Directional Standard Deviation of ocean waves

To compute the directional standard deviation of the ocean waves using ERA5 data, please have a look at the following document (from Jean Bidlot, ECMWF):


Moreover, to complement the mean direction parameters, ERA5 data also provides the wave spectral directional width parameters for the total sea, wind waves and total swell

For more details, see section 10.3.5, of part VII of the ifs documentation:

Hi, the link to the document is dead. May I know if I could find it elsewhere?



could you please try again?



Dear Colleagues,

why is the link not visible to the outside world?


Dear Colleagues,

Is there a way to convert the wave spectral directional width to directional standard deviation? 

Best regards,


Dear Mohamed,

In the document 


 (1) is the square of the directional standard deviation, as defined as the one sided directional width (make sure to scroll down in the document to find the copy of Holthuijsen's book).

I then show that the parameter we provide for the wave spectral directional width is the square root of (6), which is nothing else than

the weighted average in frequency space of (1)

Note that besides the 2d spectrum, all other wave parameters are integral parameters,

namely, they no longer depend on frequency and/or direction, hence why we decided to provide the directional width parameter for the total sea as weighted average.

If you need the directional standard deviation for each frequency as given in (1), then you will need to get the 2d wave spectra and compute (1) for each frequency.

Note that, as explained in the IFS documentation, part VII, chapter 10, we decided that for the windsea and total swell, we would instead use the peak frequency to compute (1).