CO2/Global Warming- is the math wrong? Convince me!

Question

If you are planning to comment on politics or the "bad and good" of the human contribution to global warming debate don't bother to answer. If you want the opportunity to change my mind with truthful facts then read on...

First, the facts. This info is undisputed and available from any number of sources. If you have other info let me know:

1. The general consensus is that HUMANS are responsible for global warming;

2. The human population has increased 700% since 1800(approximate figures are being used);

3. The CO2 concentration has increased 27% since 1800.

Now, the time to convince me...

By simple math we can determine the per capita (per person) amount of CO2 in the atmosphere in 1800. If we were to use that same number today then the levels would be 700% higher, not 27% higher. This leads to a conclusion that we are "cleaner" now than in 1800- not by just a little bit, but by 99%... um... lets call it 99.97%.

So, if human activities, particularly the emission of CO2, are the major reason for global warming and our production has decreased more than 99%, then don't you think that there is some other reason... like the NATURAL cycles of the earth and as a result we have virtually no ability to change it?

Answer 1

It's relatively straightforward, but whether you think this is simple math or not is another matter.  To get an estimate of how fast CO2 is building up in the atmosphere, you need to solve this differential equation:

dC/dt = (M(in) - M(out))/V

where C is the concentration of CO2 in the atmosphere, M(in) is the total mass of CO2 entering the atmosphere, M(out) is the total mass of CO2 leaving the atmosphere, and V is the volume of the atmosphere.  V is trivial to compute and it's constant.  The other two terms are more problematic.

M(in) can be defined as:

M(in) = M(humans) + M(natural)

where M(humans) is the CO2 produced by humans and M(natural) is all the atmospheric CO2 sources from natural processes.  For this example, assume M(natural) is constant.  M(humans) can be broken down into:

M(humans) = N(humans)P(human/time)

where N(humans) is the total number of humans and P(human/time) is the per capita production of CO2 per unit time.  It is incorrect to assume P(human/time) is constant.  The energy use per capita today is huge compared to what it was in 1800.  N(human) is exponential with time so:

N(humans) = N0*exp(a*t)

where N0 is the population in 1800 and a is whatever rate constant makes the population in 2000 equal to the world's population.  The functionality of P(human/time) is less clear to me, linear is always a good choice if you don't know what else to use:

P(human/time) = b*t + P0

where P0 is the CO2 production in 1800 and b is whatever constant you need to make that equal to the CO2 production in 2000.  

M(out) can be written as:

M(out) = M(out-terrestrial) - M(out-ocean)

where I would start off assuming M(out-terrestrial is constant) but I have no idea how to estimate what it might be.  M(out-ocean) does have a known functional form:

M(out-ocean) = k * A * (C - H*C(ocean))

where k is the air-sea transfer velocity, A is the area of the ocean, H is the Henry's Law solubility of CO2, and C(Ocean) is the average concentration of CO2 at the ocean surface (note, this is not equal to the bicarbonate concentration).  

Ok, so put all that c**p together and you get:

dC/dt = ( (N0*exp(a*t))*(b*t+P0) + M(natural) - M(out-terrestrial) - k*A(C-H*C(ocean)))/V

If you use realistic numbers for the various terms in that equation and integrate it numerically, starting from 280 ppmv, you will come up with a pretty decent fit to the actual long-term rise in atmospheric CO2.  

There is no real issue with the numbers.  Humans, can and are affecting atmospheric CO2 concentrations.

Answer 2

I'm really not following your logic here.  The planet doesn't care what the per capita CO2 emissions are, it cares about total CO2 emissions and total atmospheric CO2 concentration.

Besides which, your math is wrong.  Before humans became industrialized, the atmospheric CO2 concentration was around 280 ppm.  The per capita CO2 concentration was zero, because humans weren't responsible for any of that 280 ppm.  But based on your math, people today are "cleaner" these humans who emitted zero CO2.

Linked below is a graph of human CO2 emissions which should help.  It even has a per capita emissions graph which shows we're at the highest level of per capita CO2 emissions in human history.

http://cdiac.esd.ornl.gov/trends/emis/gl...

It's perfectly possible to distinguish between natural and human atmospheric CO2.  Like I said, prior to industrialization the level was about 280 ppm.  This had nothing to do with human breathing, which is part of the natural carbon cycle which is in balance (natural sources absorb as much as they emit).

Now atmospheric CO2 is over 380 ppm (37% increase).  By examining the isotopic ratios of carbon atoms in the atmosphere, scientists have determined that this increase is entirely due to human activities (burning fossil fuels and deforestation).

http://www.realclimate.org/index.php?p=8...

Bottom line is that you can't assign all atmospheric CO2 to humans.  That's a faulty assumption which partially leads to your faulty conclusion.

Answer 3

Well as far as consensus goes I will not comment because it is not validation through scientific method.

Point number two agreed the population has increased that much.

Point number three is admitted to by most if not all, but the cause is questioned.

Conclusions are difficult because most people on both sides of the question are not aware that many of the temperature numbers used to develop the global warming/climate change predictions have been found to be well off from reality and NASA has been verifying them and fixing the ones found to be wrong. Currently NASA has corrected the numbers for the US and is working on the ones from other countries. NASA has not released any fixes on the international numbers as yet but the person who discovered the problem originally and reported it to them does report that NASA has found them to be at least as far off as the now fixed US ones were and that it will take some time to fix all of the errant ones and publish the correct ones.

It is beginning to look as if the whole AGW thing was built on foundations of sand and the tides of truth are coming and washing the sand away. Science always wins out in the long run for those who accept nothing less than truth!

Answer 4

1 is an opinion

2 is not a fact, an estimate

3 is not a fact, but an estimate

You jump to a cause and effect automatically, no facts to prove the link.

A famous theory concludes that because pirates are decreasing they lack of pirates causes global warming.

My theory is that the sun is warming the earth and the slight increase has caused the CO2 in solution in the ceans is being released making CO2 to go up.

Answer 5

To understand the faulty in your math, you have to understand the basics of the earth's carbon cycle.

Look at this picture: http://global-warming.accuweather.com/bl...

What it tries to show is that there are many natural causes to the CO2 in our atmosphere. In fact, human emissions are just a small fraction of the total. The important thing is that the other "natural" sources are in balance. Actually, they absorb more carbon then they emit. The human contribution on the other hand is only adding more CO2 to the atmosphere.

So here's a question for you: If you increase a "small fraction" with 700%, what will happen with the total?

Once you know the answer to that question you know ONE of the reasons why your math is wrong.

Answer 6

People were clear-cutting, raising beef cattle and exhaling before industrialization, so Dana is simply incorrect to argue that NONE of the pre-industrial 280 ppm could have been contributed by humans.

Answer 7

You are assuming that human population is correlated with CO2 concentration.  This is a false assumption.  It is not the number people that causes an increase in CO2.  Perhaps you are reasoning that human exhaling is causing an increase in CO2.  That is not the cause, the carbon that we breath out comes from the food we eat which ultimately comes from plants that get the CO2 from the air.  As you can see this is all part of the normal carbon cycle and does not contribute to an increase in CO2.

The increase in CO2 is primarily from the burning of fossil fuels.  Most of the people on earth burn very little to no fossil fuels.  The correlation is the amount of fossil fuels being burned, not the population.