Comparison of Formal Errors
Each monthly gravity field comes with a full set of formal errors of the spherical harmonic coefficients. In general these are the result of an error propagation of observation and background model errors, taking into account the orbit geometry. Due to the limited knowledge of observation and background model noise, formal errors are chronically optimistic and highly dependent on the applied noise model. These dependencies lead to differences between AIUB, GFZ and GRGS.
ITSG as the only processing center applies an empirical noise model based on K-Band residual analysis. This leads to much more realistic calibrated error estimates. The error estimates of ITSG are the only ones that also show order-specific features that are explained by cross-order correlations and resonances with the orbital period of the satellites. Similar features are visible in the triangle plots of the coefficient wise anomalies.
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Calibration of Formal Errors
The very diverse formal error levels pose a problem for the combination of the gravity fields on normal equation level. Standard procedures like Variance Component Estimation for the determination of relative weights lead to unrealistic results (favouring normal equations with small formal errors).
Figures 1-12 show the ratio between the formal errors of the monthly gravity fields of the individual analysis centers and the formal errors of GFZ (taken as reference). Order-specific features are obvious and GRGS moreover displays a specific degradation of the sectorial terms.
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Fig. 1 Fig. 2
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Fig. 3 Fig. 4
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Fig. 5 Fig, 6
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Fig. 7 Fig. 8
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Fig, 9 Fig. 10
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Fig, 11 Fig. 12
In Figs. 13-24 finally the mean ratios per degree, per order, or over all coefficients are computed, again taking GFZ formal errors as reference. A strong dependence on order as well as degree is visible, the overall mean ratio is not representative for all coefficients. We conclude that a meaningful error calibration will necessitate coefficient wise calibration factors.
A corresponding scaling of the individual normal matrices prior to combination is currently being studied.
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Fig. 13 Fig. 14
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Fig. 15 Fig. 16
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Fig. 17 Fig. 18
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Fig. 19 Fig. 20
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Fig. 21 Fig. 22
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Fig. 23 Fig. 24
