N-Layer Atmosphere Radiative Balance

Atmosphere

Greenhouse gas layers (N) 3

Solar constant S 1361 W/m²

Planetary albedo α 0.30

Photon speed 1.0×

Equilibrium Temperatures

No-atmosphere T_eff

–

Surface T_s

–

Greenhouse warming ΔT = T_s − T_eff

–

How it works

This is the classic grey N-layer atmosphere energy-balance model. Each of the N layers is transparent to incoming sunlight but opaque to outgoing infrared, and every layer (and the surface) is in radiative equilibrium: energy absorbed = energy emitted, obeying the Stefan–Boltzmann law F = σT⁴.

No-atmosphere equilibrium:  T_eff⁴ = S(1−α) / (4σ)
With N opaque IR layers:    T_surface⁴ = (N+1)·T_eff⁴
Layer k (k=1 nearest surface, k=N at top):
                             T_k⁴ = (N−k+1)·T_eff⁴

Solving these simultaneous balance equations for a stack of layers shows each added layer raises the surface temperature — this is exactly why more CO₂ / water vapour / methane (more effective absorbing layers) warms the surface even though total outgoing radiation to space is unchanged at equilibrium.

N layers slider — the number of IR-opaque absorbing layers, standing in for greenhouse gas concentration.
Solar constant S — incoming solar flux at the top of the atmosphere (Earth ≈ 1361 W/m²).
Albedo α — fraction of sunlight reflected straight back to space without being absorbed (Earth ≈ 0.30, mostly clouds and ice).
Yellow photons fall straight through every layer (sunlight is not absorbed by the grey IR layers). Orange/red photons are the infrared the warm ground re-emits — each layer they hit has a chance to absorb and re-emit them up or down, exactly the "bouncing" that traps heat and raises T_surface above T_eff.

Real climate models add gas-specific absorption bands, clouds, convection, and ocean heat transport on top of this skeleton — but the N-layer picture is the actual textbook derivation of why an atmosphere with greenhouse gases has a warmer surface than the same planet with none.

Incoming sunlight Outgoing infrared Absorbing layer

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.

Climate Greenhouse Effect Simulation