Comparison between Dual-Doppler and EnKF Storm ... - AMS Journals

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Comparison between Dual-Doppler and EnKF Storm-Scale Wind Analyses: Observing System Simulation Experiments with a Supercell Thunderstorm COREY K. POTVIN AND LOUIS J. WICKER NOAA/National Severe Storms Laboratory, Norman, Oklahoma (Manuscript received 8 February 2012, in final form 29 May 2012) ABSTRACT Kinematical analyses of mobile radar observations are critical to advancing the understanding of supercell thunderstorms. Maximizing the accuracy of these and subsequent dynamical analyses, and appropriately characterizing the uncertainty in ensuing conclusions about storm structure and processes, requires thorough knowledge of the typical errors obtained using different retrieval techniques. This study adopts an observing system simulation experiment (OSSE) framework to explore the errors obtained from ensemble Kalman filter (EnKF) assimilation versus dual-Doppler analysis (DDA) of storm-scale mobile radar data. The radar characteristics and EnKF model errors are varied to explore a range of plausible scenarios. When dual-radar data are assimilated, the EnKF produces substantially better wind retrievals at higher altitudes, where DDAs are more sensitive to unaccounted flow evolution, and in data-sparse regions such as the storm inflow sector. Near the ground, however, the EnKF analyses are comparable to the DDAs when the radar cross-beam angles (CBAs) are poor, and slightly worse than the DDAs when the CBAs are optimal. In the single-radar case, the wind analyses benefit substantially from using finer grid spacing than in the dualradar case for the objective analysis of radar observations. The analyses generally degrade when only singleradar data are assimilated, particularly when microphysical parameterization or low-level environmental wind errors are introduced. In some instances, this leads to large errors in low-level vorticity stretching and Lagrangian circulation calculations. Nevertheless, the results show that while multiradar observations of supercells are always preferable, judicious use of single-radar EnKF assimilation can yield useful analyses.

1. Introduction One of the most valuable applications of Doppler radar data is the retrieval of convective storm wind fields. Since radars generally provide the only dense observations of storms above the ground, these retrievals and the analyses commonly derived from them (e.g., parcel trajectories, circulation calculations, etc.) are critical to illuminating supercell and tornado dynamics. Mobile dual-Doppler datasets have proven particularly useful in this regard. Low-level wind retrievals have been obtained on scales as fine as O[100 m, 10–100 s] by positioning the radars as near to the region of interest as possible and using a very shallow scanning strategy (Beck et al. 2006; Wurman et al. 2007a,b; Marquis et al. 2008; Wurman et al. 2010). In this study,

Corresponding author address: Dr. Corey K. Potvin, National Severe Storms Laboratory, National Weather Center, 120 David L. Boren Blvd., Norman, OK 73072. E-mail: [email protected] DOI: 10.1175/MWR-D-12-00044.1 Ó 2012 American Meteorological Society

we are primarily concerned with the somewhat largerscale (O[1 km, 100 s]) kinematical analyses typically obtained from mobile radar observations of the lowest ;5–15 km of the storm (e.g., Payne et al. 2010; Betten et al. 2011). Maximizing the scientific value of mobile radar datasets, including those collected during the Second Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX2), will require improvements to our knowledge of the expected analysis errors for the various retrieval techniques applied to such datasets. Such knowledge is required to 1) select the technique (and technique settings) most likely to minimize analysis errors for a particular case, 2) estimate analysis errors and determine how much confidence to place in inferences drawn from the analysis, and 3) help design future mobile radar deployment and scanning strategies that address significant sources of analysis error. These considerations motivated a recent observing system simulation experiment (OSSE) study of threedimensional variational data assimilation (3D-VAR)

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dual-Doppler analysis (DDA) errors under various observational scenarios (e.g., deep versus shallow radar scanning and optimal versus poor radar cross-beam angle; Potvin et al. 2012b). The present work extends this analysis to a second technique that is increasingly used to investigate supercell kinematics and dynamics: ensemble Kalman filter (EnKF; Evensen 1994) radar data assimilation (Snyder and Zhang 2003). DDA techniques provide a relatively straightforward and sophisticated way to retrieve the 3D storm wind field from radar observations, particularly when the 3D-VAR framework is used (Potvin et al. 2012c). However, substantial DDA errors can arise from a number of sources including finite observational resolution, incomplete Doppler velocity coverage due to Earth’s curvature and low-reflectivity regions, and rapid flow evolution during the analysis period. The EnKF ideally mitigates these errors by producing analyses consistent with both the radar observations and a numerical weather prediction (NWP) model. In practice, however, violations of the optimality conditions for the EnKF and errors in the observation operators and NWP model inevitably limit, and may conceivably reverse, improvements to wind retrievals. It is therefore not immediately clear under what conditions EnKF wind analyses are generally better or worse than DDAs. On the other hand, in the common scenario where part or all of the storm is observed by only one radar, it is reasonable to expect that the EnKF will permit more accurate wind retrievals than could be obtained from traditional single-Doppler retrieval methods. This hypothesis is supported by previous, perfect-model EnKF experiments with simulated supercells, in which assimilating data from a single radar produced mean retrieved wind component errors commensurate with the random errors in the radial velocity observations (Snyder and Zhang 2003; Zhang et al. 2004; Caya et al. 2005; Tong and Xue 2005; Xue et al. 2006; Yussouf and Stensrud 2010). Excellent results have even been obtained in OSSEs with large, structural errors in the microphysical parameterization scheme and/or radar reflectivity factor (hereafter ‘‘reflectivity’’) forward operator (Xue et al. 2010). In addition, in comparisons of DDAs and single-radar EnKF wind analyses of real supercells (Dowell et al. 2004; Marquis et al. 2010, 2012), the two methods have produced qualitatively similar low-level wind retrievals once enough radar volumes have been assimilated. All these results indicate that the use of an NWP model in the EnKF constrains the 3D wind solution sufficiently to recover a substantial portion of the cross-beam and vertical wind components. This is encouraging given that highquality dual-Doppler supercell observations are difficult

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to obtain. However, since the true 3D wind field was uncertain in the aforementioned real-data studies, the accuracy of the single-radar EnKF analyses relative to the DDAs was indeterminate. Our use of an OSSE framework, in which the true wind field is known, removes this limitation, allowing us to further investigate to what degree the EnKF compensates for the lack of dual-Doppler data. To further investigate the suitability of the EnKF for kinematical supercell retrieval, and to identify strengths and weaknesses of the EnKF relative to DDA, we compare 3D wind retrievals, vertical vorticity analyses, parcel trajectories, and circulation time series obtained from the two methods for a numerically simulated supercell. The observational characteristics (number of radars, scanning strategy, and cross-beam angle) as well as the sources of model error in the EnKF (coarse resolution, incorrect microphysical parameterization, and/ or imperfect model sounding) are varied over a range of plausible scenarios. The results are intended to help guide the creation and interpretation of kinematical analyses of real supercells, as well as the design of mobile radar deployment and scanning strategies that mitigate significant analysis errors. The rest of the paper is organized as follows. Section 2 describes the numerical supercell simulation, radar emulation, DDA and EnKF schemes, vorticity, parcel trajectory and circulation calculations, and verification procedure. Analyses obtained using DDA and singleand dual-radar EnKF are compared in section 3. A summary and conclusions follow in section 4.

2. Methods a. Numerical supercell simulation and radar emulation The numerical supercell analyzed in our experiments was generated by the National Severe Storms Laboratory Collaborative Model for Multiscale Atmospheric Simulation (NCOMMAS; Wicker and Skamarock 2002; Coniglio et al. 2006). The simulation proceeded on a stationary 102.4 km 3 102.4 km 3 20 km domain with 200-m horizontal and vertical spacing. The model was integrated over 2 h using large and small time steps of 2 and 0.25 s, respectively. The storm was initiated with an ellipsoidal 4-K thermal bubble with horizontal and vertical radii of 10 and 1.4 km, respectively. A fully dualmoment version of the Ziegler (1985) microphysics scheme (Mansell et al. 2010), referred to herein as the Ziegler Variable Density (ZVD) scheme, was used. Further details about the supercell simulation can be found in Potvin et al. (2012b).

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As in Lei et al. (2007) and Yussouf and Stensrud (2010), we increase the realism of the assimilated pseudo-observations by computing them on the (spherical) radar grid rather than the model grid, and by emulating the radar beam rather than assuming point measurements. Pseudo-observations of reflectivity Zobs (mm6 mm23) and Doppler velocity Vrobs are generated from the model reflectivity Z, wind components u, y, and w, and hydrometeor fall speeds wt using the technique of Wood et al. (2009). This technique emulates the power-weighted averaging of radial velocities and reflectivities of scatterers within a Gaussian radar beam. Earth curvature and beam refraction are also represented. The same hydrometeor fall speed formula is used in the calculation of the Vrobs , the Vr forward operator in the EnKF, and the model: wt 5 22.6Z0.107 (1.2/rsim)0.4, where rsim (kg m23) is the height-varying base-state air density in the simulation and Z is given in mm6 mm23 (Joss and Waldvogel 1970). Reflectivity observations ,0 dBZ are set to 0 dBZ to imitate the common practice of treating missing or very low reflectivities as ‘‘no precipitation’’ observations to suppress spurious convection in the ensemble (Dowell et al. 2004; Tong and Xue 2005; Aksoy et al. 2009). To emulate the lack of radial velocity data in regions of low signal-to-noise ratio, radial velocity observations are only computed in regions with Zobs . 5 dBZ. Random errors having 2 m s21 (2 dBZ) standard deviation are added to the radial velocity (reflectivity) observations. The measurement characteristics, scanning strategies, and positioning of the emulated radars are consistent with previous storm-scale deployments of the Shared Mobile Atmospheric Research and Teaching (SMART; Biggerstaff et al. 2005) radars (Payne et al. 2010; Betten et al. 2011). The positions of the emulated radars relative to the simulated supercell are depicted in Fig. 1. The location of the eastern radar is alternated in our experiments to achieve a cross-beam angle (CBA) of roughly 908 (default experiments) or 308 (‘‘-CBA30’’ experiments) over the reflectivity hook echo roughly midway through the data assimilation period. The radars sample every 150 m in range and 1.08 in azimuth and have halfpower and effective beam widths of 0.898 and 1.398, respectively. Observations are collected using either a deep (default experiments) or shallow (‘‘-SHAL’’ experiments) volume coverage pattern (VCP; Table 1). In each case, the two radars scan the same elevation angle at the same time, beginning at 0.58 and progressing to steeper tilts. To simulate observational nonsimultaneity, the individual sweeps in each VCP are binned by elevation angle, and blocks of sweeps valid at higher elevation angles are computed from model fields valid at later simulation times. To reduce the storage requirements and

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FIG. 1. Experimental configuration. Axes indicate distance from the southwest corner of the truth simulation and EnKF domains. The model reflectivity field at z 5 1 km is shown at the beginning (t 5 30 min) and end (t 5 84 min) of the data assimilation period. The black dots indicate the positions of the emulated radars in the majority of our experiments. In the ‘‘-CBA30’’ experiments, the eastern radar is located at the blue dot. The 308 dual-Doppler lobe is shown for each case. The verification domain (shown for t 5 30 min; black dashed square) is periodically shifted eastward to prevent excessive truncation of the storm.

to speed up the radar pseudo-observation generation, successive blocks of sweeps are computed from the model data valid at 30-s intervals.

b. EnKF configuration The EnKF settings used in our experiments are representative of recent storm-scale EnKF radar data assimilation studies. The NCOMMAS EnKF data assimilation scheme is based on the ensemble square root filter of Whitaker and Hamill (2002). Observations are therefore assimilated serially, an approximation that is justified to the extent that observational errors are uncorrelated in space and time. The ensemble consists of 40 members. The data assimilation domain has roughly the same dimensions as the truth simulation domain,1 but has 600 m (rather than 200 m) grid spacing in all three dimensions. The coarse resolution of the ensemble member grids relative to the truth simulation grid is a source of model error in all of our EnKF experiments. The covariance localization factor is calculated using the Gaspari and Cohn (1999) correlation function with

The EnKF domain was set 0.2 km 3 0.2 km 3 0.4 km larger than the truth simulation domain to make its dimensions divisible by the desired grid spacing of 0.6 km. 1

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TABLE 1. Two volume coverage patterns used in retrieval experiments. DT (min)

Elevation angles u (8)

DEEP

2.5

SHALLOW

1.5

0.5, 1.5, 2.5, 3.5, 4.5, 6.0, 7.5, 9.0, 10.5, 12.5, 14.5, 16.5, 19.0, 21.5, 24.0, 27.0, 30.0, 33.0 0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5, 10.5, 11.5

covariance estimation cutoff radii of 6 and 3 km in the horizontal and vertical directions, respectively. The sounding input to each ensemble member is obtained by adding random (s 5 2 m s21) perturbations to the 1D u and y profiles used for the truth simulation (Aksoy et al. 2009). Ellipsoidal thermal bubbles having random spatial dimensions and magnitudes are inserted in each member at t 5 0 to initiate storms. The bubbles are randomly positioned within a 40-km horizontal box roughly centered on the initiation location of the storm in the truth simulation. The ensemble members are then integrated 30 min forward to the beginning of the data assimilation period (t 5 30 min). This allows physically realistic covariances to develop in the ensemble, thus maximizing the utility of radar data early in the assimilation period (e.g., Snyder and Zhang 2003; Dowell et al. 2004). Prior to assimilation, the Zobs and Vrobs are analyzed to Cartesian grids upon their respective conical radar scan surfaces. This practice is common in contemporary EnKF analyses (e.g., Sun and Crook 2001; Dowell et al. 2004; Dowell and Wicker 2009; Aksoy et al. 2009; Marquis et al. 2012) since it reduces the impact of spatially correlated observational errors (which violate the Kalman filter formulation) and of representativeness errors due to the contributions to observations of processes unrepresented in the model, mitigates deficient ensemble spread in data-dense regions, and reduces computational cost. We perform the objective analysis using Cressman interpolation with the cutoff radius set to half the observational grid spacing. In the dual-radar assimilation experiments, observations are interpolated to 2-km grids; decreasing the grid spacing to 1 km produced very little improvement in preliminary analyses. On the other hand, 1-km observational grids are adopted in the single-radar assimilation experiments since the latter were substantially improved by the finer observational resolution (the importance of optimizing the observational grid spacing in the single-radar case is depicted in section 3h). To account for storm motion between the times at which observations are valid and the times at which they are analyzed, the interpolated observations are shifted to locations determined by the estimated storm translational velocity components U

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and V. The U and V (5 10 and 0 m s21, respectively) are treated as constants in space and time and were determined by visually tracking features in the Zobs field. Though more sophisticated advection velocity retrieval methods are available (e.g., Shapiro et al. 2010a,b), we elected to use this simpler approach since it is commonly used in storm-scale analyses. Observations are assimilated every 2 min using a 2-min window centered on t. As in most EnKF radar data assimilation studies, to reduce computational cost, the observation operator H trilinearly interpolates model fields to observational locations, and thus makes no provision for the shape of, nor inhomogeneous reflectivity distribution within, the radar beam. Following Dowell and Wicker (2009), to save computational time, observations are not used to update p and Km since the impacts are negligible. Observational error standard deviations of 2 m s21 and 5 dBZ are assumed in the filter. We used larger filterassumed Zobs errors (5 dBZ) than were actually added to the Zobs (2 dBZ) to reduce the impact of errors in the forecast hydrometeor fields and reflectivity operator. This strategy was partly motivated by the real-data experiments of Dowell et al. (2011), in which the wind analyses appeared to improve when the assumed Zobs error standard deviation was increased from 2 to 5 dBZ (it was not determined whether the improvements resulted mainly from increased ensemble spread or the reduced impact of model, Zobs and/or observation operator errors). The assimilation proceeds for 54 min, during which the supercell travels eastward from north of the western radar to north-northwest of the default location of the eastern radar in our experiments (Fig. 1). A procedure similar to the additive noise method (Dowell and Wicker 2009; based on the ensemble initialization procedure of Caya et al. 2005) is used to maintain ensemble spread consistent with the ensemble forecast error variance. Smoothed perturbations having horizontal and vertical length scales of 4 and 2 km, respectively, are added to u, y, u, and dewpoint temperature Td below z 5 10 km wherever Zobs . 20 dBZ during the data assimilation. Prior to being smoothed, the u, y, u, and Td perturbations have standard deviations of 2.5 m s21, 2.5 m s21, 2.0 K, and 0.5 K, respectively. Several factors are varied in the EnKF experiments. The number of radars contributing data to the assimilation procedure is indicated by the prefix ‘‘1-’’ or ‘‘2-.’’ The NWP model used to integrate the ensemble members forward to the next assimilation time is either identical, apart from the differing grid spacings (and slightly differing grid dimensions), to that used to generate the truth simulation, or parameterizes microphysical processes using the Gilmore et al. (2004) version of the Lin et al. (1983) scheme (hereafter

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‘‘LFO’’) rather than the ZVD scheme. Given the important differences between these two schemes (e.g., ZVD is a two-moment scheme that treats hail and graupel separately, while LFO is a single-moment scheme that includes graupel/hail in a single category), EnKF experiments using LFO (indicated by LFO in the label) have substantial model errors. In experiments with the suffix ‘‘-SNDERR’’ in the label, errors are added to the lowest 3 km of the sounding y used to initialize the ensemble members (Fig. 2). These errors are meant to represent cases where the low-level jet intensifies after the collection time of the model sounding. The errors are patterned after the evolution (due largely to low-level jet intensification) of velocity–azimuth display (VAD) profiles near the time and location of the Greensburg, Kansas, tornado (Dawson et al. 2012).

c. Variational dual-Doppler analysis technique The DDAs are obtained using the 3D-VAR technique described in Shapiro et al. (2009) and Potvin et al. (2012a). The technique weakly satisfies the radial wind observations, the anelastic mass conservation equation and a smoothness constraint, and exactly satisfies the impermeability condition at the ground (the vorticity equation constraint tested in the referenced studies was not used in our experiments). The DDAs proceed on a 40 km 3 40 km 3 6 km domain with grid spacing equal to that of the data assimilation domain (D 5 600 m). The DDA grid is periodically recentered on the storm during the data assimilation period. Provision is made for wind field translation between the analysis and observational times using the same advection-correction procedure as in the EnKF experiments.

d. Vorticity and parcel trajectory retrievals In one set of experiments, vertical vorticity, z [ ›y/›x 2 ›u/›y, and vertical vorticity stretching, z_ stre [ 2z(›u/ ›x 1 ›y/›y) are computed from the various wind analyses using centered finite differences valid over 2D. In addition, the fourth-order Runge–Kutta method is used to backward-compute parcel trajectories from t 5 60 min to t 5 45 min using the model wind fields output every 30 s (‘‘true’’ trajectories) and series of DDAs or EnKF wind retrievals (analyzed trajectories) valid every 2 min. A trajectory time step of 1 s is used in all cases. Finally, circulation, G [ åC V dl, where V is the mean wind vector along a line segment position vector dl, is computed around material circuits C connecting the parcel trajectories at successive times.

e. Verification The verification wind fields are generated from the simulated fields in two steps. First, to match the motion

FIG. 2. Hodograph used in truth simulation and most of the EnKF experiments (solid), and the modified hodograph used in the ‘‘-SNDERR’’ experiments (dashed). Altitudes of 1, 2, and 3 km are marked on each hodograph.

scales in the analyses that can be resolved on the analysis grid, a sixth-order implicit filter (Raymond 1988) is used to strongly damp wavelengths ,1.2 km (the minimum resolvable wavelength on the 600-m analysis grid) in the 200-m simulated wind fields. Second, the verification wind is computed at each analysis point by taking a weighted average of all the filtered 200-m winds located on and within a (600 m)3 grid box centered on the analysis point. The filtered winds valid on surfaces and edges of the (600 m)3 grid box are weighted ½ and 1/ 4 as much, respectively, as winds valid within the 600-m grid box. Since the velocities on the staggered (Arakawa C) EnKF analysis grid and unstaggered (Arakawa A) DDA grid are not collocated, separate verification (hereafter, ‘‘DDA true’’ or ‘‘EnKF true’’) wind fields must be computed for each in our procedure. Horizontal cross sections of the DDA true and EnKF true w fields are very similar since w is computed at the same heights on each grid. Thus, only the EnKF true w is shown in visual comparisons of the w obtained from the two methods. On the other hand, the u and y obtained from the two methods are vertically offset by 300 m, thus requiring that both verification fields be used when visually comparing the performance of the two methods (except in cases where u and y change little between the two levels). The true z and z_ stre are computed from the true u, y, and w in each case using the same finite-differencing stencil as in the analysis procedure. All root-mean-square (RMS) and RMS error (RMSE) statistics presented herein are computed at each analysis level within the ‘‘dual-Doppler region’’ of the DDA domain. In this study, the dual-Doppler region

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FIG. 3. Vertical profiles of (left) RMSE u and (right) RMSE w in t 5 60-min DEEP EnKF analyses with (dashed) and without (solid) reflectivity assimilation. The following plotting conventions are used in this and subsequent RMSE plots: (red) 2-ZVD, (blue) 2-LFO, (green) 1-ZVD, and (violet) 1-LFO.

is the set of points located within 750 m of at least one radial velocity observation from each radar when the DEEP VCP (Table 1) is used. Analyzed variables outside this region are not shown in many of the horizontal cross-section plots that appear in later sections. The DDA u and y are not verified at z 5 0 since this would require downward extrapolation of the model u and y at z 5 100 m, the lowest level on which the horizontal winds are computed on the 200-m simulation grid.

3. Results a. Ineffectiveness of reflectivity assimilation Assimilating reflectivity observations into cloud models is more problematic than assimilating radial velocity (Tong and Xue 2005; Dowell et al. 2011). Much of the difficulty arises from the frequently large errors in model-predicted reflectivity due to inaccuracies in the microphysical parameterization scheme. Significant errors can also occur in the reflectivity observation operator, which adopts the same assumptions about hydrometeor size distributions as does the microphysics scheme, and often does not realistically simulate energy backscatter. In addition, reflectivity is nonlinearly related to the model state, and so reflectivity errors may become substantially non-Gaussian (even were the microphysics scheme and reflectivity observation operator to be perfect), rendering EnKF updates suboptimal.2 In light of all these difficulties, we compared wind

2 Reflectivity biases due to beam attenuation and radar miscalibration, for example, can further limit the utility of reflectivity assimilation. However, we do not simulate these effects in our experiments.

retrievals valid at t 5 36, 60 (Fig. 3), and 84 min from 2-ZVD, 2-LFO, 1-ZVD, and 1-LFO experiments (see section 2b for experiment naming conventions) performed with or without Zobs assimilation (no-precipitation and radial velocity observations were assimilated in all experiments). In the dual-radar experiments, reflectivity was only assimilated from the western radar since Zobs from the second radar would provide very little independent observational information. In these and subsequent experiments, the presented RMSE plots were confirmed to be representative of RMSE plots at adjacent analysis times. Assimilating reflectivity degraded the 2-LFO and 2-ZVD u, y, and (especially) w at all times. The degradation of the 2-ZVD (i.e., perfect microphysics) analysis is somewhat surprising. As stated in section 1, however, the advantage of assimilating radar observations can be voided by model errors or errors/suboptimalities in the EnKF system. Possibly substantial error sources in the 2-ZVD analysis include the relatively coarse model resolution, non-Gaussian reflectivity errors, and the simplified reflectivity operator (section 2b). Overall, assimilating reflectivity improved the 1-ZVD analysis and had a mixed impact on the 1-LFO analysis at t 5 36 min, but substantially degraded both analyses (particularly 1-LFO) at the later times. The less detrimental impact of Zobs assimilation early in the single-radar experiments suggests the additional observational information accelerated the development of accurate ensemble covariances. After the ensemble spinup phase, however, the wind field evidently was sufficiently constrained by the single-radar Vrobs and no-precipitation observations that assimilating Zobs was counterproductive. In light of these results, we did not assimilate Zobs in any of our subsequent experiments. Given that assimilating reflectivity generally degraded even our perfect-microphysics

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FIG. 4. (a),(c),(e) RMSE u and (b),(d),(f) RMSE w in DEEP DDAs and EnKF analyses at (a),(b) t 5 36 min, (c),(d) t 5 60 min, and (e),(f) t 5 84 min. The ‘‘-SNDERR’’ experiments are represented by dashed curves.

analyses, and that reflectivity measurement biases will often introduce additional errors in practice, it may generally be prudent to avoid assimilating Zobs when using the EnKF to retrieve convective wind fields, unless a more sophisticated reflectivity assimilation method (e.g., updating only a subset of the state variables from Zobs as in Dowell et al. 2011) can be shown to improve the wind analyses.

b. Impact of microphysical and low-level environmental wind errors We now compare the analysis errors obtained in the default DDA and EnKF experiments (Fig. 4), paying

special attention to the impact of the model errors introduced in some of the latter. The dual-radar EnKF analysis errors are generally larger than the DDA errors at lower levels of the analysis domain, and smaller than the DDA errors at middle and upper levels. Encouragingly, the inclusion of microphysical parameterization errors has little impact on the dual-radar EnKF analyses at all three times shown. Evidently, the wind field is sufficiently constrained by the dual-Doppler Vrobs that the errors in the ensemble cross covariances between the wind and microphysical state variables do not substantially degrade the wind retrieval. This is consistent with the fact that the model u, y, and w are more strongly

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FIG. 5. (a) EnKF true w, and w retrieved in DEEP experiments at t 5 60 min, z 5 1.2 km: (b) DDA, (c) 2-ZVD, (d) 1-ZVD, (e) 1-LFO, and (f) 1-LFO-SNDERR.

correlated with the model Vr, and therefore with Vrobs , than with the microphysical variables. The dual-Doppler Vrobs also correct much of the error in the low-level basestate wind profile in the -SNDERR experiments. The single-radar EnKF analyses, which are more dependent than the dual-radar analyses on the ensemble member forecasts for the recovery of the unsampled wind components, are more strongly impacted by the microphysical and low-level environmental wind errors. The errors generally degrade the single-radar EnKF analyses near the ground, and have a mixed effect at middle and upper levels. Because of the ensemble spinup, both the 1-LFO and 1-ZVD analyses are substantially worse than the dual-radar EnKF analyses and the DDA at t 5 36 min (Figs. 4a,b), particularly at lower levels. As more data are assimilated, the gaps between the single-radar and dual-radar EnKF errors decrease. At the end of the assimilation period, however, the dualradar EnKF analyses remain superior to the single-radar analyses, especially when the microphysical errors are included (Figs. 4e,f). These results suggest that despite the advantages of the EnKF, multiradar observations are still needed to maximize the accuracy of kinematical supercell retrievals.

c. Low-level analysis errors Since the flow near the ground is typically of greatest interest to investigations of (particularly tornadic) supercells, we now focus upon the differences in the lowlevel (z # 1.2 km) wind retrievals obtained among our experiments. In addition to examining the RMSEs (Fig. 4), we compared horizontal cross sections of the true and retrieved u, y, and w at the first several analysis levels above the ground. The w fields retrieved at t 5 60 min, z 5 1.2 km in several of the experiments are shown in Fig. 5; the analysis errors therein are characteristic of the errors in all three wind components at low levels in our experiments. The low-level DDAs are very good throughout the data assimilation period (Figs. 4 and 5), which is expected given the favorable CBAs and the proximity of the observation times near the ground to the analysis time (e.g., Potvin et al. 2012b). The lowlevel wind analyses obtained in the dual-radar EnKF experiments, though quite good, have slightly larger RMSE than the DDAs (Fig. 4). This suggests that errors arising from the relative coarseness of the ensemble member grids, the simplified observational operator, and/or suboptimalities in the EnKF system prevent the

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filter from improving upon the low-level dual-Doppler wind retrievals. In light of these results, the EnKF probably should not be expected to provide better lowlevel wind retrievals than DDA in cases where the CBAs are large. Both the single- and dual-radar EnKF analyses strongly resemble the DDA on larger scales, but more poorly resolve smaller-scale features present in the true wind field (instances of this are present in Fig. 5).3 As a result, local wind extrema are systematically underestimated in the EnKF analyses. The low-level singleradar EnKF analyses are considerably less accurate than both the DDA and dual-radar EnKF analyses at t 5 36 min (Figs. 4a,b) due to the ensemble spinup. At t 5 60 min (Figs. 4c,d) and t 5 84 min (Figs. 4e,f), however, the 1-ZVD analysis is only slightly worse than the 2-ZVD analysis near the ground. The low-level 1-LFOSNDERR analysis has substantially larger errors than the dual-radar EnKF analyses and DDA at all three times, underscoring the greater sensitivity of the singleradar analyses to model error. Despite its larger RMSE, however, the 1-LFO-SNDERR analysis is qualitatively quite similar to the dual-radar EnKF analyses. This suggests the lack of dual-radar data may not be a major impediment to EnKF wind retrieval once enough observations have been assimilated. It should be noted, however, that small errors in the analyzed wind field can be amplified during subsequent analyses of the retrieved winds. The importance of the additional errors in the single-radar wind analyses to calculations of vorticity, vorticity tendency terms, parcel trajectories, and circulation time series is explored in section 3h.

d. Impact of unobserved flow evolution The RMSE in the DDAs increase faster with height than in the EnKF analyses (Fig. 4). We attribute part of this trend to the sensitivity of the DDA to unaccounted evolution of the wind field between the analysis time and the times at which observations impacting the analysis were collected (examined in more detail for this case in Potvin et al. 2012b). A somewhat extreme, but illustrative, example of the locally severe errors that result from these effects is given in Fig. 6. The DDA y more closely resembles the true y at t 5 62 min, which is shortly after the time the radar sweeps in that region were collected (t 5 61.5 min), than the true y at the analysis time (t 5 60 min). The EnKF y, on the other hand, is much more

3 Another difference between the DDA and dual-radar EnKF w analyses is the random error in the former, which arises largely from the noisy Vrobs . These errors, however, are very minor and so are not further discussed.

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representative of the true y at the analysis time. This is partly because the observations assimilated in that part of the domain were collected at t 5 59 min, resulting in an EnKF observation-analysis time interval (1 min) that is less than the DDA observation-analysis time interval (1.5 min) in that region. Since the average observationanalysis period at higher altitudes is less in the EnKF than in the DDA (whose observation-analysis periods aloft are in many areas equal to the volume scan time), errors due to unobserved flow evolution are correspondingly reduced in the EnKF analyses. In addition, the EnKF is inherently more tolerant of unobserved flow evolution since the analyses are partly constrained by the NWP model. For example, the 2-ZVD prior (i.e., 2-min forecast) valid at t 5 62 min (Fig. 6e) captures the rapid advection and weakening of the y maximum reasonably well, thus decreasing the impact of the temporally displaced observations on the posterior (i.e., analysis) at t 5 62 min (Fig. 6f). The resulting improvements in the EnKF analyses relative to the DDAs increase with height since the observational-analysis time intervals (and, thus, errors due to unaccounted flow evolution) increase with elevation angle in the latter. The greater resilience of EnKF wind analysis to rapidly changing flow should permit more accurate mid- and upper-level wind retrievals to be obtained when the two radars observe very different regions of the storm at a given time. This is encouraging given that coordinating mobile radar scans can be difficult, particularly when storms are moving quickly.

e. Impact of shallow scanning strategy Shallower scanning strategies are often used to increase spatial and/or temporal sampling of low-level features of interest (e.g., mesocyclone). Shallower VCPs can also permit shorter volume scan times, thereby improving dynamical analyses obtained from wind retrievals at successive times. To examine the relative performance of DDA and single-radar and dual-radar EnKF wind analysis when such a scanning strategy is adopted, we repeated our experiments using the SHALLOW VCP (Table 1). Both radars in these experiments provided coverage up to z ’ 6 km at t 5 60 min. However, the domain of the western (eastern) radar extended up to only z ’ 4.5 km at t 5 36 min (t 5 84 min) near the region of greatest interest due to the increased distance of the storm. To quantify the analysis degradation due to the vertically-truncated dual-Doppler coverage, vertical RMSE profiles were computed up to z 5 6 km over the same horizontal domain as in the default experiments. The differences between the RMSE u and w from the SHAL and DEEP experiments are presented in Fig. 7.

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FIG. 6. Illustration of impact of flow evolution at z 5 9.6 km (9.9 km) in DEEP DDAs (EnKF analyses). EnKF true y at (a) t 5 60 min and (b) t 5 62 min, y retrieved at t 5 60 min in (c) 2-ZVD and (d) DDA, and (e) mean 2-ZVD forecast and (f) analysis of y at t 5 62 min.

Not surprisingly, the dual-Doppler data cutoff substantially degraded the DDA u and/or w near the top of the analysis domain at all three examined times (Fig. 7). The most significant degradation of the DDA occurred

within the midlevel mesocyclone (centered near x 5 42.5 km, y 5 35 km), which is captured well in the original DDA, but is largely missing in the DDA-SHAL retrievals at t 5 36 min (Fig. 8) and t 5 84 min

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FIG. 7. (a),(c),(e) SHAL RMSE u 2 DEEP RMSE u and (b),(d),(f) SHAL RMSE w 2 DEEP RMSE w at (a),(b) t 5 36 min, (c),(d) t 5 60 min, and (e),(f) t 5 84 min.

(not shown). In addition, the main updraft is too broad in the DDA-SHAL analyses at these times. The dualradar EnKF analyses, on the other hand, are much less impacted aloft by the data cutoff (Figs. 7 and 8), and in many instances appear to mildly benefit from the finer vertical sampling of the SHALLOW VCP (Fig. 7). The single-radar EnKF analyses are substantially degraded near the analysis domain top (where no observations are available) at t 5 36 min (Figs. 7a,b), but are much less degraded at t 5 60 min (Figs. 7c,d), and generally are not degraded at t 5 84 min (Figs. 7e,f) despite the lack of observations above z 5 4.5 km at that time. Evidently, the ensemble covariances between model variables

above and below the data cutoff remain sufficiently accurate for observations below the data cutoff to improve the analysis above. These results suggest that the EnKF is particularly valuable in cases where the use of a shallow VCP inadvertently truncates the radar domain within the region of interest. Both the DDAs and, once the ensemble covariances are well developed, the EnKF wind analyses are generally insensitive to the choice of VCP (DEEP or SHALLOW) near the ground. This suggests the dependence of low-level wind analysis errors on the analysis method used (DDA, dual-radar EnKF or single-radar EnKF) may not vary substantially within the range of

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FIG. 8. Storm-relative horizontal winds (vectors) at z 5 5.4 km (5.7 km) in DDAs (EnKF analyses), and w (shading) at z 5 5.4 km, both valid at t 5 36 min: (a) DDA truth, (b) DDA, (c) DDA-SHAL, (d) 2-ZVD, (e) 1ZVD-SHAL, and (f) 2-ZVD-SHAL. The EnKF true u and y are not shown since they are very similar to the DDA true u and y.

commonly used storm-scale radar scanning strategies, and that the results of this study are broadly applicable. Since parcel trajectories and other 4D retrievals derived from successive wind analyses are more often computed from

observations collected using shallower scanning strategies (due to the reduced volume scan times and, thus, temporal discretization errors), we adopt the SHALLOW VCP in our parcel trajectory and vorticity analyses in section 3h.

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FIG. 9. Storm-relative horizontal winds (arrows) and w (shading) at t 5 60 min, z 5 0.6 km: (a) DDA truth, (b) DDASHAL, (c) EnKF truth, (d) 2-ZVD-SHAL, (e) 1-ZVD-SHAL, and (f) 1-ZVD-SNDERR-SHAL.

f. Wind retrievals outside radar domain The above-demonstrated ability of the EnKF to accurately recover the wind field above the dual-Doppler domain constitutes a clear advantage over DDA. We now assess the ability of the EnKF to recover the wind field outside the radar data domain. The wind fields retrieved at z 5 0.6 km in the majority of the SHALLOW experiments (section 3e) at t 5 60 min are shown in Fig. 9; the following conclusions are valid at other analysis levels and through the data assimilation period subsequent to the ensemble spinup phase. The DDASHAL analyses contain severe errors within the inflow

sector as well as south and west of the rear flank, an expected result given the lack of Vobs in those regions. It may be possible to mitigate these errors by imposing a background wind field (e.g., from the sounding) as an analysis constraint. Given the degree to which the inflow sector is modified by the supercell, however, it seems unlikely that a background constraint would substantially improve the wind retrieval there in most cases. Fortunately, the 2-ZVD-SHAL analysis is much better than the DDA-SHAL analysis within the inflow sector, and the 1-ZVD-SHAL analysis is only slightly worse than the 2-ZVD-SHAL analysis. The apparent ability of the EnKF to obtain useful analyses even outside the

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FIG. 10. As in Fig. 4, but for ‘‘-CBA30’’ retrievals and with ‘‘-SNDERR’’ results omitted to increase readability.

radar data domain is encouraging given that air parcels arriving in the potential tornadic region of supercells may traverse the (potentially echo free) inflow sector (e.g., Fig. 13; Markowski et al. 2012).

g. Impact of poor cross-beam angle In all the above experiments, the radar CBAs within the supercell are close to optimal (908) throughout the data assimilation period. In reality, such ideal CBAs are rarely achieved in mobile radar deployments. Since DDA, being more dependent upon the radar observations, benefits more than the EnKF from larger CBAs, the results presented so far provide an upper-limit estimate of the performance of DDA relative to dual-radar EnKF assimilation. To examine the relative impact of smaller CBAs in our experiments, we repeated several of the default experiments (section 3b) with the eastern radar shifted southwestward such that the CBA over the

hook echo was ;308 during the middle of the data assimilation period (Fig. 1). The analysis RMSE (Fig. 10) were computed over the same domain as in the default experiments (the error curves from the single-radar EnKF experiments are reproduced in Fig. 10 for comparison purposes). Using the suboptimal radar geometry generally degrades the DDA more than the dual-radar EnKF analyses except at upper levels of the analysis domain (Fig. 11). This is especially true at later times, by which the ensemble covariances are well developed, and particularly at t 5 84 min (Figs. 11e,f), by which the CBAs have decreased to ;208 over much of the storm. This result is consistent with the skill of the single-radar EnKF in recovering the unsampled wind components in our previous experiments (e.g., Fig. 4), and with the expectation that DDAs will be more adversely impacted than dual-radar EnKF analyses by suboptimal CBAs.

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FIG. 11. Differences in (a),(c),(e) RMSE u and (b),(d),(f) RMSE w between ‘‘-CBA30’’ and default retrievals at (a),(b) t 5 36 min, (c),(d) t 5 60 min, and (e),(f) t 5 84 min.

These results strongly suggest the EnKF should be favored over DDA when radar CBAs are poor. By t 5 84 min, even the single-radar EnKF analyses generally have smaller RMSE than the DDA, even at lower levels (particularly the 1-ZVD analysis; Figs. 10e,f). Unlike in the default experiments (Fig. 4), the advantage of assimilating data from the second radar disappears by the end of the assimilation period, a consequence of the reduced information content of radar observations collected with a narrower CBA. On the other hand, the dualradar EnKF analyses still improve upon the single-radar EnKF analyses at earlier times.

h. Vorticity, parcel trajectory, and circulation analyses To more directly illuminate storm dynamics, threedimensional wind retrievals are often used to derive, for example, vorticity and vorticity tendency fields, parcel

trajectories, and Lagrangian kinematical time series. Since these analyses are subject to spatial and/or temporal discretization errors in the retrieved wind fields, it is plausible that gross errors will occur in some cases. Improved knowledge of the typical errors in these analyses under different observational scenarios and for different wind retrieval methods is required to maximize their contributions to our understanding of convective storms. Toward this end, we computed and evaluated z and z_ stre (section 2d) at t 5 54 min and t 5 60 min, z 5 0.6 km from analyses obtained in DDA-SHAL-CBA30, 2-ZVD-SHAL-CBA30, 1-ZVD-SHAL, and 1-ZVDSNDERR-SHAL experiments (t 5 60 min results shown in Fig. 12; t 5 54 min results were similar). We will first examine the analyses within the data domain, which is approximately demarcated by the dBZ 5 5 contour in Fig. 12. The DDA-SHAL-CBA30 and 2-ZVD-SHALCBA30 wind retrievals produced roughly commensurate

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FIG. 12. z (s21) at z 5 0.6 km, t 5 60 min and z_ stre (3100 s22) at z 5 0.9 km, t 5 60 min: (a),(g) EnKF truth; (b),(h) 2-ZVD-SHALCBA30; (c),(i) 1-ZVD-SHAL; (d),(j) DDA truth; (e),(k) DDA-SHAL-CBA30; and (f),(l) 1-ZVD-SNDERR-SHAL. The model dBZ 5 5 contour (roughly collocated with the radar data edge) is shown.

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analyses of both z and z_ stre within the data domain. Both analyses well represent the strong cyclonic vorticity and vorticity stretching ahead of the northern portion of the gust front and (to a lesser degree) the anticyclonic vorticity and vorticity stretching behind the gust front. However, locally large errors occur in both analyses, the most significant being the severe underestimation of the magnitudes of z and z_ stre within the RFD (along the rear flank of the hook echo). The z computed from the single-radar EnKF analyses was roughly as good as the z from the dual-radar EnKF analyses, even when microphysical and/or low-level wind errors were added (1-LFO-SHAL and 1-LFO-SHAL-SNDERR not shown). The z_ stre , on the other hand, was substantially underestimated in the single-radar EnKF analyses ahead (rearward) of the northern (southern) part of the gust front. These results indicate that EnKF analyses involving spatial derivatives of the wind field can benefit from dual-radar data, but even then may contain locally large errors. We now examine the analyses outside the data domain. The 2-ZVD-SHAL-CBA30 analysis produced better z and z_ stre than did the DDA-SHAL-CBA30 analysis over the inflow sector and rearward of the hook echo, consistent with the results in section 3f. The z and z_ stre were analyzed roughly equally well in 1-ZVDSHAL as in 2-ZVD-SHAL, and were only mildly degraded when the additional model errors were included. In all the EnKF analyses, however, the z and z_ stre were overestimated along the southern part of the gust front. This suggests that caution be used when interpreting vorticity and vorticity budget analyses in data-void regions. For each of the wind analyses used to calculate z and z_ stre above, 1000 parcel trajectories were backward computed from a 3-km-radius ring centered between the main updraft and downdraft at t 5 60 min, z 5 1.2 km. Trajectories were also computed from wind analyses produced in an experiment identical to 1-ZVDSNDERR-SHAL but using observations that were objectively analyzed to 2-km (rather than 1 km) grids (1-ZVD-SNDERR-SHAL-2 km). Horizontal and x–z projections of the material circuits connecting the true, DDA-SHAL-CBA30, 2-ZVD-SHAL-CBA30, 1-ZVDSNDERR-SHAL, and 1-ZVD-SNDERR-SHAL-2 km trajectories at t 5 57 min and t 5 50 min are shown in Figs. 13a,b, respectively. In addition, circulation time series were computed for each of the circuits (Fig. 13c). We defer discussion of the 1-ZVD-SNDERR-SHAL-2 km analyses until the end of the section. The remaining analyzed circuits are qualitatively accurate, consistent with their corresponding wind analyses being quite good at t 5 60 min even over the portion of the storm inflow sector just outside the data cutoff (not shown). On the other

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hand, the circulation time series computed from the EnKF analyses contain much larger errors than those computed from the DDA. The 2-ZVD-SHAL-CBA30 analysis underestimates the true circulation throughout the period, but especially prior to t ’ 55 min (by up to 20 000 m2 s21, or 50%). The consequently substantial overestimate of the increase in circulation after t ’ 50 min would imply (via the Bjerknes circulation theorem) much larger baroclinic contribution to circulation (;8 3 105 m2 s21) than actually occurred during this period (;6 3 105 m2 s21)4. The errors in the 1-ZVDSNDERR-SHAL circulation analysis are even more serious. For example, the increase in circulation after t ’ 50 min is underestimated by roughly 50%. This result, along with the locally substantial underestimation of z_ stre in the single-radar EnKF analyses (Fig. 12), highlight the potential for errors arising from lack of dual-radar data to be compounded in derived analyses that more directly illuminate storm dynamics. Repeating the trajectory and circulation analyses for the SHALLOW-CBA90 case produced similar results, except that the DDASHAL and (especially) the ZVD-SHAL circulation time series were both improved, making the 1-ZVDSNDERR-SHAL circulation analysis even more of an outlier (not shown). The circuits computed from the 1-ZVD-SNDERRSHAL-2 km wind analyses contain much larger errors than the 1-ZVD-SNDERR-SHAL circuits, thus seriously misrepresenting the source region of air in the potentially tornadic region of the storm. It is not surprising, then, that the 1-ZVD-SNDERR-SHAL-2 km circulation time series also contain larger errors than in the 1-ZVD-SNDERR-SHAL case. These results underline the importance of using finer observational grid spacing when assimilating only single-radar data, particularly when analyses that potentially compound wind retrieval errors are performed.

4. Summary and conclusions Kinematical analyses of mobile radar datasets are vital to advancing the understanding of supercell thunderstorms. Maximizing the scientific value of these analyses requires thorough knowledge of the characteristic errors obtained using different methods under different observational scenarios. Our results suggest that when data are available from two radars, using the EnKF rather than DDA can improve wind retrievals in

4

Since we did not include the Coriolis effect in our truth simulation and data assimilation experiments, it did not contribute to circulation generation in either case.

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FIG. 13. (a) Horizontal projections of material circuits valid at t 5 57 min (green curves) and t 5 50 min (blue curves) for parcel trajectories initiated around a 3-km-radius ring (black circle) at t 5 60 min, z 5 1.2 km. The trajectories were computed from the true (thick, solid, dark), DDA-SHAL-CBA30 (thin, solid, dark), 2-ZVDSHAL-CBA30 (thick, dashed, dark), 1-ZVD-SNDERR-SHAL (thick, solid, light), and 1-ZVD-SNDERR-SHAL2 km (thin, dashed, dark) wind fields. The model dBZ valid at z 5 1.2 km, t 5 60 min (shading) is displayed in the background. (b) Vertical (x–z) projections of the material circuits. (c) Time series of circulation computed around the circuits. The plots in (b) and (c) use the same line style conventions as in (a).

at least two ways. First, the ability of the EnKF to obtain shorter (than the volume scan period) analysisobservation intervals and to constrain the analysis with an NWP model makes the analyses less prone to errors from unobserved flow translation and evolution than

DDAs. Thus, the EnKF should permit accurate midand upper-level wind retrievals to be obtained using less coordinated multiradar scanning strategies than are required for DDA. Second, the ability of the EnKF to utilize estimated covariances between Doppler velocity

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observations and state variables outside the data domain (e.g., in low-reflectivity portions of the storm-inflow sector and above the dual-Doppler cutoff) appears to substantially improve wind retrievals in those regions. However, our results also indicate that when the radar CBAs are large, EnKF radar data assimilation may produce poorer low-level wind retrievals than DDA. We attributed this to the wind field already being well constrained by the Doppler velocity observations in this scenario, and the inevitable EnKF analysis errors arising from, among other sources, violations of the EnKF optimality conditions and resolution errors in the model forecasts (priors). Though the error increases in the EnKF analyses were relatively small, this result is significant given the importance of the low-level flow to supercell dynamics, including tornadogenesis. Single-radar EnKF wind retrievals were more sensitive than dual-radar EnKF wind retrievals to errors in the microphysical parameterization scheme and in the low-level model sounding winds, particularly early in the assimilation period (during ensemble spinup). In addition, larger errors occurred in circulation time series computed from single-radar versus dual-radar EnKF wind analyses. These results indicate that EnKF wind analyses benefit from assimilating observations from multiple radars, particularly when large model errors occur. Nevertheless, our experiments suggest that when only single-radar data are available, EnKF data assimilation can produce better wind retrievals over the midand upper levels of the storm than are typically obtained in DDAs with large CBAs, and (additionally) better wind retrievals over lower levels of the storm than are typically obtained in DDAs with small CBAs. Singleradar EnKF analyses may also be superior to DDAs outside the Doppler velocity domain, including over data-sparse regions of the storm inflow sector. Finally, backward-computed parcel trajectories were qualitatively accurate in the single-radar case. To maximize the accuracy of single-radar EnKF analyses, particularly of analyses derived from the retrieved winds, it is necessary to use finer observational grid spacing than is required to optimize dual-radar EnKF analyses. The OSSE framework adopted for our experiments enables straightforward comparisons of analyses obtained from DDA and the EnKF under a variety of observational and model-error scenarios. However, it should be borne in mind that since the characteristics of typical storm-scale observational and model errors are not well known, neither is the representativeness of the errors simulated in our experiments (given the relative insensitivity of the dual-radar EnKF wind analyses to the microphysical parameterization and low-level wind profile errors introduced in some of our experiments, the

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question of model error representativeness is mainly of concern in the single-radar case). This problem will be alleviated in future experiments with real radar observations (but at the cost of having imperfect knowledge of the true wind field). Nevertheless, we consider the present study to be an important step toward comprehensive understanding of wind retrieval errors obtained from EnKF radar data assimilation versus DDA. We hope that our findings will help guide the creation and interpretation of future kinematical supercell analyses. Acknowledgments. The first author was supported by a National Research Council Postdoctoral Award at the National Severe Storms Laboratory (NSSL). We thank Edward Mansell (NSSL) and two anonymous reviewers for their helpful suggestions for improving the manuscript. We are particularly grateful to one of the reviewers for their invaluable recommendation that we repeat our initial single-radar EnKF experiments using finer observational grid spacing. REFERENCES Aksoy, A., D. C. Dowell, and C. Snyder, 2009: A multicase comparative assessment of the ensemble Kalman filter for assimilation of radar observations. Part I: Storm-scale analyses. Mon. Wea. Rev., 137, 1805–1824. Beck, J. R., J. L. Schroeder, and J. M. Wurman, 2006: Highresolution dual-Doppler analyses of the 29 May 2001 Kress, Texas, cyclic supercell. Mon. Wea. Rev., 134, 3125–3148. Betten, D., M. I. Biggerstaff, and G. Carrie, 2011: Observations of low-level mesocyclogenesis using a new trajectory mapping technique. Preprints, Sixth European Conf. on Severe Storms, Palma de Mallorca, Spain, European Severe Storms Laboratory. [Available online at http://www.essl.org/ECSS/2011/ programme/abstracts/81.pdf.] Biggerstaff, M. I., and Coauthors, 2005: The Shared Mobile Atmospheric Research and Teaching Radar: A collaboration to enhance research and teaching. Bull. Amer. Meteor. Soc., 86, 1263–1274. Caya, A., J. Sun, and C. Snyder, 2005: A comparison between the 4DVAR and the ensemble Kalman filter techniques for radar data assimilation. Mon. Wea. Rev., 133, 3081–3094. Coniglio, M. C., D. J. Stensrud, and L. J. Wicker, 2006: Effects of upper-level shear on the structure and maintenance of strong quasi-linear mesoscale convective systems. J. Atmos. Sci., 63, 1231–1252. Dawson, D. T., L. J. Wicker, E. R. Mansell, and R. L. Tanamachi, 2012: Impact of the environmental low-level wind profile on ensemble forecasts of the 4 May 2007 Greensburg, Kansas, tornadic storm and associated mesocyclones. Mon. Wea. Rev., 140, 696–716. Dowell, D. C., and L. J. Wicker, 2009: Additive noise for stormscale ensemble data assimilation. J. Atmos. Oceanic Technol., 26, 911–927. ——, F. Zhang, L. J. Wicker, C. Snyder, and N. Andrew Crook, 2004: Wind and temperature retrievals in the 17 May 1981 Arcadia, Oklahoma, supercell: Ensemble Kalman filter experiments. Mon. Wea. Rev., 132, 1982–2005.

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