Various natural or industrial processes are affected by the interaction between a turbulent boundary layer with a rough permeable surface. Focusing on river application, I will present measurements resulting from a fast particle image velocimetry protocol on turbulent flows adjacent to an inclined porous bed. Working with refractive-index-matched materials makes it possible to scan the medium continuously in the transverse direction, and thus to reconstruct two of the three velocity components of the flow (3D2C-PIV). Recording first and second order turbulent statistics continuously while translating the laser sheet at a constant speed requires meeting certain criteria. The protocol leads to space-and time-averaged profiles as defined by the double-averaging procedure (Nikora et al., J. Hydr. Eng. 127, 123-133, 2001). A turbulent boundary layer over the rough bed was observed while experiments were run at intermediate Reynolds numbers, i.e. Re = O (1000). Under these flow conditions, viscosity played a non-negligible role through the van Driest damping effect. Based on the Prandtl mixing length theory, I propose a model for the turbulent stress that takes into account the continuous porosity profile as well as dispersive and damping effects. Finally, a good agreement is shown between the model and classic flow resistance laws employed for river studies. The model contrasts with existing boundary-layer models which assume a discontinuous porosity profile at bed interface (be the bed permeable or impermeable).