Better way to smooth bathymetry than "repeated interpolation"?

[glwagner]

Right now we rely on a sort of crude and uncontrolled method to smooth bathymetry, eg from the bathymetry generation example

h_rough = regrid_bathymetry(grid; interpolation_passes = 3)
h_smooth = regrid_bathymetry(grid; interpolation_passes = 40)

It doesn't really seem possible to predict what the effect of the "interpolation passes" is. Obviously more of them smooths, but how much do they smooth? How much do we need? Is there any way to understand what the net outcome is, regardless of the grid we are on?

I think this method was implemented not because it is a good method to use, but because it was convenient to simply "keep interpolating". Convenience isn't always the best motivation...

I think diffusion or a moving average might be a better way to smooth bathymetry. This would preserve the total ocean volume. Also, rather than specifying "number of passes" I feel like it would be more useful to be able to specify something like the "maximum gradient" or "maximum curvature" and iterate until that criterion is reached.

[NoraLoose]

I think diffusion or a moving average might be a better way to smooth bathymetry. This would preserve the total ocean volume. Also, rather than specifying "number of passes" I feel like it would be more useful to be able to specify something like the "maximum gradient" or "maximum curvature" and iterate until that criterion is reached.

That's basically what we do when we prepare the bathymetry for a ROMS simulation. We perform two consecutive steps, first a domain-wide smoothing (to avoid grid-scale instabilities) and then an iterative local smoothing until the maximum slope criterion is satisfied. For more details, see the ROMS-Tools documentation.

[NoraLoose]

The domain-wide smoothing step might be more relevant for a terrain-following coordinate (as in ROMS) than for a z-coordinate.