Seth Borenstein: "Man-made heat put in oceans has doubled since 1997"

1sky1,
There is little, if any, heat flow from hot to cold down through the thermocline and most of the transfer between hot and old occurs as weather and surface circulation currents. Note that the atmosphere is the primary connection between hot and cold and as I said before, the thermocline is acting like an insulator consequential to gravity acting on the density/temperature profile of water. Otherwise, how can you explain the existence of 0C water in the deep ocean directly under the equator an how can you explain the inflection points that define the thermocline?
There’s a small flow upward of about 1 W/m^2 which is the average heating from the solid surface below and of course, warmer water is less dense and rises which is counter to the expected flow from hot (surface) to cold (deep). The thermohaline circulation is the hydraulic action of cold water sinking at the poles, connecting at the equator and pushing water up, replacing that which was evaporated since the net flow of surface water via evaporation and rain is from the equator to the poles.
If you think of the planets energy storage as a temperature difference between warm surface waters and the deep ocean cold separated by an insluator (thermocline), the planet stores energy much like an electrical capacitor. The math works out the same as well, if Pi(t) and Po(t) are the instantaneous incident and emitted power of the planet, when the instantaneous difference is > 0, the energy stored by the planets surface increases and it warrms and when it’s < 0, the energy stored by the planets surface decreases and it cools. If E(t) is the instantaneous total energy stored by the surface relative to average, its also linearly proportional to the surface temperature, T(t). We can write this as,
Pi(t) = Po(t) + dE(t)/dt
If we now define an arbitrary amount of time, tau, such that all of E can be emitted at the rate Po in time tau, we can rewrite this as,
Po(t) = E(t)/tau
Pi(t) = E(t)/tau + dE/dt
which should be recognized as the LTI that describes an RC circuit with a time constant of tau. Note that in an electrical circuit a DC voltage bias on both plates of a capacitor is irrelevant to the stored energy, just as the average temperature 'bias' of the planet does not effect the stored energy. There's one additional constraint arising from the heat capacity and Stefan-Boltzmann where,
Po(t) = k*E(t)^4
The constant k combines the effective emissivity, the SB constant and the heat capacity. This illustrates a second order effect similar to a temperature dependent dielectric constant where tau must decrease as E increases which in this case, is a result of Stefan-Boltzmann, which is that Po(i) is proportional to T^4, thus E^4 and since k is mostly constant (1 cal, 1 gm water, 1C), tau must decrease as E (and T) increases. This simple set of equations can then be extended to account for cloud dependent emissivity and albedo on a gridded basis and becomes a very good predictor of the planets thermodynamic response to variable TSI and quantifiably establishes a sensitivity well below the lower bound claimed by the IPCC.
Note that the cold side of this 'capacitor' (the water below the thermocline) remains constant between about 0C and 4C regardless of the surface temperature and this will true as long as the poles provide a source of cold, dense water. The delta T and hence energy stored by the planet is then proportional to the average ocean surface temperature where a thermocline exists minus 4C which is the temperature at the bottom of the thermocline.

1sky1,
There’s no more hand waving involved with the LTI model of the climate system then there is for using it to model an RC circuit. The operation of an RC circuit can also be quantified in terms of more primitive first principles at many levels of abstraction all the way down to statistical Quantum Mechanics. For an RC circuit, the LTI model is an exact representation of the averages underlying the most primitive statistical behavior of the molecules comprising the circuit and is provable so by its macroscopic conservation requirements. In the same way, COE constrains the LTI climate model to be an exact representation of the climate system, moreover; superposition tells us that the only way the climate state can behave, where the state variable is the stored energy required to establish the instantaneous surface temperature, E(t), is as the sum of solutions to the aforementioned differential equation, Pi(t) = E(t)/tau + dE(t)/dt.
The thermal conductivity of water is about 0.58 W/(m K). While it’s no where near as good a conductor of heat as copper at about 400 W/(m K), nor as good an insulator as air at about .024 W/(m K), it becomes a good insulator at a sufficient thickness and 24 meters of water insulates as well as 1 meter of air. To be clear though, while the thermocline is behaving like an insulator separating deep cold from a warm tropical surface, it got that way as a consequence of gravity organizing water by its physical properties It’s interesting to note that the poles are also thermally connected to each other by a path going underneath the tropics.

1sky1,
Conservation of Energy is about as first principles as you can get, and this is the only constraint, in fact the only possible constraint, on the LTI model of the planets climate system that I’ve described. What happens at lower levels of abstraction is meaningless unless you can also account for this overriding top level constraint and conforming to this top level constraint is something that pedantic climate science does not do. If as you say, this kind of modelling was explored 50 years ago, then climate science would have been settled long ago in favor of the skeptics. Either you are wrong about this being considered in the past, or it was never given the due consideration it deserves The predictive power of this approach is to much to ignore, especially seasonal and diurnal variability.
Here’s a simple though experiment. Start with an ideal gray body representation of the planet (emissivity = 0.62), all aspects of which can be completely quantified by first principles (SB is also a first principles LAW) and then explain how the planet can exhibit the outward behavior of an ideal gray body, which the data is unambiguously clear about, yet manifest bulk properties far different from that of a gray body (the consensus claims a sensitivity 3-4 times larger)?