The total surface area of the ocean absorbing CO₂ from the atmosphere is very large and it is a continuous process because CO₂ is always in the atmosphere (and of course, is increasing due to human activities).
Fresh water from melting ice caps *will* dilute the effect somewhat, but water locked up as ice in polar regions accounts for about 3% the mass of all the water on Earth. So even if it all melted tomorrow it wouldn’t make a huge difference, plus then you’ve still got the ongoing absorption of atmospheric CO₂ (not to mention your global sea level is a couple of hundred metres higher, oops).
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