# Hydstra rating plots explained

When viewing discharge data at the Victorian Water Monitoring website, one option is to see a Gaugings vs. Ratings Plot (Figure 1).

Figure 1: A gauging v rating plot can be created for each gauge

An example for the Avon River at Stratford is shown in Figure 2.  This plot may make perfect sense for a hydrographer but was challenging for me to understand, and I imagine many others.

First, check out the y axis label:

• 100 – Stream Water Level (m) plotted against CTF of 1.225 in metres

Also look at the  labels on the y-axis tick marks:

• 1.226, 1.235, 2.225, 11.225.

Figure 2: Avon River at Stratford, gauging vs. ratings plot

What this is referring to is the rating equation that has been used to establish the rating curve.  This is likely to be in the form:

$Q = C(h - h_o)^m \quad \mathrm{Equation \; 1}$

Where: Q is discharge,  C is a constant, h is gauge level,  ho is the cease to flow (CTF) level, m is a constant exponent with typical value 1.5 to 2.5.  These three parameters are fitted based on gauging data.

For the Avon River at Stratford, ho is 1.225 m.  This explains the comment about CTF in the y-axis label.  The ‘100’ in the y-axis label is a value used in Hydstra to refer to water levels. There is a corresponding ‘141’ in the x-axis label, which Hydstra uses to refer to discharge which is created from levels by use of the rating curve.  A list of Hydstra codes is here.

Now to the y-axis labels.  These are based on log-cycles with the addition of a constant representing the CTF level.

• 101   + 1.225 = 11.225
• 100  + 1.225 = 2.225
• 10-1 + 1.225 = 1.325
• 10-2 + 1.225 = 1.235
• 10-3 + 1.225 = 1.226

So, Figure 2 is a plot of the following:

• $\log_{10}(Q)$ on the $x$ axis
• $\log_{10}(L - 1.225)$ on the $y$ axis.

Where, $Q$ is the discharge and $L$ is the stream water level (the gauge reading).  These transformations relate to equation 1.

Stream gaugings are available from the Australian Bureau of Meteorology website http://www.bom.gov.au/waterdata/.  Rating curves are also available from the website and from the Victorian warehouse http://data.water.vic.gov.au/monitoring.htm?ppbm=225201&rs&1&rspf_org.

I’ve plotted the gaugings and the rating curves in the Hydstra format in Figure 3 below. This graph is the same as Figure 2 with the added value of colouring points based on when data was collected.  Clearly there is a lot of scatter in the low end gaugings and its not just based on when the data were collected.  There are ‘red’ points (recent gaugings) above and below the current rating.  At higher discharges, it looks like the water levels are increasing for a given flow.

Figure 3: Plot of ratings and gaugings for the Avon River at Stratford.  Colours indicate when gaugings were made.

The upshot is, that it is possible to construct these Hydstra style plots given gauging data and an estimate of the cease to flow level.

Code to create this plot is available as a gist.

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