Exercise 1 solution

Volume V = 1.3 x 10^18 m3. Flow Q = 17 x 10^6 m3/s = 1.7 x 10^7 m3/s.

Time = V / Q = 1.3 x 10^18 / 1.7 x 10^7 = about 7.6 x 10^10 seconds.

One year is about 3.15 x 10^7 s, so time = 7.6 x 10^10 / 3.15 x 10^7 = about 2,400 years.

This is the time to move one ocean-volume of water at 17 Sv. It is the same order of magnitude as the quoted loop time of several hundred to a thousand years, which is consistent: the overturning does not pass through the whole ocean (much of the water is in basins and layers it never visits at that rate, and the Antarctic overturning adds flow), so the simple division gives only a rough upper bound. The point is that the deep ocean turns over on a scale of centuries to millennia.