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Blog - carbon cycle box models (part 1)

This page is a blog article in progress, written by Staffan Liljegren. To discuss this article while it is being written, visit the Azimuth Forum.


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. Here is a NASA animation on satellite measurements superposed on top of the Keeling Mauna Loa measurements from 2002 to 2009:

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:

m˙=sourcessinks\dot m = \sum {sources} - \sum {sinks}

Here mm 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 Gt per year and the fossil fuel emission source 8.7 Gt carbon and the remainder that did not end up in the atmosphere was the ocean 2. 1 Gt C per year. Land also acts as a sink at 2.5 GtC per year.

Next time I will do a survey of the results from the 2-box land and atmosphere models and also the importance to understand and manage non-linearity in the models of 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.