station density weighting

[nicholasloveday]

Weather stations are typically not evenly spaced out. It may be important to weight the stations based on network density so that areas with high station density don't overwhelm the final score.

We should build a function that generates these station weights.

We can follow the ECMWF approach in section 9 of https://rmets.onlinelibrary.wiley.com/doi/pdfdirect/10.1002/qj.656

[nicholasloveday]

I've managed to create station density weightings that varies based on a 2D array (e.g., station_number and time dims). It needs to vary due to NaN handling (e.g., there may not be data at some stations at certain timesteps, so those stations should be excluded from the weighting of other stations). The current prototype approach loops through the time dimension and isn't vectorised.

We can to one of the following:

• implement 1D/2D version
• extend it to N dimensions (this may be slow if we start looping within loops)
• someone else has a go at trying to vectorise it