Water depth ($d$)

Water depth is the local vertical distance from the bed to the free surface. If the bed has elevation $b(x,y)$ and the surface has elevation $\eta (x,y,t)$ in the same vertical coordinate, then $h=\eta -b$. The datum used to define the two elevations cancels from their difference.

Keeping the distinction matters in the shallow water equations: the horizontal hydrostatic pressure gradient depends on surface elevation, while the transported volume depends on depth. A sloping bed with a horizontal free surface can have a varying water depth without a horizontal gravitational driving term. Conversely, the same bed can support a flow driven by a sloping surface.