To add to Mark's answer, the Surface Storage options available with the Implicit and SWMM solvers in SewerGEMS and CivilStorm provide an option to define with a depth-area curve, but you'll need to enter those values in the table. As you noticed, the Trex and Terrain model tools will populate node ground elevations. There are likely other programs that can extract a cross section from a TIN, which you could use to populate the depth-area table in CivilStorm or SewerGEMS.
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