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We also truncate the flow model at degree 14 and damp using the Bloxham 'strong' norm (Bloxham 1988) which effectively reduces the influence of the model SV above degree 8.
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The RMS difference per degree shows that the field model forecast by the IGRF-10 SV prediction (grey solid line, circle marker) differs strongly from the CHAOS-2 model at degrees 1-5.
Its elements are given by, where ∆P (l) is the difference between the powers of two MF models at degree l.
The final version of CHAOS-6 was obtained by taking the model coefficients from CHAOS-6l (as described above) and replacing the static field Gauss coefficients above degree (n=24) with the static field coefficients from the CHAOS-6h model, truncated at degree (n=110).
Figure 10 again shows that although there are differences with other models, especially at degree 5, the BGS model is well within the range of variability of other models.
When comparing the two SV models truncated at degree 8 (Fig. 6 and Table 2), we obtain differences with similar geographical patterns and comparable intensity values as for the MF model comparison.
Figure 5-right indeed illustrates that model D has the smallest correlation to the mean model at large degrees n with a most significant difference from SH degree 11, thus corresponding to small spatial scales.
From the data obtained, an inverse kinematic model at seven degrees of freedom was realized.
Our method can therefore overcome those computational complexity issues, and identify complex interactions (between two or more factors) that contribute to the response model, at varying degrees of sparsity (controlled by the penalization component).
To evaluate the significance of the AICs' difference, we calculated a chi-square (difference between -2log likelihood of both models) at a degree of freedom (difference between degrees of freedom of both models).
The absolute differences are relatively similar in magnitude and somewhat complementary the errors of the IGRF-7 field model are lower at degree 1 and 2 and similar for degree 3 and 4, while the errors of the flow model SV forecast are lower at degrees 5 12.
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