# Metrological Evaluation of Deep-Ocean Thermometers

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

- -
- SBE35 (Sea-Bird Scientific, formerly Sea-Bird Electronics) —reference thermistor thermometer with claimed 0.2 mK accuracy, 0.14 mK∙yr
^{−1}stability and 0.5 s response time. - -
- SBE3 (Sea-Bird Scientific, formerly Sea-Bird Electronics)—CTD profiling thermistor thermometer with claimed 0.7 mK accuracy, 2 mK∙yr
^{−1}stability, and 0.07 s response time.

^{−1}to 2.24 mK∙(60 MPa)

^{−1}, see [5]), under the assumption that the SBE35 response is pressure-independent.

^{−1}for only one individual SBE35 unit in an experiment in which temperature was not controlled and Joung et al. [8] obtained a repeatable pressure dependence ≤1 mK∙(60 MPa)

^{−1}for 2 of the 3 investigated SBE35, and no pressure dependence, within the measurement uncertainty, for the other SBE35.

## 2. Calibration of SBE35 and SBE3

#### 2.1. Manufacturer Calibration of SBE35 and SBE3

- -
- Initially, the unit is calibrated by comparison in a water bath at 11 temperatures between −1.5 °C and 32.5 °C.
- -
- Subsequently, an interpolation of the calibration data is performed using the Steinhart and Hart equation:

_{90}is the ITS-90 temperature in °C, f is the frequency output of the unit, f

_{0}= 1000 Hz is an arbitrary scaling factor used for computational efficiency, and a

_{i}are the 5 coefficients determined by the interpolation.

- -
- Finally, a linear adjustment is applied to the interpolation by calibrating the unit at the triple point of water, TPW, (t
_{90}= 0.01 °C) and at the gallium melting point (t_{90}= 29.7646 °C), using standard ITS-90 fixed-point cells:$${t}_{90}^{adj}=m\xb7{t}_{90}+q$$

#### 2.2. Fixed-Point Recalibration of SBE35

#### 2.3. Calibration by Comparison of SBE35 and SBE3 in a Water Bath

## 3. Pressure Dependence

_{SBE}− t

_{90}, between the SBE35 units and the reference temperature provided by the reference SPRTs (see Figure 10).

_{SBE35}and the water bath reference temperature t

_{90}as a function of t

_{90}, suggests that a large part of the scatter was due to the temperature stability of the water bath during the measurements—while for the s/n 0081, the scatter in the reference temperature was slightly larger than 0.5 mK, for the s/n 0015 the scatter exceeded 1.5 mK.

- -
- A pressure effect linear on the applied pressure p was assumed: t
_{SBE35}− t_{90}= a_{0}+ a_{1}∙p - -
- The set of N (N = 27 for the s/n 0015 set and N = 112 for the s/n 0081 set) experimental points (p
_{i}, (t_{SBE35}− t_{90})_{i}) was randomized as:`o`- p
_{i},_{k}= p_{i}+ R_{k}(−1, 1)∙u(p) `o`- (t
_{SBE35}− t_{90})_{i,k}= (t_{SBE35}− t_{90})_{i}+ R_{k}(−1, 1)∙u(t)

_{k}(−1, 1) is a random generator comprised between −1 and +1 with rectangular distribution, u(p) = 0.003 MPa is the standard uncertainty of pressure, and u(t) = 0.153 mK is the standard uncertainty of the bath temperature.

- -
- For each of the 8192 randomized sets of experimental data, a linear regression of the relationship t
_{SBE35}− t_{90}= a_{0}+ a_{1}∙p provided the pressure sensitivity a_{1}.

_{1}are shown in Figure 13 and Figure 14. The best estimates and the variances of the obtained pressure sensitivities were: a

_{1}= 0.0045 mK∙MPa

^{−1}and σ = 0.0008 mK∙MPa

^{−1}for the SBE35 s/n 0015, and a

_{1}= 0.0053 mK∙MPa

^{−1}and σ = 0.0004 mK∙MPa

^{−1}for the SBE35 s/n 0081. These pressure sensitivities translated into pressure effects of 0.27 mK and 0.32 mK, for the s/n 0015 and the s/n 0081, respectively.

## 4. Conclusions

^{−1}mK∙MPa

^{−1}for the SBE35 s/n 0015 and 0.0053 mK∙MPa

^{−1}for the SBE35 s/n 0081). Although the observed pressure effect was very small (approximately 0.3 mK at 60 MPa) for these two specific units, this result could not be generalized to all SBE35 units, as evidenced by the different results obtained by different authors [7,8,9] in different units.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Hansen, J.; Sato, M.; Kharecha, P.; von Schuckmann, K. Earth’s energy imbalance and implications. Atmos. Chem. Phys.
**2011**, 11, 13421–13449. [Google Scholar] [CrossRef][Green Version] - Van Schckmann, K.; Cheng, L.; Palmer, M.D.; Hansen, J.; Tassone, C.; Aich, V.; Adusumilli, S.; Beltrami, H.; Boyer, T.; Cuesta-Valero, F.J. Heat stored in the Earth system: Where does the energy go? Earth Syst. Sci. Data
**2020**, 12, 2013–2041. [Google Scholar] [CrossRef] - Wunsch, C. Global Ocean Integrals and Means, with Trend Implications. Ann. Rev. Mar. Sci.
**2016**, 8, 1–33. [Google Scholar] [CrossRef] [PubMed][Green Version] - Budeus, G.; Schneider, W. In-situ temperature calibration: A remark on instruments and methods. In International WOCE Newsletter, No. 30; WOCE International Project Office: Southampton, UK, 1998; pp. 16–18. [Google Scholar]
- Uchida, H.; Ohyama, K.; Ozawa, S.; Fukasawa, M. In situ calibration of the SeaBird 9 plus CTD thermometer. J. Atmos. Ocean. Technol.
**2007**, 24, 1961–1967. [Google Scholar] [CrossRef] - Uchida, H.; Nakano, T.; Tamba, J.; Widiatmo, J.V.; Yamazawa, K.; Ozawa, S.; Kawano, T. Deep ocean temperature measurement with an uncertainty of 0.7 mK. J. Atmos. Ocean. Technol.
**2015**, 32, 2199–2210. [Google Scholar] [CrossRef] - Peruzzi, A.; Ober, S.; Bosma, R. Effect of Pressure on Deep-Ocean Thermometers. Int. J. Thermophys.
**2017**, 38, 163. [Google Scholar] [CrossRef] - Joung, W.; Gam, K.; Pearce, J.V. Pressure Dependence of Reference Deep-Ocean Thermometers. Meteorol. Appl.
**2020**, 27, e1870. [Google Scholar] [CrossRef] - Preston-Thomas, H. The International Temperature Scale of 1990(ITS-90). Metrologia
**1990**, 27, 3–10. [Google Scholar] [CrossRef] - Bosma, R.; Peruzzi, A.; van Breugel, R.; Bruin-Barendregt, C. A Sub-Millikelvin Calibration Facility in the Range 0 °C to 30 °C. Int. J. Thermophys.
**2017**, 38, 37. [Google Scholar] [CrossRef]

**Figure 1.**Deep-ocean thermometers from Sea-Bird Scientific—(

**a**) SBE3, needle length 56 mm and (

**b**) SBE35, stem length 465 mm.

**Figure 2.**500 readings (one every 4 s) with SBE35 s/n 0019 at the TPW (solid line and left scale) and at the Ga (dashed line and right scale). The peak-to-peak noise is 0.3 mK and 1.1 mK and the standard deviation is 0.054 mK and 0.185 mK, at the TPW and at the Ga, respectively.

**Figure 3.**Fixed-point recalibration of 4 different SBE35 units—s/n 0019 from NIOZ, s/n 0086 from LNE/CNAM, s/n 0015 from SHOM, and s/n 0081 from NIOZ. The circles corresponds to TPW calibrations and the squares corresponds to Ga calibrations. The bars represent the uncertainties in the fixed-point recalibration (0.186 mK for TPW and 0.464 mK for Ga, see Table 1).

**Figure 4.**SBE3, SBE35 (not visible), and two reference SPRTs mounted in the brass comparator block of the sub-millikelvin calibration facility.

**Figure 5.**Recalibration of SBE35 and SBE3 units in a water bath (WB)—(

**a**) SBE35 s/n 0019 and SBE3 s/n 4812 and (

**b**) SBE35 s/n 0015, SBE35 s/n 0081. For convenience, the average of the SBE-35 fixed-point (FP) calibrations (TPW and Ga) are also reported in full symbols (full circle for SBE35 s/n 0019, full square for SBE35 s/n 0015, and full triangle for SBE35 s/n 0081).

**Figure 8.**Time evolution of the SBE35 temperature reading (

**a**) at and after pressurization from atmospheric pressure to 50 MPa and (

**b**) at and after de-pressurization from 50 MPa to 30 MPa. The dotted blue line and the continuous red line corresponds to the same SBE35 temperature reading, showed on different temperature scales (left scale for the dotted blue line and right scale for the continuous red line), in order to show both the whole peak and the stabilization after the peak.

**Figure 9.**Pressure drift (left scale) and consequent temperature drift (right scale) during measurements at the highest pressure (≈60 MPa).

**Figure 10.**Temperature difference between the SBE35 reading and the reference thermometers as a function of the pressure.

**Figure 11.**Temperature difference between the SBE35 reading, t

_{SBE35}, and the water bath reference temperature, t

_{90}, as a function of t

_{90}for two SBE35 units (s/n 0015 and s/n 0081).

**Figure 12.**SBE35 s/n 0081 at 0.1 MPa and at 60 MPa. The experimental points at 60 MPa had clearly shifted up with respect to the experimental points at 0.1 MPa.

**Figure 13.**Sensitivity coefficient of the SBE35 s/n 0015 obtained with the Monte Carlo method with 8192 trials—best estimate a

_{1}= 0.0045 mK∙MPa

^{−1}and variance σ = 0.0008 mK∙MPa

^{−1}.

**Figure 14.**Sensitivity coefficient of the SBE35 s/n 0081 obtained with the Monte Carlo method with 8192 trials—best estimate a

_{1}= 0.0053 mK∙MPa

^{−1}and variance σ = 0.0004 mK∙MPa

^{−1}.

Uncertainty Component | Uncertainty/mK | |
---|---|---|

TPW | Ga | |

National Reference | ||

Chemical impurities | 0.020 | 0.079 |

Isotopic composition | 0.002 | 0.000 |

Residual gas pressure in the cell | 0.003 | 0.040 |

Stability | 0.005 | 0.010 |

SBE35 Calibration | ||

Stability of reading (standard deviation of 500 consecutive readings in 10 min) | 0.054 | 0.185 |

Reproducibility for different days | 0.072 | 0.085 |

Hydrostatic head correction | 0.005 | 0.012 |

Thermal conditions | 0.005 | 0.067 |

Combined standard uncertainty (k = 1) | 0.093 | 0.232 |

Expanded uncertainty (k = 2) | 0.186 | 0.464 |

**Table 2.**Uncertainty budget for the recalibration of the SBE35 and the SBE3, by comparison to reference SPRTs in the sub-millikelvin calibration facility.

Uncertainty Component | Uncertainty/mK | |
---|---|---|

SBE35 | SBE3 | |

Standard resistor | 0.112 | 0.112 |

Resistance ratio bridge linearity | 0.049 | 0.049 |

SPRT calibration | 0.138 | 0.138 |

Time stability and spatial uniformity of temperature | 0.153 | 0.183 |

ITS-90 non-uniqueness | 0.162 | 0.162 |

Interpolation | 0.191 | 0.236 |

Combined standard uncertainty (k = 1) | 0.348 | 0.387 |

Expanded uncertainty (k = 2) | 0.696 | 0.774 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Peruzzi, A.; Bosma, R.; van Geel, J.; Ober, S. Metrological Evaluation of Deep-Ocean Thermometers. *J. Mar. Sci. Eng.* **2021**, *9*, 398.
https://doi.org/10.3390/jmse9040398

**AMA Style**

Peruzzi A, Bosma R, van Geel J, Ober S. Metrological Evaluation of Deep-Ocean Thermometers. *Journal of Marine Science and Engineering*. 2021; 9(4):398.
https://doi.org/10.3390/jmse9040398

**Chicago/Turabian Style**

Peruzzi, Andrea, Rien Bosma, Jan van Geel, and Sven Ober. 2021. "Metrological Evaluation of Deep-Ocean Thermometers" *Journal of Marine Science and Engineering* 9, no. 4: 398.
https://doi.org/10.3390/jmse9040398