Concise Notes on Global Temperature and Greenhouse Effect

Global Temperature Models

  • Models range from simple calculations to complex 3D atmospheric general circulation models (GCMs).
  • These models predict climate on regional and seasonal basis.
  • Focus on factors influencing global temperature.
  • Crucial climate variables: winds, ocean currents, precipitation, soil moisture, runoff, snow cover, polar sea ice, and glaciers.

Earth as a Blackbody

  • Blackbody: an object that absorbs all radiation and radiates at the maximum rate.
  • Solar constant (S): average annual intensity of solar radiation, S = 1372 W/m^2
  • Rate of energy absorption: E_a = S \pi R^2
  • Energy radiated: E_r = \sigma 4 \pi R^2 T^4 where \\sigma = 5.67 \times 10^{-8} W/m^2K^4
  • Under steady-state conditions, energy absorbed equals energy radiated: S \pi R^2 = \sigma 4 \pi R^2 T^4
  • Solving for Earth's temperature (T): T = \sqrt[4]{\frac{S}{4\sigma}} = 279 K

Radiation Balance Model with Albedo

  • Albedo (\alpha): fraction of incoming solar radiation that is reflected.
  • Earth's albedo is about 30%.
  • Absorbed energy equals reradiated energy: S(1-\alpha)\pi R^2 = \sigma 4 \pi R^2 T_e^4
  • Effective temperature (Te): Te = \sqrt[4]{\frac{S(1-\alpha)}{4\sigma}}
  • Substituting values: T_e = 255 K

The Greenhouse Effect

  • Wien's displacement rule: \lambda_{max} = \frac{2898}{T}
  • Incoming solar energy is short-wavelength radiation; energy radiated from Earth is long-wavelength (thermal) radiation.
  • Oxygen and ozone absorb incoming solar radiation with wavelengths less than 0.3 μm (ultraviolet).
  • Greenhouse gases: water vapor (H2O), carbon dioxide (CO2), nitrous oxide (N2O), and methane (CH4).
  • Atmospheric radiative window: between 7 and 12 μm.
  • Greenhouse gases trap outgoing thermal radiation, heating the atmosphere, which radiates energy back to Earth.
  • Greenhouse effect (°C) = Ts - Te
  • Earth's greenhouse effect adds 33 °C of warming.
  • Incoming solar radiation: \frac{S \pi R^2}{4 \pi R^2} = \frac{S}{4} = 343 W/m^2
  • Incoming radiation reflected: 0.30 \times 343 W/m^2 = 103 W/m^2
  • Incoming radiation absorbed: 0.70 \times 343 W/m^2 = 240 W/m^2
  • Energy radiated by surface: \sigma T^4 = 5.67 \times 10^{-8} W/m^2K^4 \times (290 K)^4 = 401 W/m^2

Global Warming Problem

  • Sources of greenhouse gases: population, economic activity, technology.
  • Other greenhouse gases: nitrous oxide, methane, and chlorofluorocarbons (CFCs).
  • Climate changes impact agriculture and ecosystems.
  • Rising temperatures cause thermal expansion of oceans.
  • Approaches to climate change: adaptation and prevention.

Carbon Dioxide

  • Arrhenius (1896) made the first calculations on global temperature as a function of atmospheric CO2 content.