Simple Eulerian-Lagrangian approach to solve equations for sinking particulate organic matter in the ocean

Abstract. A gravitational sinking of the particulate organic matter (POM) is a key mechanism of 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 the primary production and various mechanisms including food web consumption. The mass of particles, as they descend, changed under aggregation, fragmentation, bacterial decomposition which depends on the water temperature and oxygen concentration, particle sinking velocity, age of the organic particles, ballasting and other factors. In this paper, we developed simple Eulerian-Lagrangian approach to solve equations for sinking particulate matter when the influence of the size and age of particles, temperature and oxygen concentration on their dynamics and degradation processes were taken into account. The model considers feedback between degradation rate and particle sinking velocity. We rely on the known parameterizations, but our Eulerian-Lagrangian approach to solving the problem differs, allowing the algorithm to be incorporated into biogeochemical global ocean models with relative ease. Two novel analytical solutions of a system of the one-dimensional Eulerian equation for POM concentration and Lagrangian equations for particle mass and position were obtained for constant and age-dependent degradation rates. At a constant rate of particle sinking, they correspond to exponential and power-law profiles of the POM concentration. It was found that feedback between degradation rate and sinking velocity results to a significant change in POM and POM flux vertical profiles. The calculations are compared with the available measurement data for POM and POM flux for the latitude band 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 POM concentration enhancing the degradation of sinking particles in the ocean’s upper layer and suppressing it in the deep layer of the ocean. The influence of oxygen concentration in all cases considered was insignificant compared to the distribution of temperature with depth.