Dedicated deep-dive site
A standalone site is published for this domain at climate.senuamedia.com — with the per-instance results, walkthroughs, and downloadable data behind every reading on this page.
Same framework, applied to Climate
The framework's value lies in its universality across disparate domains. The brake operator \(\mathcal{B}\), dispersion \(\mathcal{S}\), consensus \(\mathcal{M}\), spectral primitive \(\mathcal{P}\), anti-shadow detector \(\mathfrak{A}\), and scope-reporter \(\mathscr{A}\) — together with Theorems 1–13 — are applied here exactly as on every other domain. Source code: github.com/senuamedia/uniformity. No per-domain calibration. No imported threshold. No bespoke fit.
Cross-domain catalogue — \(\beta\)-strip
Every brake-exponent reading across every domain. The same operator \(\mathcal{B}\) produced every point. This domain's points are highlighted; the rest of the catalogue is visible for cross-domain context.
Click any point for the full reading: instance, domain, \(\beta\) value, and a link to the source code.
What the framework provides for climate science
Climate science already has rich diagnostic toolkits: model-comparison protocols, paleoclimate reconstructions, change-point detection. What it does not have is a single dimensionless lens that applies uniformly across CMIP6 ensembles, observational satellite records, and paleoclimate ice-core data — without importing a domain-specific tipping threshold or scale. The σ-Uniformity Framework provides exactly that lens: a model-agnostic cross-ensemble robustness measurement applied identically across tipping elements, observational records, and paleoclimate proxies. 15 catalogue instances on climate alone (instances 16–30).
Headline results across 15 instances
- Anthropogenic vs natural CO\(_2\) separated at 5.7σ (instance 23). Modern Mauna Loa β = +4.04; paleo Vostok/EPICA β ≈ +2.96–3.00; within-paleo cross-cadence σ = 0.024.
- CMIP6 Arctic sea-ice decline cross-model unanimous (instance 16). 21/21 models agree on direction; relative ΔΦ = -73%.
- Earth-system energy-budget closure 78% (instance 18). Reproduces Trenberth–Fasullo "missing energy" finding from first principles, in domain-internal units.
- Permafrost early threshold +0.36 ± 0.12 K (instance 26) — far below literature ±1.5–2.0 °C tipping window.
- NSIDC observational regime breaks at 1990 and 2007 (instance 17) via PELT, BIC penalty — recovers literature "Arctic Dipole Shift" hypothesis with no imported regime dates.
- Mid-Pleistocene Transition resonance shift 41 kyr → 100 kyr (instance 22). Framework class-declares MPT as resonance reorganisation, not cascade-class change.
- Stratospheric ozone Montreal Protocol (instance 25). Theorem 10 anchor: \(\mathfrak{A} = 22.4\) anti-shadow detection — hole-minimum and zonal-mean shadow different cascades.
- Cross-model timing-of-tipping prediction (instance 27). Framework beats naive Φ→Φ₀/2 baseline (20–25 yr error vs 38–41 yr).
- Tropical cyclones (instance 30). Wind-vs-pressure shadow disagreement in 5/6 basins — third Theorem-10 anchor.
Experiments
45 scripts at domains/climate/experiments/.
Selected:
cmip6_tipping_cross_shadow.py— instance 16arctic_sea_ice_v2.py— instance 17 (Theorem 3 precision-floor anchor)conservation_decomposition_v2.py— instance 18 (Pattern-4 introduction)younger_dryas_v2.py— instance 20 (Layer-C primitive)mid_pleistocene_transition_v2.py— instance 22 (T9, T13 anchor)co2_atmospheric_trajectory_v2.py— instance 23stratospheric_ozone_v2.py— instance 25 (T10 anchor)permafrost_carbon_cascade.py— instance 26timing_of_tipping_prediction.py— instance 27tropical_cyclone_intensity.py— instance 30
Detail — anthropogenic vs natural CO\(_2\) (instance 23)
| Cadence | \(\beta\) | \(R^2\) | \(\sigma_{\text{cross}}\) |
|---|---|---|---|
| Modern (Mauna Loa, 1958–2024) | +4.04 | 0.68 | 0.45 |
| Holocene (200 yr–12 ka) | −2.54 | 0.03 | fails Theorem 3 gate |
| Vostok (0–420 ka) | +3.00 | 0.09 | — |
| EPICA (0–800 ka) | +2.96 | 0.08 | — |
Within-paleo cross-cadence \(\sigma = 0.024\) — natural CO\(_2\) is scale-invariant millennial → 100-millennial. \(|\beta_{\text{anth}} - \beta_{\text{nat}}| = 2.13\) → 5.7σ separation. EMD-trend on Vostok: once Milankovitch cycles peeled, residual brake \(\beta = -0.24 \pm 0.45\) (below threshold). Framework reads anthropogenic CO\(_2\) as a distinct cascade class.
Framework reading and caveats
Theorems 3 and 11 anchor every climate reading: where brake-p fits cleanly (long timescales, anthropogenic CO\(_2\)) the result is sharp; where the precision floor binds (annual cadence, narrow log-range) the framework declines and falls back to a direction-and-rate-sign consensus that retains real informational content. The framework's two-layer / three-layer reading correctly separates ensemble robustness from temporal smoothness — Arctic sea-ice (robust) is distinguished from Amazon NPP (genuinely inconclusive) without imposing a domain-specific threshold.
Deep dive
The full climate analysis lives at climate.senuamedia.com.