The general structure of a biogeochemical model with state variables expressed as ensemble averaged concentrations is given by the following set of equations:
The gradient term on the left hand side of (263) is the total transport, for which typically surface and bottom boundary conditions
We basically consider two types of ecosystem models. In the simple NPZ (nutrient-phytoplankton-zooplankton) type models all state variables are based on the same measurable unit such as [mmol N m] for nitrogen-based models. In such NPZ models the reactive terms do only exchange mass between state variables with
In many biogeochemical models most state variables are known to be positive or at least non-negative quantities. For non-negative initial conditions one can easily show by a simple contradiction argument that the condition
However, for many applications such simple models are too restrictive. Often different spatial references are involved for the state variables, such as the detritus concentration in the water column, measured in [mmol N m] and the fluff layer concentration at the bed, measured in [mmol N m]. Many biogeochemical processes involve more than two substances such as the photosynthesis where different nutrients (e.g. nitrate and phosphorus) are taken up by phytoplankta and oxygen is produced. The ratios between these substances dissipated or produced are usually fixed, in the example of photosynthesis uptake of 16 mmol m nitrate is connected to an uptake of 1 mmol m phosphorus and a production of 8.125 mmol m oxygen.
For state variables which may be negative (such as oxygen concentration which also includes oxygen demand units, all sink and source terms are added up in the production terms , with a negative sign for the sink terms. For the Neumann et al. (2002) model discussed in sections , further deviations from the conservation formulation are introduced since biogeochemical reactions include substances which are not budgeted by the model (mostly because they are assumed to be not limiting). One typical example is nitrogen fixated by blue-green algae which builds up biomass by using atmospheric nitrogen which is later recycled to nitrate. Such non-conservative terms are lumped into the diagonal terms and .
Karsten Bolding 2012-01-24