Carbon Dioxide Puzzles

I like it when people do interesting calculations and help me put their results on this blog. Renato Iturriaga has plotted a graph that raises some interesting questions about carbon dioxide in the Earth’s atmosphere. Maybe you can help us out!

The atmospheric CO₂ concentration, as measured at Mauna Loa in Hawaii, looks like it’s rising quite smoothly apart from seasonal variations:

However, if you take the annual averages from here:

• NOAA Earth System Laboratory, Global Monitoring Division, Recent Mauna Loa CO₂.

and plot how much the average rises each year, the graph is pretty bumpy. You’ll see what I mean in a minute.

In comparison, if you plot the carbon dioxide emissions produced by burning fossil fuels, you get a rather smooth curve, at least according to these numbers:

• U. S. Energy Information Administration Total carbon dioxide emissions from the consumption of energy, 1980-2008.

Renato decided to plot both of these curves and their difference. Here’s his result:

The blue curve shows how much CO₂ we put into the atmosphere each year by burning fossil fuels, measured in parts per million.

The red curve shows the observed increase in atmospheric CO₂.

The green curve is the difference.

The puzzle is to explain this graph. Why is the red curve roughly 40% lower than the blue one? Why is the red curve so jagged?

Of course, a lot of research has already been done on these issues. There are a lot of subtleties! So if you like, think of our puzzle as an invitation to read the existing literature and tell us how well it does at explaining this graph. You might start here, and then read the references, and then keep digging.

But first, let me explain exactly how Renato Iturriaga created this graph! If he’s making a mistake, maybe you can catch it.

The red curve is straightforward: he took the annual mean growth rate of CO₂ from the NOAA website I mentioned above, and graphed it. Let me do a spot check to see if he did it correctly. I see a big spike in the red curve around 1998: it looks like the CO₂ went up around 2.75 ppm that year. But then the next year it seems to have gone up just about 1 ppm. On the website it says 2.97 ppm for 1998, and 0.91 for 1999. So that looks roughly right, though I’m not completely happy about 1998.

[Note added later: as you’ll see below, he actually got his data from here; this explains the small discrepancy.]

Renato got the blue curve by taking the US Energy Information Administration numbers and converting them from gigatons of CO₂ to parts per million moles. He assumed that that the atmosphere weighs 5 × 10¹⁵ tons and that CO₂ gets well mixed with the whole atmosphere each year. Given this, we can simply say that one gigaton is 0.2 parts per million of the atmosphere’s mass.

But people usually measure CO₂ in parts per million volume. Now, a mole is just a certain large number of molecules. Furthermore, the volume of a gas at fixed pressure is almost exactly proportional to the number of molecules, regardless of its composition. So parts per million volume is essentially the same as parts per million moles.

So we just need to do a little conversion. Remember:

• The molecular mass of N₂ is 28, and about 79% of the atmosphere’s volume is nitrogen.

• The molecular mass of O₂ is 32, and about 21% of the atmosphere’s volume is oxygen.

• By comparison, there’s very little of the other gases.

So, the average molecular mass of air is

28 × .79 + 32 × .21 = 28.84

On the other hand, the molecular mass of CO₂ is 44. So one ppm mass of CO₂ is less than one ppm volume: it’s just

28.84/44 = 0.655

parts per million volume. So, a gigaton of CO₂ is about 0.2 ppm mass, but only about

0.2 × 0.655 = 0.13

parts per million volume (or moles).

So to get the blue curve, Renato took gigatons of CO₂ and multiplied by 0.13 to get ppm volume. Let me do another spot check! The blue curve reaches about 4 ppm in 2008. Dividing 4 by 0.13 we get about 30, and that’s good, because energy consumption put about 30 gigatons of CO₂ into the atmosphere in 2008.

And then, of course, the green curve is the blue one minus the red one:

Now, more about the puzzles.

One puzzle is why the red curve is so much lower than the blue one. The atmospheric CO₂ concentration is only going up by about 60% of the CO₂ emitted, on average — though the fluctuations are huge. So, you might ask, where’s the rest of the CO₂ going?

Probably into the ocean, plants, and soil:

But at first glance, the fact that only 60% stays in the atmosphere seems to contract this famous graph:

This shows it taking many years for a dose of CO₂ added to the atmosphere to decrease to 60% of its original level!

Is the famous graph wrong? There are other possible explanations!

Here’s a non-explanation. Humans are putting CO₂ into the atmosphere in other ways besides burning fossil fuels. For example, deforestation and other changes in land use put somewhere between 0.5 and 2.7 gigatons of carbon into the atmosphere each year. There’s a lot of uncertainty here. But this doesn’t help solve our puzzle: it means there’s more carbon to account for.

Here’s a possible explanation. Maybe my estimate of 5 × 10¹⁵ tons for the mass of the atmosphere is too high! That would change everything. I got my estimate off the internet somewhere — does anyone know a really accurate figure?

Renato came up with a more interesting possible explanation. It’s very important, and very well-known, that CO₂ doesn’t leave the atmosphere in a simple exponential decay process. Imagine for simplicity that carbon stays in three boxes:

• Box A: the atmosphere.

• Box B: places that exchange carbon with the atmosphere quite rapidly.

• Box C: places that exchange carbon with the atmosphere and box B quite slowly.

As we pump CO₂ into box A, a lot of it quickly flows into box B. It then slowly flows from boxes A and B into box C.

The quick flow from box A to box B accounts for the large amounts of ‘missing’ CO₂ in Renato’s graph. But if we stop putting CO₂ into box A, it will soon come into equilibrium with box B. At that point, we will not see the CO₂ level continue to quickly drop. Instead, CO₂ will continue to slowly flow from boxes A and B into box C. So, it can take many years for the atmospheric CO₂ concentration to drop to 60% of its original level — as the famous graph suggests.

This makes sense to me. It shows that the red curve can be a lot lower than the blue one even if the famous graph is right.

But I’m still puzzled by the dramatic fluctuations in the red curve! That’s the other puzzle.

Stabilization Wedges (Part 4)

Okay, here are the last two of Pacala and Socolow’s stabilization wedges. Remember, these wedges are ways to reduce carbon emissions. Each one is supposed to ramp up from 2004 to 2054, so that by the end it reduces carbon emissions by 1 gigaton per year. They claimed that seven wedges would be enough to keep emissions flat:

In Part 1 of this series we talked about four wedges involving increased efficiency and conservation. In Part 2 we covered one about shifting from coal to natural gas, and three about carbon capture and storage. In Part 3 we discussed five involving nuclear power and renewable energy. The last two wedges involve forests and agriculture:

14. Stop deforestation, start reforestation. They say we could stop half a gigaton of carbon emissions per if we completely stopped clear-cutting tropical forests over 50 years, instead of just halving the rate at which they’re getting cut down. For another half gigaton, plant 250 million hectares of new forests in the tropics, or 400 million hectares in the temperate zone!

To get a sense of the magnitude here, note that current areas of tropical and temperate forests are 1500 and 700 million hectares, respectively.

Pacala and Socolow also say that another half gigaton of carbon emissions could be prevented by created by establishing approximately 300 million hectares of plantations on nonforested land.

15. Soil management. When forest or grassland is converted to cropland, up to one-half of the soil carbon gets converted to CO₂, mainly because tilling increases the rate of decomposition by aerating undecomposed organic matter. Over the course of history, they claim, 55 gigatons of carbon has gone into the atmosphere this way. That’s the equivalent of two wedges. (Note that one wedge, ramping up linearly to 1 gigaton/year for 50 years, adds up to 25 gigatons of carbon by 2054.)

However, good agricultural practices like no-till farming can reverse these losses — also reduce erosion! By 1995, these practices had been adopted on 110 million of the world’s 1600 million hectares of cropland. If this could be extended to all cropland, accompanied by a verification program that enforces practices that actually work as advertised, somewhere between half and one gigaton of carbon per year could be stored in this way. So: maybe half a wedge, maybe a whole wedge!

I’ve seen a lot of argument about both these topics, and I’d love to learn more facts. Some of the controversy concerns the UN’s <a href="REDD+ program, which got a big boost in Cancún. “REDD” stands for Reducing Emissions from Deforestation and Forest Degradation — while the plus sign hints at the the role of conservation, sustainable management of forests, and enhancement of forest carbon stocks.

Some people think REDD+ is great, while others think it could actually hurt. The Wikipedia article says, among other things:

REDD is presented as an “offset” scheme of the carbon markets and thus, will produce carbon credits. Carbon offsets are “emissions-saving projects” that in theory “compensate” for the polluters’ emissions. Offsets allow polluting governments and corporations, which have the historical responsibility to clean up the atmosphere, to buy their way out of the problem with cheap projects that exacerbate social and environmental conflicts in the South. Moreover, it delays any real domestic action where a historical responsibility lies and allows the expansion of more fossil fuel explorations and extractions. The “carbon credits” generated by these projects can be used by industrialised governments and corporations to meet their targets and/or to be traded within the carbon markets.

There’s also a lot of argument about just how much long-term impact on atmospheric CO₂ a standing forest has, though everyone seems to agree that cutting one down releases a lot of CO₂.

For a bit more, try:

• About REDD+, United Nations.

• REDD+: Reducing Emissions from Deforestation and Forest Degradation, Center for International Forestry Research.

Next time I’ll give you a update on the stabilization wedges from Stephen Pacala himself, based on a talk he gave in 2008. It’s a bit scary…

Carbon Trading in California

It’s for real!

Or — to be more cautious — it might soon be for real!

On Thursday December 16th, 2010, California’s Air Resources Board began a cap and trade system for carbon. This system will implement the state’s law mandating that carbon emissions be reduced back to 1990 levels by 2020.

This will amount to a 15% decrease from current emissions.

The system will let greenhouse gas emitters buy and sell emission allowances. It covers everyone who emits more than 5,000 tons of carbon dioxide per year. That’s about 360 businesses, who taken together emit about 85% of the CO₂.

At first these business will receive free allowances that cover most of their emissions, but as time passes, they’ll have to buy those allowances through quarterly auctions. According to the plan, there will be two phases. By 2012, all major industrial sources and utilities will be covered. By 2015, distributors of fuels and natural gas will also be included.

The chair of the Air Resources Board, Mary Nichols, gave a speech. Among other things, she said:

This program is the capstone of our climate policy, and will accelerate California’s progress toward a clean energy economy. It rewards efficiency and provides companies with the greatest flexibility to find innovative solutions that drive green jobs, clean our environment, increase our energy security and ensure that California stands ready to compete in the booming global market for clean and renewable energy.

The governor also showed up at this historic board meeting, and gave a speech.

But I can guess what you’re wondering, or at least one of the many things you should be wondering.

“How much can California do by itself?”

Luckily, California is not doing this by itself. By the time the program gets rolling in 2012, California plans to have built a framework for carbon trading with New Mexico, British Columbia, Ontario and Quebec — some of its partners in the Western Climate Initiative.

The green guys are the ‘partners’; the other guys, blue because they’re watching carefully but sadly not taking part, are the ‘observers’.

Furthermore, ten states of the US — New York, New Jersey, Delaware, Maryland and the New England states — have started up another system, the Regional Greenhouse Gas Initiative, which covers only electric utilities. They are already doing auctions.

So, while in theory it might make sense to institute carbon trading on a national basis, political realities have pushed North America down a different path, where smaller regions take the lead in groupings that may transcend national boundaries! And that is very interesting in itself.

Stabilization Wedges (Part 3)

I bet you thought I’d never get back to this! Sorry, I like to do lots of things.

Remember the idea: in 2004, Stephen Pacala and Robert Socolow wrote a now-famous paper on how we could hold atmospheric carbon dioxide below 500 parts per million. They said that to do this, it would be enough to find 7 ways to reduce carbon emissions, each one ramping up linearly to the point of reducing carbon emissions by 1 gigaton per year by 2054.

They called these stabilization wedges, for the obvious reason:

Their paper listed 15 of these wedges. The idea here is to go through them and critique them. In Part 1 of this series we talked about four wedges involving increased efficiency and conservation. In Part 2 we covered one about shifting from coal to natural gas, and three about carbon capture and storage.

Now let’s do nuclear power and renewable energy!

9. Nuclear power. As Pacala and Socolow already argued in wedge 5, replacing 700 gigawatts of efficient coal-fired power plants with some carbon-neutral form of power would save us a gigaton of carbon per year. This would require 700 gigawatts of nuclear power plants running at 90% capacity (just as assumed for the coal plants). The means doubling the world production of nuclear power. The global pace of nuclear power plant construction from 1975 to 1990 could do this! So, this is one of the few wedges that doesn’t seem to require heroic technical feats. But of course, there’s still a downside: we can only substantially boost the use of nuclear power if people become confident about all aspects of its safety.

10. Wind power. Wind power is intermittent: Pacala and Socolow estimate that the ‘peak’ capacity (the amount you get under ideal circumstances) is about 3 times the ‘baseload’ capacity (the amount you can count on). So, to save a gigaton of carbon per year by replacing 700 gigawatts of coal-fired power plants, we need roughly 2000 gigawatts of peak wind power. Wind power was growing at about 30% per year when they wrote their paper, and it had reached a world total of 40 gigawatts. So, getting to 2000 gigawatts would mean multiplying the world production of wind power by a factor of 50. The wind turbines would “occupy” about 30 million hectares, or about 30-45 square meters per person — some on land and some offshore. But because windmills are widely spaced, land with windmills can have multiple uses.

11. Photovoltaic solar power. This too is intermittent, so to save a gigaton of carbon per year we need 2000 gigawatts of peak photovoltaic solar power to replace coal. Like wind, photovoltaic solar was growing at 30% per year when Pacala and Socolow wrote their paper. However, only 3 gigawatts had been installed worldwide. So, getting to 2000 gigawatts would require multiplying the world production of photovoltaic solar power by a factor of 700. See what I mean about ‘heroic feats’? In terms of land, this would take about 2 million hectares, or 2-3 square meters per person.

12. Renewable hydrogen. You’ve probably heard about hydrogen-powered cars. Of course you’ve got to make the hydrogen. Renewable electricity can produce hydrogen for vehicle fuel. 4000 gigawatts of peak wind power, for example, used in high-efficiency fuel-cell cars, could keep us from burning a gigaton of carbon each year in the form of gasoline or diesel fuel. Unfortunately, this is twice as much wind power as we’d need in wedge 10, where we use wind to eliminate the need for burning some coal. Why? Gasoline and diesel have less carbon per unit of energy than coal does.

13. Biofuels. Fossil-carbon fuels can also be replaced by biofuels such as ethanol. To save a gigaton per year of carbon, we could make 5.4 gigaliters per day of ethanol as a replacement for gasoline — provided the process of making this ethanol didn’t burn fossil fuels! Doing this would require multiplying the world production of bioethanol by a factor of 50. It would require 250 million hectares committed to high-yield plantations, or 250-375 square meters per person. That’s an area equal to about one-sixth of the world’s cropland. An even larger area would be required to the extent that the biofuels require fossil-fuel inputs. Clearly this could cut into the land used for growing food.

There you go… let me hear your critique! Which of these measures seem best to you? Which seem worst? But more importantly: why?

Remember: it takes a total of 7 wedges to save the world, according to this paper by Pacala and Socolow.

Next time I’ll tell you about the final two stabilization wedges… and then I’ll give you an update on their idea.

Cancún

What happened at the United Nations Climate Change Conference in Cancún this year? I’m trying to figure that out, and I could use your help.

But if you’re just as confused as I am, this is an easy place to start:

• Climate talks wrap with hope for developing nations, Weekend Edition Saturday, National Public Radio.

Here’s what I’ve learned so far.

The good news is, first, that the negotiations didn’t completely collapse. That was a real fear.

Second, 190 countries agreed to start a Green Climate Fund to raise and disburse $100 billion per year to help developing countries deal with climate change… starting in 2020.

A good idea, but maybe too late. The World Bank estimates that the cost of adapting to a world that’s 2 °C warmer by 2050 will be about $75-100 billion per year. The International Energy Agency estimates that the cost of supporting clean energy technology in developing countries is $110 billion per year if we’re going to keep the temperature rise below 2 °C. But these organizations say we need to start now, not a decade from now!

And how to raise the money? The Prime Minister of Norway, Jens Stoltenberg, leads the UN committee that’s supposed to answer this question. He told the BBC that the best approach would be a price on carbon that begins to reflect the damage it does:

Carbon pricing has a double climate effect — it’s a huge source for revenue, but also gives the right incentives for reducing emissions by making it expensive to pollute. The more ambitious we are, the higher the price will be – so there’s a very close link between the ceiling we set for emissions and the price. We estimate that we need a price of about $20/25 per tonne to mobilise the $100bn.

Third, our leaders made some steps towards saving the world’s forests. Every year, forests equal to the area of England get cut down. T This has got to stop, for all sorts of reasons. For one thing, it causes 20% of the world’s greenhouse gas emissions — about the same as transportation worldwide!

Cancun set up a framework called REDD+, which stands for Reducing Emissions from Deforestation and Degrading Emissions, with the cute little + standing for broader ecosystem conservation. This is supposed to create incentives to keep forests standing. But there’s a lot of work left. For example, while a $4.1 billion start-up fund is already in place, there’s no long-term plan for financing REDD+ yet.

The bad news? Well, the main bad news is that there’s still a gap between what countries have pledged to do to reduce carbon emissions, and what they’d need to do to keep the expected rise in temperature below 2 °C — or if you want a clearer goal, keeping CO₂ concentrations below 450 parts per million.

But it’s not as bad as you might think… at least if you believe this chart put out by the Center for American Progress. They say:

We found that even prior to the Copenhagen climate summit, if all parties did everything they claimed they would do at the time, the world was only five gigatons of annual emissions shy of the estimated 17 gigatons of carbon dioxide or CO₂ equivalent annual reductions needed to put us on a reasonable 2°C pathway. Since three gigatons of the projected reductions came from the economic downturn and improved projections on deforestation and peat emissions, the actual pledges of countries for additional reductions were slightly less than two-thirds of what was needed. But they were still not sufficient for the 2°C target.

and then:

After the Copenhagen Accord was finalized at the December 2009 climate summit, a January 2010 deadline was established for countries to submit pledges for actions by 2020 consistent with the accord’s 2°C goal. Two breakdowns of the pledges in February, and later in March, by Project Catalyst estimated that the five-gigaton gap had shrunk somewhat and more pledges had come in from developing countries. Part of the reason that pledges increased from developing countries was that the Copenhagen Accord had finally made a significant step forward on establishing a system of cooperation between developed and developing countries that had a chance at providing incentives for additional reductions.

And now, they say, the gap is down to 4 gigatons per year. This chart details it… click to make it bigger:

That 4-gigaton gap doesn’t sound so bad. But of course, this estimate assumes that pledges translate into reality!

So, the fingernail-biting saga of our planet continues…

Stabilization Wedges (Part 2)

Okay. We’re going through this paper, which you can read yourself:

• Stephen Pacala and Robert Socolow, Stabilization wedges: solving the climate problem for the next 50 years using current technologies, Science 305 (2004), 968-972.

The paper lists 15 ‘wedges’, each of which could ramp up to reducing carbon emissions by 1 gigaton/year by 2054. We’re going through all these wedges and discussing them. And the Azimuth Project is lucky to have a new member on board — Frederik De Roo — who is summarizing our discussion here:

• Azimuth Project, Stabilization wedges.

So, let’s get going!

Last time we covered four wedges related to energy conservation and increased efficiency. Wedge 5 is in a category of its own:

5. Shifting from coal to natural gas. Natural gas puts out half as much CO₂ as coal does when you burn them to make a given amount of electricity. After all, it’s mainly methane, which is made from hydrogen as well as carbon. Suppose by 2054 we have coal power plants working at 90% of capacity with an efficiency of 50%. 700 gigawatts worth of coal plants like this emit 1 gigaton of carbon per year. So, we can reduce carbon emissions by one ‘wedge’ if we replace 1400 gigawatts of such plants with gas-burning plants. That’s four times the 2004 worldwide total of gas-burning plants.

Wedges 6-8 involve carbon capture and storage:

6. Capturing CO₂ at power plants. Carbon capture and storage at power plants can stop about 90% of the carbon from reaching the atmosphere, so we can get a wedge by doing this for 800 GW of coal-burning power plants or 1600 GW of gas-burning power plants by 2054. One way to do carbon capture and storage is to make hydrogen and CO₂ from fossil fuels, burn the hydrogen in a power plant, and inject the CO₂ into the ground. So, from one viewpoint, building a wedge’s worth of carbon capture and storage would resemble a tenfold expansion of the plants that were manufacturing hydrogen in 2004. But it would also require multiplying by 100 the amount of CO₂ injected into the ground.

7. Capturing CO₂ at plants that make hydrogen for fuel. You’ve probably heard people dream of a hydrogen economy. But it takes energy to make hydrogen. One way is to copy wedge 6, but then ship the hydrogen off for use as fuel instead of burning it to make electricity at power plants. To capture a wedge’s worth of carbon this way, we’d have to make 250 megatons of hydrogen per year from coal, or 500 megatons per year from natural gas. This would require a substantial scale-up from the 2004 total of 40 megatons of hydrogen manufactured by all methods. There would also be the task of building the infrastructure for a hydrogen economy. The challenge of injecting CO₂ into the ground would be the same as in wedge 6.

8. Capturing CO₂ at plants that turn coal into synthetic fuels. As the world starts running out of oil, people may start turning coal into synfuels, via a process called coal liquefaction. Of course burning these synfuels will release carbon. But suppose only half of the carbon entering a synfuels plant leaves as fuel, while the other half can be captured as CO₂ and injected underground. Then we can capture a wedge’s worth of CO₂ from coal synfuels plants that produce 1.8 teraliters of synfuels per year. For comparison, total yearly world oil production in 2004 was 4.7 teraliters.

Now: What are the pros and cons of these four wedges? What is the biggest thing that Pacala and Socolow overlooked?

I’m puzzled about the last wedge. Pacala and Socolow say 1 gigaton carbon/year is the flow of carbon in 24 million barrels/day, or 1.4 teraliters/year. They assume the same value for synfuels and allow for imperfect capture, which leads them to conclude that carbon capture at synfuels plants producing 1.8 teraliters/year of synfuel can catch 1 GtC/year. But this calculation doesn’t make sense to me. If we’re catching just half the carbon, and 1 GtC/year = 1.4 teraliters oil/year, don’t we need to generate at least twice that — 2.8 teraliters synfuel/year — to catch wedge’s worth of carbon?

I’m also unclear what percentage of the carbon you can actually capture while turning coal into synfuels. Can you really capture half of it?

There’s also another funny feature of this last wedge. If we assume people are already committed to making synfuels from coal, then I guess it’s true, they’ll emit less carbon if they use carbon capture and storage as part of the manufacturing process. But compared to making electricity or hydrogen as in wedges 6 and 7, turning coal into synfuels seems bound to emit more carbon, even with the help of carbon capture and storage.

In general, it only makes sense to talk about how much carbon emission some action prevents when we compare it to some alternative action. That’s pretty obvious, but it gets a bit confusing when some of Pacala and Socolow’s wedges look like plausible alternatives to other ones.

Another question: how does carbon capture and storage work, actually? Summarizing Pacala and Socolow, I wrote:

One way to do carbon capture and storage is to make hydrogen and CO₂ from fossil fuels, burn the hydrogen in a power plant, and inject the CO₂ into the ground.

But I’d like to learn the details!

Carbon Emissions in 2009

A news item relayed to us from David Roberts:

• Richard Black, 2009 carbon emissions fall smaller than expected, BBC News, 21 November 2010.

“What we find is a drop in emissions from fossil fuels in 2009 of 1.3%, which is not dramatic,” said lead researcher Pierre Friedlingstein from the UK’s University of Exeter.

“Based on GDP projections last year, we were expecting much more.

“If you think about it, it’s like four days’ worth of emissions; it’s peanuts,” he told BBC News.

The headline figure masked big differences between trends in different groups of countries.

Broadly, developed nations saw emissions fall – Japan fell by 11.8%, the UK by 8.6%, and Germany by 7% – whereas they continued to rise in developing countries with significant industrial output.

China’s emissions grew by 8%, and India’s by 6.2% – connected to the fact that during the recession, it was the industrialised world that really felt the pinch.

The news story is based on this article, which is apparently not freely available:

• P. Friedlingstein et al., Update on CO₂ emissions Nature Geoscience, 21 November 2010.

By the way: how come I can afford to create a link to the original article, while the BBC and other mass media cannot? Is it really so bloody difficult? Isn’t it just basic good journalism?

Also by the way: I really like getting good suggestions for environmental news stories to blog about… but I love it when people join the Azimuth Forum and post links to these news articles under News and Information.

Some puzzles. Guess before you google:

1) Which nation has the highest carbon emissions per person? In 2007 its per capita carbon emissions were almost 3 times that of the USA. I bet it’s still the champion today.

2) Say I make some round-trip flights from Los Angeles to Singapore, with one stop each way. How many flights would it take to burn as much carbon as an average US citizen does in a year? A rough estimate, please!

3) How many such flights would equal the yearly carbon emissions of an average world citizen?

(I am calculating the footprint of a flight using Terrapass. I have no idea how accurate it is or how it works. Also: all my figures only count carbon emissions from burning fossil fuels.)