A quasi-physical dynamic reduced order model for thermospheric mass density via Hermitian Space Dynamic Mode Decomposition

TL;DR

This paper introduces a quasi-physical reduced order model for thermospheric mass density using Hermitian Space Dynamic Mode Decomposition, enabling fast and accurate satellite drag predictions from high-dimensional physics-based models.

Contribution

It develops a novel ROM approach based on DMDc in Hermitian space, capturing thermospheric dynamics with high accuracy from 12 years of TIE-GCM data.

Findings

ROM maintains forecast error within 5% after 24 hours

Model effectively captures thermospheric behavior across a solar cycle

Provides a fast surrogate for complex physics-based models

Abstract

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 have yet to be developed. Empirical models are fast to evaluate, but offer very limited forecasting abilities. This paper presents a methodology of developing a reduced-order dynamic model from high-dimensional physics-based models by capturing the underlying dynamical behavior. This work develops a quasi-physical reduced order model (ROM) for thermospheric mass density using simulated output from NCAR's Thermosphere-Ionosphere-Electrodynamics General Circular Model (TIE-GCM). The ROM is derived using a dynamic system formulation from a large dataset of TIE-GCM simulations spanning 12 years and covering a complete solar cycle. Towards this end, a new reduced order modeling approach, based on Dynamic Mode Decomposition with control (DMDc), that uses the Hermitian space of the problem to derive the dynamics and input matrices in a tractable manner is developed. Results show that the ROM 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 hours.