# Study on the Thermospheric Density Distribution Pattern during Geomagnetic Activity
## 1 Introduction  
Existing atmospheric models are primarily classified into physical models and empirical models [1; 2]. Both models have their own advantages and application areas. Physical models attempt to describe the fundamental physical characteristics through equations [3]. These models include thermospheric general circulation models (TGCM) and local high-resolution flow models [4], which simulate temperature, density, atmospheric composition, horizontal wind, and atmospheric responses to different energy inputs. Compared with the empirical model, the physical model requires far more calculations, so the operator must have a very professional knowledge of physics [5]. Empirical models consist of several relatively simple functions that generally exhibit excellent performance in representing long-term and large-scale atmospheric characteristic changes. However, these functions contain parameters that are fitted using existing observational data, and hence require significant observational data to improve model accuracy. The prediction accuracy of existing atmospheric models, whether physical or empirical, depends on the forecast accuracy of solar and geomagnetic activity indices. Studying thermospheric density distribution under extreme atmospheric conditions (geomagnetic storms) can significantly prevent economic losses and disasters. [PERSON] et al. researched the effects of solar activity on the thermospheric density over the South Atlantic Anomaly (SAA) [6]. The researchers found that, during periods of high solar activity, the density in the SAA increased, while during periods of low solar activity, the density decreased. [PERSON], [PERSON] et al. analyzed irregular changes in the Earth's ionosphere caused by the 2013 St. Patrick's Day geomagnetic storm [7]. They found that during storms, irregular changes in the upper atmosphere's density can significantly impact the operation of satellites. This article utilizes the inversion results of the Swarm-C accelerometer [8; 9; 10] and employs the empirical orthogonal function analysis method to study the spatiotemporal distribution of atmospheric density during geomagnetic storms. Scientific studies have used satellite spaceborne accelerometer data to detect atmospheric density [11; 12; 13; 14; 15]. The most popular satellites for studying thermospheric density are GRACE and CHAMP [16; 17]. [PERSON] et al. [18] used the CHAMP and GRACE satellites' accelerometer data inversion to obtain the latest atmospheric density dataset. They found that the difference between the new and existing datasets is 14-18% compared with CHAMP, and 10-24% compared with GRACE. [PERSON] et al. [19] calculated the measured results of the thermal layer's atmospheric density and the empirical model's average error, with an error range of approximately 15-20%. This error would increase during solar activity. [PERSON] et al. [20] use the TDW (thermospheric density and wind) and GHOST (GPS high precision orbit determination software tools) software provided by NASA to invert the GRACE and CHAMP satellites' thermal atmosphere and horizontal wind field. Thermospheric density is mainly influenced by solar and geomagnetic activity cycles. Therefore, the thermospheric density is correlated with solar and geomagnetic activities. However, the change in geomagnetic activity is delayed by 5 min to 10 h compared to solar activity [21; 22; 23]. In relevant studies on space climate, the value of solar radiation index F10.7 helps evaluate solar activity. When there is no strong geomagnetic disturbance, the period of change of atmospheric density in the thermal layer is 27 days, the same as the sun's rotation period [24]. A significant positive correlation exists between the daily change in atmospheric density and solar radiation index F10.7 [25]. However, once a geomagnetic storm occurs, the thermospheric atmosphere heats up rapidly. The density of the thermosphere near the equator increases by 50 percent or more in the hours after the storm begins [26].