The Kalmag model as a candidate for IGRF-13

Earth, Planets and Space

Table 2 Magnetic sources parameters as described in "Magnetic sources" section

Field	Spectrum	Radius \(a_i\) (km)	\(A_i\) (nT)	\(M_i\)	\(\alpha_i\)
Core	Flat	3456	D: \(2.52 \times 10^5\) \(9.74 \times 10^4\)	\(\tau_{\text{c}}(1)\): 935 years \(M(\ell \ge 2) = 514\) years	1.06
Lithospheric	C-based	6287	0.16	\(\infty\)	0
Close magnetospheric	C-based	12524	D: 9.16 1.88	\(\tau_{\text{m}}(1)\): 1.54 days \(M(\ell \ge 2) = 18\) min	0
Remote magnetospheric	C-based	235570	7.3	10.31 years	0
Fluctuating magnetospheric	C-based	13028	D: 3 4.56	\(\tau_{\text{fm}}(1)\): 0.36 day \(\tau_{\text{fm}}(2)\): 0.55 days \(M(\ell \ge 3) = 4\) days	\(1.15\)
Residual ionospheric/ induced	Flat	6324	D: 5.48 4.39	\(\tau_{\text{ii}}(1)\): 0.71 day \(M(\ell \ge 2) = 1.76\) day	0.93
Field-aligned currents	C-based	7917	D: 0 1.22	\(\tau_{\text{fac}}(1)\): 0 \(M(\ell \ge 2) = 1\) min	\(0\)

The prior spatial covariance matrices are derived from energy spectra expressed at some radii \(a_i\) which are are either flat with \(E_i^\infty (\ell ) = A_i^2\) or of the C-based type with the form \(E_i^\infty (\ell ) = A_i^2 (2\ell +1) S(\ell )\) where \(S(\ell )=\ell +1\) and \(S(\ell )=\ell\) for, respectively, internal and external sources. The characteristic timescales of Eqs. 5, 7 and 8 are parameterized by \(\tau_i(\ell ) = M_i \ell ^{-\alpha_i}\). In the \(A_i\) column, D corresponds to the magnitude of the dipole component