Dynamical models

Let’s call \(X\) the model state defined on a spatial grid (regular or not). Its temporal evolution is given by the dynamical operator \(\mathcal{M}\), such as:

\[\frac{\partial X}{\partial t} = \mathcal{M}(X,t)\]

The codes for the dynamical models are gathered in the mapping/src/mod.py script. For each model, a specific class is implemented. Each class M has the following functions:

• M.step: forward propagation in time

• M.step_tgl: forward propagation in time of the linear tangent model

• M.step_adj: backward propagation in time of the adjoint model

For some models, the class call an external library located in mapping/models/.

In the configuration file, you can select a specific model by setting the value of name_model.

Here is a detailed description of the dynamical models used in MASSH and how to parametrize them:

• Diffusion model
  • Equation solved
  • Numerical implementation
  • Configuration parameters
• 1.5-layers Quasi-Geostrophic model
  • Equations solved
  • Formulation with Sea Level Anomalies
  • Numerical implementations
  • Configuration parameters
• Linear Shallow-Water model
  • Equations solved
  • Open boundary conditions
  • Numerical implementations
  • Specific implementation of OBCs
  • Configuration parameters
• External boundary conditions