Convergence of Zeitlin truncation for multilayer critical latitude predictions of quasi-geostrophic flow on an Earth-like planet

Long-term predictions of large-scale flow features on an Earth-like planet are crucial for developing global atmospheric model systems. Such predictions require computational models, i.e., governing PDE systems combined with appropriate numerical methods, to preserve essential structures of the underlying physical model over extended simulation periods. We present a Lie–Poisson formulation of the multi-layer quasi-geostrophhic (QG) equations on the full globe, mimicking the dynamics in the troposphere extended over the first 10 km of the atmosphere. The chosen computational modeling ensures consistency with the underlying structure and enables long-term simulations without the need for additional regularization, forcing, or numerical dissipation. Recent advancements in Lie–Poisson discretization that preserve energy, enstrophy, and higher-order moments of potential vorticity are extended to stratified QG multilayer systems on the sphere. We adopt Zeitlin discretization, which yields a finite-dimensional dynamical system conserving all numerically resolved Casimirs with machine-precision. Particular attention is given to the convergence of critical latitude ($ \phi_{cl} $) predictions upon increasing the spatial resolution per layer ($ N $) and the number of layers in the model ($ M $). A systematic parameter study quantifies (ⅰ) that the dependency of $ \phi_{cl} $ on the resolution per layer $ N $ scales quadratically, showing near grid-independency for $ N \geq 96 $, and (ⅱ) the critical latitude decreases with the number of layers $ M $ for modest radial resolutions of $ M \leq 32 $.