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An introductory global CO2 model

World Scientific


IMAGE: An Introductory Global CO2 Model -- the model is based on just seven ordinary differential equations (ODEs) and is therefore intended as an introduction to some basic concepts and as... view more

Credit: World Scientific, 2015

On May 10, 2013, the New York Times reported [1] that for the first time in several million years, the CO2 level in the Earth's atmosphere passed 400 ppm (parts per million). Consequently, extreme heat waves, droughts, wildfires, melting glaciers and sea level rise may be a preview of the future, i.e., these unprecedented events will most likely be due to the accumulation of greenhouse gases (GHGs) in the atmosphere, principally CO2 from the burning of fossil fuels.

A mathematical model can be particularly informative and helpful for under-standing what is happening. In World Scientific's latest book An Introductory Global CO2 Model, an introductory global CO2 model that gives some key numbers, for example, atmospheric CO2 concentration in ppm as a function of time such as for the calendar years 1850 (preindustrial) to 2100 (a modest projection into the future), is presented.

The model is based on just seven ordinary differential equations (ODEs) and is therefore intended as an introduction to some basic concepts and as a starting point for more detailed studies. The ODEs are carbon balances for seven reservoirs: upper atmosphere, lower atmosphere, long-lived biota, short-lived biota, ocean upper layer, ocean deep layer and marine biosphere.

Authors Anthony J McHugh, Graham W Griffiths, and William E Schiesser highlighted that the model also includes ocean chemistry calculations that address acidification with ocean pH typically ranging from 8.2 to 7.8 (pH decreases with increasing acidity).

These calculations illustrate some basic numerical procedures, e.g., a Newton solver applied to a fourth order polynomial to calculate ocean pH and spline interpolation to provide additional model outputs. The problem of acidification has important implications for coral and the associated marine life through the chemistry of calcium carbonate.

The model is available (gratis) as a set of commented routines in Matlab [2] and R [3], with documentation and references, from

The book retails for US$48 / £32 at leading bookstores. More information about the book can be found at A companion media pack comes with the book.


Questions concerning the model can be directed to

A. J. Mchugh G. W. Griffiths W. E. Schiesser

[1] long-feared-milestone.html

[2] Matlab is a commercial scientific programming system available from the Math Works, Natick, MA.

[3] R is an open source scientific programming system that can be easily downloaded from the Internet.

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