Heat reservoir versus heat sink - A heat reservoir is bi-directional and a heat sink is one way. Most heat sinks aren't even close to ideal but they never reverse direction during normal operation. For climate science the oceans are a good reservoir the atmosphere is a poor reservoir and the poles are heat sinks.

Zeroth Law of Thermodynamics - A "Thermodynamic Temperature", source temperature or sink temperature, has to accurately describe the energy available in the source and sink. "Average" temperature of a process is pretty much meaningless. "The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other." Since energy varies with the forth power of temperature, a "half way" temperature would indicate different energy flows to source and sink so it would not be in equilibrium or steady state relative to both source and sink. It is an invalid frame of reference. For example, 0K (0 Wm-2) to 288K(390 Wm-2) would have an average temperature of 144K and an average energy of 195 Wm-2 which has an equivalent temperature of 242 K degrees. If you use 242 K degrees as a frame of reference with respect to 288K degrees or 0K degrees there is a huge error. The 33 C "greenhouse effect" temperature and energy range is meaningless by itself.

Latent and Convective Heat in an open system is a bitch. Since latent heat and convection are inter-related, higher surface convection increases the rate of evaporation, and the flow of the latent heat is driven by more than just temperature differential, plus there is phase change in the stream that varies with turbulent mixing which can change the flow rate, you have a marvelously complex fluid dynamics problem without a reliable solution. You may be able to approximate a range of possible solutions, but the problem is essentially chaotic.

All this makes for a wonderful puzzle with no perfectly correct solution. You can "ASSUME" any number of sources and sinks which is nothing more than varying your frames of reference. You can pigeonhole each frame with some neat sciency sounding name, like maximum entropy production, minimum entropy production, construction theory, dissipation theory and probably a few dozen others and it is pretty likely that no two independent methods will agree "exactly". If the methods are done correctly and the data valid, you will end up with a range of possible "answers" which should define a range or region of probability.

If you consider the thoughts of S. Manabe, THE greenhouse effect should produce about 60 C of "surface" warming. Convection which is intertwined with latent heat should produce about -30C of negative feedback to the GHE from that "surface" reference. If the GHE and the Convective feedback are not perfectly linear, very likely, you have the potential for regime changes The trick is to find the likely range of temperatures AND the offset that may be produced by man cause CO2e "forcing".

You can reduce all this down to a simplified partial differential equation that includes all of the inter-dependencies of the known variables, but that gets you right back to the fluid dynamics problem which is essentially chaotic. You can "complex model" the system various ways, but the results will always be depend on initial conditions resulting in hopefully the same range or region of probabilities you get with a suite of simple models.

The Climate Illuminati despise chaos but thrive on uncertainty which is a bit bizarre. A range is a range regardless of how you get there. Since all you will ever get is a range, you need to embrace it and make decisions based on the highest probability, which is currently about 0.8 C more from our current conditions.

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