1. Introduction
The assimilation of radar data into convective-scale numerical weather prediction (NWP) models has gained considerable attention in recent years with increased operational implementation and use in the warning decision process (e.g., the “Warn-on-Forecast” initiative; Stensrud et al. 2009, 2013). Weather radar is one of the only sources of data available that provides information at a temporal and spatial resolution comparable to convection-allowing NWP models. Thus, radar data assimilation’s ability to promote deep moist convection and its attendant perturbations in NWP models and to reduce the spinup time has been and continues to be explored. However, most efforts to date have been limited to measurements of reflectivity at horizontal polarization (hereafter, Z) and radial velocity.
Many methods of assimilating Z have been studied over the past two decades. One of the earliest methods examined was four-dimensional variational data assimilation (4DVAR), which uses the forecast model as a dynamical constraint during the assimilation process. While results have been encouraging (e.g., Sun and Crook 1997, 1998; Sun 2005; Sun and Zhang 2008; Wang et al. 2013b), the difficulty of developing and maintaining an adjoint model and the inherent nonlinearities of the microphysics scheme often hinder proper convergence of the cost function. As such, 4DVAR methods have not been widely used for convective-scale radar data assimilation and have typically been limited to warm rain microphysics, although recent work has begun to investigate the inclusion of some ice phases (Chang et al. 2016). The simpler and more computationally efficient three-dimensional variational data assimilation (3DVAR) method has provided positive results (e.g., Xiao et al. 2005, 2007; Gao and Stensrud 2012; Wang et al. 2013a). However, 3DVAR lacks flow-dependent error covariances, which may limit the ability to update unobserved variables, and requires limiting assumptions about the model microphysics. In recent years, the ensemble Kalman filter method (EnKF; Evensen 1994) has become increasingly popular for convective-scale radar data assimilation with very promising results for producing accurate storm-scale analyses (e.g., Dowell et al. 2004, 2011; Tong and Xue 2005; Xue et al. 2006; Aksoy et al. 2009; Yussouf and Stensrud 2010; Snook et al. 2011, 2012; Yussouf et al. 2013; Wheatley et al. 2015). However, ensemble methods are computationally expensive, may suffer from issues related to rank deficiency (e.g., filter divergence due to sampling errors; Gao et al. 2014), and have not yet seen widespread operational implementation. Hybrid methods combining the strengths of variational and ensemble methods by defining ensemble-derived flow-dependent covariances for the variational scheme are being developed (e.g., Wang et al. 2008a,b) and investigated for use with radar data assimilation at the convective scale (e.g., Gao et al. 2013, 2016; Gao and Stensrud 2014).
Other assimilation techniques assimilate state variables indirectly retrieved from Z. These methods include latent heating nudging (e.g., Jones and Macpherson 1997; Macpherson 2001; Leuenberger and Rossa 2007; Stephan et al. 2008), specific humidity nudging (Davolio and Buzzi 2004), and divergence nudging (Korsholm et al. 2015), as well as techniques that use regions of observed Z to activate a convective parameterization scheme (Rogers et al. 2000) or variationally assimilate retrieved relative humidity profiles (Caumont et al. 2010). One of the most prominent methods is the Advanced Regional Prediction System’s (ARPS) cloud analysis (hereafter “cloud analysis”; Zhang et al. 1998; Zhang 1999; Brewster 2002; Hu et al. 2006a). The cloud analysis is based on the Local Analysis Prediction System (Albers et al. 1996) and makes adjustments to the model relative humidity, hydrometeor mixing ratios, and temperature based on radar, satellite, and surface observation data. Cloud analysis techniques are conceptually straightforward, computationally efficient, and have been shown to be useful for reducing the spinup of observed storms and improving short-term convective forecasts (e.g., Xue et al. 2003, 2014; Souto et al. 2003; Dawson and Xue 2006; Hu et al. 2006a; Zhao and Xue 2009; Schenkman et al. 2011; Dawson et al. 2015; Zhuang et al. 2016). Benefits can be amplified when the cloud analysis is used in conjunction with radial velocity information. To update multiple unobserved model variables from Z alone, however, cloud analysis techniques rely on semiempirical quantitative relations (e.g., retrieving hydrometeor mixing ratios from Z) and general rules relating Z to the aforementioned variables (e.g., saturating regions within a given Z threshold). These relations and rules require simplifications that can introduce errors (e.g., Gao et al. 2009; Carlin et al. 2016).
The operational WSR-88D network in the United States has been upgraded to dual-polarization, with other countries, including Germany, Canada, and the United Kingdom, following suit. These networks now provide an unprecedented volume of polarimetric observations. In contrast to single-polarization radars, dual-polarization radars transmit and receive orthogonally polarized electromagnetic waves from which information about a target’s size, shape, orientation, and composition can be garnered (e.g., Kumjian 2013a). In addition to Z, measured variables include differential reflectivity 
In recent years, numerous distinct polarimetric “signatures” have been identified and tied to dynamical and microphysical processes within storms. One of the most ubiquitous polarimetric signatures observed in deep moist convection is the 
In addition to the aforementioned 
Despite the connection between dual-polarization radar and the microphysical and thermodynamic characteristics of deep moist convection, leveraging polarimetric data for NWP is a relatively new area of research. Predicated on the idea that a physically accurate microphysics scheme should be able to reproduce realistic polarimetric signatures, many studies have explored the use of polarimetric radar forward operators (e.g., Jung et al. 2008a, 2010a; Pfeifer et al. 2008; Ryzhkov et al. 2011) to evaluate the performance of microphysics schemes (e.g., Jung et al. 2008a, 2010a, 2012; Ryzhkov et al. 2011, 2013a; Kumjian and Ryzhkov 2012; Dawson et al. 2013, 2014; Kumjian et al. 2014; Putnam et al. 2014; Johnson et al. 2016; Snyder et al. 2017a,b). If large discrepancies are present between the model-derived polarimetric signatures and those observed in nature, it can be indicative of deficiencies in the microphysics scheme. Alternatively, if a model faithfully reproduces polarimetric signatures as they are observed in nature, the model can be used to investigate what physical processes are responsible for a given signature. Some studies have used polarimetric data to assimilate improved estimates of rainwater mixing ratio using both 3DVAR (Li and Mecikalski 2010, 2012) and EnKF (Yokota et al. 2016) methods and found positive impacts compared to experiments that assimilated mixing ratios retrieved from Z alone. However, ice phases were neglected. Wu et al. (2000) attempted to use 
This study explores the impact of assimilating observed polarimetric data through a modified cloud analysis routine. The cloud analysis technique was chosen because of its proven success in reducing spinup time and ease of implementation into existing code infrastructure. Direct insertion of the retrieved temperature and moisture perturbations is currently more straightforward than assimilating the polarimetric variables using variational techniques, which require cross covariances between model state variables and the polarimetric variables that are not currently well formulated. Section 2 details the modifications made to the existing cloud analysis routine, and section 3 describes the experimental setup used in this study. Results are presented in section 4, followed by a summary and discussion in section 5.
2. Description of data assimilation routine
a. ARPS 3DVAR routine
The first step of the assimilation cycling procedure makes use of the ARPS 3DVAR routine (Gao et al. 2004; Hu et al. 2006b). ARPS 3DVAR minimizes a cost function with a recursive filter containing terms for the background and observations as well as an anelastic mass continuity term as a weak constraint to produce a more balanced three-dimensional analysis of the model state variables from multiple data sources. The system is designed to work with a number of observation types including surface and upper-air observations and radial velocity. As it was designed for use at the storm scale, the routine includes multiple analysis passes with varying scales of spatial influence to help resolve flows at different scales. The resultant analysis is then used as the background when invoking the cloud analysis routine.
b. Existing cloud analysis
In the current cloud analysis, the radar data are first quality controlled and interpolated to the model grid (Brewster et al. 2005; Brewster and Stratman 2015). The process for the polarimetric variables follows that of radial velocity and Z. Radar data at ranges between 3 and 230 km from the radar site are processed. Anomalous propagation is removed using gradients and texture fields of Z and low wind speeds, with additional filtering of nonmeteorological echoes using a user-defined 
An initial cloud fraction field is diagnosed from the background relative humidity field following a similar approach as Koch et al. (1997). Subsequently, clouds are directly inserted by setting the cloud fraction to 100% above the surface-based lifted condensation level anywhere Z exceeds a threshold, set to 15 dBZ above 2 km by default. Cloud water and ice content can be determined either adiabatically or, as in this case, using the Smith–Feddes model (Haines et al. 1989) with a reduction for entrainment following Hu et al. (2006a). Next, the dominant hydrometeor species in each grid box is determined using temperature and Z thresholds, where snow (rain) is considered when the temperature is below (above) 0°C, and where hail is considered when the Z exceeds 45 dBZ (Albers et al. 1996; Pan et al. 2016). In the case of cycling, the species can also be determined by the existing species in the model background. The mixing ratios of each species are then typically retrieved using single-moment retrieval equations for rain, snow, and hail based on Smith et al. (1975) and Lin et al. (1983). Summaries of these equations can be found in Dowell et al. (2011), Carlin et al. (2016), and Pan et al. (2016). However, recent work has initialized intercept parameters (and, if needed, shape parameters) for multimoment microphysics schemes using iterative techniques (Brewster and Stratman 2015), while other studies have found positive impacts from using single-moment microphysics schemes with intercept parameters diagnosed from hydrometeor mixing ratios (e.g., Wainwright et al. 2014; Pan et al. 2016), as developed in Zhang et al. (2008).
A temperature adjustment is then made to account for latent heat release. This can be done by simply adding the latent heating associated with the added cloud water and ice content (Zhang et al. 1998) or by assuming a moist-adiabatic temperature profile from cloud base with entrainment effects included (Brewster 2002). In this study, the latter method is applied to regions with vertical velocity w 
c. Modified cloud analysis
The modifications made to the cloud analysis in this study involve the final two steps of moistening and heating in updraft areas. Many studies have shown that both temperature perturbations (e.g., Hu et al. 2006a) and the initial moisture field (e.g., Weygandt et al. 2002; Ge et al. 2013) can play primary roles in determining the accuracy of modeled convection. The insertion of too much water vapor can result in an overestimate of the intensity and areal coverage of convection, leading to a degradation of the forecast (e.g., Schenkman et al. 2011; Schenkman 2012). This issue was examined in detail in Tong (2015), who found that saturating based on a Z threshold can result in too much moisture being added and large degradations in forecast skill. Forecast skill was greatly improved when a more accurate initial moisture field was provided in an observing system simulation experiment. Because of the lack of a direct relationship between in-cloud moisture and conventional observations, Tong (2015) proposed a modification to the cloud analysis in which the relative humidity in downdraft regions, which are generally unsaturated, is reduced. Notable improvements were found for both the analysis and forecast for all state variables examined, further highlighting the importance of improving the initial moisture field for convective storm-scale modeling. Despite these encouraging results, certain issues remain. While unsaturated regions correspond well with downdrafts overall, the specific quantitative relationship between water vapor mixing ratio 
To investigate the validity of the proposed modifications, vertical cross sections of relative humidity, latent heating rate, 
Vertical cross sections of simulated deep moist convection from the Hebrew University Cloud Model showing relative humidity (shaded gray above 90%), the 100 K h−1 latent heating rate contour (orange), the 1.0-dB 
Citation: Monthly Weather Review 145, 12; 10.1175/MWR-D-17-0103.1
In this study, polarimetric data are first quality controlled and mapped to the model grid as described in section 2b. Areas of interest are limited to regions in which Z 
Summary of the criteria used to detect 
As opposed to warming in areas with w 
An example of the differences in potential temperature and water vapor mixing ratio analysis increments between the traditional cloud analysis and the modified cloud analysis is shown in Fig. 2 for the initial 2000 UTC assimilation cycle of the 19 May 2013 Oklahoma case (discussed below). While the magnitudes of the moistening and warming are comparable, the location and extent of the increments vary between the two. The traditional cloud analysis (Fig. 2a) shows a large area of moistening with two primary areas of warming west-northwest of Oklahoma City associated with the first developing supercell, and smaller areas of moistening and warming northwest and west-southwest of Oklahoma City. In contrast, the modified cloud analysis employing detected 
The 2000 UTC analysis increments of water vapor mixing ratio (shading, g kg−1) and potential temperature (black contours every 1 K) at approximately 5 km AGL for (a) the traditional cloud analysis and (b) the modified cloud analysis for the 19 May 2013 Oklahoma case.
Citation: Monthly Weather Review 145, 12; 10.1175/MWR-D-17-0103.1
3. Experimental setup
To investigate the impact of the modified cloud analysis, two tornadic supercell events were studied: the 19 May 2013 tornado outbreak in central Oklahoma (“the OK case”) and the tornadic supercell of 25 May 2016 in north-central Kansas (“the KS case”).
a. Case descriptions
Around 2000 UTC 19 May 2013, thunderstorms initiated near a dryline just west of the Oklahoma City, Oklahoma, metropolitan area in an environment characterized by strong vertical wind shear and high potential convective instability (i.e., CAPE). These storms developed quickly, and the three supercells that emerged from the convection moved toward the east-northeast; two of the supercells produced a total of eight tornadoes, whereas the third supercell was not tornadic. The northernmost supercell produced two brief tornadoes north and northeast of Oklahoma City before producing a long-lived tornado that produced EF3 damage near Carney, Oklahoma, between 2141 and 2224 UTC that resulted in 4 injuries; the southernmost supercell spawned a tornado that produced EF4 damage near Shawnee, Oklahoma, between 2300 and 2350 UTC that resulted in 2 fatalities and 10 injuries (NWS 2017a).
In the KS case, an isolated supercell formed in north-central Kansas just north of a warm front around 2200 UTC 25 May 2016 and moved slowly east-southeastward. The storm produced a total of four tornadoes, including a long-track tornado just east-northeast of Salina, Kansas, that lasted over 1.5 h (0007–0140 UTC) (NWS 2017b).
For both cases, observed tornado tracks are retrieved from shapefiles created from damage survey reports.
b. Model setup
The model used in this study is the ARPS (Xue et al. 2000, 2001, 2003), a nonhydrostatic, compressible, numerical model designed to function at multiple scales with an emphasis on the explicit prediction of convection. Terrain data were derived from the U.S. Geological Survey 3-arc-s dataset. Subgrid-scale turbulence was parameterized using a 1.5-order TKE turbulence scheme, with the evolution of the planetary boundary layer using the formulation of Sun and Chang (1986). Cloud microphysics were parameterized using the Milbrandt–Yau double-moment scheme (Milbrandt and Yau 2005a,b), and both short- and longwave radiation were parameterized using the NASA Goddard schemes (Chou 1990, 1992). A two-layer force-restore soil model based on Noilhan and Planton (1989) was used with surface fluxes based on stability-dependent drag coefficients using surface temperature and volumetric water content. More information about the full ARPS physics suite can be found in Xue et al. (2001).
Experiments were conducted using a one-way nested grid configuration. The parent domain has a size of 1200 km × 1200 km with a horizontal grid spacing of 4 km, and the inner nest a size of 500 km × 500 km with a horizontal grid spacing of 1 km. The domains for the OK and KS cases were centered on 35.45°N, 97.25°W and 38.65°N, 97.55°W, respectively. Both nests used a stretched vertical grid containing 53 vertical levels with an average spacing of 400 m and a minimum spacing of 100 m near the surface. The model top was rigid with a Rayleigh damping layer above 12 km to absorb vertically propagating waves. Lateral boundary conditions were externally forced. The simulated Z fields were computed using the T-matrix-based algorithm of Jung et al. (2010a). The domains used for each case are shown in Fig. 3, and a summary of the model setup used for these experiments is provided in Table 2.
Model domains used for the (left) 19 May 2013 Oklahoma case and the (right) 25 May 2016 Kansas case. The larger outer nest is shown in a thick black line, the inner nest is shown in a thin black line, and the zoomed-in domain plotted in subsequent figures is shown with a dotted line. The radar site used for each case is labeled.
Citation: Monthly Weather Review 145, 12; 10.1175/MWR-D-17-0103.1
Summary of ARPS model setup used for all experiments.
c. Assimilation procedures
The 12-km North American Mesoscale Forecast System (NAM) model analysis and forecast data were used to initialize the parent domain. For the OK case, the 1800 UTC 19 May 2013 NAM analysis was used, and for the KS case the 2-h forecast from the 1800 UTC 25 May 2016 NAM analysis (valid at 2000 UTC) was used. The NAM data were interpolated onto the 4-km ARPS grid, which was then integrated forward for 1 h using 3-h lateral boundary conditions derived from the NAM. This forecast was then further interpolated down to the inner nest and integrated forward another 1 h, with boundary conditions on the inner nest updated at 30-min intervals from the outer nest, for a total spinup period of 2 h. This forecast was then used as the background for all assimilation experiments performed.
Assimilation cycles were performed every 10 min following Hu and Xue (2007), who found this to be the optimal cycling frequency in their experiments. Radial velocity data were assimilated using the ARPS 3DVAR routine (Gao et al. 2004; Hu et al. 2006b), after which the cloud analysis routine was called. For the OK case, Oklahoma Mesonet data (Brock et al. 1995) were also assimilated using the 3DVAR routine. After 30 min, a separate 1-h forecast was made, with 10-min assimilation cycles continuing. Then 1-h forecasts were subsequently initiated every 30-min for 3 h after the initial analysis time. A diagram of the spinup, cycling, and assimilation process is shown in Fig. 4. For the OK case, radar data from the Twin Lakes, Oklahoma, WSR-88D (KTLX) were used, while the KS case used data from the Topeka, Kansas, WSR-88D (KTWX) (Fig. 3). For each case, two runs were performed: a control run (hereafter “Control”), in which the legacy cloud analysis is used (see section 2b), and an experimental run (hereafter “ZDRCOL”), which employed the modified polarimetric cloud analysis described in section 2c.
Diagram showing the spinup and assimilation cycles used for the (a) OK case and the (b) KS case. “FX” represents forecasts, while “A” represents assimilation cycles encompassing the ARPS 3DVAR + Cloud Analysis routines. The 0–1-h forecasts initiated every 30 min are denoted by red arrows. The dotted lines indicate a continuation of the 10-min assimilation cycles in addition to the initiated 0–1-h forecast.
Citation: Monthly Weather Review 145, 12; 10.1175/MWR-D-17-0103.1
Specific nomenclature for each experiment will be referred to hereafter by their case and which cloud analysis method was used (i.e., “KS_ZDRCOL” refers to the 25 May 2016 KS case experiment employing the modified cloud analysis).
4. Results
a. 19 May 2013 case
To investigate the performance of the 
Composited remapped Z (15-dBZ contour in gray) and analyzed 
Citation: Monthly Weather Review 145, 12; 10.1175/MWR-D-17-0103.1
The areas encompassed by the 15-dBZ threshold are much larger and extend farther to the north and east of the analyzed 
Composite plots of the maximum analyzed w (contoured at 30 m s−1) at each grid point for both OK_Control and OK_ZDRCOL through the assimilation period (2000–2300 UTC) are shown in Fig. 6. OK_Control exhibits a rather noisy w field composed of many spurious updrafts, along with a pronounced northward bias compared to the observed tornado tracks. This northern and positive forward speed bias has been observed in many storm-scale modeling studies (e.g., Potvin et al. 2014; Xue et al. 2014; Stratman and Brewster 2015; Wheatley et al. 2015). In sharp contrast, OK_ZDRCOL features much more consolidated updraft tracks that closely follow the analyzed 
Composited maximum vertical velocity in each grid column for each of the postassimilation analyses from 2000 to 2300 UTC for the 19 May 2013 case for the (a) OK_Control case and (b) OK_ZDRCOL case, colored according to their corresponding analysis time and showing the 30 m s−1 vertical velocity contour line. Observed tornado tracks are shown in black and gray, with gray tracks indicating observed tornadoes that fall outside of the period of study.
Citation: Monthly Weather Review 145, 12; 10.1175/MWR-D-17-0103.1
The composited 1–6 km above ground level (AGL) updraft helicity (Kain et al. 2008) swaths for three different forecast periods are shown in Fig. 7. Model output was saved every 5 min and composited over the 1-h forecast, with the maximum for the forecast period shown at each grid point. The 1–6-km updraft helicity provides a reasonable depiction of the path of mesocyclones and overall storm track. To aid in verifying the forecast updraft helicity swaths, rotation tracks derived from the Multi-Radar Multi-Sensor (MRMS; Smith et al. 2016) system, which are composited maximum values of radar-derived azimuthal shear (Smith and Elmore 2004) in a layer through a given time period, are included in Fig. 7. While the traditional azimuthal shear product uses 0–2- or 3–6-km AGL layers, the 1–6-km AGL azimuthal shear was used in this study to better correspond with the 1–6-km updraft helicity derived from the model output. The rotation tracks shown in Fig. 7 correspond to the 1-h forecast periods shown in each panel.
Composited 1–6-km AGL updraft helicity (m2 s−2, red shading) at each grid point for (a),(c),(e) OK_Control and (b),(d),(f) OK_ZDRCOL for the 0–1-h forecasts beginning at (a),(b) 2030; (c),(d) 2130; and (e),(f) 2230 UTC. MRMS-derived 1–6-km AGL rotation tracks (black contours, 0.01 s−1 shown) are included for each 1-h period. The initial 1-km Z of each 1-h period is shown for reference (grayscale shading).
Citation: Monthly Weather Review 145, 12; 10.1175/MWR-D-17-0103.1
During the first 0–1-h forecast at 2030 UTC (Figs. 7a,b), both OK_Control and OK_ZDRCOL feature a storm track for Supercell 1 that is located too far north. The updraft helicity swath in OK_ZDRCOL, however, is more consolidated and features a smaller northward bias compared to OK_Control. Supercell 1 in OK_ZDRCOL has a slower mean storm motion, with the center of the updraft helicity swath covering approximately 10 fewer kilometers than OK_Control during the forecast period. Finally, OK_ZDRCOL features a weak updraft helicity swath associated with the second developing storm (Supercell 2, southwest of Oklahoma City) that is absent in the OK_Control run.
The improvements of OK_ZDRCOL over OK_Control are most pronounced in the forecast initiated at 2130 UTC (Figs. 7c,d), approximately 10 min before the start of the long-track tornado northeast of Oklahoma City. OK_Control features multiple updraft helicity swaths. There is no identifiable strong updraft helicity swath coincident with the observed rotation track of Supercell 1, with instead a very strong and prominent updraft helicty swath displaced far to the northeast of the observed rotation track and corresponding tornado. Moreover, there are two notable updraft helicity swaths corresponding to the weakening rotation track of Supercell 2 southeast of Oklahoma City, with no updraft helicity swath that clearly corresponds with the rotation track for Supercell 3. In stark contrast, OK_ZDRCOL captures the updraft helicty swath of Supercell 1 well, with the forecast swath nearly coincident with the observed rotation track and with only a slight bias in forward speed. It also correctly captures the updraft helicity swath associated with Supercell 2 that weakens as it moves to the northeast. Finally, the early development of strong rotation in the southernmost supercell (Supercell 3) that would go on to produce the Shawnee tornado is depicted to the south of Oklahoma City while being absent in OK_Control.
The 2230 UTC 0–1-h forecast (Figs. 7e,f) show many of the same improvements. Both Supercells 1 and 2 were nontornadic and beginning to weaken, with less pronounced updraft helicity swaths in OK_ZDRCOL. In contrast, OK_Control has strong but noisy updraft helicity swaths for these storms displaced to the northeast of their observed locations. For Supercell 3, both OK_Control and OK_ZDRCOL exhibit updraft helicity associated with the strong and broad observed rotation track south of Oklahoma City. However, the updraft helicity swath in OK_Control is primarily north and east of the observed rotation track, while OK_ZDRCOL captures the rotation (albeit with a slight north bias) and its timing well.
To further examine the improvements in the OK_ZDRCOL forecasts over OK_Control, the 1-km AGL Z is shown for the forecasts initiated at 2130 UTC in 20-min increments and compared to the observed radar fields in Fig. 8. This time period represents the duration of the northern long-track tornado northeast of Oklahoma City, which was on the ground between 2141 and 2224 UTC, as well as the leadup period to the long-track tornado produced by Supercell 3, which first touched down at 2300 UTC. For both the OK_Control and OK_ZDRCOL runs, an adjustment period is seen in the first 20 min (Figs. 8e,f) with small, yet intense, precipitation cores (Z 
Plots of (left) observed 1-km AGL Z from KTLX remapped to the ARPS grid, and corresponding forecasts from the (middle) OK_Control and (right) OK_ZDRCOL runs for the 0–1-h forecast beginning at 2130 UTC for the 19 May 2013 case. Plots are shown for (a)–(c) the analysis at 2130 UTC, (d)–(f) 20-min forecast at 2150 UTC, (g)–(i) 40-min forecast at 2210 UTC, and (j)–(l) 60-min forecast at 2230 UTC. Observed tornado tracks are shown in black.
Citation: Monthly Weather Review 145, 12; 10.1175/MWR-D-17-0103.1
Equitable threat score and bias of composite Z at (a),(b) 20-; (c),(d) 30-; and (e),(f) 40-dBZ thresholds for each of the 0–1-h forecasts for the OK case.
Citation: Monthly Weather Review 145, 12; 10.1175/MWR-D-17-0103.1
b. 25 May 2016 case
The KS case presents a somewhat more challenging forecast scenario owing to a complex evolution of the supercell and the greater distance between the supercell and the radar. After becoming mature, the main supercell began moving slowly to the southeast. A new storm developed to the southwest of the main supercell, which produced a left-moving supercell that moved off to the north-northeast before merging with the primary supercell. Additional convection also formed along, and was absorbed into, the southern flank of the forward-flank downdraft in the supercell. This storm was farther away from the radar than the storms in the OK case were (initiation occurred approximately 140 km away from the radar compared to 65 km away from the radar in the OK case), resulting in a decrease of the quality of radar data available for assimilation due to both decreased low-level coverage and increasing radar resolution volume (
A long, continuous swath of 
Composited remapped Z (15-dBZ contour in gray) and analyzed 
Citation: Monthly Weather Review 145, 12; 10.1175/MWR-D-17-0103.1
The composite plot of maximum w in the analyses for the KS case shows many of the same improvements documented in the OK case. The KS_Control case shows a more disorganized and less coherent updraft path, with many spurious updrafts to the north of the main supercell path and observed tornado tracks (Fig. 11a). Considering that the end of the assimilation period is near the ending time of the long-track tornado, the general progression of the analyzed updrafts is also too fast. In contrast, KS_ZDRCOL features a much more coherent updraft swath with a slower forward motion to the east-southeast and a path closer to the observed tornado track (Fig. 11b). KS_ZDRCOL also features less spurious convection than KS_Control in the central and southern parts of the domain.
Composited maximum vertical velocity in each grid column for each of the postassimilation analyses from 2200 to 0100 UTC for the 25 May 2016 case for the (a) KS_Control case and (b) KS_ZDRCOL case, colored according to their corresponding analysis time and showing the 30 m s−1 vertical velocity contour line. Observed tornado tracks are shown in black and gray, with gray tracks indicating observed tornadoes that fall outside of the period of study.
Citation: Monthly Weather Review 145, 12; 10.1175/MWR-D-17-0103.1
A comparison of 1–6-km updraft helicity with MRMS-derived rotation tracks, similar to Fig. 7, is shown for the KS case in Fig. 12. The forecasts selected here were chosen to coincide with the long-track tornado. In the forecast initiated at 2300 UTC (Figs. 12a,b), both KS_Control and KS_ZDRCOL produce a developing supercell north of Salina with an unorganized updraft and an east-northeast motion. The observed rotation tracks show only slight, messy rotation during this period. Starker differences are apparent for the 0000 UTC forecast (Figs. 12c,d). KS_Control features a disorganized updraft helicity swath displaced far to the north of the observed rotation track. In contrast, KS_ZDRCOL features a consolidated updraft helicity swath through the duration of the forecast period along and just north of the observed rotation track, although a slight slow bias in forward speed is apparent. These same general patterns are also observed for the 0100 UTC forecast, with a noisy updraft helicity field too far to the northeast in KS_Control; KS_ZDRCOL exhibits a large, southeastward-directed updraft helicity swath displaced slightly southwest of the observed rotation track.
Composited 1–6-km AGL updraft helicity (m2 s−2, red shading) at each grid point for (a),(c),(e) KS_Control and (b),(d),(f) KS_ZDRCOL for the 0–1-h forecasts beginning at (a),(b) 2300; (c),(d) 0000; and (e),(f) 0100 UTC. MRMS-derived 1–6-km AGL rotation tracks (black contours, 0.01 s−1 shown) are included for each 1-h period. The initial 1-km Z of each 1-h period is shown for reference (grayscale shading).
Citation: Monthly Weather Review 145, 12; 10.1175/MWR-D-17-0103.1
An example of observed and forecast Z for both KS_Control and KS_ZDRCOL is shown in Fig. 13 for the 0000 UTC forecast. This 1-h period begins near the start time of the primary long-track tornado and features a complex evolution involving the secondary storm to the southwest splitting and merging with the main supercell (Figs. 13a,d,g,j). As such, both KS_Control and KS_ZDRCOL struggle to accurately predict the evolution of the storm during this period. A very large and elongated forward-flank downdraft not seen in the radar observations quickly develops and extends to the east-southeast and east-northeast in KS_Control and KS_ZDRCOL, respectively. This forward-flank precipitation appears to stem from weak upper-level Z in the anvil in the observations. Despite this, KS_ZDRCOL features a more realistic supercell structure 20-min into the forecast (Fig. 13f) compared to KS_Control (Fig. 13e), with a well-defined hook echo and rear-flank downdraft near the observed tornado track. Neither KS_Control nor KS_ZDRCOL clearly capture the left-splitting supercell. An erroneous region of moderate Z (i.e., 25–35 dBZ) within the inflow region of the supercell is also seen in the KS_Control run (Fig. 13e) that is not seen in the KS_ZDRCOL run. Both KS_Control and KS_ZDRCOL generally feature Z values that are too low (by 5–10 dBZ) compared to observations outside of the forward-flank downdraft. Overall, KS_ZDRCOL features a slower and noticeably more accurate forecast track of the hook echo than KS_Control (as also seen Figs. 12c,d), as well as a more realistic looking hook echo (Figs. 13i,l vs Figs. 13h,k).
(left) Observed 1-km AGL Z from KTWX remapped to the ARPS grid, and corresponding forecasts from the (middle) KS_Control and (right) KS_ZDRCOL runs for the 0–1-h forecast beginning at 0000 UTC (on 26 May) for the 25 May 2016 case. (a)–(c) The analysis at 0000 UTC, (d)–(f) 20-min forecast at 0020 UTC, (g)–(i) 40-min forecast at 0040 UTC, and (j)–(l) 60-min forecast at 0100 UTC. Observed tornado tracks are shown in black and gray, with gray tracks indicating observed tornadoes that fall outside of the period of study.
Citation: Monthly Weather Review 145, 12; 10.1175/MWR-D-17-0103.1
Quantitatively, KS_ZDRCOL generally exhibits improvements over KS_Control with higher ETS scores and lower biases, although the improvements in ETS scores are more mixed than in the OK case, with lower scores for the first two forecasts in the period (Fig. 14). Overall scores are lower in the KS case, in part due to the challenging nature of the forecast and in part due to the aforementioned biases in Z (e.g., Figs. 14b,d,f) and the extensive forward-flank downdrafts, which generally exceed the biases seen for the OK case, particularly for later forecasts.
As in Fig. 9, but for the KS case.
Citation: Monthly Weather Review 145, 12; 10.1175/MWR-D-17-0103.1
5. Summary and discussion
In this study, the potential for the assimilation of polarimetric radar data observations via a cloud analysis technique to aid in the spinup and forecast of convection in storm-scale models is examined. Differential reflectivity columns are ubiquitous features of deep moist convection that are coincident with updrafts and, thus, with areas of saturation and latent heat release. Based on this premise, a 
The 
These experiments represent a basic proof-of-concept investigation of the potential for assimilating 
While being a relatively simple and efficient method for assimilating Z, cloud analysis techniques may not be optimal owing to their inherent empirical relationships that can compromise initial adjustments in the model. As temperature and moisture increments appear to play large roles in aiding the spinup of observed storms in storm-scale models, future work will seek to explore the possibility of assimilating cloud analysis-derived temperature and moisture increments based on detected 
The authors thank the three anonymous reviewers for their constructive feedback, as well as Keith Brewster and Elizabeth Smith for their helpful discussions and Alexandre Fierro for providing useful feedback about the manuscript. Funding was provided by NOAA/Office of Oceanic and Atmospheric Research under NOAA–University of Oklahoma Cooperative Agreement NA11OAR4320072, U.S. Department of Commerce. Additional funding was provided by the U.S. Department of Energy Atmospheric System Research Grant DE-SC0014295 and by NSF Grant AGS-1341878. The computing for this project was performed at the OU Supercomputing Center for Education and Research (OSCER) at the University of Oklahoma (OU).
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