Water-vegetation interactions in a sea of water: Plankton in mesoscale turbulence

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2 Water-vegetation interactions in a sea of water: Plankton in mesoscale turbulence A. Provenzale ISAC-CNR, Torino and CIMA, Savona, Italy Work done with: Annalisa Bracco, Claudia Pasquero Adrian Martin, Kelvin Richards, Istvan Scheuring

3 Motivation: climate dynamics and the marine ecosystem Phytoplankton activity in the ocean significantly affects carbon fluxes between the atmosphere and the ocean (photosythesis and respiration) An indirect measure of CO 2 fluxes is the rate of phytoplankton production (PP: Primary Production)

4 Trophic web in the ocean Nutrients (N, P, Fe) Phytoplankton (primary producers) bacteria Zooplankton grazers (fish) highest predators

5 Trophic web in the ocean Large number of coexisting planktonic species (the Paradox of the Plankton ) Complexity of the community structure Large spatial-temporal variability

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7 Limiting factors for phytoplankton: light and nutrients Photosynthetic phytoplankton need light: Phytoplankton are confined in the upper layer of the ocean (euphotic layer)

8 Photosynthetic phytoplankton need nutrients: Where do nutrients come from? Upwelling from deeper water Regeneration Dust deposition

9 The structure of the upper ocean Sunlight Nutrients

10 The structure of the upper ocean (Oran-Almeria front)

11 The structure of the upper ocean (the Gulf Stream)

12 The structure of the upper ocean: Localized upwelling areas: inhomogeneous nutrient fluxes Strong horizontal advection of nutrients, phytoplankton and zooplankton Finite reaction times of phyto and zooplankton: Phytoplankton time scale of about 1-2 days Zooplankton time scale of about two weeks

13 Spatial patchiness of phytoplankton

14 Bloom of Nodularia spumigena in the Baltic Sea (notice the effect of mesoscale structures)

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16 Development of a mathematical model of the interaction between fluid dynamics and biology (at meso and large scales): Reaction-advection-diffusion equations

17 Interaction between fluid dynamics and biology: Advection and diffusion of reactive tracers Horizontal advection: large-scale and mesoscale flows Vertical motions: upwelling and downwelling (nutrient input) Diffusion: parameterization of small-scale turbulence

18 Interaction between fluid dynamics and biology: Advection and diffusion of reactive tracers DP Dt = P t + u r P + w P z = f (P) + κ 2 P P + z K P z e.g. DP Dt = α P + κ P 2 P DP Dt = α P(1 P) + κ P 2 P

19 Nutrient-phytoplankton-zooplankton dynamics:

20 Nutrient-phytoplankton-zooplankton dynamics: DN = input uptake + regeneration Dt DP = growth mortality predation Dt DZ = growth mortality predation Dt

21 Nutrient-phytoplankton-zooplankton dynamics: DN = input f(n,p) + g(p,z) Dt DP Dt = α f(n,p) h P P (P) q(p,z) DZ Dt = α q(p,z) h Z Z (Z) r(z)

22 Simplified plankton dynamics: the homogeneous NPZ model dn dt N =Φ(N) β k N + N P + µ N (1 γ) aεp 2 a + εp Z + µ PP + µ 2 Z Z 2 dp dt = β N k N + N P aεp 2 a + εp Z µ PP 2 dz dt = γ aεp 2 a + εp 2 Z µ Z Z 2

23 A simplified model of mesoscale flows: the quasigeostrophic approximation δ = H/L << 1 neglect of vertical accelerations Ro = U/f 0 L << 1 neglect of fast modes (gravity waves) Dq Dt q t + u q x + v q y q t + ψ, q [ ]= F + D u = ψ y q = 2 ψ + z, v = ψ x 2 f 0 ψ + f N 2 (z) z f 0 = 2Ωsinφ, β = 2Ω R E cosφ, f = f 0 + β y N 2 (z) = g ρ ρ z

24 QuickTime and a Compact Video decompressor are needed to see this picture. Simulation by Jeff Weiss et al

25 Α A further simplification: A layer of homogeneous flow, rigid lids, f-plane: 2D turbulence

26 In the absence of dissipation and forcing, quasigeostrophic flows conserve two quadratic invariants: energy and enstrophy E = 1 A A Z = 1 A A 1 2 ψ 2 dxdy ( 2 ψ ) 2 dxdy (for 2D turbulence) As a result, one has a direct enstrophy cascade and an inverse energy cascade

27 QuickTime and a Cinepak decompressor are needed to see this picture.

28 Forced-dissipated barotropic turbulence

29 A numerical simulation of horizontal advection with the NPZ model in forced-dissipated barotropic turbulence

30 What we want to explore here: Impact of the interplay between the spatio-temporal variability of nutrient fluxes and horizontal advection on primary productivity in the ocean. How does the size and the nature of nutrient input regions affect PP estimates in the presence of horizontal advection?

31 Our simple model of N-P-Z dynamics DN Dt = s(x, y,t)(n N) β N 0 k N + N P + µ N (1 γ) aεp 2 a + εp Z + µ P + µ Z 2 2 P Z DP Dt = β N k N + N P aεp 2 a + εp Z µ PP 2 DZ Dt = γ aεp 2 a + εp 2 Z µ Z Z 2 D Dt = t + u x + v y s = s n = day 1 s = s a = day 1

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33 The advecting flow is modelled with forced-dissipated barotropic turbulence

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37 Fluid parcels are advected past active upwelling regions The increase in primary productivity is due to the alternance between active and quiescent regions and to the asymmetry between growth and decay of phytoplankton and flux changes from active to normal and back

38 A fluid parcel subject to a periodic alternance between active and quiescent conditions:

39 A fluid parcel subject to a periodic alternance between active and quiescent conditions: Effect of the duration of upwelling events

40 The spatial and temporal distribution of the nutrient input plays an important role, due to the presence of mesoscale (and submesoscale) structures and the associated mixing processes Models that do not resolve mesoscale features can severely mis-estimate primary production Bounds on primary production

41 Mesoscale turbulence and reaction rates

42 Mesoscale turbulence affects reaction rates DN Dt = s ( N N 0 0) 1 β 1 NP 1 ρ 1 k 1 + N 1 β 2 NP 2 ρ 2 k 2 + N + κ 2 N N DP 1 Dt = β 1 NP 1 k 1 + N µ 1 P 1 + κ 1 2 P 1 DP 2 Dt = β 2 NP 2 k 2 + N µ 2 P 2 + κ 2 2 P 2

43 Principle of competitive exclusion: in equilibrium conditions, when two species compete for the same resource only the most favoured species survives.

44 Horizontal advection by 1) A Langevin stochastic process (with no coherent flow structure) 2) 2D Turbulence (with vortices)

45 Ornstein-Uhlenbeck (Langevin) process dx = udt du = u dt + 2σ 2 T L T L 1/2 dw dw = 0 dw (t)dw (t') = δ(t t')dt R(τ) = u(t)u(t + τ) = exp( τ /T L ) 1 u2 p(u) = exp 2πσ 2σ 2

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47 Vortices provide a shelter that allows longer survival of the less-favoured species Bracco, Provenzale, Scheuring, Proc. R. Soc. B (2000) Pasquero, Bracco, Provenzale, in Shallow Flows (2004)

48 The presence of vortices significantly affects (chemical and biological) reaction rates Bracco, Provenzale, Scheuring, Proc. R. Soc. B (2000) Pasquero, Bracco, Provenzale, in Shallow Flows (2004)

49 An important challenge: parameterising the effect of mesoscale structures on biogeochemical reactions

50 Mesoscale turbulence acts as one component of the marine ecosystem

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53 Parameterization of plankton advection in mesoscale turbulence (Pasquero 2005) r X t = r u P t = D eff 2 P D eff = 2E kin T L

54 Parameterization of plankton advection in mesoscale turbulence: Estimate of primary productivity

55 Parameterization of plankton advection in mesoscale turbulence: dispersion of a reactive scalar (Plumb 1978)

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57 Eulerian method P t + r u P = f (P) + κ P 2 P dp j dt Semi-Lagrangian method d r X j dt ( ) = u r X r j,t = f (P j ) + κ P W( X r j X r k )P k k

58 Dynamics of reactive tracers

59 Dynamics of reactive tracers