Comment by Retric

That’s overly simplified, and these lakes normally only fully mix every few years. In winter surface water is colder than sub surface water so if you start pumping water to create a cold and more dense column of water in a pipe you can stop the pump and let physics move the through that pipe for months with zero energy expenditure. It’s the same basic reason lakes normally mix in the first place. Decomposing organic mater etc then warm up the deep water over time

Even without that it’s way more efficient to pump water when you have near zero difference in pressure and only need to move a short distance. The column of water outside the pump and the column of water inside the pump are only going to vary by the difference in weight due to differences in temperature. So you’re effectively pumping water up ~10cm even though the column is much longer than that.

If we assume we need ultra fast circulation and mixing every year… 19 gigaliter ~= 19 billion kg lifted ~0.1 m is 9.8 * 19 ^9 * 0.1 J / 60 / 24 / 365 = 600 Kw which is a fair bit of energy perhaps 1 MW with losses, definitely expensive for an individual but not much compared to what cities are spending pumping water around. But again you’re likely fine doing less than 1% of that.