382 John Woods
signal: noise ratio. 1 shall describe a Virtual Plankton Ecosystem with mutating
plankton in 18.9.3. For now, we conclude that evolution does not prevent primitive- equation modelling of the plankton ecosystem.
18.4 Plankton
Plankton were discovered at Scheveningen on 27 th July 1676 by Antony van
Leeuwenhoeck (1677). Theyare micro-organisms that drift in the sea. Or more precisely (my definition), plankton are pelagic organisms, which cannot swim fast
enough to change their ambient environment usefully by swimming horizontally.
Ofcourse, many species ofplankton can swim fast enough to benefit from migrating vertically through the water. This anisotropy arises from the fact that the correlation scale of environmental variables is much shorter in the vertical than in the
horizontal, in the ratio ofthe Coriolis frequency to the Brunt-Vaisala frequency.
18.4.1 One-dimensional modelling
Thus the plankton ecosystem is essentially one-dimensional. The environment is
controlled by vertical fluxes from the sea surface, as in a classical boundary layer,
and the plankton move up and down through the water. This suggests that to first
order we can treat vertical and horizontal variation separately in our models. We
can do this by simulating the ecological processes with strictly one-dimensional
equations. If horizontal fluxes exist, their divergence is assumed to be negligible.
This is like simulating the plankton ecosystem in a vertical water column, which
outcrops at the sea surface and extends down into the ocean. The water colurnn has
an arbitrary horizontal area: one square kilometre is convenient. We as sume that
the fluxes through the sea surf ace are uniform across that area. The plankton populations in the water column are expres sed as either the number of organisms or biomass per unit area (e.g. copepods/m 2 or mgC/m 2 ). Vertical variation is expressed
per unit volume (e.g. copepods/m 3 ). The water column has open sidewalls: water
flows freely through them. That is unlike experimental ecosystem enclosures, the
sidewalls of which cause unwanted disturbance (Lalli & Parsons 1997). In onedimensional modelling, the neglect of horizontal flux divergence is assumed to
cause insignificant error in the simulation of plankton demography.
However, observations do show horizontal variation. We can divide it into two
categories: smaller and larger than the Rhines scale, which is about 100 km. That is
the maximum size oftransient eddies in the ocean; any larger and they Iose energy
to Rossby waves (Rhines 1979). Satellite images of ocean colour show that there is
substantial horizontal variation of phytoplankton concentration on scales smaller
than the Rhines limit. This is known as "patchiness" (Fasham 1978; Steele 1978).
It is caused by the transient eddies and jets of mesoscale turbulence, the oceanic
equivalent ofweather (Woods 1988). Simulating patchiness demands three-dimensional models. Martin et al. (2001) show that horizontally-averaged properties of a
patchiness-resolving three-dimensional model differ significantly from that simu-
signal: noise ratio. 1 shall describe a Virtual Plankton Ecosystem with mutating
plankton in 18.9.3. For now, we conclude that evolution does not prevent primitive- equation modelling of the plankton ecosystem.
18.4 Plankton
Plankton were discovered at Scheveningen on 27 th July 1676 by Antony van
Leeuwenhoeck (1677). Theyare micro-organisms that drift in the sea. Or more precisely (my definition), plankton are pelagic organisms, which cannot swim fast
enough to change their ambient environment usefully by swimming horizontally.
Ofcourse, many species ofplankton can swim fast enough to benefit from migrating vertically through the water. This anisotropy arises from the fact that the correlation scale of environmental variables is much shorter in the vertical than in the
horizontal, in the ratio ofthe Coriolis frequency to the Brunt-Vaisala frequency.
18.4.1 One-dimensional modelling
Thus the plankton ecosystem is essentially one-dimensional. The environment is
controlled by vertical fluxes from the sea surface, as in a classical boundary layer,
and the plankton move up and down through the water. This suggests that to first
order we can treat vertical and horizontal variation separately in our models. We
can do this by simulating the ecological processes with strictly one-dimensional
equations. If horizontal fluxes exist, their divergence is assumed to be negligible.
This is like simulating the plankton ecosystem in a vertical water column, which
outcrops at the sea surface and extends down into the ocean. The water colurnn has
an arbitrary horizontal area: one square kilometre is convenient. We as sume that
the fluxes through the sea surf ace are uniform across that area. The plankton populations in the water column are expres sed as either the number of organisms or biomass per unit area (e.g. copepods/m 2 or mgC/m 2 ). Vertical variation is expressed
per unit volume (e.g. copepods/m 3 ). The water column has open sidewalls: water
flows freely through them. That is unlike experimental ecosystem enclosures, the
sidewalls of which cause unwanted disturbance (Lalli & Parsons 1997). In onedimensional modelling, the neglect of horizontal flux divergence is assumed to
cause insignificant error in the simulation of plankton demography.
However, observations do show horizontal variation. We can divide it into two
categories: smaller and larger than the Rhines scale, which is about 100 km. That is
the maximum size oftransient eddies in the ocean; any larger and they Iose energy
to Rossby waves (Rhines 1979). Satellite images of ocean colour show that there is
substantial horizontal variation of phytoplankton concentration on scales smaller
than the Rhines limit. This is known as "patchiness" (Fasham 1978; Steele 1978).
It is caused by the transient eddies and jets of mesoscale turbulence, the oceanic
equivalent ofweather (Woods 1988). Simulating patchiness demands three-dimensional models. Martin et al. (2001) show that horizontally-averaged properties of a
patchiness-resolving three-dimensional model differ significantly from that simu-