Figure: From sea-level measurements to ocean heat uptake estimates. The panel a shows global-mean sea level rise (black), and its contributing components: ocean mass changes measured by GRACE (blue) and thermal expansion as observed by the Argo float network (orange). The residual is shown in red. Panel b shows the estimated changes in ocean heat content. We can estimate the heat content by subtracting the ocean mass change from the total sea-level change, and multiplying the difference with the expansion efficiency of sea water (blue). The direct measurements from Argo (down to 2000m) are shown in orange. The difference between both (red) shows a much larger heat uptake than what limited deep-ocean measurements below 2000m (turquoise) show. Panel c shows the year-to-year variability of the ocean heat uptake, and a comparison with top-of-atmosphere radiative fluxes measured by CERES. Both ocean heat uptake estimates show more variability than CERES, but the total sea level minus ocean mass estimate shows a much higher correlation (0.8) with CERES than the Argo observations.

In response to increasing emissions of greenhouse gases and the radiative forcings and feedbacks they impose, Earth gains heat energy and its climate changes. Often referred to as Earth’s energy imbalance (EEI), the contemporary energy gain of 0.5-1 W/m2 is quite small compared to the radiation fluxes that enter and exit the Earth system at the top of the atmosphere. Therefore, it is difficult to accurately measure the small but crucial EEI as the residual of observed incoming and outgoing radiative fluxes. An alternative approach to estimating EEI is to take inventory of the heat content changes in Earth’s ocean, land, atmosphere, and cryosphere. Since the voluminous ocean absorbs ~90% of Earth’s energy gain, ocean heat uptake provides a major constraint for EEI and its uncertainty. Direct observations of sub-surface ocean temperature change form the basis for estimating ocean heat uptake and constraining EEI. As with many in-situ sensor networks, the coverage by ocean profiling floats (e.g., Argo) is incomplete in space and time, which may introduce biases. For example, the deep ocean below 2000 m (comprising approx. 50% of the total ocean volume) is not covered by the current Argo float network. Independent estimates of ocean heat uptake are therefore required to complement the sensor-float results and to better constrain EEI.

Satellite observations of total sea level change (altimetry: Jason 2,3, Sentinel 6-MF) and ocean mass change (gravimetry: GRACE and GRACE-FO) allow us to dissect the sea level budget into its mass and thermosteric (thermal) components (Figure a). From the latter, ocean heat content is derived (Figure b), using the expansion efficiency of sea water to convert from thermosteric sea level heights to heat energy (for details see Hakuba et al., 2021). From the temporal change in ocean heat content, we can estimate the rate of ocean heat uptake (W/m2) and its year-to-year variability (Figure c). Over 2005-2019, ocean heat uptake amounts to 0.86 W/m2 (at the top of the atmosphere, not just the ocean surface area!) as Earth continues to get warmer. Although the radiation fluxes provided by the Cloud’s and Earth Radiant Energy System (CERES) do not resolve the absolute magnitude of EEI, they track the temporal EEI variability accurately. The ocean heat uptake series derived from the geodetic satellite observations correlates very well with the net radiative flux, but exhibits a larger variability. Both these data sets agree that there is a significant increasing trend in EEI, which implies an accelerated warming of Earth by at least 0.4 W/m2 per decade.


Dataset NameProcessing
Start/StopFormatSpatial ResolutionTemporal
ECCO Ocean Temperature and Salinity - Monthly Mean llc90 Grid (Version 4 Release 4)4 to PresentNETCDF-41 degrees (Latitude) x 1 degrees (Longitude)Monthly - < Annual