Emissions & Physics

CO2 emission rate 40 GtCO2/yr

Climate feedback λ 1.15 W/m²/K

Ocean heat uptake γ 0.70 W/m²/K

Polar amplification 2.4×

Time

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Atmospheric CO2

420 ppm

Radiative forcing

2.15 W/m²

Global ΔT

+1.3°C

Deep ocean ΔT

+0.2°C

Arctic ΔT

+3.1°C

Tropical ΔT

+0.7°C

How it works

This is a two-layer ocean-atmosphere energy balance model — the same structure used to derive transient climate response (TCR) from equilibrium climate sensitivity (ECS) in IPCC assessments. It separates fast atmosphere/mixed-layer warming from slow deep-ocean heat storage, so temperature lags forcing instead of jumping straight to equilibrium.

CO2 forcing:      F = 5.35 · ln(C / 280)      [W/m²]
Upper layer:      C_u dT_u/dt = F − λT_u − γ(T_u − T_d)
Deep layer:       C_d dT_d/dt = γ(T_u − T_d)
Carbon budget:    dC/dt = 0.45 · E / 7.81     [ppm/yr]

Emission rate E — annual CO2 output (GtCO2/yr). ~45% stays airborne each year (the rest is absorbed by oceans and land sinks); 7.81 GtCO2 raises the atmosphere by 1 ppm.
Feedback λ — how strongly outgoing radiation resists warming. Equilibrium sensitivity to doubled CO2 is F₂ₓ/λ = 3.7/λ; a smaller λ means more eventual warming per watt of forcing.
Ocean heat uptake γ — how fast heat drains from the mixed layer into the deep ocean. A larger γ slows surface warming today but stores more "warming in the pipeline" that surfaces later even if emissions stop.
Polar amplification — Arctic warming runs ahead of the global mean (ice-albedo feedback, thinner cold atmosphere); the tropics lag behind it. The globe's ice caps and colour bands scale with this split.

Real-world relevance: this lag between forcing and full equilibrium warming — driven by ocean thermal inertia — is why global temperatures keep rising for decades after emissions plateau, and why cutting emissions today still leaves "committed" warming already stored in the deep ocean.

Year 2026

CO2 molecules (shell density) Polar ice extent Warmer surface

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Climate Change Simulation — CO2 Emissions to Transient Warming