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Earth and Space Sciences · Glossary

What is Two-layer energy-balance model?

Definition 22.7 University Earth and Space Sciences — Year 3 · Chapter 22 — Climate Models

A two-layer energy-balance model represents the climate by a surface layer of temperature anomaly TT and heat capacity CC, and a deep ocean of temperature anomaly TdT_d and heat capacity CdC_d, coupled by a heat exchange coefficient γ>0\gamma > 0:

C dTdt=F+λT−γ(T−Td),Cd dTddt=γ(T−Td).C\,\frac{\mathrm dT}{\mathrm dt} = F + \lambda T - \gamma(T - T_d), \qquad C_d\,\frac{\mathrm dT_d}{\mathrm dt} = \gamma(T - T_d) .
The two-layer model with the mean parameters of the emulator of the sixth assessment and the forcing F_2× = 3.93\, W/ m2 of a doubling. Left, an abrupt quadrupling of carbon dioxide: 62\,\% of the final 5.9\, C after 10 years, 78\,\% after 100 and 95\,\% after 500. Right, carbon dioxide rising by 1\,\% a year: at the doubling, year 70, the surface has warmed by 1.99\, C, the TCR of the model, while the equilibrium warming for that forcing, its ECS, is 2.95\, C; the surface lags because the deep ocean is still taking up heat.
The two-layer model with the mean parameters of the emulator of the sixth assessment and the forcing F2×=3.93 W/m2F_{2\times} = 3.93\,\mathrm{W}/\mathrm{m}^{2} of a doubling. Left, an abrupt quadrupling of carbon dioxide: 62 %62\,\% of the final 5.9 ∘C5.9\,{}^{\circ}\mathrm{C} after 10 years, 78 %78\,\% after 100 and 95 %95\,\% after 500. Right, carbon dioxide rising by 1 %1\,\% a year: at the doubling, year 70, the surface has warmed by 1.99 ∘C1.99\,{}^{\circ}\mathrm{C}, the TCR of the model, while the equilibrium warming for that forcing, its ECS, is 2.95 ∘C2.95\,{}^{\circ}\mathrm{C}; the surface lags because the deep ocean is still taking up heat.
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