## måndag 12 april 2010

### On Climate Sensitivity 2

On the Importance of of Black Bodies remind us that according to Stefan-Boltzmann's Radiation Law (heat radiated by a black body is proportional to the fourth power of temperature):
• The ideal black body temperature of the Earth surface is 21 times smaller than that of the Sun, say 5700/21 = 273 K = 0 Celcius.
• Taking variations from albedo and Sun radiation into account, the Radiation Law gives an estimated Earth surface of temperature of  273 - 33 = 240K = -33 C.
• Taking an estimated reduction of emissivity, from "total radiative forcing"  from water vapour and CO2, into account in the Radiation Law, the temperature increases to 288 K = 15 C, which is surprisingly close to the real global mean temperature.
• Changing the emissivity 1% changes the temperature 0.25%.
But how is now "total radiative forcing" determined? So that the corresponding Radiation Law gives the expected 288K? Probably.

Is this the way to compute the "radiative forcing" from doubling CO2 to be about 4 Watts/K m^2? Probably.

Is this the way the corresponding climate sensitivity of 1 C (upon doubling of CO2) is computed? (4 Watts is about 1% of total insolation which gives 0.25% of 273 about 0.7 C temperature increase). Probably.

But in Climate Sensitivity 1 we showed that the Earth with atmosphere does not radiate from the Earth's surface like a black body, because convection coupled with evaporation/condensation changes the heat flux and temperature profile.

Instead it seems to be the top of the stratosphere which radiates according the original Radiation Law at a temperature of 273 K, which seems close to reality.

The computation of radiative forcing from CO2 with corresponding climate sensitivity
0f 1 C, seems to be based on applying the Radiation Law to the surface of the Earth, which
does not seem to reflect correct physics.

From where does then the crucial CO2 radiative forcing of 4 Watts/m^2 with its associated
climate sensitivity of about 1 K upon doubling of C02? Climate Audit traces its origins
to the following formula expressing the "radiative forcing" F in Watts/m^2
upon changing the CO2 concentration to C from a reference value C_0:

F= 5.35 ln C/C_0 ~ 4  if   C/C_0 = 2.

From where does this formula come? Nobody seems to know.  Does the logarithm reflect
some deep law of physics? And the constant 5.35? In IPCC AR4 2007 a reference
is made to IPCC 1990 with a reference to Hansen et al  1988 with the following reference to Lacis et al GRL 1981:
• Radiative forcing of the climate system can be specified by the global surface air temperature change ΔT0 that would be required to maintain energy balance with space if no climate feedbacks occurred (paper 2). Radiative forcings for a variety of changes of climate boundary conditions are compared in Figure B1, based on calculations with a one-dimensional radiative-convective model (Lacis et al, 1981).
But Lacis does not contain the logarithmic formula, only a sketchy derivation of a 1-d model.

This was so far Climate Audit came in Jan 2007. Any progress since then in the search for a derivation of the formula? The formula that underlies the whole of AGW.

The very concept of radiative forcing from CO2 is dubious if the Earth surface insolation is
supposed to be kept constant, since it is this heat which eventually will have to be radiated from the top of the atmosphere,  at about 273 K.

The Earth surface temperature depends on the convection-evaporation/condensation and radiation through the atmosphere as shown in Climate Sensitivity 1 with vastly different temperature profiles with vastly different sensitivity to varying forcing (e.g. varying insolation). The broken temperature profile with small sensitivity seems to be closer to reality.

The most direct way of estimating climate sensitivity is to consider the 280 W/m^2
being absorbed by the Earth surface, which is eventually re-emitted from the top of the atmosphere at 273 K while the surface temperature is 288 K.  The temperature sensitivity
total insolation would thus be 15/280.

A radiative forcing perturbation of say 2.8 W/m^2 would then give rise to an increase of surface temperature of 0.15 K. To be compared with the above 0.7 K inflated by feedback to 1.5 - 4.5 K or more by IPCC.