Climate Change: CO2 Forcing & Ocean Heat Lag

Climate Change — Two-Layer Model

Atmospheric CO2 560 ppm

Climate feedback λ 1.30 W/m²/K

Ocean heat uptake γ 0.70 W/m²/K

Sim speed 6 yr/s

Readouts

Radiative forcing F

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Sim time

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Surface ΔT

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Deep ocean ΔT

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TOA imbalance N

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Equilibrium ΔT

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How it works

This is the standard two-layer energy balance model used in simplified-climate-model literature (e.g. Held et al. 2010) to explain why surface warming lags behind the CO2 already in the air. A fast-mixing surface+upper-ocean layer exchanges heat with a slow, huge deep-ocean layer:

F  = 5.35 · ln(CO2 / 280)                (IPCC CO2 forcing, W/m²)
Cs·dTs/dt = F − λ·Ts − γ·(Ts − Td)
Cd·dTd/dt = γ·(Ts − Td)
N  = F − λ·Ts                            (top-of-atmosphere imbalance)

CO2 concentration — sets the forcing F via the logarithmic CO2 law; each doubling adds a fixed ~3.7 W/m², not a fixed ppm step.
Climate feedback λ — how strongly a warmer surface radiates extra heat back to space; a smaller λ means a more sensitive climate (larger equilibrium warming per W/m²).
Ocean heat uptake γ — how fast heat mixes from the warm surface layer into the deep ocean; a larger γ slows surface warming but banks more heat for later ("warming in the pipeline").
TOA imbalance N — while N > 0 the planet is still absorbing more sunlight than it radiates away, so surface temperature keeps climbing even if CO2 is held constant from here.

In the scene, greenhouse-gas density in the translucent shell scales with CO2 ppm. Photons launched from the surface pass upward; the fraction re-emitted back down by the shell (visualized as a bounce) scales with the current forcing, the same optical-depth idea behind the log(CO2) law — more absorbers, more re-radiation back toward the surface.

Outgoing IR — escapes Outgoing IR — re-absorbed

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Surface ΔT Deep ocean ΔT