Stage-discharge (H-Q) curves

The stage-discharge relationship (often called H-Q curve) is fundamental for stream-gauging sites. Everybody knows that higher water levels in the river generally mean greater discharge. But for a natural cross-section (no weir structure), the exact relationship between water level (stage or H) and discharge (Q) must be determined through field measurements. Stream-gauging sites normally have a pressure sensor and data logger which records water level at say 10 minute intervals, so that we can plot the stage hydrograph. The H-Q curve allows us to estimate discharge from stage, so that we can plot the discharge hydrograph.

Every time we visit Takiya River we make a discharge measurement and read the stage. We can then plot a new point on the stage-discharge curve, either confirming the existing H-Q curve, or sometimes showing us that there has been a shift in the curve. Shifts in the curve can happen during big floods when there is a change in the supply of sediment, causing a change in the elevation of the stream bottom. The big flood of 23 June last month caused such a shift in the H-Q curve as shown below:

The pink data points show the two most recent discharge measurements, indicating a shift to the right of about 10cm for the H-Q curve. This means that for the same discharge amount, the water level is now about 10cm higher than it was before the 23 June flood event, due to accumulation of gravel in the channel. Also plotted are the three previous H-Q curves and we can see that recently the curve has shifted every year. This means that we have to work hard to keep establishing the new H-Q curve each year before there is another shift! Ideally we need about 20-30 measurements across a wide range of flows, but often we have to make do with much less data and a less well defined H-Q curve.

The river is too dangerous during big floods to be able to take a discharge measurement by wading in the water, and so we have no points on the H-Q curve for high stage values. We must extrapolate the H-Q curve to estimate these peak flow discharge values, and therefore we have large degrees of uncertainty. The chart below shows the previous H-Q curves extrapolated up to 2m, indicating that the flood peak of 23 June had a discharge of approximately 100 m3/s! However, we must try alternative techniques for measuring discharge during peak flows to try to confirm the H-Q curve at these high flow levels.