PEAR: Equal Area Weather Forecasting on the Sphere

TL;DR

The paper argues that equiangular spherical grids introduce sampling biases in ML weather forecasting and proposes PEAR, a transformer that operates directly on the native HEALPix grid. PEAR employs patch embedding, windowed attention, and hierarchical down/up-sampling to forecast global surface and upper variables up to 10 days ahead, outperforming an equiangular-grid baseline with a substantially larger model and no extra overhead. The results demonstrate improved ACC and RMSE on ERA5-lite data, highlighting the practical benefits of a fully HEALPix-native approach for unbiased, globally consistent forecasts. This work sets the stage for leveraging high-resolution HEALPix data in next-generation, data-driven weather and climate prediction systems, aligned with initiatives like ECMWF DestinE.

Abstract

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 limitation shared by many of these models is their reliance on an equiangular discretization of the sphere which suffers from 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, removing unphysical biases. 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 without any computational overhead.

Figures (11)

• Figure 1: Left: Predicted surface level temperature from PEAR. Green lines show the HEALPix cell boundaries at 3 levels of course-graining above the model resolution. Right: Anomaly correlation coefficient (ACC) (higher is better) for surface level northward wind component with forecast horizon up to 10 days. PEAR outperforms the almost 8 times larger PanguLarge at longer forecast horizons.
• Figure 2: Shift and corresponding mask for windowed attention. Illustration of a scalar tensor with the 1d HEALPix index in the horizontal direction and the vertical direction corresponding to the discretized vertical direction above the surface. Ring indexing is used in the HEALPix direction, with the north pole to the left, and south pole to the right. The lower grid shows where the indicated voxels from the top grid end up after a negative shift of half a window in both directions. Note that the voxels from region a, b, c and d are all from spatially separated regions, and thus the window in the lower right needs to be masked accordingly. The colored striped regions indicate the mask for windows along the borders, where each window contains two regions instead of four as in the corner window.
• Figure 3: PEAR architecture schematic. Violet slices correspond to the variables visualized on the sphere for the input and output tensors. Each block indicates the tensor shape after the layer with the corresponding name. Patch embedding by convolution, shifted windowed multi-head attention (SW-MHA) with learned positional embedding, downsampling and upsampling by patch merging and splitting and patch recovery by transpose convolutions. Green block indicates the skip connection, where the output of the first attention layer is concatenated along the embedding dimension before the final patch recovery by transpose convolutions. Green lines on the spherical visualizations indicate the HEALPix grid at 3 levels of course-graining above the model resolution.
• Figure 4: Mean anomaly correlation coefficient (ACC), higher is better, for the surface and upper variables after iterated model inference to perform multiple day forecasting. The upper variables are averaged over the 13 vertical levels. The metrics are mean sea level pressure (msl), temperature at 2m (t2m), eastward horizontal wind velocity at 10m (u10), northward horizontal wind velocity at 10m (v10), specific humidity (q), temperature (t), eastward wind velocity (u), northward wind velocity (v), geopotential (z). PEAR consistently outperforms Pangu at the same architecture hyperparameters, and is on par (t2m) or better (msl, u10, v10, t, u, v, z) at longer lead times compared to the almost 8 times larger PanguLarge model.
• Figure A1: Patches (green) and windows (red) at the first attention layer. Each green patch contains four pixels of the input resolution $n_\mathrm{side}=64$ on the HEALPix grid, and each window contains 64 patches at this level. The window also include one vertical level above, not shown in the figure.