Radar Data Assimilation with WRF 4D-Var. Part II: Comparison with 3D-Var for a Squall Line over the U.S. Great Plains

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1 JULY 2013 S U N A N D W A N G 2245 Radar Data Assimilation with WRF 4D-Var. Part II: Comparison with 3D-Var for a Squall Line over the U.S. Great Plains JUANZHEN SUN AND HONGLI WANG National Center for Atmospheric Research,* Boulder, Colorado (Manuscript received 8 June 2012, in final form 5 November 2012) ABSTRACT The Weather Research and Forecasting Model (WRF) four-dimensional variational data assimilation (4D-Var) system described in Part I of this study is compared with its corresponding three-dimensional variational data assimilation (3D-Var) system using a Great Plains squall line observed during the International H 2 O Project. Two 3D-Var schemes are used in the comparison: a standard 3D-Var radar data assimilation (DA) that is the same as the 4D-Var except for the exclusion of the constraining dynamical model and an enhanced 3D-Var that includes a scheme to assimilate an estimated in-cloud humidity field. The comparison is made by verifying their skills in 0 6-h quantitative precipitation forecast (QPF) against stage-iv analysis, as well as in wind forecasts against radial velocity observations. The relative impacts of assimilating radial velocity and reflectivity on QPF are also compared between the 4D-Var and 3D-Var by conducting data-denial experiments. The results indicate that 4D-Var substantially improves the QPF skill over the standard 3D-Var for the entire 6-h forecast range and over the enhanced 3D-Var for most forecast hours. Radial velocity has a larger impact relative to reflectivity in 4D-Var than in 3D-Var in the first 3 h because of a quicker precipitation spinup. The analyses and forecasts from the 4D-Var and 3D-Var schemes are further compared by examining the meridional wind, horizontal convergence, low-level cold pool, and midlevel temperature perturbation, using analyses from the Variational Doppler Radar Analysis System (VDRAS) as references. The diagnoses of these fields suggest that the 4D-Var analyzes the low-level cold pool, its leading edge convergence, and midlevel latent heating in closer resemblance to the VDRAS analyses than the 3D-Var schemes. 1. Introduction In Wang et al. (2013b, hereafter Part I), we described the development of a radar data assimilation (DA) scheme within the Advanced Research Weather Research and Forecasting Model s (ARW-WRF; Skamarock et al. 2008; hereafter referred to as WRF) four-dimensional variational data assimilation (4D-Var) system (Huang et al. 2009). This system uses an incremental formulation (Courtier et al. 1994), in which the forward model that constrains the atmospheric motion within an assimilation window is the tangent linear approximation of a nonlinear forecast model. The analysis variables in the * The National Center for Atmospheric Research is sponsored by the National Science Foundation. Corresponding author address: Juanzhen Sun, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO sunj@ucar.edu cost function are the increments from the nonlinear basic state that is updated in an outer loop outside the minimization inner loop. Preliminary testing showed in Part I of this two-part paper suggested the system had a stable performance when tested with assimilation windows up to 30-min duration. In this second part of the study, we demonstrate the enhanced capability of the WRF 4D-Var radar data assimilation system by comparing it with a WRF threedimensional variational data assimilation (3D-Var) system. The WRF 3D-Var system was first developed for the assimilation of conventional large-scale observations using the incremental formulation (Barker et al. 2005, 2012). Xiao et al. (2005) and Xiao et al. (2007) added a radar DA scheme for the convective-scale analysis and forecasting. The WRF 3D-Var radar DA system has been evaluated using real data case studies (Xiao et al. 2005, 2007; Xiao and Sun 2007) and with an operational implementation in the Korea Meteorological Administration (KMA; Xiao et al. 2008). Sugimoto et al. (2009) further examined the system s strengths and DOI: /MWR-D Ó 2013 American Meteorological Society

2 2246 M O N T H L Y W E A T H E R R E V I E W VOLUME 141 weaknesses in an observing system simulation experiment (OSSE) study. In this study, they also demonstrated the importance of including a cloud analysis in the first guess to improve the performance of precipitation forecasts. It was shown that the cloud analysis helped warm up and moisten the cloud region and hence strengthen the updraft. Recently, Sun et al. (2012) further evaluated the capability of the WRF 3D-Var radar DA by running sensitivity experiments over a consecutive 6-day period that involved substantial convective activities documented during the International H 2 O Project (IHOP_2002; Weckwerth et al. 2004; Sun et al. 2012). They examined the performance of the WRF 3D- Var radar DA with a 3-hourly cycled configuration as well as the sensitivity to the assimilation of radial velocity, reflectivity, or both and found that the assimilation of radar observations with the WRF 3D-Var resulted in improved precipitation prediction up to 8 to 9 h. A cloud analysis scheme similar to that of Sugimoto et al. (2009) was used to enhance the impact of reflectivity. Studies using other 3D-Var systems have also been conducted and the findings were consistent with those using the WRF 3D-Var. Hu et al. (2006) and Hu and Xue (2007) showed that a tornadic storm was successfully forecasted two hours ahead when the 3D-Var radar DA system of the Center for Analysis and Prediction of Storms (CAPS; Gao et al. 2004) was used in combination with a cloud analysis scheme. Recently, the CAPS 3D-Var system was demonstrated in real time during the spring seasons of 2008 and 2009 and the results were reported in Xue et al. (2010) and Kain et al. (2010). They found that all measures (subjective and objective) for the two seasons indicated a clear advantage of the run with the 3D-Var radar DA through about 6 h, when compared with a run that was initialized by interpolation of the North American Mesoscale Model (NAM) analysis. Rennie et al. (2011) conducted a three-case study on the assimilation of clear-air radial winds using the 3D-Var system of the Met Office Unified Model and showed potential positive impact on the improvement of precipitation forecast. Ballard et al. (2012a,b) described the impact of radar data assimilation including both clear-air and precipitation echoes in the Met Office 3D- Var system and demonstrated promising results. Although the above studies are encouraging, limitations for the assimilation of radar observations with 3D- Var are also revealed. It was found that the impact of the radar radial velocity assimilation could be rather small (Rennie et al. 2011), and the precipitation obtained without the assimilation of radar reflectivity could dissipate quickly. Additionally, it was commonly known that a simple assimilation of reflectivity without an adjustment of other model fields could also result in a quick dissipation of precipitation. Remedies for the problem were provided based on techniques of diabatic initialization (Krishnamurti et al. 1991). Hu et al. (2006) showed that a cloud analysis scheme that adjusts heating and humidity within the cloud improved the prediction of a tornadic storm. Schenkman et al. (2011a,b) further examined the impacts of the Advanced Regional Prediction System (ARPS) cloud analysis procedure on the analysis and prediction of a mesoscale convective system. Zhao and Xue (2009) documented the significant impact of cloud analysis and in-cloud moisture adjustment on the prediction of a hurricane. Dixon et al. (2009) reported that the nudging of latent heat and cloud inferred from radar reflectivity and other data resulted in a significant improvement of precipitation forecast skill on a study using five convection-dominated precipitation events. Weygandt et al. (2008) showed that the use of a diabatic digital filter initialization (DDFI) that adjusts latent heating based on radar reflectivity resulted in improved short-term forecasts. Recently, Liu et al. (2012) described a method to estimate the in-cloud updraft and assimilated that information in a 3D-Var system. They showed that the method had a positive impact on precipitation forecasts when applied to a typhoon case. Wang et al. (2013a) presented a recent upgrade to the WRF 3D-Var radar DA scheme by adding the assimilation of in-cloud humidity estimated from reflectivity observations. They demonstrated that the method positively impacted forecasts up to 6 h for four convective cases that occurred in Beijing, China. Although these approaches have their merits in enhancing the benefit of the reflectivity data, they are all simple treatments and thus cannot get rid of the inherent weakness of the 3D-Var technique resulting from the neglect of time tendency of atmospheric flow and the inability to dynamically fit data distributed in time. Hence, it has a limited ability in accurately retrieving the unobserved quantities, such as radar cross-beam wind, buoyancy, and in-cloud humidity. In their OSSE study, Sugimoto et al. (2009) showed that the 3D-Var only partially retrieved the tangential wind component that is not observed by radar. Without the retrieved buoyancy and the resulting updraft, the rainwater obtained by the assimilation of reflectivity (or its derived microphysics) can fall to the ground quickly, unable to maintain a storm. The 4D-Var technique uses a numerical weather prediction (NWP) model as a dynamical constraint, thereby the time tendency terms, which are important for the convective scale, are not excluded. The NWP model constraint naturally links the microphysical fields with the dynamical and thermodynamical fields. It can be potentially a superior technique for convective-scale

3 JULY 2013 S U N A N D W A N G 2247 FIG. 1. Synoptic conditions at 1200 UTC 12 Jun 2002 as determined from 13-km Rapid Update Cycle (RUC) model analyses. Plots are of 500-hPa winds (full barb 5 5ms 21, half barb m s 21, and pennant 5 25 m s 21 ), wind speed (shaded), geopotential height (solid lines with 6-decameter contour interval), and temperature (dashed lines with 28C contour interval). The bold lines with barbed symbols indicate the approximate positions of surface fronts. The IHOP region is indicated by the boldface rectangle. DA that depends primarily on radar observations. To further examine the potential ability of the WRF 4D-Var radar DA system described in Part I of this study, in this paper we compare the WRF 4D-Var with the 3D-Var. We use two slightly different 3D-Var schemes in the comparison. One is the standard 3D-Var, which is the same as the 4D-Var except for the exclusion of the constraining dynamical model, and the other is an enhanced 3D-Var developed by Wang et al. (2013a) that includes a scheme to assimilate an estimated in-cloud humidity field. The latter is included in the current study to investigate how much the 4D-Var can improve over a 3D-Var that is enhanced by a diabatic initialization method. The comparison is performed with the squallline case of 13 June 2002 that was observed during IHOP_2002. The performances of these systems are evaluated by verifying their skills in 0 6-h quantitative precipitation forecast (QPF) against stage-iv precipitation analyses (Fulton et al. 1998), as well as in wind forecasts against radial velocity observations. In addition, the analyses and forecasts of wind, temperature, and humidity are compared with the Variational Doppler Radar Analysis System (VDRAS; Sun and Crook 1997) to investigate the causes of the improved forecasts. We also compare the relative impacts of radial velocity and reflectivity for both 3D-Var and 4D-Var by conducting data-denial experiments. The paper is organized as follows. In section 2, the case and data used in this study are described. In section 3, we present the experimental design. The performances of the three DA systems in terms of QPF are compared in section 4. In section 5, we further evaluate their performances by comparing the wind, convergence, and temperature fields. Summary and discussions are given in the last section. 2. Case description The upper-level flow pattern at 1200 UTC 12 June 2002, 12 h before our data assimilation experiment start time, is shown by the 500-hPa winds, temperature, and geopotential height in Fig. 1. The IHOP region (indicated by the rectangle) is located in a transition zone with relatively weak westerly flows. A surface cold front is located across the region. Several convective systems

4 2248 M O N T H L Y W E A T H E R R E V I E W VOLUME 141 FIG. 2. (a) Composite radar reflectivity observations (color) and surface observations of temperature, dewpoint temperature, and wind speed and direction at 2100 UTC 12 Jun The positions of the cold front (blue line), dryline (brown line), and outflow boundary (pink line) are depicted (from Xiao and Sun 2007). (b) The experimental domain and the WSR-88D radars used in this study. occurred during 12 and 13 June 2002 in the IHOP domain. This study focuses on a squall line initiated east of a triple point (intersection of an outflow and a dryline, Fig. 2a) near the Oklahoma Kansas border around 2100 UTC 12 June and propagated southeastward. The cold-air outflow boundary is a result of the decaying convective system located in Arkansas at and before 2100 UTC. A mesoscale circulation (mesoscale low) around the triple point is evident as shown by the surface observations. The warm, moist air mass to the east of the dryline and south of the outflow boundary contained CAPE near 2000 J kg 21 and little convective inhibition (CIN) around 2100 UTC 12 June. The air mass to the north of the outflow boundary is slightly cooler. Figure 3 shows the hourly accumulated precipitation from stage-iv analysis at four different times. Shortly before 2200 UTC 12 June (Fig. 3a), a few isolated convective cells were initiated near the border of Oklahoma and Kansas and in south Kansas. In the next two hours more convective storms were developed, along two intersecting lines (Fig. 3b). By 0200 UTC, a well-organized squall line had developed and became substantial at 0300 UTC (Fig. 3c). The precipitation magnitude of the squall line was reduced but the spatial coverage was

5 JULY 2013 S U N A N D W A N G 2249 FIG. 3. Hourly accumulated precipitation (mm h 21 ) from stage-iv analysis at (a) 2200 UTC 12 Jun, (b) 0000 UTC 13 Jun, (c) 0300 UTC 13 Jun, and (d) 0600 UTC 13 Jun extended at 0600 UTC (Fig. 3d). The system completely dissipated around 0900 UTC. The National Centers for Environmental Prediction (NCEP) stage-iv precipitation analysis reported a maximum 3-h rainfall accumulation of 89.5 mm at 0300 UTC in northern Oklahoma. Damaging winds and large hail were reported in conjunction with some of the storms. The severe storm near the triple point produced golf ball sized hail, maximum outflow wind speeds exceeding 30 m s 21, flash flooding, and at least one tornado. Weckwerth et al. (2008) conducted a study using detailed observations to examine the initiation mechanism of the convective cells that later expand to form the squall line. Liu and Xue (2008) simulated convective initiation and storm evolution of this case by assimilating special IHOP observations with good success. Xiao and Sun (2007) conducted 3D-Var radar data assimilation experiments to investigate the potential of QPF using this case. Sun and Zhang (2008) applied this case to VDRAS to examine detailed wind analysis and prediction as well as QPF. Similar to Xiao and Sun (2007) and Sun and Zhang (2008), our focus in the current study is not on the prediction of the initial storm development, but predicting the evolution of existing storms and the development of new ones from outflow interaction. Predicting storm initiations requires a subkilometer resolution that can resolve the finescale structure of the atmosphere. Liu and Xue (2008) used 3-km grid spacing that enables the capturing of secondary initiation due to outflow boundary-preexisting boundary collision, but Xue and Martin (2006) suggested that higher resolutions are needed to resolve boundary layer processes important for convective initiation without preexisting mesoscale boundaries. 3. Description of the experiments A total of seven experiments were conducted for this study. A summary of the experiments is provided in Table 1. The experimental domain is shown in Fig. 2b. The Weather Surveillance Radar-1988 Doppler (WSR- 88D) radars that are assimilated in these experiments

6 2250 M O N T H L Y W E A T H E R R E V I E W VOLUME 141 TABLE 1. Summary of experiments. Expt 3DV 3DVQV 4DV 3DV_RF 3DV_RV 4DV_RF 4DV_RV Description 3DVAR assimilating both radial velocity and reflectivity Same as 3DVAR, but with the addition of relatively humidity assimilation 4DVAR assimilating both radial velocity and reflectivity Same as 3DV, but without the assimilation of radial velocity Same as 3DV, but without the assimilation of reflectivity Same as 4DV, but without the assimilation of radial velocity Same as 4DV, but without the assimilation of reflectivity are also shown in this figure. The quality control and error estimate of the radar observations are conducted using the same data preprocessing and quality control package in VDRAS. The reader is referred to Sun (2005) for a description. The first three experiments 3DV, 3DVQV, and 4DV assimilate both radar radial velocity and reflectivity using the WRF 3D-Var, the enhanced WRF 3D-Var, and the 4D-Var, respectively. The enhanced WRF 3D-Var includes an additional term in the cost function to assimilate the estimated in-cloud humidity by assuming saturation of air when reflectivity is greater than a prespecified value. The reader can find a detailed description of the methodology in Wang et al. (2013a). Experiments 3DV_RF and 4DV_RF are the same as 3DV and 4DV, respectively, except that the radial velocity data are not assimilated. Similarly, the experiments 3DV_RV and 4DV_RV assimilate only radial velocity data by excluding reflectivity. A schematic diagram is provided by Fig. 4 to illustrate the assimilation and forecast setup for both 4D-Var and 3D-Var. The assimilation period is 30 min from 0000 UTC to 0030 UTC 13 June. The 4D-Var experiments 4DV, 4DV_RF, and 4DV_RV are run in this window assimilating all radar volumes (approximately 5 min apart) from the six radars shown in Fig. 2b. The background is provided by an Eta Model 40-km analysis. Six outer loops are performed in the 4D-Var experiments, meaning the nonlinear model is updated 6 times during the minimization of the cost function. For each outer loop, 21 iterations are carried out for the minimization of the cost function in the inner loop. Both the outer loop and inner loop use the same horizontal resolution of 4 km and vertical resolution of 31 vertical terrain following levels. The reader is referred to Part I of this study for more information about the minimization procedure of the incremental approach. The description of the tangent linear model (TLM) and the FIG. 4. Schematic diagram of 3D-Var and 4D-Var data assimilation experiments. Eta Model and WRF in parentheses indicate the sources of background fields; Tangent linear model (TLM) and adjoint model integrations (ADM). adjoint model (ADM) of the Kessler warm-rain scheme is also given in Part I of this study. The 3D-Var experiments 3DV, 3DVQV, 3DV_RF, and 3DV_RV perform the first data assimilation at the beginning of the 30-min assimilation window using the 40-km Eta Model as background and assimilate the radar volume closest to 0000 UTC from each radar. A 30-min forecast is then executed from the 3D-Var analysis, and this forecast is used as background for the second 3D-Var assimilation at the end of the assimilation window (0030 UTC). Since there are no significant highly nonlinear operators in 3D-Var, one outer loop is sufficient for the 3D-Var minimization to converge. For all experiments, a forecast is conducted up to 0600 UTC after the data assimilation. The same physical options are used during the assimilation ( UTC) and the subsequent forecast except for the microphysical parameterization scheme. These options are as follows: the Rapid Radiative Transfer Model (RRTM) longwave radiation, Dudhia shortwave radiation, Yonsei University (YSU) PBL, and the Noah land surface model. The Kessler warm-rain scheme is used during the assimilation period in TLM, ADJ, as well as in the outer loop nonlinear model in 4D-Var and in the short forecast from 0000 to 0030 UTC in 3D-Var, while the WRF single-moment 5-class microphysics scheme (WSM5) that has ice and snow physics are used during the forecast period. The description of the above schemes can be found in the WRF-ARW technical report (Skamarock et al. 2008). 4. Results a. Comparison of QPF Since the main motivation of the current study is to improve short-term QPF, the 3D-Var and 4D-Var techniques are compared by first examining their accuracy in precipitation forecasting. Hourly precipitation

7 JULY 2013 S U N A N D W A N G 2251 FIG. 5. FSS vs forecast hour of hourly accumulated precipitation (mm h 21 ) for thresholds (a) (c) 1, (d) (f) 5, and (g) (i) 10 mm. The FSSs in the three columns are computed with the ROI of 8, 24, and 48 km, respectively. accumulation is verified against stage-iv analysis using bias and fractions skill score (FSS) following Schwartz et al. (2009). The stage-iv precipitation was interpolated to the WRF grid to compute the verification statistics. The results of the FSS from the experiments 3DV, 3DVQV, and 4DV are compared in Fig. 5 for the thresholds of 1, 5, and 10 mm, respectively, with three radii of influence [(ROI) 5 8, 24, and 48 km] for each threshold, respectively. Since the uninterrupted forecasts start at 0030 UTC (see Fig. 4), the accumulated precipitation at t 5 1 h (corresponding to 0100 UTC) includes that during the 30 min assimilation period. It is shown in Fig. 5 that the standard 3D-Var has lowest scores for all thresholds and ROIs during the entire forecast period. The 4D-Var experiment 4DV has higher FSSs beyond t h than the experiment 3DVQV for the lower threshold of 1 mm (Figs. 5a c). It outperforms 3D-Var for the 5-mm threshold during the entire forecast period (Figs. 5d f) and the same is true for the higher threshold of 10 mm (Figs. 5g i) except for the last hour. The reason for the lower score at t 5 6hwill be given in the discussion of Fig. 6. A distinct feature shown in the FSS of 4DV for the 5- and 10-mm thresholds is the initial skill, which is maintained throughout the entire forecast range. In contrast, 3DV shows a rapid decrease of FSS between t 5 1 and 2 h for the 1- and 5-mm

8 2252 MONTHLY WEATHER REVIEW VOLUME 141 FIG. 6. Hourly accumulated precipitation (mm) valid at (left) 0100 UTC, (middle) 0300 UTC, and (right) 0600 UTC. Forecasts at these times from experiments (d) (f) 3DV, (g) (i) 3DV_QV, and (j) (l) 4DV are compared with (a) (c) the stage-iv precipitation analyses. thresholds and between t 5 1 and 3 h for the 10-mm threshold, indicating a lack of dynamical response of other fields to support the assimilated rainwater. The diabatic initialization through the assimilation of the estimated in-cloud humidity in 3DVQV provides a favorable moisture environment to support the convection; hence, the decrease of the skill in 3DVQV is alleviated. The forecasted hourly precipitation patterns at t 5 1, 3, and 6 h are compared in Fig. 6 using the stage-iv precipitation analysis as the truth. At t 5 1 h, all three

9 JULY 2013 S U N A N D W A N G 2253 experiments (Figs. 6d,h,j) capture the three major convective clusters A, B, and D, but their strengths vary among the experiments and in general are all weaker than the observed (Fig. 6a). At t 5 3 h, 3DV (Fig. 6e) fails to forecast the line structure as shown by the observations in Fig. 6b by missing the storms in the west segment. 3DVQV (Fig. 6h) improves over 3DV by producing more precipitation in that area. The best result is obtained by 4DV (Fig. 6k), which forecasts the line structure and the location of the convective system with noticeable improvement over 3DVQV. At t 5 6h,3DV(Fig.6f) is still unable to predict the full squall line. 3DVQV (Fig. 6i) and 4DV (Fig. 6l) both successfully forecast the squall line but the 4DV result has a closer resemblance in terms of location, spatial extension, and strength. Both experiments produce a false convective cluster near (35.58N, 988W), which results in the decrease of FSS for the higher threshold of 10 mm at the last forecast hour for 4DV (Fig. 5i). Overall, the experiment 3DVQV overpredicts the strength of the precipitation and has a slower propagation in comparison with 4DV. The overprediction is confirmed by the higher bias shown in Fig. 7. Next we examine whether radar radial velocity and reflectivity impact the precipitation analyses and forecasts differently between 4D-Var and 3D-Var. In Fig. 8, the FSSs from 4DV_RF and 4DV_RV are plotted by green lines and from 3DV_RF and 3DV_RV by blue lines for the thresholds of 1 (Fig. 8a), 5 (Fig. 8b), and 10 mm (Fig. 8c) with a 25-km ROI. For all the three thresholds, it is shown that assimilating radial velocity (4DV_RV) generally results in higher FSS than assimilating reflectivity (4DV_RF) except for the beginning forecast hours. In contrast, the 3D-Var results are opposite in that the assimilation of radial velocity generally gives lower score except for a short period around t 5 4 h for the 1-mm threshold. The FSS shows a larger difference between 3DV_RV and 3DV_RF than that between 4DV_RV and 4DV_RF in the first 2 h due to the fact that the 3D-Var assimilation of radial velocity is not as effective, resulting in a longer spinup period than that of the 4D-Var. The lower scores in the first 2 h in 4DV_RV suggest that an initial precipitation spinup is still required if only radial velocity data are assimilated although the spinup period is clearly shorter than that required in 3DV_RV. This result is not surprising because the use of the dynamical model in 4D-Var help balance the initial state. The precipitation patterns from the above experiments are compared in Fig. 9. The assimilation of radial velocity with 4D-Var clearly results in quicker precipitation spinup than with 3D-Var (Figs. 9a vs 9d). Comparing with the observed precipitation (Fig. 6a), FIG. 7. Bias of hourly accumulated precipitation vs forecast time for the thresholds of (a) 1, (b) 5, and (c) 10 mm.

10 2254 M O N T H L Y W E A T H E R R E V I E W VOLUME 141 FIG. 8. FSS of hourly accumulated precipitation from the experiments 4DV_RF, 4DV_RV, 3DV_RF, and 3DV_RV with the radius of influence of 25 km for thresholds of (a) 1, (b) 5, and (c) 10 mm. however, the forecast from 4DV_RV is more scattered. At t 5 3 h, a precipitation band is formed by 4DV_RV (Fig. 9b), while the precipitation by 3DV_RV (Fig. 9e) concentrates in the northeast corner and around the Oklahoma and Kansas border. At t 5 6 h, the forecasted precipitation band from 4DV_RV (Fig. 9c) moves to the east central Oklahoma and the pattern agrees reasonably well with the observations (Fig. 6b). In contrast, the 3DV_RV (Fig. 9f) forecasts mostly scattered convection at both t 5 3 and t 5 6 h. Since the reflectivity directly provides rainwater information, the precipitation forecast at t 5 1 h is close to the observations for both 3DV_RF and 4DV_RF as shown by Figs. 9g,j. At t 5 3 and 6 h, the forecasted precipitations from 3DV_RF (Figs. 9k,l) are better organized than their counterparts from 3DV_RV in Figs. 9e,f. The forecasts from 4DV_RF (Figs. 9h,i) capture larger areas of the squall-line precipitation, showing clear improvements over 3DV_RF. However, the squall line moves slower compared with those observed (Figs. 6b,c) and forecasted by 4DV_RV (Figs. 9b,c), which results in a lower FSS than 4DV_RV in Fig. 8. In summary, the results shown in Figs. 8 and 9 indicate that the 4D-Var has a better ability in spinning up the precipitation when only radial velocity data are assimilated, apparently due to the use of the model constraint during the data assimilation. After t 5 4 h, however, the impact of radial velocity relative to reflectivity is comparable in both techniques although slightly improved FSSs are shown by 4DV_RV than by 3DV_RV compared to their respective experiment of reflectivity assimilation. It was also shown from the above comparison of experiments that the assimilation of reflectivity in 3D-Var played an important role in mitigating the spinup issue and thereby improved the precipitation forecasts in the first 3 h. b. Examining wind and temperature In this subsection, we examine the wind and temperature fields from the three experiments 3DV, 3DVQV, and 4DV. The wind forecast is verified against radial velocity observations by computing the relative root-meansquare error (RRMSE) between the model-predicted radial wind and the observed radial wind from the six radars in the experiment domain. A qualitative evaluation of the wind and temperature analyses and forecasts will also be provided using VDRAS analyses as references. The modeled radial wind is calculated by projecting its3dwindfieldtotheradialdirectionofeachradar and to the radar-scanning elevations. The RRMSE calculation is performed with a 15-min interval, which includes multiple radar volumes. The RRMSE is defined by RRMSE 5 s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi, sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi å 6 å N å M nr51 nt51 i51 (y m r 2 yo r )2 i,nt,nr å 6 å N å M (y m r )2 i,nt,nr nr51 nt51 i51, (1)

11 JULY 2013 SUN AND WANG 2255 FIG. 9. Hourly accumulated precipitation forecasts (mm) from experiments (a) (c) 4DV_RV, (d) (f) 3DV_RV, (g) (i) 4DV_RF, and (j) (l) 3DV_RF valid at (a),(d),(g),( j) 0100 UTC; (b),(e),(h),(k) 0300 UTC; and (c),(f),(i),(l) 0600 UTC 13 Jun where yor is radial velocity observation and ym r is the radial velocity calculated from model velocity components u, y, and w, and rainwater mixing ratio qr using Eqs. (3) and (4) in Part I of the paper. The indices i, nt, and nr represent the ith observation grid point, the ntth radar data volumes, and the nrth radar, respectively. The total number of observations is represented by M and the total number of radar volumes by N. The total number of radars is six.

12 2256 M O N T H L Y W E A T H E R R E V I E W VOLUME 141 FIG. 10. (a) RRMSE with respect to forecast time verified against radial velocity observations of the six radars over the experimental domain. (b) Vertical distribution of the RRMSE at 0030 (solid lines) and 0300 UTC (dashed lines). The RRMSEs from the experiments 3DV, 3DVQV, and 4DV against the radar radial wind are shown in Fig. 10. All radars scanned 14 elevation angles during the experiment period. It should be noted that the verification only applies to those grid points where there are radar echoes, which are confined to the convective region for storm echoes or near the radar in the first two elevation angles for clear-air echoes. Figure 10a plots the RRMSE over all elevation angles with respect to forecast time. The experiment 4DV has the lowest RRMSE over the entire forecast period. In contrast, it is noted that 3DVQV improves the wind forecasts over 3DV only in the last 3 h and it degrades the wind forecasts from 3DV up to t 5 3 h. The degradation is caused by a dynamical readjustment in the convective region resulting from the estimated in-cloud humidity assimilation. To see how the errors vary vertically, the vertical distribution of the RRMSEs at the end of the analysis time (t 5 30 min) and at t h from the three experiments are shown in Fig. 10b. Evidently, the experiment 4DV produces an improved analysis at all levels over both 3DV and 3DVQV. 3DVQV only slightly improves the wind analysis over 3DV only slightly. At t h, 4DV improves the wind forecast over 3DV below the fourth elevation angle but worsens slightly above. The main degradation of the 3DVQV wind forecast is between the fourth and ninth elevation angles. Overall, Fig. 10 suggests that the accuracy of wind analysis and forecast is not significantly improved by the 4D-Var relative to the large error in wind forecast. In the following, we will examine the analysis and forecast fields of wind and temperature using VDRAS analysis as the truth to make further comparison of the performances of the three experiments. For this purpose, continuous analyses with a rapid update cycle of 15 min are produced for the period UTC 13 June by VDRAS. VDRAS is a 4D-Var data assimilation system that produces frequent high-resolution analyses by fitting a cloud-scale model to observations from radars and a surface network with WRF model output as a background. Its analysis has been used since 1998 in real time for nowcasting convective weather in several operation centers and mission agencies. VDRAS wind analysis has been verified against aircraft observations (Sun and Crook 2001), dual-doppler analyses (Crook and Sun 2004), and profiler data (Sun et al. 2010). These verifications revealed that VDRAS produces accurate winds under convective conditions with a typical root-mean-square difference of 2 3 m s 21 from independent data. Good agreement of VDRAS temperature analyses with surface observations in convective cases with strong cold pools was demonstrated in Sun et al. (2010). Since VDRAS has a different vertical coordinate from WRF, WRF forecasts are mapped to the VDRAS grid, which has Dx, Dy 5 4 km and Dz km to facilitate the comparison. As shown by the black line in Fig. 10a, the VDRAS analysis has substantially smaller errors than the WRF forecasts. The y component of wind at 0.2 km above ground level (AGL) is compared in Figs. 11 and 12 for the final analysis at t 5 30 min and the forecast at t 5 3 h, respectively. The horizontal wind vectors and rainwater greater than 0.2 g kg 21 (corresponding to ;30 dbz) are overlaid. The VDRAS wind analysis (Fig. 11a) shows northerly wind north of storm A and a strong northerly outflow coming out of the storm. Weaker outflows are also produced by storms B, C, and D, forming a northwest southwest band of northerly flow. The wind in the prestorm environment is southerly. The analyses from 3DV and 3DVQV (Figs. 11b,c) only have minor differences, both showing northerly flow in the northwest corner

13 JULY 2013 SUN AND WANG 2257 FIG. 11. The y component of velocity (m s21) at z km overlaid by wind vectors and 0.2 g kg21 rainwater mixing ratio (white contours) from (a) VDRAS, (b) 3DV, (c) 3DVQV, and (d) 4DV valid at 0030 UTC. Note that the plots are on a subdomain, the experimental domain. The distance labels are respect to the center of the experimental domain. The thin white line shows the Oklahoma and Kansas state border. of the domain weaker than that in VDRAS. Although there is an indication of the outflow from storm A as shown by the weakened southerly wind south of storm A, it is not strong enough to change the wind direction to northerly. The analysis from 4DV (Fig. 11d) results in a stronger northerly wind in the northwest corner and slightly stronger outflow from the storm A (northerly wind between 0 and 5 m s21 as shown by the forest green color scale). Note that the sizes of the storms B, C, and D are noticeably smaller in the 4DV analysis compared with the observations. As we will show later, however, the 4DV not only improves the analysis of the meridional wind component but also the low-level convergence, cold pool, as well as the midlevel latent heating. As a result, the modeled convective system experiences a quick precipitation spinup and thus an improved forecast skill. At the third hour into the forecast shown by Fig. 12, the VDRAS analysis shows strong north-northwesterly outflows from the squall line (indicated by the white contour line of 0.2 g kg21

14 2258 MONTHLY WEATHER REVIEW VOLUME 141 FIG. 12. As in Fig. 11, but valid at 0300 UTC. rainwater in Fig. 12a). The forecast from 3DV misses the squall line and most of its associated outflow winds. The 3DVQV improves the rainwater forecast, producing stronger south-southwesterly winds behind the squall line and the northwesterly winds near the rainband. 4DV successfully forecasts the northerly wind band although the strength is weaker than the VDRAS analysis. The horizontal convergence fields at t 5 30 min (analysis) and t 5 1 h (30 min forecast) are shown in Figs. 13 and 14, respectively, with the warm shades for convergence and cold shades for divergence. The VDRAS analysis clearly shows an outflow convergence boundary, and its location is indicated by the bold black line. This convergence boundary moves to the southeast in the next hour and leads to the formation of the squall line. The 4DV analysis of the convergence field (Fig. 13d) shows that the 4D-Var produces a leading edge convergence boundary that agrees better with that produced by VDRAS than those from 3DV and 3DVQV. At t 5 1 h, 4DV and VDRAS continue to have a closer resemblance and the 3DV and 3DVQV further depart from VDRAS. The two major storms (represented by the white contours of rainwater and marked by A and B in Figs. 14a and 14d) behind the leading convergence

15 JULY 2013 SUN AND WANG 2259 FIG. 13. Convergence (cold color) and divergence (warm color) (m s21 km21) at 200 m AGL at 0030 UTC 13 Jun 2002 from (a) VDRAS analysis, (b) 3DV, (c) 3DVQV, and (d) 4DV. The storms are indicated by rainwater mixing ratio of 0.2 g kg21 (white contour). For comparison purpose, the outflow convergence boundary from VDRAS is indicated by the black line. Note that the plots are on a subdomain of the experimental domain. The distance labels are with respect to the center of the experimental domain. The thin white line shows the Oklahoma and Kansas state border. line are captured by 4DV although the area coverage is smaller. In contrast, the storms from 3DV (Fig. 14b) decay as a result of the lack of dynamical support. Although these storms are better maintained in 3DVQV (A and B in Fig. 14c), their positions are farther away from the convergence line analyzed by VDRAS. The perturbation temperature from the horizontal mean is shown by Fig. 15 for the height of 0.2 km AGL and Fig. 16 for the height of 5.8 km, respectively. The VDRAS analysis shows a cold pool with a maximum cooling of approximately 288C, which is consistent with surface observations (not shown). None of the WRF data assimilation experiments capture the cold pool at that magnitude. Among the three experiments, 4DV is best at analyzing the cold pools associated with the storms near the Oklahoma and Kansas border and in northwest Oklahoma although the magnitude (about 248C) is less than that from VDRAS and the spatial

16 2260 MONTHLY WEATHER REVIEW VOLUME 141 FIG. 14. As in Fig. 13, but valid at 0100 UTC. extent is also smaller. On the higher level (5.8 km shown by Fig. 16), VDRAS analyzes a large area of heating in the convective area (Fig. 16a), resulting from the latent heating effect of the storms. Near the storm clusters A, B, and C, heating over 28C with a maximum value of ;68C is identified. In contrast, 3DV only shows a few spots of heating in the convective area (Fig. 16b). 3DVQV and 4DV show similar heating patterns and magnitudes (Figs. 16c,d), but 4DV produces stronger heating near the developing storms A and B, which is consistent with the VDRAS result. The above qualitative examination reveals that the 4D-Var technique is able to obtain balanced convective-scale initial conditions as suggested by the consistent analysis of low-level cold pool, its associated leading edge convergence, and midlevel latent heating with those from VDRAS analysis. In contrast, the 3D-Var technique has limited ability in obtaining small-scale structures associated with convection. The enhanced 3D-Var with in-cloud humidity assimilation is able to get the midlevel heating from latent heat release that plays a role in maintaining the storms, but is unable to analyze the low-level cold pool and its associated leading edge convergence, which leads to an overprediction of the convective system and a slower propagation.

17 JULY 2013 S U N A N D W A N G 2261 FIG. 15. Perturbation temperature (from horizontal mean; 8C) at 200 m AGL at 0030 UTC 13 Jun 2002 from (a) VDRAS analysis, (b) 3DV, (c) 3DVQV, and (d) 4DV. The storms are indicated by rainwater mixing ratio of 0.2 g kg 21 (white contour). Note that the plots are on a subdomain of the experimental domain. The distance labels are with respect to the center of the experimental domain. The thin white line shows the Oklahoma and Kansas state border. 5. Summary and conclusions The WRF-based 4D-Var radar data assimilation system with an incremental framework was developed and tested. In Part I of this two-part study, we described the features of this system and conducted preliminary testing. In the paper, we evaluated the system by comparing data assimilation and forecasting experiments on a squall line observed during IHOP_2002 with those from two WRF 3D-Var schemes. One is the standard 3D-Var, which is the same as the 4D-Var except for the exclusion of the constraining dynamical model and the other is an enhanced 3D-Var developed by Wang et al. (2013a) that includes an algorithm to assimilate estimated incloud humidity. Continuous volumetric radar observations of radial velocity and reflectivity from six WSR-88D radars are assimilated over a 30-min window in the 4D-Var data assimilation experiments, while the cycled 3D-Var schemes assimilate those radar volumes that are closest to the start or the end of the 30-min window. The

18 2262 MONTHLY WEATHER REVIEW VOLUME 141 FIG. 16. As in Fig. 15, but at 5.8 km AGL. comparison is made by verifying their skills in 0 6-h QPF against stage-iv hourly precipitation analysis, as well as in wind forecasts against radial velocity observations from the six radars. The relative impacts of assimilating radial velocity and reflectivity on QPF are also compared between 4D-Var and 3D-Var by conducting data denial experiments. The analyses and forecasts from the 4D-Var and 3D-Var schemes are further compared by examining the meridional wind, low-level horizontal convergence, low-level cold pool, and midlevel temperature perturbation, using analyses from VDRAS as references. The major conclusions from the current case study are summarized below. 1) The WRF incremental 4D-Var substantially improved the QPF skill over the WRF standard 3D-Var for the 6-h forecast range for the three thresholds of 1, 5, and 10 mm as measured by FSS. 4D-Var overcame the problem of initial precipitation spindown manifested in the 3D-Var schemes. 2) The 4D-Var improved the QPF skill over the enhanced 3D-Var except for the last forecast hour at the threshold of 10 mm. The precipitation forecast from the enhanced 3D-Var has higher bias than 4D-Var beyond the second forecast hour for the thresholds of 5 and 10 mm. 3) Compared to reflectivity assimilation, radial velocity assimilation using 4D-Var has a larger impact on

19 JULY 2013 S U N A N D W A N G 2263 precipitation forecasts in the first 4 h than using 3D-Var due to a quicker precipitation spinup. 4) The 4D-Var improved the wind analysis and forecast over both 3D-Var schemes as verified against radial velocity observations using the relative RMSE, but the improvement is only slight relative to the large error in wind forecast. 5) The diagnosis study of analysis fields suggest that the 4D-Var technique produced improved convectivescale initial conditions as suggested by the consistent analysis of low-level cold pool, its associated leading edge convergence, and midlevel latent heating with those from VDRAS analysis. The improved balance of the initial conditions resulted in a quicker spinup, avoiding the dynamical readjustment as in the 3D-Var schemes. 6) The enhanced 3D-Var with the in-cloud humidity assimilation was able to analyze the midlevel heating from latent heat release that plays a role in maintaining the storms, but it is unable to analyze the low-level cold pool and its associated convergence leading edge convergence, which leads to an overprediction of the convective system and a slower propagation. It is obvious that more convective cases that have different characteristicsshouldbeexaminedinthe future to obtain a general conclusion about the performance of the WRF 4D-Var. Experiments with continuous cycles will be conducted to further improve the system. 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