What it does
River gauges record the stage, the height of the water surface, every few minutes. Discharge, the volume of water passing each second, is measured only now and then, by gaugings with a current meter or an acoustic profiler. A rating curve links the two, so the stage record can be turned into a flow record.
Most rating curves follow a power law set by the channel’s control (a riffle, a weir, or the channel itself):
Q = a (h − h0)^b
where h0 is the stage at which flow stops, a scales the curve and b describes the shape of the control (about 1.5 for a rectangular section or a weir, 2.5 for a V shape, about 1.6 to 1.7 for a natural channel).
This tool fits the curve to your gaugings, shows how well they agree, and turns stages into discharges.
How to use it
- Paste or open your gaugings: stage and discharge per row. Columns named stage, level or gauge height and discharge, flow or Q are found by name; dates and notes are ignored.
- Type the units for the labels.
- Leave h0 blank to fit it, or type a surveyed value (the lowest point of the control).
- Choose two segments if the control changes, for example when the river spills onto its floodplain, and give the break stage. Each segment gets its own curve; the tool shows the step between them at the break so you can move the break until they meet.
- Set the percentage for flagging gaugings that sit far off the curve.
- Use the last card for the discharge at a stage, the stage for a discharge, and a rating table at any step, ready to download as CSV.
What the results mean
- Scatter gives the range that 95 % of single gaugings fall within around the curve, as a percentage. Good stations manage about ±5 to 10 %.
- Gaugings off the curve may be measurement errors, or a sign that the channel has changed (weed growth, a flood that moved the gravel). A run of gaugings all on one side over time means the rating needs a shift or a new curve.
- The 95 % range in the table is for the mean curve; it widens quickly beyond the gauged range.
Worked example
The 24 made-up gaugings run from 0.64 m to 3.04 m stage and 1.6 to 62 m³/s. The fit gives Q = 11.61 (h − 0.3406)^1.681, with single gaugings within about −7.0 % to +7.5 % of the curve. At 2.5 m the curve gives 42.4 m³/s; 30 m³/s needs a stage of about 2.1 m. Typing a surveyed h0 of 0.30 m instead gives Q = 10.60 (h − 0.30)^1.764.
FAQ
Can I extend the curve above my highest gauging? Only with care. Flow above the gauged range often follows a different control (the floodplain), so extrapolation can be badly wrong. A hydraulic calculation such as the Manning and weir flow calculator can help check it.
Why fit on logarithms? Gauging errors are roughly a fixed percentage of the flow, so fitting the logarithms weighs a 5 % error the same at low and high flows.
Does it handle hysteresis or shifts? No. Loops from rising and falling floods and gradual shifts need dated gaugings and more advanced methods.
Where the numbers come from
- The power-law rating curve Q = a (h − h0)^b fitted by least squares on logarithms, with h0 as the stage of zero flow: standard hydrometric practice, as described for example in the WMO Manual on Stream Gauging (WMO-No. 1044, 2010) and ISO 18320 (equations only; no tables reproduced).
- Confidence ranges from ordinary least-squares regression on the logarithms with Student's t; the zero-flow stage is found by a one-dimensional search that minimises the misfit.
- Checked against SciPy curve_fit and linregress in the tests. The example gaugings are made up, drawn at random by fibub.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-08.