Stellarator wrote:For context, the Millenium II simulation in 2009 contained a little over 1010 particles. 1010 particles means about 1020 interactions to compute per time step. The simulation was run for 22,000 time steps. It took 1.4 million computer hours on 2048 cores, or in other words about a month on a world-class supercomputer. If we make the generous assumption that the Moore's Law for the number of computations per second per consumer dollar continues to hold for the future, then when would we expect a computer in typical consumer price range to be able to do something like that in a few seconds or minutes? Maybe in another 20 years. But again this assumes that trend continues, that we don't hit a ceiling in terms of transistor density on a chip, or the ability to dissipate the heat away when it has to be doing that many computations that quickly in a confined space...So, short answer for when you can expect this to be possible? Don't hold your breath.
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Actually, this is serious question: when might computers be powerful enough to model this 'in-game'?.
PlutonianEmpire wrote:Yes, very slightly! Burning fossil fuels consumes O2 to create CO2, so for each molecule of CO2 produced, we add 1 carbon atom to the atmosphere. This increases the mass of the atmosphere, which in turn increases the pressure at the surface.
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By pumping all our greenhouse gasses into the atmosphere, are we also simultaneously increasing the air pressure?
By how much? Let's do the math. This might feel a bit roundabout, but stick with me. The payoff should be worth it.
The total mass of the atmosphere can be found by integrating the density of the atmosphere with respect to altitude from the surface to infinity, (which gives us the mass of atmosphere over each square meter of surface), and then multiplying that by the surface area of the Earth.
The density of the atmosphere follows an exponential of the form
Doing a simple substitution, we can pull out a factor of kT/mg from the integral, leaving the integral of e-u
du from 0 to infinity, which is 1. The total mass of the atmosphere becomes
is the density at the surface.
Now we invoke the Ideal Gas Law, PV=NkT. Divide both sides by VkT to get the number density: N/V = P/kT. Then multiply by the mass per molecule to get the mass density ρ. So we can sub this in for ρ0
at the surface, giving us
Now at last we have a relation between the surface pressure P and the mass of the atmosphere. And we know how much the mass of atmosphere changes when we burn carbon fuels to convert O2 to CO2 in the air. So solve for P in terms of everything else:
This is a pretty nice and simple result that could also have been found from intuition: the pressure at the surface is simply the weight of the atmosphere, which is its mass times gravitational acceleration, divided by the surface area.
What happens if we change the mass of atmosphere slightly? Then the pressure changes by
Plug in the values for the radius of the Earth (R = 6371km), g=9.81m/s2
, and let ΔM = 1 ton. Then this tells us the pressure at Earth's surface goes up by1.92x10-11 pascals per ton of carbon burned.
Note: The mass of a carbon atom is about 12 atomic mass units, while a CO2 molecule is 44. So for each ton of carbon burned, 44/12 = 3.67 tons of CO2 is "emitted", and 2.67 tons of oxygen is consumed.
Right now, humans are emitting about 10 billion
tons of carbon per year into the atmosphere. So this corresponds to an annual pressure increase of0.192 pascals per year. Or 1.9x10-6 atm.
Not very much.
Nor is the decrease in atmospheric oxygen associated with the combustion easily measurable. What is measurable is the effect of the greenhouse gas on the Earth's energy balance, warming the surface and cooling the upper atmosphere.