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On the effective resolution of AI weather prediction models
Tobias Selz1, W. P. Bruinsma, George C. Craig1, S. Markou, R. E. Turner, and A. Vaughan
1Ludwig-Maximilians-Universität München
First published:
Feb. 14, 2025
No permanent ID assigned yet. URL: https://opendata.physik.lmu.de/H66gKyhITQ7qS51
Keywords:
Artificial intelligence
weather prediction

Selz, T., Bruinsma, W., P., Craig, G., C., Markou, S., Turner, R., E., and Vaughan, A. (2025): On the effective resolution of AI weather prediction models. LMU Munich, Faculty of Physics. (Dataset). URL: https://opendata.physik.lmu.de/H66gKyhITQ7qS51

wget and curl are the two standard tools that are available on most Linux and macOS computers. wget contains a feature for downloading a list of files: 
wget -x -nH -i 'https://opendata.physik.lmu.de/H66gKyhITQ7qS51/?list'
curl is missing a feature like that, but the same functionality can be created by combining curl and xargs: 
curl 'https://opendata.physik.lmu.de/H66gKyhITQ7qS51/?list' | xargs -I URL -n1 bash -c 'curl --create-dirs -o ${1:31} ${1}' -- URL
Abstract
In this study, we investigate the effective resolution of deterministic AI weather prediction models. We find that an ideal, perfectly trained AI model follows the mean of the predictive distribution for the lead time interval which is used in its loss function during training. We demonstrate the consequences and limitations of this result with forecast data from various AI models, including Aurora, Pangu, GraphCast and GenCast and we compare them to ensemble and deterministic forecasts from the European Centre for Medium Range Weather Forecasting. We further demonstrate the impact of the resolution on mean-square error scores and suggest a method for a fairer comparison of two models with different effective resolution.
README.md

Data of Selz et al., 2025

The zip-file contains the data which is required to reproduce the figures of "Selz et al., 2025: On the effective resolution of AI weather models (preprint version)". It consists of the following NetCDF files, one for each AI model experiment. The label used in the paper is given in brackets.

spharm_aurora-ft-i.nc (Aurora-S)
spharm_aurora-ftl-i.nc (Aurora-L)
spharm_gencast-hro-i.nc (GenCast)
spharm_graphcast-op-i.nc (GraphCast)
spharm_pangu-1h-i.nc (Pangu-1h)
spharm_pangu-3h-i.nc (Pangu-3h)
spharm_pangu-6h-i.nc (Pangu-6h)
spharm_pangu-24h-i.nc (Pangu-24h)

Each nc-file contains spherical harmonics expansion coefficients (spharm) of divergence (div) and vorticity (vo).

Important note: The spherical harmonics coefficients are complex numbers. Hence, a HDF5 backend is required to read the data, e.g. in python:

ds = xr.open_dataset('spharm_pangu-24h-i.nc', engine='h5netcdf')

In case of problems or questions, please contact: tobias.selz@lmu.de

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