Exploration of a Composite Index to Describe Magnetospheric Activity: Reduction of the Magnetospheric State Vector to a Single Scalar

Abstract

Geomagnetic activity is usually gauged by a single time‐dependent geomagnetic index. One drawback is that an individual geomagnetic index measures only one aspect of the activity in the Earth's magnetosphere. Here we construct a time‐dependent 11‐element magnetospheric state vector E for Earth that consists of measures of high‐latitude currents, polar cap current, magnetospheric convection, plasma pressure, ion and electron precipitation rates, the intensity of substorm‐injected electrons, and the elapsed time since the last substorm onset. At the same time we construct an eight‐element time‐dependent solar‐wind state vector S from the measured properties of the solar wind at Earth. In this S → E picture a time‐dependent “magnetospheric‐activity index” E(1) is created from a weighted sum of the 11 variables in the magnetospheric state vector, with the weights chosen by the vector correlation properties between the magnetospheric state vector E and the solar wind state vector S. The properties and advantages of this E(1) index are examined for the years 1991–2007. Comparing fits made on different subsets of the data demonstrates the robustness of the definition of E(1); tests using out‐of‐sample data demonstrate the accuracy of solar wind predictions of E(1). The advantages of the composite index E(1) include a more direct association with the solar wind, linearity, high predictability, and versatility with respect to (a) storm‐versus‐quiet intervals, (b) solar maximum versus solar minimum, and (c) the various types of solar wind plasma. Defining magnetospheric storms with the composite index E(1) is explored, and categorizing magnetospheric storms using the magnetospheric state vector E is considered.

On the Saturation (or Not) of Geomagnetic Indices

“…Note that other E (1) and S (1) variables composed of other geomagnetic indices and other solar-wind variables (with and without a R quick dt term) also show linearity in the response (no saturation): c.f. Figure 1 of Borovsky (2014), Figure 2A of Borovsky and Denton (2018), and…”

“…2a of Borovsky (2014), Eq. 8 of Borovsky and Denton (2018), and Eq. 1a of Borovsky and Osmane (2019)], hence the lack of saturation in these cases is not dependent on the ability of the solar-wind driver function to know the value of Q.…”

“…One motivation for investigating the nature of geomagneticindex saturation is the development of composite geomagnetic indices (Borovsky and Denton, 2018;Borovsky and Osmane, 2019) that do not exhibit saturation at strong driving, even though some of the geomagnetic indices used to create the composite indices do exhibit saturation.…”

The Need for a System Science Approach to Global Magnetospheric Models

“…These models provide information 1) that can be used to test our physical understanding about how the solar-wind-driven system works, 2) that can inform us about which parameters in the solar wind are key to controlling the reaction of the magnetosphere-ionosphere system, 3) about the global modes of reaction of the magnetosphere to the solar wind, 4) about the flow of information into and through the system, and 5) about where in the system chaotic behaviors emerges. These system methods can improve our scientific knowledge of the magnetosphere (e.g., the uncovering of secondary modes of reaction of the Earth system to the solar wind (Borovsky and Osmane, 2019) and can uncover improved ways to predict space weather (e.g., the expectation of accurately predicting the reaction of the Earthsystem to as-yet-unseen severe levels of solar-wind driving (Borovsky and Denton, 2018)). Note that, at present, system science methods do not appear to be used yet in their most general form for space weather prediction outside academia.…”

A Nonlinear System Science Approach to Find the Robust Solar Wind Drivers of the Multivariate Magnetosphere

“…These complications of overfitting becomes even more relevant as the magnetospheric system is a high dimensional system that seems to evolve in a low dimensional attractor (Valdivia et al., 1996) so that these models should represent, to some approximation, the robust dynamics of the system. Hence, a robust multivariate nonlinear system science description, that for example includes the coupling of these three geomagnetic indices (GI) and with solar wind drivers (Borovsky & Denton, 2018; Valdivia et al., 1999) can further our understanding of these interactions and their time scales (Adhikari et al., 2019), and could pave the way to robust Space Weather applications. This is what we are going to start analyzing in this manuscript.…”