251:
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water than in shallow water. At low tide, some plates are dry, and wave growth has to start all over again. Close to the shore (beyond the Gat van
Borssele), there's a tall salt marsh; at low tide, there are no waves there, at average tide, the wave height decreases to almost nothing at the dike, and at high tide, there's still a wave height of 1 m present. The measure of period shown in these graphs is the
4813:
276:. The waves are also separated by their direction of propagation. The model domain size can range from regional to the global ocean. Smaller domains can be nested within a global domain to provide higher resolution in a region of interest. The sea state evolves according to physical equations â based on a spectral representation of the conservation of
139:
relevant for the development of the sea state in two dimensions. The wave modeling project (WAM), an international effort, led to the refinement of modern wave modeling techniques during the decade 1984-1994. Improvements included two-way coupling between wind and waves, assimilation of satellite wave data, and medium-range operational forecasting.
20:
255:
France, around the island of
Ouessant, which lies 20 km from the mainland. The bottom panel show the heights and directions of waves, computed with the numerical model WAVEWATCH III (R), using a triangular mesh with variable resolution. The strong currents south of Ouessant deflect the waves away from the measuring buoy at low tide.
154:, the study of wave growth garnered significant attention. The global nature of the war, encompassing battles in the Pacific, Atlantic, and Mediterranean seas, necessitated the execution of landing operations on enemy-held coasts. Safe landing was paramount, given that choppy waters posed the danger of capsizing
292:, and a source function which allows for wave energy to be augmented or diminished. The source function has at least three terms: wind forcing, nonlinear transfer, and dissipation by whitecapping. Wind data are typically provided from a separate atmospheric model from an operational weather forecasting center.
354:
interactions, sub-grid representations of unresolved islands, and dynamically updated ice coverage. Wind data is provided from the GDAS data assimilation system for the GFS weather model. Up to 2008, the model was limited to regions outside the surf zone where the waves are not strongly impacted by
2377:
The computation time for a calculation with SWAN is in the order of seconds. In one-dimensional mode, results are available from the input of a cross-sectional profile and wind information. In many cases, this can yield a sufficiently reliable value for the local wave spectrum, particularly when the
246:
can also be important, in particular in western boundary currents such as the Gulf Stream, Kuroshio or
Agulhas current, or in coastal areas where tidal currents are strong. Waves are also affected by sea ice and icebergs, and all operational global wave models take at least the sea ice into account.
138:
First generation wave models did not consider nonlinear wave interactions. Second generation models, available by the early 1980s, parameterized these interactions. They included the âcoupled hybridâ and âcoupled discreteâ formulations. Third generation models explicitly represent all the physics
2538:
Robert
Montagne, The swell forecasting service in Morocco (In French), 1922, Annales Hydrographiques, pp. 157-186. This paper describes the use of the method published by Gain in the same journal (1918) which combines a classification of North Atlantic Storms with the use of observations in Azores
2402:
The calculation was made for low water, average water level, and high water. At high tide, the salt marsh is under water; at low tide, only the salt marsh is submerged (the tidal difference here is about 5 metres). At high tide, there is a constant increase in wave height, which is faster in deep
416:
Another model, CCHE2D-COAST is a processes-based integrated model which is capable of simulating coastal processes in different coasts with complex shorelines such as irregular wave deformation from offshore to onshore, nearshore currents induced by radiation stresses, wave set-up, wave set-down,
254:
This figures show an example of the effects of currents on the wave heights. This example is adapted from scientific paper published in the
Journal of Physical Oceanography (vol. 42, December 2012). The top panels show the tidal currents at 3 AM and 11 AM on 28 October 2008, off the West coast of
2473:
from the ECMWF. Such resources permit the creation of monthly wave climatologies, and can track the variation of wave activity on interannual and multi-decadal time scales. During the northern hemisphere winter, the most intense wave activity is located in the central North
Pacific south of the
2431:
occurs, or where the coastline is irregular, the one-dimensional method falls short, necessitating the use of a field model. Even in a relatively rectangular lake like Lake Garda, a two-dimensional calculation provides considerably more information, especially in its southern regions. The figure
238:
A wave model requires as initial conditions information describing the state of the sea. An analysis of the sea or ocean can be created through data assimilation, where observations such as buoy or satellite altimeter measurements are combined with a background guess from a previous forecast or
125:
During the 1950s and 1960s, much of the theoretical groundwork necessary for numerical descriptions of wave evolution was laid. For forecasting purposes, it was realized that the random nature of the sea state was best described by a spectral decomposition in which the energy of the waves was
1063:
When plotted against the dimensionless wind fetch, both dimensionless wave height and wave period tend to align linearly. However, this trend becomes notably more flattened for more extended dimensionless wind fetches. Various researchers have endeavoured to formulate equations capturing this
349:
are based on the WAVEWATCH III model. This system has a global domain of approximately 50 km resolution, with nested regional domains for the northern hemisphere oceanic basins at approximately 18 km and approximately 7 km resolution. Physics includes wave field refraction,
2244:
of 3.5 m and a period of roughly 7 s (assuming the storm persists for at least 4 hours). The Young and
Verhagen formula, however, predicts a lower wave height of 2.6 m. This diminished result is attributed to the formula's calibration for shallow waters, whilst Lake Garda is notably deep.
130:
and swells. The first numerical model based on the spectral decomposition of the sea state was operated in 1956 by the French
Weather Service, and focused on the North Atlantic. The 1970s saw the first operational, hemispheric wave model: the spectral wave ocean model (SWOM) at the
1775:
Integrating the water depth into the same chart was problematic as it introduced too many input parameters. Therefore, during the primary usage of nomograms, separate nomograms were crafted for distinct depths. The use of computers has resulted in reduced reliance on nomograms.
2435:
This case highlights another limitation of the one-dimensional approach: at certain points, the actual wave growth is less than predicted by the one-dimensional model. This discrepancy arises because the model assumes a broad wave field, which isn't the case for narrow lakes.
142:
Wind wave models are used in the context of a forecasting or hindcasting system. Differences in model results arise (with decreasing order of importance) from: differences in wind and sea ice forcing, differences in parameterizations of physical processes, the use of
2386:
As an example, a calculation of the wave growth in the
Westerschelde has been made. For this example, the one-dimensional version of SWAN and the open-source user interface SwanOne were used. The wave height at the base of the sea dike near Goudorpe on
374:
was allowed to evolve freely (up to a cut-off frequency) with no constraints on the spectral shape. The model underwent a series of software updates from its inception in the late 1980s. The last official release is Cycle 4.5, maintained by the German
2115:
1892:
3029:
Janssen, P. A. E. M., J. D. Doyle, J. Bidlot, B. Hansen, L. Isaksen and P. Viterbo, 2002: "Impact and feedback of ocean waves on the atmosphere", in
Advances in Fluid Mechanics, Atmosphere-Ocean Interactions, Vol. I, WITpress, Ed. W.Perrie., pp
225:. This work concluded that the 1973 Bretschneider formula was the most suitable. However, subsequent studies by Young and Verhagen in 1997 suggested that adjusting certain coefficients enhanced the formula's efficacy in shallow water regions.
2474:
Aleutians, and in the central North Atlantic south of Iceland. During the southern hemisphere winter, intense wave activity circumscribes the pole at around 50°S, with 5 m significant wave heights typical in the southern Indian Ocean.
3540:
2358:, and many institutions and companies have since developed their own user environments for SWAN. The program has become a global standard for such calculations, and can be used in both one-dimensional and two-dimensional modes.
208:, which underwent subsequent refinements and data integrations. The method, in due course, came to be popularly referred to as the SMB method, an acronym derived from its founders Sverdrup, Munk, and Charles L. Bretschneider.
1632:
2468:
A retrospective analysis, or reanalysis, combines all available observations with a physical model to describe the state of a system over a time period of decades. Wind waves are a part of both the NCEP Reanalysis and the
1520:
2444:
Comparison of the wave model forecasts with observations is essential for characterizing model deficiencies and identifying areas for improvement. In-situ observations are obtained from buoys, ships and oil platforms.
1150:
1220:
390:(IFS). The model currently comprises 36 frequency bins and 36 propagation directions at an average spatial resolution of 25 km. The model has been coupled to the atmospheric component of IFS since 1998.
315:
Wind waves also act to modify atmospheric properties through frictional drag of near-surface winds and heat fluxes. Two-way coupled models allow the wave activity to feed back upon the atmosphere. The
1722:
2986:
2548:
Gelci, R., H. CazalĂŠ, J. Vassal (1957) Sea state forecasting. The spectral method (In French), Bulletin d'information du ComitĂŠ d'OcĂŠanographie et d'Etude des CĂ´tes, Vol. 9 (1957), pp. 416-435.
2220:
242:
A more critical input is the "forcing" by wind fields: a time-varying map of wind speed and directions. The most common sources of errors in wave model results are the errors in the wind field.
1997:
500:
746:
2168:
1945:
674:
The constants in these formulas are deduced from empirical data. Factoring in water depth, wind fetch, and storm duration complicates the equations considerably. However, the application of
2240:
in Italy is a deep, elongated lake, measuring about 350 m in depth and spanning 45 km in length. With a wind speed of 25 m/s from the SSW, the Bretschneider and Wilson formulas suggest an H
1425:
1325:
931:
870:
809:
555:
1442:
Graph depicting the variation of significant wave height with dimensionless fetch based on the Young & Verhagen wave growth formula, set against a specific water depth and wind speed.
1779:
For deep water, the distinctions between the various formulas are subtle. However, for shallow water, the formula modified by Young & Verhagen proves more suitable. It's defined as:
1763:
987:
303:
The output of a wind wave model is a description of the wave spectra, with amplitudes associated with each frequency and propagation direction. Results are typically summarized by the
239:
climatology to create the best estimate of the ongoing conditions. In practice, many forecasting system rely only on the previous forecast, without any assimilation of observations.
211:
Between 1950 and 1980, various formulae were proposed. Given that two-dimensional field models had not been formulated during that time, studies were initiated in the Netherlands by
1667:
1555:
2008:
2395:, was calculated, with the wind coming from the SW at a speed of 25m/s (force 9 to 10). In the graph, this is from left to right. The dike is quite far from deep water, with a
1785:
295:
For intermediate water depths the effect of bottom friction should also be added. At ocean scales, the dissipation of swells - without breaking - is a very important term.
2935:
Komen, GJ and Cavaleri, L. and Donelan, M. and Hasselmann, K. and Hasselmann, S. and Janssen, P. et al, 1994: "Dynamics and Modelling of Ocean Waves", Cambridge, 534 pp
2591:
G.J. Komen, L. Cavaleri, M. Donelan, K. Hasselmann, S. Hasselmann and P.A.E.M. Janssen, 1994. Dynamics and Modelling of Ocean Waves. Cambridge University Press, 532p.
3326:
668:
639:
610:
118:
relationships between the present state of the sea, the expected wind conditions, the fetch/duration, and the direction of the wave propagation. Alternatively, the
1057:
1035:
1013:
581:
2323:
and WAM are not reliable in shallow water areas near the coast. To address this issue, the SWAN (Simulating WAves Nearshore) program was developed in 1993 by
2990:
321:
3501:"Evaluation of Contemporary Ocean Wave Models in Rare Extreme Events: The "Halloween Storm" of October 1991 and the "Storm of the Century" of March 1993"
1561:
3013:
1768:
During periods when programmable computers weren't commonly utilised, these formulas were cumbersome to use. Consequently, for practical applications,
317:
1772:
were developed which did away with dimensionless units, instead presenting wave heights in metres, storm duration in hours, and the wind fetch in km.
1452:
4543:
376:
4533:
3592:
2495:
126:
attributed to as many wave trains as necessary, each with a specific direction and period. This approach allowed to make combined forecasts of
1086:
1156:
221:(TAW - Technical Advisory Committee for Flood Defences) to discern the most appropriate formula to compute wave height at the base of a
3197:
3558:
2560:
4449:
2664:
1673:
54:. These simulations consider atmospheric wind forcing, nonlinear wave interactions, and frictional dissipation, and they output
4816:
3864:
3632:
2522:
3371:
2638:
307:, which is the average height of the one-third largest waves, and the period and propagation direction of the dominant wave.
4096:
2173:
3585:
178:
132:
3986:
1950:
446:
4691:
4118:
4006:
3077:
684:
3541:"Evaluation Of NCEP-NCAR Reanalysis Project Marine Surface Wind Products For A Long Term North Atlantic Wave Hindcast"
2121:
1898:
158:. Consequently, the precise forecasting of weather and wave conditions became essential, prompting the recruitment of
4538:
3809:
277:
1331:
1231:
1071:
Dimensionless wave height and period against the backdrop of the dimensionless fetch (data courtesy of Wilson, 1965)
3996:
3956:
2616:
876:
815:
752:
506:
4726:
3712:
1727:
186:
3525:
3500:
2971:
2946:
2896:
2871:
2802:
2777:
4849:
4806:
4399:
3578:
2324:
937:
678:
facilitates the identification of patterns for all these variables. The dimensionless parameters employed are:
410:
2643:
35th Summer Training Course Lecture Collection, Japan Society of Civil Engineers Coastal Engineering Committee
2335:
in the United States. Initially, the main focus of this development was on wave changes due to the effects of
3010:
370:
The wave model WAM was the first so-called third generation prognostic wave model where the two-dimensional
3854:
2523:"Thirty Years of Operational Ocean Wave Forecasting at Fleet Numerical Meteorology and Oceanography Center"
2110:{\displaystyle {\widehat {T}}=7.519\left(\tanh {A_{T}}\tanh {{B_{T}} \over {\tanh {A_{T}}}}\right)^{0.387}}
1637:
2503:
7th International Workshop on Wave Hindcasting and Forecasting October 21â25, 2002, Banff, Alberta, Canada
1887:{\displaystyle {\widehat {H}}=0.241\left(\tanh {A_{H}}\tanh {{B_{H}} \over {\tanh {A_{H}}}}\right)^{0.87}}
1525:
320:(ECMWF) coupled atmosphere-wave forecast system described below facilitates this through exchange of the
3914:
4051:
3475:
3402:
3257:
3189:
3115:
2729:
2423:
Calculation of wave growth (and decline) on Lake Garda due to strong wind (25 m/s) from the SSW (210°).
387:
147:
and associated methods, and the numerical techniques used to solve the wave energy evolution equation.
3556:"Forty-year European Re-Analysis of the Global Atmosphere; Ocean wave product validation and analysis"
2681:
4586:
3991:
3951:
3220:"The Growth of Fetch Limited Waves in Water of Finite Depth. Part 1. Total Energy and Peak Frequency"
3351:
2460:
Hindcasts of wave models during extreme conditions also serves as a useful test bed for the models.
4716:
4091:
4081:
4021:
3657:
3627:
2778:"Swell transformation across the continental shelf. part I: Attenuation and directional broadening"
2332:
198:
182:
102:, have led to the developments of wind wave models specifically designed for coastal applications.
4753:
4736:
4573:
4066:
3931:
3869:
3859:
3752:
3219:
3060:
406:
304:
205:
177:
embarked on wave prediction research. In the U.S., comprehensive studies were carried out at the
2817:
Ardhuin, F.; Chapron, B.; Collard, F. (2009). "Observation of swell dissipation across oceans".
4748:
4686:
4113:
3799:
675:
1446:
In the Netherlands, a formula devised by Groen & Dorrestein (1976) is also in common use:
4581:
4563:
4071:
3966:
3601:
3296:
2748:
2404:
3048:
2923:
2911:
2666:
North Atlantic Coast Wave Statistics: Hindcast by Bretschneider-Revised Sverdrup-Munk Method
2602:
2343:, and the like. The program was subsequently developed to include analysis of wave growth.
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4768:
4601:
4304:
4161:
4026:
3737:
3555:
3512:
3152:
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2883:
2836:
2789:
2355:
646:
617:
588:
429:
383:
273:
8:
4763:
4648:
4643:
4369:
4041:
4001:
3717:
3039:
Janssen, P. A. E. M., 2004: The interaction of ocean waves and wind, Cambridge, 300 pages
2557:
2392:
351:
99:
3516:
3156:
3078:"CCHE2D-Coast | the National Center for Computational Hydroscience and Engineering"
2962:
2887:
2840:
2793:
250:
4706:
4419:
4409:
4374:
4274:
4259:
4156:
3377:
3363:
3140:
2852:
2826:
1042:
1020:
998:
566:
421:
399:
194:
155:
3235:
4788:
4778:
4721:
4701:
4384:
4349:
4284:
4264:
4254:
4136:
3824:
3682:
3433:"Wave Hindcast in Enclosed Basins: Comparison among SWAN, STWAVE and CMS-Wave Models"
3381:
3367:
2703:
325:
144:
81:
19:
358:
The model can incorporate the effects of currents on waves from its early design by
80:
are extremely important for commercial interests on the high seas. For example, the
4743:
4711:
4681:
4490:
4475:
4344:
4279:
4171:
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4016:
3941:
3722:
3692:
3622:
3617:
3520:
3454:
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3359:
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3160:
3101:
3070:
2966:
2891:
2856:
2844:
2797:
2693:
2351:
2297:
Young & Verhagen's formula, which typically applies to shallow waters, yields:
328:. This allows the atmosphere to respond to changes in the surface roughness as the
281:
1627:{\displaystyle {\widehat {T}}=2\pi \tanh \left(0.0345{\widehat {F}}\right)^{0.37}}
427:
122:
part of the state has been forecasted as early as 1920 using remote observations.
4548:
4444:
4394:
4359:
4319:
4211:
4181:
4031:
3981:
3849:
3782:
3707:
3667:
3562:
3259:
The Accuracy of the Young and Verhagen Formula for Waves in Water of Finite Depth
3017:
2872:"Modification of the Physics and Numerics in a Third-Generation Ocean Wave Model"
2564:
2371:
2328:
212:
2225:
Research by Bart demonstrated that, under Dutch conditions (for example, in the
1515:{\displaystyle {\widehat {H}}=0.24\tanh \left(0.015{\widehat {F}}\right)^{0.45}}
91:
For the specific case of predicting wind wave statistics on the ocean, the term
4658:
4653:
4558:
4553:
4389:
4329:
4324:
4056:
3946:
3767:
3702:
3677:
2388:
2366:
359:
265:
243:
51:
35:
3903:
4843:
4828:
4676:
4596:
4485:
4404:
4379:
4314:
4244:
4151:
4046:
3923:
3844:
3804:
3777:
3687:
3637:
3141:"Numerical Prediction of Ocean Waves in the North Atlantic for December 1959"
2707:
2527:
Symposium on the 50th Anniversary of Operational Numerical Weather Prediction
2419:
2347:
2336:
371:
289:
174:
159:
119:
3081:
1430:
4783:
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4671:
4622:
4500:
4495:
4470:
4454:
4429:
4146:
4036:
3976:
3762:
3672:
3647:
2580:
2350:) and derives the significant wave height from this spectrum. SWAN lacks a
163:
151:
3301:
Proceedings International Symposium on Ocean Wave Measurement and Analysis
2354:
for easily creating input files and presenting the output. The program is
4773:
4505:
4434:
4299:
4239:
4206:
4196:
4191:
4076:
4011:
3971:
3961:
3936:
3819:
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3732:
3697:
3459:
3430:
2848:
2749:"User manual and system documentation of WAVEWATCH III TM version 3.14 â "
2639:"On the Historical Development of the Mathematical Theory of Water Waves"
2346:
SWAN essentially calculates the energy of a wave field (in the form of a
190:
76:
63:
59:
3570:
3431:
Favaretto, C.; Martinelli, L.; Philipine Vigneron, E.; Ruol, P. (2022).
4591:
4439:
4414:
4309:
4289:
4216:
4201:
4186:
4176:
4141:
4061:
3881:
3876:
3839:
3834:
3829:
3727:
3164:
2776:
Ardhuin, F.; O'Reilly, W. C.; Herbers, T. H. C.; Jessen, P. F. (2003).
2609:
On the Historical Development of the Mathematical Theory of Water Waves
2428:
2396:
2340:
2237:
2226:
1067:
437:
285:
85:
66:, and propagation directions for regional seas or global oceans. Such
28:
4823:
3449:
3432:
3403:"A practical method for design of coastal structures in shallow water"
2698:
2381:
1145:{\displaystyle {\widehat {H}}=0.283\tanh(0.0125{\widehat {F}})^{0.42}}
4663:
4525:
4510:
4424:
4269:
4108:
4103:
3886:
3814:
3742:
3662:
3652:
3609:
2446:
2320:
405:
Regional wave predictions are also produced by universities, such as
269:
115:
111:
55:
43:
3281:
2945:
Hasselmann, S; Hasselmann, K; Janssen, P A E M; et al. (1988).
1215:{\displaystyle {\widehat {T}}=7.54\tanh(0.077{\widehat {F}})^{0.25}}
4758:
4480:
4339:
4231:
4221:
4166:
3642:
1769:
329:
127:
69:
2924:
User manual and system documentation of WAVEWATCH-III version 2.22
2831:
436:
For determining wave growth in deep waters subjected to prolonged
4627:
4617:
3787:
3757:
1434:
Wave growth chart based on the formulas by Groen & Dorrestein
2947:"The WAM model - A third generation ocean wave prediction model"
2944:
2775:
2493:
1438:
4334:
3747:
3499:
Cardone, V.; Jensen, R.; Resio, D.; Swail, V.; Cox, A. (1996).
2470:
2457:, can also be used to infer the characteristics of wind waves.
2450:
362:
in the 1990s, and is now extended for near shore applications.
47:
23:
NOAA WAVEWATCH III (R) 120-hour Forecast for the North Atlantic
3400:
4696:
4515:
4294:
4249:
2454:
222:
170:
193:
devised an avant-garde wave calculation methodology for the
4128:
3526:
10.1175/1520-0426(1996)013<0198:eocowm>2.0.co;2
3401:
Verhagen, H.J.; van Vledder, G.P.; Eslami Arab, S. (2008).
2972:
10.1175/1520-0485(1988)018<1775:twmtgo>2.0.co;2
2897:
10.1175/1520-0426(1996)013<0726:motpan>2.0.co;2
2803:
10.1175/1520-0485(2003)033<1921:statcs>2.0.co;2
2292:
346:
1717:{\displaystyle {\widehat {T}}=0.502{\widehat {F}}^{0.225}}
268:; the sea surface can be decomposed into waves of varying
3102:"Validation Test Report for the Navy Standard Surf Model"
3061:"Surf's Up: Professor Using Models To Predict Huge Waves"
3554:
Caires, S., A. Sterl, G. Burgers, and G. Komen, ERA-40,
84:
requires guidance for operational planning and tactical
3498:
2682:"Revisions in Wave Forecasting: Deep and Shallow Water"
2432:
below demonstrates the results of such a calculation.
382:
ECMWF has incorporated WAM into its deterministic and
3352:"Shallow water wave modelling in the nearshore (SWAN)"
2926:. NOAA / NWS / NCEP / MMAB Technical Note 222, 133 pp.
417:
sediment transport, and seabed morphological changes.
2816:
2756:
National Oceanographic and Atmospheric Administration
2496:"20 Years Of Operational Forecasting At Oceanweather"
2176:
2124:
2011:
1953:
1901:
1788:
1730:
1676:
1640:
1564:
1528:
1455:
1334:
1234:
1159:
1089:
1045:
1023:
1001:
940:
879:
818:
755:
687:
649:
620:
591:
569:
509:
449:
3477:
A reanalysis of the wave observations in Lake George
3020:, European Centre for Medium-Range Weather Forecasts
2551:
2248:
2215:{\displaystyle B_{T}=0.0005215{\widehat {F}}^{0.73}}
3294:
2581:"The Wave Modeling Group, a historical perspective"
2382:
Example: wave growth calculation in The Netherlands
2214:
2162:
2109:
1992:{\displaystyle B_{H}=0.00313{\widehat {F}}^{0.57}}
1991:
1939:
1886:
1757:
1716:
1661:
1626:
1549:
1514:
1419:
1319:
1214:
1144:
1051:
1029:
1007:
981:
925:
864:
803:
740:
662:
633:
604:
575:
549:
495:{\displaystyle {{gH_{s}} \over {u_{w}^{2}}}=0.283}
494:
318:European Centre for Medium-Range Weather Forecasts
204:This pioneering effort led to the creation of the
4544:North West Shelf Operational Oceanographic System
2489:
2487:
2275:Utilizing Wilson's formula, the predictions are:
1075:
741:{\displaystyle {\widehat {H}}={gH_{s}/u_{w}^{2}}}
4841:
3295:Holthuijsen, L.H.; Booij, N.; Ris, R.C. (1993).
2916:
2494:Cox, Andrew T. & Vincent J. Cardone (2002).
2163:{\displaystyle A_{T}=0.331{\widehat {d}}^{1.01}}
1940:{\displaystyle A_{H}=0.493{\widehat {d}}^{0.75}}
218:Technische Adviescommissie voor de Waterkeringen
4534:Deep-ocean Assessment and Reporting of Tsunamis
3407:International Conference on Coastal Engineering
3349:
3187:
2539:and Portugal to forecast the swells in Morocco.
2484:
1420:{\displaystyle {\widehat {T}}=1.37\{1-^{-5}\}}
1320:{\displaystyle {\widehat {H}}=0.30\{1-^{-2}\}}
3586:
3217:
2876:Journal of Atmospheric and Oceanic Technology
2679:
2314:
2270:
926:{\displaystyle {\widehat {F}}={gF/u_{w}^{2}}}
865:{\displaystyle {\widehat {d}}={gd/u_{w}^{2}}}
804:{\displaystyle {\widehat {T}}={gT_{s}/u_{w}}}
550:{\displaystyle {{gT_{s}} \over {u_{w}}}=7.54}
398:Wind wave forecasts are issued regionally by
3297:"A spectral wave model for the coastal zone"
3054:
3033:
1414:
1353:
1314:
1253:
345:The operational wave forecasting systems at
2727:
2414:
2361:
1758:{\displaystyle 10<{\widehat {F}}<400}
413:) to forecast waves in the Gulf of Mexico.
216:
3593:
3579:
3198:Royal Netherlands Meteorological Institute
3600:
3550:
3548:
3524:
3458:
3448:
2970:
2929:
2904:
2895:
2830:
2801:
2697:
2529:, 14â17 June 2004, University of Maryland
982:{\displaystyle {\widehat {t}}={gt/u_{w}}}
3183:
3181:
2418:
2365:
2293:Young & Verhagen Formula: Lake Garda
1437:
1429:
1066:
249:
197:and later refined this approach for the
27:For broader coverage of this topic, see
18:
3492:
3473:
3113:
3023:
2938:
2662:
2575:
2573:
2532:
2515:
409:âs use of the SWAN model (developed by
4842:
3865:one-dimensional Saint-Venant equations
3545:
3138:
3042:
2869:
2863:
2232:
105:
3574:
3178:
3004:
2585:
1662:{\displaystyle {\widehat {F}}>400}
4812:
3533:
3284:. TU Delft, fluid mechanics section.
3255:
3218:Young, I.R.; Verhagen, L.A. (1996).
3095:
2636:
2600:
2570:
1550:{\displaystyle {\widehat {F}}>10}
16:Numerical modelling of the sea state
3539:Cox, A., V. Cardone, and V. Swail,
2979:
420:Other wind wave models include the
228:
179:Scripps Institution of Oceanography
133:Fleet Numerical Oceanography Center
42:describes the effort to depict the
13:
4692:National Oceanographic Data Center
4119:World Ocean Circulation Experiment
4007:Global Ocean Data Analysis Project
3364:10.1016/b978-0-08-102927-5.00017-5
3188:Groen, P.; Dorrestein, R. (1976).
2746:
2253:Based on Bretschneider's formula:
583:= gravitational acceleration (m/s)
98:Other applications, in particular
14:
4866:
4539:Global Sea Level Observing System
2987:"Entwicklungen KSD WAM Cycle 4.5"
2912:"WAVEWATCH III Model Description"
2378:wind path crosses shallow areas.
2249:Bretschneider Formula: Lake Garda
310:
259:
114:were created manually based upon
46:and predict the evolution of the
4822:
4811:
4802:
4801:
3997:Geochemical Ocean Sections Study
3913:
3902:
2951:Journal of Physical Oceanography
2652:– via TU Delft Repository.
2617:Japan Society of Civil Engineers
2521:Wittmann, Paul and Mike Clancy,
2427:In situations where significant
2319:Global wind wave models such as
264:The sea state is described as a
4727:Ocean thermal energy conversion
4450:VineâMatthewsâMorley hypothesis
3467:
3424:
3394:
3343:
3319:
3288:
3274:
3249:
3211:
3132:
3107:
2810:
2769:
2740:
2721:
2686:Coastal Engineering Proceedings
2673:
2656:
428:The formulae of Bretschneider,
393:
3358:, Elsevier, pp. 391â419,
2630:
2594:
2542:
2449:data from satellites, such as
2325:Delft University of Technology
1402:
1362:
1302:
1262:
1203:
1184:
1133:
1114:
1076:Common Formulas for Deep Water
411:Delft University of Technology
288:(by bathymetry and currents),
1:
3236:10.1016/S0378-3839(96)00006-3
3049:"Operational Model Forecasts"
2730:"Methods for wave prediction"
2477:
2463:
2439:
2229:), this formula is reliable.
641:= significant wave period (s)
612:= significant wave height (m)
377:Helmholtz Zentrum, Geesthacht
3987:El NiĂąoâSouthern Oscillation
3957:CraikâLeibovich vortex force
3713:Luke's variational principle
3350:Guisado-Pintado, E. (2020),
2680:Bretschneider, C.L. (2011).
1080:Bretschneider (1952, 1977):
440:, the basic formula set is:
424:Standard Surf Model (NSSM).
340:
7:
3145:German Hydrographic Journal
2669:. U.S. Beach Erosion Board.
384:ensemble forecasting system
335:
10:
4871:
4052:Ocean dynamical thermostat
3900:
3356:Sandy Beach Morphodynamics
2728:Holthuijsen, L.H. (1980).
2315:Shallow and coastal waters
2271:Wilson Formula: Lake Garda
432:, and Young & Verhagen
388:Integrated Forecast System
26:
4797:
4636:
4610:
4587:Ocean acoustic tomography
4572:
4524:
4463:
4400:MohoroviÄiÄ discontinuity
4358:
4230:
4127:
3992:General circulation model
3922:
3628:BenjaminâFeir instability
3608:
3505:J. Atmos. Oceanic Technol
298:
169:During this period, both
4717:Ocean surface topography
4092:Thermohaline circulation
4082:Subsurface ocean current
4022:Hydrothermal circulation
3855:Waveâcurrent interaction
3633:Boussinesq approximation
2736:. Rijkswaterstaat - TAW.
2415:Two-dimensional approach
2362:One-dimensional approach
2333:Office of Naval Research
2327:, in collaboration with
407:Texas A&M University
233:
199:Office of Naval Research
185:. Under the guidance of
183:University of California
166:by the warring nations.
93:ocean surface wave model
4754:Sea surface temperature
4737:Outline of oceanography
3932:Atmospheric circulation
3870:shallow water equations
3860:Waves and shallow water
3753:Significant wave height
3104:, US Naval Research Lab
2307:Predicted wave period:
2301:Predicted wave height:
2285:Predicted wave period:
2279:Predicted wave height:
2263:Predicted wave period:
2257:Predicted wave height:
305:significant wave height
272:using the principle of
206:significant wave method
110:Early forecasts of the
4749:Sea surface microlayer
4114:Wind generated current
3114:Battjes, J.A. (1982).
3011:"The Ocean Wave Model"
2615:(in Japanese). Tokyo:
2424:
2374:
2216:
2164:
2111:
1993:
1941:
1888:
1759:
1718:
1663:
1628:
1551:
1516:
1443:
1435:
1421:
1321:
1216:
1146:
1072:
1053:
1031:
1009:
983:
927:
866:
805:
742:
664:
635:
606:
577:
551:
496:
365:
256:
217:
24:
4850:Physical oceanography
4582:Deep scattering layer
4564:World Geodetic System
4072:Princeton Ocean Model
3952:CoriolisâStokes force
3602:Physical oceanography
3139:Wilson, B.W. (1965).
2870:Bender, L.C. (1996).
2422:
2369:
2217:
2165:
2112:
1994:
1942:
1889:
1760:
1719:
1664:
1629:
1552:
1517:
1441:
1433:
1422:
1322:
1217:
1147:
1070:
1054:
1032:
1010:
984:
928:
867:
806:
743:
665:
663:{\displaystyle u_{w}}
636:
634:{\displaystyle T_{s}}
607:
605:{\displaystyle H_{s}}
578:
552:
497:
332:builds up or decays.
326:sea surface roughness
253:
22:
4602:Underwater acoustics
4162:Perigean spring tide
4027:Langmuir circulation
3738:Rossby-gravity waves
3474:Breugem, A. (2003).
3051:, Environment Canada
2849:10.1029/2008GL037030
2663:Saville, T. (1954).
2174:
2122:
2009:
1951:
1899:
1786:
1728:
1674:
1638:
1562:
1526:
1453:
1332:
1232:
1157:
1087:
1064:observed behaviour.
1059:= storm duration (s)
1043:
1021:
999:
938:
877:
816:
753:
685:
676:dimensionless values
647:
618:
589:
567:
507:
447:
181:affiliated with the
150:In the aftermath of
52:numerical techniques
50:of wind waves using
4764:Science On a Sphere
4370:Convergent boundary
4042:Modular Ocean Model
4002:Geostrophic current
3718:Mild-slope equation
3517:1996JAtOT..13..198C
3224:Coastal Engineering
3157:1965DeHyZ..18..114W
2963:1988JPO....18.1775W
2888:1996JAtOT..13..726B
2841:2009GeoRL..36.6607A
2794:2003JPO....33.1921A
2393:Westerscheldetunnel
2391:, just west of the
2370:Wave growth in the
2233:Example: Lake Garda
921:
860:
736:
482:
324:which controls the
106:Historical overview
100:coastal engineering
4420:Seafloor spreading
4410:Outer trench swell
4375:Divergent boundary
4275:Continental margin
4260:Carbonate platform
4157:Lunitidal interval
3561:2007-02-07 at the
3194:Knmi Publicatie 11
3165:10.1007/BF02333333
3016:2008-06-03 at the
2819:Geophys. Res. Lett
2567:, Oceanweather Inc
2563:2001-11-21 at the
2425:
2375:
2212:
2160:
2107:
1989:
1937:
1884:
1755:
1714:
1659:
1624:
1547:
1512:
1444:
1436:
1417:
1317:
1212:
1142:
1073:
1049:
1027:
1005:
979:
923:
907:
862:
846:
801:
738:
722:
670:= wind speed (m/s)
660:
631:
602:
573:
547:
492:
468:
400:Environment Canada
352:nonlinear resonant
322:Charnock parameter
257:
195:United States Navy
40:wind wave modeling
25:
4837:
4836:
4829:Oceans portal
4789:World Ocean Atlas
4779:Underwater glider
4722:Ocean temperature
4385:Hydrothermal vent
4350:Submarine volcano
4285:Continental shelf
4265:Coastal geography
4255:Bathymetric chart
4137:Amphidromic point
3825:Wave nonlinearity
3683:Infragravity wave
3450:10.3390/w14071087
3373:978-0-08-102927-5
3256:Bart, L. (2013).
2957:(12): 1775â1810.
2782:J. Phys. Oceanogr
2747:Tolman, Hendrik.
2699:10.9753/icce.v6.3
2637:Goda, Y. (1999).
2601:Goda, Y. (1999).
2579:Komen, Gerbrand,
2399:in front of it.
2203:
2151:
2094:
2021:
1980:
1928:
1871:
1798:
1746:
1705:
1686:
1650:
1610:
1574:
1538:
1498:
1465:
1384:
1344:
1284:
1244:
1199:
1169:
1129:
1099:
1052:{\displaystyle t}
1030:{\displaystyle F}
1015:= water depth (m)
1008:{\displaystyle d}
950:
889:
828:
765:
697:
576:{\displaystyle g}
539:
484:
280:â which include:
145:data assimilation
82:shipping industry
4862:
4827:
4826:
4815:
4814:
4805:
4804:
4744:Pelagic sediment
4682:Marine pollution
4476:Deep ocean water
4345:Submarine canyon
4280:Continental rise
4172:Rule of twelfths
4087:Sverdrup balance
4017:Humboldt Current
3942:Boundary current
3917:
3906:
3723:Radiation stress
3693:Iribarren number
3668:Equatorial waves
3623:Ballantine scale
3618:Airy wave theory
3595:
3588:
3581:
3572:
3571:
3565:
3552:
3543:
3537:
3531:
3530:
3528:
3496:
3490:
3489:
3487:
3485:
3471:
3465:
3464:
3462:
3452:
3428:
3422:
3421:
3419:
3417:
3398:
3392:
3391:
3390:
3388:
3347:
3341:
3340:
3338:
3337:
3323:
3317:
3316:
3314:
3312:
3292:
3286:
3285:
3278:
3272:
3271:
3269:
3267:
3253:
3247:
3246:
3244:
3242:
3215:
3209:
3208:
3206:
3204:
3185:
3176:
3175:
3173:
3171:
3136:
3130:
3129:
3127:
3125:
3111:
3105:
3099:
3093:
3092:
3090:
3089:
3080:. Archived from
3074:
3068:
3058:
3052:
3046:
3040:
3037:
3031:
3027:
3021:
3008:
3002:
3001:
2999:
2998:
2989:. Archived from
2983:
2977:
2976:
2974:
2942:
2936:
2933:
2927:
2920:
2914:
2908:
2902:
2901:
2899:
2867:
2861:
2860:
2834:
2814:
2808:
2807:
2805:
2788:(9): 1921â1939.
2773:
2767:
2766:
2764:
2762:
2753:
2744:
2738:
2737:
2725:
2719:
2718:
2716:
2714:
2701:
2677:
2671:
2670:
2660:
2654:
2653:
2651:
2649:
2634:
2628:
2627:
2625:
2623:
2614:
2598:
2592:
2589:
2583:
2577:
2568:
2555:
2549:
2546:
2540:
2536:
2530:
2519:
2513:
2512:
2510:
2509:
2500:
2491:
2221:
2219:
2218:
2213:
2211:
2210:
2205:
2204:
2196:
2186:
2185:
2169:
2167:
2166:
2161:
2159:
2158:
2153:
2152:
2144:
2134:
2133:
2116:
2114:
2113:
2108:
2106:
2105:
2100:
2096:
2095:
2093:
2092:
2091:
2090:
2073:
2072:
2071:
2061:
2053:
2052:
2051:
2023:
2022:
2014:
1998:
1996:
1995:
1990:
1988:
1987:
1982:
1981:
1973:
1963:
1962:
1946:
1944:
1943:
1938:
1936:
1935:
1930:
1929:
1921:
1911:
1910:
1893:
1891:
1890:
1885:
1883:
1882:
1877:
1873:
1872:
1870:
1869:
1868:
1867:
1850:
1849:
1848:
1838:
1830:
1829:
1828:
1800:
1799:
1791:
1764:
1762:
1761:
1756:
1748:
1747:
1739:
1723:
1721:
1720:
1715:
1713:
1712:
1707:
1706:
1698:
1688:
1687:
1679:
1668:
1666:
1665:
1660:
1652:
1651:
1643:
1633:
1631:
1630:
1625:
1623:
1622:
1617:
1613:
1612:
1611:
1603:
1576:
1575:
1567:
1556:
1554:
1553:
1548:
1540:
1539:
1531:
1521:
1519:
1518:
1513:
1511:
1510:
1505:
1501:
1500:
1499:
1491:
1467:
1466:
1458:
1426:
1424:
1423:
1418:
1413:
1412:
1400:
1399:
1395:
1386:
1385:
1377:
1346:
1345:
1337:
1326:
1324:
1323:
1318:
1313:
1312:
1300:
1299:
1295:
1286:
1285:
1277:
1246:
1245:
1237:
1221:
1219:
1218:
1213:
1211:
1210:
1201:
1200:
1192:
1171:
1170:
1162:
1151:
1149:
1148:
1143:
1141:
1140:
1131:
1130:
1122:
1101:
1100:
1092:
1058:
1056:
1055:
1050:
1037:= wind fetch (m)
1036:
1034:
1033:
1028:
1014:
1012:
1011:
1006:
988:
986:
985:
980:
978:
977:
976:
967:
952:
951:
943:
932:
930:
929:
924:
922:
920:
915:
906:
891:
890:
882:
871:
869:
868:
863:
861:
859:
854:
845:
830:
829:
821:
810:
808:
807:
802:
800:
799:
798:
789:
784:
783:
767:
766:
758:
747:
745:
744:
739:
737:
735:
730:
721:
716:
715:
699:
698:
690:
669:
667:
666:
661:
659:
658:
640:
638:
637:
632:
630:
629:
611:
609:
608:
603:
601:
600:
582:
580:
579:
574:
556:
554:
553:
548:
540:
538:
537:
536:
526:
525:
524:
511:
501:
499:
498:
493:
485:
483:
481:
476:
466:
465:
464:
451:
386:., known as the
355:shallow depths.
282:wave propagation
229:General strategy
220:
4870:
4869:
4865:
4864:
4863:
4861:
4860:
4859:
4840:
4839:
4838:
4833:
4821:
4793:
4632:
4606:
4568:
4549:Sea-level curve
4520:
4459:
4445:Transform fault
4395:Mid-ocean ridge
4361:
4354:
4320:Oceanic plateau
4226:
4212:Tidal resonance
4182:Theory of tides
4123:
4032:Longshore drift
3982:Ekman transport
3918:
3912:
3911:
3910:
3909:
3908:
3907:
3898:
3850:Wave turbulence
3783:Trochoidal wave
3708:Longshore drift
3604:
3599:
3569:
3568:
3563:Wayback Machine
3553:
3546:
3538:
3534:
3497:
3493:
3483:
3481:
3472:
3468:
3429:
3425:
3415:
3413:
3399:
3395:
3386:
3384:
3374:
3348:
3344:
3335:
3333:
3325:
3324:
3320:
3310:
3308:
3293:
3289:
3282:"SWAN homepage"
3280:
3279:
3275:
3265:
3263:
3254:
3250:
3240:
3238:
3216:
3212:
3202:
3200:
3186:
3179:
3169:
3167:
3137:
3133:
3123:
3121:
3112:
3108:
3100:
3096:
3087:
3085:
3076:
3075:
3071:
3067:, Feb. 23, 2005
3059:
3055:
3047:
3043:
3038:
3034:
3028:
3024:
3018:Wayback Machine
3009:
3005:
2996:
2994:
2985:
2984:
2980:
2943:
2939:
2934:
2930:
2922:Tolman, 2002g:
2921:
2917:
2910:Tolman, H. L.,
2909:
2905:
2868:
2864:
2815:
2811:
2774:
2770:
2760:
2758:
2751:
2745:
2741:
2726:
2722:
2712:
2710:
2678:
2674:
2661:
2657:
2647:
2645:
2635:
2631:
2621:
2619:
2612:
2599:
2595:
2590:
2586:
2578:
2571:
2565:Wayback Machine
2558:"Wave Modeling"
2556:
2552:
2547:
2543:
2537:
2533:
2520:
2516:
2507:
2505:
2498:
2492:
2485:
2480:
2466:
2442:
2417:
2410:
2405:spectral period
2384:
2372:Western Scheldt
2364:
2329:Rijkswaterstaat
2317:
2295:
2273:
2251:
2243:
2235:
2206:
2195:
2194:
2193:
2181:
2177:
2175:
2172:
2171:
2154:
2143:
2142:
2141:
2129:
2125:
2123:
2120:
2119:
2101:
2086:
2082:
2081:
2074:
2067:
2063:
2062:
2060:
2047:
2043:
2042:
2035:
2031:
2030:
2013:
2012:
2010:
2007:
2006:
1983:
1972:
1971:
1970:
1958:
1954:
1952:
1949:
1948:
1931:
1920:
1919:
1918:
1906:
1902:
1900:
1897:
1896:
1878:
1863:
1859:
1858:
1851:
1844:
1840:
1839:
1837:
1824:
1820:
1819:
1812:
1808:
1807:
1790:
1789:
1787:
1784:
1783:
1738:
1737:
1729:
1726:
1725:
1708:
1697:
1696:
1695:
1678:
1677:
1675:
1672:
1671:
1642:
1641:
1639:
1636:
1635:
1618:
1602:
1601:
1597:
1593:
1592:
1566:
1565:
1563:
1560:
1559:
1530:
1529:
1527:
1524:
1523:
1506:
1490:
1489:
1485:
1481:
1480:
1457:
1456:
1454:
1451:
1450:
1405:
1401:
1391:
1387:
1376:
1375:
1374:
1336:
1335:
1333:
1330:
1329:
1305:
1301:
1291:
1287:
1276:
1275:
1274:
1236:
1235:
1233:
1230:
1229:
1225:Wilson (1965):
1206:
1202:
1191:
1190:
1161:
1160:
1158:
1155:
1154:
1136:
1132:
1121:
1120:
1091:
1090:
1088:
1085:
1084:
1078:
1044:
1041:
1040:
1022:
1019:
1018:
1000:
997:
996:
972:
968:
963:
956:
942:
941:
939:
936:
935:
916:
911:
902:
895:
881:
880:
878:
875:
874:
855:
850:
841:
834:
820:
819:
817:
814:
813:
794:
790:
785:
779:
775:
771:
757:
756:
754:
751:
750:
731:
726:
717:
711:
707:
703:
689:
688:
686:
683:
682:
654:
650:
648:
645:
644:
625:
621:
619:
616:
615:
596:
592:
590:
587:
586:
568:
565:
564:
532:
528:
527:
520:
516:
512:
510:
508:
505:
504:
477:
472:
467:
460:
456:
452:
450:
448:
445:
444:
434:
396:
368:
343:
338:
313:
301:
262:
236:
231:
213:Rijkswaterstaat
108:
32:
17:
12:
11:
5:
4868:
4858:
4857:
4852:
4835:
4834:
4832:
4831:
4819:
4809:
4798:
4795:
4794:
4792:
4791:
4786:
4781:
4776:
4771:
4769:Stratification
4766:
4761:
4756:
4751:
4746:
4741:
4740:
4739:
4729:
4724:
4719:
4714:
4709:
4704:
4699:
4694:
4689:
4684:
4679:
4674:
4669:
4661:
4659:Color of water
4656:
4654:Benthic lander
4651:
4646:
4640:
4638:
4634:
4633:
4631:
4630:
4625:
4620:
4614:
4612:
4608:
4607:
4605:
4604:
4599:
4594:
4589:
4584:
4578:
4576:
4570:
4569:
4567:
4566:
4561:
4559:Sea level rise
4556:
4554:Sea level drop
4551:
4546:
4541:
4536:
4530:
4528:
4522:
4521:
4519:
4518:
4513:
4508:
4503:
4498:
4493:
4488:
4483:
4478:
4473:
4467:
4465:
4461:
4460:
4458:
4457:
4452:
4447:
4442:
4437:
4432:
4427:
4422:
4417:
4412:
4407:
4402:
4397:
4392:
4390:Marine geology
4387:
4382:
4377:
4372:
4366:
4364:
4356:
4355:
4353:
4352:
4347:
4342:
4337:
4332:
4330:Passive margin
4327:
4325:Oceanic trench
4322:
4317:
4312:
4307:
4302:
4297:
4292:
4287:
4282:
4277:
4272:
4267:
4262:
4257:
4252:
4247:
4242:
4236:
4234:
4228:
4227:
4225:
4224:
4219:
4214:
4209:
4204:
4199:
4194:
4189:
4184:
4179:
4174:
4169:
4164:
4159:
4154:
4149:
4144:
4139:
4133:
4131:
4125:
4124:
4122:
4121:
4116:
4111:
4106:
4101:
4100:
4099:
4089:
4084:
4079:
4074:
4069:
4064:
4059:
4057:Ocean dynamics
4054:
4049:
4044:
4039:
4034:
4029:
4024:
4019:
4014:
4009:
4004:
3999:
3994:
3989:
3984:
3979:
3974:
3969:
3964:
3959:
3954:
3949:
3947:Coriolis force
3944:
3939:
3934:
3928:
3926:
3920:
3919:
3901:
3899:
3897:
3896:
3895:
3894:
3884:
3879:
3874:
3873:
3872:
3867:
3857:
3852:
3847:
3842:
3837:
3832:
3827:
3822:
3817:
3812:
3807:
3802:
3797:
3796:
3795:
3785:
3780:
3775:
3770:
3768:Stokes problem
3765:
3760:
3755:
3750:
3745:
3740:
3735:
3730:
3725:
3720:
3715:
3710:
3705:
3703:Kinematic wave
3700:
3695:
3690:
3685:
3680:
3675:
3670:
3665:
3660:
3655:
3650:
3645:
3640:
3635:
3630:
3625:
3620:
3614:
3612:
3606:
3605:
3598:
3597:
3590:
3583:
3575:
3567:
3566:
3544:
3532:
3511:(1): 198â230.
3491:
3466:
3423:
3393:
3372:
3342:
3318:
3287:
3273:
3248:
3230:(1â2): 47â78.
3210:
3177:
3151:(3): 114â130.
3131:
3106:
3094:
3069:
3053:
3041:
3032:
3022:
3003:
2978:
2937:
2928:
2915:
2903:
2882:(3): 726â750.
2862:
2809:
2768:
2739:
2720:
2672:
2655:
2629:
2593:
2584:
2569:
2550:
2541:
2531:
2514:
2482:
2481:
2479:
2476:
2465:
2462:
2441:
2438:
2416:
2413:
2408:
2389:South Beveland
2383:
2380:
2363:
2360:
2352:user interface
2316:
2313:
2312:
2311:
2305:
2294:
2291:
2290:
2289:
2283:
2272:
2269:
2268:
2267:
2261:
2250:
2247:
2241:
2234:
2231:
2223:
2222:
2209:
2202:
2199:
2192:
2189:
2184:
2180:
2157:
2150:
2147:
2140:
2137:
2132:
2128:
2117:
2104:
2099:
2089:
2085:
2080:
2077:
2070:
2066:
2059:
2056:
2050:
2046:
2041:
2038:
2034:
2029:
2026:
2020:
2017:
2000:
1999:
1986:
1979:
1976:
1969:
1966:
1961:
1957:
1934:
1927:
1924:
1917:
1914:
1909:
1905:
1894:
1881:
1876:
1866:
1862:
1857:
1854:
1847:
1843:
1836:
1833:
1827:
1823:
1818:
1815:
1811:
1806:
1803:
1797:
1794:
1766:
1765:
1754:
1751:
1745:
1742:
1736:
1733:
1711:
1704:
1701:
1694:
1691:
1685:
1682:
1669:
1658:
1655:
1649:
1646:
1621:
1616:
1609:
1606:
1600:
1596:
1591:
1588:
1585:
1582:
1579:
1573:
1570:
1557:
1546:
1543:
1537:
1534:
1509:
1504:
1497:
1494:
1488:
1484:
1479:
1476:
1473:
1470:
1464:
1461:
1428:
1427:
1416:
1411:
1408:
1404:
1398:
1394:
1390:
1383:
1380:
1373:
1370:
1367:
1364:
1361:
1358:
1355:
1352:
1349:
1343:
1340:
1327:
1316:
1311:
1308:
1304:
1298:
1294:
1290:
1283:
1280:
1273:
1270:
1267:
1264:
1261:
1258:
1255:
1252:
1249:
1243:
1240:
1223:
1222:
1209:
1205:
1198:
1195:
1189:
1186:
1183:
1180:
1177:
1174:
1168:
1165:
1152:
1139:
1135:
1128:
1125:
1119:
1116:
1113:
1110:
1107:
1104:
1098:
1095:
1077:
1074:
1061:
1060:
1048:
1038:
1026:
1016:
1004:
990:
989:
975:
971:
966:
962:
959:
955:
949:
946:
933:
919:
914:
910:
905:
901:
898:
894:
888:
885:
872:
858:
853:
849:
844:
840:
837:
833:
827:
824:
811:
797:
793:
788:
782:
778:
774:
770:
764:
761:
748:
734:
729:
725:
720:
714:
710:
706:
702:
696:
693:
672:
671:
657:
653:
642:
628:
624:
613:
599:
595:
584:
572:
558:
557:
546:
543:
535:
531:
523:
519:
515:
502:
491:
488:
480:
475:
471:
463:
459:
455:
433:
426:
395:
392:
367:
364:
360:Hendrik Tolman
342:
339:
337:
334:
312:
311:Coupled models
309:
300:
297:
261:
260:Representation
258:
244:Ocean currents
235:
232:
230:
227:
187:Harald Svedrup
164:oceanographers
160:meteorologists
107:
104:
36:fluid dynamics
15:
9:
6:
4:
3:
2:
4867:
4856:
4853:
4851:
4848:
4847:
4845:
4830:
4825:
4820:
4818:
4810:
4808:
4800:
4799:
4796:
4790:
4787:
4785:
4782:
4780:
4777:
4775:
4772:
4770:
4767:
4765:
4762:
4760:
4757:
4755:
4752:
4750:
4747:
4745:
4742:
4738:
4735:
4734:
4733:
4730:
4728:
4725:
4723:
4720:
4718:
4715:
4713:
4710:
4708:
4705:
4703:
4700:
4698:
4695:
4693:
4690:
4688:
4685:
4683:
4680:
4678:
4677:Marine energy
4675:
4673:
4670:
4668:
4667:
4662:
4660:
4657:
4655:
4652:
4650:
4647:
4645:
4644:Acidification
4642:
4641:
4639:
4635:
4629:
4626:
4624:
4621:
4619:
4616:
4615:
4613:
4609:
4603:
4600:
4598:
4597:SOFAR channel
4595:
4593:
4590:
4588:
4585:
4583:
4580:
4579:
4577:
4575:
4571:
4565:
4562:
4560:
4557:
4555:
4552:
4550:
4547:
4545:
4542:
4540:
4537:
4535:
4532:
4531:
4529:
4527:
4523:
4517:
4514:
4512:
4509:
4507:
4504:
4502:
4499:
4497:
4494:
4492:
4489:
4487:
4484:
4482:
4479:
4477:
4474:
4472:
4469:
4468:
4466:
4462:
4456:
4453:
4451:
4448:
4446:
4443:
4441:
4438:
4436:
4433:
4431:
4428:
4426:
4423:
4421:
4418:
4416:
4413:
4411:
4408:
4406:
4405:Oceanic crust
4403:
4401:
4398:
4396:
4393:
4391:
4388:
4386:
4383:
4381:
4380:Fracture zone
4378:
4376:
4373:
4371:
4368:
4367:
4365:
4363:
4357:
4351:
4348:
4346:
4343:
4341:
4338:
4336:
4333:
4331:
4328:
4326:
4323:
4321:
4318:
4316:
4315:Oceanic basin
4313:
4311:
4308:
4306:
4303:
4301:
4298:
4296:
4293:
4291:
4288:
4286:
4283:
4281:
4278:
4276:
4273:
4271:
4268:
4266:
4263:
4261:
4258:
4256:
4253:
4251:
4248:
4246:
4245:Abyssal plain
4243:
4241:
4238:
4237:
4235:
4233:
4229:
4223:
4220:
4218:
4215:
4213:
4210:
4208:
4205:
4203:
4200:
4198:
4195:
4193:
4190:
4188:
4185:
4183:
4180:
4178:
4175:
4173:
4170:
4168:
4165:
4163:
4160:
4158:
4155:
4153:
4152:Internal tide
4150:
4148:
4145:
4143:
4140:
4138:
4135:
4134:
4132:
4130:
4126:
4120:
4117:
4115:
4112:
4110:
4107:
4105:
4102:
4098:
4095:
4094:
4093:
4090:
4088:
4085:
4083:
4080:
4078:
4075:
4073:
4070:
4068:
4065:
4063:
4060:
4058:
4055:
4053:
4050:
4048:
4047:Ocean current
4045:
4043:
4040:
4038:
4035:
4033:
4030:
4028:
4025:
4023:
4020:
4018:
4015:
4013:
4010:
4008:
4005:
4003:
4000:
3998:
3995:
3993:
3990:
3988:
3985:
3983:
3980:
3978:
3975:
3973:
3970:
3968:
3965:
3963:
3960:
3958:
3955:
3953:
3950:
3948:
3945:
3943:
3940:
3938:
3935:
3933:
3930:
3929:
3927:
3925:
3921:
3916:
3905:
3893:
3890:
3889:
3888:
3885:
3883:
3880:
3878:
3875:
3871:
3868:
3866:
3863:
3862:
3861:
3858:
3856:
3853:
3851:
3848:
3846:
3845:Wave shoaling
3843:
3841:
3838:
3836:
3833:
3831:
3828:
3826:
3823:
3821:
3818:
3816:
3813:
3811:
3808:
3806:
3805:Ursell number
3803:
3801:
3798:
3794:
3791:
3790:
3789:
3786:
3784:
3781:
3779:
3776:
3774:
3771:
3769:
3766:
3764:
3761:
3759:
3756:
3754:
3751:
3749:
3746:
3744:
3741:
3739:
3736:
3734:
3731:
3729:
3726:
3724:
3721:
3719:
3716:
3714:
3711:
3709:
3706:
3704:
3701:
3699:
3696:
3694:
3691:
3689:
3688:Internal wave
3686:
3684:
3681:
3679:
3676:
3674:
3671:
3669:
3666:
3664:
3661:
3659:
3656:
3654:
3651:
3649:
3646:
3644:
3641:
3639:
3638:Breaking wave
3636:
3634:
3631:
3629:
3626:
3624:
3621:
3619:
3616:
3615:
3613:
3611:
3607:
3603:
3596:
3591:
3589:
3584:
3582:
3577:
3576:
3573:
3564:
3560:
3557:
3551:
3549:
3542:
3536:
3527:
3522:
3518:
3514:
3510:
3506:
3502:
3495:
3479:
3478:
3470:
3461:
3460:11577/3439620
3456:
3451:
3446:
3442:
3438:
3434:
3427:
3412:
3408:
3404:
3397:
3383:
3379:
3375:
3369:
3365:
3361:
3357:
3353:
3346:
3332:
3328:
3322:
3306:
3302:
3298:
3291:
3283:
3277:
3261:
3260:
3252:
3237:
3233:
3229:
3225:
3221:
3214:
3199:
3195:
3191:
3184:
3182:
3166:
3162:
3158:
3154:
3150:
3146:
3142:
3135:
3119:
3118:
3110:
3103:
3098:
3084:on 2016-03-04
3083:
3079:
3073:
3066:
3062:
3057:
3050:
3045:
3036:
3026:
3019:
3015:
3012:
3007:
2993:on 2013-08-23
2992:
2988:
2982:
2973:
2968:
2964:
2960:
2956:
2952:
2948:
2941:
2932:
2925:
2919:
2913:
2907:
2898:
2893:
2889:
2885:
2881:
2877:
2873:
2866:
2858:
2854:
2850:
2846:
2842:
2838:
2833:
2828:
2825:(6): L06607.
2824:
2820:
2813:
2804:
2799:
2795:
2791:
2787:
2783:
2779:
2772:
2757:
2750:
2743:
2735:
2731:
2724:
2709:
2705:
2700:
2695:
2691:
2687:
2683:
2676:
2668:
2667:
2659:
2644:
2640:
2633:
2618:
2610:
2606:
2605:
2597:
2588:
2582:
2576:
2574:
2566:
2562:
2559:
2554:
2545:
2535:
2528:
2524:
2518:
2504:
2497:
2490:
2488:
2483:
2475:
2472:
2461:
2458:
2456:
2452:
2448:
2437:
2433:
2430:
2421:
2412:
2406:
2400:
2398:
2394:
2390:
2379:
2373:
2368:
2359:
2357:
2353:
2349:
2348:wave spectrum
2344:
2342:
2338:
2334:
2330:
2326:
2322:
2310:
2306:
2304:
2300:
2299:
2298:
2288:
2284:
2282:
2278:
2277:
2276:
2266:
2262:
2260:
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2015:
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718:
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681:
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677:
655:
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403:
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391:
389:
385:
380:
378:
373:
372:wave spectrum
363:
361:
356:
353:
348:
333:
331:
327:
323:
319:
308:
306:
296:
293:
291:
287:
284:/ advection,
283:
279:
275:
274:superposition
271:
267:
252:
248:
245:
240:
226:
224:
219:
214:
209:
207:
202:
200:
196:
192:
188:
184:
180:
176:
175:United States
172:
167:
165:
161:
157:
156:landing craft
153:
148:
146:
140:
136:
134:
129:
123:
121:
117:
113:
103:
101:
96:
94:
89:
87:
83:
79:
78:
72:
71:
65:
61:
57:
53:
49:
45:
41:
37:
30:
21:
4784:Water column
4732:Oceanography
4707:Observations
4702:Explorations
4672:Marginal sea
4665:
4623:OSTM/Jason-2
4455:Volcanic arc
4430:Slab suction
4147:Head of tide
4037:Loop Current
3977:Ekman spiral
3891:
3763:Stokes drift
3673:Gravity wave
3648:Cnoidal wave
3535:
3508:
3504:
3494:
3482:. Retrieved
3476:
3469:
3440:
3436:
3426:
3414:. Retrieved
3410:
3406:
3396:
3385:, retrieved
3355:
3345:
3334:. Retrieved
3330:
3321:
3309:. Retrieved
3304:
3300:
3290:
3276:
3264:. Retrieved
3258:
3251:
3239:. Retrieved
3227:
3223:
3213:
3201:. Retrieved
3193:
3168:. Retrieved
3148:
3144:
3134:
3122:. Retrieved
3116:
3109:
3097:
3086:. Retrieved
3082:the original
3072:
3065:ScienceDaily
3064:
3056:
3044:
3035:
3025:
3006:
2995:. Retrieved
2991:the original
2981:
2954:
2950:
2940:
2931:
2918:
2906:
2879:
2875:
2865:
2822:
2818:
2812:
2785:
2781:
2771:
2759:. Retrieved
2755:
2742:
2733:
2723:
2711:. Retrieved
2689:
2685:
2675:
2665:
2658:
2646:. Retrieved
2642:
2632:
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2608:
2604:ă波ĺĺéĄăăŽć´ĺ˛çĺ¤éˇ
2603:
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2506:. Retrieved
2502:
2467:
2459:
2443:
2434:
2426:
2401:
2385:
2376:
2345:
2318:
2309:6.89 seconds
2308:
2302:
2296:
2287:7.01 seconds
2286:
2280:
2274:
2265:7.02 seconds
2264:
2258:
2252:
2236:
2224:
2001:
1778:
1774:
1767:
1445:
1224:
1079:
1062:
991:
673:
559:
435:
419:
415:
404:
397:
394:Other models
381:
369:
357:
344:
314:
302:
294:
263:
241:
237:
210:
203:
168:
152:World War II
149:
141:
137:
124:
109:
97:
92:
90:
74:
67:
60:wave heights
39:
33:
4855:Water waves
4774:Thermocline
4491:Mesopelagic
4464:Ocean zones
4435:Slab window
4300:Hydrography
4240:Abyssal fan
4207:Tidal range
4197:Tidal power
4192:Tidal force
4077:Rip current
4012:Gulf Stream
3972:Ekman layer
3962:Downwelling
3937:Baroclinity
3924:Circulation
3820:Wave height
3810:Wave action
3793:megatsunami
3773:Stokes wave
3733:Rossby wave
3698:Kelvin wave
3678:Green's law
3443:(7): 1087.
3190:"Sea Waves"
2356:open-source
2303:2.63 meters
2281:3.56 meters
2259:3.54 meters
278:wave action
270:frequencies
191:Walter Munk
58:describing
4844:Categories
4712:Reanalysis
4611:Satellites
4592:Sofar bomb
4440:Subduction
4415:Ridge push
4310:Ocean bank
4290:Contourite
4217:Tide gauge
4202:Tidal race
4187:Tidal bore
4177:Slack tide
4142:Earth tide
4062:Ocean gyre
3882:Wind setup
3877:Wind fetch
3840:Wave setup
3835:Wave radar
3830:Wave power
3728:Rogue wave
3658:Dispersion
3480:. TU Delft
3336:2023-08-27
3262:. TU Delft
3120:. TU Delft
3117:Wind Waves
3088:2015-06-01
2997:2012-03-22
2508:2008-11-21
2478:References
2464:Reanalyses
2440:Validation
2429:refraction
2397:salt marsh
2341:refraction
2238:Lake Garda
2227:IJsselmeer
286:refraction
88:purposes.
86:seakeeping
56:statistics
29:Wind waves
4574:Acoustics
4526:Sea level
4425:Slab pull
4362:tectonics
4270:Cold seep
4232:Landforms
4109:Whirlpool
4104:Upwelling
3887:Wind wave
3815:Wave base
3743:Sea state
3663:Edge wave
3653:Cross sea
3484:11 August
3416:11 August
3387:27 August
3382:219883066
3311:11 August
3307:: 630â641
3266:10 August
3241:10 August
3203:10 August
3170:10 August
3124:10 August
2832:0809.2497
2713:11 August
2708:2156-1028
2648:27 August
2622:27 August
2447:Altimetry
2321:WAVEWATCH
2201:^
2191:0.0005215
2149:^
2079:
2058:
2040:
2019:^
1978:^
1926:^
1856:
1835:
1817:
1796:^
1770:nomograms
1744:^
1703:^
1684:^
1648:^
1608:^
1590:
1584:π
1572:^
1536:^
1496:^
1478:
1463:^
1407:−
1382:^
1360:−
1342:^
1307:−
1282:^
1260:−
1242:^
1197:^
1182:
1167:^
1127:^
1112:
1097:^
948:^
887:^
826:^
763:^
695:^
422:U.S. Navy
341:WAVEWATCH
128:wind seas
116:empirical
112:sea state
95:is used.
77:forecasts
70:hindcasts
44:sea state
4807:Category
4759:Seawater
4486:Littoral
4481:Deep sea
4340:Seamount
4222:Tideline
4167:Rip tide
4097:shutdown
4067:Overflow
3800:Undertow
3643:Clapotis
3559:Archived
3331:TU Delft
3014:Archived
2761:22 March
2692:(6): 3.
2561:Archived
2337:breaking
2331:and the
336:Examples
330:wind sea
290:shoaling
266:spectrum
215:and the
173:and the
4817:Commons
4687:Mooring
4637:Related
4628:Jason-3
4618:Jason-1
4501:Pelagic
4496:Oceanic
4471:Benthic
3788:Tsunami
3758:Soliton
3513:Bibcode
3153:Bibcode
3030:155-197
2959:Bibcode
2884:Bibcode
2857:6470677
2837:Bibcode
2790:Bibcode
1968:0.00313
992:Where:
560:Where:
64:periods
4506:Photic
4335:Seabed
3748:Seiche
3380:
3370:
3327:"SWAN"
2855:
2734:P80-01
2706:
2611:]
2471:ERA-40
2451:GEOSAT
1599:0.0345
1118:0.0125
430:Wilson
299:Output
48:energy
4697:Ocean
4666:Alvin
4516:Swash
4360:Plate
4305:Knoll
4295:Guyot
4250:Atoll
4129:Tides
3892:model
3778:Swell
3610:Waves
3437:Water
3378:S2CID
2853:S2CID
2827:arXiv
2752:(PDF)
2613:(PDF)
2607:[
2499:(PDF)
2455:TOPEX
2409:m-1,0
2139:0.331
2103:0.387
2028:7.519
1916:0.493
1805:0.241
1710:0.225
1693:0.502
1487:0.015
1372:0.008
1272:0.004
1188:0.077
1106:0.283
490:0.283
438:fetch
234:Input
171:Japan
120:swell
75:wave
68:wave
4664:DSV
4649:Argo
4511:Surf
3967:Eddy
3486:2023
3418:2023
3389:2023
3368:ISBN
3313:2023
3268:2023
3243:2023
3205:2023
3172:2023
3126:2023
2763:2022
2715:2023
2704:ISSN
2650:2023
2624:2023
2453:and
2208:0.73
2170:and
2156:1.01
2076:tanh
2055:tanh
2037:tanh
2002:and
1985:0.57
1947:and
1933:0.75
1880:0.87
1853:tanh
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1251:0.30
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1179:tanh
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1138:0.42
1109:tanh
545:7.54
347:NOAA
223:dike
162:and
73:and
3521:doi
3455:hdl
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