# Algorithmic Optimal Control - CO2 Uptake of the Ocean

Our research group worked on the project "CO2-Uptake of the Ocean" during the first phase of the cluster of excellence "Future Ocean" within the framework of the “excellence initiative” of the German Research Foundation (DFG) on behalf of the German government and the federal states of Germany. During the second phase we are part of the research field R11 - Predicted Ocean.

### What is Algorithmic Optimal Control?

Many scientific and technic applications pose problems of optimization which can be described by differential equations. Such problems are called problems of optimal control. Our research group works on the variety of challenges posed by the mathematical analysis as well as the numeric and algorithmic implementation of such problems of optimal control.

Important research areas are:

- Mathematical analysis and development of algorithms for optimal control problems
- Non-linear Optimization
- Optimal Control of ordinary and partial differential equations, particularly in fluid mechanics, including non-Newtonian fluids and area optimization
- Numerical Mathematics of partial differential equations, particularly of fluid mechanics equations, finite element method
- Algorithmic/Automatic Differentiation, Algorithmic Differentiation of functions based on computer programms, particularly of clima models

### What is CO2 Uptake?

Chemical, biological and physical processes ensure that atmospheric carbon dioxide is bound and saved in the ocean and hence temporarily extracted from the atmosphere. The ocean thus functions as a huge carbon sink and absorbs about a third of the human-caused carbon dioxide. This trait is of central importance during the current climate discussion, which concentrates on the effects of the greenhouse gas carbon dioxide on the global climate. A crucial aspect is the question how the CO2 Uptake of the ocean changes during climate changes (e.g. an increase of temperature). As CO2 uptake is a biochemical process, the main goals of the project A3 are sensitivity analysis and data assimilation (i.e. adjustment of model parameters using measured data) in biochemical models which are linked to ocean circulation models. At this point, the research areas of Applied Mathematics and Computer Science come into play.