Nested Boundary Conditions

A recent paper by Tomy Jensen, JMS, 16,297,1998 (mercifully for us) tests various boundary conditions for a multi-layer model; and finds out, among other things, that under relatively hostile situations relaxing to an almost correct boundary conditions [nudging on a band of a few points], the (3) layer model responds adequately.

The fine grid does have the potential access to the 'almost' correct values. These values are provided by the coarse grid. Under these circumstances, the boundary values can be nearly be approximated in the fine grid as one approaches the boundary. The nudging can be accomplished, say inside a band with a width of about half wavelength of the coarse grid (4-8 points).

The implementation can be done in various ways. The strictly correct one [ keeping track of terms, energetics, etc.] is:

1. to finish the time step for the volume variables in the coarse grid
2. interpolate -without the restriction- to the boundary in the fine grid.
3. Fine grid then does its time step for the volume data, including nudging to the approximated value;
4. the rest of the 2-way nesting flow remains the same.

Questions:

1. do you see an adverse impact for the 3-level zoom nesting?
2. The nudging can be done less strictly. One way that does not requires a modification of the present (99-nesting) 2-way flow of information can be done by nudging after the regular fine grid model does its time step. [ala time splitting form]. This requires to access the volume data for time tau. All of this is done external to clinic and tracer. To account for the influence to external component forcing and quantifying the influence of this into the terms of the equation and energetics requires further additional work. What do you think?

The idea can be used as well for the standard nesting. Here the almost correct values at the boundary can be constructed using a simpler schema. The gain is the smoothing properties of the algorithm. The smoothing is derived from the spatial scale in the relaxation.

Questions:

3. What initial lower order estimates for the boundary values can be used?

Carlos