Fig. 6: Lagrangian biomass anomaly from ensemble simulations.

We show the Lagrangian biomass anomaly (LBA) measured in tonnes of carbon [Mg C] for an ensemble of well-mixed (a) and spatially-heterogeneous (b) patches across realistic ranges of strain [day⁻¹] and diffusion [km²day⁻¹] for one month of integration. Panel (c) shows the LBA difference between heterogeneous and well-mixed ensembles. The values reported for strain and diffusion are referred to the initial time of the simulations, as the patch size increases, they change accordingly to the respective scaling laws. All the other model parameters are kept constant (Methods). Each pixel of the heatmaps corresponds to the LBA attained by a single simulated patch under the effect of a specific combination of strain and diffusion. In (a) spatial heterogeneity is neglected by switching off the second moments of the tracer distributions. The maximum LBA values are reached for the minimums of both strain and diffusion i.e. for the smaller dilution rates. Instead, in (b), spatial heterogeneity is explicitly considered by modeling the second moments of the tracer distributions. The LBA in this case reaches much higher values than in the well mixed case as explicitly shown in (c). LBA maxima for the heterogeneous case populate an extended ridge in the LBA surface highlighting the fact that the associated optimal dilution values can be obtained from various combinations of strain and diffusion.