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Spherical harmonic transform available in NCL and pyNGL for lat/lon data.
Interpolate EAM native grid output to a (N+1)x2N lat/lon cap grid
For cubed sphere grid with resolution NE, take N>=NE*6 (degrees of freedom, pole to pole)
Interpolate using TR’s “highorder” algorithm.
Need instantaneous output of (U,V) or (vor,div) and PS on the GLL grid (not the PG2) grid. PS is needed if interpolating to pressure levels
in EAM, U and V may be on the PG2 grid in EAMv2. To get GLL output, use U_DYN and V_DYN. VOR and DIV output is always on the GLL grid.
fincl3 = ‘VOR:I','DIV:I','PS:I' or: ‘U_DYN:I’,'V_DYN:I','PS:I'
For smoother results, need spectra from ~60 snapshots. 2x per day for 1 month will produce nice results. What about hourly over 3 days?
At NE256, interpolating and computing the spectra for each snapshot takes about 5min and 30GB of memory. At NE1024 this will probably require ~500GB of memory and could take 320min per snapshot.
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KE spectra is useful for understanding and tuning the dissipation mechanisms in the model. For a global model, it can be computed via a vector spherical harmonic transform of the instantaneous velocity field, or two spherical harmonic transforms of the instantaneous vorticity and divergence scalars on a spherical surface. For all the data below, we interpolate to 250mb (I think because this is the most energetic part of the atmosphere - check this?). Spherical harmonics can be thought of as polynomials in Cartesian coordinates (x,y,z) restricted to the sphere. For each degree k there will be 2k+1 polynomials of total degree k, or 2k+1 spherical harmonics of degree n. To compute the KE spectra, E(k), we sum the coefficient squared over all degree n spherical harmonics.
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The spectra above from single snaphots have a lot of noise which can be removed by averaging. We next analyze how much averaging is necessary from an aqua planet NE256 simulation with 1 month of daily snapshots. The legend indicates how many snapshots (spaced 1 day apart) were used when averaging E(k). With 28 snapshots the data is still a touch noisy at the lower frequencies, so we recommend at least 60 snapshots. Need to test the minimum spacing: 60 snapshots from hourly data is probably not as good as 60 snapshots from daily data. In the plot below, each curves are all shifted downward so they would not be plotted on top of each other.
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Software needed
To generate a TR “highorder” mapping file for GLL data if not already available.
ncremap -G ttl="lat-lon-cap-grid"#latlon=1537,3072#lat_typ=fv#lon_typ=grn_ctr -g latlon_scrip.nc
GenerateCSMesh --res 256 --out_format Netcdf4 --file atmgrid.g
GenerateOverlapMesh --b atmgrid.g --a latlon_scrip.nc --out overlap_mesh.g
GenerateOfflineMap --in_mesh atmgrid.g --out_mesh latlon_scrip.nc --ov_mesh overlap_mesh.g --in_type cgll --in_np 4 --out_type fv --out_double --out_format Netcdf4 --correct_areas --out_map map_ne256np4_to_1537x3072_highorder.nc
Remap a native grid EAM output file:
ncremap -m map_ne256np4_to_1537x3072_highorder.nc -i casename.cam.h2.0001-02-02-00000.nc -o casename.cam.h2.0001-02-02-00000.latlon.nc
Compute spectra.
todo: add link to “ke.ncl” script