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Home/Biophysics, Fluids & Geoscience/Greenhouse: One vs Two Slabs

Greenhouse: One vs Two Slabs

Compare gray-atmosphere surface temperature for one IR slab vs two coupled slabs; albedo α and absorptivities.

Solar & albedo

1361 W/m²
0.3

Blackbody shells in radiative balance: effective emission temperature T_eff satisfies σT_eff⁴ = (1−α)S/4. One isothermal atmospheric shell raises the surface to σT₁⁴ = 2·(1−α)S/4; two nested shells give σT₂⁴ = 4·(1−α)S/4 — a textbook ladder explaining why multiple absorbing layers warm the surface more than a single slab at the same albedo.

Measured values

T_eff (σT⁴=S₀)-18.6 °C
T_surf one shell29.6 °C
T_surf two shells86.9 °C

S₀ = (1−α)S/4 is absorbed shortwave per unit area in this cartoon; see also the single gray-slab simulator in Astronomy for emissivity-based variants.

Live graphs

About this model

A stack of blackbody isothermal atmospheric shells in radiative balance with shortwave absorption (1−α)S/4 at the surface illustrates how adding layers increases surface temperature while keeping effective emission temperature tied to outgoing longwave. Compare one shell (σT₁⁴ = 2S₀) with two shells (σT₂⁴ = 4S₀) in the same normalized flux units.

Who it's for: Climate physics introductions contrasting gray-slab counts.

Key terms

  • Greenhouse effect
  • Energy balance
  • Albedo
  • Effective temperature

How it works

Analytic comparison of effective temperature versus surface temperature for idealized one- and two-shell greenhouse models at the same planetary albedo.

Frequently asked questions

Why black shells instead of emissivity sliders?
To keep the algebra closed-form; see the astronomy single-slab simulator for emissivity-based gray variants.