ERA5: How to calculate wind speed and wind direction from u and v components of the wind?

Last modified on Mar 26, 2024 09:20

The meteorological wind direction is the direction from which the wind is blowing.

Wind direction increases clockwise such that a northerly wind is 0°, an easterly wind is 90°, a southerly wind is 180°, and a westerly wind is 270°.
Because trigonometry uses a polar coordinate system in which 0° is along the x axis, the meteorological angle definition can wreak havoc on typical angle calculations.
Fortunately, it is still easy to compute the wind components, u and v, given the meteorological wind angle. Let Φ be the meteorological wind direction angle, then the following equations can be applied:

\[ \begin{align*} u &= - \mid\overrightarrow{\rm V}\mid \sin \phi \\ v &= - \mid\overrightarrow{\rm V}\mid \cos \phi \\ \mid\overrightarrow{\rm V}\mid &= \sqrt{u^2 + v^2} \end{align*} \]

Note that Φ must be in radians. If Φ is in degrees, multiply the angle by π/180 before using the trig functions.

It is also possible to compute Φ from u and v using the atan2 function.

On a spreadsheet, use the following equation to get an answer in degrees in the range 0 ≤ Φ < 360:

\[ \phi =\mod\left(180 + \frac{180}{\pi}atan2(u,v),360\right) \]

The atan2 arguments vary by type of software and in some applications the arguments (u,v) are switched around. For more details please have a look at the section 'Realizations of the function in common computer languages' in the following link: https://en.wikipedia.org/wiki/Atan2.

_{This document has been produced in the context of the Copernicus Climate Change Service (C3S).}

_{The activities leading to these results have been contracted by the European Centre for Medium-Range Weather Forecasts, operator of C3S on behalf of the European Union (Delegation Agreement signed on 11/11/2014 and Contribution Agreement signed on 22/07/2021). All information in this document is provided "as is" and no guarantee or warranty is given that the information is fit for any particular purpose.}

_{The users thereof use the information at their sole risk and liability. For the avoidance of all doubt , the European Commission and the European Centre for Medium - Range Weather Forecasts have no liability in respect of this document, which is merely representing the author's view.}

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