Impact of assimilating Formosat-7/COSMIC-II GNSS radio occultation data on heavy rainfall prediction in Taiwan

This study investigates the impact of assimilating Formosat-7/COSMIC-II (FS7/C2) radio occultation (RO) refractivity data on predicting the heavy rainfall event that occurred in Taiwan on August 13, 2019. This event was characterized by heavy rainfall over the coastal region of central and southwestern Taiwan. Our investigation is performed using the Weather Research and Forecasting-Local Ensemble Transform Kalman Filter. Generally, assimilating the RO data increases the amount of moisture over the northern South China Sea (SCS) and the Pearl River area in southern China. It was expected that assimilating the RO data would improve low-level moisture analysis, given that more RO data are available for the lower atmosphere compared to those from Formosat-3/COSMIC-I. However, our results show that the experiment that does not include the RO data below 3 km facilitates better rainfall prediction over Taiwan in terms of the intensity and location of heavy rainfall. This heavy rainfall event can be attributed to moisture transport from the Pearl River area, where the RO data at the altitude of 3–5 km provide effective moisture enhancement to deepen the high-moisture layer. The experiment using the local spectral width (LSW) to conduct the quality control (QC) also helps improve rainfall prediction. However, such an LSW-based QC procedure tends to reject significant amounts of RO data 3 km above the land. Based on this case study, our results show that the QC procedure brings a larger impact to rainfall prediction than counterparts that adjust the observation error variance. A sophisticated QC procedure should be developed to optimize the impact of low-level RO data. Assimilating FS7/C2 RO data above 3 km improves moisture and rainfall prediction. LSW-based QC shows that RO data quality is sensitive to the land-sea distribution. QC is more crucial to optimize the low-level RO assimilation than R adjustment. Assimilating FS7/C2 RO data above 3 km improves moisture and rainfall prediction. LSW-based QC shows that RO data quality is sensitive to the land-sea distribution. QC is more crucial to optimize the low-level RO assimilation than R adjustment.


Terrestrial, Atmospheric and Oceanic Sciences
Page 2 of 24 Chang and Yang Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:7 Ionosphere and Climate (FORMOSAT-3/COSMIC; Anthes et al. 2008, hereafter FS3/C). GNSS-RO complements microwave and infrared satellite observations with a high vertical resolution under all weather conditions, providing valuable information about temperature and moisture. FS3/C has six low-earth orbiting (LEO) satellites. This constellation system receives an average of 1800 atmospheric profiles each day (Fong et al. 2009) and has contributed the most RO profiles since its launch in April 2006 . FS3/C adopts high inclination angles, with a coverage focusing on mid latitudes. In relative terms, data availability becomes limited at lower latitudes, especially in the tropics, where many severe weather systems originate. Therefore, the likelihood of collecting RO data in an area sensitive to severe weather systems is low. As the follow-on mission of FS3/C, the FORMOSAT-7/COSMIC-2 (FS7/C2) project has been proposed with another six LEOs to replenish the RO data. The FS7/C2 constellation is designed to have a smaller inclination angle in order to ensure better coverage over the lower latitudes. Following its successful launch on June 25, 2019, FS7/C2 has offered up to 5000 profiles per day with the ability to receive signals from both GNSS and GLObal NAvigation Satellite System (GLONASS). In addition, FS7/C2 uses an advanced GNSS receiver, which allows deeper penetration into the lower atmosphere, enabling more data to be attained from here ). Many studies of RO assimilation have demonstrated its positive impacts on the prediction of severe events, such as heavy rainfall episodes caused by the Mei-Yu front Huang et al. 2016), and tropical cyclones Hsiao et al. 2012). These benefits have been attributed to either the improvement of the low-level moisture field after the assimilation of low-level RO data Yang et al. 2014) or the use of an advanced observational operator (Healy et al. 2007;Yang et al. 2014;Chen et al. 2018Chen et al. , 2020. Using RO data below 1 km (the altitude means the geometric height in this study without a specific note), Yang et al. (2014) have shown that assimilating FS3/C's RO bending angle improves heavy rainfall prediction due to the enhancement of moisture transport from the ocean upstream. The improvement of the moisture field also enhances low-level convergence, which is essential for predicting the intensity and the location of heavy precipitation. These findings help anticipate the positive impact of FS7/C2 assimilation on predictions of moisture transport and precipitation.
Before the FS7/C2 reaches their designated mission orbits to offer the entire designed RO coverage, many studies have been conducted to investigate the characteristics of FS7/C2's RO observation and its application to numerical weather prediction (NWP). Ho et al. (2020) have compared the first few weeks of FS7/C2's RO observation with Vaisala RS41 radiosonde data to examine the former's data quality. They show that the mean refractivity biases and the uncertainty of FS7/C2 are compatible with those of FS3/C. The retrieved water vapor exhibits negative biases from the surface to an altitude of 5 km geometric height. Chen et al. (2021) have compared FS7/C2's observations against airborne and ship soundings from a chartered mission over the oceanic region of the South China Sea (SCS), and demonstrate that FS7/C2 has negative biases in vapor pressure in the lower troposphere. The negative biases of FS7/C2 data are consistent with other RO data sets (e.g., EUMET-SAT Metop-A/B/C) and global analyses (e.g., National Centers for Environmental Prediction Final operational global analysis, NCEP FNL). Chen et al. (2021) have also noted that almost 80% of FS7/C2 observations penetrate below 1 km, while this is only true of 40% of FS3/C observations. As regards the application of NWP, Lien et al. (2021) are the first to assimilate FS7/C2 observations with the operational global NWP system at Central Weather Bureau (CWB). With a 7-month parallel semioperational experiment, the FS7/C2 RO assimilation exhibits significantly positive impacts on temperature, height and wind fields in the tropical regions and moisture fields in the mid-troposphere. The assimilation of FS7/C2's RO observation became operational at the European Centre for Medium-Range Weather Forecasts (ECMWF; Healy 2020) and NCEP  in March and May 2020, respectively.
The quality of RO data, especially at lower levels, is crucial to optimizing their impact in NWP. The superior penetration rate of FS7/C2 to FS3/C allows more RO products (such as refractivity and bending angle) to be retrieved near the surface, but it does not guarantee the quality of the retrieval products (Gorbunov 2020). In particular, the uncertainty of RO data depends on the spatial variability of the moisture (Ho et al. 2020), which becomes larger in the lower troposphere. Hence, although FS7/C2 shares similar characteristics with FS3/C, issues regarding quality control (QC) and the reestimation of the observation error are essential to optimizing the assimilation of FS7/C2 data.
Many QC processes have been proposed to identify the data quality of RO (Cucurull et al. 2007(Cucurull et al. , 2013Poli et al. 2009;Cucurull 2010), such as the super-refractivity issue in the lower troposphere. Recently, Liu et al. (2018; hereafter L18) introduced a new QC process with the local spectral width (LSW) of RO signals. LSW is used to measure uncertainties of the retrieved bending angle and refractivity; detailed information is given by L18. An increase in the LSW in the lower troposphere is mostly related to random refractivity irregularities, resulting in uncertainties of the retrieved variables. L18 suggest that the LSW can be used to detect low quality RO retrievals, serving as an indicator for the QC procedure. They further suggest that when the LSW exceeds 35%, the RO retrievals are of poor quality, and so all data below this altitude should be discarded. Hence, in this study, the highest altitude of the LSW exceeding 35% is denoted as the LSWH. L18 demonstrate that a positive impact can be obtained by using LSW-based QC processes rather than traditional innovation-based QC processes.
Various studies have shown that the RO observation error depends on the altitude, latitude, and season (Kuo et al. 2004;Chen et al. 2011;Bowler 2020;Xu and Zou 2021). For instance, Kuo et al. (2004) have shown that the lower tropical troposphere has a large observation error, attributed to the complicated structure of humidity, super-refraction and receiver tracking errors. Rather than pursuing the observation error directly related to the season and latitude, Bowler (2020) has suggested that the average background temperature between the surface and 20 km impact height can be used as a new predictor for estimating the RO observation error. The observation uncertainty estimated by the average temperature, altitude and satellite identifier improves the forecast skill at the Met Office NWP system. L18 also suggest that the LSW could be used to adjust the RO observation error covariance. To explore the possibility of using FS7/C2's RO observation more effectively, different QC procedures and observation error estimation strategies are examined in this study.
In Taiwan, predicting heavy rainfall events under multi-scale interactions is challenging. Factors that affect the prediction of extreme precipitation over southwestern Taiwan include the intensity and the location of tropical cyclones (TC), the transport of moist and warm flow and heat via the prevailing southwesterly monsoonal flow, the complex orography, and the land-sea breeze in the coastal region. Even if they are not directly affected by TC, some heavy rainfall events here result from the Asian monsoon circulation's interactions with the TC circulation (Chen and Wu 2016). Yu and Cheng (2014) have found that when a westward-moving typhoon passes central or northern Taiwan, the prevailing southwesterly monsoonal flow is enhanced by the outer circulation of TC, intensifying the rainfall over Taiwan. From mid-July to August, the convective systems embedded in the monsoon flow are an important source of rainfall in southwestern Taiwan (Chen et al. 2004). These convective systems can initiate over southern China with the help of the oceanic low-level flow (Du et al. 2020). Lin et al. (2001) have demonstrated that synoptic and mesoscale environmental features, such as the presence of a very moist low-level jet, can aggravate orographic precipitation. Given the complex, high-altitude, mountainous terrain of Taiwan, the orographic effect further adds to the complexity of the location of heavy rainfall. Focusing on moisture transport, this study aims to investigate the impact of RO assimilation with different strategies by adjusting the QC processes and observation error variance.
This paper is organized as follows. Section 2 describes the experimental settings, including the selected precipitation case, the setup of the Weather Research and Forecasting (WRF)-Local Ensemble Transform Kalman Filter (WRF-LETKF) system, and the design of the sensitivity experiments. Section 3 presents the moisture analyses. Section 4 provides the results of the deterministic forecast for predicting heavy rainfall in Taiwan. Section 5 discusses the importance of the QC processes and the estimation of observation error variance for RO assimilation. Finally, Sect. 6 provides a conclusion. The rainfall event that occurred in Taiwan during mid-August 2019 was mainly caused by the interaction between the southwesterly flow and the circulation of Typhoon Lekima. However, the development of the weather systems near Taiwan also became tangled with Typhoon Krosa, given the latter's large size circulation. Based on the synoptic weather conditions, this rainfall episode can be categorized into three stages, each with its own rainfall types and patterns over Taiwan. At stage one (August 10-11, Fig. 1a), Typhoon Lekima had passed northern Taiwan and moved northward to inland China. Enhanced by the circulation of Lekima, the moist southwesterly flow moved across the northern SCS and extended to the Bashi Channel. Precipitation at this stage was mainly accumulated over the mountain region because the moist airflow impinged on the Central Mountain Range. At stage two (August 12-14, Fig. 1b), Typhoon Lekima had moved far away from Taiwan. Given that the enhancement caused by TC was declined, the southwesterly flow became weaker and changed to westerly to west-southwesterly over the SCS. Meanwhile, Typhoon Krosa moved northwestward. Its circulation was approaching but was yet to affect Taiwan. At this stage, the impact from both TC circulations was actually limited in the Taiwan area. Instead, this area was dominated by the prevailing southwesterly flow, the low-level flow split around the southwestern coast of Taiwan, and an orographic blocking effect was induced. As a consequence, heavy rainfall was concentrated in the coastal region of western Taiwan. At stage three (August 15-17, Fig. 1c), Typhoon Krosa moved further northwestward and made landfall in Japan at this stage. However, due to this typhoon's large size (the radius of 34 kts reached 400 km before landfall), its circulation was still able to enhance the southwesterly monsoonal flow. Heavy precipitation was observed in the mountainous area of southern Taiwan. The heavy precipitation during the second stage has lower predictability than the other stages owing to the multi-scale interaction and coastal-type precipitation. It is challenging to predict the location and the amount of the heaviest rainfall in this event because a good rainfall prediction requires a good description of moisture transport, a proper representation of TC circulation, the southwesterly flow, and its interaction with the mountainous terrain in southern Taiwan. Therefore, the rainfall event during the second stage is used below as a case study for investigating FS7/C2's RO assimilation. The primary focus of this study is the impact of RO assimilation on moisture modification and the follow-up rainfall prediction.

The WRF-LETKF system
WRF-LETKF (Yang et al. 2012) is a regional data assimilation system that combines the LETKF (Hunt et al. 2007) with the WRF model (Skamarock et al. 2008). The ensemble data assimilation system has the advantage of using the flow-dependent background error covariance. This data assimilation (DA) system has been used to investigate the predictability of the severe mesoscale weather systems that affect Taiwan, including TC (Yang et al. 2012;Chang et al. 2014Chang et al. , 2020Lin et al. 2018) and the Mei-Yu frontal system .
This system assimilates surface pressure from synoptic surface stations, wind and temperature from soundings and upper-air reports, satellite winds from atmospheric motion vectors (AMV), and refractivity from FS7/C2's RO observation with a local operator ). These observations are preprocessed with the standard QC processes of WRFDA (Barker et al. 2012). This study uses refractivity as the first step to verify the impact of RO assimilation. Figure 2 presents the locations of the RO profiles on different days. The red, purple, green, blue and black dots mean that the RO profiles penetrate to 500 m, 500 m to 1 km, 1-2 km, 2-3 km, and above 3 km, respectively. Over the ocean, there are considerable RO data available within the planetary boundary layer (PBL). During our assimilation period, 74.6% of the RO profiles Page 5 of 24 Chang and Yang Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:7 reach below 1 km and 94.8% below 3 km. Therefore, it is expected that numerous low-level observations will provide moisture adjustment. We note that the observation error of the RO refractivity used in WRF-LETKF follows the lookup table provided by Chen et al. (2011). It depends on the altitude, with a maximum value of 3% at the surface. In the QC step, all the observations pass the QC processes (such as the super-refraction check) of WRFDA as an off-line quality control.

Experimental setup
WRF model version 4.0 is used in this study. During the assimilation cycles, the WRF is run with a single domain with a horizontal grid spacing of 15 km (366 × 246 grid points) and 54 stretched vertical layers with the model top arranged at 50 hPa. An additional nested domain with a 2 km horizontal resolution (471 × 356 grid points) is used for the deterministic forecast. The physical parameterizations include the Goddard Scheme (Tao et al. 2016) for the cloud microphysics, the Rapid Radiative Transfer Model (RRTM) Longwave Scheme (Mlawer et al. 1997), and the Goddard Shortwave Scheme (Chou and Suarez 1994) for radiative forcing, and Yonsei University (YSU) for the PBL scheme (Hong et al. 2006). An additional physics setting associated with the YSU PBL scheme is used to correct the surface winds (Jiménez et al. 2012). The Kain-Fritsch Scheme (Kain 2004) for cumulus parameterization is applied only in the outer domain.
To initialize the ensemble for data assimilation, two sets of ensemble forecasts with a total of 42 members are generated with the initial conditions taken from the NCEP Global Ensemble Forecast System's (GEFS) one-degree data at 1800 UTC, August 8, 2019, and 0000 UTC, August 9, 2019, and are spun up to 1200 UTC August 9, 2019. With these 42 ensemble members, the WRF-LETKF analysis is performed with an assimilation interval of 6 h from 1200 UTC, August 9 to 1200 UTC, August 12. Deterministic forecasts with Fig. 2 The distribution of RO profiles on August a 9, b 10, c 11, and d 12, 2019. The cross, star, x and dot symbols denote the RO observations available at 0000, 0600, 1200, and 1800 UTC, respectively. The red, purple, green, blue and black indicate that the lowest altitude of the RO profile is below 500 m, 500 m to 1 km, 1-2 km, 2-3 km, and above 3 km, respectively Page 6 of 24 Chang and Yang Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:7 nested domains are then initialized with the mean of the analysis ensemble, with a focus of the precipitation on August 13. Table 1 lists the assimilation experiments. The CNTL experiment only assimilates the conventional observations and satellite air motion vector (AMV). In addition to the observations used in CNTL, the RO_all experiment assimilates the RO refractivity data obtained from FS7/C2. A comparison of the CNTL and RO_all experiments demonstrates the impact of FS7/C2's RO observation assimilation on this extreme heavy rainfall case. Assimilating better quality RO data with an appropriate observation error covariance is essential to optimizing the current RO assimilation. Thus, two sets of sensitivity experiments are conducted to investigate the impact of using different strategies of data QC processes and the observation error variance. The QC sensitivity experiments investigate the impact of adding additional QC criteria to the standard QC processes. According to Lien et al. (2021), large amounts of low-level RO data are rejected below 3 km with the QC procedure in the Gridpoint Statistical Interpolation (GSI) DA system. Since the QC procedure used in the WRFDA is different from the GSI, an experiment referred to as RO_3kmQC, is designed to brutally reject all RO observations below 3 km. Another experiment, RO_LSWQC, follows the suggestion of L18 to reject all RO data below the LSWH. This sensitivity test anticipates understanding the impact of the low-level RO observation and whether the LSW can serve as an indicator of QC. Rather than rejecting the low-level observation, keeping it but adjusting the observation error covariance provides an alternative way of taking advantage of the observational information. Therefore, the error variance for the RO observation below 3 km is adjusted, increasing linearly from the default value at 3 km to 10% at the surface. This experiment is referred to as RO_modR. We note that the optimal estimation of the observation error variance should depend on the DA system and the NWP model. However, the re-estimation for the WRF-LETKF should be conducted after the FS7/C2 satellites have fully entered their mission orbits, enabling the uniform observation distribution to be obtained.

Impacts of RO data assimilation on the moisture field
We first illustrate that assimilating the RO refractivity can modify the moisture field with the analysis increment of the water vapor mixing ratio at the levels of 950 and 700 hPa at 0000 UTC, August 10 (i.e., the third DA cycle; Fig. 3). Due to the absence of observations in the open ocean, the CNTL experiment has very limited moisture increment over the ocean at 950 hPa except a slight adjustment is found over the SCS in the lower troposphere ( Fig. 3a) and has almost no moisture correction derived at 700 hPa over the SCS. In the RO_all experiment, significant moisture corrections are associated with the TC circulation and southwesterly wind over the SCS. For example, a strong moisture correction is presented around the island of Hainan at 950 hPa ( Fig. 3b), which is greatly affected by the FS7/C2 observations below 1 km. A significant correction in the Bashi Channel at 700 hPa corresponds to the RO observations there (the green box in Fig. 3d). This correction affects the subsequent establishment of a moist environment for convection and precipitation. Furthermore, the RO observation is able to correct the moisture field embedded in the circulation of Typhoon Krosa (the blue box in Fig. 3d) and further enhances its intensity with more assimilation cycles (not shown). It is obvious that assimilating FS7/C2's RO observation provides significant moisture adjustments in the lower troposphere, over both land and ocean.
The differences among the analysis increments of CNTL, RO_all and RO_3kmQC highlight the impact of the RO data below 3 km on the moisture in the lower troposphere. Although the RO data in the lower troposphere are discarded in RO_3kmQC, the WRF-LETKF is able to correct the variables at lower levels through the vertical error correlation estimated by the ensemble. With the purpose of predicting the heavy rainfall in Taiwan on August 13, we focus on the moisture analysis and corresponding analysis increments at 950 hPa and 700 hPa at 0000 UTC, August 12 (Fig. 4). Nevertheless, we should emphasize that the impact is accumulated through analysis cycles. First, the CNTL experiment has a positive moisture increment in Guangdong province at 950 hPa. However, this adjustment becomes weaker in the RO_all and even shows a negative adjustment (green box). Discarding the RO observation below 3 km maintains this positive increment over southern China as highlighted in the green box of Fig. 4c. This difference further affects the low-level moisture transport with the prevailing westerly wind. At 700 hPa, the positive increment of RO_3kmQC over southern China extends to the coastline of southeastern China, while RO_all exhibits increment with a scattered pattern. Compared with CNTL, the positive increment shown in RO_3kmQC is larger over the northern Pearl River basin, but has a less extension toward upstream. It should also be noted that the RO observation southwest of Taiwan provides a positive moisture increment at 700 hPa, while CNTL exhibits a negative increment extending from the Taiwan Strait to the northern part of the SCS. The comparison of moisture increment at 700 hPa indicates that the deep moisture layer (moisture content) is expected to be significantly different among different analyses. We use the moisture analysis at 700 hPa ( Fig. 5) from 1200 UTC 11 August to 0000 UTC 12 August to illustrate how RO_3kmQC gradually establishes the high moisture content from southern China to SCS. At 1200 UTC 11 August, all the experiments have exhibited a high moisture zone from southern China to offshore of southeastern China and the Taiwan Strait and the RO_3kmQC has the moistest environment over SCS in general. Compared with CNTL and RO_all, the higher moisture content in RO_3kmQC becomes even more evident in the Pearl River basin and its upstream at 1800 UTC 11 August. We also note that at this time, deep convections developed vigorously over southern China, according to the infrared Page 8 of 24 Chang and Yang Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:7 satellite images. Combining a moist background evolving from Fig. 5f and broad positive moisture increment (Fig. 4f ), the high moisture zone in RO_3kmQC is well established from the Pearl River basin to the northern SCS and southwest of Taiwan at 0000 UTC 12 August, while the CNTL and RO_all analyses show a relatively drier zone from southwest to south of Taiwan. The characteristic of the deep moisture layer is further demonstrated by a cross-section of the moisture field, extending from the Pearl River area to southwestern Taiwan (the red dashed line in Fig. 5g). As shown in Fig. 6, three analyses exhibit moist conditions (higher than 16 g kg −1 ) below 850 hPa, particularly over the ocean. As indicated by the isopleth of the water vapor mixing ratio of 12 g kg −1 of RO_3kmQC, the moisture layer of RO_3kmQC in the Pearl River estuary (112.5-116E) is much deeper than that of the other experiments. With the prevailing westerly wind in this region, one can expect more moisture to be transported eastward. Moisture transport and its impact on precipitation prediction will be discussed further in Sect. 4.2. Our results suggest that RO assimilation increases the amount of moisture over southern China, SCS and southern Taiwan. Assimilating the RO observation above 3 km is very effective in providing a moister environment due to the moisture correction above the PBL, which could be critical for the heavy rainfall downstream in Taiwan.
We should note that all three experiments have weaker southerly wind components in southern Taiwan compared with the ECMWF reanalysis at 0000 UTC, August 12. This is attributed to the over-estimated intensity and size of the simulated Typhoon Krosa in all experiments. At 1200 UTC, 10 August, the simulated Typhoon Krosa in CNTL reaches its strongest intensity during the assimilation period, with a minimum sea level pressure (MSLP) of 953 hPa. The MSLP Are as in a-c, but at 700 hPa. The black, red, and blue cross symbols indicate the location of RO profile with LSW smaller than 35%, LSW larger than 35% at the altitude above and below 3 km, respectively Page 9 of 24 Chang and Yang Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:7 issued by the Japan Meteorological Agency (JMA) was 965 hPa at that time. During the whole assimilation period, the MSLP of the simulated typhoon in CNTL is lower than 970 hPa, which is stronger than the intensity issued by the JMA. With the RO assimilation, the MSLP of Typhoon Krosa in RO_all is about 2-hPa lower than that in CNTL during the assimilation window. Such difference in TC development affects the TC circulation as well. Several reasons could cause a less realistic intensification in Krosa's development, such as neglecting the TC-ocean interaction. The cause of why RO assimilation leads to a less realistic intensification in Krosa's development is under investigation. The intense simulated typhoon leads to a larger TC circulation that affects the prevailing wind near southern Page 10 of 24 Chang and Yang Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:7 Taiwan. However, assimilating the RO data only slightly increases the southerly wind component over the northern SCS, and thus the westerly wind dominates.

Moisture analysis of the sensitivity experiments
The anticipation of RO assimilation is to provide a more accurate moisture analysis, especially with the aid of the RO observation available in the lower troposphere. However, the result shown above implies that assimilating the observations below 3 km could lead to a drier environment, which does not support the convection in the reality. The question arises whether the moisture adjustment is less robust due to the uncertainty in the data quality. Thus, a sensitivity test was conducted to apply the LSWbased QC to identify the good quality RO observations below 3 km and to reject the poor quality RO data. Figures 7a and 7b show the moisture analysis increment of RO_LSWQC at 0000 UTC, August 12. The RO locations denoted in black, red and blue indicate that the profile has no LSW exceeding 35%, or the LSWH above or below 3 km, respectively. That is, according to L18, for the RO profile with LSWH above 3 km (denoted in red), the RO observations below 3 km are correctly discarded in RO_3kmQC. Conversely, discarding the RO observations below 3 km could be inappropriate for the profiles denoted in black and blue, because the data below 3 km may have good quality and provide an effective correction. Compared with RO_all, RO_LSWQC is expected to further detect the RO data with large uncertainties mainly caused by the retrieval processes, discarding the unsuitable observations.
We first focus on the RO profile located offshore of southwestern Taiwan (denoted as profile A in Fig. 7a). Compare with the RO_all (Fig. 4e) and the RO_3kmQC (Fig. 4f ), RO_LSWQC does not gain any increment near this profile at lower levels. Figure 7d shows the LSW (the thick black line) and the moisture increment interpolated to this RO location for the RO_all (red line), the RO_3kmQC (blue line), and the RO_LSWQC (purple line). As shown in Fig. 7d, the LSWH of this profile is 5 km. Therefore, the analysis increment of RO_LSWQC is small below 5 km, but RO_all and RO_3kmQC reveal a large adjustment there. At around 2 km, RO_all shows a negative adjustment, in contrast to the other experiments with the QC process. Such different impacts on the RO assimilation will be accumulated as the number of DA cycle increases. Figure 7c shows the moisture Fig. 6 Cross-section of the a CNTL, b RO_all and c RO_3kmQC analyses of the water vapor mixing ratio. The slant path is along the Pearl River area to southwestern Taiwan, indicated as the red dashed line in Fig. 5g. The dashed line is the isopleth of 12 g kg −1 from c Page 11 of 24 Chang and Yang Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:7 analysis of RO_LSWQC at 700 hPa. The black, red, and blue contours in Fig. 7c show the 12 g kg −1 isopleth of the RO_LSWQC, the RO_all, and the RO_3kmQC moisture analysis, respectively. Although RO_LSWQC has less increment over the Taiwan Strait, it is clearly moister than the RO_all and RO_3kmQC due to the accumulated impacts of cycled DA. However, the RO_LSWQC is drier than the RO_3kmQC in the Pearl River area. Another example is the RO profile B located around the Pearl River estuary. This profile indicates that the RO data between 1 and 3 km is still qualified because the LSWH is below 1 km. Thus, between 1.5 and 3 km, the adjustment of RO_all and RO_LSWQC are similar. Below 1.5 km, there is no RO observation for this profile and the adjustment of RO_LSWQC is affected by the vertical background error correlation. Without the RO observations below 3 km, the RO_3kmQC results in a negative adjustment in general. Although the analysis increment also depends on the background field, such adjustment leads to a clear difference in the moisture distribution of northern SCS at 700 hPa (Fig. 7c). This comparison implies that the selection of the QC method is crucial to RO data assimilation. At the very least, Fig. 7f shows that a strong correction could happen, especially in the lower troposphere, if there is no special QC procedure applied, such as the RO profile C, located near the Changsha city of Hunan Province in China. The low-level adjustment difference between RO_all and RO_3kmQC reaches almost 7 g kg −1 . Therefore, a large negative increment is found around this RO profile at 950 hPa (Fig. 4b).
Without knowing the truth, it is difficult to judge whether the moisture adjustment is accurate. For the verification purpose, we compare the observation-minusbackground (OMB) and observation-minus-analysis (OMA) against the radiosonde observation located at (113.0 • E, 25.8 • N) which is nearest to the RO profile C. Figure 8a shows that the background of RO_all is much moister than the radiosonde observation at 850 hPa and Fig. 7 Increment of the water vapor mixing ratio of RO_LSWQC at a 950 hPa, and b 700 hPa at 0000 UTC, August 12, 2019. The black, red, and blue cross symbols indicate the location of RO profile with LSW smaller than 35%, LSW larger than 35% at the altitude above and below 3 km, respectively. c The analysis moisture at 700 hPa. The black, red and blue contours represent the 12 g kg −1 isopleth of RO_LSWQC, RO_all (Fig. 5h), and RO_3kmQC (Fig. 5i) Page 12 of 24 Chang and Yang Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:7 the background fields of RO_3kmQC and RO_LSWQC are closer to this radiosonde observation than that of RO_all. To make a clearer verification, we conduct sensitivity tests by removing this radiosonde observation and using the identical background field from the RO_all experiment to assimilate the RO observations with different QC strategies. This sensitivity experiment is named with the suffix '_nSA' . By comparing the RO_all and the RO_all_nSA, the moisture correction at this location is dominated by the RO data. The moisture correction is valid to reduce the moisture at 850 hPa but results in an overcorrection at the lower atmosphere (e.g. 950 hPa), leading to a dryer condition than the radiosonde. Removing the RO data below 3 km (RO_3kmQC_nSA) and 1 km (RO_1kmQC_nSA) avoid the large negative increment shown in RO_all_nSA. We should also note that even though the moisture correction could be valid at 850 hPa, such a strong adjustment after many assimilation cycles may induce an imbalance of model dynamics and is unwelcome from the perspective of data assimilation. With the effect accumulated from previous cycles, both RO_3kmQC (Fig. 4c) and RO_LSWQC (Fig. 7b) successfully avoid such an issue, implying the importance of proper QC processes. An alternative way to better use the RO observations is to keep all the RO observations but modify the observation error during the data assimilation. The modification to the RO refractivity error is conducted as another sensitivity test to explore the impact. Increasing the observation error variance below 3 km aims to mimic the expected larger uncertainties of RO observations in the lower troposphere. The RO_modR experiment linearly increases the observation error variance from its default value at 3 km to 10% at the surface. It can be noted that the purpose of this sensitivity test is to understand the impact of tuning the observation variance in the lower troposphere rather than optimizing the performance of RO assimilation. In general, the characteristics of the analysis increments at 700 hPa (Fig. 9a) are similar to those from RO_3kmQC (Fig. 4i). For instance, the RO_modR also has a small dry zone around southwestern Taiwan (Fig. 9c) that is caused by the dry adjustment from RO assimilation. The positive moisture adjustment across southern China and southwest of Taiwan is broader in RO_modR relative to the RO_3kmQC. Compared to the RO_all, the significant negative adjustment over the inland China at 950 hPa does not exist as observation error variance increased (Fig. 9b). In addition, it should also be pointed out that there is a large negative increment over the Pearl River area in RO_modR at 700 hPa (Fig. 9a). Through the westerly wind there, these increments further affect the moisture flux in southwestern Taiwan and the precipitation prediction.
In general, it can be concluded that assimilating all the RO observations below 3 km leads to a large negative adjustment in the lower atmosphere, which may be related to issues of data quality and overwhelm the accuracy of the low-level moisture analysis. Applying the QC process, such as brutally rejecting the RO data below 3 km or based on the LSW information, and increasing the RO observation error variance below 3 km can avoid the strong adjustment. It implies that further Fig. 8 The observation-minus-background (OMB) and observation-minus-analysis (OMA) against the radiosonde observation located at 0000 UTC 12 August 2019 for a the RO_all, the RO_3kmQC, and the RO_LSWQC experiments, and b the sensitivity experiments by using an identical background from the RO_all experiment and without assimilating this radiosonde observation Page 13 of 24 Chang and Yang Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:7 modification is needed for using the FS7/C2 observations, especially for the lower atmosphere. Relative to the moisture analysis of RO_all, RO assimilation with additional QC processes (RO_3kmQC and RO_LSWQC) leads to a moister environment over the Taiwan Strait, while increasing the observation error variance produces a drier environment. In the following, we compare how these differences in the moisture analysis can lead to different precipitation predictions. Figure 10 shows the one-day accumulated rainfall on August 13 of the deterministic forecast initialized from the analysis ensemble mean at 0000 UTC, 0600 UTC, and 1200 UTC, respectively, on August 12. Generally, all experiments exhibit heavy rainfall in the Bashi Channel. For the rainfall prediction initialized at 0000 UTC, August 12, the CNTL forecast has a very limited ability to reproduce the coastal rainfall. The forecasts assimilating the RO observations can generate the coastal rainfall, except for the RO_all experiment. For the forecast initialized at 0600 UTC, August 12, RO_all is still unable to predict the heavy rainfall over the southwestern Taiwan. CNTL captures some heavy rainfall signals in the mountainous area even without assimilating the RO observation. RO_3kmQC has the best performance in predicting the heavy rainfall in the coastal region, while RO_LSWQC shows heavy precipitation not only in southern Taiwan but also extending to the Bashi Channel.

Results from all experiments
To further identify the ability of producing a suitable environment for heavy rainfall, Fig. 11 demonstrates the convective available potential energy (CAPE) over Taiwan from the 21-h forecast initialized at 0000 UTC, August 12, 2019. All the experiments show a high CAPE (larger than 2000 J kg −1 ) over the southwestern sea area of Taiwan, indicating that the environment provides a good potential condition for convection. In southwestern Taiwan, it is noticed that RO_3kmQC has the highest CAPE and CNTL has the least CAPE. A better environmental condition (e.g. high CAPE) and a stronger westerly wind component justify the better performance of the RO_3kmQC forecast in producing heavy accumulated rainfall over the southwestern Taiwan as shown in Fig. 10. Compared with the RO_3kmQC, the smaller CAPE of RO_all also implies that assimilating the RO observation below 3 km obliterates the benefit of the moisture adjustment obtained from assimilating the higher RO data above 3 km. Thus, the use of low-level FS7/C2 data needs careful consideration.
We note that the deterministic forecasts of all the experiments initialized at 1200 UTC, August 12 show the worst predictions compared to the forecasts initialized at other times. This is because the simulated typhoon Krosa in all experiments is too intense and the size is too large (e.g. the radius of 34 kts issued by the Joint Typhoon Warning Center is 450 km, but it is 800 km in CNTL). This affects the local wind field and the precipitation around the southern Taiwan. Only RO_3kmQC is able to predict the rainfall in southern Taiwan with a stronger westerly wind component (shown in Fig. 12). With the same reason, none of the experiments are able to capture the extreme rainfall over central Taiwan. The oversized Krosa pulls the flow around Taiwan to merge with Krosa's circulation. Taking the CNTL analysis as an example (Fig. 12a), the wind southwest and south of Taiwan has Page 14 of 24 Chang and Yang Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:7 a stronger northerly wind component and inhibits the moisture transport. Assimilating the RO data, unfortunately, cannot correct the intensity and the exaggerated size of Typhoon Krosa.

Impact on moisture transport
As shown in Sect. 3, analyses of all experiments at 0000 UTC, August 12 offer the moist environment around southern Taiwan. This benefit accumulates and can be seen in the subsequent analysis at 0600 UTC, August 12. We should note that all the experiments exhibit conditions of high low-level moisture offshore of Taiwan at 0000 UTC, August 12. However, sustaining moisture transport into the Taiwan region is the key to predicting the heavy rainfall in Taiwan on August 13, such as in the RO_3kmQC forecast initialized at 0600 UTC, August 12. Figure 12 shows the moisture and wind fields at 950 hPa of the 21-h forecast, which is crucial for the intensity and location of the rainfall in Taiwan on August 13. All the experiments have a moist environment at this level. While the high moisture band of CNTL, RO_all, and RO_LSWQC extends from the SCS to the southern Taiwan, a larger northerly wind component appears in the Taiwan Strait near 23° N. The northerly wind component brings the dry air to the western Taiwan, as found in RO_all and RO_LSWQC. Both the RO_3kmQC and RO_modR have a relatively stronger westerly wind over the northern SCS and the offshore southwestern Taiwan. The stronger westerly wind can provide a stronger moisture transport into the southwestern Taiwan. With the moistest environment at the lower atmosphere, RO_3kmQC has an environment favorable for producing rainfall over the southwest Taiwan. The wind field difference of those experiments indicates that assimilating the RO observation below 3 km also changes the low-level prevailing wind, which is crucial to determine the location of the local convergence (Chen et al. 2005). Page 15 of 24 Chang and Yang Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:7 To quantify the moisture transport, the moisture flux is calculated to demonstrate how the moisture travels from upstream to southwestern Taiwan. The zonal (qu) and meridional (qv) components of the integrated moisture transport (IVT) are defined as: where u and v are the horizontal and meridional winds, q is the water vapor mixing ratio, and P s and P t denote the pressure at the surface and the model top, respectively. Given that the moisture variation resides below 500 hPa, this altitude can be regarded as the top level of the atmosphere for calculating the moisture flux. In addition, the net IVT flux is calculated to represent a moisture sink or source in the area. The high IVT flux may owe either to a high moisture content or a high wind (1) qu = 1 g Pt Ps qu dp, (2) qv = 1 g Pt Ps qv dp, speed, but both are important for moisture transport and the consequence of the extreme precipitation. Figure 13 shows the IVT flux of CNTL, RO_all and RO_3kmQC at 0000 UTC, August 12, as each demonstrates a different characteristic of moisture distribution during the deterministic forecast. Three regions are selected to represent the upstream area, the transition zone and the precipitating area of southwestern Taiwan, denoted as blue, red and yellow boxes, respectively. It is evident that zonal transport dominates the IVT flux. The moisture originating in the Pearl River area is the main source of moisture, which is transported toward southwestern Taiwan with the prevailing west-southwesterly wind. In the upstream area, the zonal inflows along the western boundary are less than the zonal outflow along the eastern boundary in all three experiments, indicating that the moisture is transported into the downstream area. The meridional moisture budget of CNTL and RO_all shows clear southward transport, while northward transport is found in RO_3kmQC. This can be attributed to the stronger northerly wind component in CNTL and RO_all, which Page 16 of 24 Chang and Yang Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:7 transports the drier airflow from the north. The clear northward transport existing in RO_3kmQC (as shown in contours in Fig. 13c) enables moisture to be supplied from the northern SCS, as a result of having more southerly wind correction in this area. In the transition zone, the zonal net IVT flux of RO_3kmQC is 63.4 kg m −1 s −1 , which is slightly smaller than RO_all with 69.8 kg m −1 s −1 . Nevertheless, the RO_3kmQC has the greatest intensity in inflow and outflow, implying greater transport. Conversely, RO_all has the weakest transport intensity, which is unfavorable for maintaining a moist environment.
In southwestern Taiwan, the characteristics of all the experiments are similar. The zonal inward IVT flux across the western boundary is larger than the zonal IVT outflux at the eastern boundary, indicating that moisture is accumulated and the wind speed is decreased due to the interaction with the terrain in this region. Notably, unlike other regions, the meridional IVT influx at the southern boundary is positive. With a negative outward IVT flux at the northern boundary, the meridional moisture transport converges in this region. The positive net IVT flux budget of these three experiments certainly favors the generation of heavy rainfall. Compared with The colored arrows and associated values denote the direction and amount of IVT flux at each boundary. The "Net" value indicates the net moisture transport in the box. Positive (negative) value implies that the moisture is accumulated (diverged). The contours indicate the stronger meridional wind of RO assimilation experiments than CNTL Page 17 of 24 Chang and Yang Terrestrial, Atmospheric and Oceanic Sciences (2022)  Page 18 of 24 Chang and Yang Terrestrial, Atmospheric and Oceanic Sciences (2022)  Page 19 of 24 Chang and Yang Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:7 CNTL and RO_all, the RO_3kmQC has the greatest net IVT flux in this region, providing a favorable environment with the largest moist convergence (source). Figure 14 shows the time series of the net IVT flux during the deterministic forecast for the selected areas in Fig. 13. In the upstream region (Fig. 14a), the CNTL and RO_all experiments have a stronger net outflow after 1500 UTC, August 12. However, in the transition zone (Fig. 14b), the moist airflow of CNTL tends to accumulate in this region rather than traveling downstream, and the RO_all has a net IVT flux close to zero. With a relatively weaker moisture transport, the net IVT flux of CNTL and RO_all are smaller than RO_3kmQC in southern Taiwan (Fig. 14c). For RO_3kmQC, the IVT flux in the upstream area serves as a moisture source during all the forecast lead times, and has the largest amount of moisture transport after 1200 UTC, August 12. In addition, its zonal outflow at the eastern boundary (dashed line) provides the greatest transport to the downstream area. This gives an ideal condition for maintaining the moist environment in RO_3kmQC. At 0000 UTC, August 13, RO_3kmQC shows the largest net IVT flux, corresponding to moisture accumulation in the transition zone. Three hours later, the moist transport in RO_3kmQC transports is largest in the downstream (Fig. 14c) and the net IVT flux indicates that the moisture in southwestern Taiwan is accumulated and sustained. Figures 13 and 14 clearly demonstrate that sustaining the moisture transport during the deterministic forecast is crucial for generating persistent precipitation.

Discussion
As shown in the previous section, assimilating the RO observations with different strategies leads to variations in predicting the extreme precipitation event in southwestern Taiwan. The main purpose of our comparison has been to understand the sensitivity of assimilating the RO observations in the lower troposphere (i.e., below 3 km) with strategies related to the quality of RO data. According to L18, we regard an RO profile as good quality if its LSW is smaller than 35% throughout all levels. As shown in Table 2, 17.8% and 26.5% of the total RO profiles exhibit good quality over the land and the ocean, respectively. That is, for the RO_all experiment, almost 56% of RO profiles are of poorer quality below a certain altitude. This is one possible reason why the increments derived from the RO_all experiment are less useful for improving predictions of precipitation.
We have also noticed that the RO observations have different characteristics over the land and the ocean with the LSW criteria. During our assimilation period, a total of 72% of the RO profiles are distributed over the ocean (Table 2). As shown in Fig. 15a, for the RO observations over the ocean (red bars), the LSWH appears at all the bins of altitude below 7 km. As listed in Table 2, the percentages of the poor RO profiles that exist below or above 3 km are comparable, indicating that over the ocean, half of the RO profiles can still provide good information below 3 km. However, for the RO observations over the land (blue bars), the LSWH tends to be above 3 km (more than 95%, as shown in Table 2). Compared to the ocean, more RO profiles over the land are regarded as being of poor quality according to L18's definition, leading RO_ LSWQC to discard more RO data over the land at an altitude higher than 3 km. Based on this case, the moisture increment at 700 hPa in the Pearl River area over southern China is crucial for generating heavy rainfall downstream, i.e., in southwestern Taiwan, so removing too much data over the land causes this benefit to disappear. The high percentage of RO profiles with an LSWH below 3 km over the ocean also explains the results with operational DA systems, where the FS7/C2 data are largely rejected in the lower levels. As shown in Lien et al. (2021), more than 90% and 50% of FS7/C2 RO data below 2 km and 3 km, respectively, are rejected by the default QC process of the CWB Global Forecast System (CWB-GFS) GSI system. However, from the point of view of L18, at least, 44% of the data below 3 km is wrongly discarded in RO_3kmQC (LSW < 35%) and potentially, 23% of the data could be good but discarded (LSWH below 3 km). Given that the LSW-based QC is an adaptive procedure for detecting the data quality of RO, it is expected that RO_LSWQC is able to provide the largest amount of useful correction. However, it is RO_3kmQC that gives the best rainfall prediction, even though more than half of the useful RO observations are discarded below 3 km. It cannot be concluded that the RO observations below 3 km are useless. Rather, we tend to think that the positive impact in the RO_all experiment is overwhelmed Table 2 Statistics of the RO profiles according to the surface type and the LSWH The first row shows the percentage of RO profile with LSW smaller than 35% at all levels. The second and third rows show the percentage of RO profiles with the lowest altitude that LSW is larger than 35% below or above 3 km, respectively. For the first row, the percentage is calculated based on the total number of RO profile (400). For the second and third rows, the percentage is calculated based on the number of RO over land (42) and ocean (181) Page 20 of 24 Chang and Yang Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:7 by the poor quality of the observations. On the other hand, the RO_LSWQC rejects too much of the data over the land and the associated good impact; therefore, the criteria of the LSW should be re-examined for the FS7/C2 data so that the good-quality data can be better preserved. Lien et al. (2021) have raised several questions regarding the suitability of the estimated observation error variance, such as whether that estimated with other available Fig. 15 a The count of the RO profiles with the LSWH exceeds 35% and does not exceed 35%. The blue and red bars indicate that the RO profiles are located over the land and the ocean, respectively. b The average RO observation error variance used in CNTL (the default value; black line), and RO_modR (red line) RO data sets (e.g., FS3/C) before FS7/C2's launch is still applicable to the FS7/C2 assimilation. Re-estimating the observation error variance is important for optimizing the use of FS7/C2's RO observations, but is beyond the scope of this study. Adjusting the observation error variance is the first step to improving the RO assimilation directly. Given concerns about the quality of RO data below 3 km, the observation error variance should be enlarged. This point echoes the finding of Lien et al. (2021) that the re-estimated observation error variance is twice as large as the GSI-default value. The RO_modR increases the observation variance linearly below 3 km. The purpose of this linear adjustment is to consider the variations in the PBL where the moisture decreases with height. The RO_modR is able to extract useful information from the RO observations below 3 km, but unfortunately, it cannot eliminate the disadvantage shown in the RO_all moisture increment.
As a short conclusion, tuning or re-estimating the observation error variance could extract more useful information from the quality observations. L18 have suggested that the uncertainty related to data retrieval, such as the LSW information, be included in the observation error estimation. Nevertheless, adjusting the observation error variance alone may not be able to optimize the impact of the RO data, because the positive impact could still be contaminated by the poor-quality data. Undoubtedly, an effective QC process that considers the retrieval quality in addition to the conventional innovation-based criteria is important. Our results suggest that in order to take full advantage of the low-level data, it is imperative to develop a proper QC procedure. Furthermore, as discussed earlier, the vertical characteristics of the LSW seem to depend on whether the surface is land or sea (Fig. 15a). Such a distinction implies a larger variation in FS7/C2's RO data quality over the land than over the ocean. This characteristic may be an important factor for the observation error variance estimation.

Conclusion
Formosat-7/COSMIC-II (FS7/C2) provides good coverage from the tropics to the subtropics with a better penetration to the lower atmosphere compared to Formosat-3/COSMIC-I (FS3/C). The amount of data yielded by FS7/C2 in the lower atmosphere also exceeds that of FS3/C. The goal of this study has been to investigate the impact of FS7/C2's RO data, focusing on regional moisture analysis and rainfall prediction. We have also attempted to identify the strategies that may be used in data assimilation in order to optimize the use of the RO data. A case study of the heavy rainfall episode in Taiwan on August 13, 2019, was selected for this purpose. This event was characterized by heavy rainfall over the coastal region of central and southwestern Taiwan. The flow pattern over the Taiwan area was influenced by Typhoon Lekima, which had made its second landfall at Shandong, China, and Typhoon Krosa, which occurred east of Taiwan and prevailing southwesterly winds over the SCS. Our investigation has been performed using the WRF-LETKF with a model grid spacing of 15 km. All experiments have been initialized at 1200 UTC, August 9, 2019, with 42 ensemble members spun up from the NCEP GEFS.
With the use of the flow-dependent background error covariance, the moisture increment from the RO assimilation has been found to be significant in areas with active moisture transport, including typhoon circulations, the northern SCS and the Pearl River area in southern China. However, assimilating all the RO observations (RO_all) with the standard innovation-based QC procedure has revealed some disadvantages for generating a moist environment that favors extreme precipitation in Taiwan, including a large dry correction over the continent that breaks the moisture zone extending from the northern SCS to southern Taiwan. Therefore, how to enhance the benefit of FS7/C2's RO assimilation has been investigated with sensitivity experiments. From the perspective of data assimilation, re-designing the QC processes and re-estimating the observation error variance (R) are the preliminary considerations for improving the use of observations. Therefore, two strategies have been adopted in the sensitivity experiment, including changing the QC procedure and modifying the observation error variance.
Two experiments use a different QC procedure, including directly discarding the RO data below 3 km (RO_3kmQC) or below the LSWH (RO_LSWQC). The other experiment adjusts the observation error variance below 3 km by linearly increasing the variance from its original value at 3 km to 10% at the surface (RO_modR). It was expected that the assimilation of FS7/C2's RO observations would improve the low-level moisture analysis, given that more RO data are available for the lower atmosphere compared to those from FS3/C. However, our results show that the experiment that does not include the RO data below 3 km leads to the best rainfall prediction over Taiwan on August 13, 2019, in terms of the intensity and the location of the heavy rainfall. The experiment with the LSW-based QC also brings benefits to rainfall prediction. Similar to RO_3kmQC, RO_ LSWQC exhibits a broad range of moisture enhancement over southern China and alleviates the large dry correction over the northern SCS during several successive analysis cycles. However, the LSW of the RO profiles over the land shows larger variations than those over the ocean and more RO profiles with an LSWH located above 3 km. Such an LSW-based QC procedure rejects more RO data above 3 km over the land. In comparison to discarding the data through QC, inflating the observation error variance saves all the RO observations, but the contributions of observations are reduced depending on uncertainties in the background information. Increasing the observation error variance linearly with a downward extent can alleviate the discontinuity of the observation error variance and reflects the characteristics in the PBL. However, without a well-tuned observation error variance, the positive impact may be contaminated by the poor-quality RO data. This indicates that simply adjusting the observation error variance alone is insufficient to the RO assimilation.
By examining the forecast initialized from the RO_3kmQC analysis, we have found that the key to predicting this heavy rainfall event is moisture transport from the Pearl River area, where the RO data at 3-5 km height provide effective moisture enhancement to deepen the high moisture layer. The eastward IVT flux in the area of the Pearl River estuary is the largest in the RO_3kmQC forecast, among all the experiments. Our results suggest that the active deep convection developed over southern China greatly deepens the high moisture layer and the prevailing westerly wind transports the moisture downstream, providing a significant IVT flux from offshore to the coastal regions of southwestern Taiwan, further leading to heavy rainfall over Taiwan. One challenge is that the flow pattern over Taiwan was affected by the circulation of Typhoon Krosa. The assimilation of RO data has a limited effect on the over-predicted Krosa. This can be partly explained by the fact that the ocean's contribution has been ignored in our experiments and the ocean analysis has indicated a cold eddy that could have suppressed Krosa's development.
Based on this case study, the results show that for the RO data assimilation, the QC procedure brings a larger impact to rainfall prediction than counterparts that adjust the observation error variance. Currently, decent efforts have been made to calculate the observation error variance. Although the artificial QC procedure that discarding RO data below 3 km seems to be brutal in this study, it confirms the quality of RO data above 3 km and their effectiveness in moisture analyses and precipitation prediction. It also implies that the use of low-level FS7/ C2 data needs careful consideration. Re-designing the QC processes and re-estimating the observation error variance (R) become the potential strategies that could optimize the use of low-level FS7/C2 data. Both the RO_ LSWQC and RO_modR experiments provide a preliminary attempt. We would like to emphasize that a more sophisticated QC procedure should be developed to consider the FS7/C2's higher penetration rate into the lower atmosphere compared to the FS3/C data. Also, a sophisticated QC procedure that is sensitive to the land/ocean should be investigated in order to optimize the impact of the low-level RO data. Such characteristics may be considered in the re-estimation of the observation error variance. Although the RO refractivity has been used in this study, further research should consider the bending angle, which is the upstream product, expected to further improve FS7/C2's RO assimilation.