Towards determining uncertainties in global oceanic mean values of heat, salt, and surface elevation

Lower-bounds on uncertainties in oceanic data and a model are calculated for the 20-year time means and their temporal evolution for oceanic temperature, salinity, and sea surface height, during the data-dense interval 1994-2013. The essential step of separating stochastic from systematic or deterministic elements of the fields is explored by suppressing the globally correlated components of the fields. Justification lies in the physics and the brevity of a 20-year estimate relative to the full oceanic adjustment time, and the inferred near-linearity of response on short time intervals. Lower-bound uncertainties reflecting the only stochastic elements of the state estimate are then calculated from bootstrap estimates. Trends are estimated as 2.2 +/- 0.2 mm/y in elevation, 0.0011 +/- 0.0001 degrees C/y, and (-2.825 +/- 0.17) x 10(-5) for surface elevation, temperature and salt, with formal 2-standard deviation uncertainties. The temperature change corresponds to a 20-year average ocean heating rate of 0.48 +/- 0.1 W/m(2) of which 0.1 W/m(2) arises from the geothermal forcing. Systematic errors must be determined separately.