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Numerical prediction of ocean waves in the North Atlantic for December, 1959

Numerische Vorausberechnung von Wellen im Nordatlantik für Dezember 1959

Prédiction numérique de vagues dans l'Atlantique Nord pour le mois de décembre 1959

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Summary

A severe storm of December 15–18, 1959, over the North Atlantic, covering great areas of ocean with high winds, was responsible for high seas which were measured by a ship-borne wave recorder on the OWS “Weather Reporter”, while proceeding from Northern Ireland to Station “J” at lat. 52 1/2°N, long. 20°W. The wave records were calibrated and analyzed for determination of significant wave heights and wave energy spectra. The present paper is an attempt to predict (for comparison) the wave conditions that would have been encountered by the moving ship from analysis of the oceanwide weather records and the use of a high-speed digital computer process for forecasting waves in moving, variable wind systems. The wave prediction technique is dependent on generalizations of emprical laws derived from observed wind-wave relationships. The proverbial non-uniformity of the latter makes possible several versions of supposedly best—fit empirical laws. Trial is made of two different generalizations, of which the second was found to yield predicted significant wave heights in fair agreement with the measurements over a period of several days. Further improvement, however, is possible and the forms of the empirical wind-wave generation laws, likely to be most nearly in agreement with the natural laws, are derived.

Zusammenfassung

In der Zeit vom 15. bis 18. Dezember 1959 erzeugte ein schwerer Sturm über dem Nordatlantik, der weite Gebiete mit starken Winden überzog, die hohen Wellen, die vom Wellenschreiber des Wetterschiffes “Weather Reporter” auf seiner Fahrt von Nordirland nach der Station “J” in 52 1/2°N, 20°W gemessen wurden. Die Wellenaufzeichnungen wurden aufbereitet und analysiert, um die maßgeblichen Wellenhöhen und Wellenenergiespektren zu bestimmen. Die vorliegende Arbeit ist ein Versuch, die Wellenverhältnisse (zum Vergleich) vorherzusagen, die von dem fahrenden Schiff nach Analyse der Seewetteraufzeichungen und der Verwendung von Schnellrechnerdaten zur Vorhersage bei wandernden, veränderlichen Windsystemen angetroffen worden wären. Die Wellenvorausberechnungstechnik ist abhängig von Verallgemeinerungen empirischer Gesetze, die aus den beobachteten Wechselbeziehungen zwischen Wind und Wellen hergeleitet sind. Die sprichwörtliche Uneinheitlichkeit letzterer ermöglicht verschiedene Versionen der mutmaßlich am besten passenden empirischen Gesetze. Zwei verschiedene Verallgemeinerungen werden untersucht, von denen die zweite eine gute Übereinstimmung zwischen vorhergesagten maßgeblichen Wellenhöhen und Messungen über einen Zeitraum von mehreren Tagen erbrachte. Eine weitere Verbesserung ist jedoch möglich, und empirische Wind-Wellen-Gesetze, die den Naturverhältnissen am nächsten kommen, werden abgeleitet.

Résumé

Du 15 au 18 décembre 1959 une violente tempête sur l'Atlantique Nord où de vastes étendues de l'océan furent soumises à l'action de vents très forts, souleva de grosses lames qui furent mesurées par un houlographe à bord du navire météorologique «Weather Reporter» se rendant d'Irlande du Nord à la station «J» par 52°30′N–20°00′W. Les enregistrements de vagues furent réduits et analysés pour obtenir les valeurs significatives des hauteurs des lames et du spectre d'énergie. La présente étude est un essai de prédiction (pour comparaisons) des vagues qu'aurait rencontrées sur sa route le navire, au moyen d'une analyse des renseignements météorologiques s'étendant à tout l'océan et effectuée en utilisant un calculateur digital à grande vitesse pour la prédiction des vagues dans des systèmes de vents variables en déplacement. La technique de prédiction des vagues repose sur des généralisations de lois empiriques tirées de l'observation des relations entre vent et vagues. L'instabilité proverbiale de ces relations autorise plusieurs versions des lois empiriques supposées les mieux adaptées. On fait l'essai de deux généralisations différentes et on trouve que la seconde permet de prédire des hauteurs de vagues qui concordent assez bien avec les hauteurs effectivement mesurées pendant plusieurs jours. Une amélioration ultérieure reste cependant possible et on en déduit des lois empiriques qui semblent se rapprocher le plus des lois naturelles.

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Abbreviations

c :

velocity in deep-water of significant waves

F :

fetch or distance over which wind blows

f 1,f 2 :

functions of variables

g :

acceleration due to gravity

H :

height of the significant wave

i :

integer subscript of distance (=1, 2, 3...)

j :

integer subscript of time (= 1, 2, 3...)

k :

integer subscript (Fig. 17) (=1, 2, 3...), defining numerical step

m :

integer subscript (Fig. 17), (=1, 2, 3...)

MOD1 (t k):

defines the fraction by which the numbert k exceeds its nearest integer

MOD10 (X k):

defines the fraction of 10 by which the numberX k exceeds 10p in whichp is the largest integer for which 10p<X k

n :

integer subscript (Fig. 17), (=1, 2, 3...)

T :

period of significant waves

t :

variable time

t j :

particular value oft [=j τ]

t k :

value oft elapsed to thekth step from the start of the digital computation (Fig. 17)

t k+1 :

value oft elapsed to the (k+1)th step from the start of the digital computation (Fig. 17)

t n :

particular value oft [=n τ]; eithert n=tk ort n=tk − MOD1(t k)

t n+1 :

particular value oft [=(n+1) τ]

°t :

incremental length of time

°t k :

particular value of °t [=t k+1−t k]

U :

component of surface wind velocity uniform along a line of fetch

U 1 :

initial value ofU at space-time lattice point (X i, tj)

U k :

value ofU at space-time lattice point (x k, tk) or (X k, tj+tk)

U m :

value ofU at space-time lattice point (X m, tn)

U m+1 :

value ofU at space-time lattice point (X m+1, tn)

U n :

value ofU at space-time lattice point (X m, tn)

U n+1 :

value ofU at space-time lattice point (X m, tn+1)

U(x) :

component surface wind velocity along a line of fetch, variable over the fetch (continuous function ofx)

V :

group-velocity of significant waves in deep water

X :

distance from coastal station along given fetch line

X k :

value ofX defining the positionx k [=X i−xk]

X m :

particular value ofX [=mλ]; eitherX m=Xk orX m=Xk − MOD10(X k)

X m+1 :

particular value ofX [=(m+1)λ]

x :

variable distance or fetch over which the wind blows

x k :

value ofx from the start to thek-th step of the digital computation (Fig. 17)

x k+1 :

value ofx from the start to the (k+1)-th step of the digital computation (Fig. 17)

Y :

dimensionless parameter [=gH/U 2]

Y′ :

differential coefficient ofY with respect togx/U 2

Z :

dimensionless parameter [=c/U]

Z′ :

differential coefficient of Z with respect togx/U 2

°x :

incremental length of fetch

°x k :

particular value of °x [=x k+1 − xk]

λ:

interval of distance in space-time lattice

π:

universal constant (3. 14159...)

τ:

interval of time in space-time lattice

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Authors and Affiliations

  1. Science Engineering Associates, San Marino, California

    Basil W. Wilson

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  1. Basil W. Wilson
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With Plate 3 with Fig. 1–10, Plate 4 with Figs. 11–14, Plate 5 with Figs. 15–20, Plates 6 and 7

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Wilson, B.W. Numerical prediction of ocean waves in the North Atlantic for December, 1959. Deutsche Hydrographische Zeitschrift 18, 114–130 (1965). https://doi.org/10.1007/BF02333333

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