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**2. The WAM Model: Solves energy balance equation, including Snonlin**

WAM Group (early 1980’s) 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 (0.5 0.5 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 (0.25 0.25) Historically: 0.5 covering the Mediterranean only. Both implementations use a discretisation of 30 frequencies 24 directions (used to be 25 freq.12 dir.) The Wave Model (ECWAM)

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**2.1. Energy Balance for Wind Sea**

Summarise knowledge in terms of empirical growth curves. Idealised situation of duration-limited waves ‘Relevant’ parameters: , u10(u*) , g , , surface tension, a , w , fo , t Physics of waves: reduction to Duration-limited growth not feasible: In practice fully- developed and fetch-limited situations are more relevant. , u10(u*) , g , t The Wave Model (ECWAM)

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**Connection between theory and experiments: wave-number spectrum:**

Old days H1/3 H1/3 Hs (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: The Wave Model (ECWAM)

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Let us now return to analysis of wave evolution: Fully-developed: Fetch-limited: However, scaling with friction velocity u is to be preferred over u10 since u10 introduces an additional length scale, z = 10 m , which is not relevant. In practice, we use u10 (as u is not available). The Wave Model (ECWAM)

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**JONSWAP fetch relations (1973):**

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

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**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]. The Wave Model (ECWAM)

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**Fetch-limited growth Remarks:**

WAM model scales with u Drag coefficient, Using wind profile CD depends on wind: Hence, scaling with u gives different results compared to scaling with u10. In terms of u10 , WAM model gives a family of growth curves! [u was not observed during JONSWAP.] The Wave Model (ECWAM)

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**Dimensionless energy:**

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

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Phillips constant is a measure of the steepness of high-frequency waves. Young waves have large steepness. 1000 p The Wave Model (ECWAM)

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**Duration-limited growth **

Infinite ocean, no advection single grid point. Wind speed, u10 = 18 m/s u = 0.85 m/s Two experiments: uncoupled: no slowing-down of air flow Charnock parameter is constant ( = ) 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) The Wave Model (ECWAM)

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**Time dependence of wave height for a reference run and a coupled run.**

The Wave Model (ECWAM)

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**Time dependence of Phillips parameter, p , for **

a reference run and a coupled run. The Wave Model (ECWAM)

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**Time dependence of wave-induced stress for **

a reference run and a coupled run. The Wave Model (ECWAM)

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**Time dependence of drag coefficient, CD , for **

a reference run and a coupled run. The Wave Model (ECWAM)

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**Evolution in time of the one-dimensional frequency **

spectral density (m2/Hz) Evolution in time of the one-dimensional frequency spectrum for the coupled run. The Wave Model (ECWAM)

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**The energy balance for young wind sea.**

The Wave Model (ECWAM)

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**The energy balance for old wind sea.**

-2 -1 The energy balance for old wind sea. The Wave Model (ECWAM)

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**SWADE case WAM model is a reliable tool.**

2.2. Wave Forecasting Sensitivity to wind-field errors. For fully developed wind sea: Hs = 0.22 u102 / g 10% error in u10 20% error in Hs from observed Hs Atmospheric state needs reliable wave model. SWADE case WAM model is a reliable tool. The Wave Model (ECWAM)

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**Verification of model wind speeds with observations**

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

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**Verification of WAM wave heights with observations**

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

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**Validation of wind & wave analysis using satellite & buoy. **

Altimeters onboard ERS-1/2, ENVISAT and Jason Quality is monitored daily. Monthly collocation plots SD 0.5 0.3 m for waves (recent SI 12-15%) SD 2.0 1.2 m/s for wind (recent SI 16-18%) Wave Buoys (and other in-situ instruments) SD 0.85 0.45 m for waves (recent SI 16-20%) SD 2.6 1.2 m/s for wind (recent SI 16-21%) The Wave Model (ECWAM)

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**Buoy observations are not representative for aerial average.**

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

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**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 Note the start of Autumn. New: 1. Anomaly correlation 2. Verification of forecast against buoy data. The Wave Model (ECWAM)

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