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A Procedure for Rapidly Forecasting Swell

CHARLES C. BATES Associate Oceanographer, U. S. Hydrographic Office, Washington, D. C.

ABSTRACT

A procedure, based on the work of Sverdrup and Munk, is described by which swell characteristics may be forecast rapidly. Specific wave generating areas defined by the fixed parameters, wind duration and fetch, and the variable parameter, wind velocity, are established. The change in swell characteristics as the swell moves away from these generating areas is illustrated by graphs which may be re-drafted as transparent overlays at the scale of the synoptic weather chart from which swell forecasts are to be made.

INTRODUCTION CONSTRUCTION OF WAVE DECAY DIAGRAMS At the request of the Army Air , The decay of waves as they move away Drs. Sverdrup and Munk of the Scripps from their area of generation may be illus- Institution of , La Jolla, Cali- trated diagrammatically. If wave-generat- fornia began work in 1942 on the problem ing areas are described as regions of fixed of discovering a method by which and minimum fetch and fixed wind duration but swell could be forecast quantitatively. This variable wind velocity, a series of diagrams work, transferred in early 1943 to the gen- are required to describe the various possible eral direction of the Hydrographic Office, values of minimum duration and fetch.i jn U. S. Navy, made such rapid progress that practice, however, rather rough values of by July of that year the basic concepts had these parameters must be used because of been determined by which such forecasting the difficulty in determining exact values could be accomplished. In late 1943, the from synoptic charts. Moreover, if the gaps Hydrographic Office published 11 Wind Waves between the selected duration times are kept and Swell—Principles in Forecasting'1 [1] sufficiently small, errors in due as the basic forecasting manual, and in to these gaps may be ignored. These two 1944 published a sister volume entitled facts permit a series of six diagrams to "Breakers and Surf—Principles in Fore- satisfactorily describe the wave-generating casting" [2]. These publications, classified areas that normally occur in Nature. at the time, served as the "Bible'' of the FIGURES 1 to 3 have been constructed Army and Navy meteorologists who were from values extracted from graphs given charged with preparing quantitative sea, in "Wind Waves and Swell—Principles in swell, and surf forecasts throughout the Forecasting'' [1]. The range of the maxi- various military theatres. mum error in height between values given The Swell Forecast Section, located at by these diagrams and values by the basic the British Admiralty in London and reference is roughly: — staffed by Royal Navy and U. S. Army Air meteorologists during 1944, was the first to test and apply this newly de- Significant Maximum veloped aspect of oceanographic forecasting Wave Height 2 Error on a large scale. During this work, it 2 to 4 feet 50% became apparent that determinations of 4 to 16 feet swell height, by requiring reference to three 30% 1 or more diagrams and a short computation 16 to 8 feet 25% for each value, were unduly protracted in 18 to 22 feet 20% the event a knowledge of swell conditions 22 feet or greater 15% was desired over an area as large as the

North Atlantic Ocean. To remedy this 1 Fetch is the length of the water surface over situation, the writer devised the method de- which the wind is blowing in a given direction, while duration is the length of time the wind has been scribed below which permits the meteorolo- blowing in that direction. 2 , as defined by Sverdrup gist to prepare swell forecasts very quickly, and Munk [3], is approximately the average height although several minor refinements in the of the one-third higher waves, i.e., the height of the higher waves which an observer tends to record standard technique must be sacrificed. in an observation lasting 5 minutes or more.

Unauthenticated | Downloaded 10/01/21 03:39 AM UTC WAVE-DECAY DIAGRAM:— (A) Generating area with duration of 6 hours and minimum fetch of at least 40 miles. (B) Generating area with duration of 12 hours and minimum fetch of at least 100 miles.

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FIGURE 2. WAVE-DECAY DIAGRAM:— (A) Generating area with duration of 18 hours and minimum fetch of at least 200 miles. (B) Generating area with duration of 24 hours and minimum fetch of at least 300 miles.

Unauthenticated | Downloaded 10/01/21 03:39 AM UTC FIGURE 3. WAVE-DECAY DIAGRAM:— (A) Generating area with duration of 36 hours and minimum fetch of at least 550 miles. (B) Generating area with duration of 36 hours and minimum fetch of at least 750 miles. Unauthenticated | Downloaded 10/01/21 03:39 AM UTC Errors greater than + 2 feet occur only EXAMPLES for wind velocities greater than 25 knots For an example of the method, assume and a duration of less than 12 hours. How- the following situation:— ever, it appears that if the wind velocity is 25 knots or more in a given area, its dura- 400 nautical miles tion is almost certain to be 12 hours, or Wind Speed 28 knots greater, making the above case uncommon. Wind Duration ... 22 hours In the FIGURES, the solid curved lines Decay distance . . . 1,400 nautical miles illustrate the significant height of the waves in feet, the slanting dashed lines the time :— in hours required by a wave to travel away from the forepart of a generating area, (1) Select the wave-decay diagram with and the dotted lines the wave period in a duration of 24 hours, since the existing seconds. In practice, the diagrams should fetch is greater than the minimum fetch be re-drawn on transparent material to the required (300 nautical miles). scale of the meteorological chart being used; (2) At the intersection of the 28-knot this makes horizontal distances on the dia- wind velocity and the decay distance of grams equivalent to those on the synoptic 1,400 nautical miles, interpolation indicates chart and permits the diagrams to be used that the swell takes 85 hours to arrive, has as overlays. a height of 3.5 feet, and a period of 13 seconds at that point. DIRECTIONS FOR USE OF DECAY DIAGRAMS Computation, using the graphs of "Wind Given a synoptic situation producing Waves and Swell—Principles in Forecast- swell which will affect the locality for which ing'? [1], gives a travel time of 88 hours, the forecast is desired, the forecaster pro- height of 2.8 feet, and period of 13 seconds. ceeds as follows: In the above situation, if the fetch is (1) Determines the wind duration, veloc- only 225 nautical miles, the wave decay ity, and fetch in the generating area. diagram previously used does not apply, (2) Selects the transparent overlay of the since that diagram required a minimum decay diagram best satisfying the wind du- fetch of 300 nautical miles. One should ration and fetch in the generating area. use the decay diagram constructed for 18 It should be remembered that wave-genera- hours duration, in which the minimum fetch tion can be limited by either the fetch or required is 200 nautical miles. This gives the duration parameter. 92 hours of travel time, a wave height of (3) Places the transparent overlay upon 2.2 feet, and period of 12.8 seconds. Com- the synoptic chart so that the line of the putation, using the basic graphs, gives a chosen direction of wave motion extends travel time of 90 hours, height of 2.5 feet, from the front of the generating area to and period of 12.4 seconds. the locality forecast for, e.g., a . (4) At the intersection of the line of REFERENCES wave motion and the locality forecast for, [I] United States Navy, Hydrographic Office, Wind read the height and period of the swell Waves and Swell—Principles in Forecasting, H. and the time taken to travel that distance. O. Misc. 11,275, 61 pp. 1943. [21 United States Navy, Hydrographic Office, Break- No allowance is made for the case of follow- ers and Surf—Principles in Forecasting, H. O. ing or opposing winds, as experience has Pub. 234, 51 pp. 1944. [3] Sverdrup, H. U., and Munk, W. H.: Empirical shown that it is very difficult to apply such and theoretical relations between wind, sea, and swell. Trans. Amer. Geophys. Union, v. 27, a correction. pp. 823-827, 1946.

Unauthenticated | Downloaded 10/01/21 03:39 AM UTC