Universal multifractals and ocean patchiness: Phytoplankton, physical fields and coastal heterogeneity

We argue that a wide-range scaling approach is demanded by standard Stommel diagrams and that it can unify the treatment of phytoplankton variability over wide ranges of scales. By investigating the effects of coastal heterogeneity on the variability of in situ salinity (S), oxygen (ρ_o), temperature (T), optical transmissivity (t) and phytoplankton proxy data (fluorescence; ρ_p) over the range ∼ 0.4-1600 m, we statistically characterize the heterogenity of these variables, determining both the range and types of scaling, as well as their scale-by-scale interrelationships. By comparing bays with systematically varying large-scale heterogeneity, we were able to investigate the influence of the latter on the variability, systematically determining the three universal multifractal parameters as well as the exponent characterizing extreme self-organized critical behaviour. We found that, consistent with turbulent dominated dynamics, T, ρ_o, S and T were scaling over essentially the entire observed range of scales, with T and ρ_o being statistically very close to passive scalars. However, ρ_p was quite different, displaying two regimes separated by a characteristic 'planktoscale' typically ∼ 100 m, but highly variable. The large-scale regime was neither passive scalar nor growth dominated (Denman-Platt), but was rather in between the two (the corresponding exponent was H_p ≈ 1/8 rather than 0 or 1/3, respectively). In addition, we fund a new small-scale regime with H_p ≈ -1/3, which is much 'rougher' than passive scalar (which has H_p = +1/3). We propose a simple model involving both growth and turbulence to account for the large scale, and grazing and turbulence (predator-prey zooplankton/phytoplankton interactions) to account for the small scale. Depending on the value of a dimensionless grazing constant Gr = D/ (τ_g²ε) (where D is the zooplankton diffusion constant, τ_g is the phytoplankton growth c onstant and ε is the turbulent energy flux), the small scale is dominated either by the turbulent grazing (Gr > 1) or by passive scalar turbulence (Gr < 1). In the grazing regime, we also theoretically predict that the density fluctuation exponent = -1/3, which is quite close to the data and quantifies the tendency of the zooplankton to uniformize the phytoplankton distribution by preferentially grazing high-concentration patches.