## 3 Results
### Morphological Characteristics of U. prolifera Distribution  
#### 3.4.1 Directionality  
The SDE can be used to show the directional characteristics of the distribution of coverage points of _U. prolifera_. Figure 9 shows the SDE corresponding to different dates in 2018. Also, the SDE of _U. prolifera_ in 2017 and 2016 can be seen in Figure 10. Because the direction angle and the oblateness of the ellipse are the two important parameters in this study, Figure 11 shows the variation curve of the standard deviation ellipse oblateness, and Figure 12 displays the directional angle of the ellipse of these three years. The coverage of _U. prolifera_ in different shapes was simplified to the SDE. The parameters of SDE can reflect the morphological characteristics of the coverage of the _U. prolifera_ margin to some extent. Overall, there were large differences in the ellipse shape over different periods, both in direction and in oblateness. The larger the oblateness, the more directional the object distribution, and thus, more attention must be paid to the time node at which the oblateness shows an upward jump. As can be seen from Figure 11a, a sharp increase in oblateness occurred three times during the monitoring period in 2018. The first period was from June 3 to June 12, with an increase from 0.47 to 0.73. In the second period, from July 19 to July 23, the ratio increased from 0.45 to 0.66. The third period was from August 2 (0.65) to August 11 (0.85). Among these periods, the oblateness reached a maximum on August 11, when directionality was significant. Figure 12a also shows that the elliptical direction rotated clockwise with the passage of time, where two large angles of rotation occurred, and the time of these angles coincided with the first two periods, with a sudden increase in oblateness. Two sudden increases in oblateness can be easily founded in 2017 (Figure 11b) during two continuous periods, June 18 (0.47) to 26 (0.67) and June 26 to July 13 (0.88). However, there was no consistent pattern of changes in the SDE direction angle in 2017, and three mutations occurred. The first period was from April 30 to May 7, the second was from June 4 to 14, and the third was from June 14 to 18. Among them, the change in third period was enormous, reaching 115\({}^{\circ}\). In 2016, the flatness of the SDE slightly fluctuated, but it was at a relatively small level most of the time, except for the period from July 24 to 29, the flattening rate increased from 0.23 to 0.82. The direction angle of the ellipse appeared over three periods of significant change. From May 25 to June 17, the direction angle continuously rotated clockwise. The second mutation occurred in July 2 to July 14, and there was a large turn in the direction angle. Thereafter, the angular rotation direction was reversed prodigiously, reaching 132.1\({}^{\circ}\). Figure 9: Standard deviation ellipse of the coverage area of _U. prolifera_ in 2018. The first standard deviation ellipse was used in this paper, containing the data with a ratio of 68% (the proportion of data contained does not affect the values of two key indicators). **(a)** The SDE on June 3. **(b)** The SDE on June 12. **(c)** The SDE on June 21. **(d)** The SDE on June 24. **(e)** The SDE on June 29. **(f)** The SDE on July 15. **(g)** The SDE on July 19. **(h)** The SDE on July 23. **(i)** The SDE on August 2. **(j)** The SDE on August 11. Four parameters of the standard deviation ellipse are marked in **(a)**. The yellow round dot is the elliptical center point, and the two green lines passing through the center point and perpendicular to each other are the X-axis and Y-axis, respectively. The angle between the north direction and the long axis is the directional angle, which is represented by an orange arc in the diagram. The annotation of these parameters is omitted from other subgraphs. The direction and oblateness of the ellipse are indicated at the bottom of each subgraph. \(q\) represents the direction angle, whereas \(e\) is the oblateness.