(RESOLVED) Correction for noisy rotation angle in geogrid.exe (for high-resolution simulation)

I deeply appreciate all of the WRF developers for their great effort.

Now I am trying to conduct high-resolution simulation (25km/5km/1km/0.2km).
When I checked the output of geogrid.exe for 0.2km domain, I found the rotation angle (COSALPHA and SINALPHA) is quite noisy
(see: cosalpha_dx200m_original.png).
I have checked the source code, and found that the difference of latitude and longitude, which is used for the calculation of rotation angle in process_tile_module.F, is close to the minimum value of single precision float for the high-resolution domain.

I found that it can be fixed if I have conducted double-precision calculation for geogrid.exe, and I also found that rotation angle calculation with 'cone', which is applied in 'wrf_fddaobs_in.F', is useful even for single-precision calculation (see: cosalpha_dx200m_modified.png).
I would like to know if there is a problem in my procedure.

Apologies for the long delay in responding! I think either of your approaches is sound: to either run geogrid in double-precision, or to recompute the rotation angle from a difference in longitude from the standard longitude multiplied by a cone factor.

From what I can recall, our objective in the geogrid program was to compute the rotation angles in a map-projection-independent way, since we envisioned that more map projections (beyond Lambert conformal, Mercator, polar stereographic, and cylindrical equidistant) might be added in the future. However, as you have noted, the finite difference approach that considers only the latitude and longitude fields on the WRF grid can lead to numerical issues when we take the difference between values that are nearly equal.

Thank you for your response! It is very helpful for me to get a clarification from the developer. I hope this information might help other WRF users who will conduct high resolution simulations (e.g. less than 1km).