# Directional Standard Deviation of ocean waves **URL:** \ **Category:** C3S - Datasets and Usage\ **Tags:** c3s, era5, global\_reanalysis\ **Created:** [13 March 2020 17:10 UTC](https://forum.ecmwf.int/t/directional-standard-deviation-of-ocean-waves/1234 "2020-03-13T17:10:58Z")\ **Posts on this page:** 9\ **Page:** 1
**Author:** ![Michela](https://forum.ecmwf.int/letter_avatar_proxy/v4/letter/m/898d66/32.png) [@Michela](https://forum.ecmwf.int/u/Michela)\ **Post date:** [13 March 2020 17:10 UTC](https://forum.ecmwf.int/t/directional-standard-deviation-of-ocean-waves/1234/1 "2020-03-13T17:10:58Z")
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): [directional\_spread\_in\_ECWAM.pdf](https://forum.ecmwf.int/uploads/short-url/fJBIxDKv7aRDUBWGMDVRA1cnrI0.pdf) (1.0 MB) 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: [https://www.ecmwf.int/en/publications/ifs-documentation](https://www.ecmwf.int/en/publications/ifs-documentation) ---
**Author:** ![JH\_Chow](https://forum.ecmwf.int/letter_avatar_proxy/v4/letter/j/c37758/32.png) [@JH\_Chow](https://forum.ecmwf.int/u/JH_Chow)\ **Post date:** [1 September 2020 09:06 UTC](https://forum.ecmwf.int/t/directional-standard-deviation-of-ocean-waves/1234/2 "2020-09-01T09:06:51Z")
Hi, the link to the document is dead. May I know if I could find it elsewhere? [directional\_width\_parameter\_in\_ECWAM.pdf](https://confluence.ecmwf.int/download/attachments/177472149/directional_width_parameter_in_ECWAM.pdf?version=1&modificationDate=1599209600130&api=v2) ---
**Author:** ![Michela](https://forum.ecmwf.int/letter_avatar_proxy/v4/letter/m/898d66/32.png) [@Michela](https://forum.ecmwf.int/u/Michela)\ **Post date:** [4 September 2020 08:55 UTC](https://forum.ecmwf.int/t/directional-standard-deviation-of-ocean-waves/1234/3 "2020-09-04T08:55:35Z")
Hi, could you please try again? Thanks Michela ---
**Author:** ![Jean\_Bidlot](https://forum.ecmwf.int/letter_avatar_proxy/v4/letter/j/f08c70/32.png) [@Jean\_Bidlot](https://forum.ecmwf.int/u/Jean_Bidlot)\ **Post date:** [2 September 2020 07:44 UTC](https://forum.ecmwf.int/t/directional-standard-deviation-of-ocean-waves/1234/4 "2020-09-02T07:44:53Z")
Dear Colleagues, why is the link not visible to the outside world? Jean ---
**Author:** ![Mohamed\_Ouda](https://forum.ecmwf.int/letter_avatar_proxy/v4/letter/m/f4b2a3/32.png) [@Mohamed\_Ouda](https://forum.ecmwf.int/u/Mohamed_Ouda)\ **Post date:** [29 January 2023 12:46 UTC](https://forum.ecmwf.int/t/directional-standard-deviation-of-ocean-waves/1234/5 "2023-01-29T12:46:29Z")
Dear Colleagues, Is there a way to convert the wave spectral directional width to directional standard deviation?  Best regards, Mohamed ---
**Author:** ![Jean\_Bidlot](https://forum.ecmwf.int/letter_avatar_proxy/v4/letter/j/f08c70/32.png) [@Jean\_Bidlot](https://forum.ecmwf.int/u/Jean_Bidlot)\ **Post date:** [29 January 2023 17:21 UTC](https://forum.ecmwf.int/t/directional-standard-deviation-of-ocean-waves/1234/6 "2023-01-29T17:21:23Z")
Dear Mohamed, In the document  [directional\_spread\_in\_ECWAM.pdf](https://confluence.ecmwf.int/download/attachments/177472149/directional_spread_in_ECWAM.pdf?version=1&modificationDate=1675012387072&api=v2)  (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). ---
**Author:** ![Mohamad\_Barani\_pm](https://forum.ecmwf.int/letter_avatar_proxy/v4/letter/m/74df32/32.png) [@Mohamad\_Barani\_pm](https://forum.ecmwf.int/u/Mohamad_Barani_pm)\ **Post date:** [13 September 2024 19:07 UTC](https://forum.ecmwf.int/t/directional-standard-deviation-of-ocean-waves/1234/7 "2024-09-13T19:07:19Z")
Hi dear Jean, thanks for your help, Unfortunately I can’t access the directional\_width\_parameter\_in\_ECWAM.pdf I don’t know why, but I get a license error… I know it is a big request, but I would be very grateful if you would email me this file. This is my email address: ---
**Author:** ![Mohamad\_Barani\_pm](https://forum.ecmwf.int/letter_avatar_proxy/v4/letter/m/74df32/32.png) [@Mohamad\_Barani\_pm](https://forum.ecmwf.int/u/Mohamad_Barani_pm)\ **Post date:** [13 September 2024 19:18 UTC](https://forum.ecmwf.int/t/directional-standard-deviation-of-ocean-waves/1234/8 "2024-09-13T19:18:15Z")
Hi dear Michela, thank you for your description, Unfortunately I can’t use your guides cause I can’t access this directional\_width\_parameter\_in\_ECWAM.pdf I don’t know why, but there is a license error…! I know it is a big request, but I would be very grateful if you would email me this file… This is my email address: Thank you in advance for your help. ---
**Author:** ![Michela](https://forum.ecmwf.int/letter_avatar_proxy/v4/letter/m/898d66/32.png) [@Michela](https://forum.ecmwf.int/u/Michela)\ **Post date:** [16 September 2024 08:37 UTC](https://forum.ecmwf.int/t/directional-standard-deviation-of-ocean-waves/1234/9 "2024-09-16T08:37:06Z")
Hi, could you please try the link in the first message now? Thanks