A state-of-the-art report is given of the Hamburg model of the oceanic carbon cycle. The model advects geochemical tracers important to the carbon cycle by the currents of a general circulation model. The geochemical cycling is driven by a Michaelis-Menten type production kinetics. The model is an extension of the Bacastow and Maier-Reimer (1990) model. It is based on a more realistic current field and includes a mechanism of lysocline-sediment interaction. Principal variables are ∑CO2, alkalinity, phosphate, oxygen, and silicate. The carbon variables are defined for 12C, 13C, and 14C separately. In addition to these carbon isotopes, 39A and δ18O of dissolved oxygen are predicted. The model predicts realistic global patterns of tracer distribution. In the equatorial eastern Pacific, however, the structures are exaggerated due to a strong upwelling which is a common feature of coarse resolution models of the general circulation of the ocean.

Geochemical cycles in an ocean general circulation model. Preindustrial tracer distributions

A three-dimensional model of the natural carbon cycle in the oceans is described. The model is an extension of the inorganic ocean-circulation carbon cycle model of Maier-Reimer and Hasselmann (1987) to include the effect of the ocean biota. It is based on a dynamic, general circulation model of the world oceans. Chemical species important to the carbon cycle are advected by the current field of the general circulation model. Mixing occurs through numerical diffusivity (related to finite box size), a small explicit horizontal diffusivity, and a convective adjustment. An atmospheric box exchanges CO2 with the surface ocean. There is no land biota provided in the present version of the model. The effect of the ocean biota on ocean chemistry is represented in a simple way and model distributions of chemical species are compared with distributions observed during the GEOSECS and other expeditions.

Ocean-circulation model of the carbon cycle

http://www.vliz.be/imisdocs/publications/103176.pdf

Review of three-dimensional ecological modelling related to the North Sea shelf system: Part 1: models and their results

Self-shading of light by algae growing in a column of water plays an important role in the dynamics of algal blooms. Thus without self-shading the algal concentration would increase more rapidly, making the nutrient limitation too strong. Apart from the practical importance of self-shading, its inherent nonlinearity in the growth dynamics leads to an interesting mathematical problem, which warrants detailed analytical investigation. Our mathematical model for the self-shading effect includes vertical diffusion, algal settling, gross production, and collective losses of algae. Steady-state solutions of the model equation are investigated in detail by the phase plane method, and their stability examined. Finally we discuss the vertical profile of algal concentration.

Analysis of the self-shading effect on algal vertical distribution in natural waters

http://www.staff.uni-oldenburg.de/alexey.ryabov/pdfs/Ryabov_et_al_Vertical_Phyto_2010.pdf

Vertical distribution and composition of phytoplankton under the influence of an upper mixed layer

/pdf/the-vertical-structure-of-phytoplankton-growth-dynamics-a-5f3cff6l0g.pdf

The vertical structure of phytoplankton growth dynamics - a mathematical model

The vertical structure of photoplankton growth dynamics a mathematical Model

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The vertical structure of phytoplankton growth dynamics - a mathematical model

The vertical structure of photoplankton growth dynamics a mathematical Model