Simple Calculation - Anthropogenic Global Warming

[MobiusPizza]

I was neither a sceptic nor a firm believer of man made climate change, that's why I was trying to use some Mathematics to estimate which I should lean towards.

My simple calculation relies on these assumptions:

1. There are accurate data on fossil fuel usage in total.
2. Good estimates of CO2 output in parts per million contributed by man in the atmosphere can be easily calculated.
3. There is theory on the radiative absorption effect of CO2 as warming effect and I presume lab tested.
4. There is good estimate of sun's energy output reaching earth
5. Ignore man-made contributions of other greenhouse gases such as methane.

3 and 4 together fall under the umbrella assumption that the Radiative forcing formula used below is reasonably accurately derived.

There is 30 billion metric tonnes of CO2 released each year and rising.
The atmosphere has a mass of about five quintillion (5e18) kg (http://en.wikipedia.org/wiki/Earth's_atmosphere)

That's 5e18 / 3e12 = 6 part per million of CO2 each year and increasing.
Current concentration of CO2 is 387ppm. It is known by the

http://en.wikipedia.org/wiki/Radiative_forcing
According to radiative forcing formula,
increase from 387 to 387+6 = 393,

Change in temperature = lamda * 5.35 * ln(393/387) = 0.06 degrees.

This equates to about 0.06 degrees per year.
So a warming of 1 degrees per decade is feasible if the emission raises each year, and given that ignoring other man-made greenhouse gases will result in an underestimate.
Also it may be slightly less than 0.6 degrees in 10 years if emission stays the same (due to decreasing effect of natural logarithm on a growing C0 in the equation).

It isn't improbable but hinges on the fact that the assumptions made are reasonable.
What do you think? Anyone know how confident scientists are in the Radiative Forcing formula? Is it backed by experimental evidence, for instance, shining light on CO2 in lab and measure absorption characteristics in different temperature and pressure?

 

[MobiusPizza]

I was neither a sceptic nor a firm believer of man made climate change, that's why I was trying to use some Mathematics to estimate which I should lean towards.

My simple calculation relies on these assumptions:

1. There are accurate data on fossil fuel usage in total.
2. Good estimates of CO2 output in parts per million contributed by man in the atmosphere can be easily calculated.
3. There is theory on the radiative absorption effect of CO2 as warming effect and I presume lab tested.
4. There is good estimate of sun's energy output reaching earth
5. Ignore man-made contributions of other greenhouse gases such as methane.

3 and 4 together fall under the umbrella assumption that the Radiative forcing formula used below is reasonably accurately derived.

There is 30 billion metric tonnes of CO2 released each year and rising.
The atmosphere has a mass of about five quintillion (5e18) kg (http://en.wikipedia.org/wiki/Earth's_atmosphere)

That's 5e18 / 3e12 = 6 part per million of CO2 each year and increasing.
Current concentration of CO2 is 387ppm. It is known by the

http://en.wikipedia.org/wiki/Radiative_forcing
According to radiative forcing formula,
increase from 387 to 387+6 = 393,

Change in temperature = lamda * 5.35 * ln(393/387) = 0.06 degrees.

This equates to about 0.06 degrees per year.
So a warming of 1 degrees per decade is feasible if the emission raises each year, and given that ignoring other man-made greenhouse gases will result in an underestimate.
Also it may be slightly less than 0.6 degrees in 10 years if emission stays the same (due to decreasing effect of natural logarithm on a growing C0 in the equation).

It isn't improbable but hinges on the fact that the assumptions made are reasonable.
What do you think? Anyone know how confident scientists are in the Radiative Forcing formula? Is it backed by experimental evidence, for instance, shining light on CO2 in lab and measure absorption characteristics in different temperature and pressure?

 

[wwswimming]

Pv = nRT ?

 

[BrownTown]

That said there are several other effects that could result in a more complex function. For example as the earth were to heat up the ice at the poles would melt and would result in more solar radiation being absorbed bt the oceans instead of reflected by the ice. Also, the amount of CO2 that can dissolve in water decreases as it heats up meaning the oceans could release CO2 as the earth warms.

Of course on the other end it could turn out that most of the CO2 dissolves in the oceans and doesn't stay in the atmosphere.

That said there are three important calculations here. One is how much the earth will warm due to CO2 releases. The second is how much this will cost our society and the third is how much the cost to stop global warming will cost. If the cost of stopping global warming is more than the cost of global warming itself then there inst really much point in stopping it.

 

[William Gaatjes]

I was neither a sceptic nor a firm believer of man made climate change, that's why I was trying to use some Mathematics to estimate which I should lean towards.

My simple calculation relies on these assumptions:

1. There are accurate data on fossil fuel usage in total.
2. Good estimates of CO2 output in parts per million contributed by man in the atmosphere can be easily calculated.
3. There is theory on the radiative absorption effect of CO2 as warming effect and I presume lab tested.
4. There is good estimate of sun's energy output reaching earth
5. Ignore man-made contributions of other greenhouse gases such as methane.

3 and 4 together fall under the umbrella assumption that the Radiative forcing formula used below is reasonably accurately derived.

There is 30 billion metric tonnes of CO2 released each year and rising.
The atmosphere has a mass of about five quintillion (5e18) kg (http://en.wikipedia.org/wiki/Earth%27s_atmosphere)

That's 5e18 / 3e12 = 6 part per million of CO2 each year and increasing.
Current concentration of CO2 is 387ppm. It is known by the

http://en.wikipedia.org/wiki/Radiative_forcing
According to radiative forcing formula,
increase from 387 to 387+6 = 393,

Change in temperature = lamda * 5.35 * ln(393/387) = 0.06 degrees.

This equates to about 0.06 degrees per year.
So a warming of 1 degrees per decade is feasible if the emission raises each year, and given that ignoring other man-made greenhouse gases will result in an underestimate.
Also it may be slightly less than 0.6 degrees in 10 years if emission stays the same (due to decreasing effect of natural logarithm on a growing C0 in the equation).

It isn't improbable but hinges on the fact that the assumptions made are reasonable.
What do you think? Anyone know how confident scientists are in the Radiative Forcing formula? Is it backed by experimental evidence, for instance, shining light on CO2 in lab and measure absorption characteristics in different temperature and pressure?

It is highly likely that our weather is influenced by many things. And the most powerful effects have the most influence. The sun, the radiation , cosmic rays. Our earth is pretty stable with respect to rotation/precession. Local earth effects are more found in the ocean. Then there are theories that bacteria influence the weather as well. Our pollution could cause a bacteria multiplying frenzy of a certain species. Now since energy conservation is present, that means the secretions of the bacteria are important. What do they secrete ? And what is more important, when are these bacteria talking with each other ?
It is everything combined that can shift the balance.

When putting on my tin foil conspiracy hat

Lots of people think that when Al Gore went around the world with his movie, he hoped to spark a whole new global industry : A green environmental friendly industry.
Truth is this industry was already started long ago.
But since it is an emerging industry it needs lot's of financial back up.

Oil was supposed to get more scarce.
The green industry would globally finally be able to reach critical mass.
Then the financial market fell apart.
And one after another the green investors where bankrupted as well.
Now many environmental projects are on hold or stopped.
Oil has become more cheap once again and THE energy source for decades to come.
Taking my tin foil hat off again.


Looking at my country...
I was surprised to read that new electrical power plants which use coal as energy source will be build with the option of being environmental friendly. The separating of polluting material is not enforced but optional. And since these coal plants needs to be lucrative, any other use of windpower and solar power is not lucrative for the same electrical energy producer/company. This al was accomplished by the same minister of environment that forced upon the people the use of compact fluorescent lamps. And the same minister that wants CO2 restrictions so heavy that the entire industry will be killed.
Now is that not amazing ?

 

[jimhsu]

It's still my belief that green industry is not only desirable socially, but that it will be inevitable economically. Simply said, fossil fuels are limited, but our desires for energy are not. Instead of giving up, we do what we've done as a species for the past few million years and adapt. Capitalist markets will prefer the cheapest solution to the problem (considering externalities of course) and eventually oil will be expensive enough that "green power" will be the more affordable solution, even before carbon subsidies and such ($150/barrel almost got us there, but then the crash happened).

PV panels for example are affected by positive feedback - more panels bought means more on-line manufacturing capacity, creating competition/economies of scale and decreasing prices even more (http://spectrum.ieee.org/blog/semiconductors/devices/tech-talk/photovoltaic_moores_law_on_tra).

 

[William Gaatjes]

it's still my belief that green industry is not only desirable socially, but that it will be inevitable economically.

I totally agree.

 

[DrPizza]

That said there are several other effects that could result in a more complex function. For example as the earth were to heat up the ice at the poles would melt and would result in more solar radiation being absorbed bt the oceans instead of reflected by the ice. Also, the amount of CO2 that can dissolve in water decreases as it heats up meaning the oceans could release CO2 as the earth warms.

Of course on the other end it could turn out that most of the CO2 dissolves in the oceans and doesn't stay in the atmosphere.

edit: I was thinking that I saw a link here in the forums, but I think it was something that was sent to me at school. There's a great presentation that was given at MIT on the topic; fairly recent.

That said there are three important calculations here. One is how much the earth will warm due to CO2 releases. The second is how much this will cost our society and the third is how much the cost to stop global warming will cost. If the cost of stopping global warming is more than the cost of global warming itself then there inst really much point in stopping it.

Actually, there is a point - there are certain "tipping points" that once we pass them, there's no turning back. One is when the permafrost thaws. It will result in a lot of greenhouse gas emissions that will increase the rate of global warming.

A lot of people think "what's the big deal, it's just a few degrees" - but the difference between right now & the peak of the ice age is actually "just a few degrees." (4 or 5 IIRC)

 

[BrownTown]

In terms of green power being "inevitable" though, that's not necessarily true at this point in history. There is still more than enough coal oil and natural gas in the ground to power to power our society as long as any of us will be alive. Not to mention the much larger amounts of nuclear fuel especially if reprocessing were allowed. Right now there really is only one "green" source of power which is anything close to economical and that is wind power. However, there are only certain parts of the country where it actually makes economic sense and building a 500 mile transmission line from those locations to the big cities can cost more than the wind turbines themselves. Also due to grid stability reasons it really isn't prudent to have wind supply more than ~10% of demand, the high variability puts much more strain on the grid than constant power from a coal or nuclear plant.

In the end the only way to supply the ever growing energy needs isn't by getting rid of the most abundant energy sources we have (coal and nuclear), you need to integrate EVERYTHING into a comprehensive approach so that teh strength of each energy source can cover for the weaknesses of others.

 

[jimhsu]

Coal is projected to last 200 or a few hundred years, last time I heard. Uranium is something like 85 (provable) (http://nuclearinfo.net/Nuclearpower/WebHomeAvailabilityOfUsableUranium), though a lot of potential reserves exist (>90&#37. Deuterium in ocean water for fusion is good for several million, I think. Actually though, any fossil fuel we have is essentially unlimited as far as economics is concerned; "Peak oil" and such are predictions that the COST of extracting oil will eventually exceed the PROFIT from selling it, given that it has to be competitive with other energy sources. We can never use up all the oil in the world, because it will simply be unprofitable to do so, and no one is crazy enough to dig up more at a loss. The sun, however, has several billion more years to go before it becomes "unprofitable" to exploit it (ie the earth gets destroyed).

 

[William Gaatjes]

Coal is projected to last 200 or a few hundred years, last time I heard. Uranium is something like 85 (provable) (http://nuclearinfo.net/Nuclearpower/WebHomeAvailabilityOfUsableUranium), though a lot of potential reserves exist (>90%). Deuterium in ocean water for fusion is good for several million, I think. Actually though, any fossil fuel we have is essentially unlimited as far as economics is concerned; "Peak oil" and such are predictions that the COST of extracting oil will eventually exceed the PROFIT from selling it, given that it has to be competitive with other energy sources. We can never use up all the oil in the world, because it will simply be unprofitable to do so, and no one is crazy enough to dig up more at a loss. The sun, however, has several billion more years to go before it becomes "unprofitable" to exploit it (ie the earth gets destroyed).

Although many people will disagree with me, i see nuclear energy also as green power. And not only because of the emitted colors in some wrong designs... :biggrin:

 

[cheesehead]

From what I understand, we're all really, really, really epically screwed. And it's already too late.

Although many people will disagree with me, i see nuclear energy also as green power. And not only because of the emitted colors in some wrong designs... :biggrin:

It's the ONLY viable green energy source. Solar and wind are unreliable, hydroelectric only works in certain areas, and geothermal is basically only practical for Finland.

Nuclear fusion is going to be ah heck-all expensive, but worth every penny.

 

[William Gaatjes]

From what I understand, we're all really, really, really epically screwed. And it's already too late.



It's the ONLY viable green energy source. Solar and wind are unreliable, hydroelectric only works in certain areas, and geothermal is basically only practical for Finland.

Do you not mean Iceland ?
Finland is great for woodgas installations.
http://en.wikipedia.org/wiki/Wood_gas

And i agree that solar and wind are secondary powersources.

Nuclear fusion is going to be ah heck-all expensive, but worth every penny.

There are a lot of viable and reliable fission designs. It is just that the overactive and uninformed green hippies have been very good at feeding wrong information to the masses and politicians.

I am still hoping for a rubbiatron, it runs on thorium and can burn up nuclear waste we have stored today. In essence, you have for a 1000 years of energy and you can burn your nuclear fuel for a 95%. I have read once that a current fission reactor uses less then 10 percent of it's fuel. All that waste still has so much energy in it. And the rubbiatron can use it. Another name for it is energy amplifier.

I never really understood why the rubbiatron is doomed.
Maybe someone has a technical answer for me ?
Do not come with that to expensive crap.
Current fusion projects has cost more then 30 billion dollars world wide and nothing is accomplished yet. While a rubbiatron can be build with readably available technology, that is if it really works.
http://en.wikipedia.org/wiki/Energy_amplifier


When thinking of fusion, The late Robert Bussard had some promising idea's...
His idea was that the tokamak can never work reliable. And thus his company devised a version that has according to him more potential.


http://en.wikipedia.org/wiki/Robert_W._Bussard

http://emc2fusion.org/

And a google techtalk with Robert W Bussard about his company and their fusion reactor design .

http://video.google.com/videoplay?docid=1996321846673788606#

And for those interested in energy from thorium...
http://www.energyfromthorium.com/forum/

 

[cheesehead]

There are a lot of viable and reliable fission designs. It is just that the overactive and uninformed green hippies have been very good at feeding wrong information to the masses and politicians.

The problem with current fission designs is twofold: There's a limited supply of uranium in the world, and they're really bleeding expensive. However, I agree that with a relatively small amount of research pebble bed reactors could become a practical and affordable source of propulsion for large container ships and the like, eliminating a huge source of CO2.

That said, regardless of type, I'm very enthusiastic about the possibility of thorium reactors. I'm also interested in the use of "CANDU"-style heavy water reactors, capable of using nuclear waste as fuel and breaking it down into less harmful isotopes in the process. (Electricity AND safer waste - what's not to like?)

That said, if we can get ITER to hit breakeven...well, I'm throwing one hell of a party.

 

[William Gaatjes]

The problem with current fission designs is twofold: There's a limited supply of uranium in the world, and they're really bleeding expensive. However, I agree that with a relatively small amount of research pebble bed reactors could become a practical and affordable source of propulsion for large container ships and the like, eliminating a huge source of CO2.

That limited supply is with current reactors. With the more efficient newer designs more of the fuel is actually used. It is amazing with how much energy is still left in that waste.

That said, regardless of type, I'm very enthusiastic about the possibility of thorium reactors. I'm also interested in the use of "CANDU"-style heavy water reactors, capable of using nuclear waste as fuel and breaking it down into less harmful isotopes in the process. (Electricity AND safer waste - what's not to like?)

i had to look that up candu.
http://en.wikipedia.org/wiki/CANDU

I totally agree with the thorium reactors. LFTR seems also to be a good candidate next to the rubbiatron and candu.
http://en.wikipedia.org/wiki/Molten_salt_reactor

That said, if we can get ITER to hit breakeven...well, I'm throwing one hell of a party.

Although i do find the design from Robert Bussard extremely interesting, I will be joining you and bring the booze

 

[Lemon law]

I would point out to the OP, if CO2 were the only factor in global warming, such a simple calculation might exist. But as we even start to scratch the surface of predicting global warming, with our existing climate models failing badly, its quite apparent that many many factors are operating at the same time. And even if an understanding single factor analysis is possible in a lab, we understand almost nothing about how all the factors interact when they all operate at the same time.

 

[drinkmorejava]

I'm confused, how does a mass ratio of 6/1000000 translate to 6ppm?
given mass atm=5e18kg and an approx molar mass of 14.67g/mol->3.4083e20moles in the atm
mass C02 added=3e12kg and molar mass of 44.01g/mol->6.817e14moles C02 added each year
6.817e14moles/3.4083e20moles*1000000=2ppm

 

[drinkmorejava]

Another question.
From your model lambda=~.73

So an increase in the c02 content of the atm by 1ppm increases the temperature of the atmosphere by .01C. Or in other other words, that 1 c02 molecule traps enough energy to increase it's temperature .01*1000000=10000C?

This of course assumes everything has the same specific heat. But I'm not convinced that that model even touches specific heat at all.

Someone mind doing an energy balance on that for me? I have more fun things to do.