Advancing Parsimonious Deep Learning Weather Prediction Using the HEALPix Mesh

We present a parsimonious deep learning weather prediction model to forecast seven atmospheric variables with 3-hr time resolution for up to 1-year lead times on a 110-km global mesh using the Hierarchical Equal Area isoLatitude Pixelization (HEALPix). In comparison to state-of-the-art (SOTA) machine learning (ML) weather forecast models, such as Pangu-Weather and GraphCast, our DLWP-HPX model uses coarser resolution and far fewer prognostic variables. Yet, at 1-week lead times, its skill is only about 1 day behind both SOTA ML forecast models and the SOTA numerical weather prediction model from the European Center for Medium-Range Weather Forecasts. We report several improvements in model design, including switching from the cubed sphere to the HEALPix mesh, inverting the channel depth of the U-Net, and introducing gated recurrent units (GRU) on each level of the U-Net hierarchy. The consistent east-west orientation of all cells on the HEALPix mesh facilitates the development of location-invariant convolution kernels that successfully propagate weather patterns across the globe without requiring separate kernels for the polar and equatorial faces of the cube sphere. Without any loss of spectral power after the first 2 days, the model can be unrolled autoregressively for hundreds of steps into the future to generate realistic states of the atmosphere that respect seasonal trends, as showcased in 1-year simulations.