Improving Afternoon Thunderstorm Prediction over Complex Terrain with the Assimilation of Dense Ground-Based Observations: Four Cases in the Taipei Basin

Shu-Chih Yang aDepartment of Atmospheric Sciences, National Central University, Taoyuan, Taiwan
bGPS Science and Research Application Center, National Central University, Taoyuan, Taiwan
cRIKEN Center for Computational Science, Kobe, Japan

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Yi-Pin Chang aDepartment of Atmospheric Sciences, National Central University, Taoyuan, Taiwan

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Hsiang-Wen Cheng aDepartment of Atmospheric Sciences, National Central University, Taoyuan, Taiwan
dTaiwan Space Agency, Hsinchu, Taiwan

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Kuan-Jen Lin aDepartment of Atmospheric Sciences, National Central University, Taoyuan, Taiwan

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Ya-Ting Tsai eCentral Weather Administration, Taipei, Taiwan

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Jing-Shan Hong eCentral Weather Administration, Taipei, Taiwan

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Yu-Chi Li eCentral Weather Administration, Taipei, Taiwan

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Abstract

In this study, we investigate the impact of assimilating densely distributed Global Navigation Satellite System (GNSS) zenith total delay (ZTD) and surface station (SFC) data on the prediction of very short-term heavy rainfall associated with afternoon thunderstorm (AT) events in the Taipei basin. Under weak synoptic-scale conditions, four cases characterized by different rainfall features are chosen for investigation. Experiments are conducted with a 3-h assimilation period, followed by 3-h forecasts. Also, various experiments are performed to explore the sensitivity of AT initialization. Data assimilation experiments are conducted with a convective-scale Weather Research and Forecasting–local ensemble transform Kalman filter (WRF-LETKF) system. The results show that ZTD assimilation can provide effective moisture corrections. Assimilating SFC wind and temperature data could additionally improve the near-surface convergence and cold bias, further increasing the impact of ZTD assimilation. Frequently assimilating SFC data every 10 min provides the best forecast performance especially for rainfall intensity predictions. Such a benefit could still be identified in the earlier forecast initialized 2 h before the start of the event. Detailed analysis of a case on 22 July 2019 reveals that frequent assimilation provides initial conditions that can lead to fast vertical expansion of the convection and trigger an intense AT. This study proposes a new metric using the fraction skill score to construct an informative diagram to evaluate the location and intensity of heavy rainfall forecast and display a clear characteristic of different cases. Issues of how assimilation strategies affect the impact of ground-based observations in a convective ensemble data assimilation system and AT development are also discussed.

Significance Statement

In this study, we investigate the impact of frequently assimilating densely distributed ground-based observations on predicting four afternoon thunderstorm events in the Taipei basin. While assimilating GNSS-ZTD data can improve the moisture fields for initializing convection, assimilating surface station data improves the prediction of rainfall location and intensity, particularly when surface data are assimilated at a very high frequency of 10 min.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Shu-Chih Yang, shuchih.yang@atm.ncu.edu.tw

Abstract

In this study, we investigate the impact of assimilating densely distributed Global Navigation Satellite System (GNSS) zenith total delay (ZTD) and surface station (SFC) data on the prediction of very short-term heavy rainfall associated with afternoon thunderstorm (AT) events in the Taipei basin. Under weak synoptic-scale conditions, four cases characterized by different rainfall features are chosen for investigation. Experiments are conducted with a 3-h assimilation period, followed by 3-h forecasts. Also, various experiments are performed to explore the sensitivity of AT initialization. Data assimilation experiments are conducted with a convective-scale Weather Research and Forecasting–local ensemble transform Kalman filter (WRF-LETKF) system. The results show that ZTD assimilation can provide effective moisture corrections. Assimilating SFC wind and temperature data could additionally improve the near-surface convergence and cold bias, further increasing the impact of ZTD assimilation. Frequently assimilating SFC data every 10 min provides the best forecast performance especially for rainfall intensity predictions. Such a benefit could still be identified in the earlier forecast initialized 2 h before the start of the event. Detailed analysis of a case on 22 July 2019 reveals that frequent assimilation provides initial conditions that can lead to fast vertical expansion of the convection and trigger an intense AT. This study proposes a new metric using the fraction skill score to construct an informative diagram to evaluate the location and intensity of heavy rainfall forecast and display a clear characteristic of different cases. Issues of how assimilation strategies affect the impact of ground-based observations in a convective ensemble data assimilation system and AT development are also discussed.

Significance Statement

In this study, we investigate the impact of frequently assimilating densely distributed ground-based observations on predicting four afternoon thunderstorm events in the Taipei basin. While assimilating GNSS-ZTD data can improve the moisture fields for initializing convection, assimilating surface station data improves the prediction of rainfall location and intensity, particularly when surface data are assimilated at a very high frequency of 10 min.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Shu-Chih Yang, shuchih.yang@atm.ncu.edu.tw

1. Introduction

Short-term precipitation prediction is a challenging and top priority issue in regional numerical weather prediction, as the decision making for disaster prevention depends on the performance of heavy rainfall prediction. Convective-scale radar data assimilation (DA) has contributed tremendous progress in improving short-term quantitative precipitation forecasting (Aksoy et al. 2009; Sun et al. 2014; Gustafsson et al. 2018). The assimilation of high-resolution radar observations combined with frequent analysis cycles greatly impacts the prediction of heavy rainfall events undergoing rapid development (Miyoshi et al. 2016). In recent years, studies show that combining radar data with innovative remote sensing observations, such as satellite-derived liquid/ice and cloud water paths, bring additional benefits for improving short-term QPF (Jones et al. 2016; Pan et al. 2021).

Different from other long-lived heavy rainfall systems, afternoon thunderstorms (ATs) are characterized by small scales, short term, and high rainfall intensities with rapid development, which can cause urban-scale flooding in a short time. However, predicting AT is difficult because it involves accurate initiation timing, location, development, and rainfall intensity. Furthermore, AT prediction is especially challenging over complex terrain, where orographic effects and the land–sea breezes can modulate the initialization and development of ATs. Local thermal effects and interactions between convection and terrain can modify the local circulation and convective instability (Tang et al. 2016; Katona and Markowski 2021).

It is critical to depict the precursors of rapidly developing ATs, but traditional radar observations such as radial velocity and reflectivity are limited before the initialization of AT events. In addition, radar cannot provide near-surface conditions due to radar scanning strategies involving minimal elevation angles and cannot directly measure variables related to thermal conditions, such as the temperature and moisture content. Efforts have been made to overcome these limitations by incorporating ground-based observations that can provide the information associated with convective development, such as in situ surface station (SFC) data and remote sensing data, including Global Navigation Satellite System (GNSS) zenith total delay (ZTD), Raman lidar, and Atmospheric Emitted Radiance Interferometer data (Yoshida et al. 2020; Seko et al. 2011; Degelia et al. 2020). Although innovative ground-based profilers can provide high vertical-resolution data frequently, they are deployed at limited locations for experimental field campaigns. By comparison, the densely distributed SFCs and ZTD stations are the main component of ground-based observation networks in many countries, and they regularly measure low-level atmospheric conditions with considerably high spatiotemporal resolution.

SFC data are assimilated every hour in most operational convective-scale DA systems (Gustafsson et al. 2018). Chen et al. (2020) showed that with the operational regional three-dimensional variational system, additionally assimilating hourly SFC data can further increase the forecast lead time of AT events relative to radar assimilation. Lin et al. (2023) showed that assimilating the New York State Mesonet data hourly using a Gridpoint Statistical Interpolation–based three-dimensional variational system is beneficial for forecasting a convective event. With a four-dimensional variational Doppler radar assimilation system, Wu et al. (2021) showed that assimilating SFC data with a 12.5-min window is critical for correcting rainfall location errors, but the role of surface moisture is less clear since the surface humidity is nearly saturated in their case.

The ground-based GNSS receiver measures the delay in the path of receiving signals from GNSS satellites, and the ZTD expresses this delay as the excess pathlength along the zenith direction. Compared to moisture-related measurements that are only available at particular times of the day, the GNSS ZTD provides fast-changing moisture content information at a high temporal resolution (30 min) for all weather conditions with relatively inexpensive instrumentation. Although precipitable water (PW) can be retrieved from the ZTD, studies have suggested that it is more preferable to assimilate the ZTD than PW (Cucurull et al. 2004). Previous works have demonstrated that ZTD assimilation improves the humidity and rainfall forecasting performance, and these results were mostly obtained with the three-dimensional variational system (Singh et al. 2019; Giannaros et al. 2020; Lagasio et al. 2019; de Haan 2013). Lindskog et al. (2017) provided a thorough investigation of ZTD assimilation in Nordic countries. They showed that the benefit of ZTD assimilation in moisture forecasting could be increased when assimilating other types of meteorological observations jointly or with an enhanced static background error covariance. With the 4DVAR system, Rohm et al. (2019) reported a mixed impact of ZTD assimilation on severe weather prediction. Yang et al. (2020) showed that assimilating ZTD data in addition to radar data helped improve the prediction of the initiation and intensity of heavy rainfall in Taiwan. To our knowledge, limited literature has examined the impact of ZTD assimilation on predicting short-term, intense rainfall events using a convective-scale ensemble data assimilation (EDA) system.

In Taiwan, the Taipei basin (Fig. 1a) is a hot spot of AT occurrence given the distinctive conditions of the complex terrain and the urban heat island effect (Kuo and Wu 2019). During the summer daytime, the local sea breeze prevails under weak synoptic-scale forcing, and onshore flows originating from the Danshui River valley and Keelung River valley transport moist air and converge in the Taipei basin (Chen et al. 2007). The blocking effect of the Snow Mountain Range also consolidates convergence. Datun Mountain, situated near the coast, can enhance moisture transport by the sea-breeze circulation (Miao and Yang 2020). These factors provide dynamic and thermodynamic conditions favorable for convective development. Even the near-surface outflow induced by the cold pool of ATs can play a crucial role in initializing new convective cells or merging them into a new major complex (Feng et al. 2015; Kuo and Wu 2019; Wu et al. 2021).

Fig. 1.
Fig. 1.

(a) Terrain height (m; shading). (b) The ground-based observation distribution. The yellow circles, cyan squares, and magenta triangles denote the manned surface stations, automatic surface stations, and ZTD stations, respectively. (c) The model domain of the experiments.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0149.1

The Central Weather Administration in Taiwan has established a dense ground-based observation network, including 29 manned SFCs, 406 automatic SFCs, and 118 GNSS ZTD stations (Fig. 1b), routinely providing near-surface atmospheric information with high spatiotemporal resolution. Given the limitation of radar observations before the start of ATs, SFC and ZTD data are the only observations with a sufficiently high spatiotemporal resolution to capture initialization and rapid development of ATs in Taiwan. Therefore, it is essential to investigate the benefit of SFC and ZTD assimilation at a high frequency for representing the precursors of AT development and how this facilitates the associated heavy rain prediction. In this study, we investigated the impact and challenges of the assimilation of dense ground-based observations on four intense AT events with the convective-scale EDA system to improve AT prediction in the Taipei basin. We addressed the following scientific questions: What is the role of assimilating ZTD and SFC data in improving the prediction of rapidly changing dynamic and thermodynamic conditions of ATs? How can assimilation strategies affect the impact of these ground-based observations in a convective-scale EDA system and influence AT development? Can frequent DA with a 10-min interval improve the initialization and prediction of ATs? In particular, the AT event on 22 July 2019 with a rainfall rate of 90 mm h−1 in the Taipei basin (Fig. 2k) was thoroughly analyzed.

Fig. 2.
Fig. 2.

(a) The maximum radar reflectivity (dBZ) of QPESUMS at 1200 LST 22 Jul 2019. The thickest to thinnest black contours indicate terrain heights of 0, 100, 250, 500, 1000, and 2000 m, respectively. (b)–(f) As in (a), but for 1300, 1400, 1500, 1600, and 1700 LST 22 Jul 2019, respectively. (g)–(l) As in (a)–(f), but for the hourly rainfall (mm) of QPESUMS from 1100 to 1200, from 1200 to 1300, from 1300 to 1400, from 1400 to 1500, from 1500 to 1600, and from 1600 to 1700 LST 22 Jul 2019, respectively.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0149.1

The rest of the paper is organized as follows: section 2 gives an overview of the four AT events. Section 3 presents the characteristics of the observations. Section 4 introduces the DA experiments, and the corresponding analysis and forecast results are provided in section 5. Section 6 examines issues related to earlier forecast and DA strategies. Finally, section 7 provides a summary of this study, including the answers to our proposed questions.

2. Overview of the four AT events

A series of DA experiments were conducted for four AT events, including 22 July 2019, 24 June 2022, 4 July 2022, and 25 August 2022 (hereafter referred to as Cases I, II, III, and IV, respectively). The four cases were chosen by considering rainfall rates in excess of 40 mm h−1 under weak synoptic-scale forcings, as indicated by the low wind speeds offshore around Taiwan (Figs. 3a–d). The 10-m wind direction at the SFCs shows notable land–sea breezes (Figs. 3e–h). Although the wind direction of the land–sea breeze is generally similar near the coast, significant differences among the cases occur surrounding the Taipei basin when the ATs initialize (Figs. 3i–l). This suggests the importance of capturing local wind variations for the purpose of improving AT prediction.

Fig. 3.
Fig. 3.

(a) Surface wind speed (m s−1; shading) and wind direction (arrows) of NCEP final analysis at 0800 LST for Case I. (b)–(d) As in (a), but for Cases II, III, and IV, respectively. (e) The 10-m wind direction of the surface stations at 0400 LST (blue arrows) and 1400 LST (red arrows) for Case I. The terrain heights (m) are shown with grayscale shading. (f)–(h) As in (e), but for Cases II, III, and IV, respectively. (i),(l) As in (e) and (h), but at 1400 LST (blue arrows) and 1500 LST (red arrows), respectively. (j),(k) As in (f) and (g), but at 1300 LST (blue arrows) and 1400 LST (red arrows), respectively.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0149.1

Figure 4 shows the Quantitative Precipitation Estimation and Segregation Using Multiple Sensors (QPESUMS) 2-h accumulated rainfall of the AT events, and the magenta box defines the target area centered on the Taipei basin (48 × 48 km2). The 2-h AT period starts from the time when the rainfall rate is higher than 40 mm h−1 (the definition of “heavy rainfall” by the Central Weather Administration) within the target area: 1500–1700 LST 22 July 2019 for Case I, 1400–1600 LST 24 June 2022 for Case II, 1400–1600 LST 4 July 2022 for Case III, and 1500–1700 LST 25 August 2022 for Case IV. During these times, several kilometer-wide thunderstorm cells quickly developed in the Taipei basin and caused severe rainfall. Among these cases, Case I had the most extreme rainfall, with 134 mm (2 h)−1 (Fig. 4a). An intense AT emerged in the middle of the Taipei basin at 1500 LST, which gradually propagated southward toward the Snow Mountain Range and dissipated. The AT in Case II also indicated southward development (Fig. A1a in the appendix), but it had the lowest rainfall intensity among the four cases, with 77 mm (2 h)−1 (Fig. 4b). The AT in Case III formed at the border between the Taipei basin and the Linkou Tableland (Fig. A1b in the appendix). In Case IV, the AT developed northward, starting from the Snow Mountain Range and ending at the Taipei basin (Fig. A1c in the appendix). The rainfall intensity was 131 and 98 mm (2 h)−1 in Cases III and IV (Figs. 4c,d), respectively.

Fig. 4.
Fig. 4.

(a) The 2-h accumulated rainfall (mm) of QPESUMS for Case I. The magenta box indicates the target area. The thickest to thinnest black contours indicate terrain heights of 0, 100, 250, 500, 1000, and 2000 m, respectively. (b)–(d) As in (a), but for Cases II, III, and IV, respectively.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0149.1

3. Ground-based observations

In this study, ground-based observations for assimilation include the ZTD, 10-m zonal wind (U10), 10-m meridional wind (V10), and 2-m temperature (T2) of SFCs. Note that the 2-m water vapor mixing ratio (Q2) of SFCs is not assimilated and is an independent observation for verification. The spatial resolutions of the SFC and ZTD stations in the target area are approximately 7 and 21 km (Fig. 1b), respectively. The SFC data are available every 10 min, and the ZTD data are available every 30 min at 15 and 45 min past the hour.

In the following, we use Case I to illustrate the ground-based observation characteristics of the AT event. Two featured stations in Taipei and Linkou are selected to demonstrate the temporal evolution of weather conditions in the Taipei basin and the Linkou Tableland. As shown in Fig. 5b, T2 was already 34°C at the Taipei station and 31°C at the Linkou station at 1130 LST. Sea breezes induced by the heated land surface entered the Taipei basin through the river valleys. The unstable thermodynamic conditions and sea-breeze convergence triggered convection over the complex terrain near the basin from 1200 LST (Figs. 2h,i). In particular, convection at the Linkou station generated rainfall after 1430 LST (the blue bars in Fig. 5b) and caused T2 to rapidly drop by 4°C h−1 (the blue line in Fig. 5b). The cold pool–associated downdraft induced wind gusts, giving rise to a dramatic change in the 10-m wind direction at the Linkou station of 70° in 30 min (the blue arrows in Fig. 5b). On the other hand, the temporal variation in the ZTD corresponds well to the PW variation (Fig. 5c), which is derived from the zenith wet delay of the ZTD. The ZTD at the Linkou station shows that the moisture content gradually increased and reached its maximum at 1445 LST when the rainfall there ended.

Fig. 5.
Fig. 5.

(a) T2 (°C; circles) and 10-m wind (arrows) at the surface stations at 1500 LST 22 Jul 2019. The locations of the Linkou and Taipei surface stations are marked with blue and dark red circles, respectively, while the locations of the Linkou and Taipei ZTD stations are marked with blue and dark red triangles, respectively. The thickest to thinnest gray contours indicate terrain heights of 0, 100, 250, 500, 1000, and 2000 m, respectively. (b) Time series of T2 (°C; lines), 10-m wind directions (arrows), and rainfall rates (mm min−1; bars) at the Taipei (in red) and Linkou (in blue) surface stations. The direction of the wind arrows corresponding to the north is “up.” (c) Time series of the ZTD (cm; solid lines) and PW (cm; dashed lines) at the Taipei (red) and Linkou (blue) ZTD stations.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0149.1

In addition to the outflow at Linkou, the outflow generated by rainfall-associated downdrafts on the southwestern side of Datun Mountain, combined with the blocking effect of the Snow Mountain Range (Fig. 2j) led to wind convergence in the Taipei basin at 1500 LST (Fig. 5a). Deep convection quickly developed there, resulting in extreme rainfall during the following 2 h (red bars in Fig. 5b). The ZTD and PW maxima at the Taipei station at 1545 LST (Fig. 5c) confirmed abundant moisture transport by local winds. This also indicates that the ZTD can resolve rapid changes in moisture content and thus can trace the signals leading up to AT formation.

In conclusion, the precursors of AT development in the Taipei basin reside in the fast-changing local dynamic and thermodynamic conditions and their interactions with the surrounding complex terrain. High-spatiotemporal resolution ground-based observations, including SFC and ZTD data, capture these features immediately.

4. DA system and experimental settings

a. Convective-scale WRF-LETKF system

The Advanced Research Weather Research and Forecasting (WRF) Model version 3.7.1 (Skamarock et al. 2008) was used in this study, configured with two-way and triple-nested domains. The domains are centered on Taiwan (Fig. 1c), and the horizontal grid spacings in each nested domain are 27, 9, and 3 km. There are 50 model layers with the first model level arranged at the 8.8-m height and the model top at 50 hPa. In total, 16 model levels reside below 1 km to resolve the variations below the planetary boundary layer (PBL). The physical parameterization settings follow those of Wu et al. (2020).

In this study, we used the convective-scale WRF–local ensemble transform Kalman filter (WRF-LETKF) system (Tsai et al. 2014; Yang et al. 2022). Two sets of NCEP GEFS ensembles initialized at 0200 and 0800 LST are spun up to the DA initial time to obtain the initial ensemble for all the experiments (i.e., the 42 members comprising Case I includes 21 members from 9-h forecasts and 21 members from 3-h forecasts). Due to changes in the NCEP GEFS configuration, there are 42 members for Case I and 62 members for each of the other cases. During the spinup period, the ensemble mean is recentered on the NCEP final analysis at 0800 LST so that the synoptic environment can be better simulated, which helps to highlight the local DA impact on predicting AT events. DA is conducted in the innermost domain for all the experiments.

The ZTD operator is implemented following the approaches of Vedel and Huang (2004) and Yang et al. (2020), considering the inconsistencies between the altitude of the GNSS stations and the model topography. The operator for simulating the 10-m wind at the SFCs is constructed by interpolating the model wind to the altitude of the station if the station altitude is higher than the first model level. If the station altitude is lower than the first model level and the altitude difference is less than 200 m, an empirical power law relation (Hsu et al. 1994), which considers the effect of the PBL, is used to diagnose the wind at the station. Otherwise, the data are discarded. Only 4.8% of the total stations encounter such large altitude inconsistencies.

The cross-variable update is restricted for both SFC and ZTD assimilation. The SFC wind and T2 only update the wind and potential temperature fields, respectively; while the ZTD only updates hydrometeors. Further discussion on this configuration is included in section 6b. In addition, we adopt mixed localization to consider multiscale corrections (Zhang et al. 2009; Lin et al. 2022). The horizontal localization length scales are 150 and 12 km for the ZTD and SFC assimilations, respectively; and a vertical localization of 4 km is used for both observations. With the choices of the localization scales, we consider that the moisture correction of ZTD assimilation aims to adjust the moisture fields from the mesoscale to convective scale (Yang et al. 2020; Do et al. 2022), while the wind and temperature corrections of SFC assimilation target the convective scale. In addition, the observation error for ZTD assimilation is 10 mm following Yang et al. (2020). Regarding SFC 10-m wind and T2 assimilation, the observation errors are 1 m s−1 and 1°C, respectively. To amplify the observation signal in the assimilation,1 the observation errors are halved in Cases II, III, and IV, which have smaller ensemble spreads than those in Case I. The relaxation to prior spread method (Whitaker and Hamill 2012) is implemented for all DA cycles using a relaxation factor of 0.9. For the first DA cycle, the multiplicative inflation method is used with an inflation factor of 1.08 to additionally inflate the initial ensemble.

b. Experimental design

Table 1 lists the experiments and DA setup. To highlight the assimilation impact on capturing convection initialization, the DA experiments perform frequent analysis cycles from 4 to 1 h before the AT event (i.e., from 1100 to 1400 LST in Cases I and IV; from 1000 to 1300 LST in Cases II and III), as shown in Fig. 6. “ZDA” assimilates the ZTD data alone, while “ZSDA” assimilates both the ZTD and SFC data. The ZTD is assimilated every 30 min at 15 and 45 min after the hour, while the SFC data are assimilated every 30 min at 0 and 30 min after the hour. The assimilation times of the ZTD and SFC data are staggered to consider the time represented by these data since ATs can develop very rapidly. “ZSDA_HT” has the same setup as ZSDA, except that it assimilates the SFC data every 10 min. “ZSDA_ALL” demonstrates the impact of the cross-variable update when assimilating the ZTD, and a related discussion is provided in section 6b. The 3-h ensemble forecasts initialized from the final analysis ensemble and mean forecasts from the final analysis mean are generated for all experiments and all cases. Without the impact of assimilation, “NoDA” denotes that the mean and ensemble forecasts start at 0800 LST.

Table 1.

List of the experiments and DA setup.

Table 1.
Fig. 6.
Fig. 6.

The experimental timeline.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0149.1

5. Results

In this section, we first describe the impact of ZTD and SFC assimilation by comparing the results of NoDA with those of ZDA and ZSDA analyses. Section 5b focuses on ZSDA_HT to highlight the impact of frequent DA. Section 5c presents the forecast performance.

a. Impact of ZTD and SFC assimilation

Figure 7 shows the cycling performance of the averaged bias and RMSE of all cases relative to SFC data. Over northern Taiwan (the verification domain is shown in Fig. 1a), all experiments indicate cold and dry biases (Figs. 7a,b). Assimilating the ZTD reduces the Q2 errors of all DA experiments after 1.5 h (the colored lines in Figs. 7b,d), but the T2 bias of ZDA is consistently higher than that of NoDA (the purple and black lines in Fig. 7a). By assimilating the SFC data, the T2 errors of ZSDA at the analysis time are largely decreased (the blue lines in Figs. 7a,c). However, the error grows to a level that is similar to that of NoDA after 30 min, suggesting that a shorter DA interval is necessary for this kind of rapidly developed AT events. The sawtooth pattern in the T2 bias suggests a systematic bias in the underlying WRF model that is constantly reintroducing this temperature bias during the ensemble forecast. This also indicates that it is difficult to remove the bias with T2 assimilation.

Fig. 7.
Fig. 7.

(a) Average T2 biases (°C) of the four cases over northern Taiwan during the DA period. The black, purple, blue, and red lines denote NoDA, ZDA, ZSDA, and ZSDA_HT, respectively. (b) As in (a), but for the Q2 biases (g kg−1). (c),(d) As in (a) and (b), but for the RMSE. (e)–(h) As in (a)–(d), but for the U10 bias, V10 bias, U10 RMSE, and V10 RMSE (m s−1), respectively. (i)–(l) As in (e)–(h), but validated within the target area.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0149.1

Compared to those of NoDA and ZDA, the wind errors of ZSDA are largely reduced over northern Taiwan in both the analysis and background (Figs. 7e–h). The V10 bias of ZSDA is effectively corrected throughout the assimilation period in both northern Taiwan and the target area, while the improvement of the U10 bias of ZSDA is evident in the target area. The wind RMSE of ZSDA is also reduced in the target area (Figs. 7k,l).

Taking the surface wind analysis of Case I at 1400 LST (the final analysis time) in the target area as an example, ZSDA can capture the local wind features by assimilating the SFC wind, but NoDA and ZDA cannot (Fig. 8). At this time, the SFC wind data exhibit northwesterly flow in the Linkou Tableland and northeasterly flow near the Dahan River valley (the red arrows inside the green circle), forming a convergence area and causing convection (Fig. 2c). The winds in NoDA and ZDA are more southerly in the Linkou Tableland, while ZSDA shows good agreement with the SFC data, indicating its potential in predicting convective initiation at Linkou and affecting the following AT in the Taipei basin. Similar improvements in ZSDA can also be found in the other cases (figure not shown). However, several issues still remain. All experiments exhibit different behaviors at the Snow Mountain Range due to the lack of corrections. In addition, the sea breezes on the northwestern coast are overestimated in all cases. The issue of sea breezes is further examined in section 6b.

Fig. 8.
Fig. 8.

(a) The 10-m wind of NoDA (gray arrows) compared to the SFC wind (red arrows) of Case I at 1400 LST. The thickest to thinnest black contours indicate terrain heights of 0, 100, 250, 500, 1000, and 2000 m, respectively. (b) As in (a), but for ZDA analysis. (c) As in (a), but for ZSDA analysis.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0149.1

The ZTD and SFC assimilations provide different spatial adjustments to the near-surface dynamic and thermodynamic fields, which can modulate the low-level moisture distribution and thus lead to different precipitation behaviors. Whether ZTD and SFC assimilation helps predict rainfall 1 h prior to the AT event is crucial, because the scattered convection during this hour is deterministic for the following AT development. Figure 9 shows a comparison of the total precipitable water (TPW) analysis and 1-h rainfall forecast of each experiment. As a benchmark, the TPW of NoDA is shown in the first row of Fig. 9. The second row shows the corresponding QPESUMS rainfall, superposed with the rainfall difference between NoDA and QPESUMS. To highlight the accumulated DA effect, the third to final rows show that the TPW of the final analysis of the DA experiments deviates from the NoDA TPW, superposed with the rainfall difference between the DA experiments and NoDA.

Fig. 9.
Fig. 9.

(a) TPW of NoDA for Case I at the final analysis time. The thickest to thinnest gray contours indicate terrain heights of 0, 100, 250, 500, 1000, and 2000 m, respectively. (b)–(d) As in (a), but for Cases II, III, and IV, respectively. (e) QPESUMS rainfall in the next hour to the final analysis time (mm; shading) and the rainfall difference between NoDA and QPESUMS for Case I. The blue and red contours indicate differences of −10 and +10 mm, respectively. (f)–(h) As in (e), but for Cases II, III, and IV, respectively. (i) TPW difference at the final analysis time (kg m−2; shading) and the rainfall difference over the next hour (contours) between ZDA and NoDA for Case I. The blue and red contours indicate differences of −10 and +10 mm, respectively. (j)–(l) As in (i), but for Cases II, III, and IV, respectively. (m)–(p) As in (i)–(l), but for the difference between the ZSDA and NoDA. (q)–(t) As in (i)–(l), but for the difference between ZSDA_HT and NoDA.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0149.1

The TPW of NoDA captures the general characteristics of the four AT events: Case II has the driest environment (Fig. 9b), and Case III has the most humid environment (Fig. 9c) among the four cases. Nonetheless, the rainfall discrepancy over the next hour between NoDA and QPESUMS indicates that NoDA fails to predict the locations of scattered convection cells given that the blue contours in Figs. 9e–h overlap with QPESUMS (shading). ZDA largely adjusts the TPW distribution and affects the rainfall locations accordingly (Figs. 9i–l). For example, the TPW and rainfall in the Western Lowlands in Cases I and II are increased, and those in the higher mountains in Case III are reduced. These results exhibit good spatial agreement with the areas where NoDA underestimates/overestimates in the forecast (blue/red contours in Figs. 9e–h), confirming the positive impact of ZTD assimilation on rainfall prediction.

Compared to ZDA, assimilating the SFC data further adjusts the TPW distribution and rainfall forecast with enhanced detail. For example, SFC assimilation enhances the TPW band in the Western Lowlands in all cases (Figs. 9m–p). In Case I, both ZDA and ZSDA have higher TPW levels than NoDA in the Linkou Tableland (Figs. 9i,m), echoing the increase in PW at the ZTD station (Fig. 5c). However, local maxima in the Linkou Tableland can only be found in ZSDA. The benefits of SFC assimilation on moisture can be explained by the following two reasons: first, assimilating 10-m wind provides wind correction that can effectively transport the moisture adjusted by ZTD assimilation; second, assimilating T2 reduces the biases in the thermal fields and thus improves the moisture content. In conclusion, both ZTD and SFC assimilation provide beneficial near-surface corrections. It should be noted that the TPW adjustment amount in the Snow Mountain Range is relatively small given that ground-based observations are limited in this area (Fig. 1b). Consequently, TPW corrections at higher terrain elevations mainly rely on ZTD assimilation using larger-scale localization. The lack of corrections from SFC assimilation can reduce the accuracy of the thermodynamic and dynamic fields, especially when the mountainous convective activity is pronounced (Cases III and IV, Figs. 9o,p).

b. Impact of 10-min SFC assimilation

In section 5a, we mentioned that SFC assimilation can reduce biases at the analysis time, but rapidly growing errors can diminish the benefits with a 30-min DA interval, especially for T2 (Fig. 7a). As a result, more frequent DA is desired to capture the fast-changing near-surface conditions for AT development. In this subsection, we investigate the DA results of ZSDA_HT to address the impact of assimilating the SFC observations at a high temporal frequency of 10 min.

As shown in Figs. 7a and 7c, the background and analysis T2 errors of ZSDA_HT are smaller than those of ZSDA. The wind biases in northern Taiwan are also reduced more quickly (Figs. 7e,f). While 2 h are needed to reduce the background U10 bias to 0.2 m s−1 in ZSDA, only 1 h is needed in ZSDA_HT. Benefits in terms of wind errors can also be observed in the target area (Figs. 7i–l). This confirms that 10-min DA is more effective for correcting surface errors relative to the standard 30-min setup. However, the wind biases over northern Taiwan of ZSDA_HT become slightly larger than those of ZSDA in the final hour (Figs. 7e,f). This phenomenon is explained in section 6b.

ZSDA_HT further enhances the positive impacts observed in the moisture distribution of ZSDA (Figs. 9m–p versus Figs. 9q–t). This indicates that frequent SFC assimilation helps to adjust the moisture distribution. The rainfall adjustment of ZSDA_HT (red contours in Figs. 9q–t) makes up for the deficiency of NoDA well (blue contours in Figs. 9e–h), especially in Cases I, II, and III.

In addition to horizontal atmospheric conditions, the vertical thermodynamic structure plays a crucial role in AT development. Due to the lack of profiling observations with a high temporal resolution, it is difficult to verify the impact of ground-based observations on the PBL thermodynamic structure. Fortunately, a newly developed radiosonde, the “Storm Tracker” (Hwang et al. 2020), is available near the event center of Case I hourly from 1200 to 1500 LST (the launch location is marked in Fig. 4a). Given that the AT starts at 1500 LST, the Storm Tracker covers the initialization period of the AT event well and provides vertical profiles of the temperature, humidity, wind, and pressure in the lower atmosphere. The Hovmöller diagrams of the equivalent potential temperature (θe) of the experiments are compared to the Storm Tracker graphs (Fig. 10). Note that data from 1200 to 1400 LST are obtained from analysis, and the data from 1400 to 1500 LST are retrieved from the mean forecast. Notably, ZSDA_HT has the highest θe value among the experiments and, qualitatively, is the most comparable with the Storm Tracker data (the shading and circles in Fig. 10d). The θe value of ZSDA_HT is greater than 350 K below 850 hPa before 1400 LST, and the high-θe structure rapidly expands to 700 hPa from 1400 to 1500 LST. By comparison, the high-θe structure of ZSDA is shallower (below 900 hPa) and does not expand upward before 1500 LST (Fig. 10c). ZDA and NoDA do not possess this high-θe feature, even though the θe value of ZDA is slightly higher than that of NoDA (Figs. 10a,b). In other words, Fig. 10 confirms that ZTD and SFC assimilation is beneficial for increasing the near-surface θe value by increasing the near-surface moisture content, improving moisture transport, and reducing the cold bias. Most importantly, performing frequent DA is the key to establishing the rapid development of high θe values, which can trigger convective development and is most consistent with the Storm Tracker data.

Fig. 10.
Fig. 10.

(a) Hovmöller diagram of θe (K; shading) of the NoDA mean forecast. The circles denote the θe values of the Storm Trackers. (b) As in (a), but for ZDA. (c) As in (b), but for ZSDA. (d) As in (b), but for ZSDA_HT. Note that in (b)–(d), the data from 1200 to 1400 LST are retrieved from analysis, and the data from 1400 to 1500 LST are obtained from the mean forecast.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0149.1

c. Rainfall forecast performance

An overview of the rainfall forecasts after 3-h DA is presented in this subsection. Since the improvement in predicting such a small-scale AT event involves both an accurate location and intensity, traditional point-based verification scores are not sufficient to evaluate the forecast skill (Roberts and Lean 2008; Mittermaier et al. 2013). In the following, the rainfall forecasts are evaluated with two metrics: the probability quantitative precipitation forecast (PQPF) and the fractions skill score (FSS). The PQPF provides a qualitative understanding of the general ensemble performance and practical information in terms of risk assessment (Chang et al. 2012). The FSS is a neighborhood-based verification metric that quantitatively evaluates the forecast skill at different spatial scales (Roberts 2008). The FSS was introduced by Roberts and Lean (2008) and is given by
FSS(n)=1FBSFBSref=11Ni=1N(F(n)iO(n)i)21N(i=1NF(n)i2+i=1kO(n)i2),
where F and O are the forecast and observed fractions, respectively, at each point for a given neighborhood of length n, and N is the number of pixels in the verification area. The numerator is the fractions Brier score, and the denominator is the reference fractions Brier score giving the possible largest (worst) case. The FSS value ranges from 0 to 1, with 0 indicating the worst possible mismatch between the forecast and observation and 1 indicating a perfect match.

It is important to determine an appropriate threshold to fairly evaluate the forecast performance by using the PQPF and FSS. Traditionally, choosing a threshold in physical units (e.g., 40 mm) verifies the quantitative rainfall forecast at a fixed rainfall intensity for all types of cases. However, choosing a threshold in terms of the occurrence frequency (percentile) focuses on the spatial error without considering the impact of the bias (Roberts and Lean 2008; Mittermaier and Roberts 2010; Mittermaier et al. 2013). Therefore, we design an adaptive threshold to combine the advantages of physical- and percentile-based thresholds. The QPESUMS rainfall in each grid within the target area was ranked to obtain the rainfall amount at the 85th and 95th percentiles, which denote the heavy and extreme rainfall amounts, respectively. The 85th percentile rainfall amounts (hereafter referred to as “R85”) in Cases I to IV are 28, 36, 33, and 41 mm, respectively. The 95th percentile rainfall amounts (hereafter referred to as “R95”) in Cases I to IV are 67, 54, 58, and 57 mm, respectively. The use of the R85/R95 threshold allows for quantitative comparisons between forecasts and observations, providing an adaptive standard for cases with different intensities.

1) PQPF

Figure 11 shows a comparison of the PQPF (shading) and QPESUMS rainfall (black contours) with the R85 threshold. In Case I, ZTD assimilation alone increases the TPW (Fig. 9i) and thus increases the rainfall in the Western Lowlands compared to NoDA (Figs. 11a,e), but the forecast probability in the Taipei basin is very low. In contrast, the PQPF of ZSDA is 30% higher than that of NoDA in the Taipei basin (Fig. 11i), and the PQPF of ZSDA_HT is 42% higher, although the location of heavy rain is shifted southeastward (Fig. 11m). Similar features can be observed in the other cases, where ZTD assimilation increases the forecast probability in the Western Lowlands (Figs. 11e–g), and SFC assimilation further improves the AT prediction skill in the Taipei basin (Figs. 11i–p). These results reveal that assimilating both kinds of ground-based observations is helpful for AT initialization and prediction, but frequent SFC assimilation is most beneficial for increasing the correctness of the AT location. Nevertheless, additional efforts are still needed for the accurate representation of heavy rainfall. For example, there is a limited impact of both kinds of observations on Case IV, where heavy rain is not captured in the Taipei basin in all experiments (Figs. 11d,h,l,p). Rainfall in the Snow Mountain Range is overestimated in Cases I and III. Additionally, the fact that all cases possess PQPFs lower than 60% in the target area suggests the need for more observations to reduce the large diversity in the ensemble forecast results.

Fig. 11.
Fig. 11.

(a) PQPF (%; shading) with the R85 threshold of NoDA for Case I. The black contours mark the area where the QPESUMS rainfall is higher than R85. The thickest to thinnest gray contours indicate terrain heights of 0, 100, 250, 500, 1000, and 2000 m, respectively. (b)–(d) As in (a), but for Cases II, III, and IV, respectively. (e)–(h) As in (a)–(d), but for ZDA. (i)–(l) As in (a)–(d), but for ZSDA. (m)–(p) As in (a)–(d), but for ZSDA_HT.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0149.1

2) FSS

In this study, we propose an innovative way to use the FSS at critical scales (Koch et al. 2017) to construct an informative verification diagram to distinguish the forecast skill with respect to the AT location and intensity that can be naturally adapted to the different cases. As shown in Fig. 12, the abscissa is the FSS with the R85 threshold and a 15-km length scale (R85-15km), reflecting the forecast skill of the smaller-scale location accuracy of heavy rainfall. The ordinate is the FSS with the R95 threshold and a 48-km length scale (R95-48km), reflecting the occurrence of extreme rainfall across the target area (48 × 48 km2). The closer the points are to the top-right corner, the better the forecast skills of both the rainfall location and intensity. To provide statistical insight into the full ensemble, the FSSs of the ensemble are sorted as the 25th, 50th and 75th percentiles (Q1, Q2 and Q3, respectively) and denoted with cross, triangle, and circle symbols, respectively, in Fig. 12.

Fig. 12.
Fig. 12.

(a) FSS verification diagram for Case I. The abscissa is the FSS with the R85 threshold and a 15-km length scale, and the ordinate is the FSS with the R95 threshold and a 48-km length scale. The crosses, triangles, and circles denote the first, second, and third quartiles, respectively, of the FSS of ensemble forecasts. The black, purple, blue, and red symbols denote NoDA, ZDA, ZSDA, and ZSDA_HT, respectively. The gray line denotes the regression line, and its slope is shown in the title. (b) As in (a), but for Case II. (c) As in (a), but for Case III. (d) As in (a), but for Case IV.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0149.1

Results in Fig. 12 clearly show that the FSS increases in the order of NoDA, ZDA, ZSDA, and ZSDA_HT for all four cases. The FSSs of all quartiles of NoDA and ZDA are mostly located at the bottom-left corner in all cases (i.e., the FSS approaches 0). The Q2 and Q3 FSSs of ZSDA lie in the middle of the diagrams, showing modest improvements in the prediction of the rainfall location and intensity. The FSSs show that ZSDA_HT significantly outperforms those of the other experiments for all quartiles. This evaluation confirms that assimilating densely distributed ZTD and SFC observations is helpful for AT prediction, and SFC assimilation every 10 min is critical to obtain the most accurate quantitative rainfall forecasts.

Furthermore, the regression line of the FSSs for all experiments is calculated for each case, and the slopes of the regression lines reflect the unique forecast features of these ATs. In Case I (Fig. 12a), the slope of the regression line is 0.68, showing that it is more challenging to capture the rainfall intensity than it is for the location, and only Q3 of the ZSDA_HT ensemble can capture extreme rainfall (the R95-48km FSS is 0.9). The predictability of the intensity and location in Case II is relatively moderate, as indicated by a slope of 1.14 (Fig. 12b). By assimilating the ZTD and adjusting moisture alone, ZDA in Case II is more improved than that in the other cases since Case II involves less wind directional changes in the Taipei basin (Fig. 3j). In Cases III and IV (Figs. 12c,d), the forecasts have lower R85-15km FSSs even for Q3 of the ZSDA_HT ensemble, as indicated by R85-15 km FSSs values of only 0.52 and 0.48, and the slopes of the regression lines are 1.81 and 1.61, respectively. This could be attributed to the fact that the ATs develop in mountainous areas where observational information is insufficient to improve the accuracy of the model state through DA cycles, and thus predicting the AT location is more challenging in these regions. Nevertheless, improvements in the intensity forecasts (R95-48km FSSs) remain obvious with ZSDA_HT in both cases. In summary, the FSS verification diagram can 1) quantitatively and concisely represent the location and intensity forecast skills of such a small-scale weather system, 2) characterize the forecast performance of various cases, and 3) highlight the benefits of frequent assimilation.

6. Discussion

a. Predictability of early forecasts

The results in section 5c show that both ZSDA and ZSDA_HT have the potential to predict the AT events 1 h in advance. However, a 1-h warning is a relatively small window for such a very short-term extreme AT event. Therefore, we further investigate whether assimilating ground-based observation can provide useful information in the earlier prediction of ATs. The earlier forecast performance of Case I is demonstrated using the FSS verification diagram (Fig. 13). Initialized with analyses after 1-, 2-, and 3-h DA, the first, second, and third mean forecasts start at 1200, 1300, and 1400 LST, respectively, each aiming to predict the AT event starting at 1500 LST. The first forecast (cross symbols, Fig. 13) in all experiments yields low FSSs and fails to capture either the rainfall location or intensity. Regarding the second forecast, both ZDA and ZSDA (purple and blue triangles, Fig. 13) underestimate the rainfall intensity (the R95-48km FSS is 0), but ZSDA captures the AT location (the R85-15km FSS is 0.6). ZSDA_HT (red triangle, Fig. 13) outperforms the other DA experiments at both FSS thresholds, suggesting that only frequent DA can provide a warning of this extreme AT event 2 h in advance. Regarding the third forecast, all of the forecasts are further improved. In particular, the R95-48km FSS increases from 0 to 0.68 for ZSDA. The ensemble-based DA relies on a spinup period to initialize a reliable forecast, and frequent DA can accumulate sufficient observational information more quickly and thus accelerate such spinup, whereas lower-frequency DA takes longer.

Fig. 13.
Fig. 13.

FSS verification diagram of the mean forecasts of Case I. The crosses, triangles, and circles denote the first, second, and third forecasts, respectively. The black, purple, blue, and red symbols denote NoDA, ZDA, ZSDA, and ZSDA_HT, respectively. Note that NoDA only has one forecast that starts at 0800 LST.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0149.1

The second forecast of ZSDA_HT reveals the key to improving early warnings in Case I. Figure 14 shows a comparison of the surface convergence field and rainfall between ZSDA and ZSDA_HT. Both analyses contain local convergence zones in the Linkou Tableland at 1300 LST (Figs. 14a,f), but ZSDA_HT exhibits stronger convergence. The convergence becomes more pronounced in ZSDA_HT than in ZSDA at 1400 LST (Figs. 14b,g). As a result, the rainfall from 1400 to 1500 LST of ZSDA_HT is heavier and better matches the QPESUMS rainfall (Figs. 14i,n), whereas the rainfall of ZSDA is limited and shifts southward to the Dahan River Valley (Fig. 14d). The rainfall induces cold outflow and divergence, gradually forming convergence zones in the Taipei basin at 1500 LST (Figs. 14c,h). Notably, the convergence of ZSDA_HT in the Taipei basin is narrower and is more meridionally aligned, so the AT develops southward of the Snow Mountain Range, similar to the QPESUMS (Figs. 14j,o). In addition, the low-level wind of ZSDA_HT converges and brings in more moisture in the observed rainfall areas (Figs. 14k–m), and the higher T2 (Fig. 7a) enhances the urban heat island effect, eventually leading to higher vertical instability and heavier rainfall. In conclusion, accurate location and intensity forecasts of such a very short-term and small-scale AT event require high-spatiotemporal resolution DA.

Fig. 14.
Fig. 14.

(a) The 10-m convergence (0.001 s−1) of the ZSDA analysis at 1300 LST. The black and thin gray arrows are the 10-m wind of the SFC data and model, respectively. The red boxes denote the area of the observed rainfall locations from 1400 to 1500 LST. The thickest to thinnest black contours indicate terrain heights of 0, 100, 250, 500, 1000, and 2000 m, respectively. (b),(c) As in (a), but for the second forecast of ZSDA at 1400 and 1500 LST. (d) Hourly rainfall of the second forecast of ZSDA from 1400 to 1500 LST. (e) As in (d), but from 1500 to 1600 LST. (f)–(j) As in (a)–(e), but for ZSDA_HT. (k)–(m) As in (a)–(c), but for the TPW difference (kg m−2) between ZSDA_HT and ZSDA. (n),(o) As in (d) and (e), but for QPESUMS.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0149.1

b. Impact of DA strategies on the surface temperature and sea breezes

Although assimilating the ZTD and SFC data has a significant impact on the AT forecasts in this study, there exist challenges in correcting the surrounding sea breeze, which enters the Taipei basin through the river valleys. This issue is reflected in 1) the dilemma from SFC wind and temperature corrections and 2) the impact of the cross-variable update of ZTD assimilation. In the following, we illustrate this issue using Case I, but the conclusions drawn here can be applied to the other cases.

In section 5a, we mentioned that the surface cold bias can be corrected at the analysis time by assimilation, despite the fact that the model integration keeps reintroducing this temperature bias (Fig. 7a). A correction is mainly applied over land due to the use of convective-scale localization. However, this increases the temperature differences between land and sea and thus unrealistically enhances the sea breeze. Figures 15a and 15b show that the sea-breeze biases in both western (more westerly flow) and eastern Taiwan (more easterly flow) increase through the DA cycles. To compensate for this effect, SFC 10-m wind assimilation continues to provide land-breeze corrections (Fig. 15c). Once T2 is assimilated more frequently, the T2 cold biases over land decrease, but the sea-breeze biases increase, resulting in higher wind biases for ZSDA_HT than for ZSDA over northern Taiwan in the final DA hour (Figs. 7e,f).

Fig. 15.
Fig. 15.

(a) U10 error (m s−1) of ZSDA_HT of the background mean compared to the SFC data at 1100 LST 22 Jul 2019. The thickest to thinnest black contours indicate terrain heights of 0, 100, 250, 500, 1000, and 2000 m, respectively. (b) As in (a), but at 1300 LST 22 Jul 2019. (c) U10 increment (m s−1) of ZSDA_HT at 1300 LST 22 Jul 2019.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0149.1

It should be noted that the model sea-breeze bias can greatly affect convection development near the coast. Strong sea breezes cause more inland convection in the Western Lowlands (Fig. 11). In addition, since the area of lowlands in western Taiwan is larger than that in eastern Taiwan, the enhancement in sea breezes is more obvious over western Taiwan. Consequently, convection develops more to the east in ZSDA_HT than it does in ZSDA for all cases (Fig. 11). To better constrain the local sea breeze and improve the location forecast of the AT event, we may need to rely on the near-surface temperature and wind observations offshore and over the Taiwan Strait (denoted in Fig. 15a).

ZTD assimilation in this study disables the cross-variable update, such as wind and temperature, and only hydrometeors are updated. With the ZSDA_ALL experiment, Fig. 16 shows the impact of ZTD assimilation with cross-variable updates (updating hydrometeors, wind, and potential temperature). Compared to those of ZSDA, ZSDA_ALL has similar Q2 errors (Figs. 16a,e), but its cold bias increases with ZTD assimilation at 15 and 45 min (Fig. 16b). Therefore, SFC assimilation at 0 and 30 min forces a larger T2 correction (Figs. 16b,f). This indicates that the T2 increment by ZTD assimilation through cross-variable correlation is an invalid correction. We speculate that the model error, such as the error in PBL parameterization or complex terrain, may affect the representativeness of the background error covariance derived from the ensemble, and thus, the cross-variable background error correlation becomes unreliable.

Fig. 16.
Fig. 16.

(a) Q2 (g kg−1) bias as compared to the SFC data over northern Taiwan during the DA period for Case I. The blue and orange lines denote ZSDA and ZSDA_ALL, respectively. (b)–(d) As in (a), but for the biases of T2 (°C), U10 (m s−1), and V10 (m s−1). (e)–(h) As in (a)–(d), but for the RMSE for each variable. (i) Analysis increments of Q2 (g kg−1) of ZSDA_ALL at 1245 LST. The thickest to thinnest black contours indicate terrain heights of 0, 100, 250, 500, 1000, and 2000 m, respectively. (j)–(l) As in (i), but for T2 (K), U10 (m s−1), and V10 (m s−1).

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0149.1

Although ZTD assimilation provides small wind increments (Figs. 16k,l) and the wind RMSE is similar between ZSDA_ALL and ZSDA (Figs. 16g,h), the 10-m wind biases decrease during model integration from 15 to 30 min and from 45 to 0 min (Figs. 16c,d). Echoing the previously mentioned findings, the increasing cold biases over land actually reduce the temperature differences between land and sea, thus weakening the overly intense sea breezes. This phenomenon is most obvious in the wide lowlands in western Taiwan and reflected in the U10 biases (Fig. 16c). This U10 error reduction is due to the indirect correction resulting from the cross-variable update. In addition, not updating the temperature field still causes higher cold biases in ZDA (Fig. 7a) since the increased moisture induces light rain and cools the surface, but it yields little benefit for local wind circulation (Figs. 7e–l).

In summary, incomplete correction due to the small localization or unrealistic cross-variable updates due to the model error actually degrades the impact of ground-based observation assimilation. In particular, frequent SFC assimilation and cross-variable updates of ZTD assimilation affect the temperature difference between land and sea and thus falsely alter the intensity of sea breezes and convective development.

7. Summary and conclusions

In this study, we investigated the impact of the frequent assimilation of dense ground-based observations, including ZTD and SFC data, on predicting the initialization of the very short-term and extreme AT events in the Taipei basin. The Taipei basin is surrounded by complex topography, including mountains and river valleys. Under weak synoptic-scale forcings, four intense cases with a rainfall rate higher than 40 mm h−1 were chosen to conduct a series of DA experiments using the convective WRF-LETKF system. The 3-h DA with frequent cycling was designed to end 1 h prior to the AT event.

Our results confirm that ZTD and SFC assimilation successfully reduces the surface humidity, temperature and wind errors in general. Regarding AT prediction, it is crucial to perform DA for better predicting convection earlier in the day near the target area, because the associated rainfall modulates the local atmospheric environment and significantly affects subsequent AT development. Assimilating ZTD every 30 min with mesoscale horizontal localization effectively adjusts the moisture distribution and improves the representation of scattered rainfall, especially in the Western Lowlands. However, ZDA still produces a low forecast probability for the AT events in the Taipei basin since the convection surrounding the Taipei basin still could not be captured. In addition to ZTD, ZSDA assimilates the densely distributed SFC data every 30 min using convective-scale horizontal localization, providing beneficial corrections to the local and near-surface wind and temperature fields, leading to largely reduced surface errors. Therefore, more moisture is transported and concentrated at the observed rainfall locations, leading to better prediction of early convection surrounding the Taipei basin and increasing the forecast probability of AT events. This finding indicates that the assimilation of both kinds of ground-based observations provides effective corrections to the near-surface dynamic and thermodynamic conditions, which is essential for AT formation.

For such a short-term and small-scale weather system, surface errors rapidly grow with a 30-min DA interval. ZSDA_HT, which performs SFC assimilation every 10 min, is designed to capture rapidly changing atmospheric conditions. Compared to ZSDA, ZSDA_HT better predicts early rainfall over complex terrain, so it can represent the rainfall outflow and wind direction change more accurately. A detailed analysis of Case I reveals that frequent SFC DA reduces the cold biases and establishes stronger convergence to transport moisture into the Taipei basin, giving rise to the rapid vertical development of high θe. By improving the local low-level dynamic and thermodynamic conditions, the ZSDA_HT forecasts outperform those of the other experiments, especially for rainfall intensity. This suggests that frequent DA is crucial to predict very short-term and extreme AT events.

A new verification metric based on the FSS is proposed in this study to comprehensively and concisely evaluate AT forecasts. Applying the concept of the critical scale, the R85-15km FSS evaluates the small-scale location accuracy, while the R95-48km FSS evaluates the forecast skill of extreme rainfall. With the use of the R85-15km (abscissa) and R95-48km FSSs (ordinate), the verification diagram displays clearly that forecast performance is improved by each DA method in increasing order: NoDA, ZDA, ZSDA, and ZSDA_HT. Furthermore, the slope of the regression line of the data points indicates the forecast behavior in each of four cases. It is more difficult to predict the AT intensity in Case I since it is the most extreme case among all cases, and it is challenging to predict the AT location in Cases III and IV because convective development occurs in mountainous areas where less station data are available to correct the model state.

We further investigated two issues regarding AT forecasting. The first issue is whether earlier forecasts can still predict the AT event accurately enough to provide practical information for civic response. The results presented here show that ZSDA and ZSDA_HT can capture the AT location 2 h in advance, while ZDA cannot. Only ZSDA_HT can predict the extreme rainfall intensity 2 h in advance among all experiments. It was found that initiating scattered and early convection by frequent SFC assimilation is the key to representing very local and fast-changing weather conditions, and thus, ZSDA_HT could provide useful early warnings. In other words, frequent DA accumulates observation information quickly and shortens the spinup period for initializing reliable forecasts.

The second issue is related to the impact of near-surface temperature correction on sea breezes, which further affects AT development. Although frequent SFC assimilation effectively reduces the T2 cold bias over land using convective-scale localization, the lack of correction offshore implicitly increases the temperature differences between land and sea, unrealistically enhancing the sea breeze. A reverse effect is observed when enabling cross-variable updates for ZTD assimilation, falsely increasing the T2 cold bias and diminishing the sea-breeze bias. The slight difference in near-surface atmospheric conditions alters the formation and development of AT, and this further influences the skill of location forecasting. Results imply that DA strategies such as mixed localization and cross-variable update can significantly affect the impact of the ground-based observations in a convective-scale EDA system, and they can be decisive when predicting the initialization of a short-term convection under weak synoptic conditions.

It should be noted that the mean forecast and ensemble forecasts share similar qualitative characteristics (Fig. 11 versus Fig. A2 in the appendix). The mean errors of the peak rainfall intensity in all cases are −45, −62, −31, and −30 mm for NoDA, ZDA, ZSDA, and ZSDA_HT, respectively. SFC assimilation undoubtedly improves the rainfall intensity forecast performance. However, the low PQPF and underestimations in the peak intensity suggest that the current ground-based observation network partially provides critical information, and thus we need more observations to reduce the errors and diversity of member forecasts in the ensembles, particularly in mountainous areas where the station density is low. It should also be noted that, for cases with smaller background ensemble spread, the observation errors are suppressed to amplify the observational impact in the assimilation. Therefore, the impact of the observations in operational forecasts may be less significant when the background ensemble spread is small with fixed observation errors. In addition, the local land–sea circulation is sensitive to the environmental conditions offshore and over the Taiwan Strait. Furthermore, the characteristics of the dynamic and thermodynamic conditions in the PBL are important for AT initialization. Therefore, vertical profiling instruments that observe the PBL at a high frequency are expected to improve the prediction of the vertical development of ATs and rainfall intensity. The complex terrain and the model error in the PBL may affect the representativeness of the ensemble-based background error covariance and thus diminish the DA impact. In future work, we will investigate the combined impact of assimilating dense ground-based observations, surrounding data from remote sensing measurements, and innovative PBL observations, such as water vapor DIAL and UAV data, on predicting extreme short-term heavy rain events.

1

The magnitude of the GEFS ensemble spread is case dependent and can vary more than double from case to case and for different areas.

Acknowledgments.

The authors thank the Central Weather Administration for providing the GNSS-ZTD and SFC data and the National Center for High-Performance Computing of the National Applied Research Laboratories for providing the computational resources. This work was supported by National Science and Technology Council Grants 110-2111-M008-029 and 110-2923-M-008-003-MY2.

Data availability statement.

The raw data supporting the conclusion of this article will be made available by the authors, without undue reservation. The NCEP GEFS ensemble is openly available at https://www.ncei.noaa.gov/products/weather-climate-models/global-ensemble-forecast. The GNSS ZTD data and 10-min surface station data can be applied for at the Central Weather Administration.

APPENDIX

Rainfall of QPESUMS and Mean Forecasts for Four Cases

Figure A1 shows the hourly rainfall of QPESUMS for Cases II to IV. Figure A2 compares the 2-h accumulated rainfall of mean forecasts with QPESUMS, and it is provided as the reference to show the similar qualitative characteristics between the PQPF from ensemble forecasts (Fig. 11) and mean forecasts.

Fig. A1.
Fig. A1.

(a1)–(a6) Hourly rainfall (mm) of the QPESUMS for Case II from 1000 to 1100, from 1100 to 1200, from 1200 to 1300, from 1300 to 1400, from 1400 to 1500, and from 1500 to 1600 LST 24 Jun 2022. The thickest to thinnest black contours indicate terrain heights of 0, 100, 250, 500, 1000, and 2000 m, respectively. (b1)–(b6) As in (a1)–(a6), but for Case III from 1000 to 1100, from 1100 to 1200, from 1200 to 1300, from 1300 to 1400, from 1400 to 1500, and from 1500 to 1600 LST 4 Jul 2022. (c1)–(c6) As in (a1)–(a6), but for Case IV from 1100 to 1200, from 1200 to 1300, from 1300 to 1400, from 1400 to 1500, from1500 to 1600, and from 1600 to 1700 LST 25 Aug 2022.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0149.1

Fig. A2.
Fig. A2.

(a) The 2-h accumulated rainfall (mm) of NoDA for Case I. The thickest to thinnest black contours indicate terrain heights of 0, 100, 250, 500, 1000, and 2000 m, respectively. (b)–(d) As in (a), but for Cases II, III, and IV, respectively. (e)–(h) As in (a)–(d), but for ZDA. (i)–(l) As in (a)–(d), but for ZSDA. (m)–(p) As in (a)–(d), but for ZSDA_HT. (q)–(t) As in (a)–(d), but for QPESUMS.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0149.1

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Save
  • Aksoy, A., D. C. Dowell, and C. Snyder, 2009: A multicase comparative assessment of the ensemble Kalman filter for assimilation of radar observations. Part I: Storm-scale analyses. Mon. Wea. Rev., 137, 18051824, https://doi.org/10.1175/2008MWR2691.1.

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    • Export Citation
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    • Search Google Scholar
    • Export Citation
  • Chen, I.-H., J.-S. Hong, Y.-T. Tsai, and C.-T. Fong, 2020: Improving afternoon thunderstorm prediction over Taiwan through 3DVar-based radar and surface data assimilation. Wea. Forecasting, 35, 26032620, https://doi.org/10.1175/WAF-D-20-0037.1.

    • Search Google Scholar
    • Export Citation
  • Chen, T.-C., S.-Y. Wang, and M.-C. Yen, 2007: Enhancement of afternoon thunderstorm activity by urbanization in a valley: Taipei. J. Appl. Meteor. Climatol., 46, 13241340, https://doi.org/10.1175/JAM2526.1.

    • Search Google Scholar
    • Export Citation
  • Cucurull, L., F. Vandenberghe, D. Barker, E. Vilaclara, and Z. Rius, 2004: Three-dimensional variational data assimilation of ground-based GPS ZTD and meteorological observations during the 14 December 2001 storm event over the western Mediterranean Sea. Mon. Wea. Rev., 132, 749763, https://doi.org/10.1175/1520-0493(2004)132<0749:TVDAOG>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Degelia, S. K., X. Wang, D. J. Stensrud, and D. D. Turner, 2020: Systematic evaluation of the impact of assimilating a network of ground-based remote sensing profilers for forecasts of nocturnal convection initiation during PECAN. Mon. Wea. Rev., 148, 47034728, https://doi.org/10.1175/MWR-D-20-0118.1.

    • Search Google Scholar
    • Export Citation
  • de Haan, S., 2013: Assimilation of GNSS ZTD and radar radial velocity for the benefit of very-short-range regional weather forecasts. Quart. J. Roy. Meteor. Soc., 139, 20972107, https://doi.org/10.1002/qj.2087.

    • Search Google Scholar
    • Export Citation
  • Do, P.-N., K.-S. Chung, P.-L. Lin, C.-Y. Ke, and S. M. Ellis, 2022: Assimilating retrieved water vapor and radar data from NCAR S-PolKa: Performance and validation using real cases. Mon. Wea. Rev., 150, 11771199, https://doi.org/10.1175/MWR-D-21-0292.1.

    • Search Google Scholar
    • Export Citation
  • Feng, Z., S. Hagos, A. K. Rowe, C. D. Burleyson, M. N. Martini, and S. P. de Szoeke, 2015: Mechanisms of convective cloud organization by cold pools over tropical warm ocean during the AMIE/DYNAMO field campaign. J. Adv. Model. Earth Syst., 7, 357381, https://doi.org/10.1002/2014MS000384.

    • Search Google Scholar
    • Export Citation
  • Giannaros, C., V. Kotroni, K. Lagouvardos, T. M. Giannaros, and C. Pikridas, 2020: Assessing the impact of GNSS ZTD data assimilation into the WRF modeling system during high-impact rainfall events over Greece. Remote Sens., 12, 383, https://doi.org/10.3390/rs12030383.

    • Search Google Scholar
    • Export Citation
  • Gustafsson, N., and Coauthors, 2018: Survey of data assimilation methods for convective-scale numerical weather prediction at operational centres. Quart. J. Roy. Meteor. Soc., 144, 12181256, https://doi.org/10.1002/qj.3179.

    • Search Google Scholar
    • Export Citation
  • Hsu, S. A., E. A. Meindl, and D. B. Gilhousen, 1994: Determining the power-law wind-profile exponent under near-neutral stability conditions at sea. J. Appl. Meteor., 33, 757765, https://doi.org/10.1175/1520-0450(1994)033<0757:DTPLWP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hwang, W.-C., P.-H. Lin, and H.-J. Yu, 2020: The development of the “Storm Tracker” and its applications for atmospheric high-resolution upper-air observations. Atmos. Meas. Tech., 13, 53955406, https://doi.org/10.5194/amt-13-5395-2020.

    • Search Google Scholar
    • Export Citation
  • Jones, T. A., K. Knopfmeier, D. Wheatley, G. Creager, P. Minnis, and R. Palikonda, 2016: Storm-scale data assimilation and ensemble forecasting with the NSSL experimental Warn-on-Forecast System. Part II: Combined radar and satellite data experiments. Wea. Forecasting, 31, 297327, https://doi.org/10.1175/WAF-D-15-0107.1.

    • Search Google Scholar
    • Export Citation
  • Katona, B., and P. Markowski, 2021: Assessing the influence of complex terrain on severe convective environments in northeastern Alabama. Wea. Forecasting, 36, 10031029, https://doi.org/10.1175/WAF-D-20-0136.1.

    • Search Google Scholar
    • Export Citation
  • Koch, J., G. Mendiguren, G. Mariethoz, and S. Stisen, 2017: Spatial sensitivity analysis of simulated land surface patterns in a catchment model using a set of innovative spatial performance metrics. J. Hydrometeor., 18, 11211142, https://doi.org/10.1175/JHM-D-16-0148.1.

    • Search Google Scholar
    • Export Citation
  • Kuo, K.-T., and C.-M. Wu, 2019: The precipitation hotspots of afternoon thunderstorms over the Taipei basin: Idealized numerical simulations. J. Meteor. Soc. Japan, 97, 501517, https://doi.org/10.2151/jmsj.2019-031.

    • Search Google Scholar
    • Export Citation
  • Lagasio, M., and Coauthors, 2019: A synergistic use of a high-resolution numerical weather prediction model and high-resolution Earth observation products to improve precipitation forecast. Remote Sens., 11, 2387, https://doi.org/10.3390/rs11202387.

    • Search Google Scholar
    • Export Citation
  • Lin, H.-C., J. Sun, T. M. Weckwerth, E. Joseph, and J. Kay, 2023: Assimilation of New York state mesonet surface and profiler data for the 21 June 2021 convective event. Mon. Wea. Rev., 151, 485507, https://doi.org/10.1175/MWR-D-22-0136.1.

    • Search Google Scholar
    • Export Citation
  • Lin, K.-J., S.-C. Yang, and S. S. Chen, 2022: Improving analysis and prediction of tropical cyclones by assimilating radar and GNSS-R wind observations: Ensemble data assimilation and observing system simulation experiments using a coupled atmosphere–ocean model. Wea. Forecasting, 37, 15331552, https://doi.org/10.1175/WAF-D-21-0202.1.

    • Search Google Scholar
    • Export Citation
  • Lindskog, M., M. Ridal, S. Thorsteinsson, and T. Ning, 2017: Data assimilation of GNSS zenith total delays from a Nordic Processing Centre. Atmos. Chem. Phys., 17, 13 98313 998, https://doi.org/10.5194/acp-17-13983-2017.

    • Search Google Scholar
    • Export Citation
  • Miao, J.-E., and M.-J. Yang, 2020: A modeling study of the severe afternoon thunderstorm event at Taipei on 14 June 2015: The roles of sea breeze, microphysics, and terrain. J. Meteor. Soc. Japan, 98, 129152, https://doi.org/10.2151/jmsj.2020-008.

    • Search Google Scholar
    • Export Citation
  • Mittermaier, M., and N. Roberts, 2010: Intercomparison of spatial forecast verification methods: Identifying skillful spatial scales using the fractions skill score. Wea. Forecasting, 25, 343354, https://doi.org/10.1175/2009WAF2222260.1.

    • Search Google Scholar
    • Export Citation
  • Mittermaier, M., N. Roberts, and S. A. Thompson, 2013: A long-term assessment of precipitation forecast skill using the fractions skill score. Meteor. Appl., 20, 176186, https://doi.org/10.1002/met.296.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., and Coauthors, 2016: “Big data assimilation” revolutionizing severe weather prediction. Bull. Amer. Meteor. Soc., 97, 13471354, https://doi.org/10.1175/BAMS-D-15-00144.1.

    • Search Google Scholar
    • Export Citation
  • Pan, S., J. Gao, T. A. Jones, Y. Wang, X. Wang, and J. Li, 2021: The impact of assimilating satellite-derived layered precipitable water, cloud water path, and radar data on short-range thunderstorm forecasts. Mon. Wea. Rev., 149, 13591380, https://doi.org/10.1175/MWR-D-20-0040.1.

    • Search Google Scholar
    • Export Citation
  • Roberts, N., 2008: Assessing the spatial and temporal variation in the skill of precipitation forecasts from an NWP model. Meteor. Appl., 15, 163169, https://doi.org/10.1002/met.57.

    • Search Google Scholar
    • Export Citation
  • Roberts, N., and H. W. Lean, 2008: Scale-selective verification of rainfall accumulations from high-resolution forecasts of convective events. Mon. Wea. Rev., 136, 7897, https://doi.org/10.1175/2007MWR2123.1.

    • Search Google Scholar
    • Export Citation
  • Rohm, W., J. Guzikowski, K. Wilgan, and M. Kryza, 2019: 4DVAR assimilation of GNSS zenith path delays and precipitable water into a numerical weather prediction model WRF. Atmos. Meas. Tech., 12, 345361, https://doi.org/10.5194/amt-12-345-2019.

    • Search Google Scholar
    • Export Citation
  • Seko, H., T. Miyoshi, Y. Shoji, and K. Saito, 2011: Data assimilation experiment of precipitable water vapor using the LETKF system: Intense rainfall event over Japan on 28 July 2008. Tellus, 63A, 402414, https://doi.org/10.1111/j.1600-0870.2010.00508.x.

    • Search Google Scholar
    • Export Citation
  • Singh, R., S. P. Ojha, N. Puviarasan, and V. Singh, 2019: Impact of GNSS signal delay assimilation on short range weather forecasts over the Indian region. J. Geophys. Res. Atmos., 124, 98559873, https://doi.org/10.1029/2019JD030866.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. NCAR Tech. Note NCAR/TN-475+STR, 113 pp., https://doi.org/10.5065/D68S4MVH.

  • Sun, J., and Coauthors, 2014: Use of NWP for nowcasting convective precipitation: Recent progress and challenges. Bull. Amer. Meteor. Soc., 95, 409426, https://doi.org/10.1175/BAMS-D-11-00263.1.

    • Search Google Scholar
    • Export Citation
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  • Fig. 1.

    (a) Terrain height (m; shading). (b) The ground-based observation distribution. The yellow circles, cyan squares, and magenta triangles denote the manned surface stations, automatic surface stations, and ZTD stations, respectively. (c) The model domain of the experiments.

  • Fig. 2.

    (a) The maximum radar reflectivity (dBZ) of QPESUMS at 1200 LST 22 Jul 2019. The thickest to thinnest black contours indicate terrain heights of 0, 100, 250, 500, 1000, and 2000 m, respectively. (b)–(f) As in (a), but for 1300, 1400, 1500, 1600, and 1700 LST 22 Jul 2019, respectively. (g)–(l) As in (a)–(f), but for the hourly rainfall (mm) of QPESUMS from 1100 to 1200, from 1200 to 1300, from 1300 to 1400, from 1400 to 1500, from 1500 to 1600, and from 1600 to 1700 LST 22 Jul 2019, respectively.

  • Fig. 3.

    (a) Surface wind speed (m s−1; shading) and wind direction (arrows) of NCEP final analysis at 0800 LST for Case I. (b)–(d) As in (a), but for Cases II, III, and IV, respectively. (e) The 10-m wind direction of the surface stations at 0400 LST (blue arrows) and 1400 LST (red arrows) for Case I. The terrain heights (m) are shown with grayscale shading. (f)–(h) As in (e), but for Cases II, III, and IV, respectively. (i),(l) As in (e) and (h), but at 1400 LST (blue arrows) and 1500 LST (red arrows), respectively. (j),(k) As in (f) and (g), but at 1300 LST (blue arrows) and 1400 LST (red arrows), respectively.

  • Fig. 4.

    (a) The 2-h accumulated rainfall (mm) of QPESUMS for Case I. The magenta box indicates the target area. The thickest to thinnest black contours indicate terrain heights of 0, 100, 250, 500, 1000, and 2000 m, respectively. (b)–(d) As in (a), but for Cases II, III, and IV, respectively.

  • Fig. 5.

    (a) T2 (°C; circles) and 10-m wind (arrows) at the surface stations at 1500 LST 22 Jul 2019. The locations of the Linkou and Taipei surface stations are marked with blue and dark red circles, respectively, while the locations of the Linkou and Taipei ZTD stations are marked with blue and dark red triangles, respectively. The thickest to thinnest gray contours indicate terrain heights of 0, 100, 250, 500, 1000, and 2000 m, respectively. (b) Time series of T2 (°C; lines), 10-m wind directions (arrows), and rainfall rates (mm min−1; bars) at the Taipei (in red) and Linkou (in blue) surface stations. The direction of the wind arrows corresponding to the north is “up.” (c) Time series of the ZTD (cm; solid lines) and PW (cm; dashed lines) at the Taipei (red) and Linkou (blue) ZTD stations.