# “Mickey Mouse is, to me, a symbol of independence. He was a means to an end.” – Walt Disney

Why is it that in hydrometry, specifically with regards to plotting rating curves, that the dependent variable (discharge) is commonly plotted on the abscissa (x axis) and the independent variable (stage) is plotted on the ordinate (y axis)? This practice is contrary to mathematical convention and is a real head-scratcher for anyone coming to hydrometry from other sciences.

## The convention of plotting discharge on the abscissa is not universal.

In some regions of the world, stage is routinely plotted on the abscissa and it is quite common to see stage on the abscissa in rating curves published in peer reviewed journal articles.

From a hydraulic perspective, if there is zero approach velocity to the control, discharge is dependent on stage. A change in stage results in a change in discharge – but what would cause the stage to change? From a hydrologic perspective stage is dependent on discharge. Catchment runoff is not affected by the channel control conditions. A change in discharge results in a change in stage. Conversely, any alteration of the control will result in a change in stage but this change in stage does not, fundamentally, result in a change in flow. Some of the flow may be diverted to, or from, temporary channel storage but continuity is maintained. Hence, discharge is the independent variable.

## Walt Disney may have had it right. Choosing a symbol of independence may just come down to finding a means to an end.

Almost invariably, people who are most offended by the convention of plotting discharge on the abscissa have never hand-drawn a rating curve. Back in the day, we used to work on ANSI C (17” x 22”) paper on which there was a 16” by 20” grid giving an aspect ratio of 1:1.25. Obviously, you want discharge on the long axis and stage on the short axis because the range of values is so much larger. I don’t know what your experience is with such a large sheet of paper but for me I would need much longer arms and much better eyesight to work with it in a portrait layout. Working in landscape is just way easier. You combine the need to plot discharge on the long axis with the ergonomics of working in landscape and – you have a means to an end.

The other thing you discover when plotting rating measurements by hand is that it is very intuitive to have stage on the vertical axis. Visualizing shift corrections just makes sense. Stage fluctuates up and down, not sideways. Discharge is a more abstract concept so it is not difficult to think of relative change on a horizontal scale. There was always a light table in the office and it was common practice to plot our cross sections using the same vertical scale as our rating curves for evaluation of break-points in the curve by overlay.

For me, working on a monitor with a VGA (4:3) aspect ratio, I want to see my discharge plotted on the abscissa. Even more so if I was to choose a monitor with the increasingly popular 16:9 aspect ratio.  I think the resolution of the media is reason enough to keep the convention of plotting discharge on the long (some would say the wrong) axis. I know some people like to set their monitors to work in portrait mode in which case the long axis would be the ordinate axis but that is not a widely adopted practice yet.

Photo Credit: Thomas | Mickey Mouse | License