The Mathematics of Planet Earth

31 October, 2012

Here’s a public lecture I gave yesterday, via videoconferencing, at the 55th annual meeting of the South African Mathematical Society:

Abstract: The International Mathematical Union has declared 2013 to be the year of The Mathematics of Planet Earth. The global warming crisis is part of a bigger transformation in which humanity realizes that the Earth is a finite system and that our population, energy usage, and the like cannot continue to grow exponentially. If civilization survives this transformation, it will affect mathematics—and be affected by it—just as dramatically as the agricultural revolution or industrial revolution. We cannot know for sure what the effect will be, but we can already make some guesses.

To watch the talk, click on the video above. To see slides of the talk, click here. To see the source of any piece of information in these slides, just click on it!

My host Bruce Bartlett, an expert on topological quantum field theory, was crucial in planning the event. He was the one who edited the video, and put it on YouTube. He also made this cute poster:

I was planning to fly there using my superpowers to avoid taking a plane and burning a ton of carbon. But it was early in the morning and I was feeling a bit tired, so I used Skype.

By the way: if you’re interested in science, energy and the environment, check out the Azimuth Project, which is a collaboration to create a focal point for scientists and engineers interested in saving the planet. We’ve got some interesting projects going. If you join the Azimuth Forum, you can talk to us, learn more, and help out as much or as little as you want. The only hard part about joining the Azimuth Forum is reading the instructions well enough that you choose your whole real name, with spaces between words, as your username.

John Harte

27 October, 2012

Earlier this week I gave a talk on the Mathematics of Planet Earth at the University of Southern California, and someone there recommended that I look into John Harte’s work on maximum entropy methods in ecology. He works at U.C. Berkeley.

I checked out his website and found that his goals resemble mine: save the planet and understand its ecosystems. He’s a lot further along than I am, since he comes from a long background in ecology while I’ve just recently blundered in from mathematical physics. I can’t really say what I think of his work since I’m just learning about it. But I thought I should point out its existence.

This free book is something a lot of people would find interesting:

• John and Mary Ellen Harte, Cool the Earth, Save the Economy: Solving the Climate Crisis Is EASY, 2008.

EASY? Well, it’s an acronym. Here’s the basic idea of the US-based plan described in this book:

Any proposed energy policy should include these two components:

Technical/Behavioral: What resources and technologies are to be used to supply energy? On the demand side, what technologies and lifestyle changes are being proposed to consumers?

Incentives/Economic Policy: How are the desired supply and demand options to be encouraged or forced? Here the options include taxes, subsidies, regulations, permits, research and development, and education.

And a successful energy policy should satisfy the AAA criteria:

Availability. The climate crisis will rapidly become costly to society if we do not take action expeditiously. We need to adopt now those technologies that are currently available, provided they meet the following two additional criteria:

Affordability. Because of the central role of energy in our society, its cost to consumers should not increase significantly. In fact, a successful energy policy could ultimately save consumers money.

Acceptability. All energy strategies have environmental, land use, and health and safety implications; these must be acceptable to the public. Moreover, while some interest groups will undoubtedly oppose any particular energy policy, political acceptability at a broad scale is necessary.

Our strategy for preventing climate catastrophe and achieving energy independence includes:

Energy Efficient Technology at home and at the workplace. Huge reductions in home energy use can be achieved with available technologies, including more efficient appliances such as refrigerators, water heaters, and light bulbs. Home retrofits and new home design features such as “smart” window coatings, lighter-colored roofs where there are hot summers, better home insulation, and passive solar designs can also reduce energy use. Together, energy efficiency in home and industry can save the U.S. up to approximately half of the energy currently consumed in those sectors, and at no net cost—just by making different choices. Sounds good, doesn’t it?

Automobile Fuel Efficiency. Phase in higher Corporate Average Fuel Economy (CAFE) standards for automobiles, SUVs and light trucks by requiring vehicles to go 35 miles per gallon of gas (mpg) by 2015, 45 mpg by 2020, and 60 mpg by 2030. This would rapidly wipe out our dependence on foreign oil and cut emissions from the vehicle sector by two-thirds. A combination of plug-in hybrid, lighter car body materials, re-design and other innovations could readily achieve these standards. This sounds good, too!

Solar and Wind Energy. Rooftop photovoltaic panels and solar water heating units should be phased in over the next 20 years, with the goal of solar installation on 75% of U.S. homes and commercial buildings by 2030. (Not all roofs receive sufficient sunlight to make solar panels practical for them.) Large wind farms, solar photovoltaic stations, and solar thermal stations should also be phased in so that by 2030, all U.S. electricity demand will be supplied by existing hydroelectric, existing and possibly some new nuclear, and, most importantly, new solar and wind units. This will require investment in expansion of the grid to bring the new supply to the demand, and in research and development to improve overnight storage systems. Achieving this goal would reduce our dependence on coal to practically zero. More good news!

You are part of the answer. Voting wisely for leaders who promote the first three components is one of the most important individual actions one can make. Other actions help, too. Just as molecules make up mountains, individual actions taken collectively have huge impacts. Improved driving skills, automobile maintenance, reusing and recycling, walking and biking, wearing sweaters in winter and light clothing in summer, installing timers on thermostats and insulating houses, carpooling, paying attention to energy efficiency labels on appliances, and many other simple practices and behaviors hugely influence energy consumption. A major education campaign, both in schools for youngsters and by the media for everyone, should be mounted to promote these consumer practices.

No part of EASY can be left out; all parts are closely integrated. Some parts might create much larger changes—for example, more efficient home appliances and automobiles—but all parts are essential. If, for example, we do not achieve the decrease in electricity demand that can be brought about with the E of EASY, then it is extremely doubtful that we could meet our electricity needs with the S of EASY.

It is equally urgent that once we start implementing the plan, we aggressively export it to other major emitting nations. We can reduce our own emissions all we want, but the planet will continue to warm if we can’t convince other major global emitters to reduce their emissions substantially, too.

What EASY will achieve. If no actions are taken to reduce carbon dioxide emissions, in the year 2030 the U.S. will be emitting about 2.2 billion tons of carbon in the form of carbon dioxide. This will be an increase of 25% from today’s emission rate of about 1.75 billion tons per year of carbon. By following the EASY plan, the U.S. share in a global effort to solve the climate crisis (that is, prevent catastrophic warming) will result in U.S emissions of only about 0.4 billion tons of carbon by 2030, which represents a little less than 25% of 2007 carbon dioxide emissions.128 Stated differently, the plan provides a way to eliminate 1.8 billion tons per year of carbon by that date.

We must act urgently: in the 14 months it took us to write this book, atmospheric CO2 levels rose by several billion tons of carbon, and more climatic consequences have been observed. Let’s assume that we conserve our forests and other natural carbon reservoirs at our current levels, as well as maintain our current nuclear and hydroelectric plants (or replace them with more solar and wind generators). Here’s what implementing EASY will achieve, as illustrated by Figure 3.1 on the next page.

Please check out this book and help me figure out if the numbers add up! I could also use help understanding his research, for example:

• John Harte, Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics, Oxford University Press, Oxford, 2011.

The book is not free but the first chapter is.

This paper looks really interesting too:

• J. Harte, T. Zillio, E. Conlisk and A. B. Smith, Maximum entropy and the state-variable approach to macroecology, Ecology 89 (2008), 2700–-2711.

Again, it’s not freely available—tut tut. Ecologists should follow physicists and make their work free online; if you’re serious about saving the planet you should let everyone know what you’re doing! However, the abstract is visible to all, and of course I can use my academic superpowers to get ahold of the paper for myself:

Abstract: The biodiversity scaling metrics widely studied in macroecology include the species-area relationship (SAR), the scale-dependent species-abundance distribution (SAD), the distribution of masses or metabolic energies of individuals within and across species, the abundance-energy or abundance-mass relationship across species, and the species-level occupancy distributions across space. We propose a theoretical framework for predicting the scaling forms of these and other metrics based on the state-variable concept and an analytical method derived from information theory. In statistical physics, a method of inference based on information entropy results in a complete macro-scale description of classical thermodynamic systems in terms of the state variables volume, temperature, and number of molecules. In analogy, we take the state variables of an ecosystem to be its total area, the total number of species within any specified taxonomic group in that area, the total number of individuals across those species, and the summed metabolic energy rate for all those individuals. In terms solely of ratios of those state variables, and without invoking any specific ecological mechanisms, we show that realistic functional forms for the macroecological metrics listed above are inferred based on information entropy. The Fisher log series SAD emerges naturally from the theory. The SAR is predicted to have negative curvature on a log-log plot, but as the ratio of the number of species to the number of individuals decreases, the SAR becomes better and better approximated by a power law, with the predicted slope z in the range of 0.14-0.20. Using the 3/4 power mass-metabolism scaling relation to relate energy requirements and measured body sizes, the Damuth scaling rule relating mass and abundance is also predicted by the theory. We argue that the predicted forms of the macroecological metrics are in reasonable agreement with the patterns observed from plant census data across habitats and spatial scales. While this is encouraging, given the absence of adjustable fitting parameters in the theory, we further argue that even small discrepancies between data and predictions can help identify ecological mechanisms that influence macroecological patterns.

Carbon Cycle Box Models

24 July, 2012

guest post by Staffan Liljegren


I think the carbon cycle must be the greatest natural invention, all things considered. It’s been the basis for all organic life on Earth through eons of time. Through evolution, it gradually creates more and more biodiversity. It is important to do more research on the carbon cycle for the earth sciences, biology and in particular global warming—or more generally, climate science and environmental science, which are among the foci of the Azimuth project.

It is a beautiful and complex nonlinear geochemical cycle, I decided to give a rough outline of its beauty and complexity. Plants eat water and carbon dioxide with help from the sun (photosynthesis) and while doing so they produce air and sugar for others to metabolize. These plants in turn may be eaten by vegan animals (herbivores), while animals may also be eaten by other animals like us humans, being meat eaters or animals that eat both animals and plants (carnivores or omnivores).

Here is an overview of the cycle, where yellow arrows show release of carbon dioxide and purple arrows show uptake:

carbon cycle

Say a plant gets eaten by an animal on land. Then the animal can use its carbon while breathing in air and breathing out water and carbon dioxide. Ruminant animals like cows and sheep also produce methane, which is a greenhouse gas like carbon dioxide. When a plant or animal dies it gets eaten by others, and any remains go down into the soil and sediments. A lot of the carbon in the sediments actually transforms into carbonate rock. This happens over millions of years. Some of this carbon makes it back into the air later through volcanoes.


Carbon is not a very abundant element on this planet: it’s only 0.08% of the total mass of the Earth. Nonetheless, we all know that many products of this atom are found throughout nature: for example in diamonds, marble, oil… and living organisms. If you remember your high school chemistry you might recall that the lab experiments with organic chemistry were the fun part of chemistry! The reason is that carbon has the ability to easily form compounds with other elements. So there is a tremendous global market that depends on the carbon cycle.

We humans are one fifth carbon. Other examples are trees, which we humans use for many things in our economic growth. But there are also fascinating flows inside the trees. I’ve read about these in Colin Tudge’s book The Secret Life of Trees – How They Live and why they Matter, so I will use this book for examples about forests and trees. You may already be familiar with these, but maybe not know a lot of details about their part in the carbon cycle.

When I stood in front of an tall monkey-puzzle tree in the genus Auracaria I was just flabbergasted by its age, and how it used to be widespread when the dinosaurs where around. But how does it manage to get the water to its leaves? Colin Tudge writes that during evolution trees invented stem-cell usage to grow the new outer layer, and developed microtechnology before we even existed as a species, where the leaves pull on several micron sized channels through osmosis and respiration to get the water up through the roots and trunk to the leaves at speeds typically around 6 meters per hour. But if needed, they can crank it up to 40 meters per hour to get it to the top in an hour or two!


Global warming is a fact and there are several remote sensing technologies that have confirmed this. You can see it nicely by clicking on this—you should see a NASA animation of satellite measurements superposed on top of Keeling’s famous graph of CO2 measured at Mauna Loa measurements from 2002 to 2009. Here’s more of that graph:

Many of the greenhouse gases that contribute to increasing temperature contains carbon: carbon dioxide, methane and carbon monoxide. I will focus on carbon dioxide. Its behavior is vastly different in air or water. In air it doesn’t react with other chemicals so its stays around for a longer time in the atmosphere. In the ocean and on land the carbon dioxide reacts a lot more, so there’s an uptake of carbon in both. But not in the ocean where it stays a lot longer mainly due to ocean buffering. I will have a lot more to say about the ocean geochemistry in the upcoming blog postings.

The carbon dioxide levels in the atmosphere in 2011 are soon approaching 400 parts per million (ppm) and the growth is increasing for every year. The parts per million is in relation to the volume of the atmosphere. David Archer says that if all the carbon dioxide were to fall as frozen carbon dioxide—’dry ice’—it would just be around 10 centimeters deep. But the important thing to understand is that we have thrown the carbon cycle seriously out of balance with our human emissions, so we might be close to some climate tipping points.

Colin my fellow ‘tree-hugger’ has looked at global warming and its implication for the trees. Intuitively it might seem that warmer temperatures and higher levels of CO2 might be beneficial for their growth. Indeed, the climate predictions of the International Panel on Climate Change assume this will happen. But there is a point where the micro-channels (stomata) start to close, due to too much photosynthesis and carbon dioxide. Taken together with higher temperature, this can make the trees’ respiration faster than its photosynthesis, so they end up supplying more carbon dioxide to atmosphere.

Trees also are very excellent at preventing floods, since one tree can divert 500 litres per day through transpiration. This easily adds up to 5000 cubic metres per square kilometre, making trees very good at reducing flood and and reducing our need for disaster preventions if they are left alone to do do their job.


One way of understanding how the carbon cycle works is to use simple models like box models where we treat the carbon as contained in various ‘boxes’ and look at how it moves between boxes as time passes. A box can represent the Earth, the ocean, the atmosphere, or depending on what I want to study, any other part of the carbon cycle.

I’ll just mention a few examples of flows in the carbon cycle, to give you a feeling for them: breathing, photosynthesis, erosion, emission and decay. Breathing is easy to grasp—try to stop doing it yourself for a short moment! But how is photosynthesis a flow? This wonderful process was invented by the cyanobacteria 3.5 billion years ago and it has been used by plants ever since. It takes carbon out of the atmosphere and moves it into plant tissues.

In a box model, the average time something stays in a box is called its residence time, e-folding time, or response time by scientists. The rest of the flows in my list I leave up to you to think about: which are uptakes which are releases, and where do they occur?

The basic equation in a box model is called the mass balance equation:

\dot m = \sum \textrm{sources} - \sum \textrm{sinks}

Here m is the mass of some substance in some box. The sources are what flows into that box together with any internal sources (production). The sinks are what flows out together with any internal sinks (loss and deposition).

In my initial experiments where I used the year 2008, when I looked at a 1-dimensional global box model of CO2 in the atmosphere with only the fossil fuel as source, I get similar results to this diagram from the Global Carbon Project (petagram of carbon per year, which is the same as gigatonnes per year):

global carbon budget 2000 - 2010

I used the observed value from measurements at Mauna Loa. The atmosphere sink is 3.9 gigatonnes of carbon per year and the fossil fuel emission source is 8.7 GtC per year. The ocean also absorbs 2.1 GtC per year, and the land acts as a sink at 2.5 GtC per year.

I hope this will be the first of a series of posts! Next time I want to talk about a box model for the ocean’s role in the carbon cycle.


• Colin Tudge, The Secret Life of Trees: How They Live and Why They Matter, Penguin, London, 2005.

• David Archer, The Global Carbon Cycle, Princeton U. Press, Princeton, NJ, 2011.

Energy, the Environment, and What We Can Do

5 April, 2012

A while ago I gave a talk at Google. Since I think we should cut unnecessary travel, I decided to stay here in Singapore and give the talk virtually, in the form of a robot:

I thank Mike Stay for arranging this talk at Google, and Trevor Blackwell and Suzanne Broctao at Anybots for letting me use one of their robots!

Here are the slides:

Energy, the Environment, and What We Can Do.

To see the source of any piece of information in these slides, just click on it!

And here’s me:

This talk was more ambitious than previous ones I’ve given—and not just because I was struggling to operate a robot, read my slides on my laptop, talk, and click the pages forward all at once! I said more about solutions to our problems this time. That’s where I want to head, but of course it’s infinitely harder to describe solutions than to list problems or even to convince people that they really are problems.

I, Robot

24 January, 2012

On 13 February 2012, I will give a talk at Google in the form of a robot. I will look like this:

My talk will be about “Energy, the Environment and What We Can Do.” Since I think we should cut unnecessary travel, I decided to stay here in Singapore and use a telepresence robot instead of flying to California.

I thank Mike Stay for arranging this at Google, and I especially thank Trevor Blackwell and everyone else at Anybots for letting me use one of their robots!

I believe Google will film this event and make a video available. But I hope reporters attend, because it should be fun, and I plan to describe some ways we can slash carbon emissions.

More detail: I will give this talk at 4 pm Monday, February 13, 2012 in the Paramaribo Room on the Google campus (Building 42, Floor 2). Visitors and reporters are invited, but they need to check in at the main visitor’s lounge in Building 43, and they’ll need to be escorted to and from the talk, so someone will pick them up 10 or 15 minutes before the talk starts.

Energy, the Environment and What We Can Do

Abstract: Our heavy reliance on fossil fuels is causing two serious problems: global warming, and the decline of cheaply available oil reserves. Unfortunately the second problem will not cancel out the first. Each one individually seems extremely hard to solve, and taken
together they demand a major worldwide effort starting now. After an overview of these problems, we turn to the question: what can we do about them?

I also need help from all of you reading this! I want to talk about solutions, not just problems—and given my audience, and the political deadlock in the US, I especially want to talk about innovative solutions that come from individuals and companies, not governments.

Can changing whole systems produce massive cuts in carbon emissions, in a way that spreads virally rather than being imposed through top-down directives? It’s possible. Curtis Faith has some inspiring thoughts on this:

I’ve been looking on various transportation and energy and environment issues for more than 5 years, and almost no one gets the idea that we can radically reduce consumption if we look at the complete systems. In economic terms, we currently have a suboptimal Nash Equilibrium with a diminishing pie when an optimal expanding pie equilibrium is possible. Just tossing around ideas a a very high level with back of the envelope estimates we can get orders of magnitude improvements with systemic changes that will make people’s lives better if we can loosen up the grip of the big corporations and government.

To borrow a physics analogy, the Nash Equilibrium is a bit like a multi-dimensional metastable state where the system is locked into a high energy configuration and any local attempts to make the change revert to the higher energy configuration locally, so it would require sufficient energy or energy in exactly the right form to move all the different metastable states off their equilibrium either simultaneously or in a cascade.

Ideally, we find the right set of systemic economic changes that can have a cascade effect, so that they are locally systemically optimal and can compete more effectively within the larger system where the Nash Equilibrium dominates. I hope I haven’t mixed up too many terms from too many fields and confused things. These terms all have overlapping and sometimes very different meaning in the different contexts as I’m sure is true even within math and science.

One great example is transportation. We assume we need electric cars or biofuel or some such thing. But the very assumption that a car is necessary is flawed. Why do people want cars? Give them a better alternative and they’ll stop wanting cars. Now, what that might be? Public transportation? No. All the money spent building a 2,000 kg vehicle to accelerate and decelerate a few hundred kg and then to replace that vehicle on a regular basis can be saved if we eliminate the need for cars.

The best alternative to cars is walking, or walking on inclined pathways up and down so we get exercise. Why don’t people walk? Not because they don’t want to but because our cities and towns have optimized for cars. Create walkable neighborhoods and give people jobs near their home and you eliminate the need for cars. I live in Savannah, GA in a very tiny place. I never use the car. Perhaps 5 miles a week. And even that wouldn’t be necessary with the right supplemental business structures to provide services more efficiently.

Or electricity for A/C. Everyone lives isolated in structures that are very inefficient to heat. Large community structures could be air conditioned naturally using various techniques and that could cut electricity demand by 50% for neighborhoods. Shade trees are better than insulation.

Or how about moving virtually entire cities to cooler climates during the hot months? That is what people used to do. Take a train North for the summer. If the destinations are low-resource destinations, this can be a huge reduction for the city. Again, getting to this state is hard without changing a lot of parts together.

These problems are not technical, or political, they are economic. We need the economic systems that support these alternatives. People want them. We’ll all be happier and use far less resources (and money). The economic system needs to be changed, and that isn’t going to happen with politics, it will happen with economic innovation. We tend to think of our current models as the way things are, but they aren’t. Most of the status quo is comprised of human inventions, money, fractional reserve banking, corporations, etc. They all brought specific improvements that made them more effective at the time they were introduce because of the conditions during those times. Our times too are different. Some new models will work much better for solving our current problems.

Your idea really starts to address the reason why people fly unnecessarily. This change in perspective is important. What if we went back to sailing ships? And instead of flying we took long leisurely educational seminar cruises on modern versions of sail yachts? What if we improved our trains? But we need to start from scratch and design new systems so they work together effectively. Why are we stuck with models of cities based on the 19th-century norms?

We aren’t, but too many people think we are because the scope of their job or academic career is just the piece of a system, not the system itself.

System level design thinking is the key to making the difference we need. Changes to the complete systems can have order of magnitude improvements. Changes to the parts will have us fighting for tens of percentages.

Do you know good references on ideas like this—preferably with actual numbers? I’ve done some research, but I feel I must be missing a lot of things.

This book, for example, is interesting:

• Michael Peters, Shane Fudge and Tim Jackson, editors, Low Carbon Communities: Imaginative Approaches to Combating Climate Change Locally, Edward Elgar Publishing Group, Cheltenham, UK, 2010.

but I wish it had more numbers on how much carbon emissions were cut by some of the projects they describe: Energy Conscious Households in Action, the HadLOW CARBON Community, the Transition Network, and so on.

Melting Permafrost (Part 3)

19 December, 2011

Melting permafrost is in the news! Check out this great slide show and article:

• Josh Hane, Hunting for clues to global warming, New York Times, 16 December 2011.

• Justin Gillis, As permafrost thaws, scientists study the risks, New York Times, 16 December 2011.

They track Katey M. Walter Anthony, an assistant professor at the Water and Environmental Research Center at the University of Alaska Fairbanks, as she studies methane bubbling up from lakes—as shown above.

These lakes form in an interesting way. Permafrost is permanently frozen soil lying beneath a layer 0.6 to 4 meters thick of soil that thaws in the summer and refreezes in the winter: the active layer. The permafrost itself can be much thicker—up to 1500 meters in parts of Siberia!

As far as I can tell, talik is permanently unfrozen soil on top of, amid or beneath the permafrost.

Permafrost is rock-hard and solid. Liquid water does not pass through it, so permafrost environments tend to be poorly drained and boggy. But when permafrost starts to melt, it becomes soft. Soil sinks down into marshy hollows separated by small hills, forming a kind of terrain called thermokarst.

Trees in this terrain can lean crazily as their roots sink, creating drunken forests.

On flat ground, melted water can pool into a thermokarst lake. On slopes, water pours downhill and the land can rip open in a thermokarst failure. Here are Breck Bowden and Michael Gooseff exploring a thermokarst failure in Alaska:

For more on this, see:

• Emily Stone, When the ground collapses like a soufflé: Studying the effect of thermokarst on the Arctic, Field Notes: the Polar Field Services Newsletter

All these are natural processes that are widespread at the end of each glacial period. Here’s a surprisingly delightful book which discusses this in detail:

• Evelyn C. Pielou, After the Ice Age: the Return of Life to Glaciated North America, U. Chicago Press, Chicago, 1991.

So, please don’t misunderstand: I’m not trying to say that thermokarst lakes, drunken forests and the like are signs of disaster. However, as the Earth warms, new regions of permafrost are melting, and we’ll see these phenomena in new regions. We need to understand how they work, and the positive and negative feedbacks. For example, thermokarst lakes are darker than their surroundings, so they absorb more sunlight and warm the area.

Most importantly, as permafrost thaws, it releases trapped carbon in the form of carbon dioxide and methane, which are both greenhouse gases. Since there are roughly 1.7 trillion tons of carbon in northern soils, with about 90% locked in permafrost, that’s a big deal.

At least once so far, the tundra has even caught fire:

One day in 2007, on the plain in northern Alaska, a lightning strike set the tundra on fire.

Historically, tundra, a landscape of lichens, mosses and delicate plants, was too damp to burn. But the climate in the area is warming and drying, and fires in both the tundra and forest regions of Alaska are increasing.

The Anaktuvuk River fire burned about 400 square miles of tundra, and work on lake sediments showed that no fire of that scale had occurred in the region in at least 5,000 years.

Scientists have calculated that the fire and its aftermath sent a huge pulse of carbon into the air — as much as would be emitted in two years by a city the size of Miami. Scientists say the fire thawed the upper layer of permafrost and set off what they fear will be permanent shifts in the landscape.

Up to now, the Arctic has been absorbing carbon, on balance, and was once expected to keep doing so throughout this century. But recent analyses suggest that the permafrost thaw could turn the Arctic into a net source of carbon, possibly within a decade or two, and those studies did not account for fire.

“I maintain that the fastest way you’re going to lose permafrost and release permafrost carbon to the atmosphere is increasing fire frequency,” said Michelle C. Mack, a University of Florida scientist who is studying the Anaktuvuk fire. “It’s a rapid and catastrophic way you could completely change everything.”

By the way, if you click on these scientists’ portraits, you’ll see where they work. If you’re a student looking for an interesting career, consider these options! For example, Michelle C. Mack—shown above—runs a lab, and you can see her postdocs and grad students, and what they do.

For previous posts in this series, see:

Melting Permafrost (Part 1).

Melting Permafrost (Part 2).

Melting Permafrost (Part 2)

14 December, 2011

This summer a Russian research ship found hundreds of plumes of methane, “of a fantastic scale”, bubbling up from the sea floor off the East Siberian coast:

• Steve Connor, Shock as retreat of Arctic sea ice releases deadly greenhouse gas, 13 December 2011.

Here are the quotes with actual new information:

In late summer, the Russian research vessel Academician Lavrentiev conducted an extensive survey of about 10,000 square miles of sea off the East Siberian coast. Scientists deployed four highly sensitive instruments, both seismic and acoustic, to monitor the “fountains” or plumes of methane bubbles rising to the sea surface from beneath the seabed.

“In a very small area, less than 10,000 square miles, we have counted more than 100 fountains, or torch-like structures, bubbling through the water column and injected directly into the atmosphere from the seabed,” Dr Semiletov said. “We carried out checks at about 115 stationary points and discovered methane fields of a fantastic scale – I think on a scale not seen before. Some plumes were a kilometre or more wide and the emissions went directly into the atmosphere – the concentration was a hundred times higher than normal.”


“This is the first time that we’ve found continuous, powerful and impressive seeping structures, more than 1,000 metres in diameter. It’s amazing,” Dr Semiletov said. “I was most impressed by the sheer scale and high density of the plumes. Over a relatively small area we found more than 100, but over a wider area there should be thousands of them.”

Scientists estimate that there are hundreds of millions of tonnes of methane gas locked away beneath the Arctic permafrost, which extends from the mainland into the seabed of the relatively shallow sea of the East Siberian Arctic Shelf. One of the greatest fears is that with the disappearance of the Arctic sea-ice in summer, and rapidly rising temperatures across the entire region, which are already melting the Siberian permafrost, the trapped methane could be suddenly released into the atmosphere leading to rapid and severe climate change.

Dr Semiletov’s team published a study in 2010 estimating that the methane emissions from this region were about eight million tonnes a year, but the latest expedition suggests this is a significant underestimate of the phenomenon.

I’d like to know more about Igor Semiletov’s work and what he’s just found. He was mentioned in this earlier very good article:

• Amanda Leigh Mascarelli, A sleeping giant?, Nature Reports Climate Change, 5 March 2009.


The Siberian Shelf alone harbours an estimated 1,400 billion tonnes of methane in gas hydrates, about twice as much carbon as is contained in all the trees, grasses and flowers on the planet. If just one per cent of this escaped into the atmosphere within a few decades, it would be enough to cause abrupt climate change, says Shakhova. “When hydrates are destabilized, gas is released under very high pressure,” she says. “So emissions could be massive and non-gradual.” Shakhova and her colleague Igor Semiletov of the University of Alaska, Fairbanks, believe the plumes they’ve observed confirm previous reports that the permafrost cap is beginning to destabilize, allowing methane to escape from the frozen hydrates below. “Subsea permafrost is like a rock,” explains Semiletov. “It works like a lid to prevent escape of any gas. We believe that the subsea permafrost is failing to seal the ancient carbon pool.”

But Carolyn Ruppel, a geophysicist with the US Geological Survey in Woods Hole, Massachusetts, isn’t yet ready to attribute the methane plumes to a breakdown in methane hydrates in the subsea permafrost. “We have proof from studies that have been carried out in the past few years that there’s a lot of methane in certain shallow marine environments offshore in the Arctic,” says Ruppel. “But can we prove that the methane comes from methane hydrates? That is a critical question.”

Why is it critical? Because people are worried about global warming melting permafrost and gas hydrates on the ocean floor. Suppose these release large amounts of methane, a greenhouse gas vastly more potent than carbon dioxide. This will then makes the Earth even warmer, and so on: we have a feedback loop. In a real nightmare scenario, we could imagine that this feedback actually leads to a ‘tipping point’, where the climate flips over to a much warmer state. And in the worst nightmare of all, we can imagine something like Paleocene-Eocene Thermal Maximum, a spike of heat that lasted about 20,000 years, causing significant extinctions.

Are any of these nightmares really possible? I wrote about this question before, assembling what facts I could easily find:

Melting permafrost (Part 1).

How much new light does Semiletov’s work shed on this question?

Luckily, a team of scientists is gearing up to answer it:

Permafrost Carbon Network (RCN).

Here’s a paper by this team:

• Edward A. G. Schuur, Benjamin Abbott and the Permafrost Carbon Network, High risk of permafrost thaw, Nature 480 (1 December 2011), 32-33.

To get the ball rolling, they surveyed themselves. That may seem like a lazy way to write a paper, but I don’t mind it as a quick way to get a sense of the conventional wisdom… and they probably wanted to do it just to find out what they all thought! Here are the results—emphasis mine:

Our survey asks what percentage of the surface permafrost is likely to thaw, how much carbon will be released, and how much of that carbon will be CH4, for three time periods and under four warming scenarios that will be part of the Intergovernmental Panel on Climate Change Fifth Assessment Report. The lowest warming scenario projects 1.5 °C Arctic warming over the 1985–2004 average by the year 2040, ramping up to 2 °C by 2100; the highest warming scenario considers 2.5 °C by 2040, and 7.5 °C by 2100. In all cases, we posited that the temperature would remain steady from 2100 to 2300 so that we could assess opinions about the time lag in the response of permafrost carbon to temperature change.

The survey was filled out this year by 41 international scientists, listed as authors here, who publish on various aspects of permafrost. The results are striking. Collectively, we hypothesize that the high warming scenario will degrade 9–15% of the top 3 metres of permafrost by 2040, increasing to 47–61% by 2100 and 67–79% by 2300 (these ranges are the 95% confidence intervals around the group’s mean estimate). The estimated carbon release from this degradation is 30 billion to 63 billion tonnes of carbon by 2040, reaching 232 billion to 380 billion tonnes by 2100 and 549 billion to 865 billion tonnes by 2300. These values, expressed in CO2 equivalents, combine the effect of carbon released as both CO2 and as CH4.

Our estimate for the amount of carbon released by 2100 is 1.7–5.2 times larger than those reported in several recent modelling studies, all of which used a similar warming scenario. This reflects, in part, our perceived importance of the abrupt thaw processes, as well as our heightened awareness of deep carbon pools. Active research is aimed at incorporating these main issues, along with others, into models.

Are our projected rapid changes to the permafrost soil carbon pool plausible? The survey predicts a 7–11% drop in the size of the permafrost carbon pool by 2100 under the high-warming scenario. That scale of carbon loss has happened before: a 7–14% decrease has been measured in soil carbon inventories across thousands of sites in the temperate-zone United Kingdom as a result of climate change. Also, data scaled up from a single permafrost field site point to a potential 5% loss over a century as a result of widespread permafrost thaw. These field results generally agree with the collective carbon-loss projection made by this survey, so it should indeed be plausible.

Across all the warming scenarios, we project that most of the released carbon will be in the form of CO2 with only about 2.7% in the form of CH4. However, because CH4 has a higher global-warming potential, almost half the effect of future permafrost-zone carbon emissions on climate forcing is likely to be from CH4. That is roughly consistent with the tens of billions of tonnes of CH4 thought to have come from oxygen-limited environments in northern ecosystems after the end of the last glacial period.

All this points towards significant carbon releases from permafrost-zone soils over policy-relevant timescales. It also highlights important lags whereby permafrost degradation and carbon emissions are expected to continue for decades or centuries after global temperatures stabilize at new, higher levels. Of course, temperatures might not reach such high levels. Our group’s estimate for carbon release under the lowest warming scenario, although still quite sizeable, is about one-third of that predicted under the strongest warming scenario.

I found this sentence is a bit confusing:

These values, expressed in CO2 equivalents, combine the effect of carbon released as both CO2 and as CH4.

But I guess that combined with a guess like “30 billion to 63 billion tonnes of carbon by 2040″, it means that they’re expecting a release of carbon dioxide and methane that’s equal, in its global warming potential, to what you’d get from burning 30 to 63 billion tonnes of carbon, turning it all into carbon dioxide, and releasing it into the atmosphere.

For comparison, in 2010 humanity burnt 8.3 billion tonnes of carbon. So, at least up to 2040, I guess they’re expecting the effect of melting permafrost to be roughly 1/8 to 1/4 of the direct effect of burning carbon.


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