Per-SSP cross-shadow σ over β
| SSP | n_models | σ_cross | β median | β IQR | R² median |
|---|---|---|---|---|---|
| SSP1-1.9 | 12 | 5.095 | −0.136 | 5.645 | 0.02 |
| SSP1-2.6 | 12 | 2.304 | +1.168 | 1.892 | 0.02 |
| SSP2-4.5 | 12 | 1.214 | +0.514 | 0.710 | 0.01 |
| SSP3-7.0 | 12 | 0.624 | −0.274 | 1.084 | 0.01 |
| SSP5-8.5 | 12 | 0.694 | −0.450 | 0.829 | 0.03 |
The σ_cross paradox
σ_cross monotonically decreases with forcing intensity. Under aggressive mitigation, internal variability dominates external forcing, so models disagree more. Under high-forcing scenarios the external signal dominates internal variability, so models agree. Implication: ensemble-mean projections of sea-ice under aggressive mitigation have wider cross-model uncertainty than under continued high emissions. Read the full paradox treatment.
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).
Three-criterion best-pathway selection
Criteria (all framework-internal, no imported thresholds beyond β=1):
- σ_cross(β) ≤ 1.214 (CMIP6 universality, Law III)
- consensus β 68% CI upper bound < 1.0 (sub-brake regime, Theorem 1, Law IV)
- PELT detects no change-point in consensus Φ(t) before 2050 (single-regime cascade)
| SSP | (i) σ_cross | (ii) β CI < 1 | (iii) no PELT pre-2050 | verdict |
|---|---|---|---|---|
| SSP1-1.9 | FAIL | PASS | FAIL | FAIL |
| SSP1-2.6 | FAIL | FAIL | FAIL | FAIL |
| SSP2-4.5 | PASS | FAIL | FAIL | FAIL |
| SSP3-7.0 | PASS | PASS | FAIL | FAIL |
| SSP5-8.5 | PASS | PASS | FAIL | FAIL |
No CMIP6 pathway clears all three criteria. The σ_cross criterion fails for low-forcing SSPs; the PELT criterion fails for all SSPs (the SSP forcing transition itself constitutes a PELT-detected regime change — the criterion was too strict for forced-physics shadows).
Source: scenario_fan_sea_ice.py