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 heterog eneity on the variability of in situ salinity (S), oxygen (rho (O)), temper ature (T), optical transmissivity (t) and phytoplankton proxy data (fluores cence; rho (p)) over the range similar to0.4-1600 m, we statistically chara cterize the heterogeneity of these variables, determining both the range an d types of scaling, as well as their scale-by-scale interrelationships. By comparing bays with systematically varying large-scale heterogeneity, we we re able to investigate the influence of the latter on the variability, syst ematically determining the three universal multifractal parameters as well as the exponent characterizing extreme self-organized critical behaviour. W e found that, consistent with turbulent dominated dynamics, T, rho (O), S a nd t were scaling over essentially the entire observed range of scales, wit h T and rho (O) being statistically very close to passive scalars. However, rho (p) was quite different, displaying two regimes separated by a charact eristic 'planktoscale' typically similar to 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 approximate to 1/8 rather than 0 or 1/3, respectively). In addition, we found a new small-scale regime with H-p approximate to -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 intera ctions) to account for the small scale. Depending on the value of a dimensi onless grazing constant Gr = D/(tau (2)(g)epsilon) (where D is the zooplank ton diffusion constant, tau (g) is the phytoplankton growth constant and ep silon 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 fluctua tion exponent = -1/3, which is quite close to the data and quantifies the t endency of the zooplankton to uniformize the phytoplankton distribution by preferentially grazing high-concentration patches.