Instance #24 — Global sea-level rise multi-shadow
Datasets: 6 GMSL shadows — Church-White 2015, CSIRO Reconstructions 2019, Frederikse et al. 2020, Jevrejeva et al. 2014, CSIRO altimetry, NOAA STAR altimetry. Spans 1807–2026 across reconstructions plus 1992–2026 altimetry.
Aggregate result
Cross-shadow σ_cross(β) = 0.479 ≈ mean within-shadow half-CI = 0.451 — at noise floor. Median β = +0.131. The cross-shadow CI half-width matches the framework's Theorem 3 precision-floor prediction (\(\mathrm{Var}(\hat\beta) \le K^2/\log^2(\text{range})\) → CI ≈ 0.5 for \(K \approx 1\) and log-range 1.08–2.08).
Component decomposition (Frederikse 2020)
Per Theorem 5 (linear cascade composition), GMSL = steric + glaciers + GrIS + AIS + TWS. Per-SSP β:
| SSP | Steric | Glaciers | GrIS | AIS | TWS |
|---|---|---|---|---|---|
| SSP1-1.9 | +1.117 | +0.213 | +1.181 | +3.757 | −0.626 |
| SSP1-2.6 | +1.176 | +0.382 | +1.281 | +3.664 | −0.312 |
| SSP2-4.5 | +1.250 | +0.634 | +1.407 | +3.479 | +0.138 |
| SSP3-7.0 | +1.293 | +0.806 | +1.478 | +3.316 | +0.427 |
| SSP5-8.5 | +1.313 | +0.899 | +1.511 | +3.210 | +0.578 |
Headline component finding
AIS is super-rate (β > 3) under all 5 SSPs including SSP1-1.9. Aggregate GMSL stays sub-rate, but its dominant component does not. Theorem 1 binds harder for components than for totals. The framework's β quantifies post-tipping cascade rate: AIS dominates GMSL's eventual rate-of-rate.
Hierarchical decomposition finding (numerical-tools update): components have narrower log-range (0.24–1.35) than total GMSL (1.08–2.08). Theorem 3 binds harder on components, not less, in this case. Components register correctly as Outcome B (distinct cascades, σ_cross = 5.37 across mechanisms — steric vs cryospheric mass loss vs hydrology are physically different).
Pattern-4 closure check
Ice components (GrIS + AIS + glaciers) → Barystatic SLR contribution at 0.05 relative residual ✓. Pattern-4 closure passes for the cryospheric subset.
Source: sea_level_rise_v2.py + scenario_fan_gmsl.py