PEAR: Equal Area Weather Forecasting on the Sphere

Artificial intelligence is rapidly reshaping the natural sciences, with weather forecasting emerging as a flagship AI4Science application where machine learning models can now rival and even surpass traditional numerical simulations. Following the success of the landmark models Pangu Weather and Graphcast, outperforming traditional numerical methods for global medium-range forecasting, many novel data-driven methods have emerged. A common design choice in many of these models is an equiangular discretization of the sphere, which has a much finer grid at the poles than around the equator. In contrast, in the Hierarchical Equal Area iso-Latitude Pixelization (HEALPix) of the sphere, each pixel covers the same surface area, avoiding unequal-area sampling and the need for latitude weights. Motivated by a growing support for this grid in meteorology and climate sciences, we propose to perform weather forecasting with deep learning models which natively operate on the HEALPix grid. To this end, we introduce Pangu Equal ARea (PEAR), a transformer-based weather forecasting model which operates directly on HEALPix-features and outperforms the corresponding model on an equiangular grid, and other baselines, without any computational overhead. Furthermore, we perform numerical experiments on azimuthal equivariance and verify the performance of PEAR on climate-model emulation.