Numerical simulations of submesoscale balanced vertical velocity forcing unsteady nutrient-phytoplankton-zooplankton distributions

The effect of submesoscale balanced ( void of waves) vertical velocity on initially steady nutrient-phytoplankton-zooplankton (NPZ) distributions is investigated numerically. First, steady vertical NPZ profiles, continuous but not continuously differentiable at several depths, are found as analytical solutions to the NPZ equations in the absence of flow. These solutions admit numerical equivalents that are continuously differentiable in the numerical sense, here meaning convergence of the vertical derivative with respect to increasing vertical resolution. These NPZ solutions require, however, large vertical resolutions, with a grid size of few centimeters, to be properly discretisized. The ecological model is next coupled to a nonhydrostatic Boussinesq f plane physical model that explicitly conserves potential vorticity on isopycnals. Then the NPZ solutions are used as steady initial ecosystem conditions to investigate the role of submesoscale balanced vertical velocity in forcing NPZ anomalies in an idealized case of a baroclinic unstable jet. The results show that the baroclinic flow rapidly develops balanced vertical velocity that in turn favors NPZ anomalies. A large cancelation between the local change and the horizontal advection occurs in the ecosystem variables. This particularly occurs for zooplankton anomalies that therefore behave as better passive tracers of the horizontal flow than phytoplankton anomalies. However, once phytoplankton and zooplankton anomalies develop locally, forced by vertical velocity, they are horizontally advected away from the upwelling or downwelling regions so that spatial distributions of vertical velocity and ecological fields become eventually uncorrelated.