全球变化知识资源中心

As the dominant reservoir of heat uptake in the climate system, the world’s oceans provide a critical measure of global climate change. Here, we infer deep-ocean warming in the context of global sea-level rise and Earth’s energy budget between January 2005 and December 2013. Direct measurements of ocean warming above 2,000 m depth explain about 32% of the observed annual rate of global mean sea-level rise. Over the entire water column, independent estimates of ocean warming yield a contribution of 0.77 ± 0.28 mm yr⁻¹ in sea-level rise and agree with the upper-ocean estimate to within the estimated uncertainties. Accounting for additional possible systematic uncertainties, the deep ocean (below 2,000 m) contributes −0.13 ± 0.72 mm yr⁻¹ to global sea-level rise and −0.08 ± 0.43 W m⁻² to Earth’s energy balance. The net warming of the ocean implies an energy imbalance for the Earth of 0.64 ± 0.44 W m⁻² from 2005 to 2013.

Sea-level rise is one of the most important consequences of human-caused global warming. Because sea-level rise is caused by a combination of freshwater increase (from the melting of land ice) and thermal expansion (from ocean warming), global mean sea-level change provides a powerful tool for monitoring the net impact of forcing on the climate system¹. Because of their accuracy, satellite observations of sea-level rise and ocean mass change are now able to provide a new constraint on the rate of thermal expansion in the ocean, and hence on ocean heat content change. Here, we consider gridded in situ temperature and salinity observations from Argo in combination with global mean sea-level rise from satellite altimetry and ocean mass change estimates (that is, fresh water inputs from melting of mountain glaciers and ice sheets) from the Gravity Recovery and Climate Experiment (GRACE). By combining these three different types of observations, we quantify warming rates of the deep ocean and place upper bounds on the net rate of global warming from 2005 to 2013.

Long-term global sea-level rise has been well established², and there have been several review papers addressing the causes of sea-level rise and their implications for global warming^{3, 4}. Since 2003, global observations of ocean temperature for depths above 2,000 m have become available on a regular basis with the advent of the Argo array of profiling floats^{5, 6, 7, 8, 9, 10}. Measurements from ships of opportunity provide observations from earlier periods but are limited to depths above 700 m (refs 3, 11). Nevertheless, the ocean layers above 700 m and 2,000 m represent only 20% and 50%, respectively, of the total ocean volume^{1, 12}. Although the temperature change remains small compared to the upper ocean, the deep-ocean contribution to sea level and energy budgets might be significant because of its large volume¹³. Studies have demonstrated deep-ocean warming below 2,000 m depth over multi-decadal timescales^{13, 14}. For instance, it has been shown that the deep ocean (below 2,000 m depth) experienced a significant slight warming of 0.068 ± 0.061 W m⁻² (95% confidence), corresponding to a global mean sea-level rise of 0.113 ± 0.1 mm yr⁻¹ (95% confidence), for the 1990s–2000s period¹³. Decadal warming in the deep ocean has recently been discussed in a review paper¹², with small but significant rates in several regions that contribute to global sea-level rise and Earth’s energy balance. Nevertheless, such estimates rely primarily on very sparse observations and are limited to decadal and longer-term rates of change, and periods before about 2005.

This lack of data has led to speculation that large amounts of heat might be entering the deep ocean undetected. For instance, it has been suggested that such deep-ocean warming (below 2,000 m) could explain the ‘missing energy’ in observations of the global energy budget¹⁵. Some have suggested that 30% of ocean warming on decadal timescales has occurred below 700 m depth¹⁶. Yet, direct observations of deep-ocean warming do not suggest such large amounts of warming in the deep ocean, at least before the mid-2000s^{12, 13, 14}. Over the most recent decade, however, the GRACE and Argo observing systems have given us a new way to estimate warming in the deep ocean and the net imbalance in Earth’s energy budget. To do so, we consider the total amount of sea-level rise observed by satellite altimeters between 2005 and 2013 and subtract the amount attributable to upper-ocean warming (as observed by Argo) and ocean mass increase (as observed by GRACE). The residual is then used to place a constraint on the possible range of deep-ocean warming during this period.

The global mean sea-level time series inferred by satellite altimetry (blue curve in Fig. 1) increases by approximately 30 mm from 2003 to 2013, showing some interannual variability fluctuating around a near-linear increase. This interannual variability is highly correlated to El Niño/La Niña climate variability¹⁷ and is linked to fresh water exchanges between the ocean and the continents¹⁸, especially the large La Niña event of 2011^{19, 20}. From 2005 to 2013, sea level rose at a rate of 2.78 ± 0.32 mm yr⁻¹. This rise is slightly lower than the rate of 3.2 ± 0.4 mm yr⁻¹ for the whole altimetric period (updated from refs 3, 4) and has been attributed to the successive La Niña events for the recent years²¹. The black curve depicts the ocean mass evolution from 2003 to 2013 based on independent satellite gravimetry observations from GRACE. Similar to observed mean sea-level variations, the ocean mass signal exhibits a linear increase plus interannual variability, especially during the large La Niña event of 2011. The ocean mass variations explain 80% of the fractional variance of the observed global mean sea-level fluctuation. Formally, from 2005 to 2013, the ocean mass time series has a linear trend of 2.0 ± 0.1 mm yr⁻¹. The uncertainties quoted here (and throughout unless otherwise noted) represent random errors plus the formal error from the linear fit estimated as described in Methods. Systematic errors (that is, temporally correlated) are dealt with separately, as discussed below and in Methods.

The estimates are observed variations by satellite altimetry (blue), ocean mass contributions based on GRACE data (solid black) and steric sea level based on in situ observations (red). The dashed black curve shows the indirect steric mean sea-level estimate inferred by removing ocean mass contributions from the observed sea-level time series. Seasonal signals have been removed from all curves. Curves are offset for clarity. Shading, where shown, denotes 1-σ uncertainty of the respective estimates.

Total sea level has been continuously observed by satellite altimetry since 1992 with the launch of TOPEX/Poseidon followed by Jason-1 and -2, launched in 2001 and 2008, respectively. This family of satellites provides a near-global coverage (±66° of latitude) of the oceans every ten days. We have considered here the global mean sea-level time series from the University of Colorado¹⁷, available at http://sealevel.colorado.edu/. These data have been processed by applying geophysical corrections and verified using independent tide gauge records. (For more information about data processing, see ref. 17.) For a period of ten days, random errors in the global average are estimated to be about 4 mm and have been verified through comparison with tide gauges^{9, 22, 29}. To compute monthly error averages, we assume that these ten-day averaged altimetric data have an e-folding correlation time of ten days. Then, the accuracy of the monthly global mean sea level is estimated to be ±2.6 mm (which represents random measurement error).

To estimate global mean ocean mass variations, we use GRACE CSR Release-05 time-variable gravity observations from April 2002 through to December 2013 (available at http://www.nature.com/nclimate/journal/v4/n11/full/ftp://podaac-ftp.jpl.nasa.gov/allData/grace/L2/CSR/RL05/). Standard processing steps were followed (details can be found in ref. 30) by accounting for geocentre motion³¹, glacial isostatic adjustment³² and changes in Earth’s dynamic oblateness (that is, C(2,0) coefficients)³³. The impact of land signals on GRACE ocean mass is reduced by omitting data within 300 km of land. The resulting ocean average represents ocean mass changes and can thus be directly compared to the steric-corrected sea level. We estimate the accuracy (which represents random measurement error) of the monthly ocean mass estimates to be ±1.2 mm (ref. 30). Additional GRACE solutions from GFZ (available at http://www.nature.com/nclimate/journal/v4/n11/full/ftp://podaac-ftp.jpl.nasa.gov/allData/grace/L2/GFZ/RL05/) and JPL (available at http://www.nature.com/nclimate/journal/v4/n11/full/ftp://podaac-ftp.jpl.nasa.gov/allData/grace/L2/JPL/RL05/) were also analysed. The standard deviation among the three solutions is ±0.4mm, which indicates that the formal error estimate above is conservative.

Gridded temperature and salinity estimates used in this study are obtained from four separate groups: Scripps Institution of Oceanography (updated from ref. 34), International Pacific Research Center (IPRC), Japan Agency for Marine-Earth Science and Technology (JAMSTEC, ref. 35) and National Oceanic and Atmospheric Administration (NOAA, ref. 24). These data can be downloaded at www.argo.ucsd.edu/Gridded_fields.html for SCRIPPS, IPRC and JAMSTEC data sets and www.nodc.noaa.gov/OC5/3M_HEAT_CONTENT/ for the NOAA data set. Contrary to the others, the NOAA and JAMSTEC data sets combine not only Argo floats, but also other in situ measurements (for example, expendable bathythermograph (XBT), CTD and mooring data). Temperature and salinity data have been passed through many quality control checks (see the Argo quality control manual for more details, ref. 36). Steric sea-level time series are computed by using temperature and salinity fields from each data product. (Further details of this computation can be found in ref. 11, section 2.1.1.) On a monthly basis, the global mean steric sea-level evolution of the upper 2,000 m of the ocean is estimated with an accuracy of ±3 mm (refs 5, 9). As for altimetry and GRACE, this uncertainty represents an estimate of random measurement error in estimating the global mean using available observations. The partitioning of heat content change above and below 700 m has been motivated because of the historical sampling for the past decades²³.

All estimates in the present study are anomalies with respect to the time-mean over their respective periods (that is, 2003–2013 for altimetry and GRACE time series and 2005–2013 for steric sea level inferred by Argo data sets). Because we are focusing on interannual to decadal changes, we have removed a monthly-climatology defined as the time-mean over the respective time periods for each calendar month. The curves are offset for clarity.

The error estimates for each observing system previously described in this section represent the accuracy of the measurement at a monthly basis. We assume that these errors are random and uncorrelated over timescales longer than one month. This is a good assumption, given that none of the analyses use data collected over a period longer than one month. To estimate uncertainty in the trend, we perform a weighted least-squares fit to the monthly observations, where the weights are chosen to equal the reciprocal of the square of the measurement accuracy for each month (as in ref. 27; Appendix A). The formal error from the fit, which represents the misfit of the observations to the trend, is added to the individual random error for each month to compute the trend uncertainty quoted throughout the manuscript. As well as the trend errors, we add systematic uncertainty for GRACE and satellite altimetry.

Coherence between two time series is quantified in terms of explained variance (EV), defined as:

where var(A − B) and var(A) denote the variance of A − B and A respectively. The measure will be equal to 1 when B completely accounts for variations of A, and less than 1 otherwise.

1. IPCC Climate Change 2013: The Physical Science Basis (eds Stocker, T. F. et al.) (Cambridge Univ. Press, 2013).
2. Church, J. A. & White, N. J. Sea-level rise from the late 19th to the early 21st century. Surv. Geophys. 32, 585–602 (2011).
   • Article
3. Cazenave, A. & Llovel, W. Contemporary sea level rise. Annu. Rev. Mar. Sci. 2, 145–173 (2010).
   • Article
4. Church, J. A. et al. Revising the Earth’s sea-level and energy budgets from 1961 to 2008. Geophys. Res. Lett. 38, L18601 (2011).
   • Article
5. Willis, J. K., Chambers, D. P. & Nerem, R. S. Assessing the globally averaged sea level budget on seasonal to interannual time scales. J. Geophys. Res. 113, C06015 (2008).
   • Article
6. Cazenave, A. et al. Sea level budget over 2003–2008: A reevaluation from GRACE space gravimetry, satellite altimetry and Argo. Glob. Planet. Change 65, 83–88 (2009).
   • ISI
   • Article
   URL: