Hello,
Well generally the negative depths of treatment 1 are not a problem (order of minus a few centimeters) and do not absolutely spoil mass conservation as these negative depths are integrated in the mass balance, and this treatment is chepar in computer time (see e.g. the test case malpasset). Now people prefer to have positive depths and also in 3D it is better because the mesh is based on the depth. Note that treatment 2 is a post-processing of treatment 1 where the fluxes that would bring negative depths are eliminated, and a better continuity equation is obtained, and this gives a second difference :
with treatment 1, the accuracy of mass conservation depends on your accuracy of the solver.
with treatment 2, the accuracy of mass conservation is the machine accuracy.
With best regards,
Jean-Michel Hervouet