Intrinsic instantaneous coarse-to-fine recoverability in multiscale chaos: The Lorenz-96 system
Year: 2026
Type: preprint
Abstract: In multiscale chaotic systems, a central question for closure is how much of an unresolved fine-scale target can be inferred from a simultaneous coarse observation. For a specified observation-target pair, we quantify instantaneous recoverability under the invariant snapshot measure as the fraction of target variance explained by conditioning on the retained coarse variables. Evaluating this quantity across scales produces a scale-resolved recoverability map. Applied to the Lorenz-96 system across a range of forcings, the maps reveal a strongly nonuniform landscape: lower-wavenumber targets have little variance explained by the retained lower modes, while a finite band of higher modes exhibits partial recoverability once the retained scales reach the energetically active intermediate range. Recoverability onset is organized around a reference cutoff at which two retained modes can directly couple to the target through the quadratic nonlinearity, although its precise location depends on attractor statistics. Across the tested forcings, this qualitative onset structure persists while recoverability decreases, leaving a larger fraction of target variance unexplained in more strongly driven regimes. This definition identifies the maximal explained-variance fraction attainable by instantaneous deterministic models under squared loss; the estimated maps provide a scale-dependent diagnostic for closure modeling.
Source: arXiv (Cornell University)
Authors: Xu, Zhongfeng, Chen, Junfeng
Language: English
Subfield: Atmospheric Science
Field: Earth and Planetary Sciences
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167902387