An analysis of the error budget for a GOCE-based estimate of the ocean's mean dynamic topography

Over the last decade, the Gravity Recovery And Climate Experiment (GRACE) mission and, more recently, the Gravity and steady state Ocean Circulation Explorer (GOCE) mission, have lead to a dramatic improvement in our ability to measure the ocean's mean dynamic topography (MDT) from space. To fully exploit this improvement and make further improvements in the observational system, however, knowledge of the MDT's error characteristics is required. Here we assess the error budget for an MDT based on a GOCE geoid and an altimetric mean sea surface (MSS). We find that for spatial scales of 250 km and greater the global mean MDT error is 3 cm, with the MSS making the greater contribution to the total error. For spatial scales within the range 133--250 km the error is 4 cm, with the MSS and geoid contributing almost equally to this. For spatial scales less than 133 km it is 17 cm, with geoid error accounting for almost all of this. Our approach also allows an assessment of the formal errors for the geoid and mean sea surface. For the former, we find that the formal error underestimates the true error by a factor of two for the medium wavelength component, but is reliable in terms of the global mean for the long and short-wavelength components. However, the formal geoid error does not accurately capture the regional variations in the true geoid error, which arise primarily where the sea floor topography is steep. For the MSS, we find that the formal errors capture the spatial variability but underestimate the error magnitude by approximately a factor of three.