A unified approach to inner magnetospheric state prediction

PUBLICATIONS Journal of Geophysical Research: Space Physics TECHNICAL REPORTS: METHODS 10.1002/2015JA021733 A uniﬁed approach to inner magnetospheric state prediction J. Bortnik 1 , W. Li 1 , R. M. Thorne 1 , and V. Angelopoulos 2 Special Section: Variability of the Sun and Its Terrestrial Impact VarSITI Key Points: • We present a general method that can be used to model any quantity in the inner magnetosphere • We demonstrate our method on the spatiotemporal distribution of elec- tron density • This model could be immensely useful for space weather and other applications Correspondence to: J. Bortnik, jbortnik@gmail.com Citation: Bortnik, J., W. Li, R. M. Thorne, and V. Angelopoulos (2016), A uniﬁed approach to inner magnetospheric state prediction, J. Geophys. Res. Space Physics, 121, 2423–2430, doi:10.1002/ 2015JA021733. Received 27 JUL 2015 Accepted 3 MAR 2016 Accepted article online 9 MAR 2016 Published online 30 MAR 2016 Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, California, USA, 2 Earth, Planetary and Space Sciences/Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California, USA Abstract This brief technique paper presents a method of reconstructing the global, time-varying distribution of some physical quantity Q that has been sparsely sampled at various locations within the magnetosphere and at different times. The quantity Q can be essentially any measurement taken on the satellite including a variety of waves (chorus, hiss, magnetosonic, and ion cyclotron), electrons of various energies ranging from cold to relativistic, and ions of various species and energies. As an illustrative example, we chose Q to be the electron number density (inferred from spacecraft potential) measured by three Time History of Events and Macroscale Interactions during Substorms (THEMIS) probes between 2008 and 2014 and use the SYM-H index, taken at a 5 min cadence for the 5 h preceding each observed data point as the main regressor, although the predictor can also be any suitable geomagnetic index or solar wind parameter. Results show that the equatorial electron number density can be accurately reconstructed throughout the whole of the inner magnetosphere as a function of space and time, even capturing the dynamics of elementary plasmaspheric plume formation and corotation, suggesting that the dynamics of various other physical quantities could be similarly captured. For our main model, we use a simple, fully connected feedforward neural network with two hidden layers having sigmoidal activation functions and an output layer with a linear activation function to perform the reconstruction. The training is performed using the Levenberg-Marquardt algorithm and gives typical RMS errors of ~1.7 and regression of >0.93, which is considered excellent. We also present a discussion on the different applications and future extensions of the present model, for modeling various physical quantities. 1. Introduction The Earth’s inner magnetosphere is a complex, interconnected system that is driven by energy inputs from the Sun and solar wind (e.g., see introductory discussions in Kivelson and Russell [1995] and Khazanov [2011]). There are a variety of components that comprise the magnetospheric environment, such as the ionosphere, background electric and magnetic ﬁelds, plasma waves, electrons ranging from cool ( 5 MeV) energies, and different species and energies of ions. These components can be externally or internally driven and typically couple to one another in subtle and often unexpected ways. Understanding the dynamical behavior of these various magneto- spheric components is interesting and important scientiﬁcally and also has important societal implications in that the near Earth space environment can impact human technological systems in dramatic ways (see, for instance, the National Research Council’s Decadal Survey report “Solar and Space Physics: A Science for a Technological Society”). A number of different approaches to specify and predict the state of the inner magnetosphere have been employed in previous studies. The ﬁrst and most familiar involves the construction of ﬁrst principles physics-based models, and a number of efforts are currently underway in pursuit of this goal [e.g., Wolf et al., 1991; Toffoletto et al., 2003, 2004; Jordanova et al., 2008, 2010; Wang et al., 2004; Wiltberger et al., 2004; Goodrich et al., 2004; Pembroke et al., 2012]. The major advantage of physics-based models is that they employ fundamental physical principles and thus can be useful in extrapolating to situations that have not been previously observed. The disadvantage is that these models are typically large, complex, and computationally intensive. The coupling between various component systems is not straightforward, and if there are missing physical processes from the models (which there inevitably always are), the models can produce erroneous results when operated in unusual regimes. ©2016. American Geophysical Union. All Rights Reserved. BORTNIK ET AL. On the other end of the spectrum, the state of the inner magnetosphere can be speciﬁed simply by plotting a particular quantity in a plane or a volume, broadly parameterized by some controlling parameter. For example, Meredith et al. [2012] plot the intensity of whistler mode chorus waves in the inner magnetosphere, parameter- ized by three ranges of the AE index representing quiet, moderate, and active conditions, based on data col- lected by the DE1, Combined Release and Radiation Effects Satellite, Cluster 1, Double Star TC1, and Time INNER MAGNETOSPHERIC STATE PREDICTION