the spring bloom contain more nitrate: 10–12 μM. Substituting those values (Fig.
4.4b), produces a strong, more delayed bloom that is eaten down by grazers. Both P
and Z then fall to very low (but not zero) values with almost all the nutrient in
inorganic form. The cycle repeats after 75 days, and then settles into similar strong
oscillations with an approximately 50-day period. A common modeling strategy can
be applied to make the model appear somewhat more realistic: a threshold amount of
phytoplankton is included, P 0 , that must be present to induce grazers to eat. This is
installed in the Ivlev function as:
(^) along with a statement forcing dP/dt to zero when P < P
0 . The grazing threshold
enforces low, constant P and Z values after the initial bloom (Fig. 4.4c). The large
amount of nutrient regenerated as the bloom is consumed is not realistic and is forced
by the closure of the upper water column.
Fig. 4.4 Annual nutrient, phytoplankton and herbivore stock variation in a Franks–
Wroblewski–Flierl model. (a) Similar to original model. (b) Vm reduced to 0.69 d−1
and initial nutrient increased to 10.6 μM. (c) Like (b), but with a threshold
phytoplankton abundance, P 0 , for grazer activity. (d) Like (c) with mixing daily from
a lower layer constantly at initial nutrient and with no phytoplankton.