The Paris Agreement (Article 4.11) runs on 5-year pledge-and-review cycles: every nation submits a Nationally Determined Contribution (NDC) — a self-set emissions-cut target — and each new NDC must represent a progression beyond the last (the "ratchet" mechanism: ambition can only go up, never down). Every cycle ends with a Global Stocktake comparing collective pledges against the temperature goal.
Ratchet: a(t+1) = a(t) + pressure · (1 − a(t)) [monotonic, a ∈ [0,1]]
Implemented: cut(t) = a(t) · (1 − gap) [gap = pledge-vs-delivery shortfall]
Emissions: E(t+1) = E(t) · (1 + bau − cut(t))
Cumulative: C(t+1) = C(t) + E(t) · 5 [5-yr cycle, GtCO₂]
Warming: ΔT(C) ≈ ΔT₀ + TCRE · C [TCRE ≈ 0.00045 °C per GtCO₂]
Each bar in the 3D field is one of 12 illustrative negotiating blocs; bar height tracks its current-cycle emissions and bar color its ambition level (red → green). The ring above the field is the shrinking 1.5°C-consistent emissions ceiling.
- Stocktake pressure — how strongly the global review pushes every bloc's ambition upward at each ratchet.
- Implementation gap — the fraction of a pledge that historically goes undelivered (policy lag, enforcement gaps).
- BAU growth — the emissions growth rate that would occur with zero climate policy.
- Run Stocktake & Ratchet — advances one 5-year cycle: ambitions ratchet up, emissions respond, and warming updates via the cumulative-emissions climate response (TCRE), the same simplified relationship IPCC AR6 uses to link cumulative CO₂ to warming.
Real-world relevance: this is the actual legal architecture behind the Paris Agreement — no external body sets national targets; ambition rises only through this repeated pledge/review/ratchet loop, which is why the "ambition gap" (pledged cuts vs. what a 1.5°C budget requires) is the single most-tracked number in international climate diplomacy.