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<front>
<journal-meta>
<journal-id journal-id-type="publisher">NPG</journal-id>
<journal-title-group>
<journal-title>Nonlinear Processes in Geophysics</journal-title>
<abbrev-journal-title abbrev-type="publisher">NPG</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Nonlin. Processes Geophys.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1607-7946</issn>
<publisher><publisher-name>Copernicus Publications</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/npg-21-347-2014</article-id>
<title-group>
<article-title>Latitudinal variation of stochastic properties of the geomagnetic field</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Wanliss</surname>
<given-names>J. A.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Shiokawa</surname>
<given-names>K.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Yumoto</surname>
<given-names>K.</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>Presbyterian College, 503 South Broad Street, Clinton, SC 29325, USA</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>Solar-Terrestrial Environment Laboratory, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi, 464-8601, Japan</addr-line>
</aff>
<aff id="aff3">
<label>3</label>
<addr-line>Space Environment Research Center, Kyushu University, 53 6-10-1 Hakozaki, Higashi-ku Fukuoka, 812-8581, Japan</addr-line>
</aff>
<pub-date pub-type="epub">
<day>03</day>
<month>03</month>
<year>2014</year>
</pub-date>
<volume>21</volume>
<issue>2</issue>
<fpage>347</fpage>
<lpage>356</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2014 J. A. Wanliss et al.</copyright-statement>
<copyright-year>2014</copyright-year>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit <ext-link ext-link-type="uri"  xlink:href="https://creativecommons.org/licenses/by/3.0/">https://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions>
<self-uri xlink:href="https://npg.copernicus.org/articles/21/347/2014/npg-21-347-2014.html">This article is available from https://npg.copernicus.org/articles/21/347/2014/npg-21-347-2014.html</self-uri>
<self-uri xlink:href="https://npg.copernicus.org/articles/21/347/2014/npg-21-347-2014.pdf">The full text article is available as a PDF file from https://npg.copernicus.org/articles/21/347/2014/npg-21-347-2014.pdf</self-uri>
<abstract>
<p>We explore the stochastic fractal qualities of the geomagnetic field from
210 mm ground-based magnetometers during quiet and active magnetospheric
conditions. We search through 10 yr of these data to find events that
qualify as quiet intervals, defined by Kp &amp;le; 1 for 1440 consecutive
minutes. Similarly, active intervals require Kp &amp;ge; 4 for 1440 consecutive
minutes. The total for quiet intervals is ~ 4.3 x 10&lt;sup&gt;6&lt;/sup&gt; and 2 x 10&lt;sup&gt;8&lt;/sup&gt; min for active data points. With this large number of data we
characterize changes in the nonlinear statistics of the geomagnetic field via
measurements of a fractal scaling. A clear difference in statistical behavior
during quiet and active intervals is implied through analysis of the scaling
exponents; active intervals generally have larger values of scaling
exponents. This suggests that although 210 mm data appear
monofractal on shorter timescales, the scaling changes, with overall
variability are more likely described as a multifractional Brownian motion. We
also find that low latitudes have scaling exponents that are consistently
larger than for high latitudes.</p>
</abstract>
<counts><page-count count="10"/></counts>
</article-meta>
</front>
<body/>
<back>
<ref-list>
<title>References</title>
<ref id="ref1">
<label>1</label><mixed-citation publication-type="other" xlink:type="simple">Anh, V., Yu, Z.-G., and Wanliss, J. A.: Analysis of global geomagnetic variability, Nonlin. Processes Geophys., 14, 701–708, &lt;a href=&quot;http://dx.doi.org/10.5194/npg-14-701-2007&quot;&gt;https://doi.org/10.5194/npg-14-701-2007&lt;/a&gt;, 2007.</mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple">Balasis, G., Daglis, I. A., Papadimitriou, C., Anastasiadis, A., Sandberg, I., and Eftaxias, K.: Quantifying Dynamical Complexity of Magnetic Storms and Solar Flares via Nonextensive Tsallis Entropy, Entropy, 13, 1865–1881, 2011.</mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple">Bartels J.: Discussion of time variations of geomagnetic indices Kp and Ap, Ann. Geophys., 19, 19323–19361, 1963.</mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple">Bartels, J., Heck, N. H., and Johnston, H. F.: The three-hour-range index measuring geomagnetic activity, J. Geophys. Res., 44, 411–454, 1939.</mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple">Bianchi, A. and Planese, A.: Modelling stock price movements: multifractality or multifractionality?, Quant. Financ., 7, 301–319, 2007.</mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple">Bryce, R. and Sprague, K.: Forecasting conflict intensity: Afghanistan, Journal of Battlefield Technology, 15, 23–29, 2012.</mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple">Chen, Z., Ivanov, P. C., Hu, K., and Stanley, H. E.: Effect of nonstationarities on detrended fluctuation analysis, Phys. Rev. E, 65, 041107, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevE.65.041107&quot;&gt;https://doi.org/10.1103/PhysRevE.65.041107&lt;/a&gt;, 2002.</mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple">Collins, J. J. and De Luca, C. J.: Upright, correlated random walks: A statistical-biomechanics approach to human postural control system, Chaos, 5, 57–63, 1994.</mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple">Consolini, G. and De Michelis, P.: Non-Gaussian distribution functions of AE-index fluctuations: Evidence for time intermittency, Geophys. Res. Lett., 25, 4087–4090, 1998.</mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple">Consolini, G. and Lui, A. T. Y.: Symmetry breaking and nonlinear wave-wave interaction in current disruption: Possible evidence for a phase transition, in: Magnetospheric Current Systems, edited by: Ohtani S.-I., Fujii, R., Hesse, M., and Lysak, R. L., Geophys. Monogr. Ser., 118, p. 395, 2000.</mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple">Consolini, G., Marcucci, M. F., and Candidi, M.: Multifractal Structure of Auroral Electrojet Index Data, Phys. Rev. Lett., 76, 4082–4085, 1996.</mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple">Dobias, P. and Wanliss, J. A.: Intermittency of Storms and Substorms: Is it Related to the Critical Behaviour?, Ann. Geophys., 27, 2011–2018,              &lt;a href=&quot;http://dx.doi.org/10.5194/angeo-27-2011-2009&quot;&gt;https://doi.org/10.5194/angeo-27-2011-2009&lt;/a&gt;, 2009.</mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple">Frisch, U.: Turbulence, Cambridge University Press, New York, 1997.</mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple">Hergarten, S.: Self-Organized Criticality in Earth Systems, Springer, Berlin, Heidelberg, New York, 2002.</mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple">Hori, T., Lui, A. T. Y., Ohtani, S., C:son Brandt, P., Mauk, B. H., McEntire, R. W., Maezawa, K., Mukai, T., Kasaba, Y., and Hayakawa, H.: Storm-time convection electric field in the near-Earth plasma sheet, J. Geophys. Res., 110, A04213, &lt;a href=&quot;http://dx.doi.org/10.1029/2004JA010449&quot;&gt;https://doi.org/10.1029/2004JA010449&lt;/a&gt;, 2005.</mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple">Hu, K., Ivanov, P. C., Chen, Z., Carpena, P., and Stanley, H. E.: Effect of trends on detrended fluctuation analysis, Phys. Rev. E, 64, 011114, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevE.64.011114&quot;&gt;https://doi.org/10.1103/PhysRevE.64.011114&lt;/a&gt;, 2001.</mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple">Kantelhardt, J. W., Zschiegner, S. A., Koscielny-Bunde, E., Havlin, S., Bunde, A., and Stanley, H. E.:, Multifractal detrended fluctuation analysis of nonstationary time series, Physica A, 316, 87–114, 2002.</mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple">Korth, A., Friedel, R. H. W., Henderson, M. G., Frutos-Alfaro, F., and Mouikis, C. G.: \chemO^{+} Transport into the ring current: Storm versus substorms, in: Disturbances in Geospace: The Storm-Substorm Relationship, edited by: Sharma, A. S., Kamide, Y., and Lakhina, G. S., AGU, Washington, DC, Geoph. Monog. Series, 142, 59–73, 2003.</mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple">Mandelbrot, B. B. and Van Ness, J. W.: Fractional Brownian Motions, Fractional Noises and Applications, SIAM Rev., 10, 422–437, 1968.</mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple">Muniandy, S. V. and Lim, S. C.: Modeling of locally self-similar processes using multifractional Brownian motion of Riemann-Liouville type, Phys. Rev. E, 63, 046104, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevE.63.046104&quot;&gt;https://doi.org/10.1103/PhysRevE.63.046104&lt;/a&gt;, 2001.</mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple">Neuman, S. P. and Federico, V. D.: Multifaceted Nature of Hydrogeologic Scaling and Its Interpretation, Rev. Geophys., 41, 1014, &lt;a href=&quot;http://dx.doi.org/10.1029./2003RG000130&quot;&gt;https://doi.org/10.1029./2003RG000130&lt;/a&gt;, 2003.</mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple">Peltier, R. and Lévy Vehel, J.: Multifractional Brownian motion: Definition and preliminary results, INRIA, Technical report No. 2645, 39 pp., 1995.</mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple">Peng, C. K., Havlin, S., Stanley, H. E., and Goldberger, A. L.: Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series, CHAOS, 5, 82–87, 1995.</mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple">Pulkkinen, T. I., Partamies, N., Huttunen, K. E. J., Reeves, G. D., and Koskinen, H. E. J.: Differences in geomagnetic storms driven by magnetic clouds and ICME sheath regions, Geophys. Res. Lett., 34, L02105, &lt;a href=&quot;http://dx.doi.org/10.1029/2006GL027775&quot;&gt;https://doi.org/10.1029/2006GL027775&lt;/a&gt;, 2007.</mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple">Rangarajan, G. K. and Iyemori, T.: Time variations of geomagnetic activity indices Kp and Ap: an update, Ann. Geophys., 15, 1271–1290, &lt;a href=&quot;http://dx.doi.org/10.1007/s00585-997-1271-z &quot;&gt;https://doi.org/10.1007/s00585-997-1271-z&lt;/a&gt;, 1997.</mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple">Seber, G. A. F. and Wild, C. J.: Nonlinear Regression, John Wiley &amp; Sons, Inc., Hoboken, NJ, USA, &lt;a href=&quot;http://dx.doi.org/10.1002/0471725315&quot;&gt;https://doi.org/10.1002/0471725315&lt;/a&gt;, 2005.</mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple">Sharma, A. S. and Veeramani, T.: Extreme events and long-range correlations in space weather, Nonlin. Processes Geophys., 18, 719–725, &lt;a href=&quot;http://dx.doi.org/10.5194/npg-18-719-2011&quot;&gt;https://doi.org/10.5194/npg-18-719-2011&lt;/a&gt;, 2011.</mixed-citation>
</ref>
<ref id="ref28">
<label>28</label><mixed-citation publication-type="other" xlink:type="simple">Stanley, H. E., Amaral, L. A. N., Goldberger, A. L., Havlin, S., Ivanov, P. Ch., and Peng, C. K.: Statistical physics and physiology: monofractal and multifractal approaches, Physica A, 270, 309–324, 1999.</mixed-citation>
</ref>
<ref id="ref29">
<label>29</label><mixed-citation publication-type="other" xlink:type="simple">Takalo, J., Timonen, J., Klimas, A., Valdivia, J., and Vassiliadis, D.: Nonlinear energy dissipation in a cellular automaton magnetotail field model, Geophys. Res. Lett., 26, 1813–1816, 1999.</mixed-citation>
</ref>
<ref id="ref30">
<label>30</label><mixed-citation publication-type="other" xlink:type="simple">Taqqu, M. S., Teverovsky, V., and Willinger, W.: Estimators for long-range dependence: An empirical study, Fractals, 3, 785–798, 1995.</mixed-citation>
</ref>
<ref id="ref31">
<label>31</label><mixed-citation publication-type="other" xlink:type="simple">Taqqu, M., Teverovsky, V., and Willinger, W.: Is network traffic self-similar or multifractal?, Fractals, 5, 63–73, 1997.</mixed-citation>
</ref>
<ref id="ref32">
<label>32</label><mixed-citation publication-type="other" xlink:type="simple">Vörös, Z.: On multifractality of high-latitude geomagnetic fluctuations, Ann. Geophys., 18, 1273–1282, &lt;a href=&quot;http://dx.doi.org/10.1007/s00585-000-1273-6&quot;&gt;https://doi.org/10.1007/s00585-000-1273-6&lt;/a&gt;, 2000.</mixed-citation>
</ref>
<ref id="ref33">
<label>33</label><mixed-citation publication-type="other" xlink:type="simple">Wanliss, J.: Fractal properties of SYM-H during quiet and active times, J. Geophys. Res., 110, A03202, &lt;a href=&quot;http://dx.doi.org/10.1029/2004JA010544&quot;&gt;https://doi.org/10.1029/2004JA010544&lt;/a&gt;, 2005.</mixed-citation>
</ref>
<ref id="ref34">
<label>34</label><mixed-citation publication-type="other" xlink:type="simple">Wanliss, J. and Uritsky, V.: Understanding bursty behavior in midlatitude geomagnetic activity, J. Geophys. Res., 115, A03215, &lt;a href=&quot;http://dx.doi.org/10.1029/2009JA014642&quot;&gt;https://doi.org/10.1029/2009JA014642&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref35">
<label>35</label><mixed-citation publication-type="other" xlink:type="simple">Wanliss, J. A.: Nonlinear variability of SYM-H over two solar cycles, Earth Planets Space, 56, e13–e16, 2004.</mixed-citation>
</ref>
<ref id="ref36">
<label>36</label><mixed-citation publication-type="other" xlink:type="simple">Wanliss, J. A. and Antoine, L. A. G.: Geomagnetic micropulsations: Implications for high resolution aeromagnetic surveys, Explor. Geophys., 26, 535–538, 1995.</mixed-citation>
</ref>
<ref id="ref37">
<label>37</label><mixed-citation publication-type="other" xlink:type="simple">Wanliss, J. A. and Dobias, P.: Space Storm as a Phase Transition, J. Atmos. Sol.-Terr. Phy., 69, 675–684, &lt;a href=&quot;http://dx.doi.org/10.1016/j.jastp.2007.01.001&quot;&gt;https://doi.org/10.1016/j.jastp.2007.01.001&lt;/a&gt;, 2007.</mixed-citation>
</ref>
<ref id="ref38">
<label>38</label><mixed-citation publication-type="other" xlink:type="simple">Wanliss, J. A. and Reynolds, M. A.: Measurement of the stochasticity of low-latitude geomagnetic temporal variations, Ann. Geophys., 21, 1–6,  &lt;a href=&quot;http://dx.doi.org/10.5194/angeo-21-2025-2003&quot;&gt;https://doi.org/10.5194/angeo-21-2025-2003&lt;/a&gt; , 2003.</mixed-citation>
</ref>
<ref id="ref39">
<label>39</label><mixed-citation publication-type="other" xlink:type="simple">Wanliss, J. A., Anh, V. V., Yu, Z.-G., and Watson, S.: Multifractal modeling of magnetic storms via symbolic dynamics analysis, J. Geophys. Res., 110, A08214, &lt;a href=&quot;http://dx.doi.org/10.1029/2004JA010996&quot;&gt;https://doi.org/10.1029/2004JA010996&lt;/a&gt;, 2005.</mixed-citation>
</ref>
<ref id="ref40">
<label>40</label><mixed-citation publication-type="other" xlink:type="simple">Wanliss, J. A. and Showalter, K. M.: High-resolution global storm index: Dst versus SYM-H, J. Geophys. Res., 111, A02202, &lt;a href=&quot;http://dx.doi.org/10.1029/2005JA011034&quot;&gt;https://doi.org/10.1029/2005JA011034&lt;/a&gt;, 2006.</mixed-citation>
</ref>
<ref id="ref41">
<label>41</label><mixed-citation publication-type="other" xlink:type="simple">Yu, Z.-G., Anh, V., Wang, Y., Mao, D., and Wanliss, J.: Modeling and simulation of the horizontal component of the geomagnetic field by fractional stochastic differential equations in conjunction with empirical mode decomposition, J. Geophys. Res., 115, A10219, &lt;a href=&quot;http://dx.doi.org/10.1029/2009JA015206&quot;&gt;https://doi.org/10.1029/2009JA015206&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref42">
<label>42</label><mixed-citation publication-type="other" xlink:type="simple">Yumoto, K. and the 210MM Magnetic Observation Group: The STEP 210 magnetic meridian network project, J. Geomagn. Geoelectr., 48, 1297–1310, 1996.</mixed-citation>
</ref>
</ref-list>
</back>
</article>