Energetic particles in the near-Earth space pose a significant risk to Earth-orbiting satellites and humans in space. During geomagnetic storms the radiation in the near-Earth space can dramatically increase, and numerous anomalies have been reported by satellite operators. Satellite measurements are usually limited to a single location in space, which complicates the data analysis geared towards reproducing the global state of the ring current and radiation belts. Up until recently, most of the research concentrated on the analysis of data from individual spacecrafts, which does not allow for inferring the global evolution of the particle radiation environment.
Analysis of satellite measurements from different spacecraft is complicated by the fact that measurements are given at various locations in space, have different instrumental errors and often vary by orders of magnitude. During the first funding period, we focused on developing data-assimilative tools for the most energetic electrons called radiation belts. These highly energetic particles can produce deep dielectric charging in satellites. In the second funding period, we will focus on another population of electrons in the near-Earth space that is usually referred to as ring current. The name is derived from the current that is generated by this particle population and the magnetic field produced by it that can be measured on the ground. The hazardous effects of the ring current include charging of satellite surfaces that can damage them, degradation of satellite solar panels, and induction of currents in power grids that can damage transformers or result in voltage instability leading to a collapse of the power system. While there are a number of existing physics-based models of the ring current and a number of operational satellites providing in-situ measurements of the ring current in space, there have only been a few attempts to assimilate the measurements in the physics-based model and there is currently no operational model that is using data assimilation for predictions.
While we will be building upon the progress achieved during the funding period, there are also significant differences between the data assimilation for the radiation belts and for the ring current. In the case of the radiation belts, the description can be reduced to 3 variables and the evolution can be described by the diffusion equation. For the ring current (in the most general case), we need to specify the 4-dimensional distribution function, as the ring current has an asymmetry in the local time (4th variable). Another complication of modeling the ring current is the fact that the dynamics are described by the advection-diffusion equation and not just the diffusion equation, as is the case for radiation belts. The ring current also shows variability on much shorter time scales and exhibits very narrow spatial structures, which makes it difficult to judge whether the observed variability is produced by global changes of the ring current, local changes associated with small spatial structures or transient phenomena.
Data assimilation for the ring current will require the development of new methods and approaches. In collaboration with a number of projects within CRC, we will explore different methods and test the applicability of non-linear parameter estimation with the EnKF for determining unknown and unobserved parameters. We will also use the EnKF to directly assimilate fluxes into the code without first transforming them into Phase Space Density (PSD). Special attention will be paid to the set up and use of the Ensemble Kalman Filter (EnKF), including set up of errors and localisation, and comparison with the Kalman Filter (KF). The new approaches and methods developed within the CRC will be tested on space physics data for multi-dimensional diffusion and diffusion-convection equations.
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