# wind velocity derivations

1. meridional wind velocity from wind speed and direction

symbol

description

unit

variable name

$$u$$

zonal wind velocity

$$m/s$$

zonal_wind_velocity {:}

$$s$$

wind speed

$$m/s$$

wind_speed {:}

$$\theta$$

wind direction

$$deg$$

wind_direction {:}

The pattern : for the dimensions can represent {vertical}, {latitude,longitude}, {latitude,longitude,vertical}, {time}, {time,vertical}, {time,latitude,longitude}, {time,latitude,longitude,vertical}, or no dimensions at all.

$u = s \cos((180 - \theta)\frac{\pi}{180})$
2. zonal wind velocity from wind speed and direction

symbol

description

unit

variable name

$$v$$

meridional wind velocity

$$m/s$$

meridional_wind_velocity {:}

$$s$$

wind speed

$$m/s$$

wind_speed {:}

$$\theta$$

wind direction

$$deg$$

wind_direction {:}

The pattern : for the dimensions can represent {vertical}, {latitude,longitude}, {latitude,longitude,vertical}, {time}, {time,vertical}, {time,latitude,longitude}, {time,latitude,longitude,vertical}, or no dimensions at all.

$v = s \sin((180 - \theta)\frac{\pi}{180})$
3. wind direction from zonal and meridional wind velocity

symbol

description

unit

variable name

$$u$$

zonal wind velocity

$$m/s$$

zonal_wind_velocity {:}

$$v$$

meridional wind velocity

$$m/s$$

meridional_wind_velocity {:}

$$\theta$$

wind direction

$$deg$$

wind_direction {:}

The pattern : for the dimensions can represent {vertical}, {latitude,longitude}, {latitude,longitude,vertical}, {time}, {time,vertical}, {time,latitude,longitude}, {time,latitude,longitude,vertical}, or no dimensions at all.

$\theta = 180 - \arctan2(u,v)\frac{180}{\pi}$
4. wind speed from zonal and meridional wind velocity

symbol

description

unit

variable name

$$u$$

zonal wind velocity

$$m/s$$

zonal_wind_velocity {:}

$$v$$

meridional wind velocity

$$m/s$$

meridional_wind_velocity {:}

$$s$$

wind speed

$$m/s$$

wind_speed {:}

The pattern : for the dimensions can represent {vertical}, {latitude,longitude}, {latitude,longitude,vertical}, {time}, {time,vertical}, {time,latitude,longitude}, {time,latitude,longitude,vertical}, or no dimensions at all.

$s = \sqrt{u^2 + v^2}$
5. surface meridional wind velocity from surface wind speed and direction

symbol

description

unit

variable name

$$u$$

zonal wind velocity

$$m/s$$

surface_zonal_wind_velocity {:}

$$s$$

wind speed

$$m/s$$

surface_wind_speed {:}

$$\theta$$

wind direction

$$deg$$

surface_wind_direction {:}

The pattern : for the dimensions can represent {vertical}, {latitude,longitude}, {latitude,longitude,vertical}, {time}, {time,vertical}, {time,latitude,longitude}, {time,latitude,longitude,vertical}, or no dimensions at all.

$u = s \cos((180 - \theta)\frac{\pi}{180})$
6. surface zonal wind velocity from surface wind speed and direction

symbol

description

unit

variable name

$$v$$

meridional wind velocity

$$m/s$$

surface_meridional_wind_velocity {:}

$$s$$

wind speed

$$m/s$$

surface_wind_speed {:}

$$\theta$$

wind direction

$$deg$$

surface_wind_direction {:}

The pattern : for the dimensions can represent {vertical}, {latitude,longitude}, {latitude,longitude,vertical}, {time}, {time,vertical}, {time,latitude,longitude}, {time,latitude,longitude,vertical}, or no dimensions at all.

$v = s \sin((180 - \theta)\frac{\pi}{180})$
7. surface wind direction from surface zonal and meridional wind velocity

symbol

description

unit

variable name

$$u$$

zonal wind velocity

$$m/s$$

surface_zonal_wind_velocity {:}

$$v$$

meridional wind velocity

$$m/s$$

surface_meridional_wind_velocity {:}

$$\theta$$

wind direction

$$deg$$

surface_wind_direction {:}

The pattern : for the dimensions can represent {vertical}, {latitude,longitude}, {latitude,longitude,vertical}, {time}, {time,vertical}, {time,latitude,longitude}, {time,latitude,longitude,vertical}, or no dimensions at all.

$\theta = 180 - \arctan2(u,v)\frac{180}{\pi}$
8. surface wind speed from surface zonal and meridional wind velocity

symbol

description

unit

variable name

$$u$$

zonal wind velocity

$$m/s$$

surface_zonal_wind_velocity {:}

$$v$$

meridional wind velocity

$$m/s$$

surface_meridional_wind_velocity {:}

$$s$$

wind speed

$$m/s$$

surface_wind_speed {:}

The pattern : for the dimensions can represent {vertical}, {latitude,longitude}, {latitude,longitude,vertical}, {time}, {time,vertical}, {time,latitude,longitude}, {time,latitude,longitude,vertical}, or no dimensions at all.

$s = \sqrt{u^2 + v^2}$