On Climate Sensitivity 1

Consider the following basic model for vertical heat transfer in an atmosphere (troposphere + stratosphere) represented by the interval [0 , 1]:

                    T_t + aT + bT_x - cT_xx = q,   

                    -c T_x(0,t)  =Q(t),   T(1,t)=0, 

where T(x,t) is temperature at position x at time t, the subindices t and  x indicate differentiation, a is coefficient of net outgoing radiation, b is convection velocity, c is coefficient of heat conduction/radiation, q internal forcing from evaporation/condensation, and Q(t) is incoming heat from the ocean (from insolation). 

The basic stationary case is Q(t)=1 constant, a =0, b=0, q=0 and c constant, which gives T=(1-x)/c with corresponding temperature sensitivity T(0)=1/c which is large if c is small. This is the right curve above with slope - 1/c reflecting that heat is transported by conduction with consistent negative temperature gradient: High temperature sensitivity to forcing Q.

Consider now the case q = -1 for x in [0, 0.5] (evaporation) , q = 1 for x in (0.5, 1] (condensation) and b =1 (upward convection), c small, with Q (t)= 1 as above, which in the stationary case gives T(x) ~ -x for x in [0,0.5] and T(x)= x - 1 for x in (0.5, 1], with T(0)=0: Low temperature sensitivity. The corresponding temperature is represented by the broken left curve, which mimics the real temperature decreasing in the tropsphere and increasing in the stratosphere. In this case heat is transported mainly by convection and the temperature gradient changes sign because of evaporation/condensation. 

We conclude that convection coupled with evaporation/condensation, like in the real atmosphere, can change temperature sensitivity drastically, and since climate sensitivity is related to temperature sensitivity,  also climate sensitivity can be drastically reduced as compared to that of the simplest radiative model underlying simple calculations of climate sensitivity based on conduction/radiation without convection.

In the boiling pot analogy increasing the forcing results in more vigorous boiling but the 

temperature stays the same, and the temperature sensitivity is zero.  It is likely that

Roy Spencer's upcoming report on climate sensitivity will have a similar message.

Compare with a common Green House GH, which has high temperature sensitivity because convection is prevented by the glass enclosure. The basic climate sensitivity of 1 degree Celscius upon doubling of CO2 in the atmosphere is computed with this model as basis, which thus may exaggerate sensitivity, which in IPCC AR4 is exaggerated even more by positive feed-back, from water in particular vapour, in contradiction to the above model with evaporation.  

To call CO2 a Green House Gas GHG, which is done by IPCC, thus appears questionable.

Nevertheless, the above analysis is supported by the following statement from IPCC 2007 Summary for Policymakers:

• Some aspects of climate have not been observed to change.
  

I will return to the dynamics of the model.