Every member of the ensemble is a one-box energy-balance model: the planet's temperature anomaly ΔT relaxes toward equilibrium under a radiative forcing ΔF, with an ocean heat-capacity term slowing the response and a red-noise term standing in for year-to-year internal variability (ocean/atmosphere weather noise, not measurement error).
C·dΔT/dt = ΔF(t) − λ·ΔT + η(t)
ΔF(t) = 5.35·ln(CO₂(t)/280) [W/m², Myhre et al.]
λ = ΔF₂ₓ / ECS, ΔF₂ₓ = 5.35·ln(2) ≈ 3.71 W/m²
η(t+dt) = η·e^(−dt/τ) + amp·N(0,1)·√(1−e^(−2dt/τ))
- Emission scenario — sets the CO₂ pathway to 2100 (SSP1-2.6 peaks and declines, SSP5-8.5 keeps accelerating). This is scenario uncertainty — the dim reference lines for the other two scenarios show how much of the long-range spread comes from policy choices, not physics.
- Climate sensitivity (ECS) — equilibrium warming per CO₂ doubling; sets the feedback strength λ that pulls ΔT back toward balance. Higher ECS means the same forcing produces more warming and a slower approach to equilibrium.
- Internal variability — amplitude of the red-noise forcing that drives the N=18 ensemble members apart. This spread saturates rather than growing forever — the reason forecast uncertainty at century scale is dominated by which scenario unfolds, not by chaos.
- Forecast speed — how fast simulated time advances; each loop back to 2025 redraws the ensemble with a fresh random seed, as a new forecast run.
This mirrors the real "cascade of uncertainty" framework climate forecasters use (Hawkins & Sutton, 2009): near-term spread is mostly internal variability, while long-term spread is mostly which emissions scenario the world follows.