Boundary conditions control for a shallow‐water model

Abstract

A variational data assimilation technique was used to estimate optimal discretization of interpolation operators and derivatives in the nodes adjacent to the rigid boundary. Assimilation of artificially generated observational data in the shallow-water model in a square box and assimilation of real observations in the model of the Black sea are discussed. It is shown in both experiments that controlling the discretization of operators near a rigid boundary can bring the model solution closer to observations as in the assimilation window and beyond the window. This type of control allows also to improve climatic variability of the model.

Variational data assimilation for optimizing boundary conditions in ocean models

“…We automatically provide the stability of the obtained discretization by choosing the rather durable assimilation window. Its conservative properties can also be provided by adding the corresponding member to the cost function as demonstrated in [24]. However, it is often needed to comprehend the obtained results from the point of view of the correspondence to the accepted physical imperatives and hypotheses.…”

Optimized boundary conditions at staircase-shaped coastlines

“…But, assimilating real data that contain a flux of an integral quantity, we should be ready to add a constraint in the cost function to ensure the conservation of an appropriate integral and avoid long-term trends. Thus, we had to add the total mass conservation requirement in Kazantsev (2012) to compensate the mass flux in the satellite observations of SSH in the Black sea.…”

“…Following Kazantsev (2010), Kazantsev (2012), instead of controlling physical boundary conditions, we use more general framework controlling the way boundary conditions are introduced in the model operators. Thus, expressions for derivatives D x , D y , are modified at the grid-nodes adjacent to the boundary, i.e.…”

Optimal boundary conditions for ORCA-2 model

“…Following [12], [14], these expressions are modified in the grid-nodes adjacent to the boundary, i.e. near the continents for interpolations in x and y directions and near the bottom and the surface for vertical interpolation.…”

“…However, the idea that other model's parameters should also be identified by data assimilation has also been studied and discussed in numerous papers. One can cite several examples of using data assimilation to identify the bottom topography of simple models ( [23], [8], [11]), to control open boundary conditions in coastal and regional models ( [32], [33], [34], [36]), boundary conditions on rigid boundaries ( [18], [21] [20], [12], [13], [14]) and to determine other parameters of a model ( [37], [30], [3]).…”