A Bad Assumption in Ed Berry's Model

Ed Berry's carbon model (top) vs US Global Change
Research Program's carbon model (bottom)

Ed Berry writes, "There is no such thing as a system being 'too simplistic.' A system should be a simple as possible to solve a problem."

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.

Berry's model's basic flaw is that it assumes that once a CO2 molecules leaves the atmosphere, it (or an identical one) cannot ever find its way back into the atmosphere, and that leaving/entering the atmosphere does not affect what is entering/leaving the atmosphere. Henry's Law is a simple example showing that it does.

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

L_b = inflow * T_e

where inflow is the net flux of CO2 into the system (= natural + anthropogenic), L_b is defined to be the "balance level, and T_e 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 L_b and T_e 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?