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Spherical harmon transform available in NCL and pyNGL for lat/lon data.
Interpolate EAM native grid output to a (N+1)x2N lat/lon cap grid
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) on the GLL grid (not the PG2) grid.
For smoother results, need spectra from ~(how many?) snapshots
At NE256, interpolating and computing the spectra for each snapshot takes about 5min and 30GB of memory. At NE1024 this will start to become challenging.
KE Spectra
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. 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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Note that in the actual spectra plot, the differences are quite small, with the lower resolution spectra matching very well at low wave numbers, and only slightly below at high wave numbers.
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Time Averaging
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.