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This question presupposes that

  1. The amount of fossil fuels on earth is limited
  2. Mankind will burn all of its fossil fuels eventually

Based on these presuppositions, the total amount of CO2 released into the atmosphere from burning fossil fuels during time X (where X is the time it takes to use up all fossil fuels) is constant.

Regulations of emissions would thus merely increase or decrease X while the total emissions remain constant.

What beneficial and/or negative effects would a shorter X (no emission guidelines) thus have over a longer X (strict emission guidelines)?

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closed as off topic by Qmechanic, Sklivvz, Manishearth Dec 28 '12 at 12:43

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This is much more than a physics question since the effects are supposed to be economic and environmental. The physics part of the question would concentrate on the time evolution of climatic variables that results from the different emission trajectories. –  Mitchell Porter Aug 22 '12 at 2:52
    
The main effect is the carbon cycle--- a one-time dump of all the CO2 is much more catastrophic, because plants fix the CO2 back into material that sediment into the ocean floor and elsewhere, and sequester the carbon back into fossils (eventually), so it makes a big difference. The physics component is actually very small, you would be better off asking on biology, since it's almost all about the carbon capture rate in plants.. –  Ron Maimon Aug 22 '12 at 6:14

2 Answers 2

The first thing to note is that we will not burn all accessible fossil fuels, at least not within the next couple of hundred years, because to do so would be to pretty much destroy human civilisation. So one of the presuppositions in the question is incorrect.

And now to the effect of the rate of release.

Greenhouse gas concentrations are a stock problem, rather than a flow problem, at human timescales.

Think of a bath with one tap part open, running water; and with the plug out. The tap is open just enough that the rate of water entering (the source), is equal to the rate of water going down the plug hole (the sink). So the level of water in the bath stays the same. Turn the tap up a notch, and the bath will steadily fill until it overflows.

The problem with what we've been doing over the last two centuries, is that we've increased the rate at which greenhouse gases enter the atmosphere (source); and at the same time, we've been cutting back the Earth's capacity to sequester $CO_2$ in the form of soil and biomass (sinks). So greenhouse gas concentrations have been rising sharply.

And that means that climate is changing, much more rapidly than it would in the normal scheme of things. The Earth has warmed and cooled before. Over millennia, and over millions of years. Which means that previous climate change, has happened at the same sort of timescales that evolution operates, and so life adapts, over hundreds of generations.

When climate changes rapidly (massive meteor strike, anthropogenic climate change), then evolution doesn't get off the starting blocks, and we have a mass extinction (we're currently in what is, as far as we can tell, the Earth's sixth mass extinction event).

And having built much of our civilisation, our cities, and our food production, on the climate and sea levels we've had for the last few centuries, it's a real problem to change those things rapidly. So the problem, for life and for civilisation, is the rate of change.

And that's why the release time, matters. Higher emissions rates, mean faster increases in global temperatures, and much less time to adapt:

From IPCC AR4, on impacts and timescales: enter image description here

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CO2 emissions obviously represent no problem regardless of the speed at which the fossil fuels are utilized. Concerning the greenhouse effect, the dependence of the temperature rise on the concentration is logarithmic and a doubling of CO2 (something we have to wait for until 2100 or so) only corresponds to 1 °C of warming (the no-feedback value may be computed to be 1.2 °C) which is pretty much undetectable without sophisticated measurement devices and complicated (and controversial) global averaging and homogenization. But even if the climate sensitivity were 3 °C, it wouldn't represent a problem although it could become noticeable locally.

However, there's a time scale at which the excess CO2 gets absorbed back to the oceans and the biosphere. Based on current absorption rates (2 ppm per year with the 115 ppm excess CO2), every 55 years, the deviation of the CO2 concentration from the equilibrium value (280 ppm for our "preindustrial interglacial" temperatures) decreases 2.718 times. During the glaciation cycles, this process may have been slower. The absorption rate is pretty much proportional to $(c-280{\rm ppm})$.

But it's clear that when the rate of CO2 emissions is slow enough, the CO2 concentration never surpasses a certain threshold. For example, if the world reduced the CO2 emissions to 50% starting from tomorrow, the CO2 concentration would be kept constant at 393 ppm in the future. That's because we're emitting 4 ppm worth of CO2 a year, it would drop to 2 ppm, and 2 ppm a year is also what the oceans and the biosphere remove from the atmosphere every year.

If the CO2 emissions were reduced to less than 50% of the current amount, the CO2 concentrations in the atmosphere would start to decrease.

More realistically, the CO2 emissions will continue to increase exponentially and gradually slower than that (especially during ice ages when the life and the oceans can't adapt so quickly: the "lag" could have been up to 800 years) and will peak at 600-800 ppm in a century or so.

So if someone thinks that elevated CO2 concentrations are a problem, the separation of the consumption of X to a longer period of time has the advantage that the maximum CO2 concentration that is ever reached will be lower. Of course, the real problem will be the dropping CO2 concentrations once the mankind stops CO2 emissions. For example, if the CO2 concentrations dropped back from current 393 ppm to 280 ppm, the "preindustrial interglacial" value, that would correspond to the drop by nearly 30% and the crop yields could decrease by 15% as a consequence because CO2 is of course a key (and in some sense the only) plant food. It's plausible that a billion of extra people on the Earth would start to starve.

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It's a little more complex in biology than physics. Most plants are not %CO2 limited and although they will evolve for higher concentrations not on industrial revolution timescales. The CO2 uptake by the oceans isn't linear with %CO2, as the absorption of more CO2 changes ocean pH and organisms are very sensitive to pH. –  Martin Beckett Aug 22 '12 at 15:37
    
Dear Martin, organisms aren't very sensitive to pH. In reality, virtually all organisms may live in pH between $p$ and $p+2$ i.e the concentration of the $H^+$ ions may be 100 times larger or smaller than "normal". pH=7 is the normal but there are organisms that prefer pH around 2.5, too. In a century, the maximum thing the CO2 emissions may achieve is to lower pH from 8.1 to 8.0 or 7.9 which is still alkaline and makes absolutely no practical difference. Extra comments: motls.blogspot.cz/2010/04/… –  Luboš Motl Aug 23 '12 at 10:30
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Concerning the question whether the growth is CO2 limited, it may be true that "most" aren't CO2-limited but this majority is dominated by algae and similar things we don't praise that much. Most of the important plants are CO2-limited even at present conditions and all "modern enough" plant species stop growing at 150 ppm of CO2. The staggering effect of higher CO2 on cowpea plants is the subject of a well-known video youtube.com/watch?v=P2qVNK6zFgE –  Luboš Motl Aug 23 '12 at 10:34
    
Concerning ocean absorption, then you're fundamentally wrong that this shouldn't pay attention to physics, just biology. The key processes are governed by Henry's law en.wikipedia.org/wiki/Henry%27s_law which is a law of physics, not biology, and in contrast with your expectations, it does start with proportionality. When all the feedbacks are included, the absorption isn't a linear function of the excess CO2 above the equilibrium but the nonlinearities don't affect any of my conclusions qualitatively. –  Luboš Motl Aug 23 '12 at 10:38

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