Abstract The in-depth investigation of the parameters of the solar wind, the zonal geomagnetic indices and the interplanetary magnetic field (IMF) is the key to furthering space weather researches. The investigations got meaning through modeling various interplanetary parameters and geomagnetic indices. These models, built on the basis of the correlations between solar wind parameters and zonal geomagnetic indices, and that must strictly obey physical principles, will not only reveal the properties of geomagnetic activity but also allow estimates of their formations. This study focuses on the 2012 March 09 phenomenon, the first intense geomagnetic storm of the 24th solar cycle. The deeper understanding of the storm depends on a correct interpretation and visualization of the relationship between solar wind plasma parameters (solar wind dynamic pressure (P), flow speed (v), electric field (E), magnetic field (Bz), proton density (N), temperature (T)) and zonal geomagnetic indices (AE, ap, Kp, Dst). The study investigates, visualizes and interprets the solar wind plasma parameters and zonal geomagnetic indices themselves. The storm variables set included of observations of ten variables from NASA are described. By this investigation a covariance matrix indicates the strength of bivariate relationships, a dendrogram indicates hierarchical clustering into groups, and factor analysis indicates three distinct eigenvectors. In addition, linear and nonlinear models about the problem are introduced to readers. The author discuses mathematically what happened in the storm on 2012 March 09 at the beginning of the 24th solar cycle. The aim of this work is to help the reader understand the storm by providing the models that the representatives of parameters and indices coexist.

中文翻译：

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2012 年 3 月 9 日强风暴的数学分析

摘要 深入研究太阳风参数、纬向地磁指数和行星际磁场（IMF）是推进空间天气研究的关键。通过对各种行星际参数和地磁指数进行建模，这些调查变得有意义。这些模型建立在太阳风参数和纬向地磁指数之间的相关性基础上，必须严格遵守物理原理，不仅可以揭示地磁活动的特性，还可以估计它们的形成。这项研究的重点是 2012 年 3 月 9 日现象，这是第 24 个太阳周期的第一次强烈地磁风暴。对风暴的更深入理解取决于对太阳风等离子体参数（太阳风动压（P）、流速（v）、电场（E）、磁场（Bz）、质子密度）之间关系的正确解释和可视化(N)、温度 (T)) 和纬向地磁指数（AE、ap、Kp、Dst）。该研究调查、可视化和解释太阳风等离子体参数和纬向地磁指数本身。描述了包含来自 NASA 的十个变量的观测的风暴变量集。通过这项调查，协方差矩阵表示双变量关系的强度，树状图表示分层聚类成组，因子分析表示三个不同的特征向量。此外，还向读者介绍了有关该问题的线性和非线性模型。作者从数学上讨论了 2012 年 3 月 9 日第 24 个太阳周期开始时风暴中发生的事情。这项工作的目的是通过提供参数和指数的代表共存的模型来帮助读者理解风暴。