I'm sure Columbia University is a fine liberal arts school ... their business and law schools are world famous ... unfortunately, they don't offer any classes on climatology, only a non-credit lecture series that's open to all students ... and this blerb you've presented seems to be a part of the lecture series, it is certainly written to the high school level
Not even high school level and that pretty much sums up the state of climate sceince...
And do you ever actually research anything at all?
Mission - The Earth Institute - Columbia University
Atmospheric Science | Earth and Environmental Sciences
Denial of the state of climate science hardly changes the fact...
The blerb describes how a gardener's greenhouse works ... as this is very accessible to the typical high school student ... something many of them have been in and experienced the warmer temperatures first hand ... the university isn't on the hook for issuing credits, so this is fine ... but the notion of different IR layers in the atmosphere is ridiculous, unless you mean the entire atmosphere, one layer ... one emissivity value ...
And no..it does not describe how a garden greenhouse works...a garden greenhouse works by blocking convection of energy radiated from the floor...there is no "second absorptive layer" which "doubles" the amount of energy being radiated from the floor...
And yes it is ridiculous, but alas, that is the state of climate science...
That is some artistic math, for liberals ... eq. 7 must be a misprint, F isn't defined anywhere ... the high schoolers' eyes have already glazed over, no one's bother to fix that ... Eq. 10 did wind up being SB greybody, set e = 1/(1+N) set N to infinity ... [smile] ... and integrate ... but no sense making the kids wet their pants ...
Again...that is the state of climate science...interesting that you are unaware of this.
from the University of Washington atmospheric sciences department which they say describes the mechanism of the greenhouse effect.
Note the equation at the bottom..the claim is that if you have a radiator emitting X W/m2 and add another radiator emitting X W/m2, you end up with a radiator emitting 2XW/m2. So if you have a pot of water at 100C and add another pot of water at 100C, you end up with a larger pot of water at 200C.
Here is one from Pen State
There are any number of graphics more or less just like this one which is just like the one from Columbia university...they all show the same thing and use the same equations...they all apply the SB equation to the atmosphere and claim that absorption and emission of IR by the atmosphere doubles the amount of energy present.
I've expressed my disdain of "climate science" ... I fully understand the foolish things they say ... but I've tried to explain blackbody radiation to high school kids as well, so I understand some liberties need to be taken ... I don't know if I would offer bogus math, but none of them was paying me either ... my mistake I guess ...
Maybe so, but you do defend the radiative greenhouse effect and you see the model of it and how it is derived... Like I said...there is no radiative greenhouse effect as described by climate science...
Eq. 8 is wrong ... where the numeral "2" is should be a gradient ... [shrugs shoulders] ... that's why God invented third year calculus ...
And yet, every atmospheric physics department associated with climatology teaches the same thing...the equation is not a misprint, or an error....it is part and parcel of the radiative greenhouse effect as described by climate science...and the basis for the AGW hypothesis...