Saturday, October 8, 2011

Just For Fun

I don't like taking life or myself too seriously. Solving that equation was fun, but no one cares. I will let everything sit for a while the do a few rewrites.

I do have a semi final form of the equation,

dF/dT=(1.32*a*Fc+4.39*b*Fl+3.3*c*Fra+1.56*d*Frs)/T where Fc is conductive flux, Fl is latent flux Fra is Radiative flux in the GHG spectrum and Frs is the radiative flux in the window to space. T, is in K and the Fs are in Wm-2.

The variables a through d are undetermined equations for the relationships between fluxes. a for example would be change in conductivity, b the change is convectivity, b change in GHG emissivity and d the change in atmospheric window emissivity. If you divide the R value by 4 you have the initial values of each impedance. i.e. 0.33 is the impedance to Fc, multiplied by 4 = 1.32, which I am calling resistance. I need to double check the Frs and Fra relationships because that may be a little more non-linear, so use with caution. So far it has worked like a dream, but I type like crap and proof worse.

As I mentioned in an earlier post, the conductive flux resistance is equal to the potential energy divided by the flux, similar to Ohms law, were V=IR. R,the conductive resistance of the atmosphere is equal to the potential 288-216 divided by thermal current or flux 24, 288-216/24=3. the coefficient for a in aFc =1/R=0.33 and I have not named that value. For bFl, Rl=(288-216)/79=0.91 b=1/Rl=1.097. For the radiative values, Rr=(288-216)/87=1.21 e=1/1.21=0.825. Why did I chose 87 when the NASA drawing shows 79? Because it appears to have a small error. 79 plus the portion of the radiation through the atmospheric window is the correct value, 87-79=8.

If you want to solve for the atmospheric effect,

dF/dT=(1.32*a*Fc+4.39*b*Fl+3.3*c*Fra+1.56*d*Frs)/T - GHE = (1.32*a*Fc+4.39*b*Fl)/To

This is a bit of a shock to some, but you can assume no radiative greenhouse effect, but the Earth still has an atmosphere even without greenhouse gases. If you assume to=255, then you will come close to the classic 155Wm-2 and 33K. without water, you can drop the Fl term. I haven't solve it, but since the atmospheric sensitivity is 2.08 to all forcing and roughly 1.31 at t=288, the no GHG sensitivity is roughly 1.16 at 255K. It would involve a few recursive calculations to hone in the correct temperature.

The 3.3Wm-2/T is very accurate for the change in forcing for the Fra term, A doubling of CO2 will cause about 0.79 K increase in temperature, with some feed back for ~1.2 but completely closing the GHG window only produces, 2.01 degrees of warming. There seems to be a very close limit to saturation.

So anyone wants to play around with what if's have a ball. Remember the R values are variable and I have not determined their equations. Anyway, the equation works like magic, but I need an interpreter to explain why it works.

The R values are for F/T = 390/288 Since they are non-linear to a point, the values are only good for a small range, +/- 50Wm-2 approximately.

The equation indicates the the atmospheric sensitivity, dF/dT, to all forcings is 2.08 and that the maximum sensitivity to CO2 is when 3.3 increases to 4.4, a little tricky since that is what varies, which change Fra.

Well, I will take some time off and try to find some work.

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