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Table 1 Summary of the numerical experiments

From: A candidate secular variation model for IGRF-13 based on MHD dynamo simulation and 4DEnVar data assimilation

Case code Window length \(\varvec{\alpha}_{S}\) \(\varvec{\alpha}_{UW}\)
[\(\times 30\)]
T (trend), B (bias) Forecast type \(\sqrt {\varvec{dP}} \varvec{ }\) 4.5 years after release [nT] \(\sqrt { \varvec{dP}_{\varvec{wo}}}\) 4.5 years after release [nT]
(O1) 10 years \(\alpha '\) 2 no T, B MHD (\(k^{\prime} = 0\)) 228.5 168.2
(O2) 10 years \(\alpha '\) 2 only B MHD (\(k^{\prime} = 0\)) 212.9 164.0
(A1) 10 years \(\alpha '\) 2 T and B Ens. wei. sum 153.8 129.9
(A2) 10 years \(\alpha '\) 2 T and B MHD (\(k^{\prime} = 0\)) 168.2 136.2
(A3) 10 years \(\alpha '\) 2 T and B MHD (\(k^{\prime} = 0\)) 155.7 131.5
(A4) 10 years \(0.1\alpha '\) 2 T and B Ens. wei. sum 100.9 95.1
(A5) 10 years 0.1 \(\alpha '\) 2 T and B MHD (\(k^{\prime} = 0\)) 107.8 102.5
(A6) 10 years 0.1 \(\alpha '\) 2 T and B KD (\(k^{\prime} = 0\)) 106.3 99.3
(B1) 5 years \(\alpha ''\) 2 T and B Ens. wei. sum 146.8 137.3
(B2) 5 years \(\alpha ''\) 2 T and B MHD (\(k^{\prime} = 0\)) 147.6 136.4
(B3) 5 years \(\alpha ''\) 2 T and B MHD (\(k^{\prime} = 0\)) 145.7 136.2
(B4) 5 years \(0.1\alpha ''\) 2 T and B Ens. wei. sum 115.0 111.4
(B5) 5 years 0.1 \(\alpha ''\) 2 T and B MHD (\(k^{\prime} = 0\)) 118.7 114.5
(B6) 5 years 0.1 \(\alpha ''\) 2 T and B KD (\(k^{\prime} = 0\)) 137.6 134.1
(C1)   IGRF-12 96.9 94.7
(C2)   Extrapolation using SV of MCM at 2014.25 72.4 73.4
(C3)   No SV from 2014.25 442.7 398.9
  1. In calculations of \(\sqrt {{\text{d}}P}\) (Eq. 40) and \(\sqrt {{\text{d}}P_{wo} }\) (Eq. 41), the MCM6 model, which covers up to 2019.50, is used as \({g_{l}^{m}}_{\text{data}}\) and \({h_{l}^{m}}_{\text{data}}\). Release times for all cases are assumed to be 2014.75, except 2015.00 for IGRF-12. In the “Forecast type” column, \(k^{\prime} = 0\) and \(k^{\prime} = K\) mean the MHD dynamo or KD simulations running from the optimized state vector at 2004.25 and 2014.25, respectively. See text for details of the three forecast types. In the \(\alpha_{S}\) and \(\alpha_{UW}\) columns, we specify those for the final 5th step in Eq. 39, where \(\alpha^{\prime} = 14\) and \(\alpha^{\prime\prime} = 7\)
  2. Italic—Case A4 was found to be the best setting in our numerical experiments