This post is primarily intended for the engineering public and the reanalysis community; it highlights a very pragmatic question, reccurent for offshore engineering practitioners: which wind field model dataset should I use for driving my spectral wave model?
[Update 2021-09-09: see also this second post with more technical details on the surface layer parametrisations in both ERA5 and CFS].
Setting the scene
Ocean waves are wind-driven, and can be modelled using spectral wave models. These models require a time-dependent surface wind field as input (typically at 10 m above the surface, every 1 to 3 hours). The simulations vary from large-scale simulations over the entire globe, to high-resolution simulations in Norwegian fjords. See the below illustrations. The choice of the wind model is then in part driven by the complexity of the flow at the location of interest.
It goes without saying that the quality of the wave modelling is not only related to the wind field, but to other drivers of the wave spectra: spatial resolution, bathymetry, wave-wave interactions, currents, all of these play an important role. Yet, the surface wind speed remains the most important parameter for most projects. See below an illustration of measured (20-minute samples, right) and modelled (3-hours averages, left) Wind Sea* significant wave heights at the HKZA floating LiDAR in the Southern North Sea (NL): this locally-generated component of the sea state is very sensitive to wind variations.
*Swell and Wind Sea have been separated using the wave age critera described in Section 5.5.3 of this study by DHI (from which the model data come from).
For engineering purposes (design of marine structures), site-specific, high-resolution modelling is carried out using models such as SWAN, WAVEWATCH III, or MIKE. The choice of the wind model is left to the modeller, and typically:
- for regional/global simulations (1-10 km resolution): reanalysis models are used, for instance: {CFSR; CFSv2}, ERA-Interim or ERA5, COSMO6;
- for local modelling (0.1-1 km resolution): either the reanalysis field is kept unchanged, or a higher-resolution wind field (for instance, a dowscaling of the reanalysis) is used.
Validating the 10 m wind
Knowing the above, the practioner is then interested in checking whether a given model wind field is accurate enough for the purpose of the study. In the below, I have compared ERA5 and CFSv2 to high-quality LiDAR data in the Southern North Sea (an offshore wind playground):
- the Hollandse Kust Zuid A (HKZA) floating LiDAR,
- the IJmuden met mast;
- the Ten noorden van de Waddeneilanden A (TNWA) floating LiDAR.
The locations of the instruments are shown with magenta circles on the map below, see this post for further information on wind LiDARs and publicly available measurements in the North Sea.
From these measurements, the 10 mMSL wind speed has been derived by fitting a power law to each wind speed profile (for each 10 min timestamp, and by selecting only the measurement heights lower than 90 mMSL). From the correlation plots below, large values of wind speeds are always underestimated by ERA5:
CSFv2, on the contrary, seems better predict wind speeds during storms, and provide slighlty conservative (design-wise) wind speeds; see below:
Are ERA5-data biased?
The underestimation of storm wind speeds in the ERA5 dataset, compared with CFSR and CFSv2, appears clearly when comparing these time series at a large number of wind farm/measurement locations offshore Northern Europe, see selected correlation plots and the map below (the map is showing the mean ratio between CFSR- and ERA5 wind speeds over the 20 m/s).
For reference, GFS (the NWP system behind CFSR anc CFSv2) and IFS CY41R2 (the one behind ERA5) use two different air-sea interaction schemes:
- GFS uses for CFSR and CFSv2 a simple relationship between wind speed and surface roughness, following (Charnock, 1955), this was also the case for the older NCEP reanalysis. The actual reference to the GFS documentation is hard to find, but here is a LINK and another LINK;
- IFS CY41R2 uses another parametrisation, see Section 3.2 of the IFS documentation, where the surface drag coefficient is a function of the sea state (a “coupled” model).
Are the results valid for these locations/datasets only? In effect, a number of publications have already pointed this bias, which was also present in ERA-Interim; for instance (list non exhaustive):
- (Stopa and Cheung, 2014) “Intercomparison of wind and wave data from the ECMWF Reanalysis Interim and the NCEP Climate Forecast System Reanalysis” LINK;
- (Guillou et al., 2017) “Strong winds in a coupled wave–atmosphere model during a North Atlantic storm event: evaluation against observations” LINK;
- (Fery et al., 2018) “Reproduction of storms over the North Sea and the Baltic with the regional reanalysis COSMO-REA6” LINK
Earlier this year, the ECMWF has updated the air-sea interaction module of the IFS, highligting that the issue is being investigated:
- (Bidlot et al., 2020) “Enhancing tropical cyclone wind forecasts” LINK
From the comparisons with measurements shown above, and against the GFS datasets, the ERA5 drag formulation seems to be biased from approximately 10 m/s and larger. The paper (Janssen, 1992) which is given as reference in the IFS CY41R2 shows good agreement between observed (at the Noordwijk meetpost, 18m water depth) and modelled friction velocities up to 1 m/s (approx. 21 m/s at 10 m/s, for neutral wind conditions). Therefore, if one is to trust the friction velocity from ERA5, the bias may then lie in the roughness length formulation in the IFS (page 15 of the wavel model documentation):
A reduction in model wind speed is caused by a larger roughness. In turn, this larger roughness is caused by a larger ratio between wave stress and atmospheric stress. As we’ve seen earlier, the friction velocity may not be biased, therefore, and I understand this is the object of (Bidlot et al., 2020) above, the focus has now been set on wave stress and the steepness of the spectra (which controls the dissipation term due to white capping). As friction velocity and roughness need to be solved in an iterative manner, the question remains: how to explain the successful validations of the friction velocity in (Janssen, 1992)? The water depth was only 18m:
- could it be that depth-induced breaking led to larger roughness (which would not have occured further from shore)?
- how to explain the “poor” performance of the simple Charnock relationship at this site? It seems to work well elsewhere (in deep water)
- could one also try to validate whether the roughness lengths values are valid?
The friction velocity and the roughness length go hand-in-hand: in the Janssen model the roughness length is larger than using simple Charnock, but the friction velocity is larger too: see the plot below where I have used the CFSv2 wind speed time series as “independent” variable. Furthermore, one of the ERA5 known issues is that the roughness length from the CDS is too small (it is derived from and incorrect friction velocity, see text on the ECMWF website): the roughness length actually used by the model is much larger (in yellow below).
Choosing a 10 m for ocean wave modelling
The overall conclusion for the practioner is that the ERA5 10 m wind speeds from the Copernicus Data Store may not be (are not, in many situations) the best choice for modelling storm situations. While for normal conditions the surface wind speeds from ERA5 are very similar (if not better) to the ones from CFSR and CFSv2, during storm conditions the ERA5 data are clearly negatively biased.
This implies that spectral wave models driven by these wind speeds are likely to underestimate large wave heights. Therefore, results from such models are not likely to be suitable for most engineering purposes.
A simple correction has been proposed, and will be tested/validated in future posts 🙂 Here is a sneak peak into the first results: these corrected 10m wind speed values are derived from a simple surface layer profile, where the friction velocity+roughness relationship is a simple Charnock , and where the atmospheric stability is characterised by z/L using the (Grachev and Fairall, 1997) bulk Richardson number parametrisation.
Comments/questions/suggestions are welcome. You fill find HERE the correlation plots in high resolution, together with some additional info (like land masks for the three datasets)
Rémi
Note: this post was updated on 2021-06-01 with more detailed plots.
