Single-Layer Energy Balance

This interactive simulator explores Single-Layer Climate (Toy) in Astronomy & The Sky. S, α, ε: T_eff vs T_surface from gray-slab balance — intuition only. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.

Who it's for: Suited to beginners and first exposure to the topic. Typical context: Astronomy & The Sky.

Key terms

  • single
  • layer
  • climate
  • toy
  • single layer climate
  • astronomy
Effective (space)
-19°C
Surface (slab model)
15°C

Bar heights are **schematic** (linear in °C for display only). Compare how **ε** lifts the surface bar while **α** lowers both.

How it works

**Energy balance** cartoon: incoming **(1−α)S/4** matches outgoing longwave in a **highly simplified** single-layer atmosphere. Turn **ε** and **α** to see why **effective** temperature (what Earth radiates to space) can stay near **255 K** while the **surface** is warmer — the usual first lecture, not a climate model.

Key equations

(1 − α)S/4 = σT_eff⁴ · slab: (1−α)S/4 + σT_a⁴ = σT_s⁴, εσT_s⁴ = 2σT_a⁴
⇒ T_s⁴ = (1−α)S / (4σ(1 − ε/2))