Atmospherics

The Volume and Mass of our atmosphere and CO2.

        Earth is a ball with a diameter of 7,909 miles, or 12,756 km.  The atmosphere in which 90% of us live is 1 mile deep, but some humans live up to 10,000 ft. or two miles and at that altitude 90% of all the air is below you, so we use a thickness of two miles or 3.226 kilometers for calculations.  To find the volume, and mass of the atmosphere we only need to determine the volume of a sphere 7,911 miles, or 12,759 kilometers in diameter, and subtract from it the volume of a sphere of 7,909 miles or 12,756 kilometers in diameter. 

        The volume of a sphere is 4/3 pi r^3, 4/3rds pi is 4.189 and when we do it for miles, 7909 cubed, or times itself three times, is 494 billion.  Before we multiply that by 4.189 you should know about scientific or engineering notation as it makes all of this much simpler.  

        In scientific notation 1,000 is 1 x 10^3, one followed by three zeros.  One million would be 1 x 10^6, one followed by six zeros.  Thus 494 billion would be 494 x 10^9.  There is a rule for numbers in this system that we quote them in terms of a unit, decimal point and usually only two more digits.  Under this rule we say 4.94 and then times 10^11 because we, in effect, reduced 494 by a factor of 100 in order to keep the first number in units as they enable easy approximation. 

        When we multiply 4.189, which is 4/3 pi from the “4/3 pi r^3” expression, we have 4.189 x 4.94 = 20.69 and we find that earth has a volume of 20.69 x 10^11 cubic miles.  And, to keep our mathematicians happy we convert that to 2.07 X 10^12.  Notice that we only moved the decimal point one place to the left so we only added one to the 10^11 part of the expression.  And, we rounded 2.069 to 2.07 as we generally like to have three significant figures. 

        Three significant figures is a hangover from the slide-rule days, as that was all they could do, but now with digital calculators we could have more and you will see numbers quoted to five and six places, but for most calculations this is unnecessary. 

        We have calculated the volume of our planet in cubic miles, 2.07 x 10^12.  The volume of our planet with the atmosphere is 2.074 x 10^12 miles and we have a problem.  By the traditions of math, science and engineering the volume of our atmosphere is an insignificant figure destined to be dropped if we stick to the slide rule tradition.  Could it be we have discovered why none of this became an issue before the invention of the digital calculator?  Our atmosphere didn’t exist in the minds of scientists?  That is not the case, but it could be the source of an interesting urban legend plus fodder for Art Bell and George Noory.  So, let us return the fourth digit to our original calculation of Earth’s volume, i.e. 2.069 X 10^12 and 2.074 by 10^12 for Earth plus atmosphere. 

        The difference is 0.005 X 10^12 cubic miles of air and as you have probably realized already the “0.005” is not right by our friends in the white coats, who will get all testy if we don’t fix it.  So, we’re going to move the decimal point three places to the right to make the 0.005 a “5” and then repair the value of this “exponential expression,” as these are called in polite company, by changing 10^12 to 10^9.  The logic is that where we increased the apparent value of 0.005 by 1000, or 10^3, we must reduce the exponent by 1000 or 10^3, so 10^12 becomes 10^9. And, we have found that our entire atmosphere has a volume of 5 X 10^9 cubic miles.  Five billion cubic miles. 

        At the surface every cubic foot of air weighs about one ounce, but at 10,000 feet the pressure has dropped to about 65% of that at sea level.  But, where air is perfectly elastic in this temperature range, the average weight/volume will be about 90% of the weight/volume at sea level.  This is the case as gravity is a relatively constant force in this range.  Gravity acts through the center of the Earth and being 7911 miles from that point is not very different from being 7909 miles away.  Thus, the force compressing the perfectly elastic gas is much the same from top to bottom.  If gravity acted from the surface we would have a wildly different atmosphere and anything taller than a cockroach would be gasping for breath.  

        Where a cubic mile is 5280 ft. cubed or 1.47 X 10^11 cubic feet and each cubic foot weighs about 0.9 ounces a cubic mile of air weighs 1.32 X 10^11 ounces or 8.25 X 10^9 pounds.  And where carbon dioxide is now 375 ppm, or 0.000375 decimally or 3.75 X 10^-4 exponentially then each cubic mile now contains 3.09 X 10^6 pounds of carbon dioxide, a little over 3 million.

        Where we have 5.0 X 10^9 cubic miles and each has 3.09 X 10^6 pounds of CO2 in it the entire atmosphere includes 15.45 X 10^15 pounds of carbon dioxide. 50 years ago the atmosphere had 280 ppm or 25% less CO2.   In the last half century the environmentalists thus claim we have put 3.86 X 10^15 pounds of CO2 into the atmosphere. 

        According to the UN's Intergovernmental Panel on Climate Change, nature releases between 150 and 153 gigatons of CO2 each year; we humans emit about six to nine gigatons. That's nature, 93 to 97 per cent; humans, three to six per cent. 

        But, the UN Intergovernmental Panel on Climate Change says we make only six to nine gigatons, the mean of which is 7.5 gigatons.  At that rate it would take us 515,000 years to make the CO2 for which we are blamed by the “greens.”  They have overestimated our importance in the problem by a factor of 10,300!  

        Studies of the world’s streams and rivers show that most of our carbon dioxide comes from limestone carbonates dissolved in rainwater.  When this water warms, becomes acidic or mixes with seawater the carbon dioxide comes out of solution and enters the atmosphere.  The next largest source of natural carbon dioxide is the decay of dead plants and animals.  The seas not only cover three fourths of the planet, but each square mile of seawater contains many times the living matter of each square mile of land. 

        The simple fact of the matter is that we could not change the climate with carbon dioxide if we wanted to and this was a conclusion reached by Svante Arrenhius over 100 years ago.  Sometimes it makes sense to look carefully into the rearview mirror.

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