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This section describes the correlation between the MMVs (both before and after filtering) and the TC intensities (V_{max} and p_{min}). All results were significant at the 99% confidence level (Fig. 5), and strong correlations were observed between the MMVs and the intensity dataset for all samples except Lionrock. In particular, the correlation coefficient between Megi’s MMV sequence before (after) filtering and p_{min} was 0.89 (0.91), and the correlation coefficient with V_{max} was –0.92 (–0.94). Clearly, the correlation coefficient (absolute value) between the filtered MMVs and the TC intensities is much higher than that before filtering; further, the correlation between the MMVs and V_{max} was stronger than that between the MMVs and p_{min}. These results indicated that the MMVs corresponded better to the TC intensities after filtering out the highfrequency fluctuations, and that the MMVs showed more information about the wind field than the pressure field. Therefore, the TC intensity can be indirectly estimated by establishing mathematical models between the filtered MMVs and V_{max}.
Figure 5. Correlation coefficients for MMVs and TC intensities. Orange (yellow) color represents the correlation coefficient between the before (after) filtering MMVs (deg^{2}) and p_{min} (hPa); blue (cyan) color represents the correlation coefficient between the before (after) filtering MMVs (deg^{2}) and V_{max} (m s^{–1}).
All filtered MMVs were classified according to the TC intensity recorded in the CMABestTrack dataset (Fig. 6a). It can be seen from the boxplot that the distribution of the MMVs were scattered when the TC intensity was weak. When the TC intensity became enhanced, the MMVs tended to decrease and become more and more concentrated. The medians of the MMVs were reduced by more than 200 deg^{2} for the processes whereby the TC intensity was transformed from WTD to TD and from TD to TS. The decrease of the medians of the MMVs was also clear given the fact that the TC intensity turned from TS to STS and from SYT to SuperTY. However, there was not much difference in the medians of the MMVs when the TC intensity changed from STS to TY and from TY to STY. Those distribution characteristics of the MMVs and the TC intensities can be fitted by a sigmoid function (Fig. 6b). In addition, the temporal scales of the CMABestTrack dataset and the MMVs were different, because the former contained largerscale information compared to the latter. This complicated the correlation analysis between the two datasets. To overcome this problem, only the medians of all the MMVs associated with a single intensity were chosen as the fitting data for regression analysis (Piñeros et al., 2011). The sigmoid equation is described as follows:
Figure 6. Relationship between the MMVs and the TC intensities. (a) Boxplot of MMVs for different TC intensities. In each box, the central mark indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentile, respectively. The whiskers extend to the most extreme data points excluding outliers, and the outliers are plotted individually using the “o” symbol. (b) The relationship between the MMVs and V_{max}. The black line is the sigmoid curve, the green points are the MMVs at all of the CMABestTrack moments, and the purple points represent the MMV medians for each TC intensity.
$${\overline v_{{\rm max}}} = \frac{{{I_{\rm max}}  {I_{\rm min}}}}{{1 + {\rm exp}[\alpha ({\sigma ^2}  \beta)]}} + {I_{\rm min}}, $$ (1) where
${\overline v_{{\rm max}}} $ is the fitting value for$ v_{{\rm max}}$ ;${\sigma ^2}$ represents the filtered MMV; and${I_{\rm max}}$ and${I_{\rm min}}$ correspond to the maximum and minimum intensity recorded by the CMABestTrack data, respectively. The range of the estimated intensity is between${I_{\rm max}}$ and${I_{\rm min}}$ . Moreover,$\alpha $ and$\beta $ are the equation parameters. In this study,${I_{\rm min}}$ is 10 m s^{–1};${I_{\rm max}}$ is 75 m s^{–1};$\alpha $ is 6.09 × 10^{–3} (ranging from 4.73 to 7.45 × 10^{–3}); and$\beta $ is 1409 (from 1378 to 1440).Based on the regression model, the estimated MMVs and the confidence interval for each intensity bin can be calculated (Table 1). Then, those fitted data can be used as threshold to determine the TC intensity, and thus help improve the ability to predict TC damage. However, it should be noted that the lower the adopted MMV threshold was, the higher the accuracy of the TC identification (true positive rate) and the higher the false negative rate would be. In contrast, when the adopted MMV threshold was high, the false negative rate would be lower, but the false alarm rate (false positive rate) would increase at the same time (Wood et al., 2015). Clearly, this aspect is very important for the monitoring and prediction of TCs.
TC intensity TD TS STS TY STY SuperTY Estimated MMV
95% CI2127 1751 1615 1513 1421 1324 1971–2352 1661–1873 1549–1700 1465–1569 1389–1453 1309–1329 Table 1. Estimated MMVs (deg^{2}) in different TC intensity bins. CI denotes confidence interval

Considering that the water vapor condition is insufficient in the early stages of a TC and the TC would be greatly affected by the topography after landfall, the characteristics of a TC in weakintensity periods would be significantly different from those in the other periods. When samples that below the TD (including TD) intensity were excluded, the RMS error of relative distances dropped dramatically compared to that for the complete lifecycle. In particular, in the cases of Meranti, which was of long duration after landfall, and Sarika, which had multiple landfalls, the RMS errors of relative distances decreased by 115.5 and 69.5 km, respectively (Table 2). Overall, there was a strong consistency between the MMV locations and the CMABestTrack dataset.
Relative distance (km) Nepartak Lionrock Meranti Megi Sarika Haima Nockten All TCs Minimum 16.7 7.5 7.7 17.0 7.7 17.4 17.1 —— Median ≥ TS intensity 73.2 44.5 54.0 52.6 54.3 81.1 44.6 56.5 Lifecycle 97.0 50.0 77.8 62.1 84.9 84.6 55.6 73.8 RMS ≥ TS intensity 126.8 85.7 76.2 74.6 90.1 101.7 97.3 95.0 Lifecycle 127.4 103.8 191.7 133.0 159.6 124.6 145.6 140.3 Table 2. Comparison of relative distances between the MMV locations and the CMABestTrack dataset
It can be seen that the range of relative distance distribution gradually becomes concentrated for an increase in the TC intensity (Fig. 7a). Further, the relative distance distribution in the TC weakintensity periods was very scattered, resulting in the correlation coefficient (–0.48) being not very large. However, when the TC reached the TD intensity, the relative distance dramatically decreased; when the TC reached the TS intensity, the relative distance became very concentrated compared to the previously dispersed distribution. In the meantime, TD is the intensity at which a TC alert needs to be given, and TS is the intensity at which a TC should be graded. These findings show that the relative distance is a good indicator of the TC genesis. Similar to the analysis of the relationship between the MMVs and the TC intensities, only the median of the relative distances corresponding to a single intensity was selected as the fitting data for regression analysis. From the distribution of scatter plots, it was appropriate to use an inverse function as the regression model (Fig. 7b). The inverse function is described as follows:
Figure 7. As in Fig. 6, except for relative distances. The black line in (b) represents an inverse function curve.
$$ \overline v_ {{{\rm max}}} = \frac{a}{{{R_{\rm d}} + b}},$$ (2) where
$\overline v_ {{{\rm max}}} $ is the fitting value for$ v_ {{{\rm max}}} $ ,${ R_{\rm d}}$ represents the relative distance, and$a$ and$b$ are equation parameters. In this study,$a$ is 1942 (from 1489 to 2395) and$b$ is –10.2 (from –27.5 to 7.1).