Is ocean warming accelerating faster than thought? – An analysis of Cheng et al (2019), Science 1 There are a number of statements in Cheng et al. (2019) 'How fast are the oceans warming?', ('the paper') that appear to be mistaken and/or potentially misleading. My analysis of these issues is followed by a reply from the paper's authors: Lijing Cheng, John Abraham, Zeke Hausfather and Kevin Trenberth. Contrary to what the paper indicates:  Contemporary estimates of the trend in 0–2000 m depth ocean heat content over 1971–2010 are closely in line with that assessed in the IPCC AR5 report five years ago  Contemporary estimates of the trend in 0–2000 m depth ocean heat content over 2005–2017 are significantly (> 95% probability) smaller than the mean CMIP5 model simulation trend. Ocean warming over 1971–2010 per IPCC AR5 and contemporary estimates 1. The paper states: "The warming is larger over the 1971–2010 period than reported in AR5. The OHC trend for the upper 2000 m in AR5 ranged from 0.20 to 0.32 Wm −2 during this period (4: AR5). The three more contemporary estimates that cover the same time period suggest a warming rate of 0.36 ± 0.05 (6: Ishii ), 0.37 ± 0.04 (10: Domingues), and 0.39 ± 0.09 (2: Cheng) Wm −2 ." [Numbered references in this article are to the same numbered references in the paper. The number is followed by the lead author's name, or AR5, where this aids clarity.] 2. AR5 (4) featured 0–700 m depth ocean heat content (OHC) 1971-2010 linear trend estimates from five studies, ranging from 0.15 to 0.27 Wm −2 of the Earth's surface. Adding the AR5 700–2000 m OHC 1971-2010 trend estimate of 0.09 Wm −2 brings the range up to 0.24 to 0.36 Wm −2 , not to 0.20 to 0.32 Wm −2 as stated. The warming rates plotted in Supplementary Figure S1 agree to my values, not to those stated in the paper. 3. Importantly, although AR5 featured several OHC trend estimates for 0–700 m depth, its assessment of the Earth's energy uptake (Section 3.2.3 and Box 3.1) used only the highest one (10: Domingues), adding the Levitus (12) 700–2000 m OHC trend to give a best estimate 0–2000 m warming rate over 1971–2010 of 0.36 Wm −2 . That rate is identical to one (6: Ishii) of the three more contemporary estimates given in the paper and extremely close to the other two of them – within the innermost one- third of their uncertainty ranges. See Figure 1, left hand section, and compare with the 'Updated OHC estimates compared with AR5' figure [Fig 2] in the paper. It is therefore misleading to claim that the warming is larger over the 1971–2010 period than reported in AR5. 4. Moreover, over the final decade covered by AR5, 2002–2011, the trend of the 0–2000 m OHC time series that AR5 adopted for its assessment, 0.60 Wm −2 , was noticeably higher than those for two of the three more contemporary estimated OHC datasets given in the paper (0.35 (6: Ishii) and 0.52 (2: Cheng) Wm −2 ) and, unsurprisingly, almost identical to the third (10: Domingues + 12: Levitus). 1 The paper does not directly claim that ocean warming is accelerating faster than thought; that is the headline of The New York Times article about the paper.