produce wave statistics for approximately a 45 20 year period. It may be of interest to note that synoptic wave fields are currently being prepared from a 2 0-year series of synoptic weather maps by FNWC. No spectral climatologies have previously been produced; therefore j the resulting spectral climatology formats de- scribed herein are considered to be experimental in nature. Although the area of application of spectral data appears to be largely unexplored, it is probable that in resonance re- lated phenomenon they will find their greatest use. Ships or ship routers might utilize deep water two-dimensional spectral climatologies to estimate the energy content from both a frequency and direction standpoint for the purpose of planning ship routes. While the actual relationship between energy densities and hull responses requires investigation, increased energy in a critical frequency or direction band may be expected to significantly affect the stability and sea-keeping characteristics of a structure or craft. For coastal engineering purposes it may be seen that the two-dimensional spectral climatology statistics (Appendices F and G) may be shoaled and refracted into intermediate or shallow water depths where they could be used for prediction of the resonant behavior of piling platforms, floating break- waters, and other coastal structures. Littoral drift rates may also be computed from computation of the longshore com- ponent of wave power derived by shoaling and refracting the deep water climatology. Wave heights in shoal water cannot be calculated from the deep water spectral climatology, however. Near-shore wave-height climatologies can be prepared 46 only by shoaling and refracting the deep water spectral analyses and recombining the resultant wave heights at a near-shore site. The one-dimensional spectral data (shown in Tables XVI and XVII and Figures 12 and 13) cannot be transformed by re- fraction to provide near-shore wave information because no directional information is available in this format. Its potential applications are, therefore, restricted to deep water use, and furthermore have no application to situations which require directional information. The one-dimensional spectral statistics appear to have their greatest potential application with regard to dynamic interaction of moored or stationary structures in deep water which are not direc- tionally sensitive. 47 LIST OF REFERENCES 1. Cardone , Vincent, 197 5. Computer Program for the Spectral Energy Distribution of the Sea Surface, program run at FNWC 2 6 March 19 75. 2. Gerst , Anthony L. , 1971. Naval Weather Service Environ- mental Detachment, Adak , Alaska, Local Area Forecaster's Handbook, 1 February 19 71. 3. Kinsman, Blair, 1965. Wind Waves their generation and propagation on the ocean surface, Prentice-Hall. H- . Lazanoff, Sheldon and Norman M. Stevenson, 1975. Fleet Numerical Weather Central Technical Note 75-3, An Evalua- tion of a Hemispheric Operational Wave Spectral Model, June 1975. 5. National Marine Consultants, Inc., 19 60. Wave Statistics for Seven Deep Water Stations Along the California Coast. 6. National Marine Consultants, Inc., 1961. Wave Statistics for Three Deep Water Stations Along the Oregon-Washington Coast, May 1961. 7. Pierson, Willard, J. Jr., Gerhart Neumann and Richard N. Jones, 195 5. Practical Methods for Observing and Fore- casting Ocean Waves by Means of Wave Spectra and Statistics , H. 0. Publication No. 603, U. S. Naval Oceanographic Office. 48 Table 1 FREQUENCY/PERIOD PARAMETERS FOR THE FNWC SOWM (modified from Lazanoff and Stevenson, 1975) Central frequency (Hz) Frequency band (Hz) Band- width (Hz) Central period (Sec) 6.1 Period band (Sec) 6.1- 0.0 Band- width (Sec) Scaling factor 0.164 .164-0° 10 0.153 .142-. 164 .0220 6.5 6.1- 7.0 .9 45 0.133 .125-. 142 .0165 7.5 7.0- 8.0 1.0 60 0.117 .108-. 125 .0165 8.6 8.0- 9.3 1.3 60 0.103 .097-. 108 .0110 9.7 9.3-10.3 1.0 90 0.092 .086-. 097 .0110 10.9 10.3-11.6 1.3 90 0.083 .080-. 086 .0055 12.0 11.6-12.5 .9 180 0.078 .075-. 080 .0055 12.9 12.5-13.3 .8 180 0.072 .069-. 075 .0055 13.8 13.3-14.5 1.2 180 0.067 .064-. 069 .0055 15.0 14.5-15.6 1.1 180 0.061 .058-. 064 .0055 16.4 15.6-17.2 1.6 180 0.056 .053-. 058 .0055 18.0 17.2-18.9 1.7 180 0.050 .047-. 053 .0055 20.0 18.9-21.3 2.4 180 0.044 .042-. 047 .0055 22.5 21.3-23.8 2.5 180 0.039 .036-. 042 .0055 25.7 23.8-27.8 4.0 180 49 Table II OCCURRENCE OF PERIOD PEAKS FOR AUGUST 1974 AND FEBRUARY 1975 Number of period peaks per analysis 0 1 2 3 4 Percentage Percentage occurrence occurrence August 1974 February 1975 6 0 36 36 26 40 20 20 12 4 Table III OCCURRENCE OF DIRECTIONAL PEAKS FOR AUGUST 19 7 4 AND FEBRUARY 19 7 5 Number of direction peaks per analysis Percentage Percentage occurrence occurrence August 1974 February 19 7 5 8 0 77 42 15 58 50 Table IV WAVE HEIGHT CODE FOR THE GROSS CLIMATOLOGY FORMATS Code H, ,,(ft) Total variance ( ft 2 ) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 Ll/3 0.0- 1.9 0.000- 0.249 2.0- 3.9 0.250- 0.999 4.0- 5.9 1.000- 2.249 6.0- 7.9 2.250- 3.999 8.0- 9.9 4.000- 6.249 10.0-11.9 6.250- 8.999 12.0-13.9 9.000-12.249 14.0-15.9 12.250-15.999 16.0-17.9 16.000-20.249 18.0-19.9 20.250-24.999 20.0-21.9 25.000-30.249 22.0-23.9 30.250-35.999 24.0-25.9 36.000-42.249 26.0-27.9 42.250-48.999 28.0-29.9 49.000-56.249 30.0-31.9 56.250-63.999 32.0-33.9 64.000-72.249 34.0-35.9 72.250-80.999 36.0-37.9 • 81.000-90.249 38.0-39.9 90.250-99.999 40.0 + 100.000 + 51 6.1 6.5 7.5 \LL D 8.6 IRECT C EN 9.7 IONS TRA L PI 10-9 |12.0 ERIO 12.9 D (SECO 13.8 |1 5.0 NDS) 16.41 FEE 18.0 , R U/ 20.0 k RY 22.5 1975 25.7 01 02 03 1 2 04 1 1 05 1 06 2 1 Q07 6 1 O O08 [ } 2 2 ►-09 X 1 ^ 10 2 2 •- 11 z 1 3 < U 12 2 1 1 Z*3 3 1 ^ 14 1 1 1 15 1 16 2 17 1 18 1 19 20 21 . Table V. Gross Wave Statistics for All Directions for February 19 7 5 52 6.1 l 6.5 V => 7.5 ML Dl 8.6 RECTIONS CENTRA 9.7 1 10.9 L PI 12.0 ERIO 12.9 D (S 13.8 ECO 15.0 NDS) 16.4J A 18.0 UGU 20.0 ST 22.5 1974 25.7 01 6 4 3 5 02 2 4 1 2 03 4 1 04 1 5 3 3 1 05 6 3 1 1 06 07 38 09 10 11 12 13 14 15 16 17 18 19 20 21 Table VI. Gross Wave Statistics for All Directions for August 1974 53 Table VII ENERGY DENSITY CODE FOR THE SPECTRAL CLIMATOLOGY FORMATS Energy Density 2 Code (ft /frequency bandwidth) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 0.00- 0.24 0.25- 0.49 0.50- 0.74 0.75- 0.99 1.00- 1.24 1.25- 1.49 1.50- 1.74 1.75- 1.99 2.00- 2.49 2.50- 2.99 3.00- 3.49 3.50- 3.99 4.00- 4.49 4.50- 4.99 5.00- 5.49 5.50- 5.99 6.00- 6.49 6.50- 6.99 7.00- 7.49 7.50- 7.99 8.00- 8.49 8.50- 8.99 9.00- 9.49 9. 50- 9.99 lQ. 00- 10.49 10.50- 10.99 54 u;=3 FEBRUARY 1975 6.1 6.5 7.5 8.6 r EN 9.7 TR A 10.9 L P* 12.0 .RIO 12.9 D (S 13.8 ECOI 15.0 16.4 18.0 20.0 22.5 25.7 01 12 5 3 5 2 11 12 15 13 12 9 7 5 3 5 02 18 20 21 1 5 4 2 3 3 3 1 03 6 3 1 4 2 2 2 2 2 04 14 4 2 1 2 1 2 2 2 1 1 05 10 5 3 3 2 1 1 06 3 5 1 1 1 2 07 4 2 4 1 08 7 3 2 2 09 1 3 1 1 3 10 2 1 11 4 2 12 3 1 13 1 1 14 15 1 1 16 ■ 17 18 19 1 20 21 1 22 23 24 25 26 , bO O rH o rd £ •H H O CD > rd C O -^ •H oo CO C m CD S ■&■ •H >-^ Q O !>• 2 cn Eh rH > 0) rH ,£! Eh 55 W = 3 FEBRUARY 1975 6.1 6.5 7.5 8.6 ■EN 9.7 TR A 10.9 L PI 12.0 :RIO 12.9 D (S 13.8 ECOI 15.0 ^DS) 16.4 18.0 20.0 22.5 25.7 01 30 25 24 12 7 15 12 15 13 12 9 7 5 3 5 02 14 7 3 2 3 3 3 1 03 10 3 4 2 2 2 2 2 04 11 1 2 1 2 2 2 1 1 05 5 3 3 2 1 1 06 5 1 1 1 2 07 2 4 1 08 3 2 2 09 1 3 1 1 3 10 2 1 11 4 2 12 3 1 13 1 1 14 15 1 1 16 17 18 19 1 20 21 1 22 23 24 25 26 [■» CD H -C >>-H fc T5 IT) H 3 2 fc t3 X3 C 0) td Pm CQ fc >> 0 o 4h c 0) >, 3 bO ct< 0 CD rH Sh O Uh -p rd h 6 id •H 3 rH cr1 o w 0) & > O ft! IJH s ID r-\ d) id -P e CO o 3 •H •r— i co id c< a) S •-N •H CO Q 1 O 2 -9- Eh N_X • X H n r-{ m -3- c < U 0 s <*■ s o N 00 O O o o 3: S rv Cjh LO r» in CD 0 H e >> =3 & h 03 +J 3 o fc 0) X3 Oh CD 00 Uh >^cn bfl r-\ U CO h e 0 w <+H X 2; H Ph r-i w —> U-t CO T3 U C O-H 4hS •"■ \ CD £ 4-> ^ =3 0 -P fc C XI -P ^ •H O 5 0) O -a PuCvJ c en rd & A >,0 b04n rH P. in cu fd 3 c cu cr1 Woo CU X r-{ rd I I— a i a z < CO z O O ^ b 58 6.1 6.5 7.5 ME i 8.6 AN r EN 9.7 WIN TR A 10.9 D D L PI 12.0 I RE( .RIO 12.9 :tio D (S 13.8 N ECOl 15.0 ^IDS) 16.4 18. Q 20.0 22.5 25.7 01 0 0 0 1 0 1 0 1 0 1 0 02 1 0 0 1 0 1 0 03 1 1 0 1 0 04 1 05 1 1 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 c co c •H cti < o 3 O 4h CO X) c £ +J a O & C 4-" >4 O (D O g^co CO >, O (1) rd C CD W CO I— I M X CO +-> ■H c a* ft! Z »- Z Q a z < CD z o 2 2 O ^ u U b 59 61 6.5 7.5 ME I 8.6 AN : en 9.7 WIN TR A 10.9 D D L PI 12.0 I RE< .RIO 12.9 :tio D (S 13.8 N ECOI 15.0 >.^ H U-t H w 3 Cj-i CO TD M C 0 -H <4H 2 *^-\ CO e +■> ^ a O -M ^ C -a -M M •H O 2 0) O 13 Puj- C oq rd fc A >^ 0 bflUn H Ph 03 0) T3 3 C 0) cr W go , rd H m a 3 s Ph 2 Ph k w 0 Uh W -a S c D -H fc 2 ■H a -p /~\ CD 0 CO a c -= oo >4 -P T3 >^o •rH bfli-n 3 & "O CD k a C 0 id W <4h J3 • > H X CD rH X3 id Eh X t- z o i— — a J ii Q < Z CO < CO Z O U 2 *2 Z O u. u T- O 61 iy=3 AUGUST 1974 CENTRAL PERIOD (SECONDS) 6.1 6.5 7.5 8.6 9.7 10.9 12.0 12.9 13.8 15.0 16.4 18.0 200 22.5 25.7 01 15 19 19 19 18 11 12 10 3 2 3 3 1 02 15 5 6 4 7 2 1 1 03 1 1 1 1 1 04 1 05 06 07 08 09 10 11 12 13 14 15 16 ■ 17 18 19 . 20 21 22 23 24 25 26 o >> O o -p O CD > /— n id OO s II r-\ td -3- c ^■^ o •H zf CO c-« C CD CD H b •H ■H Q CO I d O bO 5 P Eh < • > X ^ 09 13 6 3 3 3 1 1 / Spect Februa 10 1 4 5 2 3 3 1 1 11 9 3 2 2 1 2 C 0 CD Mh 12 1 7 3 1 3 2 1 3 CT* CO CD ,C 13 2 3 4 2 2 2 Dnal Fr andwidt 14 3 3 4 1 15 3 1 2 1 •H CQ CO 16 ■ 1 1 1 CD ac ■H lo 17 1 1 1 1 I o CD O 18 2 G • O o 19 1 1 1 1 • H > 20 X CD 21 2 22 23 1 1 1 24 1 25 26 1 63 6.1 6.5 7.5 M.LD i 8.6 IREC : en 9.7 rioN TR A 10.9 s L PE 12.0 RIO 12.9 D (S 13.8 ECOI 15.0 >4DS) 16.4 AL 18. 0 JGU 20.0 ST 1 22.5 974 25.7 01 61 61 55 49 50 56 59 59 60 59 60 61 61 61 61 02 6 12 1 1 5 1 1 1 1 03 1 1 1 04 1 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 • 23 24 25 26 o 6 CD D rH U -M -H O CO 31 || Ov -O *"■ ■u - 1 t 0 •a 3 3 o ' -O 1 2 a "\ "! "7 •o ~> •0 j 3 —i «) ® jj] « a s ■ o ol oi -^ r-\| 1 , XJ 4 .o o iA > ^71 2 3b| 2 si 0J i « J o z 3 OS o; J ' " _ o « rJ ol J "7 ~a o ■ - w. so + a* 0 3 ^ ^ 1 1 1 ! 1 A 3 a 3 2 1 II 13 2 z 3 (5| j o; i : i ; \-x a 3 -< so i a* "J "1 r1 ■ o a* o -o oil >A ■ "} , 1 •d 0 4) | ol O ,-JI • 2 + 1 ^3 •o 2 ^ ^ 1 ^j S 2 o "? ■o ml • •' ■6 * 3 -r 2 *o -| o 3 -i\ » « ""3 , j ^ j ■ g oi ^ ol *0 . o TJ -J 3 1A i 3 * a -a ■"1 i "} i -O ' n ll i -i\ ^ 3 ^ p^i m OV j _ ' ' ol ' j' •o a ^ x 3 Oil SI ol 1 O *o o* •o •0 uvl XI I vO Jl ol J 3 +■ , s c 3 « i S "lj ml O i 3 ; ■l ! i o 3 ojj ^ 1 •O "i\ 2 53 o a „ Lo j •: Mill 2 o «> j 2 - 5 2 1 3 *o 3 ■A I o 3 *"* i| ~ • : 1 I* 00 o - : ^_ ■O 00 1 X o; i o\ o a* ' 0> o 1 a* io|oll-»t>o!+tri 7 7 f i t i :w u •0 o o- o o s •o 1 o « a o O O o a D » Ed ■x. O X Cb o :j 10 >A h + -o" 3 3 1 -1 l-l "» ■» 3 I ^!^ J i o I A O ■O | oi -* « i| "! 1 ^ o ■* ^ - f 2 3,1 IV 4 1 O c^ •o Jl so 2 j o> : l-I •o "" i 5 "11 -r o jl flo j i 3 +1 ■O J 3 o 3 ' 1 -i I 1 ol CO ^ oil J ; -f •o •0 i J ">| J ■* o "I "^ ! I : a 3 + i 3 rt 1 |"2 ^ J 00 2 1' °:: 1 -| o r4 O •» ^ "1 3 ~r x> j ■" n j I j i 1 v.. a + •O i 3 3 | 1 ^ i to 3 m o <> •0 "t | ol ! Jl j -' O N w4 1 W ™ + 3 3 1 3E ! ■B o | ^N 1 sO A ■ O ™ 1 J I oil J * * 1 °1 "I : -i X - 4- 1 <; O 3 J "1 ■°. Ov I 3 m o ol 1 ^ 4 50 i" "! 12 ~f O | oj | *0 ■ 3 ■*A 3 + 3 3 i ^ i ■ £ 33 3 ^- . 1 A O -0 Oj -i i rj J "° ;l ^ A ■* 2 + 1 1 1 -i 1 1 i 3 3 >o j- « 3 ■O o> 4 o °:i °: v. - - '3 3 3 i 35 -o o 1 o *j | * o o i ' >o 3= 1 t? / r » <*> O O 1 • to r- ■ > 1 °* °5 o> i o> o> pi -1 1 O a) j <*■. l i^ O- CT» r- U CD > id rH s id 00 W rH 4-J CD C en td H -P p o en S c s 0 o s 0 0) Sh C 4h •H ^»-x ^H d >, S bO 0 H r-i rd 0 C ■M 0 rd •H S ■P •H rd i— 1 S CJ H H > X cu rH rd Eh 65 fi 0 CO 0) c x: cu ■p > CD <4H -M 0 OQ C X3 0 C •H fti -P 0 4-i CD 4-4 •i — i 0 0 C & rd cu N d 0 J •H c e o 0 s & 0 4h C ~^ CD 1 CO ,— 1 c «j d P. aj -a a CD o rC id X3 ^ en r-i LO 0 fc o- 0 0 en H S . » oo oooooooon U"t oo-JOcaOssooa «4 o oa-'Coa aonooo M • ••••■«•«•••■ • oo aoeoooaoa i — ' \fi ooloooooooooo ir o o oomooooooooo fo o • •••••••••••• • ^ r-> o cnoaoaoao • i J> *. cm a uasoaojcoooo eo i_3 oa ooooooooo z M _J(\jN. OOLPOCOOOOOOO u> mo oo-aocaocriao «4 o • • •■•••«•••••* « c >^a ccoacooao o— a ooaaaoooaooo a v> • ••••••••«••• « t_ 3 oo aooaoooo o oooaooo O O N. r"10«-l 00<»-IMP>»000 0000 es ..u-h oaaanooaoaoo jr II LU • • • • • • . . 3 0_ oo (jOooooo *"— — • "° — -^C5m '_30(\jM»*oOOOuOO *-l ZZ.-I oooom»hOooooo «y oOm • •*•■••# • * f t • • OHZ OO OOOOOO — >— ! i POO W ' aeuj ir> oaoosNaoooaa *■> O-} »H LOOONrlOOaCOO |*J J-O i • I p^Of oooe aoooaa II 0. H-3 v£> OOO-i-l—lT-lOOOOOO ml Q ^0 ^h o oo oooooo«r>oo ej • ••■•••••■••« • uoa oooooo ** r- uj»-iwr\jir>L,\v^s.«ea,o«*f\j u. o +J ft O S SI 3 o O o CO iH CO CJ CO 2 o d-i r^ CM (D bfl •H 67 u +J 0 PH 0) 0 Ph'-H C/l Cfl >^.c a ■H c X) a) •H 3 3 C^X) CD G & d Ph CQ H >^ rti 0 G G 0 CD •H 3 Cfl cr •-N G cd NI 0) r M — i 6 Ph O •H H Q a co 1 2 30 cu s; o G PL| ^r Q ^-^ r- •i § : ! .3 - 2 P-. ZH/,id.SN3Q yyA a ♦— C3 m i i ii re Q h 68 -M & O 0 CD '-H P, 00 CO rC >, 4- o T3 c •H CD 3 3 X3 cr C CD id >H CQ tin >> rH O rd c C CD 0 3 •H cr CO a; •-» c f-i N] CD P-H O g o •H i-H rH Q rfl CO 1 3 CO CD era C jq J- O ^*x c-%. ZH/^'SN3Q Wh a - a — C3 mi i LxJCC 69 0 — • I • o o * o * • o • • o • * o • o • • o • • o • * • <) • (I II • (I • o • • o • o o • o • • o a * • o o * • o a * o • a * o • * o • o • o • o * • o * • o * • o « • * o • * O O • * o • * 0*0 o • * o • ro o en O CN 00 CN t^ CN o CN lO CN CN m CN CN o CN O LU If) < ■«■ Q ¥"■ rn *~ CN o 00 en cn q CN O <> eo in s If) <6 a c CD a CT4 a) Fn Uh a> rH Ph •H J- -p r^ H cn a M S -P <4h CO 0 =3 bfl 0) 3 a < C , S Ph tt) Mh 3 0 & £) 0) > CJ rH CD fc fc •H •H xj Q -a ^H CD •"N HJ TD — C 0 CO O CJ rH •H ^^ CO -M C IS] c 0) o ■H e o O •H H a P m I CO X! 0) o ■H c J- fc o r- 00 CD bO •H 72 & 0 Mh i-1 J- 0 c- •H en -M H O !< ,JQ T3 0) c O rO c Q) lO h r» b Ol 3 rH a 0 >! o & fd -M D C (h CD W U-i CO Sh bO •H Ph 73 LO C*- co en 0 H co S-i CD 0) c > 0 -a 03 U •H (t) u o C > a tt -H 03 S S 3 a z • > CD > CD h 3 M •H Uh o a q a z z z z o o o o en ^ m ((cmsnrav) lx /C/ln ) via3iiao ss3Nd3 iis 74 6.1 6.5 7.5 8.6 C EN 9.7 TRA 10.9 L PI 12.0 ERIO 12.9 D (S 13.8 ECO 15.0 NDS) 16.4' 18.0 20.0 22.5 25.7 01 02 03 1 04 1 05 1 06 1 07 1 38 1 D9 1 10 1 11 1 12 1 13 1 14 1 15 1 16 1 17 1 18 1 19 1 20 1 21 — 1 Figure 10. Wave Steepness Criterion Envelope of H1/3/T12(A.djusted) >_ 0.125 75 FNWC VARIABLE FREQUENCY BANDWIDTHS T = 20SEC T = 8.6 SEC 0.37 o z < u Z u_ 047 .050 .053 H — 0.0055 FREQ (Hz) 0.37 .117 — 0.0165 - FREQ (Hz) 125 EQUAL FREQUENCY BANDWIDTHS T = 20SEC T=8.6 SEC 0.37 z < CO < D O uu O 00 O lO zt CO 0 CM J- CO 00 K rH • • rH ffi rH • • rH W 00 CM c-~ p» • CM rH CO • 2 Q rH Hf r-i rH Oh 2 CM CM W M W 2 P o CD rH -H LO CD O Eh id LO CO CO id CM CO CO 00 Eh y— \ 00 • • rH CO • • rH O LO id rH r» r- • id rH rH CO • Q 2 r~ CD 0) rH rH 2 « CD 00 00 < rH o C o CD o c CD ["- CM 00 LO •> CU lO CM CO cu lO CO J" PS CU en LO • • rH GO LO • • rH W Q C •H rH C^ r» • •H rH O LO • Eh 2 0 P. H rH rH CQ W < T3 < < 2 b X < - m 5^ o co LO > [-- CM CO H C£ O o rH LO CD CM rH J" O LO Q < =t rH CM • . rH rH CM • • rH 2 Cu s 3 H c^ r^ • 3 rH CD Hr • W o 0 U-, Ph rH Oh ►rj o p. v*^ ^-^ cu ^ 4h < 2 en o CO CO GO r-> CO CO O - ID 4-J CO CO ht P> lO H^ lO OS o CU ^ CD • • rH « CD • • rH CD cm ■H 4h o CO CO • O CO rH rH • W « •H CM CO > o TD < Uh O o CO r~ o CM CO s 6 • • CO CD =t • • CD r~ CO < Vw' T3 CO • • rH TD CO • • rH J H 0) LO Hr • cu CO CO • < C* CU CU OS w a Pu Eh Eh 00 00 O M CO CO LO o o J- W PS -a LO rH i> TJ co CD r» Cu CJ c CD • • rH G CO • • rH 00 ■H go P. P G 0 ■H P CO a CU CO ^—/ cu P CM • "0 cu P GO •n T3 id •H 2 GO u c o •H P LO CJ cu GO /*— s -o cu p J" CU P GO •f— 1 rd 00 • — \ GO id GO ^-s GO U a p GO CM p. 3 p GO OJ 0 •1 — 1 CO CD CO TD ^^ co cu c C "*s. CU ">>, C \ cu •H H rH +J rH •H H rH P1 r 2 Eh Iffi 00 IE IS Eh Iffi 00 IX 80 o J- CM o o =t o • • H co 00 CO • O CO H O CO CO =f . • rH /— \ CM lO H cd CM • CO Pi 3 o co CD 0 o o CM K rH • • rH CM lO CD • J- rH CM CM +J CD rH LO fl CO CO CO CO • • rH fl H CM c-~ • CD r-\ CM co c O CD C- cu O CD co en LO • • rH •H H CM CO • Pi H CM < >> LO CO LO rH CM CO CO rH CM • • rH ^ H rH o • rH CM CO CD J" O -M LO CD CO >4 CD • • H o X3 CD cu a CO -a c •H CO o o CD O CD CO [-» CO co CO CO o CO H o LO J- r- . • rH CM CO rH LO • O r~\ LO o CO CO J" • • rH S~ N CM CO rH CO • CO Pi 3 CO CM rH 0 CO J" LO K rH • • rH CM CO o • o rH J- CO ■p O co CO rd o c» CO 00 • • r-^ rd H LO CO • CD rH CO CO C O CD CO a) o CO J- CO LO • • rH •H rH LO CO • u rH CO < >\ LO CD CO rH 00 CD LO rH CM • • rH 3 rH CO CD • rH CM CO CO CO CD -H CO CM LO X CD CM CO rH o rH CM LO LO O CO »■ CM CO CD X3 CO • • rH CD CD CO •X3 C •H CO LO CO CM LO co CO P« K c o •H -P rd Pi TJ C •H O CD CO T5 CD -H CO •n -a ■H Iffi CD P CO •I — I CO co CD ft CD CD +-1 CO CM Iffi CO Pi C 0 •H p rd Pi c •H T3 CD P CO •i — i 1TJ P T3 CD P CO •r—i H IK co CO CD c 0) CD P CO CM rH Eh IK 81 APPENDIX C SPECTRAL ENERGY DISTRIBUTION FOR FULLY ARISEN SEAS FROM WIND SPEEDS OF 20, 30, i+0, AND 5 0 KNOTS FOR A 30° DIRECTION BAND (modified from Cardone , 1975) Tables C-l thru C-4 contain the spectral energy-period band distribution for wind speeds of 20, 30, M-0, and 50 knots respectively. The 30° direction band is centered about the direction of the mean wind. The energy distribu- tion is presented for both the FNWC and the common band- widths . 82 Table C-l Fully Arisen Sea (20 knots) Wind speed: 20 kts Time to fully- arisen conditions: 21 hrs Tav : 5.69 sees U... : .74 H1/3: 7.4 2 ft Var: 3.44 ft Frequency Period AE/FNWC Energy in AE/0. 0055Hz (Hz) (sees ) bandwidth 30° band bandwidth .039 25.7 .0U4 22.5 .050 20.0 .055 18.0 .061 16.4 .067 15.0 .072 13.8 .078 12.9 :0003 .0001 .0001 .083 12.0 .0020 .0008 .0008 .092 10.9 .0351 .0132 .0066 .103 9.7 .1614 .0605 .0302 .117 8.6 .5025 .1884 .0628 .133 7.5 .6199 .2325 .0775 .153 6.5 .7074 .2653 .0663 .164 6.1 1.4094 .5285 .0294 E =3.4375 83 Table C-2 Fully Arisen Sea (30 knots) Wind speed: 3 0 kts Time to fully arisen < conditions : 24 hrs Tav: 8. 18 sees u* : 1. 26 Hl/3: 16 .49 ft .99 ft2 Var: 16 Frequency Period AE/ 'FNWC Energy in AE/0. 0055Hz (Hz) ( sees ) 25.7 bandwidth 30° band bandwidth .039 .01+14 22.5 .050 20.0 < ,0003 .0001 .0001 .056 18.0 . 0131 .0049 .0049 .051 16.4 1158 .0434 .0434 .067 15.0 4 ,4032 .1512 .1512 .072 13.8 ■ ,8177 .3066 .3066 .078 12.9 1. ,1983 .4494 .4494 .083 12.0 1. ,4363 .5386 .5386 .092 10.9 2. ,9903 1.1214 .5607 .103 9.7 2. ,5722 .9646 .4823 .117 8.6 2. ,7401 1.0275 . 3425 .133 7.5 1. ,6863 .6324 .2108 .153 6.5 1. ,2767 .4788 .1197 .164 6.1 1. Et=16. ,7370 ,9873 .6514 .0362 84 Table C-3 Fully Arisen Sea (40 knots) Wind sp« Bed : 40 kts Time to fully arisen < conditions : 24 hrs Tav: 10 .78 sees " U,. : l.i 35 Sl/3: 29 .38 ft .97 ft2 Var: 53 Frequency Period AE/FNWC Energy in AE/0. 0055Hz (Hz) ( sees ) 25.7 bandwidth .0056 30° band .0021 bandwidth .039 .0021 .044 22.5 . 2749 .1031 .1031 .050 20.0 1.7222 .6458 .6458 .056 18.0 4.0634 1.5238 1.5238 .061 16.4 5. 8309 2.1866 2.1866 .067 15.0 6.4152 2.4057 2.4057 .072 13.8 6.0960 2.2860 2.2860 .078 12.9 5.3359 2.0010 2.0010 .083 12.0 4.4611 1.6729 1.5729 .092 10.9 6.5687 2.4633 1.2317 .103 9.7 4.2319 1.5870 .7935 .117 8.6 3.7227 1.3960 .4700 .133 7.5 2.0158 .7559 .2520 .153 6.5 1.4182 .5318 .1330 .164 6.1 V 1.8043 =53.9668 .6766 .0376 Table C-4 Fully Arisen Sea (50 knots) Wind speed: 5 0 knots Time to fully arisen conditions: 30 hrs Tav: 13.41 sees U:V: 2.51 H1/3: 46.04 ft Var: 13 2.49 ft Frequency Period AE/FNWC Energy in AE/0. 0055Hz (Hz) (sees) bandwidth 30° band bandwidth .039 25.7 4. 0088 1.5033 1.5033 .044 22. 5 12.5661 4.7123 4.7123 .050 20.0 18. 7274 7.0228 7.0228 .056 18.0 19.4475 7 .2928 7. 2928 .061 16.4 16.9890 6 . 3709 6. 3709 .067 15.0 13.6499 5.1187 5.1187 .072 13.8 10.5468 3.9551 3.9551 .078 12.9 8.0207 3.0073 3.0078 .083 12.0 6.0780 2.2793 2 . 2793 .092 10.9 8.1547 3.0580 1.5290 .103 9.7 4.8500 1. 8188 .9094 .117 8.6 4. 0489 1.5183 . 5061 .133 7.5 2.1166 .7937 .2646 .153 6.5 1.4595 .5473 .1368 .164 6.1 1.3233 .6837 . 0380 Et=132.4872 86 APPENDIX D CLI11AT0 LOGICAL WAVE TABLES OF THE GROSS STATISTICS FOR FEBRUARY 19 7 5 Tables D-l thru D-12 contain the coded wave height-equal period band distribution for the meteorological direction bands 1 thru 12 for grid point 164- in subprojection 3 at latitude 50.9° North, longitude 145.6° West. The February 197 5 wave statistics were derived from 4-5 FNWC SOWM 12-hourly synoptic analyses. The wave height codes are found in Table IV. The directional bandwidth codes are contained in item 11 of Figure 2. The tabular entries reflect the number of event occurrences of 12-hourly analyses for February 197 5. 87 1^ = 1 FEBRUARY 1975 I 6.1 6.5 1 7.5 I 8.6 C EN 9.7 TRAL PERIOD (SECO 10.9 I"I2.0 [12.9 113.8 J15.0 N DS) 16.4 J 18.0 20.0 22.5 25.7 01 02 03 04 1 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 i ■ | Table D-l J 6.1 { [6.5 V=2 7.5 | 8.6 CENTRAL PERIOD (SECO I 9.7 ho.9_Jj2.oJl2 .9 f 13.8 |l5 0 ^ DS) 16.4' FEE 13.0 ir u; !20.0 22.5 1975 25.7 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 •— - Table D-2 89 U>=3 FEBRUARY 1975 CENTRAL PERIOD (SECONDS) ! 6.1 6.5 I 7.5 ! 8.6 1 9.7 '10.9 !12.0 112.9 f 1 3.8 1 1 5.0 1 16.4 ' 18.0 :20.0 | 22.5 25.7 01 02 03 1 04 1 05 1 06 1 07 1 D8 09 10 1 11 2 12 13 1 1 14 1 15 1 16 2 17 1 18 19 20 21 U Table D-3 90 W =4 FEBRUARY 1975 I 6.1 [6.5 7.5 ! 8 6 C EN 9.7 T RA L PE RIOD (SECO 10.9 |12.0 i 1 2 9 f 1 3 8 [l5 0 N DS) '16.41 18.0 !20.0 I 22.5 25.7 01 02 03 04 05 06 1 O07 1 u -i a O08 1 »-09 X ^ 10 3T ■ i •- 11 z i < U 12 z13 w 14 15 16 17 18 1 19 20 21 >' i Table D-4 91 W =5 FEBRUARY 1975 I 6.1 (6.5 7.5 ! 8.6 CENTRAL P ! 9.7 1 10.9(12.0 ERIOD (SECO ' 12.9 Il3.8 |l5.0 NDS) 16.4 18.0 !20.0 22.5 25.7 01 02 03 04 05 06 O07 a O08 i } «... i h-09 X o w 10 "T" — - 1 *- 11 z 1 < ■ Table D-ll 98 ! 6.1 I [6.5 0i = I 7.5 12 ! 8.6 CENTRAL PERIOD (SECONDS) 1 9.7 |10.9 |12.0 112.9 113.8 15.0 16.4 FEBR U> 18.0 [lO.O ^RY 22.5 1975 ! 25.7 01 02 03 04 05 06 Q07 O08 u •-09 x . S to «- 11 z < _ 1 06 07 08 09 10 11 12 13 14 15 16 17 18 : 19 20 21 Table. E-4- 104 J 6.1 I 6.5 | 7.5 5 8.6 CENTRAL PERIOD (SECO 9.7 10.9 |12.0 |12.9 J13.8 |15.0 NDS; 116.4 AUGUST 118.0 J20.0I22.5 1974 ! 25.7 01 2 3 02 1 03 1 04 1 3 05 1 1 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 Table .E-5 105 1 6.1 6.5 | 7.5 > 8.6 C EN 9.7 T RA 10.9 L P 12.0 ERIOD (SECONDS) 12.9 |13.8 1 1 5.0 16.4 ' AUGUST |18.0 |20.0l22.5 1974 25.7 01 3 02 03 04 05 1 06 07 D8 39 10 11 12 13 14 15 16 17 18 19 20 21 «— Table. E-6 106 6.1 I 6.5 7.5 7 8.6 CENTRAL PERIOD (SECONDS) 9.7 1 1 0.9 |12.0 12.9 13.8 f 15.0 1 16.4 AUGUST Ii8.0j20.0!?2.5 1974 | 25.7 01 02 03 1 04 1 05 1 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 Table E-7 107 UJ=8 AUGUST 1974 6.1 6.5 7.5 8.6 CENTRA 9.7 1 10.9 L P 12.0 ERIOD (SECONDS) 12.9 |13.8 |15.0 1 16.4 18.0 20.0 (22.5 ! 25.7 01 02 03 04 05 06 07 38 39 10 11 12 13 14 15 16 17 18 • 19 20 21 Table- E-: 108 UJ = 9 AUGUST 1974 6.1 6.5 I 7.5 8.6 | 9.7 ho 9 |12.0 12.9 il3.8 1 15.0 I 16.4 J18.0 (20.0I22.5 1.25.7 01 02 03 04 05 06 07 D8 09 10 11 12 13 14 15 16 17 18 19 20 21 Table E-9 109 6.1 6.5 | 7.5 10 I 8.6 CENTRAL P 9.7 |10.9|12.0 ERIOD (SECONDS) 12.9 |13.8 1 15.0 116.4 AUGUST |18.0 |20.0|22.5 1974 25.7 01 i 02 03 04 05 06 O07 »■« r O08 »-09 X w 10 »- 11 z < U 12 213 w 14 15 16 17 18 19 20 21 — -- — ■ Table E-10 110 W = 11 AUGUST 1974 6.1 6.5 7.5 8.6 C EN 9.7 TRAL PERIOD (SECO 10.9 |12.0 |12.9 13.8 |15.0 NDS) 116.4 (18.0 20.0 |22.5 | 25.7 01 1 t i ■ 02 03 04 05 06 O07 h-09 X w 10 x — ■ •- 11 z < U 12 2 13 v2 mm" Zi 14 15 16 17 18 • 19 20 21 _ Table- E-ll 111 J 6.1 6.5 V = I75 Y2 I 8.6 C EN 9.7 TRA L P 10.9 12.0 ERIOD (SECO 12.9 |13.S Jl 5.0 NDS) 116.4 AUGUST |18.0 I20.0I22.5 1974 25.7 01 4 1 02 1 03 04 05 06 07 38 09 W 11 12 13 14 15 16 17 18 19 20 21 Table- E-12 112 APPENDIX F CLIMATO LOGICAL WAVE TABLES OF THE TWO-DIMENSIONAL WAVE STATISTICS FOR FEBRUARY 19 7 5 Tables F-l thru F-12 contain the coded energy density - FNWC period band distribution for the meteorological direc- tion bands 1 thru 12 for grid point 164 in subprojection 3 at latitude 50.9° North, longitude 145.6° West. The Febru- ary 1975 wave statistics were derived from 45 FNWC SOWM 12- hourly synoptic analyses. The energy density codes are found in Table VII. The directional bandwidth codes are contained in item 11 of Figure 2 . The tabular entries re- flect the number of event occurrences of 12 hourly analyses for February 197 5. 113 iy = i FEBRUARY 1975 6 1 6.5 7.5 < 8.6 :en 9.7 TR A 10.9 l PERIO 12.0 12.9 D (S 13.8 ECO 15.0 MDS) 16.4 180 I20.0 22.5 25.7 01 24 24 21 20 18 23 19 17 9 21 5 2 1 02 11 3 7 6 3 3 4 2 2 4 2 03 4 3 2 1 1 2 04 1 3 05 1 1 06 07 08 09 10 11 12 13 14 15 16 ■ 17 18 19 20 21 22 23 24 25 26 I PL, 114 UJ=2 FEBRUARY 1975 6.1 Um 7.5 < 8.6 : en 9.7 TRAL PERIOD (S 10 9l 12.0 12.9 13 8 ECO N OS) 15.0 16 -1 18.0 I20.0 22.5 257 01 15 15 12 13 8 12 19 24 21 25 16 11 6 1 2 02 14 12 15 5 3 4 5 7 3 3 3 1 03 11 5 2 2 3 5 2 2 1 04 3 9 1 2 1 1 05 1 3 1 1 2 1 06 3 1 2 07 .. 2 1 08 09 10 11 12 13 14 15 16 ■ 17 18 19 20 21 22 23 24 25 26 I J2 E-< 115 iy=3 FEBRUARY 1975 O u X »— a a z < CO O C£ u. Z Z Lu > . 6.1 6 5 7.5 8.6 CENTRAL PI 9.7 j 1 0 . 9 1 1 2 . 0 ERIOD (S 12.9 Jl 3.8 ECO 15.0 NDS) 1 16 A I18.0 20.0 22.5 |25.7 01 12 5 3 5 2 11 12 15 13 12 9 1 7 5 3 5 02 18 20 21 1 5 4 2 3 3 3 1 03 6 3 1 4 2 2 2 2 2 04 14 4 2 1 2 1 2 2 2 1 1 05 • 10 5 3 3 2 1 1 06 3 5 1 1 1 2 07 4 2 4 1 08 7 3 2 2 09 1 3 1 1 3 10 2 1 11 4 2 12 3 1 13 1 1 14 15 1 1 16 ■ 17 18 19 1 20 21 1 22 23 24 25 26 -J « 1 CO I CD H XI rti Eh 116 qj = 4 FEBRUARY 1975 o UJ O O u a z < m O UJ en Z Z o cr LU z UJ 6.1 6.5 7.5 < 8.6 : en 9.7 TRA 10.9 L PI 12.0 IRIO 12.9 D (S 13 8 ECO 15.0 MDS) 16.4 18 0 200 22.5 25.7 01 4 3 2 1 6 6 8 10 6 6 8 2 1 3 02 20 21 21 5 5 6 2 2 5 4 1 1 03 1 1 6 7 2 5 1 2 1 1 1 04 13 6 1 5 5 1 1 1 1 05 5 5 4 2 1 1 1 06 1 1 1 2 07 ._ 3 2 1 1 08 3 1 1 09 2 2 10 3 1 11 2 1 12 2 1 13 1 1 14 15 16 1 17 18 19 20 21 22 23 24 25 26 l 0) rH Xi 117 UJ=5 FEBRUARY 1975 a O o X a a z < CO O UJ cc Lb u z to Z © UJ Z UJ 6.1 6.5 7.5 8 6 :en 9.7 TR A L P* 10.91 12 0 L RIO 12.9 D (S 13.8 ECONDS) 150 [16.4 18.0 20.0 22.5 [25.7 01 7 6 5 7 7 7 8 7 6 7 6 5 9 2 3 02 17 17 19 2 5 1 6 3 3 2 2 2 03 10 6 7 2 3 2 3 1 2 8 1 04 5 6 1 4 2 1 1 05 3 3 4 1 2 1 2 06 5 1 3 2 1 07 3 3 2 1 1 08 1 3 1 1 09 1 1 10 11 12 13 14 15 16 ■ 17 18 19 20 21 22 23 24 25 26 LO I Eh 118 Uf = 6 FEBRUARY 1975 6.1 6.5 7.5 8 6 : en 9 7 TR A 10.9 L PERIO 1 2 . 0 1 2 .9 D (S 13 8 ECO 15.0 ^ DS) 16.4 18.0 200 22.5 25.7 01 14 13 16 13 14 20 17 19 14 8 10 9 2 1 02 10 6 6 4 6 2 3 4 5 2 1 2 1 03 4 2 2 1 3 2 4 1 1 04 4 3 2 2 4 05 2 2 1 06 1 1 07 ._ 2 08 O < > 09 1 X 10 11 o z < 12 ca O 13 OS u. 14 z 15 u. > 16 ■ T 17 bu O 18 or: 19 Z ut 20 21 22 23 24 25 26 I 0) H rd 119 6.1 6.5 7.5 7 8.6 : en 9.7 TRA 10.9 L PE 12.0 RIO 12.9 o (S 13 8 ECOI 15.0 16.4 FEB 18 0 R UA 20.0 RY 22.5 1975 25.7 01 16 11 12 16 17 14 11 10 11 10 11 8 3 02 4 3 5 4 4 4 4 4 2 1 03 1 1 2 1 1 1 04 3 1 1 1 1 2 05 2 1 2 1 06 1 07 ._ 1 08 1 09 10 11 12 13 14 15 16 ■ 17 18 19 20 21 22 23 24 25 26 I Eh 120 6.1 6 5 7.5 3 < 8 6 r EN 9.7 TRA 10.9 L Pf 12.0 .RIO 12.9 D (S 13.8 ECO 15.0 16.4 rtb 18.0 2 00 i K T 22.5 1 V / D 25.7 01 10 12 8 11 14 14 13 13 14 4 4 4 3 02 5 2 7 2 1 3 3 5 3 5 2 2 03 5 4 2 1 1 04 2 2 2 3 1 1 1 05 1 1 1 06 2 1 07 ._ 08 09 10 11 12 13 14 15 16 ■ 17 18 19 20 21 22 23 24 25 26 oo I H ,£} «d Eh 121 W = 9 FEBRUARY 1975 O O U o z < CD u z z >- c UJ Z UJ 6.1 6.5 7.5 8.6 : en 9.7 TR A 10.9 L PI 12.0 :rio 12.9 D (S 13 8 ECO 15 0 16.4 18 0 200 22.5 2 5.7 01 7 6 12 13 18 22 18 20 10 2 3 1 4 2 02 8 9 9 1 2 1 4 1 2 1 2 03 1 3 2 1 1 1 1 2 04 10 5 2 1 05 4 2 2 1 1 2 1 06 1 1 2 1 1 07 -_ 2 08 2 09 10 11 12 13 14 15 16 ■ 17 18 19 20 21 22 23 24 25 26 CD I P-. 0) ,£! 122 UJ=10 FEBRUARY 1975 a O - o a: 6.1 6.5 7.5 < 3 6 : en 9.7 TR A 10.9 L Pf 12.0 ;rio 12.9 D (S 13 8 ECO 15.0 1 16,1 18.0 200 22.5 257 01 5 6 5 5 9 10 10 13 9 4 2 1 1 1 02 12 11 12 2 2 2 3 1 1 1 2 03 9 8 6 3 1 1 04 4 5 2 1 1 1 05 1 1 1 2 1 2 1 06 1 1 07 ._ 1 08 2 09 10 11 12 13 14 15 16 • 17 18 19 20 21 22 23 24 25 26 0) H ft) Eh 123 o UJ O O a z < CO O UJ Of u. U z z >- oe UJ Z UJ 6.1 6.5 7.5 11 < 8.6 : en 9.7 TR A 10.9 L PI 12.0 LRIO 12.9 D (S 13 8 ECO 15.0 MDS) 1 16.-4 FEB |18.0 ku; [20.0 k R Y 22.5 1975 25.7 01 8 12 4 3 1 1 1 2 2 4 2 2 1 02 13 8 10 1 1 2 4 2 2 1 1 03 6 5 2 9 1 1 04 5 8 1 1 1 05 1 1 1 06 2 07 -. 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 I rH 124 a Ul Q o u a z < 03 o Ul ee u. Z Z o ui Z 6.1 6.5 7.5 12 < 8.6 : en 9.7 TR A 10.9 l PERIO 12.0 12.9 D (S 13 8 ECON DS) 15.0 1 16.4 t t b 18.0 200 k K Y 22.5 19/5 257 01 20 22 22 17 14 13 9 10 10 5 2 2 02 9 3 5 7 6 1 1 3 03 3 4 2 1 04 2 1 05 1 06 07 -. 08 09 10 11 12 13 14 15 16 ■ 17 18 19 20 21 22 23 24 25 26 I Pi-. OJ rH Eh 125 APPENDIX G CLIMATO LOGICAL WAVE TABLES OF THE TWO-DIMENSIONAL WAVE STATISTICS FOR AUGUST 19 7 4 Tables G-l thru G-12 contain the coded energy density- FNWC period band distribution for the meteorological direc- tion bands 1 thru 12 for grid point 164 in subprojection 3 at latitude 50.9° North, longitude 145.6° West. The August 1974 wave statistics were derived from 61 FNWC SOWM 12- hourly synoptic analyses. The energy density codes are found in Table VII. The directional bandwidth codes are contained in item 11 of Figure 2 . The tabular entries re- flect the number of event occurrences of 12 hourly analyses for August 1974. 126 61 6.5 7.5 1 8 6 r EN 9.7 TR A 10.9 L Pi 12.0 :rio 12.9 D (S 13.8 ECO 15.0 16.4 Al 18. 0 JGU 20.0 ST 1 22.5 974 25.7 01 16 3 3 2 2 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 • 17 18 19 20 21 22 23 24 25 26 H I CD CD r-i rd Eh 127 Ur=2 AUGUST 1974 6 1 6.5 7.5 < 8.6 : en 9.7 TR A 10 9 L Pi 12.0 ;rio 12.9 D (S 13.8 ECONDS) 15.0 16.4 18.0 20.0 '22.5 25.7 01 23 15 19 14 23 14 6 6 2 1 3 02 2 2 03 04 05 06 07 ._ 08 09 10 11 • 12 13 14 15 16 ■ 17 18 19 20 21 22 23 24 25 26 CM I CD 128 6.1 6 5 7.5 3 < 8.6 r EN 9.7 TR A 10.9 L P* 12.0 .RIO 12.9 D (S 13.8 ECO 150 -IDS) 16.4 Al 18.0 JGU 20.0 ST I 22.5 974 25.7 01 15 19 19 19 18 11 12 10 3 2 3 3 1 02 15 5 6 4 7 2 1 1 03 1 1 1 1 1 04 1 05 06 07 08 09 10 11 ■ 12 13 14 15 16 - 17 18 19 20 i 21 22 23 24 25 26 CO I CD 0) r-H Eh 129 6 1 6.5 7.5 4 i 8.6 : en 9.7 TR A 10.9 I Pf 12.0 .RIO 12.9 D (S 13.8 ECOI 15.0 16.4 AUGU 18.0 j 2 0.0 ST 1 22.5 974 25.7 01 16 27 28 22 27 15 16 15 5 1 17 02 15 3 4 7 2 1 03 04 05 06 07 08 09 10 11 12 13 14 15 16 • 17 18 19 20 21 22 23 24 25 26 I CD rd 130 lj;=5 AUGUST 1974 CENTRAL PERIOD (SECONDS) a O o z < £3 O LU OS u. U Z CO Z o Of Uf Z 61 6.5 7.5 | 8.6 9.7 10.9 12.0 12.9 13.8 15 0 16.4 18.0 200 22.5 257 01 26 38 24 16 11 7 7 5 3 1 1 02 9 5 8 7 4 1 03 1 2 04 05 06 07 ._ 08 09 10 11 12 13 14 15 16 ■ 17 18 19 20 21 22 23 24 25 26 I =7 CENTRAL PERIOD (SECONDS) AUGUST 1974 61 6.5 " 8 6 9.7 109 12.0 12.9 13.8 15 0 16.4 18.0 20.0 22.5 25.7 01 6 5 5 3 3 1 02 5 2 1 2 03 04 05 06 07 ._ 03 09 10 11 12 13 14 15 16 - 17 18 19 20 21 22 23 24 25 26 I 133 a O o a z < ca O UJ 0£ z Z Ul O >- ce UJ Z UJ W = 8 CENTRAL PERIOD (SECONDS) AUGUST 1974 6.1 6 5 7.5 8.6 9.7 10 9 12.0 12.9 13.8 15.0 16.4 18 0 20.0 22.5 J25.7 01 7 5 4 4 2 1 02 4 03 04 05 06 07 ._ 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 00 I CD Eh 134 W=9 AUGUST 1974 61 6.5 7.5 8 6 r EN 9.7 TR A 10 9 L PI 12.0 ;rio 12.9 D (S 13.8 ECO 15.0 ^DS) 16.4 18.0 20.0 22.5 |25.7 01 6 4 ■ 4 3 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 ■ 17 18 19 20 21 22 23 24 25 26 CD I e> a) H A td Eh 135 UJ a O u Q Z < CO O LU ee u. U z to z >- o H jQ rtJ Eh 136 U) =-| -J AUGUST 1974 CENTRAL PERIOD (SECONDS) a O a z < CO O UJ fi£ u. U Z z >- o UJ z [6.1 6.5 7.5 8.6 9.7 10.9 12.0 12.9 13.8 15 0 16.4 18 0 2 0.0 22.5 25.7 01 4 02 03 04 05 06 07 -_ 08 09 10 11 12 13 14 15 16 ■ 17 18 19 20 21 22 23 24 25 26 r-\ r-\ I CD 137 W = 12 AUGUST 1974 61 6.5 7.5 < 8 6 "EN 9.7 TR A 10 9 L P« 12.0 :RlO 12.9 D (S 13.0 ECO 15 0 16.4 18.0 20.0 22.5 25.7 01 10 3 02 03 04 05 06 07 -_ 08 09 10 11 12 13 14 15 16 • 17 18 19 20 21 • 22 23 24 25 26 I a; rd 138 INITIAL DISTRIBUTION LIST No. Copies 1. Mr. John S. Habel 6 Department of Navigation and Ocean Development State of California 1416 9th Street Sacramento, California 9 5 814 2. Defense Documentation Center 2 Cameron Station Alexandria, Virginia 22314 3. Department of Oceanography, Code 6 8 3 Naval Postgraduate School Monterey, California 93940 4. Library (Code 0212) 2 Naval Postgraduate School Monterey, California 93940 5. Professor W. C. Thompson, Code 68 2 Department of Oceanography Naval Postgraduate School Monterey, California 93940 6. Professor Edward B. Thornton 1 Department of Oceanography Naval Postgraduate School Monterey, California 93940 7. LT F. M. Reynolds, USN 1 1307 Fechteler Drive Monterey, California 9 3 940 8. Oceanographer of the Navy 1 Hoffman Building No. 2 200 Stovall Street Alexandria, Virginia 22332 9. Office of Naval Research 1 Code 480 Arlington, Virginia 22217 10. Library, Code 3 3 30 1 Naval Oceanographic Office V/ashington, D. C. 2 037 3 139 11. Commanding Officer 1 Fleet Numerical Weather Central Monterey, California 93940 12 . Commanding Officer 1 Navy Environmental Prediction Research Facility Monterey, California 93940 13. Department of the Navy 1 Commander Oceanographic System Pacific Box 1390 FPO San Francisco 96610 14. Director, Naval Oceanography and Meteorology 1 Building 200 Washington Navy Yard Washington, D. C. 20374 15. Commanding Officer 1 Naval Civil Engineering Laboratory Port Hueneme , California 93043 16. Dr. Robert E. Stevenson 1 Scientific Liaison Office, ONR Scripps Institution of Oceanography La Jolla, California 92037 17. Commanding Officer 2 San Francisco District U. S. Army Corps of Engineers 100 Mc Allister Street San Francisco, California 9 4111 18. Mr. Orville T. Magoon 1 Coastal Engineering Branch Planning Division U. S. Army Engineering Division, South Pacific 630 Sansome Street San Francisco, California 94111 19. Mr. Charles Fisher, Chief 1 Coastal Engineering Branch U. S. Army Corps of Engineers P. 0. Box 2711 Los Angeles, California 90053 20. Dr. Rudolph P. Savage 1 Technical Director Coastal Engineering Research Center 5201 Little Falls Road, N.W. Washington, D. C. 20016 140 21. Dr. D. Lee Harris Coasting Engineering Research Center 5201 Little Falls Road, N.W. Washington, D. C. 20016 22. SIO Library University of California, San Diego P. 0. Box 2367 La Jolla, California 92037 23. Department of Oceanography Library University of Washington Seattle, Washington 98105 2 4. Department of Oceanography Library Oregon State University Corvallis, Oregon 97331 25. Dr. James S. Bailey Director, Geography Programs (Code 46 2) Office of Naval Research Arlington, Virginia 22217 141 Thesis 166625 R3685 Reynolds c.l CI i ma to logical wave statistics derived from 'es FNWC synoptic spectral i o J wave) analyses. 2 6010 es 166625 Thesis R3685 Reynolds c.l C lima to logical wave statistics derived from FNWC synoptic spectral wave analyses. thesR3685 Climatological wave statistics derived ii 111 mi n 111 iiiiii inn in ii n pi mill mi n mil nun ii in mi n in iii ml :i Ii il III lull 3 2768 002 01328 6 DUDLEY KNOX LIBRARY