atmospheric heating
Or, some people just have too much time on their hands.
There was a question, "How much has man warmed the earth? How much energy have we added to the environment?"
At this point, there's a bit less than a rise of 1 degree in the average planetary temperature.
If I consider only the atmosphere, and ignore ocean heating, ice melting, etc, think I can actually calculate this.
First, one ought to point out that we didn't make a big fire and heat stuff up.
What we did is similar to putting on an extra blanket, so that the heat we get from the sun does not get lost.
The average temp of the earth is the balance between the energy we receive from the sun, + the energy that is conducted up from the center of the earth, balanced by the amount of energy radiated away from the earth.
And the 40% increase in CO2 in the atmosphere has reduced the amount of energy radiated away from the earth.
After considerable searching, I think I found how to look at the air temp increase.
What I propose to do is see what the effect would be if the atmospheric heating were to be applied to the 5 great lakes.
This will, in fact, minimize what we think of as the heating somewhat, because water is hard to heat. It absorbs more energy, per pound, than almost anything else, for a given temperature rise. To a large degree, that's why we don't see a large temperature change on the earth. The ocean is absorbing all the energy, and changing temperature very slowly. The first thing to do is go look for the data we'll need.
http://environment.newscientist.com/channel/earth/climate-change/dn11639
The graph indicates a temp increase about 0.8 degrees C (from -0.3 to +0.5) in the last 100 years.
specific heat capacity of air is about 1000 J / kg
water with a specific heat of 4200 J / (kg oC).
So how much air is there? first calculate surface area of earth.
Sphere Surface Area = 4 • π • r² = π • d²
or (8000*5280)^2*pi or
((8 000 * 5 280)^2) * pi = 5.6052849 × 10^15 <== surface area of earth, in sq ft.
Now over every sq in of earth, there are 14.7 pounds of air (that's what makes air pressure)
so, converting to sq ft 14.7*144
And the total weight of atmosphere is (8000*5280)^2*pi*14.7*144 or
((8 000 * 5 280)^2) * pi * 14.7 * 144 = 1.18652671 × 10^19 <== total weight of air in pounds.
http://www.epa.gov/glnpo/statsrefs.html -- next, how much water is there in the great lakes?
The water volume is 22,600 Km^3 in the the 5 great lakes
Since 1 kilometer = 3,280.8399 feet the total weight of water in the great lakes is
3281^3*62.4 or (3 281^3) * 62.4 = 2.20395783 × 10^12 <== total weight of water in all 5 lakes.
So now, we have the total weight of air and water in the great lakes.
We note that the air is surprisingly heavier.
Oh, we've used Joules. what are they? One joule = the energy required to heat one gram of dry, cool air by 1 degree Celsius. Or, in our case, 1/453.6 pounds 1 degree C.
We've raised the temperature of the atmosphere 0.8 degrees C in the last 100 years.
So, if we were to apply the energy of that temperature change, to the water in the great lakes, what would it do?
Above, we've noted that the specific heat of water is 4 times that of air.
So what we want to calculate is how many degrees would the great lakes heat up, if the energy we've added to the atmosphere was concentrated in the water of the great lakes.
To do that, we calculate #air/#lake*1000/4200/453.6 or
--- air weight--- !- water weight -!-air/water specific heat-!-grams/pounds-!- 0.8 degree rise
((8000*5280)^2*pi*14.7*144)/(3281^3*62.4)*1000/4200/453.6*0.8 --- or that's enough heat/energy to raise the temperature of all the water in the 5 great lakes by:
(((((((8 000 * 5 280)^2) * pi * 14.7 * 144) / ((3 281^3) * 62.4)) * 1 000) / 4 200) / 453.6) * 0.8 = 2 260.69456 degrees. (I sure like google calculator.)
The energy that's been accumulated is enough to raise the temp of all the water in all 5 great lakes 2,260 degrees.
Or, raise the temp of all 5 lakes, top to bottom, from freezing to boiling, 22 times over.
Or, raise the temp of all 5 lakes, top to bottom, from freezing to boiling, AND boil them all dry, 3 1/2 times over.
That's only considering the energy we've added to the atmosphere, and skipping the ocean heating and ice we melted in glaciers, ice fields, permafrost, and floating ice, which, if i could figure out how to calculate it, would likely be much larger.
Today, i wondered how much CO2 has been added to the atmosphere. Eg, over your house, how much CO2 is there? So, let's say you have a 2,000 sq ft house. How much CO2 is in the air column over your house?
14.7 * (44 / 29) * (380 / 1 000 000) * (2 000 * 144) = 2,440 pounds.
(That's atmospheric pressure * weight of CO2/air * volume of CO2 * area of your house. And we get ...)
Well over a ton. A couple hundred years ago, it would only have been 1,800 pounds. there are 600 pounds more CO2, just over your house, than there were not long ago.