## 3 Results and Discussion
### Analysis of Rainfall  
Whether it is PWV, atmospheric circulation, temperature, water vapor flux, or water vapor flux divergence, the ultimate focus is on precipitation, so changes in precipitation characteristics are important characterizations in the lower atmosphere. For precipitation characteristics, the two cyclones mentioned above continuously transport water vapor to the surrounding areas of Tonga, and the water vapor delivery may bring rainfall [10; 43]. The eruption of the HTHH volcano may have had an impact on the precipitation around Tonga. In this paper, the precipitation in January and February in Tonga in the recent seven years was analyzed, and the precipitation distribution in the surrounding area of Tonga in January and February was obtained. As shown in Figure 11a-e, the precipitation in the eastern part of Tonga in January was significantly less than in the central part of Tonga. However, in January 2022 (Figure 11f), the precipitation in the Tonga region increased significantly, especially in the eastern part of Tonga, forming a large precipitation region. This area of precipitation was consistent with the location of the low-pressure center in eastern Tonga [52; 53; 54]. As can be seen in Figure 11g-k, there was significant precipitation in the central and eastern parts of Tonga in February. The precipitation area in the east of Tonga was more extensive, but in February 2022 (Figure 11), the precipitation area in the east of Tonga was significantly reduced. Figure 10: The 850 hPa water vapor flux divergence anomaly fields (color shaded areas, unit: g\(\cdot\)cm\({}^{-2}\)\(\cdot\)h\(\cdot\)Pa\({}^{-1}\)\(\cdot\)s\({}^{-1}\)) and 850 hPa water vapor flux (arrows, unit: g\(\cdot\)cm\({}^{-1}\)\(\cdot\)hPa\({}^{-1}\)\(\cdot\)s\({}^{-1}\)) anomaly fields from 14 to 17 January 2022 at 23:00 (UT). Red boxes and green boxes indicate areas of abnormal water vapor flux. All red and green boxes indicate variations in the same water vapor flux concentration area. Taking the average precipitation in January of the past six years as the background value, the precipitation anomaly map for January 2022 (Figure 12a) was obtained, which shows that the precipitation in Tonga and the eastern region has significantly increased. Taking the average precipitation in February in the recent six years as the background value, the precipitation anomaly map for February 2022 was obtained (Figure 12b). It can be seen that only Tonga and a few areas (concentrated around 20\({}^{\circ}\) S) experienced an increase in precipitation, while most of the rest experienced a decrease in precipitation. In February 2022, the surface temperature decreased (Figure 7), PWV values around Tonga generally reduced (Figure 4), and precipitation around Tonga also decreased significantly (Figure 11). It can be concluded that there is a strong correlation between volcanic activity and rainfall characteristics. Figure 11: Precipitation distribution maps for January (**a–f**) and February (**g–l**) for Tonga region from 2017 to 2022 (color shaded areas, unit: mm); red triangles are HTHH volcano locations. Dashed boxes indicate precipitation in January (**a–f**) and February (**g–l**) of previous years, and solid boxes indicate precipitation in January (**a–f**) and February (**g–l**) of 2022. In conclusion, it can be seen that PWV, water vapor flux, temperature, and precipitation are closely related [55; 56]. When the water vapor flux increases abnormally, the PWV value also changes, precipitation increases, and surface temperature increases. When PWV generally decreases, precipitation decreases, and surface temperature decreases. At the time of a volcanic eruption, the temperature of the surrounding sea rises, and the PWV located in the troposphere begins to be anomalous. The water vapor flux at the height of 500 hpa from the surface is transported to the low-pressure center by the circulation.