## Tuesday, May 26, 2015

### Storms are powerful heat engines!

Storms are incredibly powerful (on human scales) heat engines - driven by the sun, the fluxes of mass and energy are simply enormous.  To see just how big, let's take a look at the big thunderstorm system that flooded large parts of the city of Houston last night (hence why I'm blogging and unable to get to campus until the waters recede).   A large storm system dumped about 20 cm of rain (!) over a land area of approximately 4000 km2 between 10:00pm and about 4:00am.   That's 8 x 1011 kg of water!

The bottom of the rain clouds was maybe 0.5 km above ground level.  That's a lower bound on how far all that rain had to fall.  Using $g \approx$10 m/s2, that's about 4 x 1015 J of energy, deposited in about 20000 sec, for an average power delivered of 2 x 1011 Watts, as much as 100 municipal-scale power stations.   That doesn't even account for the energy contained in the wind and the lightning discharges.

Remember, this is all being driven by the sun, through temperature differences that are at most 20 K.  Thermodynamics tells us that the most efficient this process could possibly be is something like 1 - (300 K/320 K) = 1/16.  That means that the total energy involved had to be at least 6.4 x 1016 J = about 18 billion kW-h, and that's only one part of a big storm system.  This is why engineering the weather is a non-starter!

Anonymous said...

nice (again)!
I vote for more back-of-a-stamp everyday physics examples :-)

Anonymous said...

I don't agree with the conclusion in your last statement. We control all kinds of large energy flows with very low-energy control systems. E.g., a municipal power plant can be controlled pretty well with a laptop. And (relatively) small amounts of CO2 in the atmosphere can/are significantly mess with the weather.

Maybe it was implicit that the "engineering" has to be done in a controlled way? In that case, I think it is more about complexity of the system and not the scale of energy flows.

Anzel said...

I'd have to agree with Anon@3.17. I'd imagine much of proper weather control would involve finding systems at tipping points, and give them (relatively) subtle nudges to push weather towards a more desirable outcome.

In other news, stay dry out there in Houston.

Douglas Natelson said...

Anon@3:17 - I understand what you're saying. When we design systems it is possible to control large energies with small inputs (e.g., removing control rods to drive a 2 GW nuclear powerplant critical). My point was about trying deterministic control of weather. Just like the oft-asked "Could we stop a hurricane with a nuclear bomb?" situation, in natural systems it is generally extremely difficult to control large mass and energy fluxes quickly with small inputs. One exception to this would be cloud seeding, where a relatively minor perturbation metaphorically tips a metastable system (water-saturated cloud) over a transition point to a different state. Regarding CO2, as you know, that's a matter of affecting the statistical distribution of weather over very long times, not trying to decide whether we want it to be warmer next week.

Anonymous said...

Thanks for clarifying. I agree with your point about "rapid" control needing large energy input. (the characteristic timescale that we use to non-dimensionalise to define "rapid" is days because it is relevant to humans, or something else?)

But your example of cloud seeding raises the question of whether we fundamentally require large energy inputs to control storms, or if we have simply not (yet) figured out if/how we can exploit some metastability to control storms.

Anon@3:17

Jonah said...

Nevermind engineering the weather... build gigantic 'rainmills' and harvest that energy! Imagine the power you could reap in the Amazon, or monsoon season in Asia...