Are you working on characterising offshore wind- and wave conditions? Have you already been b*tching at CFSR and CFSv2 for only having a 10mMSL wind speed, and no corresponding near-hub height wind speed?
In this post, I will show you a simple recipe for deriving a wind speed time series at elevations from 10 m and up to 200 mMSL, only using the 10m CFS wind speed and ERA5 surface parameters. For validating the method, I will use the HKZA Floating LiDAR System dataset; the instrument was deployed off the coast of the Netherland for about two years; see the map below (here is the link to the data). All measurement data have been hourly averaged. The Figures are available in high-resolution here.
Step 1: deriving the Obukhov length
As explained in an earlier post, the wind speed profile is best described in the boundary layer with the Monin-Obukhov similarity theory, combined with some stress-dependent roughness length, and additional lenght-scale parametrisations above the surface layer.
Extrapolating the wind speed from 10 to 100 mMSL therefore requires to quantify the atmospheric stability, which we can do by calculating the Obulhov length using ERA5 data and the bulk Richardson method from Grachev and Fairall (see the earlier post).
Step 2: deriving the friction velocity and the roughness length
Once we know the Obukhov length, we can compute the friction velocity by solving the following implicit equation:
$$u_{*} = \frac{ U(z)\kappa} { \ln \left( \frac{z}{z_{0}(u_{*})} \right) }$$
Where
$$z_{0}(u_{*})=\alpha\frac{u_{*}^{2}}{g}$$
is the Charnock relationship (I have used 
Step 3: deriving the wind speed near hub height
Now, the wind speed at any elevation can easily be derived using:
- The Monin-Obukhov similarity theory (referred to as “MOST” in the below);
- The model from (Gryning, 2007), which extends the MOST above the surface later (referred as “GRYNING2007” in the below);
- An alternative method, which consists in scaling the 10m wind speed time series using a single, mean power law exponent derived from measurements. This is the method used in DHI’s Hollandse Kust Nord study (see its Section 3.3.1.4), therefore it is called “DHI” in the below).
The results are provided below for 160 mMSL. The model data are compared with measurement data, and, in particular in stable conditions, the model from Sven-Erik Gryning works better than the two other models.
That was all folks, here is a near-hub height wind speed you can use ^^.
What about the wind-wave correlation (btw) ?
After all, we also want to get the wind-wave correlation right. I have used the wave buoy data to extract a Wind-Sea component from the directional spectra (reconstructed from the Fourier coefficients and the Maximum Entropy Method from (Lygre and Krogstad, 1986), in the same way as the Wind-Sea is extracted from the DHI model data (see Section 5.3.3 of their report). Note: I only took the data for the long offshore fetch wind directions ([190; 60[°N).
Again, we see that in stable conditions the model from Sven-Erik Gryning works better. How interesting.
Remaining issues
The one thing we have not modelled, is the change of wind direction with elevation (wind veer). In stable- and very stable conditions, the wind veer is large (up to ~30° across a modern wind turbine rotor). This needs to be taken into account in your analyses. See an example from the FINO1 LiDAR below:
Work in progress then..
Comments and questions are welcome.
Rémi.
