Error assessment of biogeochemical models by lower bound methods (NOMMA-1.0)

Biogeochemical models, capturing the major feedbacks of the pelagic ecosystem of the world ocean, are today often embedded into Earth system models which are increasingly used for decision making regarding climate policies. These models contain poorly constrained parameters (e.g., maximum phytoplankton growth rate), which are typically adjusted until the model shows reasonable behavior. Systematic approaches determine these parameters by minimizing the misfit between the model and observational data. In most common model approaches, however, the underlying functions mimicking the biogeochemical processes are nonlinear and non-convex. Thus, systematic optimization algorithms are likely to get trapped in local minima and might lead to non-optimal results. To judge the quality of an obtained parameter estimate, we propose determining a preferably large lower bound for the global optimum that is relatively easy to obtain and that will help to assess the quality of an optimum, generated by an optimization algorithm. Due to the unavoidable noise component in all observations, such a lower bound is typically larger than zero. We suggest deriving such lower bounds based on typical properties of biogeochemical models (e.g., a limited number of extremes and a bounded time derivative). We illustrate the applicability of the method with two real-world examples. The first example uses real-world observations of the Baltic Sea in a box model setup. The second example considers a three-dimensional coupled ocean circulation model in combination with satellite chlorophyll a.