The Earth is warming as a result of increasing greenhouse gas concentrations. About 90% of the additional energy stored in the climate system since the 1950s is in the ocean, with about 60% of the ocean storage in the upper 700 db.

Our recent research (Web link to GRL paper) has shown that accurate estimates of the ocean warming require accurate interpolation between the sparse sampling depths of historical profiles. Using a non-linear vertical interpolation scheme (Multiply-Rotated Piecewise Cubic Hermite Interpolating Polynomials, MR-PCHIP) that better approximates the change in temperature with depth results in about 14% larger estimates of ocean warming and ocean thermal expansion than a simple but biased estimate using linear interpolation


Insert panels a and b from the following figure – just showing the MRST and linear lines. 

Tina Rolf / Unsplash

Upper ocean (to 700 db) heat content (a) thermosteric and (b) sea level change for the MR-PCHIP (black) and linear (red) vertical interpolation schemes. The dotted/solid lines use 3/11 years of data to estimate the heat content changes.  The data can be found here (Weblink to data for MRST and Linear with 95% uncertainty estimates for both series).


Ocean Heat Content trends in the upper 700 m for 1970 to 2015. (a) The equivalent surface flux into the ocean in W m-2, (b) the differences between the MRST and Linear vertical interpolation equivalent surface flux into the ocean in W m-2, and (c) the zonal integral of the accumulated heat content in ZJ °lat yr-1 (MRST black and LIN red, and their differences blue). The dashed black and red lines show the zonally integrated thermosteric in mm yr-1 (upper axis).

The data for this figure and the equivalent thermosteric and halosteric can be found here (Weblink to data). 

Reference:  To be completed. 

For further information contact Professor Trevor McDougall (, Dr Paul Barker (, Professor John Church ( or Dr Yuehua Li (