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Ocean Wave Forecasting

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Ocean Wave Forecasting Ocean Wave Forecasting Jean-Raymond Bidlot* Marine Prediction Section Predictability Division of the Research Department European Centre for Medium-range Weather Forecasts (E.C.M.W.F.) Reading, UK * With contributions from my colleagues in the JCOMM/ Expert Team in Waves and Coastal Hazards Slide 1 Ocean waves: We are dealing with wind generated waves at the surface of the oceans, from gentle to rough … Ocean wave Forecasting Slide 2 Ocean Waves Forcing: earthquake wind moon/sun Restoring: gravity surface tension Coriolis force 10.0 1.0 0.03 3x10-3 2x10-5 1x10-5 Frequency (Hz) Ocean wave Forecasting Slide 3 What we are dealing with? Water surface elevation, Wave Period, T Wave Length, Wave Height, H Ocean wave Forecasting Slide 4 A Wave Record Individual Waves, Significant Wave Height, Hs, Maximum Individual Wave Height, Hmax Individual waves … etc. Hmax Hs= H1/3 Surface elevation time series from platform Draupner in the North Sea Ocean wave Forecasting Slide 5 Wave Spectrum The irregular water surface can be decomposed into (infinite) number of simple sinusoidal components with different frequencies (f) and propagation directions ( ) and amplitudes. The distribution of wave energy among those components is called: “wave spectrum”, F(f,). Ocean wave Forecasting Slide 6 Modern ocean wave prediction systems are based on statistical description of oceans waves (i.e. ensemble average of individual waves). The sea state is described by the two-dimensional variance spectrum F(f,) of the surface elevation. Ocean Ocean Wave Modelling Ocean wave Forecasting Slide 7 Ocean Wave Modelling Once the spectrum is known, information about the sea state can be derived. For example, the mean variance of the sea surface elevation due to waves is given by: 2 F( f ,)dfd The statistical measure for wave height, called the significant wave height (Hs): 2 4 H s The term significant wave height is historical as this value appeared to be well correlated with visual estimates of wave height from experienced observers. It can be shown to correspond to the rd average 1/3 highest waves (H1/3). Ocean wave Forecasting Slide 8 Ocean Wave Modelling The 2-D spectrum follows from the energy balance equation (in its simplest form: deep water case): F V F S S S t g in nl diss Where the group velocity Vg is derived from the dispersion relationship which relates angular frequency and wave number: 2 g k Sin: wind input source term (generation). Snl: non-linear 4-wave interaction (redistribution). S : dissipation term due to whitecapping (dissipation). diss Ocean wave Forecasting Slide 9 Wind input in pictures Linear growth But once waves are present, they distort the air flow above: Figures from “Waves in Oceanic and Coastal Waters” by exponential growth Leo Holthuijsen. Cambridge University Press Ocean wave Forecasting Slide 10 Non-linear inter-action in pictures 3-waves interaction (triad) 4-waves interaction (quadruplet) not possible in deep water possible in deep water Figures from “Waves in Oceanic and Coastal Waters” by Leo Holthuijsen. Cambridge University Press Ocean wave Forecasting Slide 11 whitecapping dissipation Ocean wave Forecasting Slide 12 Wave Model Configurations ECMWF Global models Tuesday20°E 14 March40°E 200660°E 00UTC80°E ECMWF100°E 120°E Forecast140°E t+36160°E VT: Wednesday180° 160°W 15 March140°W 2006120°W 12UTC100°W Surface:80°W significant60°W 40°W wave20°W height Global from 81°S to 90°N, 10.29 70°N 70°N 9.75 60°N 60°N including all inland seas. 9 50°N 50°N 40°N 40°N 8.25 30°N 30°N 7.5 20°N 20°N 6.75 Coupled to the atmospheric model 10°N 10°N 6 0° 0° 5.25 (IFS) with feedback of the sea 10°S 10°S 4.5 20°S 20°S 3.75 30°S 30°S 3 surface roughness change due to 40°S 40°S 2.25 50°S 50°S 1.5 60°S 60°S waves. 0.75 70°S 70°S 0 20°E 40°E 60°E 80°E 100°E 120°E 140°E 160°E 180° 160°W 140°W 120°W 100°W 80°W 60°W 40°W 20°W The interface between WAM and Forecast wave height on 15/03/2006 12UTC. the IFS has been generalised to neutral wind include air density and gustiness effects on wave growth and wind gustiness neutral winds. air density Data assimilation Jason-2 altimeter wave heights. model Wave model Wave Atmospheric roughness Ocean wave Forecasting Slide 13 ECMWF Wave Model Configurations Deterministic model Probabilistic forecasts (EPS) 28 km grid spacing. 55 km grid spacing. 36 frequencies. 30 25 frequencies *. 36 directions. 24 12 directions *. Coupled to the TL1279 model. Coupled to TL639 TL319 model *. (50+1) (10+5) day forecasts from 0 and 12Z (monthly once a week). Analysis every 6 hrs and 10 day forecasts from 0 and 12Z. * Change in resolutions after 10 days NB: also in seasonal forecast at lower resolutions Ocean wave Forecasting Slide 14 Wave Model Products Wave model The complete description of the sea state is given by the 2-D spectrum, however, it is a fairly large amount of data (e.g. 1296 values at each grid point in the global model (36x36). It is therefore reduced to integrated quantities: 1-D spectrum obtained by integrating the 2-D spectrum 2-D over all directions and/or over spectrum a frequency range. 1-D spectrum Ocean wave Forecasting Slide 15 Wave Model Products When simple numbers are required, the following parameters are available: ) peak f The significant wave height ( E (Hs). The peak period (period of the peak of the 1-D 2 spectrum). area under spectrum = < > Mean period(s) obtained H 4 2 from weighted integration s of the 2-D spectrum. Integrated mean direction. f fp < f > Few others. (peak frequency) (mean frequency) T = 1 / f Complete list at: http://www.ecmwf.int/services/archive/d/parameters/order=/table=140/ Ocean wave Forecasting Slide 16 Wave Model Products Plot of 2-D spectrum can become very busy ! windsea swell total sea Ocean wave Forecasting Slide 17 Wave Model Products Except if you only look at one location … Ocean wave Forecasting Slide 18 Wave Model Products Use simple parameters: total wave height and mean propagation direction 10m winds and mean sea level pressure: Wave height and mean direction: Analysis : 14 February 2009, 00 UTC Analysis : 14 February 2009, 00 UTC Ocean wave Forecasting Slide 19 Wave Model Products Wave height and mean direction: Analysis : 14 February 2009, 00 UTC PEAK PERIOD: Analysis : 14 February 2009, 00 UTC Ocean wave Forecasting Slide 20 Wave Model Products Situation might be more complicated ! 10m winds and mean sea level pressure: Wave height and mean direction: Analysis : 15 February 2009, 00 UTC Analysis : 15 February 2009, 00 UTC Ocean wave Forecasting Slide 21 Wave Model Products Situation might be more complicated: Wave height and mean direction: Analysis : 15 February 2009, 00 UTC Ocean wave Forecasting Slide 22 Wave Model Products A scheme is used to split the global wave fields into waves which are under the direct influence of the forcing wind, the so-called windsea or wind waves, and those waves that are no longer bound to the forcing wind, generally referred to as swell. Period and mean direction are also determined for these split fields. Wave height and windsea mean direction: Wave height and swell mean direction: Analysis : 15 February 2009, 00 UTC Analysis : 15 February 2009, 00 UTC Ocean wave Forecasting Slide 23 Wave Model Products Windsea and swell: opposing sea Ocean wave Forecasting Slide 24 Wave Model Products Windsea and swell: cross sea swell Ocean wave Forecasting Slide 25 Wave Model Products yet it has been introduced at JMA to indicate cross sea areas ! Predicted wave spectrum field (upper) and an image wave map in which crossing area is marked. (Source: JMA) Ocean wave Forecasting Slide 26 Wave model deterministic products on the web* Wave products available by default on the centre‟s web pages: (Home -> Products -> Forecasts -> Ocean Wave Forecasts : http://www.ecmwf.int/products/forecasts/wavecharts/index.html#forecasts Significant wave height and mean direction Ocean wave Forecasting Slide 27 Wave model deterministic products on the web Also windsea and swell plots: Windsea wave height and direction Swell wave height and direction Windsea Mean period and direction Swell Mean period and direction Ocean wave Forecasting Slide 28 spectral partitioning Operational: total windsea Swell 2 windsea Swell Swell 1 New decomposition: Ocean wave Forecasting Slide 29 Can we derive more information from the wave spectra? Significant wave height and low frequency wave energy propagation, as derived by integrating the 2d spectra over directions and frequency bands (shown here in terms of equivalent wave height) Hs 25-29s 21-29s 11 May, 2007, 12 UTC 17-21s 14-17s 12-14s Ocean wave Forecasting Slide 30 Large swell reaching la Réunion: Can we derive more information from the wave spectra? Significant wave height and low frequency wave energy propagation, as derived by integrating the 2d spectra over directions and frequency bands (shown here in terms of equivalent wave height) Hs 25-29s 21-29s 11 May, 2007, 18 UTC 17-21s 14-17s 12-14s Ocean wave Forecasting Slide 31 Large swell reaching la Réunion: Can we derive more information from the wave spectra? Significant wave height and low frequency wave energy propagation, as derived by integrating the 2d spectra over directions and frequency bands (shown here in terms of equivalent wave height) Hs 25-29s 21-29s 12 May, 2007, 0 UTC 17-21s 14-17s 12-14s Ocean wave Forecasting Slide 32 Large swell reaching la Réunion: Can we derive more information from the wave spectra? Significant wave height and low frequency wave energy propagation, as derived by integrating the 2d spectra over directions and frequency bands (shown here in terms of equivalent wave height) Hs 25-29s 21-29s 12 May, 2007, 6 UTC 17-21s 14-17s 12-14s Ocean wave Forecasting Slide 33 spectral partitioning Transformation of topographically partitioned North Pacific significant wave height data (left) into systems (right) by NCEP‟s swell tracking routine.
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