Choice of normalization for tradewind predictability estimates

Determine whether the unnormalized or normalized Ricci curvature is the more plausible quantity for replacing Arnold’s sectional-curvature parameter in tradewind error-growth estimates.

Background

The paper replaces Arnold’s sectional-curvature quantity in a heuristic weather-predictability estimate with two alternatives: the unnormalized Ricci curvature and its normalized version. These choices produce substantially different predicted error amplification factors after two months. The authors do not resolve which normalization has the more meaningful physical or geometric interpretation.

References

At this point, we are unaware which of the unnormalized or normalized Ricci curvature value is a more plausible choice.

— Ricci curvature for fluid models on the torus via Zeitlin's quantization  (2609.01259 - Ishida et al., 1 Sep 2026) in Section 4, subsection “Tradewind current”