Gradient calculation techniques for multi-point ionosphere/thermosphere measurements from GDC

The upcoming Geospace Dynamics Constellation (GDC) mission aims to investigate dynamic processes active in Earth’s upper atmosphere and their local, regional, and global characteristics. Achieving this goal will involve resolving and distinguishing spatial and temporal variability of ionospheric and thermospheric (IT) structures in a quantitative manner. This, in turn, calls for the development of sophisticated algorithms that are optimal in combining information from multiple in-situ platforms. This manuscript introduces an implementation of the least-squares gradient calculation approach previously developed by J. De Keyser with the focus of its application to the GDC mission. This approach robustly calculates spatial and temporal gradients of IT parameters from in-situ measurements from multiple spacecraft that form a flexible constellation. The previous work by De Keyser, originally developed for analysis of Cluster data, focused on 3-D Cartesian geometry, while the current work extends the approach to spherical geometry suitable for missions in Low Earth Orbit (LEO). The algorithm automatically provides error bars for the estimated gradients as well as the scales over which the gradients are expected to be constant. We evaluate the performance of the software on outputs of high-resolution global ionospheric/thermospheric simulations. It is shown that the software will be a powerful tool to explore GDC’s ability to answer science questions that require gradient calculations. The code can also be employed in support of Observing System Simulation Experiments to evaluate suitability of various constellation geometries and assess the impact of measurement sensitivities on addressing GDC’s science objectives.