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Wave Model Description

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The second-generation (2G) spectral wave model

The Met Office runs a second-generation (2G) spectral wave model, with both global and nested regional configurations. Spectral models work by calculating the levels of wave energy that can be assigned to a two-dimensional frequency-direction domain (termed the wave spectrum) used to describe motion of the sea-surface under waves (the sea-state). Essentially the spectrum decomposes a given sea-state into a set of constituent sine waves, each with a different direction, period (inverse of frequency) and amplitude (energy).

Field experiments have established families of wave spectra appropriate to different forcing circumstances, and upon which spectral wave models have been based. In the instance of the Met Office 2G model, the spectra used are those derived from the JONSWAP experiment that recorded wave growth over a fetch in the North Sea (Hasselmann, 1973).

From the two-dimensional frequency-direction spectrum standard integrated parameters representing wave conditions are generated (.e.g. significant wave height, wave peak and zero-upcrossing period, principal wave direction). With knowledge of wind strength and direction, these integrated parameters can also be assigned to wave field components defined as wind-sea or swell (see Wind-Sea/Swell Partitioning).

Summary of the 2G wave model scheme

The wave models are forced using hourly wind fields generated in Met Office Numerical Weather Prediction (NWP) models, which include observational data from satellite, ship and data buoy networks in their assimilation schemes. Based on the local wind speed and direction, energy is input to waves through a parameterization of the exponential growth of existing wind-sea energy (linear growth in the early development stage). Wind-sea spectral peakedness and peak frequency are used to select an appropriate member of the JONSWAP family of spectra to describe the growing wind-sea energy distribution in frequency space. Directional distribution of wind-sea energy is defined using a cosine squared distribution about the mean wind-sea direction. Frequency dependency for the rate of turn of wave energy in response to turning winds is also parameterized.

As the waves grow, a balance is reached between parameterizations for the input, nonlinear transfer between frequencies and dissipation of wave energy. This ensures that for a given wind speed, with sufficient fetch and duration, the limiting JONSWAP form (known as the Pierson-Moskowitz spectrum) is reached but not exceeded.

Wave energy is advected through the model domain using a 2nd order Lax-Wendroff scheme. In the Global wave model, longer period swell energy direction of propagation is modified to ensure that the energy follows a Great Circle. In shallow water (<200m depth) wave group speed depth dependency, bottom friction and depth refraction are represented in the model physics. The UK Waters Wave Model additionally includes the effects of time-varying currents on the UK continental shelf, taking hourly currents from the 12km Storm Surge model.

Model grid and forcing data

The model runs on prescribed regular latitude-longitude spatial grids. Parameter values are derived at collocated positions corresponding to grid cell centre (i.e. the grid is not staggered). Cell types comprise 'sea points', where the full set of calculations for wind-sea growth/dissipation and wave energy advection are applied; 'land points' where no calculations are performed; and 'coast points', where advective/dissipative schemes only are applied and which act as a buffer zone for the land.

Depth information is held on the model grid using a representative average for each cell. This assumption may prove important in some near coastal grid cells where the average depth (for example taken over a 12km grid cell in the UK Waters model, 60km cell in the global model) may mask bathymetric features affecting the local distribution of wave energy. A cut-off depth is set in the model scheme at 200m, since at depths greater than this value shallow water effects are negligible even for wave energy in the lowest frequency range.

The importance of increased spatial resolution is clearest in the near coastal zone, since this allows a better representation of the coastline itself and will increasingly resolve shallow water bathymetric features. The trade off for making these resolution changes lies in run-time, with shorter calculation timesteps required for increased spatial resolution in order not to violate conditions for energy advection (see Wave Energy Advection).

Models are calibrated to be forced by representative 19.5m mean wind speed and direction, such that for correct wind speed, duration and fetch the wave model will attain the limiting Pierson-Moskowitz wave height. In the operational models this forcing is provided by NWP atmospheric models operated on rotated grids. As a result the winds must first be converted to the regular latitude-longitude grid prior to ingestion by the wave model. In assessing an appropriate wave model spatial grid size, the resolution at which the forcing winds are provided is an important constraint.

Operational configurations

The Met Office suite of operational global and regional nested wave models produces regularly updated wave forecasts with lead times of up to five days. Operationally the models are configured with a spectral resolution of 13 frequency bins and 16 directional bins, representing waves with a range of periods between 25 seconds and 3 seconds (deep-water wavelengths from 975 m to 15 m).

Wave conditions worldwide are forecast using the Global Wave Model on a 5/9 degree latitude by 5/6 degree longitude grid (approximately. 60km square grid at mid-latitudes), with fields output at 3-hourly resolution to a lead time of 5 days (T+120). This model is forced using the Met Office's Global domain NWP 10m wind field and run twice daily based on 0000 and 1200 UTC analysis times. The extent of ice cover at high latitudes is updated daily using NWP global analysis data.

Boundary conditions from the Global Wave Model are used as input to a European Wave Model, based on a 1/4 degree latitude by 2/5 degree longitude grid (approximately 35km) covering the area from 30°.75N to 67°.00N and 14°.46W to 41°.14E and with a forecast range out to 36 hours (T+36). Similarly to the Global Wave Model, this model is forced using the Met Office Global domain NWP 10m wind field and run twice daily based on 0000 and 1200 UTC analysis times.

A further increase in resolution is made for the UK Waters Wave Model, which is nested using boundary conditions from the Global Wave Model. The UK Waters Wave Model uses a 1/9 degree latitude by 1/6 degree longitude grid (approximately 12km) covering the north-west European continental shelf from 12°W between 48°N and 63°N. Two configurations of the UK Waters Wave Model are run. The first configuration is forced by high resolution (~12km grid) Mesoscale NWP 10m winds and includes effects of time-varying currents on the UK continental shelf as generated by the Met Office's operational 12km Storm Surge Model. This model is run four times daily using analysis times 0000, 0600, 1200 and 1800 UTC and provides hourly forecasts out to T+36. The second configuration (Extended UK Waters Wave Model) does not include current effects, and is run twice daily (0000 and 1200 UTC analyses) forced by Global NWP 10m winds to provide 3-hourly forecast data out to T+120.

Third generation (3G) versus second-generation (2G) models

The 2G model scheme mainly differs from its 3G counterparts (e.g. WAM, WAVEWATCH III) in its use of parameterization schemes for wave growth, nonlinear transfer of energy and dissipation, whereas the more recently devised 3G models calculate some of these explicitly (details in Holt and Hall 1992). Nevertheless, the 2G scheme is still considered robust for operational wave modeling applications and compares favourably with 3G counterparts operated by other meteorological bureau in an ongoing international data exchange (Bidlot et al., 2000, 2002).

Output

Data are output from the model and variously retained in commercially available fast-access hindcast archives and research based forecast model archives. Due to data handling constraints two-dimensional (frequency-direction) spectral data are output at specific model points only and are not archived. The hindcast archives are based upon one-dimensional (frequency) spectral data output for all model grid points. These data are used to construct integrated wave parameters including significant wave height, period and direction based on the total spectrum, wind-sea and swell components. The decomposition between swell and wind-sea is made using analyses based upon archived model values of wind speed and direction. Hindcast and forecast integrated parameters (e.g. significant wave height) are generated at model run-time for each model grid point and are retained in the research forecast model archive.

References

Bidlot, J.R., Holmes-Bell, D.J., Wittmann, P.A., Lalbeharry, R., Chen, H.S., 2000. Intercomparison of the performance of operational ocean wave forecasting systems with buoy data. European Centre for Medium-Range Weather Forecasts (ECMWF) Technical Memorandum Number 315 also 2002, Weather and Forecasting, 17, 287-310.

Golding, B., 1983. A wave prediction system for real-time sea-state forecasting. Quarterly Journal Royal Meteorological Society, 109, 393-416. Golding, B.A., 1983.

Hasselmann, K., Barnett, T.P., Bouws, E., Carlson, H., Cartwright, D.E., Enke, K., Ewing, J.A., Gienapp, H., Hasselmann, D.E., Kruseman, P., Meerburg, A., Muller, P., Olbers, D.J., Richter, K., Sell, W., Walden, H., 1973. Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Deutsches Hydrographisches Institut, Hamburg, UDC 551.466.31; ANE German Bight.

Holt, M.W., and Hall, B.J., 1992. A comparison of 2nd generation and 3rd generation wave model physics. Unpublished Met Office Short-Range Forecasting Research Division Technical Report Number 10.

(Last Updated: 30-01-2008)