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@ARTICLE{2025SpWea..2304317G,
       author = {{Guo}, Yu and {Guo}, Fei and {Zhang}, Xiaohong and {Yang}, Yan and {Mei}, Dengkui and {Ren}, Xiaodong},
        title = "{A Two-Step Method for Enhancing Thermospheric Mass Density Empirical Model}",
      journal = {Space Weather},
     keywords = {thermosphere, neutral total mass density, SWARM-C, GRACE-A, NRLMSIS 2.1 model, empirical model enhancement},
         year = 2025,
        month = may,
       volume = {23},
       number = {5},
          eid = {e2024SW004317},
        pages = {e2024SW004317},
     abstract = "{With the rapid development of Low Earth Orbit constellations, the
        importance of accurately estimating thermospheric mass density
        is steadily increasing. Current empirical models still exhibit
        unavoidable biases in estimating thermospheric mass density. In
        this paper, we propose a novel two-step empirical model
        calibration enhancement method. The enhancement coefficients are
        constructed by the second-order spherical harmonic function and
        the machine learning method. The daily in situ mass density
        observations collected by the SWARM-C and GRACE-A satellites
        between 2015 and 2017 are used to generate coefficients and test
        the model. The two-step enhancement method performs well under
        various conditions, including different satellites, altitudes,
        and space weather scenarios. During storm periods, using
        satellite observations as the references, the enhanced MSIS 2.1
        model can achieve estimation error reduction of over 15\%.
        During long-term testing in 2015, 2016, and 2017, the average
        RMSEs of the enhanced thermospheric mass density decreased by
        23.06\%, 20.33\%, and 30.95\%, respectively.}",
          doi = {10.1029/2024SW004317},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2025SpWea..2304317G},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}