Linear Control Theory to Introduce PeriodicParameters for a Marine Ecosystem Model

Global ocean biogeochemical models are of great importance for the assessment of the role of the ocean in the global carbon cycle and for the estimation of the impact of the climate change on marine ecosystems. The ocean acts as a major sink of carbon dioxide and takes up about one third of anthropogenic CO2. This characteristic plays a central role with respect to the climate discussion. The CO2-uptake of the ocean refers to biogeochemical processes which are simulated by corresponding parameterized models. The evaluation of these models leads to a sensitivity analysis of the model parameters and a model state estimation using associated measurement data. Usually, the biogeochemical models are coupled to ocean circulation models. This work comprises an investigation and application of control theory and optimization methodologies using discrete linear quadratic optimal control with both closed loop and open loop and the Kalman filter method. The fundamental aim of this work is to explore the potentialities of those proposed methods regarding an enhancement of a one-dimensional non-linear marine ecosystem model of NPZD (N for dissolved inorganic nitrogen, P for phytoplankton, Z for zooplankton and D for detritus) type. This ecosystem model, developed by Oschlies and Garcon, simulates the distribution of nitrogen, phytoplankton, zooplankton and detritus in a water column and is driven by ocean circulation data. The proposed methods are used to introduce annually periodic model parameters in a linearized version of the model. Firstly, I use the closed loop discrete linear quadratic optimal control (LQOC). It will be shown that the obtained version of the model gives a significant reduction of the modeldata misfit, compared to the misfit obtained for the original model with optimized constant parameters. The found inner-annual variability of the optimized parameters provides hints for an improvement of the original model. The obtained optimal periodic parameters are also used in validation and prediction experiments with the original non-linear version of the model. The experiments indicate that the considered method is very suitable for the considered marine ecosystem models. Secondly, I use the obtained periodic parameters in a state estimation applying the Kalman filter method. A comparison with results obtained by using optimized constant parameters in the Kalman filter state estimation approach is performed. We show that the Kalman filter method provides a very reasonable solution with periodic parameters compared to that with constant parameters. Thirdly, I use the open loop discrete linear quadratic optimal control (DOLOC) to investigate the impact of the linearization scheme about the state variables on the model-data-fit by using these periodic parameters in the original non-linear NPZD model. The proposed methodologies, particularly the closed loop discrete linear quadratic optimal control approach, serve as initial steps towards a tool for an efficient enhancement of marine ecosystem models. The investigation of further improvements of the presented algorithms as well as other promising approaches in the framework of linear quadratic optimal control optimization are considered to be highly valuable.