## 3 Results  
### Distribution and Coverage Area of U. prolifera  
By synthesizing the observation conditions and taking into account the calculation of the distribution probability of _U. prolifera_ in the later stage, 10 groups of relatively ideal results in 2018 with as equal time intervals as possible were obtained by screening (Figure 4); nine groups of results in 2017 and 2016 were shown in Figures 5 and 6, respectively. In 2018, due to continuous thick cloud cover, the MODIS images of the Yellow Sea region in May were deleted during the screening stage. Therefore, the earliest time and place of _U. prolifera_ could not be accurately determined by interpretation of the MODIS images. The growth of _U. prolifera_ had begun to take shape on June 3, when it was detected for the first time (Figure 4a). The distribution and coverage area were about 17,788 and 365 km\({}^{2}\) respectively. The maximum distribution and coverage area of _U. prolifera_ occurred on June 24, 2018, with a distribution area of 33,502 km\({}^{2}\) and a coverage area of 2301 km\({}^{2}\) (Figure 4d). The growth of _U. prolifera_ began on the coast of Jiangsu Province, gradually drifted northward, and finally disappeared near the coast of Qingdao. The change in the coverage area of _U. prolifera_ was divided into four stages with the passage of time: a slow growth period, an eruption period, a stable period, and a rapid extinction period. From early to mid-June, the growth rate of _U. prolifera_ was slow. The outbreak began in mid- to late June. Compared with the beginning of June, the distribution area was about twice as large, and the coverage area was about seven times as large. From late June to late July, _U. prolifera_ entered a stable state. Its distribution area gradually decreased, but its coverage area stabilized at 800 to 900 km\({}^{2}\). In early August, _U. prolifera_ entered a period of rapid extinction. The distribution and the coverage area decreased rapidly, and the algae disappeared completely from mid- to late August. Compared with 2018, the temporal and spatial characteristics of the _U. prolifera_ distribution in 2017 were quite different. At the end of April 2017, a large area of _U. prolifera_ was found in the southeast corner of the Yellow Sea, with a distribution area of 18,643 km\({}^{2}\) and a coverage area of 841 km\({}^{2}\) (Figure 5a). In May, the _U. prolifera_ gradually drifted northwest, and the distribution reached a maximum of 42261 km\({}^{2}\) on May 18 (Figure 5c). In mid-late May, _U. prolifera_ appeared in the sea water near Jiangsu Province, and its scale expanded gradually. The _U. prolifera_ in the southern part of the Yellow Sea disappeared quickly in June, and the large-scale outbreak of _U. prolifera_ in the sea region near Shandong Province reached a maximum of 1871 km\({}^{2}\) on June 14 (Figure 5f). Since then, _U. prolifera_ has decreased rapidly and died out near Qingdao in mid-July. In 2017, two outbreaks of _U. prolifera_ in different locations were found, with a time-span of about one month. _U. prolifera_ initially appeared in 2016 at around mid-May, located near Jiangsu Province, which was similar to that in 2018. The initial distribution area and the coverage area of _U. prolifera_ were 6952 km\({}^{2}\) and 381 km\({}^{2}\), respectively (Figure 6a). The growth of _U. prolifera_ was slow in late May. From the beginning of June to the end of June, _U. prolifera_ broke out on a large scale, with the maximum distribution area and coverage area reaching 57,384 km\({}^{2}\) and 2906 km\({}^{2}\) on June 25 (Figure 5e). In July, on a decreasing scale, the distribution of _U. prolifera_ was continuously close to the coastline of Shandong Province scale, and died out near Qingdao at the end of July. Figure 4: _Cont._  
Figure 4: Spatial and temporal distribution of _U. prolifera_ in the Yellow Sea, China in 2018. The area within the red line represents the distribution of _U. prolifera_. The blue gradient band represents the coverage area of _U.