Temporal variance normalization

[clessig]

Is your feature request related to a problem? Please describe.

GraphCast uses a temporal variance normalization in the loss of the form || pred - target || / \sigma_t. Replicating this with observations is non-trivial since \sigma_t is usually computed based the grid-point wise difference between adjacent time step. This is not defined for most observations.

Describe the solution you'd like

@iluise suggested to use the deviation from the mean instead of the grid point-wise difference between adjacent frames. For ERA5 (or any gridded datasets), this can be compared to the original approach. If the suggested approach yields qualitatively the same results as the original one, then it should be used for the WeatherGenerator. Otherwise, the original approach should be used where possible with \sigma_t = 1 for datasets where it cannot be computed (yet).

Describe alternatives you've considered

\sigma_t = 1 yields sub-optimal results for the different physical fields that have widely different de-correlation times. This becomes even more extreme when other Earth system components are considered.

Additional context

No response

Organisation

ECMWF