Abstract

The uncertainty of deep ocean temperature (~1°C) measurement was evaluated. The time drifts of six deep ocean standards thermometers were examined based on laboratory calibrations as performed by the manufacturer in triple point of water (TPW) cells and gallium-melting-point (GaMP) cells. The time drifts ranged from −0.11 to 0.14 mK yr−1. Three of the six thermometers were evaluated at the National Metrology Institute of Japan in five TPW cells and a GaMP cell, and the temperature readings agreed with the realized temperature of the national standard cells of Japan within ±0.14 and ±0.41 mK for TPW and GaMP, respectively. The pressure sensitivities of the deep ocean standards thermometers were estimated by comparison with conductivity–temperature–depth (CTD) thermometers in the deep ocean, and no notable difference was detected. Pressure sensitivities of the two CTD thermometers were examined by laboratory tests, and the results suggest that the deep ocean standards thermometers have no pressure sensitivity, at least up to 65 MPa. The position and attitude motion of the CTD system can affect temperature and salinity data quality. The overall expanded uncertainty of the deep ocean temperature measurement (up to 65 MPa) by the CTD thermometer calibrated in reference to the deep ocean standards thermometer is estimated to be 0.7 mK.

1. Introduction

The earth’s climate system is driven by energy from the sun, and the ocean’s central role in the climate system results from its great capacity to store and transport heat. Recent high-quality land-to-land global hydrographic observations have revealed bottom water warming along the pathway of the deep-water circulation only around 2 mK decade−1 in the North Pacific (Fukasawa et al. 2004; Kawano et al. 2010) and around 30 mK decade−1 in the Southern Ocean closer to the source region of the deep water (Purkey and Johnson 2010; Rhein et al. 2013). A supercomputer simulation has shown that surface warming events in the Southern Ocean may cause significant changes in the North Pacific deep waters in only 4 decades (Masuda et al. 2010). Heat content changes below 3000-m depths are estimated to be 8%–20% of those in the upper layer (typically the upper 700-m depths), suggesting that the heat content changes below 3000-m depths cannot be neglected in the precise estimation of heat content changes in the global ocean (Kouketsu et al. 2011). For quantitative evaluation and monitoring of these slight temperature changes by the decadal repeat hydrographic observations, the temperature should be measured with a 1-mK level of uncertainty, which allow us to estimate the temperature difference between the two observations with 1.4 mK of uncertainty. Furthermore, the General Conference on Weights and Measures [Conférence Générale des Poids et Mesures (CGPM)], which is the supreme authority under the Meter Convention (BIPM 2010), recommends that all measurements used to make observations that may be used for climate studies are made fully traceable to the International System of Units (SI units).

For such high-quality hydrographic measurements, the SBE 9plus conductivity–temperature–depth (CTD) system (Sea-Bird Electronics, Inc., Bellevue, Washington) is widely used (Swift 2010). In the deep ocean, however, the SBE 9plus CTD system measures temperatures that may be higher than their actual values due to pressure sensitivity (~2 mK at 60 MPa) (Budeus and Schneider 1998; Uchida et al. 2007) and viscous heating (~0.5 mK) of the thermometer (Larson and Pedersen 1996; Uchida et al. 2007). These systematic errors, including the time drift of the thermometer [SBE 3, a negative temperature coefficient (NTC) thermistor (CTD thermometer)], can be corrected relative to a deep ocean standards thermometer (SBE 35, an NTC thermistor (reference thermometer)] (Uchida et al. 2007; McTaggart et al. 2010). The reference thermometer is an ultrastable aged thermistor with the unique ability to be used both in fixed-point cells and in the ocean at depths up to 6800 m (about 70 MPa). However, the pressure sensitivity of the in situ reference thermometer has not yet been examined. In addition, although the manufacturer conservatively claims that the initial accuracy of the reference thermometer is 1 mK in a laboratory, we need a closer estimation of the measurement uncertainty to judge whether the temperature in the deep ocean can be measured with a 1-mK level of uncertainty.

In this paper, we evaluate the overall uncertainty of deep ocean temperature measurement. For this purpose, we present the time drifts of six reference thermometers based on the manufacturer’s laboratory calibrations. Three of the six reference thermometers were evaluated at the National Metrology Institute of Japan (NMIJ). Details of the evaluation of the reference thermometer not only at the triple point of water (TPW) and gallium-melting-point (GaMP) but also for the oceanographic temperature range (0.5°–30°C) are described in a separate paper (I. Saito et al. 2015, unpublished manuscript). We deduce the pressure sensitivity of the reference thermometers based on in situ comparisons with the CTD thermometers and a laboratory test for the CTD thermometers. And we estimate the uncertainty of the deep ocean temperature measurement by the in situ calibrated CTD thermometer in reference to the reference thermometer. We also discuss how the position of the CTD system affects the quality of the temperature and salinity data.

2. Laboratory calibration

The laboratory calibrations for the reference thermometers were performed by the manufacturer. The calibration of a reference thermometer is accomplished in two steps. The first is to characterize the sensor with a standard platinum resistance thermometer (SPRT) maintained by the manufacturer in a toroidal circulation temperature bath at 11 points (typically −1.5°, 1.0°, 4.5°, 8.0°, 11.5°, 15.0°, 18.5°, 20.0°, 25.5°, 29.0°, and 32.5°C) in the oceanographic temperature range from low to high. The second step is repeated the calibration of the sensor at the TPW (0.01°C) and GaMP (29.7646°C) cells. The temperature offsets at the fixed temperature points are adjusted by slope and offset corrections to the nonlinear calibration equation (the Steinhart–Hart fourth-order polynomial for thermistors; Bennett 1972). The TPW measurement is typically determined by using a group of four TPW cells, with the first measured cell repeated at the end of the series of measurements, and then all the measurements are averaged, although a group of two TPW cells was used before mid-2005. The GaMP measurement is determined by using a GaMP cell.

The manufacturer’s calibration procedure was then modified in 2011. While the calibration had been based on the International Temperature Scale of 1990 (ITS-90)-defined temperatures for TPW (0.01°C) and GaMP (29.7646°C) before 2011, the calibration has been based on the realized temperatures of the TPW and GaMP cells traceable to National Institute of Standards and Technology (NIST) temperature standards. Temperature biases for the fixed-point cells used in the calibration were estimated in reference to the cells traceable to NIST temperature standards (e.g., Table 1) and corrected since late 2011. For TPW, only one cell traceable to NIST temperature standards is directly used in the manufacturer’s calibration of the reference thermometers since 2014.

Table 1.

Temperature biases for the fixed-point cells used in the manufacturer’s calibration estimated in reference to the cells traceable to NIST temperature standards. The temperature biases of GaMP for serial numbers 22m and 45 were not given in the manufacturer’s calibration reports and were provided by the manufacturer later (Sea-Bird Electronics, Inc., 2015, personal communication).

Temperature biases for the fixed-point cells used in the manufacturer’s calibration estimated in reference to the cells traceable to NIST temperature standards. The temperature biases of GaMP for serial numbers 22m and 45 were not given in the manufacturer’s calibration reports and were provided by the manufacturer later (Sea-Bird Electronics, Inc., 2015, personal communication).
Temperature biases for the fixed-point cells used in the manufacturer’s calibration estimated in reference to the cells traceable to NIST temperature standards. The temperature biases of GaMP for serial numbers 22m and 45 were not given in the manufacturer’s calibration reports and were provided by the manufacturer later (Sea-Bird Electronics, Inc., 2015, personal communication).

We examined the time drifts of six reference thermometers from measurements in TPW and GaMP cells reported in the manufacturer’s calibration (Fig. 1). One reference thermometer (serial number 22) showed an irregularly large offset in 2009. Therefore, that temperature probe was replaced, and the new probe was distinguished from the original with the serial number of 22m. The time drifts estimated from the regression lines (not shown) ranged from −0.11 to 0.14 mK yr−1 for both the TPW and GaMP measurements for the data obtained after June 2004, except for the GaMP measurements of the serial number of 22. Maximum absolute deviations from the regression lines were determined to be 0.23 and 0.29 mK for TPW and GaMP, respectively.

Fig. 1.

Time drifts (temperature offsets relative to the first calibration) of six reference thermometers (SBE 35) based on laboratory calibrations performed by Sea-Bird Electronics in (a) TPW (0.01°C) and (b) GaMP (29.7646°C) cells. TPW and GaMP cells used in the calibrations are traceable to NIST temperature standards since 2011.

Fig. 1.

Time drifts (temperature offsets relative to the first calibration) of six reference thermometers (SBE 35) based on laboratory calibrations performed by Sea-Bird Electronics in (a) TPW (0.01°C) and (b) GaMP (29.7646°C) cells. TPW and GaMP cells used in the calibrations are traceable to NIST temperature standards since 2011.

The laboratory calibrations for the CTD thermometers were also performed by the manufacturer. The calibration of a CTD thermometer is accomplished in the same way as the first step for the laboratory calibration for the reference thermometer mentioned above.

3. Evaluation at the National Metrology Institute of Japan

Three reference thermometers calibrated by the manufacturer based on fixed-point cells traceable to NIST temperature standards (Table 1) were evaluated for stability and repeatability of their measurements in the national standard fixed-point cells (five TPW cells and one GaMP cell) of Japan at the NMIJ. Temperature measurements at the NMIJ were made within 5 months before and/or after the manufacturer’s calibration of the reference thermometers in 2011. For measurements before the manufacturer’s calibration, temperature readings from the reference thermometers were recalculated by using the manufacturer’s calibration coefficients after the measurements. The standard uncertainties of a single calibration of the reference thermometer by the national standard cells of Japan are estimated to be 0.078 and 0.163 mK for TPW and GaMP, respectively (Yamazawa et al. 2012). Details of the estimated uncertainties are listed in Table 2. Differences between the temperature readings and the realized temperature of the fixed-point cells were within ±0.14 and ±0.41 mK for TPW and GaMP cells, respectively (Fig. 2). Repeatability of the fixed-point calibrations are estimated to be 0.09 and 0.10 mK for TPW and GaMP, respectively, from the standard deviations (SDs) of the temperature differences for serial number 53. Therefore, the uncertainty of the comparisons was estimated from the root sum square of the uncertainty of the single calibration at the national standard cells of Japan and the repeatability of the fixed-point calibrations.

Table 2.

Uncertainty budget for a single calibration of the reference thermometer (SBE 35) at the national standard TPW and GaMP cells of Japan (Yamazawa et al. 2012).

Uncertainty budget for a single calibration of the reference thermometer (SBE 35) at the national standard TPW and GaMP cells of Japan (Yamazawa et al. 2012).
Uncertainty budget for a single calibration of the reference thermometer (SBE 35) at the national standard TPW and GaMP cells of Japan (Yamazawa et al. 2012).
Fig. 2.

Temperature differences between reference thermometer readings and realized temperatures of the national standard TPW and GaMP cells in Japan (open circles). The differences were averaged over each reference thermometer (SBE 35) serial number (closed circles). Numbers of measurements are shown over each mark. Vertical bars represent the expanded uncertainties (k = 2) of the comparisons (see text for details).

Fig. 2.

Temperature differences between reference thermometer readings and realized temperatures of the national standard TPW and GaMP cells in Japan (open circles). The differences were averaged over each reference thermometer (SBE 35) serial number (closed circles). Numbers of measurements are shown over each mark. Vertical bars represent the expanded uncertainties (k = 2) of the comparisons (see text for details).

Although the mean differences between the temperature readings of the reference thermometers and the realized temperatures of the national standard cells of Japan were within the expanded uncertainties (k = 2) of the comparison, there exists some deviations for the mean differences and their maximum absolute deviations were 0.09 and 0.31 mK for TPW and GaMP, respectively (Fig. 2). Since these evaluations at NMIJ were conducted immediately before and after the manufacturer’s calibrations, there should be some causes for these deviations. However, we could not independently discriminate these causes from the available data; thus, these causes remain unresolved. Therefore, we call these deviations unresolved deviations in the evaluation of the measurement uncertainty (section 5).

A relatively large difference (−0.31 mK on average) for the GaMP with serial number 53 of the reference thermometer may have resulted from a significantly large error of the estimate of the temperature bias for the GaMP cell (Isotech serial number 149) used in the manufacturer’s calibration (Sea-Bird Electronics, Inc., 2015, personal communication). In fact, the time drift of this GaMP (open triangles in Fig. 1b) shows that the temperature offset in 2011 strongly deviated (0.29 mK) from a regression line calculated from the results obtained after June 2004. The positive deviation is considered to indicate a temperature reading lower than the actual temperature, and the anticipated temperature error (−0.29 mK) is similar to the large difference (−0.31 mK) in Fig. 2 (GaMP, serial number 53).

4. Pressure sensitivity

In previous studies, the pressure sensitivities of CTD thermometers were evaluated with reference to reference thermometers in the deep ocean (Budeus and Schneider 1998; Uchida et al. 2007). However, no proof was given that the reference thermometers lack pressure sensitivity. Here, the pressure sensitivities of reference thermometers are deduced in two steps. The first is to examine the individual differences of the pressure sensitivity of reference thermometers compared with common CTD thermometers in the deep ocean. Although to examine the pressure sensitivity of the reference thermometers in the laboratory is straightforward, there is a risk of damage to the reference thermometers by the laboratory test. Therefore, the second step is to examine the pressure sensitivity of the CTD thermometer in the laboratory and to compare it with the pressure sensitivity estimated with reference to the reference thermometers in the deep ocean. If these two estimates of the pressure sensitivity of the CTD thermometer agree with each other, then the reference thermometers would have no pressure sensitivity.

For the six CTD thermometers, the pressure sensitivity could be estimated by comparing them with two or three reference thermometers in the deep ocean up to 65 MPa by using the same method as a previous study: Tc = T − (c0 + c1P + c2 t), where Tc is in situ corrected temperature of the CTD thermometer, T is temperature reading of the CTD thermometer, P is pressure, t is time from the laboratory calibration of the CTD thermometer, c0c2 are the in situ correction coefficients determined by minimizing the Tc and temperature reading of the reference thermometer for each cruise, and c1 is used to estimate the pressure sensitivity (Uchida et al. 2007) (Fig. 3). The difference in the estimate of the pressure sensitivity for each CTD thermometer was typically within the estimation error (SD of the estimates). For example, for the serial number 4216 of the CTD thermometer, both of the two estimates of the pressure sensitivity with reference to the serial numbers 22 and 45 of the reference thermometers were around 0 mK at 60 MPa. This result suggests that the two reference thermometers either do not have pressure sensitivity or have unknown similar pressure sensitivity. For serial number 1359 of the CTD thermometer, the three estimates of the pressure sensitivity with reference to the serial numbers 22m, 45, and 53 of the reference thermometers were around 1 mK at 60 MPa. This result also suggests that the three reference thermometers either do not have pressure sensitivity or have unknown similar pressure sensitivity. Therefore, these two results suggest that the four reference thermometers (serial numbers 22, 22m, 45, and 53) either do not have pressure sensitivity or have unknown similar pressure sensitivity. Similarly, from all the results in Fig. 3, it is confirmed that the six reference thermometers either do not have pressure sensitivity or have unknown similar pressure sensitivity. In addition, the time histories of the pressure sensitivities for four of the CTD thermometers estimated for each cruise show no time dependency (Fig. 4). It is extremely likely that the pressure sensitivities of the reference thermometers and the CTD thermometers do not change with time.

Fig. 3.

Average pressure sensitivities at 60 MPa of eight CTD thermometers (SBE 3) estimated from different reference thermometers (SBE 35). The number of pressure sensitivity estimations for each mark is noted immediately below that mark. Vertical bars show their SDs.

Fig. 3.

Average pressure sensitivities at 60 MPa of eight CTD thermometers (SBE 3) estimated from different reference thermometers (SBE 35). The number of pressure sensitivity estimations for each mark is noted immediately below that mark. Vertical bars show their SDs.

Fig. 4.

Time histories of pressure sensitivities at 60 MPa for four CTD thermometers (SBE 3) estimated for each cruise.

Fig. 4.

Time histories of pressure sensitivities at 60 MPa for four CTD thermometers (SBE 3) estimated for each cruise.

To examine whether the reference thermometers have pressure sensitivity, the pressure sensitivities of two CTD thermometers were evaluated by a laboratory test. One CTD thermometer (serial number 4216) was estimated to have little pressure sensitivity (0.06 ± 0.23 mK at 60 MPa), and another CTD thermometer (serial number 4188) was estimated to have relatively large pressure sensitivity (1.94 ± 0.29 mK at 60 MPa) with reference to the reference thermometer in the deep ocean (Fig. 3). The thermistor probe of the CTD thermometer was inserted into a pressure vessel made from stainless steel, and the two pressure vessels were filled with water and immersed in a refrigerated temperature calibration bath (model 7011, Fluke Co., Everett, Washington) (Fig. 5). Data from the CTD thermometers were acquired by using the SBE 9plus CTD system. Pressure in the vessels was generated by an oil hydraulic pump (model P-1B, Riken Kiki Co., Ltd., Tokyo, Japan) connected with stainless steel tubes. A liquid-to-liquid separator (model 38, Budenberg Ltd., Manchester, United Kingdom) was used between the oil hydraulic pump and the pressure vessels to prevent cross contamination of water and oil. The pressure in the vessels was monitored by a reference pressure monitor (model E-DWT A70M, Fluke Co.) and was manually adjusted to the following target pressures (in order): 0, 20, 30, 40, 50, 0, 10, and 0 MPa within ±5 kPa for 30 min to stabilize the temperature in the vessels. The temperature of the bath was set to 1°C, similar to the temperature of the deep ocean. The reference pressure monitor was calibrated by Ohte Giken, Inc. (Ibaraki, Japan) 6 months before the measurements and pressure readings were traceable to NIST pressure standards with an uncertainty (k = 2) of 0.02% of pressure reading.

Fig. 5.

Schematic view of the laboratory pressure test. The thermistor probe of the CTD thermometer (SBE 3) was inserted into a pressure vessel filled with water, and the two pressure vessels were immersed in a refrigerated temperature-calibration bath.

Fig. 5.

Schematic view of the laboratory pressure test. The thermistor probe of the CTD thermometer (SBE 3) was inserted into a pressure vessel filled with water, and the two pressure vessels were immersed in a refrigerated temperature-calibration bath.

At each pressure, the temperature and pressure readings were averaged over 10 min. The SDs of the temperature and pressure were smaller than 0.16 mK and 3.2 kPa, respectively. The root-mean-square of the three estimates of the mean temperature at 0 MPa (atmospheric pressure) was to be 0.06 mK. The pressure sensitivities of the two CTD thermometers were estimated as temperature anomalies from the mean of three estimates at 0 MPa for each sensor (Fig. 6). The pressure sensitivities at 60 MPa with standard uncertainty estimated from the regression lines were 0.06 ± 0.04 and 5.07 ± 0.07 mK for the serial numbers 4216 and 4188, respectively. The CTD thermometer of serial number 4216 was estimated to have little pressure sensitivity, and the result agrees with the value estimated with reference to the reference thermometer in the deep ocean within the uncertainty (0.08 mK at 60 MPa) of the estimate (0.23/√8). These results suggest that the reference thermometers have no pressure sensitivity, at least up to 65 MPa.

Fig. 6.

Pressure sensitivities of two CTD thermometers (SBE 3) estimated from laboratory tests. Regression lines through the origin are shown.

Fig. 6.

Pressure sensitivities of two CTD thermometers (SBE 3) estimated from laboratory tests. Regression lines through the origin are shown.

However, the pressure sensitivity at 60 MPa of the latter estimate (5.07 mK) was 2.6 times the value (1.94 mK) estimated with reference to the reference thermometer in the deep ocean (Fig. 3). One difference between the laboratory test and the in situ comparison is the presence of pump-controlled steady flow (~1 m s−1) around the thermistor probe of the CTD thermometer. Flow around the probe might diffuse part of the temperature anomaly caused by mechanical stress received when the thermistor is compressed at high pressure. The other difference is the simultaneous temperature and pressure cycling in the field that is not being modeled in the laboratory where only the pressure is being cycled. However, there are no clear differences between the pressure sensitivities estimated at low latitude, where the surface temperature is much higher than the temperature of the deep ocean, and at high latitude, where the temperature is relatively uniform throughout the water column.

A thermistor bead that is slightly larger than its specification inside a 0.8-mm-diameter needle may receive mechanical stress when the gap between the thermistor and the needle wall becomes small enough to allow increased efficiency of pressure transmission through the particles in the thermal grease (Sea-Bird Electronics, Inc., 2015, personal communication). Therefore, a negative value of the pressure sensitivity is not unlikely. However, one CTD thermometer (serial number 1464) showed slight negative pressure sensitivity (−0.5 mK at 60 MPa) (Fig. 3). For this CTD thermometer, the tendency of the pressure sensitivity changed from positive to negative at around 20 MPa (Fig. 4b in Uchida et al. 2007). Therefore, no notable pressure sensitivity (−0.05 mK at 60 MPa) was estimated when all data (from surface to bottom) of Fig. 4b in Uchida et al. (2007) were used for estimation of the linear pressure dependency.

5. Uncertainty

Establishing the chain of traceability through evaluating the measurement uncertainty when the reference thermometer and CTD thermometer are in actual use in the ocean is absolutely essential to ensure the data quality, especially for climate studies. In this section, we characterize the uncertainty of the deep ocean temperature measurement by the CTD thermometer calibrated in reference to the reference thermometer in the deep ocean (depths greater than 20 MPa), where temperatures range around 0°–3°C. Here, the uncertainty is investigated in three steps. The first is to assess uncertainties for laboratory calibration of the reference thermometer at the fixed temperature points based on the evaluation at the NMIJ. The second is to assess uncertainty for the temperature measurement in the deep ocean by the reference thermometer. The last step is to assess uncertainty for the temperature measurement in the deep ocean by the CTD thermometer calibrated in situ by the reference thermometer. The uncertainty budget described below is summarized in Table 3.

Table 3.

Uncertainty budget for the deep ocean (depths greater than 20 MPa) temperature measurement by the in situ calibrated CTD thermometer (SBE 3) in reference to the reference thermometer (SBE 35). Serial number is abbreviated as SN.

Uncertainty budget for the deep ocean (depths greater than 20 MPa) temperature measurement by the in situ calibrated CTD thermometer (SBE 3) in reference to the reference thermometer (SBE 35). Serial number is abbreviated as SN.
Uncertainty budget for the deep ocean (depths greater than 20 MPa) temperature measurement by the in situ calibrated CTD thermometer (SBE 3) in reference to the reference thermometer (SBE 35). Serial number is abbreviated as SN.

a. Laboratory calibrations of reference thermometer at TPW and GaMP

The standard uncertainties of a single calibration of the reference thermometer by the national standard cells of Japan are estimated to be 0.078 and 0.163 mK for TPW and GaMP, respectively (Yamazawa et al. 2012) (Table 2).

Repeatability of the fixed-point calibrations are estimated to be 0.09 and 0.10 mK for TPW and GaMP, respectively, from the SDs of the differences between the temperature readings of the reference thermometer (serial number 53) and the realized temperature of the national standard cells of Japan (Fig. 2).

Unresolved deviations are estimated to be 0.05 and 0.18 mK for TPW and GaMP, respectively, from maximum absolute deviations of the mean differences between the temperature readings of the reference thermometer and the realized temperature of the national standard cells of Japan (Fig. 2), assuming a uniform probability distribution.

The overall standard uncertainties for laboratory calibration of the reference thermometer are estimated to be 0.13 and 0.26 mK for TPW and GaMP, respectively.

b. Reference thermometer measurement in the deep ocean at 0°–3°C

As described in section 2, temperature offsets at TPW and GaMP are adjusted by slope and offset corrections in the manufacturer’s calibration. Thus, the uncertainty contribution from the fixed-point calibrations of the reference thermometer for the temperature range between 0° and 3°C is estimated to be 0.15 mK [√(0.132 × 27/30 + 0.262 × 3/30)] from the maximum uncertainty at 3°C propagated from the fixed-point calibrations at TPW and GaMP.

Nonlinearity of the reference thermometer was estimated to be typically within ±0.1 mK for the temperature range between the TPW and GaMP from the temperature difference between the reference thermometer and SPRT after the slope and offset corrections (Yamazawa et al. 2012). Therefore, the uncertainty contribution from the nonlinearity of the reference thermometer is estimated to be 0.06 mK, assuming a uniform probability distribution.

The maximum time drift of the reference thermometers was 0.14 mK yr–1 (section 2). Therefore, the uncertainty contribution from the time drift of a reference thermometer used within a year from the laboratory calibration is estimated to be 0.08 mK, assuming a uniform probability distribution.

The uncertainty contribution from the pressure sensitivity of the reference thermometers at 65 MPa was estimated to be 0.09 mK (0.08 mK/60 MPa × 65 MPa) (section 4).

The uncertainty contribution from the temperature noise of the reference thermometer was 0.04 mK in a thermally quiet environment (Sea-Bird Electronics 2015) when four measurement cycles were taken and averaged at each sample (Uchida et al. 2007).

The overall standard uncertainty for the temperature measurement in the deep ocean by the reference thermometer is estimated to be 0.21 mK.

c. CTD thermometer measurement in the deep ocean calibrated in situ by the reference thermometer

The uncertainty contribution from the temperature measurement in the deep ocean by the reference thermometer is estimated to be 0.21 mK (from section 5b).

The uncertainty contribution from the variability of the temperature measurement in the deep ocean by the CTD thermometer was estimated to be 0.20 mK from the mean of the SDs of the difference between the in situ calibrated CTD thermometer and the reference thermometer (Uchida et al. 2007).

The uncertainty of the correction for pressure sensitivity of the CTD thermometer is estimated to be 0.21 mK at 60 MPa from the mean of the SDs of the estimated pressure sensitivities for each CTD thermometer (Fig. 3). Therefore, the uncertainty contribution from the correction at 65 MPa is estimated to be 0.23 mK (0.21 mK/60 MPa × 65 MPa).

The uncertainty contribution from the resolution (0.2 mK) of a CTD thermometer is 0.06 mK by a uniform probability distribution.

The overall expanded uncertainty (k = 2) of the deep ocean temperature measurement (up to 65 MPa) by the CTD thermometer calibrated in situ by the reference thermometer is estimated to be 0.7 mK (Table 3).

6. Discussion

In this section, we discuss three issues: 1) comparison of the manufacturer’s calibrations before and after introduction of the fixed-point cells traceable to NIST temperature standards, 2) temperature error due to the changing viscous heating effect, and 3) temperature hysteresis of the thermometers.

Consistency of the calibrations of the reference thermometers at the TPW is critical for monitoring the deep ocean temperature changes on a decadal time scale. However, there had been a transition during the past decade in the definition of the unit kelvin under the SI units. In 2005, the definition of the TPW was clarified by relating it to the isotopic composition of Vienna Standard Mean Ocean Water (VSMOW), based on the findings of the international comparison of TPW cells among national metrology institutes (Stock et al. 2006). In the manufacturer’s calibration before the introduction of the TPW cell traceable to NIST temperature standards following the revised definition, only borosilicate TPW cells were used except for a short period from 8 November to 10 December 2010 (Sea-Bird Electronics, Inc., 2015, personal communication), and the temperature bias for the TPW cells was estimated to be −0.13 mK, on average, in 2011 (Table 1). However, the realized temperature of a borosilicate TPW cell may, on average, drift in time with a rate of about −0.013 mK yr–1 due to impurities leaching from the glass envelopes, while the rate of a time drift is small (about −0.002 mK yr−1) for a fused-quartz TPW cell (Strouse and Zhao 2007). Hill (2014) also estimated an average rate of time drift of −0.006 mK yr−1 relative to their fused-quart cells. Therefore, the temperature biases of the borosilicate TPW cells of Sea-Bird Electronics before 2011 might be closer to zero than the temperature biases (about −0.13 mK) in 2011, since two of the borosilicate TPW cells (serial numbers 1682 and 1866) used in 2011 were always used in the manufacturer’s calibration before 2011 (Fig. 1).

Viscous heating occurs for pump-controlled flow around the thermistor probe of the CTD thermometer. The effect of this heating can change if the flow speed in the pumping system changes. The position of the CTD system can affect the temperature data quality and thus the salinity calculated from conductivity and temperature (see the  appendix). If the SBE 9plus is deployed in a vertical position, the downcast (upcast) temperature profile might be systematically lower (higher) by about 0.3 mK than the temperature profile measured at the discrete bottle-firing stops. Even if the SBE 9plus is deployed in a horizontal position, the attitude fluctuation of the SBE 9plus may cause temperature fluctuations with peak-to-peak amplitudes of about 0.6 mK. The salinity fluctuation resulting from the temperature fluctuation is remarkable in the deep ocean. The temperature fluctuation could be eliminated by using a relatively heavy frame of the CTD package and by attaching a large plate (0.5 m × 0.9 m) to the CTD package to prevent its rotation (Uchida and Fukasawa 2005).

Three of the six reference thermometers were evaluated over the oceanographic temperature range (0.5° to around 30°C) against SPRTs at the NMIJ; it was found that two of the three reference thermometers had a temperature hysteresis (Saito et al. 2014). The maximum difference among the temperature readings between the down trace (from high to low temperature) and up trace (from low to high temperature) was about −0.4 mK. The reference thermometer is calibrated from a low to high temperature during the manufacturer’s procedure (section 2). Therefore, the temperature readings of the reference thermometer for the down-trace (from high to low) temperature measurement can be affected by the temperature hysteresis. Since the temperature measurements by the reference thermometer are conducted at the bottle-firing stops from the deep ocean to the sea surface and the deep ocean temperature is usually lower than the surface water temperature, the reference thermometer measures from low (usually within a few degrees Celsius from the lowest temperature of the manufacturer’s calibration) to high temperature during the CTD measurement. Therefore, the in situ temperature measurements in the deep ocean by the reference thermometer conducted during the upcast of the CTD measurement may not be affected by the temperature hysteresis. Moreover, continuous temperature measurements by the CTD thermometer are usually conducted in the downcast, while the CTD thermometer is calibrated in situ by using data obtained at bottle-firing stops during the upcast. Therefore, the continuous temperature profiles might be affected by a temperature hysteresis if the CTD thermometer has one. However, the effect of a temperature hysteresis will be small for the deep ocean because the temperature range there is usually small.

Acknowledgments

We are grateful to the Arctic Ocean and Climate System Research Group (Japan Agency for Marine-Earth Science and Technology) for allowing us to use its reference thermometer (serial number 53). We thank the technicians of Marine Works Japan, who conducted in situ calibration of the CTD thermometers. We also thank Naoko Miyamoto (Marine Works Japan) for assisting with the laboratory pressure test. We also thank Dick Guenther (Sea-Bird Electronics, Inc.) for providing the information about the fixed-point cells of Sea-Bird Electronics. Comments by two anonymous reviewers helped to improve the paper.

APPENDIX

Temperature Error due to the Effect of Changing Viscous Heating

The SBE 9plus CTD system uses a pumping system. Therefore, viscous heating (~0.5 mK) occurs during pump-controlled steady flow (~1 m s−1) around the thermistor probe of the CTD thermometer (Larson and Pedersen 1996; Uchida et al. 2007). The viscous heating effect can change if the flow speed of the pumping system changes (Larson and Pedersen 1996). In fact, the temperature reading from the CTD thermometer increased 0.7 mK relative to the reference thermometer when the conductivity sensor (SBE 4) was removed from the pumping system, probably because the flow resistance decreased by removing the conductivity sensor, and the flow speed increased in the duct.

The flow speed of the pumping system may change in a CTD measurement between the downcast, upcast, and bottle-firing stops, when the SBE 9plus CTD system is deployed in a vertical position. Figure A1 shows an example of the temperature differences in the deep ocean between the upcast and downcast for the SBE 9plus deployed in both vertical and horizontal positions. The mean values with SDs of the temperature differences for depths greater than 53 MPa were 0.63 ± 0.11 mK and −0.07 ± 0.11 mK for the vertical and horizontal positions, respectively. The cross section of an exhaust tube of the pumping system is typically 4 times the cross section of the intake of the temperature−conductivity (TC) duct. When the SBE 9plus is deployed in a vertical position, both the intake and exhaust of the pumping system are directed downward. The flow speed in the duct might be reduced during the downcast by the effect of the dynamic pressure derived from the descending speed (~1 m s−1) of the CTD package, so that the downcast temperature profile might be systematically lower by about 0.3 mK than the temperature profile measured at the discrete bottle-firing stops. Similarly, the temperature profile during the upcast might be systematically higher by 0.3 mK.

Fig. A1.

Examples of temperature differences between upcast and downcast profiles near the sea floor. The SBE 9plus CTD was deployed in a vertical position (R/V Mirai cruise MR99-K02, location 50°N, 165°E) and in a horizontal position (R/V Mirai cruise MR14–04, location 43°N, 153°E).

Fig. A1.

Examples of temperature differences between upcast and downcast profiles near the sea floor. The SBE 9plus CTD was deployed in a vertical position (R/V Mirai cruise MR99-K02, location 50°N, 165°E) and in a horizontal position (R/V Mirai cruise MR14–04, location 43°N, 153°E).

Even if the SBE 9plus is deployed in a horizontal position, the flow speed of the pumping system may also change during a CTD measurement by the attitude motion of the CTD package. Figure A2 shows examples of the temperature differences between two CTD thermometers and the attitude motion of the CTD package measured by a lowered acoustic Doppler current profiler (LADCP) for two CTD measurements (downcasts). The temperature differences fluctuated (peak-to-peak amplitude of about 0.6 mK), corresponding to the attitude (pitching, rolling, and heading) changes of the SBE 9plus, although the conductivity differences did not fluctuate. When the SBE 9plus was in a horizontal position, the intake of the TC duct was directed horizontally, and the exhaust of the pump, the cross section of which is about 2 times the cross section of the intake of the TC duct, was directed 45° from upward. The attitude motion might change the effect of the dynamic pressure, so that the flow speed in the duct might fluctuate. The temperature difference between the two CTD thermometers fluctuated because the phase between the two temperature fluctuations was slightly different.

Fig. A2.

Examples of temperature differences between two CTD thermometers and attitude motion of the CTD package measured by an LADCP for two CTD measurements (downcasts) during the R/V Mirai MR01-K04 cruise.

Fig. A2.

Examples of temperature differences between two CTD thermometers and attitude motion of the CTD package measured by an LADCP for two CTD measurements (downcasts) during the R/V Mirai MR01-K04 cruise.

The temperature fluctuation for each CTD thermometer was estimated from the temperature–salinity relation in the deep ocean (Fig. A3) because the temperature fluctuation was too small to detect from the highly variable temperature profile itself. In Fig. A3, the ratio of the temperature range (70 mK) to the salinity range (9 mg kg−1) is an order of magnitude greater than the ratio of the temperature fluctuation (~0.3 mK) to the salinity fluctuation (~0.3 mg kg−1) caused by the temperature fluctuation, so that the salinity fluctuation is dominant in the temperature–salinity relation. The amplitude of the salinity deviation from the regression line was estimated by fitting a sine function in time. The correlation between the amplitude of the salinity deviation and the tilt of the CTD package in the range from 1° to 23° was examined by using 19 CTD profiles obtained from three types of CTD packages whose weights were 650, 730, and 970 kg in air. The correlation coefficient was 0.82, and the slope of the regression line was 0.013 mg kg−1 deg−1. Therefore, the relationship between the amplitude of the temperature deviation and the tilt of the CTD package was estimated to be 0.013 mK deg−1.

Fig. A3.

Potential temperature–salinity relationship in the deep ocean (depths deeper than ~35 MPa) for the same CTD measurements shown in Fig. A2. Contour lines indicate the potential density anomaly (kg m−3).

Fig. A3.

Potential temperature–salinity relationship in the deep ocean (depths deeper than ~35 MPa) for the same CTD measurements shown in Fig. A2. Contour lines indicate the potential density anomaly (kg m−3).

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