Introduction to the twenty year hindcast climatology

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L.K. Kupras

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i _Introduction

i

Forecast Technique _i

Hindcast Technique ₂

Grid point ₄

The Hindcast Spectrum ₆

Basic Parameters of Hindcast Spectrum

9

More About Parameters

13

Stratified Spectral Family ₂₂

Data Format ₂₆

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PREFACE

This report gives a short introduction to The Twenty Year Hindoast Climatology.

The original Twenty Year Hindcast Climatology consists of a

5.84 i

10' directional spectra hindcasted for a period of twenty years and for 2000 grid points covering the Northern Hemisphere. This data base can be applied to the real-time prediction of ship responses. The remaining two data bases postprocessed and edited in the form of climatic atlasses are less voluminous and can be efficiently applied for probabilistic models. A compact data base in the form of stratified spectral families is arinoun ced to be published soon.

It was proved by different users that The Twenty Year Hindcast Climato

logy is a unique source of wind and wave data, which can be used for design of seaborn structures. Maximum ship responses for short and long term prediction, optimal routing and seakeeping performance of seagoing

and stationary- floating structures can be more precisely predicted.

Because of a compact form of postprocessed data, they can be handy used in the first stage of design specially when the time is spare and hardware less sofisticated.

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INTRODUCTION

It is not clear who first initiated the concept of hindcasting. The first break through in numerical wave prediction came during World War 2 when wave forecasting were needed to support amphibious operations. Barber and

Ursel at the A.R.L. in Teddington, England were able to forecast the

lo-cation of storms from classical wave theory and the analysis of component wave trains from wave recorder data. In 1942, at Scripps Institution of'

Oceanography in La Jolis, California, Svedrup and Munk used synoptic data to quantitatively forecast sea, swell and surf condition. In 1966 Pierson, Tick and Baer presented their Computer Wave Prediction Model, which a de-cade later became operational on full scale.

2 FORECAST TECHNIQUE

Wave prediction model, developed by Pierson and his associates is based on the numerical solution of the spectral energy ballance equation, whose source function contains terms intended to represent wave generation, wave breaking and wave dissipation. The solution is a directional wave spectrum in matrix form which consists of spectral components (variances) for a set of specified frequency bandwidths and around-the-clock wave directions. The wave prediction model as developed by Pierson and his assiociates was adopted in 1974 by F.N.O.C. (see list of abbreviations) to provide weather routing guidance to naval and commercial ships. The mode known as the Spec tral Ocean Wave Model (SOWM) is run twice daily to provide 12,24,..72 hour forecast of wave conditions for about 2000 locations (grid points) throu-ghout the Northern Hemisphere. Grid points are at 90 to 180 N-miles spacing both basins North Atlantic and North Pacific and The North Sea, The Gulf of Mexico, The Sea of Japan, The Bering Sea and The South China Sea. The input local wind fields are updated every six hours together with the characteristics of waves propagating into an area (grid point) from distant disturbances in order to predict the then existing local sea spectrum. At each of the grid points, the propagated wave energies are summed to pro vide the current local prediction and the starting point for the next twelve hour prediction. The SOWM is essentially a deep water model, and does not include effects such as refraction, diffraction, shoaling and bottom friction, so it should be interpreted with a great of care for sha-llow water applications.

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3. HINDCAST TECHNIQUE

For evaluating the effects of envirimnent of ships and other marine struc tures Climatological Data Base On Waves and Winds is required. The SOWM was adapted to simulate such data base. This technique called hindcasting

provide in summary a time history of the ocean. The first of the SOWM

hindcast were developed at PNOC in Ionterey, California in

_1976.

The hindcast are developed somewhat differently from the forecast. Instead of extrapolating the predictions into the future by forecasting the driving wind fields, the hindcast use wind fields derived from analyses of surface presure fields archived at NCC, in Asheville, so that they reflect what "truly" occured. Lajd and ship observations are included to improve input data. Historical wind fields were reconstructed by blending wind and pre ssure data. The reasonablenses of the data depends on the restrictions of the model being met

- the data point is in deep water (water depth is twice the wave length,

- the data point is sufficiently far from land to preclude interferen ce with wave patterns,

- the wind field used to drive the model is representative of the actual winds.

Because the variability from year to year was considered to be so great that there would be an extended period before a sufficient number of sea-sonal weather cycles would provide a reliable statistical basis. In connec tion to that FNOC proposed to use historical meteorogical data, sufficien tly archived for about 20 years, as a starting point for the wave predic-tion process and then use "hindcast" wave condipredic-tions throughout the

Nor-thern Hemisphere

at

sequential time steps. The product would be a Set of

Directional Wave Spectra, at 6 hour intervals , for all seasons. Such

a Data Base would be free from observational and geographical biases and would provide the type of environmental specifications needed for the quan

tification of ship performance. Presure fields data as recorded in the periods of 20 and. 10 years were input for Hindcast Climatology (HCC).

The

20

Year Hindcast Climatology covers about

450

locations (grid points)

in The North Atlantic for years 1956 to

₁₉₇₅

and 10 Year Hindcast Climato

logy covers

900

grid points in The North Pacific for years

1964

to

1975.

Finally about

2.5

i hindcasting directional wave spectra were then

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re-quired to translate this data base into useful engineering _and/or opera-tional tools are substantial. Hindeast data were forwarded to The David

W. Taylor Naval Ship Research And Development Center (DTNSRDC) _for

ana-lysis and paraineterization. As the result of this work first _{two atlases}

were published. The first one is The Standardized Wave And Wind _Environ

ments Por NATO Operational Areas, published in 1981. This _{report provides}

seasonal (Annual, Winter, Spring, Summer and Pall) and _geographical

dis-tribution ( 18 areas ) of wind and wave parameters and specifies inathema tical models by which wave spectra , required by any ship seakeeping

per-formance methodology can be developed. _{The second atlas The US Navy}

Hindcast Spectral Ocean Wave Model Climatic Atlas: North Atlantic, publi

shed in 1983 includes climatology variation on monthly basis and _{for 63}

grid points. Some additional wave parameters were concerned and _persisten

ce data for six months (January, February,

April, July, August and Octo-ber) were included. The entire 20-year Hindcast Data Set stored on the magnetic tapes as well the atlases are available from NOCD in Asheville.

Fig. i provides an organizational overview of the climatology _development

by the US Navy for engineering applications.

H ISTOR I CAL

WIND \ELD

III FNOC

I)) FLEET NUMERICAL OCEANOGRAPHY CENTER IFNOCI 121 DAVIO W. TAYLOI) NAVAL SHIP R&D CENTER IDTNTIIDC) ¿31 NAVAL OCEANOGRAPHY COMMAND DETACHMENT

INOCO). ASHEVILLE

Pig.1 PARTICIPANTS IN TWiTY YEAR HIDCAST CLIMATOLOGY _DEVELOPMENT. See publ.( 4 ). IEI2MATRIX. 4TIMESDAILY. FOR 25 YEARS 2000 LOCATIONSAT SPECTRAL HIN OCASTS 121 DTNSRDC PARAMETER SETC <(BO NM INTERVALS INN. HEMISPHERE PHYSICAL PARAMETERS 3) NDCO,

ASHEVILLE PUB LICATIONATLAS

VALIDATION <20 VALUES HEIGHT. PERIOD. DIRECTIONALITY FOR

-UP TO 2 SIMULTANEOUS FREO.OFOCC.OF WAVE SYSTEMS E G.,

SEA AND SWELL) PHYSICAL PARAMETERS

DYNAMIC SEASON DEFINITION (JOINT) EXTREME VALUE EVALUATION PERSISTENCE OF

VALIDATION _EXTREMES

IMPROVED UESIGN _{WAVE SLOPE}

ANO OPERATIONAL DISTRIBUTIONS APPLICATIONS SEASONAL AND GEOGRAPHIC VARIATIONS NOTE. POINTS OP CONTACT

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4.

GRID POINT

The grid points are laid out on groinonic subprojections of an icosahedron (a solid whose surface is 20 equilateral triangles) so as to allow great circle propagation. For each of the 20 triangles, a gnomonic projection is used. Thus, a straight line with any orientation on any of the 20

subpro-jections is a great circle. On the sphere, the sides of the eqilateral spherical triangle intersect at an angle of 720 and, thus, five triangles meet at a common point. The triangles are not oriented in a simple way rela tive to the latitudes and longitudes on the Earth. Instead, the icosahedron was located so as to maximize the number of the number of verticies on land. Fig.2 shows the 20 triangles as their verticies and edges appear on a Miller1 projection. Each triangle covers exactly the same area.

Fig. 2 THE TWENTY EQUILATERAL TRIAÌGLES OF THE ICOSAHEDRAL GNOMONIC

OF THE SOWM. ALL TRIMGLES ARE THE SMIlE SIZE ON THE EARTH' ,

BUT THE MILLER PROJECTION DISTORTS THEM (Lit.: publ.(1O )

_).

Two sides of a triangle form a natural

set of

axes for each subprojection

and the grid

of

points at which the SOWM spectra are computed are

_formed

by

the intersections

of

equally spaced lines drawn pai'allel to the two

chosen sides o± each subprojection as shown in Fig.

_3.

Each grid point,

in principle, ought to be representative of wave spectra anywhere within the hexagon surrounding the grid point.

1- A

Miller projection is a cylindrical projection similar to a Mercator

projection with less exaggerated spacing of the parallels at high latitudes.

20* 230" 40' 50' 60" 1700280'WIlO' 60 50' 40' 30' 20' IO' I80 90 40 70' 60' 50* 40* 20* SIT 40* *0' E 10' 20' 30' 40' 50* 60 70 60" 80' 214)' IO' 120

220

______ _

70, l

lLiiUt!

iÍupiiiiív1r

*

lidi!!,

IUUL

Ql

4U

UEiIU!!!uUU1iMUl!!ÌUUUUIUIIi.

lllliiÌ!!iIi!41llllIllll!!

200' I70BI80'WI10' 140* 450*440' 20' Ir 110'100' 40' &r 70' 40' SO' 40' 30' 20' I0'W 0' 410' 80' r 40' 50' 40' 70'

ÌiìÌ!!UUi1ÏiÏU!!iÏHÌi!!iiII.

40' 40'

,

Jill

140 ISO' 100'IZO' 180'

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The great circle property is indicated by the fact that waves can travel to a given grid point along a great circle path from any one of the six

surrounding grid points, thus accounting for six of the 12 direction

bands in the model. The other six direction bands have directions of travel halfway between those for each of the primary directions. These spectral components are effectively treated as if they come from a source on the inner hexagon surrounding each grid point at a point halfway between two grid points. The distance involved is thus only about 85% of the primary distance as shown in Fig. 4

s

.

.uu

s

5/

Ou

s

.

_{O.( ®'}

O

i

OD s

.

.uu

. .

.

s

SIX PRIMARY DIRECTIONS _{SIX SECONDARY DIRECTIONS}

Fig. 4. GRID POINTS INVOLVED IN PROPAGATION. The large dots on the left are for the six primary directions. For the circled point a downward pro pagating spectral component requiring an upstream point, an upper upstream point and a downstream point are shown. For secondary directions, the points on the inner hexagon are treated as if located at the open cines

- for one time step. The shift is reserved for the next time step. (After Pierson, 1982).

Fig. 3 The 325 GRID POINTS ON

A TRIANGULAR GNOMONIC

SUBPROJEC-TION FOR THE SOWM. Any strait line isa great circle .The hexagon around the circled dot shows the area represented by a grid point. The inner hexagon of heavy dots and the outer hexagon of X's show those grid points required to treat wave propagation effects at the cir cled point.(After Pierson, 1982).

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Land boundaries and a prescribed ice limit act as sinks for spectral components. Grid points just south of the equator are treated as an arti ficial land boundary to provide appropriate sinks for southward moving

o- .

spectral compnents and artificially fetch limited waves for southerly winds at the equator. No swell from the Southern Hemisphere exists in the model althougIthey could be appreciable just north of the equator during the Southern Hemisphere winter. Also there is no specific provision for tropi cal cyclones in the model. Once the grid, the spectral resolution, and the time step are prescribed, the model can compute what the spectrum will be at each grid point x hours later, given an initial wave spectrum and the

winds at all grid points at the time, t = to In the SOWM, this is accom:

plished by computing : how much the wind-generated sea will increase or

grow (if at all) during the next time step at each grid point; how much

+ o

the waves traveling against the wind (- 90 ) will be dissipated: how far each spectral component will propagate at a representative group velocity along a great circle path in x hours; and, then reassembling the spectra for the end of the time step. Por brevity, these steps are called Grow, Dissipate, and Propagate. For the SOWM hindcasts at the end of a six-hours

time step, within the resolution of the model, the new spectra at the grid points represented the waves at t = t + 6 hours; new winds were then used,

and the process of Grow, Dissipate , and Propagate were repeated.

5. THE HINDCAST SPECTRUM

The output from a SOWM hindcast includes a Directional Variance Spectrum at each grid point as represented by 12 equally divided direction bands

and 15 frequency bands of varying widths as depicted in Tables 1 and 2.

The direction bands are unique for each grid point, but the frequency bands remain constant for all grid points (Table 2). The lowest possible frequen

cy in a SOWTYI spectrum is 0.0390 Hz which corresponds to a period of 25.6 seconds. Conversely, the highest frequency is 0.308 Hz which corresponds to a period of 3.24 seconds. The SOWM generates "energy Variances" (mean square displacement of the free surface) in each cell within the 180 ele-ment matrix from input wind fields, The variances in the columns are added to provide a frequency point spectrum or frequency "marginal" distribution. Similarly, the rows are added to provide a "directional marginal" distribu tion. The sum of all the elements of the matrix is the well known parameter "E", or the Mean Sqare Wave Surface Displacement. Other parameters of inte

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rest and available for use are compas wind direction, wind velocity in knots, white cap percentage, frictional wind velocity, and the significant wave height in feet.

Wind Direction 1600 Wind Speed 21.5 kn

Central Frequency hz)

Derived parameters: m0= 9.3 ft., T= 8.57 s., a = 0.085, PWD = 212°, Pc = 0.77

TABLE i AI' EXAMPLE OF A DIRECTIONAL VARIANCE SPEC TRIJT (Pubi. (i o) )

(x)- white cap percentage and frictional wind velocity are not shown on this table.

There is a certain amount of confusion in the terminology "energy variance" since the values within each cell are not energies. In a stedy Sea State the record of the waves (a continuous time series of the rise and fall of the sea surface at a point) does not repeat itself exactly from one wave to the next because the waves are a superposition of sinusoids with many different frequencies and directions of travel. Every wave record of finite

length as a function of time, however, can be decomposed into harmonics.

The zeroth harmonic is the mean elevation of the sea and is assumed to be zero for the analysis since the contributions from much longer periods such as the tides are constants during the time of observation. The first harmonic, is a least squares fit of a sinusoid with a period equal to the wave record with its peak positioned such that Its amplitude is maximazed.

The first harmonic has one maximum and minimum for the entire wave record. The second harmonic has a period of one-half the wave record with its two peaks positioned such that it too has maximum amplitude. Each subsequent

Direction (deg) .308 .208 .158 .133 .117 .103 .092 .081 .072 .067 .062 .056 .050 .044 .039 Directional Total 96.6 66.6 36.6 6.6 336.6 306.6 276.6 .01 .06 .10 .15 .42 .15 .02 .02 .93 246.6 216.6 .04 .06 .13 .20 .18 .35 .13 .29 .13 .33 .11 .18 .05 .06 .03 .02 .01 .01 .82 1.49 186.6 .06 .20 .37 .30 .28 .01 .09 .02 1.33 156.6 .04 .14 .20 .14 .12 .01 .03 .01 .69 126.6 .03 .08 .04 .03 .18 Frequency Spectrum .23 .75 1.10 .91 .95 .41 .38 .50 .16 02 .03 5.44 Total

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TABLE 2. BAND NUMBER,BAND WIDTH,

CENTRAL FREQUENCY,PERIOD,ANI) BAI'D

WIDTH BOtTNDS(After Pierson,1982)

harmonic can be thought of as a least squares fit of a sinusoid with the number of peaks and valleys (or the period) increasing (decreasing) cor responding to the harmonic number.

By adding each new harmonic to the

preceding harmonics, the harmonics or the "Fourier Series" begin to resemble the wave record. If the number of observations on the wave

record is N, then

_N/2

harmonics will

completely describe the wave record.

The average energy in the wave motion per unit area is described by

E = i /2J'

g a2

where

_5'

is the density of the ocean

water, g is the acceleration of gra

vity, and a is the wave amplitude.

Half of the energy is kinetic, and the other half is potential.

Recalling that each wave record can be decomposed into a number of harmo nics, theu,if the amplitude of each is squared, multiplied by (iI2fg), and plotted on a graph as the ordinate using the associated frequency or period of the harmonic as the abcissa, the resulting graph is a "wave energy spectrum". In the present presentation the multiplication of () is omitted. This is the format of the data generated in the SOWM hìndcasts.

Each cell in Pable 1 can be summed to yield the quantity

(1/2 a2).

The omission of

(f

g) transforms the "wave energy spectrum" into an "energy

variance spectrum" or more appropriately "variance spectrum", since the

sum of each cell in Table i will equal the variance of the spectrum of the

wave record it is representing. Likewise, the are under a variance spectrum

curve as derived from the frequency spectrum totals in Table i will equal

the variance of the spectrum represented.

Band Number Band Width x 180 Central Frequency Central Frequency Pariod Lower Bound x 180 Upper Bound x 180 1 24 55.5/180 0,3083 3.24 43.5 67.5 2 12 37.5/180 0.20833 4.8 31.5 43.5 3 6 28.5/180 0.15833 6.32 25.5 31.5 4 3 24.0/1BO 0.13333 7.5 22.5 25.5 5 3 21.0/180 O.1i66 8.57 19.5 22.5 6 2 18.5/180 0.10277 9.73 17.5 19.5 7 2 16.5/180 0.0916 10.91 15.5 17.5 8 2 14.5/180 0.0805 12.4 13.5 15.5 9 1 13.0/180 0.0722 13.85 12.5 13.5 10 1 12.0/180 0.066g 15.0 11.5 12.5 11 1 11.0/180 0.06111 16.4 10.5 11.5 12 1 10.0/180 0.0555 18.0 9.5 10.5 13 1 9.0/180 0.0500 20.0 8.5 9.5 14 1 8.0/180 0.0444 22.5 7.5 8.5 15 1 7.0/180 0.0388 25.7 6.5 7.5

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6. BASIC PARAMETERS OF HINDCAST SPECTRUM

Wave Height H

In the Table 1 each quantity within the cells of the table has units of

ft2 , and cells without any values contain component variances less than

0.01 ft2 . Such small values were considered insignificant , and were not

retained in the output generated from the SOWM hindcast. The total variance of each spectrum cari be converted to a spectral wave height parameter

(H) which closely corresponds to the significant wave height (Hwl/3). The significant wave height on a wave record is defined as the average height of the highest one-third of the wave heights. The quantity (H1/3)

has been shown to roughly approximate the characteristics _{wave height}

observed visually (Catwright, 1964, Nordenstrom, 1969 ). The spectral

wave height parameter (H) from Rayleigh statistics is defined as

H = 4

(m)h/2

where m is the sum of the component variances of all cells of Table 1.

The quantity (m) is commonly refered to as the moment of order zero.

The correspondence between Hmo and is stricly valid for a spectrum

with most of its enerr or variance concentrated over a narrow range of frequencies, but the approximation in the cases with a broader spectrum is sufficiently close for most practical applications.

Wave Period T

The choice of the Modal or Peak Wave Period (T ) is based upon the

"variance densities" with dimension of Pt -sec are obtained by dividing

the variances by the frequency bandwidth. In the S0W the bandwidths

vary in size from 0.0056 to 0.1₃₃₃ Hz. After dividing by the bandwidth,

the energies are standardized with respect to one another. T can

then be obtained by choosing the central frequency, or corresponding

period, associated with the peak variance density. In Table 1, T _is

assiociated with the central frequency of _{0.117 Hz, which equates to}

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Primary Wave Direction and Directionality : PWD

The Primary Wave Direction (PWD) and the DIRECTIONALITY (j') are two

parameters which are derived from the directional spectrum totals as opposed to the frequency spectrum totals. The definition of the PWD is

taken directly from the PIENUMOCEANCEN's (see abbreviations) 1981 version

of their operational SOWIV! computer program (Lazanoff, 1981). The PWD is determined by a multi-step process. First , the maximum variance (Vm) in

the directional totals is identified, where ni is one of the twelfe

directional bands. Next, the following true-false tests are performed in sequence ¡ 12

v"{(t V1)

i ni (a) j=1 12 V

> v'T(Y

V. ) i m, m+1 (b) in,m+i 1=1 12 V

> v'

( V1 ) i - m,m*1 ,in-1 (c) m,m+1 ,m1

where i is one of the 12 directional bands, and V+, is the higher

of the two adjacent directional variances. 1±' qu.(a) is true , then the

PWD is the direction associated with V. If (a) is false, Equ.(b) is tes ted; and thusly for Equ. (e). For the first succesful test of Equ. (b) or

(c) , the vectors defined by the directions and variances of the quantities

on the left-hand side of the inequalities are summed and the resultant

direction defined as the PWD. If Equ. (c) is false, then the PWD is no

defined, and a confused sea state is assumed. The methodology used for defining the PWD is somewhat arbitrary, but the technique has proved quite useful operationally (Lazanoff, 1981).

The degree of directionality is defined by

j)

_{= (3'}

p2)1/2

_(d)

where:

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12

= (1/rn) V. cos 6 (f)

i i

The angle 6 is the direction associated with the variances in the dire

ctional spectrum totals. The directionality has a value of one for an uni directional sea state, and a value of zero when there is a completely s mmetricdistribution of variance around the compass. This parameter has the same properties as the "constancy" parameter, often used in climatological wind summaries.

Air Cap

Air Cap is a sorne kind of ameasure of the air-sea interaction0 It is

more of interest to the oceanographers and less to the naval architects. It is included in the routine calculations of the SOWM.

Numerical Check of Sample Parameters H11 , PWD , e and

as for sample directional variance spectrum.

Primary Wave Direction

Equ. (a) :

1.49>

V'

3.95 false

Equ. (b) : 2.82

> V

2.62 false _,

Equ. (c) :

3.64> Y3 1.80

true

Dir. Var. Moment

216.6 1.49 = _322.734

186.6 3E 1.33 = 248.178

246.6

3

0.82 = 202.212

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TABLE 3.

Significant Wave Height and Directionality

H 4 IET0T = 4 V 5.44 = 9.32 Ft.

f

= (t/ETOT)

si

= (115.44)3(-2.29909) = -0.422627

f) = (1/ETOT)

3

S2 = (1/5,44)3(-3.47672) = -0.639103

(J'

_S2

)1/2 = (0.422627 2 + 0.6391035 2) = 0.77

Main Direction

e

= ATN

(Ç1If

) = _{ATN(-2.29909 / -3.476723 ) =}

e.

_i

E.(9.)

_i

sin e.

_i

E.sin e.

_i

cos O.

E.cos O.

276.6 0.93 -0.99337 -0.923836 0.114937 0.10689 246.6 0.82 _-0.917754 _-0.752558 _-0.397147 _-0.32566 216.6 1.49 -0.59622 -0.888375 -0.802817 -1.19619 186.6 1.33 -0.114937 -0.152866 -0.99337 -1 .32118 156.6 _0.69 _0.397148 _0.274032 _-0,91775 _-0.63325 126.6 0.18 0.802817 0.144507 -0.5962 -0.10732 ETOT = 5.44

Sl =

-2.29909 32 = -3.47672

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L.

7.

MORE ABOUT SPETRAL PARAMETERS

In order to discuss a set of spectra meaningfully, and to generalize the

characteristics most significant to the naval architects, it is desirable

and almost essential to define nemerical parameters witich can be used to measure these characteristics. Some of these parameters were already discussed. It should be noted that more than one parameter can be used to describe a particular characteristic. In most cases, this duplication is due to conflicting requirements. The most meaningful parameter for measu ring a characteristic may require significant computing time and thus be to costly to apply to the entire hindcast data base. Its use is necessari ly limited to the discussion of samples (Stratified or completely random

taken from the total set.

The parameters mostly used in the discussion of hindcast spectra are

Moments m

n These are given by

m E.(".)

n / i i i

where J

.

is circular frequency . Por n = O

m _=' E1 = E (b)

o _/

Various moments are used in the formulas for wave period and wave slope parameters. The higher order moments diverge for certain theoretical dis tributions (for example, m4 and higher for the Bretschneider spectral

formulation). However , since the hindcast directional spectra are bounded in frequency, this is not a problem here.

Significant Wave Height

11w1/3

This parameter is defined as the average of the one thierd highest (crest

to trogh). It is equal to 4

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2.

H113

= 4'%f (c)

Comment The factor 4 in the formula holds when the spectrum is

narrow in which case the so called spectral width factor (broadness factor)

2

1-m /(m

m )

2 o 4

is approximately zero with the consequence that the distri.

bution of wave heights is approximately Rayleighan . Such

a distribution obtains only for swell and not for rising

and fully arisen wind-seas. In such case , the

wave height distribution approaches Gäussian and the factor

decreases from 4 to 3 The later value is consistent

with the idealized spectra of Bretschneider and of Pierson

- Moskowitz. SOWM however makes no allowance for spectral

width and if it did, the predicted significant wave heights would be decreased.

Variance or Mean Enery Density, E

This parameter is the variance of the instantaneous surface displacement.

Note that E = in , E = 2 VARIANCE.

o

Periods

Historically, a variety of wave periods have been used to characterize the spectrum and its associated waves and they are usually derived from the various moments.

Modal Period or Peak Wave Period, T

o

The modal period, T0 is the exception, in that it corresponds to the

central frequency, , of the cell of the frequency marginal with

the heighest density

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T z . C T =

2'TI'(m2

Im4

)1/2

C

This is the mean period between crests at a point.

Period Corresponding to the Average Frequency , T1

T1 =

211m

Im1

(h)

Average Period ,

T1

=-

2e)1m, Im

To

211/ ciJa

(e)

Comment : T is a simple parameter with intuitive appeal, but has

poor sampling qualities. It is in any case arbitrarily de fined within the cell, and its significance is further weakened by its dependence upon the hindcast variances

in three adjacent cells, all of which are subject to er

ror. The modal period is more useful in treating groups of spectra (sample family spectra), where the errors ave rage out, than in describing a particular spectrum. As they depend upon the weights of all the cells, the periods based upon moments are better defined. These periods are described bellow

Zero Crossing Period , T .

1 /2

f

,

= 2 it m

O /

m)

This is the average of the periods between zero up - crossings of the wave surface displacement againts time

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Comment The T1 is recommended by the ITTC for characterizing

a spectrum but is not used here because lt corelates

strongly with T. The _T is prefered because of its greater physical significance.

Wave Slope

This parameter is intended to measure a quality of surface roughness. The slope associated with very high waves is considered by many ship desi gners to be a major contribution to operational failures. The wave slope

is often estimated using the ratio of the wave height (H) to the wave

length (L). However, the relationship usually used to obtain the wave

length

L = 5.12 T2 (j)

where T is the wave period in seconds and L is the wave length in

feet is valid only when the wave is a simple periodic sine wave. Pierson

(1955) clearly states that Equ.(j) does not hold for the irregular aea sur face. The assumptions under which Equ.(j) was derived are violated outside of the wave tank. An alternative method of estimating the wave slope is needed. Since the SOWM provides a frequency spectrum of wave energy this informatIon is used directly to calculate a wave slope parameter (a).

The wave slope parameter, "c' , is defined by

ç=

(rn4)h1'2/g

_(k)

where m4 is the moment of order four. The moments are defined by:

k

m = V.(A)

n

:1=1 1

i

(1)

where (.J is the circular frequency, n is the order of the moment, V1

is a component variance, and k is the number of frequency bands. The

parameter 0C is the roòt mean square of the absolute slope at any fixed

point. Cummings and Bales(1980) derived the wave slope parameter ,C . It

should be noted that o is more strongly influenced by the shorter, higher frequency components of the spectrum than by the larger longer but not so steep waves near the modal frequency. Thus, a "rough sea" as measured

by oC , does not necessarily imply a "high sea" Information regarding

(20)

tion of the root mean square wave slope of a regular wave. The resulting equation is (Gentile, 1982)

(7V7 V)

( HI

L ) (m)

where H is the wave height (crest to trough) and L is the wave length.

Information in Table 4 is based upon Equ. (m).

TABLE 4 APPROXIMATE VALUES OF WAVE

LENGTH TO WAVE HEIGHT FOR ASSOCIATED

VALUES OF THE WAVE SLOPE PARATTER1

Comments : Wave slope is considered by many naval architects to be

almost as important as wave height, and for some purpo-ses, even more important. It is strongly depended upon the shorter waves in the spectrum which respond rapidly to the wind, and the wave slope might be expected to grow faster than the significant wave height, which is an un-weighted sum of all of the wave components and grows

slowly in the longer components. Short-crested waves have a higher oC value than long-crested waves at the sa-me height and period.

Directional Distribution or Spread, s

This is a measure of the angular spread or width of the directional mar gin about the mean direction. It has the form of a second moment, and is the radius of gyration of the weighted unit circle about its mean direc tion axis Wave Slope Parameter Ratio Wave Length to Wave Height Lw/Hw Angle of Wa ve

Sf

ope Tan (HwILw) 0.01 222.0 0.3° 0.02 111.0 O.5 0.03 74.0 0.8° 0.04 55.5 1.0° 0.05 44.4 1.3° 0.06 37.0 1.5° 0.08 27.8 2,1° 0.10 22.2 2.6° 0.13 17.1

330

0.14 15.9 3.6° 0,15 14,8

390

(21)

assuming - spreading angle - wave direction - sector width =

( 1/ E ) EE.

sin2(e.

-where

e

is main direction

C

e

_c = ATN

_(I'

)

s(e)

=

_{E/cos2(((- e)/)(fr/}

₂₎₎

(p) for -

< O

c o S(e) = O elsewhere _(r) Sample

=7T'i

2 _{( 90 degr.)}

e

- e

_='Tr,

₍ _{45 degr.)} c oC _{=rri 12 (} _{15 degr.)}

Spreading weight factor

w

= 1/ cos2((

e - e

)I

)(7r/

2))3.

= 1/6 _cos2( _{/ 4}

) = 0.0833 ₍ _{see Table 5}

(22)

c'J

The spreading parameter has the form

= 1/2

(

11 - (i

- (2

/f()2)_1

(

sin

)/ (2))

(s)

20 40 60 80 100 120 140 160 180

FIG. 5 THE SPREADING PARA1V1ETER m2 FOR THE

COSINE SQUARED DISTRIBUTION ( Ref. 4 )

TABLE

5.

SAMPLE SPREADING WEIGHTS

FOR SECTOR WIDTHS

OPt5

DECREES

WAVEAN

ANGLE S (SECTOR)

ANGLE

OF

SPREADING

90

75

60

45 30

15

0

90

0.000 -

-

-75

0.011 0.000

-

-60

0.042 0.019 0.000

-

-45

0.083 0.069 0.037 0.000

-

-30

0.125 0.131 0.125 0.083 0.000

-

-15

0.156 0.181 0.213 0.250 0.250 0.000,0.000

o

0.167 O.2000.25O0.333O.5OO 1.000 1,000

15

0.156 0.181 o.213ro.25o 0.250 0.000 0.000

30

0.125 0.131 0.125 0.083 0.000

-

-45

0.083 0.069 0.037 0.000

-

--

-60

0.042 0.019 0.000

-

-75

0.011 0.000

-

-90

0.000 -

-

(23)

-This function is shown in Fig.5. The usual assumption that 4) is 900

2 2 ° o

yields a value of ni of 0.25 while a cas distribution over +180

yields a value of 0.5. Superimposing a swell on a cas2 distribution

generally increases ni2 uness the swell is near the axis of the cos2

distribution. Values of ni greater than 0.5 suggest that several

disturbances from widely different directions are present.

Comment : The significance of the ni factor to the naval architect is

evident, while unidirectional seas are rare, the assumption

of a cos2 distribution over +- 900 corresponds to the wide

range of observed values. For any ship response characteristics which is sensitive to the degree of directional spreading,

2

the range of possible values of m should be taken into

consideration, together with an appropriate probability mea sure. So it can be suggested that a variable model of direc-tionality should be employed in some design studies (e.g., those studies which concentrate on particular operational

scenarios in specific geographical areas).

Centralness of Spreading , p2

The centralness of spreading , p2 corresponds to a moment of inertia

of the wave spreading ; large values of p2 (e.g. p2>0.t ) suggest

a non - central distribution of wave directionality such as is present when two or more systems propagate into an area. The relationship between

p2 and ni2 for cosine squared spreading is shown in fig. 6.

_m1

Fig. 6 SPREADING PARAMETER

and PARAMETER p2 VERSUS COSINE

SQUARED SPREADING MGLE,

(Ref.4

)

/

d 11-

/

a, Di

.3

I I i I 20 60

II

I 160 180

spreading angle, 00 (degr.)

0)

/

(24)

Skewness Parameter

q.

If the asymetry of a distribution is of interest, this property is quanti tified by the third central moment or by dimensionless coefficient of

skewness , q. This parameter is given

q = (i/E)

e-1

sin 2 ( &.

i

- 9 ) (t)

C

It is assumed that further discussion will deal only with absolute values

of skewness parameter , . Small values reflect slightly central distri

bution while large values, particulary in conjuction with large values

of p2 , suggest wave systems from multiple sources.

Discussion : Fig. 7 provides cumulative distribution of p2. The variation

between locations, while atatistically significant, is small,

so only one curve is drawn. The median occurs at p2 of

2

0.05 and p exceeds 0.1 about 25 percent of the time.

This implies that two or more systems are evident about

half the time, and that about one quarter of the time the

effect is large. Prom these data and histogram of ni2

versus p2 (not shown), it is concluded that about one-third

of the hindcast directional distributions cannot be fit with a cosine-squared distribution.

Fig. 8 shows the cumulative distribution of for Grid

Point 149 for various wave heights. More skew is shown for lower wave heights at this location but otherwise the pattern is similar to that at the two locations.

In summary, it is suggested that about half of the hindcast

directional spectra for these three locations (as considered

in Fig. 7 ) can be approximated with a cosine-squared distri

(25)

1.0 0.8 0.6 o GP. 127 o GP 14 0.2 GP 279 o.o I I I I I

I

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 08

FIG. 7' _{CUMOTLATIVE FREQUENCY DISTRIBUTION OF PARAMETER}

p2

FOR THREE GRID POINTS, _{1959 TO 1969}

C FROM REF. 4 ) LO

'J

GP 149 o G-1m O 1-2m o 2-o 3-441% o 4-sn o Sii. OS-441% .O 0m 00 DO 0.1 12 L 14 0.5 0.6 0.7 04 SKEWNESS PARAMEVR.qI

PIG. 8 _{CUTDIJATIVE FREQUENCY DISTRIBUTION OF SKEWNESS}

PARAMETER, iqi _{, FOR VARIOUS SIGNIFICANT WAVE HEIGHT}

RANGES FOR GRID POINT 149, 1959 TO 1969 (FROM _REF.4

)

8. _{STRATIFIED SPECTRAL FAMILY}

Frequency domain analysis

utilizes theoretical point spectra coupled _with

a spreading function to evaluate ship motions _{and fatigue}

characteristics.

Such theoretical spectral formulation _{do not account for the random}

varia tions from its mean value in spectral

shape. This is caused by a variety of oceanographic

conditions (duration and fetch of wind, _{presence of swell}

...etc), geographical location and a _{season of a year. From}

this reason a single theoretical

spectral formulation may not be realistically

applied

in predicting _{responses of a ship which}

may encounter an _{infinite variety} of wave conditions

during her life time. One approach

to account fot such variations in wave spectral

energy contents, Is the use of the Wave _Spectra

Family Concept.

Instead of using a single theoretical

spectrum to repre-sent a given sea state, several

spectra of the same level of _{sea severity,}

characterized by its

(26)

The concept of wave spectr&famlly was first proposed by Ochi (2 ) and by Hoffman (ii). For evaluating ship longitudinal strength, A.B.S. has for the past several years been using a stratified spectral family based on actual measured data. The wave spectral family concept offers another advantage. Twenty and ten years hindcast climatology represents unique source of data could be used for design purposes. However number of data is so big that direct use of them is almost impossible because of a large computing time as required. Applying stratified spectral families , number ol' data can be reduced considerably, so computation of motions and respon ses can be performed quickly even on smaller and slower computers.

The procedure for the selection of a stratified spectral family is simple. First of all, the distinction should be made between a familles used

either for short or long term prediction. In the case of long term

pre-diction , the spectral families should be averaged over several years,

and all seasons and for one location (grid point ). In the case of short term prediction, the entire sample covers only one selected season avera ged for several years (5,10 or 20 years).

The procedure is as follows

- divide a total sample in required number of groups C strata )

which correspond to tequired significant wave heights (e.g. 9 groups (H113)1

(111,3)2 )

- for each group calculate mean values of

- modal period T0

- broadness factor _E

-

standard devalation of

spectral energy SD(H113)

These four parameters _111,3 , T0 , SD(H113) were chosen because

together they represent the overall character. of the spectrum

- 111/3 - significant wave height represents the energy of

the spectrum

- T - mean perlod represents the distribution of the

energy with frequency,

- _E

-

broadness represents the process as relatively

narrow or broad - band ,

- SD - standard deviation of spectral energy as represen

(27)

After of these values has been averaged for the entire group, a Monte Carlo process or another technique using random generator is undertaken

to choose N spectra from the entire group which , based on the average

parameters for the N best, represent the group. The N spectra thus

become the spectral family representing the spectral group. A simplified

flow diagram of this procedure is shown on Fig. 9

The application of spectral family concept for response calculations

(28)

STORE THIS SET INTO

BOX: "CURRENT

SET"

CALCULATE A "PENALTY" : PEN =

N

₌

-tç

2()2 E-E 2

+(-)

₍

SD-SD)2

T _E SD

Y

REPLACE

_{"THE LAST BEST SET"}

BY A "CURRENT SET"

N

START

SORT ALL SPECTRA

INTO dNG_"GROUPS AND CALCULATE EMT PARAMETER VALU

ES:

H113,T0,

E. ,

FOR EACH GROUP

-'Y

FI =PEN

o

STORE THIS SET INTO

EOX:"LAST BEST"

THE BEST _{SAMPLES IN EACH}

GROUP, I.E.

STRATIFIED SPECTRAL

FAMIL,77

'N

FIG. 9 FLOW CHART POR _{THE SELE}

CTION 0F STRATIFIED SPECTRAL FAMILIES

DATA BASE

ENTIRE SAMPLE OP SPECTRA(RANDOM SAMPLE)

- E1

, E2

_,

_EMTOT

AND THEIR PARAMETER VALUES

-

H1 T ,

E

, SD(H1/3)

ALL _{SPECTRA SORTED INTO} NG GROUPS

GROUP NO TOT.NUMBER OF SPECTRA IN EACH GROUP: SPECTRA AS SE LECTED: MEAN PARAMETER VALUES OP THE WHOLE GROUP

î

MCi)

_{E11 ,..E1M1}

H1

'

1'o1

2

M(2)

E

NG M(NG) _ENG1

,. ENG(NGG...

lT _{SELECTED SPECTRA IN EACH GROUP}

GROUP "CURRENT SET" "LAST BEST SET"

i

NG

FOR P=1 STEP 1 UNTIL NG :2;

FOR L=1 STth' 1 UNTIL 200CC

-R.G.

SELECT RANDOMLY N SPECTRA

z

FOR THIS SET CALCULATE

[RAN VALUES

OF:

(29)

9. DATA FORMAT

The 20 year _{Hjndcast Data}

are available in different formats. _{They are}

- the entire 20 _year

hindcast data set _{stored on magnetic}

tapes under the title

" SPECTRAL OCEAN WAVE MODEL _HINDCAST

DATA

_{SET ",}

and in the form of atlasses - the first atlas

"THE _{STANDARIZED WAVE AND WIND}

ENVIRONMENTS

FOR NATO

OPERATIONAL AREAS ", published in 1981 ,

- the second atlas

: " THE US NAVY

HINDCAST SPECTRAL _OCEAN

WAVE MODEL CLIMATIC ATLAS _NORTH _{ATLANTIC ", published}

in 1983 , and

- the third atlas, which

will contain data of THE STRATIFIED SPECTRAL FAMILIES,

as announced to be _{published in}

1984.

These data formats

are briefly described _{as follows}

SPECTRAl OCEAN WAVE MODEL HINDCAST _{DATA SET.}

Version 1 NAÌE:

SPECTRAL OCEAN WAVE MODEL

(P13-9782) HINDCAST DATA SET.

TIME PERIOD:

Atlantic Ocean;

January 8, 1956 through Decem

ber _{30, 1975, Pacific}

Ocean; September 1 ,

1964 through February 23, _1977.

GEOGRAPHIC COVERAGE: _{Atlantic and Pacific}

Oceans, FORMAT:

FILE SIZE:

PILE STRUCTURE:

ANSI D format,

blocked variable length records, ASh

characters. Each block contains a maximum of 5000 characters, with

an average record length of 4800 characters.

The first four characters of each record

are counters that indicate the number of

characters in the record. If read

with standard FORTRAN or _{COBOL, the counters}

are transparent

and should be ignored.

90 magnetic _{tapes; 9-trac,}

odd parity, 6250 _bpi,

ASCII mode.

The data in this file _{were originally created}

by the U.S. Navy Fleet _{Numerical Oceanographic}

(30)

CONTENTS:

controlled, and converted to ANSI format by

the NCDC and are sorted .s follows:

Gridpoint sorted files; the files are in gridpoint time sort with a tape mark

C file mark, standard ANSI label) between

gridpoints. Each tape contains 10 to 70

gridpoints, depending upon the gegraphical locations. NCDC can select particular grids from this file.

Synoptic sorted file; this file is sorted by year, month, day, hour. Each tape for the Atlantic Ocean contains approximately 12 month data - each tape for the Pacific Ocean contains 6 to 9 month data. NCC can select by timer from this file.

These magnetic tapes are available for purchase from NCC.

To generate true wind and wave direction and gegraphical location (latitude-longitude) of the point, a program is required which is also available from NCC.

The SOWM is a deep water model that produces estimates of wave conditions from a wind field. Historical wind fields were reconstructed by

blending wind and pressure data. The SOW data

are not observations.

The reasonables of the data depends on the restrictions of the model being met

The data point is in deep water (water depth is twice the wavelength),

The data point is sufficiently far from land to preclude interference with wave patterns, The wind field: used to drive the model is representative of the actual winds.

The major parameters in this file are wind di-rection (with respect to the subprojection

orientation - not the true direction), wind

speed (knots to the nearest tenth), white caps ( percent coverage ), array elements (the num ber of array positions to be encountered), array position (location in the 180 element array of the next energy value), and energy (value of the array position in feet squares to the nearest hundreth). Only non-zero vales will appear on the tape. Therefore, the position

in the array is given with the corresponding energy value.

(31)

Version 2 NAME: TillE PERIOD: GEOGRAPHIC COVERAGE: FORMAT: FILE SIZE: FILE STRUCTURE: CONTENTS:

SPECTRAL OCEAN WAVE MODEL (TD-9783) HINDCAST DATA SET.

Atlantic Ocean; January 8, 1956 through Decem

ber 30, 1975 , Pacific Ocean; September 1

1964 through February

23,

1977.

Atlantic and Pacific Oceans.

60-bit word binar7. This is an internal format to CDC 6000 series computers. Maximum block length is 2000 60-bit words.

44 magnetic tapes; 9-track, odd parity, 6250 bpi, binary.

The data in this file were originally created by the U.S. Navy Fleet Numerical Oceanographic Center. These data were processed and quality

controlled by the NCC , and are sorted as

follows:

Gridpoint sorted files; the files are in grid point, time sort with a tape mark between

gridpoints. Each tape contains from 20 to 60 gridpoints, depending upon geographical

location

Synoptic sorted files; this file is sorted

by time, gridpoint. There are no tape marks

between data-time groups. Each tape contains approximately two years of data.

The magnetic tapes in this file are available for purchase from the NCC but they are only useful to customers with CDC 6000 series computers. NCC can also run a program called SOWM-PRINT that will print out data for selected grids and dates.

To generate true wind and wave direction and geo graphical location (latitude-longitude) of the point, a program is required which is also avail able from the NCC.

The data in this file are identical to that in TD-9782 file (reference page 27) but In a diffe rant format.

The program you can receive is a copy of an active piece of software on the UNIVAC 1100 System used by the NCC for its internal use and as such is in

the public domain. All commercial requests should be mailed to the

U.S. Department of Connnerce, National Oceanic and Atmospheric Administra tion, Environmental Data and Information Service, National Climatic Center, Ashevilee, North Carolina, 28801-2696.

(32)

NAME:

TIME PERIOD:

CONTENTS:

THE ATLAS: THE STANDARIED WkVE AND WIND ENVIRONMENTS FOR NATO OPERATIONAL AREAS

GEOGRAPHIC COVERAGE:

THE STANDARIZED WAVE AND WIND ENVIRONMENTS FOR NATO OPERATIONAL AREAS

Mjor portion of the data contained herein are derived from the TWENTY YEAR HINDCAST

WIND AND WAVE CLIMATOLOGY,

(1956 - 1975 ).

Regions considered as appropriate for joint operations of NATO naval forces.

Pig. 10 identifies the three generic opera-tional areas. They are

Open ocean North Atlantic from the Tropic of Cancer northward,

Mediterranen Sea,

Coastal and landlocked waters (e.g. North, Baltic and Black Seas ).

Furthermore the open ocean area is divided into sub-areas which are identified in Fig.11.

Because of the previous usage of the wave sta

tistics provided by Hogben and Lumb ( i. ),

it was decided to adopt their definition of geographical zones where possible. Areas i ,2,

3,4,6,7,8,9,10

and 11 are taken as defined

by Hogben and Lunib. Areas

15,16,17

and 18 are

also taken as defined by Hogben and Lumb but

o

truncated at the Tropic of Cancer (23 N).

Areas 00 and O are new areas. The darkened

circles about the grid points within each area

on Fig, li indicate the SOWM grid points

indu

ded in this atlas.

The following natural environment data distri butions for their respective oceanographic locations are given

I. Surface Natural Environment Summary,see

sample as the Table

6.

Ii. Waves and Wind

11. Significant wave height versus modal

wave period,

Significant wave height vs. wind speed, Significant wave height vs. primary wave direction,

Wind speed vs. wind direction,

Significant wave height vs. wind speed III. Persistence:

Significant wave height vs. duration Wind speed vs. duration.

For samples of wind and wave distributions

see Figures 12 -

16

and for wind and wave

persistence, Figures 17 and 18.

Note: persistence data are given on the annual basis.

(33)

PREPARED BY:

Both annual and seasonal distributions are provided. The seasons are defined by:

i Winter - December to February,

Spring - March to May, Summer - June to August, Pall - September to November.

IV. Seasonal Variations of Surface Currents (directional and speed) throughout the Nato Operational Areas, See sample, Fig.19. David W.Taylor Naval Ship Research And

Develop-ment Center,Bethesda,Md. 20084.Authors: Susan

Bales,Wah T. Lee and Joyce M. Voelker. July 1981.

120

90

60 30 W O

E

30

PIG. 10. GENERIC NAVAL OPERATIONAL

AREAS FOR NATO FORCES

70

60

50

40

30

20

10 o

(34)

700 N 60° 30° za 90° _60°

MODAL WAVE PERIOD(SEC) FIG. 12

SIGNIFICANT WAVE HEIGHT BY MODAL WAVE PERIOD

30°

FIG. 11

_{SELECTION OF}

REPRESENTATIVE AREAS IN THE NORTH _ATLANTIC _BASIN

20 I E-i H E-i

çM

111

0

fr: p-i , s H ta 1 1 3 20 0 202243

WIND SPEED AT 19.5 M (KNOTS)

FIG. 13

_{SIGNIFICANT WAVE HEIGHT}

BY WIND SPEED VV 0° E SPRING _{AREA O} 30° r

I

!:

s

4Q)4

H,0oi.

.0

í4.*T

el.;o

-

0 20 -:

2t-- SP2 p.303 0 _c

.°

o o 9.2- ₀ o 41 0 ¿

1 016

.17

/

f o _{.3220-4 320 ..aS..ata.200ò.2020.}

-

2. 0 53 52 13 lOO .5 .2 .2 .5 .5 .1 .3 .3 .8 .3 i: i: .: .: .7 .3 .6 .2 .4 .2 4.4 .3 ₃₅ 2 .7 .3 .5 .2 _/.3 .6 2 8 3.3 5.7 .9 . _.3 . _9.8 .6 4.5 3.5 2.9 .6 .0 .7 .4 35.5 '.6 6.3 6.3 3.3 3.o .7 3.3 .0 .6 .4 23.3 .0 2.2 3.8 3.2 3 3.8 2.7 .7 .8 .7 .3 1.0 .3 21.9 .2 1.6 5.9 1.92.3 .6 .3 .3 .7 .5 .3 .1 72.8 .2 .2 3.3 7.3 70.3 56.7 12.7 18.3 11.37.8 4.9 3.7 :2.6 .0 700.0 .2 .5 1.5 2.6 3.5 lO 5 1 7-2 tO 5.0 - _5,5

1121

SPRING _{AREA O} 20.0 23.7 1.1 3.4 6.0 34 S.l _{. 7!0.I2.0il.3IS.0I&.0} 6.0 00.0

(35)

20

!6

'0

knEE

SE

*?PA0! WAVE DI*(CTÌOW

o.: 6.0 6.0 2.5 1.25 0.5 0.l o 10106 SAMPLES 3.?!? ISO 1VTA S.S

FIG. 16. SIGNIFICANT WAVE HEIGHT BY

WIND SPEED TOTAl. OMPtE! 3.387 00 75 50 25 .1 .5 .1 5 .1 .2 .3 8 1 .1 I .2 5 L? 0 .5 .0 2.4 I 6 0 .3 1.1 r 24 IS I II 1,3 I.) I,? .2 7,! 2.! 2 .9 0 2.2 5.! 5.8 6.5 0 .0 .3 0.0 5,6 3.' ' 5.5 07 2 .0 39 5.7 5.0 0.0 .0 253 09 2 10

:121

2 50 '50 .5 .i .1 .i .2 .r 5 .6 .5 _.8 _.3 .8 .2 .5 3.2 5.0 .5 .6 .7 2.5 .2 5.0 .6 8.2 2.0 .8 5.2 2.) 2.5 2.2 .6 5.2 53.6 3.5 .6 2.2 3.? 3.2 2.1 5.3 5L2

::

:::

::

:; :

::

.2 I.'. I.? 5.0 . I.? 50.2

'1156

1:

i

152.1 .:

,: i.

0 .5 .5 5.0 .5 (.3 56.5 3.9 p3.7 5.3 5.0 o 2.0 5.8 51.? I5.3 05.8 5.0 56.6 56.: .5 500.0

FIG. 14. SIGNIFICANT WAVE HEIGHT

FIG. 15

WIND SPEED BY WIND DIRECTION

BY WAVE DIRECTION

SP! NC TOTAL A6IPLEN 3.307

0 6 0 6 2 27 '.7 55 63 TOTALS I8E0 SPEED AT 0 M (KNOT

70 _4$ 4? 36 za 50 22 - 17 1? 1 5E 5 0W 15MC 25!tT!OW A

(36)

55 48 TOTA&S

E-'

H .

z,

H'

ca 30 36 42 .8 56 0UU1128 (o0uS

FIG.

18. PERSISTENCE OF WIND SPEED

I,

DURATION (HOURS)

FIG. 17. PERSISTENCE OF SIGNIFICANT WAVE HEIGHT

TOFU %ti) fl.J5i

's E

z

o

P-i 2S I 2 2 7 22 '2 7 U aS I) I 3 n 27 27 $ 1 I I I Ill it) $1 7 1 22) ISO II 50 15 I 7 2 1 ¿It Ib 54 23 5 S I I ¡'S I) Ii bO 2) Ii 2 2 I b I I i bi) 14* 14$ 27 Sl 1*

2)221,

lO * I 7 710

13 Ill III 14 *5 4) a 22 71 6 4 3 5 It iii

I)) F01 III

¡

55 37 71 1) II II 1 bi 4$

ill

11411

II-i

:

:1:::

IO I I 12 38 6 2 61 108 65 23 16 6 3 2 221 275 37 6 25 7 lb 665 238 99 62 II 13 5 5 6 I 3(6 678 306 65 75 30 3 6 3 3 2 I 2 1268 654 434 ISO 113 59 29 ¡5 10 8 7 2 6 7 3 561 726 ¿61 115 79 29 II 6 7 2 2 I 2 1 1262 67: l7 63 30 1 2 ¿ 762 023 67 3. 21. 6 6 I I 359 368f 689 715 423 161 35 27 20 12 1. 9 7 4851 APnIUAL TOT1LS.TPLS ' ¡8 26 60 4' 72 78 TOTAl. S 08 22 17 100 75

(37)

SURFACE CURRENTS lo.

J-M'

44 JOlI I01 111CC 1100111 111011140

O 1011111 40011.11n0( 110 11 1O'1 111011110 - 1011101 01111101 0 1W lIJO ni Il Ill

'/: 'o- _{.3. .0} 'I - _. Y.r .- -r__r I, '-___10 ; _ II Iq.31 I 01,_111 I1C0I I " 11 ('

'i

,

-!11'0i.

",A ," "w ... IO 0'

-

-:--0

-1//4'

I,

7

-_ 0 III

/ 1/;

t II ,'

fr,-f

JO-..' 'lIli ':4 "1 , O + I

tl'

II, C t

'

'.40 -'I ' '

/1

_-'Iç

l\

_-____\ ,'--r

, I1 I

/

/ :

s l

't'

100011111110 DAlA ,

1c"-'.'' «---::.

I4 A i JOl

/

/ //

,

fi lOAllt

"

I

:-'

I /ç'

-//

/1 "o

't.. \\t1 \ \ 'Il 41 . lI\

-

"Ill i '

-I

40 I _\ \ . It'..._ _4,__ 'It .14 S''' " I 'IO /111 II' 20' 00'

(,

fI1(' I1' --' "lh. VIl'

ç

-I.' ÇIJ

MAY

r

FIG. 19

GENERALIZED OCEAN CURRENTS FOR NATO OPERATIONAL AREAS FOR MAY

/ /

.'

/,'

r...

-

it0--Io. -J loo'

r

lo' IO. O. IO' 10' 40'

(38)

TABLE 6

SURFACE NATURAL ENVIRONMENT SUMMARY

Season: Annual; Location. 62.851° N, 3.916° W Natural EnvIronment Minimum (5 PercentIle) Median (50 Percentile) Maximum (95 Percentile) Mean Most Probable Sea Surface

Sig. Wave Height, m. Wave Period, sec Direction

.5 6 -3 ₁₀ -7 _16.5 -3 11.5 -SW - W Winds

Speed, knots Corresponding Mean SIg. Wave Heght, ni. Direction

¡4 I -15 2.5 -33 6.5 -16 2.5 -14 S - SW

Vi5ibiiity, nautical miles

2

10

25

-Cloud Cover

Total clouds, In eighths of sky obscured low clouds, In eighths of sky

obscured

1 1

7 6 8 8

-

-Precipitat ion (Occurrence)

All precipitation

-22%

of the tim.

Snow

-9% of the time (Dec - Mary

Relative Humidity, Z 614 814 97 -Air Temperature, 'C 3.5 8 12.5 8

Surface Water Temperature, 'C

6.5

9

12

-Sea Level Pressure, millibars

993 1,008 1,028 -Ice None Refractivity

Mean Surface Refractivity Sub-Refraction (1

kin, Annual)

Super-Ref rection or Ductlng (I km, Annual)

-

-j

-319: 1% of the time None

(39)

THE ATLAS: _{U.S. NAVY7 HINDCAST SPECTRAL OCEAN WAVE MODEL} CLIMATIC ATLAS: NORTH ATLANTIC OCEAN

NAME: _{U.S. NAVY HINDCAST SPECTRAL OCEAN WAVE MODEL}

CLIMATIC ATLAS: NORTH _{ATLANTIC OCEAN}

TIME PERIOD: _{Data contained herein are derived from the TWENTY}

YEAR HINDCAST WIND AND WAVE CLIMATOLOGY, (1956-1975) North Atlantic Ocean. Data concerns 63 gridpoints which are shown on the North Atlantic map, see Pig.2O. The following natural environment data distributions foT the whole Atlantic Ocean and for gridpoints are given:

1) Isopleths of: wind speed, see Pig.21 wave height, see Fig. 22, wave slope (cL), see Pig. 23. These isopleth are given on monthly and annual. basis.

Contigency Tables of:

wind direction and speed,see Fig.24, wave height and wind speed, see Fig.25,

wave height and wave slope, _{see Fig.26,}

wave height and period, see Fig.27, wave height and directionality,

see Fig. 28,

wave height and primary wave direction, see Fig. 29,

primary wave direction and wind direction, see Fig. 30.

These data are given on monthly and annual basis. Duration - Interval Tables of:

wind speed duration, _{see Fig.31}

wind speed intervals, _{see Fig.32,}

wave height durations, see Pig. 3Y', wave height intervals, see Fig. 34.

wave slope (eZ) _{durations, see Pig. 35,}

wave slope (cK) intervals, see Pig. 36, wave height and slope (.:() duration,

see Fig. 37,

wave height and slope (oC) intervals, see Pig. 38.

These data concems following months! _seasons:

January, February, April1July, August, October and Annual.

PREPARED BY:

Naval Oceanography Command Detachment, Asheville, N.C., October 1983.

GEOGRAPHIC COVERAGE:

(40)

Fig

20 GRID POINT-SUBPROJECTION AND SEQUENCE NUMBERS

105° 600 500_ 40 300 20° N 100° 900 80° 700 60° 50° 40° 300 200 10° w 0° E loo 20° 300 400

i

-J -) . 1073 1 o n: 1103 111-3 - -

-

=

-: -II .

/

13-3 304-2 171-3 279-2 -2 269-' lo 25J 8 129-3 128-3 n 9 10 149-3 147-3 187-3 1843 : 218-3 216.3 215-3 -241.2

-242i 2202 203.2 * 40 287-3 _0 151-2 48 127-3 18 _214-3 27 1 -124-3

'

-=

-

L =

ç

226-1 -1 22-1

'---263-2 261-2 32

202

224-2 21 -2 4 207-2 61-2 243-2 228-2 216-2 - 214-2 182-2 4/

I7

265-3'°'

-- ,-1050 L

0oL[IjI!l

124-2 4 85-2 81.2 _\ 37-4 500 40 -692 18-2 2 I 4fl0 139-2 100° 90° 80° 70° Go 3fb 20° 10° w 00 E 10° 20° 30°

(41)

105° 1000 70° 60° 90 80 7)) u Itt _I (I W ii

1I

,t I

/

f

\

,0

5 f 5A

/

coJ t.U5s. _l0'

t

k

¡ 4 .5 \

.'

r lo i. j)) r 1

Solid Lines (dotted intermediates)

- Percent

Frequency of wind speeds

1O knots

Dashed Lines (short intermediates)

-Percent

frequency of wind speeds 34 knots

PIG. 21

ISOPLETHS OP WIND SPEED

500 ₄₀₀ 300 20° 100 Ø0 30-1_5'-' -20 5- 3) i ,20 f iii i i I 20

liii!

WIND SPEED (1O AND 34 KNOTS)

JANUARY

I

iL

J1i I iJi ii

titi 1.1 I ii i iii t ii

I il±LL

20° 10 W 0° E 10' 20-30 30' 50' 40' 1050 100° 90° 80° 70° 60°

(42)

FIG. 22. ISOPLETHS OF WAVE HEIGHT

1050 1000 1 (50 500 400

M'

90°

ri( rrrr1j

4 80 ₅₀ 80 700 00° 50 11)

rfl1T

r ii-r-r f I TfTTI I i I I

I [I L!U I

i 11)5 10)) 90° bO 90

50-

60 50 60

IHIHIiilIIItI11lIHi

K) 70 20 r

/

1/

_/

/

2/

/

---II

\

\ '0 ) i'1

+ L!

20jj

r! °'l

Solid Lines (dttd intermediotes)- Percent

Ire-'

quency of wave heights <5 feet (<1.5 meters) Dashed Lines (short intermediates) - Percent

;

frequency of wave heights <8 feet (<2.4 meters)

40°

r. ¡

Lii' i I iii

LioLi

iI

I j I

lili

I I

iii

IO W 0" E IO" 20' 30° 40°

JANUARY

WAVE HEIGHT (<5 AND <8 FEET)

3() 20° 10 N 1) 20

]iIIrIIl,,III

/

40

-

21 (il)' 50' 4)°

(43)

90° 80°

y

' L JILt1JL I 01 I (f1) 9(J 80 70 60° 500 400 30° 20 10 w 0° E 10°

[rrTr[IJT rnT1-1TrTIrIT[T ¡ 1 iijii !Fn1T1rlT

ri ¡j

'r1'

J20 20

10

\\L

30

¶30

i

\

---4. '

Or k0 O°)yf

4

10

(Ç

, IL) L

í-1-'

k,'

r

.iI} LLLLJ±.

Iii)

H

iLIH Ill)

7f) 00 50° 1ft 4 IO iJ L 11h] 1 1)1 I 14) 2(1 II) V 0 l 20° 30°

Dashed Lines (short intermediates) - Percent frequency of wove slope parameter (a)

O.1O

N

-Solid Lines dotted intermediates) - Percent frequency of wave slope parameter (a)

O.O5

10

20°

30°'

FIG. 23,

ISOPLETHS OF WAVE SLOPE

JANUARY

WAVE SLOPE (a) (O.O5 AND O.1O)

50° 4'

f

20° I (I N

)IIIIIIIIIIIIIIIIIILIL()

I I I

iii

(44)

i

_Io Io 70 so 40 0.079 2437 1

UUUUUIUU

uUu.uRUuIuu

ix so

so UUUUU.UDIUU

70 .usDanuL1uuU

so

u..UIIUUDUUE

io

gflfll4JUURff

gtJIJDflt3J1lUuRUIE

_{liOUUIUuIIuUUi}

er

WAVE SLOPE 38-3 30 30 10 o . . . o. o DIRECTIONALITY law 4.v 3414 25E 241 30G 11 H 12 T et 3 e Si 90 A loe 40V 90 31E so 2114 70 24E so 301 1I *50 40 12T 30 If _z et 10 3 o O

N)LESWU T

PRIMARY WAVE DIRECTION 2437 1 1 38-3 4 7 11 17 22 25 34 Ii 4e 54 eT WIND SPEED I

PIG. 24. WIND DIRECTION AN])

PIG. 25. WAVE HEIGHT AND

SPEED WIND SPEED

øaaaaauui

aoujirnenauia

auflUDLIflflUllDUU

_nounanuu.u

a'rnL1nn'rn..u.c

auu.uuuuuø

aIIIUINRUUU..D

o t WAVE HEIGHT ft 38-3 e 64 56w 4o 34 24 16H 12 st 3 o V.7 24.0 21.2 16.9 17.1 15.7 E 13.3 11.6 I 10.3 o 9.2 D 6.0 7.1 5.7 4.'

y

64 56W 40, 34 24 20G 12T Ir st 3 o

..11.

i

131

5

122

6 I 1 I 4 6 1 13

13594

22 1 2 4 6 6 19 1 2 6 4 15 i 2 4

sIi I

12 1.1.1111 1 I I i

I

2

HI

¡3 3 21 34 21

2UUUL

Il I 1 I 15 I i I I O

i

14

12.15 3..26

i I 1 1 6 1 3 ¡3 32

12711522

2 2 1 1 2 6 1 1 4 19 2 2 1 I 3 1 4 IS 1 2 2 2 I 3 12

wuNirwu

-.11

... 4

1 11111

.5

1 IiI11I1.6

I 2 2 2 2 2 2 I ¡3

123333331 22

i 3 3 2 3 3 2 1 1 1 I 2 2 3 I 2 2 2 I 16 I ¡ 2 1 I i 1 i 1 * 12 lI*I*J.I.I,I.I.I..3

-64 _ix 48 r 90 41 so 34 70 28 90 22 5o 17 40 k X

7n

z 4 io o

PIG. 26. WAVE HEIGHT AND

FIG. 27. WAVE HEIGHT AND

WAVE SLOPE PERIOD

PIG. 28. WAVE HEIGHT AND

FIG. 29. WAVE HEIGHT AND PRIMARY

DIRECTIONK[Ipy

WAVE DIRECTION

2437 i 38-3

13 3 2437 i

N

IE

S sw W M C T

11.9 2441 45 211-2

(45)

W64 ¿»4e D »

»34

HOURS DURATION OF EVENTS

PIG. 31

WIND SPEED DURATION

H Q

tjH

HZJ H

au

H

o

H TI 18 4 s 36 42 48 4 s 66 2

6 64 9.9.+

MflX T T H z rn o> -I

zo--inr.-D oz-*

- ,

t

...

Î

t - LA - t

-I

-IA Î t

t

;li4flîT:1WsI

IITIL'WM

3 62-3

(46)

>64 I 1 P'41 >48 > >34 -i. S '28e 11I'

-.

r_

1 £U I

fl

P >22j1 --I

rrrv

>17 k >11 u>7 k > 4 1 1

1'

n 2 18 ¿ 30 36 2 -ti j 66 ¡2 78 tu 90tub MAX TI T Ts

HOURS INTERVAL BETWEEN EVENTS

w

PIG. 32.

WIND SPEED INTERVALS

6

12 18 24

30 38

42 48 54

60 66 72 76 64 9096+

PTG.

4.

WAVE HEIGHT INTERVALS

>64 _'*1_,z1p1

i1'W4

>64 W >56 >46 >40 >34 M >28 Ç >24 1>20 >16 >12 >9 ç >6 t >3

-IU11ZK1

-_____

_--________IiJTIW1i1Kfl

ThW-wI

a y >48 >40 »34 H '28 Ç >24 & '20

>16 B4

1U 1'El.

IC*.'UUP#1II441sI;)

»12 I%N'I'

'9 U!NIII

f > 6 UCIi4 t. '3

IIIlE*stsU4

i

38-3

2 37-3

6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96+ MAX TE T T

FIG. 33.

WAVE HEIGHT DURATIONS

i

38-3

MAX

(47)

. 15 .14 W >13 .12 .10 S >.06 L >.06 F >.03 >.02 .0t >64 i .

1.UNi}lil'ThiJ

1i*l.f I

i1Ii

11CIL.NÁ*1

I I

I-6

FIG. 35.

WAVE SLOPE DURATIONS

i

. 15 . 14 W , 13 . 12

: 1111

. 11 .10 s >.c

(WII'i'i'

6 12 18 24 30 36 42 48 54 60 66 72 78 84 9096+ MX T

FIG. 36.

WAVE SLOPE INTERVALS

6 12 18 24 30 6 42 48 54 bU bb f tu JUb

107-3

38-3

>w

-->20 I

-->16

--1; >12 9

U'

6

--_Il__________

t

3 _1__

--TE T MAX

FIG. 37.

WAV1

ETHP ANP

TOP1 flTTRAPTnr

1;1;J1J

i.1f.1'ThJ

57 283-1

12 18 24 30 36 42 46 54 60 66 72 78 84 9096+

tlx

T T

(48)

>f;4 >48 >40 >34 tI >28 Ç >24 1>20 >16 >12 >9 t. >3

55

6

12 18 24 30 36 42 48 54 60 66 72 78 84 9096f _{HOURS INTERVAL BETWEEN EVENTS}

FIG. 38.

WAVE HEIGHT AND SLOPE INTERVALS

69-2

II

I_____

u._--u_____

--

;_;

EI,:P:.0

JWsI'.I II.IIW'I;I')4I'$

1 1;R'i.UIIPPAi'UPl

¡

I'-I) 4P AS