Page - 19 - in Contributions to GRACE Gravity Field Recovery - Improvements in Dynamic Orbit Integration, Stochastic Modelling of the Antenna Offset Correction, and Co-Estimation of Satellite Orientations

3.4.2 Degree Amplitudes When analysing and describing gravity fields, they are often compared to some reference field, usually a mean potential field. This reference field is also given as a series of Stokes coefficients. The signal degree amplitude of a gravity field for one degree n, along with its formal error, is defined as ηn= √ n ∑ m=0 (c2nm+s2nm) and σn= √ n ∑ m=0 (σ2nm+σ 2 nm) (3.4.8) where σ2nm, σ2nm are the formal errors of the Stokes coefficients. The difference degree amplitude is,with∆cnm and∆snm thedifferenceof theStokescoefficients to thereference field, ∆ηn= √ n ∑ m=0 (∆c2nm+∆s2nm) . (3.4.9) Figure 3.1 shows the signal and difference degree amplitudes of two arbitrary models. The GRACE baseline, a pre-launch estimate of the expected accuracy for GRACE monthly gravity field solutions, is also displayed. This curve will feature in many of the degree amplitude plots in this thesis, without being labelled in the legend each time. 0 20 40 60 80 100 120 Degree 10−5 10−4 10−3 10−2 10−1 100 101 Reference Model Baseline Figure 3.1: Illustration of signal degree amplitudes for a reference field and difference degree amplitudes for the analysed model. 3.4 Representation of the Gravitational Potential 19