## Arking on NIR Water Vapor

The theory of anthropogenic CO2 forcing is that outbound IR radiation is plugged up a little more in the atmosphere, causing a steeper lapse rate and warmer surface. The issue of inbound NIR water vapor absorption is that, if inbound NIR solar radiation is plugged up a little more in the atmosphere, then you would presumably have the opposite effect. If NIR water vapor absorption parameters were under-estimated (as appears to have been the case in GCMs, it seems to me that you would have an over-estimate of water vapor feedback effects, which could be quite important as climate change projections seem to me to be levered to water vapor multiplier effects. It also seems to me that errors in NIR parameterization could explain some GCM defects, such as a too negative tropopause temperature. Some of these questions were passed very indirectly to Alan Arking, who argued that such errors do not matter. Here are some of his comments. more

1. Jeff Norman
Posted May 3, 2005 at 5:53 AM | Permalink

This summary is difficult to read until you have figured out who is responding to whom.

A program of the players would have been useful.

Otherwise some interesting thoughts and comments.

2. John Creighton
Posted Jul 5, 2006 at 9:19 PM | Permalink

Can we model this with simple physics?

Black body radiation is proportional to the power squared:
F=k1*T^4 (1)
Differencing with respect to x:
dF/dx=4*k1*T^3*dT/DX (2)
The fraction of the power absorbed per distance is proportional to the percentage of gas:
dF/dx=k2*rho*F——- (3)
Thus:
k2*rho*F=4*k1*T^3*dT/Dx ——- (4)
The change in pressure with respect to altitude is given by:
dP/dx=rho*g*x ——- (5)
From the ideal gas law and the above equation
P=rho RT ——- (6)
Thus:
rho*(g/R)*x=R*(T*d{rho}/dx+rho*dT/dx) ——- (7)

The last piece of the puzzle is the inverse greenhouse effect as the earth must emit what it absorbs. The power absorbed over a given height is over the cross section a circle (A1) while the power emitted is over the area of a sphere (A2).

Fin/dx=-k3*rho*Fin ——- (8)

dF/dx=1/(d(A2)/dx)*Fin*(A1/A2) ——- (9)
dF/dx=1/(2*4*pi*(x+xo))*Fin*(pi*(x+xo)^2)/(4*pi*(x*xo)^2) ——- (10)
dF/dx =Fin/(32*(x+xo) ——- (11)

Thus ignoring convection and conduction which I think we can do at high altitudes, the laps rate is described by the system of differential equations (7), (4) (8) and (11). To include conduction and convection just change equation 1 and the rest follows. The fractionating of the gases can be dealt with by statistical thermodynamics.

I might try this sometime in the future to see how close an answer it gives us to the actual lapse rate and see how changing the constants k2 and k3 affect the laps rate. As of now I am not sure if the change in the lapse rate is the most significant factor or if it is the pushing of the isothermal curves to higher altitudes.