It looks to me like the combination FSCHAPMAN/M2FLATHER/M3RADIATION are not radiating fully. I am experimenting with a barotropic model driven only by a free surface boundary condition on a western boundary in the southern hemisphere. The northern boundary is a coastal wall (the depth shoals). The wave travels eastward along the northern boundary and should pass transparently out the eastern boundary, but part of the energy turns south along the eastern boundary instead of disappearing. I do not have RADIATION_2D turned on because it looks like that is irrelevant to these BCs, Am I wrong there? Also I am not using a sponge, because it shouldn't be necessary.
This is a pretty standard set of BCs that I think are widely used. Either I am doing something wrong, or a lot of people are contaminating their interiors, at least the areas close to boundaries. Any thoughts?
I'd also like to know where the energy goes that DOES radiate out.
My thoughts: We do what we can to get the best results. If that means trying RADIATION_2D, then I'll try it. Also, SPONGE does help, but still isn't perfect. We put the boundaries far enough from the region of interest so that we're not completely in trouble from boundary artifacts.
Then there was that boundary condition talk Sasha gave at one of the ROMS meetings. We still don't have his better BC in our code.
These boundary conditions are not perfect by any means, but have been found to work well enough in many applications. The paper describing them http://tinyurl.com/ChapmanJPO1985 gives some indication about how well they work and how sensitive different numerical choices are to the outcome.
John.
John Wilkin: DMCS Rutgers University
71 Dudley Rd, New Brunswick, NJ 08901-8521, USA. ph: 609-630-0559 jwilkin@rutgers.edu
Thanks Kate and John W for your responses. The Chapman paper makes the point that there is no universally best method in all the types he tested, and that the choice can have profound effects on the solution well away from the boundary. In my tests (which are similar to the Kelvin test case, but with an open southern boundary and a mode 1 wave forcing instead of Kelvin), M2RADIATION results in unrealistic sea levels everywhere (but realistic geostrophic velocities at the boundary). The problem with M2FLATHER is that while the model sea levels are generally realistic, a cross-shelf jet when the wave meets the reaches the eastern boundary (some energy passes through the boundary). I notice that when you choose EAST_M2FLATHER, v2dbc_im.f90 (the tangential velocity at the eastern boundary) contains a "Chapman" condition. So the normal bc is "Flather" but the tangential bc is "Chapman", That's hardwired in when you choose M2FLATHER. I am speaking here of the vertically-integrated velocity of course. I am not familiar with specifying tangential velocity boundary conditions and it isn't mentioned in the literature I have at hand. I just wonder if the tangential velocity BC is causing the cross-shelf jet? Anyone else seen this?
The good news is that a short distance in from the boundary, the velocities are the same regardless of whether M2RADIATION or M2FLATHER is used.
Well, in case anyone has a clue, here is a snapshot of what happens at the boundary.
The aberrant velocities are at column Iend-1. (The ubar BCs at the eastern boundary are calculated at Iend+1; they are not plotted). ubar is too small at Iend; vbar is too big at Iend-1.
The colours here are sea level. The sea levels look fine. So it seems like the overlarge velocity is due to continuity (ubar too small at Iend).
I read in the boundary condition ubar_east and zeta_east from a netcdf file. They are both set to zero at the eastern boundary. As before, it is an FSChapman+M2Flather boundary condition.
Well I would not be happy with that phrase "... a few cells inside things in velocity field is OK." We have seen this in our application for the Adriatic Sea when one can get strong along boundary current that is due only to boundary conditions; like yours.. Imagine that you have some tracer like T that is supposed to leave domain, with your figure fr ubar I am pretty sure that you'll have return inside the domain and endup with building up of T in a long run...
So be careful with that, a few cells are not enough!
Cheers
Ivica
