For those of you into light reading,you may have noticed that the polar flux readings are wild and crazy, particularly in the Antarctic. I firmly believe that understanding what is going on way down under is key to figuring out what changes CO2 would have on the Atmospheric effect. The numbers available, well, they ask more questions than they answer.
Simplifying the down under, looks to be possible with considering the changes in thermal conductivity and Kenimatic viscosity in the coldest of climates. Basically, the conductive flux in the Antarctic is nearly twice the global average and CO2 has a small but apparently significant impact on the thermal conductivity. Very interesting. This tends to indicate that flux changes in and above the tropopause have much greater impacts on surface cooling in the Antartic region. That is nothing new, only that the conductive change still appears to be the main known unknown and that the Kimoto Equation using surface and mid tropospheric temperatures may provide a simplified method of analyzing the impacts which appear to be becoming more obvious each day. For those playing with the Equation, ~0.61Fc and ~0.71Fr are the new Antarctic approximations with Fl being unknown but much smalerl because of the cold dry environment. Using -24.7 C and 600mb as the tropospheric reference to determine change in atmospheric effect.
Since the Thermal conductivity and kenimatic viscosity can be approximated with known surface temperature and pressure, the approximations for the equation should be fairly close. It will still require some tweaking, but it should be possible to estimate surface flux values with reasonable accuracy.
Basic Reasoning: Thermal Flux Boundaries
Since the Kimoto Equation is a touch novel, somewhat novel approaches may be required to estimate the significance of physical properties that impact the flow of thermal energy. Boundary layers are well known and mainly applied to conductive and convective heat transfer with radiant a bit of an afterthought or considered separately
Looking at the Antarctic data available, the thermal conductivity and convectivity need to be considered separate to the Latent flux, i.e.,Fc proportional to F(I) plus F(v) for (i) conductive and (v) convective or viscous flux. This allows the application to be expanded to denser gases and liquids. The latent associated phase change also includes a sensible component, Fl = Fl(l) plus Fl(s). Then if the atmosphere being analyzed does not include significant phase change, The Fl term can be approximated as zero.
This is beneficial in the Antarctic where water phase change at the surface is minimal. However, phase change of both water and carbon dioxide cannot be ruled out in higher layers where microscopic scale changes are possible with extreme low temperatures and photon interaction and at extremely high pressures, near constant temperatures and densities in the deep oceans, the 4C boundary for example.
The equation should be adaptable to all layers and boundary conditions.
This allows some minor trickery to be used. By considering a parallel circuit so to speak, only one flux at a time can be used to determine an approximate maximum value for that portion of the total flux with local conditions. In the Antarctic, using the simplified form, aFc+bFl+eFr with surface temperature ~224 (-49C) Maximum values for a and e can be determined assuming b is small. Then the approximate values of a and e can be compared to the properties of air at local temperature and pressure to a standard reference, -24.7C @ 600mb, the global average potential temperature and pressure of the atmospheric effect.
As noted previously, this standard reference is subject to change by +/- 4C approximately due to the uncertainty of the Virgin Earth surface temperature and Tropopause altitude. That adds to the complexity of the solution, but is not insurmountable.