PLANKTON PATCHINESS

“[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 Ulloa Politician, explorer, scientist ( Discoverer of platinum)

Physical processes implicated in patchiness Diffusion-related processes Patches Filaments Turing Mechanism Plankton waves Lateral stirring Early observations of phytoplankton spectra Physical turbulence Explaining phytoplankton spectra Zooplankton and spectra Pitfalls of spectral analysis Biological 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.  ~L 1.15 Okubo (1971)

Physical processes implicated in patchiness Diffusion-related processes Patches Filaments Turing Mechanism Plankton waves Lateral stirring Early observations of phytoplankton spectra Physical turbulence Explaining phytoplankton spectra Zooplankton and spectra Pitfalls of spectral analysis Biological forcing at intermediate scales Vertical-horizontal coupling

Including grazing (Wroblewski et al., 1975; Denman and Platt, 1975) P t =  P xx +  P - R[1-exp(- P)] - R P L c =  [  /(  -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 exists Logistic growth rate, (Petrovskii, 1999a, 1999b)  P  P(1-P/P 0 ) 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 processes Patches Filaments Turing Mechanism Plankton waves Lateral stirring Early observations of phytoplankton spectra Physical turbulence Explaining phytoplankton spectra Zooplankton and spectra Pitfalls of spectral analysis Biological forcing at intermediate scales Vertical-horizontal coupling

Inert tracers in 2d turbulence Garrett, C. (1983). Dynamics of Atmospheres and Oceans, 7, Consider an initially very small patch of tracer. 3 regimes: L<L S,spreads diffusively,  =  s L S <L<L L,filamented L L <L,spreads diffusively,  =  l Lengthscales: LS=(s/) LS=(s/) L L =  (  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 structure quicker 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- C C

Filaments formed, predominantly, in shear-dominated regions A 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

L fil =  (   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:  =5m 2 s -1, =5x10 -6 s -1 L fil ~1km Converges 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 L fil ~  (   )

Physical processes implicated in patchiness Diffusion-related processes Patches Filaments Turing Mechanism Plankton waves Lateral stirring Early observations of phytoplankton spectra Physical turbulence Explaining phytoplankton spectra Zooplankton and spectra Pitfalls of spectral analysis Biological forcing at intermediate scales Vertical-horizontal coupling

A.M.Turing The chemical basis for morphogenesis Phil.Trans.Roy.Soc. B, 237, 37-72, 1952

Murray, 1988

Different diffusivities for different marine tracers?  zoo  phy Zooplankton have greater swimming speeds than phytoplankton. Levin and Segel, 1976; Matthews and Brindley, 1997  phy  nit 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 motility Underwater 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 processes Patches Filaments Turing Mechanism Plankton waves Lateral stirring Early observations of phytoplankton spectra Physical turbulence Explaining phytoplankton spectra Zooplankton and spectra Pitfalls of spectral analysis Biological forcing at intermediate scales Vertical-horizontal coupling

Dubois, 1975

Neufeld, 2001

Captain James Cook “…on the 9 th 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.”

P N

V=2  (  )

From Matthews and Brindley, du/dt=f(u,v) dv/dt=g(u,v)