changes. State variables N, P, and H are in units of nutrient (as nitrogen)
concentration, μmol liter−1. The symbol ζ+(t) means that change in concentrations (N
and P) due to altered mixed-layer depth (Fig. 4.5) only occurs when the mixed layer
deepens, not when it shoals. This is not applied to herbivores, H, which are assumed
to swim up to stay above the limit to mixing; thus mixed-layer deepening dilutes
them, shoaling concentrates them. Mixing also includes 0.025Mz exchange between
the mixing layer and deeper water each day. Phytoplankton growth rate, when limited
by available light, is related to it by a saturating P vs. E curve. Almost any suitable
function will serve, and a simple one used by Denman and Peña (1999), Vmax (1 −
exp[–αEz/Vmax]), is used here. The quantity 1 − exp(–αEz/Vmax) varies from 0 to 1.
Estimates of available sea-surface light, E 0 , are from standard irradiance functions for
the latitude and date (Brock 1981), ignoring variations due to clouds (although cloud
effects can be added). Extinction down the water column is done here by a numerical
integration from dawn to sunset on every model day, meter-by-meter down through
the mixed layer. Both phytoplankton and zooplankton have daily mortality losses, mP
and carnH, proportional to their abundance. Grazing has a hyperbolic relationship to
P and is proportional to H, but with a threshold, P 0 , below which grazing stops.
Herbivores grow with an efficiency f, i.e. added H = f graz HP. A program for this
model is shown in Box 4.4. Initial variable and parameter values (changed from
Evans & Parslow 1985) are those shown in the program.
Fig. 4.5 Mixed-layer depth cycle imposed in the Evans–Parslow model.