A black body cavity is any energy source where the temperature of that source can be accurately approximated with the Stefan-Boltzmann Law. That definition varies a bit from others, but it is the bottom line. If the black body source is less than ideal, then you have to consider individual elements and their radiant spectra to adjust for the less than ideal source. Depending on the level of precision that your application demands, you can assume "ideal" behavior as long as you remember the degree of uncertainty.
Pretty simple for most radiant physics/climate science geeks, there is uncertainty that needs to be considered whenever assuming ideal conditions. ASSUME is the first real law of thermodynamics.
If you consider what makes a good black body cavity, the first thing would be consistency or stability. The black body cavity is a reference, if your reference is noisy the adjustments for "less than ideal" behavior become more complex. If you want to simplify the problem you pick a stable FRAME OF REFERENCE (FOR). FOR is the second real law of thermodynamics.
By selecting a stable FOR and avoiding ASSUMEd precision that may not exist, you are following the first and most important real law of thermodynamics, KEEP IT SIMPLE STUPID, KISS.
SteveF at Lucia's has a post on removing natural variability from the global surface temperature record to show that another attempt to remove natural variability from the global surface temperature record was flawed and that the actual "trend" in actual global surface temperature is a gnat's ass less that estimated in the flawed attempt to remove the gnat's ass. The author of the original gnat's ass paper snidely points out that SteveF's paper has residual gnat's asses circa 1976 which totally invalidates SteveF's gnat's ass removal procedure.
Welcome to climate science, home of fat tails, gnat's asses and elephant avoidance.
The elephant is still the black body cavity that provides the energy which everything else responds to. Instead of a slit in a furnace or high precision optical source we have about 362 million kilometers squared of slit which can have non-uniformly distribute sea ice that can vary the slit area by 20 to 50 million kilometers squared or about 5.5% to 13.8% roughly on times scales of months to millions of years. With all that range of possible variation, the temperature of the black body cavity, the global oceans, varies by about 3 degrees from a low of ~1 C to a high of ~4 C if you consider the "average" temperature of the black body cavity. With the temperature of the black body cavity at the high end of the range, 4 C, which if it were an ideal black body cavity, would have an effective emissive energy of 334.5 Wm-2. The Black body cavity is not ideal. The temperature/effective energy varies from nearly 30 C at the equator to nearly -2 C at the poles for the surface or slit/aperture which is oddly the selected FOR for the gnat's ass assessors who ASSUME the energy is uniformly distributed and can only be significantly impacted by radiant forcing in a nearly linear manner. Is that KISS?
The simple fact avoided is that the black body cavity cannot emit energy any more quickly than that energy can be internal transferred from the "average" of the black body cavity to the "slit", aperture, surface or radiant "shell", i.e. the ocean-atmosphere boundary layer. How efficiently the black body cavity can transfer that energy internally determines the "average" energy of the black body source.
There can be several volumes published on the different factors that have different degrees of influence on the "average" temperature of the oceans aka black body source. For now just consider that the oceans have an "average" temperature and that there is an "average" ice free ocean area. With that average temperature equal to 4C (334.5Wm-2) and the average area equal to 360 kilometers square or 71 % of the total "surface" area of the globe, the "average" energy at any arbitrarily selected altitude would be equal to 334.5 Wm-2 times the ice free ocean area divided by the area of the arbitrarily selected "shell". If we select a "shell" equal to that total sea level surface area of the Earth, then the effect radiant energy at that "shell" would be 334.5 time 0.71 equals 236 Wm-2, that is the FOR selected by climate science convention. What about that other 29%?
During the black body mode or night mode, a large portion of that area is covered by ice and the remainer has a lower specific heat content relative to the black body source with much lower rates of internal heat transfer. Where the "land" portion, as in not ice covered, has higher moisture content, that portion would have a significant impact on the "average" energy at the arbitrarily selected "shell", but energy from the true energy source would be transferred at differing degrees of efficiency to the "land" area. By selecting the 236 Wm-2 altitude as a reference, the climate scientist now has to consider the ocean internal heat transfer efficiency and the ocean-atmosphere heat transfer efficiency and the ocean-"land" heat transfer efficiency.
Since the "land" is not symmetrically distributed, the ocean internal energy would not be uniformly distributed and with a rotating black body source, the hemispheres of the spherical source would be somewhat isolated by Coriolis effects. Even with all this to consider, there is still an "average" energy of the oceans and an "average" energy of any arbitrarily selected radiant "shell". By selecting a less arbitrary "shell", one that is more stable and uniformly distributed, like say the Turbopause, one could determine a range of natural variability, if either has a reasonably accurate long term estimated temperature/energy range.
Since both the energy and the ice free surface area varies over long times scales, the most stable FORs still do not eliminate uncertainty. With a 1 C to 4 C "average" ocean temperature range, there would be an "average" 2.5 C (327.4 Wm-2) temperature/effective energy with a +/- 1.5 C (7.12Wm-2) range for the more recent glacial/interglacial periods. If the focus is on either interglacial or glacial, the range could be reduced by half to +/-0.75 C (3.62 Wm-2).
So while I am just tickled to death that SteveF is winning the gnat's ass war, the real focus should be the expected range of natural variability on all relevant times scales, not just dreaming up more creative ways of removing a portion of the natural variability on arbitrary times scales, since the chart above doesn't paint the same pictures and these next two charts.
The more variably Northern Hemisphere versus the Indo-Pacific Warm Pool and
the rest of the world "surface" temperatures. Which indicates a range in the ballpark of +/- 0.75 C (3.62Wm-2) uncertainty with time scales of at least 400 years. Which by the way is roughly the time required for the "global" (0-2000 meters) ocean average temperature to rise, 0.75 C degrees.
As a final note, while there are plenty of theories, part of the equation is sea ice area and hemispherical distribution. The solar-lunar connection with climate likely plays a role in this variability since sea ice floats and orbital forcing also effect tides which can free or fix sea ice. That is a non-radiant "forcing" or "unforced variable" in the currently radiant centric gnat's ass modeling approach.
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