## Methods

#### Numerical experimentation

Numerical models of the climate system provide important tools for climate scientists. They can be used as a kind of laboratory to carry out controlled experiments with the climate system. By comparing a model experiment with increased greenhouse gas forcing to one with pre-industrial values, for example, it is possible to study anthropogenic influences on climate. Numerical experimentation is also used to determine the predictability of a system by studying the sensitivity of forecasts to small initial and forcing perturbations (→ Chaos).

Since the value of this approach depends on the realism of the used models,  scientists in the Climate Dynamics section work continuously on improving numerical models of the climate system. One example is the development of the new finite element sea ice ocean model (FESOM).

#### Data assimilation

In the oceanic and atmospheric sciences data assimilation encapsulates the process of combining observational data with models. By doing so the strength of both the observational data (i.e. information about the true state of the system) and models (physically plausible solutions) are combined in some optimal way. Data assimilation has many applications such as state estimation, generation of initial conditions for subsequent forecasts, observing system simulation experiments and model error diagnosis.

#### Data analysis

One of the main tasks in climate research is finding structures such as trends in large data sets. Advanced data analysis helps unraveling these structures in data and allows making statements about their robustness (interesting signal versus “interestingly looking” noise).

#### Theoretical work

The mathematical equations governing the evolution of the climate systems, which are based on first physical principles, are well-known, at least for large-scale aspects of the climate system. Unfortunately, these equations are impossible to solve analytically (i.e. with a pencil on a piece of paper) due to their complexity. However, if the focus is on understanding certain phenomena it is often not necessary to consider the full complexity of the equations to find a solution. Numerous successful applications of this approach in the past have proven the usefulness of the theoretical approach to further our understanding of some of the key phenomena of the climate system.