It's an interesting question, here's some napkin math.
There's almost 19 gigaliters of water in Crater Lake. To pump that amount of water in a year would require pumping 52 megaliters of water per day. A small city produces about 200 megaliters of sewage in a day. (LA produces about 2 gigaliters per day.)
So it should be possible but would be very expensive. Maybe on the order of running the drinking water infrastructure for a town. I suspect I'm overestimating though, I think you might only have to pump half of the water to achieve good mixing. (ETA: After a tiny bit of research I think you might be able to do it with much less than half due to entrainment.)
You would also kill a lot of animals and microorganisms in the process. Pumps driven by impellers create cavitation that cracks open microorganisms, and things like peristaltic pumps which avoid this can't handle these volumes. As this material is decomposed by bacteria, they will reproduce and increase the biological oxygen demand in the water, which might end up making the lake anoxic anyway.
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.
I wonder if there are any elegant passive solutions... like a floating sun-exposed surface that conducts heat down to a lower anchored point. Or lake-bottom structures that re-channel water movements from subtle tides or seiches.
I think that's the wrong way round: climate change causes longer summers and shorter winters, so the problem is one of cooling, not heating.
Shade balls[0] could work, but then they'd have to cover part of the lake with that.
EDIT: And of course, that also comes with a reduction in total light reaching the lake, which may have different side effects beyond temperature alone.
Look at the full picture. The cycling is reduced due a reduction in temperature gradient. That reduction in temperature gradient is due to water not cooling down enough in winter and warming up for longer in summer.
Could you increase cycling by creating a temperature gradient by capturing the heat from the sun to warm up the water at the bottom of the lake? Maybe, but that also would imply an even greater increase of average water temperature than the effects of climate change. Which would have all kinds of other ecological side-effects.
Or put another way: global warming increases thermal energy being added to the system, resulting in a change of the dynamics of the lake. Cooling it would counteract that increase. Capturing more heat would add even more thermal energy. Even if they both could affect cycling in the same way, adding even more thermal energy is almost guaranteed to create other ecosystemic imbalances.
Modern society is falling apart over the cost of getting to net zero. I don't think we have the funds to put lakes on artificial life support in the foreseeable future.
Is it the cost of net zero? Or is it the cost of everything else pretending to be relevant to net zero?
Of the interests pushing for net zero, the bulk of them are only doing it insofar as it can be done in a way that basically guarantees them incomes and all of these earmarks are what's driving the non-starter cost while simultaneously souring people on the whole premise. You'd think that people who allege to think on environmental time scales wouldn't need to be told that a movement that looks like branded rent seeking and legalized corruption when viewed through the perspective of anyone who isn't rolling in money isn't gonna last long enough to do its job.
Germany and their out of control energy costs (while still only being at best 1/5 of the way there if you count things like thermal heat), are a good example.
California has a dramatically easier climate, and is similarly struggling - without even taking into account goods shipping/transportation, thermal heat in the less nice climate zones, etc.
California might have a chance of getting to actual net zero without completely breaking the bank. But it’s not obvious it will. Germany is an order of
magnitude harder.
Renewable electricity in Germany is already at over 50% per year and climbing steadily, but heating, mobility, land/resource/artificial fertilizer use, pollution and circular economy are still lagging (esp. accounting for the fact we're externalizing some of those by cross-border trade).
I guess we're trying much harder than most, but it's expensive, as you said, and politicians have become very careful to push things further. That said, I do think it's totally feasible in theory, it's just there's a lot of powerful bad actors out there throwing wrenches in the works.
The challenge is with the remainder, which is actually a much bigger problem.
Thermal heating for example, even using heat pumps, will require more than 5x the existing electrical grids peak energy capacity - just on its own. I’ve done the math several times, it’s staggering.
And it will do it during typically minimal insolation times.
Germany has made good progress, don’t get me wrong, but it highlights just how hard of a problem this really is.
