I've read "Design of Small Dams", and don't see a method to calculate this force.
I've read references to an uplift force that results from the formation of the hydraulic jump in a stilling basin, and it is not the uplift force from seepage or hydrostatic head. Unfortunately I can't find a way to calculate this force despite searching through the Corps of Engineers, FERC, and USBR.
I did find an Indian Standard, IS 11527 that has an equation for this force, but the material I was able to download is missing figures that are needed for some of the variables.