Error calibration of geopotential harmonics in recent and past gravitational fields

The geopotential coefficients of a number of recent and past models have been examined with the aim of calibrating their formal (or published) errors, principally by direct comparison with the same coefficients of a precise and wholly independent satellite-only reference field determined (in 2010) predominantly from over 7 years of μ/s low–low GRACE inter-satellite range rate observations (ITG-GRACE2010S). In all of these comparisons the reference field used, over specified spectral ranges, has much smaller reported errors than the ones to be calibrated. In particular we find that a recently published field (in 2010) using gravity gradient and position data from ESA’s GOCE satellite, GO_CONS_GCF_2_TIM_R1, has formal errors which are significantly optimistic for the lowest degrees (n) but with increasing realism where the gradiometer gains influence over the position information (15 < n < 120). Other GOCE models do not afford an unbiased error calibration. Validating error calibration with the independent reference model, of two past comprehensive fields (containing both satellite and surface data), confirms that one of them (JGM3, published in 1994, complete to n = 70) reported generally realistic formal errors while another (EGM96, published in 1998, complete to n = 360, tested only for n < 150) had significantly optimistic ones for most n < 100 but with better realism when affected only by the surface information.

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