Capability of pure water calibrated time-of-flight sensors for the determination of speed of sound in seawater

Knowledge of the speed of sound in seawater with high accuracy is fundamental to the application of acoustic systems and technologies in the marine environment. The speed of sound is physically related to other thermodynamic properties and is therefore important for establishing equations of state for fluids. In oceanography, the Thermodynamic Equation of Seawater–2010 (TEOS-10) was adopted in 2010 as a new standard for the calculation of the thermodynamic properties of seawater (Feistel et al., 2008; Intergovernmental Oceanographic Commission et al., 2010). However, speed-of-sound data for seawater covering the oceanographic range for temperature, salinity, and pressure with sufficiently low uncertainties to meet current requirements are scarce. The TEOS-10 formulation with respect to the speed of sound is mainly based on the absolute measurements of Del Grosso and Mader (1972) who indirectly determined the acoustic wavelength with variable path acoustic and laser interferometry. Chen and Millero (1977) measured the speed of sound relative to pure water using commercial sensors working with the sing-around technique. The phased-out international standard algorithm (EOS-80, Fofonoff and Millard, 1983) is based on these results. Together, equations from both studies still represent the standard references for the speed of sound in oceanography, although systematic differences partially larger than the claimed uncertainties between both equations exist, at least at elevated pressures. Thus, the demand for precise sound speed data in conjunction with other thermophysical properties remains high, e.g., in view of ocean and ocean-climate modeling. However, the speed of sound is still preferentially calculated from in situ conductivity, temperature, and pressure data (CTD) using the given equations rather than directly measured with sound speed sensors. Each of the CTD measurands brings its own uncertainty as well as the applied equations. Furthermore, calculated sound speeds do not consider possible effects of variations in the relative composition of dissolved matter in seawater (e.g., Feistel et al., 2010). This substantiates the need for further development and the respective metrological investigations of direct measurement techniques.

For laboratory speed-of-sound measurements in liquids, various techniques based on the transmission of sound pulses have been established. Sound pulses are emitted into a fluid sample over a distance of a few centimeters by a transducer and detected by the same element after reflection or by a second transducer. The speed of sound is then calculated from the measured travel times of the pulses along the known sound path. A technique used for decades is the sing-around technique, where pulse generation is triggered by detection of the previous pulse (e.g., Mackenzie, 1972). The pulse repetition rate as a function of the sound speed is the measurement signal. However, mainly ringing effects generally limit the uncertainty of this method. A modern but more extensive approach is the double pulse echo technique, where sound pulses are emitted by the same transducer simultaneously in opposite directions into the liquid along paths of different length (Meier and Kabelac, 2006; Lin and Trusler, 2012; Albo et al., 2013). The travel time is given by the pulse repetition rate which causes cancelation of the two successively arriving echoes which are brought to overlap. It is inherent to these methods that the length of the sound path in general has to be determined by calibration, e.g., in pure water under reference conditions. Mechanical models then have to be applied to account for thermal expansion and pressure deformation effects acting on the mechanical parts constituting the sound path. Also, diffraction effects causing systematic phase shifts of the real transducer generated sound wave compared to an ideal planar wave have to be included by appropriate correction models. Similar problems are known in conjunction with high-precision measurements of density and salinity, respectively, in seawater, where a device calibration with respect to pure water and standard seawater is performed to reduce the uncertainty (Wolf, 2008; Seitz et al., 2010). Attempts to trace the acoustic path length to an absolute measurement do not provide sufficient accuracy to avoid calibration (Benedetto et al., 2005a,b).

A further experimental issue complicating high precision speed-of-sound measurements in seawater is its electrical conductivity and especially its strong corrosiveness. Besides the undesirable degrading effect on the components of the measurement cells, the demands on the purity of the samples may not be fulfilled due to contamination with the corroded material.

As an alternative and a practice-oriented approach we investigated oceanographic time-of-flight sensors for high accuracy speed-of-sound measurements in a laboratory study. This type of sensor is optimized by manufacturers for in situ measurements in seawater under field conditions. They provide strong corrosion resistance by their construction and choice of materials. With respect to the measurement principle, they were developed to measure the time of flight of single acoustic pulses. An important advantage is that errors from multiple echoes or ringing effects, which are typical for sing-around sensors (Eaton and Dakin, 1996), can be avoided. Furthermore, modern devices provide a high resolution of the time-of-flight determination (Table I), so that this is no longer a limiting factor for the overall uncertainty of the speed of sound.

The investigated sensors are AML Micro SV2000, AML SV XChange (OEM), Valeport miniSVS, and Valeport miniSVS (OEM), hereinafter referred to as MSV, SVX, VP, and VP OEM,¹ respectively. They all consist of a single transducer and a reflector, which are kept apart at a fixed distance by means of fixed rods (Fig. 1). The distance is 10 cm (3.4 cm for the SVX). The variable to be determined is the time of flight of an acoustic pulse which is detected by the same transducer after reflection. Materials are chosen to suppress effective thermal expansion and pressure effects to a negligible level. The sound path of the older analog sensor (MSV) is composed of different materials for the reflector and the rods in such a way that they virtually compensate for thermal expansion. Novel sensors (SVX, VP, VP OEM) are equipped with carbon composite rods with a stated negligible effective thermal expansion. The MSV uses analog timing circuits for time-of-flight determination, whereas SVX, VP, and VP OEM use modern digital signal processing and timing techniques. For VP and VP OEM, the manufacturer claims uncertainties smaller than 0.02 m s^–1 (<14 ppm) after a two-point calibration in pure water at atmospheric pressure. More detailed information on the built-in method of time determination (e.g., correlation techniques or threshold level based methods) or on the calibration procedures was not available.

We discuss our results with respect to the potential of the sensors to produce high precision speed-of-sound data and compare them to values in literature. Although the sensors are intended to be applied also at high pressures, the results presented here are restricted to atmospheric pressure.

After our own recalibration in pure water, relative measurements of the speed of sound have been conducted in aqueous solutions of salts (NaCl, MgCl₂, Na₂SO₄) which constitute the main components of sea salt, as well as in two original and pure water diluted samples of North Atlantic seawater.

Sensor calibration and speed-of-sound measurements were carried out in the bulk volume of a 55 l thermostat (Kambič OB-50/2, Semic, Slovenia) which was completely filled with the sample liquid (Fig. 2). Because the thermostat had no cooling function, cooling was provided by a separate cryothermostat (Lauda ProLine RP845, Lauda-Königshofen, Germany). Two PTB-calibrated SPRTs (Standard Platinum Resistance Thermometers, Rosemount, Chanhassen, MN) connected to a high precision resistance bridge (MicroK 70, Isotech, Southport, UK) were installed for temperature measurement. The temporal and spatial temperature stability was generally within 1 mK in the vicinity of the sensors during the periods of sound speed records of typically less than 1 minute. To suppress the formation of bubbles due to degassing of dissolved air from the samples, the measurement courses were generally run from warm to cold, starting with a period for partial degassing at a temperature higher than the first measurement point. The setting time for each preselected temperature was about 1.5 h. Evaporation and heat exchange through the sample surface were minimized by an insulating cover widely sealing the thermostat volume. The conductivity was observed using a pure water cell (LR 325/01, WTW, Weilheim, Germany) as purity check in pure water, or, in the case of salt solutions and seawater, with oceanographic conductivity cells (SBE-4, SBE-37 MicroCat, Sea-Bird Electronics, Bellevue, WA) to track the stability of the sample salinity and to determine the absolute values of Practical Salinity (S_P) of the seawater samples. The pure water (initial resistivity >15 MΩ cm, according to an electrical conductivity <0.067 μS cm^–1) for calibration was produced by a reverse osmosis purification system (Milli-Q Integral, Merck Millipore, Billerica, MA). During the calibration runs or measurements in pure water, the conductivity converted to 25 °C typically increased slightly from less than 1 μS cm^–1 after thermostat vessel filling (dominated by dissolution of atmospheric CO₂) to at most (2 to 3) μS cm^–1. This level of “contamination” is negligible with respect to its effect on the speed of sound within our range of uncertainty. It is clear that owing to the open character of the setup, the pure water for calibration as well as the samples for measurements are not completely degassed.

The measurement cycles were run at typically 8 to 14 preselected temperatures covering the range of 50 °C to 1 °C. The relevant sensors were used simultaneously where possible to assure virtually identical conditions. After stabilization of the preselected temperatures, 20 to 40 single pulses were recorded with each sensor at a rate of 1 Hz and afterward averaged for further data processing. A complete cycle was generally extended over two working days.

During the initial tests of the setup, we observed in continuous records at adjusted temperatures that starting with clean sensors, the speed of sound continuously increased on a time scale of less than 1 hour before turning into a certain plateau (Fig. 3). The magnitude of this effect varied between 0.01 m s^–1 up to several 0.1 m s^–1 in water and salt water samples at different temperatures. We address this in terms of the formation of small, invisible bubbles (microbubbles) at the transducer and reflector surfaces, either formed from dissolved gases, or continuously produced in the actively circulating bath and concentrated on the surfaces. Mechanical cleaning with a soft tissue drew the readings back to well reproducible, i.e., not influenced, values. The cleaning immediately before recording the speed-of-sound data therefore became part of our measurement routine. This observation confirmed the annotations given by Mackenzie (1972) and Eaton and Dakin (1996) and illustrated that caution is advised in stirred measurement and calibration baths open to the atmosphere.

The sensors were calibrated by the manufacturers or distributors before delivery. Data from the sensors can therefore be recorded as values converted to the speed of sound in SI units using the stored original calibration coefficients, but also as raw timing counts from the built-in signal processing. As specified in the calibration documents, the MSV, VP, and VP OEM sensors are calibrated in pure water using a function of the form w = A/(t−B), where t is the measured time of flight, and A and B the parameters to be determined. It is obvious that this type of calibration function is physically motivated by assuming the validity of the linear relationship between the reciprocal sound speed and the flight time of the signal. In this case, A can be associated with a fixed effective acoustic path length and B with a constant electronic time delay.

The MSV sensor was originally calibrated in pure water in the temperature range of 1 °C to 50 °C with ∼1000 data points. For the VP and VP OEM sensors a simple two point calibration, also in pure water at reference points (∼2 °C and ∼15 °C), is documented. No information on the method or liquids for calibration was available for the SVX sensor.

Pure water is the preferred reference liquid for which absolute speed-of-sound data and equations for the temperature dependence are available with low uncertainties of ≤0.005% at atmospheric pressure (Wagner and Pruß, 2002). The calibration conditions are well reproducible because temperature is—besides the purity of the liquid—the only parameter to be controlled. To assure comparability of the investigated sensors and to be independent of the manufacturer's specific procedures, we conducted a recalibration in pure water. Our subsequent measurements in salt solutions and seawater samples were built upon this recalibration. A calibration in standard seawater was not considered because of the inconsistency of existent speed-of-sound equations and also for reasons of cost. Reporting sound-speed measurements of seawater relative to pure water also leaves open the beneficial option of correcting the pure water equation in the future. The impossibility of doing so was the main reason for discarding the Chen and Millero (1978) sound speed data when the seawater standard changed from EOS-80 to TEOS-10 (see Feistel, 2003; IOC et al., 2010).

However, we still relied on the signal algorithms for time-of-flight determination performed by the sensor electronics which could vary with the sensor model. The temperature range for calibration was 1 °C to 50 °C. This ensured the coverage of measurements in seawater with a salinity of 36 g kg^–1 at temperatures up to about 30 °C (Fig. 4).

In Fig. 5, the calibration results were compared for all sensors after application of different calibration functions. The majority of the data was recorded with the described experimental setup (Fig. 2). A small part of the data set was taken exclusively with the more compact OEM sensors (SVX and VP OEM), using another cryothermostat with a smaller (∼5 l) sample volume. As a pure water reference for the speed of sound we used the Seawater-Ice-Air (SIA) library of TEOS-10 (IOC et al., 2010) which contains subroutines for pure water based on the IAPWS-95 equations of state [Wagner and Pruß, 2002; International Association for the Properties of Water and Steam (IAPWS), 2014].

Figure 5 shows the pure water sound speed calculated with the equation of state versus the time-of-flight output of the sensors at the preselected temperatures (circles). In the second row, the speed-of-sound deviation from the TEOS-10 values derived from the calibration coefficients given by the manufacturer is plotted. A part of the deviation (<0.05 m s^–1) may be attributed to a possible use of a different pure water sound speed equation for the original calibration by the manufacturers. However, larger differences could be attributed to these fittings.

For the MSV sensor we fairly reproduced the general course of the original calibration (not shown). The apparently constant offset for the SVX (open circles, the zero line is shifted by −0.2 m s^–1 in this panel) is primarily due to several discrete leaps in the readings in one direction, which occurred during the first days of calibration measurements with the brand-new sensor (crosses in Fig. 5). They sum up to ∼0.28 m s^–1. Afterward the sensor stabilized. We therefore did not include these “unstable” data into the further analysis. The subsequent stable records show at most a weak increasing deviation with pulse transit time. Both the VP and VP OEM coincide and show increasing deviations from the equation of state with shorter pulse transit times (higher temperatures).

Besides the initial instability of the SVX, the VP and VP OEM results were not satisfying with respect to the certified accuracy (Table I). Together with the systematics of the residuals, this motivated the recalibration. Whenever possible, calibration measurements were carried out simultaneously for all sensors. In a first approach, we applied the same equation w = A/(t−B) for calibration (third row in Fig. 5) as was originally done by the manufacturers. The systematic deviations which remained after applying the original calibration (second row) essentially persist with the new fit coefficients, at least for the MSV, VP, and VP OEM. This indicates that the relationship w = A/(t−B) does not satisfactorily describe the sensor behavior and needs improvement. Because of limited information about the construction and functioning of the sensors we did not attempt a more detailed physically based approach. Instead we fitted fourth-order polynomials to the data (fourth row in Fig. 5). With exception of the SVX, this resulted in a significant reduction of the standard deviations in the fits, leaving no significant systematic pattern in the residuals. Because our investigations comprise repeated measurements over a period of up to about 1.5 year, the standard deviations can be seen as overall reproducibility which includes possible small sensor drifts and variability because of experimental sources.

The working principle of the speed-of-sound determination using time-of-flight sensors can be described by the simple equation $w=2L/(t+δt)$⁠, where L is the distance between transducer and reflector, and t and δt are the measured time of flight and a time delay, respectively. The distance L should be seen as an effective parameter in which possible small path length changes due to the measurement conditions (especially temperature) are absorbed. By means of the elastic material properties, i.e., the thermal expansion (α) and the compressibility (β) of the sensor elements defining the sound path, the physical path length generally depends on temperature and pressure. Consequently, this would require a path length correction using an appropriate value for the coefficient α (and β if working under elevated pressure) (Benedetto et al., 2005b; Meier and Kabelac, 2006; Lin and Trusler, 2012). However, the materials used to construct the supports for the reflectors of the investigated units are chosen to minimize these effects. The total thermal expansion effect on the path length and therefore on the speed of sound over the (1 to 50) °C temperature interval of our measurements corresponds to less than 0.01 m s^–1 (7 ppm), assuming α = 1.3 × 10^–7 K^–1 for the carbon composite rods [Advanced Composites Manufacturing Centre (ACMC), Plymouth University, Plymouth, UK].

As our measurements are conducted at ambient pressure, the experimental pressure uncertainty u(p) is only given by the changes of the atmospheric pressure and the sensor immersion depth in the sample bath. Possible effects on the path length due to the compressibility of the sensor material and therefore on the sound speed would amount to <2 × 10^–5 m s^–1. The point is that besides their small magnitude, both effects are covered by our calibration in pure water.

Because of the dissolved salts, the speed of sound in seawater and in pure water is the same for temperatures differing up to ∼20 K (see Fig. 4). Therefore a systematic speed-of-sound offset exists because of the thermal expansion connected to this temperature shift when using pure water calibrated sensors in seawater. However, the effect is smaller than 0.004 m s^–1 (3 ppm) and therefore negligible.

The calibration also covers a possible time delay δt caused by the electronics, as well as time-of-flight shifts because of sound wave diffraction, and possible further unknown effects. The magnitude of the diffraction is determined by the sensor geometry and working frequency, and varies with the sound speed itself (Meier and Kabelac, 2006; Lin and Trusler, 2012). Because the geometry and frequency are fixed and because the sensors are calibrated in terms of time-of-flight (i.e., speed of sound), the diffraction effect is covered by the pure water calibration as well.

The relevant uncertainty contributions for speed-of-sound measurements in pure water (calibration) are summarized in Table II. They comprise the repeatability and resolution of the time of flight, the standard deviations of the polynomial fits for calibration, and the contributions from temperature and pressure readings during the calibration, which are typically u(T) = 2 mK and u(p) = 4000 Pa. For an evaluation of the speed of sound with respect to absolute values, the uncertainty associated with the equation of state of the calibration liquid (currently 50 ppm ≈ 0.075 m s^–1 in our case of IAPWS-95 and TEOS-10, respectively, for pure liquid water at ambient pressure) has to be taken into account. We did not specify this contribution in Table II, because it is separate from our sensor analysis and also subject to possible future changes of the reference equations.

The uncertainties due to experimental errors of temperature, pressure, and salinity in sample preparations of seawater or salt solutions have to be considered separately, because they are independent of the calibration. With sensitivities derived from the equations of state we estimated uncertainty contributions using representative values for u(T), u(S), and u(p), respectively. They are shown in Table III.

In a first step, we started with speed-of-sound measurements in solutions with single dissolved salts instead of seawater as a multi-component mixture. Solutions were prepared by dissolution of laboratory grade NaCl, MgCl₂ (as hexahydrate), and Na₂SO₄ (as decahydrate) in pure water. These salts constitute the main components in natural seawater. The speed of sound was then measured using the same setup as that for pure water. To account for salinity changes due to evaporation and possible contamination, we determined a representative relative value of 0.05% for the uncertainty of the salt concentrations as a conservative value, although the samples have been gravimetrically prepared with an initial uncertainty of 0.002 g kg^–1 (grams per kilogram of the solution). This estimate is based on conductivity records and covers the variability seen in repeated measurements at different stages of the measurement cycles in a certain sample.

Figure 6 summarizes the results which are also listed as values relative to pure water in Tables IV–VI. For NaCl and MgCl₂ the speed-of-sound data relative to pure water (w−w_pure) document the expected increase with salt concentration. Whereas the absolute speed of sound always increases with temperature (see Fig. 4), the difference to pure water values shows a decrease. The lower rows in Fig. 6 show differences in the measured speed of sound to values calculated with the existing equations of state given by Millero et al. (1987) (w−w_Mi87) for the same temperature and salt concentrations. This representation provides an appropriate scale which helps to focus on the variations of interest of the measured sound speeds with T and S and among the different sensors and, secondarily, on the relation of the results to reference values from the literature. The error bars represent the combined standard uncertainties given in Tables II and III.

At higher temperature and salinity, the values for the NaCl solutions partly exceed the calibration range (∼1550 m s^–1), which is indicated by enlarged error bars.

For the NaCl results, deviations are obvious, becoming larger with increasing sound speed (decreasing time of flight) and increasing salt concentration. Considering the MSV sensor only, the amplitude is ∼0.4 m s^–1 (compare data for S = 9.997 g kg⁻¹ and S = 34.999 g kg⁻¹ at large w). Furthermore, differences to simultaneously measured data with a different sensor are existent (MSV and VP, S = 23.979 g kg^–1 NaCl, open symbols).

The inconsistency among the sensors found for different NaCl solutions resembles those of the S = 4.714 g kg^–1 and S = 13.335 g kg^–1 MgCl₂ solutions. Whereas the VP and VP OEM sensors coincide as already observed during calibration in pure water, the MSV again differs toward higher values, increasing both with temperature (speed of sound) and concentration. The SVX in turn shows an offset toward lower values (13.335 g kg^–1 MgCl₂). These patterns reveal a strongly systematic cause which is obviously not covered by the simultaneous calibration of the sensors. They also clearly exceed the known uncertainties discussed in the uncertainty section.

For the Na₂SO₄ solution a single data set at only one salt concentration was measured with the MSV (right column of the upper panel). It supports the finding that the variability within all data sets as well as the differences to the reference data are not particularly sensitive to the certain solute species. The apparent increase with temperature, which is present for most of the other results, is absent here, suggesting that this is not necessarily attributable to the sensor.

For an absolute comparison with the equations of Millero et al. (1987), the comparatively large standard deviations of their fits (dashed lines in Fig. 6) have to be considered. Agreement at a level of 200 ppm or better can then be stated for the S = 9.997 g kg^–1 NaCl, the major part of MgCl₂, and for the Na₂SO₄ solutions.

Taking into account the variability of temperature, pressure, and salt concentration (Table III), the high precision of the sensors as seen for pure water essentially holds for salt solutions. This can be stated from successive records under virtually identical conditions as well as from a repetition of measurements in newly prepared samples.

The speed of sound in seawater was measured in two unfiltered samples of North Atlantic water (NA I and NA II), taken in the summer of 2012 and the spring of 2013 near Madeira, and in dilutions of these samples with pure water. The practical salinities S_P [in the sense of dimensionless practical salinity units (PSU); Perkin and Lewis, 1980] calculated from conductivity measurements were S_P = 36.574 ± 0.050 and S_P = 36.208 ± 0.010, and S_P = 16.660 ± 0.030 and S_P = 7.765 ± 0.007 for the dilutions, respectively. For measurements and dilution procedures, the samples were directly transferred from the sample cans (100 l) into the 55 l thermostat volume. The motivation for speed-of-sound measurements in diluted samples was the same as for the salt solutions, i.e., to identify possible speed-of-sound deviations of the different sensors which are apparently related to salinity. Although the use of commercially available Standard Seawater with certified conductivity or salinity would in principle have been more appropriate from the metrological point of view, this was not considered for cost reasons because of the large required sample volumes in our setup.

The measurement results are summarized in Fig. 7 in the same format as for salt solutions (Fig. 6) and are listed as values relative to pure water in Tables VII–IX. As reference we chose the TEOS-10 equation for sound speed in seawater. Each sample was measured with at least three of the sensors, in most cases simultaneously.

The overall pattern of the seawater results resembles that of the salt solutions: Besides the coincidence of the VP and VP OEM sensors in all samples, the measurements reveal a high reproducibility of all sensors within the range of the quantified uncertainties. However, again systematic deviations occur among the MSV, VP, and SVX sensors with increasing sound speed, i.e., with temperature. Also, an increasing difference between the MSV and both VP sensors with increasing salinity at least at higher speed-of-sound values can be stated when comparing the results from the diluted samples and the original ones. Most of these deviations exceed the calculated uncertainties. The difference between the SVX and the VP sensors amounts at maximum to ∼0.35 m s^–1 (230 ppm).

The deviations of the speed-of-sound results of different sensors after simultaneous calibration in pure water substantiate the existence of systematic effects. They are probably caused by different properties of the manufacturer's specific methods of signal analysis for the time-of-flight determination. The methods might to a different extent be sensitive to phase shifts or amplitude changes in conjunction with slight changes in the oscillation characteristics of the piezoelectric transducer, with the sound coupling to the sample liquid, or with different sound attenuation in saltwater and pure water. A significant temperature sensitivity of the electronic circuits can be excluded. The outputs at simultaneous measurements coincide for the VP and VP OEM sensors, although the VP housing containing the electronics felt the sample temperature whereas the electronic board of the VP OEM (as well as the board of the SVX) was outside the bath at room conditions.

As we could not access and evaluate the built-in procedures and because we did not apply our own signal processing within this study, we treated these discrepancies as an additional source of uncertainty. The use of a self-developed procedure for time-of-flight determination applied to both sensors types (i.e., not using the manufacturer electronics) may help to recover the inconsistencies and to further reduce the uncertainty. This is part of the continuing activities.

The level of the sound speed deviations clearly exceeds the combination of the known uncertainty contributions (Tables II and III). Therefore, the maximum difference found between VP (or VP OEM) and SVX derived sound speeds may give an indication of the overall uncertainty of speed-of-sound measurements at atmospheric pressure using modern digital time-of-flight sensors. Because of its obsolete technique, the analogue MSV sensor is of declining importance for oceanographic practice. Therefore, we did not include its results in this final uncertainty assessment, as well as in the following discussion.

In spite of the observed systematic differences up to 0.35 m s^–1 (230 ppm), the results of the modern sensors (VP, VP OEM, and SVX) are consistent with values from TEOS-10 and therefore of Del Grosso (1974) within about 0.3 m s^–1 (200 ppm). This is valid for the two original Atlantic samples with salinities representative for seawater (36.747 g kg^–1 and 36.379 g kg^–1), at least for the major part of the measured range at sound speeds lower than ∼1560 m s^–1 (see Fig. 7). Note that the uncertainty of the Del Grosso (1974) formula is 0.05 m s^–1, indicated with dashed lines. Our uncertainty estimate is supported by this consensus, particularly because sound speed calculated from TEOS-10 is expected to be most reliable in the vicinity of the standard salinity (35.165 g kg^–1).

The results at sound speeds exceeding about 1560 m s^–1 (i.e., exceeding ∼40 °C for our measurements) indicate a closer inspection. In this context, a demonstrative decline is confirmed by all sensors in both original Atlantic samples. Assuming the validity of the overall uncertainty estimate, the sound speed deviation from TEOS-10 seems to show significance. This might provide evidence of an enhanced deviance of TEOS-10 in that range. A similar argumentation might be appropriate for our results in the diluted seawater samples (16.738 g kg^–1 and 7.801 g kg^–1): The obvious tilt of the data courses (i.e., in terms of temperature) relative to TEOS-10 in both samples (Fig. 7) also may reflect significant deviations. We confirmed this with a third record in a sample of diluted Standard Seawater (OSIL, Havant, UK) with S_A = 17.893 g kg^–1 (not shown).

The restricted range of the measurements of Del Grosso (1974) [T = (0 to 35) °C, S_A = (29 to 43) g kg^–1 at atmospheric pressure], which is the speed-of-sound data base for the respective TEOS-10 formula (Feistel, 2008), should be considered as part of an explanation. On the basis of recent data combined with earlier studies, Millero and Huang (2011) published equations for sound speed in seawater at atmospheric pressure covering the temperature and salinity range of our study. We therefore also compared our results to values calculated with their expression for the temperature range of (0 to 95) °C (Fig. 8). It shows that the decline as well as the tilt are clearly less pronounced (compare to Fig. 7). Although our data equally fit both equations in the original seawater samples at temperatures <40 °C, we see confirmation of our conclusion of enhanced deviations of the TEOS-10 sound speeds at higher temperatures and in the diluted samples.

The primary intention of our investigations was to test the capabilities of the time-of-flight sensors as instruments for routine practice of in situ sound speed measurements. Beyond the introduction of the time-of-flight approach by Eaton and Dakin (1996) (Applied Microsystems Ltd., Sidney, BC, Canada) and a study focusing on the calibration of such an analogue time-of-flight sound velocimeter in seawater at atmospheric pressure and discussing pressure effects from an at-sea test by Sweeney et al. (2006), no metrologically oriented and manufacturer-independent study on state-of-the-art digital time-of-flight sensors for oceanography is available to our knowledge. We see the results as the first step of a thorough characterization which illustrates and substantiates the potential of digital time-of-flight sensors as a routine tool in oceanographic research; however, it also discloses the current limitations when used as delivered by the manufacturers.

With the estimated uncertainty level of our measurements after extended recalibration in pure water, we cannot confirm a deviation from the recent TEOS-10 sound speed output at atmospheric pressure and salinities around Standard Salinity (S_P = 35). However, at sound speeds (temperatures) exceeding the oceanic range as well as for diluted seawater we could reproduce significant systematic deviations which might indicate a degree of inconsistency on the part of TEOS-10 in those ranges.

The next step will need to extend the laboratory investigations on time-of-flight sensors to elevated pressures according to oceanic conditions by mounting the OEM units in an appropriate pressure vessel for the samples.

With their design optimized for seawater, the sensors are also interesting for studies under laboratory conditions as complementation or alternative to established pulse-echo methods, for which measurements in electrically conductive and highly corrosive liquids like seawater are generally connected with considerable experimental difficulty. Although their application is restricted with respect to temperature in favor of their stability in seawater, the speed of sound should in principle also be measurable with improved accuracy in a number of other liquids.

We thank S. Weinreben and R. Feistel at the Leibniz Institute for Baltic Sea Research in Rostock-Warnemünde (Germany) for supplying the Atlantic seawater samples and support with salinity measurements (S. Weinreben), and for the technical discussion (R. Feistel). We also thank the two reviewers for their thoughtful comments which helped to improve the manuscript. This research was undertaken within the project EMRP ENV05. The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union.