1. Introduction
The primary purpose of data assimilation at convective scales is to improve short-term forecasts, especially for severe weather events with heavy precipitation. The weather radar is a remote sensing tool that provides high temporal and spatial data useful for analyzing extreme weather phenomena (Houze et al. 1989; Germann and Zawadzki 2002, 2004). Numerous studies have discussed the advantages of including radar observations in various assimilation algorithms. For instance, radar data have been successfully assimilated in three-dimensional variational (3DVAR) algorithms (Xiao and Sun 2007; Chung et al. 2009; Sugimoto et al. 2009), four-dimensional variational (4DVAR) algorithms (Sun and Crook 1997, 2001; Sun and Zhang 2008; Sun et al. 2010; Tai et al. 2011; Chang et al. 2014, 2016), and ensemble-based data assimilation systems (Snyder and Zhang 2003; Zhang et al. 2004; Tong and Xue 2005; Aksoy et al. 2009; Yussouf and Stensrud 2010; Dowell et al. 2011; Tsai et al. 2014). These studies have indicated that the assimilation of radar data [e.g., radial wind (Vr) and reflectivity (Z)] in numerical weather prediction (NWP) can enhance the simulated structure of the weather system and improve quantitative precipitation forecasting (QPF) for severe weather events, such as squall lines, supercell storms, and typhoons.
However, the assimilation of Z and Vr from weather radar has some limitations in regards to improving the analysis and forecast of convective weather systems. Ge et al. (2013) conducted observing system simulation experiments (OSSEs) to assimilate various state variables, emphasizing the influential roles of humidity in addition to that of horizontal wind in storm analysis and forecast. The assimilation of Z and Vr offers an opportunity to adjust the hydrometeors and wind fields inside precipitation systems; however, how such assimilation properly modifies temperature and humidity remains an active research topic. Many studies have applied various approaches to obtain and assimilate humidity information at convective scales. Wang et al. (2013) introduced a scheme to assimilate retrieved rainwater and water vapor data derived from Z and demonstrated that both the location and intensity of convection were accurately forecast in four cases of convective heavy rain. Caumont et al. (2010) and Wattrelot et al. (2014) employed the 1D + 3DVar method in which the retrieved humidity is based on 1D Bayesian formalism and the observed Z is assimilated with the conventional 3DVar assimilation system. Their results indicated a notable enhancement in the performance of short-term accumulated precipitation forecasting. Through the assimilation of rainfall observed by radar and surface observations, Sun et al. (2020) revealed that rainfall data are critical for adjusting humidity and temperature; reflectivity assimilation, however, only partially contributes to humidity correction. Alternatively, temperature and humidity fields can be modified through a semiempirical complex cloud analysis procedure. This semiempirical method demonstrates the ability to effectively analyze the in-cloud humidity field and improve storm forecasting (Hu et al. 2006; Pan and Wang 2019; Pan et al. 2020). Lai et al. (2019) derived vertically integrated liquid water from three-dimensional reflectivity and assimilated it with Z and Vr, alleviating the overprediction of storm cells. Despite the positive effects of assimilating retrieved moisture information, the aforementioned studies have largely focused on providing humidity information inside precipitation systems.
Crook (1996) and Fabry and Meunier (2020) indicated that slight changes in environmental humidity can modify rain patterns and intensity considerably. Information on the humidity surrounding severe weather systems is crucial for the prediction of storm initiation. Through assimilating the zenith total delay of ground-based global navigation satellite systems and radar data, Yang et al. (2020) demonstrated that assimilating the extra humidity in radar data–void regions can enhance moisture convergence, resulting in short-term forecast improvements. Furthermore, radar-derived refractivity, which provides near-surface humidity information nearby the precipitation system, was assimilated and investigated by Gasperoni et al. (2013). A series of sensitivity tests based on the OSSEs revealed that refractivity assimilation can correct low-level moisture errors. In addition to these two types of humidity information, Ellis and Vivekanandan (2010) demonstrated the ability to infer environmental water vapor profiles through the lower troposphere by using the attenuation difference between the S-band and Ka-band measurements of the National Center for Atmospheric Research (NCAR) S- and Ka-band dual‐wavelength (S-PolKa) radar. The retrieved humidity was obtained outside the precipitation system and represented the moisture of the nonprecipitation area at low levels. The potential for utilizing dual-frequency for retrieving moisture information has been investigated in other studies (Tian et al. 2007; Ellis and Vivekanandan 2011), but the impact of retrieved water vapor data from S-PolKa has not yet been examined.
This study examined the effect of assimilating S-PolKa-retrieved water vapor data with Z and Vr data for convective-scale weather systems. The assimilation strategy for the retrieved water vapor information was also investigated. Two organized heavy rainfall events and a scattered convection event from the Dynamics of the Madden–Julian Oscillation (DYNAMO) field campaign (Yoneyama et al. 2013) were selected for analysis. The organization of this paper is as follows. Section 2 introduces the assimilation system and observational dataset for assimilation. The experimental design and three case studies are described in section 3. Section 4 details the improvement in rain forecasting using different strategies of retrieved moisture assimilation. Finally, section 5 presents the summary and discussion.
2. Assimilation system and data description
a. WRF-Local ensemble transform Kalman filter radar assimilation system
In Eq. (5), I is an identity matrix and ρ is a multiplicative covariance inflation factor (Anderson 2001). This study assigned a covariance inflation of 1.08 (Tsai et al. 2014) to reduce underdispersiveness.
Yang et al. (2009) developed a system that combines the LETKF algorithm with the WRF Model. Tsai et al. (2014) extended this system to assimilate radar data in their WRF-Local ensemble transform Kalman filter radar assimilation system (WLRAS) and improve the very short-term forecast for the convective scale. Several studies (Cheng et al. 2020; Tsai and Chung 2020; Wu et al. 2020; Yang et al. 2020) have successfully applied the WLRAS to examine severe weather cases. The WLRAS updates every single model variable, including wind, geopotential height, potential temperature perturbation, and the mixing ratio of water vapor (Qv) and hydrometeors; different model variables use different error covariance localization radii. The localization radius set up for the system in this study is based on that by Tsai et al. (2014), with the exception of Qv localization, which adapts retrieved Qv assimilated in nonprecipitation areas. The localization for horizontal wind (U and V) was set as 36 km, the temperature and hydrometeor mixing ratio of cloud as 24 km, and the vertical velocity and hydrometeor mixing ratio of rain, snow, and graupel as 12 km. The study utilized a broader localization for the radius for updating moisture (i.e., 48 km), as suggested by Yang et al. (2020). The features of background error correlations (BECRs) in this study also supported this setup (see section 3b). For the vertical localization, 4 km was set for all variables, following Tsai et al. (2014).
b. Model configuration
The two-way nesting WRF Model version 3.9.1 was employed in the experiments. The model uses three nested domains, with horizontal grid spacing of 27, 9, and 3 km for domain 1 (131 × 129 grid points), domain 2 (175 × 169 grid points), and domain 3 (139 × 133 grid points), respectively (Fig. 1a). The outermost and innermost domains cover the northern part of the Indian Ocean and the Maldives, respectively. All experiments were performed with 52 vertical levels (top at 10 hPa), and all physics parameterizations remained unchanged. In particular, the longwave and shortwave radiation parameterization schemes were the Rapid Radiative Transfer Model (RRTM; Mlawer et al. 1997) and Dudhia (1989) scheme, respectively. The Yonsei University planetary boundary layer scheme was also employed (Hong et al. 2006). The Grell–Dévényi cumulus scheme (Grell and Dévényi 2002) was only used in domain 1 and domain 2. To manage microphysics explicitly, the Goddard Cumulus Ensemble (GCE) scheme (Tao et al. 2003) was used for domain 3.
(a) The WRF Model domains. The black dot indicates the S-PolKa location. The horizontal grid spacing of domains 1, 2, and 3 are 27 km (131 × 129 points), 9 km (175 × 169 points), and 3 km (139 × 133 points), respectively. (b) The experimental design schematic. The triple dash lines represent the model spinup period, and the triple dotted lines and solid lines represent the ensemble forecast and data assimilation period, respectively. The single solid lines indicate the mean forecast. The vertical dash bars represent the assimilation cycles.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
(a) The WRF Model domains. The black dot indicates the S-PolKa location. The horizontal grid spacing of domains 1, 2, and 3 are 27 km (131 × 129 points), 9 km (175 × 169 points), and 3 km (139 × 133 points), respectively. (b) The experimental design schematic. The triple dash lines represent the model spinup period, and the triple dotted lines and solid lines represent the ensemble forecast and data assimilation period, respectively. The single solid lines indicate the mean forecast. The vertical dash bars represent the assimilation cycles.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
(a) The WRF Model domains. The black dot indicates the S-PolKa location. The horizontal grid spacing of domains 1, 2, and 3 are 27 km (131 × 129 points), 9 km (175 × 169 points), and 3 km (139 × 133 points), respectively. (b) The experimental design schematic. The triple dash lines represent the model spinup period, and the triple dotted lines and solid lines represent the ensemble forecast and data assimilation period, respectively. The single solid lines indicate the mean forecast. The vertical dash bars represent the assimilation cycles.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
c. Radar observations
The Z and Vr datasets from the NCAR S-Pol (10-cm wavelength) located at Addu Atoll (0.63°S, 73.10°E) in the Maldives were utilized for this study. The NCAR/Earth Observing Laboratory (EOL) provides quality-controlled radar data. The beamwidth and maximum range of the S-Pol radar are 0.91° and 150 km, respectively. The plan position indicator (PPI) scanning covers 360° of azimuth with eight elevation angles (from 0.5° to 11.0°) and 1° azimuthal resolution. The superobbing strategy (Lindskog et al. 2004; Alpert and Kumar 2007) was adopted to thin the data and avoid spatial correlations between observations. The Z and Vr were gridded to 3 km and 3° intervals in the radial and azimuthal directions. The observation errors were set as 3 m s−1 and 5 dB(Z) for Vr and Z, respectively (Tsai et al. 2014).
d. S-PolKa-retrieved water vapor density
Ellis and Vivekanandan (2010) introduced a method to retrieve water vapor density based on the difference in atmospheric attenuation at two different wavelength radar observations. The Ka-band (8-mm wavelength) attenuation has a much stronger dependence on water vapor than S-band attenuation. Therefore, S-band attenuation can be neglected, and the mean water vapor content can be estimated based on Ka-band atmospheric attenuation. Through a cloud- and precipitation-free atmosphere, at the end of radar ray segments, the Ka-band Z value is subtracted from the S-band Z and combined with the range to obtain the Ka-band total atmospheric attenuation. Of the two types of ray segments, the more common primary rays start at the radar and end at the closest edge of an echo, whereas secondary rays connect between the back edge of an echo and the front edge of another echo further in range. To obtain ray segments, the data must be from Rayleigh scatterers at both the Ka and S bands, and the effect of measurement noise must be small compared with the attenuation. Furthermore, ray segments must be at least 15 km in length, with a minimum of 10 radar range gates averaged in a 2D patch at the front edge of the echoes. With the attenuation obtained on several ray segments, the water vapor density is estimated using the relation between humidity and attenuation that was identified with Liebe’s microwave propagation model. The Liebe (1985) model was run numerous times to compute the water vapor density under different pressures, temperatures, and attenuations, and a polynomial fit was used to develop an equation for humidity as a function of attenuation. The estimated water vapor density could then be assigned to the height of the midpoint of the ray segment. This retrieved water vapor was fundamentally unbiased compared with the sounding measurements (Ellis et al. 2017). However, when heavy rain spreads over the radar, the identification of usable ray segments may not be possible, and this retrieval method thus cannot be applied. The observation error of the Qv was 1.5 g kg−1 in this study.
e. Observation operator
The selected time of Gan sounding data must be closest to the time of the S-PolKa-retrieved water vapor density (15-min frequency).
3. Case description and experimental design
a. Description of the three study cases
In this study, three cases were selected for investigation. The first two cases occurred on 18 October 2011 and 16 October 2011, and constituted the two events with the most rain during the DYNAMO campaign (Zuluaga and Houze 2013). In the first case (i.e., 18 October 2011), two cyclones were detected over the Arabian Sea, west of the S-PolKa location. The intertropical convergence zone (ITCZ) remained to the south of Gan Island, with a low pressure system over the north causing the development of many convective systems around the island. Within the S-PolKa domain, from 1600 to 1700 UTC (Figs. 2a,d), two strong convective lines oriented southwest–northeast (denoted by two black boxes with the letters A and B in Fig. 2a) formed to the southeast of S-PolKa. Convective lines continued to develop, strengthen, and move toward the radar site. Convection A approached and covered the radar at approximately 1800 UTC (Fig. 2g). From 1900 to 2100 UTC (Figs. 2j,m,p), convection A intensified and moved to the northwest and convection B dissipated.
Hourly column maximum Z observation of the three cases. (a),(d),(g),(j),(m),(p) The first case from 1600 to 2100 UTC 18 Oct 2011, (b),(e),(h),(k),(n),(q) the second case from 0000 to 0500 UTC 16 Oct 2011, and (c),(f),(i),(l),(o),(r) the third case from 1030 to 1530 UTC 12 Oct 2011. Two convective lines in the first case are denoted by two black boxes with the letters A and B. The encircled black cross indicates the S-PolKa location.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
Hourly column maximum Z observation of the three cases. (a),(d),(g),(j),(m),(p) The first case from 1600 to 2100 UTC 18 Oct 2011, (b),(e),(h),(k),(n),(q) the second case from 0000 to 0500 UTC 16 Oct 2011, and (c),(f),(i),(l),(o),(r) the third case from 1030 to 1530 UTC 12 Oct 2011. Two convective lines in the first case are denoted by two black boxes with the letters A and B. The encircled black cross indicates the S-PolKa location.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
Hourly column maximum Z observation of the three cases. (a),(d),(g),(j),(m),(p) The first case from 1600 to 2100 UTC 18 Oct 2011, (b),(e),(h),(k),(n),(q) the second case from 0000 to 0500 UTC 16 Oct 2011, and (c),(f),(i),(l),(o),(r) the third case from 1030 to 1530 UTC 12 Oct 2011. Two convective lines in the first case are denoted by two black boxes with the letters A and B. The encircled black cross indicates the S-PolKa location.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
In the second case (i.e., 16 October 2011), weak twin cyclones were situated to the south and north of the equator. Low-level northwesterly winds at 925 hPa appeared between the cyclones and covered the Gan site. At the surface, a strong westerly wind component was dominant. At 0000 UTC (Fig. 2b), large clusters of convective cells developed within the S-PolKa domain, and in the following 3 h, these clusters continued developing, expanding and merging to form intensive rainbands at 0300 UTC (Figs. 2e,h,k). The convection strengthened and covered almost the entire radar domain from 0400 to 0500 UTC (Figs. 2n,q), with the most robust convective line located to the north of S-PolKa.
The third case (i.e., 12 October 2011; Figs. 2c,f,i,l,o,r) is different from the first two cases, with easterly winds between two anticyclonic gyres at 200 hPa dominating over Gan Island. At low levels, moderate southwesterly winds covered the S-PolKa domain, over which convective cells were scattered and localized. Some convective cells formed in the S-PolKa domain at approximately 1030 UTC (Fig. 2c), intensified and continued to move northwest until 1530 UTC (Fig. 2r).
b. Experimental design
This study used the high-resolution (0.75° × 0.75°, every 6 h) ERA-Interim reanalysis data as the initial and lateral boundary conditions. Based on the ERA-Interim and WRF-3DVar random perturbation (Barker et al. 2004), 40 ensemble members were generated in domain 1, then downscaled to domains 2 and 3. After the 10–16 h of spinup for each case, observations of the Z, Vr, and retrieved Qv from the NCAR S-PolKa were assimilated in domain 3.
To design an effective strategy for assimilating retrieved moisture information, the Qv in the second case (i.e., at 0000 UTC 16 October 2011) was selected to demonstrate the Qv distribution. Figure 3a depicts the original retrieved Qv locations for all levels, which were all within 25 km from the radar center. Two approaches for thinning the Qv were employed because of the close distance between each Qv location. The first method combined the average of all observations and results in one Qv profile (Fig. 3b); the averaged Qv was then located at the mean latitude and longitude of all points (Fig. 3c). The second method consisted of separating the Qv data into four quadrants (northeast, southeast, southwest, and northwest of the radar site; Ellis et al. 2017), computing an averaged Qv profile in each quadrant, and locating it at the point of the mean latitude and longitude of points in the same quadrant (Figs. 3d,e). Figure 4 depicts the standard deviation between the vertical profile observations of one averaged Qv profile and four-quadrant Qv profiles used for the three cases. The retrieved Qv height ranged between 0.05 and 2.5 km. Among the three cases, the deviation of four-quadrant Qv profiles relative to the averaged Qv profile was more evident in the second case than in the other two cases.
(a) The original S-PolKa-retrieved Qv location for all levels. (b),(d) The vertical profiles of one averaged Qv profile and four-quadrant Qv profiles (solid color lines), and the original retrieved Qv values (black crosses). (c),(e) The location of one averaged Qv profile and four-quadrant Qv profiles (black dot); the encircled blue cross indicates the radar location, and the red triangle represents the Gan sounding station. These figures are plotted at 0000 UTC 16 Oct 2011.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
(a) The original S-PolKa-retrieved Qv location for all levels. (b),(d) The vertical profiles of one averaged Qv profile and four-quadrant Qv profiles (solid color lines), and the original retrieved Qv values (black crosses). (c),(e) The location of one averaged Qv profile and four-quadrant Qv profiles (black dot); the encircled blue cross indicates the radar location, and the red triangle represents the Gan sounding station. These figures are plotted at 0000 UTC 16 Oct 2011.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
(a) The original S-PolKa-retrieved Qv location for all levels. (b),(d) The vertical profiles of one averaged Qv profile and four-quadrant Qv profiles (solid color lines), and the original retrieved Qv values (black crosses). (c),(e) The location of one averaged Qv profile and four-quadrant Qv profiles (black dot); the encircled blue cross indicates the radar location, and the red triangle represents the Gan sounding station. These figures are plotted at 0000 UTC 16 Oct 2011.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
The standard deviation (SD) between Qv derived through the average profile method (i.e., one averaged Qv profile) and four-quadrant method (i.e., northeast, southeast, southwest, and northwest) for the three study cases: (a)–(e) 18 Oct 2011, (f)–(j) 16 Oct 2011, and (k)–(o) 12 Oct 2011. The figures are plotted every 30 min in each case beginning from the first cycle.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
The standard deviation (SD) between Qv derived through the average profile method (i.e., one averaged Qv profile) and four-quadrant method (i.e., northeast, southeast, southwest, and northwest) for the three study cases: (a)–(e) 18 Oct 2011, (f)–(j) 16 Oct 2011, and (k)–(o) 12 Oct 2011. The figures are plotted every 30 min in each case beginning from the first cycle.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
The standard deviation (SD) between Qv derived through the average profile method (i.e., one averaged Qv profile) and four-quadrant method (i.e., northeast, southeast, southwest, and northwest) for the three study cases: (a)–(e) 18 Oct 2011, (f)–(j) 16 Oct 2011, and (k)–(o) 12 Oct 2011. The figures are plotted every 30 min in each case beginning from the first cycle.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
To properly set up the localization radius for updating moisture information, the BECRs between the Qv and itself and with U and V, computed with respect to the reference point at the S-PolKa location (nonprecipitation area), are illustrated in Fig. 5. The BECRs are presented at the time of the first cycle before assimilation. The high values and long correlation lengths in the space of the BECRs were demonstrated in all three cases, except for the BECR between the Qv and wind (U and V) in the third case. This indicated that the humidity field in nonprecipitation areas can propagate the information to adjust the moisture and wind fields in broad ranges. Because the retrieved Qv was only available in the nonprecipitation area, experiments were conducted for each case based on the characteristics of the retrieved water vapor. The NODA experiment entailed downscaling ensemble forecasts to domain 3. In experiment ZVr, radar data (Z and Vr) were assimilated, and in experiments ZVrQv_a and ZVrQv_4q, radar data were assimilated with the retrieved Qv (Z and Vr were assimilated sequentially after Qv assimilation); ZVrQv_a used one averaged Qv profile, and ZVrQv_4q used four-quadrant Qv profiles. The information of one averaged Qv profile and four-quadrant Qv profiles was utilized in experiments Qv_ZVr_a and Qv_ZVr_4q, respectively, assimilating only water vapor information in the first hour and Z and Vr data in the second hour. The six experiments are summarized in Table 1. The assimilation period for all data assimilation experiments was 2 h, with a 15-min frequency (i.e., nine cycles). All experiments were initialized with an ensemble mean analysis of the final cycle to obtain a 6-h deterministic forecast. The experimental design diagram is presented in Fig. 1b, and the study case and each case’s experimental time setting are detailed in Table 2.
The BECRs estimated using the ensemble between (left) Qv and Qv, (center) Qv and U, and (right) Qv and V at 1 km, with the S-PolKa location (encircled black cross) serving as the reference point for the (a)–(c) first case, (d)–(f) second case, and (g)–(i) third case. The correlations are presented at the time of the first cycle before assimilation.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
The BECRs estimated using the ensemble between (left) Qv and Qv, (center) Qv and U, and (right) Qv and V at 1 km, with the S-PolKa location (encircled black cross) serving as the reference point for the (a)–(c) first case, (d)–(f) second case, and (g)–(i) third case. The correlations are presented at the time of the first cycle before assimilation.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
The BECRs estimated using the ensemble between (left) Qv and Qv, (center) Qv and U, and (right) Qv and V at 1 km, with the S-PolKa location (encircled black cross) serving as the reference point for the (a)–(c) first case, (d)–(f) second case, and (g)–(i) third case. The correlations are presented at the time of the first cycle before assimilation.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
Summary of experiments. The symbols “_” and “x” indicate that the information was not assimilated and was assimilated, respectively.
Summary of study cases and time period settings for each case.
4. Results of the analysis and forecast
The effect of assimilation of S-PolKa-retrieved Qv, Vr, and Z for convective scale is evaluated in this section. First, the accuracy of the analysis was examined using the radar observations and the S-PolKa-retrieved Qv. Then the short-term forecast was assessed using the S-Pol-derived estimated rainfall (Dolan et al. 2017) and Gan station data.
a. Performance of the analysis
To investigate the impact of assimilating additional retrieved Qv, we first examined experiments ZVr, ZVrQv_a, and ZVrQv_4q. Figure 6 depicts the Qv increment of these three experiments at 1 km at the first assimilation cycle for the three cases. In the first case (Figs. 6a–c), at the first cycle (i.e., 1600 UTC 18 October 2011), experiments ZVrQv_a and ZVrQv_4q increased the moisture of the nonprecipitation area near the S-PolKa location, with a marked enhancement observed in ZVrQv_a. Figure 7a illustrates a comparison of the Qv root-mean-square errors (RMSEs) with the S-PolKa-retrieved Qv for the first case. The Qv correction of experiment ZVrQv_a and ZVrQv_4q was more precise than that of ZVr for most assimilation cycles. Additionally, assimilating four-quadrant Qv profiles could more accurately represent the moisture environment than assimilating one averaged Qv profile. In the second case, at the first cycle (i.e., 0000 UTC 16 October 2011), similar to the first case, retrieved Qv assimilation could adjust the moisture in the nonprecipitation areas (Figs. 6e,f versus Fig. 6d). The moisture corrections generated through assimilating four-quadrant Qv profiles were more notable than those generated through assimilating one averaged Qv profile. The Qv modifications in the ZVrQv_a and ZVrQv_4q experiments were verified to be more precise than that in ZVr across nine assimilation cycles (Fig. 7b). Moreover, ZVrQv_4q had a lower Qv RMSE than ZVrQv_a. The Qv increments in experiments ZVr, ZVrQv_a, and ZVrQv_4q for the third case at the first cycle (i.e., 1030 UTC 12 October 2011) are presented in Figs. 6g–i. The retrieved Qv assimilation could modify the moisture environment near S-PolKa, and the more obvious moisture corrections occurred in the experiment utilizing the four-quadrant Qv profiles (Fig. 6i). The RMSEs illustrated in Fig. 7c verified that the Qv adjustment in experiments ZVrQv_a and ZVrQv_4q was more accurate than that in ZVr. Among these three experiments, the lowest Qv errors occurred in experiment ZVrQv_4q for most assimilation cycles.
The Qv analysis increment at 1 km at the first cycle for the (a)–(c) first case, (d)–(f) second case, and (g)–(i) third case. The increments are from experiment (left) ZVr, (center) ZVrQv_a, and (right) ZVrQv_4q. The encircled black cross indicates the S-PolKa location.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
The Qv analysis increment at 1 km at the first cycle for the (a)–(c) first case, (d)–(f) second case, and (g)–(i) third case. The increments are from experiment (left) ZVr, (center) ZVrQv_a, and (right) ZVrQv_4q. The encircled black cross indicates the S-PolKa location.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
The Qv analysis increment at 1 km at the first cycle for the (a)–(c) first case, (d)–(f) second case, and (g)–(i) third case. The increments are from experiment (left) ZVr, (center) ZVrQv_a, and (right) ZVrQv_4q. The encircled black cross indicates the S-PolKa location.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
RMSEs of Qv verified against S-PolKa-retrieved Qv across nine assimilation cycles for the three cases.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
RMSEs of Qv verified against S-PolKa-retrieved Qv across nine assimilation cycles for the three cases.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
RMSEs of Qv verified against S-PolKa-retrieved Qv across nine assimilation cycles for the three cases.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
The moisture increment in all three cases indicated that assimilating one averaged Qv profile or four-quadrant Qv profiles more effectively modifies the moisture environment than assimilating only Z and Vr. More accurate modifications occurred when four-quadrant Qv profiles were included in the assimilation process. Furthermore, among the three cases, the second case exhibited more marked Qv improvement in ZVrQv_4q than in ZVrQv_a and ZVr. The benefit was most like related to the more complete four-quadrant Qv profiles in the second case. Additionally, this case had more variety in the humidity profiles in different directions (Fig. 4).
Figures 8a–f present the analysis of the column maximum Z at 1800 UTC 18 October 2011, for the six experiments. Compared with the observations in Fig. 2g, the NODA experiment (Fig. 8a) could not capture strong convection in the right positions. By contrast, all experiments assimilating the Z and Vr simulated the intense convection in the right area (Figs. 8b–f). Additionally, most false alarms in the convective area of NODA could be alleviated in the data assimilation experiments. The difference between the observation and analysis mean of the Z at 1 km in the final cycle is illustrated in Figs. 8g–l; the greatest Z deviation was noted in NODA (Fig. 8g). Slight improvements were observed in terms of the Z deviation in ZVrQv_a and ZVrQv_4q compared with that in ZVr after nine assimilation cycles (Figs. 8h,i,k). Conversely, experiments Qv_ZVr_a and Qv_ZVr_4q (Figs. 8j,l) generated Z simulations that most closely matched the observations among the six experiments.
(a)–(f) Column maximum Z. (g)–(l) The difference between the observation and analysis mean of the Z at 1 km at the final cycle of the first case (1800 UTC 18 Oct 2011). Shown are NODA in (a) and (g), ZVr in (b) and (h), ZVrQv_a in (c) and (i), Qv_ZVr_a in (d) and (j), ZVrQv_4q in (e) and (k), and Qv_ZVr_4q in (f) and (l). The encircled black cross indicates the S-PolKa location.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
(a)–(f) Column maximum Z. (g)–(l) The difference between the observation and analysis mean of the Z at 1 km at the final cycle of the first case (1800 UTC 18 Oct 2011). Shown are NODA in (a) and (g), ZVr in (b) and (h), ZVrQv_a in (c) and (i), Qv_ZVr_a in (d) and (j), ZVrQv_4q in (e) and (k), and Qv_ZVr_4q in (f) and (l). The encircled black cross indicates the S-PolKa location.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
(a)–(f) Column maximum Z. (g)–(l) The difference between the observation and analysis mean of the Z at 1 km at the final cycle of the first case (1800 UTC 18 Oct 2011). Shown are NODA in (a) and (g), ZVr in (b) and (h), ZVrQv_a in (c) and (i), Qv_ZVr_a in (d) and (j), ZVrQv_4q in (e) and (k), and Qv_ZVr_4q in (f) and (l). The encircled black cross indicates the S-PolKa location.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
Figures 9a–f depict the column maximum Z of the six experiments for the second case at the analysis time of 0200 UTC 16 October 2011. Compared with the observed convective lines (Fig. 2h), the simulated convection was weaker but more widespread, covering the entire NODA experiment domain. Conversely, all experiments resulted in strong convective cells after radar data assimilation (Figs. 9b–f). Some false alarms occurred in the southeast corner domain in experiments ZVr, ZVrQv_a, and ZVrQv_4q (Figs. 9b,c,e) but were slightly improved in Qv_ZVr_a and Qv_ZVr_4q (Figs. 9d,f). Additionally, Qv_ZVr_a and Qv_ZVr_4q enhanced the most intense convective line to the north of the radar compared with other experiments. Figures 9g–l describe the deviation between the observation and analysis mean of the Z in the six experiments at 1 km in the final cycle. The results indicated that the simulated Z in the Qv_ZVr_a and Qv_ZVr_4q experiments was more accurate than that in the NODA, ZVr, ZVrQv_a, and ZVrQv_4q experiments (Figs. 9j,l versus Figs. 9g,h,i,k).
As in Fig. 8, but for the second case at 0200 UTC 16 Oct 2011.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
As in Fig. 8, but for the second case at 0200 UTC 16 Oct 2011.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
As in Fig. 8, but for the second case at 0200 UTC 16 Oct 2011.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
Figure 10 presents the column maximum Z in the final analysis step of the third case (1230 UTC 12 October 2011). Compared with the observation (Fig. 2i), the NODA experiments exhibited widespread coverage of Z from 10 to 20 dBZ (Fig. 10a). The highest Z in NODA was less than 30 dBZ; however, in all the data assimilation experiments, the highest Z value ranged between 45 and 50 dBZ (Figs. 10b–f). The comparison between the observation and analysis mean of the Z in the six experiments at 1 km in the final cycle is depicted in Figs. 10g–l. Some improvements were noted near S-PolKa in experiments ZVrQv_a and ZVrQv_4q. The least deviation from the observation was observed in experiments Qv_ZVr_a and Qv_ZVr_4q.
As in Fig. 8, but for the third case at 1230 UTC 12 Oct 2011.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
As in Fig. 8, but for the third case at 1230 UTC 12 Oct 2011.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
As in Fig. 8, but for the third case at 1230 UTC 12 Oct 2011.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
For a more detailed comparison, the RMSEs of the Z, Vr, and Qv in the final analysis cycle were calculated and are listed in Table 3; the smallest RMSEs of these three variables in each case are indicated in bold font. Overall, the Qv assimilation experiments had lower Z, Vr, and Qv RMSEs compared with the experiments assimilating only the Z and Vr in all three cases. The most marked improvement in the assimilation of the Qv was obtained in the second case, which may be attributed to the more varied humidity profiles in this case, as mentioned in section 3b. Additionally, experiments Qv_ZVr_a and Qv_ZVr_4q resulted in more accurate Z, Vr, and Qv simulations than did ZVrQv_a and ZVrQv_4q.
RMSEs of the Z, Vr (compared with S-band radar), and Qv (compared with S-PolKa-retrieved Qv) at the final analysis cycle for the three cases. The smallest RMSEs of these three variables in each case are indicated in bold font.
The analysis results indicated that the assimilation of additional S-PolKa-retrieved Qv can enhance the modification of moisture more effectively than the assimilation of Z and Vr alone. However, assimilating only the Qv in nonprecipitation areas in the first hour of the assimilation period generated a more precise moisture environment than assimilating all data over the entire 2 h and resulted in the outperformed simulation of Z, Vr, and Qv. Furthermore, in the comparison of the two thinning methods (i.e., one averaged Qv profile and four-quadrant Qv profiles), moisture was more significantly and precisely modified in the four-quadrant Qv profile assimilation.
b. Performance of the short-term deterministic forecast
The analysis results revealed the outperformance of the data assimilation experiments (i.e., ZVr, ZVrQv_a, ZVrQv_4q, Qv_ZVr_a, and Qv_ZVr_4q) compared with the NODA experiment. Therefore, we focused on evaluating the short-term forecast performance of the data assimilation experiments. Figure 11 depicts the 3-h (from 1800 to 2100 UTC 18 October 2011) accumulated rainfall in the first case. Compared with the radar-derived total rainfall (Dolan et al. 2017; Fig. 11a), all data assimilation experiments predicted heavy rainfall in this event. In addition, these experiments exhibited similar rainfall patterns to the observation despite some overestimated areas (Figs. 11b–f). The more accurate analysis of the Z, Vr, and Qv in experiments Qv_ZVr_a and Qv_ZVr_4q (Table 3, Figs. 8j,l) resulted in more precise heavy precipitation areas than those in experiments ZVr, ZVrQv_a, and ZVrQv_4q (in the north domain, denoted by the black boxes).
Accumulated 3-h rainfall from 1800 to 2100 UTC 18 Oct 2011 for the first case. (a) Observation, (b) ZVr, (c) ZVrQv_a, (d) Qv_ZVr_a, (e) ZVrQv_4q, and (f) Qv_ZVr_4q. The encircled black cross represents the S-PolKa location. The black boxes denote the more accurate heavy rain forecasts of Qv_ZVr_a and Qv_ZVr_4q compared with those of the other experiments.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
Accumulated 3-h rainfall from 1800 to 2100 UTC 18 Oct 2011 for the first case. (a) Observation, (b) ZVr, (c) ZVrQv_a, (d) Qv_ZVr_a, (e) ZVrQv_4q, and (f) Qv_ZVr_4q. The encircled black cross represents the S-PolKa location. The black boxes denote the more accurate heavy rain forecasts of Qv_ZVr_a and Qv_ZVr_4q compared with those of the other experiments.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
Accumulated 3-h rainfall from 1800 to 2100 UTC 18 Oct 2011 for the first case. (a) Observation, (b) ZVr, (c) ZVrQv_a, (d) Qv_ZVr_a, (e) ZVrQv_4q, and (f) Qv_ZVr_4q. The encircled black cross represents the S-PolKa location. The black boxes denote the more accurate heavy rain forecasts of Qv_ZVr_a and Qv_ZVr_4q compared with those of the other experiments.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
Figure 12 presents the 3-h accumulated rainfall for the second case. As in the first case, all data assimilation experiments predicted heavy rainfall. The main rainband in the northern S-PolKa coverage area was captured in these experiments. However, the forecast rainband moved faster than the observation, resulting in underestimated and overestimated rainfall to the southwest and southeast of the domain, respectively (Figs. 12b–f versus Fig. 12a). As revealed in the analysis results, experiments Qv_ZVr_a and Qv_ZVr_4q exhibited less overestimation in the southeast corner domain and less underestimation at the most intense convective line to the north of the radar (Figs. 9j,l versus Figs. 9h,i,k). Therefore, these two experiments alleviated overprediction in the southeast domain and enhanced the intensity of the main rainband (Figs. 12d, f). Consequently, among the five data assimilation experiments, Qv_ZVr_a and Qv_ZVr_4q generated the results closest to the observations.
As in Fig. 11, but for 3 h (from 0200 to 0500 UTC 16 Oct 2011) for the second case.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
As in Fig. 11, but for 3 h (from 0200 to 0500 UTC 16 Oct 2011) for the second case.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
As in Fig. 11, but for 3 h (from 0200 to 0500 UTC 16 Oct 2011) for the second case.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
Figure 13 details the 3-h cumulative precipitation distribution for the third case. All data assimilation experiments (Figs. 13b–f) could predict heavy rainfall greater than 20 mm. However, the location of the scattered convective system was difficult to identify accurately. Compared with experiment ZVr, more heavy rain was forecast in the southeast domain in all Qv assimilation experiments (Figs. 13c–f versus Fig. 13b). The most complete and heaviest rainfall occurred in Qv_ZVr_a and Qv_ZVr_4q (Figs. 13d,f), which generated results that were the most consistent with the observation. This may link to the closer analysis of Qv_ZVr_a and Qv_ZVr_4q to the observation compared with that of ZVr, ZVrQv_a, and ZVrQv_4q (Figs. 10j,l versus Figs. 10h,i,k).
As in Fig. 11, but for 3 h (from 1230 to 1530 UTC 12 Oct 2011) for the third case.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
As in Fig. 11, but for 3 h (from 1230 to 1530 UTC 12 Oct 2011) for the third case.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
As in Fig. 11, but for 3 h (from 1230 to 1530 UTC 12 Oct 2011) for the third case.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
Figure 14 presents the FSS of accumulated rainfall from 1 to 4 h averaged over the three cases. In general, the FSS decreases with increasing rainfall thresholds. The most obvious enhancement occurred in experiment Qv_ZVr_4q for almost all thresholds throughout the 2–4-h forecast. In the comparison among the other four experiments, generally, assimilating either one averaged Qv profile or four-quadrant Qv profiles provided higher FSSs than assimilating only the Z and Vr during the first 3 h. Furthermore, in the 1-h forecast, assimilating four-quadrant Qv profiles with Z and Vr for the entire assimilation period produced a more favorable forecasting of heavy rain greater than 20 mm than the assimilation in the other experiments. Moreover, the FSS revealed that the assimilation of four-quadrant Qv profiles generated more accurate rain forecasts than the assimilation of one averaged Qv profile.
The FSS score of the (a) 1-, (b) 2-, (c) 3-, and (d) 4-h accumulated rainfall. Scores are averaged across the three cases.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
The FSS score of the (a) 1-, (b) 2-, (c) 3-, and (d) 4-h accumulated rainfall. Scores are averaged across the three cases.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
The FSS score of the (a) 1-, (b) 2-, (c) 3-, and (d) 4-h accumulated rainfall. Scores are averaged across the three cases.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
For further evaluation, the surface and sounding data from the Gan station and the S-PolKa-retrieved Qv were compared with the output from the data assimilation experiments. Figures 15a–e illustrate the RMSEs of the accumulated rainfall and that of the relative humidity (RH), T, U, and V variables at the Gan sounding station. The RMSEs were calculated during 1–4-h forecasts and were averaged across the three cases. In the prediction of accumulated rainfall at the Gan station (Fig. 15a), experiments Qv_ZVr_a and Qv_ZVr_4q exhibited lower RMSEs than the other three experiments during the 4-h forecast; the most accurate forecast was generated in the Qv_ZVr_a experiment. Among the other three experiments, ZVrQv_4q had the lowest RMSE in the first 2 h, but the RMSE later increased, eventually becoming the largest RMSE in the last 2 h. In comparison with the Gan sounding data (Figs. 15b–e), in general, all experiments that assimilated the additional Qv alternately offered the lowest RMSEs for the RH, T, U, and V during the first 3-h forecast, except for the least accurate forecast of the V in experiment ZVrQv_4q. Because the S-PolKa-retrieved Qv was unavailable for the 4-h forecast time in the first and second cases, the Qv RMSE was only calculated for the third case, as detailed in Fig. 15f. The results revealed that more improvement in the Qv forecast was achieved in experiments Qv_ZVr_4q and Qv_ZVr_a in the first 2 h. In the last 2 h, lower RMSEs were exhibited in experiments ZVrQv_a and ZVrQv_4q.
The 1–4-h RMSEs of the data assimilation experiments of (a) accumulated rainfall compared with surface rainfall at the Gan station; (b)–(e) the RH, T, U, and V compared with the Gan sounding station data, averaged for the entire profile; and (f) the Qv compared with the S-PolKa-retrieved Qv. The Qv RMSE is only calculated for the third case; other RMSEs are averaged across the three cases.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
The 1–4-h RMSEs of the data assimilation experiments of (a) accumulated rainfall compared with surface rainfall at the Gan station; (b)–(e) the RH, T, U, and V compared with the Gan sounding station data, averaged for the entire profile; and (f) the Qv compared with the S-PolKa-retrieved Qv. The Qv RMSE is only calculated for the third case; other RMSEs are averaged across the three cases.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
The 1–4-h RMSEs of the data assimilation experiments of (a) accumulated rainfall compared with surface rainfall at the Gan station; (b)–(e) the RH, T, U, and V compared with the Gan sounding station data, averaged for the entire profile; and (f) the Qv compared with the S-PolKa-retrieved Qv. The Qv RMSE is only calculated for the third case; other RMSEs are averaged across the three cases.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0292.1
The quantitative evaluation results further verified the effect of assimilating radar data and the S-PolKa-retrieved Qv for convective scales. The assimilation of Z and Vr with the retrieved Qv generates more accurate forecasts than the assimilation of Z and Vr only. Optimal forecasts can be obtained if the retrieved Qv is assimilated before Z and Vr in the first hour of the assimilation period. Furthermore, the assimilation of four-quadrant Qv profiles resulted in more accurate forecasts than the assimilation of one averaged Qv profile.
5. Summary and discussion
This study examined the assimilation of the Z, Vr, and retrieved Qv from the NCAR S-PolKa radar in convective forecasts. The retrieved Qv was thinned into one averaged Qv and four-quadrant Qv profiles and then assimilated using two strategies. Three real cases comprising two heaviest rain events and one scattered convection event in the DYNAMO campaign were examined. For each case, six experiments were conducted using the WLRAS. All data assimilation experiments consisted of 2-h assimilation with 15-min frequency and 6-h deterministic forecasts. Our main conclusions are summarized as follows:
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For the retrieved Qv, assimilating thinned humidity information into four quadrants provided a more effective analysis than assimilating the information in one averaged Qv profile, leading to a more markedly improved QPF in ZVrQv_4q and Qv_ZVr_4q than that in ZVrQv_a and Qv_ZVr_a, respectively. The performance results were particularly obvious in the second case because of the greater variety of humidity profiles in different directions in this case.
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The S-PolKa-retrieved Qv was only available when the precipitation system approached but did not cover the radar site. Therefore, the following two strategies were applied when conducting experiments: assimilating the retrieved Qv, Z, and Vr for the entire assimilation period, and assimilating only the retrieved Qv beforehand in the first hour of the assimilation period. Both approaches can more effectively improve the analysis of the environmental moisture nearby precipitation system compared with only assimilating the Vr and Z. In addition, more precise moisture adjustments were obtained when only the retrieved Qv was assimilated in the first hour of the assimilation period prior to other assimilation processes. Consequently, experiments Qv_ZVr_a and Qv_ZVr_4q exhibited more accurate analysis fields than other experiments as compared to the observation. The qualitative and quantitative evaluation for the short-term forecasts indicated that additionally assimilating the Qv with Z and Vr could improve the QPF and obtain a higher FSS in the 0–3-h forecast lead time compared with assimilating only the Z and Vr. The two experiments that assimilated the retrieved Qv alone in the first hour of the assimilation period generated the most comparable rainfall to the observations in terms of intensity and pattern, resulting in their highest FSSs. When further compared with the surface observation, sounding data, and S-PolKa-retrieved Qv, the results demonstrated that the experiments assimilating the retrieved Qv improved the short-term forecast of wind, temperature, and humidity at least up to 3 h. Overall, the assimilation of the additional S-PolKa-retrieved Qv is beneficial for short-term forecasting.
This study examined three cases. In the future, more cases, particularly those incorporating different weather scenarios such as hurricanes, can be investigated to increase the robustness and generalizability of the findings. Additionally, radar refractivity data, which provide thermodynamic information for the environment near the surface and significantly supplement the lacking of surface station observations (Feng et al. 2021), can be combined with the S-PolKa-retrieved Qv to construct a more complete environmental dataset. A comparison between the assimilation of the retrieved Qv and that of refractivity and an investigation into the effect of the combined assimilation of these two components are required.
Acknowledgments.
We appreciate three anonymous reviewers for their invaluable comments to improve the quality of the manuscript. This work was supported by the Ministry of Science and Technology of Taiwan under Research Grants 110-2111-M-008-023 and 104-2923-M-008-003-MY5.
Data availability statement.
NCAR’s Earth Observing Laboratory provided the data utilized in this study. The data included S-PolKa radar, fully corrected, final moments data in cfRadial format, S-band only (https://doi.org/10.5065/D6S75F50), Gan ARM AMF radiosonde L3 data, ESC format (https://data.eol.ucar.edu/dataset/347.008), NCAR S-PolKa radar rain rate data (https://doi.org/10.26023/3CX2-GQCY-3G04), and Gan, Addu Atoll, Maldives AMF-2 surface meteorology data (https://doi.org/10.26023/XB43-BSRF-VH04). The S-PolKa-retrieved water vapor data of the DYNAMO campaign were provided by Dr. Scott M. Ellis at the National Center for Atmospheric Research; this experimental dataset was not part of the base data delivered to the principal investigators.
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