How to correctly average wind speeds/directions and wave heights/directions?

Hi there,

I want to take some of the ERA5 datasets for the last 10 years, and calculate the average values for different weather parameters for each month over 10 years.
Some of these parameters are wind speeds/directions and wind wave heights/mean directions.

For the wind, i started by averaging the u and v components and then calculating the wind speeds and directions from the averaged u and v components.
This seemed to be the correct way to do it, according to: How to average winds? | Copernicus Marine Help Center
However, i just noticed this: How to compute mean wind speed from ERA5 u and v wind components?, which says that wind speeds should first be calculated from the u and v components, and then averaged.

However, for the wave directions, I’m wondering what’s the most correct way of averaging them:

  1. using the arithmetic mean
  2. using a weighted average, where the weights are the wave heights
  3. converting the wave directions and heights into u and v components, averaging the u and v components, and then converting the averaged u and v components back into heights and directions.

My guess would be that (3) is the correct way, but when i take the mean direction of wind waves + significant heights from the “ERA5 hourly data on single levels from 1940 to present” for 1h intervals for a full day, average the values following (1), (2), and (3), and then compare to the corresponding daily means in “ERA5 post-processed daily statistics on single levels from 1940 to present”, (1) is the closest to the values in this latter dataset.
Looking at earthkit (used to do the postprocessing), it seems indeed that the arithmetic mean is used to average the wave directions.
Is this how it should be? Am i missing something?

Thanks in advance!
Marta