First, the SB equation is inappropriately applied to the whole business of atmospheric physics.
The SB equation shows that all objects can radiate toward each other no matter the temperature difference. That happens in atmospheric physics.
The SB equation shows no such thing. In its fundamental form it states that in a vacuum, the amount of radiation emitted by a black body per second of its area is proportional to the fourth power of its absolute temperature. It its more common form which shows a radiator emitting into its cooler surroundings it states that the amount of radiation emitted by the radiator is equal to its emissivity, times the SB constant times the area of the radiator times the difference between the temperature of the radiator to the 4th power and the temperature of the surroundings to the 4th power)......that is all that it states....nothing more....nothing less.
Emissivity is accounted for in the SB equation.
And precisely, what is the emissivity of the earth and its atmosphere? Don't know do you?...that's all right...no one does...Emissivity figures are assumptions...not known numbers....there goes another monkey wrench into your belief system.
Not true. See Crick's explanation.
Crick is an idiot child....he...and the rest of you warmers have no problem pointing out the cooling stratosphere which was predicted by the AGW hypothesis...problem is, that you can't accept one prediction that happens and then reject the other more important failure. Crick is relying on a comic book author for his climate science...cook went way out on a limb when he suggested that the hot spot wasn't caused by the greenhouse effect..his heroes disagree with him.. Look in the IPCC AR4, Chapter 8, or read Hansen et al 1984 : they call it “Water Vapor” feedback. The IPCC (for a change) don’t mince words,
“Water vapour is the most important greenhouse gas in the atmosphere.” Hansen is specific in his 1984 paper. His reference to “infrared opacity” is another way of saying “greenhouse effect”: "Water vapor feedback arises from the ability of the atmosphere to hold more water vapor as temperature increases. The added water vapor increases the infrared opacity of the atmosphere, raising the mean level of infrared emission to space to greater altitude, where it is colder."
Every important GCM has predicted a tropospheric hot spot...it is a fundamental prediction made by the AGW hypothesis....it has failed....again, how many fundamental predictive errors do you believe a hypothesis should get before it is scrapped?