Dynamical Properties of Peak and Time-Integrated Geomagnetic Events Inferred From Sample Entropy

<p class="rtejustify">We provide a comprehensive statistical analysis of the sample entropy of peak and time-integrated geomagnetic events in 2001\textendash2017, considering different measures of event strength, different geomagnetic indices, and a simplified solar wind-magnetosphere coupling function <img alt="urn:x-wiley:jgra:media:jgra55526:jgra55526-math-0001" class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/612fc9aa-04ac-42f4-b25d-c21651568041/jgra55526-math-0001.png" />. Our investigations reveal the existence of significant correlations between the entropies of <img alt="urn:x-wiley:jgra:media:jgra55526:jgra55526-math-0002" class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/8ea9e610-a2cc-462d-ba2a-8ab2d561e994/jgra55526-math-0002.png" />, <img alt="urn:x-wiley:jgra:media:jgra55526:jgra55526-math-0003" class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/b305181e-7877-4aca-8f46-b534967df450/jgra55526-math-0003.png" />, and <img alt="urn:x-wiley:jgra:media:jgra55526:jgra55526-math-0004" class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/7908a179-7493-4026-bbf0-74b9f5ed28d7/jgra55526-math-0004.png" />, and between such entropies and event strengths, as well as good correlations between peak levels of solar wind-magnetosphere coupling and ring current ( <img alt="urn:x-wiley:jgra:media:jgra55526:jgra55526-math-0005" class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/8198433d-2cab-4b59-914a-9496dfb2e8a5/jgra55526-math-0005.png" />) and <img alt="urn:x-wiley:jgra:media:jgra55526:jgra55526-math-0006" class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/11417ba1-2fe2-4c50-bd36-79374f8cd701/jgra55526-math-0006.png" /> entropies, suggesting a potential predictability of significant <img alt="urn:x-wiley:jgra:media:jgra55526:jgra55526-math-0007" class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/f4f5471c-5456-4bde-97dd-e6e056cef2f8/jgra55526-math-0007.png" /> and <img alt="urn:x-wiley:jgra:media:jgra55526:jgra55526-math-0008" class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/6c3e0941-6b9e-4754-a9bd-a6acf2bb11ae/jgra55526-math-0008.png" /> events on the basis of appropriate functions of <img alt="urn:x-wiley:jgra:media:jgra55526:jgra55526-math-0009" class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/e5181b56-8958-428a-b599-7c2340dca629/jgra55526-math-0009.png" />. Sensibly weaker correlations are found with <img alt="urn:x-wiley:jgra:media:jgra55526:jgra55526-math-0010" class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/81baf902-d4ce-45be-bcf4-132474ccc528/jgra55526-math-0010.png" /> entropy. We further show the presence of several significant entropy correlations between geomagnetic indices, solar wind-magnetosphere coupling, and trapped or precipitated energetic electron and ion fluxes measured by geostationary and low Earth orbit satellites in the outer radiation belt during the same periods. Entropy correlations between <img alt="urn:x-wiley:jgra:media:jgra55526:jgra55526-math-0011" class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/989d1ae2-c613-48ce-8918-aa3f2a8ce64c/jgra55526-math-0011.png" /> and trapped or precipitated 30- to 80-keV ion fluxes at low <img alt="urn:x-wiley:jgra:media:jgra55526:jgra55526-math-0012" class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/30012910-3771-4497-85ae-0e906d17d21a/jgra55526-math-0012.png" /> and between <img alt="urn:x-wiley:jgra:media:jgra55526:jgra55526-math-0013" class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/8c553e90-e91f-4cb6-b552-35e4ccac788d/jgra55526-math-0013.png" /> and trapped 40-keV electron fluxes at geostationary orbit correspond well with ring current properties and substorm-induced injections, respectively. Entropy correlations between <img alt="urn:x-wiley:jgra:media:jgra55526:jgra55526-math-0014" class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/a04a1e52-2b80-4f1e-a324-c2e77114fdff/jgra55526-math-0014.png" /> and precipitation rates of energetic ion and electron fluxes demonstrate the sensibility of <img alt="urn:x-wiley:jgra:media:jgra55526:jgra55526-math-0015" class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/d0371314-063c-4634-90a6-e82e57793116/jgra55526-math-0015.png" /> index entropy to both low-energy (5\textendash30 keV) electron injections and ring current. The stronger entropy correlation between solar wind-magnetosphere coupling and <img alt="urn:x-wiley:jgra:media:jgra55526:jgra55526-math-0016" class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/f7ec6651-8da6-41d3-8420-b4b155abf118/jgra55526-math-0016.png" /> than <img alt="urn:x-wiley:jgra:media:jgra55526:jgra55526-math-0017" class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/070fbb92-7613-466e-ad70-0c3bfc8384c0/jgra55526-math-0017.png" /> likely stems from the more stochastic behavior of electron injections and fast losses near geostationary orbit.</p>