Comparative Investigation of Canadian, US, and Australian Stage-Discharge Rating Curve Development

Stuart Hamilton, Ray Maynard, Terry Kenny - Aquatic Informatics, Qld Department of Natural Resources and Mines, United States Geological Survey , 21 November, 2017

For any well-selected gauging location there is a unique relation between stage and discharge that is valid for a specified period of time. However, it is up to the stream hydrographer to discover the form of this relation, for a given epoch, by a combination of stream gauging and inference-making.

The importance of inference in rating curve development cannot be over-stated. Even if given the same data it is unlikely that any ten hydrographers would produce identical hydrographs, with the differences being primarily due to inferences made about curve form, extrapolation, and response to dynamic in-stream conditions. There are many factors that influence inference-making, including: standards, training, techniques and technologies – all of which vary between monitoring jurisdictions.

All three countries generally use the same non-linear shifted power law rating equation, Q = a∙ (GH – e)m, where Q is discharge, GH is gauge height, and a, e, and m are calibrated parameters. They mostly also use log-log rating curve plots, although some areas in Australia use GH vs Q0.4 plots, and a small subset use the more flexible GH vs Q1/m plots.

The main difference in rating curve development is that a single height offset is used in Australia for each rating curve, presumably as a legacy of paper log-log plots. Canada and the US can use a unique height offset for up to three rating segments, which typically gives more flexible rating curves that can need less rating points to span a given range.

The three parameters of a properly-fitted shifted power law rating equation convey meaningful information about the local site hydraulics, whereas those poorly fitted using a sub-optimal height offset are hydraulically uninterpretable, due to parameter interaction in the fitting process.

Another notable difference in rating curve development is the Australian use of families of rating curves, whereas Canada and the US favour multiple base rating curves that are then modified by 3-point height shifts to account for subsequent small temporary rating changes.

Rating extrapolation methods are fairly similar in all three countries. However, some areas in Australia tend to use the Σad½ method or its later derivative Σad2/3.

More use could be made in all three countries of prior rating information from cross section shapes and shape changes in the context of the influence of vegetation, particularly for over-bank flow. Stream channels in Australia are often of complex shape, although areas with regular high runoff tend towards simpler U-shaped channels similar to many streams in Canada and the USA.

Increased recognition that a unique stage-discharge rating is not possible at many sites is driving an increase in the number of deployments of ADVMs in North America. ADVM usage is also likely to increase in Australia because of flood access and boat gauging safety concerns.