Rating curve development and river surveys: getting flood levels right

Almost every flood level you will see in a warning, a design report or a flood map passes through a rating curve or a hydraulic model, and usually both. Rating curve development means measuring discharge across the range of river levels, tying every level to one surveyed datum, fitting a curve with honest uncertainty, and being careful above the highest gauging. Get those steps right and flood levels can be trusted; get one wrong and every number downstream inherits the error.

What a stage-discharge rating curve is

A stage-discharge rating curve is the relation between the water level at a gauging station and the flow passing it. The US Geological Survey defines a discharge rating as the relation of discharge to stage "and sometimes also to other variables", and distinguishes simple ratings, where stage alone sets the flow, from complex ones that also use the rate of change in stage, the water-surface slope or an index velocity [1]. Level is cheap to record continuously; flow is not. The rating curve is what turns a level record into a flow record, and a forecast flow back into a level people recognise.

The international standard on the subject, ISO 1100-2, states that the relation needs enough paired discharge and stage measurements to define it to the required accuracy, and covers both stable and unstable channels, including shifting controls, variable backwater and hysteresis [2]. It was withdrawn and replaced by ISO 18320:2020, so new work should cite the current standard [2].

Controls: why the curve has the shape it has

The level at a gauge is set by a control downstream of it. At low flow this is often a section control: a rock bar, a riffle or a weir. At higher flow the channel itself takes over, through its slope, shape and roughness. When the river overtops its banks the geometry changes again. Each control gives a different segment of the curve, which is why a single smooth line fitted through all the points is often wrong at both ends.

Controls also move. Sand bars build and wash out, weeds grow in the dry season, a flood scours the bed. A rating that fitted well last year may be biased now. Regular gaugings are how you find out, and the reason WMO's Manual on Stream Gauging treats fieldwork and the computation of discharge as one subject [3].

Gauging: ADCP discharge measurement and current meters

A gauging is a measurement of discharge at a known stage. On rivers deep enough for a boat, the usual tool today is an acoustic Doppler current profiler. USGS guidance on ADCP discharge measurement from a moving boat covers planning before deployment, collecting the data in the field and processing it afterwards, and gives particular attention to moving-bed conditions, where sediment moving along the bed biases the measured flow unless it is tested for and corrected [4]. Where the water is shallow or the ADCP cannot be used, wading measurements with a current meter remain standard [3].

The most useful gaugings are the hardest to get: those at high flow. A rating built only from dry-season measurements says little about floods. Plan for crews and safe access during high water, and record every gauging with its stage, time, method and any problems.

River cross-section survey and datum checks

A river cross-section survey records the shape of the channel and floodplain at chosen sections, and it is the raw material for both hydraulic models and any attempt to extend a rating curve. The surveys only help if every number shares one datum. Before fitting a curve, run these datum checks:

• Is the gauge zero tied to a permanent benchmark, and has it been levelled since the staff gauge or sensor was last moved or replaced?
• Are the cross-sections, flood marks and gauge zero all on the same vertical datum, not a mix of local and national ones?
• Do logger readings agree with the staff gauge at each visit?
• Has the gauge been relocated during the record? If so, the record must be split or corrected.

A datum error looks like a shift in the rating and is easy to "fit away". It is better to find it with a level and a notebook than with a curve.

Fitting the curve

Most ratings are fitted, segment by segment, as a power law of the form Q = C (h − e)^b, where h is the stage, e is the stage of zero flow for that control, and C and b are fitted. Kennedy's USGS chapter describes the logarithmic plotting behind this approach and its use in rating development [1]. Good practice is to plot every gauging with its date, fit each control separately, look at the residuals over time to spot shifts, and show an uncertainty band rather than a single line.

Rating curve extrapolation: the flood end

The flows that matter most for flood warnings and design are usually above the highest gauging. Rating curve extrapolation simply extends the fitted power law, and that assumes the control does not change. Once the river spills onto its floodplain, conveyance increases sharply and the low-flow curve can badly misjudge the flow at a given level, or the level for a given flow.

Better ways to extend a rating are to use the surveyed cross-sections and a hydraulic model of the reach, to estimate past flood peaks from surveyed flood marks and the channel slope, or, best, to gauge a flood. Whatever the method, mark the extrapolated part clearly, widen its uncertainty, and say in the report how far beyond the measured range the curve has been pushed.

Hysteresis: rising and falling limbs

On flat rivers, or during fast floods, the same stage can carry more flow on the rising limb than on the falling limb, because the water-surface slope is steeper as the flood wave arrives. Plotted against stage, the gaugings form a loop rather than a line. This hysteresis is one of the effects ISO 1100-2 describes [2], and it is the reason complex ratings add the rate of change in stage or the water-surface slope as a second variable [1]. If gaugings at the same stage disagree, check whether they were taken on rising or falling water before calling them outliers.

HEC-RAS model calibration

A hydraulic model turns flows into levels and extents along a whole reach, not just at the gauge. The US Army Corps of Engineers' HEC-RAS manual sets out a calibration sequence for unsteady flow models: first calibrate Manning's n values against "established rating curves at gages and known high water marks", then choose events covering low, high and returning flows, adjust storage and lateral structures to reproduce the timing, peak, volume and shape of flow hydrographs, adjust n values to reproduce stage hydrographs, and finally verify the model on events or periods not used in calibration [5].

That sequence explains why rating curves and models belong together. The rating curve calibrates the model in the gauged range; the model, built on surveyed cross-sections, helps extend the rating where there are no gaugings. Both depend on the same datum and the same surveys, so keeping them in one place avoids rebuilding the geometry for every study.

Why this matters for flood warnings

Warning thresholds are usually agreed as levels on a staff gauge, while forecast models usually produce flows. The rating curve sits between them. A biased rating moves every Watch and Warning level, and an extrapolated rating can make a forecast flood look smaller or larger than it will be. Our guide on flood early warning system design covers the forecasting side of the same chain.

What KAI offers

As a service, KAI processes ADCP discharge data, updates rating curves and survey datums, and builds and calibrates 1D and 2D HEC-RAS models against observed events, delivering flood lines, depths and a report. This is described on our river surveys and hydraulic models solution page. KAI-River, the software that will keep every cross-section, gauging, rating curve and survey datum in one shared database and export straight to HEC-RAS 1D and 2D, is in development; early access is free.

Next step

Send us what you already hold: stage records, gaugings, cross-sections and any flood marks, with their datums. We will tell you how far the existing rating can be trusted, where it is extrapolated, and what extra field data would change the answer. Start from the river surveys and hydraulic models page, or join early access on the KAI-River page.