A data processing method to obtain high-quality data from an expendable conductivity–temperature–depth (XCTD) profiler is proposed. By adjusting the mismatch of the response time of the temperature and conductivity sensors, systematic error (on the order of −0.05) in XCTD salinity data can be eliminated from regions having a strong vertical temperature gradient (>0.2°C m−1), such as the main thermocline of the nearshore side of the Kuroshio axis and the seasonal thermocline of the subarctic North Pacific. The systematic errors in XCTD depth and temperature data from two cruises were evaluated by comparing the CTD and XCTD data taken simultaneously during each cruise. The XCTD depths were in good agreement with the CTD depths from one cruise, but depth-dependent depth errors from the other cruise were found. The cause of the depth error is unknown but may have occurred because the terminal velocity for the XCTD probes was much less (−0.0428 m s−1) than that provided by the manufacturer for the later cruise. The results suggest that XCTD and expendable bathythermograph (XBT) observations may have a similar depth error because XBT and XCTD do not have pressure sensors, and therefore depth is inferred from the fall rate of the probe. Systematic positive biases (0.018°C on average) were found in XCTD temperature data. The viscous heating effect may contribute to the thermal bias because flow past the XCTD temperature probe is relatively fast (>3 m s−1). Evaluation of XBT/XCTD data by using simultaneous CTD observations data is valuable for validation of statistical corrections of the global XBT/XCTD dataset.
Since the 1960s, the expendable bathythermograph (XBT) has been widely used globally to measure upper-ocean thermal structures (e.g., Wijffels et al. 2008); and since the 1990s, upper-ocean salinity structures have been measured by using an expendable conductivity–temperature–depth profiler (XCTD) (e.g., Johnson 1995; Uehara et al. 2008). Although XBT/XCTD data can be easily collected from research vessels and other ships on a voluntary basis, systematic errors can be a problem because the XBT and XCTD do not have pressure sensors, and therefore depth is inferred from the fall rate of the probe, which can be biased (e.g., Hanawa et al. 1995; Johnson 1995; Kizu et al. 2008; Wijffels et al. 2008; Ishii and Kimoto 2009; Gouretski and Reseghetti 2010). In addition, postcruise calibration of temperature and conductivity sensors is not possible for expendable instruments. For example, Gouretski and Koltermann (2007) suggested that the global XBT dataset has a time-varying warm bias. Some models correcting the global XBT dataset appear to fit the data well with a time-dependent fall-rate error alone (Wijffels et al. 2008; Ishii and Kimoto 2009), while other models appear to require a time-independent fall-rate error along with a temperature- and a time-dependent temperature bias (Gouretski and Reseghetti 2010).
Furthermore, a need for the adjustment of the mismatch in the response time of the temperature and conductivity sensors was pointed out for early XCTD probes in a pioneer study of evaluation of XCTD performance (Sy 1993), and similarly for conductivity–temperature–depth profiler (CTD) instruments (e.g., Fofonoff et al. 1974; Gregg and Hess 1985; Johnson et al. 2007). However, Sy (1998) reported that the time-lag problem was not detected for recent XCTD probes. Mizuno and Watanabe (1998) also concluded that the response time of the XCTD temperature and conductivity sensors agreed with each other because salinity spikes were inconspicuous, although the XCTD data used in their study were collected in the subtropical and tropical ocean where vertical temperature gradients are relatively weak. Therefore, few studies of evaluation for the mismatch in the response time of the XCTD temperature and conductivity sensors have been done.
To use XBT/XCTD data for climate change research, we must apply data processing and quality control measures that go beyond the manufacturer’s specifications (Table 1). In this study, we propose a data processing method for obtaining high-quality XCTD data. The method eliminates systematic error in XCTD salinity data that is due to the mismatch of the response time of the temperature and conductivity sensors. We also evaluated systematic errors in XCTD depth and temperature data by comparing XCTD data to simultaneously measured CTD data.
We used Tsurumi-Seiki (TSK; Kanagawa, Japan) XCTD-1 and XCTD-2 probes for this study. The TSK XCTD uses an inductive conductivity sensor and thermistor, and details of the XCTD system are described in Mizuno and Watanabe (1998). The fall-rate equation provided by the manufacturer was used to infer depth Z (m),
where t is the elapsed time in seconds from probe entry into the water, and a (terminal velocity) and b (acceleration) are the empirical coefficients (Mizuno and Watanabe 1998; Koso et al. 2005; see also Table 2). The data sampling interval was 0.04 s.
XCTD data were obtained in the Pacific Ocean (Fig. 1) during the Research Vessel (R/V) Hakuho-maru cruise KH-02-3 leg 1 [15–20 September 2002; see Uchida et al. (2008)], and the R/V Mirai cruises MR07-04 [12–14 August 2007; see Kawano et al. (2009)] and MR09-01 legs 1 and 2 [21 April–14 June 2009; see Uchida et al. (2011)]. XCTD data were acquired with the MK-130 data acquisition system (Tsurumi-Seiki) for the KH-02-3 and MR09-01 cruises and with the MK-100 data acquisition system (Tsurumi-Seiki) for the MR07-04 cruise.
We used a Sea-Bird Electronics (SBE; Bellevue, Washington) 9plus CTD system as the comparative system on these cruises. Accuracy of the CTD data is about an order of magnitude higher than the accuracy of the XCTD data, making the CTD data a valuable benchmark. The CTD pressure sensors were calibrated before each cruise against a dead-weight piston gauge (Bundenberg Gauge, Manchester, United Kingdom), and the CTD temperature sensors were calibrated in situ against a Sea-Bird Electronics (SBE 35) deep ocean reference thermometer (Uchida et al. 2007) for the R/V Mirai cruises. For the R/V Hakuho-maru cruise, the CTD pressure and temperature sensors were calibrated before the cruise by the manufacturer. The CTD salinity data were corrected using the in situ water sample data. Salinity measurements for the water samples were conducted with a Guildline Autosal model 8400B salinometer (Guildline Instruments, Smiths Falls, Ontario, Canada) for the R/V Mirai cruises and with a Guildline Portasal model 8410A salinometer for the R/V Hakuho-maru cruise. The salinometers were standardized with the International Association for Physical Science of the Ocean (IAPSO) Standard Seawater from batches P142, P148, and P150 for the cruises KH-02-3, MR07-04, and MR09-01, respectively. The batch-to-batch differences in recent batches from P130 to P150 of the Standard Seawater were less than 0.001 (Kawano et al. 2006).
Simultaneous observations using the XCTD and CTD probes were carried out during cruises KH-02-3 and MR09-01, except for the easternmost five casts of cruise MR09-01. The XCTD probes were usually launched about 10 min after the start of CTD measurements. For cruise MR07-04, XCTD observations were carried out between the CTD stations. CTD data averaged over 1-dbar intervals were used for comparison with the XCTD data.
3. Data processing
a. Data processing sequence
Processing and quality control of the XCTD data were based on a method described in Uchida and Imawaki (2008) with slight modification. The data processing sequence used in the reduction of XCTD data was as follows:
Raw temperature and conductivity data from the first 32 scans (about 4.3 m) of the XCTD data were deleted to remove the effect of the start-up transient change (Kizu and Hanawa 2002) of XCTD measurements. Data were also deleted after the probe made contact with the bottom, judging from the abrupt shift of the conductivity data. Spikes in the temperature and conductivity profiles were manually removed. Gaps caused by the deletion of data were linearly interpolated when the data gap was ≤15 scans (about 2 m).
Temperature and conductivity data were low-pass filtered using a Hamming filter with a window of 19 scans (about 2.4 m).
Conductivity data were advanced by 1.1 scans (about 0.15 m), instead of 2 scans, as described in Uchida and Imawaki (2008), relative to the temperature data to correct the mismatch in the response time of the sensors.
Salinity was calculated from pressure, temperature, and conductivity data. The pressure data were calculated by using the relation between hydrostatic pressure and depth.
The data were linearly interpolated and subsampled at 1-dbar or 1-m intervals.
Salinity biases of the XCTD data were estimated by comparing temperature and salinity relationships in the deep ocean obtained from the CTD and XCTD data, and the estimated salinity biases were subtracted from the original XCTD salinity data.
The characteristics of the XCTD data regarding the data processing procedures for steps 2–4 and 6 above are described in detail in the following subsections.
b. Noise reduction
The manufacturer’s data processing software interpolates and samples XCTD temperature and salinity data at 1-m intervals to reduce the size of the dataset. Salinity data are low-pass filtered using the running mean filter with a window of 13 scans (about 1.7 m) before interpolation to reduce salinity noise. However, distinct spectral spikes are present in not only conductivity profiles but also temperature profiles at frequencies of 5 and 10 Hz, corresponding to one and two cycles per five scans (Gille et al. 2009). Low-pass-filtered data using the filters of Gille et al. (2009) are biased (1 mK for temperature and 0.01 for salinity) because the sum of the coefficients does not equal 1 because of round-off errors in the reported filter coefficients. All of the coefficients should be multiplied by a factor of 0.9997 (1.0003) for the 21 (11)-point filter to eliminate the biases. Although the filters of Gille et al. (2009) can remove the anomalous spikes from the XCTD temperature and conductivity data, the XCTD data are still noisy compared to the CTD data averaged over 1-dbar intervals. Using a Hamming filter with a window of 19 scans for both the XCTD temperature and conductivity data can effectively remove the anomalous spectral spikes and noise (Fig. 2). The standard deviation (SD) of the differences in XCTD salinity interpolated onto temperature surfaces at 1-dbar intervals and CTD data was 0.0065, 0.0041, and 0.0028 for the raw data, data with the anomalous spikes removed, and data subjected to a low-pass filter by using a Hamming filter with a window of 19 scans, respectively, for a temperature range between 4.5° and 12.0°C.
c. Correction of mismatch in response times
Time constants of the XCTD temperature and conductivity sensors were reported to be the same (0.1 s or less; see Mizuno and Watanabe 1998). However, temperature–salinity profiles measured by the XCTD often show a loop shape in the main thermocline resulting from a mismatch in the response times of the sensors (label L in Fig. 2). This mismatch was examined by using the XCTD data obtained from the nearshore side of the Kuroshio axis during cruise KH-02-3 (Fig. 1). Conductivity is strongly dependent on temperature, so these two variables are generally well correlated in the ocean. The conductivity sensor will always lead the temperature sensor by about one scan. The differences in sensor response times are just more noticeable in regions of strong vertical temperature gradients (Fig. 3). This slight mismatch in the response times causes a large artificial fluctuation in the calculated salinity data (about 0.05) that is not seen in the CTD salinity data (Fig. 4). Although often sensor responses can be better matched by sharpening temperature for the CTD sensor (Johnson et al. 2007), the noise of the calculated salinity data tends to be increased by instrument noise (Fofonoff et al. 1974). In this study, the mismatch was compensated for by advancing the conductivity data in time relative to the temperature data. For this example, the correlation coefficient between the high-pass-filtered conductivity and temperature data between 10- and 700-m depth was highest (0.995 87) after advancing the conductivity data by 1.375 scans. The lag that maximizes the correlation was examined for the 60 XCTD profiles used in this study (Fig. 5) and the optimal lag was estimated be 1.1 scans on average. The advance of 1.1 scans simply resulted in less artificial fluctuation in the calculated salinity data (Fig. 4). The corrected conductivity data (C′) at a scan number i can be calculated from the following equation:
where C is the original conductivity data. To check the correction, we analyzed 512-point segments (170–239 dbar) of raw temperature and conductivity data from the 60 XCTD profiles, similar to Johnson et al. (2007). The mean-squared coherence was slightly improved (on the order of 0.01) and the spectral phase came close to 0 at region around 0.15, 0.3, and 0.5 Hz (with vertical wavelengths of around 23, 11, and 7 dbar).
Using the example of the nearshore side of the Kuroshio axis, the salinity error caused by the mismatch in response times is obvious from the XCTD data by examining the density inversions (loop shapes of the temperature–salinity profile). For the subarctic North Pacific, however, the salinity error is found in the seasonal thermocline without density inversions. Because simultaneous collocated CTD observation was not carried out for cruise MR07-04, the temperature–salinity profiles from the XCTD and CTD observed at neighboring stations were compared (Fig. 6). In the region of a strong vertical temperature gradient (>0.2°C m−1) between 20- and 40-m depth, the XCTD salinity was systematically lower than the CTD salinity observed at neighboring stations (Fig. 6a). The temperature–salinity profiles from the XCTD data corrected for the mismatch of the response time showing almost straight lines between 20- and 100-m depths, similar to the CTD data, as might be expected from vertical mixing in the seasonal thermocline (Fig. 6b). The difference in the average salinity from the surface to 100-m depth between the original and corrected XCTD data was −0.015 for both of the XCTD profiles in Fig. 6 and −0.014 ± 0.0011 (SD) for the 17 XCTD profiles obtained during cruise MR07-04 (Fig. 1), and it became small with depth (−0.005 ± 0.0007 from 100- to 200-m depth and −0.001 ± 0.0003 from 200- to 300-m depth). Although the magnitude of the error is smaller than the manufacturer’s specification (0.042; Table 1), it is one-quarter of the surface layer salinity change (−0.057) recorded in the subpolar North Pacific during recent decades (Hosoda et al. 2009), so this systematic error must be removed for climate change research.
d. Salinity calculations
For the TSK MK-100 data acquisition system, salinity is calculated erroneously using depth instead of pressure. Because the pressure is about 1% greater than the depth at depths less than 1000 m, a depth-dependent systematic error (about +0.005 at 1000-m depth) exists in the salinity data from the MK-100. Although the magnitude of the error is again much less than the manufacturer’s specification (Table 1), it is much greater than the observed salinity change (0.002) in the eastern South Pacific Antarctic Intermediate Water between 1992 and 2003 (Schneider et al. 2005), and this systematic error must also be removed for climate change research.
Hence, for data collected with the MK-100, the XCTD salinity is recalculated using pressure estimated from the XCTD data and location (latitude) as follows:
where P is pressure; ρ is density; g is gravitational acceleration; ρ is a function of pressure, temperature, and salinity; and g is a function of pressure and latitude (Fofonoff and Millard 1983). At the sea surface, P0 and Z0 are zero. Temperature and conductivity data for just beneath the sea surface were assigned the same values as the shallowest valid data. For the calculation of ρi+1 and gi+1, the pressure of Pi was used as an approximation because the error induced by this approximation is negligible. XCTD salinity was calculated from the estimated pressure, temperature, and conductivity by using a reference conductivity of 42.896 mS cm−1 corresponding to a salinity of 35, temperature of 15°C, and pressure of 0 dbar. This reference conductivity value is used in the manufacturer’s data processing software. The MK-130 system correctly uses pressure for calculating salinity, so no such correction is required for data collected using the MK-130.
e. Offset correction of salinity data
For the deep ocean, changes in salinity in time and space may often be much smaller than the XCTD salinity error, and the XCTD salinity offset correction is effective in such cases. If temperature–salinity relationships are known, or appropriate CTD data are available for the observed region, then the XCTD salinity data can be corrected with sufficient accuracy, assuming that the XCTD temperature data are accurate enough (Itoh and Shimada 2003; Uchida and Imawaki 2008). For the XCTD salinity data used in this study, salinity offset errors were estimated from tight relationships between temperature and salinity obtained from the CTD data (Table 3). The temperature–salinity relationship for the XCTD-2 data was taken at a temperature of 2.5°C, and the XCTD-1 data obtained from KH-02-3, MR07-04, and MR09-01 cruises were at temperatures of 14.1°, 2.75°, and 4.5°C, respectively. The difference in salinity at the reference temperature between the XCTD and CTD data was defined as the bias of the individual XCTD data and subtracted from the XCTD salinity profile. In the absence of contemporary CTD data, a salinity correction method using climatological temperature–salinity relationships similar to the more sophisticated method developed for autonomous CTD profiling floats (Wong et al. 2003; Böhme and Send 2005) might be useful. The bias-corrected XCTD data should be used for climate change research.
4. Evaluation of the XCTD errors
a. Depth error
Biases in estimated XCTD depth can make a significant contribution to data errors from these instruments. Although global statistical studies with large numbers of probes have attempted, with some success, to remediate XBT depth errors (e.g., Gouretski and Reseghetti 2010), the best way to assess the depth error in XCTD data is to conduct side-by-side comparisons with CTD data using a temperature error-free method as documented in previous studies (e.g., Hanawa et al. 1995; Kizu et al. 2008). The errors in XCTD depth data were examined by using side-by-side XCTD and CTD data obtained from cruises KH-02-3 and MR09-01. To remove any biaslike temperature error, the large-scale temperature structure, and small-scale noise, the individual temperature profiles of XCTD and CTD pairs were bandpass filtered by subtracting temperature profiles that were low-pass filtered by the running mean filter with a window of 81 m from those with a window of 31 m (Fig. 7). The obtained high-wavenumber temperature profiles of the XCTD and CTD pairs have a similar pattern, although differences in depth (e.g., about 20 m at 1600-m depth) are evident in the profiles from cruise MR09-01.
We assumed that the XCTD depth error is constant over a range of ±100-m depth, and we estimated the XCTD depth bias that maximized the correlation coefficient between the CTD and XCTD bandpass-filtered temperature within a specified depth range (±100 m) at 100-m intervals. The estimated depth biases were averaged for each depth, cruise, and probe type (Fig. 8). Although the results for cruises KH-02-3 and MR09-01 are within the manufacturer’s specifications, the XCTD depths for cruise MR09-01 were significantly underestimated for both XCTD-1 and XCTD-2 (Fig. 8b). If the error is caused by a discrepancy between coefficient a in the fall-rate equation and true terminal velocity, the error of coefficient a can be estimated from the regression line. The estimated error of the terminal velocity was −0.0428 m s−1 for cruise MR09-01.
As a check on the XCTD depth error, grounding depths of the XCTD were compared with bottom depths measured by the ship’s multiple narrowbeam echo sounder during cruise MR09-01 (Uchida et al. 2011). The echo sounding data were corrected by using sound velocity profiles calculated from the CTD data, and the data were gridded with a resolution of 0.001 25° (about 133 m) for both longitude and latitude and then interpolated for the location where the XCTD was deployed (Fig. 9). Differences between the grounding depth of the XCTD and the echo sounding depth were similar to the differences between the grounding depth of the XCTD and the bottom depth estimated from the maximum depth of the CTD plus the height above the bottom as measured by the altimeter attached to the CTD package. These differences were consistent with the depth error of the XCTD (Fig. 8).
b. Thermal bias
Thermal biases in XCTD temperature can also make a considerable contribution to data errors from these instruments as suggested by Gouretski and Reseghetti (2010). Differences of temperature on pressure surfaces were examined by using side-by-side XCTD and CTD data obtained from MR09-01 and KH-02-3 (Fig. 10). For cruise MR09-01, the XCTD data were corrected for the depth error by using the estimated terminal velocity. Although the difference was not significant for shallow water (<1000 dbar), in which vertical gradient of temperature was strong systematic warm biases were found in both cruises below the thermocline. Average thermal biases below 1100 dbar were 0.016°C for MR09-01 and 0.019°C for KH-02-3. These biases are just within the manufacturer’s error specifications.
In this study, we propose a data processing method for obtaining high-quality XCTD data. We statistically evaluated the mismatch in the response time of the XCTD temperature and conductivity sensors, which was not taken into consideration in previous XCTD data processing methods. By adjusting the mismatch of the response time, systematic error (on the order of −0.05) in XCTD salinity data can be eliminated in a region having a strong vertical temperature gradient (>0.2°C m−1).
Perhaps the most problematic result of this study is the statistically different fall rates estimated for XCTDs on two different cruises presented in section 4. While these depth errors are within manufacturer’s specifications (Table 1), they are problematic for climate research. There are a number of possible reasons for these, including 1) differences in physical characteristics of the probes and 2) differences in ambient conditions.
Regarding differences in physical characteristics of the probes, nonuniformity in weight of the XCTD probes may change the terminal velocity of the probe. Assuming that the terminal velocity error is caused by a weight discrepancy between the actual weight of the probe and the weight specified by the manufacturer, the weight discrepancy is calculated to be about 8–9 g less than the normal probe in seawater by using a bulk dynamic model for a vertically falling probe (Green 1984). However, all of the XCTD probes were weighed in air by the manufacturer before they were shipped (Tsurumi-Seiki 2009, personal communication) and were listed as 1068 ± 1 g for XCTD-1 and 1076 ± 1 g for XCTD-2. Moreover, the XCTD-1 probes produced in 2003 and the XCTD-2 probes produced in 2008 showed a similar depth error, suggesting that the depth error is not caused by nonuniformity of the products.
Regarding differences in ambient conditions, differences in the ambient water temperature may change the terminal velocity by changing the viscous drag. Temperature-dependent coefficients for the XCTD have been proposed by Kizu et al. (2008). However, the difference between the original depth data for the XCTD obtained during cruise MR09-01 and the depth calculated by using temperature-dependent coefficients of the fall-rate equation proposed by Kizu et al. (2008) is less than 4 m. Moreover, ambient temperature profiles for cruise MR09-01 and KH-02-3 are similar (Fig. 10a). Therefore, the depth error cannot be explained by differences in the ambient temperature. In addition, the terminal velocity for the XCTDs deployed during cruise MR09-01 must be less than that during cruise KH-02-3 because gravitational acceleration is less in lower latitudes. However, the difference (−0.0015 m s−1) in the terminal velocity caused by the difference in the gravitational acceleration is much less than the terminal velocity error (−0.0428 m s−1) estimated in section 4a.
The problem of systematic thermal biases (+0.018°C on average) of the XCTD temperature data are also serious for climate research, although the errors are within manufacturer’s specifications (Table 1). Because viscous heating occurs for any flow past the temperature probe (Larson and Pedersen 1996; Uchida et al. 2007), this effect may contribute to the thermal biases because flow past the XCTD temperature probe is relatively fast (>3 m s−1). However, it would require much more thermal sensitivity on the XCTD thermistor to viscous heating than either the SBE 3 thermometer or the temperature correction to approach 0.018°C at a fall rate of 3 m s−1 (Larson and Pedersen 1996). Similar systematic thermal biases in XBT temperature data were estimated from a global statistical study (Gouretski and Reseghetti 2010); error-weighted mean thermal bias was +0.017°C for the XBT T-7 and Deep Blue data and +0.016°C for the T-4 and T-6 data after 1990. Salinity calculated from the XCTD data can be biased (by about −0.02) due to the thermal biases (+0.018°C on average). The XCTD salinity offset errors (Table 3) estimated from the temperature–salinity relationship were consistent with the salinity biases because of the thermal biases, except for cruise KH-02-3 whose standard deviation of the estimated salinity biases was relatively large.
Although the systematic depth and temperature errors are less than the manufacturer’s specification, they must be taken into consideration for climate change research. The steric height error between 0 and 1800 dbar caused by the depth error was about −1 cm, and the steric height error caused by the thermal bias (0.018°C) was about +3 cm when the offset correction of salinity data was not applied, although it was about +0.5 cm when the offset correction was applied. The magnitude of these steric height errors is comparable to the magnitude of the steric height rise over a decade (2.8 ± 0.9 cm) south of Japan (Uchida and Imawaki 2008). However, more work is needed to clarify the cause of the systematic depth error of the XCTD for cruise MR09-01 and the systematic thermal biases. A common systematic thermal bias, such as viscous heating of the thermistor, should be corrected, along with any pressure error, before recalculating salinity for step 4 of the data processing procedures presented in section 3a. In future studies we must keep in mind that XBT/XCTD observations may have similar depth errors and that simultaneous CTD observations are the most appropriate method to evaluate these errors and valuable for validation of corrections of the global XBT/XCTD dataset.
We are grateful to the technicians of Global Ocean Development, Inc., who conducted the XCTD and the multiple narrowbeam echo sounder observations during cruise MR07-04 and MR09-01, legs 1 and 2. The XCTD observations during cruise KH-02-3 leg 1 were jointly carried out by Shiro Imawaki (Japan Agency for Marine-Earth Science and Technology), Kaoru Ichikawa (Research Institute for Applied Mechanics, Kyushu University), Tomowo Watanabe (National Research Institute of Fisheries Science, Yokohama, Japan), and Tsurumi Seiki. We also thank two anonymous reviewers for valuable comments, which improved the paper considerably.