Migrant Pump Depth-Time Model: Diel Vertical Migration Flux (2D)

The ocean's biological carbon pump isn't just sinking "marine snow" — a large share of it rides on animals swimming up and down every day. Instead of animating individual copepods, this simulation solves a continuum advection-diffusion (Fokker-Planck) equation for the population's depth density n(z,t): a light-driven isolume-tracking target depth pulls the profile up at night and down by day, an adjustable diffusivity spreads it to reflect real behavioural variability, and a finite-volume solver computes the exact flux crossing the mixed-layer depth every frame. The result renders as a scrolling depth-time echogram — the same kind of view oceanographers read off real ADCP backscatter data — alongside a live carbon-export flux, mean depth, and a mass-conservation check confirming the numerical scheme keeps the population exactly conserved.