Radar, ultrasonic, float and pressure water level sensors compared: physics, error budgets and field behaviour

Choosing a stage sensor is an engineering decision with a measurable cost of getting it wrong. Stage (water level) is the primary variable in hydrometry. Almost every other quantity, discharge above all, is computed from it. This article compares the four technologies in routine use for rivers, canals and reservoirs: non-contact radar, non-contact ultrasonic, float and shaft encoder in a stilling well, and submersible pressure. For each we set out how it measures, what limits its accuracy, and what the standards and field studies report. We make radar sensors, so we say so, and we have tried to keep the comparison to physics and published evidence.

Why millimetres matter: from stage error to discharge error

Discharge is not measured continuously. It is calculated from stage with a rating curve, usually of the form:

Q = C · (h − h0)^b

where h is the stage, h0 the stage of zero flow, C a site constant, and b an exponent set by the channel control. For a rectangular weir b is 1.5, for a triangular (V-notch) weir 2.5, and natural channel controls usually fall between the two. Differentiating gives the relationship that governs the whole sensor decision:

ΔQ / Q  ≈  b · Δh / (h − h0)

The relative discharge error is the stage error divided by the depth over the control, multiplied by b. It is largest at low flow, where h − h0 is small. The WMO Manual on Stream Gauging makes the same point with a station-sensitivity example: a stage uncertainty of 5 mm at a station where a 1 % change in discharge moves the stage by 5 mm gives a 1 % discharge uncertainty, which is acceptable. At a station where a 1 % change moves the stage by only 0.5 mm, the same 5 mm stage error gives 10 %, which the Manual calls unacceptable [1].

For b = 2, the table shows what a given stage error costs:

The practical consequence is that the right sensor depends on the use. A flood warning threshold is crossed by tens of centimetres and tolerates a centimetre of error. A low-flow record, water allocation or a rating curve built on gaugings needs millimetres, because that is where discharge sensitivity to stage is highest.

What the standards ask for

Two reference documents set the baseline:

• WMO Manual on Stream Gauging (WMO-No. 1044). Gauge readings should normally be made to the nearest 0.003 m (0.01 ft). For pressure transducers it states an acceptable error of 0.003 m or 0.10 % of the effective stage, whichever is greater, which works out to 3 mm for a 3 m stage, 10 mm for 10 m and 15 mm for 15 m. For non-contact devices it says that ultrasonic and radar instruments "are used extensively and successfully in Europe", that under very controlled conditions some are accurate to within 0.003 m, and it lists temperature variation, density variation and the composition of the transmission path among their error sources. It also notes that radar gauges "are often affected by waves on the water surface" [1].
• ISO 4373:2022, Hydrometry: Water level measuring devices. It specifies the functional requirements of automatic level instruments for both contact and non-contact methods, with an annex giving guidance on the types available and the uncertainty associated with them [3].

The Central Water Commission's field manual adds an operating practice worth keeping in mind for any sensor: where the surface is unstable from wind or turbulence, the observer takes the mean of the fluctuation over about 30 seconds, and the staff gauge is retained to check the recorder at intervals [2]. In other words, a good automatic station averages, and it stays tied to a visible reference.

Non-contact radar

How it measures

A radar level sensor emits a radio wave towards the water and measures the round-trip time of the echo. The distance is d = c · t / 2, where c is the speed of light, and the level is the mounting height minus d. Two modulation schemes are common in level radar:

• Pulse radar sends short pulses and times the return directly.
• FMCW (frequency-modulated continuous-wave) radar sweeps its frequency across a bandwidth B and measures the frequency difference between the transmitted and received signal. That difference is proportional to distance.

For FMCW, the theoretical range resolution is Δr = c / (2B). A wider sweep resolves finer distances:

Resolution is not accuracy. Millimetre-level accuracy comes from processing the phase and the shape of the echo, not from separating two targets millimetres apart. Resolution does decide how well a sensor can tell the water surface from a nearby structure, which matters on bridges.

Level radars commonly operate in the K band around 24 to 26 GHz or the W band around 76 to 81 GHz. Higher frequency allows a narrower beam from a smaller antenna, and the choice of frequency, bandwidth and antenna sets the practical accuracy [8].

Why water is an easy target

A flat water surface reflects radio waves strongly. Water has a relative permittivity of about 80. At normal incidence the fraction of power reflected is:

R = ((√εr − 1) / (√εr + 1))²   →   εr = 80:  R = 0.64

About 64 % of the incident power returns, against roughly 7 to 11 % for a material with εr of 3 to 4, such as many dry solids. This is why radar works so well on rivers and why it needs little power.

Beam footprint

The beam spreads with distance. The footprint diameter is 2 · h · tan(θ/2) for beam angle θ and range h:

This table is a mounting checklist. A sensor on a bridge deck 10 m above the water with a 12° beam illuminates a spot 2.1 m across. Any pier, abutment or rail inside that spot, or inside the side lobes around it, can return an echo that competes with the water. Choosing the mounting point, the beam and the minimum range is how you keep structures out of the beam.

What affects radar accuracy

• Surface motion. The sensor measures the mean distance to a moving surface. Waves, standing waves and turbulence add scatter. The WMO Manual notes that radar gauges are often affected by waves [1]. Averaging over many samples reduces it.
• Air properties. The speed of radio waves in air depends slightly on temperature, pressure and humidity. The radio refractivity is N = 77.6/T · (P + 4810 e/T) [9]. Between dry air at 20 °C and humid air at 35 °C at the same pressure, N changes by about 160 parts per million, which is about 1.6 mm over a 10 m range and 4.9 mm over 30 m. That is small, and it is the reason datasheet accuracy is quoted for reference conditions. Compare it with ultrasonic in the next section.
• Rain, fog and wind. Their effect on the radio signal at these frequencies is small. Wind matters mainly because it roughens the water surface, which changes the scatter.
• Mounting. Tilt, a structure in the beam, and a bracket that flexes with temperature or wind are often larger than any electronic error.
• Very shallow flow. One field comparison of stream radars against conventional gauges reported accurate stage as long as the depth was not less than about 0.08 ft (2.4 cm) [7].

What field tests report

A USGS conference paper on radar stage uncertainty found that radar measurements were more accurate than uncorrected pressure sensors at higher stages, but less accurate than pressure sensors at low stages, and that radar showed a small negative bias that grew slightly with stage when compared with wire-weight measurements [4]. A USGS Hydrologic Instrumentation Facility laboratory evaluation of a radar water-level sensor confirmed a manufacturer specification of ±0.01 ft (about ±3 mm) over the sensor's temperature range at distances from 3 to 15 ft, and judged that specification adequate for a primary stage sensor at a streamgage [5]. Laboratory results and field results are not the same thing: the lab removes waves, mounting movement and weather, which is why field verification against a staff gauge is part of any acceptance test.

Non-contact ultrasonic

An ultrasonic sensor works on the same time-of-flight principle with sound. The difficulty is that sound is slow and its speed depends on the air it travels through:

c ≈ 331.3 · √(1 + T / 273.15)   m/s      (T in °C, dry air)

Near 20 °C, c changes by about 0.17 % per °C. A sensor that assumed 20 °C and was operating in 40 °C air would read the distance about 3.3 % too long. Every ultrasonic gauge therefore includes an air temperature sensor for compensation [10]. The uncorrected error is large:

Compensation removes most of this, but not all. The probe measures the temperature at the sensor, while the sound travels through the whole air column. Over a river, that column can be several degrees different from the air at the sensor, especially when sun heats the bridge deck or when cool air lies over water. A 5 °C mismatch over a 5 m column gives 0.17 % × 5 × 5 m ≈ 4 cm. Wind and gradients also bend and disturb the beam, and the beam is typically wider than a radar beam, so structures near the path can return false echoes. Ultrasonic is a good tool for sheltered sites, tanks and short ranges. For wide open rivers with large seasonal swings it needs careful siting.

Float and shaft encoder in a stilling well

How it measures

A well connected to the river by intake pipes holds a float. As the level rises the float lifts and turns a wheel, and a shaft encoder converts the rotation into stage. The well damps waves and turbulence, which is its purpose [1].

Where the error comes from

The WMO Manual is direct about this method's failure modes:

• Intake lag. Water has to flow through the intake pipes to change the level in the well, so during a rapid rise the well lags the river. The Manual gives an equation for the lag that depends on the pipe length and diameter, the well area and the rate of change of stage, and references the USGS study of intake lag [1][6].
• Drawdown and pile-up. High velocity at the outer end of the intakes can lower or raise the level inside the well by "on the order of 0.15 m or more", and the Manual advises checking it with simultaneous inside and outside readings at high stage, and using static tubes or relocating the intakes to reduce it [1].
• Silting and blockage. Clogged intakes or sediment in the well "usually result in a complete loss of data" [1].
• Float and tape errors. A leaking float floats lower and reads too low. The float tape and pulley produce a line-shift error that is positive on a rising stage and negative on a falling one [1].
• Thermal movement. A tall metal well exposed to a 40 °C change in temperature can raise its instrument shelf by about 12 mm for a 25 m well [1].

A well in good order, with clean intakes and a verified inside-outside relationship, is a sound, proven method, and the WMO Manual notes that stilling wells are still widely used [1]. The cost is construction and upkeep, and during a flood, when the intakes are most likely to clog, the lag is greatest.

Submersible pressure sensors

A pressure sensor below the surface measures hydrostatic pressure, P = ρ · g · h. For fresh water at 20 °C, 1 m of water is about 9.79 kPa, so the sensor must resolve about 10 Pa to see 1 mm. The measurement has three corrections:

1. Atmospheric pressure. A vented (gauge) transducer is connected to the air by a vent tube in the cable and measures only water pressure. An absolute sensor measures water plus atmosphere and needs a barometer, because 1 hPa of air pressure is about 1.02 cm of water, so a 10 hPa weather swing is a 10 cm error if uncorrected.
2. Water density. The conversion from pressure to depth assumes a density. Temperature changes it, and so does suspended sediment.
3. Calibration drift. The WMO Manual states that pressure transducers "may have or may develop calibration errors" and that the standard for acceptable error is 0.003 m or 0.10 % of the effective stage, whichever is greater [1].

The density terms can be computed. Compared with a calibration at 998.2 kg/m³ (fresh water at 20 °C):

(The sediment rows assume a particle density of 2650 kg/m³ and are computed from ρ = ρw + C · (1 − ρw/ρs).) For clear rivers the effect is a fraction of a percent. For very sediment-laden streams it is not: the USGS describes the Rio Puerco in New Mexico, where suspended sediment concentrations regularly range from 10 to 200 g/L, as a stream where this matters [11]. A pressure sensor is also in the stream, so floods can bury it, damage it or foul it, which is the practical reason many agencies prefer non-contact sensors for flood-prone channels.

Side-by-side summary

Verifying any sensor in the field

Whatever you choose, accuracy on the datasheet is not accuracy at your site. Acceptance should include:

1. Reference gauge. A staff gauge or surveyed reference read to the nearest 3 mm, with simultaneous readings at several stages across the working range [1][2].
2. High-stage check. Comparison during a high-flow event, where lag, drawdown, waves and mounting movement are largest.
3. Averaging and filtering. Burst sampling (for example 10 to 30 seconds of samples) with a median or mean reported, which mirrors the observer's practice of averaging a fluctuating surface [2].
4. Drift check. A repeat comparison each season, and a record of every adjustment.
5. Data quality rules. Range limits, rate-of-change limits, flat-line detection and gap flags in the logger or the server.

Where ClimMaTech fits

Tarang is our non-contact radar level sensor: ±1 mm accuracy, 0.5 mm resolution and a measuring range up to 50 m, for AWLR stations where the sensor has to stay out of the water and the reading should hold steady across the seasons. Pravaah adds surface velocity to the same measurement for AWVLR stations. For a description of what a complete station contains, see our guide to AWLR and AWVLR stations, and for the specification checklist, how to choose a river water level sensor.

References

1. World Meteorological Organization, Manual on Stream Gauging, Volume I: Fieldwork, WMO-No. 1044 (2010), Chapter 3 (sensitivity of controls), Chapter 4 (measurement of stage). WMO publication page.
2. Central Water Commission, India, Gauge and Discharge Measurement Field Manual. cwc.gov.in.
3. ISO 4373:2022, Hydrometry: Water level measuring devices. ANSI Webstore.
4. U.S. Geological Survey, Radar stage uncertainty. usgs.gov.
5. U.S. Geological Survey, Hydrologic Instrumentation Facility, Laboratory evaluation of a radar water-level sensor. usgs.gov.
6. U.S. Geological Survey, Study of intake lag in conventional stream gaging stilling wells, Open-File Report 65-150. pubs.usgs.gov.
7. Remote sensing of hydrologic variables in rivers (field comparison of stream radars against conventional gauges). shareok.org.
8. The impacts of frequency and antenna selection for free-space radar transmitters, Control Engineering. controleng.com.
9. ITU-R Recommendation P.453, The radio refractive index: its formula and refractivity data. itu.int.
10. Sensors One, Ultrasonic liquid level sensors (temperature compensation). sensorsone.com.
11. U.S. Geological Survey, In situ densimetric measurements as a surrogate for suspended-sediment concentrations in the Rio Puerco, New Mexico. pubs.usgs.gov.

The worked numbers in this article (speed of sound, radar reflectivity, beam footprint, range resolution, discharge sensitivity, refractivity and density effects) are computed from the stated relations. They illustrate the size of each effect. They are not the specification of any particular product.