1. Introduction
Since heavy rainfall from landfalling tropical cyclones (TCs) can cause hazardous impacts in coastal areas, a better understanding of the factors that control the rainfall distribution is very important for real-time operational rainfall forecasts. Marks (1985) analyzed the reflectivity data from airborne radar systems on board three National Oceanic and Atmospheric Administration (NOAA) aircraft during 6 days for Hurricane Allen (1980) and found that changes in both the storm intensity and the eyewall radius had little impact on the total rainfall of the storm. But in recent years, the relationship between TC intensity and rainfall has gradually become a topic of considerable interest. Lonfat et al. (2004) examined the radial distributions of the axisymmetric rainfall component for TCs of different intensity categories (tropical storms, hurricanes with category-1 and category-2 strengths, and hurricanes with strengths in categories 3–5) using TRMM-retrieved rain data during 1998–2000 over global oceans. They showed that the axisymmetric rain rates greater than 5 mm h−1 were located within 50 km of the TC center for all TCs. Axisymmetric rain rates decreased outward to 1 mm h−1 at a radius of around 250 km. The peak mean axisymmetric rain rates increased with increasing TC intensity, namely, 3.0, 7.0, and 12.5 mm h−1 for tropical storms, category-1 and -2 hurricanes, and category-3–5 hurricanes, respectively. The radius where the peak rainfall occurred decreased from 50 km from the TC center for tropical storms to 35 km for TCs in categories 3–5. Harnos and Nesbitt (2011) used microwave remote measurements to find that rapidly intensifying (RI) TCs have different structures from TCs of lesser intensification rates, with 85-GHz signatures showing a convective ring surrounding the TC center. This indicated that the convective axisymmetry prior to RI onset may have potential for RI forecasts. Kieper and Jiang (2012) analyzed the Naval Research Laboratory 37-GHz passive microwave composite color product for 84 TCs in the Atlantic Ocean basin and showed that the RI of TCs is related to a distinctive satellite-derived precipitation ring pattern around the TC centers. They showed that TC intensity change is related to the rainfall patterns. Jiang and Ramirez (2013) showed that in the inner core, the rain area and total volumetric rain were always larger for rapidly, as compared with slowly, intensifying TCs. Based on 209 images from the lower-fuselage 5.6-cm radar, on board the two NOAA WP-3Ds, Barnes and Barnes (2014) analyzed the eye and eyewall traits (including mean rain rate) of 37 TCs in the Atlantic basin during 1991–2012. They concluded that when a TC intensified, the eye area decreased while the eyewall area increased and rain rates were higher for faster-moving TCs. They also ascertained that larger vertical wind shear (VWS) was related to more asymmetric eyewall reflectivity. Alvey et al. (2015) analyzed the relationship between the rainfall properties and TC intensity change and found that the axisymmetric TC rainfall distribution was correlated with TC intensity change. Harnos and Nesbitt (2016) made two 1-km Weather Research and Forecasting Model simulations of the RI periods of Hurricanes Ike (2008) and Earl (2010) and evaluated mechanisms linked to the initiation and maintenance of RI. They found that despite similar simulated intensification time series, the exhibited hydrometeor characteristics differed between the two TCs since Ike possessed less asymmetry and less vigorous convection than Earl. Those findings confirmed that TC intensity and intensity change are closely related with rainfall and rainfall change over the ocean.
In the past decade or so, the relationship between the asymmetric distribution of TC rainfall over the ocean and environmental VWS has been extensively studied using observations of lightning and precipitation (Rogers et al. 2003; Chen et al. 2006; Lonfat et al. 2007; Ueno 2007; Wingo and Cecil 2010; Hence and Houze 2011; Reasor et al. 2013). Lonfat et al. (2004) also investigated the relationship between TC rainfall distribution and TC intensity, geographic location, and motion and found that the maximum rainfall was located in the front quadrant for the global average but changed with TC intensity. Using the same TRMM rain data as was used by Lonfat et al. (2004), Chen et al. (2006) analyzed the TC rainfall asymmetry relative to the environmental VWS and found that the rainfall asymmetry was significantly affected by VWS when VWS was greater than 5 m s−1. Most previous studies have demonstrated that when a TC is embedded within a unidirectional VWS, inflow and convergence would develop at lower levels and outflow and divergence at upper levels on the downshear side of the TC center, suggesting deep convection over the downshear sector [see a review in Wang (2012)]. The VWS may even predominantly affect the asymmetric wind distribution as well (Uhlhorn et al. 2014).
Asymmetric rainfall in a landfalling TC may be influenced by not only VWS, but also TC motion, nonuniform surface characteristics (such as land–sea contrast, coastline, and topography), and mesoscale convective activities (Tuleya and Kurihara 1978; Tuleya et al. 1984; Jones 1987; Wang and Holland 1996; Bender 1997; Kepert and Wang 2001; Chen and Yau 2001; Chan et al. 2004; Rogers et al. 2003; Lonfat et al. 2004; Chen et al. 2006; Lonfat et al. 2007; Ueno 2007; Kimball 2008; Ramsay et al. 2009; Wingo and Cecil 2010; Yu et al. 2010a,b; Yu and Yu 2012; Hence and Houze 2011; Reasor et al. 2013; Li and Duan 2013; Li et al. 2014, 2015; Xu et al. 2014). Some numerical studies (Kepert 2002, 2006a,b; Chan and Liang 2003; Chan et al. 2004; Chen and Yau 2001; Wong and Chan 2006, 2007) have shown that the asymmetric structure, including the asymmetric rainfall distribution in both the eyewall and spiral rainbands, could be forced by land–sea contrasts. Recently, Li et al. (2014) performed idealized simulations for landfalling TCs on an f plane and found that with large VWS, the rainfall asymmetry became larger after landfall. They further found in a later study that the rainfall–VWS relationship (both environmental VWS and shear due to storm-scale dynamics) evolved during landfall (Li et al. 2015). The land surface roughness would first affect the rainfall distribution in the outer region, and then the effect of environmental VWS dominated. Xu et al. (2014) noticed that the rainfall percentage toward the right quadrant relative to the coastline would experience an obvious increase in landfalling TCs, which might be caused by the land–sea roughness gradient.
Some earlier observational studies of landfalling TC rainfall showed that rainfall was often large to the right of the TC track when the TC was near the coast (Koteswaram and Gaspar 1956; Miller 1964; Powell 1982, 1987). Dunn and Miller (1960) speculated that this kind of rainfall asymmetry was mainly due to low-level convergence associated with the land–sea surface frictional contrast to the right of the TC track. However, some other observational studies documented rainfall maxima to the left of the track in some landfalling TCs (Parrish et al. 1982; Blackwell 2000), suggesting that land–sea surface frictional contrast may not always dominate the TC rainfall asymmetry during landfall.
Recently, Uhlhorn et al. (2014) analyzed the relationships of TC motion and VWS with the wind asymmetries based on aircraft observations and showed that TC translational speed could contribute to the wind asymmetry at the flight level about 700 hPa. Yu et al. (2015) studied the rainfall asymmetries in TCs making landfall in China using the TRMM satellite 3B42 rainfall data. They showed that the TC motion direction generally could not explain the rainfall asymmetries, and landfalling TCs regularly had the maximum rainfall downshear to downshear left when in environmental VWS. In addition, Meng and Wang (2016) found that the precipitation-induced surface cold pool triggered by cold-air intrusion was also important to the rainfall asymmetry in landfalling TC Utor (2013).
The current study aims to document the evolution of the rainfall distribution in landfalling TCs over China and to analyze the relationship between TC intensity and both the axisymmetric and asymmetric rainfall distributions from 24 h prior to landfall to 24 h after landfall. The study will also systematically examine the effects of TC intensity, land–sea contrast, and TC translational speed on the asymmetric rainfall distribution. Section 2 introduces the data used along with the analysis methods. Sections 3 and 4 present, respectively, the axisymmetric and asymmetric rainfall distributions in landfalling TCs in relation to TC intensity and intensity change. Section 5 summarizes the major results.
2. Data and analysis methods
a. Data
The TRMM 3B42 [version 6 (V6) during 2001–10 and V7 during 2011–151] rainfall estimates (3 hourly, 0.25° × 0.25°) as described by Yu et al. (2009, 2015) are used to analyze the axisymmetric and asymmetric rainfall distributions in TCs from 24 h prior to landfall to 24 h after landfall. As indicated by Yu et al. (2015), since rain gauge data are rare over the ocean (only over some small islands) and are sometimes sparse even over land, and the weather radar spatial coverage is very limited, the satellite rainfall estimates are the most suitable data for the analysis of rainfall characteristics, in particular for TCs in coastal regions.
Although the TRMM 3B42 rainfall estimates are more accurate over the ocean than over land for heavy rain in TCs as evaluated by Chen et al. (2013b), they still provide quite reasonable rain estimates for landfalling TCs when compared with radar estimates or gauge data (Jiang et al. 2008a,b; Yu et al. 2009; Chen et al. 2013a). Therefore, the TRMM 3B42 rainfall data are utilized in this study, although we note that the data tend to underestimate heavy rainfall amounts for landfalling TCs (Yu et al. 2009; Chen et al. 2013a). To indicate the spread in observations, we have used box-and-whisker plots (showing medians and outliers) to illustrate the rainfall characteristics (such as maximum rain rates) related with TC intensity. The box-and-whisker plots are a quantitative way of illustrating the random errors in the data. Also, 90% and 10% percentiles are used to denote the extremely high and extremely low values in the box-and-whisker plots.
For the maximum rain rate, we have chosen the maximum rain value within a 500-km radius (with 0.25° data resolution) for every TC sample. The maximum rain rate might be underestimated by the TRMM 3B42 dataset to some extent, but this study has avoided examining the absolute values of the maximum rain rate. We only compare the relative amplitudes of the TC samples of different intensity categories. Since the 3B42 product relies on passive microwave estimates, which have higher signal to noise over water than land as a result of the radiometrically cold ocean background, it is likely that part of the land–ocean differences are actually due to algorithm differences. As a result, the rainfall over land, and the rainfall change between land and ocean, would be affected by the 3B42 data limits. Since our study is mainly focused on the relationship between landfalling TC intensity and rainfall, this would not significantly affect the major conclusions in this study.
To analyze the relationship between asymmetric rainfall evolution and environmental VWS, the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) global reanalysis dataset (Kalnay et al. 1996) as used in Yu et al. (2015) is utilized to obtain the wind fields. The environmental VWS is defined as the difference between the 200- and 850-hPa winds averaged within 500-km radius from the TC center at 6-h intervals, as in Yu et al. (2015).
Intensities and positions of TCs during 2001–15 are extracted from the best-track data of the China Meteorological Administration, which are available from the Shanghai Typhoon Institute. The intensity is defined as the maximum wind speed of TCs in this study, and the related intensity categories, samples, and frequencies in landfalling TCs over China from 24 h prior to landfall (t = −24 h) to 24 h after landfall (t = 24 h) every 6 h are shown in Table 1. Since the landfall time (t = 0) is not always the exact synoptic time (0000, 0600, 1200, and 1800 UTC), the nearest synoptic time is linearly interpolated and then treated as the landfall time. The TC translational speed and direction at each TRMM observation time are calculated using the two closest best-track records at 6-h intervals. TC intensity and intensity change are deduced from the maximum near-surface wind speeds in the best-track data at 6-h intervals.
Samples and frequencies (%) of TC intensity of the five categories (CAT) 2–6 from 24 h prior to landfall (t = −24 h), to landfall (t = 0 h), to 24 h after landfall (t = 24 h) every 6 h. The intensity is defined by the maximum sustained 10-m wind speed.
There are in total 133 TCs that were of at least tropical-storm intensity (category 2) during the 24 h prior to landfall (t = −24 h) to landfall time (t = 0 h), among which there are 24, 39, 32, 29, and 9 TCs making landfall along the coasts of Hainan (HN), Guangdong (GD), Taiwan (TW), Fujian (FJ), and Zhejiang (ZJ) Provinces, respectively, as shown in Figs. 1a–e. Note that among the 29 landfalling TCs of FJ, 19 TCs first made landfall over TW and arrived at FJ for their second landfall, while 10 TCs directly made landfall at FJ without landfall at TW.
Tracks of TCs that made landfall in different regions over China during 2001–15: (a) Hainan (HN), (b) Guangdong (GD), (c) Taiwan (TW), (d) Fujian (FJ), and (e) Zhejiang (ZJ). Numbers of TCs making landfall in individual regions are indicated in each panel. (f) The names and locations of the five regions, and their coastlines.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-16-0334.1
Finally, to analyze the land–sea contrast effects on the rainfall asymmetry, the coastline directions of the previously defined five regions of China are obtained from the most northern point to the most southern point of the coastlines as shown in Fig. 1f. The orientations of the coastlines of HN, GD, TW, FJ, and ZJ are 45°, 16°, 76°, 53°, and 45° from the east, respectively.
One point that should be mentioned is that this study does not consider the effect of TC size on the rainfall. This is mainly because reliable estimates of TC size are not available. Therefore, the TC size impacts on landfalling TC rainfall need to be considered in a future study with methods that can estimate the TC size and size changes.
b. Analysis method
3. Axisymmetric rainfall distribution in landfalling TCs
Figure 2 compares the axisymmetric rainfall distributions in TCs 24 h prior to and 24 h after landfall in five regions across China (see Fig. 1). In general, the peak rainfall is located about 60 km from the TC center and is about 5.5 mm h−1 at 24 h prior to landfall (Fig. 2a), which is close to the peak mean rain rate in TCs over the northwestern Pacific Ocean, as shown in Fig. 13 in Lonfat et al. (2004). By 24 h after landfall, however, the maximum mean rain rate is only about 3 mm h−1 and is located near the TC center (Fig. 2b). Therefore, the peak axisymmetric rain rate mostly decreases during landfall but shifts inward after landfall perhaps due to the enhanced surface frictional convergence and the eyewall contraction and collapse (Chen and Yau 2003). In addition, the radial profiles of the azimuthally averaged rain rate are different for TCs making landfall in different regions over China, similar to those different profiles among five oceanic basins shown in Lonfat et al. (2004). This may be related to the different averaged angles (107.5°, 126.6°, 89.3,° 85.7°, and 63.7°) between the storm motions and the coastlines at landfall time in the different regions (HN, GD, TW, FJ, and ZJ, respectively).
Radial profiles of the azimuthally averaged rain rates in TCs making landfall in different regions (a) 24 h prior to and (b) 24 h after landfall.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-16-0334.1
a. TC intensity and averaged axisymmetric rainfall
Figure 3 illustrates the relationship between TC intensity and the axisymmetric rainfall for landfalling TCs as a whole as well as in five regions over China. Figure 3a shows the averaged TC intensity in terms of maximum wind speed from 24 h prior to landfall to 24 h after landfall. It is interesting to note that during 24–12 h (from t =−24 h to t =−12 h) prior to landfall, the averaged maximum wind speeds of TCs making landfall in HN, GD, TW, and ZJ are increasing while that in FJ is decreasing, which is likely related to the effect of Taiwan on TC intensity. Note that among all the 29 landfalling TCs at FJ, 19 TCs had their first landfall at Taiwan, and then made a second landfall over mainland China. We did not separately analyze the rainfall differences between the 10 and 19 TCs, because we did not think the sample size was large enough to extract the systematic differences associated with the interaction with Taiwan or not.
Evolution at 6-hourly intervals of rainfall from 24 h prior to 24 h after landfall for (a) the averaged intensity indicated by the maximum sustained 10-m wind speed, (b) the averaged minimum sea level pressure, and (c) the area averaged rain rate within 500-km radius of the storm center for all TCs. (d) Radial profiles of the azimuthally averaged rain rates for different TC intensity groups.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-16-0334.1
At landfall time (t = 0 h), the maximum wind speed of all TCs decreased. Although the interpolation of the landfall times to the nearest 6-h synoptic time would cause time errors of about 0–3 h, the actual distance errors between the TC centers and landfall locations are about 0–54 km (considering the averaged TC motion speed of 18 km h−1 in this study). Assuming the inner-core diameters to be about 100 km, the TC structures would have already been affected by land at the analyzed landfall time (t = 0 h). Therefore, although the landfall time errors exist, we would expect that the intensity decrease at landfall time (t = 0 h) was mainly caused by the land effect.
As seen from Fig. 3a, in general, the averaged TC maximum wind speed for all landfalling TCs is about 34 m s−1 prior to landfall, and begins to decrease at the time of landfall and continues weakening to about 20 m s−1 at 24 h after landfall. Figure 3b shows the averaged minimum sea level pressure change from 24 h prior to landfall to 24 h after landfall, which is generally similar to the variations in TC intensity in terms of maximum sustained near-surface wind speed (Fig. 3a). But note that for ZJ the maximum wind speed is the same (dV/dt = 0) from −12 to −6 h, but the minimum sea level pressure is slightly increasing (dP/dt > 0). This suggests that the pressure–wind relationship may change near landfall from −12 to −6 h in some cases. Figure 3c shows the areal averaged rain rate within 500-km radius from the TC center. It is about 1.6 mm h−1 at 24 h prior to landfall, starts to decrease 18 h before landfall, and decreases to about 1.0 mm h−1 at 24 h after landfall. The averaged TC maximum wind speed decreased by 41% (in 48 h) from t = −24 to 24 h, which is close to the decreasing rate of the areal averaged rain rate [38% (48 h)−1]. This indicates that the areal-averaged total rain rate is positively correlated with TC intensity. This is perhaps not too surprising, since TC intensity is likely linked to the mean rain rate and the associated diabatic heating, which drives the secondary circulation and the maintenance of a TC system.
To see more clearly the relationship between TC intensity and the axisymmetric rain rate at landfall, we first categorize the landfalling TCs based on their landfall status. Two groups of ALL/−24h and ALL/0h (shown in Fig. 3d) represent the averaged rain rates of TCs within two integrated periods—prior to landfall (from t = −24 h to t = −6 h) and after landfall (t = +6–24 h), respectively. This comparison can obviously reflect the impacts of landfall on TC rainfall. Second, we group the TCs on the basis of their intensities (categories 2–6). At 24 h prior to landfall (t = −24 h), TCs are grouped into CAT23 and CAT456 TCs. The averaged rain rates of the CAT23 and CAT456 TCs before landfall within the t range from −24 to −6 h are shown as CAT23/−24h and CAT456/−24h, respectively, in Fig. 3d. Similarly, TCs at the time of landfall (t = 0) are also grouped into CAT456 and CAT23. The averaged rain rates of the CAT23 and CAT456 TCs after landfall within t=+6–24 h are shown as CAT23/0h and CAT456/0h, respectively, in Fig. 3d. The results show that the mean rain rate of TCs prior to landfall (ALL/−24h in Fig. 3d) is much higher than that after landfall (ALL/0h in Fig. 3d), which is consistent with the results shown in Figs. 2 and 3c. The averaged rain rates of both the CAT456/−24h and CAT456/0h groups are, respectively, higher than those of CAT23/−24h and CAT23/0h. This also indicates that the axisymmetric rain rate decreases with TC intensity from 24 h prior to landfall to 24 h after landfall, especially within a radius of 150 km from the TC center.
Note that in our later discussion (see Figs. 4–8 and Fig. 12) we have treated all TC cases in categories 2–6 (not including tropical depressions; i.e., category 1) at all times (t = −24, −18, −12, −6, 0, 6, 12, 18, and 24 h) as samples. We have focused on the rain traits of the samples of different intensity categories (categories 2–6). For example, for category 6, first, we chose all cases that are category 6 during the time period from t = −24 to 24 h. Second, we did an analysis of the rain traits for the category-6 TC samples. Last, we obtained the results for category-6 TCs shown in Figs. 4–8 (and later in Fig. 12). In the same way, we obtained results for TCs in categories 2–6.
(a) Frequencies of the total rain (the area-averaged rain rate within 500 km of the storm center) for CAT23 and CAT456 TCs. (b) The total rain distributions for TC categories 2–6 during landfall from 24 h prior to 24 h after landfall (medians and outliers in the box plots in subsequent figures are defined the same as here).
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-16-0334.1
Fractional rain area (× 100%) relative to the total area within a 500-km radius of the storm center with different rain rates [R > (a) 0, (b) 2, and (c) 5 mm h−1] for TC categories 2–6 during landfall from 24 h prior to 24 h after landfall.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-16-0334.1
The fractional rain area of the total area within a 500-km radius of the storm center with rain rates greater than 0, 2 and 5 mm h−1 for CAT456 (red lines with open circles) and CAT23 (black lines) TCs during landfall from 24 h prior to 24 h after landfall.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-16-0334.1
The maximum rain rate (mm h−1) within a 500-km radius of each TC center for TC categories 2–6 during landfall from 24 h prior to 24 h after landfall.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-16-0334.1
Time evolution of the 6-hourly wavenumber-0–4 rainfall components and the total rainfall (mm) during the period from 24 h prior to 24 h after landfall for (a) CAT23 and (b) CAT456 TCs. The time-integrated mean values of total rainfall, wavenumber-0, and asymmetric rainfall (wavenumbers 1–4) are marked above the lines in (a) and (b). (c),(d) As in (a) and (b), but for the 6-hourly amplitudes (%/100) of the wavenumber-0–4 rainfall components relative to the total rainfall. The time-integrated mean values of amplitudes of wavenumber 0 and asymmetric parts (wavenumbers 1–4, respectively) are marked above the lines in (c) and (d).
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-16-0334.1
Figure 4a shows the probability distribution of total rain (the areal-averaged rain rate within 500 km of the storm center) for TCs of CAT23 and CAT456 from 24 h prior to landfall to 24 h after landfall, respectively. For CAT23 TCs, the highest probability is about 28% for a rain rate of 0.5–1 mm h−1, while for CAT456 TCs, the highest probability is about 23% for a rain rate of 1.5–2.0 mm h−1. The rainfall distribution of CAT456 is clearly shifted to the right. Note that higher rain rates are more widespread in more intense TCs while weaker TCs generally have lower rain rates. Therefore, stronger TCs would generally have higher probabilities of higher total rain. This is expected since the stronger TCs are often accompanied by larger diabatic heating and thus rain rate.
b. TC intensity and maximum total rain, rain area, and rain rate
Though TC intensity is positively correlated with the averaged axisymmetric rainfall in landfalling TCs, it would also be valuable to examine whether and how extreme rainfall events may be related to TC intensity. To do so, we introduce several rainfall parameters below:
maximum rain rate, which is the largest rain rate over all grid points within 500 km of each TC center;
maximum total rain, which is the largest value of accumulated rainfall within 500 km of the TC center among category-2–6 TC samples; and
maximum area of rain, which is the largest value of fractional rain area relative to the TC area within 500-km radius from the TC center among category-2–6 TC samples.
Figure 4b shows the total rain of category‐2–6 TCs from 24 h prior to landfall to 24 h after landfall. The mean total rain increases with increasing TC intensity: highest in category-6 TCs and lowest in category-2 TCs. However, the maximum total rain of category-6 TCs is smaller than that of category-2 TCs. That is, intensity generally correlates with total rain but this relationship is not absolute as evidenced by the peak total rain value being the lowest for category 6 among all intensity classifications. Note that, although here we mainly focus on the relationship between the landfalling TC intensity and the maximum rainfall, because of the rain-rate underestimation of the 3B42 data, the results are preliminary and need to be verified in more case studies and with better rain estimates in the future.
Since the total rain is related to both the rain area and the rain rate, we have further analyzed the relationship between the rain area, the rain rate, and TC intensity. Figure 5 shows the rain area distributions of three different rain rates (>0, 2, and 5 mm h−1, respectively) for TCs in categories 2–6 from 24 h prior to landfall to 24 h after landfall. On average, the rain area increases with increasing TC intensity for all rain rates. In other words, category-6 TCs have the largest rain area and category-2 TCs have the smallest. With increasing rain rates from 0 to 5 mm h−1, the rain areas decrease so that the heavy rain (R > 5 mm h−1) area is the smallest. However, the maximum (minimum) rain area of category-6 TCs is not always larger (smaller) than that of category-2 TCs, indicating that the rain area is related to more than just the TC intensity.
Figure 6 shows the averaged rain area variations of the three different rain rates for TCs of CAT23 and CAT456 from 24 h prior to landfall to 24 h after landfall. On average, the rain area (nonzero rain rate, R > 0 mm h−1) is about 55% of the total area within a 500-km radius from the storm center for CAT456 TCs 24 h before landfall. The rain area decreases to about 41% of the total area 24 h after landfall. For TCs of both CAT23 and CAT456, the rain area shrinks during landfall. In general, the rain area of all three rain rates for CAT456 TCs is larger than that for CAT23 TCs. For rain rates > 5 mm h−1, the rain area decreases to <10% of the total area.
Figure 7 shows the maximum rain rates of TCs in categories 2–6 from 24 h prior to landfall to 24 h after landfall. For large maximum rain rates in these samples, namely the high outliers in the diagram, category-2 TCs have even higher and more frequent maximum rain rates than category-6 TCs. For the mean maximum rain rates of all TCs, category-6 TCs do not show systematically higher rates than category-2–5 TCs. Indeed, very large maximum rain rates (the outliers in the box-and-whisker plots in Fig. 7) seem more likely to occur in weaker storms. This is an interesting feature but needs further investigation in the future.
The above analyses on the total rain, the rain area, and the rain rate suggest that the averaged total rain, rain area, and rain rate are all related to TC intensity, but the maximum total rain, maximum rain area, and maximum rain rate are not necessarily so. Based on samples analyzed here, weak TCs are more likely to produce large values of maximum rain rate than strong TCs. We plan to explore the reasons behind this interesting relationship in a future study since understanding the processes associated with these very large maximum rain rates is critical to disaster prevention for extreme rain events associated with landfalling TCs.
c. TC intensity and axisymmetric contribution to the total rainfall
As discussed above, TC intensity is important for azimuthally averaged rainfall. The axisymmetric rainfall component (wavenumber 0) relative to the total rainfall within a radius of 500 km from the TC center from 24 h prior to landfall to 24 h after landfall is further analyzed by grouping TCs into CAT456 and CAT23 (Fig. 8). Figures 8a and 8b show the total rainfall and the wavenumber-0–4 rainfall components in TCs of CAT23 and CAT456, respectively. We can see that the time-integrated mean values of total rainfall, wavenumber 0, and asymmetric rainfall (wavenumbers 1–4) for CAT456 TCs are 187.1, 92.1, and 95.1, respectively, while they are 157.1, 67.1, and 89.6 for CAT23 TCs. Both the asymmetric rainfall and axisymmetric rainfall of CAT456 TCs are higher than those of CAT23 TCs (Figs. 8a and 8b). Although the absolute values of the asymmetric rainfall components of wavenumbers 1–4 are higher in CAT456 TCs than those in CAT23 TCs, their amplitudes relative to the total rainfall are lower in the former than in the latter (Figs. 8c and 8d). In addition, the axisymmetric rainfall component relative to the total rainfall is much higher in CAT456 TCs (49%) than in CAT23 TCs (42%). This means that the total rainfall in stronger TCs has a larger contribution from the axisymmetric component, while that in weaker TCs has a larger contribution from the asymmetric components. We suggest that the results in section 3b on the relationship between TC intensity and maximum rain rate, total rain, and rain area may be related to this aspect of the behavior of weak TCs. We plan to explore this aspect in more detail in a future study.
d. TC intensity change and the axisymmetric rain change
Table 2 shows the intensity change information (including calculation methods and samples) in the study. According to the rate of TC intensity change, TCs are categorized into five groups: rapidly decaying (RD), slowly decaying (SD), unchanged, slowly intensifying (SI), and rapidly intensifying (RI). We define the RI threshold of 15 m s−1 based on the 95th percentile of 24-h maximum wind speed change of 14.8 m s−1 in the western North Pacific, as shown in Shu et al. (2012). A decreasing threshold of −15 m s−1 in 24-h intensity change is defined as RD. Therefore, the RI, SI, unchanged, SD, and RD TCs have their 24-h intensity changes of ≥ 15, from 0 to 15, 0, from −15 to 0, and ≤ −15 m s−1. Note that the unchanged category is exactly defined as 0 m s−1 here, which occurs quite frequently, especially during the 24 h prior to landfall. Note that the sample of 21 RI TCs is not large; the other kinds of TC sample sizes in this study are much larger. Therefore, the results here still need further verification with more samples in future studies.
Samples of TC intensity changes across the five categories (RI, SI, unchanged, SD, and RD) from 24 h prior to landfall (t = −24 h), to landfall (t = 0 h), to 24 h after landfall (t = 24 h) every 6 h. The V is the maximum sustained 10-m wind speed.
Figure 9a shows the variations of the rate of TC intensity change from 24 h prior to landfall to 24 h after landfall. Generally, the rate of TC intensity change 24 h prior to landfall is nearly zero or positive (0–0.1 m s−1 in 6 h), which implies that the averaged TC intensity is maintained or even increased 24 h prior to landfall. In contrast, at the time of landfall, the rate of intensity change becomes negative (about −0.1 m s−1 in 6 h), indicating that TCs begin to weaken at landfall. At 6 h after landfall, the averaged rate of intensity change reaches the maximum negative value of −0.2 m s−1 in 6 h. During the 24 h after landfall, the intensity change rate varies between −0.1 and −0.2 m s−1 in 6 h. Correspondingly, the areal-averaged rain rate within 500-km radius from the TC center has a similar change from t = −24 to −18 h. But it has started to be negative before landfall at t = −12 and −6 h while the intensity change rates are still positive, which is likely related to the outer-core rainfall between 200- and 500-km radii where rainfall is first affected by land. Interestingly, at landfall (t = 0) the areal-averaged rain rate within 500-km radius from the TC center shows a similar pattern of behavior to the rate of TC intensity change (Fig. 9b). At t = 6 h after landfall, the averaged rate of total rain change reaches its maximum decreasing rate.
The 6-hourly time evolution from 24 h prior to 24 h after landfall for (a) the rate of averaged TC intensity change (meters per second per 6 h), (b) the rate of change of the areal-averaged rain rate (within 500-km radius of the storm center; mm h−1) for all TCs, and (c) the frequency of TCs of RD, SD, unchanged, SI, and RI. (d) Radial profiles of the azimuthally averaged rain rates for different intensity change groups, based on the integration across all analysis times (from t = −24 h to t = +24 h).
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-16-0334.1
To see more clearly the relationship between the intensity change and rain change, we calculated the correlation coefficients between the intensity change rates and the rain change rates for individual regions. They are 0.47, 0.67, 0.57, 0.86, and 0.75, respectively, for HN, GD, TW, FJ, and ZJ. The correlation coefficient for the whole sample is 0.77. Therefore, the rate of TC intensity change is well correlated with the rate of TC rain-rate change during landfall.
Figures 9c and 9d show the frequencies of TC intensity change and their corresponding radial rainfall distributions. From Fig. 9c, we can see that during the 24 h prior to landfall, 70%–90% of TCs maintain or increase their intensities, but during the 24 h after landfall, more than 60% of TCs decay slowly, while about 20%–30% of TCs decay rapidly. During the whole 48-h period, RI rarely occurs and less than 10% of TCs are SI after landfall. The five TC groups show quite different radial rain rate distributions based on the integration across all analysis times (from t = −24 h to t = +24 h) (Fig. 9d). The RD TCs have the lowest peak averaged rain rate of 3 mm h−1 and the largest radius of maximum rain rate at about 160 km. For the SD TCs, the maximum averaged rain rate increases to 4 mm h−1 with a smaller radius of maximum rain rate at about 80 km. The SI TCs have a rain rate of 5 mm h−1 with the radius of maximum rain rate at about 50 km. Finally, the RI TCs have the highest peak azimuthal-mean rain rate of >13 mm h−1 with the smallest radius of maximum rain rate at about 40 km.
Figure 10 shows the relationship between different rates of TC intensity change (SI, RI, unchanged, SD, and RD) and total rain-rate change from 24 h prior to landfall to 24 h after landfall. For the TC intensity varying from RI to RD, the total rain rate changes mostly from increasing to decreasing. In addition to decaying TCs, the axisymmetric (wavenumber 0) rainfall contribution relative to the total rainfall decreases steadily with decreasing TC intensity, while the asymmetric (wavenumbers 1–4) rainfall increases (Fig. 11).
The relationship between different TC intensity changes (RI, SI, unchanged, SD, and RD) and the total rainfall change during the time period from 24 h prior to 24 h after landfall.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-16-0334.1
The relationship between different TC intensity changes (RI, SI, unchanged, SD, and RD) and (a) axisymmetric rainfall contribution (relative to the total rain) change and (b) asymmetric rainfall contribution change, during the time period from 24 h prior to 24 h after landfall.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-16-0334.1
The above results suggest that the axisymmetric rain rate in landfalling TCs is related to both TC intensity and intensity change. TCs of higher intensity have higher peak azimuthal-mean rain rates. TCs with a larger rate of intensity change have a larger rate of mean rain-rate change. That is, the more rapidly a TC decays during landfall, the more the rain rate decreases. The lower the peak rain rate is, the larger the radius is at which the peak rain rate occurs. Further study into understanding these characteristics is needed, which will be important for improving rainfall forecasts for TCs during landfall.
4. Asymmetric rainfall distribution in landfalling TCs
The relationship between the asymmetric rainfall distribution and TC intensity from 24 h prior to landfall to 24 h after landfall is analyzed in this section. Because the wavenumber-1 asymmetry of rainfall is in general much larger than the higher wavenumber rainfall asymmetries (wavenumbers 2–4) (Yu et al. 2015), we have mainly analyzed the wavenumber-1 asymmetry with the results shown in Fig. 12. Overall, the maximum rainfall in both CAT23 and CAT456 TCs is often located downshear and downshear left from 24 h prior to landfall (I), to the time of landfall (II), and to 24 h after landfall (III). But CAT456 TCs appear to have much weaker averaged shear magnitudes. The averaged shear for CAT23 TCs is 8.6 m s−1, much higher than that for CAT456 (6 m s−1). The maximum wavenumber-1 rain rate is larger in CAT23 TCs than in CAT456 TCs prior to landfall. The rainfall asymmetries of CAT456 TCs are rotated cyclonically from the shear vector relative to CAT23 cases. This might be related to the different VWS magnitudes. When the shear is strong, the maximum rainfall is located downshear and downshear left. When the shear is weak, the maximum rainfall may turn cyclonically away. This means that there are some subtle differences in the asymmetric rainfall distributions between strong and weak TCs. Together with the results from section 3b, the implication is that the relationship between TC intensity and maximum rainfall is not absolute. Further work is needed to understand this relationship.
The wavenumber-1 rainfall asymmetry (color shaded; mm) for (a) CAT23 and (b) CAT456 TCs. The solid arrows denote the averaged VWS vector. The X and Y axes are distances in longitude and latitude (°) from the TC center (origin). Stage I is 24 h prior to landfall, stage II is at the time of landfall, and stage III is 24 h after landfall.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-16-0334.1
Hsu and Kuo (2013) examined the effect of Taiwan’s topography on TC motion. They found that for slow-moving TCs, the convective heating pattern acted to reduce the TC motion and thus led to more prolonged rainfall. Recently, however, Yu et al. (2015) found that the rainfall asymmetries in landfalling TCs over mainland China were not significantly related to TC motion. Instead, they showed that the location of the maximum asymmetric rainfall in landfalling TCs was generally dominated by the effect of environmental VWS. Nevertheless, except for VWS, the effects of translational speed and land–sea contrasts on rainfall asymmetries in landfalling TCs have not been systematically analyzed based on observations. Further analysis of these effects would help identify factors influencing rainfall distributions in landfalling TCs. Figure 13 shows the wavenumber-1 rainfall asymmetries in TCs with translational speeds of <12, 12–20, and >20 km h−1. The illustrated coastlines in Fig. 13 considered the displacement of 8 km h−1 × 24 h = ~200 km (~1.8° latitude), 16 km h−1 × 24 h = ~400 km (~3.6° latitude), and 21 km h−1× 24 h = ~500 km (~4.5° latitude) under low, modest, and high TC translational speeds. We can see that whatever the translational speed is, the maximum rainfall is mostly located in the left and even rear-right quadrants facing down toward the direction of TC motion. This indicates that TC translation has little effect on the asymmetric rainfall distribution in landfalling TCs over China analyzed in this study. Since TC translation is mainly controlled by the large-scale environmental flow, but not directly related to the environmental VWS, which often largely controls the rainfall asymmetry, it is not surprising that the rainfall asymmetry is not well correlated with TC motion.
The wavenumber-1 rainfall asymmetry (color shaded; mm) relative to the coastlines for TCs with different translational speeds: (a) <12, (b) 12–20, and (c) >20 km h−1. The coastline is aligned with the positive X axis to the right (shown by the black solid lines). The arrows denote the mean motion direction.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-16-0334.1
In contrast, the maximum wavenumber-1 rainfall asymmetry increases with increasing VWS, as we can see from Figs. 14a–c for TCs under VWSs of <5, 5–7.5, and >7.5 m s−1, respectively. Furthermore, the maximum rainfall asymmetry in the inner core (within a radius of 2° latitude) of landfalling TCs is always located offshore and downshear left under all shear conditions. However, in the outer-core region (2°–5° latitude from the TC center), the maximum rainfall location is cyclonically rotated from offshore gradually to onshore when environmental VWS decreases from >7.5 to <5 m s−1. These results are generally consistent with those of a numerical study by Xu et al. (2014), who suggested that the land–sea surface frictional gradient might cause an increase in the rainfall percentage toward the right quadrant relative to the coastline for landfalling TCs. However, they did not consider the difference in TC rainfall asymmetries in different shear magnitudes. Our observational study clearly shows different rainfall asymmetries in landfalling TCs embedded in different environmental VWSs. Especially at the time of landfall, the maximum rainfall amounts in both the inner core and outer core appear onshore and upshear when the VWS is <5 m s−1 (Fig. 14a). This indicates that under weak VWS conditions, the combined effects of VWS and the coastline (land–sea contrast) might influence the distribution of the rainfall asymmetry in landfalling TCs, especially in the outer-core region and at the time of landfall.
As in Fig. 13, but for TCs with different VWS magnitudes: (a) <5, (b) 5–7.5, and (c) >7.5 m s−1. The solid arrows denote the averaged VWS vectors.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-16-0334.1
5. Conclusions
In this study, we have analyzed the relationship between TC intensity and rainfall distribution (both axisymmetric and asymmetric components) in landfalling TCs over China from 2001 to 2015, based on TRMM rainfall estimates. The main purpose has been to document how the patterns of evolution of axisymmetric and asymmetric rainfall distributions in landfalling TCs are related to TC intensity and intensity change. It is found that, on average, the axisymmetric rainfall amount is closely related to TC intensity. TCs with higher intensity have higher averaged rain rates, higher averaged peak axisymmetric rain rates, more average total rain, larger averaged rain areas, higher averaged amplitudes of their axisymmetric rainfall components relative to the total rainfall, and lower amplitudes of wavenumber-1–4 rainfall components relative to the total rainfall. It is also shown that the evolution of rainfall is related to TC intensity change from 24 h prior to landfall to 24 h after landfall. Among different intensity change categories, rapidly decaying TCs show the most rapid decrease in both the total rainfall and the axisymmetric rainfall relative to the total rain.
In contrast, the maximum total rain, maximum area of rain, and maximum rain rate are not absolutely correlated with TC intensity. Indeed results show evidence that weak storms are likely to produce even larger maximum rain rates than strong storms. One such recently documented case is TC Bilis (Deng et al. 2017). The asymmetric rainfall distribution is not significantly correlated with TC intensity either, but is likely controlled by other factors, such as environmental VWS. Maximum rainfall asymmetries in both CAT23 and CAT456 TCs are generally located downshear to downshear left, while they are cyclonically rotated relative to the VWS vectors for the CAT456 TCs with a weaker averaged VWS. This suggests that there are some subtle differences between TCs with different intensities.
Although the averaged rainfall structure (including average axisymmetric rainfall, average rain rate, and average rain area) is closely related to TC intensity, the asymmetric rainfall structure (including maximum rainfall location) is mainly controlled by environmental VWS. Further analysis on the effects of translational speed and land–sea contrast on rainfall asymmetry, following Yu et al. (2015), reveals that TC translational speed does not significantly affect rainfall asymmetries in landfalling TCs studied here, since fast-moving TCs show rainfall asymmetries similar to slow-moving TCs.
The asymmetric rainfall maximum varies with the magnitude of environmental VWS and shows a cyclonic rotation from downshear and offshore to upshear and onshore when environmental VWS decreases from >7.5 to <5 m s−1, especially in the outer-core region and at the time of landfall. Particularly at the time of landfall, the rainfall maxima in both the inner- and outer-core regions are located onshore and upshear under weak VWS conditions. This indicates that when the environmental VWS is weak, the coastline may contribute to the rainfall asymmetry in landfalling TCs, leading to onshore rainfall maxima. Of particular interest are the very large maximum rain rates that occur in weak TCs. We have demonstrated that, even with the limitations of the TRMM rain estimates, strong TCs do not have systematically higher maximum rain rates when compared with weak TCs, while very large maximum rain rates seem most likely to occur in weak TCs.
Consistent with previous studies of TCs over the ocean (Jiang and Ramirez 2013; Alvey et al. 2015; Harnos and Nesbitt 2016), this study has shown that landfalling TC intensity, on average, is closely related to the rain rate, the rain area, and the total rain. This finding could suggest that the averaged rain characteristics (including rain rate, rain area, and total rain) are related to the averaged TC circulation and the horizontal distribution of convection during landfall. In addition, TC intensity does not have a clear relationship with maximum values of rain rate, rain area, and total rain. Category-2 TCs may regularly have maximum rain rates larger than category-6 TCs. However, since 3B42 often underestimates the large rain intensity, the maximum rain rates do have some uncertainties. In this regard, our results need to be evaluated in the future with better rain estimates when available.
Note that since TC best-track data frequently lack information on TC size, particularly for TCs after landfall, this study has not considered the possible effect of TC size on rainfall characteristics. In the future, it may be possible to use geostationary imagery or some other dataset to obtain information on TC size, and then to study this aspect. Furthermore, to analyze the relationship between TC intensity and rainfall, we stratified the TC samples according to intensity and intensity change. Although the total sample size is large, the stratification led to relatively limited numbers in each category. In addition, because of some limitations in the TRMM satellite rain estimates, this study has analyzed composites of rainfall characteristics and tried to reduce the uncertainties by using the box-plot analysis method. The 3B42 data often underestimate the rainfall over land and, therefore, can produce rainfall differences between land and sea. Although this would not significantly affect the major conclusions in this study, we still need to be aware of the limitations in future studies. Also there are still some remaining issues that need further investigation, including the mechanisms responsible for the relationships between the rainfall distribution and TC intensity during landfall and the possible effect of TC size. Nevertheless, results from this study can help further our understanding of the rainfall processes in TCs from 24 h prior to landfall to 24 h after landfall and provide a background for prediction of rainfall in landfalling TCs in other regions as well.
Acknowledgments
We thank Dr. Elizabeth Ebert, Dr. Yinjun Chen, Dr. Zhian Sun, Dr. Hongyan Zhu, and Dr. Yimin Ma of BOM for their very helpful comments. The study also benefitted from very thorough and thoughtful review comments by anonymous reviewers. The work is supported in part by the State 973 programs (2013CB430305) and the Public Welfare Industry (Meteorology) Research Program (GYHY201506007), in part by the National Natural Science Foundation of China (41305049, 41475058, and 41405060), and in part by NSF Grant AGS-1326524 and a JAMSTEC grant to the University of Hawaii at Manoa.
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Note that although the two versions have some differences, our results based on the two versions show only slight variations. This is demonstrated by removing the analysis for the latest 5 yr (not shown).
