Several animations were given during the talk, which we think illustrate quite nicely the fact that in some situations, the hypothesis of a unique relationship may not hold. This is something already well known, but we thought that seeing some real data helps.
The first animation shows data obtained in a low land stream in North Carolina when 'back water conditions' are regularly obtained (slope 0.01%; dates in 1998). The curves drawn are sometimes called 'looped stage-discharge curves' and show a hysteresis of the stage-discharge relationship.
The second animation was obtained in a more upland stream in Nozay in France (44; dates in 2004). The hypothesis of a unique relationship between stage and discharge seems to be a lot better verified.
In both cases, however, there are some uncertainties that may have some consequences, particularly on the cumulative flow volumes, as can be seen on the presentation.
The reason for that is that the rating curves that may be drawn from manual gauging and that are used to calculate instantaneous flow depend on:
- the presence or not of a hysteresis in the stage-discharge relation
- the number of points from which the best fit rating curve is established
- the range of stage and discharge covered to establish the rating curve
Below are two animations showing, for 20 gauging points, how different the rating curves can be depending on when they were obtained. The first animation with the red dots show dramatic differences between consecutive rating curves and correspond to the lowland stream in North Carolina where back water conditions were known to happen.
The second with the green dots show differences in rating curves for the upland stream in France where the unique rating curve was thought to hold quite well. It becomes obvious that the curves do not vary nearly as much as they do for the lowland stream, although there are some variations despite the fact that the curve was fit extremely well through the points for each (r²>0.98).
The consequences on the cumulative flow volumes can be seen on the presentation.