Interpolating values of a vector with Gaussian Process / Kriging in Python

Question

I'm attempting to interpolate wind speed and direction values on a map given some lat/long coordinates and then compare those values to my observed values. A couple papers suggest that Gaussian Process / Kriging are effective methods for this, but I don't understand the maths well enough to implement their models directly.

My dataframe looks something like:

lons_   lats_   U2M_    V2M_
.
.
.

I can follow the examples on SciPy, but am unsure if I can use their methods since I am attempting to interpolate vectors - wind speed and direction have both u & v components:

 ws_   = np.sqrt((U2M_ ** 2) + (V2M_ ** 2))
 dir_  = np.arctan2(V2M_,U2M_)

Where U2M_.... are just pd.Series(...) of the respective row-wise u,v components. Could I perform the calculation on each component separately, and then reconstruct the speed and direction values from the interpolated u,v values? I guess my questions is, is this a mathematically sound process?

Answer 1

Wind speed can be interpolated directly from observations, but wind direction is more complicated. The standard approach is to convert into vectors - you're half-way towards this having computed the u and v components. You can average and interpolate these two values, before converting back into your ws and dir variables using the formulae you've given. The background to this is explained far better than I can in this really helpful resource:

Grange, Stuart. (2014). Technical note: Averaging wind speeds and directions. 10.13140/RG.2.1.3349.2006. https://www.researchgate.net/publication/262766424_Technical_note_Averaging_wind_speeds_and_directions