Global reconstruction of historical ocean heat storage and transport

Significance Since the 19th century, rising greenhouse gas concentrations have caused the ocean to absorb most of the Earth’s excess heat and warm up. Before the 1990s, most ocean temperature measurements were above 700 m and therefore, insufficient for an accurate global estimate of ocean warming. We present a method to reconstruct ocean temperature changes with global, full-depth ocean coverage, revealing warming of 436 ×1021 J since 1871. Our reconstruction, which agrees with other estimates for the well-observed period, demonstrates that the ocean absorbed as much heat during 1921–1946 as during 1990–2015. Since the 1950s, up to one-half of excess heat in the Atlantic Ocean at midlatitudes has come from other regions via circulation-related changes in heat transport.

(1-4). However, a comparison of simulated bomb radiocarbon with observations suggests that shallow-to-deep exchange in ECCO-GODAE may be too efficient (5,6). Despite this bias, the inventory and spatial distribution of anthropogenic CO2 simulated by ECCO-GODAE have been shown to be in line with observational estimates (6,7). In addition, a detailed analysis (8) using a more recent version of ECCO, which is not qualitatively different from previous ECCO versions (except for the longer period of assimilation), produces abyssal heat content changes at high Southern latitudes that are consistent with those of (9) (as also shown here in Fig. 1C).
Nonetheless, ECCO-GODAE pathways are derived from an ocean model at 1 • horizontal resolution which inevitably possesses some biases, despite being constrained by observations. To include this uncertainty, without having to recalculate the GFs for several ocean reanalyses, which is computationally challenging, we have opted to perturb our estimates of the GFs. The uncertainty in observationally-based, basin-averaged GFs has been estimated to be O(10-20%) (10). In addition, crude estimates derived from previous studies (5,6) suggest O(20-30%) error in shallow to deep exchange of water. Finally, comparison of ocean reanalysis products (11) shows a 20 to 30% spread in the amplitude of the upper and lower overturning cells. Therefore, we perturb the GFs by 20% in the upper 2000 m and 40% below 2000m in an attempt to represent the transport uncertainty derived from ocean reanalyses, and tracer-based observational estimates. The perturbations are applied while imposing mass conservation by renormalizing the GFs. This uncertainty representation is potentially conservative and will be investigated in future work by using GFs estimated from different observation-based products (e.g., other ECCO state estimates, or direct climatological products such as GLODAP), and/or over different time periods.
Finally, we convolve the GFs with 10 different realizations from HadISST v2.0, rather than using HadISST v1 alone to include uncertainty in surface boundary conditions. The ensemble-mean estimate of OHC, from 1955 onwards, based on HadISST v2.0 is only within 2% of the one based on HadISST v1. The error prior to 1955 is large due to the reduced availability of surface temperatures. Using two additional SST estimates from the NOAA Extended Reconstruction SSTs V4 (12) or from COBE (13) did not result in different OHC estimates (less than a few percents change) and those estimates are therefore left out of the present study.
Overall, the OHC and associated errors from the GFs are comparable to the ensemble-mean and the spread from different observational estimates (e.g., 14, 15, and Fig.1 here). The values of regional trends in OHC and thermosteric sea level rise mentioned in the manuscript are only discussed if the discrepancies between observations and GF estimates are larger than the error estimates derived here.  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62 D. Error estimates: observational products. There is a vast literature describing observational products and associated errors (e.g., [16][17][18]. In addition to the sparsity of the data, especially at high latitudes and in the early part of the historical record, there are other factors leading to uncertainty in OHC estimates: error related to the measurements themselves (i.e., instrumental error), and errors due to the methods used to filling the gap in data sampling. The methods include infilling of data gaps via statistical methods, which often relies on knowledge of temporal and spatial covariance of the data. The uncertainty associated with mapping techniques has been well documented in previous studies (18,19). Other methods to cover the gap in sampling is to rely on data assimilation techniques, which combines observations with a numerical model -none used in the present study (20). As shown in Fig. 1, there are substantial differences among the observationally-based estimates using direct in-filling. Our GFs estimates are often situated within the bounds of the different products, except perhaps for the early part of the record -however error uncertainty estimates might also be underestimated in all products. To easily compare with observations, we have presented the observational linear trends in Fig. 1 (and associated discussion in the main manuscript) as an ensemble-mean, with the error given by the one standard deviation. This type of quantification of uncertainty estimate is likely optimistic, as discussed by (4), especially given that the uncertainty associated with the sparsity of data in the earlier part of the record are not adequately represented by such an unbiased uncertainty quantification.

E. Timeseries of OHC as a function of latitudes.
Heat redistribution by changes in ocean circulation integrates to zero globally; a property that is respected by the use of GFs. However, as shown in Fig. 3, a signature of ocean circulation change is present on a regional scale in the North Atlantic. Since the OHC trends are not necessarily linear, and exhibit strong variability on a wide range of timescales (Figs. 1 and 3), let us consider the temporal evolution of OHC. In the Southern Ocean between 80 • S and 60 • S, there are weak trends over 1955-2017 in both observations (Figs. S3, grey shading representing observational estimates) and GFs (orange curves). Note that the lack of trends in the Southern Ocean could be due to lack of observations (21). Between 60 • S and 40 • S, the increase in heat storage is weaker in the GF estimates than that observed (0.03 ZJ/ • lat), yet still within observational uncertainty. There is a warming trend at all latitudes ranging from 60 • S to 20 • N in both GF estimates and observations, with magnitudes of 1-2 and 0.5-1 ZJ/ • lat, respectively, occurring in the upper 2000 m over the last 60 years. Between 20 • N and 50 • N, discrepancies in trends and variability between the GF and observational estimates are further discernible, indicating strong changes in ocean transport on all timescales.