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3.3 Grid nesting 
Starting with a coarse grid coverage, the grid is refined in a part of the model domain. In 
this part of the domain, coarse grid cells are split into smaller cells. The grid mesh ratio is 
a fixed integer. In the BSH model, the grid refinement is applied to the German coastal 
waters. Compared to the reference grid for the entire North Sea and Baltic Sea, a sixfold 
magnification is used. Each coarse grid cell contains 36 fine grid cells, except where the 
fine grid coastline runs through the encompassing coarse grid cell, in which case the 
number of cells is smaller. 
At the open boundary of the fine grid, mass is transported into and out of the fine grid. 
The grid construction is such that the outer edge line of the fine grid coincides with a line 
of coarse grid cell edges (In our Arakawa C model, the grid placement of discrete 
variables is the same for both coarse mesh and fine mesh). Treatment of the mass 
budget on both sides is simple. Mass fluxes (of normal flow) situated on the boundary 
line are required for cells on both sides, both fine grid and coarse grid cells. To ensure 
continuity, the fluxes controlling either side should be related to those acting on the other 
side. In our setting, the fluxes acting on the coarse grid network are primary quantities 
subject to the momentum equation. These coarse grid fluxes are broken down to fine grid 
fluxes as secondary quantities which give the flow (inflow/outflow) at the boundary edges 
of the adjacent fine grid cells. 
In our setting, the outermost fine grid quantities are cell midpoints, half a grid length away 
from the demarcation line. In treating the mass budget of such a cell, at least one mass 
flux comes from the coarse grid calculation. In return, a number of fine grid cells in the 
vicinity of the outer edge are taken into account as feedback to the coarse grid fluxes on 
and normal to the demarcation line. These fluxes respond to pressure on both sides, and 
one of them is taken as a mean quantity from the fine grid by appropriate averaging. 
It is evident that some interpolation and averaging is inevitable when grids having a 
different resolution are joined together. However, apart from this transfer of information, 
there is no other limitation to the dynamic performance of the grid joint. In particular, if 
both grids had the same resolution the coupling method would work as though the joint 
were not present. It is obvious that our joining method allows full two-way interaction. 
Long gravity waves (tidal signal) are transmitted across the grid joint with no other 
deformation than that caused by the stepwise transition of grid mesh length. 
The entire construction may be considered as a single grid composed of domains having 
different resolutions. Viewed as a coupling problem, our approach can be simply 
described as follows: Due to the staggered arrangement, the (discrete) evolution of any 
grid quantity is controlled by adjacent quantities placed on the surrounding grid stencil. If 
any of these positions falls into a grid area of a different spacing (refined or coarsened), 
averaging or interpolation is applied for fitting. The dynamic performance of a grid joint 
thus does not constitute a problem in principle, and the grid coupling is inherently two- 
way interactive. 
To achieve a locally higher resolution of the model, a refined grid may be laid above any