# Model Simulations

## What are sea ice models used for?

The Arctic areas - ocean even more than land - are difficult to reach, for several winter months not at all. Instruments must be able to work at very low temperatures. These are all reasons which limit research on site. It is complex, expensive and potentially dangerous.

With models one can perform theoretical experiments that would be impossible in reality. By using models you can look to some extent, into the future.

One can analyze processes in minute detail thus gaining a deeper insight. Additionally, the work takes place in the office and is comparatively cheap despite the use of mainframe computers.

### How does a sea ice model look like?

The basic properties that will determine the ice are thickness, coverage (percentage of surface area covered with ice) and speed. These properties are highly variable in space and time. Variability is determined e.g. by air and ocean temperature. The velocity in turn depends on the thickness of the ice, the wind conditions and the ocean current.

The changes of the sea ice over time, however, can be described by relatively simple equations. The state at the next time is calculated from the previous state plus the change over the time interval. This explains the expression "compute the model forward in time". The area of interest- here the Arctic Ocean is overlaid with a three-dimensional grid. The geometry of this grid can be as simple or complicated as one likes. Numerical properties of different grids determine the choice.#

The calculations are then carried out at the midpoints of the grid's substructure (e.g. cuboids). The side length of the cuboids are called resolution. In our case coarse resolution mean 1-2 degrees geographic, 1/10 to 1/12 degrees geographic are regarded as high resolution (see graphic above).

To calculate the change, variables outside of the ice are necessary as air temperature over the ice and the water temperature below the ice. Wind speed over the ice and the ocean movement under the ice influence the ice velocity and with that the transport of ice.

### How reliable are the results/statements of a model?

The reliability of model results is much discussed in public. Whenever results such as e.g. the IPCC report are released and reported by the non-scientific press, a more or less heated debate on this issue follows.

### Quality of a model

The basic equations, see above, based on physical laws and are thus correct. However, problems can arise through

• the solution of the system by computer
• the chosen numerical method
• the accuracy of the computer (now rarely a problem)
• the resolution (size of cubes, see above)
• the initial and forcing (atmospheric) data: Measurements are rather incomplete in space and time especially in high latitudes (see above)
• data products are measurements completed by models. A large community is engaged in the production and evaluation of these data.

Some processes in the ocean are taking place on scales that are smaller than the cube, e.g. mixing. For these processes,  the correct but not directly solvable equation is approximated with an educated guess, often just one number. Mostly one can rely on studies that have systematically compared a solution of the equation with the approximation. No one, however, is immune against processes turning out to be important for the overall solution that have not been included so far.

### How to check the quality of a model? Keyword validation

A direct comparison will only work with simulations of the actual situation and a well-known past. Then you can compare model values to data, insofar as there are data available. It is particularly useful, not to compare the values of the basic variables point-wise, but area wide integrated values. In the Arctic, that would be e.g. transport of ice or water through Fram Strait. AWI has collected long time series of measurements across the Fram which can be used for model validation.

A thorough discussion of this topic can be found here (ocean model only but the fundamentals apply for ice and atmosphere models as well): Griffies, S. M. , Gnanadesikan, A. , Dixon, K. W. , Dunne, J. P. , Gerdes, R. , Harrison, M. J. , Rosati, A. , Russell, J. , Samuels, B. L. , Spelman, M. , Winton, M. and Zhang, R. (2005): Formulation of an ocean model for global climate simulations , Ocean Science, 1 , pp. 45-79 .