Wind is a vector quantity, so it has a **magnitude** `ws`

(`wind_speed`

) and a **direction** (`wind_direction`

). Alternatively, the wind vector can be split into two orthogonal components: the zonal wind `u`

(`eastward_wind`

) and the meridional wind `v`

(`northward_wind`

).

Wind speed is instead calculated from the wind components through `ws = sqrt(u^2 + v^2)`

.

There are two distinct methods to average winds, either by calculating the scalar average or the vector average (example : Grange, S.K., 2014).

The

**scalar average**is the mean of the wind magnitudes (speed),**not**taking into account the wind direction. For example, the scalar average of a southerly and a northerly wind of`5 m s^-1^`

results in a mean wind speed of`5 m s^-1^`

.The

**vector average**takes into account the wind direction and is equal to or smaller than the scalar average. The vector average of a southerly and a northerly wind of`5 m s^-1^`

gives a mean wind speed of`0 m s^-1^`

because there is no resultant`wind_speed`

.

### Scalar Average

The **scalar mean wind speed** over a period of interest can be obtained in two ways:

calculating wind speed from the components

`u`

and`v`

for each time step and then averaging over the period;averaging the

`wind_speed`

from the product over the period.

Both methods should give very similar results, except for the local interpolation biases explained below, which give **preference to using method 1**.

### Vector Average

The **vector mean wind speed** is obtained by first averaging `u`

and `v`

over the period of interest and then calculating the `wind_speed`

from the averaged `u`

and `v`

.

## Which calculation method to choose?

The appropriate method depends on whether wind direction plays a role in the User's application.

The scalar average should be used it the application is focused in the wind speed **magnitude**. In this case, users will need to know how hard the wind blows, for example when considering the kinetic energy associated with winds.

The vector average should be used when the wind **direction** matters as well. For example in the transport of particles by the wind, because winds in opposite directions cancel out in terms of transport.

*Figure 1** - Scalar mean and vector mean wind speed for January 2021 (ascending passes). *

**Interpolation Issue **

In locations with large gradients in the wind components, biases occur, that can be seen from a comparison with the zonal and meridional component plots.

In WIND product processing, the wind components (`u`

and `v`

) are derived from `wind_speed`

and `wind_direction`

at Level 2 (grid aligned with the satellite tracks) and subsequently interpolated to Level 3 (regular latitude, longitude grid).

At locations with large gradients in `u`

and `v`

, the interpolated `wind_speed`

variable may differ from the `wind_speed`

calculated from the interpolated `u`

and `v`

components. The effects are small when looking at the global scale, but may be significant at regional scales.

For consistent wind components and `wind_speed`

for regional study, then the choice be to calculate `wind_speed`

from the components at Level 3.

*Figure 2 - **Zonal and meridional wind speed for 15 January 2021 (ascending passes). The third panel shows the difference between wind speed calculated from the components and provided in the product. *

If you need more information about this topic or an expert advice for your specific application, you can always contact us:

through a chat session available in the bottom right corner of the page

via our contact webpage

via e-mail to our support team (servicedesk.cmemsATmercator-ocean.eu)