Bathymetry smoothing

[mathieu]

Dear all,

a rough bathymetry creates unstability of the model
because of the terrain following coordinates.
One solution is to use smoothing but I have some
more questions below.

(1) What are the means of measuring the roughness?
The roughness factor, i.e. the maximum of |h1-h2| / (h1+h2)
over adjacent wet points is the usual measure.
Are there other quantities that needs to be taken into account?

(2) How the smoothing should be done?
I know the method of taking average over neighboring wet points
and I wrote a linear programing problem which for a fixed r finds
the bathymetry satisfying
|h1 -h2| < r (h1+h2) and which is nearer to the real bathymetry.
There are also some other methods in the ROMS Numerical
Toolbox (http://www.o3d.org/RNT/).
What would you recommend?

(3) Appart from smoothing, what are the ways of resolving
rough bathymetry?
I can think of two ways: increasing the number of vertical levels
and increasing the number of time steps.
What would you recommend?

thank you

[kate]

(1) What are the means of measuring the roughness?
The roughness factor, i.e. the maximum of |h1-h2| / (h1+h2)
over adjacent wet points is the usual measure.
Are there other quantities that needs to be taken into account?

ROMS prints out two measures of steepness, the above being the Beckmann and Haidvogel number. There is also a Haney number. Note that the steepness is only part of the problem, there is also the stratification because both enter into errors in the pressure gradient term - or did Sasha fix that entirely?

(2) How the smoothing should be done?
I know the method of taking average over neighboring wet points
and I wrote a linear programing problem which for a fixed r finds
the bathymetry satisfying
|h1 -h2| < r (h1+h2) and which is nearer to the real bathymetry.
There are also some other methods in the ROMS Numerical
Toolbox (http://www.o3d.org/RNT/).
What would you recommend?

If it works, use it.

(3) Appart from smoothing, what are the ways of resolving
rough bathymetry?
I can think of two ways: increasing the number of vertical levels
and increasing the number of time steps.
What would you recommend?

Neither of these is the right answer - you need horizontal resolution. If you look at the function above, you get into trouble where the bathymetry is shallow and where the water depth changes drastically from one box to another. Say you've got a continental slope where one rho point is at 100 m and the next is at 2000 m. What you need is more points between these two in order to capture intermediate depths. I know it's costly, but it does point to the need for unstructured grids to put the resolution where it's needed to resolve the slopes.

[mathieu]

Thank you for the above explainations. I have a better understanding of
the problem.

The linear programming smoothing, which I mentionned earlier is available
from http://www.liga.ens.fr/~dutour/Bathymetry/index.html.
All critics are accepted.