Sensitivity of Observationally Based Estimates of Ocean Heat Content and Thermal Expansion to Vertical Interpolation Schemes

Changes in ocean heat content are a critical element of climate change, with the oceans containing about 90% of the excess heat stored in the climate system and 60% in the upper 700 db. Estimates of these changes are sensitive to horizontal mapping of the sparse historical data and errors in eXpendable BathyThermograph data. Here we show that they are also sensitive to the vertical interpolation of sparsely sampled data through the water column. We estimate, using carefully constructed vertical interpolation methods with high‐quality hydrographic (bottle and CTD) data, the observationally based upper ocean heat content increase (thermosteric sea level rise) from 1956 to 2020 is 285 Zeta Joules (0.55 mm yr−1), 14% (14%) larger than estimates relying on simple but biased linear interpolation schemes. The underestimates have a clear spatial pattern with their maximum near 15°N and 12°S, around the maxima in the curvature of the temperature‐depth profile. Plain Language Summary Change in ocean heat content is a critical element of anthropogenic climate change, with the oceans containing about 90% of the excess heat stored in the climates system. We show that linear vertical interpolation of sparse ocean temperature observations results in warm biases in upper ocean heat storage because of the curvature of the depth‐temperature profile. Because the vertical sampling has increased in recent years, these biases result in underestimates of heat content trends. Our results show that more sophisticated vertical interpolation methods (rather than linear interpolation) result in 14% larger trends in upper ocean heat content increase and thermosteric sea level rise from 1956 to 2020. The underestimates have a clear spatial pattern with their maximum near 15°N and 12°S around the location with the maxima in the curvature of the temperature depth profile. Key Points Estimates of upper ocean warming with an improved vertical interpolation method are 14% larger than linear interpolation (LIN) schemes The corresponding upper ocean thermal expansion is 14% larger than LIN The larger values occur most strongly near 15°N and 12°S, near the maxima in the curvature of the temperature depth profile