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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.
How accurate is
each method?
It is important to differentiate between relative accuracy (precision)
and absolute accuracy. Effectively, 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 relative and absolute accuracy, which can lead to confusion;
the relative accuracy figure will always be a smaller, more impressive
figure than the absolute accuracy.
Relative Accuracy
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.
Sing around sensors do have considerable error sources; there is
an electronics delay between receiving one pulse and starting the
next, and they can be subject to echoes and ringing, which combine
to blur the sound pulses. Generally speaking these devices offer a
relative accuracy of around ±0.25m/s.
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 is of the order of 140µs. 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 ±0.06m/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. Without going too far into
the detail, this technique gives a repeatability figure of ±0.002m/s.
Allowing for maximum possible errors in the sensor timing circuit
and the calibration procedure, we state a relative accuracy of ±0.03m/s.
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. We
will leave aside discussion of the sing around type, partly because
Valeport do not manufacture that type, but mainly because its relative
accuracy is not really comparable to that of either a CTD or time
of flight type measurement.
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 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 ±0.03m/s and an absolute
accuracy of ±0.045m/s.
So why would anyone
buy a CTD?
Two reasons:
- 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.
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 (the time of flight of a single sound pulse); 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 SVX. 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
reasonably achieved. In the short 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 comparison.
Bibliography
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 1442-1446
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