J. Meteor. Res.  2017, Vol. 31 Issue (4): 747-766   PDF    
http://dx.doi.org/10.1007/s13351-017-6007-8
The Chinese Meteorological Society
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Article Information

Xuwei BAO, Dan WU, Xiaotu LEI, Leiming MA, Dongliang WANG, Kun ZHAO, Ben Jong-Dao JOU . 2017.
Improving the Extreme Rainfall Forecast of Typhoon Morakot (2009) by Assimilating Radar Data from Taiwan Island and Mainland China. 2017.
J. Meteor. Res., 31(4): 747-766
http://dx.doi.org/10.1007/s13351-017-6007-8

Article History

Received November 6, 2016
in final form December 19, 2016
Improving the Extreme Rainfall Forecast of Typhoon Morakot (2009) by Assimilating Radar Data from Taiwan Island and Mainland China
Xuwei BAO1, Dan WU1, Xiaotu LEI1, Leiming MA1, Dongliang WANG1, Kun ZHAO2, Ben Jong-Dao JOU3     
1. Shanghai Typhoon Institute, China Meteorological Administration, Shanghai 200030;
2. Key Laboratory of Mesoscale Severe Weather/Ministry of Education, and School of Atmospheric Sciences, Nanjing University, Nanjing 210023;
3. Department of Atmospheric Sciences, National Taiwan University, Taipei 10617
ABSTRACT: This study examined the impact of an improved initial field through assimilating ground-based radar data from mainland China and Taiwan Island to simulate the long-lasting and extreme rainfall caused by Morakot (2009). The vortex location and the subsequent track analyzed through the radial velocity data assimilation (VDA) are generally consistent with the best track. The initial humidity within the radar detecting region and Morakot's northward translation speed can be significantly improved by the radar reflectivity data assimilation (ZDA). As a result, the heavy rainfall on both sides of Taiwan Strait can be reproduced with the joint application of VDA and ZDA. Based on sensitivity experiments, it was found that, without ZDA, the simulated storm underwent an unrealistic inward contraction after 12-h integration, due to underestimation of humidity in the global reanalysis, leading to underestimation of rainfall amount and coverage. Without the vortex relocation via VDA, the moister (drier) initial field with (without) ZDA will produce a more southward (northward) track, so that the rainfall location on both sides of Taiwan Strait will be affected. It was further found that the improvement in the humidity field of Morakot is mainly due to assimilation of high-value reflectivity (strong convection) observed by the radars in Taiwan Island, especially at Kenting station. By analysis of parcel trajectories and calculation of water vapor flux divergence, it was also found that the improved typhoon circulation through assimilating radar data can draw more water vapor from the environment during the subsequent simulation, eventually contributing to the extreme rainfall on both sides of Taiwan Strait.
Key words: Morakot     radar     assimilation     rainfall     simulation    
1 Introduction

Typhoon Morakot (2009) is known as the most devastating typhoon to have struck Taiwan in the past 50 years, causing the deaths of 673 people and a further 26 to be missing and presumed dead (Wu, 2013). According to the official report of the China Meteorological Administration (CMA), Morakot made landfall in Hualien at around 1500 UTC 7 August, and then took more than 40 h to pass through the Central Mountain Range (CMR) and Taiwan Strait; it subsequently made landfall once again on the east coast of mainland China later on 9 August. Morakot produced a huge accumulated rainfall amount (with a record-breaking peak of 2965 mm) in southern Taiwan during 7–10 August, and resulted in numerous devastating mudslides. A tragic burying incident occurred at Shiao-lin Village (near 23.3°N, 120.6°E) in which approximately 500 people were killed (Lee et al., 2011; Lin et al., 2011; Wu, 2013). The estimated agricultural and industrial losses exceed $3.8 billion (Chanson, 2010). Beyond that, Morakot also produced more than 800 mm of accumulated rainfall in mainland China, which caused 12 deaths and economic damage of about $2 billion, according to the CMA's Yearbook of Tropical Cyclones (TCs) in 2009.

After the severe rainfall event, extensive studies were conducted to explore the underlying mechanisms of this record-breaking rainfall. Ge et al. (2010) and Hong et al. (2010) identified that the interaction of Morakot's circulation, large-scale environmental circulation (e.g., monsoon gyre), and orographic lift by the CMR contributed to the extreme rainfall in southern Taiwan. Within the southern periphery of the monsoon circulation, strong southwesterly flow prevailed during the period from the first landfall in Taiwan Island to the second landfall in mainland China, which provided abundant water vapor toward southern CMR (Lin et al., 2011). Figure 1 shows the evidence for an east–west-oriented convective rainband oscillating between 22.5° and 23.5°N, as a result of the convergence of the northerly wind of Morakot's circulation and the southwesterly flow over southern Taiwan Strait documented by previous studies (Wang et al., 2010; Lee et al., 2011; Jou et al., 2012; Wei et al., 2014).

Figure 1 The observed composite radar reflectivity (dBZ) from Taiwan Island and mainland China every 6 h from 0600 UTC 7 August to 0000 UTC 9 August 2009, except for 1500 UTC 7 August 2009.

Hall et al. (2013) identified that the maintenance and development of the deep rainband in the southwest quadrant of the typhoon circulation were combined with the vortex Rossby waves moving into the downshear side. In addition, Morakot's unique slow movement after its first landfall prolonged the precipitation duration, ultimately leading to the huge amount of accumulated rainfall in southern Taiwan (Chien and Kuo, 2011). In summary, the effect of topographic lift, the slow translation speed of Morakot after its first landfall, and the abundant water vapor transport from the southwesterly flow, are considered as three important factors that led to the production of the unprecedented rainfall in southern Taiwan during 7–10 August (Fang et al., 2011; Xie and Zhang, 2012; Yu and Cheng, 2013; Huang et al., 2014).

In addition to the sophisticated formation mechanism of TC rainfall, quantitative forecasting of TC precipitation also remains a challenge at present, especially for extreme rainfall like that associated with Morakot. In the real-time forecast, numerical models exhibited rather high accuracy in their prediction of Morakot's track and notable asymmetric rainfall, but grossly underestimated its slow moving speed and accumulated rainfall amount in Taiwan (Hendricks et al., 2011; Wu et al., 2011; Huang et al., 2014). A number of previous studies (Zhang et al., 2010; Nguyen and Chen, 2011; Schwartz et al., 2012; Wu, 2013) have suggested that high-resolution mesoscale models with reasonable initial atmospheric and oceanic conditions are required to reproduce and understand such a devastating rainfall event. By assimilating Doppler radar data, Zhao et al. (2012) proved that an improved initial field for Typhoon Meranti (2010) (a typhoon that formed over Taiwan Strait) can improve the subsequent short-term (12-h) forecast of its track, intensity, and rainfall. Because almost half of Morakot's total rainfall amount fell on 8 August [close to 1500 mm within the 24 h from 0000 UTC 8 August to 0000 UTC 9 August; see Fig. 2b in Wang et al. (2012)], in the present study, we examined whether an improved initial field achieved via radar data assimilation (DA) before landfall can successfully reproduce Morakot's slow motion and water vapor condition as well as the extreme rainfall on 8 August (with a forecast time of 24 h or more). In addition, sensitivity experiments were designed to explore where the abundant water vapor came from, and what factors can affect the simulated track as well as the heavy rainfall.

This remainder of this paper is organized as follows. Section 2 describes the data sources and numerical experimental design. The analysis and forecast results based on assimilating the radar data from both sides of Taiwan Strait are described in Section 3. Section 4 discusses the role of radar DA in reproducing the extreme rainfall, based on an analysis of the sensitivity experiments. The study's conclusions are summarized in Section 5.

2 Data and numerical experiment 2.1 Data

In this study, the initial and boundary conditions of the numerical model were provided by the operational analyses of the NCEP/GFS (Global Forecast System) model at a resolution of 0.5° × 0.5°. The radar data assimilated into the numerical model came from the same seven radars located on both sides of Taiwan Strait as used by Zhao et al. (2012) except Longyan station (Fig. 2), because the coverage of Xiamen radar almost overlaps with that of Longyan radar. Figure 1 shows that the three radar stations in Taiwan can cover the core area and the strong convection over southern Taiwan prior to Morakot's landfall in Hualien. All of the radars in mainland China and Taiwan operated with the same volume coverage pattern 21 (VCP21) scanning mode of WSR-88D (Crum et al., 1993). Because of the topographic blocking of the CMR, when the radar wave scanning beam was blocked or interfered with by the mountains, the radar data detected at this scanning beam were not assimilated into the numerical model in this study. The track and intensity data of Typhoon Morakot were obtained from the CMA best-track dataset. The rainfall observational data were from rain gauges in mainland China and Taiwan Island.

Figure 2 The model domain with a resolution of 3 km. The solid circles denote the observed Typhoon Morakot locations every 6 h from 1200 UTC 7 August to 1200 UTC 9 August, based on the best-track data of the China Meteorological Administration. The locations of the radar stations (WZ, Wenzhou station; FZ, Fuzhou station; XM, Xiamen station; HL, Hualien station; ST, Shantou station; CG, Chigu station; KT, Kenting station) are marked by filled triangles, and their maximum ranges of coverage are indicated by the circles.
2.2 Numerical model, radar data processing and assimilation system

The three-dimensional variational (3DVAR) DA system and complex cloud analysis system of ARPS (Advanced Regional Prediction System) were adopted in this study (Xue et al., 2000; Xue et al., 2003; Hu et al., 2006a, b; Zhao and Xue, 2009; Dong and Xue, 2013), because it has been proven by Zhao et al. (2012) to be a simple and effective method to improve the initial field through assimilating radar data for a typhoon over Taiwan Strait. The observation error (standard deviation) for the radial velocity and reflectivity is 1 m s–1 and 2 dBZ, and the quality control of the radar data is designed in the 88d2arps program, which includes ground clutter removal and velocity dealiasing, relying upon the SOLO software (Oye et al., 1995) to further check and manually edit the data. The Advanced Research Weather Research and Forecasting (WRF) model, version 3.3 (Skamarock et al., 2008), was used during the 1-h forecast-analysis cycle to generate the background state and the following 45-h forecast. This combined system based on WRF and radar software has been successfully used in scientific research on TC prediction (Howard et al., 2009; Lamberton et al., 2009). Figure 2 shows the model domain, with 601 × 502 grids at a resolution of 3 km. The domain has 35 eta (η) vertical levels at a finer resolution near the boundary layer and with an upper limit at 50 hPa. The WSM6 (single-moment six-class microphysics) scheme (Hong et al., 2004), RRTM (Rapid Radiative Transfer Model) for longwave radiation (Mlawer and Clough, 1997), and Dudhia shortwave radiation scheme (Dudhia, 1989), were used in this study. The terrain dataset and land-use information were obtained from the U. S. Geological Survey at a resolution of 30 s.

2.3 Experimental design

The same initial and boundary conditions from GFS were used for all the experiments. The control experiment (CTRL) without radar DA were from 1200 UTC 7 August to 1200 UTC 9 August (Fig. 3). For the other DA experiments, four DA cycles [the same as that in Zhao and Jin (2008)] were performed at 1200, 1300, 1400, and 1500 UTC 7 August, respectively. In this study, all of the experiments were divided into two groups. In order to examine the individual impact of assimilating radar reflectivity and radial velocity, in addition to CTRL, the first group included three other experiments: (i) Exp-all, which assimilated both radar reflectivity and radial velocity; (ii) Exp-dbz, which assimilated radar reflectivity only; and (iii) Exp-rv, which assimilated radial velocity only. Moreover, in order to examine the impact of assimilating each set of radar data from Taiwan Island and mainland China, and where the water vapor came from, another set of three experiments was designed: (iv) Exp-ml, which assimilated the radar reflectivity and radial velocity from mainland China only; (v) Exp-tw, which assimilated the radar reflectivity and radial velocity from Taiwan only; and (vi) Exp-kt, which only assimilated the radar reflectivity and radial velocity from Kenting station. All the experiments are listed in Table 1.

Table 1 Description of the experimental design
Experiment Description
CTRL No radar data assimilation
Exp-all Assimilation of radial velocity and reflectivity
Exp-dbz Assimilation of radar reflectivity only
Exp-rv Assimilation of radial velocity only
Exp-ml Assimilation of radar data from mainland China only
Exp-tw Assimilation of radar data from Taiwan only
Exp-kt Assimilation of radar data from Kenting station only
Figure 3 Illustration of the experimental design and data assimilation (DA) scheme. Except for CTRL, with a 48-h forecast starting at 1200 UTC 7 August, the other experiments performed 45-h forecasts after 4-h DA cycles at 1500 UTC 7 August.
Figure 4 Analysis increments of column-integrated water vapor (g kg–1) and horizontal wind (≥ 2.5 m s–1) at z = 3 km for (a–c) the first analysis at 1200 UTC 7 August and (d–f) the second analysis at 1300 UTC 7 August from (a, d) Exp-all, (b, e) Exp-dbz, and (c, f) Exp-rv.
Figure 5 The increments of (a, c) tangential and (b, d) radial wind components at z = 3 km from Exp-all for (a, b) the first analysis at 1200 UTC 7 August and (c, d) the second analysis at 1300 UTC 7 August.
3 Analysis and forecast results 3.1 Effects of radar DA on TC structure 3.1.1 Analysis increment

Figure 4 shows the analysis increments of column-integrated water vapor deviation and horizontal wind at 3-km height from Exp-all, Exp-dbz, and Exp-rv at 1200 and 1300 UTC 7 August. In the first cycle, the column-integrated water vapor in Exp-all generally increases within the composite detecting range of radar, and the high values concentrate in the west and south flanks of the typhoon circulation where the strong convection is located (Fig. 1). For the horizontal wind increment, on first impression, it looks irregular, e.g., the wind analysis increment does not exhibit a well-organized cyclonic structure in the primary circulation. In order to clarify the contribution of velocity DA (VDA) to the typhoon vortex, the wind increment is decomposed into the tangential and radial components (Figs. 5a, b). The tangential wind increment produces a cyclonic structure within approximately 180 km (inner-core area) from the typhoon center, compared with the initial vortex derived from the GFS; while in the rest of the radar coverage, the cyclonic wind component is not as evident (Fig. 5a). Figure 5b shows that the strong radial inflow increment concentrates in the northeast quadrant of the inner-core area. Outside the inner-core area, one radial inflow appears in the northwest quadrant, due to assimilating the radar data from mainland China; and another strong inflow is in the southwest quadrant, which is closely associated with the southwesterly wind. In the second cycle, the humidity improvement still concentrates in the south periphery of the typhoon circulation, and its increasing magnitude is much higher than that in the first cycle. In addition to the inherent model adjustment, this is partly because the convection over the southern CMR enhanced as Morakot moved toward the eastern coast of Taiwan (Fig. 1), but the horizontal wind increment is still less organized in the second cycle. As is further shown in Figs. 5c, d, in the inner-core area the tangential wind increment even results in an anticyclonic structure, and the radial outflow is dominant in the southwest quadrant instead of the inflow in the first cycle, because the 1-h simulated southwesterly wind based on the first analysis is stronger than the radar observation. In general, different to previous studies (Zhao et al., 2012), the wind increments in the first two analysis cycles do not produce a remarkable cyclonic flow against the initial circulation, partly because the initial vortex of Morakot from the GFS is rather strong, such that the primary circulation is not significantly improved by VDA with the ground-based radar. The topographic effect may be another reason, because the detection of radial velocity on the west flank of the central circulation was interfered with by the CMR when Morakot was very close to the east shore of Taiwan at the beginning of the DA period. The characteristics and structures of subsequent analysis increments in the last two cycles (1400 and 1500 UTC 7 August) are very similar to that in the second cycle, and are therefore not presented in this paper.

Figures 6ag show the simulated column-integrated water vapor at the end of the DA cycles (1500 UTC 7 August) against the initial field at 1200 UTC 7 August. If we roughly define the radius of maximum wind (RMW) of Morakot as about 180 km, based on the first group of experiments (Fig. 7), the typhoon circulation discussed in this study is mainly within a radius of 600 km from the TC center [about three times the RMW in Wang (2009)]. Thus, the column-integrated water vapor in the typhoon circulation simulated in Exp-all and Exp-dbz is apparently larger than that in CTRL and Exp-rv (Fig. 6h).

Figure 6 Deviation of column-integrated analyzed water vapor (shading; g kg–1) from (a) CTRL, (b) Exp-all, (c) Exp-dbz, (d) Exp-rv, (e) Exp-ml, (f) Exp-tw, and (g) Exp-kt, at 1500 UTC 7 August, against the initial field at 1200 UTC 7 August (the typhoon symbols denote the locations of the simulated typhoon centers at 1500 UTC 7 August), and (h) the column-integrated water vapor (qv; g kg–1) of each experiment, every 120-km-width annular within 600 km from the CMA best track at 1500 UTC 7 August.
Figure 7 Radius–time cross-sections of the azimuthally averaged (a) observed composite radar reflectivity (shading; dBZ), (b–e) simulated radar reflectivity (shading; dBZ), and (f–i) tangential wind (contour interval: 5 m s–1, with the heavy contour for 30 m s–1) at z = 3 km, and hourly accumulated rainfall (shading; mm) in (b, f) CTRL, (c, g) Exp-all, (d, h) Exp-dbz, and (e, i) Exp-rv from 1800 UTC 7 August to 0000 UTC 9 August (the dashed line denotes the radius of maximum wind).
Figure 8 (a) The central minimum sea level pressure (MSLP; hPa) and (b) best track of Typhoon Morakot (from the China Meteorological Administration; black line with triangles) every 6 h from 1200 UTC 7 August to 1200 UTC 9 August, and the simulated tracks in CTRL (blue line with circles), Exp-all (red line with circles), Exp-dbz (khaki line with circles), and Exp-rv (green line with circles). (c) The forecast mean flow [full (half) barbs are 4 (2) m s–1] within 300–700 hPa and a radius of 600 km from the TC center from 1800 UTC 7 August to 0000 UTC 9 August.
3.1.2 Vortex evolution

Following the final DA cycle at 1500 UTC 7 August (the final hour prior to landfall), a 45-h forecast was subsequently carried out until 1200 UTC 9 August in the first group of DA experiments. As investigated by Hu et al. (2006a, b), the spin-up time for the 3DVAR and cloud analysis scheme should be 2–3 h, so Fig. 7 shows the temporal evolution of several azimuthal mean variables of the simulated Morakot from 1800 UTC 7 August (3-h integration after the final DA cycle) to 0000 UTC 9 August. In comparison with Exp-all and Exp-dbz, CTRL and Exp-rv simulate weaker storms (Fig. 8a), as well as weaker convection (Fig. 7), and even the storm sizes simultaneously become small after 0600 UTC 8 August, accompanied by the rapid inward contraction of the high convection zone ( > 15 dBZ). Until 1800 UTC 8 August, the RMWs of the simulated storms in Exp-rv and CTRL are only half of those in Exp-all and Exp-dbz, as well as the strong convection zone (Fig. 7). This is because CTRL and Exp-rv have drier analyzed fields in the typhoon circulation (Fig. 6). This result is in good agreement with the viewpoint that "a relatively drier initial environment leads to weaker spiral rainbands, limiting the outward expansion of wind fields and thus favoring the small inner-core size of the simulated TC", as proposed by Xu and Wang (2010).

Figure 9 shows the wind from QuikSCAT and the simulated 10-m winds in the first group of experiments at around 1030 UTC 8 August 2009. Consistent with the above discussion, Exp-all and Exp-dbz simulate stronger winds in the inner-core area than CTRL and Exp-rv, as well as stronger southwesterly wind over southern Taiwan. In agreement with the analysis in Fig. 7, the radii of moderate gale wind (13.9–17.1 m s–1) simulated by Exp-all and Exp-dbz are slightly larger than the QuikSCAT observation, while the radii of gale wind in CTRL and Exp-rv are grossly underestimated as compared with the observation. The location of the simulated storm center in Exp-all is most consistent with the QuikSCAT observation, in comparison with the north-biased (south-biased) track simulated in CTRL and Exp-rv (Exp-dbz). The reason will be discussed in the following subsection.

Figure 9 Horizontal distributions of 10-m winds (m s–1) from (a) QuikSCAT observations and the numerical experiments of (b) CTRL, (c) Exp-all, (d) Exp-dbz, and (e) Exp-rv at around 1030 UTC 8 August.
Table 2 Simulated track errors of each numerical experiment against the best track, and the mean ETS (equitable threat score), BS (bias score) and RMSE (root-mean-square error) of composite radar reflectivity from each numerical experiment against the observation every hour from 1800 UTC 7 to 0000 UTC 9 August 2009
Experiment Track error (km) Mean ETS Mean BS Mean RMSE (dBZ)
Max Min Mean
CTRL 133.4 11.3 60.2 0.082 0.81 11.23
Exp-all 77.7 0.0 33.4 0.110 0.92 11.44
Exp-dbz 146.7 16.7 98.5 0.072 0.86 11.82
Exp-rv 77.8 5.8 37.9 0.095 0.78 10.05
Exp-ml 57.0 11.3 34.8 0.097 0.89 11.34
Exp-tw 79.4 11.1 44.8 0.075 0.99 11.62
Exp-kt 116.2 11.1 76.4 0.088 1.02 11.46
3.2 Effects on the TC track and intensity forecast

As shown by Fig. 8, CTRL simulates the most northward track, while Exp-dbz has the most westward track. The track error of each numerical experiment against the best track demonstrates that the simulated tracks in Exp-all and Exp-rv are more consistent with the best track (Table 2). It is well-known that the interaction of typhoon circulation and the ambient environment field is the main factor affecting the movement of a typhoon. In Exp-rv and Exp-all, VDA can improve the wind structure of the typhoon and relocate the analyzed typhoon center, such that the locations of the analyzed storm are consistent with the observation at 1500 UTC 7 August (Fig. 6). Even at 1800 UTC 7 August, the simulated storm centers in Exp-all and Exp-rv (also including Exp-tw in Section 4) almost overlap with the observed location (Fig. 8b). However, the northward bias of the storm track (Fig. 8b) and the evolution of the vortex structure (discussed in Section 3.1.2) simulated by Exp-rv in the later stage, hints that it is not enough to improve Morakot's forecast only based on the wind adjustment with VDA. As proposed in Wang et al. (2012), release of latent heating through increasing humidity can reduce the northward moving component of Morakot (resulting in a more southward track), so the humidity should be another important factor affecting the track forecast through improving the typhoon structure. In agreement with their result, in this study, the experiments with reflectivity DA (ZDA; Exp-all and Exp-dbz) also simulate a more southward track than those without ZDA (CTRL and Exp-rv). Figure 8c shows the evolution of mean flow within a radius of 600 km from the typhoon centers in each experiment during the forecast period. CTRL generally has the largest northward wind, while Exp-dbz has the weakest southerly wind component and the strongest easterly wind component in correspondence to its most westward track. This is because the analyzed humidity in the typhoon circulation with ZDA affects the typhoon structure (storm size, asymmetric convection distribution, etc.) and its subsequent evolution, meaning the interaction of the typhoon circulation and the ambient environmental field affects the movement of the typhoon (Fig. 8c). In addition, higher humidity can produce stronger storms (Fig. 8a), as identified by Xu and Wang (2010). Similarly, Exp-all and Exp-dbz also simulate stronger storms because of higher analyzed humidity, meaning they can cross the CMR more easily, instead of deflecting northward along the east side of Taiwan like CTRL, due to the topographic blocking (Wang, 1980). It is important to note that the simulated storm in Exp-dbz exhibits a movement trend toward the strong convection area over southern Taiwan because of the absence of the vortex relocation during the DA window, leading to earlier landfall (Fig. 6c) and a subsequent southward-biased track.

For the intensity forecast, all numerical experiments overestimate the intensity of Morakot, even though they generally simulate the decreasing tendency after landfall. Exp-all and Exp-dbz (with ZDA) simulate a stronger storm, because of a moister analyzed field, as discussed above. It should be noted that the storm in Exp-all is located on the leeside of the mountains (central western Taiwan) at 0600 UTC 8 August (when the simulated storm reaches maximum intensity); the downslope warming and depressing effect could superpose on the intensity (Wu, 2001).

3.3 Effects on rainfall prediction

Figure 10 shows the simulated radar reflectivity and wind vectors at the fifth model level (η = 0.934) from the first group of experiments. In general, the simulated convections in Exp-all and Exp-dbz are stronger than those in CTRL and Exp-rv, in correspondence to the higher analyzed humidity (Fig. 6). At 0000 UTC 8 August, the composite radar observation shows that an important rainband extends northwestward along the east side of Taiwan, with its tongue approaching the eastern coast of mainland China (Fig. 1), which partly contributed to the subsequent heavy rainfall in mainland China. This rainband is successfully simulated by Exp-all and Exp-dbz (with ZDA; Figs. 10c2, d2). However, the convection pattern in Exp-dbz generally presents some differences with the radar observation because of its westward-biased track. Until 0000 UTC 9 August, it seems that only Exp-all reproduces a strong rainband near between 22.5° and 23.5°N, and toward southern Taiwan [as discussed by Jou et al. (2012)], which is consistent with the observation in Fig. 1. In contrast, the rainband on the south flank of the storm in Exp-dbz does not cover Taiwan Island, due to its westward track; while the rainbands in CTRL and Exp-rv are located over the north part of Taiwan, in correspondence with their northward tracks and smaller sizes, as discussed above.

Figure 10 (a1–a4) Observed composite and (b1–b4) simulated radar reflectivity (color shading; dBZ) and wind vectors (full barb is 10 m s–1) at the fifth model level (η = 0.934), in (b1–b4) CTRL, (c1–c4) Exp-all, (d1–d4) Exp-dbz, and (e1–e4) Exp-rv at 1800 UTC 7 (first column), 0000 UTC 8 (second column), 1200 UTC 8 (third column), and 0000 UTC 9 August (fourth column).
Table 3 Station numbers at different rainfall thresholds against 605 observation stations from mainland China and Taiwan Island, based on the observed and simulated 24-h accumulated rainfall on 8 August 2009
Rainfall threshold (mm) Station numbers at different rainfall thresholds
OBS CTRL Exp-all Exp-dbz Exp-rv Exp-ml Exp-tw Exp-kt
100 270 224 250 221 240 252 247 245
200 205 132 165 159 157 174 164 123
300 163 59 94 96 95 104 108 77
400 122 31 67 62 49 56 75 45
500 89 20 45 37 26 32 48 30
600 63 7 25 23 18 21 27 18
700 47 3 16 16 9 13 17 12
800 35 1 11 11 7 8 9 5
900 30 0 10 5 0 3 8 5
1000 24 0 7 1 0 2 7 4
1100 13 0 4 0 0 1 4 2
1200 10 0 2 0 0 0 1 0
1300 7 0 1 0 0 0 0 0
1400 4 0 0 0 0 0 0 0
1500 3 0 0 0 0 0 0 0

As shown by Fig. 11, from the rainfall pattern, all of the numerical experiments reproduce the heavy rainfall in southern Taiwan. However, from the comparison of station numbers at different rainfall thresholds based on the 24-h accumulated rainfall observed by 605 rain gauges from both sides of Taiwan Strait and simulated by the first group of experiments on 8 August (Table 3), it is apparent that the simulated station number at each threshold is smaller than the observation. If there are more rain gauges in the high mountain regions, the possibility that the simulated result will become worse cannot be excluded. In particular, for more than 900 mm of rainfall, CTRL and Exp-rv produce missed forecasts. This indicates that a numerical model without ZDA remains deficient in forecasting such extreme rainfall in southern Taiwan, which is in agreement with previous studies (Hendricks et al., 2011; Wu et al., 2011, Huang et al., 2014). The improved humidity with ZDA in Exp-all and Exp-dbz significantly increases the simulated rainfall magnitude. The equitable threat score (ETS) of simulated rainfall against the observation from Taiwan Island and mainland China further confirms this result (Fig. 11i). At more than 400-mm rainfall thresholds, the ETSs of Exp-all and Exp-dbz are obviously higher than those of CTRL and Exp-rv. Furthermore, Exp-all even obtains an ETS for the rainfall forecast of more than 1200 mm, in correspondence with a simulated rainfall peak of 1387 mm in Kaohsiung County against the observation, which increases by approximately 30% as compared to the simulated rainfall peak in CTRL and Exp-rv. Note that, although CTRL also simulates a rainfall peak of more than 1000 mm (Fig. 11b), its location is biased to the north, meaning that it has no ETS at rainfall thresholds of more than 800 mm (Fig. 11i). For the rainfall simulation over eastern mainland China (Fig. 12), Exp-all also simulates the best rainfall. CTRL and Exp-rv remarkably underestimate the rainfall amount (only half of the observation), while Exp-dbz wrongly simulates the location of the rainfall peak, due to the southward track, even though the simulated maximum rainfall magnitude is close to the observation.

Figure 11 Maps of 24-h accumulated rainfall (mm) from 0000 UTC 8 August to 0000 UTC 9 August: (a) observed by rain gauges in Taiwan, and simulated by (b) CTRL, (c) Exp-all, (d) Exp-dbz, (e) Exp-rv, (f) Exp-ml, (g) Exp-tw, and (h) Exp-kt (the county boundaries are marked by black lines, and the number denotes the peak rainfall amount). (i) Equitable threat scores of 24-h accumulated rainfall verified against surface rain gauges in Taiwan Island and mainland China.
Figure 12 As in Fig. 11, but for eastern China.
4 Discussion on the improvement of the rainfall forecast

In the above section, we discussed the influence of assimilating the radar data from both sides of Taiwan Strait on the reproduction of the track and the water vapor condition, as well as the heavy rainfall, in Morakot. This section further examines where the water vapor in the analyzed field came from, and what could affect the simulated track, as well as the rainfall distribution. Accordingly, sensitivity experiments that assimilated individual sets of radar data from Taiwan Island and mainland China, and only from Kenting station, were designed. As shown by Figs. 6e, f, the contribution of assimilating the radar data from Taiwan to the analyzed humidity is larger than assimilating the radar data from mainland China, especially within a radius of 360 km from the TC center. This is because the strong convection (high radar echo) concentrated in the south periphery of the TC circulation (Fig. 4), and it was captured well by the radars in Taiwan (Fig. 13a), while the rainband captured by the radar in mainland China was far away from the typhoon center. As a result, Exp-tw produces a similar analyzed humidity to Exp-all and Exp-dbz, while in Exp-ml the analyzed humidity within a radius of 360 km from the TC center is very small compared with Exp-tw (Fig. 6h). It is interesting that Exp-kt produces almost the same humidity as Exp-tw, except within a radius of 120 km. The reason for this is because Kenting radar almost covered the main high-value reflectivity area, even though it did not entirely cover the inner core of the TC (Fig. 13a). Thus, it can be confirmed that the humidity field in Morakot's circulation can be reproduced through assimilating the radar reflectivity over southern Taiwan. Figure 14 shows the backward trajectories of air parcels starting from the points at several heights surrounding stations Zherong and Meishan at 0600 UTC 8 August, when Morakot had moved over Taiwan Strait. The air parcel trajectories were calculated by the Flexible Particle Dispersion Model with WRF (FLEXPART-WRF; Stohl et al., 2005; Fast and Easter, 2006). In addition to a few parcels at low levels from the east, the air parcels over Meishan and Zherong generally come from the southwesterly jet and the southern part of the TC circulation. Note that the trajectories at 0.5 km show that the air parcels firstly flow around Taiwan and then reach over Meishan, due to the topographic blocking. This situation is different to those above 2 km, which look to directly flow over the CMR from east to west. Because the air parcels over Zherong are far away from the center of the typhoon circulation (weak entrainment effect), their trajectories at different heights look more consistent. In general, the trajectories of air parcels over Meishan hint that the production of heavy rainfall in southern Taiwan was very closely associated with the southwesterly wind, in agreement with previous studies. The area-averaged and vertically integrated horizontal flux divergence of water vapor in the region of the typhoon circulation also shows that the improved typhoon circulations draw more water vapor from the environment (Fig. 14i). In general, ZDA can result in more water vapor transport than VDA by enhancing the TC circulation, while the effect of assimilating the radar data only from Taiwan Island is greater than only from mainland China. This also indicates that, although the higher analyzed humidity is 240 km outside the typhoon center in Exp-ml, through assimilating the radar data from mainland China (Fig. 6h), this higher moisture (especially over southern Taiwan Strait) can be transported into the inner core of the TC to improve the TC circulation (Figs. 6e, 14a), so that the improved TC circulation can draw more water vapor from the environment in the subsequent simulation (Fig. 14i), eventually resulting in larger rainfall than in Exp-rv and CTRL (Fig. 11). Similarly, Exp-tw and Exp-kt produce larger rainfall than Exp-ml because of more water vapor transport from the environment. Moreover, Exp-tw and Exp-kt even produce larger rainfall than Exp-all, due to their southward tracks in the latter half of 8 August (Fig. 13b).

Figure 13 (a) Valid points of radar reflectivity (≥ 15 dBZ, marked by crosses) at 3-km height and Morakot's location (typhoon symbol) at 1500 UTC 7 August (final data assimilation cycle). The locations of radar stations (FZ, XM, HL, CG, and KT) are marked by black dots. (b) As in Fig. 8b, but for Exp-ml, Exp-tw, and Exp-kt.
Figure 14 Fifteen-hour backward trajectories of air parcels near (a) Meishan at 0600 UTC 8 August (the center of the box with 600-km-long sides is the typhoon center at 1200 UTC 8 August), and (b–d) the vertical height of each parcel at 4.0 km (green points), 2.0 km (red points), 0.5 km (blue points) and above ground level every hour from 1500 UTC 7 August to 0600 UTC 8 August, based on the 1-h output of Exp-all. (e–h) As in (a–d), except for Zherong station. (i) Area-averaged [in the box in (a)] and vertically integrated horizontal flux divergence of water vapor [–1e–5 g (hPa m2s)–1] in every experiment.
Figure 15 (a) Equitable threat score (ETS), (b) bias score above the 15-dBZ threshold, and (c) root-mean-square error (RMSE; dBZ) of hourly simulated composite radar reflectivity against observed composite radar reflectivity in Taiwan Island and mainland China from 1800 UTC 7 August to 0000 UTC 9 August.

Table 2 lists the mean ETS, bias score (BS), and root-mean-square error (RMSE) of hourly simulated composite radar reflectivity of each numerical experiment against the observed composite radar reflectivity from Taiwan Island and mainland China at more than the 15-dBZ threshold from 1800 UTC 7 August to 0000 UTC 9 August 2009. As identified by Xie and Zhang (2012), a good rainfall forecast of Morakot foremost requires a good simulated track. Similarly, in this study, Exp-all, Exp-rv, and Exp-ml have the higher mean ETSs, due to their smaller simulated track errors than other experiments. However, the evolution of the ETS during this period shows that the high ETSs in Exp-rv and Exp-ml occurred before 0600 UTC 8 August, and then they rapidly dropped to the same score as in other experiments, except Exp-all. In addition to the simulated track, the structure associated with the rainband of the simulated TC should thus be another important factor affecting the rainfall distribution. In order to further understand the impact of storm structure on the rainfall forecast, Fig. 16 shows the evolution of hourly area-averaged rainfall near Meishan and Zherong from 0000 UTC 8 August to 0000 UTC 9 August, based on the rainfall observed by rain gauges and simulated by the first group of experiments. It can be seen that, in the first 6 hours, the simulated rainfall near Meishan from each experiment was highly consistent with the observation, and Exp-rv nearly had the same rainfall amount, as well as RMW, as Exp-all. However, after that the hourly rainfall amount simulated by Exp-rv started to decline and gradually deviated from the observation (Fig. 16c), in correspondence with the reduction of RMW in Exp-rv (Fig. 7). In contrast, the continuous increasing tendency of the rainfall amount was captured by Exp-all during 0600–1200 UTC 8 August. After 1200 UTC 8 August, although all of the experiments underpredicted the hourly rainfall amount as compared with the observation, Exp-all (with VDA and ZDA) produced a better simulation than Exp-rv (with VDA only) (Fig. 16c). The time series of the radar reflectivity and wind vectors near the latitudes of Meishan and Zherong were given in Fig. 17. Because Exp-rv simulated a more northward track (Fig. 8b) and smaller inner-core size (Fig. 7), the strong rainband cannot cover Meishan, in correspondence with the rapid decline in rainfall amount after 12 UTC 8 August. In the meantime, the rainfall near Zherong started to increase after 1200 UTC 8 August (Fig. 16d). This indicates that the heavy precipitation areas simulated by Exp-rv cannot simultaneously cover both Meishan and Zherong, in agreement with the demonstration in Fig. 17. In contrast, both Meishan and Zherong can be covered in the heavy precipitation area simulated by Exp-all and Exp-dbz (with ZDA) on 8 August, which is closely consistent with the observation (Fig. 10 and Fig. 17). This is also in agreement with the fact that the larger humidity field ultimately produces a large-sized storm, leading to the increase in the precipitation area and rainfall magnitude, as discussed in Section 3.

Figure 16 (a) Map of 24-h accumulated rainfall (mm) observed by the rain gauges in Taiwan Island and mainland China on 8 August. (b) Simulated track errors against the China Meteorological Administration best track every 6 h. (c, d) Hourly area-averaged rainfall in a 100-km2 box near (c) Meishan and (d) Zherong (shown in Fig. 15a), observed by rain gauges and simulated by CTRL, Exp-all, Exp-dbz, and Exp-rv from 0000 UTC 8 August to 0000 UTC 9 August.
Figure 17 Time series of (a, f) observed and (b, g) CTRL simulated, (c, h) Exp-all simulated, (d, i) Exp-dbz simulated, and (e, j) Exp-rv simulated radar reflectivity (dBZ; color shading) and wind vectors (m s–1; full barb is 10 m s–1) at z = 3.0 km near (a–e) 27.25°N (Zherong) and (f–j) 23.27 °N (Meishan) from 1800 UTC 7 August to 0000 UTC 9 August.
5 Summary and conclusions

Typhoon Morakot (2009) lasted approximate 48 h from its first landfall in Taiwan to its second landfall on the east coast of mainland China, and resulted in long-lasting rainfall and devastating floods on both sides of Taiwan Strait. As proposed by previous studies, the heavy rainfall in Morakot was produced due to the interaction of slow moving speed, the supplement of abundant water vapor associated with southwesterly wind, and topographic lift. Accordingly, in this study, seven experiments were conducted to examine whether assimilating the radar data from Taiwan Island and mainland China can reproduce Morakot's slow motion and abundant water vapor condition, as well as the heavy rainfall on both sides of Taiwan Strait, caused by these important factors.

In this study, VDA was found to present little ability in terms of providing a cyclonic structure comparable to the primary circulation derived from the GFS data, but was found to keep the analyzed vortex location consistent with the best track through adjusting the wind field within the radar detecting region, subsequently improving the track forecast. Meanwhile, ZDA was found to not only significantly increase the humidity in the typhoon circulation, but also to reduce the northward moving speed, due to improved typhoon structure and evolution associated with the release of latent heating, ultimately enhancing the rainfall amount in southern Taiwan. Therefore, the track forecast can be improved through the vortex relocation with VDA and increased initial humidity with ZDA, as well as the forecast of rainfall distribution associated with the track, while the precipitation area and rainfall magnitude can be significantly improved through ZDA. It indicates that the high-resolution numerical model with the hybrid application of VDA and ZDA can successfully simulate Morakot's water vapor field and track. Based on the sensitivity experiments, it was found that, because of the drier humidity field, the simulated storm in the experiments without ZDA features unrealistic inward contraction after 12 h of integration, meaning that the heavy precipitation area, as well as the rainfall amount, is underestimated. In contrast, in the absence of the vortex relocation with VDA, the moister (drier) humidity field with (without) ZDA will produce a more southward/westward (northward) track, which will also affect the rainfall location, especially for the location of the rainfall peak. From the experiment assimilating the radar data from Kenting station, it was further found that the improved analyzed humidity is mainly contributed by assimilating the high-value radar reflectivity (strong convection) over southern Taiwan. The analysis of parcel trajectories over Meishan further showed that the long-lasting and extreme rainfall in southern Taiwan caused by Morakot was very closely related with the southwesterly wind, in agreement with previous studies. Moreover, the area-averaged and vertically integrated horizontal flux divergence of water vapor further confirmed that the improved typhoon circulation through assimilating the radar data draws more water vapor from the environment, and eventually produces such extreme rainfall in Taiwan.

This study shows that a numerical model with radar DA may be capable of forecasting long-lasting and extreme rainfall like that in Morakot. It should be noted, however, that the extension of this conclusion needs further verification based on more case studies. In addition to the combination of the dynamical interaction among TC circulation, southwesterly flow, and orographic lift, the precipitation processes in Morakot were governed by the microphysical processes associated with the injection of abundant water vapor from the southwesterly flow (Hendricks et al., 2011; Wu, 2013; Huang et al., 2014), which also needs further investigation.

Acknowledgments. The authors are grateful to Dr. Fuqing Zhang and the two anonymous reviewers for providing valuable comments and suggestions that improved our original manuscript.

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