We examine volume average temperature anomalies (ΔT) for the upper 700 m of the global ocean (see Methods). Figure 1a compares uncorrected observational ΔT estimates ISH-UNCOR (ref. 10) and LEV-UNCOR (ref. 11) with improved versions, ISH (ref. 8) and LEV (ref.  9), which incorporate corrections for expendable bathythermograph (XBT) biases. The bias-corrected temperature analysis⁷ from a third group (DOM) is also shown. Bias corrections have a substantial impact on the time evolution of ΔT, particularly during the 1970s–1980s, when they markedly reduce spurious decadal variability.

[Delta]T (0-700[thinsp]m) with respect to a 1957-1990 climatology." />

a, Estimates of Domingues et al. ⁷ (DOM), Ishii et al. ⁸ (ISH) and Levitus et al. ⁹ (LEV), all of which have been corrected for XBT biases. Earlier (uncorrected) estimates of Ishii et al. ¹⁰ (ISH-UNCOR) and Levitus et al. ¹¹ (LEV-UNCOR) are also shown. b, ISH and LEV ΔT_IF (solid lines) and ΔT_SS (dotted lines) results. c, Recent observed ΔT estimates compared with the CMIP3 20CEN MMR for the subsets of models including VOL and NoV. MMR results are also shown for the CMIP3 SRES A1B scenarios, constructed from the same VOL and NoV subsets defined by the 20CEN models. The SRES A1B results include fewer model simulations than were available in the 20CEN MMRs. All time series are computed from spatially complete data, except the dotted lines in b. For visual display purposes only, all observational data are five-year running averages.

As shown below, these bias adjustments have important implications for detection and attribution (D&A) studies. Although there are no significant differences between the ΔT trends (which range from 0.022 to 0.028 °C per decade) in the three improved observational data sets, Fig. 1a illustrates that substantial structural uncertainties remain. The impact of different XBT bias corrections is a major source of this uncertainty¹².

Another important component of observational uncertainty relates to the sparseness of ocean temperature measurements and to the different methods used to objectively infill data where and when measurements are not available^{13, 14, 15}. ISH and LEV use objective mapping techniques to carry out infilling, generating anomalies that are biased towards zero in data-sparse regions. The infilling method of DOM employs statistics of observed ocean variability estimated from altimeter data. We compare the spatially complete infilled estimates (ΔT_IF) with subsampled ΔT data (ΔT_SS) restricted to available in situ measurements (see Methods). Not surprisingly, the ΔT_SS variability in Fig. 1b is greater than that of ΔT_IF, particularly at the times/locations of the sparsest sampling (early in the record and in the southern oceans; Supplementary Fig. S1).

We use results from phase 3 of the Coupled Model Intercomparison Project (CMIP3; see Methods and Supplementary Information) to obtain information on the behaviour of ΔT in unforced (control) simulations and in externally forced twentieth-century runs (20CEN). External forcing is by a variety of anthropogenic factors (primarily greenhouse gases and sulphate aerosols). In some models, the applied forcing also includes natural changes in volcanic aerosols and solar irradiance. The seven CMIP3 models (with the data required for our analysis) incorporating the effects of volcanic eruptions (VOL) in the 20CEN simulations uptake less heat than the six that do not (NoV)¹⁶.

Accounting for residual simulation drift (see Methods), the multimodel VOL global mean ΔT time series are within the spread of observational estimates over the entire observational record, whereas the warming in the NoV multimodel average is larger than observed in the most recent decades (Fig. 1c). Twenty-first-century ΔT changes in CMIP3 future projections are also shown¹⁷, and are based on the SRES A1B scenario from the Intergovernmental Panel on Climate Change Special Report on Emissions Scenarios (SRES). The small discontinuity between the 20CEN and SRES A1B results arises because fewer simulations are available for the scenario runs and forcing discontinuities are known to exist in some simulations¹⁸ (see Supplementary Information). Note that inclusion of volcanic forcing increases the simulated variability^{7, 15, 19}.

Figure 2 shows linear trends over 1960–1999 in observed and simulated ΔT_SS and ΔT_IF data. Results are for global averages and each of the six ocean basins. Observed ΔT_IFtrends are generally smaller than their ΔT_SScounterparts, probably because the ΔT_IF results are biased low in data-sparse regions. Note that in both models and observations, the Atlantic warming is larger than in the Pacific.

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