“…To estimate the water velocity distribution in the section, we hypothesize that the law of the wall applied to the whole water column (details in Appendix A), so that where u ( x , z , H ) is the water velocity at lateral position x , depth z , and height H ; X lb and X rb respectively represent the left and right bank abscissa; S e ( H ), the energy slope for water elevation H ; g , the gravity constant; κ , the Von Karman constant taken at 0.41; z B ( x , H ), the local bottom depth counted from the water surface; and k s , the effective roughness height here defined by 3 × D 50 = 0.22 m from the pebble median size measured on local Narayani gravel bars (supporting information Table S2; Attal & Lavé, ; Dingle et al, ; Mezaki & Yabiku, ). In equation , S e ( H ), is assumed to be constant around 0.05% (see justification and sensitivity test in supporting information S7).…”