A discrete interaction numerical model for coagulation and fragmentation of marine detritic particulate matter

Abstract. A simplified model, representing the dynamics of marine organic particles in a given size range experiencing coagulation and fragmentation reactions is developed. The framework is based on a discrete size spectrum on which reactions act to exchange properties between different particle sizes. The reactions are prescribed according to triplets interactions. Coagulation combines two particle sizes to yield a third one, while fragmentation breaks a given particle size into two (i.e. the inverse of the coagulation reaction). The complete set of reactions is given by all the permutations of two particle sizes associated with a third one. Since, by design, some reactions yield particle sizes that are outside the resolved size range of the spectrum, a closure is developed to take into account this unresolved range and satisfy global constraints such as mass conservation. In order to minimize the number of tracers required to apply this model to an Ocean General Circulation Model focus is placed on the robustness of the model to the particle size resolution. Thus, numerical experiments were designed to study the dependence of the results on i) the number of particle size bins used to discretize a given size range (i.e. the resolution) and ii) the type of discretization (i.e. linear vs nonlinear). The results demonstrate that in a linearly size discretized configuration, the model is independent of the resolution. However, important biases are observed in a nonlinear discretization. A first attempt to mitigate the effect of nonlinearity of the size spectrum is then presented and shows significant improvement in reducing the observed biases.