Backwater Curves

Last updated: 2026  ·  US Army Corps of Engineers

A backwater curve describes the gradually-varied water surface profile that forms in an open channel when a downstream control (dam, bridge, or tidal boundary) forces the water surface to deviate from normal depth. HEC-RAS computes these profiles using the standard step method, marching from a known boundary condition upstream through each cross-section.

The M1 (mild-slope, backwater) curve is the most common profile in practice. It occurs whenever a downstream barrier raises the tailwater above normal depth, creating a gradually-increasing water surface that asymptotically approaches normal depth upstream.

Why Backwater Matters

  • Flood stage prediction — backwater from bridges, culverts, and dams determines how far upstream flooding extends.
  • Levee freeboard — the backwater profile sets the design water surface against which levee heights are checked.
  • Navigation depth — lock-and-dam operations maintain a target pool elevation whose backwater curve defines the navigable channel depth upstream.

Energy Equation

The one-dimensional energy equation for steady, gradually-varied flow balances the total energy head between two cross-sections separated by a reach of length L: 

WSE₂ + V₂²/(2g) = WSE₁ + V₁²/(2g) + hf

where:
  WSE  = water surface elevation (bed elev + depth)
  V    = mean velocity = Q / A
  A    = flow area = W × y  (rectangular channel)
  hf   = friction head loss = Sf_avg × L
  Sf   = friction slope = (n·V / (K·R^⅔))²
  R    = hydraulic radius = A / P
  P    = wetted perimeter = W + 2y
  K    = 1.486 (US customary) or 1.0 (SI)
  n    = Manning's roughness coefficient

The subscripts 1 and 2 refer to the upstream and downstream sections respectively. For subcritical flow (Froude < 1), computation proceeds from downstream to upstream because the downstream boundary condition controls the profile.

Friction Slope

Manning's equation gives the friction slope at any section as a function of velocity, roughness, and hydraulic radius. The average friction slope over a reach is taken as the arithmetic mean of the upstream and downstream values — a second-order accurate approximation for gradually-varied flow.

Standard Step Method

The standard step method is an iterative procedure that solves the energy equation reach-by-reach. Starting from the known downstream water surface elevation, the algorithm marches upstream:

  1. Known: downstream WSE, bed elevations at both stations, discharge Q, channel geometry.
  2. Compute downstream hydraulics: depth y, area A, velocity V, hydraulic radius R, and friction slope Sf.
  3. Guess upstream WSE (initial guess = downstream WSE + bed slope × reach length).
  4. Compute upstream hydraulics using the guessed WSE.
  5. Average friction slope: Sf_avg = (Sf_up + Sf_down) / 2.
  6. Compute energy-balanced WSE: WSE_up = WSE_down + hf + V²_down/(2g) − V²_up/(2g).
  7. Compare and iterate: apply 0.5 relaxation until |ΔWSE| < 0.001 ft.

The relaxation factor of 0.5 prevents overshoot in the Newton-like iteration. For most subcritical M1 profiles on mild slopes, convergence is reached in 3–8 iterations per reach.

Interactive Profile

The visualization below shows a simplified rectangular channel with four cross-sections (stations 0, 200, 400, 600 ft). Drag the bed elevation handles or the downstream boundary WSE to see the backwater profile recompute in real time using the standard step method described above.

Phase 1 — Channel bed draws left to right.  Phase 2 — Downstream boundary water level rises.  Phase 3 — Standard step computation animates upstream.  Phase 4 — Interactive: drag handles and adjust inputs.

Handles: Green handles control bed elevations at each station. The cyan handle sets the downstream boundary WSE. The teal marker shows the computed upstream WSE. The values panel on the right displays intermediate hydraulic variables at every station.