Given a sample set of wind data (speed and direction parallel to the earth), I would like to identify the consistency of wind samples. Standard deviation comes to mind, but I don't know if it is appropriate for use with vector data.
I am proposing that the mean vector $\vec{V}$ is defined as:
$\vec{V} = \frac{1}{N} \sum_{i=1}^N \vec{v}_i$
And the standard deviation $s$ is defined as:
$s = \sqrt{\frac{1}{N-1} \sum_{i=1}^N (\vec{v}_i - \vec{V})^2}.$
Is this sort of calculation ever used? Is it statistically relevant, or is there a better way of measuring variation in vector data?