The arctic ice is basically a giant floating sheet of ice laid upon the ocean so the ocean and ice are (probably) at equilibrium in the arctic. And since all oceans are connected shouldn't all of them be at equilibrium with arctic ice. This impress that every single ocean on the earth must have a very low temperature near 0C. But this is very obviously not the case. So how can an ice-water system stay in equilibrium without constant temperature across itself

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    $\begingroup$ Not in equilibrium. Always moving, dynamically changing to heat from Sun, that's one reason why all the currents. It is a sort of dynamic equilibrium over the mid term $\endgroup$ – Bob Bee Dec 5 '17 at 0:51

You can have an equilibrium without things being equal. If you heat one end of a copper rod while the other end is in an ice bath, there will be a thermal gradient along the rod such that the rate at which heat flows along the gradient equals the rate at which heat enters the rod at the hot end (and leaves at the cold end).

The same thing, but on a much more complex scale, happens in the oceans. The main complicating factors:

  1. Convection: currents exist in the ocean due to prevailing winds (rotation of the earth), salinity of the sea water (and lack of salt in the melting water of the arctic), and the changing density of water with temperature (with the densest water having a temperature of about 4°C)
  2. Solar heating: the oceans absorb a MASSIVE amount of heat per second from the sun's rays. This heating is greatest at the point where the sun is perpendicular to the surface of the sea (near the equator), and least near the poles (which is one important reason why it's colder near the poles).
  3. Evaporative cooling: the oceans lose heat by evaporation - the hotter they are, the more evaporation there is. That tends to offset some of the solar heating
  4. Other sources of water: rain, rivers add water that is at a different temperature
  5. El Niño: a thermal fluctuation in the Pacific ocean that causes a shift of warm water, and that greatly affects the climate for a number of months.

Locally, these effects greatly change the temperature of the ocean; but there is some stability (over a period of years) in the temperature distribution - all these things happen in a way that leaves the temperatures "roughly the same" (not counting longer term changes to the heat content of the Earth due to changes in the atmospheric composition etc).

In short - there is equilibrium, but not equality. Not by a long stretch. NASA has published a beautiful map of the temperature distribution (https://svs.gsfc.nasa.gov/vis/a000000/a003600/a003652/SSTMap_8000x4000.jpg): you can see the effect of solar heating near the equator very clearly.

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