## Section: Scientific Foundations

### Numerical Modelling

**Models** allow a global view of the dynamics, consistent in time and space on a wide spectrum of
scales. They are based on fluid mechanics equations and are complex since they deal with the
irregular shape of domains, and include a number of specific parameterizations (for example, to
account for small-scale turbulence, boundary layers, or rheological effects). Another fundamental
aspect of geophysical flows is the importance of non-linearities, i.e. the strong interactions between
spatial and temporal scales, and the associated cascade of energy, which of course makes their modelling more complicated.

Since the behavior of a geophysical fluid generally depends on its interactions with others (e.g.
interactions between ocean, continental water, atmosphere and ice for climate modelling), building a
forecasting system often requires **coupling different models**. Several kinds of problems can be encountered, since the models to be coupled may differ in numerous respects: time and space resolution, physics, dimensions. Depending on the problem, different types of
methods can be used, which are mainly based on open and absorbing boundary conditions, multi-grid theory, domain decomposition methods, and optimal control methods.