# Ultrasonic tide gauges

In the 1980s, to upgrade the existing network of tide gauges in the US, the Naval Oceanographic Survey (NOS) undertook a study showing that the airborne acoustics method for measuring distances was likely to achieve the best compromise between the quality of sea level measurements and the overall cost of the network. This cost included acquisition, operation and maintenance for a period of 20 years. The operation of ultrasonic gauges (ultrasonic transducers) is simple: the air draft between the tide gauge and the sea surface is measured by the transmission and reception of ultrasonic waves emitted into the air at 41.5 kHz. After calculation, the measured air draft can be used to determine the water height. The speed of sound in the air varies and depends on three parameters: - pressure, humidity and temperature. Due to the potential errors caused by the temperature gradient in stilling wells in sites with high tidal ranges, ultrasonic gauge technology was abandoned in the early 2000s in favour of radar gauges.

## Deployment

Although ultrasonic sensors are able to operate without protection, subject to sufficient transmit power, they are used in stilling wells to increase their shelf life, avoiding the influence of weather, and to ensure a plane water surface limiting the reflection losses of the acoustic wave. Any unevenness of the well may cause disruptive interference reflections. For this reason, it is recommended to channel the beam in a smooth rigid tube made of PVC for example. Multiple reflections on the walls of this type of cylinder are not a problem, as long as careful calibration is performed.

## How it works

The measurement principle is simple: a transducer located above the surface of the water emits an ultrasonic signal vertically downward and then captures the reflected signal. Knowing the speed of sound in the air (c) the round trip transit time (DT) provides the distance (l), air draft between the transducer and the surface: l = c Δt / 2

Where d is the altitude of the base of the acoustic transponder compared to a reference level (usually the chart datum), the height h of the sea level is therefore expressed by:

H = d – l = d – (c Δt / 2)

With sufficient accuracy for our applications, the speed of sound in the air (c) (expressed in m/s) is given by the following formula, where T is the temperature in degrees Celsius (° C), pa is the atmospheric pressure in hectopascals (hPa) and w is the relative humidity of the air.

c = 331.2 [ 1 + 0.97(w/pa) + 1.9 10-3T] m/s

Experience shows that the variation in the relative humidity of the air is negligible in a closed well where the air is nearly saturated with water. However, because temperature plays an important role, assuming c0 = 331.2, we have:

## Influence of temperature

Because of the relationship which gives = - this corresponds to an opposite sign error on h of nearly 2 mm per meter of air draft (l) and per degree Celsius.

Two methods are used to compensate for the significant influence of temperature:

• The first is to place a reflector under the probe at a known distance Io. The transit time Δt0 (round trip of the signal from the transponder to the reflector) gives the speed:

• The second is to place a temperature sensor close to the transducer and to calculate the speed of sound, depending on the temperature measured.

Both methods have their faults. The first gives the mean speed of sound on the probe-reflector route, but not all along the air draft of the wells. The second is even less efficient because it considers the speed at just one level. Experiences have shown that changes in temperature and its vertical gradient in the well induce significant errors on the level measurement, especially when daytime heating of the tide gauge structure raises the temperature of the air inside the wells. In this case, a temperature gradient appears in the well that is undetectable by the sensor. There is no truly satisfactory solution to this problem.

However, for the purposes of ocean dynamics studies, special gauges were developed, with different levels of watertight temperature sensors that can be immersed with no problem. But this expensive solution is seldom used for hydrography. Thus ultrasonic gauges are hardly used at all in France today.

To find out more:

Reference

• Simon B. (2007). La Marée - La marée océanique et côtière. Edition Institut océanographique, 434pp.

Last updated: 12/12/2012

Other tide gauge instruments to explore: