A Quasi-Physical Dynamic Reduced Order Model for Thermospheric Mass Density via Hermitian Space-Dynamic Mode Decomposition

Thermospheric mass density is a major driver of satellite drag, the largest source of uncertainty in accurately predicting the orbit of satellites in low Earth orbit (LEO) pertinent to space situational awareness. Most existing models for thermosphere are either physics based or empirical. Physics-based models offer the potential for good predictive/forecast capabilities but require dedicated parallel resources for real-time evaluation and data assimilative capabilities that are still under development. Empirical models are fast to evaluate but offer very limited forecasting abilities. This paper presents methodology for developing a reduced order dynamic model from high-dimensional physics-based models by capturing the underlying dynamical behavior. The quasi-physical reduced order model for thermospheric mass density is developed using a large dataset of Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIE-GCM) simulations spanning 12 years and covering a complete solar cycle. Toward this end, a new reduced order modeling approach, based on dynamic mode decomposition with control that uses the Hermitian space of the problem to derive the dynamic and input matrices in a tractable manner is developed. Results show that the reduced order model performs well in serving as a reduced order surrogate for TIE-GCM while almost always maintaining the forecast error to within 5% of the simulated densities after 24 hrs.