It has been stated that the pre-balanced formulation of the Shallow water models is advantageous in terms of well balancing. But another argument is that the pre-balanced formulation is not in conservative form (the free surface is not a conserved quantity). In my opinion, the pre-balanced form is easier to work with, but at the same time, I think that conservation Laws should be left in conserved quantities if the Finite volume formulation is to be adopted, as the FV method is based on this conservation property.
What do you think about this pre-balanced formulation?
I found one article for your research interest
Liang, Q. (2010). ”Flood Simulation Using a Well-Balanced Shallow Flow Model.” J. Hydraul. Eng., 136(9), 669–675.
It is always better to use conservative forms if you use finite volume methods
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