Rating Curves: Part 2 - Representation and Approximation

A rating curve represents a supposedly-unique relationship between the stage (surface elevation) of water at a gauging station and the flow past that station. A significant problem is that the flow can vary from none to that of large floods, and this whole range has to be represented, including everyday small flows. A traditional way of doing this is to use log-log axes, but these have a number of problems. This paper considers the simple hydraulics of typical natural geometries of controls and river cross-sections and shows that in many situations the stage at the gauging station will vary roughly like the square root of the discharge, but with different relationships at different flow ranges. This suggests routinely plotting stage against the square root of discharge as representing and approximating rating curves.