column. Since there is no spatial variation, such a model is termed zero-dimensional
(even though time is a “dimension”). Nutrients are taken up by phytoplankton and
converted to phytoplankton stock. Phytoplankton are eaten by zooplankton and
converted to tissue, with losses to metabolism. Those losses appear immediately as
nutrient available to phytoplankton. Both phytoplankton and zooplankton die and
decay at significant rates, the nutrients released appearing immediately as dissolved
and available nutrients. The most important oversimplification is that the system is
closed; nothing mixes in or sinks out. The flow diagram for these interactions is
shown in Fig. 4.3.
Fig. 4.3 A box diagram of the Franks–Wroblewski–Flierl NPZ model.
The difference equations can be written out in words, often a useful modeling
exercise:
(^)
(^)
(^) Next, these equations are written out as differential (or directly as difference)
equations. The key challenge at this step is to find suitable and effective functional
relations to represent the interactions accurately. The functions used here differ from
those of Franks et al. (1986) only in letting γ, not (1 − γ), be zooplankton growth
efficiency (0.3 of ingested food). They are:
(^)
(^)
(^) A Matlab script with suitable code for solving these equations is shown in Box 4.3.