From barotropic velocity to surface velocity

[maucollu]

Dear all,
I have more of a theoretical question.
pyTMD, as far as I understood, provides the tidal current barotropic velocity. i.e. approximately equal to the dapth-averaged velocity.

The question is: does anyone know a methodology to derive, from the barotropic velocity, the surface tidal current velocity? It does not need to be super-accurate, since it is for a conceptual/preliminary design.

The only reference to this I found is in DNV-RP-C205, section 4.1.4.2:
When detailed field measurements are not available the variation in shallow of tidal current velocity water with depth may be modelled as a simple power law, assuming uni-directional current

but it does not seem to suggest a typical value for the alpha exponend in the in case data are not available to determine this parameter.

Many thanks