Hi Theodoropoulos,
I am not an expert, but I will try to be helpful.
About Thompson boundary conditions, you have to take in account that you are prescribing one of three possible variables (Discharge, Velocities or Elevation), considering that the other 2 variables are computed by TELEMAC, what Thompson boundary condition does is, according to the theory of characteristics, to give a reasonably value to one of those variables and compute the other.
Considering this, it is not possible to prescribe an elevation and, using the Thompson condition, get a different value of elevation. The elevation will be the same; the values computed with the theory of characteristics would be velocity and discharge.
Maybe somebody else with more experience could be clearer about this.
On other hand, I believe you could try to prescribe flowrate at both inlet and outlet boundaries. Thus, you could get values of the depth/elevation at outflow boundary, this using Thompson boundary condition. Maybe this is a way of getting H values, since you want to ‘estimate them’. That is the only way I see at this moment. Surely, Jean-Michel or Leo can say whether this is ok or not, since they have more experience.
I hope it helps.
Cheers,
José Andrés.