6.1 Radiation Budget
Earth's energy budget balances incoming solar radiation with outgoing longwave radiation. This balance determines global temperature.
Energy Balance
$$\frac{S_0(1-\alpha)}{4} = \sigma T_e^4$$
Incoming solar = Outgoing longwave at equilibrium
340 W/m²
Avg incoming solar
~100 W/m²
Reflected (albedo 0.30)
~240 W/m²
OLR to space
Python: Energy Budget
#!/usr/bin/env python3
"""radiation_budget.py"""
import numpy as np
sigma = 5.67e-8
S0 = 1361
alpha = 0.30
T_e = ((S0*(1-alpha))/(4*sigma))**0.25
print(f"Effective temperature: {T_e:.1f} K ({T_e-273:.1f}°C)")
print(f"Actual surface temp: ~288 K (15°C)")
print(f"Greenhouse effect: {288-T_e:.0f} K")