## Tuesday, November 8, 2011

### The Learning Equation - Kimoto Modified

I played around with the Atmospheric R values, just to show there is more than one way to skin a cat fish. The best way I am firmly convinced is the modified Kimoto equation.

As a refresher, Kimoto is base on the simplification of the S-B relationship where dF/dT=4F/T, or the change in flux with respect to the change in temperature is equal to or "proportional" to four times the flux divided by the temperature. That is an approximation and it is not truly a linear relationship.

Depending on your choice of a frame of reference, the approximation could be 5F/T or just F/T, S-B has a forth power relationship between temperature and flux.

Using the 4F/T is equivalent to using 255K as a reference temperature. If I use the surface as my frame of reference, then the modification, a*4F/T is required where a is a variable dependent on the thermodynamic reference with respect to 255K. Only you can make a suitable to any other reference temperature just by changing the charact5eristics of a. Simple right? Evidently not so much for a lot of people, but that is how it works.

Once people get beyond that silly 4, they begin to realize you can make the equation approximately a linear relationship for small changes from any consistent Thermodynamic frame of reference.

The neat part is once that sinks in, you can see how flexible that simple equation can be. aFt + bFl + eFr, for thermal, latent and radiant. I mentioned in a previous post the F? should always be considered. We are dealing with a dynamic system so there are going to be surprises. That is the beauty of the modified equation, it can learn with you.

Fr can be split into Fr(GHG) + Fr(water,liquid) + ... F sub whatever you either have good information on or wish to learn more about. Fr can be separated into a complete line by line(LBL) spectral analysis if you wish.

The whole equation can be used for dF/dT surface, dF/dT 600mb or any reference layer you wish to study in any direction by just adjusting the coefficients for the reference temperatures of source and sink. dF/dT tropics with dF/dT sub-tropics could be used for average energy transfer between regions. It is a powerful equation, as long as you reference back to a common frame of reference.

Since boundary layers are plentiful and hard to deal with in fluid dynamics, using a boundary as a reference from in two directions could simplify resolution of changes in boundary layer flex changes with time. I haven't tried that yet, but it appears very likely.

By skipping boundary layers, ie surface to tropopause versus surface to stratopause you can compare effective emissivities to help resolve solar impacts in the atmosphere. As long as you have sufficient temperature and pressure resolution of the target layers, you can double check flux relationships between layers.

Most importantly, you can select layers where the best temperature data is available, like the 500mb mid-troposphere satellite data.

The more physical data you have, the more you can learn about F?