Extreme value and rare occurrence wave statistics for northern hemispheric shipping lanes

5 JW4L 1960

ARCH

EF

EXTREME VALUE AND RARE OCCURRENCE

WAVE STATISTICS FOR NORTHERN HEMISPHERIC

SHIPPING LANES

by

William E. Cuxnmins

David W. Taylor Naval Ship R&D Center

Senior Research Scientist

DTNSRDC, Code 1513, Bethesda, MD

20084

202/227-1868

Fellow, SNAME

and

Susan L. Bales

David W. Taylor Naval Ship R&D Center

Group Leader, Surface Ship Dynamics Branch

DTNSRDC, Code 1568, Bethesda, MD

20084

202/227-1107

Member, SNA

(SNNE/STAR, June 1980)

Lab. v. Scheepsbouwkun e

Technische Hogeschool

Deiff

ABSTRACT

In 1975 the U.S. Navy initiated a

-. project to develop a new ocean wind and

wave climatology using its Spectral Ocean Wave Model (SOWN). The project was to consist of the hindcasting and subsequent parameterization of dirc-tional wave spectra fOr about twO thou-sand locations, systematically Spread throughout the Northern Hemisphere. The

Process vas to be performed at six hour time intervals over a twenty year time

span. This paper presents some initial results de±ived from the emerging hind-cast data set and concentrates on extreme

and rare sea conditions.. Extreme seas are taken to be those characterized by a

ignificant height of 10 m or greater and are presented for locations in the Atlantic basin that are on or near major shipping lanes. Comparisons with

loca-tions along Pacific shipping lanes are also provided. The slope of extreme waves, believed to be a majcr coritribu-tor to operational failures, is examined. Seasonal variations, important to the selection of optimum shipping routes, are shown, and variations in extremes for different years are identified and com-pared with averaged annual extremes. Finally, comparisons with historical sta-tisticaldatã as well as point spectra derived from buoy measurements are given. It is concluded that the sea condition data developed by hindcasting offer a substan-. tial new capability to the ship designer. For example, the identification of long wave periods associated with extremely high wave is valuable in the seakeep-ing and survivability analyses of larger commercial and naval ships as well as those.advanced ship concepts with low frequency resonances.

INTRODUCTION

Just over twenty-five years ago, St. Denis and Pierson (1)1 introduced the concept of the ocean wave spectrum to the naval architectural rofession,

and this period has seen wOrldwide research efforts devoted to the study of how ships respond to natural waves. Special facilities have been built, many

full scale trials have been conducted, and much significant theoretical.

research has been published. Technology has now reached the state in which

application of theory alone provides quite good estimates of ship performance

for most cases when the form of the ship and the wave spectrum can be specified. While there remain some areas that require further research (nonlinear responses, the effect of above water

shape, and maneuvering in quartering seas), the primary interest today is directed toward the merging of this maturing technology into the ship design

process. More specifically, current interest is focused on both the develop-ment of a design practice which permits

the establishment of. quantitative mea-sures of desired or needed seakeeping performance and the confirmation that

this performance is actually achieved in

the real world.

The U.S. Navy has had a continuing interest in the problems of seakeeping and is currently modifying its design procedures in recognition of the impor-tance of its needs in this area. In

1975, the Naval Sea Systems Command sponsored a workshop, held at the U.S. Naval Academy, to consider the problems of incorporating seakeeping cons idera-tions into ship design (2). Representa-tives of industry, universities, and various government and private labora-tories participated in this conference. As a result of the workshop, there has been a strong shift in direction in the Navy's research on seakeeping, with less attention being given to the mecha-nism of ship response and thore attention to the development of usable r.easures of ship performance. For example, particu-lar attention has been given to quariti-Lying the degradation of various ship systems in seas of increasing severity. The objective is to assign meaningful numerical measures to the required level of performance and then to design o

these measures.

Numbers in parentheses designate references at end of the paper.

As these ideas be.gantocrystalize at the Seakeeping Workshop, it becarae

clear that an element essential, to the.

development of quantitative performance measures was missing. This was an

unbiased, universal wave climatology which could be used as a foundation for

accurate assignment of measures in ship specification and as the basis for an objective comparison of design optiOns. While it was recognized that catalogs of estimates of wave height and wave period, such as that developed by Hogben and Lumb (3), exist it was generally recog-nized that their usefulness was limited by several factors. For example, though such data bases are quite useful, they contain visual estimates by many ent observers on ships of widely differ-ent sizes and limited to particular ship-ping routes. The presence of error and bias cannot be ignored. Also one criti-cal element, namely the joint directional and frequency distribution of all wave trains simultaneously converging on the area of observation, is completely neglected. In fact, in spite of the twenty-five years of progress made since the St. Denis and Pierson paper (1), only a miniscule number of measured directional wave spectra are available, and hence no reliable statistical sum manes of them have been developed for application by the naval architect.

Though it was clear at the Seakeep-ing Workshop that the required wave data base does not exist, it was also deter-mined that the technology for generating

it did exist and in fact, was already operational at the Navy's Fleet

Numeri-cal Oceanography Center (FNOC)2 in Monterey, California. In brief, FNOC utilizes the wave prediction model developed by Pierson and his associates

(4) at New York University. The model is based on the numerical solution of

the spectral energy balance 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 spec-tral components (variances) for a set of specified frequency bandwidths and around-the-clock wave directions.

The operational FNOC model, known as the Spectral. Ocean Wave Model (SOWN), is run twice daily to provide 12, 24,... 72 hour forecasts of wave conditions for about 2000 locations or grid points throughout the Northern Hemisphere (5). These forecasts are routinely used for weather routing of U.S. Navy and Military Sealift Command ships. Wind fields, derived from certain meteorological data, are used as input to SOWN from which wave systems are predicted and followed

2

Until 1979, this organization was known as Fleet Numerical Weather Central

(FNWC).

2

.:as thy propagate throughout the ocean

-basins. At each of the grid.points, the propagated wave energies are summed to provide the current local prediction and

the starting point for the next twelve hourly prediction.

While retaining these operational forecasts could eventually provide a useful data base for ship design applica-tions, the variability from year to year

'5 considered to be so great that there

would be an extended period before a suf-ficient number of seasonal weather cycles would provide a reliable statistical

basis. A more attractive possibility was proposed by FNOC participants at the Sea-keeping Workshop. That was to use

his-torical meteorological data, sufficiently archived for about twenty years, as a starting point for the wave prediction process, and thence 'hindcast" wave con-ditions throughout the Northern Hemi-sphere at sequential time steps. The

product would be a set of directional wave spectra, at six hour intervals, for all seasons, throughout most of the operational area of the U.S. Navy. Such a data base would be free from observa-tional and geographic biases and would provide the type of environmental speci-fications needed for the quantification

of ship performance..

It is not surprising that the development of the proposed hindcast wave climatology became an essential

component of the Navy's seakeeping research program initiated in 1975. While the number of spectra to be

calcu-lated was very large (up to about 2.92 x 10° Northern Hemisphere spectra per year), all of the spectra would neces-sarily be generated in the hindcasting process, and so it was decided to retain the entire data set.

Much of this data base has now been hindcast by FNOC for both the Atlantic and Pacific basins. As of the Fall of 1979, about eighteen years of hindcasts are completed for the Atlantic and over twelve and a half years are completed for the Pacific basins. Hindcasts for the Indian Ocean and the Mediterranean Sea have not yet been initiated. As the data is hindcast, it is forwarded to the David W. Taylor Naval Ship R&D Center

(DTNSRDC) for analysis and

parameteriza-tion. Enough of the DTNSRDC work has now been completed to make it worthwhile to extract some useful information which previously has been unavailabl,e to

the naval architect. This paper is the first public release of findings from

this source.

Based on tl"e.theme of this Star Symposium, a number of important results

for ship safety are p.esented together with other findings of interest to the

profession. Much of the hindcast data were only recently received and analysis

Table. 1 Typicai Hindcast DreCtiOna1 Spectrum (Vanancea)

USTR .89

H1/3 10.35 FT SIGNIFICANT WAVE

HEIGHT

is incomplete. The results presented in this paper are limited to a ten year period from September 1959 to August 1969 for the North Atlantic, though a s&'all amount of comparison data are also included for locations along Northern Pacific shipping lanes. As it will be several years before the total task of analysis is finished, it was considered appropriate to present some of the àvailãble significant information. Although the cOnclusions should be

treated as tentative pending the analysis of the total data base, most appear to be rather well established based on convincing material.

It is noted that the Navy intends to disseminate the entire Twenty Year Hindcast Wave Climatology to the public as soon as it is. completed and in a manageable form. The Naval Oceanography Command Detachment in Asheville, North Carolina, will be largely responsible for this dissemination as well as for the publication of atlases derived from

the data set. Appendix 1 provides an organizational overview of the clima-'tology development and a brief summary of present intentions for the first atlas publication which is expected to go to print by theSpring of 1951.

THE H':NDCAST SPECTRJN

The hindcast. directional wave spec-trum at any, point of the geographic grid is represented by dividing the frequency scale into 15 bands and the directions into 12 thirty degree sectors. The variance (mean square displacement of the free surface) due tO the waves in each combination of direction and

fre-WINO DIRECTION AND SPEED. WHITE CAP PERCENTAGE. FRICTIONAL WIND VELOCITY

TOTAL

ENERGY

quency is identified, modified by the calculated local winds, and propagated to provide the next six hourly spectrum. Thus, the 180 element matrix represents the sum of 'all the wave energies beIng propagated into the grid point area from all directions, plus the contributions of local winds to the growth of each

element.

An example of a spectrum is shown

in Table 1. _{The variances in the}

col-umns are

_added

to provide a frequency point sectrum or frequency "marginal" distrIbution. Similarly, the rows are added to provide a directional marginal distribution. The sum of' all the

ele-ments of the matrix is the well, known parameter E, or the mean square wave surface displacement. Other parameters of interest and available for use are compass wind directIon, wind velocity in knots, white cap percentage, fric-tional wind velocity, and the signif i-cant wave height in feet. The compass direction of wave propagation at the center of each sector is shown as these differ from grid point to grid point. From this basic information, a nuniber of other parameters have been calculated as measures of certain aspects of the spectrum, and many of these will be

reviewed in this' paper.

The basic grid for the forecast or hindcast calculation utilized by SOWM is an array of geographically fixed points arranged in a triangular pattern each of which consists of 325 grid points with

a spacing of up to about 180 nautical miles between them. There are about 450 'grid points in the North Atlantic, 900

points in the North Pacific, and 225 WAVE UENCY DATETIME WIND SPD LOCATION 9Z 31 MAR 68 WIND DIR 267.6 58.292N i2.297W 216 WHITECPS 0 (FRED _{.308 .208 .158 .133 .117} .103 .092 .081 .072 IN ! HZ .00 .00 .01 .00 .00 .01 .00 .02 .06 .03 .08 .15 .15 .17 .07 .00 .03 .00 VARIANCE .05 .15 .27 .25 .30 .22 .01 .04 .00 ENERGY .06 .21 .38 .38 .56 .42 .31 .00 .00 .08 .19 .34 .30 .40 .06 .18 .11 .00 .04 .12 .19 .14 .14 .00 .01 .03 .00 POINT .24 .75 1.34 1.22 1.57 .78 .51 .23 .06 SPECTRuM .00 .00 .00 .00 .00 6.7 WAVE DIRECTIONS .067 .061 .056 .050 .044 .039 DIR (FROM) .00 .00 .00 .00 .00 .00 6.58 .00 .00 .00 .00 .00 .00 .7 335.58 .00 .00 .00 .00 .00 .00 1.3 306.58 .00 .00 .00 .00 .00 .00 2.3 276.58 .00 .00 .00 .00 .00 .00 1.6 246.58 .00 .00 .00 .00 .00 .00 .7 _216.58

points in the Indian Ocean. There is also a grid in the Mediterranean (about 450 points), but this is of a different geometry from those for the other basins.

The resolution of the 180 element spectrum is not as fine as desirable for wave climatology applications or for propagation purposes, but the cômputa-tional reqiirements are so great that such a compromise was necessary. _The fine structure of some available point spectra that were calculated from wave records is missing from the hindcast

spectra. However, the combination of directional and frequency information, without geographical or seasonal biases, makes the set of hindcast spectra of great value to the naval, architectural

Community.

VALIDATION OF THE FORECAST/EINDCAST MODEL

In order to develop confidence in the use of a climatology based on these hindcast spectra, it is essential to obtain and examine evidence to establish

the validity of SOWN. It was concluded at the Seakeeping Worksho that for the intended purposes, which are primarily statistical, it is not necessary that each spectrum be a completely accurate representation of the surface at each point in space and time. It was only considered necessary that collectively, the set should include no serious biases which could affect decisions in the ship design process. For example, since the waves depend upon winds, which in turn depend upon atmospheric pressures, any error in the latter may result in an error in a storm track, which might cause a sea condition to be spacially

displaced. Thi- would not seriotis-ly

affect the climatology because effects lost at one grid point would be recovered at another, and all spectra would remain representative of location and season.

It should be recognized that the coarse spatial gfld of SOWN has an anal-ogous effect to the coarse spectral matrix. In other words, the fine geo-graphic structure of. a storm is lost. In fact, this leads to one of the most serious failings of the SOWN, which is that intense local storms may be so limited in geographical area as to be missed compltely in the hindcasts. Thus, hurricanes and typhoons are not adequately represented in

the

clima-tology data base. While it is feasible to model the wave generation and propa-gation of a hurricane, it would require a very fine grid and the appropriate meteorological input to make the coinpu-tation successful. In fact, one of the most impressive validations of the prin-ciples involved in SOWM is a study Of Hurricane Camille by Professcr Cardone

and his associates (6).. His hindcasts agreed extremely well with measurements of the local seas at fixed platfOrms in

the Gulf of Mexico.

4

The validation of any numerical model is frequently a long term process,

and that of SOWM is no exception. The

sparcity of good measured data to use as "sea truth," as well as the complexities of the model, present a difficult task. At least two criteria should be used in the evaluation of SOWN. The first is per-haps the thost difficult and is simply its ability to predict realistic directiOnal wave spectra for given wind fields that vary in both space and time. The second, which may permit the determination of the ultimate resolutiOn required by future variants of SOWN, is its ability to per-mit the accurate prediction of ship

responses and related events in a

direc-tional seaway. While this second cri-terion is of great interest to the naval architect, a discussion of its

applica-tion will be postponed pending the results of recently initiated work with FNOC and the Royal Netherlands Navy.

The first criterion, i.e., the accu-rate prediction of directional wave spec-tra, is difficult to apply because mea-sured directional spectra are rarely

available. Hence, it is commonly assumed that linear superposition applies and the point spectra provided by SOWN are com-pared with those developed from wave, buoys satellite mounted radar altimeters, and other wave sensors. An initial evalua-tion of the operaevalua-tional model was con-ducted by Lãzhnoff and Stevenson (5), and they concluded that SOWN can accurately predict the propagation of low frequency energy; can cope with simultaneous wave trains; compares reasonably well with observations from an operational spectral observing station (NOA buoy); and per-mits realistic growth of high waves for

sustained high wind conditions. In a

more recent paper, Lazanoff and Stevenson (7) summarize the current status of SOWN by stating that the model generally pro-vides rather good results on a routine

basis. Further, they state that most of the errors are traceable to inaccurate wimd velocity inputs. Because of this, the wind field inputs, derived from the U.S. National Climatic Center archives for the Twenty Year Hindcasts have, under FNOC direction, been reanalyzed and modi-fied so as to provide the most represen-tative prediction of sea characteristics.

Two other validation efforts should be mentioned. A comparison of SOWN fore-casts with point spectra derived from wave buoy measurements collected by-the Royal Netherlands Navy during several sea-keeping trials (8) in the winters of 1978 and 1979 in the North Atlantic Ocean has recently been completed. The forecasts were provided to the ships -on a daily basis in order to aid in the planning of the next day's activities. The results, to be published subsequently, indicate

-that

1. Spectral shape is more áccu-rately predicted for extreme

a

3.2 0.4 06 SE 3 1.2

FREGUENCY. RE!

Fig. 1 Typical Comparison of Forecast and Measured Wave

Spectra for Significant Wave Heights of 10 m

or Greater

sea conditions with significant heights of 10 neters or more

The SOWM spectral peaks are sometimes shifted to the left or the right in comparison with those derived using wave buoy measurements for moderate/low

sea cotditions; this may be due partly to poor sampling charac-teristics associated with the modal frequency, although

spec-t.ral shape is generally better

predicted in 48 hour forecasts than with more short term

fore-casts

Parameters derived from the SOWN spectra, for example, significant wave height, pri-mary direction, secondary direction, etc., generally provide a good statistical fit

to those derived from the buoy or shipboard obseriations although ship observations may

improperly

classify longer, higher waves

The importance ef spectral shape discrepancies can be determined by sensitivity studies of predicted ship responses and related events such as keel slamming and bow wetness

2EE9 tRIO "140LL014

t 3

ISF.D SPEED 38 KNOTS

530W 7730 GUT A sowu 310.781 WO SPEED 44 KNOTS 307... 45.5W 1220 GUY SAME DAY FORECAST

to 14 12 4 B DEC1976 1YDEMAN TRIALS 0 5 DECOMOER 1979 BUOY Iw1113 738. WIND SPEED 20 KNOTS

38.IN. 20.1W

1455 GUT

£

It.),,3 7.581

WIND SPEED 26 KNOTS 40.8N. 29.7W t2 5811 SAME DAY FORECAST

0"

-a

'1.-2C0 SAY TYOEMAN' TRIALS 6407 50744 FORECASTS 3&IR. 25t'W 4008.

ORSE OWED WINO 101104957010

WINDS

Fig. 3 Typical SOWM Forecasts of Significant Wave Height.

with Corresponding Wind Speeds, for Successive Days

lB 12 IS

2NDO/\

\

3110047 10 25 30 :9 0.2 3,4 86 06 to 1.2 RRPOUENCY. RPS

Fig. 2 Typical Comparison of Forecast and Measured Wave

Spectra for Significant Wave Heights of 7 to 8 m

IS

'0

I, '2

S

;ues 1, 2, and 3 show some results from this comparative work. _{Figure 1}

rcvides a cothparisonof a SOWN forecatht with a buoy derived point spectrum for

extreme condition. Not only is the peak of the spectrum, with respect to

freency, rather well located by the

forecast,, but the significant wave

hei;t,

_(w)1/3.

also compares very well. The forecast was made for a grid point apr:ximately 540 nautical miles from the buoy and for a time approximately five hours later than the buoy measurement.

It _{s likely the SOWN misplaced this pe}

dict.on spatially due to p00± resolution the input winds. Figure 2 provides a ccmtarson of a SOWN forecast with a buoy deri-:ed spectrum for less severe _seas than those represented in Figure 1. _In this ease, the forecast is for a grid

cinz located about 113 nautical miles

frc the buoy and at a time áboüt three h.rs eariië± than the buoy measurement.

-hile the forecast significant wave height compares very well with the mea-Lured value, the spectral shape and

ially the location of the peak are ite different. _{The significance of} :hese differences can best be evaluated

NOTE: EVERY 5th GRID POINT IN EACH SUBPROJEcTION IS LABELLED. CIRCLED

GRID POINTS ARE THE SET OF 65 USED AS A SAMPLE FOR ThIS PAPER.

---

_'

Fig. 4 Selection of Representative Grid POints in the North Atlantic Basin

by calculating their relative impacts on

predicted ship performance parameters and will be pursued in subsequent

studies.

Figure 3 provides a typical'comparj-son of updated predicted significant wave heights bver a period of successive days as compared to that derived from the buoy

measurements. _{Additionally, the updated}

wind speeds used as input to SOWN are

shown for comparison to the observed

wind. Clearly the wave height parameter is correctly predicted for this typical

case and this' is partly due to the rea-sonable agreement between the tine coin-cident wind speeds.

Another evaluation of SOWN predic-tioris has recently been reported by Pierson and Salfi (9). _{They compared} GEOS 3 satellite radar altimeter wave heights with those forecast by SOWN for orbits in 1975 and 1976. In general, they found that the SOWN predictions of significant wave height were somewhat lower than those indicated by the altim-. eter and that the larger differences between the. two may be due to poor wind

field specification fOr SOWN.

As Lazanoff-arid Stevenson (7) con-cluded after completing comparisons with Ocean Stat-jun Papa measurements, the wind sPeeds input to SOWN have been biased to the low side in the past, but the signif-icant wave height differences tend to be

random. This is an important conclusion for purposes of the Twenty Year

_Hindcast

Climatology. - it is far more important to the naval architect for the long term errors to be random than for the model to provide absolute accuracy with regard to space and time. Thus, it is

noted

again

that the Twenty Year Hindcast Wave Clima-tology is

intended

_{to provide a} statisti-cal basis for evaluating the effects of the environment on ship and other marine

structures. _{To expect the climatology to}

provide accurate sace-tirrte predictions such, as those required by casualty

analy-ses-- o _{other exacting- studies 'is in'}

vio-lation of the assumptions upon which -it

is derived.

In any event, the wind fields input to the SOWN model for the twenty year hindcasting have been refined so that they are somewhat stronger for moderate to high conditions. It is noted that the next generation SOWN, based on a longi-tude-latitude grid and with twice the

directional

resolution of the current node-i, is under development by FNOC. It is expected that the, finer directional resolution may make validation a simpler task when shi.p responses are used as a basis for the comparisons.

One further comment regarding SOWN validation is in order. Though, it has not yet-been conclusively establishd, there is some concern that SOWN predic-tions in the lower latitudes may be

mis-leading. This is due to the fact that inputs to the model f-ron south of the equator

simply

do not exist and that wi-nd

inputs just north of the equator may be suspect in both strength

and

direction.

Tab le.2 Location of Selected Grid Points in North Atlantic

As the equatorial regions generally offer little threat to shipping (except, of course, during tropical cyclones), this pOtential inaccuracy in SOWN should not be of great

concern

to the naval

archi-tect.

EXTE'IT OF PRESENT STUDY

Because of the large size of the data base which is the foundation of the Twenty Year Hindcast Wave Climatology and for the purposes of this paper, it has been necessary to sample the total set of

spectra, rather than to use the entire

collection. _{However, this has been done}

in-such a way as to provide meaningful and reliable conclusions. _{As indicated} previously, the study is primarily limi-ted to "the period September 1959 to August 1969 and to a set of 65 grid points in the North Atlantic. The sample locations are identified in Figure 4 as the circled points, and they provide fairly complete coverage from the trade wind belt up to the No±wegian Sea. Other points indicated on Figure 4 are the- remaining grid points in the 6 North Atlantic subprojections

(triar.gles)

included

in the Twenty Year

Hindcast

Wave Climatology. The 65

loca-tiOns of this sample include all of the North Atlantic Weather Ships except E

and N, the locations of naval interest defined by Bales

_and

Foley (10),

and 50

locations for which weather data is rou-tinely provided,

in

an operatiOnal sense, by FNOC and the Air Force. _{The 10 year} time period is considered sufficiently long to provide both a moderate degree of

seasonal variability'

and

a sufficiently large sample of points for stable statis-tics. The results presented

in this

paper are derived for one or more of the

65 pts. Those individual pOints

ingled out for analysis generally are located along heavily traveled shipping lanes and are identified on Table 2.

GRID POINT SUBPROJECTION LATITUDE (NI LONGITUDE 'W)

129 - 3 . 58.6 . 24.0 128 3 --- 58.5 182. 127 3 - - - 58.3 12.3 -149 3 - 55.9 _26.6 147 .3 55.8 15.7 184 - - 3 50.6 _-21.5 279 2 - 46.2 44.9 244 - 3 39.9 21.8 228 . 2 34.1 52.8

?AR!.ETERIzATIQN OF DIRECTIONAL SPECTRA

The wave spectrum at any locatIon at any :articular instant is, in principle, as unicue as a fingerprint, since it is the s- of local weather conditions and waves from many different disturbances at many d.fferent times. This potential variailitv is significant, but in order to- discuss a set of spectra meaningfully, and to ceneralize the characteristics most significant to the naval architect,

it

is desirable and aimost essential to define nu.erical parameters which can be used to measure these characteristics. Some of these parameters are already well known (for example, significant wave height- and will be used in the following

discuss:on. However, since this paper centers on a massive set of data not pre-viousiv available, it has been necessary

to deveiop some new parameter types. All of these, old- and new, will be defined in

this

3GCOfl.

It should be noted that more than

one arameter can be used to describe a Particuar characteristic. In most cases, this duplication is due to

con-flictinc recuirements. The most

meaning-ful arameter for measuring a

character--isoic ma require significant computing time and thus be too costly to apply to the entire hindcast data base. Its use is necessarily limited to the discussion of sampLes (stratified or completely random) taken from the total set.

The arameters used in the Presenta-tion and discussion of data in this paper

are

4oments, in0. These are given

n

=EE1(..)...jfl

(1)-1aricus moments are used in the formulas for wave eriod and wave slope

parame-ters. The higher order moments diverge for certain theoetical distributions

(for example, in, and higher for the

Bret-schneider spectral formulation).

How-ever, since the hindcast directional spectra are bounded in frecuency, this is not a :rcbiem here. It should be remem-bered that i. conparing moments of the hindoast spectra with those derived fo z:eoret.cai spectra, this truncation

could h-ave an import-ant effect,

partic-uiariv in calculations which are

influ-enced the high frequency tail.

2. 5ignficant Wave -Height,

. Thisparète

s defined as

the a'érage of the one third highest waves crest to trough). It is eual to

Variance or mean energy density, H. This parameter is the variance of the instantaneous surface displacement. Note

that E = in0.

Periods, T. Historically, a variety of wave periods have been used to characterize the spectrum and its associ-ated waves and they are usually derived

froth the-various moments. The modal period, T0, is the exception, in that it

corresponds to the central frequer.cy,

_0'

of the cell of the frequency marginal with the highest density. Then,

T0 = 2r/0 (3)

T0 is a simple parameter with intuitive appeal, but has poor sampling qualities. It is in any case arbitrarily defined 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 error. The modal period is more useful in treat-ing groups of spectra, where the errors may average out, than in describing a particular spectrum. As they depend upon

the- weights of -all the cells, the periods

based uon moments are better defined. These periods are described below.

Zero crossing period, T.

T = 2ir(m0/m2)½

-- (4)

This is the average of the periods between zero up-crossings of the wave

surface displacement against time.

Crest period, T.

-T = 2r(m2/m,)½

This is the mean period between crests

at a point.

Other periods coziinOnly in use,

though not treated here, are , the

period corresponding to the average frequency and T-1,- the average period

Since this is a. new parameter, its den-= 2rm0/m.1 (6)

T_1 = 2rxn1/m0 (7)

The first of these is recommended by the ITTC for characterizing a spectrum but is not used here because it correlates so strongly with T that they can hardly be considered inãependent measures. The

zero crossing period is preferred

because of its greater physical

signifi-cance.

5. Wave Slope Parameter, n. This

is the root mean square of the absolute slope at a fixed point. It is given by

0 =

(3)

where is circular freuency. For n = 0,

vatcn is given. The surface elevation,

;, in pace and time may be written in the form

;(x,y,t)

=Eaj

cos(k(x cos5 +

y sin)

-I,.

where k1 is tha wave number,

_/g, of any component,

_j

is the direc-tion of the source of the waves, and is a random phase angle.

=

-Ea.kjcosG.

..

sin(k. (x cos.

+ v

sinE..)

1 - 1

-.t

.1

=

-Ea.ksine.

sin(k(x

cosE.

- y sine.)

i.t +

E.3 1. 1 = (d.;/dx)2 -i- (d;/dy)2

a1akkccs.cosE.

1 J sin( 3 .sin(

Ea.a.k.ksin.sinE.

sin[

_Jsin[

_3.

;veraging over

_x,

y,

and t

=

½{Ea;:"o:

= a.2k.2 since sin[ ].sin[ = unless i

= j.

-.it since

(;)2 =(l/2g2)a._._

=(l/g2).._E

since ½a12 is the variance, E,

component. Thus

-.2 =

= m./g2

6. Nean direction, e. This is obtained from the directional marginal

distribution by assuming the directional

distribution to be a weight distribution

around the unit circle.

The centroid

of

the

weighted circle is

or

The rectangular coordinates are

given by

(18)

=(i/E)EE(e)cose

(19)

and

The usual division of the yearly cycle into spring,

summer, fall and

winter suggests a sinusoidal variation

-at least in the mean.. While

it

is

generally recognized that this model is

father simplistic, and that deviations

within

a

year and between Vears

can

be

large, an accurate discussion of the

seasons

has up to now been

impossible.

The hindcast climatology provides data

which permit an accurate analysis of

these patterns.

k. = (15) VARIATION OF SEASONAL FATTERN

C =

(P2

+

(20)

x is toward the East while Sj is

the

(10) compass direction of the ith marginal

sector. The parameter p also has

sig-nificance. It is one of three

paraxn-eters which help characterize the shape

of

the directional marginal. A value

near one implies a nearly unidirectional

seaway, while a value of zero implies a distrIbution without any definable mean direction (for example, symmetric about the point of observation).

7. Directional spread, m. This is.

a measure of the angular spread or width

of the directional margin about the mean

direction.

It has the form of a second

moitènt, and is the radius of gyration of

the weighted unit circle about its

mean (12)

direction axis.

2 _{=(i/E)EEjsin2(ej_O)}

(21)

8. Skewness parameter, q. This

parameter 1s nt used in the present

paper, but

it

may be noted that the five

paameters E, p,

m,

and

g

are suffir

cient to determine

the first five

coeffi-cients of the Fourier series for the

directional marginal. These are the

coefficients which can be deterxniited froi

a

recording

of all the motions of

buoy

which is free to

respond

to the waves.

The parameter q is given by

12

2/

2

V1V63 0/1/03 I

Fig. 5 Fourier Mean for Significant Wave Height. Grid Point

147. 1962/1963. With Range of Values for Each Week.

The variation

of wave conditions

during a year consists of a succession of mild and severe conditions, each of a

few days duration, superinposed upon a mean seasonal effect. For this

discus-sion, it is this latter effect ich is

of interest. The device which has been used is a five term Fourier series given by

()

1/

(t) =

a0 +

a1ccs.:

+a2cos2.t bsin2...t (23)

where the period, is 365.25 days. The presentation is a least scuares fit

(up to the second harmonic) and it smooths out all oscillations shorter than about three months. I:

permits

the

fall rise and the spring fecline to occur independently, and the winter peak and swnrner low need not be directly opposite. While the shape of the

result-ing mean is somewhat influenced

by the

character of the five tern famil,

includi.ng additional terms would

tend to give greater emphasis to fine structure

(individual long storms

Cr

lows) rather

than

the

gross characteristics which are

of

interest here. The

constant

term is

the mean significant wave height over

the year. The other coefficients have meaning collectively and are not treated as independent parameters.

The relation of this near. curve to the actual conditions of a wearly cycle is

shown in Figure 5, where the high and

low

of

the range of significant wave

height in each week i

superimposed on

the mean curve for grid point 147 for the year 1 September 1960

to 31 August

1963.

Figure 6 shows r.ir.e

earl

cycles

for grid point 127.

This location

experiences some of the wcrst

wave

con-ditions in the North Atlantic and is

representative of

a large area extending east towards the Irish Coast, north to

10

2

3/

S/I IC/I 77/1 13/1 Ill 2/1 21 4/1 5,1 S/I I US

t'

MONTH/DAY

Fig. 7 Average Variation of Significant Wave Height for Grid

Point 127 for Years 1959/60 to 1968/69 SI to/I

5/1.57 10 II 12 I 2 3 4 5 1 7 I 9/1

MoNt.omAv,ynn

Fig. 8 Seasonal Variation for 1967/1968 for Various Grid

Points in the North Atlantic

I/I 7., Ill In

Fig. 9 Nine Year Averags for 7 Grid Points in the North Atlantic

2/1 3/I Ill O/l WI

Fig. 6 Seasonal Variation of Significant Wave Height at Grid

Iceland, and south and west or some hun-dreds of miles. Figure 7 presents a

nine

year average for grid point 127 (the year 1965/1966 was not Inc1ded because of. a seven month gap in the parameterized hindcast data which irival-idates the Fourier representation).

Considering the nine year average first, the most moderate conditicos usually occur in late. July, with a mean significant wave height of about 1.5 m, and rise rapidly to a peak of abcut 5 m around 1 February. If a alue of 3 m

(about 10 feet) is considered as the threshold of severe waves, the average significant wave height exceeds this value over six months of the year (from

early November to early May) . Using a value of 1.5 m or about 3 feet as the upper limit of modeate coflditions

(usually described as Sea State 4) , it

may be noted that the mean line exceeds this level for the entire year

Returning now to the curves forthe separate years, it is noted that varia-tiOns from the 9 year mean are great. The initial, rise above 3 m can occur from

ear-ly September to 'late November nd the drop below 3 m from early April to late

June. The peak can be in late Novezber, or-as late as mid May. The suzrner 1ot is

equally ill-defined, ranging frc:r. early

June to mid September. The peak iaries from 3.8 to 5.6 m and the low from 1.4 to

2.1 m. The average annual significant wave height ranges from 3 to 4 n. It is

evident that wave data taken even over a whole cycle can be very misleading as to

the-

onditions

that catt be expected in

this region over an extended period. It

is also evident that seakeepirig qualities should be-considered highly important for any s-hip which is expected to operate effectiie1y here, since the 3 signifi-cant wave height is exceeded on the

aver-age during 61 of' 108-months considered.

The seasonal variation for seven

grid, points- for 1967/6 8 is shown in Figure 8. The variation between differ-ent regions is great but this is to be, expected as the conditions are expected to be more moderate in the south (grid points 244 and 228). More surrising is

the variation within the severe wave region west of Ireland. While the four grid points 127, 129, 147, and 149' are all in this region, and examination of the hindcast directional spectra shows that they usually experience the same storms, the winter peak occurs earlier to the south and west (early March at 149) and latest in the northeast early May -at '127)

As h-as already been stated, conclu-sions based on a single years data may be misleading, so the nine year average curves hown in Figure 9 are better

-suited for showing regional variation.

-Here the fOur nearby grid points clearly'

show, the same character, and the modal month is about the same fOr all. Point

279, east of Labradot, is a heavy traffic area which also- experiences heavy weather with a 5 m peak average, but the differ-ent character of the curve is eviddiffer-ent. The 3 m season starts a full month

later. Grid points 244 and 228 reflect conditions in the southeast and south-west zones, both moderate, exceedinc three meters for about three months, but with conditions peaking about two months

earlier in the eastern zone.

.14

.12

.10

WAVE SLOPE

Wave slope is considered by many naval architects to be almost as irc-tant as wave height, and for scme pur-poses, even more important. It is

strongly dependent-upon the shorter waves in the spectrum which respond rapidly to the wind; andthe-'ave slope might be expected to grow faster than

the

significant

wave height, which- is

an unweighted sum of all of the wave components and grows slowly in the

longer components.

-+

.04

+

0 -' 3 6

9-SIGNIFICANT WAVE HEIGHT. N

Fig. 10 Wave Slope vs. Significant Wave Height at 30 Hour

- Intervals Between 1 September 1967 and 31

December 1987 at Grid Poiñt127

12' +

The parameter ., fined as the

root mean square slope at any poir.t (whatever its direction) is used here as a measure of this characteristic. As

this parameter has not been widely used? the significance of its range of values may not be immediately actreciated. A

reular wave with the ratio of length to height (trough to crest) of 22.2 has a value of - of about 0. 1, a very steep

wave. In the current 10 year sample, hindcast spectra have bee found with values exceeding 0.14, about a 16 to 1

wave. Short-crested waves have a higher 'alue than long-crested waves at the same height a±d period.

The parameter has no: -been

calcu-lated routinely for the entire data base, and more studies of wave slope are expected to be carried out using

care-fully elected samples. '. other words,

this study is just beg.nnin. However,

there are several tentative conclusions which can be presented at this time. Figure 10 shws a plot of against

sig-nificant wave height for grid point 127 for every 30 hours between 1 September and 3 December 1977. While clearly there exists a correlation, it appears to dis-appear for significant wave heights of less than 5 m. To exaoine the ccrrela-tion at higher wave lenoths, Figure 11

was prepared. _{This shows the succession} of peak values of exceeding 0.1 for the entire year of 1967/68, with the corre-sponding significant wave heights. Again, it is evident that there is a

relationship, but the increasing scatter for higher wave heights suggests that it

is weak.

Recalling th. cOrr-en: at the start of this section that wa-ic sloce night be expected to follow wind speed very closely, the same pea-k values of shown

- in Figure 11 are plotted :n Fiure 12

against wind speed in knots. bove 30 knots the scatter is very moderate and the relation &ppears sz±bngl linear.

.14

+

.08

0 3 6 9 12

- SIGNIFICANT W. VS )4EIGHT. M

Fig. 11 Peak Values of Wave Slope vs Significant Wave Height..

During 1967/68 at Grid Point 127

12

Fig. 12 Wave Slopevs. Wind Speed for Peak Values of Wave

Slope During 1967/68 at Grid Point 127

The line shown was obtained by linear

regression. The correlation coefficient of the dath points in relation to this

line is 0.935. Figure 12 permits the tentative conclusion that wave slope can be expected to be a linear function of wind speed above 30 knots.

DIRCTIONAL DISTRIBUTIONS

The sea condition at a given location is the sum of locally generated waves and waves or swell coming from other distur-bance areas at various points of the

com-pass. The locally generated waves have a continuous distribution over a range of directions, while the swells may be nearly unidfrectional (from distant sources) or approach the degree of con-tinuousspreading of local seas (as would

be the. ease for nearby storms). In the absehce of a body of. data, it has been the practice in ship design to assume that the waves are either unidirectional or that the energy varies proportionally

to cos2(-e0). The difference between these two assumptions is considerable in the effect on many ship responses,

par-ticularly roll. However, there have been no statistics of any degree of reliabil-ity to neasure the merit of either

-assumption.

-A full treatment of this direc-tional quality is beyond the scope of this paper, as it involves difficult com-putational algorithms which will necessi-tate selective sampling techniques.

How-ever, it is possible to exhibit the nature of the evidence which bear upon

this question from the Twenty Year Hind-cast Wave Climatology.

It is assumed that a unit circle is weighted by the directional marginal

dis-tribution. That is, the density of the circle circumference in any direction is equal to the variance density in that

direction. A unidirectional source would be a discrete point mass on the

.12 -Lu C -S U, Lu S .10

-unit, circle.

_{In the r.zr.x}

:_nt-tion of the family of hindcast sPectra, there would be twelve discrete masses centered in the twelve sectors. As a measure of directional sreading, rn2 is

taken where m is the radius of gyration of this weighted unit circle about the

axis through its centroid.

The value of m2 can rance from 0 to

1. Zero implies that all the wave energy is arising from one direction, or from two opposite directions. If the distri-bution has the form of a cos-

distribu-tion over a range of andes, 2:, the

marginal distribution with respect to direction has the form

5(3) = E/;0 C0S21[(t3_3c)/;o] (-/2)t (24)

for 3-3 <c

= 0 elsewhere ₍₂₅₎

The spreading parameter has the form

= ½{i - [l_(2c0/)_] . (sin270)/(2;0)} .5 .4 3 0 .2 .1 0 (26) 13

It is clear that this parameter is far from definitive as to what is being mea-sured. The combination, m2 and _{, where}

is the radius vector of the centroid of our weighted unit circle, is much more

informative, but this is beyond the scope of this paper. 30 uJ 0 a uJ 0 U C., C I.-a Cu 10 Cu a. .1 .2 3 .4 .5 .6 .7 SPREADING PARAMETER, m2

Fig. 14 Histogram for Values of Spreading Parameter m2 from

Hindcasts for 1967/68 at Grid Point 127

The relation of m2 and significant wave height has been examined

superfi-cially by a count of occurrences in joint cells for the year 1967/68 at grid

point 127. The marginal histogram for obtained from this count is given in

Fig-ure 14. The count suggested that these parameters are virtually independent. This might be expected for lower wave heights, which are usually a nix of sea and swell, but is surprising for higher waves, which are more typically the result of strong local disturbances and would be expected to be rather uniform in their directional structure. _However, the values of m2 range from .05 to .43 for waves greater than 5 meters. The

peak in Figure 14 at m =

0.25

corresonds

to a value of of 90°, see Figure 13, but these two figures show that values of

o from 60 to 120° are frequent.

A full explanation of the behavior of this parameter must await an analysis

carried out in much greater depth. _But the significance for the naval architact

is evident. While unidirectional seas are rare, at least at this geographic location, the assumption of a cos2 dis-tribution over + 90° corresponds to the peak in a fairly wide range of observed

values. For any ship response charac-teristic which is sensitive to the degree of directional spreading, the range of possible values of m2 should be taken into consideration, together with an appropriate probability measure. This

aspect of the data base will receive extensive treatment in future studies. 20 40 60 80 100 120 ¶40 160 180

DEG

Fig. 13 The Spreading Parameter m2

This function is shown in Figure 13. The

usual assumption that : is 90: ields a value of m of 0.25, while a ccs2 distri-bution over+ 1800 yields a vaiue of 0.5. Superimposing a swell on acos- distribu-tion generally increases n-, unless the swell is r.ear the axis of the ccs2

dis-trthution. Values of m- reater than 0.5 suggest that several disturbances from widely different directitns are present.

:x:RF.z SEAS

For ourposes of this taper, extreme seas have been identified as those with a s:tnf:cant wave height of 10 in or

creaer. it was considered to be of interest to the naval architect to

iden-those occurrences for the 65 point, year sample under in.'est:gation in

this taper. Without excet.on, all of

the rcatons in the samcle nQrth of lat-30° indicated at least 3

occur-rencas of 10 in waves. The total number cf tcurrences for the lC year sample '.zas

373, some of which occurred at adjacent

t1-e stes. Figure 15 shows a contour of the nzther of occurrences throughout the ;eographic sample. The greatest

mci-dance is for those locations between 55

and N, and, in that regon, occur-rences are somewhat more n'.erous on the western s:de of the basin. :ch1e the sc;: node is not an idea: redictor for the :rth Sea region, it is noted that 18 occurrences were indicated for that

ntcrtant marine area. The most extreme

70:_

N

0-W 0° E

I P

NOTE: NUMBERS AT GRID POINTS INDICATE NUMBER OF OCCURRENCES OF 1OM OR GREATER

200 &

,,.

>_-___ 90° L

_k

) -,-

_{.-_,&}

_'

;-;: :, ---

i.,.

₀ 0 0

.7':_

-.

100

- 50

25 .,

0.

conditior,s predicted exceeded significant wave heihts of 20 m and examination of the corresponding directional spectra reveals the modal wave periods to be 20 seconds or greater and the directional spread to be reasonably symmetric. As

one might expect, the extreme point spec-tra typically resemble that of the

Pierson-Moskowitz fully developed spec-trum and the T parameter, discussed earlier, is typically about 15 seconds

or so.

The winter of 1967/1968 has previ-ously been described as a rather severe

season. Figure 16 presents a time

his-tory of significant wave height and wind speed for the month of March 1968 at grid point 127. The most extreme height

(significant wave height 17.8 in, wind

speed 48 knots) occurs on the 17th of the month and is, in fact, the extreme occur-rence of wave height, at that location,

for the season. It should be noted that the extreme wind speeds either match or just precede the extreme wave height

_; f SP2

'1

,-. 133

\r:

---,----r

1_,

196 11+ 'a -w

/

o ' 05

-

0 _o

;'

-...

,__J...,-Is..

-

_-.,

-p. -I.-.

.'s-

S

-,---

-21 SP4 218₀ 161 I 185 ;:: :'

_'-'--:

S.. SP5 SP6

.

Fig. 15 Contours of 10 Meter or Greater Significant Wave Height Occurrences During 1959 to 1969

¼ 'S

S..-

/

/-'.

..-...-p.

S.-30: 30° 60

Table 3 Persistence of Significant Wave Height at Grid Point 127 During March 1968

0

15

Fig. 16 Sample Storm Growth and Decay at Grid Point 127 SIG. WAVE HT. (METERS) EXCEEDENCE OCCURRENCE TIME BETWEEN OCCURRENCES (HOURS) OCCURRENCE DURATION (HOURS) TOTAL EXCEEDENCE TIME (HOURS) 1.5 1 0 744 744 3.0 1 36 6 2 6 72 3 108 42 4 210 30 5 60 24 6 _{132 552} 7.0 1 ₄₈ 216 2 120 162 3 48 216 10.0 1 ₁₂ 258 2 48 60 2 I-=

I'

A 0 'U

II

w 12 > SI I It 4 2

jil

I- I I 2 4 I I C.,

28

0 I

II

F., j I I

jI

I) I) WAVES 20 - - - WIND I;

-I

lvi

I Al 16 2 4 8 10 12 14 16 18 MARCH 1968 T I Y t1

II

S

I)

26 28 30 50 40 2 2 a a, -a 30 a, a 2 0 In 20 10

Table 4 6xtrerrie Spectium Hindcast for Grid Point 127 on 17 March 1968

9z 17MAr58 58.292N 12.297W

WIND !R 252.5 WIND SF0 48.4 WHITE CPS19 USTR 2.46 100

80

60

40

TEN YEAR HINOCASTS GRID POINT 127 1959/69

HOGBEN AND LUMB AREA 2 1953/61 .072 .067 .061 .096 .050 .044 .039 DIR (FROM) .01 .00 .00 .00 .00 .00 .00. 2.23 2.07 2.25 12.05 13.28. .00 .00 3.16 4,49 6.27 8.77 11.42 7.60 1.45 3.15 4.55 6.72 0.15 14.91 16.54 5.68 2.17 3.01 415 5.66 6.70 5.85 1.13 .26 1.31 3.76 3.86 85 .77 .10 .01 1099 .17 15.60 .01, 2316 .00 40.49 .04 47,20 .02 30.78 .01 8.37 3.0 336.58 38.8 306.58 52.4 276.58 71.2 246.58 35.7 216.58 11.8 . 186.58 .3 . 156.58 213. 4 8 12 18

SIGNIFICANT WAVE HEIGHT M

Fig. 18 Comparison of Hindcast and Observed Wave Heighi Occurrences

only one month's data is not sufficient

to provide a prediction of. 1o.g term

per-sistence at that location, it ticarly indicates that extreme seas can last for up to 2 or 3 days and hence pose a very serious threat to shipping. Furthernoe,

Figure 16 indiOates that the severity of the sea can change rather drastically as indicated by the rise from 7 at the end of 15 Máräh to the maximu of 17.8 in

on 17 March. Durin this sa.e period,

.2 .4 .6 1.0

RE0UENCV.RP

Fig. 17 Density Spectrum of Extreme Seas at Grid Point 127 on 17 March 1968

occurrences. Table 3 suar.:z,es the per-sistënce or duration of var: signifi-cant wave heights throughout this sanple.

In this case, all condit::s eceeded

1.5 in while 3 m was exceeded during about

3/4 of the month and at i:-ter-;ais of 1

to 3 days. . Only three izter-.'as thdicãte exceedances of 7 m and these are from about 7 to 9 day apart. To

.nter-vals of. 10 in

or greater c' =

about 11 days apart,. While the exa:nation of

FREQ .308 .208 .168 133 .11 .c3 .092 .081 .05 .11 .17 .18 .39

.5

.68 .96 .09 .20 .33 .38 .73 .59 1.53 2.77 .12 .29 .45 .49 .9 115 2.32 3.77 .12 .33 .54 .56 1.0 1.19 2.03 3.76 .09 .26 .41 .42 .7 .67 L49 2.70 .00 .00 .00 .00 .00 .03 .17 .66 .00 .00 .00 .00 .00 .00 .00 .01 .47 1.19 1.90 2.03 3.8 .5E 7.92 14.62

.3 S6.33F7

WOODEN AND LUMB NINOCAST CLIMATOLOGY

ITENIATIVEI

,

- MODAL WAVE P08100.1

Fig. 19 Comparison of Hindcast and Most Probable Modal

Periods. Given Height, for the North Atlantic Basin During-Winter

the winds increased from 13.5 to 54

knots and then decreased to 48 knots.

Table 4 presents the extreme

direc-tional wave spectrum hindcast for this

winter storm.

MOst of the wave energy is

from the southwest ar.d the energy

direc-tions are slightly skewed tO the west.

Figure

17

presents the hindcast point

density spectrum of the extreme seas on

17 March 1968.

100

'

80L

Fig. 20 Significant Wa'je Height Exceedances Hindcast

for Selected North Atlantic Locations for a

10-Year Sample

17

Figure 18 presents a comparison of

significant wave height for grid point

127.with Area 2 of the Hogben and Luxnb

data set (3).

The observed heights

reported in Hogben and Luinb were

con-verted to significant heights by a

tech-nique which utilizes the well-known

Norderiströmu relationship (11).

Taken

over the 10 year period, the heights

forecast for grid point

127

are fairly

typical for the entire region bounded by

Area

2

(5 to

30°W, 50

tO 6ODN) though

they exhibit a lesser occurrence of

extieme values.

Clearly, Figure 18

indi-cates that the hindcast heights provide

a much greater occurrence of higher waves

than the visual data.

The highest

wave system hindcastfor grid point

127

is characterized by a significant height

of

17.8 rn

an

a modal period of about

23

seconds.

The highest significant wave

height in the Hogben and Lumb sample is

only about

12.8 in

and its estimated modal

period is between 10 and 11 seconds.

Figure 19 presents another

compari-son of the hindcast sample with most

probable modal wave periods derived from

Hogben and Lumb

Though the mode is a

weak parameter due to poor sampling

char-acteristics, it is useful to the naval

architect who may use it to specify

fami-lies of wave spectra fOr seakeeping

anal-yses.

This is the case in studies which

utilize the well-known Bretschneider

two-parameter formulation.

In some

stud-ies in which many hull variations must

100

Fig. 21 Significant Wave Height Exceederlces Hincicast

for Selected North Pacific Locations for a

5-Year Sample

4 B 2 16 4 8 12 IS

SIGNIFICANT WAVE HEIGHT. M SIGNIFICANT WAVE HEIGHT. M

be quickiy examined by seine seakeeing

measure, it is not uncornrr.on to use a

range of significant wave heights and their corresponding most prcbable periods to specify the required spectral family. Thus, the tentative results indicated by Figure 19 are quite important to the naval architect. For example, the hind-casts indicate longer probable periods for seas above about 3 m and at about 12 m the difference has risen to about 3

seconds. These results could signif

i-cantly alter the severity of resonses predicted for longer ships or these advanced craft (for example, SWATH) with high resonant periods.

Figure 20 provides a summary of wave height exceedences f c± the 10 year

sample at selected North Atlantic

loca-tions. Those locations from 460 north-ward generally fall within about 0.5 rn of each other for the same exceedence

levels. The two more southerly loca-tions indicate much milder ccndiloca-tions though even here 3 in significant waves are exceeded at least 17.5 percent of

the time.

Figure 21 provides wave height exceedences for selected oints in the North Pacific which are identified on

Table 5. The data is derived frcn a paralneterization of only about 5 years of hindcast spectra, so one might expect a greater occurrence of high waves with

the inclusion of the remaining 15 years of hindcasts. Even so, for similar latitudes, the Pacific data indicates a much greater occurrence of high waves than does the Atlantic data set.

A summary of the highest wave occurrences, in the analyzed sam1es, for both basins is provided in Table 6. Modal periods are defined simply as the periods corresponding to the frecuencies of maximum variance energy. Clearly, the extreme seas occur with modal

periods far longer than may have been previously suggested by wave

observa-tions (3) or wave elevation measurements (12). It is also noted that extremes may occasionally exceed the values

ndi-cated on Table 6 .as evidenced by the

Table 5 Location of Selected Grid Points in North Pacific

18

SOWM operational forecast of about 22 rn

for 12 December 1978 for a location near 46.3°N, 27.3°W (13). _{During this storm,} a German LPSH ship was lost in the general proximity of the location.

CONCLUSIONS

This paper has presented a sample of the information which will be pro-vided to the naval architect by the Navy's iave Climatology based on hind-cast directional spectra. The data presented are primarily limited to a ten year period and for a selection of 65 grid points from the 450 grid points in the North Atlantic. Nevertheless, the broad distribution of these points in the

basin

and the moderately long period suggest that the following cc,n-clusions may be quite accurate.

There is a band across the North Atlantic from Ireland to Newfoundland which exeriences severe sea condi-tions (over 3 in average significant wave height) for over six months of the year. Significant wave heights exceeding 1.5 m can be expected throughbut the year. By analysis of a five year sample, there is also a suggestion that there is a simi-lar bamd of roughly the same latitude in the North Pacific. _{Several times a year} storms may be expected in this North Atlantic region with significant wave

heights exceeding 10 in and ra±ely

reach-ing 20 =. Nodal wave periods signif i-cantly exceed values that would be esti-mated from observed data such as found in Hogben and Lwth (3), particularly for the higher waves, and the frequency Of occur-rence of high waves also exceeds Hogben and Luxr (3) estimates. These storms are widespread in area, extending over many

grid points.. _{The duration above the 10 n}

threshold may reach 48 hours., and dura-tion of 200 hours for waves greater than

in have been hindcast.

Mean wave slopes (as measured by the root mean sqaze instantareous slope) are hindcast to exceed 0.14, which is the value for a regular

sinu-soidal wave of /=i6.

For winds above 30 knots, wave s1ope appear to follow

GRID POINT SLJBPROJECTION LATITUDE LONGITUDE (°W)

28 - 3 51.3 162.0

164 3 50.9 145.6

56 3 50.0 tBO.0

152 2 - - 34.2 163.8(°E)

the wind very closely as a linear

func-tio

of wind speed, whatever the

spec-tral forn and modal per:cd

of

the sea.

ndirectiona1 seas

are -rare, but

t:-e cozrunon assumption that the

direc-tional spectrum follows a

cos

distribu

tior. over a

+90°

ranqe

nust

e

inter-preted

as tne "most

prcbahle" occur-rence. The hindcast spectra suggest that values as low as +60° and as great at

are not rare. Further exploration

is needed of this tentative conclusion

and

.ts- inpl-ications,

by

locking into the

effeot of. an underlying

swell

upon the sPreading parameter, n.

Validation will continue, whenever

and wherever, "sea truth data can be

cbzaned. However,

the

val:dation to

daze seers

sufficient

to

:uszif-y the use

of the hindcast spectra to

develop a wave

clinatoicy. More

inPortant,

though not

discussed

in thiS pap er,

are the

itpli--ca:icns of a fully validated SOWM odel with improved directional resolution for

forecasting pposes. The esent model

has

been

:n use by the :avy for about five years as the basis

for

weather rout-ing.

But the

power-

of

a worldwide model with good accuracy

out

to 48- hours in

the

future could

be the

basis of a vastly

ipr.oved

weather buzir.g

systen

which ou1i greatly increase shio Safety and

profitab.itv. The technology

is

avail able; it :s only necessary

_to

establish a

systen

to use it.

19

ACKNOWj5DGE:.NTS

The authors acknowledge the support received from Mr. Norman Stevenson of Fleet Numerical Oceanography Center and

Mr. James

Ownbey of the Naval Oceanog.

raphy Command Detachment, Asheville,

under

the joint Twenty Year Hindcast

Climatology dévelopmeht program. The

authors also gratefully acknowledge the assistance of Ms. Joyce Voelker of DTNSBDC and Mr. Paul Schnitt, Ms. Dana Gentile, Mr. Claude Williams, and Mr. James Noel,

all of CR1, Incorporated, for their assis-tance in

the

_{extensive software} develop-xnent and data generation required to

produce the results presented in this

paper.

The responsibility for all

state-ments of

fact

_{and -opinion rests with the}

authors.

REFERENCES

M. St.

enis and W. J. Pierson, "On

the Motion of Ships in Confused Seas," TRANS. SNAME,

Vol. 61,

1953.

"Seakeering in the S-hip Design.

Process," Report of the

Seakeep-ing '.Scrkshop at the U.S. Naval

Academy, NAVSEA Research and

echr.ology Directorate Report,

Prepared by NAVSEC and NSRDC,

uly, 1975.

Table 6 Highest Significant Heights Hindcast for-the North Atlantic (10 Years) and North Pacific (5 Years)

BASIN GRIDPOINT/ SUBPROJECTION SIG.WAVEHT. (METERS) MOD.WAVEPER. (SECONDS) NORTH ATLANTIC 129/3 16.5 20 128/3 18.5 20 127/3 17.8 - 23 147/3 185 20 -- 184/3 16.5 20 27912 19.5 25 244/3 16.5 -228/2 - 13.5 17 NORTH PACIFIC 128/3 19.5 -20 164/3 17.5 23 - - - 16.5 20 152/2 15.5 20 102'2 . 9.0 17

N. Hogben and F. E. .Lumb, Ocean Wave Statistics, London, Her Majesty's Stationary Office,

1967.

W. J. Pierson, L.

3.

Tick,

and

L. Baer, "Computer Based Proce-dures for Preparing Global Wave Forecasts- and Wind Field Analyses Capable of Using Wave Data

Obtained by a Spacecraft," in

S-i-th Naval Hydrod.rnamics

Sytnpoiam, Washington, D.C.,

Officeof Naval Research, 1966.

S. M. Lazanoff and N. M. Stevenson,

"An Evaluation of a Hemispheric

Operational Wave Spectral Model,"

FNWC Technical Note 75-3, June,

1975.

V. 3. Cardone, W. J. Pierson, and E. G. Ward, "Hindcasting the

Directional Soectra of Hurricane

Generated Waves," Journal of

Petroleum Technology, Vol. 28,

1976.

5. M. Lazanoff and N. N. Stevenson, "A Twenty Yar Northern Hémis-phere Wae Spectral Climatology," in Turbulent Fluxes Through the Sea Surface; Wave

Dynamits,

and

Prediction, edited by A. Favre and 1<. Hasselrann, New York

and

London, Plenum Press, 1978.

H ISTO R CAL WIND FIELDS (1) FNOC lSxT2MATRIX. 4TIMES DAILY, FOR 20 YEARS 2000 LOCATIONS AT 18ONM INTERVALS IN N. HEMISPHERE VAUDATION SPECTRAL I-IINDCASTS (2) DTNSRDC o PHYSICAL PARAMETERS, <20VALIJES HEIGHT, PERIOD, DIRECTIONALITY FOR UP TO 2 SIMULTANEOUS WAVE SYSTEMS (E.G., SEA AND SWELL)

DYNAMIC SEASON DEFINITION EXTREMEVALUE EVALUATION

VALIDATION

IMPROVED DESIGN AND OPERATIONAL APP LICTIONS

NOTE: POINTS OFCONTACT

Ii) FLEET NUMER ICAL OCEANOGRAPHY CENTER FNOC) (2) DAVID W. TAYLOR NAVAL SHIP R&D CENTER (DTNSRDC)

131 NAVAL OCEANOGRAPHY COMMAND DETACHMENT (NOCD). ASHEVILLE

Fig. 22 Participants in Twenty Year Hindccst Climatology Development

20

8.

3.

Gerrjtsrna, M. Buitenhek, and

C. W. Jorens, "Wave and Wind

Measurements During KNLMS TYDENAN

Full Scale Trials," Technische Hogeschool Delft, Laboratorium

- voor Scheeps Hydromechanica

Report 464, May, 1978.

W. 3. Pierson and R. E. Salfi, "A Brief Summary of Verification Results for the Spectral Ocean Wave Model (SOWN) by-Means of Wave Height Measurements Obtained

by Geos 3," Journal of

Geophysical Research, Vol. 84,

No-. B8, July, 1979.

-5. L. Bales and E. W. Foley, "Atlas of Naval Operational Environments: The Natural Marine Environment," Report DTNSRDC/SPD-0795-0l, September, 1979.

S. L. Bales and W. E. Cummins,

"Wave Data Requirements for Ship

Design and Operation," in Ocean

Wave Climate.,

edited by M. D. Earle and A. Malahoff, New York and London, Plenum Press, 1979.

"Analysis of a Stratified Sample

of Ocean Wave Records at

Station

'India,'" Society of Na'ai

Architects and-Marine ngineers T&R Bulletin, May1976.

PARAMETER SETS

I

FREQ.OFOCC.OF PHYSICAL PARAMETERS (JOINT) PERSISTENCE-OF -EXTREMES WAVE SLOPE DISTRIBUTIONS -SEASONALAND GEOGRAPHIC VARIATIONS e USER ACCESS (3) NOCO, ATLAS ASHEVILLE- PUBLICATION

13. Personal cOmmunication with Ni. N.

Stevenson of Fleet Nuzrerica1

Weather Central, January 1979.

APPENDIX 1 - DEVELOPMENT AND ISSEMINA-TION OF THE TWENTY YEAR HINDCAST WAVE CLIMATOLOGY

The development of the. enty Year Hindcast Wave Climatology was iriitiated in 1976 primarily in response to the needs of the ship design community iden-tified at the Seàkeepthg Workshop (2) held at the U.S. Naval Academy in June,

1975. The project has drawn on the expertise of scientists and engineers from a wide variety of disciplines including oceanography, meteorology, naval architecture, ship operations, and

data base itianagement and disse.aination.

The three naval aOtivities primarily responsible for the effort are identi-fied On Figure 22.

As indicated in the nain text of this paper, though the project is not

yet complete, it. is considered

appropri-ate to begin disseminating data, as soon as feasible, to the interested public. In this coitext, it is exected that the first Atlas of wave and wind statistics derived from the climatology will go to print by the Spring of 1981. The Atlas will contain seasonal and annual

parame-ter distributions drawn from the 65 locations identified in Figure 4 and for the time period September, 1959 to August, 1969. Parameters, tentatively planned fOr inclusion, are

1. Significant wave height vs. modal wave period

21

2. Significant wave neight vs. primary wave direction

- 3. Primary wave direction vs.

secondary wave direction

Wind speed vs. wind direction

Wind speed vs. significant wave height

Primary spectral width vs primary wave direction

Secondary pectral width vs. secondary wave direction

Wave slope

Special attention will be paid to refinement of parameter values.

Persis-tance of extreme values as well as an investigation of a dynamic season defi-nition (for example, of variable length) will be reported. In addition to the data distributions, the Atlas will ten-tativelv contain sections which provide a discuásion of

Parameter derivation

Parameter validation

Spectral validation

4.. SOWN theory, strengths, and

weakness

Design applications

Operational applications

A user survey, aimed at developing

cOnstructive feedback which tha impact future Atlas publications, will be