Somewhere along the line I heard the quote that “The air heat is just the oceans by other means” (or something close to that). Well, it’s pretty obvious if you have an instinctive grasp of specific heats, but I got to wondering about how to make it clear to folks without 3 or 4 years of chemistry classes…
So it occurred to me, one could show how much ocean equals all the air above it, clear to space, in terms of heat capacity. That ought to give an intuitive grasp.
So the atmosphere weighs about 14.5 pounds (or 1 BAR) per square inch. (Yes, I’m mixing weight and pressure units. It doesn’t matter for this purpose). How far down in the ocean is the same weight (pressure) of water? In this case my old scuba diving units make it easy. 33 feet or 10 meters.
Yes, I’m ignoring the tiny bits past the decimal point. We’re finding an intuitive rule of thumb, not measuring gold ingots… I’m also going to ignore the small change of specific heat with air density…
Ok, but water holds more heat per unit weight (or more precisely, mass) than does air. How much? (Or what are their specific heat values?) Well, air is about 1, and water is about 4.
So we need about 1/4 that depth of water to hold the same heat as one atmosphere of air, or about 8.25 feet or 2.5 meters. Hardly enough to float a small boat.
Now the Earth is only 2/3 oceans, so that would be about 12 feet of the ocean to equal ALL of the air, even that over land too. Call it obout 3.75 meters or 375 cm of ocean. Just about two people deep.
So, to offset a 1 C rise in air temperatures, only a little more cold deep ocean needs to be overturned by wind and tides. Conversely, even a minor change to lighter winds or tides would let the air warm a degree C.
Consider just how deep the oceans are, thousands of meters, and you can see it would take a very precise knowledge of exact ocean temperatures and depths to prove any air temperature change was not just due to minor variations in the ocean.
About rain & ice
But Wait, There’s More!
As I remember it, the heat of fusion of water is about 80. (Someone can check me on that)
So about 1/80th that much water turning to ice would be the same. Call it 1.8 inches or about 5 cm.
Now that seems pretty small to me. Maybe I’ve blown a calculation somewhere… but I don’t think so…
So when a few feet of ice form over the arctic ocean, that is one heck of a lot of air equivalent heat getting radiated out to space.
The heat of vaporization is even bigger. The Specific Heat of Vaporization for water being about 540.
So our 375 cm of ocean divided by 540 = 0.7 cm of rain. So to completely remove 1 C of temperature rise in the air would require 3/4 cm of ocean to evaporate, rise to the top of the troposphere, dump that heat to space (it can radiate out through the stratosphere just fine) as it condenses to a small cloud, then fall back to earth as rain. Call it 1/4 inch of rain.
So that’s all it would take to cause 1 C global increase in warming (1/4 inch less rain) or to reduce the globe 1 C (1/4 inch more rain). Do we even know how much global rain changes year to year or decade to decade?
Now I’ve done this all “off the cuff” and only one pass, and those numbers look mighty small to me, so definitly needs a cross check. Still, I think it isn’t too far wrong.
33 feet /4 / 540 ×12 = .183 inches.
Water ft./ air equiv. ht. / Sp. Ht. V. X ft. Per inch.
Seems to cross foot.
So provided I didn’t mess up too badly, those are some human sizes for water vs air on Earth. Measuring air temperature is exactly wrong for finding global heat. It’s the ocean and the rains…