Hi, I'm interested in topography smoothing and was wondering if there are any variational method for topography smoothing, other than the ones where geometric properties (grid stiffness, "roughness" etc.) are penalized.
Are there any methods that smooth by minimizing a cost function which penalizes kinetic energy resulting from the discretized pressure gradient? For example the integrated kinetic energy after one timestep in a resting ocean with horizontally homogeneous T/S profile, i.e. the first timestep of the "usual" trial-and-error method. Perhaps not with all terms of the momentum equations, just the pressure term. And with an additional term that penalized too large deviations from the actual bathymetry. And perhaps with one penalizing geometric properties?
Is it possible to formulate a well-posed problem out of this? I would like have a function where I put in the values for
1) horizontally homogeneous T/S profile
2) bathymetry and a horizontal field sig(x,y) which is the allowed deviation
3) coordinate system paramters (N, thetha_s, hc etc.)
and out comes the perfect h(x,y)!
Thanks for any help.