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Considering that the basic features of BTCs are “mutual counterclockwise spinning and moving closer to each other”, we focus on the behavior of interaction between two coexisting TCs. Figure 2 presents frequency−distance distributions of two-TC coexistence for the CMA and the JTWC TC datasets. It can be seen that the frequencies in the two datasets both show a unimodal distribution with a peak at 2100 km, while the frequency in the JTWC dataset shows a weak secondary peak at 1900 km. In addition, as the CMA dataset contains more independent TCs than the JTWC dataset (Ren et al., 2011), the frequency of two coexisting TCs in the CMA dataset is greater than that in the JTWC dataset.
Figure 2. Frequency−distance distributions of two-TC coexistence for the CMA and the JTWC TC datasets. Here, “distance” is the amount of space between two TC centers, while “frequency” means the number of TC pairs. The distance interval for the statistics is 100 km, with the maximum value representing the interval, e.g., 1500 for (1400, 1500].
Figure 3 shows the ratio−distance distributions of TCs that are moving apart and approaching each other for the two datasets. The CMA dataset (Fig. 3a) shows that the ratio for two TCs approaching each other increases as the distance decreases, with a ratio of 0.387 at 3000 km and 0.701 at 500 km. By contrast, the ratio for two TCs that are moving apart decreases as the distance decreases. The two ratio lines intersect over a range from 1800 to 2300 km, in which the ratios for both TCs approaching each other and TCs that are moving apart oscillate around 0.5, which means that the probabilities of occurrences for approaching and escaping are equivalent. The JTWC dataset (Fig. 3b) shows similar features with the same range of intersection. The range of intersection means that within a separation distance of 1800 km, the ratio for TCs approaching each other is > 0.5, which means that the probability of occurrence for approaching becomes dominant and increases as the distance decreases.
Figure 3. Approaching and escaping ratio−distance distributions of two TCs coexisting in the CMA and the JTWC datasets. Here, “ratio” means the ratio of number of coexisting TC pairs approaching or escaping to the total number of coexisting TC pairs. The distance interval for the statistics is 100 km, with the maximum value representing the interval, e.g., 1500 for (1400, 1500]. (a) CMA dataset. (b) JTWC dataset.
Figure 4 depicts the counterclockwise and clockwise ratio−distance distributions and can be used to examine the mutual angular velocity between two coexisting TCs. The JTWC dataset (Fig. 4b) shows that the counterclockwise ratio increases as the distance decreases, with a ratio of 0.416 at 3000 km and 0.846 at 500 km. By contrast, the clockwise ratio decreases as the distance decreases, with a ratio of 0.558 at 3000 km and 0.154 at 500 km. The counterclockwise and clockwise ratios intersect over a range from 1800 to 2000 km, in which both ratios oscillate around 0.5, which means that the probabilities of occurrences for counterclockwise and clockwise are equivalent. The CMA dataset (Fig. 4a) also displays highly consistent features with the same range of intersection. The intersection range also means that within a separation distance of 1800 km, the counterclockwise ratio is > 0.5, which means that the probability of occurrence for counterclockwise becomes dominant and increases as the distance decreases.
Figure 4. As in Fig. 3 but for counterclockwise and clockwise ratio−distance distributions. Here, “ratio” indicates the ratio of number of coexisting TC pairs with counterclockwise rotation or clockwise rotation to the total number of coexisting TC pairs. (a) CMA dataset. (b) JTWC dataset.
Based on these analyses, the two datasets both show that 1800 km is a key distance in defining BTCs: within a separation distance of 1800 km, the approaching ratio and counterclockwise ratio are both > 0.5 and increase as the distance decreases. As a result, 1800 km was selected as the threshold distance to define a BTC in Eq. (3). Taking into consideration the requirement for the duration T in Eq. (4), an objective standard for a BTC in the WNP can be established. If the distance between the centers of two coexisting TCs is ≤ d0 (1800 km) and the duration is at least 12 h, then they can be defined as a BTC:
where
$ \Delta t $ is the time interval (6 h) between two adjacent observations of a tropical cyclone and$ m $ ($ m\geqslant 2 $ ) is the number of consecutive observations with d ≤ d0.The distance threshold, 1800 km, which is larger than those of the three existing definitions of BTCs, is a key parameter in the objective standard. The distance between the centers of the two TC centers defines 900 km as an important TC size. According to Chavas et al. (2016), the median and mean sizes of the outer radius of a TC in the WNP are 957.6 and 993.5 km, respectively. These three TC sizes are clearly of the same order of magnitude. This suggests that the distance threshold, 1800 km, can be understood to be twice the mean outer radius within which two TCs easily interact with each other and show clear characteristics of BTCs.
Our results are consistent with previous studies (Brand, 1970; Dong, 1980, 1981; Dong and Neumann, 1983; Kuo et al., 2000; Wu et al., 2011) in which the significance of the Fujiwara effect in a pair of TCs is dependent on the distance between the centers of two TCs. Other factors include the size, structure, and the intensity of the two TCs, as well as the environmental steering currents.
However, an approaching ratio and counterclockwise ratio both > 0.5 does not mean that the two TCs will simultaneously perform a mutual counterclockwise spin and approach each other. It is necessary to introduce a secondary standard to distinguish whether a particular example is a typical BTC. For this purpose, we consider two different conditions: (1) there is at least one observation of
$ \Delta d $ < 0 and at least one observation of$ {r}_{t} $ > 0 during the duration of the BTC; and (2) there is at least one simultaneous observation of both$ \Delta d $ < 0 and$ {r}_{t} $ > 0 during the duration of the BTC. Table 1 presents the statistics of typical BTCs with the two different conditions. It is revealed that, though the BTC frequencies are considerably different between the CMA and JTWC datasets, the typical BTC ratios are highly consistent with each other, being 0.680−0.689 under condition 1 and 0.642−0.650 under condition 2. Based on the comparison, condition 2, which means both$ \Delta d $ < 0 and$ {r}_{t} $ > 0 are observed simultaneously, and the ratios under which for the CMA and JTWC datasets are more consistent than those under condition 1, is selected as the standard for defining typical BTCs. Accordingly, a BTC that does not satisfy condition 2 is defined as an atypical BTC.CMA JTWC Frequency Ratio Frequency Ratio Condition 1 481 0.680 348 0.689 Condition 2 454 0.642 328 0.650 BTC 707 − 505 − Table 1. Statistics of typical BTCs with two different phenomena. Condition 1: at least one observation of
$ \Delta d $ < 0 and at least one observation of$ {r}_{t} $ > 0 exists during the BTC’s duration. Condition 2: at least one observation of both$ \Delta d $ < 0 and$ {r}_{t} $ > 0 exists simultaneously during the BTC’s duration.
CMA | JTWC | ||||
Frequency | Ratio | Frequency | Ratio | ||
Condition 1 | 481 | 0.680 | 348 | 0.689 | |
Condition 2 | 454 | 0.642 | 328 | 0.650 | |
BTC | 707 | − | 505 | − |