An Inverse Approach for Ocean Heat Content Estimation Using Altimetry, Gravimetry, and In-situ Data

The ocean, thanks to its vast heat capacity, plays a central role in the Earth’s climate system by absorbing most of the radiative imbalance caused by anthropogenic emissions. Over the past decades, more than 90% of the excess energy has been stored in the ocean, thereby moderating surface warming and influencing the global radiation budget. Understanding Ocean Heat Content (OHC), its temporal variability, and spatial distribution is essential for projecting climate evolution and associated impacts, notably sea-level rise.

Traditionally, OHC has been estimated from in-situ measurements, particularly through the ARGO network, which provides temperature and salinity profiles down to 2000 m. ARGO still suffers from incomplete spatial and temporal coverage, especially under sea ice, in marginal seas, and in the deep ocean. Algorithms have been developed to address these gaps, but they introduce significant uncertainties, particularly in dynamically active regions.

To overcome these limitations, satellite observations are used. Hybrid methods combine altimetry and in-situ data, leveraging correlations between sea surface height and OHC to improve sampling. Other approaches, referred to as geodetic methods, such as this work, combine altimetry and gravimetry to estimate thermosteric sea level and derive OHC. Here,   for the first time, we combine in-situ, altimetric, and gravimetric data through an inverse approach. 

Residuals between in-situ OHC and geodetic OHC are optimised and interpolated using an objective mapping algorithm to produce OHC fields along with their associated uncertainties. 

The OHC product is validated in a leave-one-out approach against non-used in-situ measurements. The uncertainty of the OHC is derived from the leave-one-out approach and a synthetic data approach. In addition, we derive the Ocean Heat Uptake (OHU) by computing the tendency of the OHC and we  compare it with an independent estimate computed as the radiation budget measured by CERES corrected from the atmospheric divergence (ERA5). With this comparison,  we assess the capacity of the OHC product to close the Earth’s energy budget over the ocean. The OHU  estimate closes the budget at the ±0.5 W/m² level on a yearly basis. This level allows tracking energy transfer at the surface of the ocean, which occurs at interannual timescales due to phenomena such as El Niño and La Niña events.