**2. Data and methodology**

produced copious amounts of rainfall in Taiwan, with a record of 3031.5 mm during August 6–13, 2009 [2]. Hurricane Katrina, one of the deadliest hurricanes in the history of the United States, brought over 15 inches (381 mm) heavy rainfall to Florida at its landfall. The recorded maximum sustained wind speed reached 175 mph (280 km/h) and wind gusts reached 220 mph (350 km/h) at New Orleans, Louisiana [3]. Typhoon Morakot left 619 people dead and the death toll due to hurricane Katrina was over 1100 [3–5]. In order to alleviate enormous loss of lives and properties in the future, it is important to notice the local population and civil authorities to make appropriate preparation for the cyclones, including evacuation of the vulnerable areas where necessary. Accurate and timely (24 and 12 h before landfall) forecasting the TC track and the potential rainfall and wind induced by TC are vital and

Most operational meteorologists rely heavily on numerical weather prediction (NWP) models in forecasting TCs. TC track forecasts have improved significantly over the past several decades [1, 7–9]. By contrast, the improvement in forecasting the TCs intensity has lagged behind the progress of TCs' track forecasting [9–12]. The capability for NWP models to predict short-term rainfall is still very limited [1, 6, 13, 14]. Quantitative forecasting of rainfall remains problematic and lags behind the TC's track forecast, although tropical cyclone forecasting is a successful enterprise with favorable benefit-to-cost returns [1]. Kidder et al. [6] report that because few observations are available while the storm is offshore, initializing numerical weather prediction models with sufficient details of the storm is impossible. Therefore, the rainfall forecasts by NWP models are not so accurate. The research of Xu et al. [15] shows that currently in China, there is no effective operational approach to forecast the heavy rainfall and wind induced by tropical cyclone. The forecast of the rainfall and wind due to TC in China all relies on NWP models and the experience of forecasters. Exploring other ways to predict short-

When TCs approach the land or move across the coast, the TCs structure and intensity change greatly [16]. Landfalling TCs usually bring about heavy rainfall over land. Regarding the forecasting of rainfall due to a TC in a certain region (at a certain rain gauge), it is reported that the rainfall is associated with the distance from the TC center, TC intensity, TC track, TC moving velocity, and TC residing time, as well as the environmental background. Rainfall induced by a TC generally decreases exponentially with distance from the TC center [6, 17, 18]. With the same environmental background, the stronger the TC intensity, the heavier the precipitation will be [18]. The distribution of precipitation due to landfalling TC is asymmetric. In the Northern Hemisphere, the land on the right-hand side of TC would usually receive more intense and spatial rainfall than the land on the left-hand side [19], since the rain bands on the right would carry more moist oceanic air than those on the left. After landfall, the slower the moving speed of the TC or the longer the residence time for the TC in a certain region, the more opportunities and longer time will be for the TC to interact with other weather systems,

The previous studies indicate that rainfall induced by a TC at a certain rain gauge is attributable to a variety of factors. However, most of those studies focused on either case studies or investigating a specific factor, and the conclusion is mostly qualitative. In this study, a statistical

essential [6].

term rainfall is therefore important and necessary.

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

which might lead to extreme rainfall accumulation [2].

This study focuses on Shenzhen to explore the potential rainfall caused by landfalling TCs. Shenzhen is a coastal and urban city in Guangdong Province, China [20–23], with the latitude from 22°27' to 22°52' and longitude from 113°46' to 114°37' (**Figure 1**). In summer and autumn, the city is often influenced by TCs. In this study, a total of 427 TCs, which made landfall along the Southeast China coast from 1953 to 2011 with the landfalling distance within 700 km to Shenzhen meteorological station (SMS), are studied.

**Figure 1.** Location of SMS; circles indicate region with radii of 100, 300, 500, and 700 km to SMS.

The records of daily rainfall from 1953 to 2011 in SMS are obtained from the Shenzhen Meteorological Bureau (SZMB). The maximum daily rainfall (from 20 pm of the previous day to 20 pm of the current day based on China standard time) and the maximum 3-day accumulative rainfall at SMS during the TC-landfalling period (within a couple of days before or after landfall) are computed. For example, if a TC makes landfall on date A, the rainfall at SMS on date A−2, A−1, A, A+1, and A+2 is collected as RA−2, RA−1, RA, RA+1, and RA+2. The maximum daily rainfall (R24) and the maximum 3-day accumulative rainfall (R72) are computed as follows:

$$\text{R.24} = \text{maximum}(R\_{A-2}, R\_{A-1}, R\_A, R\_{A+1}, R\_{A+2}) \tag{1}$$

$$\text{R.72} = \text{maximum}(R\_{A-2}R\_{A-1}R\_A, R\_{A+1}R\_AR\_{A+1}, R\_AR\_{A+1}R\_{A+2})\tag{2}$$

where RA−2RA−1RA refers to the accumulative rainfall on date A−2, A−1, A, etc.

TC characteristics from 1953 to 2011 are collected from China Meteorological Administration (CMA). The TC characteristics include the landfalling track, the distance between the TClandfalling center and SMS, and the intensity (maximum wind speed near the TC center), which are proved to be strongly related to the rainfall caused by TCs in a certain region [6, 17– 19].

As the rainfall distribution and intensity on the right side of TC track is different from those on the left side of TC track [19], all the TCs are first grouped into two categories: A, TCs landfalling to the west of SMS (landfalling longitude <114°E); and B, TCs landfalling to the east of SMS (landfalling longitude >114°E). Next, A and B are further grouped into seven categories according to the landfalling distance to SMS, for example, A1, within 100 km; A2, 100–200 km; A3, 200–300 km; … A7, 600–700 km and B1, within 100 km; … B7, 600–700 km. Finally, A1, A2, …, B7 are grouped according to their landfalling intensity. According to the typhoon categorizing criterion of CMA (**Table 1**), there are six categories of TCs, which are super typhoon, severe typhoon, typhoon, severe tropical storm, tropical storm, and tropical depression. Among the 427 TCs, no landfalling TC was super typhoon. In this study, the TC intensity is stratified into three categories based on their respective TC-landfalling intensity scale (**Table 1**): TTY (total typhoon), which includes SuTY, STY, and TY; TTS (total tropical storm), which includes STS and TS; and TD. A1, A2, …, B7 are therefore grouped into A1-TTY, A1-TTS, A1- TD, A2-TTY, A2-TTS, A2-TD, …, B7-TTY, B7-TTS, and B7-TD. The flowchart of the TCs' categorizing steps is depicted in **Figure 2**.


**Table 1.** Tropical Cyclone Intensity Scale according to CMA.

An Operational Statistical Scheme for Tropical Cyclone-Induced Rainfall Forecast http://dx.doi.org/10.5772/64859 221

R24 maximum( , , , , ) = *R R RR R A A AA A* - - ++ 21 12 (1)

R72 maximum( , , ) = *R R R R RR RR R A A A A AA AA A* - - - + ++ 21 1 1 12 (2)

where RA−2RA−1RA refers to the accumulative rainfall on date A−2, A−1, A, etc.

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

**Category Abbreviation Sustained maximum winds near the center of TCs**

19].

categorizing steps is depicted in **Figure 2**.

Super typhoon SuTY ≥51 m/s

Severe typhoon STY 41.5–50.9 m/s

Typhoon TY 32.7–41.4 m/s

Severe tropical storm STS 24.5–32.6 m/s

Tropical storm TS 17.2–24.4 m/s

Tropical depression TD 10.8–17.1 m/s

**Table 1.** Tropical Cyclone Intensity Scale according to CMA.

TC characteristics from 1953 to 2011 are collected from China Meteorological Administration (CMA). The TC characteristics include the landfalling track, the distance between the TClandfalling center and SMS, and the intensity (maximum wind speed near the TC center), which are proved to be strongly related to the rainfall caused by TCs in a certain region [6, 17–

As the rainfall distribution and intensity on the right side of TC track is different from those on the left side of TC track [19], all the TCs are first grouped into two categories: A, TCs landfalling to the west of SMS (landfalling longitude <114°E); and B, TCs landfalling to the east of SMS (landfalling longitude >114°E). Next, A and B are further grouped into seven categories according to the landfalling distance to SMS, for example, A1, within 100 km; A2, 100–200 km; A3, 200–300 km; … A7, 600–700 km and B1, within 100 km; … B7, 600–700 km. Finally, A1, A2, …, B7 are grouped according to their landfalling intensity. According to the typhoon categorizing criterion of CMA (**Table 1**), there are six categories of TCs, which are super typhoon, severe typhoon, typhoon, severe tropical storm, tropical storm, and tropical depression. Among the 427 TCs, no landfalling TC was super typhoon. In this study, the TC intensity is stratified into three categories based on their respective TC-landfalling intensity scale (**Table 1**): TTY (total typhoon), which includes SuTY, STY, and TY; TTS (total tropical storm), which includes STS and TS; and TD. A1, A2, …, B7 are therefore grouped into A1-TTY, A1-TTS, A1- TD, A2-TTY, A2-TTS, A2-TD, …, B7-TTY, B7-TTS, and B7-TD. The flowchart of the TCs'

**Figure 2.** Flowchart of grouping process for landfalling tropical cyclone along the Southeast China coast.

Due to its nature of nonnormal distribution for precipitation [24], nonparametric method is a preferable approach to analyze typhoon-induced precipitation than parametric method [25]. A nonparametric statistical method, percentile estimation, is used to analyze the rainfall data in this study. Boxplots are applied to illustrate the analysis results. The detailed procedures are as follows:

Given *n* sorted rainfall observation {*ri*}, *i* = 1, …, *n*, for a TC category, 0 < *r*1 < *r*<sup>2</sup> < … < *rn*, the corresponding percentile for a rainfall record, *ri* , is computed to be [26]

$$P\_i = \frac{100}{n} \left( i - \frac{1}{2} \right) \tag{3}$$

When computing the rainfall of any percentile *P*, it needs to find two consecutive *pk* and *pk*+1, where *pk* < *P* < *pk*+1. The rainfall for this *p* percentile is therefore

$$r = r\_k + \frac{p - p\_k}{p\_{k+1} - p\_k} (r\_{k+1} - r\_k) \tag{4}$$

Using this approach, the 25th, 50th, and 75th percentile rainfall for each TC category can be computed. The analysis results are illustrated by a boxplot (**Figure 3**) to display the differences between sample populations [27]. There are five-number summaries for a boxplot: the lower 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 minimum observation), which is not an outlier.

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

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