Speed of sound

The speed of sound is important when computing velocity from the measured Doppler shift as seen in equation 2 in the Doppler effect section. The instrument also uses the speed of sound and the time lag between the transmitted and received pulse to indirectly measure distance and determine how far the pulse traveled before it was reflected.

Speed of sound increases with increased temperature, salinity and pressure. The instruments compute the speed of sound based on the measured temperature. A constant salinity is assumed, and set by the user during the configuration of the instrument before deployment. This assumption works relatively well because the speed of sound is more sensitive to temperature variation than it is to salinity variation.

• A variation of 1°C translates to approximately 4.5 m/s in speed of sound variation.
• The average salinity of sea water is around 35 psu. The rate of variation of speed of sound is approximately 1.2 m/s for a 1 psu alteration in salinity.
• Pressure is a function of depth and the rate of change of sound velocity is approximately 1.6 m/s for every alteration of 10 atm, i.e. approximately 100 m of water depth (derived by the hydrostatic equation). This is not compensated for by the instrument.

The estimates of the horizontal velocities will not be affected by vertical variations of speed of sound through the water column. Such vertical variations can occur as a consequence of thermoclines (changes in temperature with depth) or haloclines (changes in salinity with depth). The interested reader can check out the theory behind Snell's law, but the concept is that the acoustic energy travels the same path from the transducer to the particles and back again, and is therefore negated. Because the instrument measures the change in frequency (and not time or distance), the instrument only needs to know the sound speed at the location of the instrument.

On the other hand, the range accuracy is dependent on how the sound speed changes over the profile. That means that the position of the measurement cells in the water column will change if the speed of sound profile changes. The only way to know for sure the vertical position of the measurement cells is then to use a Sound Velocity Profiler or a CTD to measure the sound velocity profile through the water column.

Speed of sound corrections

Sound speed errors are typically small, but if it is necessary to correct for errors or changes in speed of sound, the correction method is relatively simple. This can for example be necessary if you have entered a salinity value that is far off from the actual salinity at the deployment site in your configuration or if the temperature sensor has malfunctioned. To correct the velocity estimates, use the following equation:

This correction is not available as an option in any of our processing software, but instead needs to be carried out manually.

To find the new true sound speed you should use the correct salinity and temperature from your deployment site.

To judge the magnitude of the potential error, start by calculating some of the extreme values (in pressure and temperature). You may find that it is sufficient to apply the same correction for all the data. If you find that you need the full correction, the true speed of sound must be calculated for each datapoint and the correction applied accordingly. 

If the salinity is changing rapidly: 

1. Use a fixed speed of sound instead of measured and an external conductivity probe to monitor salinity. This will let you calculate speed of sound as a function of time and correct the measurements for the changing conditions.
2. Use an average value for the experiment if the change in speed of sound is small enough that its resulting uncertainty is small.