Flood dynamics in low-relief landscapes control the lateral exchange of water and sediment between a river and its floodplain. Locations where these exchanges occur for any given river discharge depend on local bank elevations, which in turn depend on the type of landform present immediately adjacent to the river channel. Our analysis separated landforms bordering a river into six categories: levee, scroll bar, counter point bar, channel-bend cutoff, erosional surface, and inactive surface. Each landform is associated with a different range of elevations. Levees are the highest, and counter point bars and cutoffs are the lowest. Using a combination of lidar-derived measurements of topography and water-surface profiles derived from U.S. Geological Survey gauge data, we show that landforms at the margins of the river change with downstream position on the coastal reach of the Trinity River in the southern United States. The fractions of counter point bars and cutoffs decrease downstream, while the fraction and continuity of levees increase to nearly 100%. This spatial change correlates with downstream reductions in channel-bend migration and deformation, and the measured range in river stage. As a result, the greatest range in bank elevations occurs upstream where variation in river stage is also highest. Meanwhile, the smallest range in bank elevation and river stage exists in the coastal backwater zone. Our analysis indicates that essentially all levees within the backwater zone are overtopped by flow associated with a single river discharge. Moving upriver, the discharge associated with levee-overtopping flow systematically increases. This study highlights the morphodynamic control on coastal river flooding.