AOGCMs have long predicted much slower warming of Antarctic oceans than the rest of the planet and some even predict modest cooling into the present. For example, Manabe’s early models predicted that it should have been cooling around Antarctica at the time. See Figure 1b in this paper, which has observations and predictions (CMIP3) for 1979-2005, a period with significant global warming and decent observations. However, the average model predicts only slightly less warming in the Antarctic oceans than globally and some predict more more warming.

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2013.0040

Abstract: “In recent decades, the Arctic has been warming and sea ice disappearing. By contrast, the Southern Ocean around Antarctica has been (mainly) cooling and sea-ice extent growing. We argue here that interhemispheric asymmetries in the mean ocean circulation, with sinking in the northern North Atlantic and upwelling around Antarctica, strongly influence the sea-surface temperature (SST) response to anthropogenic greenhouse gas (GHG) forcing, accelerating warming in the Arctic while delaying it in the Antarctic. Furthermore, while the amplitude of GHG forcing has been similar at the poles, significant ozone depletion only occurs over Antarctica. We suggest that the initial response of SST around Antarctica to ozone depletion is one of cooling and only later adds to the GHG-induced warming trend as upwelling of sub-surface warm water associated with stronger surface westerlies impacts surface properties…”

I find this explanation somewhat confusing because I also know that Antarctic Bottom water subsides in the same region. This Figure shows how complicated the currents near Antarctica are and perhaps explains why models are more likely to disagree in this location than others.

https://external-content.duckduckgo.com/iu/?u=http%3A%2F%2Fasl.umbc.edu%2Fpub%2Fchepplew%2FSouthernOcean_Overturn.png&f=1&nofb=1

Over a half year has gone since the paper came out. And I have not yet seen the climate change police at work. When will the data be corrected like earlier reports of ocean heat reduction, and where is the RC debunking? ]]>

https://www.ipcc.ch/site/assets/uploads/2018/02/WG1AR5_Chapter09_FINAL.pdf

The ultimate proof of the reliability of ocean heat transport in AOGCMs would be for those models to reproduce the temperatures and temperature gradients we observe given different starting conditions. The ocean and atmospheric modules of AOGCMs are “spun up” separately so that slow heat transport in the ocean can be modeled over long periods of time with large time steps. However ocean currents are driven by atmospheric winds, and it is computationally impractical for the full AOGCM to equilibrate the ocean via multiple circuits of the thermohaline circulation. Even after a long spin up, the surface temperature in some AOGCMs is steadily and slowly changing without forcing – suggesting to me that the deep ocean hasn’t equilibrated with surface temperature.

]]>Fick’s Law of Diffusion says that heat flux is the temperature gradient multiplied by the diffusion coefficient. Fourier’s Law says that conductivity is proportional to the temperature difference between two locations divided by the distance between those locations – also temperature gradient. So thermal diffusivity expresses heat flux in the “continuous” terms of a gradient while thermal conductivity expresses heat flux in “discrete” terms between two locations. Box models are inherently discrete. Fourier’s thermal conductivity (measured in units of W/m-K) divided by volumetric heat capacity (J/m3/K, = density times specific heat capacity) gives Fick’s thermal diffusivity (measured in units of m2/s). Conductivity and thermal diffusivity appear to be different names for quantifying heat flow driven by a temperature difference.

The thermal conductivity of water (0.59 W/m-K) and its volumetric heat capacity (4.18 J/cm3-K) affords a thermal diffusivity for stationary water of 0.0014 cm2/s, about 700 times smaller than the thermal diffusivity assumed by Hansen for a global ocean mixed by bulk motion/convection/turbulence. Mechanistically, thermal diffusion explains a negligible fraction of heat transport in the ocean

Isaac Held analyzes the ocean heat uptake of AOGCMs in terms of two-box models: a mixed layer (T) and a colder deep ocean with effectively infinite heat capacity (T_0):

https://www.gfdl.noaa.gov/blog_held/3-transient-vs-equilibrium-climate-responses/

Heat transport from the mixed layer to the deeper ocean in response to the rising temperature of the mixed layer is modeled as being proportional to the temperature difference between these two compartments. Held says that typical AOGCMs send 0.7+/-0.2 W/m2 more heat from the mixed layer to the deeper ocean per 1K of surface warming. He calls this the “ocean heat uptake efficiency”. Let’s assume that the initial temperature difference (T – T_0) between these two compartments is 10 K and rises to 11 K (T’ – T_0). Let’s also assume the distance between these two compartment 1 km. Using Fourier’s Law, the “effective thermal conductivity” would be 700 W/m-K. The volumetric heat capacity of water is 4.18 J/cm3/K, making the “effective thermal diffusivity” in this version of Held’s two-box model 1.67 cm2/s.

So a thermal conductivity for copper of 3.84 W/m-K and a thermal diffusivity of 1 cm2/s and an ocean heat uptake efficiency of 0.7 W/m2/K all could represent roughly similar easy of heat transfer when driven by a temperature gradient.

If I assumed an initial 20, 5, or 2 K difference between the two compartments, I would have calculated exactly the SAME thermal diffusivity associated with an ocean heat uptake efficiency of 0.7 W/m2/K. Only the change in the gradient matters. If I assumed heat transport over 0.5 or 2 km, however, the thermal diffusivity would have been double or half.

However, Held didn’t discuss what MUST BE HAPPENING BEFORE A FORCING IS APPLIED. Postulating ANY TEMPERATURE DIFFERENCE between two compartments connected by effective thermal diffusivity of 1.0 or 1.6 cm2/s, creates a system that is not at steady state. The only way to have a steady-state model for the ocean expressed in terms of thermal diffusion is for there to be NO temperature difference between the surface and the deep ocean or for the thermal diffusivity of the ocean to be near zero. This suggests that we should be using the 0.0014 cm2/s thermal diffusivity of stationary water, not values a thousand-fold bigger.

In order for our planet to have tropical and temperate oceans with surface temperatures 20 K and 10 K warmer than the deep ocean, the local effective thermal diffusivity in these regions must be low enough that the temperature of bottom water formed in polar regions is negligibly changed on its 1500-year trip via the thermohaline circulation. Some heat must be diffusing into bottom water. The thermohaline circulation is the only way for that heat to escape! The mechanisms that rapidly carry heat and tracers somewhat below the mixed layer in equatorial and temperate zones certainly can’t reach all the way to bottom waters.

Most heat transport in the ocean is by fluid flow. Downward fluid flow is OPPOSED by the local temperature/density gradient – NOT speeded up by a steeper temperature gradient. Bulk motion of water against the local temperature/density gradient requires doing work against gravity. The concept of thermal diffusion mistakenly predicts that the greatest heat transfer will occur in the tropics, where the steepest temperature gradients are found. It wrongly predicts that there should be no temperature difference between the deep ocean and the surface. The concept of heat transfer by fluid flow correctly predicts that most heat uptake after forcing occurs in polar regions and that the temperature of the deep ocean is controlled by the temperature in polar regions. Thermal diffusion proportional to a temperature gradient is a conceptually flawed approach to heat transfer in the ocean.

]]>As one who did diffusion models in the semiconductor industry, being able to deduce the shortcuts taken is not hard. Sorry, no shortcuts are allowed in characterizing diffusion during wafer fab.

]]>Frank replied with a long comment amateurishly discussing mechanisms by which bulk motion of water transports heat from the surface into the ocean. The reference linked below analyzed six separate mechanisms in three AOGCMs: advection, convection, mixed layer turbulence, eddy-induced advection, isopycnal diffusion and diapycnal diffusion. Figure 1 shows each model uses different mechanisms to different extents at different depths. In CMIP5 models, total heat uptake in historic runs from 1971 to 2005 ranged from and 8 to 36*10^22 J. (AR5 WG1 Figure 9.17) Ocean heat uptake – and the related, more-critical ocean uptake of CO2 – appear to be another aspect of “settled climate science” with large uncertainties

https://journals.ametsoc.org/doi/pdf/10.1175/JCLI-D-14-00235.1

In a separate comment, I noted that the energy balance models used by dozens of researchers (including Lewis) relied on observations of warming of the ocean, but AOGCM’s did need to get all of these mechanisms right and some require parameterization. And, in 1981, Hansen didn’t model any mechanisms of ocean heat uptake.

Now geoenergymath claims I misrepresented Hansen’s work: “Wrong. By incorporating diffusion with a 1 cm^2/s term, James Hansen did an infinite slab model and did it correctly, instead of this one-box or two-box junk that Nic Lewis is doing. You don’t “connect” one box with another via a diffusivity term. When you decide to use D then you either do the complete slab model numerically or you can use the analytical form, involving erf formulations or the simplified form that I have described elsewhere.”

Hansen’s publication dealt with several 1-dimensional models for the planet. 1-D models do have infinite slabs in the horizontal directions. However, Hansen himself referred using “box diffusion model[s]” on p 595. “Figure 1 : “Heat is rapidly mixed in the upper 100 m of the ocean and diffused to 1000 m with diffusion coefficient k”. k is either 1 cm2/s or infinity. That figure had two 1-box models for the ocean and two 2-box models for the ocean. So the brilliant James Hansen is using the same box models as the disdained Nic Lewis. And Hansen’s diffusion coefficient of 1 cm2/s, was derived (with significant uncertainty) from box diffusion models of analyzing ocean uptake of C-14 carbon dioxide and tritium.

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