|Ed Berry's carbon model (top) vs US Global Change
Research Program's carbon model (bottom)
But, alas, there is such a thing. The figure to the right compares Berry's model (top) to a physics-based model.
In the figure to the right, I've put Berry's model on top and that from the US Global Change Research Program's SOCCR-2 Report (Fig 1.2 pg 46) published in 2018. You can decide who's doing proper physics.
For example, another unrealistic feature is that Berry assumes the flux of CO2 into the atmosphere -- natural + human -- is a constant. Equation 4 on Berry's preprint proposes
Lb = inflow * Te
where inflow is the net flux of CO2 into the system (= natural + anthropogenic), Lb is defined to be the "balance level, and Te is the "e-folding time" -- how long it takes for 1/e of atmospheric CO2 to leave. (And he assumes Te is independent of how much CO2 is in the atmosphere.)
Berry then restricts his model by assuming
“....in the special case when Lb and Te are constant…”He’s thus choosing
Inflow = constant
which is not what is happening in the real world -- it's certainly not true for the anthropogenic component, and I doubt that nature is giving off less CO2 as the temperature warms. (It isn't true for soil, not true for volcanoes, and not true for the ocean, which is acidifying and whose CO2 uptake is in fact increasing.)
It'd be a miracle if all three of those natural changes, plus others, just happened to cancel out the human emissions (and every year, as human emissions increase!) to leave inflow = constant.
Is there any data or evidence showing the amount of CO2 entering the atmosphere is constant?