# Statistical Characterization of the Magnetic Field in Space during Magnetic Storms
## 1 Magnetic Storms
(**a**) Dst from 0:00 on 6 March 2016, to 23:00 on 7 March 2016; (**b**) Components of the magnetic field from 0:00 on 6 March 2016, to 23:00 on 7 March 2016; (**c**) Dst from 0:00 on 13 October 2016, to 23:00 on 14 October 2016; (**d**) Components of the magnetic field from 0:00 on 13 October 2016, to 23:00 on 14 October 2016; (**e**) Dst from 0:00 on 27 May 2017, to 23:00 on 28 May 2017; (**f**) components of the magnetic field from 0:00 on 27 May 2017, to 23:00 on 28 May 2017; (**g**) components of the magnetic field from 0:00 on 8 September 2017, to 23:00 on 9 September 2017; (**i**) Dst from 00:00 on 27 September 2020, to 23:00 on 28 September 2020; (**j**) components of the magnetic field from 00:00 on 27 September 2020, to 23:00 on 28 September 2020; (**k**) Dst from 00:00 4 November 2021, to 23:00 4 November 2021; (**l**) components of the magnetic field from 00:00 on 4 November 2021, to 23:00 on 5 November 2021.  
in the paper is obtained from the rapid-view data released in real-time by WDC Kyoto, the Tokyo station of the World Data System ([[https://wdc.kugi.kyoto-u.ac.jp/index.html](https://wdc.kugi.kyoto-u.ac.jp/index.html)]([https://wdc.kugi.kyoto-u.ac.jp/index.html](https://wdc.kugi.kyoto-u.ac.jp/index.html)) (accessed on 10 July 2022)). Magnetic storm forecasting for alerts at the L1 point can also be used by monitoring the solar wind in real-time using various satellites, such as the ACE satellites. The ACE satellites were launched by NASA as part of the Explorer program on 25 August 1997 and are currently in the vicinity of L1 Liza in orbit. The point is located on a straight line between the Sun and Earth, approximately 1.5 million kilometers from Earth, and is used to study the solar and outer space regions, including solar wind energy particles, interplanetary and interstellar media, and types of galactic matter. Additionally, the real-time information transmitted by ACE satellites is used by the Space Weather Forecasting Center to improve the reliability of solar storm forecasts and warnings. The data for magnetic field components (Bx, By, and Bz) in the text are provided by the ACE satellites. In Figure 1, the horizontal axis represents the date, and the vertical axis represents the Dst index and magnetic field strength, both in nT. The plots show that when the Dst index decreases significantly, indicating the occurrence of a magnetic storm, all three components of the magnetic field detected by the ACE satellites display positive and negative jitter, indicating that the magnetic field at the detection point fluctuates greatly during a storm. There is a clear temporal relationship between the fluctuations in the magnetic field components and the decrease in the Dst index, with the variation in the Dst index appearing several hours later than the large fluctuations in the magnetic field components, indicating that the magnetic storm first passes through the Lagrangian point and then through the magnetosphere and ionosphere, consequently affecting the magnetic field components near the ground. Probability Density Estimates of the Magnitudes of the Components of the Magnetic Field during a Magnetic Storm  
Probability density is one of the important characteristics of stochastic processes, especially for digital communication, radar, and navigation systems. The probability density of a signal is directly related to the signal information entropy, correlation function, correlation matrix, and other parameters [16; 17; 18], thus affecting the output performance of radar, navigation, and communication systems. For example, classification, denoising, and target detection for synthetic aperture radar imaging are dependent on the amplitude distribution of the received signal [19; 20; 21]. In wireless communication systems, the statistical properties of the channels will have an impact on parameter estimation for the target signal [22]. Additionally, the robustness and accuracy of navigation systems are highly dependent on the probability density function [23; 24].