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Home/Biophysics, Fluids & Geoscience/Urban Heat Island Energy Balance

Urban Heat Island Energy Balance

Urban heat islands arise because city surfaces absorb, store, and release energy differently from vegetated rural surfaces. This simulator compares two zero-dimensional surface slabs, urban and rural, each obeying C dT/dt = (1−α)S(t) + Q_F − εσ(T⁴−T_sky⁴) − h(T−T_air). Albedo α controls absorbed sunlight, heat capacity C controls thermal inertia and phase lag, anthropogenic heat Q_F represents waste heat from buildings and traffic, and h is a bulk turbulent exchange coefficient with the air. The model integrates several days and plots the final diurnal cycle: urban and rural surface temperatures, air temperature, and ΔT = T_urban − T_rural. Low albedo and waste heat raise daytime temperature, while high urban heat capacity delays the peak and sustains a night-time heat island after sunset.

Who it's for: Students in environmental physics, urban climate, meteorology, and sustainability courses learning first-order energy-balance controls on urban heat.

Key terms

  • Urban heat island
  • Surface energy balance
  • Albedo
  • Heat capacity
  • Anthropogenic heat
  • Diurnal cycle
  • Thermal inertia
  • Longwave radiation

Live graphs

Urban surface

0.12
0.24
4.5 MJ/m²/K
1.6 MJ/m²/K
45 W/m²
850 W/m²
25 °C
6 °C
18 W/m²/K
17 h

Two 0-D surface slabs: C dT/dt = (1−α)S(t) + Q_F − εσ(T⁴−T_sky⁴) − h(T−T_air). Large C delays the peak and releases heat at night; low α and Q_F increase urban temperature.

Measured values

Current ΔT_u-r-2.23 °C
Max ΔT_u-r2.99 °C
Night ΔT at 05:001.55 °C
Urban peak lag29.4 h after noon

How it works

Urban heat island energy balance: albedo, heat capacity, anthropogenic heat, and day/night temperature lag.

Key equations

C dT/dt = (1−α)S(t) + Q_F − εσ(T⁴−T_sky⁴) − h(T−T_air)
UHI(t) = T_urban(t) − T_rural(t); larger C → day/night lag

Frequently asked questions

Why can the heat island be strongest at night?
Dense materials such as asphalt, concrete, and masonry store heat during the day and release it after sunset. Rural surfaces with lower effective heat capacity and more evaporative cooling cool faster, so the urban-rural temperature difference often peaks at night.
What does albedo change?
Albedo is the reflected fraction of shortwave sunlight. Lower α means more absorbed solar power and warmer surfaces; cool roofs and brighter pavements raise α and reduce daytime heating.
What is anthropogenic heat?
It is waste heat from air conditioning, traffic, industry, and buildings. In the model it is a constant W/m² source, which especially matters at night when solar input is zero.
What is left out?
Evapotranspiration, wind profiles in street canyons, building geometry, shading, clouds, moisture, horizontal advection, and human heat-stress indices are not modeled.