When Does Forecast-Error Energy Grow Logistically in Geophysical Turbulence?

[2608.26492] When is logistic error growth a spectral reduction? Skip to main content Search Submit Donate Log in Physics > Atmospheric and Oceanic Physics arXiv:2608.26492 (physics) [Submitted on 27 Aug 2026 ( v1 ), last revised 22 Sep 2026 (this version, v3)] Title: When is logistic error growth a spectral reduction? Authors: Malaquias Peña View PDF HTML (experimental) Abstract: Forecast-error growth has been studied through complementary approaches: scalar models describe the evolution of bulk error, whereas spectral theories follow decorrelation and error transfer across scales. Their connection matters when a fitted growth curve is used to infer a physical mechanism or a limit of predictability. We establish a conditional link between these approaches. Within a bilinear spectral exchange model, assume a stationary reference spectrum and a remainder that vanishes on the proposed common-shape evolution. For a common initial decorrelation fraction strictly between zero and one, the spectral shape is preserved and its amplitude grows logistically exactly when every participating scale shares one positive growth coefficient. The converse inference fails: a logistic aggregate need not imply proportional decorrelation or a common coefficient. An exact two-shell construction demonstrates this failure with identical aggregate curves and different spectral dynamics. For heterogeneous amplitudes, an exact averaging identity separates the contributions of growth-rate mismatch, shape variance, rate--shape covariance, evolving spectral weights, and residual tendencies. A finite-time bound relates their combined effect to departure from a reference logistic curve. Forced surface-quasigeostrophic simulations illustrate how similar retrospective agreement with a logistic reference can coexist with heterogeneous effective shell rates and substantial instantaneous tendency discrepancies. Thus a scalar growth curve alone cannot identify how uncertainty is distributed across scales or justify interpreting a fitted rate as a common spectral growth coefficient. The framework specifies the additional spectral and budget evidence needed to give scalar predictability models that interpretation. Comments: 17 pages, 3 figures Subjects: Atmospheric and Oceanic Physics (physics.ao-ph) ; Chaotic Dynamics (nlin.CD) Cite as: arXiv:2608.26492 [physics.ao-ph] (or arXiv:2608.26492v3 [physics.ao-ph] for this version) https://doi.org/10.48550/arXiv.2608.26492 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Malaquias Peña [ view email ] [v1] Thu, 27 Aug 2026 00:27:47 UTC (180 KB) [v2] Fri, 28 Aug 2026 03:12:12 UTC (180 KB) [v3] Tue, 22 Sep 2026 00:51:39 UTC (158 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: physics.ao-ph < prev | next > new | recent | 2026-08 Change to browse by: nlin nlin.CD physics References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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