tisdag 5 april 2011

Simple Climate Model: Thermodynamics, Radiation and Observation

In the spirit of my article in Slaying the Sky Dragon, consider the following facts:
  • The Earth with atmosphere absorbs 240 W/m2 sunlight and emits 240 W/m2 IR.
  • The Earth surface temperature is 288 K.
  • By Stefan Boltzmann 240 W/m2 corresponds to an effective blackbody temperature of 255 K (with an albedo of 0.3). The difference 288 - 255 = 33 C can be seen as the total warming effect of the atmosphere.
  • 40 W/m2 is emitted directly from the Earth surface through an "atmospheric window".
  • The climate system acts as an air conditioner in a combined thermodynamic-radiation cycle processing the remaining 200 W/m2.
  • The effect of this process is to reduce the lapse from the base (dry adiabatic) value of 9.81 C/km to the observed 6.5 C/km, thus with a reduction of 3.5 C/km per 200 W/m2 or total cooling effect of 18 C, since the temperature is observed to be 255 K at a height of 5 km.
  • The reduction of the lapse results mainly from the thermodynamics by evaporation/condensation, which has a cooling effect by lowering the temperature at low altitudes by evaporation and increasing the temperature by condensation at higher altitudes.
  • Suppose now the atmospheric window is decreased by additional greenhouse gases by 4 W/m2, which are to be handled by the combined thermodynamic-radiation process.
  • Suppose the 4 W/m2 are splitted equally between thermodynamics and radiation.
  • Additional 2 W/m2 to be processed by thermodynamics means 1% reduction of the lapse rate with corresponding cooling effect of about 0.18 ~ 0.2 C.
  • Additional 2 W/m2 to radiation gives a warming effect of about 0.5 C by Stefan-Boltzmann.
  • The net is a warming effect of 0.3 C.
  • In other words, with standard terminology, we find a climate sensitivity of 0.3 C, to be compared with IPCC´s value in the range 1.5 - 4.5 C, which is 5 - 15 times bigger.
I believe this argument is the simplest possible combining thermodynamics with radiation and observations. It is possible that it contains an element of truth.

2 kommentarer:

  1. Claes, maybe it is simple but it simply leaves out considerations of heat transfer by convection at the surface particularly at the ocean surface and also evaporation. This simple analysis by E M Smith http://chiefio.wordpress.com/2011/04/03/perspective-on-rain-and-heat/ is worth considering (I have not checked the maths but from a rough look seems OK).
    Both convection and evaporation are affected by the wind velocity and involve the Nusselt and Reynolds dimensionless numbers.
    Actually, I wonder why you do not use the mathemetics of dimensional analysis.
    Then, one has to take account the insignificant absoption of radiant energy by CO2 when considered in empirical relations found principly by Prof Hoyt Hottel in measurements on gases in furnaces and heat exchangers. Hottel found a relation which involved the theoretical emissivity of CO2 (from the absorption spectrum) at the temperature of the source, the product of gas partial pressure and the beam length, the actual total pressure and the temperature of the gas.

  2. Yes, it is simple. The question is if this simple model contains an element of truth. Evaporation (and condensation) is included as the main mechanism of reducing the lapse rate by 3.5 C/km, a dominant effect.