The Stefan-Boltzmann constant states the amount of radiation emitted by matter (watts per square meter) at any particular temperature. Then emissivity adjusts that amount slightly for each type of substance.
 
The estimate of 40 times too much radiation is based on physicists' calculated percent radiation given off by the surface of the Earth being 79% as required by the Kiehl-Trenberth model (below), when that radiation should not be more than 2%, probably less, by realistic estimates.

With the Stefan-Boltzmann constant being excessively high, an extremely large amount of radiation from the surface of the Earth is indicated to be available to be absorbed by carbon dioxide in the atmosphere. Reduce the radiation, and the greenhouse effect is a joke.

With a corrected amount of radiation, so little radiation is available to carbon dioxide that it gets absorbed by a small amount of carbon dioxide by the time the radiation travels ten meters in the atmosphere, so more carbon dioxide cannot absorb more radiation, which is called saturation. The ten meters was measured by Heinz Hug in a laboratory as described in the global warming section.

Scientists determined the limitations of saturation more than a century ago, while incompetents in physics persisted with their ignorance and motives in hyping a false greenhouse effect.

Only radiation from the surface of the Earth can be absorbed by carbon dioxide in the atmosphere, because the sun's radiation is too high of a frequency. There is no significant amount of radiation given off by cold substances such as the Earth's surface. The average temperature of the surface of the Earth is only 59°F (15°C), which is too cold for significant radiation.

The 2% is my estimate of a maximum possibility having worked extensively with temperature effects in electronics; but only a maximum possibility can be estimated through elimination, while the actual would be less. Radiation is so minuscule that it is ignored in most heat analysis, which means it could not be more than 2% of heat loss, while the actual would be less but cannot be estimated at such a low level. Physicists have not determined what the number should be, which is why they could produce the absurd 79%.

Here's how the analysis works:

The Stefan-Boltzmann constant is this:

     W/m² = 5.67 x 10^-8 x K⁴

It says, watts per square meter radiation equals a constant times degrees Kelvin to the fourth power.

The average temperature of the earth's surface is said to be 15°C, which is 288°K. So 5.67 x 10^-8 x 288⁴ = 390 watts per square meter given off by the surface of the earth on average.
 
The 390 W/m² is extremely large and places restrictive demands upon analyses. In 1997, this number was used to create a model for the Earth's energy flows, called the Kiehl-Trenberth model, which defines analysis of the supposed greenhouse effect.
 
The Kiehl-Trenberth model is this: link at IPCC

A condensed, net effect, of the Kiehl-Trenberth Model is this:

The radiation leaving the surface of the earth consists of two parts: 350 W/m² going from earth to atmosphere, and 40 W/m² going from earth to outer space, for a total of 390 W/m² leaving the surface of the Earth.

The amount of energy leaving the surface of the Earth through conduction and convection is 24 W/m². There is 16 times as much radiation as conduction and convection. It's like a fan blowing over a rough surface and only carrying away one sixteenth as much energy as radiates away. Fans would never be used for 1/16 improvement. It's the other way around; the radiation is miniscule, which is why fans are used.

These numbers are forced onto the subject by the constraints which the Stefan-Boltzmann (SBC) constant created. There has to be 390 W/m² of radiation leaving the Earth based on the SBC. The sun's energy coming in is only 235 W/m². The atmosphere is assumed to radiate a lot of energy, which must total 235 W/m² going into space. The other numbers are locked in by these constraints.

The result is 79% of the energy leaving the surface of the earth as radiation [390 ÷ (390 + 102)], which is radiation divided the total leaving with conduction-convection (24) plus evaporation (78).

Instead of saying there is something wrong with the SBC, physicists showed absurd amounts of radiation. The absurdly large amount of radiation is supposed to make a greenhouse effect look more real. Could anyone assume trapped radiation would be relevant if total radiation were only 2% of the energy instead of 79%? The radiation should be 2%.
 
Those numbers were included in the NASA energy budget which is this: