Explain why rotationally equivariant padding and positional/solar-zenith conditioning degrade DiffObs performance

Determine why the modified DiffObs model—using circular-padding in the zonal (longitude) direction, additional longitude positional channels cos(lon) and sin(lon), and a zonally averaged cosine of the solar zenith angle as a temporal conditioning input—produces worse atmospheric variability and structure than the baseline model, despite preserving periodicity across the dateline.

Background

The authors observed a dateline discontinuity at 180°E/W in long autoregressive rollouts. To address this, they modified the model to enforce rotational equivariance by using circular-padding in the zonal direction and added static positional inputs (cos(lon), sin(lon)) and a temporal conditioning input derived from the zonal average of the solar zenith angle.

Despite these changes removing the spatial binding at the dateline and preserving periodicity, the resulting model exhibited degraded performance, failing to capture key atmospheric structures (e.g., identifiable landmasses and oscillatory wave signals) compared to the baseline. The authors explicitly state that the reason for this degradation is not clear.