Advection in plankton models with variable elemental ratios

As ocean biogeochemical models evolve to permit the elemental composition of plankton populations and dissolved organic matter to vary, each element is normally assigned a separate state variable, which is advected and mixed independently of the others. In a population of cells with varying elemental quotas, the proper currency of the advection operator is subpopulations of similar cells. The spatial gradient in total C, N, or P summed over the spectrum of such subpopulations is identical to that calculated for the population means, so treating the various elements as independent should generally be a valid approximation. However, errors can arise in high-order advection schemes with nonlinear corrector terms, which are not additive across the subpopulations. Some numerical examples indicate that these errors are relatively small [O(10⁻³–10⁻⁴)] but can be as high as O(10⁻²) in certain cases. As grid resolution varies, the error scales approximately to the Courant number.