Quantifying forecast blurriness over time

[bnubald]

In this paper shared by Scott, Neural general circulation models for weather and climate [1], it mentions the use of power spectra to quantify blurriness (Fig. 17 in supplementary shows power spectra plots).

I wonder if this would be of use when considering longer-term forecast to see how well a model does for the smaller scales over time. Maybe useful in informing and defining a cut-off/truncation of leadtime if we're trying to forecast too far ahead when the model starts to perform poorly?

Relevant snippet:

Figure 17 from supplementary:

References:

1. Kochkov, D., Yuval, J., Langmore, I. et al. Neural general circulation models for weather and climate. Nature (2024). https://doi.org/10.1038/s41586-024-07744-y