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Slide 1The Wave Model (ECWAM) 2. The WAM Model: Solves energy balance equation, including S nonlin WAM Group (early 1980s) State of the art models could not handle rapidly varying conditions. Super-computers. Satellite observations: Radar Altimeter, Scatterometer, Synthetic Aperture Radar (SAR). Two implementations at ECMWF: Global ( reduced latitude-longitude). Coupled with the atmospheric model (2-way). Historically: 3, 1.5 then 0.5 (Future: 0.36 ) Limited Area covering North Atlantic + European Seas ( ) Historically: 0.5 covering the Mediterranean only. Both implementations use a discretisation of 30 frequencies 24 directions (used to be 25 freq. 12 dir.)

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Slide 2The Wave Model (ECWAM) 2.1. Energy Balance for Wind Sea Summarise knowledge in terms of empirical growth curves. Idealised situation of duration-limited wavesRelevant parameters:, u 10 (u * ), g,, surface tension, a, w, f o, t Physics of waves: reduction to Duration-limited growth not feasible: In practice fully- developed and fetch-limited situations are more relevant., u 10 (u * ), g, t

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Slide 3The Wave Model (ECWAM) Connection between theory and experiments: wave-number spectrum: Old days H 1/3 H 1/3 H s (exact for narrow-band spectrum) 2-D wave number spectrum is hard to observe frequency spectrum One-dimensional frequency spectrum Use same symbol, F, for:

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Slide 4The Wave Model (ECWAM) Let us now return to analysis of wave evolution: Fully-developed: Fetch-limited: However, scaling with friction velocity u is to be preferred over u 10 since u 10 introduces an additional length scale, z = 10 m, which is not relevant. In practice, we use u 10 (as u is not available).

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Slide 5The Wave Model (ECWAM) JONSWAP fetch relations (1973): Empirical growth relations against measurements Evolution of spectra with fetch (JONSWAP) Hz km

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Slide 6The Wave Model (ECWAM) Distinction between wind sea and swell wind sea: A term used for waves that are under the effect of their generating wind. Occurs in storm tracks of NH and SH. Nonlinear. swell: A term used for wave energy that propagates out of storm area. Dominant in the Tropics. Nearly linear. Results with WAM model: fetch-limited. duration-limited [wind-wave interaction].

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Slide 7The Wave Model (ECWAM) Fetch-limited growth Remarks: 1.WAM model scales with u Drag coefficient, Using wind profile C D depends on wind: Hence, scaling with u gives different results compared to scaling with u 10. In terms of u 10, WAM model gives a family of growth curves! [u was not observed during JONSWAP.]

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Slide 8The Wave Model (ECWAM) Dimensionless energy: Note: JONSWAP mean wind ~ m/s Dimensionless peak frequency:

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Slide 9The Wave Model (ECWAM) 2.Phillips constant is a measure of the steepness of high-frequency waves. Young waves have large steepness p

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Slide 10The Wave Model (ECWAM) Duration-limited growth Infinite ocean, no advection single grid point. Wind speed, u 10 = 18 m/s u = 0.85 m/s Two experiments: 1.uncoupled: no slowing-down of air flow Charnock parameter is constant ( = ) 2.coupled: slowing-down of air flow is taken into account by a parameterisation of Charnock parameter that depends on w : = { w / } (Komen et al., 1994)

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Slide 11The Wave Model (ECWAM) Time dependence of wave height for a reference run and a coupled run.

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Slide 12The Wave Model (ECWAM) Time dependence of Phillips parameter, p, for a reference run and a coupled run.

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Slide 13The Wave Model (ECWAM) Time dependence of wave-induced stress for a reference run and a coupled run.

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Slide 14The Wave Model (ECWAM) Time dependence of drag coefficient, C D, for a reference run and a coupled run.

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Slide 15The Wave Model (ECWAM) Evolution in time of the one-dimensional frequency spectrum for the coupled run. spectral density (m 2 /Hz)

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Slide 16The Wave Model (ECWAM) The energy balance for young wind sea.

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Slide 17The Wave Model (ECWAM) The energy balance for old wind sea. 0 -2

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Slide 18The Wave Model (ECWAM) 2.2. Wave Forecasting Sensitivity to wind-field errors. For fully developed wind sea: H s = 0.22 u 10 2 / g 10% error in u 10 20% error in H s from observed H s Atmospheric state needs reliable wave model. SWADE case WAM model is a reliable tool.

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Slide 19The Wave Model (ECWAM) Verification of model wind speeds with observations observations OW/AES winds …… ECMWF winds (OW/AES: Ocean Weather/Atmospheric Environment Service)

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Slide 20The Wave Model (ECWAM) Verification of WAM wave heights with observations observations OW/AES winds …… ECMWF winds (OW/AES: Ocean Weather/Atmospheric Environment Service)

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Slide 21The Wave Model (ECWAM) Validation of wind & wave analysis using satellite & buoy. Altimeters onboard ERS-1/2, ENVISAT and Jason Quality is monitored daily. Monthly collocation plots SD m for waves (recent SI 12-15%) SD m/s for wind (recent SI 16-18%) Wave Buoys (and other in-situ instruments) Monthly collocation plots SD m for waves (recent SI 16-20%) SD m/s for wind (recent SI 16-21%)

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Slide 22The Wave Model (ECWAM) Problems with buoys: 1.Atmospheric model assimilates winds from buoys (height ~ 4m) but regards them as 10 m winds [~10% error] 2.Buoy observations are not representative for aerial average. Problems with satellite Altimeters:

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Slide 23The Wave Model (ECWAM) Quality of wave forecast Compare forecast with verifying analysis. Forecast error, standard deviation of error ( ), persistence. Period: three months (January-March 1995). Tropics is better predictable because of swell: Daily errors for July-September 1994 Note the start of Autumn. New: 1. Anomaly correlation 2. Verification of forecast against buoy data.

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