PLANKTONPATCHINESS

“[Encountered coloured water] extending about two miles from North to South and about six to eight hundred fathoms from West to East. The colour of the water was yellow.” May 1735

Don Antonio de Ulloa1716-1795

Politician, explorer, scientist(Discoverer of platinum)

Physical processes implicated in patchiness

Diffusion-related processesPatchesFilamentsTuring MechanismPlankton waves

Lateral stirringEarly observations of phytoplankton spectraPhysical turbulenceExplaining phytoplankton spectraZooplankton and spectraPitfalls of spectral analysisBiological forcing at intermediate scales

Vertical-horizontal coupling

Diffusion

Technically “effective diffusion”

Simplest (and crudest) representation of the effect of turbulent stirring and mixing.

A necessary evil at some scale for most models.

~L1.15

Okubo (1971)

Physical processes implicated in patchiness

Diffusion-related processesPatchesFilamentsTuring MechanismPlankton waves

Lateral stirringEarly observations of phytoplankton spectraPhysical turbulenceExplaining phytoplankton spectraZooplankton and spectraPitfalls of spectral analysisBiological forcing at intermediate scales

Vertical-horizontal coupling

Including grazing(Wroblewski et al., 1975; Denman and Platt, 1975)

Pt = Pxx + P - R[1-exp(-P)] - RP

Lc=[/(-R)]

But this is only for small times…

Scale dependent diffusivity

Results are very sensitive to biological model used.

Constant growth rate,(Okubo, 1978; Ozmidov, 1998)

critical length still existsLogistic growth rate, (Petrovskii, 1999a, 1999b)

PP(1-P/P0)no critical length

Other added complexity…

Diurnal light cycle (Wroblewski and O’Brien, 1976)

Zooplankton vertical migration(Wroblewski and O’Brien, 1976)

Prey detection by zooplankton(Wroblewski, 1977)

All question the existence of a well-defined critical length scale.

Data from

Dundee Satellite

Receiving Station

Processed by

Steve Groom,

RSDAS, PML

Physical processes implicated in patchiness

Diffusion-related processesPatchesFilamentsTuring MechanismPlankton waves

Lateral stirringEarly observations of phytoplankton spectraPhysical turbulenceExplaining phytoplankton spectraZooplankton and spectraPitfalls of spectral analysisBiological forcing at intermediate scales

Vertical-horizontal coupling

Inert tracers in 2d turbulenceGarrett, C. (1983). Dynamics of Atmospheres and Oceans, 7, 265-277

Consider an initially very small patch of tracer.

3 regimes:L<LS, spreads diffusively, =s

LS<L<LL, filamentedLL<L, spreads diffusively, =l

Lengthscales: LS=(s/) LL= (l/)

Ledwell, Watson and Law (1998)

Filament width~()

Why should plankton disperse like an inert tracer?

An initial “patch” requires some localised forcing,e.g. upwelling, stratification etc.

The nature of this forcing may play a strong role in the subsequent dispersion of the patch.

Will the filamental dispersion stage occur?

If the forcing is permanent and restores structurequicker than it is dispersed will this prevent formation

of filaments?

When do filaments form?Neufeld, Lopez and Haynes, 1999

Filaments if…F>C

C/ t = u.C+ax-CC

Filaments formed, predominantly, in shear-dominated regionsA patch of tracer in such a region suffers

exponential expansion of its length contraction width

Shear induced contraction of the patch will be opposed by biological growth and diffusion

The flow can be divided at any point into…

a rotation + a deformation

Lfil = ( is effective diffusivity is strain rate

For exponential growth, final width of filament is independent of growth rate

identical to that for an inert tracer

Typical values:=5m2s-1, =5x10-6 s-1

Lfil~1kmConverges in ~ 1-2 days

For limited growth, (McLeod et al., 2001)2 regimes: <2.5: as exponentially growing/inert tracer

>2.5: width dependent on growth rate larger than for exponential growth

Lfil ~ ()

Physical processes implicated in patchiness

Diffusion-related processesPatchesFilamentsTuring MechanismPlankton waves

Lateral stirringEarly observations of phytoplankton spectraPhysical turbulenceExplaining phytoplankton spectraZooplankton and spectraPitfalls of spectral analysisBiological forcing at intermediate scales

Vertical-horizontal coupling

A.M.TuringThe chemical basis for morphogenesis

Phil.Trans.Roy.Soc. B, 237, 37-72, 1952

Murray, 1988

Different diffusivities for different marine tracers?

zoophy

Zooplankton have greater swimming speeds than phytoplankton.Levin and Segel, 1976; Matthews and Brindley, 1997

phynit

Different vertical profiles for nitrate and phytoplankton in the presence of shear.Okubo, 1974, 1978

Too little data to tell…

•Occurrence very dependent on biological model Turing instability does not occur with Lotka-Volterra system

• Few measurements of plankton motilityUnderwater hologrammetry may finally allow in situ measurements

• Uncertainty in how individual motility manifests itself as population motility

Matthews and Brindley (1997) claim differences are not great enough for PZ system

Physical processes implicated in patchiness

Diffusion-related processesPatchesFilamentsTuring MechanismPlankton waves

Lateral stirringEarly observations of phytoplankton spectraPhysical turbulenceExplaining phytoplankton spectraZooplankton and spectraPitfalls of spectral analysisBiological forcing at intermediate scales

Vertical-horizontal coupling

Dubois, 1975

Neufeld, 2001

Captain James Cook1728-1779

“…on the 9th December 1768 we observed the sea to be covered with broad streaks of a yellowish colour, several of them a mile long, and three or four hundred yards wide.”

PN

V=2()

From Matthews and Brindley, 1994.

du/dt=f(u,v)dv/dt=g(u,v)