You claim that more sun heats deeper into the water and heats it more. While this is true, in a balanced environment it would be exactly offset by the increase in heat loss from the warmer ocean water to the atmosphere.
Water evaporates from the surface and moves heat from the ocean to the air. Also, the water radiates heat into space (black-body radiation) based solely on its temperature. Together, these have been in balance with the energy coming from the sun since our atmosphere was formed. As the sun sends us more, heat lost back out to space increases. This is rapid because heat transfer due to radiation is proportional to THE FOURTH POWER of temperature. That's massive. It means that with a nearly immeasurable increase in temp, the Earth would dump much more heat back into space. Very small concentrations of CO2 and other greenhouse gasses, including water vapor, regulate this. This is why a tiny change in their concentration has such an extreme effect on heating. They throw the energy in vs. energy out completely out of balance. We call the over/under shooting an ice age or a warming period. These have taken thousands of years to show the effects with the ideal fastest natural time being calculated at around 700 years PER DEGREE. You simply can't heat something as large as a planet up any faster... unless you insulate it from losing heat back out to space. If you do that, like we are, you get warming of one degree in centuries or even decades. This is huge because no feedback system on Earth can get rid of that kind of heat in less than 'around 700 years'.
In 'natural' warming periods, the temp rose from a combination of factors working in concert. This warming caused an increase in CO2 which eventually caused more warming. It was only when other negative loops kicked in enough that we returned to regular temps.
This time, we're forcing the CO2 to cause the warming at a rate that nothing can catch up and stop it. Never before has CO2 risen so high so quickly.
Now, take that CO2 effected warming and note that it decreases the CO2 absorption of the ocean, leaving more of it in the air to stop heat from radiating to space. Now add in an increase in water vapor. Now add in sublimated methane ice (which is 20X more insulating to heat loss. These feedbacks dwarf the little things like 'darker oceans absorb more heat while ice re-radiates more to space'. Those are 1X feedbacks and what we're talking about is multiplication factors on 4X magnifiers. It's not even in the same playing field.
This entire issue is NOT for the light hearted or the entry level science layman. Keep in mind that I'm NOT saying people aren't trying to game both sides for profit. They definitely are but that has no bearing on the real science. They are simply two separate debates.
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