The HEALPix grid is a promising new approach to the problem of discretizing the surface of the globe. Its use in climate model analysis is still in its infancy, and so in this work, we investigate its performance for spectral analysis of climate data. We measure the error introduced by remapping from an icosahedral grid (ICON) to the HEALPix grid and compare it to the error introduced by remapping to a Gaussian-Grid. Specifically, we investigate the error for the spectral analysis of input data by generating a set of spherical harmonics up to a degree of 100 (wave-length of ΋ 400km) on the ICON grid, remapping them to HEALPix/Gaussian grids, and then comparing the results of spectral analysis on the remapped grids to the expected results. We find that the error for the HEALPix grid is roughly an order of magnitude larger then for a gaussian grid with a similar cell count (on average 5.1 10^-6 Mean-Absolute-Error for a HEALPix grid with nside=1024, and 6.8 10^-7 for the N1024 Gaussian-Grid ). While the error might be higher, the HEALPix method might still be preferable for analysis when using lower-resolution grids (down to nside=128), due to much lower resource requirements of resolutions, if an Mean-Absolute-Error of 10^(-5)is acceptable for the spectrum.

@misc{HFCMASBOST23,
	author	 = {Jakob Ludwig Sachs},
	title	 = {{HEALPix For Climate Model Analysis: Scaling Behavior of Spectral-Analysis Tasks}},
	advisors	 = {Jannek Squar and Anna Fuchs and Florian Ziemen},
	year	 = {2023},
	month	 = {09},
	school	 = {Universität Hamburg},
	howpublished	 = {{Online \url{https://wr.informatik.uni-hamburg.de/_media/research:theses:jakob_ludwig_sachs_healpix_for_climate_model_analysis_scaling_behavior_of_spectral_analysis_tasks.pdf}}},
	type	 = {Bachelor's Thesis},
	abstract	 = {The HEALPix grid is a promising new approach to the problem of discretizing the
			surface of the globe. Its use in climate model analysis is still in its infancy, and so in
			this work, we investigate its performance for spectral analysis of climate data. We measure
			the error introduced by remapping from an icosahedral grid (ICON) to the HEALPix grid and
			compare it to the error introduced by remapping to a Gaussian-Grid. Specifically, we
			investigate the error for the spectral analysis of input data by generating a set of spherical
			harmonics up to a degree of 100 (wave-length of ΋ 400km) on the ICON grid, remapping them to
			HEALPix/Gaussian grids, and then comparing the results of spectral analysis on the remapped
			grids to the expected results. We find that the error for the HEALPix grid is roughly an order
			of magnitude larger then for a gaussian grid with a similar cell count (on average 5.1 10^-6
			Mean-Absolute-Error for a HEALPix grid with nside=1024, and 6.8 10^-7 for the N1024
			Gaussian-Grid ). While the error might be higher, the HEALPix method might still be preferable
			for analysis when using lower-resolution grids (down to nside=128), due to much lower resource
			requirements of resolutions, if an Mean-Absolute-Error of 10^(-5)is acceptable for the
			spectrum.},
}