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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]

A blackbody absorbs all incident radiation and, in thermal equilibrium, emits the Planck law spectrum with integrated flux $\sigma T^4$. Earth reflects some incoming sunlight, while its surface and atmosphere absorb and emit selectively with wavelength. With solar irradiance $S_0$ and Bond albedo A, the equilibrium planetary effective radiating temperature isReflection lowers this temperature relative to the zero-albedo value. The greenhouse effect makes the surface warmer than the effective emitting temperature: in a simple diagnostic $\mathrm{OLR}={ϵ}_{\mathrm{eff}}\sigma T_s^4$, $T_{\mathrm{eff}}={ϵ}_{\mathrm{eff}}^{1/4}{T}_s$. This effective emissivity summarizes atmospheric transfer, not a universal material constant. At fixed absorbed sunlight, greenhouse warming does not require a different equilibrium outgoing flux. ^[ref]

The stated $0.9\mathrm{W}{\mathrm{m}}^{-2}$ is positive net energy uptake, not necessarily the imposed radiative forcing itself. A linear climate forcing-response energy balance isHere F is the perturbing forcing, $\lambda \Delta T$ is the net stabilizing radiative response and C is an effective areal heat capacity. The residual heats the Earth system, mainly through ocean heat uptake, with additional storage and melting. Finite heat capacity and ocean exchange delay equilibration. The imbalance alone determines neither F, the warming rate without C, nor the eventual equilibrium warming $F/\lambda$. Feedbacks change the response coefficient. The given number is treated as the examination's premise, not a present-day observational estimate. ^[ref]

Clouds reflect shortwave sunlight, usually cooling the planet, and absorb and emit thermal infrared radiation, usually warming the surface relative to clear sky. Their net effect depends on altitude, temperature, optical depth, phase and the underlying surface: thick low clouds often have strong shortwave cooling, while cold high clouds can have a comparatively strong longwave warming effect. Surface and top-of-atmosphere budgets must be distinguished; absorbing radiation within a cloud can heat the atmospheric layer while shading the ground.

Condensation and freezing release latent heat; evaporation and melting absorb it. These processes change buoyancy, stability and convective transport. Entrainment of dry air can evaporate droplets and cool the cloud edge, while precipitation removes condensate and water.

Microphysics controls the radiative properties. For liquid droplets with a fixed liquid-water path W, the cloud optical depth at fixed liquid-water path is approximatelyThus more numerous smaller droplets at fixed W give a brighter, optically thicker cloud: the Twomey effect. Ice habit, phase and particle-size distribution also alter scattering, absorption and precipitation. Cloud-water and lifetime adjustments need not preserve W, so a microphysical perturbation has no universal net radiative sign. ^[ref]

There are several distinct radiative pathways:

Solubility and optical absorption are independent properties: insoluble does not mean absorbing, and soluble does not mean nonabsorbing. Coarse particles can also affect terrestrial infrared radiation, while dark-particle deposition on snow can lower surface albedo. These effects should not be folded into a single universal aerosol cooling rule. ^[ref]

For a gas whose lifetime is much less than the selected horizon, the numerator of its global warming potential has nearly saturated: ${\int }_0^H{a}_i{m}_i(t)dt\simeq a_i{m}_i(0){\tau }_i$. The carbon-dioxide denominator continues to accumulate because of its long-lived response. Consequently a shorter horizon usually gives a larger GWP for this short-lived substitute; a longer horizon gives a smaller GWP. If the horizon becomes comparable to, or shorter than, the substitute's lifetime, the numerator also depends strongly on the horizon and cannot be replaced by its infinite-time limit.

The horizon is a value choice, and integrated forcing is not the same as temperature at a chosen future date. Equal-GWP pulses can therefore have different near-term warming and long-term temperature paths. The result also depends on greenhouse gas radiative efficiency, background concentrations, lifetime estimates and which indirect chemical effects or feedbacks are included. A pulse-based metric does not by itself describe a continuing emissions trajectory, nor does it measure ozone depletion or local air-pollution impacts. Comparisons should state the horizon, the emission scenario and the chosen climate outcome.^[ref]

For a liquid cloud at fixed water content and geometrical thickness, more cloud condensation nuclei can produce more, smaller droplets. The increased total extinction area raises optical depth and reflected sunlight: the Twomey effect gives negative shortwave radiative forcing. It is an indirect aerosol effect mediated by cloud microphysics, rather than direct aerosol scattering.^[ref]

Smaller droplets can also delay collision-coalescence and drizzle, potentially increasing liquid-water retention, cloud lifetime or coverage; that adjustment would usually strengthen cooling for low reflective clouds. It is not universal: evaporation and mixing with dry air can reduce water content or cloud cover, and dynamical changes can oppose the simple lifetime argument. Absorbing particles can heat an atmospheric layer, sometimes evaporating cloud and producing a positive semi-direct forcing, but their vertical position can instead stabilize a cloud layer and reverse the response. Aerosols can additionally alter ice nucleation and mixed-phase precipitation, with no single forcing sign independent of cloud type. The net response combines shortwave reflection and longwave thermal effects, and depends on cloud height, optical depth and adjustments. Thus the fixed-water Twomey sign is robust within its assumptions; adjustment and ice-cloud signs require context.^[ref]

Piers Forster works on the planetary energy budget, radiative forcing, climate feedback and climate sensitivity. He is a coordinating author of an assessment chapter bringing those quantities into one quantitative framework.^[ref]

The distinctions matter physically: a forcing perturbs the energy budget, while feedback describes how the radiative response changes as the climate state changes. The inferred sensitivity also depends on the response timescale and on how those quantities are defined and estimated.