Enhance MET to calculate power spectra on global domains using spherical harmonics

[gsketefian]

Describe the Enhancement

Once PR #3411 is merged, MET will have the ability to calculate power spectra on regional grids using the discrete cosine transform (DCT).

However, the DCT is appropriate only for regional grids because it assumes a symmetric extension of the domain in both directions (an assumption that is not valid for a global domain). Thus, it should not be applied to global domains. For global domains (which are periodic in the zonal direction but not in the meridional), the proper transform to use is the spherical harmonics. This uses the Fourier transform in the zonal direction and the Legendre transform in the meridional. Thus, add to MET the capability to calculate the spherical harmonic transform of a global field.

Also consider the following options:

• For grids that wrap the earth but do not include the poles, a hybrid approach would be appropriate. Use spherical harmonics in the horizontal paired with DCT in the vertical.
• Consider whether adding support for DFT (Discrete Fourier Transform) would be worthwhile. If added, we'd need to revisit how the wavelenghts are reported. A source paper groups together adjacent DCT bins to make the DCT output comparable to DFT.
• Consider where the decomposition method choice should be made configurable. Recommend that the code "choose" the recommended option based on the grid geometry, but should users be able to override that default?

Time Estimate

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Issues should represent approximately 1 to 3 days of work.

Sub-Issues

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Define Related Issue(s)

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• METplus, MET, METdataio, METviewer, METexpress, METcalcpy, METplotpy
• Need a new METplus issue to enhance the Grid-Diag wrapper to support changes to the GridDiagConfig file for Add power spectra calculation capability to the Grid-Diag tool in MET #3304 and this issue.

Enhancement Checklist

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• Complete the issue definition above, including the Time Estimate and Funding Source.
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[gsketefian]

@JohnHalleyGotway FYI just created this. Feel free to modify.