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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 with TempestRemap’s “highorder” (native SE shape function) algorithm.
For cubed sphere grid with resolution NE, take N>=NE*6 (degrees of freedom, pole to pole)
Need instantaneous output of (U,V) or (vor,div) vorticity, divergence 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 DYN_U and DYN_V. VOR and DIV output is always on the GLL grid. fincl3 = , use: ‘VOR:I','DIV:I','DYN_PS:I' or: ‘DYN_U:I’,'DYN_V:I','DYN_PS:I'
Need ‘DYN_PS’ instead of ‘PS’ to get PS on the GLL grid instead of the PG2 grid.
For smoother results, need spectra from ~60 snapshots. 2x per day for 1 month will produce nice results in Aqua planet. What about hourly over 3 days? Are there seasonal effects in Real planet?
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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SPHEREPACK requires gridded data on either a Gaussian grid or an equal angle lat/lon “cap” grid which includes points at the poles. It relies on a combination of associated Legendre transforms and FFTs. For efficiency the grid should have dimensions N x 2N (Gaussian), or (N+1) x 2N (equal angle cap) with N the product of powers of small primes. The most common lat/lon data is an equal angle offset grid, which avoids pole points (see. CAM-FV Grid Overview ). Data on this offset grid would have to first be interpolated to a cap grid before computing spherical harmonic transforms.
Choice of variables.
SPHEREPACK contains both vector and scalar transforms. KE spectra can be computed from either (U,V) using the vector transform, or (VOR,DIV) using the scalar transforms. We recommend using VOR & DIV above for two reasons:
Interpolating (U,V) from a cubed-sphere grid to a lat/lon grid needs to be done carefully at the poles. The common approach of treating U and V components as scalars and interpolating them individually will be very inaccurate at the poles. This is due to the fact that even for a smooth velocity vector, the individual components U and V will be discontinuous at the poles. Although it’s not clear how much this error would impact the KE spectra. For correct interpolation of (U,V) near the poles, one needs to represent the velocity vector in a more well behaved coordinate system, interpolating these coefficients, and then transform back to a spherical coordinate representation. (The E3SM coupler uses Cartesian coordinates when mapping vectors between components).
Using (VOR,DIV) also allows one to separate the spectra into the rotational and compressible parts. This can be done using (U,V) but requires twice as many spherical harmonic transforms.
Choice of interpolation algorithm and resolution
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