Diffusion model

Equation solved

The diffusion model is the simplest model used in MASSH. Its unique prognostic equation applies to the SSH \(\eta\) :

\[\partial_t \eta - K_{diff} \nabla^2 \eta = 0\]

where \(\nabla^2 = \partial^2_x + \partial^2_y\) and \(K_{diffus}\) is the diffusion coefficient, indicating the strenght of the diffusion.

This model is linear and auto-adjoint, greatly facilating its implementation with 4Dvar data assimilation technique. Note that setting \(K_{diffus}=0\) gives the identity model, which can be used for static inversions.

Numerical implementation

As the numerical implementation is straightforward, the code is located directly in the class Diffusion in the mapping/src/mod.py directory. The discretization is done with a forward Euler scheme and a first order central spatial scheme.

Configuration parameters

Here are the parameters specific to the model to be prescribed in the configuration file. If some are not prescribed, then the default values shown hereafter will be used.

# Name of the model
name_model = 'Diffusion'

# Diffusion coefficient
Kdiffus = 0