nominal resolution

[chrisdane]

Hi

On feat/cmip7-awiesm3-veg-hr (3299a99), the dars2 mesh is set to have a nominal resolution of 10 km:

awi-esm3-veg-hr-variables/core_ocean/cmip7_awiesm3-veg-hr_ocean.yaml

inherit:
  grid_file: /work/ab0246/a270092/input/fesom2/dars2/mesh.nc
  grid: "FESOM 2.6 unstructured grid DARS (3146761 surface nodes)"
  nominal_resolution: "10 km"

(also it's written FESOM2.6, but 2.7 is used, right?)

How did you get this value? From the conclusion section of Danilov 2022:

A rather good estimate is provided by the square root of the area of unit cell (twice the triangle area or area of the dual cell) which is only 9% coarser than the real resolution.

and

On the other hand, if the square root of
triangle area is used as a measure of resolution for a discretization placing DOFs on cells, it gives the estimate
3−1/4h ≈ 0.75h which is 25% finer than the real resolution.

So, as far as I understand, dmax = sqrt(2*A_elem) is a good estimate for the horizontal resolution, while dmax = sqrt(A_node) is not because it's too fine:

cd /work/ab1095/a270073/mesh/fesom2/dars2

cdo -setunit,km -expr,'dmax=sqrt(2*cell_area)/1e3' griddes_dars2_elem.nc dmax_elem.nc # result of spheRlab with `fesom2velocities` = true
cdo -setunit,km -expr,'dmax=sqrt(cell_area)/1e3' griddes_dars2_node.nc dmax_node.nc

cdo --pedantic -s -output -fldmean dmax_elem.nc
16.6316 # km

cdo --pedantic -s -output -fldmean dmax_node.nc
16.6274 # km

So the global average horizontal resolution of the dars2 mesh 16.6 ~ 17 km (for both estimates: cell area defined on nodes and on elems).

Taylor et al.'s DR attribute documentation says that:

So I think the nominal resolution of the dars2 mesh is 25 km and not 10 km.

Cheers,
Chris

[chrisdane]

The 25 km and not 10 km nominal resolution of the dars2 mesh is also obtained by using PCMDI's nominal_resolution repo (https://github.com/PCMDI/nominal_resolution.git), which calculates the resolution based on https://en.wikipedia.org/wiki/Great-circle_distance:

griddes = "/work/ab0246/a270092/input/fesom2/dars2/mesh.nc" # dars2 mesh

import sys, netCDF4, numpy
sys.path.insert(0, "~/proj/cmip/cmor/nominal_resolution")
from lib import mean_resolution, nominal_resolution

ds = netCDF4.Dataset(griddes)
cell_area = ds.variables["cell_area"][:]   # m2, (ncells,)
lat_bnds  = ds.variables["lat_bnds"][:]    # deg, (ncells, vertices)
lon_bnds  = ds.variables["lon_bnds"][:]
ds.close()

mean_res = mean_resolution(cell_area, lat_bnds, lon_bnds, convertdeg2rad=True)
nom_res = nominal_resolution(mean_res)

print(mean_res, nom_res)
20.86033708177036 25 km

This globally averaged ~20.9 km resolution is 25% coarser than the ~16.6 km following Danilov 2022 (see initial post). The geometric great circle distance approach hence rather seems to represent an upper estimate compared to Danilov's wavenumber approach. I wonder if these are comparable and which should be used in the 'nominal resolution' context.