Why is sound velocity (SV) computed from a CTD better than sound velocity from direct measuring instruments?
Direct SV probes measure the time (flight time) required for a sound pulse to travel over a fixed length, using a high-speed clock to measure time. The clock starts when the pulse is emitted, and stops when the pulse is received. Theoretically, you only need to know the path length (and frequency of the clock ‑ an easy matter) to compute SV:
SV = acoustic path length / flight time.
For a typical acoustic path of 0.1 m, a flight time of 67 microseconds is expected for SV = 1492 m/s.
Two problems associated with direct SV probes are:
- The path length is not readily determined by a ruler measurement. The true length includes some depth into the acoustic transducer at which the pulse actually arises and again some depth where it is actually detected. Consider for example an typical instrument with specified accuracy of 0.05 m/s. For a typical water SV of 1500 m/s and a probe acoustic path of 100 mm, achieving this accuracy requires that length be determined to within (0.05/1500) x 100 mm = 0.003 mm (approximately 1/25 the thickness of a sheet of paper). The acoustic transducer would be of order 1 mm thick, so its dimension is much larger (300 times) than the length associated with the specified accuracy.
- Determining the actual flight time is not as simple as counting clock pulses. There are other time delays in determining both the start of the acoustic pulse and the time of its reception. Recalling that the time sound requires to travel 100 mm is approximately 67 microseconds, to measure SV to within 0.05 m, the flight time must be determined to within (0.05/1492) x 67 microseconds = 2.2 nanoseconds. It is exceedingly difficult to measure time to such precision, especially as the time lag associated with the acoustic transducer is much larger than this ‑ typically of order 1 microsecond (hundreds of times larger than the permitted error).
The fact is that in designing a direct path SV probe, the determination of length by ruler is only good to 5 or 10% (approximately 100 m/s equivalent uncertainty in SV). The actual determination of SV response therefore must be made in a calibration bath (using a CTD as a reference!), which is how all SV probes are calibrated.
Direct SV probes are often marketed on the principle that the measurement is based only on fundamental physical values of length and time. That is true in theory, but the practice is a different story! Direct SV probe manufacturers do not know the length (or the time) — they just fit the probe response to CTD-computed SV. There is a place for direct SV probes. Having been calibrated in water against a CTD, they do a competent job of measuring SV in other liquids. They will go on working in oil, petrol, milk, beer, etc. — liquids in which CTD measurements have no meaning.