Abstract: Energetic charged particles trapped by the Earth’s magnetic field present a significant hazard for Earth-orbiting satellites and humans in space. Application of the data assimilation tools allows us to reconstruct the global state of the radiation particle environment from sparse single-point observations. The measurements from different satellites with different observational errors can be blended in an optimal way with physics-based models. The mathematical formulation on the diffusion and diffusion-advection equations for the Earth’s Van Allen radiation belts and ring current is described. We further describe several recent studies that successfully applied the data assimilation tools to the near-Earth space radiation environment. The applications to the reanalysis of the radiation belts and ring current, real-time predictions, and analysis of the missing physical processes are described and motivation for these studies is provided. We further discuss various assimilation techniques and potential topics for future research.

The Sun-Earth interaction is a complex system of multi-scale processes. The spatial scales of interest vary from the mega-meter size of solar corona structures to the few hundred kilometers of the terrestrial magnetopause and even less when kinetic effects need to be considered. The temporal variations also span a wide range of scales, from thousands of years for the hydrological ocean cycles driven by the total solar radiation to scales of minutes and below for particle acceleration in magnetic reconnection. In this chapter we introduce the building blocks of the Sun-Earth system and briefly describe its important components. Solar disturbances such as solar flares and coronal mass ejection (CME) have the largest impact on geomagnetic activity, especially magnetic storms. Magnetic storms are responsible for large depressions in the horizontal (H) component of the Earth’ surface magnetic field. The strength of a storm is quantified by the Dst index, which is a local time average of the depression measured along the magnetic equator. The depression during a storm is caused by a ring current around the Earth with additional contributions from the magnetopause and tail currents. We review recent developments of empirical prediction algorithms for the Dst index using observations made upstream of the Earth, and alternative procedures based on the same concept including neural networks and the NARMAX method. Future improvements in empirical prediction will require more data from extreme events, additional physical insight to identify the role of other processes, and better measurements of the inputs to the system.

Since the discovery of the magnetosphere-magnetotail system in the1950s-1960s), and the associated beginning of the satellite era, we have gained a well-informed understanding of this space plasma region permeated by the geomagnetic field and home to a variety of charged particle populations and plasma waves. Over the last six decades, IAGA has played an important role in supporting international magnetospheric research. Here we provide an overview of recent developments in energy transport from the solar wind into the Earth’s environment. Topics include, magnetosphere energy input, the role of the boundary layer. Solar wind interaction with the magnetosphere creates geomagnetic activity and the response of the region leading to sub-storms and steady magnetospheric convection are discussed. The charged particle energy (eV to MeV) inherent/contained in the magnetospheric ring current and Van Allen radiation belts establish many properties of the region, giving rise to boundary regions and waves. Results from recent state of the art and currently operating Earth orbiting satellites (Cluster, THEMIS, Van Allen Probes, Magnetosphere MultiScale), are providing exciting new results. Waves from magnetospheric scale ultra-low frequency (ULF) from a few milliHertz, up to upper hybrid waves and continuum radiation in the 1-2 MHz band. Finally, current understanding of the plasmasphere and associated boundary the plasmapause, are considered.