The greenhouse effect is the most fundamental mechanism in climate science: atmospheric gases trap outgoing infrared radiation, warming Earth's surface above the temperature dictated by simple radiative equilibrium with the Sun.
This simulator implements the Stefan-Boltzmann framework with greenhouse optical depth. Without greenhouse gases, Earth's effective temperature T_eff is determined solely by the balance between absorbed solar radiation S(1-α)/4 and emitted thermal radiation σT⁴. For Earth's current albedo (α ≈ 0.3) and solar constant (S ≈ 1361 W/m²), this gives T_eff ≈ 255 K = -18°C — far below the observed ~15°C.
The difference is the greenhouse effect. Atmospheric gases create an optical depth τ that traps a fraction of outgoing IR, warming the surface to T_surface = T_eff·(1+τ/2)^(1/4). The optical depth increases logarithmically with CO₂ concentration, meaning each doubling of CO₂ produces roughly the same additional warming — about 3°C according to the IPCC's best estimate.
Arrhenius was the first to quantify this in 1896, calculating that doubling CO₂ would warm the planet by ~5°C. His physics was sound; the overestimate came partly from neglecting negative feedbacks. Manabe and Wetherald (1967) produced the first rigorous general circulation model confirming the logarithmic relationship.
The largest uncertainty in modern climate projections comes from cloud feedback. Low clouds reflect sunlight (cooling), but may decrease in a warmer world, amplifying warming. High clouds trap IR (warming) and may increase. The net effect of clouds on climate sensitivity remains the dominant source of uncertainty in IPCC assessments.