Methods for scale decomposition of the global atmospheric circulation

The nonlinear dynamics of atmospheric circulation is complex and covers a range of scales spanning several orders of magnitude. Analyzing the distribution and transfer of kinetic energy (KE) at different scales is central to understanding and predicting atmospheric evolution. Traditionally, such analysis relied on spherical harmonics, which are inherently global and cannot provide local information connecting scales with circulation patterns geographically. To this end, we present the coarse-graining (CG) framework to analyze multi-scale dynamics on the sphere. This is made possible by generalizing the definition of convolution to ensure that for arbitrary kernel shapes, including wavelets, the filtering operator and spatial derivatives on the sphere commute, thereby allowing us to derive the PDEs governing any set of scales. The approach is very general, allows for probing the dynamics simultaneously in scale and in space, and is not restricted by usual assumption of homogeneity. Using a new method for extracting spectra by CG, we demonstrate the application of this framework to global reanalysis data. We compare the KE spectra from CG to those from spherical harmonics and highlight some of its advantages in providing geographical information.