plankton patchiness
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“[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.
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/)
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?
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
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
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.”
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