**3. Statistical boxplots for TCs rainfall**

Following the procedures mentioned in Section 2, all the historical TCs from 1953 to 2011, which made landfall within the distance of 700 km to SMS, are grouped into 42 categories. Because of the natural selection, it is impossible that each subgroup has approximately equal number of TCs. **Table 2** shows the groupings for TCs landfalling on the west of SMS, for example, "tms" in the table means the times of TCs for each category. For instance, there are 10 TTYs (2 severe typhoons and 8 typhoons) landfalling on the west of Shenzhen within 100 km distance to SMS (A1-TTY). The "tms" for other categories are from 4 to 29. For such small sample sizes, nonparametric statistics is seriously suggested to be suitable to analyze the datasets [25]. For each category of the TCs, the minimum, maximum, 25th percentile (Q1), 50th percentile (Q2), and 75th percentile (Q3) of the observed R24 and R72 are computed (**Table 2**).

whisker (LW), lower quartile (Q1), median (Q2), upper quartile (Q3), and upper whisker (UW). Q1, Q2, and Q3 are the 25th, 50th, and 75th percentile of the population, respectively. Points are drawn as outliers if they are larger than Q3 + 1.5 × (Q3 - Q1) or smaller than Q1 − 1.5 × (Q3 − Q1). In **Figure 3**, two observations are considered as outliers, which are depicted by a red plus sign (+). The plotted whisker, UW (or LW) in the figure, is the maximum observation (or

For practical use to forecast the rainfall due to a landfalling TC, the category of the landfalling TC is first determined based on the information of TC-landfalling distance to SMS from NWP models' forecast and the landfalling intensity from NWP models' forecast, as well as from the empirical experience of the forecasters. Then, referring to the boxplot corresponding to the landfalling TC category, the rainfall of R24 and R72 at the meteorological station can be estimated that the landfalling TC might cause the medium rainfall, 25–75% interquartile

Following the procedures mentioned in Section 2, all the historical TCs from 1953 to 2011, which made landfall within the distance of 700 km to SMS, are grouped into 42 categories. Because of the natural selection, it is impossible that each subgroup has approximately equal number of TCs. **Table 2** shows the groupings for TCs landfalling on the west of SMS, for example, "tms" in the table means the times of TCs for each category. For instance, there are 10 TTYs (2 severe typhoons and 8 typhoons) landfalling on the west of Shenzhen within 100

rainfall range, LW, UW, minimum rainfall, and maximum rainfall.

**3. Statistical boxplots for TCs rainfall**

minimum observation), which is not an outlier.

222 Recent Developments in Tropical Cyclone Dynamics, Prediction, and Detection

**Figure 3.** Boxplot as an example.


**Table 2.** Times of each TC category and the corresponding percentile for R-24 and R-72 for TCs landfalling on the west of SMS.

The boxplots of the historical rainfall records of R24 and R72 at SMS due to all the categories of TCs from 1953 to 2011 are plotted in **Figure 4**. **Figure 4a** and **b** are for the category TTY, (c and d) are for TTS and (e and f) are for TD. The thick vertical line in each of the subplots of **Figure 4** refers to SMS. A7, A6, A5, A4, A3, A2, and A1 of the *x*-axis label refer to the TCs landfalling location, which are 600–700, 500–600, 400–500, 300–400, 200–300, 100–200 km, and within 100 km on the west of SMS. The meanings of B1, B2, …, B7 are similar, but for the TCs landfalling on the east of SMS. Therefore, from **Figure 4**, the rainfall of R24 and R72 at SMS can be determined that each category of the landfalling TC might cause the 25–75% interquartile rainfall range, the lower whisker, upper whisker, minimum rainfall, and maximum rainfall.

**Figure 4.** Boxplots for R24 and R72 rainfall at SMS from 1953 to 2011 due to TTYs (a and b), TTSs (c and d), and TDs (e and f). The vertical black thick line in the middle of each subplot denotes SMS. A on the *x*-label refers to the landfalling area, which is to the west of SMS, and B on the *x*-label refers to the landfalling area, which is to the east of SMS. The numbers after A and B on the *x*-label refer to the distance to SMS.

From **Figure 4**, it can be seen that the shape of the rainfall boxplots is not symmetric compared to the boxplots on the west and on the east of SMS. Generally, the TCs that make landfall on the west of SMS within the distance of 400 km would generally bring more rainfall to SMS than those TCs that make landfall on the east of SMS with similar landfalling intensity and distance. The median (Q2) records of R24 and R72 for TTY and TTS (**Figure 4a**–**d**) generally decrease with the increase of the landfalling distance to SMS, especially for TCs landfalling on the west of SMS. However, when the landfalling distance is outside 400 km, Q2 does not decrease as clearly as its change within 400 km. From **Figure 4a**–**d**, it can be seen that TCs that make landfall at B5 (with the distance of 400–500 km on the east of SMS) and B6 (with the distance of 500– 600 km on the east of SMS) sometimes might cause very heavy rainfall at SMS. The reason might be that after those TCs land at B5-B6, they do not dissipate soon and continue to move west or east. During their continuous movement, they will probably interact with other weather system, such as southwesterly monsoon and mid-latitude trough, and bring plenty of moisture and energy over Southeast China. If SMS is on the passageway or near the passageway to transport such moisture and energy, heavy rainfall would occur in Shenzhen. In addition from **Figure 4**, the variation of rainfall due to TDs does not change with distance as clearly as rainfall due to other categories of TCs. Furthermore, it can be seen from the figure that within the distance of 200 km, the median of the rainfall records (Q2) is generally larger when the strength of the TCs is higher (i.e., Q2TTY>Q2TTS>Q2TD). However, when outside 200 km, this pattern might change. For example, rainfall at SMS due to TTSs and TDs, which make landfall at B3, is even higher than rainfall due to TTYs landfalling at B3. TTSs that make landfall at B5 (more than 400 km away from SMS) might sometimes induce very large rainfall at SMS (**Figure 4c**, **d**), compared to TTYs that make landfall at the B5. This might be due to the influence of other factors, such as TC track, TC-moving velocity after landfalling, and the environmental background.
