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Table II: Dipole and Non-dipole Energies in the Earth’s Magnetic Field. Calculated by Equations (10) and (11) from IGRF geomagnetic data for the entire twentieth century (Mandea et al., 2000). Energies are in petajoules (1 PJ = 1015 joules). The rms error is the root mean square difference, in nanoteslas, between the magnetic field intensity B at the earth’s surface according to the IGRF model and the observed values, as estimated by Lowe (2000). The sigmas (s) are the corresponding errors in the dipole, nondipole, and total energies.
1900
1905
1910
1915
1920
1925
1930
1935
1940
1945
1950
Dipole Energy
5514
5487
5449
5401
5349
5303
5263
5233
5213
5193
5179
Quadrupole E
196
202
209
216
221
227
235
242
249
260
269
Octopole E
284
290
299
310
323
337
351
366
382
399
411
4th Harmonic
311
317
323
329
333
336
340
344
351
371
375
5th Harmonic
158
156
153
151
149
148
147
148
151
159
163
6th Harmonic
157
159
160
163
165
168
170
173
175
170
169
7th Harmonic
95
94
95
95
96
95
95
94
93
77
79
8th Harmonic
60
60
60
60
63
63
65
66
67
70
110
9th Harmonic
87
87
87
87
88
88
90
92
95
211
160
10th Harmonic
55
55
55
54
55
55
55
55
55
183
256
Total Energy
6916
6906
6890
6866
6843
6820
6810
6813
6830
7093
7172
Dipole Energy
5514
5487
5449
5401
5349
5303
5263
5233
5213
5193
5179
Nondipole E
1402
1420
1441
1465
1494
1517
1548
1580
1617
1900
1993
s Total Energy
25
25
24
24
24
24
24
23
23
70
54
s Dipole E
25
24
24
24
24
24
23
23
23
69
54
s Nondipole E
47
47
46
46
46
46
45
45
45
139
108
rms error
100
100
100
100
100
100
100
100
100
300
233
Year
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
Dipole Energy
5179
5161
5133
5103
5062
5019
4979
4934
4896
4860
4831
Quadrupole E
269
279
288
296
306
317
331
344
356
369
383
Octopole E
411
423
431
439
445
452
461
469
478
486
492
4th Harmonic
375
373
372
368
364
358
350
344
341
338
333
5th Harmonic
163
171
178
179
184
188
190
189
187
186
184
6th Harmonic
169
169
165
160
150
142
136
130
126
123
119
7th Harmonic
79
85
89
98
100
104
112
118
119
121
120
8th Harmonic
110
89
89
77
74
75
84
91
95
100
116
9th Harmonic
160
53
57
103
99
100
104
102
102
99
101
10th Harmonic
256
76
51
46
42
43
53
54
51
51
58
Total Energy
7172
6879
6853
6869
6827
6797
6800
6775
6751
6732
6737
Dipole Energy
5179
5161
5133
5103
5062
5019
4979
4934
4896
4860
4831
Nondipole E
1993
1718
1720
1767
1764
1778
1821
1842
1855
1872
1906
s Total Energy
54
39
23
11
11
11
2
11
11
22
11
s Dipole E
54
38
23
11
11
11
2
11
11
22
11
s Nondipole E
108
76
45
23
22
22
4
22
22
44
22
rms error
233
167
100
50
50
50
10
50
50
100
50

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