  Atmospheric states derived from reanalysis comprise a substantial portion of
weather and climate simulation outputs. Many stakeholders -- such as
researchers, policy makers, and insurers -- use this data to better understand
the earth system and guide policy decisions. Atmospheric states have also
received increased interest as machine learning approaches to weather
prediction have shown promising results. A key issue for all audiences is that
dense time series of these high-dimensional states comprise an enormous amount
of data, precluding all but the most well resourced groups from accessing and
using historical data and future projections. To address this problem, we
propose a method for compressing atmospheric states using methods from the
neural network literature, adapting spherical data to processing by
conventional neural architectures through the use of the area-preserving
HEALPix projection. We investigate two model classes for building neural
compressors: the hyperprior model from the neural image compression literature
and recent vector-quantised models. We show that both families of models
satisfy the desiderata of small average error, a small number of high-error
reconstructed pixels, faithful reproduction of extreme events such as
hurricanes and heatwaves, preservation of the spectral power distribution
across spatial scales. We demonstrate compression ratios in excess of 1000x,
with compression and decompression at a rate of approximately one second per
global atmospheric state.
