The Earth isn't a blackbody, it's a greybody.
Approximating the planets as black bodies works just fine for calculating their average temperature as long as they do not have an atmosphere with greenhouse gasses in it.
I didn’t get past the first paragraph before it became apparent this is the typical Spencer blogging crap. Spencer’s blogging has only a passing resemblance to what he actually publishes, and he typically says things he knows he would never get passed peer review and is driven by his political and religious beliefs far more then anything appears in the actual science.
Allow me to quote that first paragraph for you:
I get an amazing number of e-mails from engineers who point out that the climate system can not be dominated by positive feedback, because that would mean the climate is unstable, in which case it would have careened out of control long ago.
I happen to be an Electrical Engineer who has done some control systems work, and the claim that if the earth (or anything else) were driven by positive feedback it would careen out of control is categorically untrue. He is either making up stories of engineers saying this or the ones who did have little to no experience with control system.
Again, positive feedback can be unstable, but that isn’t even close to being universally true. In fact open loop low gain systems (like the earths climate) with positive feedback are generally stable. In systems like this positive feedback manifests as making it more sensitive to input changes, something we know is true of the earths climate.
Next he goes on to say:
But in the climate research world, the dividing line between ‘positive’ and ‘negative’ feedback is not whether extra energy is gained or lost with warming, but whether the increase is greater (or not) than the ‘temperature-only’ increase in infrared energy loss with warming.
While the earth does radiate more IR as it warms this
IS NOT feedback in and of itself. Feedback, as the name implies, means part of the output is fed back to the input. Outgoing IR on it’s own does not add to or subtract from the effective incoming energy. In contrast greenhouse gasses create “back radiation”, they intercept outgoing IR and redirect it back down so it effectively adds to the incoming solar energy.
In the absence of feedbacks, this temperature-only response is estimated to be about 3.3 Watts per sq. meter per degree C at the effective radiating temperature of the Earth, which is about 255 Kelvin (-18 deg. C).
Of course, what this also means is that if positive feedbacks exceeded that 3.3 Watts, then we really DO have an unstable climate system. So, in some sense, the climate system is always 3.3 Watts in positive feedback away from oblivion.
The simplest form criteria for stability of a positive feedback system is that the open loop gain A * the feedback factor B is less then 1. A*B < 1 (in this case A > 1 would violate conservation of energy) What he’s doing above if throwing out a red herring to disguise the fact he’s assuming a rather massive B (the feedback factor)
He’s also pulling a little bate and switch, talking about W/M^2/Deg C and then simply dropping the /Deg C part and implying any back radiation above 3.3 W would make the system unstable. In short the whole thing falls into the “that’s not right. that’s not even wrong” category.
Here is what really happens when you have positive feedback:
Lets assume A = 1 and B = 0.5 and the Sun warms up enough to increase the planets blackbody temperature 1 deg C.
The warming causes some effect (say an increase in water vapor) that causes the earth to retain more heat. In this case 0.5 Deg C (1 Deg * A * B)
That 0.5 deg cause a further increase in water vapor, which causes more warming but this time only 0.25 deg (0.5 * A * B)
That 0.25 also triggers more warming, and so on.
The final amount of warming you actually see therefore is 1 + 1/2 + 1/4 +1/8…
If you do the math you will find this series converges on 2 Deg C. I.E. an increase in solar energy that would normally cause 1 deg of warming ends up causing 2 instead.
If we had looked at negative feedback instead then the final change would have been less then 1.