# The mathematics of leaf decay

#### By By Jennifer Chu, MIT News Office | 10 Oct 2012

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The colorful leaves piling up in your backyard this fall can be thought of as natural stores of carbon. In the springtime, leaves soak up carbon dioxide from the atmosphere, converting the gas into organic carbon compounds. Come autumn, trees shed their leaves, leaving them to decompose in the soil as they are eaten by microbes.  Over time, decaying leaves release carbon back into the atmosphere as carbon dioxide.

In fact, the natural decay of organic carbon contributes more than 90 percent of the yearly carbon dioxide released into Earth's atmosphere and oceans. Understanding the rate at which leaves decay can help scientists predict this global flux of carbon dioxide, and develop better models for climate change. But this is a thorny problem: A single leaf may undergo different rates of decay depending on a number of variables: local climate, soil, microbes and a leaf's composition. Differentiating the decay rates among various species, let alone forests, is a monumental task.

Instead, MIT researchers have analysed data from a variety of forests and ecosystems across North America, and discovered general trends in decay rates among all leaves. The scientists devised a mathematical procedure to transform observations of decay into distributions of rates. They found that the shape of the resulting curve is independent of climate, location and leaf composition. However, the details of that shape - the range of rates that it spans, and the mean rate - vary with climatic conditions and plant composition. In general, the scientists found that plant composition determines the range of rates, and that as temperatures increase, all plant matter decays faster.

''There is a debate in the literature: If the climate warms, do all rates become faster by the same factor, or will some become much faster while some are not affected?'' says Daniel Rothman, a co-founder of MIT's Lorenz Center, and professor of geophysics in the Department of Earth, Atmospheric and Planetary Sciences. ''The conclusion is that all rates scale uniformly as the temperature increases.''

Rothman and co-author David Forney, a PhD graduate in the Department of Mechanical Engineering, have published the results of their study, based largely on Forney's PhD thesis, in the Journal of the Royal Society Interface.

Litter delivery
The team obtained data from an independent 10-year analysis of North American forests called the Long-term Intersite Decomposition Experiment Team (LIDET) study. For this study, researchers collected leaf litter - including grass, roots, leaves and needles - from 27 locations throughout North and Central America, ranging from Alaskan tundra to Panamanian rainforests.

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