I have a nasty habit of comparing the the Tropopause and the 4C ocean thermal boundary layer in a way that is not very clear. This is mainly due to my looking at the situation more as a puzzle than a serious fluid dynamics problem. As I mentioned in a previous post, I am looking for a simple back of the envelope method of proving the limits of CO2 radiant forcing to a reasonable level of accuracy.
The main similarity is that both are thermal boundaries with sufficiently large sink capacity to buffer changes in radiant forcing. Their mechanisms are different but the impacts are very similar.
The ocean 4C boundary is a combination of thermal and density mechanisms that result in interesting thermal properties. Warming the 4C boundary from above results in upward convection which tends to reduce the impact of the warming. The heat loss from the 4C layer has to be from warmer, 4C to colder but also has to allow for constant density. If not, there would be turbulent mixing and there would be no 4C boundary layer.
So cooling or actually maintenance, of the 4C boundary occurs mainly in the Antarctic region where the air temperature is cold enough to cause the formation of sea ice. This also occurs in the Arctic, but seasonal melting produce less dense fresh water that has to mix, with turbulence, with the denser saltwater. If there were no turbulent mixing there would be lens of fresh water constantly in Arctic summer. In the Antarctic, much more of the sea ice survives the summer months, so there is continuous replenishment of the 4C maximum density salt water slowly sinking in the southern pole that creates the deep ocean currents. Turbulent warming of the 4C layer in or near the tropics causes rising convection from the 4C boundary layer which impacts the rate of replenishment from both poles. It is a very elegant thermostat for the deep oceans, laminar replenishment versus turbulent withdrawal.
The Tropopause is similar but different. Non-condensation greenhouse gas radiant forcing balance conductive, convective and latent cooling response. The Antarctic winter conditions are controlled by the non-condensible radiant effect primarily which result in a maximum low temperature equal to the amount of non-condensible radiant forcing for that temperature range.
The lowest temperature ever recorded in the Antarctic is about -90C and that would be the lowest temperature in the Tropopause if it were not for non-radiant energy flux. The average temperature of the Tropopause is closer to -60C, which indicates that the average impact on non-radiant energy flux is on the order of 30C in the Tropopause. That is a fairly large buffer range. In addition to that range, the Tropopause altitude can vary so for short term perturbations, the temperature can drop to -100C possibly a little more. The Tropopause temperature cannot decrease much lower because stratospheric warming due to ultra violent solar radiation interacting with oxygen in the dry region above the Tropopause.
Non-interactive outgoing long wave radiation, the atmospheric window portion of the spectrum is less in the Antarctic due to the Stefan-Boltzmann relationship, ans should be on the order of 9Wm-2 at -90C implying that the actual CO2 portion of the Tropopause limit is on the order of 55 to 60 Wm-2. As more CO2 forcing is applied, the percentage of non-interactive OLR would increase, offsetting approximately 15% of the impact.
As surface temperature increases, the non-interactive response would continue to offset approximately 15% or the non-condensible GHG forcing and the conductive/convective and latent fluxes would offset more with the changes in temperature, gas mix and pressure. Convection, which is a function of temperature, density and conductive properties, is the non-linear part of the puzzle that causes the uncertainty in a pure energy perspective while albedo, surface and atmospheric, change just adds a new layer of complexity.
In both the 4C and tropopause boundary layers, virtually immeasurable changes can have a significant impact on the heat sink capacity of each and each have extremely different time constants. More complexity, making this an outstanding puzzle!
So this post hopefully will explain why I compare these two thermodynamic layers as I do, though the mechanisms are very different.