Spectra for GCM configuration

[valeriabarra]

Purpose

Spectra on the sphere via spherical harmonics are a feature needed for diagnostic purposes.

Link to any relevant PRs/issues: https://github.com/CliMA/ClimaDiagnostics/issues/1

Some of this diagnostic functionality existed in ClimateMachine but will need to be ported over to ClimaCore and adapted to use its API/objects, and potentially optimized using existing Julia packages.

Cost/benefits/risks

Having spherical harmonics will allow us to calculate and plot the energy spectra to analyze turbulence or numerical dissipation (e.g., from hyperdiffusion).

Producers

Lead: @valeriabarra Potential collaborators: @LenkaNovak , @akshaysridhar , @jiahe23

Components

On the sphere we want both 1D and 2D spectra. For these we need:

• Porting existing code:
  • [x] For 1D: Calculate the 1D (zonal) power spectra using the Fourier transform at each latitude and level from the 2D horizontal velocity field
  • [x] For 2D: Transform variable on lat-lon grid to the 2D spectral (spherical harmonic) space using fft on latitude circles (as for the 1D spectrum) and associated Legendre polynomials for meridians, and calculate spectra.
• Enhancement
  • [ ] Reuse existing Julia libraries to favor library reuse to the extent possible, e.g., AssociatedLegendrePolynomials.jl for the calulation of the associated normalized Legendre polynomials and QuadGK.jl for Gaussian integration

Inputs

References:

• ClimateMachine Spectra module and references therein:
  • Baer, "An Alternate Scale Representation of Atmospheric Energy Spectra", 1972
  • Ehrendorfer, "Spectral Numerical Weather Prediction Models", 2011

Results and deliverables

• [x] A ClimaCore subpackage that will live under lib, e.g., lib/ClimaCoreSpectra, which will include both library code under src and related tests under test, exercised through the usual runtests.jl.
• [x] Unit test(s)
  • [x] visual component for a specific spherical harmonic as the one in ClimateMachine did
  • [x] test against existing Python packages (e.g., https://shtools.github.io/SHTOOLS/complex-spherical-harmonics.html) (this was done in the original implementation)
  • [x] integration test / example that show the workflow: from a Field defined on the ClimaCore cubed-sphere to the regridding and specrta calculation
• [x] Documentation in ClimaCore

Integration in downstream repositories/packages:

• [x] See ClimaAtmos Issue # 994 and follow-up one in ClimaCoupler

Task breakdown

A preliminary list of PRs and a preliminary timeline of PRs, milestones, and key results.

• [x] Development of the lib/ClimaCoreSpectra package [1 week?]
• [x] unit testing
• [x] documentation
• [x] integration test/example that shows the full workflow (starting from a CC cubed-sphere, remapping to rll grid, and transforming to spectral space)

The four tasks above are implemented in https://github.com/CliMA/ClimaCore.jl/pull/979

Additional tasks for follow-up PRs:

• [ ] Improved interface that uses ClimaCore Fields directly with internal calls to remapping infrastructure so to remove the burned from the user

...

Details are subject to change as well as tasks/subtasks as things and plans are refined.

Working branch

valeria/spherical-harmonics

Reviewers

@charleskawczynski and possibly other folks who have worked on/with the prior implementation (e.g., @LenkaNovak , @akshaysridhar )

[LenkaNovak]

Looks good! I would say the porting over would take 1 week, so if we want to investigate other Julia packages, I would allow more time (an additional week or so). Also, in the long term this should live wherever we compute diagnostics on the regridded data (ClimaDiagnostics.jl?) but, for the time being, I agree that ClimaCore/lib seems most appropriate.

[LenkaNovak]

@jiahe23 and @akshaysridhar , you guys experimented with CM's Spectra code recently. Would you have any pointers/branches/tips/preferences?

[jiahe23]

I have a very outdated branch in CA that I adopted the CM spectra calculation. It worked fine. I have generated KE spectra plots that looked reasonable by that time.

[valeriabarra]

Thanks for the pointers!

[valeriabarra]

Now that #979 is finally merged, I would propose opening a new SDI/issue for the enhanced interface and remaining enhancements (i.e., potential use of external packages). I prefer keep things organized and this was already a pretty long SDI/PR

What do you think, @charleskawczynski ?

[valeriabarra]

I will mark this as complete and will open issues in the downstream repos (ClimaAtmos and ClimaCoupler) for the integration in them. I would also leave the 2 enhancement bullet points to a separate issue/SDI for the future revamping of the interface

[charleskawczynski]

.... What do you think, @charleskawczynski ?

That sounds good. If using features in this package require many lines of code (e.g., more than 20) in an existing script, then I suggest we break off a subtask of trying to make a good wrapper around the remapping pipeline.