Microscopic algae that are suspended in the world's ocean absorb 45,000,000,000,000,000 grams of carbon dioxide every year. That's over 7 times the total emissions of carbon dioxide by cars, power plants, agriculture and all other emissions by humans. What controls the amount of carbon absorbed? Where does it go when the microalgae die? Mathematical models can be used to study these questions.

First an equation to describe the dynamics of microscopic algae must be developed. Here's one I use for a 3 dimensional ocean:

where P is the algae concentration, t is time, v is the velocity field, K is a diffusion coefficient, R_N and R_I are nutrient and light stores of the algae, Φ,γ,Z and μ_Z parameterise losses to predators, m_N and μ_P^max are coefficients relating to algal growth and w_P is a sinking rate.

In the above equation, advection and diffusion are ocean circulation processes. Phytoplankton growth requires carbon (which comes from the ocean water, allowing atmosphere CO2 to be absorbed to replace it). Sinking provides a possible permanent removal of carbon by burial of the organic matter in sediments (later to become fossil fuel if buried long enough). Grazing passes the carbon up the food chain to animals where the carbon sink (as dying animals), or be released back into the water due to respiration.

The solution of this equation is complex, requiring prediction of circulation for a particular region of the ocean among other physical processes. The diagram to the right shows the amount of algae predicted off NSW in a numerical simulation. The ocean can be seen on 4 levels: the surface, 33 m and 66m and 99m depth. The surfaces extend along the whole NSW coast, and to about 500 km offshore. The colour represents concentration of algae. Note the high concentrations in the surface south of Coffs Harbour. At this location high nutrient water has been brought to the surface and caused an algae bloom while it is swept south with the currents. From these simulations, estimates of carbon removal from the atmosphere in the waters off NSW can be calculated.

For articles about other mathematical topics see the complete list of homepage articles.