Why are the tropical oceans still cold in the depths?

A new comment on the post "Conkered?"  http://scienceblogs.com/stoat/2014/09/20/conkered/

Author : Climate Scientist
Comment:

Why are the tropical oceans still cold in the depths?  Why don't they become isothermal like you think the troposphere would have been without that most-prolific of all greenhouse pollutants, water vapour sending all that warming back radiation back to the surface to warm it to a higher temperature than it was when it sent the original radiation and cooled in doing so.

Well the tropical oceans are colder in the depths because the poles act as a heat sink.  Isothermals (such as 4 degrees C) are deep down in the tropics, but break out at the surface in the polar regions.

So too would the atmosphere be colder at the base for the same reason.  If the whole globe were paved in black asphalt the surface would be about 235K - nearly 40 degrees below freezing.  You can work it out yourself with an on-line Stefan Boltzmann calculator using solar radiative flux of 161W/m^2 and emissivity 0.93.

So there is a lot of thermal energy entering the ocean surface in non-polar regions, moving downwards through the thermocline and exiting in the polar regions.

But why is the thin transparent ocean surface so hot?  Before you say it's the back radiation, I have to tell you that radiation from colder regions does not penetrate the warmer ocean surface more than a few nanometres.  It is "pseudo scattered" because it merely raises electrons to higher energy states and then those electrons immediately drop back and emit an identical photon.  The electro-magnetic energy is not converted to thermal energy, and so it does not raise the temperature.

In fact there is a gravitationally induced temperature gradient (aka lapse rate) in any planetary troposphere, and thermal energy absorbed from solar radiation in the upper troposphere can flow up that sloping thermal profile restoring thermodynamic equilibrium as it does so, and even entering the oceans. Water vapour reduces the temperature gradient (fortunately) making the surface about 10 to 12 degrees cooler.  Carbon dioxide makes it another 0.1 degree cooler for the same reason.