• Abraham, J. P., and Coauthors, 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
  • Adcroft, A., and J.-M. Campin, 2004: Rescaled height coordinates for accurate representation of free-surface flows in ocean circulation models. Ocean Modell., 7, 269284, https://doi.org/10.1016/j.ocemod.2003.09.003.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Adcroft, A., C. Hill, and J. Marshall, 1997: The representation of topography by shaved cells in a height coordinate model. Mon. Wea. Rev., 125, 22932315, https://doi.org/10.1175/1520-0493(1997)125<2293:ROTBSC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • ATOC Consortium, 1998: Ocean climate change: Comparison of acoustic tomography, satellite altimetry, and modeling. Science, 281, 13271332, https://doi.org/10.1126/science.281.5381.1327.

    • Search Google Scholar
    • Export Citation
  • Balmaseda, M. A., K. E. Trenberth, and E. Källén, 2013: Distinctive climate signals in reanalysis of global ocean heat content. Geophys. Res. Lett., 40, 17541759, https://doi.org/10.1002/grl.50382.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Boyer, T., and Coauthors, 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
  • Buckley, M. W., R. M. Ponte, G. Forget, and P. Heimbach, 2015: Determining the origins of advective heat transport convergence variability in the North Atlantic. J. Climate, 28, 39433956, https://doi.org/10.1175/JCLI-D-14-00579.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Campin, J.-M., A. Adcroft, C. Hill, and J. Marshall, 2004: Conservation of properties in a free surface model. Ocean Modell., 6, 221244, https://doi.org/10.1016/S1463-5003(03)00009-X.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chambers, D. P. A., N. Cazenave, H. Champollion, W. Dieng, R. Llovel, and R. Forsberg, 2017: Evaluation of the global mean sea level budget between 1993 and 2014. Surv. Geophys., 38, 309327, https://doi.org/10.1007/s10712-016-9381-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chaudhuri, A. H., R. M. Ponte, G. Forget, and P. Heimbach, 2013: A comparison of atmospheric reanalysis surface products over the ocean and implications for uncertainties in air–sea boundary forcing. J. Climate, 26, 153170, https://doi.org/10.1175/JCLI-D-12-00090.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cheng, L., K. E. 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
  • Church, J. A., and Coauthors, 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
  • Church, J. A., and Coauthors, 2013: Sea level change. Climate Change 2013, The Physical Science Basis, T. F. Stocker et al., Eds., Cambridge University Press, 11371216.

    • Search Google Scholar
    • Export Citation
  • Colosi, J. A., and W. Munk, 2006: Tales of the venerable Honolulu tide gauge. J. Phys. Oceanogr., 36, 967996, https://doi.org/10.1175/JPO2876.1.

  • Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553597, https://doi.org/10.1002/qj.828.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Desbruyères, D. G., S. G. Purkey, E. L. McDonagh, G. C. Johnson, and B. A. King, 2016: Deep and abyssal ocean warming from 35 years of repeat hydrography. Geophys. Res. Lett., 43, 10 35610 365, https://doi.org/10.1002/2016GL070413.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Domingues, C. M., J. A. Church, N. J. White, P. J. Gleckler, S. E. Wijffels, P. M. Barker, and J. R. 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
  • Durack, P. J., and S. E. Wijffels, 2010: Fifty-year trends in global ocean salinities and their relationship to broad-scale warming. J. Climate, 23, 43424362, https://doi.org/10.1175/2010JCLI3377.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dushaw, B. D., and Coauthors, 2009: A decade of acoustic thermometry in the North Pacific Ocean. J. Geophys. Res., 114, C07021, https://doi.org/10.1029/2008JC005124.

    • Search Google Scholar
    • Export Citation
  • Fasullo, J. T., and P. R. Gent, 2017: On the relationship between regional ocean heat content and sea surface height. J. Climate, 30, 91959211, https://doi.org/10.1175/JCLI-D-16-0920.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Forget, G., J.-M. Campin, P. Heimbach, C. N. Hill, R. M. Ponte, and C. Wunsch, 2015: ECCO version 4: An integrated framework for nonlinear inverse modeling and global ocean state estimation. Geosci. Model Dev., 8, 30713104, https://doi.org/10.5194/gmd-8-3071-2015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fournier, S., T. Lee, X. Wang, T. W. K. Armitage, O. Wang, I. Fukumori, and R. Kwok, 2020: Sea surface salinity as a proxy for Arctic Ocean freshwater changes. J. Geophys. Res. Oceans, 125, e2020JC016110, https://doi.org/10.1029/2020JC016110.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fukumori, I., O. Wang, I. Fenty, G. Forget, P. Heimbach, and R. M. Ponte, 2017: ECCO version 4 release 3. JPL Rep., 10 pp., http://hdl.handle.net/1721.1/110380.

    • Search Google Scholar
    • Export Citation
  • Garry, F. K., E. L. McDonagh, A. T. Blaker, C. D. Roberts, D. G. Desbruyères, E. Frajka-Williams, and B. A. King, 2019: Model-derived uncertainties in deep ocean temperature trends between 1990 and 2010. J. Geophys. Res. Oceans, 124, 11551169, https://doi.org/10.1029/2018JC014225.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gaspar, P., Y. Grégoris, and J.-M. LeFevre, 1990: A simple eddy kinetic energy model for simulations of the oceanic vertical mixing: Tests at Station Papa and long-term upper ocean study site. J. Geophys. Res., 95, 16 17916 193, https://doi.org/10.1029/JC095iC09p16179.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gasparin, F., M. Hamon, E. Rémy, and P.-Y. Le Traon, 2020: How deep Argo will improve the deep ocean in an ocean reanalysis. J. Climate, 33, 7794, https://doi.org/10.1175/JCLI-D-19-0208.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gent, P. R., and J. C. McWilliams, 1990: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20, 150155, https://doi.org/10.1175/1520-0485(1990)020<0150:IMIOCM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Giering, R., and T. Kaminski, 1998: Recipes for adjoint code construction. ACM Trans. Math. Software, 24, 437474, https://doi.org/10.1145/293686.293695.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gilbert, J. C., and C. Lemarechal, 1989: Some numerical experiments with variable-storage quasi-Newton algorithms. Math. Program., 45, 407435, https://doi.org/10.1007/BF01589113.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gleckler, P. J., P. J. Durack, R. J. Stouffer, G. C. Johnson, and C. E. Forest, 2016: Industrial-era global ocean heat uptake doubles in recent decades. Nat. Climate Change, 6, 394398, https://doi.org/10.1038/nclimate2915.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gregory, J. M., and Coauthors, 2013: Twentieth-century global-mean sea level rise: Is the whole greater than the sum of the parts? J. Climate, 26, 44764499, https://doi.org/10.1175/JCLI-D-12-00319.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Griewank, A., 1992: Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation. Optim. Methods Software, 1, 3554, https://doi.org/10.1080/10556789208805505.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hamlington, B. D., and Coauthors, 2020: Understanding of contemporary regional sea-level change and the implications for the future. Rev. Geophys., 58, e2019RG000672, https://doi.org/10.1029/2019RG000672.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hastie, T., R. Tibshirani, and J. Friedman, 2001: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Verlag, 533 pp.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heimbach, P., D. Menemenlis, M. Losch, J. M. Campin, and C. Hill, 2010: On the formulation of sea-ice models. Part 2: Lessons from multi-year adjoint sea ice export sensitivities through the Canadian Arctic Archipelago. Ocean Modell., 33, 145158, https://doi.org/10.1016/j.ocemod.2010.02.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heimbach, P., and Coauthors, 2019: Putting it all together: Adding value to the global ocean and climate observing systems with complete self-consistent ocean state and parameter estimates. Front. Mar. Sci., 6, 55, https://doi.org/10.3389/fmars.2019.00055.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Howe, B. M., and Coauthors, 2019: SMART cables for observing the global ocean: Science and implementation. Front. Mar. Sci., 6, 424, https://doi.org/10.3389/fmars.2019.00424.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hsieh, W. W., and B. Tang, 1998: Applying neural network models to prediction and data analysis in meteorology and oceanography. Bull. Amer. Meteor. Soc., 79, 18551870, https://doi.org/10.1175/1520-0477(1998)079<1855:ANNMTP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Irrgang, C., J. Saynisch, and M. Thomas, 2017: Utilizing oceanic electromagnetic induction to constrain an ocean general circulation model: A data assimilation twin experiment. J. Adv. Model. Earth Syst., 9, 17031720, https://doi.org/10.1002/2017MS000951.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Irrgang, C., J. Saynisch, and M. Thomas, 2019: Estimating global ocean heat content from tidal magnetic satellite observations. Sci. Rep., 9, 7893, https://doi.org/10.1038/s41598-019-44397-8.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 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
  • Ishii, M., and Coauthors, 2017: Accuracy of global upper ocean heat content estimation expected from present observational data sets. SOLA, 13, 163167, https://doi.org/10.2151/sola.2017-030.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jayne, S. R., J. M. Wahr, and F. O. Bryan, 2003: Observing ocean heat content using satellite gravity and altimetry. J. Geophys. Res., 108, 3031, https://doi.org/10.1029/2002JC001619.

    • Search Google Scholar
    • Export Citation
  • Johnson, G. C., S. G. Purkey, N. V. Zilberman, and D. Roemmich, 2019: Deep Argo quantifies bottom water warming rates in the southwest Pacific basin. Geophys. Res. Lett., 46, 26622669, https://doi.org/10.1029/2018GL081685.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kouketsu, S., and Coauthors, 2011: Deep ocean heat content changes estimated from observation and reanalysis product and their influence on sea level change. J. Geophys. Res., 116, C03012, https://doi.org/10.1029/2010JC006464.

    • Search Google Scholar
    • Export Citation
  • Kunze, E., 2017: Internal-wave-driven mixing: Global geography and budgets. J. Phys. Oceanogr., 47, 13251345, https://doi.org/10.1175/JPO-D-16-0141.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lary, D. J., A. H. Alavi, A. H. Gandomi, and A. L. Walker, 2016: Machine learning in geosciences and remote sensing. Geosci. Front., 7, 310, https://doi.org/10.1016/j.gsf.2015.07.003.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • L’Ecuyer, T., H. K. Beaudoing, M. Rodell, W. Olson, B. Lin, and S. Kato, 2015: The observed state of the energy budget in the early 21st century. J. Climate, 28, 83198346, https://doi.org/10.1175/JCLI-D-14-00556.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Levitus, S., J. I. Antonov, J. Wang, T. L. Delworth, K. W. Dixon, and A. J. Broccoli, 2001: Anthropogenic warming of Earth’s climate system. Science, 292, 267270, https://doi.org/10.1126/science.1058154.

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

    • Search Google Scholar
    • Export Citation
  • Llovel, W., J. K. Willis, F. W. Landerer, and I. Fukumori, 2014: Deep-ocean contribution to sea level and energy budget not detectable over the past decade. Nat. Climate Change, 4, 10311035, https://doi.org/10.1038/nclimate2387.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Losch, M., D. Menemenlis, J. M. Campin, P. Heimbach, and C. Hill, 2010: On the formulation of sea-ice models. Part 1: Effects of different solver implementations and parameterizations. Ocean Modell., 33, 129144, https://doi.org/10.1016/j.ocemod.2009.12.008.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lozier, M. S., and Coauthors, 2019: A sea change in our view of overturning in the subpolar North Atlantic. Science, 363, 516521, https://doi.org/10.1126/science.aau6592.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lyman, J. M., and G. C. Johnson, 2014: Estimating global ocean heat content changes in the upper 1800 m since 1950 and the influence of climatology choice. J. Climate, 27, 19451957, https://doi.org/10.1175/JCLI-D-12-00752.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Manoj, C., A. Kuvshinov, S. Neetu, and T. Harinarayana, 2010: Can undersea voltage measurements detect tsunamis? Earth Planets Space, 62, 353358, https://doi.org/10.5047/eps.2009.10.001.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McDougall, T. J., and P. M. Barker, 2011: Getting started with TEOS-10 and the Gibbs Seawater (GSW) Oceanographic Toolbox. SCOR/IAPSO Rep. WG127, 28 pp.

    • Search Google Scholar
    • Export Citation
  • Menemenlis, D., and Coauthors, 2005: NASA supercomputer improves prospects for ocean climate research. Eos, Trans. Amer. Geophys. Union, 86, 8996, https://doi.org/10.1029/2005EO090002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Meyssignac, B., and Coauthors, 2019: Measuring global ocean heat content to estimate the Earth energy imbalance. Front. Mar. Sci., 6, 432, https://doi.org/10.3389/fmars.2019.00432.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Minami, T., 2017: Motional induction by tsunamis and ocean tides: 10 years of progress. Surv. Geophys., 38, 10971132, https://doi.org/10.1007/s10712-017-9417-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Minami, T., H. Toh, and R. H. Tyler, 2015: Properties of electromagnetic fields generated by tsunami first arrivals: Classification based on the ocean depth. Geophys. Res. Lett., 42, 21712178, https://doi.org/10.1002/2015GL063055.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Munk, W., and C. Wunsch, 1979: Ocean acoustic tomography: A scheme for large scale monitoring. Deep-Sea Res., 26A, 123161, https://doi.org/10.1016/0198-0149(79)90073-6.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nocedal, J., 1980: Updating quasi-Newton matrices with limited storage. Math. Comput., 35, 773782, https://doi.org/10.1090/S0025-5718-1980-0572855-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Osse, T. J., and C. C. Eriksen, 2007: The Deepglider: A full ocean depth glider for oceanographic research. Oceans 2007, Vancouver, BC, Canada, IEEE, https://doi.org/10.1109/OCEANS.2007.4449125.

    • Search Google Scholar
    • Export Citation
  • Palmer, M. D., and Coauthors, 2017: Ocean heat content variability and change in an ensemble of ocean reanalyses. Climate Dyn., 49, 909930, https://doi.org/10.1007/s00382-015-2801-0.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ponte, R. M., K. J. Quinn, C. Wunsch, and P. Heimbach, 2007: A comparison of model and GRACE estimates of the large-scale seasonal cycle in ocean bottom pressure. Geophys. Res. Lett., 34, L09603, https://doi.org/10.1029/2007GL029599.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Purkey, S. G., and G. C. Johnson, 2010: Warming of global abyssal and deep Southern Ocean between the 1990s and the 2000s: Contributions to global heat and sea level rise budgets. J. Climate, 23, 63366351, https://doi.org/10.1175/2010JCLI3682.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Redi, M. H., 1982: Oceanic isopycnal mixing by coordinate rotation. J. Phys. Oceanogr., 12, 11541158, https://doi.org/10.1175/1520-0485(1982)012<1154:OIMBCR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Resplandy, L., and Coauthors, 2019: Quantification of ocean heat uptake from changes in atmospheric O2 and CO2 composition. Sci. Rep., 9, 20244, https://doi.org/10.1038/s41598-019-56490-z.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Riser, S. C., and Coauthors, 2016: Fifteen years of ocean observations with the global Argo array. Nat. Climate Change, 6, 145153, https://doi.org/10.1038/nclimate2872.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Roemmich, D., J. Church, J. Gilson, D. Monselesan, P. Sutton, and S. Wijffels, 2015: Unabated planetary warming and its ocean structure since 2006. Nat. Climate Change, 5, 240245, https://doi.org/10.1038/nclimate2513.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sanford, T. B., 1971: Motionally induced electric and magnetic fields in the sea. J. Geophys. Res., 76, 34763492, https://doi.org/10.1029/JC076i015p03476.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schindelegger, M., A. A. Harker, R. M. Ponte, H. Dobslaw, D. A. Salstein, 2021: Convergence of daily GRACE solutions and models of submonthly ocean bottom pressure variability. J. Geophys. Res. Oceans, 126, e2020JC017031, https://doi.org/10.1029/2020JC017031.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schnepf, N. R., M. C. Nair, J. Velímský, and N. P. Thomas, 2021: Can seafloor voltage cables be used to study large-scale circulation? An investigation in the Pacific Ocean. Ocean Sci., 17, 383392, https://doi.org/10.5194/os-2019-129.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stammer, D., M. Balmaseda, P. Heimbach, A. Köhl, and A. Weaver, 2016: Ocean data assimilation in support of climate applications: Status and perspectives. Annu. Rev. Mar. Sci., 8, 491518, https://doi.org/10.1146/annurev-marine-122414-034113.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Trenberth, K. E., J. T. 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
  • Trenberth, K. E., J. T. Fasullo, K. von Schuckmann, and L. Cheng, 2016: Insights into Earth’s energy imbalance from multiple sources. J. Climate, 29, 74957505, https://doi.org/10.1175/JCLI-D-16-0339.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Trossman, D. S., and R. H. Tyler, 2019: Predictability of ocean heat content from electrical conductance. J. Geophys. Res. Oceans, 124, 667679, https://doi.org/10.1029/2018JC014740.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Trossman, D. S., L. Thompson, and S. L. Hautala, 2011: Application of thin-plate splines in two-dimensions to oceanographic tracer data. J. Atmos. Oceanic Technol., 28, 15221538, https://doi.org/10.1175/JTECH-D-10-05024.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tyler, R. H., 2005: A simple formula for estimating the magnetic fields generated by tsunami flow. Geophys. Res. Lett., 32, L09608, https://doi.org/10.1029/2005GL022429.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tyler, R. H., 2017: Mathematical modeling of electrodynamics near the surface of Earth and planetary water worlds. NASA Tech. Rep. TM-2017-219022, 62 pp., https://ntrs.nasa.gov/citations/20170011279.

    • Search Google Scholar
    • Export Citation
  • Tyler, R. H., 2021: A century of tidal variability in the North Pacific extracted from hourly geomagnetic observatory measurements at Honolulu. Geophys. Res. Lett., 48, e2021GL094435, https://doi.org/10.1029/2021GL094435.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tyler, R. H., and L. Mysak, 1995: Electrodynamics in a rotating frame of reference with application to global ocean circulation. Can. J. Phys., 73, 393402, https://doi.org/10.1139/p95-055.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tyler, R. H., and T. J. Sabaka, 2016: Magnetic remote sensing of ocean heat content. 2016 Fall Meeting, San Francisco, CA, Amer. Geophys. Union, Abstract GC31D-1142, https://agu.confex.com/agu/fm16/meetingapp.cgi/Paper/191894.

    • Search Google Scholar
    • Export Citation
  • Vishwakarma, B. D., S. Royston, R. E. M. Riva, R. M. Westaway, and J. L. Bamber, 2020: Sea level budgets should account for ocean bottom deformation. Geophys. Res. Lett., 47, e2019GL086492, https://doi.org/10.1029/2019GL086492.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • von Schuckmann, K., and Coauthors, 2016: An imperative to monitor Earth’s energy imbalance. Nat. Climate Change, 6, 138144, https://doi.org/10.1038/nclimate2876.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wahle, K., J. Staneva, and H. Guenther, 2015: Data assimilation of ocean wind waves using neural networks. A case study for the German Bight. Ocean Modell., 96, 117125, https://doi.org/10.1016/j.ocemod.2015.07.007.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • WCRP Global Sea Level Budget Group, 2018: Global sea-level budget 1993–present. Earth Syst. Sci. Data, 10, 15511590, https://doi.org/10.5194/essd-10-1551-2018.

    • Search Google Scholar
    • Export Citation
  • Wood, S. N., 2006: Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC Press, 410 pp.

  • Wu, W., Z. Zhan, S. Peng, S. Ni, and J. Callies, 2020: Seismic ocean thermometry. Science, 369, 15101515, https://doi.org/10.1126/science.abb9519.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wunsch, C., and P. Heimbach, 2013: Dynamically and kinematically consistent global ocean circulation and ice state estimates. Ocean Circulation and Climate, 2nd ed. G. Siedler et al., Eds., Elsevier, 553580.

    • Search Google Scholar
    • Export Citation
  • Zanna, L., S. Khatiwala, J. M. Gregory, J. Ison, and P. Heimbach, 2019: Global reconstruction of historical ocean heat storage and transport. Proc. Natl. Acad. Sci. USA, 116, 11261131, https://doi.org/10.1073/pnas.1808838115.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhao, Z., 2016: Internal tide oceanic tomography. Geophys. Res. Lett., 43, 91579164, https://doi.org/10.1002/2016GL070567.

All Time Past Year Past 30 Days
Abstract Views 393 215 0
Full Text Views 83 59 14
PDF Downloads 88 60 11

A Prototype for Remote Monitoring of Ocean Heat Content Anomalies

David S. TrossmanaDepartment of Oceanography and Coastal Sciences, Louisiana State University, Baton Rouge, Louisiana
bCenter for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana
cGlobal Science and Technology, NOAA/NESDIS/STAR, College Park, Maryland

Search for other papers by David S. Trossman in
Current site
Google Scholar
PubMed
Close
and
Robert H. TylerdGeodesy and Geophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, Maryland
eJoint Center for Earth Systems Technology, University of Maryland, Baltimore County, Baltimore, Maryland

Search for other papers by Robert H. Tyler in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

To overcome challenges with observing ocean heat content (OHC) over the entire ocean, we propose a novel approach that exploits the abundance of satellite data, including data from modern satellite geomagnetic surveys such as Swarm. The method considers a novel combination of conventional in situ (temperature and pressure) as well as satellite (altimetry and gravimetry) data with estimates of ocean electrical conductance (depth-integrated conductivity), which can potentially be obtained from magnetic observations (by satellite, land, seafloor, ocean, and airborne magnetometers). To demonstrate the potential benefit of the proposed method, we sample model output of an ocean state estimate to reflect existing observations and train a machine learning algorithm [Generalized Additive Model (GAM)] on these samples. We then calculate OHC everywhere using information potentially derivable from various global satellite coverage—including magnetic observations—to gauge the GAM’s goodness of fit on a global scale. Inclusion of in situ observations of OHC in the upper 2000 m from Argo-like floats and conductance data each reduce the root-mean-square error by an order of magnitude. Retraining the GAM with recent ship-based hydrographic data attains a smaller RMSE in polar oceans than training the GAM only once on all available historical ship-based hydrographic data; the opposite is true elsewhere. The GAM more accurately calculates OHC anomalies throughout the water column than below 2000 m and can detect global OHC anomalies over multiyear time scales, even when considering hypothetical measurement errors. Our method could complement existing methods and its accuracy could be improved through careful ship-based campaign planning.

Significance Statement

The purpose of this manuscript is to demonstrate the potential for practical implementation of a remote monitoring method for ocean heat content (OHC) anomalies. To do this, we sample data from a reanalysis product primarily because of the dearth of observations below 2000 m depth that can be used for validation and the fact that full-depth-integrated electrical seawater conductivity data products derived from satellite magnetometry are not yet available. We evaluate multiple factors related to the accuracy of OHC anomaly estimation and find that, even with hypothetical measurement errors, our method can be used to monitor OHC anomalies on multiyear time scales.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: David Trossman, david.s.trossman@gmail.com

Abstract

To overcome challenges with observing ocean heat content (OHC) over the entire ocean, we propose a novel approach that exploits the abundance of satellite data, including data from modern satellite geomagnetic surveys such as Swarm. The method considers a novel combination of conventional in situ (temperature and pressure) as well as satellite (altimetry and gravimetry) data with estimates of ocean electrical conductance (depth-integrated conductivity), which can potentially be obtained from magnetic observations (by satellite, land, seafloor, ocean, and airborne magnetometers). To demonstrate the potential benefit of the proposed method, we sample model output of an ocean state estimate to reflect existing observations and train a machine learning algorithm [Generalized Additive Model (GAM)] on these samples. We then calculate OHC everywhere using information potentially derivable from various global satellite coverage—including magnetic observations—to gauge the GAM’s goodness of fit on a global scale. Inclusion of in situ observations of OHC in the upper 2000 m from Argo-like floats and conductance data each reduce the root-mean-square error by an order of magnitude. Retraining the GAM with recent ship-based hydrographic data attains a smaller RMSE in polar oceans than training the GAM only once on all available historical ship-based hydrographic data; the opposite is true elsewhere. The GAM more accurately calculates OHC anomalies throughout the water column than below 2000 m and can detect global OHC anomalies over multiyear time scales, even when considering hypothetical measurement errors. Our method could complement existing methods and its accuracy could be improved through careful ship-based campaign planning.

Significance Statement

The purpose of this manuscript is to demonstrate the potential for practical implementation of a remote monitoring method for ocean heat content (OHC) anomalies. To do this, we sample data from a reanalysis product primarily because of the dearth of observations below 2000 m depth that can be used for validation and the fact that full-depth-integrated electrical seawater conductivity data products derived from satellite magnetometry are not yet available. We evaluate multiple factors related to the accuracy of OHC anomaly estimation and find that, even with hypothetical measurement errors, our method can be used to monitor OHC anomalies on multiyear time scales.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: David Trossman, david.s.trossman@gmail.com
Save