# Study on the Thermospheric Density Distribution Pattern during Geomagnetic Activity
## 3 Results  
### Comparison of EOF Density Fields of Different Orders  
The three-day thermospheric density data during storm events are selected to carry out empirical orthogonal decomposition to study the spatiotemporal decomposition of thermospheric density during a geomagnetic storm. The specific steps for empirical orthogonal decomposition of thermospheric atmospheric density data are as follows:  
Firstly, the measured thermospheric density field obtained by inverting the accelerometer data for the above three days is processed by subtracting the mean value, with a latitude interval of 5 degrees and a time interval of 1 h. This produces a matrix of anomalies in the measured thermospheric density field. Next, using Equation (3), the matrix is multiplied by its transpose matrix to obtain a real symmetric matrix. Finally, the eigenvalues and eigenvectors of the real symmetric matrix are calculated to obtain the characteristic vector fields of the accelerometer-measured thermospheric density variable field for each order. Figure 3 shows the temporal and latitudinal distribution of thermospheric density in the thermosphere drawn by the characteristic vector fields of the thermospheric density of different orders obtained by empirical orthogonal decomposition. Figure 3: The third-order vector fields were obtained after the decomposition of the measured atmospheric density on 8 September 2017. (**a**) The measured density field of the original accelerometer; (**b**) the first-order EOF density field; (**c**) the first two-order EOF density field; (**d**) the first three-order EOF density field. As shown in Figure 3, on 8 September 2017, the atmospheric density increased due to the geomagnetic storm. As a result, the middle of the original measured atmospheric density field showed bright yellow. The distribution of the first-order atmospheric density eigenvector field obtained by EOF decomposition is similar to the original measured atmospheric density field distribution, but the details are different. The high-density area in the middle of the first-order EOF atmospheric density feature vector field is significantly larger than the original measured atmospheric density field. As a result, the color of the high-density area (orange-yellow) is brighter and more concentrated. Consequently, the color contrast with the surrounding area is more pronounced. Compared with the original measured atmospheric density field, the density range of the first-order EOF atmospheric density eigenvector field is smaller than that of the original measured atmospheric density field. After the second-order EOF, the atmospheric density eigenvector field is superimposed. As a result, the first two EOF atmospheric density eigenvector fields' distribution is closer to the original measured atmospheric density field. As a result, the continuous range of orange-yellow high-density areas in the figure is expanded. After superimposing the third-order EOF atmospheric density eigenvector field, the first three EOF atmospheric density eigenvector fields have almost identical characteristics to the original measured atmospheric density field. The first-order thermospheric atmospheric density characteristic vector field represents significant large-scale changes in the measured atmospheric density field, with relatively less detailed information. As higher-order characteristic vector fields are gradually added, the short-term and local features of atmospheric density become apparent. The more orders of characteristic vector fields that are included, the more similar their distribution is to the original measured atmospheric density distribution, and the more comprehensive the description of the measured atmospheric density field becomes. The high-order characteristic vector fields often reveal features with small amplitudes and randomness, while the low-order vector fields typically reveal significant features with large amplitudes and long durations, whose physical meaning is clearer.