On the mathematical formulation and parameter estimation of the Norwegian Sea plankton system

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Abstract
The mathematical description of the oceanic plankton system is often characterised by a simple structure where the major components of the system are governed by the dissolved nutrient concentration N, the phytoplankton biomass P, and the zooplankton biomass Z (also known as the NPZ model). The flows between the variables can be formulated in a variety of ways that, in general, alter the time development of the model. In this study we investigate how the numerical value of model parameters that are hard to determine experimentally can be estimated from in situ field observations. By that, we can assign parameter values to each model formulation such that they should follow a prescribed time development that is consistent with data. Accordingly, this gives us a tool to compare model formulations in a consistent way. The study emphasises the importance of analysing the model with respect to stability and multiple solutions. The study is exemplified using observations from Ocean Weather Station Mike (66°N, 2°E) in the Norwegian Sea, illustrating the need for a proper model formulation in order to reproduce measurements.

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