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.

   \[s = \sqrt{u^2 + v^2}\]