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PEAR: Equal Area Weather Forecasting on the Sphere

The paper introduces PEAR, a transformer-based weather forecasting model that natively operates on the HEALPix equal-area grid to eliminate unphysical polar biases and outperform existing equiangular-grid models without computational overhead.

Original authors: Hampus Linander, Tage Tykesson, Pietro Rosso, Christoffer Petersson, Daniel Persson, Jan E. Gerken

Published 2026-05-28

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CC BY 4.0

Original authors: Hampus Linander, Tage Tykesson, Pietro Rosso, Christoffer Petersson, Daniel Persson, Jan E. Gerken

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to paint a perfect picture of the entire Earth's weather on a flat map. The traditional way scientists have done this for decades is by drawing a grid of squares, like a checkerboard, over the globe.

The Problem with the Old Grid
The trouble with this "checkerboard" method is that it gets distorted near the poles (the North and South). To make the squares fit the curve of the Earth, the squares near the equator are wide and comfortable, but as you move toward the poles, the squares get squeezed into tiny, cramped slivers.

This creates a "traffic jam" of data at the poles. The computer has to do a lot of extra work to process these tiny, crowded squares, while the equator gets a lazy, easy ride. This unevenness introduces a "bias," like trying to measure a round room with a ruler that stretches and shrinks depending on where you hold it.

The New Solution: The Equal-Area Tiling
The authors of this paper, PEAR, decided to try a different tiling method called HEALPix.

Think of HEALPix not as a checkerboard, but as a perfectly fitted soccer ball.

Equal Size: Every single patch on this soccer ball is exactly the same size. No matter if you are at the equator or the North Pole, every "pixel" covers the exact same amount of ground.
No Distortion: Because every patch is the same size, the computer doesn't have to do extra work at the poles. It treats the whole planet fairly.

The PEAR Model
The team built a new AI weather forecaster named PEAR (Pangu Equal Area) that speaks the language of this soccer-ball grid natively.

Native Speaker: Previous AI models had to translate the weather data from the "squeezed" checkerboard grid into the "equal" soccer-ball grid just to process it, and then translate it back. PEAR skips the translation. It thinks, learns, and predicts directly on the soccer-ball grid.
The Transformer Engine: PEAR uses a powerful type of AI architecture (a Transformer) that looks at the weather in "windows." Because the grid is uniform, these windows are perfectly consistent everywhere.

What They Found
The researchers tested PEAR against the current top AI weather models (like Pangu-Weather, GraphCast, and FengWu) and the old "checkerboard" versions of their own model.

Better Accuracy: PEAR predicted the weather more accurately than all the other models, especially for forecasts up to 10 days out. It was better at predicting temperature, wind, and pressure.
Faster and Lighter: Despite being more accurate, PEAR didn't need more computer power to run. In fact, it was faster than some competitors and used fewer "brain cells" (parameters) than the massive Pangu model.
Fairness: By removing the "pole distortion," the model learned the physics of the atmosphere more naturally, without being tricked by the weird geometry of the old grid.

The Bottom Line
The paper argues that if you want to predict the weather for the whole planet, you shouldn't use a grid that treats the poles like a crowded subway station and the equator like an empty park. By switching to a grid where every piece of the puzzle is the same size (HEALPix), the AI can see the whole picture more clearly and make better predictions without needing a bigger, slower computer.

They also showed that this new approach works well for simulating long-term climate models, proving that the "soccer ball" grid is a solid foundation for understanding our planet's future.

Technical Summary: PEAR - Equal Area Weather Forecasting on the Sphere

Problem Statement

Artificial intelligence has rapidly advanced weather forecasting, with models like Pangu-Weather and GraphCast surpassing traditional numerical methods in global medium-range predictions. However, a critical limitation persists: most data-driven models rely on equiangular discretizations of the sphere (latitude-longitude or Gaussian grids). These grids suffer from non-uniform resolution, where grid cells become significantly smaller near the poles compared to the equator. This geometric distortion introduces unphysical biases and artifacts into learning-based models, as the sampling density varies arbitrarily across the globe.

While the Hierarchical Equal Area iso-Latitude Pixelization (HEALPix) grid offers a solution by ensuring every pixel covers the exact same surface area, previous attempts to utilize it in weather forecasting have been limited. Some models project data onto planar grids, while others use HEALPix only for preprocessing, requiring learnable encoders/decoders to map between equiangular and HEALPix representations. This paper addresses the need for a model that operates natively on the HEALPix grid to eliminate these unphysical biases and align with the sphere's inherent symmetries.

Methodology

The authors propose PEAR (Pangu Equal Area), a transformer-based weather forecasting model designed to operate entirely on the HEALPix grid without intermediate projections.

Data and Setup

Dataset: The model is trained on the ERA5-Lite dataset, a subset of the full ERA5 reanalysis data (2007–2017), resampled to the HEALPix grid with $n_{side} = 64$ . This resolution saturates the angular resolution of the available equiangular ERA5 data.
Input/Output: The task is a regression problem predicting the global weather state at $t + \Delta t$ (24 hours) given the state at $t$ . Inputs include surface variables (wind, temperature, pressure) and upper-atmosphere variables (wind, temperature, humidity, geopotential) across 13 vertical levels.
Architecture: PEAR utilizes a volumetric transformer architecture adapted for the spherical domain:
- Patch Embedding: Uses 1D and 2D convolutions to embed surface and upper variables, respectively.
- Windowed Attention: Leverages the nested hierarchical structure of HEALPix to partition the sphere into contiguous windows. Unlike Pangu-Weather, PEAR uses a simplified learned relative positional embedding shared across windows, capitalizing on the equal-area nature of the grid.
- Shifted Windows: To propagate information across disjoint windows, the model employs a ring shifting strategy (adapted from HEAL-SWIN) along the spherical directions and a simple shift in the vertical direction.
- Masked Attention: Due to the cyclic nature of the ring shifting and the polar regions, a masking mechanism is implemented to prevent attention between spatially disjoint voxels (e.g., those jumping from the North to the South pole).
- Downsampling/Upsampling: The hierarchical structure of HEALPix allows for efficient downsampling (merging 4 neighboring pixels) and upsampling (splitting one pixel into four) via tensor reshaping, avoiding complex interpolation.

Key Contributions

Native HEALPix Modeling: PEAR is the first machine learning weather forecasting model to operate entirely on the HEALPix grid, eliminating the need for spatial weights in loss functions and removing unphysical biases associated with equiangular grids.
Architectural Efficiency: The model achieves no computational overhead compared to an equivalent model running on a traditional equiangular grid. The hierarchical structure of HEALPix enables efficient implementation of downsampling and windowed attention.
Performance Superiority: PEAR outperforms its equiangular counterpart (Pangu) and other state-of-the-art baselines (GraphCast, FengWu) across various variables and forecast horizons, despite having fewer trainable parameters than Pangu.
Equivariance Verification: The authors verify that daily sampling (ERA5-Lite) does not degrade the model's learned equivariance properties under rotation, confirming the robustness of the approach.
Climate Emulation: The architecture demonstrates competitive performance in emulating Earth System Models (ESMs) across multiple climate models, outperforming UNet baselines in precipitation prediction.

Experimental Results

Forecast Accuracy: Evaluated on the ERA5-Lite dataset with forecast horizons up to 10 days, PEAR consistently achieves higher Anomaly Correlation Coefficient (ACC) scores than FengWu, GraphCast, and Pangu across surface and upper-level variables.
- For example, at a 9-day lead time for surface temperature (t2m), PEAR achieves an ACC of 0.439, outperforming GraphCast (0.384) and FengWu (0.350).
Efficiency: PEAR has 4.3 million trainable parameters, comparable to GraphCast but significantly smaller than Pangu (11.3M) and FengWu (14.3M). Inference time is 17 ms, faster than Pangu (25 ms), GraphCast (27 ms), and FengWu (98 ms).
Equivariance: Experiments comparing models trained on 24-hour vs. 2-hour sampling intervals show that the 24-hour ERA5-Lite dataset is sufficient for learning rotational equivariance. The error patterns align with the HEALPix grid's symmetry (peaking at 45° rotations), confirming the grid's structural influence.
Climate Modeling: In climate model emulation tasks using the ClimateSet dataset, PEAR (4.3M parameters) outperforms a UNet baseline (18.3M parameters) in 13 of 15 climate models for overall RMSE and achieves the lowest precipitation RMSE in 8 of 15 models.

Significance and Claims

The paper asserts that the HEALPix grid is the physically appropriate native grid for learning-based weather forecasting. By removing the geometric distortions of equiangular grids, PEAR demonstrates that equal-area modeling leads to superior predictive performance without sacrificing computational efficiency.

The authors highlight that as next-generation data sources (such as the ECMWF's Destination Earth initiative) move toward high-resolution HEALPix native data, models like PEAR are essential for leveraging this data efficiently. The work suggests that this approach could improve extreme weather forecasting and provides a foundation for future research into more accurate, bias-free global climate models. The authors remain modest, acknowledging limitations such as the use of ERA5-Lite (rather than full ERA5) due to compute constraints and the inherent limitations of data-driven models regarding long-term stability and physical conservation laws.