Climate feedback

A climate feedback is a response to climate change that alters the initial warming or cooling. Positive feedback amplifies the change; negative feedback opposes it. Positive feedback alone does not prove an irreversible transition.

A perturbation energy balance $\dot{T}\propto F-AT+B{T}^2$ with positive $A,B$ has a stable lower-temperature root and an unstable upper root for $F<A^2/(4B)$. They merge at $T=A/(2B)$; equality is marginal. Extrapolation of this local model is not an empirical runaway threshold for a real planet.

With positive-downward net top-of-atmosphere flux N, imposed forcing F and positive stabilizing coefficient lambda, a simple global model has $N=F-\lambda \Delta T=Cd\Delta T/dt$. A positive imbalance means energy storage, not an independent measurement of F. Ocean uptake and multiple response times complicate the one-capacity approximation. Feedback sign conventions differ between references; writing the full equation prevents confusion. ^[ref]

Lapse-rate feedback is the radiative effect of changes in the vertical temperature profile beyond a vertically uniform temperature change. In the tropics, enhanced warming aloft often increases radiative cooling and is stabilizing. In a stably stratified polar atmosphere, warming concentrated near the surface can yield less compensating cooling aloft and help produce polar amplification. The sign and magnitude depend on the profile and radiation physics.

The Planck feedback is the stabilizing increase in outgoing thermal radiation when temperatures rise, with other properties held fixed. For a blackbody the local derivative is $4\sigma T^3$, so a colder emitter has a smaller absolute radiation increase per kelvin. The atmospheric response requires radiative transfer, and cannot be obtained by replacing the entire climate system with a single surface blackbody.

Water-vapor feedback is the climate feedback from changing atmospheric water vapor as temperature changes. Fixed relative humidity allows more water vapor in a warmer column, altering radiative transfer and often amplifying warming. Fixing absolute humidity suppresses this response. The net restoring coefficient must still include the other climate feedbacks; this individual positive contribution does not establish instability.

Warming can mobilize frozen organic material or change sediment conditions, increasing methane emissions and strengthening the greenhouse effect. Production, transport and atmospheric release must be distinguished: methane can dissolve or be oxidized before reaching the atmosphere. Observed seabed bubbles alone do not establish the magnitude or timing of a global atmospheric feedback.

Replacing bright ice or snow with darker water or ground decreases surface albedo, increases absorbed sunlight and can cause further melting. Locally the extra absorbed heat flux is $({\alpha }_{\mathrm{ice}}-{\alpha }_{\mathrm{water}})S_{\downarrow }$ on the newly exposed surface. The effect depends on season, cloud cover and incident sunlight.