Disentangling density and geometry in weather regime dimensions using stochastic twins.

Large-scale atmospheric variability can be summarized by recurring patterns called weather regimes. Their properties, including predictability, have been studied using the local dimension, a geometrical estimate of degrees of freedom from multifractal theory. Local dimension estimates vary across regimes, decrease when a single regime dominates, and increase during transitions, supporting their dynamical significance. However, these variations stem not only from geometry but also from sampling density. We develop a null-hypothesis test using stochastic twins-Gaussian mixture-based surrogates matching atmospheric sampling density but with constant geometry-applied to ERA5 500 hPa fields. Density effects alone explain over 25% of local dimension variance and reproduce the dimension drop near regime peaks, indicating this behavior is density-driven, not geometric. The remaining variability is plausibly geometry-driven. This approach, applicable to any observed system with known sampling distribution, offers a new framework for interpreting local dimension estimates in atmospheric and oceanic data.