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<P><PB REF="00000001.tif" SEQ="00000001" RES="600dpi" FMT="TIFF6.0" FTR="TPG" CNF="842" N="">
THE  UN I VE RS I TY  OF  MI C H I GAN
COLLEGE OF ENGINEERING
Department of Meteorology and Oceanography
Final Report
WAVE HINDCASTS VS. RECORDED WAVES
Supplement No. 1
(1965 Data)
A.lP/ian L. QCle
Associate i Researc Kieteorolog i st
John C. Ayer s
Proj ect Director
ORA Project  06768
under contract with.
U.S. ARMY ENGINEER DISTRICT, LAKE SURVEY
CONTRACT DA-20-064-CIVENG-65-6
DETROIT, MICHIGAN
administered through:
OFFICE OF RESEARCH ADMINISTRATION, ANN ARBOR
May 1967



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I ( t    CCH



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<P><PB REF="00000003.tif" SEQ="00000003" RES="600dpi" FMT="TIFF6.0" FTR="TOC" CNF="871" N="III">
TABLE  OF  CONTENTS
Page
LIST OF TABLES
LIST OF FIGURES
ABSTRACT
1. INTRODUCTION                                           1
2. GENERAL CONSIDERATIONS                                  3
3. WIND ANALYSES                                           9
4.  HINDCAST AND OBSERVED WAVES                            15
5.  STRONG WIND CONDITIONS                                 20
6. SUMMARY AND CONCLUSIONS                                 23
APPENDIX
A.  1965 WIND DATA AND SCATTER DIAGRAMS
FOR MUSKEGON, MICHIGAN                        28
B. 1965 WAVE DATA AND SCATTER DIAGRAMS
FOR MUSKEGON, MICHIGAN                        37
C.  1965 WAVE DATA FOR POINT BETSIE AND
PORT HURON, MICHIGAN                          63
D.  COMPARISON OF 1964 WAVE DATA AT
MUSKEGON, MICHIGAN                            66
E o SUCCESSIVE APPROXIMATION TECHNIQUE
FOR ANALYSIS OF PRESSURE AND WIND
FIELDS                                        70
Fo  DERIVATION OF THE SIGNIFICANT WAVE
HEIGHT AS A FUNCTION OF THE STANDARD
DEVIATION                                     83
BIBLIOGRAPHY                                               86



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LIST OF TABLES
Table                                                                Page
3-1            Fetches and upwind land stations used in               12
the calculation of Richards winds at the Muskegon
tower.
4-1            Summary of wind data used with each wave                17
hindcast method.
5-1            Summary of wind and wave conditions, 0100E,             20
29 November 1966. USCGC ACACIA. (44-29.5N
82-53W)
6-1            Wind analysis correlation summary.                      23
6-2            Significant wave height correlation summary.            24
6-3            Wave period correlation summary.                        25
A-1            Surface wind for 1965 wave hindcast                     29
period.
B-1            Significant wave heights during 1965 hind-              38
cast periods.
B-2            Significant period or period of maximum                 43
energy for 1965 wave hindcast times.
B-3            Period band and maximum wave height for 1965            48
wave hindcast times.
C-1            Significant wave heights and periods for                64
1965 wave hindcast times. Point Betsie, Michigan.
C-2            Significant wave heights and periods for                65
1965 wave hindcast times. Port Huron, Michigan.
D-1            Comparison of SMB, PNJ, PM and OBS wave data            67
for 1964 hindcast periods. Muskegon Research Tower.
v



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I



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LIST OF FIGURES
Figure                                                           Page
1-1.    Flow chart of wind and wave analyses.                    2
4-1.    Typical wave spectra at Muskegon research                19
tower as produced by the U.S. Army Coastal
Engineering Research Center.
5-1.    Wind conditions measured by the U.S.C.G.C.               21
ACACIA on 28 November 1966. The base of
the arrow indicates the location of the ship
while the arrow shows wind direction and
speed. The numbers by each arrow are the
E.S.T. of the observation.
A-1.    Scatter diagram of Bretschneider winds                    34
vs. surface (10 meters) measured winds.
A-2.    Scatter diagram of the Jacobs 7.5 meter winds             34
vs. surface (7.5 meters) measured winds.
A-3.    Scatter diagram of the Jacobs 19.5 meter winds            35
vs. surface (16 meters) measured winds.
A-4.    Scatter diagram of the Richards winds vs.                 35
surface (16 meters) measured winds.
A-5.    Scatter diagram of the Richards winds vs.                 36
surface (10 meters) measured winds.
B-1.    Scatter diagram of CERC observed significant              52
wave heights vs. those calculated from the
standard deviation of the staff gage data.
B-2.    Scatter diagram of hindcast significant                   52
wave heights calculated by the SMB
(Bretschneider winds) method vs. the
observed significant wave heights.
B-3.    Scatter diagram of hindcast significant                   53
wave heights calculated by the PNJ
(Jacobs 7.5 meter winds) method vs. the
observed significant wave heights.
vii



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Figure                                                            Page
B-4.    Scatter diagram of hindcast significant                   53
wave heights calculated by the PM (Jacobs
19o5 meter winds) method vs. the observed
significant wave heights,
B-5.    Scatter diagram of hindcast significant                   54
wave heights calculated by the SMB
(Richards winds) method vs. the observed
significant wave heights.
B-6.    Scatter diagram of hindcast significant                   54
wave heights calculated by the PNJ
(Richards winds) method vs. the observed
significant wave heights.
B-7.    Scatter diagram of hindcast significant                   55
wave heights calculated by the PM
(Richards winds) method vs. the observed
significant wave heights0
B-8~    Scatter diagram of hindcast significant                   55
wave heights calculated by the SMB
(measured winds) method vs. the observed
significant wave heights.
3E-9.    Scatter diagram of hindcast significant                   56
wave heights calculated by the PNJ
(measured winds) method vs. the observed
significant wave heights,
B-10    Scatter diagram of hindcast significant                    56
wave heights calculated by the PM
(measured winds) method vs. the observed
significant wave heights,
B-1llo   Scatter diagram of hindcast significant                   57
period calculated by the SMB (Bretschneider
winds) method vs. the observed period of
maximum energy.
B-12.   Scatter diagram of hindcast period of                      57
maximum energy calculated by the PNJ
(Jacobs' 7,5 meter winds) method vs,
the observed period of maximum energy.
Oi 5, 



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Figure                                                           Page
B-13.   Scatter diagram of hindcast period of                    58
maximum energy calculated by the PM
(Jacobs' 19.5 meter winds) method vs.
the observed period of maximum energy.
B-14o   Scatter diagram of hindcast significant                  58
period calculated by the SMB (Richards'
winds) method vs. the observed periods of
maximum energy.
B-15.   Scatter diagram of hindcast of period                    59
of maximum energy calculated by the
PNJ (Richards winds) method vs.
the observed period of maximum energy.
B-16.   Scatter diagram of hindcast of period                    59
of maximum energy calculated by the
PM (Richards winds) method vs. the
observed period of maximum energy.
B-17.   Scatter diagram of hindcast significant                  60
wave period calculated by the SMB
(measured winds) method vs. the observed
period of maximum energy.
B-18.   Scatter diagram of hindcast wave period                  60
of maximum energy calculated by the
PNJ (measured winds) method vs. the
observed period of maximum energy.
B-19.   Scatter diagram of hindcast wave period                  61
of maximum energy calculated by the PM
(measured winds) method vs. the observed
period of maximum energy.
B-20.   Frequency distribution of significant                    62
wave heights as calculated by the SMBBretschneider wind method and the PNJJacobs 7.5 meter wind method and as
observed by the staff wave gage.
ix



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Figure                                                           Page
E-1.  The analysis grid and the locations of                     72
data sources for the Successive Approximation
Technique.
E-2.  A portion of the Successive Approximation                  78
Technique map output.
E-3.  Computer listing of input pressures for the                79
Successive Approximation Technique analysis.
E-4.  Gridpoint pressures as calculated by the                   80
Successive Approximation Technique.
E-5.  Contours of the calculated pressure field.                 81



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ABSTRACT
This study was conducted to evaluate existing methods of
wind analysis and wave hindcasting for utilization in the determination of wave climatology for Lakes Huron and Superior.
Various calculated and measured winds were used as inputs to the
Sverdrup, Munk and Bretschneider (SMB), the Pierson, Newmann and
James (PNJ) and the Pierson Moskowitz (PM) wave hindcasting
schemes.  Of these techniques, the wind analysis of Bretschneider
and the SMB wave hindcast method showed better correlations with
observed wind and wave data.
The predominant finding of this investigation is that all
aspects of wave hindcasting for the Great Lakes are subject to
question.    Further investigation and development are needed to
improve the final product. Despite the preceeding statement, the
determination of a wave climatology by hindcast methods is feasible
at this time.
xi



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1  INTRODUCTION
This report is a supplement to the final report of the research program "Wave Hindcasts vs. Recorded Waves", Contract DA20-064-CIVENG-65-6. The aim of this investigation has been to
evaluate wind analyses and wave hindcasting techniques in order to
specify the best methods for use in the development of a wave
climatology for Lakes Huron and Superior.  The original research
compared wave hindcasts with measured wave parameters for the intervals from August 1 through August 10 and September 13 through
September 23, 1964. The Pierson, Neumann and James, (PNJ) and
Pierson and Moskowitz, (PM) wave spectral methods were used to calculate significant wave heights and periods from 1964 data.  This
supplemental report presents the results of research carried out
on 1965 data using the Sverdrup, Munk and Bretschneider (SMB)
significant wave height method as well as the PNJ and PM wave
spectral techniques.
For the 1965 data, the wave hindcasting was split into three
phases. The first phase was a determination of a mesoscale wind
field over the lakes while the second phase was the calculation of
the surface wind field,  Thirdly, with a surface or'"anemometer
height" wind established, the wave statistics were determined.
Figure 1-1 illustrates the combinations of wind analyses and wave
hindcast methods that were utilized. The general considerations
of the wave hindcast problem are treated in Chapter 2. The wind
analyses are discussed in Chapter 3 and the wave hindcasts in
Chapter 4. Comparisons made between calculated and observed
values of wind and wave parameters are reported in Chapter 6.
The availability of wind and wave measurements from the research tower in Lake Michigan near Muskegon operated by the Great
Lakes Division of the University of Michigan determined the dates
and times for wave hindcasts during September, October, and
November, 1965o In general, these time periods represented growing or fully developed seas.
In addition to the analyses of 1965 data, the SMB method was
applied to the 1964 data and results compared with the earlier
findings.
In late November, 1966  an intense storm passed over Lake
Huron with winds reported to 44 knots and waves to 20 feet. Wind
analyses and wave hindcasts were made for the high wind conditions
of this storm~



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Pressure  Analysis
Geostrophic    f Wind
Upwind Land
Bretschneider      Gradient,, Wind            Station Wind
(1951)
Jacobs               Richards    Dragert and
(1965)              Mc I ntyre    (1966)
Anemometer        Height             Wind        Richards   Wind            Observed   Wind
10 m      16m       7.5 m
SMB         PM      PNJ            SMB      PM       PNJ       SM         PM         PNJ
WAVE FIELD              WAVE  SPECTRA
Figure 1-1.   Flow chart of wind and wave analyses.



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2. GENERAL  CONS IDERATI ONS
Introduct ion
The Great Lakes are bodies of water with a maximum dimension
of the order of 300 nautical miles embedded in a large continental
land mass.  Weather and climate of the surrounding land areas are
continental with maritime modifications that decrease with distance
from the lakes. A true maritime weather or climate does not exist
anywhere in the area; however the maritime modification of the continental climate can be very pronounced at times while being minimal
at other times. Over the lakes, the atmospheric conditions are
normally in a state of transition from the continental character
shown over the upwind land areas toward a maritime character over
the water. This transition was clearly shown by Richards, Dragert
and McIntyre (1966) in their discussion of the variation of the surface wind from a land station to a downwind ship location. They
showed that length of overwater fetch and air-sea temperature differences may cause the overwater wind to be as much as three times
the land wind. Likewise, Strong and Bellaire (1965) have shown that
the reduction of geostrophic winds to surface winds and the heights
of Great Lakes waves depend strongly on the stability of the lowest
levels of the atmosphere over the lakes. The atmospheric stability
has been shown by Bellaire (1965) and Lansing (1965) to have a decided seasonal variation over the lakes. The atmosphere is generally rather stable during the spring and early summer while during the fall and winter it becomes quite unstable. As an unstable
atmosphere will transport more momemtum downward, the waves should
be more energetic in fall and winter. That this is true is easily
observed. Likewise, different stability regimes would be expected
to produce different wave spectra. No experimental data have been
published to show the extent of these variations.
Wave Hindcasts
The direct approach to the problem of determining wave
statistics at any location would be to record the wave heights and
periods and apply well known statistical methods to the resulting
data,  However, adequate wave records do not exist and an indirect
method of wave hindcasting must be usedo By use of wave hindcasting techniques, meteorological records of pressure, wind, temperature, humidity, etco were analysed to produce a wind field over
the bodies of water for which wave statistics were required.  From
- 3


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this field the resultant wave field was determined and the wave
statistics calculated. This technique has at least three advantages.
First, meteorological records have been kept for many years and
many stations in the Great Lakes area as compared with wave records
at a few locationsand only for limited times. Second, the wave
hindcast technique can be applied anywhere on the lakes and especially at locations where the installation of a wave sensor and
recorder would be impossible or very costly. Indeed, after the
wind field for the Great Lakes area has been calculated, wave statistics can be produced rather rapidly and relatively inexpensively
at any new location. Third, with an input of current meteorological
data plus a weather forecast the wave hindcast becomes a wave forecast which may be of considerable value to anyone using the lakes
for commerce or recreation.
The disadvantages of the wave hindcast method is that it is
an indirect method requiring the use of analyses that were developed from ocean data that may not be applicable to the Great Lakes.
Indeed the purpose of this investigation was to evaluate these
oceanic analytical methods and determine the best one for use on
the Great Lakes.
Theoretically, the process of wave hindcasting consists of the
following steps:
1. The determination by meteorological methods of a wind field over
the water area under consideration.
20 The reduction of the wind field to a wind stress field at the
height or heights which are responsible for transferring energy to
the wave field.
3. The calculation of the energy transfer from wind field to wave
field and the resulting wave lengths, heights and periods as a
function of time and location.
4. The computation of the statistics of the wave field,
Of the above four steps, only the first and last have been
achieved with any certainty at the present time, and then only with
simplifying assumptions, i.e. a geostrophic or gradient wind field
can be calculated from the surface pressure field as reduced to sea
level. Also, according to Longuet-Higgens (1952), wave height
statistics can be calculated if, over a limited frequency range, a
Rayleigh distribution can be assumed.
4 -



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The reduction of the gradient wind field to a wind stress
field and its effect on wave generation are areas of micrometeorology and air-sea interaction that are extremely complicated.
Much research effort has been expended on these fields and much
more will be required before they become amenable to routine calculationso
In practice, steps 2, 3, and 4 have been combined into semiempirical relations which generate wave statistics when the wind
speed, fetch and duration are known at some prescribed anemometer
height.  The SMB and PNJ wave hindcasting techniques are examples
of these relations.
The investigations conducted for this project were divided
into the following three phases1o  The determination of a meso-scale wind field over the Great
Lakes area.
2.  The reduction of this wind field to'"anemometer height" or
"surface winds" over the lakes.
3. The determination of the wave statistics from the speed, fetch
and duration of the surface winds.
Phase 1    The Determination of the Meso-Scale Wind Field
A direct determination of the meso-scale wind field by an
analysis of streamlines (lines everywhere tangent to the wind vector)
and isogons (lines of constant wind speed) from a chart of plotted
wind reports often leads to erroneous results, especially for low
wind speeds. An anemometer and a wind vane sample the wind only at
one point which may be quite non-representative of the actual wind
field due to the exposure of the instruments to the wind, ie, a
wind vane located near a river flowing between sand dunes into Lake
Michigan will most likely be biased by the channeling effect of the
valley. Likewise, the data from anemometers mounted on Great Lakes
vessels may well be biased due to the proximity of smoke stacks,
wheel houses, and other parts of the superstructure.
Unlike the wind field, the pressure field is a scalar quantity
and lends itself to accurate measurement. By use of the geostrophic
and/or gradient wind assumptions, a wind field can be computed in a
straightforward manner. If there is no change of pressure gradient
in the lower atmosphere, an actual wind equal to the gradient wind
may be found above the friction layer~ However, a vertical change
-5


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of horizontal pressure gradient usually exists and the gradient wind
is generally a fictious wind, however, it is one that is reproducible
for any given pressure distribution, well known to all meteorologists, and constitutes a convenient and reliable entry into analysis
problems such as wave hindcasting.
A program for the IBM 7090 computer has been developed to
analyze the pressure field, compute the geostrophic wind, curvature of the isobars, and the gradient wind at grid points spaced
75 km apart over the western Great Lakes area. This objective
analysis for the meso-scale wind constitutes a step towards the complete computer program for wave hindcasts that must be perfected
eventually.
Phase 2    The Reduction of the Geostrophic or Gradient Wind Field
to a Surface Wind.
The geostrophic wind field is calculated from the pressure
field under the assumptions that the isobars are straight and parallel, there are no friction forces, and the pressure pattern is invariant with time. The geostrophic wind is thus a result of the
balance between pressure gradient and Coriolis forces. The gradient
wind is similar except the isobars are assumed to be circular and
the wind is the resultant motion due to a balance of pressure
gradient, Coriolis and centrifugal forces. In the boundary layer
near the surface of the Earth these assumptions are never fully satisfied and rarely approached. Indeed, the exact detailed solution
of the problem with friction, randomly curved and spaced isobars,
energy and humidity exchanges, time dependence of all variables and
parameters, etc. is an extremely difficult if not impossible task.
The lack of requisite data is a prime reason for relatively little
progress in this field. Therefore, the common practice is to calculate the geostrophic or gradient wind and determine, empirically,
the deviations of speed and direction at or near the surface. These
deviations have been studied as functions of atmospheric stability,
isobaric curvature, overwater fetch, etc.
Bretschneider (1952) published a surface wind chart showing
the ratio between the surface wind (defined as 10 meters above the
mean sea surface) and the geostrophic wind vso the difference in seaair temperature (T  - T ) for various radii of cyclonic and anticyclonic curvature. The chart was based on oceanic data originally
obtained by Arthur (1947).
Richards, Dragert and McIntyre (1966) have reported on the influence of atmospheric stability and length of overwater fetch on
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<P><PB REF="00000018.tif" SEQ="00000018" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="890" N="7">
the ratio  U /U   where U  is the wind as measured on a vessel on
Lake Erie or Lake Ontario and U is the wind speed at an upwind
land station. This report showed the lake winds to be greater than
the land winds except under very stable conditions. They also showed that under unstable over-lake conditions the wind increased with
fetch up to a fetch of about 25 nautical miles, but no further increase
occurred with additional fetch. They did not consider geostrophic
or gradient winds and did not display equations for calculating surface lake winds. This method of calculating winds has been tested
with the SMB, PNJ, and PM wave hindcasting methods.
Strong and Bellaire (1965) published data on the effect of
air stability, as measured by the air-lake temperature difference,
on wind and waves for Lake Michigan.  This report included regression
equations for the computation of surface winds from geostrophic
winds. These findings were based on ship observations of wave
height, which are estimates only and on ship reports of winds, which
are sometimes biased by the location of the wind sensors. However,
these data and the equations derived from them by Jacobs (1965) constitute an available technique for reducing gradient wind speed to
surface wind speed for the Great Lakes and they were used for computing winds for the PNJ wave hindcasting method.
Phase 3    The Determination of the Wave Statistics From Surface
Winds.
The term wave statistics is used in a broad sense and includes
any result of statistical manipulations of wave height data. Under
this definition, wave spectra are wave statistics as are such obvious quantities as mean wave height, significant wave height, etc.
The wave statistics produced by this investigation are the significant wave height and the significant wave period.
The field of ocean wave spectra and wave statistics is an
active research area in which the theories of Bretschneider and
associates and Pierson-Neumann and associates predominate with
Darbyshire, Longuet-Higgens, Wilson and others making significant
contributions.  There has been no agreement as to which of the
wave spectra forms advocated by these leaders in the field will best
describe ocean-wave fields. However, recent, Pierson (1965), publications indicate their results may be approaching each other as
they better define such quantities as "the anemometer height wind".
The SMB, PNJ and PM methods were evaluated in this study and the
SMB found to correlate best with measured wave data.
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<P><PB REF="00000019.tif" SEQ="00000019" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="894" N="8">
Observed Winds and Waves
Wind and wave values, for comparison with those calculated
from the various schemes, were obtained from the data taken at the
research tower in Lake Michigan near Muskegon, Michigan.  This
tower, operated by the Great Lakes Division of the Institute of
Science and Technology of the University of Michigan extended 16
meters above the water and was located approximately one mile from
the shore. An Aerovane wind speed and direction sensor was mounted
at the top and Climet 3-cup anemometers and resistance thermometers
were installed on the tower to provide wind profile and lapse rate
data. Thermometers in the water measured water temperature and a
staff gage on the tower gave wave data. Humidity measurements were
also taken.
When these instruments and their recorders were operational, they
provided the data for comparison and evaluation with the calculated
parameters. However, failures did occur and all desired data were
not available at all times.



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3. WIND  ANALYSES
Introduction
One of the major factors in any wave hindcasting method and
often one of the greatest causes of error is the calculation of the
wind field responsible for the wave development. The problems of
wind field analysis may be conveniently divided into two categories.
First, there is no agreement among authorities in the field as to
what wind should be determined and secondly, the methods of obtaining the desired wind or wind profile or wind spectra are not well
understood. This report will not treat the first problem as the input wind requirements for each wave hindcasting scheme have been
accepted as published. Methods of obtaining mean winds at various
specified heights of the atmosphere have been evaluated by comparing
calculated winds with measured winds at the Muskegon research tower.
Bretschneider Wind
The name "Bretschneider Wind" has been applied to the wind input for the SMB wave hindcasting method as outlined by the U.S. Army
Corps of Engineers (1961). A surface wind scale, Bretschneider (1951),
relates the sea-air temperature difference to the ratio of surface
wind vso geostrophic wind for a family of curves of varying cyclonic
and anticyclonic curvature. From the surface wind vso geostrophic
wind ratio and the geostrophic wind the surface wind was easily calculated.
The data used to determine the sea-air temperature difference
came from a number of sources. Lake temperatures were obtained from
the water temperature measurements at the Muskegon research tower
and the instrumented ships on the Great Lakeso Air temperatures
came from the above sources and from U.S. Weather Bureau reports at
land stations near the lake. Continuity and extrapolation were widely
employed to arrive at a best estimate of the temperatures in the
wave generating area, The lake-air temperature data are poor but
probably contain no greater error than other aspects of the wave hindcast procedures. There is no account taken of the spatial variability of surface temperature and none can be expected in the near
future due to a serious lack of measurements.
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The geostrophic wind speeds and the radii of curvature of the
streamlines were obtained from weather maps using a geostrophic
wind scale and a curvature scale. The weather maps, obtained from
the Chicago forecast center of the U.S.W.B., were reanalyzed for 1
mb isobars in the vicinity of Lake Michigan prior to the calculation of geostrophic wind speed and curvature. The calculated wind
direction was taken to be the direction of the isobar located nearest to Muskegon, Michigan.
The calculated Bretschneider winds for the 1965 data are listed in Table A-1 of Appendix A and should be compared with the 10
meter observed winds at the Muskegon tower listed in the same table.
Figure A-1 is a scatter diagram of the Bretschneider winds vs. the
observed 10 meter winds. The correlation coefficient of 0,63 between the Bretschneider winds and the observed winds was the best
obtained for any calculated wind.
Jacobs 7.5 meter winds
For the PNJ wave hindcast scheme, Jacobs (1965) presented the
following empirical equations for the calculation of the surface
(7.5 meters) wind from the gradient wind.
V  =  wind speed at 7.5 meters in knots
=  7.9 +.28 V             AT &lt; -50F         Stable        (3-1)
g
=  9.5 +.27 V             -50F I AT &lt; 5~F  Neutral         (3-2)
= 13.1 +.31 V             AT &gt; 50F          Unstable      (3-3)
where V   is the gradient wind calculated from surface pressure data
and A Tg is the water-air temperature difference, ioeo a stability
factor.
The gradient wind, V, was calculated by the standard
meteorological equations:
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<P><PB REF="00000022.tif" SEQ="00000022" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="871" N="11">
V     2       4-   -  f pV                  for anticyclonic
geo                  curvature
V-= -Q  +          +  fpV                   for cyclonic
g   2        4          geo                  curvature
where  V      =  the geostrophic wind in knots,
geo
p     =  radius of curvature of isobar lines in nautical
miles
f      =  Coriolis parameter
The results of these calculations are shown in Table A-lo
The corresponding measured winds, for comparison, are listed under
the heading of Muskegon Tower 7.5 meter winds. Figure A-2, a
scatter diagram of the Jacobs 7.5 meter winds vs. the measured 7.5
meter winds shows the calculated winds to be generally larger than
the measured winds. The linear correlation coefficient between these
winds was 0.56.
Jacobs 19.5 meter winds
Wave statistics as determined from the Pierson-Moskowitz
spectrum require a mean wind input for 19.5 meters. Jacobs (1965)
developed ratios between the 7.5 and 19.5 meter winds as measured
in 1963 and 1964 on the Muskegon tower (Elder, 1965) 
V     wind speed at 7.5 m
U     wind speed at 19.5 m.85    AT &lt; -50F                                  (3-6)
95    -5~F &lt; AT &lt;  + 5 F                          (3-7)
=  1.00   AT &gt; 50F                                 (3-8)
- 11 -



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<P><PB REF="00000023.tif" SEQ="00000023" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="884" N="12">
These ratios were used with the Jacobs 7.5 meter winds to obtain the Jacobs 19.5 meter winds which are listed in Table A-i.  The
Muskegon tower was 16 meters high with an Aerovane wind speed and
direction sensor on top. The data from the Aerovane system was used
to compare with the Jacobs 19.5 meter wind as illustrated by the
scatter diagram, Figure A-3. The wide scatter of these data is obvious and is confirmed by the low correlation coefficient of 027.
Richards Winds
In the Monthly Weather Review, Richards, Dragert and McIntyre
(1965) reported ratios of overwater wind to overland wind as functions
of the atmospheric stability and the fetch from land to the overwater wind observation location. They used ship winds and water
temperatures with upwind land station winds and air temperatures to
calculate the ratios of overwater wind to overland windo These
ratios were then tabulated according to fetch and the stability
parameter, Ta - Tw
These ratios were used to calculate an overwater wind at the
Muskegon tower using the Muskegon tower water temperature and an upwind land-station air temperature and wind speed. The up-wind landstations were chosen on the basis of the wind direction at the
Muskegon tower or the Muskegon UoS.W.B.    The wind directions considered, their fetches and the upwind land stations used are listed
in Table 3-1 below:
Table  3-1
Fetches and upwind land stations used in the calculation of
Richards winds at the Muskegon tower.
Overwater fetch
Wind Direction            n mi.
Upwind Land Station
1800                50                      5/3 St. Joseph, Micho
1900                80                      SBN  South Bend, Indo
2000                98                      SBN
2100                102                     ORD O'Hare Airport
Chicago, Ill.
220~                91                      ORD
2300                86                      ORD
2400                77                      MKE, 53/ Milwaukee, Wiso
250~                68                      MKE, 53/
- 12 -



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<P><PB REF="00000024.tif" SEQ="00000024" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="890" N="13">
Overwater fetch
Wind Direction            n mi.                    Upwind Land Station
2600                69                     MKE, 53/ Milwaukee, Wiso
2700                70                     MKE, 53/
2800                69                     MKE, 53/
2900                68                     MKE, 53/
300                 71                     GRB, MTW, Green Bay or
Manitowac, Wis.
3100                79                     GRB, MTW
3200                84                     GRB, MTW
330                 100                    GRB, MTW
The Richards winds data are tabulated in Table A-1 and compared with the Aerovane winds from the Muskegon tower on the scatter
diagram, Figure A-4. These data show the calculated winds to be
generally lower than the corresponding Aerovane measured winds.
When compared with the 10 meter Muskegon tower winds, Figure
A-5, the Richards winds are seen to scatter rather widely but have
no particular trend with respect to the observed winds.
The concept of determining the overwater wind by the technique
used above seems very sound from a conceptual view; however, practical
considerations appear to make it not acceptable. The major sources
of error probably are due to the strong dependence of the method on
the value of the upwind land station winds and the stability factor
over the lake. The latter are not measured with any regularity and
the former suffer from being non-representative short time averages
at single locations. Jacobs (1965) showed that the Muskegon UoSoW.B.
wind speed data correlated poorly with either Muskegon tower winds
or with ship winds.
Wind Direction
The only calculated wind directions were obtained by assuming
that the geostrophic and gradient winds have the same direction as the
isobars from which they were derived. These wind direction data are
listed in Table A-1 with the corresponding wind directions as measured by the Aerovane instrument on the Muskegon tower. As predicted
by the theory and observations, the measured wind shows a tendency
to flow across the isobars toward lower pressure. A mean deviation
13 -



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<P><PB REF="00000025.tif" SEQ="00000025" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="890" N="14">
of 290 from the isobaric direction was calculated from the data.
There is nothing new or unusual about these findings. They merely
verify accepted data and hypotheses.
Successive Approximation Technique
The successive approximation technique of Cressman (1959) has
been applied to a pressure analysis of the Great Lakes area. From
the pressure analysis, geostrophic and gradient wind can be computed.
While the technique is described in detail in Appendix E, it is
pertinent at this point to mention that it is a computer analysis
technique that produces a smoothed pressure and geostrophic wind
analysis. The smoothing built into this program should make the results more representative of the wind over an area the size of Lake
Michigan and therefore better wave hindcasts should result.
Discussion and Recommendations
The Bretschneider winds correlated with the observed wind better
than any other wind analysis technique. However, a correlation coefficient of 0.63 for 36 pairs of data is not a high correlation. It
is apparent that additional knowledge of the lower level wind systems
must be obtained before improved accuracy in wave hindcasting can be
achieved. The successive approximation technique should be the first
step in an improved analysis method. From the calculated pressure
field, geostrophic wind field, or gradient wind field, a surface
wind must be calculated taking into account the overwater stability,
the upper air stability, fetch, wind speed, etc. Indeed, according to
Pierson (1964) and Harris, (1967) the measurement of a mean wind at
one level provides insufficient data for the determination of surface stress and wave spectra. Thus the more difficult problem of calculating the surface stress or wind profiles from the synoptically
observed data has been posed0 Progress along these lines will not be
quick and it appears the best procedure at this time is to compute
the geostrophic wind which can be reduced to a lake level (10 meters)
wind by Bretschneider's surface wind speed curves~ Research should
continue to upgrade these procedures.
- 14


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<P><PB REF="00000026.tif" SEQ="00000026" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="892" N="15">
4. HINDCAST AND OBSERVED WAVES
Introduction
Two wave hindcasting methods have achieved prominence in the
United States. These are the Sverdrup, Munk and Bretschneider,
(SMB) method and the Pierson, Neumann and James (PNJ) method. Both
methods are applicable to fetch and duration limited seas as well as
fully developed seas and both are semi-empirical as experimental
data was used in some phase of their derivations. The SMB method
predicts two statistics of the wave field: the significant wave
height and the significant wave period. From these two statistics
wave spectra and other statistics can be calculated using the wave
distribution of Longuet-Higgins (1952). The PNJ method predicts the
wave spectra, from which wave statistics can be computed by use of
the wave distribution of Longuet-Higgins (1952). In recent years the
wave spectra and wave statistics derived from both methods have become more nearly equal.
A third hindcast method, the PM method, due to Pierson and
Moskowitz (1964) is very similar to the PNJ method except that a
different spectra is calculated from the input data. However, no
procedure has been published for wave spectra calculations when
fetch and duration are limited. This limitation seriously curtails
the usefulness of the method for Great Lakes wave hindcasting.
The SMB Wave Hindcast Method
The SMB method originated with Sverdrup and Munk's (1947) consideration of the transfer of energy from the wind field to the wave
by both normal and tangential stresses. They assumed the energy of
the wave field would increase until an equilibrium condition was
reached where the rate of energy transfer from the wind to the waves
equalled the rate of energy dissipation from the waves. This condition was called the fully developed sea and was characterized by
a condition of maximum wave heights, periods, and speeds for a given
wind speed. The fully developed sea is also independent of fetch
and wind duration, The theoretical work of Sverdrup and Munk required knowledge of coefficients and constants that could be determined only from empirical data, which at the time were rather meager.
With additional data, Bretschneider (1951 and 1958) revised the forecasting relations of Sverdrup and Munk (1947) into the SMB method~
- 15 -



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<P><PB REF="00000027.tif" SEQ="00000027" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="892" N="16">
From these relations a series of deep water wave forecasting curves
were developed which now appear in many reports and books; Uo.S Army
Corps of Engineers (1961) and Bretschneider (1965).
The SMB wave forecasting (hindcasting) method requires the
following input parameters:
a. The surface (10 meters) wind speed.
b. The duration of the wind from the given direction.
c. The overwater fetch.
With these wind parameters and the SMB wave hindcasting curves, the
wave parameters of significant wave height and significant wave
period can be obtained. The significant wave height is defined as
the average of the highest 1/3 of the wave heights of a given wave
train of at least 100 consecutive waves, while the significant wave
period is the average period of these same waves. Bretschneider
(1965) pointed out that the significant wave period is also a period around which is concentrated the maximum wave energy. This
latter concept allows the SMB significant wave period to be compared with the period of maximum energy as determined from measured
wave data. Longuet-Higgins' (1952) presentation of the Rayleigh
distribution for wave height variability based on a narrow spectrum
and its subsequent verification by Bretschneider (1957 and 1959) and
others permits many statistical parameters to be determined from
the significant wave height. Bretschneider (1965) has reviewed the
state of the art of wave generation in general and the SMB method
in particular; therefore, the method will be discussed no further
except as it relates directly to the problem of Great Lakes wave
hindcasting.
The PNJ Wave Hindcast Method
The PNJ wave hindcasting method is attributed to Pierson,
Neumann and James (1955) and is a development of Neumann's (1952)
theoretical wave spectrum of energy. The PNJ method predicts an
E-value, where E is related to the generated wave energy; from
which, by use of the theoretical wave distribution of Longuet-Higgins
(1952), wave statistics can be calculated. In particular, the significant wave height, the period of maximum energy, the average wave
height, and the upper period and lower period for significant wave
energy were calculatedo Jacobs (1965) has discussed the PNJ method
in considerable detail, as have other authors, hence it will not be
reviewed further except when pertinent to Great Lakes wave hindcasting 
- 16 -



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<P><PB REF="00000028.tif" SEQ="00000028" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="882" N="17">
The input data for the PNJ method are listed below:
a.  Average surface (7.5 meter) wind speed,
b. Duration of surface wind from given direction.
c. Fetch of surface wind.
It will be noted that these parameters are the same as those
for the SMB method except the surface wind is specified to be at 7.5
meters rather than 10 meters.
The Pierson-Moskowitz Spectrum
For a fully developed sea, Pierson and Moskowitz (1964) proposed a wave spectrum based on the similarity theory of Kitaigorodski
(1961)  Jacobs (1965) has reviewed this spectrum and tabulated the
equations used to calculate appropriate wave statistics. However,
the requirement of a fully developed sea severely restricts the
application of this spectrum to the wave hindcasting problem.
The Calculated Wave Statistics
Wave statistics were determined using the SMB, PNJ, and PM
methods with calculated and measured wind inputs. Table 4-1
summarizes the input wind data used with each wave hindcast method.
Table 4-1
Summary of wind data used with each wave hindcast method.
Wave Hindcast Method                  Input Wind Data
1.  Bretschneider Wind
SMB                           2.  Richards Wind
3. 10 meter Measured Wind
1. Jacobs 7.5 meter Wind
PNJ                           2.  Richards Wind
3. 7.5 meter Measured Wind
1.  Jacobs 19,5 meter Wind
PM              2o  Richards Wind
3. 16 meter Measured Wind
- 17 -



</P>
<P><PB REF="00000029.tif" SEQ="00000029" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="885" N="18">
The significant wave height and the significant wave period
or period of maximum energy were calculated for each of these cases
and compared with measured significant wave heights and periods of
maximum energy. In addition, the period band, within which resides
92% of the wave energy, was calculated from the PNJ method using
the Jacobs 7.5 meter wind.
Observed Wave Statistics
The U.S. Lake Survey operated a staff wave-gage on the Muskegon
tower during the 1965 wave hindcast periods. Data from this gage were
used to calculate the observed significant wave height and period of
maximum energy during the hindcast periods. These calculated heights
and periods were used as the standard or "correct" value for comparison with hindcast heights and periods.
Staff-gage data for the selected wave hindcast periods of
1965 were analyzed by the U.S. Army Coastal Engineering Research Center using their wave spectrum analyzer, Caldwell and Williams (1961).
The wave analyzer output, Figure 4-1, is a spectral curve of the
frequency distribution of the linear average and square average wave
heights taken over a twenty minute time interval with a filter band
width of 0.027 cycles per second. In addition, the cumulative peak
wave height is displayed. The period of maximum energy is read directly from the spectrum as the abscissa of the maximum value of the
square average wave height curve.  The significant wave height for a
spectrum is readily obtained from the relation:
Significant Wave Height =Maximum Linear Average Value
Significant Wave Height    =  0e45
0.45
due to Caldwell (1963).
The significant wave height can also be obtained by calculating the standard deviation of the staff-gage data and multiplying by
four. This relation is derived in Appendix F. The standard deviation was computed as a running mean of the preceeding twenty minutes
of real-time staff-gage record using the hybrid analog/digital computer
of the Department of Meteorology and Oceanography, University of
Michigan.
The significant wave heights as computed by the standard deviation method and the periods of maximum energy as read from the
spectral curves constituted the check data for evaluation of the wave
hindcasts,
-18 -



</P>
<P><PB REF="00000030.tif" SEQ="00000030" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="320" N="19">
Wave Frequency (Cycles Per Second)
0.04.06.08    0.10.12.14.16.18     0.20.22.24.26.28    0.30.32
STATION-'1'               O^OE~~~.,  -' -F;   B'.       -71
GAGE3-S IU  TAP      ~ -'T~l
DATE  -~ 8tgG~  TIME  /,OQ.
ANALYSIS-STANDARD &mdash; ISPECIA LREMARKS  /O,,r,-v -
ANALYZED BY-QZ4_DAT     i:  Ma~ 19F 9
&mdash; 5-  FILTER O1PENING  FOR STANDARD
ANALYSIS IS 0.027 Cy/Sec.  -
&mdash;!                                                                       _' 2 I,, eL I  II!26 ml  - 128'   13OI.3'IIl
25
~~20'   II &mdash;- I~1 &mdash;-~o   -JI J II  i   I    -    -L              -''                                                        4L III  II1I1I    1                -   II
~1                                                            1;    il,,~  F-... I   I      I'r  II I II  11  II II I I    0     i'
u,~~~~~~~~~~~~~~~~~~~~~~~~;. I    -
--                     i   5                          -I I1]~ % &mdash; ~    m                                                     --..c
i                i.~~5
-':~:~;l  c-t~,' k  ~   
-:~'Ji    I'  L 
-' Period(Sec
Figure  4-1~~~~~~~~~~~~. Typica   wave  spcr2tMseo          eerhtwra                      rdcdb          
At   ResearchC:enter.
tl~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~l~~~~~~~~~~~~~.
I,, _.. 
O O~,
30520115     1      1         8       76... ~'i':
Wav!eiod (                ~.,:.
Figure 4-1.   Typical wave spectra  at Muskegon research tower as produced by the~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~'
U.S. Army Coastal Engineering  Research  Center~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,,



</P>
<P><PB REF="00000031.tif" SEQ="00000031" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="884" N="20">
5. STRONG WIND CONDITIONS
A sizeable fraction of the wave hindcasts of this study were
made for wind speeds, in knots, ranging from the low teens to the high
twenties. Indeed, 28 knots was the highest observed wind speed of
all the 1965 data. However, wave destruction on the Great Lakes is
usually caused by winds that exceed 28 knots. One opportunity for
study of a strong wind situation occurred during late November, 1966
when a low pressure system deepened over northern Lake Huron and produced abnormally high winds and waves. On the 28th. of November the
U.S.C.G.C. ACACIA ventured into southern Lake Huron and recorded
winds to 44 knots and waves estimated to 20 feet. Figure 5-1 shows
her location and the measured wind at various times. Wind analyses
and wave hindcasts were made for 0100E on 29 November 1966 when the
ACACIA was well into Lake Huron and the wind and waves were near
their maximum values. The results of these analyses are listed below:
Table 5-1
SUMMARY OF WIND AND WAVE CONDITIONS
0100E 29 NOVEMBER 1966
U.S.C.G.C. ACACIA  (44-29.5 N  82-53 W)
S ignificant
Winds       Wave Height      Wave
(kts.)        (ft.)         Period
SMB- Bretschneider Winds               68
PNJ- Jacobs 7.5 meter Winds            25
Richards Winds                         28-46
Bretschneider- Jacobs Average
Winds                             47
SMB- Bretschne ider-Jacobs
Average Winds                                     19          1003
PNJ- Bretschne ider-Jacobs
Average Winds                                     14           8.1
USCGC  ACACIA                          42              20
- 20


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<P><PB REF="00000032.tif" SEQ="00000032" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="764" N="21">
'"'""/  )2   ICE
A P~o      LAKE HURON
FNSCT 
1928 Nov 1966
FNT                 10    I.
MTC                ACACIA
Figure 5-1.      ind conditions measured by the U.S.C.G. C.
Acacia on 28 November 1966. The base of the arrow indicates
the location of the ship while the arrow shows wind direction
and speed.  The numbers by each arrow are the E.S.T. of the
observation.
- 21


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<P><PB REF="00000033.tif" SEQ="00000033" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="890" N="22">
After calculating the Bretschneider wind to be 68 knots and
the Jacobs 7.5 meter wind to be 25 knots it became apparent that
both schemes were badly in error. With a strong wind and extremely
unstable atmosphere conditions, TLake - Tair = +80 to + 180F, there
should be very little difference between a 10 meter wind speed and
a 7.5 meter wind speed. Therefore, averages of the Bretschneider
winds and Jacobs 7.5 meter winds were calculated and used for wave
hindcasting. This average of 47 knots for 0100E on 29 November
1966 compares favorably with the ACACIA's measured wind of 42 knots.
The Richards wind of 38 to 46 knots very nicely bracketed the 42
knot observed wind. Using the average winds with the SMB and PNJ
wave hindcast methods, significant wave heights of 19 and 14 feet,
respectively, were obtained. The estimate of 20 foot wave heights
from the ACACIA compares well with the SMB significant wave height
of 19 feet.
This exercise in wave hindcasting for strong wind conditions
points out inadequacies in the wind analysis schemes. Possibly
these techniques were developed from data biased toward lower wind
conditions and do not extrapolate well to stronger winds. It appears
that investigations into high wind conditions are required in order
to accomplish further improvements in the wind analyses and wave hindcast procedures.
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<P><PB REF="00000034.tif" SEQ="00000034" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="887" N="23">
6. SUMMARY AND CONCLUSIONS
Summary of results
Tables A-1i B-l, and B-2 of Appendices A and B tabulate all
observed and hindcast values of the surface wind, the significant
wave heights and the significant wave periods, respectively for the
1965 data at the Muskegon research tower. Figures A-1 through A-5
of Appendix A and Figures B-1 through B-19 of Appendix B are scatter
diagrams of calculated vs. observed values of winds, significant
wave heights, and significant wave geriods. On each scatter diagram,
the line of perfect correlation (45 line) has been drawn as well
as the least-squares regression line. The regression equation for
the plotted data and the correlation coefficient are also displayed
on each scatter diagram.
Figure B-20 is a frequency distribution of significant wave
heights for the SMB-Bretschneider wind method, the PNJ-Jacobs 7.5
meter wind method and the observed values. These curves show a
similar gross behavior. However, a chi square test indicated that
the hypothesis that the SMB and PNJ data were drawn from the same
set of random variables as the observed data must be rejected at the
99.5% significance level.
Table 6-1, a summary of the correlation coefficients between
calculated and measured wind speeds, shows how the Bretschneider
winds correlated better with measured winds than did the other analyzed winds. The 10 meter, 7.5 meter and 16 meter winds used for
comparison were those measured on the Muskegon research tower.
Table 6-1
WIND  ANALYSES  CORRELATI ON  SUMMARY
n       r
Bretschneider Winds vs. 10 meter winds                36.63
Jacobs 7.5 meter winds vs. 7.5 meter winds            43.55
Jacobs 19.5 meter winds vs. 16 meter winds            49.37
Richards winds vs. 16 meter winds                     44.36
Richards winds vs. 10 meter winds                     36.24
n = number of data pairs
r = correlation coefficient
- 23 -



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<P><PB REF="00000035.tif" SEQ="00000035" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="885" N="24">
Table 6-2 summarizes the significant wave height results of
this research and clearly shows how the SMB wave hindcast values
correlate better than either the PNJ or the PM. It should be noted
that the SMB method correlates best with measured wind input as well
as with the calculated Bretschneider wind input. In all cases, the
significant wave height listed was correlated with that obtained
from the standard deviation calculation, Appendix F.   The CERC observed significant wave heights were calculated from the CERC wave
spectra.
Table 6-2
SIGNIFICANT WAVE HEIGHT CORRELATION SUMMARY
n       r
CERC observed significant wave heights                 85.89
SMB-Bretschneider Wind                                 69.60
PNJ-Jacobs 7.5 meter wind                              73.35
PM-Jacobs 19.5 meter wind                             30.32
SMB-Richards wind                                      59.36
PNJ-Richards wind                                      74.46
PM -Richards wind                                      36.15
SMB-Measured wind                                      53.62
PNJ-Measured wind                                      37.47
PM-Measured wind                                      16.34
n  =  number of data pairs
r  =  correlation coefficient
Table 6-3 summarizes the wave-period correlation coefficients
obtained by comparing hindcast values with those measured by the
CERC spectrum analysis. With the Richards wind input and with the
measured wind input, the SMB method showed a higher correlation of
wave periods than did PNJ or PM. However, PM with Jacobs 19,5
meter wind input correlated better than SMB with Bretschneider wind
input or PNJ with Jacobs 7.5 meter wind input.
The latter three correlation coefficients are all so small
that none of these techniques can be designated as a reliable method.
- 24


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<P><PB REF="00000036.tif" SEQ="00000036" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="887" N="25">
Table 6-3
WAVE  PERIOD  CORRELATION  SUMMARY
n       r
SMB-Bretschneider Winds                                68.20
PNJ-Jacobs 7.5 meter winds                             72.11
PM-Jacobs 19.5 meter winds                            31.31
SMB-Richards winds                                     50.40
PNJ-Richards winds                                     54       o37
PM -Richards winds                                     32.17
SMB-Measured 10 meter winds                            51.67
PNJ-Measured 7.5 meter winds                           31.51
PM-Measured 16 meter winds                            13.64
n = number of data pairs
r  =  correlation coefficient
Table C-1 of Appendix C lists significant wave heights and
periods calculated for Point Betsie, Michigan during some of the
time intervals studied at Muskegon. As comparative observed values
were not readily available these data do not contribute to the
evaluation of wind analysis and wave hindcasting techniques for the
Great Lakes.
Table C-2 lists significant wave heights and periods for
Port Huron, Michigan during the same times.  As the Muskegon data
were selected for onshore winds on the eastern shore of Lake
Michigan, most days considered showed offshore winds at Port Huron
and drastically short fetches. Therefore, these data are very limited and of no value in the evaluation.
Table D-1 of Appendix D compares significant wave heights and
periods for the days in 1964 that were previously considered by
Jacobs, The PNJ, PM, and OBS values are repeated from Jacobs (1965)
report while the SMB values are new. The wind speed and fetches
were too low for an SMB analysis in many cases, so the points that
can be compared are rather limited. Perusal of these data does not
point out any marked superiority of any technique.
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</P>
<P><PB REF="00000037.tif" SEQ="00000037" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="889" N="26">
Conclusion
The results of this investigation show the Bretschneider wind
analysis method produced the best surface mean winds and the SMB
wave hindcast method calculated the best significant wave heights.
The latter result is undoubtedly due in part to the better fit of
the Bretschneider winds to the measured winds. However, the SMB
method also produced better wave hindcasts when measured winds
were used as input to the hindcast schemes, thus the combination of
Bretschneider winds and SMB wave hindcasts appears to be the best
method to be utilized, at this time, for wave statistics studies
on the Great Lakes.
Despite being the best method available, neither the Bretschneider wind correlation coefficient of 0.63 nor the SMB Bretschneider significant-wave correlation coefficient of 0.60 are outstanding. The SMB-Bretschneider wave-period correlation coefficient
of.20 is an indication that wave periods on the Great Lakes can
not be hindcast with any accuracy. Indeed, a coefficient of.20
indicates almost a lack of correlation; a fact that is born out by
the scatter diagram, Figure B-ll.
Both the wind analysis and the wave hindcasting methods are
not totally adequate and research in both fields must continue in
order to improve the existing methods or develop new ones. However,
more data will be necessary before significant advances can be expected.
The results of the investigation of the November, 1966 storm
indicate the wind analysis schemes are biased toward low wind speed
data. Indeed, the Jacobs wind equations were derived with data
containing very few wind speeds greater than 30 knots. While the
results of one study of one storm compared with the observations
from one ship can not refute existing wind analysis and wave hindcast techniques, these results do raise questions as to the applicability of these techniques to high wind conditions. As the high
wind conditions are the most important for any user of a wave climatology, it is imperative that they be studied in greater detail.
Wave Climatology for Lakes Huron and Superior
The production of a wave climatology for the Great Lakes
should proceed at this time using the following procedure.
26 -



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<P><PB REF="00000038.tif" SEQ="00000038" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="892" N="27">
1. With synoptic weather data (0000, 0600, 1200, 1800 GCT),
use the successive approximation technique machineanalysis to calculate a surface pressure field and a
geostrophic wind field. All output data should be
stored on computer tape for future input to newly developed programs.
2.  Determine a stability factor, Twater - Tair  from a
subjective analysis of water temperature climatology,
ship records, etc.  Continuity, smoothing, interpolation and extrapolation must be judiciously applied to
this process. Measure isobaric curvature on a weather
chart.
3a. Use the Bretschneider surface wind chart with the
stability factor and the isobaric curvature to determine the ratio of surface-wind to geostrophic-wind.
Calculate the surface (10 meter) wind field upwind of
each wave hindcast location.
3b. If the calculated surface wind exceeds 30 knots, Jacobs
empirical wind equations and the Richards, Dragert and
McIntyre computations should be utilized to obtain
additional wind estimates. These must be considered,
along with ship and land wind reports, in the final determination of surface wind speed.
4. Use the SMB wave hindcast charts to determine the significant wave height and significant wave period.
5. For high wind or fast moving storm conditions, reduce
the time between analyses from 6 hours to 3 hours.
The wind analysis and wave hindcast schemes discussed in this
report and proposed above for the development of a wave climatology
should be considered to be the best available now but improvements
in the future are vitally needed and must be anticipated. The program of wave climatology production must remain flexible so that any
new developments can be rapidly exploited.
- 27 -



</P>
<P><PB REF="00000039.tif" SEQ="00000039" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="853" N="28">
APPENDIX A
1965 WIND DATA AND SCATTER
DIAGRAMS FOR MUSKEGON,  MICHIGAN
- 28



</P>
<P><PB REF="00000040.tif" SEQ="00000040" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="863" N="29">
TABLE A - 1
SURFACE WIND FOR 1965 WAVE HINDCAST PERIOD
Muskegon Research Tower
V  = Geostrophic Wind
g
V   = Gradient Wind
gr
VR  = Richards Wind
V   = Jacobs Wind (19.5 meters )
VB = Bretschneider Wind (10 meters )
V   = Jacobs Wind (7.5 meters )
J1
Wind Speed (kts)
Observed                                Calculated                      Wind Direction
QD                                                                                          (degrees)
Date:Time(C.S.T.)16m  10m  7.5m            V     g    Vg     VR J    VB  VJ1      Observed  Gradient
September, 1965
23:0000           15   16   14.6         25   25    15   17    16  17             240        260
23:0600           12         17          33   31    11   19    22  19             230        260
23:1200           24   22   24           28   28    16   22    20  22             210        250
23:1800           20   19   20           30   30    19   22    19  22             260        310
24:0000           14   12   13           25   25    16   21    17  21             290        290
24:0600           16   14   15           23   18    13   19    16  19             290        310
24:1200           17   14   15           25   28    15   22    21  22             280        310
24:1800           18   16   16           28   35    11   24    25  24             260        290
25:0000           20   18   18           35   35    13   24    26  24             260        270
25:0600           22   20   20           48   39    17   25    33  25             240        270
25:1200           24   21   20           35   61    18   32    29  32             210        250
25:1800           22   18   18           16   17    19   15    10  15             200        240
26:0000           11   11   11           0    0       22   0      0   0
26:0600           20   13   12           35   26            21    23  21         cont'd
cont'd



</P>
<P><PB REF="00000041.tif" SEQ="00000041" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="805" N="30">
Wind Speed  (kts)
Ob s er ved                             Calculated                       Wind Direction
(degrees)
Date:Time(C.S.T4) 16m  1Cm  7.5m             V                            VV    V B    Observed  Gradient
28:0000                      12           20   19           19   16   19             140        180
28:0600                                   19   19           19   14   19             140        050
28:1200                                   24   24           21   16   21             130        200
28:1800                                   12   12           13   6    13             160        190
29:0000                                   19   12           17   11   17             160        170
29:0600                                    6           11          3                 200        170
29:1200                                    6    6    10   15    4   15               180        190
30:0600                                   40   40           21   25   21             140         190
30:1200                                   40   40           21   24   21             170         200
30:1800                                   32   25    12   17   16   17               180         240
0
October 1965
01:0000'          24                      38   44    19   23   26   23               240         290
01:0600           25                      48   31    10   23   30   23               280        320
01:1200           23                      37   52    15   29   32   29               320         340
02:0600           17                      40   40    16   21   26   21               220         260
02:1200           25                      60   60    23   27   38   27               200         250
02:1800           23                      48   39    13   22   22   22               220         280
03:0000           30                      50   42    16   23   27   23               310         340
03:0600           30                      45   39    26   21   26   21               330         360
03:1200                                   28   34           24   24   24             340         360
05:1200                                   16   20           19   14   19             150         190
05:1800           13   10                  19   17    13   15   12   15              180         200
06:0000           18   18                 28   26           21   19   21             160         220
06:0600           20                      52   35    15   20   28   20               210         230
06:1200           23   19                 33   33    15   19   22   19               190         220
06:1800           13                      17   15           14    8   14             170         230
Cont'd



</P>
<P><PB REF="00000042.tif" SEQ="00000042" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="856" N="31">
Wind Speed (kts)
Observed                                Calculated                       Wind Direction
(degrees )
Date:Time(C.S.T.) 16m  lom  7.5m             V    Vgr   V    VJ    VB   V            Observed
g  r    V    V,. Observed  Gradient
2             1
07:0000           12                       21   22    17   17   13   17               190        210
07:0600           19                       48   36           20   27   20             160        220
07:1200           24                       35   26    17   17   18   17               180         240
07:1800           18                       23   21    15   16   14   16               230         230
08:0000           22                       50   43    19   24   26   24               280        300
08:0600           27                       65   44    21   22   38   22               280        310
08:1200           27                       45   31    19   19   26   19               290        310
08:1800           28                       62   41    18   22   35   22               280         300
09:0000           21                       50   36    13   20   29   20               310         320
09:0600           25                       48   31    21   23   29   23               320         340
11:0600           9                        15   21    13   16   10   16               310        340
11:1200           17                       23   23    18   20   16   20               290        330
11:1800           19                       26   24    12   17   16   17               300        300
12:0000           25                       45   26    19   17   26   17               290         310
12:0600           28                       43   39    13   25   29   25               300         320
22:1800           11   8    12             28   43    12   22   22   22               300         310
23:0000           20   18   19                         11
23:0600           19   17   14
23:1200           22   20   25             42   63           33   37   33             350         350
23:1800                      20            30   28           22   20   22             350         350
24:0000                      16            52   44           27   40   27             350         360
24:0600           16         13            52   52           29   40   29             010         060
24:1200           11   11   14             19   19    13   19   14   19               330         350
24:1800            6    5    7             19   19    12   19   15   19               260         260
25-0000           20   18   18             34   31    15   23   26   23               240         360
25:0600           27   24   24             30   30      9   22   22   22              200         260
cont'd



</P>
<P><PB REF="00000043.tif" SEQ="00000043" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="865" N="32">
Wind Speed (kts)
Observed                                Calculated                      Wind Direction
(degrees)
Date:Time(C.S.T.) 16m  10m  7.5m             Vg  Vgr   VR   V       VB   V         Observed  Gradient
2           1
25:1200                19   19            27   22    15   20   17   20
25: 1800                                  23   18    10   19   14   19
29:0600                18   17            28   28    15   22   20   22
29:1200                21   21            55   89    16   41   48   41
29: 1800               23   21            80   80    10   38   56   38
30:0000                22   22            60   60    16   27   40   27
30:0600                17   16            30   30    15   19   19   19
30:1200                12   11            50   20    14   24   20   24
30:1800                       8           27   16    16   18   16   18
31:0.000               22   22            62   54    19   27   32   27                           270
31:0600,               27   28            80   80    18   33   47   33                          350
31:1200                21   22            53   53    18   27   31   27                          330
31:1800                18   18            32   37    13   20   24   20                          330
November 1965
01:0000                18   18            19   15    16   14   10   14                           330
01:0600                12   13            37   23    16   16   20   16                           310
01:1200                16   18            25   24    18   17   14   17                           310
01:1800                 7    7             19   19    11   15   13   15                          280
03:0600                17   19            37   37            21   22   21                        230
03:1200                19   20            48   43    24   22   28   22                           230
03:1800                                                16
04:0000                                                17
04:0600                                                16
04:1200                                                16
04:1800                                   10   8                   6
cont'd



</P>
<P><PB REF="00000044.tif" SEQ="00000044" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="834" N="33">
Wind Speed (kts)
Observed                                 Calculated                      Wind Direction
(degrees)
Date:Time(C.S.T.) 16m  10m  7.5m           Vg   Vgr   VR   VJ    VB   VJ1           Observed  Gradient
05:0000                                  9    8                   5
05:0600                                  18   13           14    10   14                         190
05:1200                                  25   16    13   21    13   21                          230
05:1800                                  33   21       8   16    15   16                        250
06:0000                                  23   19           16    12   16                         270
06:0600                                  13   15           14    9    14                        270
IA.



</P>
<P><PB REF="00000045.tif" SEQ="00000045" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="834" N="34">
30
Y  10.4+.27X
20
MKG
Tower                                   + +       +/
Winds
IOm.
kts. 15
+ /  /   | Wind Comparison
Muskegon Tower 10 m. vs
10                                              Bretschneider
Correlation    r. 63'
5                         4
5        10        15       20        25       30        35        40
Bretschneider Winds kts.
Figure A-1.    Scatter diagram of Bretschneider winds vs. surface (10 meters) measured winds.
30
+
20                   x                                            /
+ /
MKG                                      + +
Tower
7. 5 m. 
kts.   15                                             +
1o0              /        +Muskegon Tower 7.5m. Winds vs
Jacobs 7. 5 m. Winds
/+ +            Correlation  r. 55
5
5        10       15        20       25        30       35
7. 5m. Jacobs Winds  kts.
Figure A-2.    Scatter diagram of the Jacobs 7.5 meter winds vs.
surface (7.5 meters) measured winds.
- 34 -



</P>
<P><PB REF="00000046.tif" SEQ="00000046" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="715" N="35">
30                                     +  t
+   /Y=x
25                                                 4
+        4/                  +
+              + 
16m.20                                                 Y 9.99+.45X
16m. 20
MKG                                +
Tower                                 +          +
Winds                                    +  *
kt. 15
/,/  t  Wind Comparison
/  /  + t'         Muskegon Tower Aerovane vs
/   +  +       Jacobs 19. 5 m.
10'                   +     Correlation  r =.37
0
5        10        15       20        25        30        35
19.5 m. Jacobs Winds  kts.
A-3.    Scatter diagram  of the Jacobs 19.5 meter winds
vs. surface (16 meters) measured winds.
30                           +                  +
+                      +
1m.2+          +
MKG  +             +  
25                                 i  + + 
Aerovane   + /+                                     Wind Comparison 16 m.
ns  I             / + +   /Muskegon Tower vs Richards
5t S.    1t                                   Correlation  r =.3 7
+ /    +
~~10           + +                  +
M KG
+
5                    ++
5        10       15        20        25        30
Richards Winds kts.
Figure       A         -4.Muskegon Tower vsdiagram   of  the         Richards winds   vs.  surfacigure A-4. Scatmeter diagram of the Richardsmeasured winds vs. sur- 35


</P>
<P><PB REF="00000047.tif" SEQ="00000047" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="841" N="36">
25
+    /Y -= 11.0 +.37X
20
MKG                                                               +
Tower                              +           +
10 m.                                      +
Winds +1+                                          +           Wind Comparison
kts.  15                                                    Muskegon Tower 10 m. wind vs
Richards Wind.
Correlation   r =. 24
10 _
5
5          10         15          20           25         30
Richards Winds  kts.
Figure A-5.    Scatter diagram of the Richards winds vs. surface  (10 meters) measured  winds.
- 36 -



</P>
<P><PB REF="00000048.tif" SEQ="00000048" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="878" N="37">
APPENDIX  B
196 5 WAVE DATA AND SCATTER
DIAGRAMS FOR MUSKEGON, MICHIGAN
- 37


</P>
<P><PB REF="00000049.tif" SEQ="00000049" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="874" N="38">
TABLE B - 1
SIGNIFICANT WAVE HEIGHTS DURING 1965 HINDCAST PERIODS
Muskegon Research Tower
SK  = SMB Wave Hindcasts with Bretschneider winds.
B
= SMB Wave Hindcasts with Richards winds.
R
= SMB Wave Hindcasts 10 meter measured winds.
M
PNJ = PNJ Wave Hindcasts with Jacobs 7.5 measured winds.
J
PNJ= PNJ Wave Hindcasts with Richards winds.
R
PNJ
PNJ= PNJ Wave Hindcasts with 7.5 meter measured winds.
M
= PM Wave Hindcasts with Jacobs 19,5  meter winds.
J2
= PM Wave Hindcasts with Richards, winds.
PM
= PM Wave Hindcasts with 16 meter measured winds.
OBS = Significant wave heights as calculated from the standard deviation of the wave record.
OBS
CERC= Significant wave heights as calculated from the CERC spectra of the wave record.
Abbreviations for sea state:  FD=fully developed, FL = fetch limited, DL = duration  limited
and Sw = swell. All significant wave heights are in feet.
cont d



</P>
<P><PB REF="00000050.tif" SEQ="00000050" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="866" N="39">
Date Time  Sea       SMB   SMB   SMB   PNJ   PNJ   PNJ  PM  PM  PM   OBS             OBS
C.S.T.   State      B      R      M      J     R      M   J2  R   M                CERC
September 1965
23:0000   DL       2.4   2.7    2.5   2.2   2.1   2.2                      2.3      3.1
23:0600  FD        5.3   2.6   4.7   6.1   1.8   4.9  6.3  2.2  2.6  3.7            3.6
23:1200  FL        5.9   3.9   6.4   5.9   4.2   7.7                       5.5      5.4
23:1800   DL       4.5   5.3    5.5   2.9   6.9   7.3                      7.0      6.1
24:0000  FL        4.8   4.4   2.8   7.4   4.5   2.7            4.7  3.6   6.1      5.3
24:0600  FD        4.5   3.3   3.5   6.7   2.7   3.5  6.5  3.1  4.7  3.7            4.5
24:1200  FL        6.5   4.0   3.7   8.7   3.8   4.0            4.1  5.3  4.6       4.1
24:1800  FL        7.7   2.5   4.4   7.8   1.8   4.6            2.2  5.9  4.2       4.1
25:0000  FL        8.2   3.0   5.2   7.8   2.7   5.9            4.7  7.3   5.1      5.1
25:0600  FL        11.0  4.4   6.1   8.0   5.1   7.7                 8.8  4.9       5.4
25:1200   FL       9.4   5.6   7.0   8.7   6.1   8.3            5.9  10.5  7.6     7.0
25:1800  FD        2.4           5.3   3.2   6.9   5.9  4.0  6.6  8.0  7.6         7.0
26:0000                                       5.1   1.9              2.2  4.6       4.6
26:0600  FL                                                                3.1      2.0
28:0000  FL        2.5                  2.2                                2.4      2.1
28:0600   DL       3.6                  7.1                                2.9      2.3
28:1200  FD        4.7                 8.4                 7.7             2.9      2.4
28:1800  FD                             2.5                3.3             2.7      2.4
29:0000  FL                            8.2                                 1.7      1.1
29:0600  FL                                    1.5                         1.0.9
29:1200  FD               2.0           3.7   1.4          4.1  1.8.9
30:0600   DL       8.0                  7.5                                1.6      1.3
30:120U  FD        8.3                  8.2                8.3             4.2      3.3
30:1800  FD        4.6                  4.7   2.0          5.4             4.4      4.4
cont'd



</P>
<P><PB REF="00000051.tif" SEQ="00000051" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="810" N="40">
Date:  Time   Sea    SMB    SMB    SMB     PNJ    PNJ   PNJ    PM    PM   PM PM   OBS    OBS
C.S.T.   State      B      R      M       J      R     M     J2    R      M            CERC
October 1965
01:0000   DL       5.1    3.4    4.2     2.3    5.1                             5,0    5.5
01:0600   FL.      8.7    2.2    7.0    9.7    1.4                  1.8         7.3    7.3
01:1200  FL        1,9    3.2    7,6     8.9    3.6                             5.8    1.2
02:0600   FL       8.3    2.5    2.5     7.5    2.2                              2.4    2,5
02:1200   FL       13.2   5.6    5.9     8.2    7.6   2.0                       5.8    5.8
02:1800   FD       7.7   3,5    6.3      6.8    2.7   4.7    9.0    3.1          6,9    5,1
03:0000   FL              4.5    8.2            4.5                 4.7          5.6    4.6
03:0600   FL              7.3   10.3            7.3                             7.1    6.2
03:1200   FL                                                                    3.6    2.9
05:1200   DL       3.4                   7.2.8
0
05:1800   FD       2.8                   3.3    2.1   2.1    4.0                 2,0    2,3
06:0000   FD       4.5                   9.1.6   8.2           5.9  3.3    4.0
06:0600   DL       8.0    2.2    2.9     6.9    2.2   5.0                        5,8    5.3
06:1200   FD       7.4   3.7    5.2      6.4    3.8  8.9    6.9    4.1          7.6    6.0
06:1800   FD                             2.2                 3.7                4,4    3.0
07:0000  FD        3.5    2.8            2.7    2.2          5.1                 2.2    2.0
07:0600   DL       7.1                   5.7          2.1                       3,7   3.5
07:1200  FD        5.4    2.8    4.2    4.8    2.2.8    5.5           10.5 5.2    4. 1
07:1800   FD       3.9    4.0    5.1    3,9    3.8   1.2    4.6    4.1   5.9  6,3   6.0
08-:000   DL       7.0    5.2    5.5     3.3    6.5                             4.2    3.4
08:0600   DL       13.0  7.4    6.8      8.5    7.9   2.2                       8.2    8.6
08:1200   FD       8.5    5,5    8.2     6.1    6.9   7.5    6.4    6,6         8.3    8.1
08:1800   FD       12.0   5.1    8,6     8.4    6.1   9.0    8.5    5.9  14.3  7.2    7,0
09: 0000   FD      10, 0   3 3    6 1    7.0    2.7  9.7    7.4    3.1   8.0  6.5    4.5
0900600   FL              5.3    7.8    10.7   5.5  4.8                   11.4  5.8   2.7
11:0600   FL                                    2.1                             2.2    1.7
cont  d



</P>
<P><PB REF="00000052.tif" SEQ="00000052" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="777" N="41">
Date:oTime   9vate    SMD    SMB    SMB          PNJ    PNJ    PNJ    PM         PM    PM    OBS       OB
C.S T a               B       R       M         J       R       M      J       R     M              CR
11:-1200   FD        4.7    4.0    2.7        8.1    4.9             7.4                   2.4     2.
11:1800   FD         4.5    2.9    4.5        4.5    2.2             5.2    2.6            4.5    3.
12:0000   FD         8.6    4,5    7.0        4.9    5.1             5.5                   5.2    5.5
12:00600   DL        10.0   3.2    7.8        7.5    2.7                     3,1           9.1     6.
22:1800   DL         3.9                       2.2    2.0                                  1.8
23:0000                      2.4    3.2                1.8                   2.2           3.6 3E
23:0600                                                                                    4.1     2.
23:1200   FL         2,3                                                                   3.4     25
23:1800   FL                                                                               4.8.
24:0000   FL         2.6                                                                   4.0.
24:0600   FL         2.6                                                                   2. 3
24:1200   FL                                           2.1                                 2.5.
H  24:1800   DL         2.1    2.7                1.6    2.2                     2.6           1C.9.
25:0000   FL                 3.7    3.3                3.8                   4.1           3.8     5.
25: 0600   DL        3.8             4.6       2.2    1.1                     1.5          7.3.
25:1200   DL,,FL    4.6    3.2    5.9          7.5    3.1                                  3.3
25:1800   FD         3.6    2.4                6.7    1.4            6.5    1.8              C5
29:0600   FL         4.8    2.3    2.9        8.5    2.1                                   59    3.
29:1200   FL         14.8   3.9    5.5         12.3   4.5                     4.7          7.      6.
29:1800   FL         21.5   2.4    7.7         10.3   1.4                     1.8          8.4     8.
30:00000   FL        14.2   3.6    7.6         8.0    4,5                                  8.4     6.
30:0600   FD         5.4    4.3    5.0         5.7    2.7                     4.1          76    6.0
30:1200   FL         6.0    3.9    3.1         7.      3.2                    3.6           5.5    4.
30:-1800   FD        4,4                       4.2    4.5             6.0    4.7            3.1    25
31.0000   DL         9.0    4,5    4.0         6.3     2.1   3.1                           4.3
3 1:-0600   FL       3,1    5,5    6.7                 4,9   8.0              5.9           7.53
31:01200   DL        6.3    3.5    4.2         2.3    2.2   3.8                             7.6E.
31:1800   FD         8.4    3.5    4.5-    7,3    5,1   6.0    7.6    3.1                   4.5    4.2



</P>
<P><PB REF="00000053.tif" SEQ="00000053" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="829" N="42">
Date: Time  Sea     SMB   SMB   SMB   PNJ    PNJ  PNJ   PM    PM  PM    OBS   OBS
C.S.T.   State    B      R      M      J       R    M    J2    R   M               CERC
November 1965
01:0000  FD              4.4   5.4   3.0    2.0  4.2   3.7   4.7             3.3   2.7
01:0600  FD       4.2   4.4   2.8   4.2    1.8  2.8   4.9   4.7             3.0   2.2
01:1200  FD       3.8   5.2   3.6   4.4            5.0   5.1   5.9          3.6   2.7
01:1800  FD       3.2   2.5           3.6          6.1   4.3   2.2           2.5   1.8
03:0600  FD       7.0          2.7   7.4.7   7.7                4.5   4.2
03:1200  FL       9.2   4.5   5.0   7.7            7.5                      6.3   7.1
03:1800                 4.4                   2.1                4.7         5.5   4.7
04:0000                  5.0                  2.2                5.3         5.0   5.2
w    04:0600                  4.7                  3.8                4.7         3.5   2.7
-P,   04:1200                 4.5                  1.1                4.7.9
04:1800  FL                                   3.1.8   2.2
05:0000                                       1.4                            1,0
05:0600  FD                           2.7                 3.4                3.7
05:1200   DL      2.7                 5.5    2.1                             3.6
05:1800  FD       3.8                 3.1    5.3          4.8   1.2          2.9
06:0000  FD       2.7                 3.6                 4.4                2.9   2.7
06:0600  FD                           3.0    2.1          3.8                2,8   2.6
06:1200                                       4.5                            1.7
06:1800                                       1.4                            o7



</P>
<P><PB REF="00000054.tif" SEQ="00000054" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="831" N="43">
TABLE B-2
SIGNIFICANT PERIOD OR PERIOD OF MAXIMUM ENERGY FOR 1965 WAVE HINDCAST TIMES
Muskegon Research Tower
SMB
= SMB Period hindcasts with Bretschneider winds.
B
SMB
= SMB Period hindcasts with Richards winds.
R
SMB
SMB Period hindcasts with measured 10 meter winds.
PNJ
PNJ Period hindcasts with Jacobs 7.5 meter winds.
Ji
PNJ
= PNJ Period hindcasts with Richards winds.
R
P   - PNJ Period hindcasts with measured 7.5 meter winds.
PM
= PM Period hindcasts with Jacobs 19.5 meter winds.
PM
PM Period hindcasts with Richards winds.
R
PM
PM Period hindcasts with measured 16 meter winds.
M
Period of Maximum Energy as determined from the CERC spectra of the wave
CERC   record.
Abbreviations for sea state: FD= Fully developed, FL= Fetch limited, DL= Duration
Limited, and Sw= Swell. All periods are in seconds.



</P>
<P><PB REF="00000055.tif" SEQ="00000055" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="835" N="44">
Date: Time    Sea     SMB    SMB    SMB    PNJ    PNJ    PNJ    PM   PM        PM      OBS
C. S.T.   State    B      R       M      J1     R      M      J2    R      M      CERC
September 1965
23:0000    DL       3.8    4.0    3.8    4.8    4.3    4.5                          4.1
23:0600    FD       5.8    4.9    5.6    7.1    4.4    6.2    7.0   4.1    4.5    4.9
23:1200    FL       6.4    5.2    6.8    9.3    7.6    7.4                           5.8
23:1800    DL       5.3    6.1    6.2    6.9    9.9    8.9                           6.6
24:0000    FL       5.9    5.7   4.8    8.4    6.5    4.9    7.0   6.0    5.3    5.8
24:0600    FD       5.8    5.2    5.2    7.6    5.3    5.5            4.9    6.0    5.0
24:1200    FL       6.7    5.5    5.3    9.7    6.1    5.7            5.6    6.4    5.0
24:1800    FL       7.2    4.7    5.7    8.7    4.4    6.0            4.1    6.8    5.0
25:0000    FL       7.3    4.8    6.1    8.7    5.3    6.7            4.9    7.5    5.4
25:0600    FL       8.2    5.4    6.5    8.5    7.8    7.4                   8.3    5.5
25:1200    FL       7.2    6.5    7.1    8.1    7.3    7.7            6.8    9.0    6.7
25:1800    FD       4.7            6.2    5.7    7.7    6.7    5.5   7.1    7.9    6.5
26:0000                                          9.4    6.9                  4.1
26:0600    FL
28:0000    FL       3.8                   4.7                                        4.6
28:0600    DL       5.4                   10.9                                       5.1
28:1200    FD       5.9                   8.3                   7.7                  5.0
28:1800    FD                             5.1                   5.0                  4.7
29:0000    FL
29:0600    FL               3.0                  4.7
29:1200    FD               4.5                  4.0                  3.8
30:0600    DL       7.3                                                              3.3
30:1200    FD       7.6                   9.9                   8.1                  5.4
30:1800    FD       5.8                   6.1    5.2            6.5                  4.9
cont'd



</P>
<P><PB REF="00000056.tif" SEQ="00000056" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="787" N="45">
Date: Time    Sea     SMB    SMB    SMB    PNJ    PNJ       PNJ   PM    PM      PM     OBS
C.S.T.     State     B       R      M     i      R         M    J2    R      M       CERC
October 1965
01:0000    DL       5.2    4.3    4.8    4.7    6.3                                  5.6
01:0600    FL       7.6    4.5    6.8    13.0   4.0                   3.8            6.6
01:1200    FL       2.7    4.7    6.8    8.3    7.2                                  6.5
02:0600    FL       7.5    3.8    3.8   9.3    4.3                                   3.9
02:1200    FL       8.7    5.9    6.0    8.6    7.9                                  5.7
02:1800    FD       6.7    5.4    6.8    7.7    5.3             8.4   4.9            6.8
03:0000    FL       2.4    5,7    7.4            6.5                  6.0            5.3
03:0600    FL       2.4    6.7    8.3            6.8                                 7.3
03:1200    FL       2.3                                                              4.5
05:1200    DL       5.0                   10.9                  5.5                  3.1
U,
05:1800    FD       5.0    3.3    2.8    5.7    5.1             8.0                  3.9
06:0000    FD       5.4                   8.6                                        4.7
06:0600    DL       6.9    3.7    4.2    10.6   4.3             7.3                  6.2
06:1200    FD       7.2    5.2    6.0    7.9    6.1             5.4   5.6           6.7
06:1800    FD                             5.3                   6.2                  5.9
07:0000    FD       5.6    4.0    3.0    6.1    4.1                                  4.0
07:0600    DL       6.5                   8.9                   6.5                  4.5
07:1200    FD       6.3    4.0    4.8    7.1    4.1             6.0                  5.6
07:1800    FD       5.7    5.5    6.2    6.1    6.1                   5.6            6.0
08:0000    DL       6.5    6,0    6.2    5.8    5.3                                  5.0
08:0600    DL       8.6    6.6    6.8    10,0   9.1             7.1                  6.7
08:1200    FD       7.4    6.3    7.2    7.3    7.7             8.1   7.1            6.7
08:1800    FD       8.3    6.1    7.4    8.3    7.3             7.5   6.8            6.4
09:0000    FD       8.0    5.2    6.6    8.1    5.3                   4.9            5.9
09:0600    FL               5.9    7.2           6.3
11:0600    FL               3,3    2.4           5.1
11:1200    FD       6.1    5.1    4.2    8.2    6.8             7.6                  3.7
cont'd



</P>
<P><PB REF="00000057.tif" SEQ="00000057" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="831" N="46">
Date:Time    Sea       SMB    SMB    SMB    PNJ    PNJ       PNJ   PM    PM      PM     OBS
C.S.T.    State      B      R      M      J1      R       M    J2    R       M       CERC
11:1800    FD        5.7    4.9    5.5    6.5    4.8             6.3   4.5            5.0
12:0000    FD        7.5    5.4    6.7    6.7    6.5             6.6                  5.6
12:0600    DL       8.0    5.2    7.2    8.3    5.3                    4.9            6.9
22:1800    DL               3.2    2.4            5.1      5.1
23:0000                     4.5    4.4            4.4     6.2          4.1
23:0600
23:1200    FL
23:1800    FL
24:0000    FL
24:0600    FL
24:1200    FL               3.3    2.9            5.2      4.4
24:1800    DL        3.6    5.7            4.7    4.8      2.6         4.5    6.8
25:0000    FL        2.4    5.2    4.4            6.1      6.8         5.6            4.8
25:0600    DL        4.7    4.6    5.0    4.7    3.6       8.4         3.4            6.7
25:1200    DL, FL    5.8    4.7    6.6    10.0   5.7             7.9
25:1800    FD        5.3    4.8            7.6    4.0                  3.8
4.3
5.2     3.0                 9.0    5.2
6.3     3.9                 4.5
29:0600    FL        5.6    3.7    4.2    9.2    4.3       4.0                        4.4
29:1200    FL        8.7    5.2    6.0    8.9    6.5       8.8         6.0            6.7
29:1800    FL        10.5   4.8    7.3    8.6    4.0       8.0         3.8    10.5   6.7
30:0000    FL        9.0    4.8    7.3    8.6    8.0       8.2                 7.9    7.1
30:0600    FD        6.2    5.8    6.2    7.1    6.1       6.1         5.6    9.4    6.9
30:1200    FL        6.5    5.7    5.2    10.3   5.7       4.5          5.3           6.5
30:1800    FD        5.7                   6.3    6.5      3.0   6.8   6.0            5.7
31:0000    DL        7 ol    6.2    4.8    7.6    9.4      4.5
31:0600    FL        3.1    6.4    6.8            7.3      6.7         6.8            6.2
cont'd



</P>
<P><PB REF="00000058.tif" SEQ="00000058" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="788" N="47">
Date: Time    Sea       SMB    SMB    SMB    PNJ    PNJ       PNJ   PM    PM      PM     OBS
C.S.T       State      B      R      M      Ji      R        M    J2    R       M      CERC
31:1200    DL        5.8    4.7    5.0    4.6    5.3       5.1                        7.8
31:1800    FD        7.6    5,5    5.5    7.9    5.3       8.8   7.7   4.9            5.7
November 1965
01:0000    FD               5,7    6.3    5.5    6.5       5.8   5.4   6.0            4.6
01:0600    FD        5.0    5.7    4,9    6.3    6.5       5.0   6.2   6.0            4.7
01:1200    FD        5.5    6.1    4.9    6.1    7.3       6.8   6.2   6.8            4.9
01:1800    FD        5.1    4.7            5.9    4.4      2.8   5.8   4.1            4.3
03:0600    FD-       7.0           4.0    7.9              4.0   7.7                  5.4
03:1200    FL        7.6    5,0    5.8    10.1   8.1       9.2                        6.6
03:1800                     5.7                   6.5                   6.0
04:0000                     6.2                   6.9                  6.4
04:0600                     6.0                   6.5                  6.0
04:1200                     5,8                   6.5                  6.0
04:1800    FL
05:0000
05:0600    FD        3.4                   5.3                   5.2
05:1200    DL        4,4    3.6            7.8    5.1
05:1800    FD        5.3                   5.6    3.2            6.1   3.0            50
06:0000    FD        4.8                   5.9                   5.8                  4.1
06:1200
06: 1800                                          6.-3



</P>
<P><PB REF="00000059.tif" SEQ="00000059" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="843" N="48">
TABLE B-3
PERIOD BAND AND MAXIMUM WAVE HEIGHT
FOR 1965 WAVE HINDCAST TIMES
PNJ = Period band and maximum wave height in preceding 20 minutes as calculated
from PNJ wave hindcasting method, using Jacobs' 7.5 meter wind.
PM = Period band as calculated from wave hindcasts based on PM spectra.
OBS = Maximum wave height as determined from wave spectra of wave gauge record.
Period Band (sec)          Maximum Wave Height (ft)
Date:Time
PNJ           PM                  PNJ      OBS
00                                       September 1965
23:0000             1.0- 4.8                            3.8       3.7
23:0600             2.4- 9.8       2.8-7.0             10.6       4.5
23:1200             2.9- 9.3                           10.2       7.5
23:1800             2.5- 6.9                            5.0       7.4
24:0000             3.1- 8.4                           12.8       7.3
24:0600             2.8-10.4       2.8-7.0             11.6       5.7
24:1200             3.3- 9.7                           15.1       4.8
24:1800             3.1- 8.7                           13.5       5.2
25:0000             3.1- 8.7                           13.5       6.2
25:0600             3.1- 8.5                           13.9       7.4
25:1200             3.1- 8.1                           15.1       9.9
25:1800             1.5- 7.8       2.2-5.5              5.5       9.3
28:0000             1.0- 4.7                            3.8       2.8
28:0600             3.0-10.9                           12.3       3.8
28:1200             3.1-11.4       3.1-7.7             14.6       2.9
28:1800             1.1- 7.2       1.8-4.6              4.3       3.1
29:0000                                                14.2       1.4
cont'd



</P>
<P><PB REF="00000060.tif" SEQ="00000060" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="868" N="49">
Period Band (sec)          Maximum Wave Height (ft)
Date: Time
PNJ           PM                 PNJ      OBS
29:1200            1.8- 8.3       2.2-5.6              6.4        -
30:0600            3.0- 9.9                           13.0       1.7
30:1200             1.8- 8.3      3.2-8.1             14.2       3.9
30:1800            2.1- 9.0       2.5-6.5              8.1      4.6
October 1965
01:0000             1.3- 4.7                           4.0       6.6
01:0600             3.5-13.0                          16.8       9.6
01:1200             3.2- 8.3                          15.4       5.6
02:0600            3.0- 9.3                           13.0       3.8
02:1200            3.1- 8.6       3.3-8.4             14.2      8.7
02:1800            2.8-10.5                           11.8       6.7
05:1200            3.0-10.9       2.2-5.6             12.5        -
05:1800             1.5- 7.8      3.1-8.0              5.7       2.9
06:0000             3.2- 7.5                          15.8       7.5
06:0600            3.0-10.6       2.9-7.3             12.0       7.5
06:1200             2.4-10.2      2.1-5.4             11.1       9.0
06:1800             1.0- 7.0      2.5-6.2              3.8       3.7
07:0000             1.5- 8.3                           4.7       3.0
07:0600            2.8- 8.9       2.6-6.5              9.9       4.6
07:1200            2.1- 9.1       2.4-6.0              8.3       5.0
07:1800             1.8- 8.3                           6.7       7.0
08:0000             1.4- 5.8                           5.7       4.7
08:0600             3.1-10.0      2.8-7.1             14.7      11.1
08:1200             2.5-10.0      3.2-8.1             10.6      10.8
cont'd



</P>
<P><PB REF="00000061.tif" SEQ="00000061" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="861" N="50">
Period Band (sec)         Maximum Wave Height (ft)
Date: Time
PNJ           PM                 PNJ      OBS
08:1800            3.1-11.4       3.0-7.5             14.6      9.6
09:0000            2.8-10.5                           12.1      6.0
09:0600            3.6                                18.5      7.2
11:1200            3.0-11.2       3.0-7.5             14.0      3.1
11:1800            2.0- 8.8       2.5-6.3              7.8      4.5
12:0000            2.2- 9.1       2.6-6.6             8.5       6.9
12:0600            3.0- 8.3                           13.0     10.3
12:1800            0.9- 4.7                            3.8
cn
25:0600            0.9- 9.1                            3.8     10.1
25:1200            3.1-10.0                           13.0
25:1800            2.8-10.4       2.8-7.1             11.6
29:0600            3.2- 9.2                           14.7      4.1
29:1200            3.7- 8.9                           21.2      7.0
29:1800            3.5- 8.6                           17.8      9.9
30:0000            3.1- 8.6                           13.8      8.7
30:0600            2.4- 9.7                            9.9      9.0
30:1200            3.1-10.3                           13.5      5.4
30:1800            1.9- 8.5       2.7-6.8              7.3      9.5
31:0000            2.9- 7.6                           10.9
31:1200            0.9- 4.6                            4.0      6.4
31:1800            2.9-10.8       3.0-7.7             12.6      4.5
cont'd



</P>
<P><PB REF="00000062.tif" SEQ="00000062" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="826" N="51">
Period Band (sec)           Maximum Wave Height (ft)
Date:Time
PNJ            PM                  PNJ       OBS
November 1965
01:0000              1.4- 7.6       2.1-5.3                5.2       3.1
01:0600              1.9- 8.5       2.4-6.2                7.3       2.7
01: 1200             1.8- 8.1       2.5-6.2                7.6       6.2
01:1800              1.7- 8.1       2.3-5.8                6.2       2.3
03:0600              2.9-10.8       3.0-7.7               12.8       5.0
03 1200              3.1-10.1                             13.3       8.8
05:0600              1.2- 7.4       2.0-5.1                4.7
05:1200              2.7- 7.8                              9.5
05:1800              1.5- 7.7       2.4-6.1                5.4       2.8
06:0000              1.7- 8.1       2.3-5.8                6.2       3.1
06:0600              1.4- 7.6       2.1-5.4                5.2       3.1



</P>
<P><PB REF="00000063.tif" SEQ="00000063" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="768" N="52">
8                        Y =. 84 +. 94X -    4   =
7                             +      +
6                             4H1/3                  + 
5                        +  /
OBS 5                  4
ft. 4                +.4./               Significant Wave Heights
4+'                 Observed vs CERC Observed
+ +          Correlation Coeffecient r =.89.,-+
3           40      I    I    I     I    I     I    I     I    l     I
I    2    3    4     5     6    7    8     9    10
Observed - CERC H113   ft.
Figure B-1.    Scatter diagram of CERC observed significant
wave heights vs. those calculated from the standard deviation
of the staff gage data.
12
~~~~10     ~~Y=x
8f    6  + /                                       +                  +
/        v *+    +                       Observed vs +MB - Bretschneider Winds
H              +/     +        +        +
1  /3     +1                                     Y I  2.55+. 35X
OBS                                       +
0       21.          6      8             12    14    16    18    20+
4                         + +  ++
+++   H                   Olserved vs SMB  - Bretschneider Winds
2                 +X4~C++     +             Correlation Coeffecient r-,60
2      4      6      8  I0        12    14    16        18    20
H/3   SMB - Bretschneider Winds   ft.
Figure B-2.    Scatter diagram of hindcast significant wave
heights calculated by the SMB (Bretschneider winds) method
vs. the observed significant wave heights.
- 52 -



</P>
<P><PB REF="00000064.tif" SEQ="00000064" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="817" N="53">
12
10 -/,   Y=X
8                             4. +
H         + +       + +
1/3      +         +           +
//|++     +                  Y= 2,90-.29X
OBS _              /   +  
ft.                                    Significant Wave Heights
4  __ +               _ + +'++       Observed vs PNJ - Jacobs Winds' +++ + t +        Correlation Coefficient, r=.35
2        +            + +
0    2    4    6    8    10   12   14   16   18   20
H 1/3   PNJ - Jacobs Winds  ft.
Figure B-3.          Scatter diagram  of hindcast significant wave
heights  calculated  by  the  PM  (Jacobs  7.5 meter winds) method
vs. the  observed  significant wave heights.
8                                 +
+                     Y=x
&mdash; _ / Y=X
446                       +
H113
OBS 5  Y=2.03+. 32X
ft. 
3                              +
Significant Wave Heights
2            /             +           a Observed vs PM - Jacobs 19. 5 m. Winds
2/                  Correlation    r =. 32
1    2    3    4    5    6    7    8    9
H113   PM - Jacobs 19. 5 m. Winds   ft.
Figure  B-4.         Scatter diagram  of hindcast significant wave
heights  calculated  by  the  PM  (Jacobs  19.5  meter winds) method
vs. the  observed  significant wave heights.
- 53


</P>
<P><PB REF="00000065.tif" SEQ="00000065" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="814" N="54">
4         +       t        Y=2.7+.63X
7/+   + 46               +       +,
1/3    5 
OBS                                 Significant Wave Heights
ft.             4.   +  Observed vs SMB - Richards Winds
4        /                      Correlation  Coeffecient r =.36
+      +
I   2    3    4   5    6    7    8   9    10
H1/3  SMB- Richards Winds  ft.
Figure B-5.          Scatter diagram  of hindcast significant wave
heights calculated by the  SMB  (Richards winds) method vs.
the observed significant wave heights.
+'
8
--     +    +                +
7                                   /    Y = 2-73 +.57X
_                     +
/      +                    O
5  +
4                4    4 
4     ++
I   2    3    4   5    6    7   8    9    10
H1/3  PNJ - Richards Winds  ft.
Figure B-6.          Scatter diagram  of hindcast significant wave
heights  calculated  by the  PNJ (Richards winds) method vs.
the  observed  significant wave heights.
- 54 -



</P>
<P><PB REF="00000066.tif" SEQ="00000066" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="806" N="55">
t
8        4/- Y:2. 32+. 68X
7 __            + +
H 113    5L _            /+          Significant Wave Heights
OBS                                  Observed vs PM - Richards Winds
ft.  4   &lt; /   +   Correlation   r. 55
4t.        +
3/         / I
I   2    3   4    5    6    7    8
H /3    PM  - Richards Winds
Figure B-7.         Scatter diagram of hindcast significant
wave heights  calculated by the  PM  (Richards winds) method
vs. the observed  significant wave heights.
9
tt e    -Y=X
8                                      /
+ t
7                    + i              +           +
+6:~,  e            Y =2.55 +.59X,t
H 113 5                                 +
OBS 
ft    4
3     /                  + 
Significant  Wave Heights
$/x +         Observed vs SMB - Measured Winds
2                           Correlation  Coeffecient r =. 62
0   1    2    3    4   5    6    7   8    9    10  11
H 113   SMB- Measured Winds  ft.
Figure B-8.          Scatter  diagram of hindcast significant wave
heights calculated by the SMB (measured winds) method vs.
the observed significant wave heights.
- 55 -



</P>
<P><PB REF="00000067.tif" SEQ="00000067" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="830" N="56">
8          +
7               +                  + / ~-+
+
6  +
H 1/         +                +
OBS                              +     Significant Wave Heights
OBS 4                             Observed vs PNJ - Measured Winds
ft.           +            +.         Correlation  r =.47
0    1    2   3    4    5   6    7    8   9    10
H1/3  PNJ - Measured Winds
Figure B-9.         Scatter diagram of hindcast significant wave
heights calculated by the PNJ (measured winds) method vs.
the observed significant wave heights.
Y =X
6                1
Y=4. 02+. 13X
5
4                           +
H 11                 /Significant fVave Heights
H1I3            t    /   t          Observed vs PM - Measured  /inds
OBS    3                        +    Correlation  r=. 34
ft.
1   2     3   4   5   6    7    8   9    10
H,,:   PM - Measured Winds   ft.
Figure B-10.    Scatter diagram  of hindcast significant
wave heights calculated by the PM (measured winds) method
vs. the observed significant wave heights.
- 56


</P>
<P><PB REF="00000068.tif" SEQ="00000068" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="813" N="57">
8                                           /    =
O*+_t+Y = 4. 90+.11 X
OBS                              +      +
Sec.              +       ++
4                   X    i+  ++
Wave Periods
Observed VS SMB- Bretschneider
2 _/Correlation  r =.20
1    2    3    4     5    6    7     8    9    10   11   12
Tsig.  SMB - Bretschneider  Sec.
Figure B-ll.   Scatter diagram of hindcast significant period
calculated by the SMB (Bretschneider winds) method vs. the
observed period of maximum energy.
8                                                Y=X
~~~7                                    4+~
6  L+               1 t+* t-t + +~ /+                    4
T+ ~      + +e +
Tm            Y = 5.02 +.05X     
OBS                                  ++ +  + +       +    +
Sec.                          /                +    +
4                     /++       t
3                                                    *
Wave Periods
CERC - Observed vs PNJ - Jacobs Winds
2                            Correlation  r =. 11
0     I    I     I    I  I       I    I    I    I       I    I  1
1    2    3    4     5    6    7    8     9    10   11   12
T   PNJ - Jacobs Winds  Sec.
m
Figure B-12.   Scatter diagram of hindcast period of maximum energy calculated by the PNJ (Jacobs' 7.5 meter winds)
method vs. the observed period of maximum energy.
- 57


</P>
<P><PB REF="00000069.tif" SEQ="00000069" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="795" N="58">
Y =X
8
T                                           +             3. 15/  +  31 
OBS  5
4                             *          +
I     /
Wave Periods
Observed VS PM - jacobs 19 5 n. Winds
2                                          Correlation  r =, 31
I    2    3     4     5    6     7     8    9     10   I 1   12
T1  PM  -Jacobs  19. 5 vn. Ninds    Sec.
Figure B-13.   Scatter diagram of hindcast period of maximum energy calculated by the PM (Jacobs' 19.5 meter winds)
method vs. the observed period of maximum energy.
Y =X
7  /+ = 0   08+.51X
7s                 it t t~+  +   + +
6 
Sec.                      +
-  / ~~+  /  Observed vs SMB - Richards Winds
/     +       Correlation r =.40
1  2    3    4      5    6     7    3     9    10   11     12
T   SVIB - Richards  Vinds    Sec.
Figure B-14.   Scatter diagram of hindcast significant
period calculated by the SMB (Richards' winds) method vs.
the observed periods of maximum energy.
58 -



</P>
<P><PB REF="00000070.tif" SEQ="00000070" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="808" N="59">
~~m~~~~~~~                   t 
t+      +
6                     +:            4, 18 +25 x
OBS    -,
sec 
4t+
Wave Periods
Observed vs PNJ - Richards Winds
2          /                       Correlation   r= 37.1   2    3    4    5    6    7    8    9   10   II   12
Tm  PNJ - Richards Ninds   sec
Figure  B-15.         Scatter  diagram  of hindcast  of period  of
maximum  energy  calculated by  the  PNJ  (Richards   winds)
method  vs.  the  observed  period  of maximum  energy.
8,                                        Y = X
7
T                           +
Tm  5           +    1 + $/+  +
6     
Iss.                                            1
OBS,                       /  
sec.  4,
-Wave  Periods
3                /                 Observed vs PM - Richards Winds
Correlation  r.17
2
O   2  3  4    5    6    7   8    9    10   11   12
Tn  PA - Richards Winds   sec
Figure  B-16.         Scatter  diagram  of hindcast of period  of
maximum  energy  calculated by  the  PM  (Richards winds)
method vs. the observed period of maximum energy.
- 59


</P>
<P><PB REF="00000071.tif" SEQ="00000071" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="814" N="60">
8
~~~7  -~~~~~~~~                   2 64 t.54X
6                     +        +
Tm                     t,    4.+  +
OBS    5   _                     +
sec
4
Nave Periods
Observed vs SMB - Measured Winds
3                             Correlation r =.67
2
I   2    3    4   5    6   7    8    9   i    I 1  12
T  SMB - Measured Winds   sec
m
Figure B-17.        Scatter diagram  of hindcast significant
wave period  calculated by the  SMB  (measured winds)
method vs. the observed period of maximum  energy.
6                              +         Y+  = 4. / &mdash; 4.o08 +.26 X
i'  ++
OBS
sec
/   Vave Periods
Observed vs PNJ - MVeasured Winds
3 _          /                  Correlation  r =.51
I   2    3   4    5    6   7    8    9   10   11  12
Tm    PNJ - Measured Winds   sec
Figure B-18.    Scatter diagram of hindcast wave period of
maximum energy calculated by the PNJ (measured winds) method
vs. the observed period  of maximum  energy.
- 60 -



</P>
<P><PB REF="00000072.tif" SEQ="00000072" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="828" N="61">
8                                                /Y =X
7                                               +
6
o    +   /Y /3       3.47 +.31 X
T     5                                                      +
OBS
sec   4
Wave Periods
Observed vs PM - Measured Winds
3                   /                   Correlation  r I.64
1     2     3     4   X   5   6-    7     8     9     10    11    12
T   PM - Measured Winds  sec.
Figure B-19.    Scatter diagram  of hindcast wave period of maximum energy calculated by the  PM  (measured winds) method vs.
the observed period of maximum energy.
- 61


</P>
<P><PB REF="00000073.tif" SEQ="00000073" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="813" N="62">
12            OBS                                      PNJ
Frequency of
Occurrence
10 
iA
8                              |\                            Significant Wave Heights
\                              Frequency of Occurrence
I il\                                       OBS, SMB, PNJ
| | I   \    /\  ~   \'/  |       \         Selected Dates Sept- Nov, 1965
6                                                            Muskegon Tower
oL  I  I  I   I      I   I   I I IA\  SM B
2 
0           I 
I   2   3   4   5   6   7   8   9   10  II  12  13  14  15
H 1 3    Classes
Figure B-20. Frequency distribution of significant wave heights as calculated by
the SMB-Bretschneider wind method and the PNJ-Jacobs 7.5 meter wind method and as
observed by the staff wave gage.



</P>
<P><PB REF="00000074.tif" SEQ="00000074" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="870" N="63">
APPENDIX C
1965 WAVE DATA FOR POINT BETSIE
AND PORT HURON, MICHIGAN
- 63 -



</P>
<P><PB REF="00000075.tif" SEQ="00000075" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="832" N="64">
TABLE C - 1
SIGNIFICANT WAVE HEIGHTS AND PERIODS
FOR 1965 WAVE HINDCAST TIMES
Point Betsie, Michigan
SMB Wave Hindcasts
Date: Time               Significant                        Significant
C.S.T.                  Wave Height (ft)                   Wave Period (sec)
28:0600                  3.4                                 4.5
28:1200                  5.3                                 6 o 2
October, 1965
23:1200                  6.2                                 5 o8
23:1800                 19.0                                 9,9
24:0000                  6.2                                 6.7
24:0600                  8.4                                 7 2
24:1200                  3.1                                 5 o 0
24:1800                  4.1                                 5 o 4
25:0000                  7.0                                 6.5
25:1200                  4.7                                 5 5
November, 1965
01: 0000                 40                                  4.80  4
01:0600                  6.4                                 6.4
01:1800                  1o9                                 4,2
05:0600                  5.3                                 5 c5
05:1200                  8.0                                 7.0
05:1800                  5.0                                 507
06. 0000                 2.8                                 4 o5
- 64 -



</P>
<P><PB REF="00000076.tif" SEQ="00000076" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="876" N="65">
TABLE C - 2
SIGNIFICANT WAVE HEIGHTS AND PERIODS
FOR 1965 WAVE HINDCAST TIMES
Port Huron, Michigan
SMB Wave Hindcasts
Date: Time               Significant                   Significant
Wave Heights (ft)            Wave Periods (sec)
October, 1965
23:1200                    4.2                           4.8
28:1800                    6.0                           6.2
24:0000                    7.5                           7.0
24:1200                   13.5                           9.3
- 65 -



</P>
<P><PB REF="00000077.tif" SEQ="00000077" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="879" N="66">
APPENDIX  D
COMPARISON OF 1964 WAVE DATA
AT MUSKEGON, MICHIGAN
- 66 -



</P>
<P><PB REF="00000078.tif" SEQ="00000078" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="870" N="67">
TABLE D-1
COMPARISON OF SMB, PNJ, PM AND OBS WAVE
DATA FOR 1964 HINDCAST PERIODS
Muskegon Research Tower
SMB = SMB Wave Hindcasts with Bretschneider Winds
PNJC PM and OBS are taken from Jacobs (1965)
Significant Wave Height                            Period  of Maximum Energy
Date:Time    Sea      SMB     PNJ     PM      OBS          SMB      PNJ     PM     OBS
C.S.T.
August, 1964
01:0600    FD      5.2      3.8     4.7                  5.3     6.1      6.0
01:1200    FD      5.5      4.5     5.3                  6.4     6.5      6.4
01:1800    FD      4.9      3.2     4.1                  6.2      5.7     5.6
02:0600    FD      3.2      2.7     4.1                  5.1      5.3     5.6
02:1200    FD      4.5      3.2     4.7                  5.5      5.7     6.0
02:1800            5.6                                   6.3
02:1926    Sw               3.2     4.7    1.6                    5.7     6.0    4.2
07:0600            4.1                                   5.0
07:0726    Sw               3.2     4.1    2.2                    5.7     5.6    4.6
07:1200    FD      4.7      3.8     4.7                  5.8     6.1      6.0
07:1736    FD               3.8     4.7    1.7                   6.1      6.0    4.6
07:1800            2.6                                   4.8
10:1200            3.2                                   4.4



</P>
<P><PB REF="00000079.tif" SEQ="00000079" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="823" N="68">
Significant Wave Height                    Period of Maximum Energy
Date:Time      Sea      SMB     PNJ     PM      OBS          SMB      PNJ     PM     OBS
C.S.T.
10:1330      Sw               3o2     4.1    1.9                    5.7     5.6    3.8
10:1530      Sw               3.2     4.1    2.0                    5.7     5.6    4.2
10:1800              5.1                                   5.9
10:1950      Sw               3.0     4.0    1.7                    5.7     5.6    5.0
11:0000              7.4                                   7.0
September, 1964
13:0000              0        0       0      0
13:0600      FD      2.5      1.2     1.6    0             3.8     3.8      3.5
13:1200      FD      3.7      2.2     3.1    1.8           5.3     4.8      4.9
00   13: 1800      FD               1.8     3.1    1.6                   4.4      4.9
14:0000      FD      2.7      3.2     4.1    2.7           4.3      5.3     5.6
14:0600      FD      4~5      4.5     5.3    3.2           5.4      6.5     6.4
20:1200      FL      3.4      2.8             0.6          4.4      5.5
20:1800      FL      4.3      2.8             0.8          5.4      5.9
21:0000      FL       2.6     3.0             2.0          4.8      5.0
21:0100                                                                            4.8
21:0300                                       3.8
21:0500                                                                            5.6
21:0600      FD      2.9      3.8     4.7                  4.4      6.1     6.0
21:0900                                       1.4                                  4.8
23:0000      FL      6.6      0.9             0.6          5.9      2.5
23:0300                                       0.9
23:0600      DL       7 7     2.8             2.8          6.3      4.0
23:0700                                                                            5.7
23:0900                                       6.6
23:1100                                                                             7.0



</P>
<P><PB REF="00000080.tif" SEQ="00000080" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="841" N="69">
Significant Wave Height                     Period Of Maximum Energy
Date: Time     Sea      SMB     PNJ      PM     OBS           SMB     PNJ      PM     OBS
C o ST o
23: 1200     DL       4.8     5 7             6.3           5.2     7.0
23:1500                                                             6.5             7.8
23:1800      FL       9,0     9.0             7.5           7.5     6.0
23:1900                                                             6.4             8.2
23:2000                                                             6.8             8.3
23:2100                                       8.7                   7.3             8.6
23:2200                                                             7.7             8.7
23:2300                                                             8.1             8.9
24:0000      FL       4.7     9.0                           5.8     8.5             8.9
i



</P>
<P><PB REF="00000081.tif" SEQ="00000081" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="885" N="70">
APPENDIX E
SUCCESSIVE APPROXIMATION TECHNIQUE
FOR ANALYSIS OF PRESSURE AND WIND FIELDS
- 70


</P>
<P><PB REF="00000082.tif" SEQ="00000082" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="887" N="71">
APPENDIX E
Successive Approximation Technique for
Pressure and Geostrophic Wind Analysis
Introduction
The successive approximateion technique, hereafter called
SAT, is an objective analysis method of computing data at the points
of a regularly arranged grid from measurements taken at irregularly
spaced locations. Figure E-1 illustrates the grid and the location
of weather stations used in the analysis.  The gridpoint array is
18 x 17 (306 gridpoints) with a 75 km ( ^ 40 n. mi.) spacing.  For
geostrophic wind calculations, the grid system reduces to 16 x 15
(240 gridpoints) while the gradient wind calculations further reduce it to 14 x 13 (182 gridpoints). The grid array has been made
large enough so that truncation does not affect the Great Lakes region. Reliable sealevel pressure analyses and geostrophic wind
analyses have been made while curvature analyses and gradient wind
analyses have been produced that show discrepancies when compared
with hand analyses or measured values.
The Analysis Method
For purposes of explanation, consider the pressure analysis
for the area shown in Figure E-lo The SAT consists essentially of
a method of successively correcting grid-point pressures using reported data. Smoothing is accomplished by the calculation of a
mean correction for each scan as well as by the introduction of
smoothing operationso
The First Guess Pressure Field
The SAT starts with a first guess grid-point pressure analysis,  The first guess used for this analysis was obtained by advection of the pressure analysis of 6 hours earlier by 50% of the
500 mb wind. For the area under consideration, the Green Bay, Wisconsin, 500 mb wind was used in most cases. If no previous computer analysis existed, a hand analysis of the previous map was produced and advected for use as the first guess 
- 71


</P>
<P><PB REF="00000083.tif" SEQ="00000083" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="357" N="72">
XL/
OQ                                 QN
yU~~~~~~5
83,
vi~~~~~~~~~~~~~~~~~~~~~~~~~
~. o~....   ~i,,, -.,f                 \    I, _
WR                TS I    Ir
l~~~~~~'~'i~"a;~'"~.~:.00,~~~cC
74                    *''
9B  Y
GI  G     PKF             0l-                             7 30( 7~31
741  RHI         IT E
EjU~J -AZ_                                               Q...
646    G6396
t ~ ~ ~ ~    I ~~~~~~~I           I   II ~~~~~~~~~OSTE                 ost
64   \IS            osH 64               GANN
~""' ~ i
~~~.
34
TAX            MKH                                OAS
FODLNR    641                          GRR          T    G
K)D                9 ~~~~~~~~~641                Aft     e
65 0                             52
&mdash; ~~~~~~3    539
AZIO BTI    5    7t  s
DSA I~~~~~~~ ORD -              0              NFB                T1 1Y~2  B F"
~~
Li  JC)Tn 5  W 5SH ~  ~     ~    ~        \\
544                      ~~~~~~~~~~~~~~~~~~~~~~~~~~.5!~~~~~~~~
10                       IT I           MFD           M
43P      HUF           0  z~~`~~
Figure E-1.    The analysis grid  and the  locations of data  sources for the  Successv
Approximation Technique.



</P>
<P><PB REF="00000084.tif" SEQ="00000084" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="884" N="73">
The First Scan
For the first scan or iterative correction process, all
pressure measurements within 4.75 grid lengths of each grid point
were used to correct the grid point pressure.  The amount of
correction contributed by any measured station pressure is weighted inversely to its distance from the grid point. Specifically,
the following procedures were followed for the first scan.
a. All weather stations within a radius of 4.75 grid lengths
of the grid point being considered were identified.
b. For each of these stations the interpolated station
pressure was calculated by bilinear interpolation from
the first guess pressure field. The difference between the interpolated and measured station pressure is
the error of the first guess field at the station location.
ER  P           - P
measured    interpolated
c.  A weight function for each weather station within the
4.75 grid length radius of the grid point in question
was calculated.
2 _ d2
WT      2    2
N + d
where N  = scanning radius
d = distance from grid point to station.
Note that the WT is unity for a station on a
grid point and is zero for a station one scanning radius from the grid point. The weight was
zero for all stations outside of the scanning
radius.
do The correction applied to the grid point wasWT * ER
correction  =             ER
Z stations
- 73 -



</P>
<P><PB REF="00000085.tif" SEQ="00000085" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="874" N="74">
where Z stations  =  the total number of stations contributing to the correction. Thus the correction was a
mean value of weighted errors.
Scans Two and Three
Scans two and three followed the same procedure as scan one
except the scanning radius, N, was decreased to 3.60 and 2.25 grid
lengths respectively. The results of each previous scan were used
as the input pressure fields. By reducing the radius of influence,
the measured data closer to each grid point more strongly influenced
the correction for the grid point.
The First Smoothing
To suppress calculation instabilities, the grid point
pressures were smoothed between scans three and four and after scan
four. Interior grid points were smoothed by the following five
point smoother. Where
+P1
+P2    +P      +P4
+P3
1      2
Smoothed p0  =  p0  +              P1
0  0          8          0
4 * P0 + P1+ P2 + P3 + P4
8
For perimeter grid points, the following smoothing was
used:
+P1
P     P P2          or           +P2
+    +    +
+P2
- 74


</P>
<P><PB REF="00000086.tif" SEQ="00000086" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="864" N="75">
2 * p0 + P1 + P2
Smoothed p0  =
The corner grid points were not smoothed.
The Fourth Scan
The technique of scan one was used for scan four with the
scanning radius  = 1.5 grid lengths and the correction given by:
Z WT * ER
correction  =               -
Z WT
The Second Smoothinq
The second smoothing was done the same as the first and the
resultant smoothed pressure values constituted the pressure analysis
according to the successive approximation technique.
The Geostrophic Wind Field
The u and v components of the geostrophic wind at each
grid point were calculated from standard meteorological equations
in centered finite difference form.
I    Pl - P3
0  p f   Y  - Y3
1    P4   P2
p f   x4 - x2
where  f  =  the Coriolis parameter
p  =  the density
+Pl
+P2     +P0    +P4
+P3
- 75


</P>
<P><PB REF="00000087.tif" SEQ="00000087" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="859" N="76">
The magnitude and direction of the geostrophic wind relative
to the grid were calculated from the following equation:
2    2
I:Vgeol =/  u  + v
Direction = 3 = arctan u/v  where 3 = the meteorological
definition of wind direction, i.e. the direction from which the
wind is blowing.
The Radius of Curvature of the Wind Field
The curvature of the wind field is required in order to compute the gradient wind or the Bretschneider wind. The radius of
curvature, R, was computed directly from the geostrophic wind direction by considering the change of wind direction between grid
points.
a+2      0        4s
Ax
K- 1~ da dx   Ha dy
R   ds   ax ds   ay ds
K        ~  )    *  cos a  +    )   s in  a
o    AX o             o    AY o         0
a4    2  *  cos ac   +   1      * sin  a
2L              o       2L             o
where:
K = the curvature of the streamlines, which is a
good approximation to  the trajectory curvature
R  =  radius of curvature
a  =  angle of the wind vector, measured clockwise
from the positive x axis



</P>
<P><PB REF="00000088.tif" SEQ="00000088" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="876" N="77">
=  37T/2 - f radians
s = distance along a steamline
L = grid spacing
The Gradient Wind Field
With the geostrophic wind and the radius of curvature computed for the grid points, the gradient wind was computed from
standard meteorological equations.
V  fR       f   for cyclonic
V2  +J V+ fRV
g      2    A      4            geo                    curvature
/ 22
fR  -.  f R    - fRV                      for anticyclonic
geo
g      2      /     4                                   curvature
The SAT pressure analysis described above and the geostrophic
and gradient wind calculations were made from input pressure values
at 114 weather stations, Bilinear interpolation provided pressure
and wind at any location in the region. For evaluation of the technique, 47 winds at shoreline locations plus pressure and wind data
from five ships per lake were entered into the computer but withheld from the analysis. The program compared these reports with the
computed values and listed input values, computed values and the
errors between them.
The output can be varied depending on use.  One map output,
a portion of which is shown in Figure E-2 lists the pressure, geostrophic wind, curvature and gradient wind at each interior grid
point. In addition, it lists the input station pressures, the shoreline station winds, the ship weather reports, computed values of all
parameters and errors, The overlake atmospheric stability, Tlake 
Tair  is listed and averaged for each lake,
The input pressure can be listed as shown in Figure E-3 and
the calculated gridpoint pressures as in Figure E-4. Contouring of
the pressure field as shown by Figure E-5 is also possible but
rather costly in time.
- 77 -



</P>
<P><PB REF="00000089.tif" SEQ="00000089" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="493" N="78">
*+**********************************************************+******+***~****+**********
*                         I                              I                            I                              I                            *
*                                                        I                            I                              I                            *
*                        (88)                           (87)                         (86)                           (85)                          *
*                                                                                                                                                 *
*                                                                                                      *****                                      i,*                                                                                                  *      *******                         (46) &mdash;*
*r~~~ ~           (88)                            (87)                         (86)                 * ********(851(46-*
* &mdash;4461                                                                                            *               **                             *
*                                                                                  **     *8**   *                     *                          *
*                                                                                       8**  *  *8*                     8*                        *
4                           **8   *8    *8    *                                                                           *88                    -
*                                                                      8   **     *                                          (                    *
*                                                       8            *   *8                                           8++*                        *
*,        150                   129                   8106   *          *    093                    080                *                          *
*          +                     +            ESC &mdash;X*   +*  *      *  -                              +                ** 
*        35/47                 00/60         (MMM)* 03/56*        *         00/36                  01/33            **   PLN                      *
8                                           (MM/MM)              ** *                                             *       X                       *
*                                                                                 * *                             *    (070)                      *
*4 ~~~~~~~ *                                                                                          *   (26/20)                     i
*                                              *                                                                  *                               *
*                              MICH           *                                                                       **                          *
/ )4(CH*.*                            *
*                          w/S               8.                                                              ***  ****                            *
*                          (*                         ***                                                          *                              *
*      048                    126    *              099                   090                    077  *                                        *
*          +                     +    *              *,         +                     *+   * ~
*       00/58                  35/66 *             * 35/49                  33/34                  31/28 * 
4 HNH~~~~MN ------ X* *++    
*                        NM                     *8* *8.* 8*                                                                                       *
4  *        +    *                                          *  *      *                                 1~~~~~~~~~~~~~~~~~~~~~~45)-*+
*.                               *     8    8                                         *     *    *                 *4**  
*-(453                              *        *    *                                             *  *    *                                         *
*                                    8      *    *.*   888*                            *                                          *
*                            *8      8$          8*                                *              *  *8                                          - 
*                           8       8  t*  *,*                                     *             **         148              *    130         *8         113                   105***                 095                                           *
*          *                                  *0 +      +                     X &mdash;---&mdash; PTB            +                                            8
8        35/54          8      34/54                 30/53                  29/55                  27/62                                          *
*                       *       *8         *                                  *                      X &mdash;&mdash; TVC                                     8
8                 08*  *  888*            *                                    *                         (096)                                    *
*                  0   8*8               8                                     *                        (25/15)                                   *
7!I42(                    *                                    *                                                                   *
*              (27/9(                   *                                     *
*                                     *....
~~~~~~~~~~~~~~~~~~~~~44-*
4~~~~~ *                                                              r
8          88                          8+*  +                                                                                                     *
159                   151                    143                   142                    137UIVRIT   F  IHIA
+                          * +  *                +          X......PT
*        34/46                 30/42*8                28/47        0         28/52                 27/58                                          *
*       ---   -------                                                   * -
*                                  8R                                 *                                044- *
*                               * 8                                                                                    (85) 
*                                                                                                                      P *  *CT  U      0
*                              8                                        8 (1::
*                             *                                                                                          8  ***8888*****~**~*
8                9                                                     *                         3 2
8         159                   151                    143             8    142                     137          *   UN(E*SNTY OP C(L8(0*E    8,*         +-.~+                + ~                                          X-+    * &mdash;-            +P  EFE ENTC                       F  ++     *
32/30                     30/34                 29/34                  28/29                 27/30 *9ETEOROLOOV *80 4           CEANON RAPGYW
3/2*                                   *  28/5
*                             8                                        8                                         8       WAVE...0..X*(80         *
*-(43)~~~~ ~~ 143I &mdash;*. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~DT &mdash;-034 ~OV1*6
* *                                                                     *                                        *    PROJECT NUMBER06768    8
3* 8r,                                                            8          -*                            * x 
*                            *                                           *                                       _**8***8************************
8                          8                                              8                                      *    OEOST*0P8(C 8(80 880    8
8                         8                                               *                                      8    PRESSURE CALCULATWIN        8
*         175            *      159                    1 153                  48                    144          *    GRI=30 NAUTCAL MILES   *
8       +              8       +                                                *. &mdash;----..G  +       *   REFERMENCE 1016 85    (0    8.
3/25                      30/25                 29/ 298/3             29/26       (149)      30/27         *   PORDT4EG.N   870EA.G 
8                          *                                                  8       (27/15)                 HDAN *
*-(43)                    8                                                    8                           (43( &mdash;*                                8
8                          *                                                    8                                8      OATE &mdash;-03 808,0965        8
8                       MKI                                                     8                1*8             8      T(ME &mdash;-18010(2400Z9   2
8                         08                                                     M &mdash;G &mdash;1 &mdash;-9 0                   *                                8
*                      (165)                                                     8              (149)            *    STA   PRESS    W(ND         8
8                     (26/20)                                                    8             (26/20)           888888*8888888*8,******8*8***8
RAC                                                                       8~* **  ESTC  -1.8N  MNM/M 
8         072                3  165                    162                   159*   0               154          *    GR0   1014.2   27/15    *
*                  +        *   +           ~                                + *...MKEL   1016.5   26/20 *
*        31/27             *   29/28                  28/31                 28/36                  28/36         8    8*0   1018.2   26/18        8
8                            *                                                  *                                6    088   1018.7   25/15 1
81 8(5                         *                                                          *    08*   1014.9   26/20 8
8                            8 &mdash;---&mdash; *                                           8                               6    MEG   1014.9   27/15 1
1*                     I       77* 8*                                                                              / TVC   1009.6   2515    *
8                            8                                                 *                                 *    PIN   1007.0   26/20    8
4  r                                              *                                 ~~~~~~~~~~~~~~~~~~~~~~****************+**************
* _*                                                                          8                                  8    (4    1012.8                8; *                                                                          8                                   8    PEP    1019.1               *
8      _180                   8 177                    175                  *j74                    169.    *    068   1021.8                 8
8          +                  8 *                       8                  8 K: G     R              *            1017.9              8
*        29/33                 28/33                  27/43               * 28/41                  28/42         *    LNR    1018.9 
888~~* 6 &mdash;----                                                                                                 MXN   1017.9 
8                     0*0.    8                                       8                                        8      * DB    1020.5 
*-(42)                                                                *                                   (42) &mdash;*    RFD   1018.6                 8
84~~ ~(182)                  8                                     1                                        8    P(A   1021.5 N
8*~~ ~(26/10)                *                                                                                    RA *  *8    1021.7         8
8                                  8                                8                                            8    LAF   1022.8                *
*                                                                 8A                                            8   -8HL   1022.3 *
8       7              1GX0 &mdash;-&mdash; 1X                             *    CH                                        *    FWA    1020.6               8
8                                                    888 &mdash;------&mdash; ~                                      *    TOL   1019.1               *
*      195                    189 (8                194***8       NO    0 188                    184           *    JXN   1016.3               8
8          +                         ( I  *           *+                  /                          +           8    FNT   0014.2                *
*        27/63                 27/36    *8          *27/76               /  28/43                  28/42         *    HTL   1011.4                *
84                          ~I      *****G                 S*N  /                                         *           1009.8 /
8                                    I           0              (187) &mdash;                                          *    APG   1007.2                *
* ILL I IND                                                    (25/15)                                           *    SSM   1008.5 *
I~~~~~~~
*                                    I                                                                                           *  10286
4~~~~~~~~~~~~~~~ * PK &mdash; ~  
* (88).17                                                1                      *.  (8)  *
8     ~          ~~~ (                                                             (                        * T8  UW11.
* OR                              D,                                 *                                          *   OBO  1020.5 *
*8t******++** *88*888***8*8888**8888***8**88*8*88888***  8*888***88*8*8*8
Figure E-2.   A portion of the Successive Approximation
Technique map output.
- 78



</P>
<P><PB REF="00000090.tif" SEQ="00000090" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="713" N="79">
21 SEP,1965   1800C(2400Z)                                                  LH*500                                                                        50C  MB WIND= 24"/55
PLO*500
MO0123
+  +  4-  +  4-     +      +      4-     +      +      +      +      4-            4-  +                +
WG4*051                                             YW*078
QK*C66          XL*070                            QN*081
4-    +      +             +      +      +      +      +      +      +      +      4-     +      4             +
JB*094
+    +      +      4     + VJ*046   +          +      +      +     +       +      +YU*101    +         +      +     +
I NL*C 32
GFK* 54 4             +      +      +      +      +      +      +      +      + WR*077   +         +      +TS'096    +         +
QT*036                                                                        V0O085
6JI*C27        +      +      +      +      +      +      +      +      +            +  +    +      +      +      +      +
HIB*008                                                                                   XR*081
FAR*C66
+  +      +             +      +      +CMX*034   +         4      +      +      +      +      +      +      +      +
DLH*014                                                                                                           MW*1~4
+     +      4      +      +      +      +   ++MQT*049   +           +      +      +      +      SB*103  YB*107   +
AXN*344                                                                       SSM*088
PKF*010
+STC*-029   +       +      +      +      +      + ESC*057 +          +      +      +ZE*094    +         +      +      +   XI*111
PLN*087
+      MSP*044    +         +      +      +      +      +      +      +     +       -+     +     +       +      +     +'..,                              Kw~~lc:~R.F* 65            EAU*051    AUW*043                                        APN*095                        QA*121
to ~~~~5) ~~~~~~~~~~~~~~~~~TVC*090                                                                                      VV*12"
+    +      +      +      +      +      + GRB*068 +          +      +      +OSC*.117   +        +      +      + 
RST.076                                                   HTL*107                                              TR*149
LSE*078                                                                       MN*5CO
4 +    +      +      +      +     +       +      +      +4     +                                 +    +  +YZ*144   +
SPC*?78
MCW*C94                LNR.066                                         MBS*500           CE*142                      ROC*175
+      +      +      +      +    MSN*O075        +      +MKG*107   +         +      +     +    XU* 150+        +4BUF*163
MKE*095         GRR*120         FNT*131                  OC.158
ALO*095
+     +       +      + 0BQ*092  +        +       +     +       +      +      +   DET*138+        +      +       +      +
RFD*088                             JXN*127
CID*106                      ORD*112                                                    ERI*171
DSM*112    +         +      +      +      +      +      +      +      +      +     4-     +      +      +       +      +
MLI*094                          SBN*131              TOL*146                    YNG
OTM*118                                                                           CLE*166. 188   OUJ*209
4+                  +      +      +      + 4  +  +     +                                  + +  +  +  +  + + +      +  + PSB*22C
LMN*111                                                              FWA*152  FDY*161              CAK*185
PIA*119                          BHL                                       PIT*20C
+      IRK*114    +         +     +      +       + LAF*152 4153 +            +     +      +      +      +       +     +A00'212
RAN*1l27                                              ZZV
UIN*IC?                                                             CMH*178   *194
MKC*118+        +      +      +      +SPI*125  +          +      +IND*167   + DAY*170 + +           4      +      + MGW*2n7 +   MRB*202
CBI1115                                   HUF*158                                       PKB*191
VLA*141                             CVG*174
STL*133                                                                              EKN*225
Figure E-3.   Computer listing of input pressures for the Successive Approximation
Technique analysis.



</P>
<P><PB REF="00000091.tif" SEQ="00000091" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="739" N="80">
21 SEP,1965  1800C(24001)
01    02    03    04    05    06    07    08    09    10    11    12    13    14    15    16    17    18
17* *  +       +     +     +      +     +     +      +     +     +      4     4     +      +     +     +      +     +  *417
58    68    13    75    78    80    82    83    86    92  101   108  112   114   115  117  116   110
16* *  +       +     4     +      4     +     +      4     +     4      4     4     +      +     +     4      4     4  4*16
61    64    63    62    63    63    68    75    77    82    92   100   106  107  105   104  105  101
15*4-   +      +     +     +      +     +     4      +     +     +      4     +     +      + +  +  +  +                 * 415
58    53    44    41    45    46    52    62    68    75    84    92    99   102  100    96    96    93
144-    +      +     + 4    +     4     4     +      4     4     4      4     4     4      4     4     +      4     4  * 414
48    39    30    28    34    34    39    49    62    71    78    84    91    96    95    89    88    87
13*4   4      4      +     4      4     4     4      4           + 4          +     4      4     +     4      4     +  *4*13
35    23    15    17    26    27    33    43    56    67    74    79    83    87    86    83    84    86
12* *  +       +     +     +      +     +     +      +     +     +      +     +     +      +     +     +      +     +  * *12
32    17    11    11    17   20    27    38    52    64    74    81    80    84    91    91    92    93
11*4-   +      +     +     +      +     +     +      +     +     +      +     +     +      +     +     +      +     +
36    25    19    15      9     9    21    36    52    68    81    86    87    90   100   105   106  103
10*4 *+        +     +     +      +     +     +      +     +     +      +     +     +      +     +      +     +     4    *4-10
42    31    29    27    18    16    25    42    56    71    84    89    91    96   107   112   112'111
09*4-   4      4     +      +     4     +      4     4     4      +     4     4      4     4     4      +     4+    +  *409
57    44    43    44    42    38    43    56    66    78    89    95    98   104   113   116   119   124
08* *  +       +     +      +     +     +      +     +     +      +     +     +      +     +     +      +     +     +  * *08
73    69    67    66    63    54    57    69    78    87    98  107  112   117  123  126  130   138
0
07*4-   +      +     +      +     +     +      +     +      +     +     +     +      +     +     +      +     +      4+  *-07
81    88    87    83    74    63    67    79    89    97   107  116  122   127   134  138   143   151
06*4-   +      +     +     +      +     +      +     +     +  - +       +     +      +     +     +      +     +     +  *4-06
90    95    93    89    80    73    78    90   100   109   117   123  129   135   145   152   158   164
054-4   +                            +     +      +     +     +      + +  4  4  4  4  4    4     4      4     +     +    *05
103   102   100    97    90    85    89   102   112   119   124   129   136   144   156   164   171   181
04*      +     +     +      +     +     +      +     +     +      +     +     +      +     +     +      +     +      +  4-4-04
110  110   109  105    96    92    99   113  123  130   134   138  146   155   165  177  188   199
03*4-   +      +     +      +     +     +      +     +     +      +     +     +      *     +     +      +     +      +    *4-03
112   115   115   111   108   107   112   123   135   143   148   152   158   165   176   189   200   209
024-4   +      +     +      +     +     +      +     +     +      +     +     +      +     +     +      +     +      +  4-402
112   118   112   10'8  117   119   121   132- 147   156  160   164  169   178  188   196  204  210
0144           +     +     +      +     +      +     +     +      +     +     +      +     +     +      +     +      +  401
108   111   114   113  120  126   131  143   157  166   167   169  176   185  192  199  206   209
01    02    03    04    05    06    07    08    09    10    11    12    13    14    15    16    17    18
Figure E-4.   Gridpoint pressures as calculated by the Successive Approximation
Technique.



</P>
<P><PB REF="00000092.tif" SEQ="00000092" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="862" N="81">
21 SEP, 1965  1800C(24002Z)
01   02   03   04   05   06   07   08   09   10   11   12   13   14   15   16   17   18
5               *    *    *    *    *    *    *                                                  11
17* *   666666                      8888888888888888888         00000000                                   * -*17
6666666666                            88888888888        00000000                           000
666666666666666666666666                     8888888       0000000000000000000000000000000
16* *  66666666666666666666666666666666                 8888888       0000000000000000000000000000000  * *16
666666                         6666666              88888        0000000000000000000000000
444444                6666666          88888          00000000000000
15* *          4444444444444444444444          6666666        888888           00000000                    * *15
444444          444444444444         666666       8888888
4444444                      4444444       66666       88888888                            8888
14* *  44444       2222222                44444    66666          88888888                  88888888888  * *14
44       22222222222                44444    66666          888888888            88888888888888
22222  22222222222222          4444    666666           8888888888  8888888888888888888
13* *      2222           22222222222         4444    666666            88888888888888888888888888888  * *13
2222              222222222222       4444    66666           888888888888888888888888888888
222                 22222222222       444    66666          8888888888888888888888888888
12* *   222                          222222    4444    6666           888888888888888                      * *12
222                          2222    4444    6666        888888888888888
22222                         2222    444   6666    8888888888888888              0000000000
11* *      2222222           0000000     222    444   666    888888888888888          0000000000000000  * *11
2222222222                  2222   444    666    8888888888888           00000000000000000
4    222222222222               222    444   666    888888888888            000000000000000000
10* *  44         2222222222           2222   444    666    888888888              000000                  * *10
4444               2222222222222   4444    666    8888888                 000000
4444                               444    6666    888888               000000
09* *      44444444444444444444        44444    66666        88888            0000000               2222  * *09
66                  4444444444444    66666         88888        0000000000            2222222222
66666666                   4444       6666      88888        000000000          222222222222
O0                                         08* *         66666666666666666             6666       888888      0000000           222222222222           * *08
H1                                                                    6666666        66666      88888       000000           22222222222          44
888888888          66666 6666666       88888       00000          22222222             44444
07* *  88888888888888888        6666666666    88888          00000        222222222            44444444   * *07
88888  88888888888         666666    88888        00000         222222222         444444444
888          8888888        6        8888       000000        222222222        44444444
06* *                   888888             8888      000000         222222222       444444          6666  * *06
888888       88888      00000         222222222        44444          6666666
88888888888888       00000         222222222         4444       6666666
05* *   G000000OOOO            8888888888    00000          2222222222         44444      6666666       8  * *05
000000000000000          88888       00000       2222222222         444444    666666        8888
OOOOCOOOOOOOOOO000000       8       0000      222222222           444444    66666        88888
04* *  000C00000C0000000                   0000    2222222              444444       66666    8888         * *04
00000000          00000    22222             444444444       66666    8888        0
0OOOOOOOOOOOOO           2222        44444444444        66666      8888       000
03* *                       0000000000        2222       444444444            666666    8888    000000  * *03
2222    4444444              6666666      8888       000000
0                 22222   44444               6666666        88888      0000000
02* *                 000              2222222   4444           66666666666        88888        0000000   * *02
0         222222222    444          666666666666        888888         00000000
0                       222222222       444      66666666666666         888888         000000000
01* *  00                     222222222       4444    66666666666666           888888          000000000  *. *01
10                                                                                                 20
01   02   03   04   05   06   07   08   09   10   11   12   13   14   15   16   17   18
Figure E-5.   Contours of the calculated pressure field.



</P>
<P><PB REF="00000093.tif" SEQ="00000093" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="898" N="82">
Evaluation of the Successive Approximation Technique
Comparisons between measured ship pressures and computed
ship pressures show the SAT does indeed analyze the pressure field.
The geostrophic wind field appears to be smooth and regular and compares well with the measured winds. The radius of curvature field
shows irregularities and inconsistencies that point out a need for
further development. The gradient wind field is not a smooth field
with reasonable values but is quite irregular and not an acceptable
analysis. The poorness of this analysis is undoubtedly due to the
poor radius of curvature input. It must be concluded, at this time,
that the SAT produces good pressure and geostrophic wind analyses
but the radius of curvature and gradient wind analyses are unreliable. For the development of a wave climatology, the SAT is
feasible for the determination of geostrophic wind. Curvature, however, should be determined from measurements on hand analyzed charts
until more consistent machine results can be obtained.
- 82 -



</P>
<P><PB REF="00000094.tif" SEQ="00000094" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="853" N="83">
APPEND IX  F
DERIVATION OF THE SIGNIFICANT WAVE
HEIGHT AS A FUNCTION OF THE STANDARD DEVIATION
- 83 -



</P>
<P><PB REF="00000095.tif" SEQ="00000095" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="832" N="84">
APPENDIX F
Derivation of the Significant Wave Height
as a Function of the Standard Deviation
The height of the lake surface, h(t), is a classical random
variable and must be analyzed by the techniques of random data
analysis. Bendat and Piersol (196t) define the mean square value,
2  of random data to be:
h'
2       1      T   2
= lim -         h (t) dt                      (F-l)
h        ToT
T-*oo
0
and the variance to be:
2       1      T              2
h  = lim            [h(t)   h    dt                    (F-2)
Th    lim~                    h
T-oo
where dh is the mean value of the lake level.
1      T
Wth = Jim T-        x(t) dt                        (F-3)
T-ooT
By a change of coordinates such that h(t) is measured from
the mean lake level, ~h can be made zero over the time period 0
to T and
2     2        1    T   2
=f   z   =lim       (    h(t) dt                       (F-4)
T I
h           T-&gt;oT
This should be compared with Jacobs'  (1965) equation (4)
chapter 2.
1  0T   2
E = 2 1im  p    h (t) dt                            (F-5)
where E is the PNJ energy parameter.
From (F-4) and (F-5), we obtain:
E
T                                              (F-6)
h    2
- 84 -



</P>
<P><PB REF="00000096.tif" SEQ="00000096" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="855" N="85">
2.
and the root mean square wave height (the positive square root of
the variance)
E /2
h   (  and   E      1.414 Th                     (F-7)
Pierson, Neumann and James (1955) have stated that the significant wave height, H1/3, can be determined from the E value of a
sea state by:
H1/3 = 2.83   E.83* 1.44 Th                    (F-8)
or
1H/3 = 4 Th                                           (F-9)
The analog computer analysis used to compute Xh removes
the mean value h from the data, so equation (F-9)   can be used
to determine H /3"
- 85


</P>
<P><PB REF="00000097.tif" SEQ="00000097" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="884" N="86">
BIBLIOGRAPHY
Arthur, R. S., 1947: Revised wave forecasting graphs and procedures.
Wave Report No. 73, Scripps Institute of Oceanography,
14 pp.
Bendat, J. S. and A. G. Piersol, 1966:  Measurement and Analysis of
Random Data. John Wiley and Sons, Inc., New York.
Bellaire, F. R., 1965: The modification of warm air moving over
cold water. Proceedings of the Eight Conference on Great
Lakes Research, March 29-30, 1965, Ann Arbor, Michigan, pp.
249-256.
Bretschneider, C. L., 1951: Revised wave forecasting curves and
procedures. Technical Report No. HE-155047, Institute of
Engineering Research, University of California, Berkeley,
28 pp. (Unpublished)., 1957:  Revisions in wave forecasting:  deep and shallow
water. Proceedings VI th. Conference on Coastal Engineering,
Chapter 3, pp. 30-67,
e 1959:  Wave variability and wave spectra for wind generated gravity vanes.   Beach Erosion Board, UoS. Army Corps
of Engineers, Technical Memo. No. 118, pp. 192.
1965:  Generation of waves by wind.  State of the Art,
Report by National Engineering Science Company, Washington,
D.C., 20036.
Caldwell, J. M., 1963:  Rapid spectrum of ocean wave trains.  Proceedings of the International Association of Hydraulic Research Congress, Volo 1, ppo 205, London., and L. C. Williams, 1963:  The Beach Erosion Board's
Wave Spectrum Analyzer and its Purpose, Ocean Wave Spectra,
Prentice Hall, pp. 259-266.
Cressman, G. P., 1959: An operational objective analysis system.
Monthly Weather Review, Vol. 87, No. 10, pp. 367-374,
- 86 -



</P>
<P><PB REF="00000098.tif" SEQ="00000098" RES="600dpi" FMT="TIFF6.0" FTR="UNSPEC" CNF="879" N="87">
Elder, Fo C., 1965: An investigation of atmospheric turbulent processes over water, report number two: data, 1963 and 1964.
Contract Cwb-10714, University of Michigan Report 05982-1-f.
pp. 71.
Harris, D. L., 1967: The air-sea boundary layer. Paper presented
at the Conference of the American Meteorological Society on
Physical Processes in the Lower Atmosphere, March 20-22, 1967,
Ann Arbor, Michigan.
Jacobs, S. J., 1965:  Wave hindcasts vs. recorded waves.  Final Report 06768-1-f. Office of Research Administration, University
of Michigan, Ann Arbor, Michigan.
Kitaigorodski, S. A., 1961:  Application of the theory of similarity
to the analysis of wind-generated wave motion as a stochastic
process. IZV, Geophys. Ser., pp. 105-117.
Lansing, L., 1965: Air mass modification by Lake Ontario during the
April-November period. Proceedings of the Eighth Conference
on Great Lakes Research, March 29-30, 1965, Ann Arbor, Michigan,
pp. 257-261.
Lonquet-Higgins, M. S., 1952.  On the standard distribution of the
heights of sea waves. Journal of Marine Research, Vol. XI,
No. 3, pp. 345-366.
Newmann, G., 1952: On ocean wave spectra and a new method of forecasting wind-generated seae  Beach Erosion Board, U.S. Army
Corps of Engineers, Tech. Memo. No. 43, pp. 42
Pierson, W. J. Jr., 1964: The interpretation of wave spectrums in
terms of the wind profile instead of the wind measured at a
constant height. Journal of Geophysical Research, Volo 69,
No. 24, pp. 5191-5203., G. Newmann, and R. James, 1955.  Practical methods for observing and forecasting ocean waves.  H.O. Publ, 603, U.S.
Navy Hydrographic Office.
_  and L. Moskowitz,1964:  A proposed spectral form for fully
developed seas based on the similarity theory of S.A.
Kitaigoradskii.   Journal of Geophysical Research,  Vol. 69,
pp. 5181-5190.
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Richards, T. Lo, H. Dragert and D. R. MacIntyre, 1966: Influence of
atmospheric stability and over-water fetch on winds over the
lower Great Lakes.   Monthly Weather Review, Vol. 94, No. 1,
pp. 448-453.
Strong, A. E., and F. R. Bellaire, 1965: The effect of air stability
on wind and waves. Proceedings of the Eight Conference on
Great Lakes Research, March 29-30, 1965, Ann Arbor, Michigan,
pp. 283-289.
Sverdrup, H. U. and W. H, Munk, 1947:  Wind, sea and swell:  theory
of relations for forecasting. Hydrographic Office Publ, No.
601. U.S. Department of the Navy, pp. 44.
U.So Army Corps of Engineers, 1961: Shore protection, planning and
design. Beach Erosion Board Technical Report No. 4 (BEB T.R.
4), Rev.
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UNIVERSITY OF MICHIGAN
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THE UNIVERSITY OF MICHIGAN
DATE DUE



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