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I am only doing gross calculations here, but...

If the Earth has warmed by about one degree Celsius in the last century or so, and the thermal expansion coefficient of water is about .0002085, then the (admittedly salty) ocean should have expanded in volume by about .02%, or 1 part in 5000. Right?

Well, the average depth of the ocean is about 10,000 feet, and if the water has (mostly) nowhere to go but up, shouldn't the seas have risen by about 2 feet, not .75 feet?

Ummm, I just thought of something... Has the ocean not warmed as much as the atmosphere?

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    $\begingroup$ Your mistake is that not the whole ocean is warmer. ncdc.noaa.gov/cag/global/time-series/globe/ocean/ytd/12/… you can find a graph of sea SURFACE temperature anomalies from 1880 - 2017 in there, which will show ~1°C warming. However, deep ocean temperatures change a lot slower. See e.g. here: agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2020GL089093 $\endgroup$
    – Joscha Fregin
    Jan 8, 2021 at 11:00
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    $\begingroup$ And from memory, circulation times are measured in 1000s of years - so we would expect it to take that sort of timescale for the 1C to be reflected in sea level rise. Of course the atmospheric temperature is still rising, and ice is melting, so sea level rise is accelerating. $\endgroup$
    – winwaed
    Jan 8, 2021 at 14:41

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You should take into account isostasy. As there's more water in the oceans, the crust underneath bends under the weight, creating more room for it. At the same time, continental crust heaves above the oceanic, hence the small value.

A question here to be careful about is where the location of the measuring point, as it very well may not be stable.

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    $\begingroup$ The question is about thermal expansion; mass of water in the oceans doesn't increase from warming, just volume. Any additional water ie mass must come from reduced water/ice on land. $\endgroup$
    – Ken Fabian
    Jan 12, 2021 at 8:33
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Firstly, the simple way to calculate a length change from a volumetric expansion coefficient is to divide that coefficient by 3 to get it for length. So with a volumetric expansion coefficient of 0.0002085, you have a linear expansion coefficient of roughly 0.0000695. Multiplying that by the average depth of 10 000 ft, you end up with a change of roughly 0.695 feet.

However, there are a multitude of factors at play. The simplest is that it is the surface temperature that has risen. It will take considerable time to heat all of the ocean.

Another factor is evaporation. Hotter air is capable of holding more moisture, and hotter temperatures result in a faster rate of evaporation. This means as the temperature of the air increases, you would expect more moisture to be in the air. This increase in water content of air reduces the amount in the ocean.

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