A momentum-based prediction model of backwater rise within and downstream of an emergent canopy in nonuniform flow

•(1) A unified phase diagram is proposed that exhibits the relationship of the water depths from downstream to upstream of an emergent canopy.•(2) The threshold for identifying strong or weak nonuniformity is explored based on the relative backwater rise in the vegetated flow.•(3) The backwater rise of an emergent canopy is predicted from a dimensionless vegetated parameter and unit discharge based on the momentum loss.•(4) The effect of downstream water depth on backwater rise is quantified by two partitions: supercritical flow and subcritical flow.