
TCP is generally defined as the rainfall within a certain distance to the TC center along with the individual track of TC, yet there is no consensus on this definition and the TCP radii are difficult to define with a range from 250 to 1100 km in previous studies (Chen and Chen, 2011; Ying et al., 2011; Bagtasa, 2017; Chen and Huang, 2019). However, researchers found that precipitation rarely changed when it exceeded the TC center by approximately 800 km (Dare et al., 2012; Wang et al., 2020). Lin et al. (2015) used satellite observed data and noticed a weak relationship between TC radius and intensity. Moreover, in a later section, when the TCP range is defined as 500 km, the precipitations rarely change at most stations, but the correlation between TCP and the SSTA index weakens. Based on the above conclusions, we apply 800 km as the effective TCP radius.
Figure 1a shows the climatology of the TCP distribution at 699 stations across the country in summer during 1980–2019. TCP gradually decreases from the southeast coast to the inland, and mainly occurs in the coastal cities of eastern and southeastern China. In general, the spatial distribution of total precipitation is relatively balanced, and the main precipitation area is still in SEC (Fig. 1b). The TCP contribution even exceeds 40% in some southeast coastal regions, and most areas in SEC reach a ratio of 10%–30% (Fig. 1c), and SEC should therefore be regarded as the main TCP area (18°–35°N, 105°–123°E) in China.

Figure 2 shows the time series of WNP TC numbers and TCP in the main TCP area per year. Butterworth’s filter extracts decadal features of time series and trends show that the number of WNP TC significantly decreased (Fig. 2a) while Fig. 2b shows that TCP in SEC increased significantly during 1980–2019. It is suggested that the TC number on the WNP is not the only critical factor that modulates the SEC TCP in summer. Moreover, due to the remarkable reduction of TC numbers in the late 1990s over the WNP, TCP also encountered an obvious reduction (Fig. 2), which was consistent with previous studies (Tu et al., 2009; He et al., 2015; Zhang et al., 2020). In order to explore the reasons for the differences between trends of time series, the 40yr data can be divided into two periods. As shown in Fig. 2a, we note a great probability of a change point on TC frequency in 1998, and the average WNP TC number in P1 (1980–1997) was about 13 TCs per year, which was larger than 10.6 TCs per year in P2 (1998–2019).
Figure 2. (a) TC number per year on the WNP and (b) TCP (mm yr^{−1}) on SEC in summer during 1980–2019. The solid lines are original time series and the yellow dashed lines are Butterworth’s filter of 10 yr. The black dotted lines are the linear trends significant at the 95% confidence level and the bars in (a) represent the conditional posterior probability mass function (PMF) of change points.
The amount of TCP at a station is determined by the rainfall rate and TC frequency, so we introduce a new empirical statistical method proposed by Li and Zhou (2015), defining the TC rainfall intensity as follows:
$$ I = \frac{P}{F}, $$ (1) where P is the total annual TCP at a station, F is the total TC days that cause rainfall, and I is the calculated TC rainfall intensity. To analyze the effects of changes in TC days on the interannual variations of TCP, the TCP anomaly with respect to its climatology is finally resolved into three main items as follows:
$$ \begin{aligned}[b] {P^\prime }& = P  \bar P = FI  \overline {FI} = (\overline F + {F^\prime })(\overline I + {I^\prime })  \overline {(\overline F + {F^\prime })(\overline I + {I^\prime })} \\ & = (\overline F \overline I + {F^\prime }\bar I + \bar F{I^\prime } + {F^\prime }{I'})  (\overline {FI } + \overline {{F^\prime }{I'}} ) \\ & = {F^\prime }\bar I + \bar F{I^\prime } + ({F^\prime }{I'}  \overline {{F^\prime }{I^\prime }} ), \\[14pt] & {} \end{aligned} $$ (2) where the first item
$ {F^\prime }\bar I $ (rainfall frequency) indicates that when the rainfall intensity is fixed, the changes in TC days contribute to the TCP anomaly; the second item$ \bar F{I^\prime } $ (rainfall intensity) examines the influence of changes in the TC rainfall intensity on the TCP anomaly when TC days are constant; and the third item$ {F^\prime }{I'}  \overline {{F^\prime }{I^\prime }} $ (nonlinear item) comprehensively considers the changes in both the TC days and intensity.Apart from the TC frequency, the TC rainfall rate is also a decisive variable regulating TC rainfall and increases remarkably with TC intensity, particularly toward the TC center (Yu et al., 2017). To verify whether there is a difference between contributions of TC days and intensity to the TCP anomaly, the rainfall frequency is measured by TC days with
$ {F}_{1} $ and by ACE with$ {F}_{2} $ . The results are shown in Table 1. In SEC, the mean contribution rate of$F_1'\overline I $ is 1.21, while that of$F_2'\overline I $ reaches 1.8 when ACE is used during 1980–2019, indicating that ACE is a more effective index reflecting the variations of TCP compared to TC days. In addition, the features of contributions in P1 and P2 are similar because ACE is an integration of TC days and intensity, and there is a distinction of$F_2'\overline I $ between P1 and P2, indicating that the ACE values fluctuate intensively in P1.$F_1'\overline I $ $\overline {{F_1}} {I'}$ $F_1'{I'}  \overline {F_1'{I'}} $ $ F_2'\overline I $ $\overline {{F_2}} {I'}$ $F_2'{I'}  \overline {F_2'{I'}} $ 1980–2019 1.21 0.27 −0.48 1.80 0.06 −0.86 1980–1997 2.46 −0.26 −1.20 3.83 −1.04 −1.79 1998–2019 0.19 0.70 0.11 0.14 0.96 −0.10 Table 1. Contributions of rainfall frequency, intensity, and nonlinear items measured by TC days (
$ {F}_{1}$ ) and ACE ($ {F}_{2}$ ) to TCP anomaly in different periods over SEC
$F_1'\overline I $  $\overline {{F_1}} {I'}$  $F_1'{I'}  \overline {F_1'{I'}} $  $ F_2'\overline I $  $\overline {{F_2}} {I'}$  $F_2'{I'}  \overline {F_2'{I'}} $  
1980–2019  1.21  0.27  −0.48  1.80  0.06  −0.86 
1980–1997  2.46  −0.26  −1.20  3.83  −1.04  −1.79 
1998–2019  0.19  0.70  0.11  0.14  0.96  −0.10 