Statistical fan (ARIMA × ±0%, ±25%, ±50% rate perturbations)
ARIMA(0,1,1) point forecast yields near-linear future trajectory; consensus β collapses to 0 (constant ρ ⇒ slope of log|ρ| against log|Φ| is 0 by construction). σ_cross retains historical curvature and is informative.
IPCC AR6 SSP fan (Fox-Kemper et al. 2021 central trajectories)
| SSP | mean ρ (mm/yr) | σ_cross | β GLS | R² GLS | β Bayesian |
|---|---|---|---|---|---|
| SSP1-1.9 | 3.97 | 0.258 | −1.119 | −66.08 | −0.032 |
| SSP1-2.6 | 4.77 | 0.256 | −0.945 | −36.71 | +0.058 |
| SSP2-4.5 | 6.24 | 0.263 | +0.296 | +0.54 | +0.026 |
| SSP3-7.0 | 7.77 | 0.257 | +0.541 | +0.45 | +0.461 |
| SSP5-8.5 | 8.89 | 0.245 | +0.521 | +0.47 | +0.451 |
When AR6 SSP curve attaches to a long, mostly-flat historical record, gls_ar1's Cochrane-Orcutt transform can be near-degenerate (R² < 0). The Bayesian AR(1) MAP/median is more stable; both reported.
Frederikse 2020 component decomposition under each SSP
| 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 |
Climate Mitigation Atlas — \(\beta\) by observable × emissions pathway
Each cell's colour is one number — the rate exponent \(\beta\). Green = stoppable (returns to rest). Orange = super-rate. Red = locked-in.
Click any cell for the full reading: \(\beta\), cross-model dispersion, theorem anchor, and the source code on GitHub.
How to read this chart · what the SSPs mean
The axes
- Rows: 8 climate observables — what is changing.
- Columns: 5 emissions pathways from "very aggressive mitigation" (left) to "no mitigation" (right).
- Cell colour: the rate exponent \(\beta\). Below 1 is stoppable; above 1 is locked-in.
- Cell label: the actual \(\beta\) value cross-model median.
The five emissions pathways (SSPs)
- SSP1-1.9 — ~1.5°C. Aggressive net-zero by mid-century. Paris lower bound.
- SSP1-2.6 — ~2°C. Moderate mitigation. Net-zero by ~2070.
- SSP2-4.5 — ~2.7°C. Current policies, middle-of-the-road.
- SSP3-7.0 — ~3.6°C. Regional rivalry, fragmented action.
- SSP5-8.5 — ~5°C. Continued fossil-fuel growth, no mitigation.
SSPs (Shared Socioeconomic Pathways) are the IPCC's standard set of emissions futures. The number after the dash is the radiative forcing in 2100 (W/m²).
AIS β > 3 under EVERY SSP
Antarctic Ice Sheet is super-rate (β = 3.21 to 3.76) under all 5 SSPs including SSP1-1.9. Aggregate GMSL stays sub-rate under aggressive mitigation, but its dominant component does not. See locked-in risks. AIS post-tipping rate scales as dΦ/dt ~ Φ³·⁵ — super-fast acceleration once tipped.
Best pathway by aggregate: SSP1-1.9 (rank-sum 7 of 24 — tightest σ_cross + smallest mean ρ + β farthest below 1).
Source: scenario_fan_gmsl.py