The dual-polarization (dual pol) Doppler radar can transmit/receive both horizontally and vertically polarized power returns. The dual-pol radar measurements have been shown to provide a more accurate precipitation estimate compared to traditional radars. In this study, the horizontal reflectivity ZH, differential reflectivity ZDR, specific differential phase KDP, and radial velocity VR collected by the C-band Advanced Radar for Meteorological and Operational Research (ARMOR) are assimilated for two convective storms. A warm-rain scheme is constructed to assimilate ZH, ZDR, and KDP data using the three-dimensional variational data assimilation (3DVAR) system with the Advanced Research Weather Research and Forecasting Model (ARW-WRF). The main goals of this study are first to demonstrate and compare the impact of various dual-pol variables in initialization of real case convective storms and second to test how the dual-pol fields may be better used with a 3DVAR system.
The results show that the ZH, ZDR, KDP, and VR data substantially improve the initial condition for two mesoscale convective storms. Significant positive impacts on short-term forecast are obtained for both storms. Additionally, KDP and ZDR data assimilation is shown to be superior to ZH and ZDR and ZH-only data assimilation when the warm-rain microphysics is adopted. With the ongoing upgrade of the current Weather Surveillance Radar-1988 Doppler (WSR-88D) network to include dual-pol capabilities (started in early 2011), the findings from this study can be a helpful reference for utilizing the dual-pol radar data in numerical simulations of severe weather and related quantitative precipitation forecasts.
Despite the steady improvement in high-resolution numerical weather prediction (NWP) models in the last two decades, accurate forecast of convective storms remains a significant challenge (Emanuel et al. 1995; Weckwerth et al. 2004; Weisman et al. 2008). At present, NWP models only have limited skill in convective storm prediction and related quantitative precipitation forecast (QPF) (Weckwerth et al. 2004). An important reason for this low skill is that modeling of convection depends very much on the quality of the initial condition (Kalnay 2003; Tong and Xue 2008). Current conventional observation systems often provide very little scale-appropriate information for convective storms (Guichard et al. 2000; Wang et al. 2002). The poorly described mesoscale features in the initial condition lead to an inability of current NWP models to accurately simulate the timing, location, and evolution of convective storms, which later lowers forecast skills as the integration time increases.
Studies have shown that radar data assimilation can help with short-term prediction of convective weather by providing more accurate and detailed information on the mesoscale structure in the initial condition (Qiu and Xu 1992; Shapiro et al. 1995; Weygandt et al. 2002; Sun 2005; Dawson and Xue 2006; Hu et al. 2006; Zhao et al. 2006; Pu et al. 2009). Three-dimensional variational data assimilation (3DVAR) is a commonly used method for radar data assimilation because of its relative simplicity and low computational cost. Xiao et al. (2005, 2006, 2007, 2008) introduced the 3DVAR methodology for radar data assimilation into the Weather Research and Forecasting Model (WRF). They demonstrated positive impact on severe weather forecasts when radar reflectivity and radial velocity data were assimilated, using both statistics analyses and case studies. Four-dimensional variational data assimilation (4DVAR) is a more advanced method, one that requires higher computational expense than 3DVAR. Sun and Crook (1997, 1998) developed a 4DVAR system to assimilate Doppler radar observations using a cloud-scale model with a warm-rain microphysical parameterization. Sun (2005) and Sun and Zhang (2008) demonstrated that 4DVAR data assimilation improved the initial condition and subsequent prediction of the evolution of convective storms. Recently, the ensemble Kalman filter (EnKF) method has gained much attention in radar data assimilation research community (Snyder and Zhang 2003; Zhang et al. 2004; Caya et al. 2005; Tong and Xue 2005; Zhang et al. 2009). As a more flexible method, EnKF requires a significantly high computational cost because of the need to run an ensemble forecast with an order of 101–102 members and the computational expensive analysis procedure.
The above studies indicated not only the benefit but also the challenges in radar data assimilation. Several issues can largely limit the performance of radar data assimilation: 1) the ability of radar observations to accurately describe cloud information and atmospheric conditions, 2) the uncertainties in radar data, 3) the sampling and assimilation strategy employed, and 4) the inadequacy of the radar forward model.
An advance in Doppler weather radars that has long been discussed is the dual-polarization (also called dual polarimetric, or simply “dual pol”) technique, which is now being implemented operationally across the United States. The dual-pol radar represents a leap above the current Weather Surveillance Radar-1988 Doppler (WSR-88D) system, given that more information about cloud and precipitation particles is observed, and our knowledge of the microphysical processes within clouds can be greatly enhanced (Seliga and Bringi 1976; Hall et al. 1984; Sachidananda and Zrnić 1987). Dual-pol radars can transmit–receive both horizontal and vertical polarized signals. From the two power returns with different polarization, information on the type, shape, size, and orientation of cloud and precipitation microphysical particles is obtained. Standard variables from the dual-pol radar may include horizontal reflectivity ZH, radial velocity VR, differential reflectivity ZDR, correlation coefficient ρHV, differential phase ΦDP, and specific differential phase KDP. Numerous studies have demonstrated that dual-pol Doppler variables provide more accurate measurement of liquid and solid cloud and precipitation particles than nonpolarimetric weather radars (Aydin et al. 1990; Chandrasekar et al. 1990; Zrnić and Ryzhkov 1996; Rinehart 1997; Ryzhkov et al. 1998; Vivekanandan et al. 1999; Carey et al. 2000; Zhang et al. 2001; Brandes et al. 2002; Bringi et al. 2003; Vivekanandan et al. 2004). Therefore, the use of dual-pol data might be a good way to reduce the uncertainties in radar estimate of precipitation and improve radar data assimilation.
The assimilation of dual-pol radar observations has not been explored much in past studies because of many reasons, including the unavailability of data, the special requirements and additional procedures needed for data processing and quality control, the complexity in developing forward models, and the determination of observational errors and noises. An early study by Wu et al. (2000) attempted to indirectly assimilate ZDR data with a 4DVAR system into a cloud model. Rain and ice mixing ratios derived from real observations of ZH and ZDR were assimilated for an isolated thunderstorm. The results showed that a large forecast error occurred because of either the deficiencies in the simple microphysics scheme used or the inability of their cloud model to simulate the nonlinear processes in the actual atmospheric systems. Their results exemplified the difficulty in assimilating dual-pol radar observations for real case studies. Jung et al. (2008a,b, 2010) represents a series of study that has successfully assimilated dual-pol radar data. With an EnKF, they directly assimilated model-simulated dual-pol variables into the observing system simulation experiments (OSSEs). Using a sophisticated microphysical scheme, ZDR, ZDP, and KDP data were incorporated into the Advanced Regional Prediction System (ARPS) model. Their studies demonstrated significant improvements that the dual-pol variables provided to vertical velocity, water vapor, and hydrometeor fields.
Collectively, the above studies revealed the benefits, as well as many unanswered questions in dual-pol radar data assimilation, which motivated our recent studies, Li et al. (2009) and Li and Mecikalski (2010, hereafter LM10). LM10 successfully assimilated dual-pol radar variables for a real case study. A radar forward operator was built in the WRF 3DVAR system to directly assimilate ZH, ZDR, and VR data collected from the Advanced Radar for Meteorological and Operational Research (ARMOR) in north-central Alabama. The result showed significantly positive impacts when assimilating ZH, ZDR, and VR observations for a mesoscale convective system (MCS) on 15 March 2008. Furthermore, the assimilation of ZDR data provided additional improvement in storm initialization, which subsequently led to better short-term precipitation forecast. This current study is a follow on to LM10, to continue exploring the methodology of dual-pol radar data assimilation for real case events. In the present paper, another dual-pol variable, the specific differential phase KDP, is assimilated. Experiments to assimilate different dual-pol variables are conducted. The main goals of the present study are to 1) examine by how much the assimilation of dual-pol radar observations can benefit the short-term precipitation forecast of real storms, 2) explore the assimilation of additional dual-pol variables beyond LM10, and 3) help understand further how dual-pol observations can be used more efficiently in NWP. The findings in this study should be especially useful when the entire National Weather Service (NWS) WSR-88D Next Generation Weather Radar (NEXRAD) radar network is upgraded to include the dual-pol characteristics (started in early 2011).
This paper is organized as follows: Section 2 introduces the observation data and the ARMOR dual-pol radar system, the methodology of radar data assimilation, the numerical model configuration, and the experiment design. In section 3, the numerical simulations and data assimilation results are analyzed and compared to evaluate the impact of the dual-pol radar data assimilation. Section 4 summarizes the study and addresses some unresolved questions.
2. Assimilation system and experimental design
a. Observation data
Dual-pol Doppler radar observations used in this study were collected by the ARMOR radar. ARMOR is a C-band Doppler radar located at Huntsville International Airport (34.6804°N, 86.7743°W). It was upgraded with dual-pol capabilities in October 2006. The ARMOR radar operates in simultaneous linear transmit and receive mode, which transmits and receives both horizontally and vertically polarized power returns. It provides real-time products of wind, precipitation, and polarimetrically diagnosed cloud information and microphysical properties on a 24/7 basis (Petersen et al. 2007). Because C-band radars suffer from attenuation during heavy rain and hail (Carey et al. 2000), ARMOR measurements are corrected for attenuation using a locally modified software that computes differential propagation phase and specific differential phase using a finite impulse response (FIR)–adaptive spatial filter approach (Bringi et al. 2001; Petersen et al. 2005). Automatic and manual quality control procedures are applied before the data are gridded into a Cartesian coordinate with 1 km × 1 km in horizontal and 0.5 km in vertical. More details about ARMOR radar measurements and the quality control procedure can be found in LM10.
Two convective storms are studies to analyze and evaluate the impact of the assimilation of ARMOR observations. In addition to the MCS event on 15 March 2008 that has been studied in LM10, an isolated summertime thunderstorm (meso-β scale) in the afternoon of 23 June 2008 is selected. A caveat to the present study is that observations from single radar often provide incomplete coverage for storms that have large horizontal spans. The result in LM10 exemplified the limitation caused by the incomplete coverage of ARMOR for the MCS. The thunderstorm on 23 June had a relatively small horizontal dimension, which put it completely within the radar coverage when it passed the ARMOR site. This storm initiated near 1500 UTC 23 June 2008 over eastern Tennessee with a size of only ~10 km in diameter. After about 3–4 h, the system intensified and grew into a meso-β-scale storm. It then propagated southeastward across southern Tennessee–northern Alabama and dissipated in northwest Georgia early on 24 June 2008. Strong winds (20–25 m s−1), lightning strikes, and hail (~2 cm) were observed in several counties in southern Tennessee–northern Alabama along its path. ARMOR has well captured this storm during the time period of 1930–2100 UTC with high-quality 14-tilt volume-scan data every 5 min. Figures 1a–d show the gridded ARMOR data of ZH, ZDR, KDP, and VR at different vertical levels, collected near 1927 UTC 23 June 2008, plotted within the innermost WRF domain. As in Fig. 1, because this storm possesses a relatively small spatial span, ARMOR recorded a complete three-dimensional view of the meso-γ-scale structure and its evolution as the storm moved across the radar domain.
As mentioned above, the MCS event on 15 March 2008 was studied in LM10, which demonstrated positive impact of ZH and ZDR data assimilation on short-term precipitation forecast. This same case is further studied in this present study. An additional experiment is added in order to investigate how the use of KDP and ZDR data influence the storm initialization when compared with ZH and ZDR data assimilation.
b. Experimental design
The Advanced Research WRF (ARW-WRF; Skamarock et al. 2008) is used to simulate the meso-β-scale thunderstorm event on 23 June 2008. Figure 1e shows the two-way interactive, double-nested domains. The dimensions of the domains are 450 × 360 × 28 and 480 × 390 × 28 with horizontal resolution of 3 and 1 km, respectively. The model physics options for both domains include the rapid radiative transfer model (RRTM; Mlawer et al. 1997) longwave radiation, Dudhia shortwave radiation (Dudhia 1989), and Yonsei University (YSU) planetary boundary layer (PBL) schemes (Hong et al. 2006). Because the resolutions of both domains are <5 km, the cumulus parameterization is not used. The warm-rain Kessler microphysics (Kessler 1969) scheme is employed to keep the model configuration compatible with the radar observational operator. The initial conditions for all the WRF simulations are interpolated from the National Centers for Environmental Prediction (NCEP) North American Mesoscale (NAM) model 12-km analysis.
Several experiments are conducted before the ARMOR radar data are assimilated. Two WRF runs, I15Z and I18Z, start at different times (1500 and 1800 UTC) in attempt to obtain a better initial depiction of the early stage of the storm. In addition, the experiment NXRD1730 assimilates the reflectivity and radial velocity data from the NEXRAD radar KGWX (Columbus Air Force Base, Mississippi, located ~160 km southwest of the ARMOR radar) into the WRF at 1730 UTC. These experiments serve the purpose to generate a relatively reasonable background field for data assimilation experiments and also provide us a view on the prediction skill of the WRF for this meso-β-scale storm.
Three experiments are conducted for the ARMOR radar data assimilation. The experiment RF assimilates only ZH and VR data. In the experiment RD, ZH, ZDR, and VR data are assimilated. In the experiment KD, KDP, ZDR, and VR data are incorporated into the WRF. All three data assimilation experiments use the WRF forecast from NXRD1730 at 1930 UTC as the background field. The ARMOR data assimilation is done for both domains between 1930 and 2030 UTC at an interval of 30 min. Because the gridded radar data have a horizontal resolution of 1 km, the observational data are thinned by averaging the values (weighted by the distance) at the points within 2-km distance from the model grids to fit the 3-km resolution of the coarser domain. Table 1 lists all the numerical experiments and the corresponding data assimilation conducted for the thunderstorm on 23 June 2008.
In LM10, experiments were conducted to compare the ZH and ZDR data assimilation with the ZH-only assimilation for the MCS on 15 March 2008. It was demonstrated that ZDR data assimilation provided additional benefit beyond the assimilation of ZH only. This result encouraged us to study further the assimilation of more dual-pol radar variables. In the present paper, one additional experiment, MCSKD, is conducted for the MCS event by assimilating KDP, ZDR, and VR data. MCSKD is compared with the two experiments from LM10, MCSRF and MCSRD, to evaluate the impacts of KDP and ZDR data. Here, MCSRF represents the experiment that assimilated ZH-only and VR data and MCSRD represents the experiment that assimilated ZH, ZDR, and VR data for the MCS event. ARMOR observations were assimilated from 0730 to 0830 UTC at an interval of 30 min in all three experiments. Detailed information about domain configuration, model physics schemes, data assimilation strategy, and forecast length for the experiments can be found in LM10. MCSKD adopts the same options as the experiments in LM10. The data assimilation setup of the experiments for the MCS is listed in Table 2.
c. Data assimilation procedure
The dual-pol Doppler radar observations from ARMOR are assimilated using the 3DVAR data assimilation system with the WRF. The algorithm of WRF 3DVAR system is based on Barker et al. (2004) with a number of improvements described in Skamarock et al. (2008). The background error for the WRF 3DVAR is calculated using the “National Meteorological Center (NMC) method” (Parrish and Derber 1992) by the averaged difference between 24- and 12-h forecasts in the month of June 2008. The background error field is calculated using the gen_be tool in the WRF 3DVAR package with the control variable (CV) option set to 5.
The methodology for ZH-only data assimilation can be referred to LM10. The forward operator for ZH and ZDR data assimilation used in this study is derived by Bringi and Chandrasekar (2001) for C-band radars as
where ZH is in mm6 m−3, ℑDR is nondimensional differential reflectivity in linear scale , and qr is the rainwater content in g m−3. It is shown in LM10 that the assimilation of ZH and ZDR significantly improved the model initial condition of the MCS. However, there remains room for further improvement. For instance, the above rain estimate equation is based on several assumptions, including that (i) drops fall with their minor axis vertically oriented, (ii) size relations are known, and (iii) the exponential raindrop size distribution is applicable. These assumptions can cause limitations in precipitation estimation (Aydin and Giridhar 1992; Ryzhkov and Zrnić 1995).
The use of the specific differential phase KDP can further improve radar estimates of rainfall (Sachidananda and Zrnić 1986; Aydin and Giridhar 1992; Ryzhkov and Zrnić 1995, 1996; Vivekanandan et al. 1999). The term KDP is the range derivative of the differential phase ΦDP and can be calculated by . Here, KDP represents the difference in propagation constants between the horizontally and vertically polarized waves. This parameter has several advantages compared to other dual-pol variables in estimating precipitation rates for anisotropic hydrometeors: it is unaffected by calibration and attenuation, immune to partial beam blockage and ground clutter canceling, less influenced by the anomalous propagation, less sensitive to the variation of drop size distribution, and unbiased by the existence of hail (Humphries 1974; Sachidananda and Zrnić 1986; Jameson 1991; Zrnić and Ryzhkov 1996; Vivekanandan et al. 1999). Humphries (1974) and Sachidananda and Zrnić (1987) showed that KDP is linearly correlated to rainfall rate. Many studies (Aydin and Giridhar 1992; Ryzhkov and Zrnić 1995, 1996; Vivekanandan et al. 1999) showed advantages of using KDP for rainfall estimate. Ryzhkov and Zrnić (1995, 1996) demonstrated that the use of the KDP and ZDR information produced more accurate rainfall estimate than the relationship based on horizontal and vertical reflectivity data. A relationship developed in Bringi and Chandrasekar (2001) for C-band radar is
where KDP is in degrees per kilometer. In the present study, we use Eq. (2) as the radar observational operator to assimilate the KDP and ZDR data collected by the ARMOR C-band radar. Figure 2 compares the rainwater content computed with the ARMOR data using Eqs. (1) and (2) for the MCS event at 0830 UTC 15 March 2008. As in Fig. 2, the most significant feature is that the use of Eq. (2) produces larger water contents than Eq. (1) over the convective core region (>40 dBZ). Accordingly, different distributions of rainwater and cloud water are produced through the data assimilation procedure, which later contribute to the difference in thermodynamic structure.
The WRF 3DVAR radar reflectivity data assimilation package utilizes a warm-rain microphysical parameterization scheme based on Dudhia (1989). The warm-rain processes include the condensation of water vapor into cloud water, accretion of clouds by rain, automatic conversion of cloud water to rainwater, and evaporation of rain to water vapor. The control variable for the radar data assimilation is the total water mixing ratio (the sum of water vapor, cloud water, and rainwater). When processing the radar data, the liquid water content is set to zero for locations where the radar observes clear air. Before conducting the data assimilation, we noticed that, at many grid points where the radar observed precipitation, the background showed clear air instead. For these grid points, we adjusted the background rainwater to 10% of the radar-retrieved rainwater before data assimilation. Sugimoto et al. (2009) showed that this is an effective method for reducing the difference between the background and the observation, which makes it easier for the data assimilation system to efficiently absorb the radar information.
The radial velocity VR data assimilation uses the operator from Xiao et al. (2005),
where (x, y, z) is the location of the radar site; (xi, yi, zi) is the location of the radar observations; ri is the distance between the radar site and the location of the radar data; (u, υ, w) are the 3D wind components; and υT is the terminal velocity calculated following Sun and Crook (1998).
a. Impact of initial condition on simulation of the 23 June 2008 thunderstorm
Simulation of meso-β-scale convective storms is a challenging problem for current NWP models. Before the ARMOR data assimilation is performed, several experiments are conducted to examine the skill of the regional WRF in predicting the afternoon thunderstorm on 23 June 2008. Because a reasonable description of the initial stage of the thunderstorm is important for generating a reasonably good forecast for the evolution of the storm, experiments are conducted serving this purpose as well. First, the WRF simulations I15Z and I18Z are started at 1500 and 1800 UTC, respectively, in an attempt to obtain a better depiction of the early stage of the storm around 1800–1900 UTC. The initial conditions for both simulations are interpolated from the NCEP NAM model 12-km analysis. Therefore, a later time run of I18Z should include a better initial condition than I15Z regarding the storm description, whereas I15Z will allow the WRF have a longer time to spin up. Figure 3 compares the composite reflectivity at 1800 and 1900 UTC from the NWS NEXRAD radars KHTX (Hytop, Alabama), KGWX, and KFFC (Atlanta, Georgia) with the WRF forecast fields from the experiments I18Z and I15Z. As shown in Figs. 3c–f, in both experiments I18Z and I15Z, no significant convection is generated in or near the area of interest. This indicates the inadequate ability of the WRF to predict this meso-β-scale storm, due to the poor representation of the storm in the initial condition. This result is not surprising, given the generally low skill of current regional mesoscale NWP models in predicting meso-β-scale convective storms, as discussed in previous sections.
The KGWX radar observed the development of this thunderstorm at its initiation and intensification stages. Therefore, experiment NXRD1730 assimilated the KGWX observations into the WRF to spin up the storm at its early stage. Using the model forecast from I15Z at 1730 UTC as background, NXRD1730 assimilates the reflectivity and VR data from KGWX at 1730 UTC. Figures 3d,h show the forecast of reflectivity from NXRD1730 at 1800 and 1900 UTC, respectively. It is seen that there are some convective clouds developing at the observed location, although the strength is much weaker than that observed. In addition, Fig. 3 shows another benefit from the NEXRAD data assimilation. Because of the assimilation of clear-air data from NEXRAD observation, it seems that the data assimilation procedure also helps remove the high-frequency noises appeared in both I15Z and I18Z experiments.
b. Impact of ARMOR data assimilation for the 23 June 2008 thunderstorm
With the forecast from NXRD1730 at 1930 UTC as background, ARMOR dual-pol radar data assimilation experiments are conducted for the 23 June 2008 thunderstorm event. Figure 4 shows the reflectivity distribution at the end of the data assimilation cycle (2030 UTC 23 June 2008) from the NEXRAD radar image (Fig. 4a), 5.5-h forecast from the experiment I15Z (Fig. 4b), 3-h forecast from NXRD1730 (Fig. 4c), the data assimilation analysis from RF (Fig. 4d), the analysis from RD (Fig. 4e), and the analysis from KD (Fig. 4f). As in Fig. 4b, the WRF run produces scattered convective clouds, but at locations far from the one observed. Figure 4c shows that the assimilation of the NEXRAD data at 1730 UTC brings improvement in storm location, but the intensity is still much weaker and it is not as organized as the observed one. This indicates that the model is not accurately predicting the development of this thunderstorm without substantial use of radar observations, particularly those from ARMOR. In contrast, after the assimilation of ARMOR data, the structure of the storm has been largely improved. Specifically, the most distinguishing feature in the NEXRAD observation is the well-organized convection over southern Tennessee to northern Alabama (Fig. 4a). Comparing with the NEXRAD observation, NXRD1730 produces weak convective cells in northwest Alabama. The cells have a horizontal scale on the order of ~100 km and are located to the west of the observed storm (Fig. 4c). With cycled assimilation of ARMOR ZH and VR data, RF produces strong convection over northern Alabama–southern Tennessee (Fig. 4d). After assimilating ZH and ZDR data, the main feature of the strong convective region over northern-central Alabama is retrieved in RD (Fig. 4e). The location is very close to the observed one, even though the size of the storm is still smaller than the observed echo. It is also noted that RD tends to overestimate the strong echo over the convective core region. The assimilation of KDP and ZDR data provides even better initialization for the storm. The bow echo shape of the convection in KD is a remarkable resemblance to the observed pattern. In addition, KD outperforms RD and RF at the convective core region in terms of the magnitude and area of high reflectivity (Fig. 4f).
The quantitative evaluation of the impact of ARMOR data assimilation can be illustrated by comparing the O − B with the O − A at the observational locations. Here, O − B represents the difference between ARMOR observed reflectivity O and the reflectivity calculated from the background field B. Subsequently, O − A represents the difference in reflectivity between the ARMOR observations and the data assimilation analysis fields A. The statistical effects of O − B and O − A at 2030 UTC 23 June 2008 are displayed by the histogram plots in Fig. 5. For successful data assimilation experiments, O − A would be much smaller than O − B. As shown in Fig. 5, the differences between the observations and the data assimilation analyses from RF, RD, and KD are significantly smaller compared to the difference between the observations and the background from NXRD1730. Specifically, in Fig. 5a, the maximum and minimum values of O − B are 25.4 and −25.6 for RF and 23.4 and −22.8 dBZ for RD, respectively. In KD, the maximum O − B is 16.7 and the minimum is −18.1 dBZ. For O − A, the maximum and minimum values are 16.8 and −15.9 for RF and 13.6 and −13.2 dBZ for the experiment RD (Fig. 5b). In KD, the maximum and minimum O − A improve to 9.3 and −10.2 dBZ, respectively. The number of the data points with O − A values within [−0.5, 0.5] dBZ also increases from 2485 in RF and 2782 in RD to 3222 in KD. Moreover, KD also shows apparent improvement for O − A values within [−15, −5] dBZ and [5, 15] dBZ, which clearly indicates the benefit of the assimilation of the KDP and ZDR data.
The impact of the ARMOR radar data varies at different vertical levels. Figure 6 plots the horizontally averaged absolute values of O − B and O − A in the first cycle of data assimilation at 1930 UTC 23 June 2008. In NXRD1730, the maximum of averaged absolute value of O − B is 11.1 dBZ. The large value of averaged O − B occurs between the surface and 6-km altitude. Above 6 km, the averaged O − B value decreases rapidly with height, which is related to the generally lower reflectivity values at high altitudes. After the assimilation of the ARMOR data, the difference between the observation and data assimilation analysis is substantially reduced. The maximum averaged O − A decreases greatly to 4.3 dBZ in RF and 3.7 dBZ in RD. In KD, the averaged O − A values are generally smaller than the values in RD and RF at most levels. Below 6-km altitude, the averaged O − A values in KD are about 0.5 dBZ less than those in RD and roughly 1 dBZ less than those in RF.
LM10 demonstrated how ZH and ZDR data assimilation is compared with ZH-only data assimilation in storm structure. In this section, a further examination is included to demonstrate how KDP and ZDR data assimilation is different from ZH and ZDR data assimilation in terms of the kinematic, thermodynamic, and hydrometeor fields. Figure 7 shows the difference fields between RD and NXRD1730 (Fig. 7a) and between KD and NXRD1730 (Fig. 7b) at 2030 UTC 23 June in water vapor mixing ratio qυ, rainwater mixing ratio qr, cloud water mixing ratio qc, and potential temperature θ fields at 2-km height. It is clearly seen that, in both Figs. 7a,b, there are significant increases in qr and qc over the stormy region due to the assimilation of the radar observation. An apparent increase in qυ is also found over northern Alabama. The increased moisture and saturation would benefit the development of convection in this area. A decrease in θ is produced because of the evaporation cooling of the added rainwater at low troposphere. Sugimoto et al. (2009) suggested that 3DVAR has limited ability in retrieving the water vapor and cloud water. The significant impact of radar data on qυ and qc in this study can be attributed to the cycled assimilation of the ARMOR data, which enhanced the structure of cloud microphysics in the WRF. Comparing Figs. 7a,b, it is found that RD produces a larger increase in qr and qc fields over the convective core region. Higher magnitudes of the qυ increase over northern Alabama are also produced in RD. This result indicates stronger convection in RD, which also explains the overestimate of reflectivity shown in Fig. 4d rather than in Fig. 4e.
Figure 8 depicts the horizontal wind components u and υ and the wind vector at 2030 UTC 23 June 2008 from RD and KD, whereas Fig. 9 shows horizontal distribution and vertical cross section of vertical velocity w field. As shown in the figures, convergence at low level is produced in low levels in both RD and KD, and hence updraft is built at northern–central Alabama. In addition, after three cycles of data assimilation, large variations in the magnitudes of u and υ are found between RD and KD (Figs. 8a–d), and hence vertical velocity field shows different structure (Figs. 9a–d). In general, RD produces higher values in vertical velocity around the stormy area (Figs. 9a,b) than KD. This may be a direct contribution to the larger amount of rainwater and cloud water produced in RD than in KD (Figs. 7a,b).
The short-term forecast of the thunderstorm is enhanced in radar data assimilation experiments. Figure 10 shows reflectivity at 2-km height from NEXRAD radar image (Fig. 10a) and forecast from NXRD1730 (Fig. 10b), RF (Fig. 10c), RD (Fig. 10d), and KD (Fig. 10e) at 2100 UTC 23 June 2008. Comparing to Fig. 10a, the forecast in NXRD1730 only produces a weak system at the location far west of the observed storm. This means the forecast storm in NXRD1730 is much weaker and propagates slower than that observed. As in Figs. 10c–e, RF, RD, and KD produce much better forecasts for the thunderstorm event. Figure 10c shows that the forecast of the storm in RF generates the convective region over northern Alabama. With the assimilation of the ZH, ZDR, and VR data in the initial condition, the forecast of the storm in RD produces a better structure than RF, although the echo within the convective core region is still stronger and has a smaller size than the one observed (Fig. 10d). This may be attributed to the overestimate of reflectivity that occurred at 2030 UTC (Fig. 4e). Using the initial condition with KDP and ZDR data assimilation, KD produces the pattern and location of the storm in very good agreement with the observation at 2100 UTC. When compared with RD and RF, the storm in KD has a broader coverage with a structure closer to the observation (Fig. 10e).
Figure 11 compares the forecasts of reflectivity at 2200 UTC 23 June 2008 from different experiments with the NEXRAD observation. Consistent with the results in Fig. 10, Fig. 11 shows that radar data assimilation experiments RD and KD produce storm structures that are much more realistic than NXRD1730, with KD in better agreement with the radar observation than RF and RD. At 2200 UTC, the NEXRAD image indicates that the thunderstorm started to dissipate. KD captures very well the timing and location of this weakening trend. This is quite remarkable for the numerical prediction of a meso-β-scale storm using a mesoscale model.
A quantitative evaluation of the ARMOR radar data assimilation impact on the short-term forecast of the thunderstorm is done using the threat score TS of different experiments. According to Xiao et al. (2005), TS can be calculated by
where C is the number of correct forecast events; F is the number of total forecast events; and R is the number of radar observed events, which is obtained from the NEXRAD observations (due to the incomplete coverage of ARMOR radar at later forecast times).
Because LM10 showed that the major impact from radar data assimilation would last no longer than a few hours after the completion of data assimilation cycles, TS comparisons are focused within 2 h after the ARMOR data assimilation cycles. Figure 12 shows the calculated TS values for each experiment from 2030 to 2230 UTC with threshold values of 10, 20, 30, and 40 dBZ. As in Fig. 12, NXRD1730 generally has a very low score at all four threshold values. In contrast, TS values for RF, RD, and KD are much higher. For example, TS values for NXRD1730 are not more than 0.06 at the threshold of 10 dBZ, whereas TS values can be as high as 0.34, 0.46, and 0.55 for RF, RD, and KD, respectively. This apparently indicates the significant positive impact of ARMOR radar data assimilation. In addition, KD generally produces larger TS values than RD and RF most of the times, which verifies the beneficial effect of assimilating the KDP and ZDR data into the initial condition. On the other hand, Fig. 12 also shows that, even with the radar data assimilation, it is still difficult for the model to fully capture all meso-γ-scale features of the storm. Specifically, the TS for KD with threshold of 40 dBZ is 0.30 at 2030 UTC. After 30 min, this score decreases rapidly to 0.22. After 2 h, the score decreases further to 0.11. This rapid decrease in TS may be related to the imperfect mesoscale model. It may also imply that the initial condition is not well balanced, which is not surprising when a relatively simple technology, such as 3DVAR, was used for data assimilation.
c. KDP and ZDR data assimilation for the 15 March 2008 MCS
In LM10, ZH and ZDR data assimilation experiment was compared with ZH-only data assimilation for the MCS event on 15 March 2008. The result indicated that assimilation of ZH and ZDR data provided additional improvement in storm initialization and short-term forecast. In this section, the assimilation of KDP and ZDR data for the MCS event is compared with the data assimilation experiments done in LM10. Figure 13 displays reflectivity at the end of the data assimilation cycle (0830 UTC 15 March 2008) from NEXRAD radars (Fig. 13a), the control run MCSCTRL (CTRL as presented in LM10; Fig. 13b), the data assimilation analysis from MCSRF (RF as presented in LM10) that assimilated ZH and ZDR data (Fig. 13c), the data assimilation analysis from MCSRD (RD as presented in LM10) that assimilated ZH and ZDR data (Fig. 13d), and the data assimilation analysis MCSKD that assimilates KDP and ZDR data (Fig. 13e). It is seen that MCSKD produces a better result than all the other experiments. Broader storm coverage is produced and the pattern of reflectivity is closer to the radar observation. As shown in both LM10 and this study, the southern part of the MCS is not captured partly because of the limited coverage of ARMOR for this MCS event.
The O − B and O − A of reflectivity at the observational locations are computed to illustrate the impact of the ARMOR KDP and ZDR data assimilation. Figure 14 compares the statistical effect of data assimilation through the histogram plots of O − B and O − A at 0830 UTC 15 March 2008. As in Fig. 14, the analysis from MCSKD is generally closer to the observation than the analysis from MCSRD. Specifically, in Fig. 14a, the maximum and minimum values for O − B in MCSRD are 19.2 and −18.6 dBZ, respectively. In comparison, the maximum and minimum values for O − B in MCSKD are 14.5 and −16.2 dBZ. For O − A, the maximum and minimum values in MCSRD are 9.4 and −8.9 dBZ, whereas they are 5.4 and −6.2 dBZ for the experiment MCSKD (Fig. 14b). In addition, Fig. 14b also shows that the number of the data points with O − A values within [−0.5, 0.5] dBZ increased from 3927 in MCSRD to 4205 in MCSKD. This clearly indicates the benefit of the assimilation of KDP and ZDR for the MCS on 15 March 2008. In Fig. 15, forecast score from MCSKD is compared with MCSRD from 0830 to 1030 UTC with threshold values of 10, 20, 35, and 40 dBZ. It is apparent that TS values for MCSKD are higher than those for MCSRD most of the times. Figures 14 and 15 verify the beneficial effect of assimilating the KDP and ZDR data, especially when the reflectivity is higher than 20 dBZ. Because LM10 demonstrated that the experiment with ZH and ZDR assimilation obtained a better forecast score than the one with assimilation of ZH only, the result shown above indicated that assimilation of KDP and ZDR data produce better initialization and short-term forecast than either ZH and ZDR data assimilation or ZH-only data assimilation.
4. Discussion and conclusions
Through two real case studies, this research demonstrates and evaluates the data assimilation of several dual-pol Doppler radar variables, using the 3DVAR data assimilation technique with a regional mesoscale WRF, for the short-term forecast of convection and the associated precipitation. Using observations from single dual-pol Doppler radar, with cycled data assimilation procedure, four dual-pol variables (ZH, ZDR, KDP, and VR) are successfully incorporated into the initial condition of the WRF. Our goals of this study are to compare and quantify the benefits associated with the assimilation of these dual-pol radar variables and to show how the dual-pol observations may be better used in a numerical modeling. Two convective storms are examined. An isolated summer thunderstorm over northern Alabama on 23 June 2008 is studied, which indicates that the ARMOR radar data assimilation significantly improve storm initialization. The result for the MCS in the afternoon of 15 March 2008 verifies the same conclusion.
In general, the results from the case studies indicate the following:
The ZH, ZDR, KDP, and VR observations from ARMOR are appropriately assimilated into the high-resolution WRF. The dual-pol radar variables bring additional benefit into the short-term precipitation forecast.
The dual-pol radar data assimilation shows significant impact on the mesoscale structure in wind (u, υ, and w), thermodynamic (qυ and θ), and microphysics fields (qr and qc) in the model initial condition.
For warm-rain radar data assimilation, KDP and ZDR provide larger improvements in storm initialization compared to ZH and ZDR assimilation and ZH-only data assimilation.
The beneficial impact from the radar data assimilation does not remain long in the model simulation; within about 2 h, the improvement decreases to about 1/2 of the original influence (as shown in Fig. 12). Therefore, cycled assimilation of radar data may be a good way to keep the forecast accuracy.
Overall, KDP and ZDR data assimilation is superior to ZH and ZDR data assimilation or ZH-only data assimilation in the initialization of the two simulated convective storms. In this light, more case studies are needed to confirm the conclusions in this paper. Several issues need to be considered prior to performing further data assimilation experiments. Specifically, KDP is not a direct measurement from the dual-pol radar, and hence it carries several shortcomings. Differential propagation measurements have accuracies of a few degrees, and they are filtered in range before the computation of KDP. This filtering process may directly cause bias in KDP values (Gorgucci et al. 1999). Sidelobe contamination may also cause bias in estimates of KDP (Sachidananda and Zrnić 1987), and KDP is found being vulnerable to random and artifact errors (Sachidananda and Zrnić 1987; Smyth et al. 1999; Brandes et al. 2001; Ryzhkov and Zrnić 1996). These data artifacts need to be considered and carefully reduced. Additional quality control procedures also should be applied before the KDP data are assimilated for real case studies. To reduce the influence of artifacts errors, so to take full advantage of the dual-pol variables, future studies should develop more sophisticated radar forward operators, in which multiple dual-pol variables are employed to describe different properties of hydrometeors and microphysical processes in clouds.
This study also implied several general areas that need further improvement. It is found that the 3DVAR system is less effective in correcting for the false convective clouds provided by the background field. For example, as in Figs. 4d,e, there are unobserved precipitation in the northeast corner of Mississippi that come from the background field. Instead, the NEXRAD observed no echoes over that region, and the data assimilation did not effectively remove all of the false convective clouds. This limitation, within the present study and implied by other previous studies (e.g., Sugimoto et al. 2009), exemplifies the extent that radar data assimilation through 3DVAR can adjust the instability of atmosphere over a stormy region. In addition, both LM10 and the present study quantify the importance of radar coverage to the effectiveness of radar data assimilation. Limited data coverage is a common issue when using observations from a single radar. Fortunately, this issue will be solved in the coming years, because the entire NEXRAD radar network will soon be upgraded with dual-pol capabilities. With the upgrade of the NEXRAD network, the 3D dual-pol products and level II variables will be constructed for most areas of the continental United States. The dual-pol radar data assimilation can then be examined and employed for both research and operational purposes.
Another issue in the present study is the use of the warm-rain microphysical processes in radar data assimilation. As with most existing radar data assimilation systems (e.g., Xiao et al. 2007; Chung et al. 2009; Sugimoto et al. 2009), this study also only considered liquid water in data assimilation procedure. As a result, unrealistic structure in cloud and precipitation were caused, especially in the middle to upper troposphere, where the ice microphysics play very important roles in kinematic and thermodynamic processes. The lack of robust ice-phased microphysical processes also limits our ability for a more accurate prediction of the convective storms. In addition, as Jung et al. (2010) showed, the use of single moment microphysical scheme could be a source of error in describing the dual-pol signatures: for example, the KDP and ZDR columns. A more sophisticated, ice-phased higher-moment microphysical scheme is needed to better represent those features.
Dual-pol radar data assimilation research is still at its very early stage. Our current ongoing research focuses on building the ice-phased microphysical processes in the WRF 3DVAR package based on the simple ice WRF Single-Moment 3-Class (WSM3; Hong et al. 2004) scheme. With the successes of dual-pol radar data assimilation in this study and LM10, we are increasingly curious, when the more sophisticated ice-phased microphysical forward model is developed for dual-pol observations, how much more information can be retrieved and incorporated into the model, which dual-pol variables would be the most informative ones for data assimilation, and to what extent the dual-pol variables can improve the NWP modeling of convective storms. In addition, due to the complicated microphysical processes and the various properties of real cloud and precipitation particles related, a more robust way to take advantage of the dual-pol variables may be the so-called hybrid algorithm (e.g., Lee 2006), using different variables and forward operators for different regions in real storms. Questions regarding how to design and implement these methods in data assimilation technology are open to future studies.
This work was supported by NSF Grants AGS-1005354 and ATM-0813603. The authors thank Drs. Lawrence Carey and Walter Petersen for their valuable comments on this study and their help with obtaining and processing the ARMOR radar observations. The authors also would also like to thank three anonymous reviewers for their contributions, which substantially improved the quality of this paper.