Representing phytoplankton aggregates in biogeochemical models

We show how to represent changes in the distribution of size and sinking speed of marine particles by a two-parameter model. In contrast to fully size-resolved models, this representation holds promise for constructing ocean biogeochemical models with detailed spatial resolution and seasonally varying sinking speed. We treat the mass and number of particles as separate state variables, each obeying its own conservation law. Average size and sinking speed of particles change as particles aggregate or the largest particles sink out. The distribution of particle sizes is assumed to follow a power law, whose exponent changes as a function of average particle size. Compared to biogeochemical models with constant particle sinking speed, our approach imposes a modest increase in computational cost and produces important effects like more rapid sinking immediately following a phytoplankton bloom. Compared to models that use hundreds of size classes to represent the detailed evolution of particle size distribution, our approach offers a major reduction in computational cost, while maintaining realistic behaviour like the sudden onset of significant aggregation when particles are sufficiently abundant.