A variational data assimilation technique applied to the identification of the optimal discretization of interpolation operators and derivatives in the nodes adjacent to the boundary of the domain is discussed in frames of the linear shallow water model.
Assimilating data that have been produced by the same model on a finer grid, in a model on a coarse grid, we have shown that optimal discretization allows us to correct such errors of the numerical scheme as under-resolved boundary layer and wrong wave velocity. In the case of the stationary solution with Munk layer, only one point near the boundary may be controlled allowing to avoid spurious oscillations due to under-resolved boundary layer. To obtain the solution almost indistinguishable from the reference one, we have to enlarge boundary region and to control operators at 4 nodes near boundary.
|U and V velocity components and sea surface height in the classical low-resolution model|
|U and V velocity components and sea surface height in the classical high-resolution model|
|U and V velocity components and sea surface height in the classical low-resolution model with optimal boundary.|