Simple Eulerian–Lagrangian approach to solving equations for sinking particulate organic matter in the ocean

Abstract. Gravitational sinking of particulate organic matter (POM) is a key mechanism of the vertical transport of carbon in the deep ocean and its subsequent sequestration. The size spectrum of these particles is formed in the euphotic layer by primary production and various mechanisms, including food web consumption. The masses of the particles, as they descend, change under aggregation, fragmentation, and bacterial decomposition. These processes depend on the water temperature and oxygen concentration, particle sinking velocity, ages of the organic particles, ballasting and other factors. In this work, we developed a simple Eulerian–Lagrangian approach to solving equations for sinking particulate matter when the effects of the sizes and ages of the particles, temperature and oxygen concentration on their dynamics and degradation processes are considered. The model considers feedback between the degradation rate and the particle sinking velocity. We rely on known parameterizations, but our Eulerian–Lagrangian approach for solving the problem differs, which enables the algorithm to be incorporated into biogeochemical global ocean models with relative ease. Two novel analytical solutions of a system of one-dimensional Euler equations for the POM concentration and Lagrange equations for the particle mass and position were obtained for constant and age-dependent degradation rates. The feedback between the degradation rate and sinking velocity leads to significant differences in the vertical profiles of the POM concentration and sinking flux, in contrast to the solutions obtained at a constant sinking velocity, where the concentration and flux profiles of the POM are similar. The calculation results are compared with the available measurement data for the POM and POM flux for the latitude bands of 20–30° N in the Atlantic and Pacific Oceans and 50–60° S in the Southern Ocean. The dependence of the degradation rate on temperature significantly affected the profiles of the POM concentration and sinking flux by enhancing the degradation of sinking particles in the ocean's upper layer and suppressing it in the deep layer of the ocean. In all cases considered, the influence of the oxygen concentration was insignificant compared to that of the distribution of temperature with depth.