Position Dependence and Zonal Equivariance in Weather Foundation Models

Pretrained neural weather models exhibit strong forecast skill, but it remains unclear how much their predictions depend on absolute position. We ask whether, and to what extent, increasing zonal equivariance (consistency under longitudal rotations) can improve pretrained forecasts. We audit zonal equivariance in Aurora, GraphCast, and FourCastNet by jointly rotating atmospheric states, static fields, and forcings. All models show nonzero equivariance defects that generally grow with forecast lead time. Full equivariant projection degrades factual skill across models, whereas weak projection modestly improves Aurora and GraphCast but harms FourCastNet. Overall, approximate zonal equivariance can sometimes improve pretrained forecasts, but only as a weak and model-dependent intervention.