The vertical mixing scheme in Frost’s (1993) model is simple, but works because
the mixing coefficients (diffusivities) were tuned to reproduce vertical profiles of
hydrographical properties and to provide the same upper-layer nutrients at the end of a
model year as at the beginning. More sophisticated mixing schemes are required if
model ecosystem cycles are to respond to some elements of climate change: more-or-
less surface irradiance (a difference in cloudiness and thus surface warming) and
changes in wind climatology. Denman et al. (2006) applied to a model of the subarctic
Pacific problem a so-called turbulence closure system (Mellor–Yamada 2.5) in which
vertical mixing is subject to surface warming and wind, modeling their effects in
layers 2 m thick down to 120 m. Other schemes are in use for this, particularly one
called Large–McWilliams–Doney (LMD) or Kv profile parameterization (KPP), not
so different from the Frost scheme, but incorporating more explicit processes.
(^) The model from Denman’s group also has a more complex set of state variables, i.e.
seven (Fig. 4.10), and thus more interactions. There are two size classes of
phytoplankton, a pico–nano group and a diatom-like group, phytoplankton growth
reduced by iron limitation (more so for the larger cells) and protozoan grazers eating
both phytoplankton groups at different rates and themselves being eaten by
mesozooplankton with a fixed cycle of abundance based on seasonal data. There is
also a silica cycle with three more state variables, added as a secondary control of the
diatoms. At this level of complexity, a model has very many parameters, 44 in this
case, some of them constrained by data and some chosen by trial-and-error in