If atmospheric CO2 rises at a constant rate, the surface temperature at any moment is always lower than what that CO2 level would produce at equilibrium. Boriana Chtirkova solves the heat equation with surface feedback analytically and shows that this gap -- the difference between transient and equilibrium temperature -- grows on human timescales before eventually saturating at a constant offset after thousands of years of quasi-steady state. On the century timescale that matters for policy, the energy imbalance at the top of the atmosphere is increasing, meaning the planet is falling further behind its own equilibrium.
The practical consequence is counterintuitive. Climate policy debates often frame stabilization targets in terms of equilibrium sensitivity -- the temperature the planet would reach if CO2 were held fixed indefinitely. But the actual path the climate follows is the transient path, and the transient path is always answering yesterday's forcing. The lag means that even if emissions were frozen today, temperatures would continue rising for centuries as the system catches up. Chtirkova's analytical solution makes the dependence explicit: the offset scales with forcing rate multiplied by the ratio of ocean heat capacity to climate feedback strength. Fast forcing and large heat capacity both widen the gap. This is not a modeling uncertainty or a parametric choice -- it is a structural feature of any system with thermal inertia responding to a ramp input. The climate is a low-pass filter applied to human activity, and the filter's time constant is long enough that we never experience the equilibrium consequence of what we are doing now. We experience the lagged consequence of what we did decades ago.
(arXiv:2603.01674)