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

Owolabi, Charles, Connor, Hyunju, Hampton, Don, Oliveira, Denny M., Calabia, Andres, Gowtam, V. Sai, and Zesta, Eftyhia, 2025. Eigen-Swarm: Swarm's Thermospheric Mass Density Modeling via Eigen-Decomposition. Space Weather, 23(7):e2025SW004351, doi:10.1029/2025SW004351.

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@ARTICLE{2025SpWea..2304351O,
       author = {{Owolabi}, Charles and {Connor}, Hyunju and {Hampton}, Don and {Oliveira}, Denny M. and {Calabia}, Andres and {Gowtam}, V. Sai and {Zesta}, Eftyhia},
        title = "{Eigen-Swarm: Swarm's Thermospheric Mass Density Modeling via Eigen-Decomposition}",
      journal = {Space Weather},
     keywords = {thermospheric mass density, eigen-decomposition, Swarm satellite, JB2008/NRLMSIS2.0 models, empirical modeling, solar activity},
         year = 2025,
        month = jul,
       volume = {23},
       number = {7},
          eid = {e2025SW004351},
        pages = {e2025SW004351},
     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{\textendash}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{\textendash}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 ({\ensuremath{\mu}}), and
        variance ({\ensuremath{\sigma}}$^{2}$), 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.}",
          doi = {10.1029/2025SW004351},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2025SpWea..2304351O},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

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