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The ECMWF Ocean Wave Model (ECWAM) describes the development and evolution of wind generated surface waves and their height, direction and period. Its domain extends across the full globe.
ECWAM is coupled to:
ECWAM is solely concerned with ocean wave forecasting and does not model the ocean itself: dynamical modelling of the ocean is done by NEMO.
ECWAM evaluates the 2-dimensional surface wave spectrum, in both oceanic and coastal (but not inshore) waters. This describes how much wave energy is present for given sea wave frequencies and associated propagation directions. The part of the spectrum under the direct influence of the local wind is called “wind-wave" or "wind-sea”; the remaining part is usually referred to as “swell”.
Changes in the wave spectrum are derived from the processes of:
ECWAM has two-way interaction with the Atmospheric models:
ECWAM has two-way interaction with NEMO and its sub-program LIM2:
Note: ECMWF uses LIM2 which is an earlier version of the Louvain-la-Neuve sea ice model currently available (Version 3.6)
ECWAM is run as:
Output is in the form of wave and swell height, direction and period. Wave energy flux, mean direction and magnitude (important for assessment of the impact of the waves on coastlines and offshore structures) is also available.
Fig2.2.1:ECMWF forecast entry page.
Fig2.2.2: Procedure to load wave parameter charts on ecCharts. Click on "Show Layers List" icon (1); Select "Add Layers" option (2); Input Wave into the "Layer select" box (3); Select desired chart by clicking on the icon (4).
Fig2.2.3: Wave parameter charts available on ecCharts (see Fig 2.2.1 and Fig2.2.2 above) and may be displayed by clicking on the desired icon.
Wavegrams are also available to show a time series of significant wave height, mean wave direction, and mean wave period for any sea location.
Fig2.2.4: Wavegrams for any oceanic location are available on ecCharts. Choose location using the Probe icon (1); Click on "Views" (2); Select "Meteograms" option on the dropdown menu (3); Select "More" on the option page that appears(4); input Wave into the "Meteogram select" box (5); select desired chart(s) by clicking on the icon (6).
Fig2.2.5: Menu to select wave parameter charts from Open Charts (See Fig2.2.1 above). Select "Range" (here medium and extended ranges); Select "Ocean Waves".
Fig2.2.6A: Wave parameter charts available on Open Charts and may be displayed by clicking on the desired icon (the above ENS products are available at post-processing steps, 12-hourly from T+0h to T+168h).
Fig2.2.6B: Seasonal forecast charts for Tropical Storm, Hurricane, Typhoons frequencies are available on Open Charts by selecting Long option in the menu (See Fig2.2.5) and then may be displayed by clicking on the desired icon.
Users should note that by convention the direction of waves (and hence also wave energy flux) is described as the direction the waves are moving towards. This is opposite from the convention for wind direction which is defined as where the winds are coming from. Thus a southwesterly wind blows from the southwest; the corresponding wind-sea moves towards the northeast and is a thus described as a northeasterly wind-sea.
The wave height is the distance between trough and crest. However, many waves co-exist at the surface of the ocean and their distribution is given by the 2D wave spectrum. From this distribution, the significant wave height is defined as 4 times the square root of the integral over frequency and direction of the wave spectrum. It can be shown to correspond to the average wave height of the one-third highest waves, commonly known as H1/3. The mean wave direction is the spectrally averaged propagation direction of the waves (weighted by amplitude).
Fig2.2.7: An example of wave heights at a platform in the North Sea. Wave height is the distance between trough and crest. The significant wave height (Hs) is defined as 4 times the square root of the integral over frequency and direction of the wave spectrum. It can be shown to correspond to the average wave height of the one-third highest waves, commonly known as H1/3. Occasionally wave of different periods reinforce and interact non-linearly giving a wave considerably larger than Hs giving a maximum trough to crest height Hmax.
The irregular surface of the sea can be decomposed into a number of components with different frequencies (f) and also directions (θ). The distribution of wave energy among these components is the Wave Spectrum E(f,θ). These can be plotted in two dimensions (Fig2.2.8A). For simplicity and ease of use the complete frequency-energy description of the sea state in 2-dimension form is simplified to 1-dimentional form by integrating over all directions and/or over a frequency range (Fig2.2.8B).
Fig2.2.8A: The irregular surface of the sea can be decomposed into a number of components with different frequencies (f) and also directions (θ). The distribution of wave energy among these components is the Wave Spectrum E(f) here plotted in two dimensions.
Fig2.2.8B: For simplicity and ease of use the complete frequency-energy description of the sea state in 2-dimension form can be simplified to 1-dimensional form by integrating over all directions and/or over a frequency range.
Other parameters are defined to characterise the sea state as prescribed by the wave spectrum. In particular, the reciprocal of the frequency corresponding to the peak of the spectrum is the wave peak period. Different mean periods are calculated by spectrally averaging the spectrum and similarly for mean wave direction (see IFS documentation part VII, chapter10).
Very often, the sea state is composed of different wave systems. If there is any sufficient wind, there will always be a wave system associated with it, referred to to "wind-wave" or "wind-sea". The part of the spectrum that is not associated with the local wind is normally called "swell".
Swell propagates at different speeds for different frequencies and if approaching from a remote source each frequency will arrive at a given location at different times but with a well defined peak in frequency and direction. Wind-sea is more variable in frequency and direction with a broad distribution of the waves around a peak. These can be plotted in 2-dimensional form or simplified to 1-dimensional form (Fig2.2.9).
Fig2.2.9: A schematic example of the Wave Spectrum at a location off the Dutch coast associated with a long wave swell propagating from the northern North Sea and wind-sea propagating across the southern North Sea. At a given time there will be a swell of relatively uniform frequency and direction, and a wind-sea of rather broader frequency and direction. A 2D plot of wave energy against frequency and direction is in the top right diagram. For simplicity this is reduced to a 1D plot of wave energy against frequency. These peak values of swell and wind-sea can be plotted in chart form.
Based on theory of wave-wave interaction, the estimate of highest equivalent weight (Hmax) is calculated from the wave spectrum.
Fig2.2.10: Wave Energy associated with a given frequency E(f) plotted against wave frequency (f). The Equivalent Wave Height (EWH) associated with a given wave frequency is derived from the area under the curve for that frequency bin. The significant wave height Hs is derived from the total area beneath the curve.
Fig2.2.11: Sequence of ocean wave forecasts. Significant wave height forecast (colours) and 10m wind (arrows) from data time 00UTC 4 January 2014, step 12 hours. Wave heights at 1.25m intervals as scale.
Swell propagates outwards well away from the source. Increased swell (e.g. reaching a coast) can give forewarning of a storm system well before any indication in the atmosphere. Fishermen have long used the arrival of long-period swell as an indication of an approaching storm even if the sky is clear. Surfers often benefit from significantly large swell in calm conditions well away from the swell source region.
Fig2.2.12: 180h forecast for significant wave height (contours) for all waves with periods between 21 and 25 seconds (shading), initialised at 00UTC 2 December 2016. The highest significant wave heights (contours) are still confined to the storm location in the Atlantic south of Iceland, while long waves from that storm are already affecting coastlines from Iberia to South Greenland (coloured).
Waves with different periods propagate with different speeds - longer periods travel fastest. These can be tracked through the forecast period and areas where different wave trains potentially interact can be identified.
Fig2.2.13: Chart showing forecast significant wave heights for several ranges of wave periods (Blue,10-12s; Green, 12-14s; Yellow,14-17s; Red,17-21s). Forecast data based on data time 00UTC 25 October 2017. The faster southward propagation of the long period waves over the shorter period waves from their source off NW Africa is clear.
The Extreme Forecast Index (EFI) can be used to indicate the significance of forecast significant wave heights when compared with the range of wave heights that might usually be expected as defined by the M-climate.
Fig2.2.14: In this example the colours west of Ireland denote a low-point in wave heights, or potentially a form of 'weather window' for certain types of marine/shipping operations. Equally this EFI can signify periods with anomalously big waves (yellow to red shading).
Use of the mean wave height and direction is the simplest method of describing the forecast wave regime in a given area and it is easy to be beguiled into just using this output for forecasts to customers. However, the mean wave direction and height is made up of contributions from wind-sea and swell with different wave periods and they interact in a complex manner. It is important to investigate the forecast wind-sea and swell separately to give an understanding of likely sea conditions in an area (e.g. for a ship requiring a particularly smooth passage) or at a location (e.g. an oil rig).
When wind-sea and swell move in similar directions the wave heights can give information on the likely sea state as one is superimposed on the other, particularly where both have a significant and comparable wave height. On occasion the swell and wind-sea may be moving in opposite directions (an opposing sea) and wave heights give information on the likely rougher sea state to be expected. Often the wind-sea and swell are at right-angles (a cross sea). Where the wind-sea and swell heights are similar the sea can be very disturbed and difficult for shipping. An illustration is given in Figs2.2.15A to E.
Fig2.2.15A: ecChart of mean wave direction (wave height is indicated by the length of the arrow). On ecCharts, wave height may be shown by use of the probe tool or more graphically by superimposing mean wave heights. This chart gives an overview of wave conditions. Northwesterly waves (i.e. moving towards the northwest) are indicated near point A. Easterly waves (i.e. moving towards the east) are indicated near point C. However, it is important to investigate the contributions to the mean wave directions and heights from inspection of the wind-sea and swell at this time.
Fig2.2.15B (left): The forecast wind-sea has developed in response to the forecast winds around a depression in mid-Atlantic. Waves move northwestwards near point A and southeastwards near point B. The length of the arrows near points A & B suggest wave heights are around 3m (wave heights are also available as charts, not shown here). Near point C wind-sea waves are relatively small and move towards the east-northeast.
Fig2.2.15C(right): The forecast total swell has been developed in response to earlier weather systems elsewhere and has propagated across the Atlantic. Swell is moving northwards near point A and southwestwards near point C with arrow length suggesting wave heights of around 2m (wave heights are also available as charts, not shown here). Near point B swell waves are relatively small and move towards the southeast.
Fig2.2.15D(left): The forecast wind-sea (blue) and swell (black) shown on a single chart. To the north of point B the wind-sea and swell waves have a similar direction of travel; to the east of point B wind-sea dominates with only weak swell contribution but almost at a right-angle. Near points A and C the wind-sea and swell waves differ widely in direction but with similar heights (a cross sea).
Fig2.2.15E(right): The forecast mean wave directions derived from the wind-sea and mean swell (as shown in Fig2.2.15A) superimposed on the previous chart (Fig2.2.15D left). This illustrates the important additional information that is gained from consideration of the wind-sea and mean swell forecasts together. The mean wave directions (FIG2.2.15A) give no indication of that a sea passage to the west of Portugal is likely to be through confused rough seas.
The interaction of waves with sea-surface currents is not yet included in the operational version of the model. In particular areas, (e.g. Gulf Stream or Agulhas current), the current effect may give rise to localised changes of up to a metre in the wave height.
Note that whilst ECMWF does provide some ocean current output, from its ocean model (as "sea water velocity fields"), the current 1/4 degree resolution of that model is insufficient to allow strong gradients in western boundary currents to be captured. This means that stronger currents that are observed around the world tend to be underestimated in this output, sometimes substantially so.
Shoaling is the deformation of waves as they move from the ocean into shallow waters causing the waves to become steeper, increase in height, and have shorter wavelength . The basic equations in ECWAM do represent the effect when the waves propagate from deep to shallow water, but the effect is not dramatic over most coastal waters. Waves inshore and at the beach, where shoaling is very strong, are not represented since the resolution of ECWAM (~ 10km) cannot represent the actual beach slope. Wave products near coasts, and, to a lesser extent, within small and enclosed basins (e.g. Baltic Sea) may be of lower quality than for the open ocean. This may be due to incomplete resolution the detail of the coast by the land-sea mask. Small islands too may not be identified and hence allow waves to propagate unhindered. Note, however, that the wave model has a scheme that attempts to represent the impact of unresolved islands on the global propagation of waves.
Fig2.2.16: An example chart of wind-wave and swell. Some shoaling is possible towards the French and British coasts as the sea becomes less deep but forecast values cannot be absolutely relied upon. See Fig2.2.17 for detail around the Azores. No parameters are shown on coasts nor where ice cover >30% (i.e. where some of the grid points used in interpolation of wave data for display are on land or ice. Users should identify whether the ice areas or coastal zones are the cause. See section regarding wave parameters near sea ice)
Fig2.2.17: The same example chart of wind-wave and swell as in Fig2.2.16, magnified near the Azores. There are some areas around the islands where wave parameters are not forecast (i.e. where some of the grid points used in interpolation of wave data are on land) but the detail of coast may not be fully resolved. ECWAM shows re-build of wind waves to the lee of the islands as the wind fetch increases and also the penetration of larger waves through the inter-island straits.
Sea ice is not static but forms or extends with low air temperature or sea-surface temperatures, and can move with winds and sea current. NEMO passes information to ECWAM regarding the extent and movement of the sea ice field forecast by LIM2, allowing a more realistic definition of what is open sea throughout the forecast period. In the current operational version of the wave model, the interaction between waves and sea-ice is not actually represented. Where sea ice cover >30% all wave parameters are set to missing (i.e. no valid values). Wave products near ice-edges may be of lower quality than for the open ocean. This may be due to uncertainty in sea-ice cover, or in the detail of an ice edge and consequently also in the boundary of the water area. Spurious areas of ice or incorrect extent of ice will act as if a coastline or island and stop waves from propagating correctly, possibly decaying the waves completely and incorrectly sheltering an otherwise exposed location.
Fig2.2.18: Illustration of the importance of distinguishing between ice cover and shallow water when an area of wave parameters is missing.
Fig2.2.19: Significant height of combined wind waves and swell (Hs). The coloured areas show the difference between the heights derived from the 2d spectra (used where >30% sea ice cover is forecast) and from the wave model (as if open sea). Some large differences are evident, illustrating the need to treat the values of wave height with caution where sea ice is present.
In the IFS, there is an active two-way coupling between the atmosphere and ocean waves - surface wind stress generates the waves and in turn the waves modulate the wind stress. The ECWAM generally forecasts realistic wave parameters (wave height, period etc).
With sufficiently strong winds, the drag on the low-level air flow is modelled using the Charnock parameter which is used to specify an aerodynamical roughness length scale. In the IFS, this roughness length scale tends to increase with 10m wind speed. However, observational evidence suggests that for exceptionally strong winds the coupling between the ocean surface and the wind becomes less efficient at transferring momentum. So, for exceptionally strong (mean) 10m winds (33m/s) the roughness length scale should be capped. This limitation avoids the effect of too much drag on the lower atmosphere and enables more realistic (stronger) winds to be forecast in the vicinity of relatively intense tropical cyclones. It should also be noted that tropical cyclone development with strengthened winds has only a limited effect upon the size and character of waves developed by the Wave model. The model change to limit the roughness length scale at very high wind speeds was introduced in cycle 47r1 in June 2020. It is important not to confuse to the aerodynamic roughness length scale with the actual roughness of the sea. The aerodynamic roughness length scale is a parameter concerning the amount of momentum that is exchanged between the atmosphere and the ocean surface via the surface stress. The actual roughness of the sea is concerned with wave heights, wave steepness and how much wave breaking is happening.
When considering forecast wave parameters in the vicinity of typhoons, hurricanes etc., it should be remembered that IFS still has difficulties in producing some intense tropical cyclones and their subsequent motion.
(Note: In older material there may be references to issues that have subsequently been addressed)
Updated/Amended 09/02/21 - updated to reflect current operation (47R1) and added clearer indication of available parameters in chart form.