Clarification on Global Mean RMSE Oscillation for Near-Surface Temperatures

Hi
I’m observing an interesting behavior while evaluating GraphCast forecasts against ERA5 data.

When plotting the global mean of near-surface temperature variables, specifically t1000 and t2m, the forecast mean oscillates in sync with ERA5, which looks physically correct and expected.

However, the global mean RMSE computed for a single 40-step (6-hour interval) run also shows a noticeable oscillatory pattern instead of a smooth or gradually increasing trend.

Is this RMSE oscillation expected, or does it indicate an underlying issue with how RMSE is being computed or with the model’s short-term stability?

Details:
Model: GraphCast-Small (1.0° / 13 levels)
Forecast length: 40 steps (6-hour intervals)
RMSE computed as global cosine-latitude-weighted mean over all grid points and times
Both forecast and ERA5 data are aligned on valid time coordinates before evaluation

RMSE typically increases smoothly with lead time, so I wanted to confirm whether oscillations in RMSE are normal behavior for GraphCast for near-surface temperature variables.

No source files or tests are named. Start by locating the evaluation entry point for GraphCast-Small forecasts and reproduce the 40-step t1000 and t2m comparison using the stated valid-time alignment and cosine-latitude weighting. Done means determining whether the oscillation comes from the RMSE calculation or documented model behavior and recording the evidence.

Written by the indexing model from the issue text.