The saltiness (salinity) of the oceans plays an important role in ocean circulat

Question

The saltiness (salinity) of the oceans plays an important role in ocean circulation because salty water is more dense than fresh water. The following question asks you to make a calculation about how much salinity can change. A heavy tropical storm drops 20 cm of rainfall in a region of the ocean in which the salinity is 35 g/kg (i.e. 35 g of salt in 1 kg of water) and the ocean surface “mixed layer” depth is 50 m. Assuming that the water is well-mixed, by how much does the salinity of the ocean surface mixed layer decrease? You can ignore the small difference between the densities of salt water and fresh water.

Explanation / Answer

After 20 cm or 0.2 m of heavy rainfall in the ocean, The volume of ocean water is increased to the extent of surface water to the bottom of the mixed layer by 0.2 / 50 = 0.004

The mass of water from surface to base of mixed layer would also increase by the same abount as mentioned above i.e. 0.004 (ignoring small density differences of salt and fresh water) = 1.0 + 0.004 = 1.004

Therefore salinity will drop to from 35 g/kg to :-

35 (g of salt) / (1+0.004) (g of water)

= 35 / 1.004

= 34.8605 g/kg

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