Carbon Cycle Box Models

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.

18 Responses to Carbon Cycle Box Models

  1. Derek Wise says:

    Staffan wrote:

    When I stood in front of an tall monkey-puzzle tree in the genus Auracaria I was just flabbergasted by its age.

    So, how old was it? And, how did you find out how old it was? I’d like to be flabbergasted too! :-)

  2. Arrow says:

    The “global warming is a fact” section is duplicated.

    Staffan: “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.”

    If its important to understand maybe you could explain it. I don’t see how a carbon cycle can be “thrown off balance,” what balance? The plants are quite happy to have more CO2, it greatly increases the efficiency of photosynthesis.

    The idea that excess CO2 would make plants give off more carbon then they absorb is just plain absurd, it makes as much sense as a claim that a human could give off more mass then he consumes, in both cases death would be swift.

    • Nathan Urban says:

      I don’t want to put words in Staffan’s mouth, but let me take a few stabs at your questions.

      “Thrown off balance” may mean that CO2 fluxes to the atmosphere are no longer in approximate balance with CO2 fluxes from the atmosphere, due to the addition of a new source, thus leading to atmospheric accumulation of CO2. But in addition, both climate change and changing atmospheric CO2 alter the carbon cycle directly (e.g. through fertilization effects, discussed below).

      Plant growth is sometimes (not always) enhanced by extra CO2. This is known as “CO2 fertilization”. But there is obviously a limit to this effect; increasing amounts of CO2 won’t cause vegetation to grow without bound. Indeed, this effect may well saturate during the 21st century, and will not continue enhancing the terrestrial carbon sink. (And fertilization isn’t the only feedback. There are opposing feedbacks that can decrease the effectiveness of the terrestrial carbon sink, quite possibly more so than fertilization can increase it.)

      As for stomatal closure, it is known that plants constrict their stoma, through which gas exchange occurs, in the presence of excess CO2. This can increase their water use efficiency, because less water vapor escapes the plant. This increased water efficiency is one CO2 fertilization effect. (Stomatal closure can also cause climate changes, due to altering the latent heat flux near the Earth’s surface, and possibly also cloud formation.)

      I recall reading of a theory that stomatal closure can occur in a positive feedback, reducing the effectiveness of plants as a CO2 sink. Perhaps this is what Staffan is talking about, although this doesn’t actually cause plants to become net CO2 sources. The idea is that when less water vapor escapes a vegetated region due to stomatal closure, the resulting atmospheric drying stimulates further stomatal closure, as the plant attempts to keep water from escaping in a dry climate. The small size of the stoma reduces the CO2 absorbed by the plant from the atmosphere. However, my understanding is that this feedback is not thought to be large. I don’t think it will kill plants, and it wouldn’t make evolutionary sense for this feedback to be too strong. I’m not sure what empirical evidence there is in its favor, either.

      • Thanks Narhan for replying! Arrow: I intended to address the non-linear nature of the carbon cycle but also felt that it’s too complex to cover in the first blog post. Hence the links to the Azimuth pages on tipping points and non-linear science!

        With “Thrown off balance”, it is like Nathan explains above.

  3. Torbjörn Larsson, OM says:

    “I think the carbon cycle must be the greatest natural invention, all things considered.”

    Very much so. There are two pity summaries of life, looking from the two ends of the redox chain.

    On the reductive end, where I hear iron reprocessed in the mantle stands for ~ 75 % of oxidation (and sulfur ~ 25 % still, with free oxygen only ~ 1-2 %), life can be said to be a geochemical way to accelerate rust production.

    On the oxidative end, where methane spontaneously is produced but at a slow rate from the primordial reduced CO2/H2 atmosphere (either globally or locally at hydrothermal vents), life can be said to be a geochemical way to accelerate methane production.

    So much so, in fact, that the latter constraint enables you to produce phylogenies based on autotrophic CO2 fixating metabolism. [“The Emergence and Early Evolution of Biological Carbon-fixation”, Braakman et al, PLoS Comp Bio, 2012] It traces back to a robust dual fixating carbon metabolism which could cope with spotty regulation during maintenance and growth. Cellular maintenance and growth would be parasitic on the often autocatalytic metabolic chains.

    This however makes the idea of 3.5 billion year old cyanobacteria problematic IMO. [Astrobiology interest here.]

    The metabolic phylogeny correlates well with recent phylogenies on protein fold families with the ability to reach back through the DNA LUCA to the RNA/protein world. [“The evolution and functional repertoire of translation proteins following the origin of life”, Goldman et al, Biol Dir, 2010; and others like that.] They describe that the RNA/protein world stands for ~ 20 % of the timeline of a protein fold origination clock proxy.

    The DNA LUCA stands for another ~ 20 %, and it is first after that the domain diversification happens that leads up to clades such as cyanobacteria. The metabolic phylogeny predicts that oxygen and energy stress constrained that diversification, which tests well against the energy constraints that are now claimed to separate the domains. (Valentin’s energy theory on archaea, ref in Braakman; Lane’s energy theory on eukaryotes, well known.)

    This timeline, early and preliminary as it is (uncalibrated clock proxies), is still hard to fit into the first billion year or Earth history. There is earlier work on protein fold families Archaean Expansion that seem to correlate a fold diversification explosion with the change from RNA protocell to DNA LUCA cell, but that was calibrated to start _after_ 3.5 billion years ago and not so surprisingly to end before the oxygenation of the atmosphere.

    Indeed the first stromatolites of perhaps 3.5 billion years ago seems ecologically alike to todays cyanobacteria based ones, with photophilic growth and extracellular matrix.

    But it could well be that early photosynthesis was generic, much less advanced akin to modern purple sulfur bacteria, anoxic (so no problem with oxygen stress), low light intensity of deep waters (so no UV problem with the lack of ozone), varied construction (so easy to evolve) and not a means to fix CO2 but to produce membrane differential energy for photophosphorylation outside of a cradle of hydrothermal vent redox potentials.

    • Torbjörn: you say:

      This however makes the idea of 3.5 billion year old cyanobacteria problematic IMO….Indeed the first stromatolites of perhaps 3.5 billion years ago seems ecologically alike to todays cyanobacteria

      I was using the same term for the first stromatolites and later cyanobacteria and I got the calculation from the book by Colin; you can also verify this with the Wikipedia article for cyanobacteria.

      BTW I am curious what this has to do with the carbon cycle and simple box models ?

  4. Torbjörn Larsson, OM says:

    @ Derek Wise:

    It is believed that the long necks of sauropod dinosaurs may have evolved specifically for browsing the foliage of the typically very tall Araucaria trees. The global distribution of vast forests of Araucaria during the Jurassic makes it likely that they were the major high energy food source for adult sauropods.[10]” [Wikipedia]

    That said, I’ve seen recent genetic work on similar (or same?) old clades, where they found species actually cycle in and out of existence with similar ages as other species. That still doesn’t predict the seeming stasis of their traits. (But here tallness can be predicted by later competition for light, natch.)

  5. John Baez says:

    Over on Google+, Kevin Clift wrote:

    I would like to suggest that (if correct, which I think it is) your writer should add a simple statement in the early simple introductory paragraphs, along these lines. “In fact most of the mass of plants comes from the air, in the form of carbon dioxide.” This is an important observation especially when one can clearly see how massive trees and other plant materials are. I contend that many smart people have not quite made this connection yet and assume that much of the mass comes from the soil or water.

    I replied:

    I bet you’re right that not everyone knows this—if you grow a little stalk of bamboo in a jar of water you’ll see firsthand that water and air can turn into leaves and wood, but not everyone does this sort of thing! If I’m feeling energetic tomorrow morning I’ll just add a remark to this effect in Staffan’s post.

    But then I realized it would be bad for me to mess with Staffan’s post unless he okays it.

    It really is amazing how plants can catalyze a reaction that comes very close to turning just water and air into leaves and wood. But now I’m wondering, somewhat irrelevantly, whether ordinary tap water has enough of the necessary extra elements (phosphorus, sulfur, sodium, calcium, magnesium,…) to hydroponically grow a full-sized bamboo plant starting from a small sprout.

    • Nathan Urban says:

      I didn’t know that most of the mass of plants came from air either, until I attended a talk by paleobotanist Kirk Johnson (curator of the Denver Museum of Natural History). He worked this concept into the title of his children’s book Gas Trees and Car Turds: Kids’ Guide to the Roots of Global Warming.

    • Giampiero Campa says:

      Very interesting, well i didn’t know until now. I wonder if we can put a numeric estimate on that “most of the mass”, in percent terms (btw your link doesn’t work).

      The fact that fertilizers are needed and that eroded soil has a reduced crop yield seem to imply that a considerable amount of mass does transition from the soil to the plants.

      • Nathan Urban says:

        The Wikipedia entry on ‘tree’ says over 90% of a tree’s biomass comes from the atmosphere. I recall Kirk Johnson also mentioning a figure around 90%.

        I don’t think you can infer much from the need for nutrients or fertilizers. They be necessary to participate in some critical reactions, but that doesn’t mean that they’re a large fraction of the mass.

        • John Baez says:

          If you burn wood very thoroughly so that no charcoal is left, you’ll see a little pile of ash, and that contains inorganic compounds that the plant was unable to get from air and water. So, it’s pretty obvious that trees are mostly made of air and water.

          But when they say 90% of the biomass comes from the atmosphere, I’m a bit suspicious: does ‘the atmosphere’ include water? Trees are mostly lignin, cellulose and other carbohydrates; the carbon and oxygen can come from air, but the hydrogen has to come from water (and probably a bunch of the oxygen does too).

          Of course most water used by trees comes from rain—which comes from the atmosphere. So, they could still be correct in a technical sense.

    • Walter Blackstock says:

      Jan Baptist van Helmont (1579-1644) “performed an experiment to determine where plants get their mass. He grew a willow tree and measured the amount of soil, the weight of the tree and the water he added. After five years the plant had gained about 164 lbs (74 kg). Since the amount of soil was basically the same as it had been when he started his experiment, he deduced that the tree’s weight gain had come from water. Since it had received nothing but water and the soil weighed practically the same as at the beginning, he argued that the increased weight of wood, bark and roots had been formed from water alone. However, this “deduction” is incomplete, as a large proportion of the mass of the tree comes from atmospheric carbon dioxide, which, in conjunction with water, is turned into carbohydrates via photosynthesis.” (Wikipedia, van Helmont)

      At the end of the 19th Century, the argument shifted to where do plants get their nitrogen? Crop rotation and legumes provided some, but guano was imported in vast amounts from South America for use as fertiliser. Using sewage on the land, as proposed by Liebig, provided only low levels of nitrogen and Crookes gave a famous British Association lecture warning of a food crisis ahead. The Times carried a spirited correspondence by Liebig and others on the merits of using sewage from London outfalls on the land. In reality sewage has less value than might be expected. The outbreak of the European War (WW1) in 1914 led to a blockade of sea routes which hastened German industrial production of ammonia in by the Haber-Bosch process.

      Today 40-60 per cent of the nitrogen in the human body has its origin in synthetic ammonia from the Haber-Bosch process. (I’d confirm the Nature 2004 reference but it’s paywalled). I like to tell my more green friends they are in part a product of high-pressure chemical engineering :)

      Apologies Staffan, a bit off-topic from Box Models …

      • John Baez says:

        Hey, great to hear from you, Walter! Lisa and I just had dinner in Fusionopolis last night—there’s a new subway stop there now—and she was asking me how you’re doing. I said we’re guys, we don’t talk about stuff like that. Now I’ll tell her you told me some fascinating facts about nitrogen and the Haber–Bosch process.

        Nitrogen is indeed the really interesting element in this game: my own remarks dodged it and focused on C, H, and O!

        • Walter Blackstock says:

          Please pass on my warm regards to Lisa – I’m still wrestling with her ‘producer-consumer’ challenge!! Being outside the paywalls, I moved into alchemy and now attempt Latin texts for exercise. The context is almost as difficult as the language!

    • I was writing up my notes on isotope geochemistry at the same time i was doing the first blog. So it was a conscious decision to leave details of the earth biomass part of the cycle. One of the references;

      is available under creative commons and it has a wonderful picture of the fluxes in a tree. Here is the picture text:

      “Overview of processes and factors determining the isotope signature of C pools and fluxes in space and time in the plant-soil-atmosphere continuum. White boxes represent pools, gray boxes show fractionation or other processes determining the C isotope composition of the involved compounds”

      My plan was to add this to the Isotope geochemistry page .But maybe we could mention this in ths blog or an upcoming on earth biomass part of the carbon cycle?

      • This was a comment on the discussion above on the air fraction of tree’s carbon cycle mostly but as i also saw that the picture has a lot of other energy resources , so maybe this could interest you too Walter!

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