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
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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
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Department of Navigation and Ocean
Development, State of California
Sacramento, California 95814
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June 1976
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141
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Naval Postgraduate School
Monterey, California 9 3940
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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EDITION OF 1 NOV 65 IS OBSOLETE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
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FEBRUARY 1975
6.1
6.5
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10.9
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12
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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
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11
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22.5
1975
25.7
01
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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
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125
Figure 11. Comparison of Energy Content for FMWC
Frequency Bandwidths and Common Frequency
Bandwidths of Af = 0.0055 Hz.
76
Figure 12. One-Dimensional Frequency Spectrum
Climatology for February 1975 (45
total event occurrences)
77
13 14 15 16 17
PERIOD (SEC)
22 23 24 25
26
Figure 13.
One-Dimensional Frequency Spectrum
Climatology for August 1974 (61
total event occurrences)
APPENDIX A
CONVERSION FORMULAE FOR COMMONLY USED WAVE HEIGHT PARAMETERS
H.O. 603 (1955)
Most frequent 1.4-1 /E
wave height
Average wave 1.77 /E
height
Significant 2.3 3 /E
wave height
Average heights 3.60 /E 5.1 /E
of l/10th highest
waves
In the wave height parameters given in H.O. 603, E = 2E ,
where E is the variance of the sea surface.
FNWC SOWM
2 /E
2.5 /E
4 /E
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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
<
<J 12
1
2 13
<j --
^ 14
1
1
15
16
17
18
■
19
20
21
— <
»■
.
Table D-5
92
W=6
FEBRUARY 1975
!
6.1
6.5
7.5
S.6
CENTRAL PERIOD (SECO
9.7 ho. 9 h2.0 |12 9 Il3.8 1 1 5.0
N DS)
16.4 1
13.0
20.0
22.5
25.7
01
i
02
03
04
05
06
07
08
09
1 ■ i
10
11
1
12
i
13
14
15
16
17
18
19
20
21
— —
<-■
Table D-6
93
CM =7
FEBRUARY 1975
I
6.1
| 6.5
7.5
8.6
CENTRAL PERIOD (SECO
1 9.7 |10. 9 |12.0 Il2 9 Il3.8 f 1 5 0
N DS)
16.4 '
18.0
J20.0
1 22.5
25.7
01
—
"— ' ■' ■
02
03
04
05
06
07
D8
09
to
11
12
1
1
13
14
15
16
17
18
19
20
21
Table D-7
94
1
6.1
UJ=8
6.5 J_7.5 { 8.6
CENTRAL PERIOD (SECO
9.7 |10.9 |l2.0 Il2.9 113.8 |l5.0
N DS)
16.4 1
F EE
18.0
R UA R Y
20.0)22.5
1975
25.7
01
'
i
02
03
04
05
06
*■
Q07
a
oos
( 1
^-09
X
w 10
•- 11
z
<
U 12
Z13
^ 14
15
16
17
18
19
20
21
«—
»■■
Table D-8
95
W =9
FEBRUARY 1975
!
6.1
I 6.5
7.5
! 8.6
CENTRAL PERIOD (SECONDS)
! 9.7 h 0.9 |1 2.0 M2.9 Il3.8 1 15.0 1 16.4 1
13.0
20.0
1 22.5
25.7
01
- — -
02
03
04
05
06
Q 07
2
1
Q I
O08
CJ — 1
1
•-09
x i
2 I
u 10
2
H
<
U 12
1
Z*3
i
2
Zt 14
15
16
17
18
19
20
21
—
»- '
Table D-9
96
UJ = 10
CENTRAL PERIOD (SECONDS)
FEBRUARY 1975
I
6.1
6.5
7.5
I 8 6
9.7
'10.9
12.0
12.9
13.8
^5.0
15.4 118.0
20.0
22.5
25.7
01
02
03
04
05
06
07
1
0 8
09
10
11
12
13
14
15
16
17
18
19
20
21
»■■
Table D-10
97
!
6.1
I
6.5
■P=1
7.5
1
8.6
CENTRAL PERIOD (SECO
9.7 |10. 9 f 1 2.0 f 12.9 1 13.8 |l5.0
NDS)
16.4'
FEBRU/
18.0 |20.0
KRY
22.5
1975
25.7
01
02
03
2
04
05
06
1
07
2
38
1
09
1
10
11
12
13
14
15
16
17
\8
19
20
21
— >
■
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
<
<J 12
z13
I
^ 14
15
16
17
18
*
19
20
21
Table D-12
99
APPENDIX E
CLIMATOLOGICAL WAVE TABLES OF THE
GROSS STATISTICS FOR AUGUST 1974
Tables E-l thru E-12 contain the coded wave height-equal
period band distribution for the meteorological direction
bands 1 thru 12 for grid point 164 in subproj ection 3 at
latitude 50.9° North, longitude 145.6° West. The August
wave statistics were derived from 61 FNWC SOWM 12-hourly syn-
optic 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 August 1974.
100
6.1
6.5
4J=-
7.5
!
| 8.6
CENTRAL PERIOD (3
1 9.7 1 1 0.9 |12.0 |12.9 13.8
ECO
M 5.0
N DS)
1 16.4
A
|18.0
UGUST
20.0(22.5
1974
25.7
01
1
02
1
03
04
05
06
07
38
39
10
11
12
13
14
15
16
17
18
.
19
20
21
Table -E-l
101
6.1
[6.5
v =:
7.5
I
8.6
CENTRAL PERIOD (SECO
! 9.7 10.9 |l2.0 Il2.9 |13.8 1 1 5.0
NDS)
1 16.4
AUGUST
(18.0 |20.0l22.5
1974
25.7|
01
02
1
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
•
19
20
21
— <
Table' E-2
102
J
| 6.1
I
6.5
7.5
3
8.6
C EN
| 9.7
TRAL PERIOD (SECO
10.9 12.0 |12.9 13.8 |l5.0
NDS)
116.4
A
(18.0
UGUST
20.0I22.5
1974
1 25.7
01
— — —
02
2
2
03
2
1
04
4
2
1
05
3
2
1
06
07
38
09
10
11
12
13
14
15
16
17
18
19
20
21
—
.._
Table E-3
103
W =4 AUGUST 1974
6.1
[6-5
7.5
| 8.6
| 9.7
1 10.9
|12.0
|12.9
|13.8
15.0
116.4
[18.0
20.0(22.5
[ 25.7
01
1
2
02
1
03
04
1
05
_>_
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
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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
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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
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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
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