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Eigen‐Swarm: Swarm's Thermospheric Mass Density Modeling via Eigen‐Decomposition

Precise thermospheric mass density (TMD) prediction is essential for satellite orbital tracking, reentry calculations, and upper atmospheric processes under varying solar and magnetospheric conditions. In this paper, we construct an… Click to show full abstract

Precise thermospheric mass density (TMD) prediction is essential for satellite orbital tracking, reentry calculations, and upper atmospheric processes under varying solar and magnetospheric conditions. In this paper, we construct an empirical model of TMD at 450 km altitude with accelerometer‐derived (ACC) TMD observations from the Swarm‐C satellite during 2014–2020. We employ the Eigen‐Decomposition technique to extract dominant spatio‐temporal modes, with the first three capturing 99.12% of the variance, forming the basis of the Swarm‐based Eigen‐Decomposition model. We study the factors controlling the observed TMD variability and investigate their relation to longitude, latitude, local solar time, seasonal effects, solar and geomagnetic indices. The Eigen‐Decomposition model performance is validated by comparison with the Jacchia‐Bowman 2008 (JB2008), Naval Research Laboratory Mass Spectrometer Incoherent Scatter 2.0 (NRLMSIS2.0), and Calabia and Jin (CAJIN) models, as well as TMD data from the Gravity Recovery and Climate Experiment Follow‐On mission during 2018–2020, using root mean square error (RMSE) as the evaluation metric. The Eigen‐Decomposition model achieves an RMSE of 19.45%, outperforming JB2008 (29.83%), NRLMSIS2.0 (65.16%), and CAJIN (45.25%). Additional metrics, including correlation coefficient (R), mean (μ), and variance (σ2), further confirm the improved accuracy and fidelity of our approach across different solar activity conditions. This work demonstrates the effectiveness of data‐driven techniques in capturing TMD dynamics and deepening our understanding of the thermospheric response to space weather conditions.

Keywords: eigen; thermospheric mass; eigen decomposition; swarm

Journal Title: Space Weather
Year Published: 2025

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