Climate physics: radiation, energy balance and feedback
Climate physics begins with conservation of energy applied to a clearly defined system. At the top of the atmosphere, incoming solar radiation is partitioned into reflected shortwave radiation and energy absorbed by the atmosphere and surface. The Earth system also emits thermal infrared radiation to space. A positive net incoming flux means energy accumulates; a negative one means the system loses energy. Temperature does not have to change instantaneously because oceans, land and the atmosphere store energy.
Geometry matters when converting an incident solar flux into a planetary average. A spherical planet intercepts sunlight over a disk of area pi R squared but has total surface area four pi R squared. A simple global model therefore divides the incident flux normal to the rays by four before comparing it with a flux averaged over the whole sphere. Albedo is the fraction of incident solar energy reflected, so absorbed sunlight in this model is (1 - albedo) times the global mean incoming solar flux.
Consider a hypothetical model with global mean incoming sunlight of 340 W per square metre and albedo 0.30. Reflected flux is 102 W per square metre and absorbed flux is 238 W per square metre. A steady top-of-atmosphere energy balance would require outgoing thermal radiation of 238 W per square metre. If outgoing radiation were instead 236, the model would accumulate energy at 2 W per square metre. These are supplied illustrative numbers, not a statement of the present measured planetary imbalance.
Thermal emission increases with absolute temperature. The ideal blackbody relation is emitted power per area = sigma T to the fourth power; a simple grey-surface model adds emissivity. This is emitted flux, not automatically the net exchange with a warmer environment. A one-layer energy-balance model cannot identify the surface temperature by equating surface emission directly to outgoing radiation at the top of a greenhouse atmosphere.
Greenhouse gases absorb and emit infrared radiation in particular spectral regions. Changes in their abundance affect how efficiently energy escapes to space, while solar input, clouds, aerosols and surface reflectivity also affect the budget. Feedback means a response changes the initial energy perturbation: melting reflective ice can reduce albedo and increase absorbed sunlight, while increased thermal emission with warming tends to restore balance. Clouds can influence both shortwave reflection and infrared emission, so their net effect cannot be inferred from color alone.
A regional radiation deficit is compatible with global balance because the atmosphere and oceans transport energy. Distinguish weather fluctuations, regional averages and long-term global energy accounting. Satellite radiation observations and other measurements constrain models; a simplified calculation illustrates mechanisms rather than providing a complete climate projection.