Multi-scale Gradient Analysis Tool Applied to Thermospheric Properties

A modern challenge in the realm of geospace is computing multi-dimensional gradients from measurements provided by a single satellite mission. While satellites offer the ability to sample a large volume of space with regularity, single satellite missions are constrained to only gathering information along the orbital track (one dimension) about a general feature or “function” in question. Satellite constellations or cluster missions, however, sample a very large physical and scientific space that has yet to be fully exploited. There are very few constellation missions that have been dedicated to performing geospace science up to this point, such as Cluster and Swarm. Constellation missions offer unique scientific opportunities due to their abilities to gather data from different, but coordinated, locations in a mission space simultaneously. One specific area of exploration this ability opens is multi-scale analysis. Geospace Dynamic Constellation (GDC), a NASA funded mission comprised of 6 satellites, provides unique avenues to exercise these unexplored opportunities. GDC broadly aims to study the tight coupling between the IT system as a whole and Earth’s magnetosphere. In turn, GDC offers the opportunity and inspiration to develop robust multi-scale analysis techniques from general multipoint and multiparameter observations along the orbit that can benefit the entire scientific community.
This developed least-squares gradient computation (LSGC) multi-scale analysis tool has been utilized in tandem with either TIEGCM or HWM14 simulations to exhibit its ability to accurately compute multi-dimensional gradients, while also being able to provide error estimates for the computed results. LSGC’s capabilities are demonstrated by simulating GDC’s satellites flying through model output and performing (1) multi-dimensional gradient computations and extracting the associated errors, and (2) computing divergences and curls of the property under scrutiny using the results from (1). All these results are verified via comparison against “truth” results computed from the model output (not subject to the multi-scale tool). In summary, the spatial/temporal ambiguities involved in the computations yield inaccurate temporal gradients, while the spatial gradients, and associated divergences/curls, yield very reliable results. Though it is recognized that further development could potentially refine the temporal results extracted from this multi-scale analysis tool, LSGC still aims to be a tool widely used by the scientific community amidst the rise of constellation missions – as constellation missions are the future.