• Abraham, J. P., and et al. , 2013: A review of global ocean temperature observations: Implications for ocean heat content estimates and climate change. Rev. Geophys., 51, 450483, https://doi.org/10.1002/rog.20022.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Boyer, T. P., and et al. , 2016: Sensitivity of global upper-ocean heat content estimates to mapping methods, XBT bias corrections, and baseline climatologies. J. Climate, 29, 48174842, https://doi.org/10.1175/JCLI-D-15-0801.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Boyer, T. P., and et al. , 2018: World Ocean Database 2018. NOAA Atlas NESDIS 87, 207 pp., https://data.nodc.noaa.gov/woa/WOD/DOC/wod_intro.pdf.

  • Breiman, L., 1996: Bagging predictors. Mach. Learn., 24, 123140, https://doi.org/10.1023/A:1018054314350.

  • Cheng, L., and J. Zhu, 2014: Uncertainties of the ocean heat content estimation induced by insufficient vertical resolution of historical ocean subsurface observations. J. Atmos. Oceanic Technol., 31, 13831396, https://doi.org/10.1175/JTECH-D-13-00220.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cheng, L., J. Zhu, F. Reseghetti, and Q. Liu, 2011: A new method to estimate the systematical biases of expendable bathythermograph. J. Atmos. Oceanic Technol., 28, 244265, https://doi.org/10.1175/2010JTECHO759.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cheng, L., J. Zhu, R. Cowley, T. Boyer, and S. Wijffels, 2014: Time, probe type, and temperature variable bias corrections to historical expendable bathythermograph observations. J. Atmos. Oceanic Technol., 31, 17931825, https://doi.org/10.1175/JTECH-D-13-00197.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cheng, L., and et al. , 2016: XBT science: Assessment of instrumental biases and errors. Bull. Amer. Meteor. Soc., 97, 924933, https://doi.org/10.1175/BAMS-D-15-00031.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cheng, L., K. Trenberth, J. Fasullo, T. Boyer, J. Abraham, and J. Zhu, 2017: Improved estimates of ocean heat content from 1960 to 2015. Sci. Adv., 3, e1601545, https://doi.org/10.1126/sciadv.1601545.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cheng, L., H. Luo, T. Boyer, R. Cowley, J. Abraham, V. Gouretski, F. Reseghetti, and J. Zhu, 2018: How well can we correct systematic errors in historical XBT data? J. Atmos. Oceanic Technol., 35, 11031125, https://doi.org/10.1175/JTECH-D-17-0122.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Church, J. N., and et al. , 2011: Revisiting the Earth’s sea-level and energy budgets from 1961 to 2008. Geophys. Res. Lett., 38, L18601, https://doi.org/10.1029/2011GL048794.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Couper, B. K., and E. C. LaFond, 1970: The mechanical bathythermograph: An historical review. Adv. Instrum, 25, 735770.

  • Cowley, R., S. Wijffels, L. Cheng, T. Boyer, and S. Kizu, 2013: Biases in expendable bathythermograph data: A new view based on historical side-by-side comparisons. J. Atmos. Oceanic Technol., 30, 11951225, https://doi.org/10.1175/JTECH-D-12-00127.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Domingues, C., J. Church, N. White, P. Gleckler, S. Wijffels, P. Barker. And, and J. Dunn, 2008: Improved estimates of upper-ocean warming and multi-decadal sea-level rise. Nature, 453, 10901093, https://doi.org/10.1038/nature07080.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Foresee, F. D., and M. T. Hagan, 1997: Gauss-Newton approximation to Bayesian learning. Proc. Int. Conf. on Neural Networks, Houston, TX, IEEE, 1930–1935, https://doi.org/10.1109/ICNN.1997.614194.

    • Crossref
    • Export Citation
  • Glorot, X., A. Bordes, and Y. Bengio, 2011: Deep sparse rectifier neural networks. 14th Int. Conf. on Artificial Intelligence and Statistics, Fort Lauderdale, FL, Proceedings of Machine Learning Research, 315–323, https://www.jmlr.org/proceedings/papers/v15/glorot11a/glorot11a.pdf.

  • Good, S., 2011: Depth biases in XBT data diagnosed using bathymetry data. J. Atmos. Oceanic Technol., 28, 287300, https://doi.org/10.1175/2010JTECHO773.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gouretski, V., 2012: Using GEBCO digital bathymetry to infer depth biases in the XBT data. Deep-Sea Res. I, 62, 4052, https://doi.org/10.1016/j.dsr.2011.12.012.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gouretski, V., and K. Koltermann, 2007: How much is the ocean really warming? Geophys. Res. Lett., 34, L01610, https://doi.org/10.1029/2006GL027834.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gouretski, V., and F. Reseghetti, 2010: On depth and temperature biases in bathythermograph data: Development of a new correction scheme based on analysis of a global ocean database. Deep-Sea Res. I, 57, 812833, https://doi.org/10.1016/j.dsr.2010.03.011.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gouretski, V., and L. Cheng, 2020: Correction for systematic errors in the global dataset of temperature profiles from mechanical bathythermographs. J. Atmos. Oceanic Technol., 37, 841855, https://doi.org/10.1175/JTECH-D-19-0205.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hagan, M. T., and M. B. Menhaj, 1994: Training feedforward networks with the Marquardt algorithm. IEEE Trans. Neural Network, 5, 989993, https://doi.org/10.1109/72.329697.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hamon, M., G. Reverdin, and P. Le Traon, 2012: Empirical correction of XBT data. J. Atmos. Oceanic Technol., 29, 960973, https://doi.org/10.1175/JTECH-D-11-00129.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hanawa, K., P. Rual, R. Bailey, A. Sy, and M. Szabados, 1995: A new depth-time equation for Sippican or TSK T-7, T-6 and T-4 expendable bathythermographs (XBT). Deep-Sea Res. I, 42, 14231451, https://doi.org/10.1016/0967-0637(95)97154-Z.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hansen, J., 2005: Earth’s energy imbalance: Confirmation and implications. Science, 308, 14311435, https://doi.org/10.1126/science.1110252.

  • Hansen, L., and P. Salamon, 1990: Neural network ensembles. IEEE Trans. Pattern Anal. Mach. Intell., 12, 9931001, https://doi.org/10.1109/34.58871.

  • Ishii, M., and M. Kimoto, 2009: Reevaluation of historical ocean heat content variations with time-varying XBT and MBT depth bias corrections. J. Oceanogr., 65, 287299, https://doi.org/10.1007/s10872-009-0027-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kizu, S., H. Yoritaka, and K. Hanawa, 2005: A new fall rate equation for T-5 expendable bathythermograph (XBT) by TSK. J. Oceanogr., 61, 115121, https://doi.org/10.1007/s10872-005-0024-4.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Levitus, S., J. Antonov, T. Boyer, R. Locarnini, H. Garcia, and A. Mishonov, 2009: Global ocean heat content 1955–2008 in light of recently revealed instrumentation problems. Geophys. Res. Lett., 36, L07608, https://doi.org/10.1029/2008GL037155.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Levitus, S., and et al. , 2012: World ocean heat content and thermosteric sea level change (0–2000 m), 1955–2010. Geophys. Res. Lett., L10603, 39, https://doi.org/10.1029/2012GL051106.

    • Search Google Scholar
    • Export Citation
  • Lincoln, W. P., and J. Skrzypek, 1990: Systematics of clustering multiple back propagation networks. Advances in Neural Information Processing Systems, D. S. Touretzky, Ed., Vol. 2, Morgan Kaufmann Publishers, 650–657.

  • Locarnini, R. A., and et al. , 2013: Temperature. Vol. 1, World Ocean Atlas 2013, NOAA Atlas NESDIS 73, 40 pp., https://data.nodc.noaa.gov/woa/WOA13/DOC/woa13_vol1.pdf.

  • Lyman, J. M., S. A. Good, V. Gouretski, M. Ishii, G. C. Johnson, M. D. Palmer, D. M. Smith, and J. Willis, 2010: Robust warming of the global upper ocean. Nature, 465, 334337, https://doi.org/10.1038/nature09043.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • MacKay, D. J., 1992: Bayesian interpolation. Neural Comput., 4, 415447, https://doi.org/10.1162/neco.1992.4.3.415.

  • Marquardt, D., 1963: An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math., 11, 431441, https://doi.org/10.1137/0111030.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Meehl, G., W. Washington, W. Collins, J. Arblaster, A. Hu, L. Buja, W. Strand, and H. Teng, 2005: How much more global warming and sea level rise? Science, 307, 17691772, https://doi.org/10.1126/science.1106663.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Prechelt, L., 1998: Automatic early stopping using cross validation: Quantifying the criteria. Neural Network, 11, 761767, https://doi.org/10.1016/S0893-6080(98)00010-0.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Reverdin, G., F. Marin, B. Bourlès, and P. Lherminier, 2009: XBT temperature errors during French research cruises (1999–2007). J. Atmos. Oceanic Technol., 26, 24622473, https://doi.org/10.1175/2009JTECHO655.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thadathil, P., A. K. Saran, V. V. Gopalakrishna, P. Vethamony, N. Araligidad, and R. Bailey, 2002: XBT fall rate in waters of extreme temperature: A case study in the Antarctic Ocean. J. Atmos. Oceanic Technol., 19, 391396, https://doi.org/10.1175/1520-0426-19.3.391.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Trenberth, K., J. Fasullo, and M. A. Balmaseda, 2014: Earth’s energy imbalance. J. Climate, 27, 31293144, https://doi.org/10.1175/JCLI-D-13-00294.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, G., L. Cheng, J. Abraham, and C. Li, 2018: Consensuses and discrepancies of basin-scale ocean heat content changes in different ocean analyses. Climate Dyn., 50, 24712487, https://doi.org/10.1007/s00382-017-3751-5.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Weigend, A. S., B. A. Huberman, and D. E. Rumelhart, 1990: Predicting the future: A connectionist approach. Int. J. Neural Syst., 01, 193209, https://doi.org/10.1142/S0129065790000102.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wijffels, S., J. Willis, C. Domingues, P. Barker, N. White, A. Gronell, K. Ridgway, and J. Church, 2008: Changing expendable bathythermograph fall rates and their impact on estimates of thermosteric sea level rise. J. Climate, 21, 56575672, https://doi.org/10.1175/2008JCLI2290.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
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Correcting Biases in Historical Bathythermograph Data Using Artificial Neural Networks

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  • 1 Interdepartmental Graduate Program in Marine Science, University of California, Santa Barbara, Santa Barbara, California
  • | 2 Department of Geography, University of California, Santa Barbara, Santa Barbara, California
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Abstract

Historical estimates of ocean heat content (OHC) are important for understanding the climate sensitivity of the Earth system and for tracking changes in Earth’s energy balance over time. Prior to 2004, these estimates rely primarily on temperature measurements from mechanical and expendable bathythermograph (BT) instruments that were deployed on large scales by naval vessels and ships of opportunity. These BT temperature measurements are subject to well-documented biases, but even the best calibration methods still exhibit residual biases when compared with high-quality temperature datasets. Here, we use a new approach to reduce biases in historical BT data after binning them to a regular grid such as would be used for estimating OHC. Our method consists of an ensemble of artificial neural networks that corrects biases with respect to depth, year, and water temperature in the top 10 m. A global correction and corrections optimized to specific BT probe types are presented for the top 1800 m. Our approach differs from most prior studies by accounting for multiple sources of error in a single correction instead of separating the bias into several independent components. These new global and probe-specific corrections perform on par with widely used calibration methods on a series of metrics that examine the residual temperature biases with respect to a high-quality reference dataset. However, distinct patterns emerge across these various calibration methods when they are extrapolated to BT data that are not included in our cross-instrument comparison, contributing to uncertainty that will ultimately impact estimates of OHC.

ORCID: 0000-0002-4010-2824.

ORCID: 0000-0002-7771-9430.

Corresponding authors: Aaron Bagnell, a-bagnell@ucsb.edu; Timothy DeVries, tdevries@geog.ucsb.edu

Abstract

Historical estimates of ocean heat content (OHC) are important for understanding the climate sensitivity of the Earth system and for tracking changes in Earth’s energy balance over time. Prior to 2004, these estimates rely primarily on temperature measurements from mechanical and expendable bathythermograph (BT) instruments that were deployed on large scales by naval vessels and ships of opportunity. These BT temperature measurements are subject to well-documented biases, but even the best calibration methods still exhibit residual biases when compared with high-quality temperature datasets. Here, we use a new approach to reduce biases in historical BT data after binning them to a regular grid such as would be used for estimating OHC. Our method consists of an ensemble of artificial neural networks that corrects biases with respect to depth, year, and water temperature in the top 10 m. A global correction and corrections optimized to specific BT probe types are presented for the top 1800 m. Our approach differs from most prior studies by accounting for multiple sources of error in a single correction instead of separating the bias into several independent components. These new global and probe-specific corrections perform on par with widely used calibration methods on a series of metrics that examine the residual temperature biases with respect to a high-quality reference dataset. However, distinct patterns emerge across these various calibration methods when they are extrapolated to BT data that are not included in our cross-instrument comparison, contributing to uncertainty that will ultimately impact estimates of OHC.

ORCID: 0000-0002-4010-2824.

ORCID: 0000-0002-7771-9430.

Corresponding authors: Aaron Bagnell, a-bagnell@ucsb.edu; Timothy DeVries, tdevries@geog.ucsb.edu
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