On the well-posedness of a coupled one-dimensional biological-physical model for the upper ocean

TL;DR

This paper proves the well-posedness of a coupled one-dimensional biological-physical ocean model, ensuring the existence and uniqueness of solutions, which supports its reliability for simulating biological activity in turbulent ocean water columns.

Contribution

It establishes the mathematical well-posedness of a novel coupled NPZD-model using variational and fixed-point methods, applicable to various biological parameterizations.

Findings

Existence of a unique positive weak solution is proven.

The analysis applies to different biological process parameterizations.

The model provides a reliable framework for biological-physical ocean simulations.

Abstract

This paper introduces a one-dimensional NPZD-model developed to simulate biological activity in a turbulent ocean water column. The model consists of a system of coupled semilinear parabolic equations. An initial-boundary value problem is formulated and the existence of a unique positive weak solution to it is proved. The existence result is derived using a variational formulation, an approximate model and a fixed-point method. It is shown that the qualitative analysis performed still applies if different parameterizations of several biological processes found in the biogeochemical modeling literature are used.