Rating curve, permanent and shifting controls

Development of a rating curve

1. Select a gauging section with a stable control and install a gauge.
2. Measure discharge by current meter (or another method) at different stages covering low to high flow, and record the stage at the same time.
3. Plot stage $G$ (y-axis) against discharge $Q$ (x-axis) on arithmetic scale, and also on log-log paper after subtracting the stage for zero flow $a$.
4. Fit a smooth curve $Q = C(G-a)^b$, with $a$, $C$ and $b$ found by trial or regression.
5. Check by correlation, and extend the curve to flood stage by extrapolation (log-log straight line or conveyance method).
6. Check the rating regularly with new measurements, and revise it when the points depart from the curve.

Control

The control is a physical feature of the channel at or downstream of the gauge that governs the stage-discharge relation.

Permanent control: the relation does not change with time. Examples: a rock ledge, a weir or a narrow rock gorge. The same stage always gives the same discharge, and a single rating curve is valid for years.

 water   ~~~~~~~~~\
 level            \___ <- rock ledge / weir (stable control)
 bed  ____________/ \_______

Shifting control: the bed or banks are made of sand or silt, so scour, deposition, vegetation growth or debris change the section and the curve shifts. A given stage then gives different discharges at different times.

  Stage
   |      /  /  /   <- curves shift with time
   |     /  /  /       (scour: right; silting: left)
   |    /  /  /
   +------------------- Q

For a shifting control, frequent discharge measurements are needed, and the rating curve is adjusted with time-varying shift corrections (a shift curve). Where the shift is caused by variable backwater, the stage-fall-discharge relation is used instead.