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Table 1 Model statistics of SIFMplus (top), \(\hbox {SIFMplus}_{{\text {noMLT}}}\) (middle) and \(\hbox {SIFM}_x\) (bottom)

From: A model of Earth’s magnetic field derived from 2 years of Swarm satellite constellation data

  SW-A SW-B SW-C SW-A – SW-C
N Mean RMS N Mean RMS N Mean RMS N Mean RMS
SIFMplus
\(F_{\text {polar}}\) 125,612 −0.36 3.39 125,598 −0.36 3.25 122,775 −0.34 3.40    
\(F_{\text {non-polar}}\) 427,979 −0.41 2.30 424,364 −0.38 2.28 420,113 −0.46 2.30    
\(B_r\) 427979 −0.25 1.93 424,364 −0.41 1.99 420,113 −0.24 1.98    
\(B_\theta \) 427,979 0.30 2.97 424,364 0.28 2.95 420,113 0.32 2.97    
\(B_\phi \) 427,979 0.02 2.49 424,364 0.01 2.48 420,113 0.02 2.50    
\(\delta F_{\text {NS, polar}}\) 268,159 −0.01 0.82 259,685 −0.02 0.76 260,085 −0.01 0.82    
\(\delta F_{\text {NS, non-polar, dark}}\) 325,453 0.00 0.18 322,491 0.01 0.17 317,916 0.00 0.18    
\(\delta B_{r,{\text {NS, dark}}}\) 215,163 −0.00 0.27 211,622 −0.00 0.27 209,694 −0.01 0.28    
\(\delta B_{\theta ,{\text {NS, dark}}}\) 215,163 −0.00 0.27 211,622 −0.01 0.26 209,694 −0.00 0.28    
\(\delta B_{\phi ,{\text {NS, dark}}}\) 215,163 −0.00 0.34 211,622 −0.00 0.34 209,694 −0.00 0.35    
\(\delta F_{\text {NS, non-polar, sunlit}}\) 356,410 0.02 0.33 355,790 0.01 0.30 349,202 0.01 0.33    
\(\delta B_{r,{\text {NS, sunlit}}}\) 232,514 −0.00 0.53 232,918 −0.01 0.51 227,049 −0.01 0.53    
\(\delta B_{\theta ,{\text {NS, sunlit}}}\) 232,514 −0.00 0.58 232,918 −0.00 0.56 227,049 −0.00 0.59    
\(\delta B_{\phi ,{\text {NS, sunlit}}}\) 232,514 0.00 0.89 232,918 0.01 0.85 227,049 0.00 0.89    
\(\delta F_{\text {EW, polar}}\)           413,933 −0.01 0.70
\(\delta F_{\text {EW, non-polar, dark}}\)           538,164 0.06 0.37
\(\delta B_{r, {\text {EW, dark}}}\)           344,719 0.01 0.48
\(\delta B_{\theta ,{\text {EW, dark}}}\)           344,719 −0.01 0.50
\(\delta B_{\phi ,{\text {EW, dark}}}\)           344,719 −0.01 0.58
\(\delta F_{\text {EW, non-polar, sunlit}}\)           592,723 0.04 0.48
\(\delta B_{\text {r,EW, sunlit}}\)           374,546 0.02 0.80
\(\delta B_{\theta , {\text {EW, sunlit}}}\)           374,546 −0.00 0.88
\(\delta B_{\phi ,{{\text {EW, sunlit}}}}\)           374,546 0.04 1.62
\(SIFMplus_{{noMLT}}\)
\(F_{\text {polar}}\) 125,612 −0.48 3.78 125,598 −0.45 3.63 122,775 −0.46 3.78    
\(F_{\text {non-polar}}\) 427,979 −0.64 2.29 424,364 −0.60 2.27 420,113 −0.69 2.31    
\(B_r\) 427,979 0.07 1.98 424,364 −0.05 1.96 420,113 0.10 2.03    
\(B_\theta \) 427,979 0.29 2.97 424,364 0.31 2.99 420,113 0.31 2.98    
\(B_\phi \) 427,979 0.26 2.53 424,364 0.26 2.51 420,113 0.24 2.54    
\(\delta F_{\text {NS, polar}}\) 268,159 −0.01 0.86 259,685 −0.01 0.79 260,085 −0.01 0.85    
\(\delta F_{\text {NS, non-polar, dark}}\) 325,453 0.00 0.18 322,491 0.00 0.17 317,916 0.00 0.18    
\(\delta B_{r,{\text {NS, dark}}}\) 215,163 −0.00 0.27 211,622 0.00 0.26 209,694 −0.00 0.28    
\(\delta B_{\theta ,{\text {NS, dark}}}\) 215,163 −0.00 0.27 211,622 −0.01 0.27 209,694 −0.00 0.28    
\(\delta B_{\phi ,{\text {NS, dark}}}\) 215,163 −0.00 0.34 211,622 −0.00 0.34 209,694 0.00 0.35    
\(\delta F_{\text {NS, non-polar, sunlit}}\) 356,410 0.03 0.34 355,790 0.03 0.31 349,202 0.03 0.34    
\(\delta B_{r,{\text {NS, sunlit}}}\) 232,514 −0.00 0.53 232,918 −0.01 0.51 227,049 −0.01 0.54    
\(\delta B_{\theta ,{\text {NS, sunlit}}}\) 232,514 −0.00 0.58 232,918 −0.00 0.56 227,049 −0.00 0.59    
\(\delta B_{\phi ,{\text {NS, sunlit}}}\) 232,514 0.00 0.89 232,918 0.01 0.85 227,049 0.00 0.89    
\(\delta F_{\text {EW, polar}}\)           413,933 −0.01 0.72
\(\delta F_{\text {EW, non-polar, dark}}\)           538,164 0.03 0.37
\(\delta B_{r, {\text {EW, dark}}}\)           344,719 0.01 0.48
\(\delta B_{\theta ,{\text {EW, dark}}}\)           344,719 −0.01 0.50
\(\delta B_{\phi ,{\text {EW, dark}}}\)           344,719 −0.01 0.58
\(\delta F_{\text {EW, non-polar, sunlit}}\)           592,723 0.05 0.49
\(\delta B_{\text {r,EW, sunlit}}\)           374,546 0.01 0.80
\(\delta B_{\theta ,\text {EW, sunlit}}\)           374,546 0.00 0.88
\(\delta B_{\phi ,\text {EW, sunlit}}\)           374,546 0.04 1.64
\(SIFM_x\)
\(F_{\text {polar}}\) 125,612 −0.47 3.71 125,598 −0.41 3.54 122,775 −0.44 3.71    
\(F_{\text {non-polar}}\) 427,979 −0.67 2.30 424,364 −0.64 2.26 420,113 −0.72 2.31    
\(B_r\) 427,979 0.08 2.00 424,364 0.06 1.98 420,113 0.10 2.05    
\(B_\theta \) 427,979 0.31 2.95 424,364 0.35 2.96 420,113 0.33 2.96    
\(B_\phi \) 427,979 0.21 2.51 424,364 0.20 2.49 420,113 0.20 2.52    
\(\delta F_{\text {NS, polar}}\) 268,159 −0.02 0.85 259,685 −0.01 0.79 260,085 −0.02 0.84    
\(\delta F_{\text {NS, non-polar, dark}}\) 325,453 0.00 0.18 322,491 0.00 0.17 317,916 0.00 0.18    
\(\delta F_{\text {NS, non-polar, sunlit}}\) 356,410 0.03 0.34 355,790 0.03 0.31 349,202 0.02 0.34    
\(\delta F_{\text {EW, polar}}\)           413,933 −0.02 0.72
\(\delta F_{\text {EW, non-polar, dark}}\)           538,164 0.03 0.36
\(\delta F_{\text {EW, non-polar, sunlit}}\)           592,723 0.05 0.49
  1. Number N of data points, (Huber-weighted) mean, and RMS misfit (in nT) of scalar (F), vector \((B_r, B_\theta , B_\phi )\), N-S gradient \((\delta F_{{\text {NS}}}, \delta B_{r,{{\text {NS}}}}, \delta B_{\theta ,{{\text {NS}}}}, \delta B_{\phi ,{{\text {NS}}}})\) and E-W gradient \((\delta F_{{\text {EW}}}, \delta B_{r,{\text {EW}}}, \delta B_{\theta ,{\text {EW}}}, \delta B_{\phi ,{\text {EW}}})\) data, at polar (>\(\pm 55^\circ \)) and non-polar (\(< \pm 55^\circ \)) QD latitudes and for dark (sun at least \(10^\circ \) below horizon) and sunlit conditions