Direct Measurement vs. CTD Calculation
There is some debate surrounding the relative merits of using a direct measurement technique to measure sound velocity as opposed to using a CTD to calculate it. As is the nature of such discussions, each school of thought believes themselves to be correct. Valeport manufactures both types of instrument, and we therefore consider that we are able to offer a (relatively) unbiased opinion. If you want a quick answer, then here it is - our reasoning and justification follows below:
- If you want to know the actual, absolute sound velocity as accurately as possible, use an instrument with a Valeport digital time of flight sound velocity sensor.
- If all your previous work has been based on CTD measurements, and you want comparable data now, use a CTD (we would recommend a Valeport CTD, naturally).
- If you want to know what the difference is between the two methods use the Valeport MIDAS SVX.
So what are the different methods?
A CTD uses Conductivity, Temperature and Pressure sensors to calculate Sound Velocity using any of a number of well known formulae. Pike & Beiboer (1993) compare these formulae, and conclude that for continental shelf work (<1000m), the formula proposed by Chen and Millero (1977) is most appropriate, whilst for deeper work the Del Grosso (1974) formula is preferred.
There are three types of direct measurement sensor:
- "Sing Around" sensors send a sound pulse over a known distance; when it is received, a further pulse is sent and so on. The repetition rate of the pulses is a function of (amongst other things) the speed of the sound pulse, which can therefore be derived.
- Analogue time of flight sensors use an accurate timing circuit to measure the time that a single pulse of sound takes to travel a known fixed distance; distance divided by time equals speed.
- Digital time of flight sensors use an even more accurate timing circuit to measure the time that a single pulse of sound takes to travel a known fixed distance; distance divided by time equals speed.
For the purposes of this discussion, we shall not consider the sing-around SV sensor type, partly because Valeport do not make one, and partly because they are demonstrably inferior in performance to time of flight SV sensors.
How accurate is each method?
It is important to differentiate here between the concepts of "Precision", "Relative Accuracy" and "Absolute Accuracy". Effectively, precision relates to how repeatable a measurement is, i.e. in a steady state, or when a sensor is repeatedly exposed to a known state, how close to one another are the readings? Relative accuracy states how good a measurement is relative to a known standard. Absolute accuracy will also include an estimate of how close the known standard is to the actual answer. Instrument manufacturers often fail to distinguish between these three, which can lead to confusion; the relative accuracy figure will always be a smaller, more impressive figure than the absolute accuracy, and the precision value should be even smaller still.
A good quality CTD, typically available from many manufacturers, will have sensor errors of the order of ±0.01°C for Temperature, ±0.01mS/cm for Conductivity, and ±0.1% for Pressure. The Pressure error value is invariably given as % of range, so for a 100Bar (~1000m) sensor, ±0.1% is ±0.1Bar (±1dBar, or approximately ±1m). Using either of the accepted formulae, these sensor errors will give a relative accuracy of around ±0.06m/s in sound velocity. What this means is that the instrument will report the sound velocity as being within ±0.06m/s of what the chosen formula says it should be for the conditions.
Time of flight sensors are much more sophisticated, using high resolution timing circuits to time a single sound pulse over a fixed distance - depending on sensor design (and obviously the sound speed) the time of flight will be in the region of 30 - 145µs. The use of a single sound pulse eliminates the echo and ringing effects, and these days composite sensor construction allows remarkable stability of the sensor path (the distance over which the sound pulse travels) over the full variation of temperatures and pressures to which it is subjected. The net result is a claimed relative accuracy of the order of ±0.05m/s for analogue time of flight sensors.
Valeport's digital time of flight sensor uses an advanced digital signal processing (DSP) timing technique to time the sound pulse to a resolution of 1/100th of a nanosecond (10 picoseconds). Allowing for maximum possible errors in the sensor timing circuit and the calibration procedure, we state a relative accuracy of ±0.02m/s. This error budget is discussed in further detail here.
But what about Absolute Accuracy?
For a CTD, the question is really "how accurate is the formula that has been used?" According to one CTD manufacturer, the author of one of the formulae in question estimates that the absolute accuracy of a CTD based sound velocity measurement is better than 0.5m/s. Of course, how much better is hard to say, but it is a reasonable assumption that we are talking about a few tens of cm/s, rather than a few mm/s, or in excess of 1m/s. It is widely held that the "formula error" of these equations is of the order of ±0.25m/s, which when added to the relative accuracy figure of ±0.06m/s would give an absolute accuracy of around ±0.3m/s; not an unreasonable figure, and broadly in agreement with the formulae authors' own estimates.
The absolute accuracy of a direct measurement sensor also depends on the accuracy of a formula (as well as the relative accuracies discussed above), and this is where the time of flight sensor really wins.
The key to understanding why a time of flight sensor beats a CTD for absolute accuracy is to remove the discussion from the oceanographic environment for a moment, and consider what we are really trying to measure. We are NOT trying to measure how the Temperature variations in the water column affect the sound velocity. We are NOT trying to measure how the Salinity variations in the water column affect the sound velocity. All we are trying to measure is time - the time taken for a single pulse of sound to travel a known distance. It doesn't matter whether the sound pulse is travelling through seawater, red wine or treacle; if we know how long it takes, we know how fast it's going. And this is equally true if the sound pulse is travelling through pure water.
As well as publishing an equation for the Speed of Sound in seawater, Del Grosso also published an equation for the Speed of Sound in pure water, this with Mader (1972). Pure water has a distinct advantage over seawater in that there are fewer variables that can affect the sound velocity, namely Pressure and Temperature. At a fixed pressure (i.e. atmospheric, under laboratory conditions) it is therefore very easy to precisely control a pure water environment in terms of temperature, and therefore also in terms of sound velocity. The Del Grosso & Mader equation is therefore estimated by the authors to have an inherent accuracy figure of ±0.015m/s; this is significantly better than that of the seawater equations.
By calibrating the time of flight sensors (both Valeport's digital type and others' analogue / digital types) in pure water, under precisely controlled temperature conditions, the performance of the sensors can therefore be characterised, and any fixed electronics delays or manufacturing tolerances removed. What we have created and calibrated is therefore a very accurate clock, and it doesn't matter what environment that clock is put in, it will measure the time of flight to the stated accuracy.
So, in summary, a CTD may have a relative accuracy of ±0.06m/s, and an absolute accuracy of ±0.3m/s, whilst a Valeport digital time of flight sensor has a relative accuracy of ±0.02m/s and an absolute accuracy of ±0.035m/s.
As relative late-comers to the SV market almost a decade ago, we did have the advantage of starting with a clean sheet of paper, which allowed us to take a quantum leap ahead in SV measurement techniques, but it does have a disadvantage in that we were obliged to follow the existing convention for stating our specifications.
As far as CTD derived SV goes, the situation is confused; some manufacturers quote relative accuracy, some quote absolute accuracy, but very few state which they are quoting. However, most quality manufacturers are achieving similar performance levels, and all use the same equations, so it is a reasonable assumption to make that if the quoted accuracy for SV measurement on a CTD is less than ±0.25m/s, then it is probably a statement of relative accuracy (i.e. it does not include formula errors). If it is more than ±0.25m/s then it is probably a statement of absolute accuracy (i.e. it includes the formula errors, generally accepted to be in the region of ±0.25m/s).
In the field of time of flight SV sensors though, the position is clear; everybody states relative accuracy. Technically speaking, the estimated formula error of ±0.015m/s should be added to create an absolute accuracy figure, but this is conventionally not done. In order to satisfy convention, and to avoid giving ourselves a competitive disadvantage by overstating the figures compared to our competition, we therefore state relative accuracy in our specifications for this particular sensor.
So why would anyone buy a CTD?
- A CTD also gives you Density and Salinity data, which may also be of value.
- If you have an ongoing project that has previously used CTD derived SV data, then it may make sense to accept the inherent error for the sake of data consistency.
Anything else to know?
It has been said that direct measurement SV sensors are easily damaged - this is not really true. Early sensors were made of Invar (chosen because of its precisely defined coefficient of thermal expansion). A steel type alloy, this did suffer to an extent from corrosion, but also being metallic it is true that if the sensors were bent, they stayed bent. Since the path length of the sensor is so critical, distorting the sensor in any way would produce errors. Having said that, Invar is still a strong steel alloy, and the abuse necessary to distort the sensor would almost certainly cause damage to any instrument.
More recently, the sensors are constructed from advanced composites, which have practically zero coefficient of thermal expansion, are resistant to corrosion, and do not bend or break without extreme violence. They are certainly more robust than most CTDs. You can find out more by clicking here.
A further advantage of a time of flight sensor is the fact that the measurement only relies on a single sensor, which has a time constant of only ~140µs at the most (the time of flight of a single sound pulse in a 100mm sensor); this is effectively an instant response sensor. CTD measurements require data from three sensors, which invariably have different response times, and this can lead to spikes in the calculated SV data. These can be eliminated by post processing the data, but there is an element of subjectivity to this.
The above discussion uses error estimates from a variety of sources, some more subjective than others, and all from different times and circumstances. The only real way to compare measured and calculated SV data is to use what we believe to be a unique instrument, the Valeport MIDAS SVX2. This device is fitted with CTD and digital time of flight SV sensors, and uses our synchronised sampling technique to measure all the sensors at the same instant rather than in sequence. Whilst even this is not a perfect method, we believe it is as close as can be reasonably achieved. In the time that this instrument has been commercially available, the data that we have seen appears to indicate that the estimated errors in the seawater formulae detailed above are not too far wide of the mark. However, more detailed comparative work would be required to give a more definitive conclusion.
J.M. Pike & F.L. Beiboer, 1993, "A Comparison Between Algorithms for the Speed of Sound in Seawater". The Hydrographic Society, Special Publication No. 34
C-T. Chen & F.J. Millero, 1977, "Speed of sound in seawater at high pressures". J Acoust Soc Am, 62(5), pp 1129-1135
V.A. Del Grosso, 1974, "New equation for the speed of sound in natural waters (with comparisons to other equations)". J Acoust Soc Am, 56(4), pp 1084-1091
V.A. Del Grosso & C.W. Mader, 1972, "Speed of Sound in Pure Water". J Acoust Soc Am, 52, pp 1442-144
Precision should either be stated as a Peak to Peak value (i.e. every point lies within this range), or as a 95% confidence value (i.e. 95% of the readings are within the stated range). Confusingly, some manufacturers use a standard deviation figure (or RMS), which is misleading, and often bears no relation to the true precision figure. Knowing your true peak to peak noise value effectively tells you how good your sensor is at detecting change; high peak to peak noise figures mean that small changes are literally lost in the noise.
The Precision of a CTD derived Sound Velocity value will depend on the precision of each individual sensor in the instrument. A Valeport CTD will have precision values (peak to peak noise) of ±0.002mS/cm for Conductivity, ±0.001°C for temperature, and ±0.002dBar for pressure (although this is slightly dependent on the range of the pressure sensor). These values will contribute to a Precision figure for SV of around ±0.006m/s. However, the issue is complicated slightly by the fact that each sensor will have a different response time; in anything other than perfectly steady conditions, this can lead to spikes in the data. Although these can be removed in post processing, it is a somewhat subjective exercise, so it easier for now to say that a CTD derived SV value should have a precision of at best, ±0.006m/s.
Measurements we have made on analogue time of flight sensors (which we do not make), and on other "digital" sensors currently available indicate a peak to peak noise value in the region of ±0.035m/s, with little to pick between the two methods. These values are actually significantly greater than the stated specification, which we therefore assume to be based on RMS data.
Valeport's digital time of flight sensor has a peak to peak noise value of ±0.002m/s.