Ensemble Kalman Filter Assimilation of Radar Observations of the 8 May 2003 Oklahoma City Supercell: Inﬂuences of Reﬂectivity Observations on Storm-Scale Analyses

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DAVID C. DOWELL Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, and NOAA/OAR National Severe Storms Laboratory, Norman, Oklahoma, and National Center for Atmospheric Research,* Boulder, Colorado

LOUIS J. WICKER NOAA/OAR National Severe Storms Laboratory, Norman, Oklahoma

CHRIS SNYDER National Center for Atmospheric Research,* Boulder, Colorado

(Manuscript received 31 March 2010, in ﬁnal form 23 July 2010)

ABSTRACT

Ensemble Kalman filter (EnKF) techniques have been proposed for obtaining atmospheric state estimates on the scale of individual convective storms from radar and other observations, but tests of these methods with observations of real convective storms are still very limited. In the current study, radar observations of the 8 May 2003 Oklahoma City tornadic supercell thunderstorm were assimilated into the National Severe Storms Laboratory (NSSL) Collaborative Model for Multiscale Atmospheric Simulation (NCOMMAS) with an EnKF method. The cloud model employed 1-km horizontal grid spacing, a single-moment bulk precipitation- microphysics scheme, and a base state initialized with sounding data. A 50-member ensemble was produced by randomly perturbing base-state wind profiles and by regularly adding random local perturbations to the horizontal wind, temperature, and water vapor fields in and near observed precipitation. In a reference experiment, only Doppler-velocity observations were assimilated into the NCOMMAS ensemble. Then, radar-reflectivity observations were assimilated together with Doppler-velocity observations in subsequent experiments. Influences that reflectivity observations have on storm-scale analyses were revealed through parameter-space experiments by varying observation availability, observation errors, ensemble spread, and choices for what model variables were updated when a reflectivity observation was assimilated. All experiments produced realistic storm-scale analyses that compared favorably with independent radar observations. Convective storms in the NCOMMAS ensemble developed more quickly when reflectivity observations and velocity observations were both assimilated rather than only velocity, presumably because the EnKF utilized covariances between reflectivity and unobserved model fields such as cloud water and vertical velocity in efficiently developing realistic storm features. Recurring spatial patterns in the differences between predicted and observed reflectivity were noted particularly at low levels, downshear of the supercell’s updraft, in the anvil of moderate-to-light precipitation, where reflectivity in the model was typically lower than observed. Bias errors in the predicted rain mixing ratios and/or the size distributions that the bulk scheme associates with these mixing ratios are likely responsible for this reflectivity underprediction. When a reflectivity observation is assimilated, bias errors in the model fields associated with reflectivity (rain, snow, and hail–graupel) can be projected into other model variables through the ensemble covariances. In the current study, temperature analyses in the downshear anvil at low levels, where reflectivity was underpredicted, were very sensitive both to details of the assimilation algorithm and to ensemble spread in temperature. This strong sensitivity suggests low confidence in analyses of low-level cold pools obtained through reflectivity-data assimilation.

* The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: David C. Dowell, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000. E-mail: [email protected]

DOI: 10.1175/2010MWR3438.1

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1. Introduction observations into the Sun and Crook (1997) cloud model, with the intent of reproducing the supercell storm The ensemble Kalman filter (EnKF) assimilation of (Browning 1968) in a reference simulation from imper- radar observations into numerical cloud models has fect observations and a simplified initial state estimate. been investigated recently as a means for producing Accurate EnKF analyses were produced after roughly detailed analyses of convective storms and initializing 6 volumes of synthetic radar data had been assimilated weather prediction models (Snyder and Zhang 2003; into the model over a 30-min period. As more radial ve- Dowell et al. 2004b; Tong and Xue 2005; Caya et al. locity observations were assimilated, supercell storms in 2005; Gao and Xue 2008; Xu et al. 2008; Jung et al. 2008b; the EnKF analyses and reference simulation became Dowell and Wicker 2009; Aksoy et al. 2009; Yussouf and more similar, and forecasts initialized from the ensemble- Stensrud 2010; Lu and Xu 2009; Xue et al. 2009; Zhang mean analyses were also improved. et al. 2009). EnKF methods use the statistics of a forecast For these first investigations of EnKF radar-data as- ensemble to estimate the background-error covariances similation, Snyder and Zhang (2003) and Zhang et al. needed for data assimilation (Evensen 1994; Houtekamer (2004) assumed that the forecast model was perfect and Mitchell 1998). These methods are relatively easy and that the synthetic observations were unbiased and to implement and parallelize (e.g., Anderson and Collins had known error characteristics. Following Snyder and 2007), and they provide both an analysis (ensemble mean) Zhang, Dowell et al. (2004b) applied a similar EnKF and an uncertainty estimate (ensemble spread). Typical method to a real supercell, for which model error is ex- formulations of EnKF methods are considered optimal pected to be significant and observation-error character- when the following assumptions are satisfied: 1) the ob- istics are not known precisely. Despite these limitations, servations are linearly related to the true model state, 2) EnKF analyses obtained by assimilating single-Doppler- observation and forecast errors have Gaussian distribu- velocity observations into the Sun and Crook (1997) tions, 3) observation and forecast errors are unbiased, cloud model had realistic features in the wind field and and 4) ensemble statistics represent true forecast errors compared favorably to independent observations, which (Evensen 1994; Houtekamer and Mitchell 1998; Anderson included Doppler-velocity observations from a second and Anderson 1999; Whitaker and Hamill 2002; Lorenc radar, a dual-Doppler analysis, and in situ wind mea- 2003; Snyder and Zhang 2003; Dowell et al. 2004b). Con- surements from the surface to 400 m AGL from a tower. sidering the localized, unbalanced, and rapidly evolving Reflectivity is a measure of how effectively a volume nature of convective storms, one might expect state es- of targets backscatters energy transmitted by a radar timation for these storms to be particularly challenging. (Doviak and Zrnic 1993). Reflectivity depends on scat- Nevertheless, results from initial tests of EnKF methods terer concentration, size, phase (liquid or ice), orien- for storm-scale radar-data assimilation have been encour- tation, and other properties. Assimilating reflectivity aging, demonstrating that flow-dependent covariances es- observations of convective storms into cloud models timated from ensembles are useful for analyzing both would seem to be more problematic than assimilating observed and unobserved fields in convective storms Doppler-velocity observations for a number of reasons. (Snyder and Zhang 2003). First, model error is expected to be particularly large Among many observation types provided by weather 1 for reflectivity predicted by cloud models (Smith et al. radars, Doppler velocity and reflectivity are the most 1975; Smith 1984; Gilmore et al. 2004b). Whereas simu- commonly used observations for both operational and related Doppler velocity is computed from the three wind search applications. Doppler velocity is a power-weighted, components, which are controlled by grid-scale dynamics, volume-averaged measure of the component of scatterer simulated reflectivity is computed from hydrometeor motion away from or toward a radar (Doviak and Zrnic fields, which are controlled by microphysical parame- 1993). Typically, the scatterer motion is approximately terizations and their inherent uncertainties. Second, even equal to the air motion plus the scatterer fall velocity. if the hydrometeor fields are predicted well, there is Several studies have shown that using an EnKF method still uncertainty in how reflectivity is diagnosed from to assimilate Doppler-velocity observations into a nu- these fields. Third, reflectivity is nonlinearly related merical cloud model is a viable method for storm-scale to the model state (Tong and Xue 2005), which means state estimation. Snyder and Zhang (2003) and then that the EnKF update is suboptimal (cf. conditions Zhang et al. (2004) assimilated synthetic radial velocity for optimality above). Fourth, unlike Doppler-velocity observation errors, reflectivity observation errors are 1 Throughout the text, we commonly use the abbreviated term affected significantly by attenuation and errors in ra- ‘‘reflectivity’’ to refer to the equivalent reflectivity factor (Doviak dar calibration (e.g., Wilson and Brandes 1979; Ulbrich and Zrnic 1993) on the customary logarithmic scale (dBZ). and Lee 1999).

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Our current expertise with EnKF assimilation of precipitation-microphysics scheme. They demonstrated reflectivity observations into cloud models has been that reflectivity-data assimilation could be used to esti- developed mainly from perfect-model experiments with mate simultaneously the atmospheric state and also synthetic radar observations. In their synthetic-data a subset of the microphysics parameters (particle densi- experiments for a simulated supercell, Caya et al. (2005) ties and/or intercept parameters), at least when the cloud assimilated observations of rainwater mixing ratio and model is otherwise perfect. radial velocity together into the Sun and Crook (1997) Experience with EnKF assimilation of reflectivity ob- cloud model. Since the model’s precipitation-microphysics servations of real convective storms is quite limited. In scheme included only a single precipitation category (rain), a recent study, Aksoy et al. (2009) assimilated Doppler- assimilating observations of the rainwater mixing ratio velocity and reflectivity observations together into was comparable to assimilating reflectivity observations, the Weather Research and Forecasting (WRF) model except that the observation operator is linear in the for- (Skamarock et al. 2005). This multi-case study included mer case and nonlinear in the latter. After rainwater and ordinary cells, convective lines, and supercells. Results velocity observations were assimilated for a few tens of were considered successful in that 1) assimilating ob- minutes, the EnKF ensemble mean was an accurate servations consistently reduced prior rms fits to ob- representation of the model state in the reference sim- servations during the first 15–30 min of the assimilation ulation. EnKF performance in the Caya et al. (2005) period, 2) comparable results were obtained for the experiments was comparable to that obtained by Snyder various convective storm types, and 3) model fields and Zhang (2003) experiments, in which only velocity obtained by assimilating observations for 1 h appeared observations were assimilated. realistic. In another recent study, Lei et al. (2009) initial- Unlike Caya et al. (2005), who used a model with ized ARPS forecasts of the supercell case that is featured a very simplified precipitation-microphysics parame- in the current study by assimilating Doppler-velocity, terization, Tong and Xue (2005) used a cloud model [the reflectivity, and surface-mesonet observations into the Advanced Regional Prediction System (ARPS); Xue model. Since reflectivity observations were assimilated et al. (2000), (2001)] with a multiclass scheme that in- together with other observations types in all experi- cluded ice. Reflectivity was diagnosed from the model’s ments in the Aksoy et al. (2009) and Lei et al. (2009) rain, snow, and hail–graupel fields. Again in a perfect- studies, it is difficult to evaluate the influences that each model scenario, Tong and Xue (2005) demonstrated that observation type has individually on the analyses. wind, thermodynamic, and microphysical fields in a ref- In our current study, we aim to provide more insight erence supercell simulation could all be reproduced into reflectivity-data assimilation for real convective accurately by assimilating synthetic Doppler-velocity storms by describing our experiences with a single case and reflectivity observations for a few tens of minutes in detail. The case we have selected is the 8 May 2003 into the same cloud model that produced the reference Oklahoma City, Oklahoma, tornadic supercell (Fig. 1), simulation. which is being used as a test case in multifaceted studies For reflectivity-data assimilation, it has proven helpful (Burgess 2004; Dowell et al. 2004a; Hu and Xue 2007; to distinguish between reflectivity observations of pre- Romine et al. 2008; Dowell and Wicker 2009; Lei et al. cipitation and reflectivity observations that have values 2009). As described in section 2, Doppler-velocity and so low that they indicate the absence of precipitation reflectivity observations of the Oklahoma City supercell (no-precipitation reflectivity observations; Aksoy et al. are available from multiple radars, together with nearby 2009). Reflectivity observations in precipitation are surface observations and a sounding. To help us un- potentially useful for analyzing inner storm details derstand how reflectivity-data assimilation works for whereas the no-precipitation observations are helpful a more typical operational situation in which a storm is mainly for suppressing spurious convective storms that observed well by only one radar, we have chosen to as- develop in ensemble members (Dowell et al. 2004b; similate observations from one radar into the cloud Tong and Xue 2005; Aksoy et al. 2009). Tong and Xue model and to use the other observations for verification. (2005) and Aksoy et al. (2009) obtained the best analy- The method used to assimilate radar data into the National ses when both types of reflectivity observations (pre- Severe Storms Laboratory (NSSL) Collaborative Model cipitation and no precipitation) were assimilated into for Multiscale Atmospheric Simulation (NCOMMAS; the model, together with radial velocity observations. Wicker and Skamarock 2002; Coniglio et al. 2006) is Tong and Xue (2008a,b) demonstrated that reflectivity summarized in section 2 and the appendix. A reference assimilation could be successful when the cloud model is storm-scale analysis is produced by assimilating only initially slightly imperfect. Specifically, they considered Doppler-velocity observations into the model, follow- uncertainty in the basic parameters in a single-moment ing the work of Snyder and Zhang (2003), Dowell et al.

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The Oklahoma City storm became more organized as it moved northeastward, developing a mesocyclone above 2 km AGL by 2120 UTC (Burgess 2004) and then a ‘‘hook echo’’ (Stout and Huff 1953; van Tassel 1955) in reflectivity near the surface at 2204 UTC (Fig. 1). Romine et al. (2008) suggest that a single tornado event occurred from 2206 to 2238 UTC, although others have classified this event as three tornadoes (Burgess 2004). Over its 27-km path, the tornado produced F2 damage (Fujita 1981) in Moore, Oklahoma, and F4 damage in Oklahoma City. Approximately 50 km south of the Oklahoma City storm’s path, other convective cells (southwest part of Fig. 1), which formed as early as 2015 UTC, failed to develop into severe thunderstorms. A National Weather Service sounding from Norman, Oklahoma (from location ‘‘KOUN’’ in Fig. 1) provides an estimate of the environmental conditions of the Oklahoma City storm (Fig. 2, which illustrates the profiles after interpolation to the NCOMMAS grid). The FIG. 1. Overview map showing the radar locations (KOUN and rawinsonde was released roughly when the Oklahoma KTLX), the sounding site (also KOUN), the surface-observation site (KOKC), tornado paths (gray lines), and KOUN radar echoes City tornado was dissipating 35 km northeast of the (20- and 40-dBZ contours) at 1 km AGL at three times (2100, 2128, sounding site. Convective available potential energy and 2204 UTC 8 May 2003). Horizontal coordinates (km) are rel- (CAPE) and convective inhibition (CIN) for the raw ative to KOUN. sounding (Fig. 3 of Romine et al. 2008) are approximately 3800 and 220 J kg21, respectively, for a parcel originating with the mean properties of the lowest 100 mb (2004b), Dowell and Wicker (2009), and others. In sec- of the sounding. The bulk Richardson number (Weisman tion 3, we describe the model’s ability to simulate reflec- and Klemp 1984) is 18. Such environmental conditions tivity in the reference (Doppler velocity only) experiment support strong supercell storms in numerical cloud models and also when reflectivity observations are assimilated (Weisman and Klemp 1984). together with velocity observations. In section 4, we de- Observations from multiple radars document the life scribe how reflectivity-data assimilation changes the storm- cycle of the Oklahoma City storm. The current study scale analyses overall, pointing out both advantages and particularly utilizes data from the KOUN radar, a 10-cm disadvantages of assimilating such observations for this radar in Norman that is essentially a Weather Surveil- case. We close with a summary, speculation about error lance Radar-88 Doppler (WSR-88D) upgraded to have sources that affect reflectivity-data assimilation, and polarimetric capability (Ryzhkov et al. 2005; Romine thoughts about future work (section 5). The current study et al. 2008). The first echoes of the Oklahoma City storm is essentially a follow-up study to Tong and Xue (2005), appeared approximately 80 km west-southwest of the except for real instead of synthetic observations, and a KOUN radar, and then the storm moved closer to and complementary study to Aksoy et al. (2009), which pro- north of the radar (Fig. 1). The Moore–Oklahoma City vides more detailed analysis of one case. tornado formed only 12 km north-northwest of KOUN. Since the KOUN radar has a 0.958 beamwidth, the beam 2. Description of the data assimilation experiments was 200–1300 m wide at these ranges of 12–80 km. The azimuthal sampling interval was 1.08, comparable to a. Case overview the beamwidth. Unfortunately, a power failure caused Since Romine et al. (2008) provide a detailed over- KOUN data loss between 2210 and 2225 UTC. The view of the Oklahoma City supercell thunderstorm and current study utilizes KOUN Doppler-velocity and re- its environment, we only provide a brief description flectivity data before 2210 UTC, from storm formation here. The Oklahoma City storm was the southernmost until tornadogenesis. Polarimetric observations of the of many tornadic supercells that formed over Oklahoma Oklahoma City storm are not used here but are described and Kansas on 8 May 2003. Initial radar echoes of what in detail by Romine et al. (2008). was to become the Oklahoma City supercell developed The KOUN velocity and reflectivity data that were near a dryline in west-central Oklahoma at 2045 UTC. assimilated into NCOMMAS (section 2b) had been

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FIG. 2. Environmental vertical profiles in NCOMMAS, obtained by interpolating the 0000 UTC 9 May 2003 Norman, OK, sounding to model grid levels. (a) Skew T–logp diagram. The solid black and gray lines indicate the temperature and dewpoint profiles, respectively. The dashed line indicates temperature for a lifted surface parcel. Wind barbs (flags) represent 10 m s21 (50 m s21). (b) Hodograph. Heights are indicated in km AGL. The ‘‘X’’ indicates the mean motion of the Oklahoma City storm between 2100 and 2200 UTC 8 May 2003 (U 5 14 m s21 and V 5 8ms21).

edited manually, which involves removing ground clut- KTLX WSR-88D (Fig. 1) observations of the Oklahoma ter, range folding, and other spurious data and unfolding City storm are also available, and we use these data aliased Doppler velocities, and then gridded. Velocity for verification purposes. The ranges from KTLX to and reflectivity data are available in precipitation and the storm features of interest are initially 110 km but also in ‘‘clear air’’ within roughly 30 km of the radar decrease to 20 km during the period of study. Terminal (Fig. 1 of Dowell and Wicker 2009). The KOUN radar Doppler weather radar observations, which provide obtained complete volumes (14 different elevation an- higher-resolution information at low levels during the gles) approximately every 6 min. Data from each ele- tornadic stage (Romine et al. 2008), are not used in the vation angle in each volume were objectively analyzed currentstudybutcouldbeusedinfuturestudiesfo- to grid points on the conical scan surfaces (Sun and cusing on topics such as tornadogenesis. Additional Crook 2001; Dowell et al. 2004b; Dowell and Wicker data we use for verification are the surface observa- 2009). The grid points are 2000 m apart in each hori- tions from KOKC, an Automated Surface Observing zontal direction, and the radius of influence for the System site (Fig. 1). Cressman (1959) objective analysis was 1000 m. The b. Data assimilation 2000-m grid spacing is roughly the same as the mean observation spacing for the more distant radar observa- The numerical model, ensemble design, and data- tions. We have confirmed for two of our data-assimilation assimilation method are similar to those used by Dowell experiments that using observations analyzed on a finer and Wicker (2009). Briefly, this study employs NCOMMAS (1000 m) grid does not change qualitative inferences (Wicker and Skamarock 2002; Coniglio et al. 2006), which about storm-scale features and processes, so we use the is a nonhydrostatic, compressible model designed for coarser observations in order to reduce computational simulating convective storms in an idealized frame- requirements. Certainly, other studies focusing on top- work, where ‘‘idealized’’ refers to a flat lower boundary, ics such as mesocyclogenesis and tornadogenesis could no surface fluxes, no radiative transfer, and a horizon- benefit from using observations at the original (higher) tally homogeneous base state. The model domain for resolution. these experiments is 100 km wide in both horizontal

Unauthenticated | Downloaded 09/26/21 11:15 PM UTC JANUARY 2011 D O W E L L E T A L . 277 directions, is 18 km tall, and follows the storm of interest (2004b), Caya et al. (2005), and Tong and Xue (2008b) by moving at U 5 14 m s21 and V 5 8ms21, where U have suggested that using smooth perturbations such as and V are the components of domain motion toward these rather than initializing the ensemble with gridpoint the east and north, respectively. The grid spacings are noise results in a more persistent ensemble spread. Also, uniformly 1.0 km (0.5 km) in the horizontal (vertical). potential problems with reflectivity-data assimilation The grid is rather coarse for simulating convective storms early in the assimilation window (Caya et al. 2005; Tong (Bryan et al. 2003), but keeps the computation man- and Xue 2005) associated with noisy ensemble covari- ageable for the numerous experiments that are required ances are mitigated (Tong and Xue 2008b). to demonstrate the sensitivities of the EnKF analyses Incipient convective storms developed in the ensem- to observation availability, ensemble design, and assim- ble members through the additive noise, model advance, ilation methodology. The model time step is 5 s. The and data assimilation, and then the additive noise helped wind, temperature, and water vapor profiles in the raw maintain ensemble spread as the different realizations 0000 UTC 9 May 2003 Norman sounding (Fig. 3 of of storms in the ensemble matured. The additive-noise Romine et al. 2008) were interpolated to model grid parameters for most experiments in our study (including 2 levels in order to initialize the base state in the model ‘‘Vr and ZdB’’ and Vr-only in Table 1) are the same as (Fig. 2). Evidence in other studies of this supercell case those in the ‘‘0.25’’ experiment described by Dowell and suggests that more realistic representation of the spa- Wicker (2009). The standard deviations, before smooth- tially- and temporally-varying mesoscale environment ing, are 1.0 (0.25) m s21, 1.0 (0.25) m s21, 1.0 (0.25) K, and is important for obtaining realistic storm-scale fore- 1.0 (0.25) K before (after) 2100 UTC for u, y, u,and casts for 1–2.5 h following the data-assimilation win- Td (dewpoint), respectively. Two sensitivity experi- dow (Hu and Xue 2007; Lei et al. 2009). However, since ments (‘‘less additive noise’’ and ‘‘more additive noise’’ the focus of the current study is instead on identifying in Table 1) used different magnitudes of additive noise, issues with reflectivity-data assimilation during the as- as described later in section 4. similation window rather than on multi-hour forecasts, The ensemble in our current study also includes per- we have opted for the simpler initialization of the model turbed base-state wind profiles for each member. The base state. Comparison with other available observa- motivations for these wind-profile perturbations are tions (not shown) suggests that the Norman sounding the uncertainty in how well the base-state sounding provides a reasonable approximation of mean environ- represents the actual storm environment and the spatial mental conditions. and temporal variability expected in this environment. We initialized a 50-member NCOMMAS ensemble at Aksoy et al. (2009) have shown that for storm-scale 2040 UTC and used additive noise (Dowell and Wicker radar-data assimilation in cloud models with simplified 2009) to introduce variability among the members. This storm environments, the increased ensemble spread re- additive noise consisted of random, smooth, local per- sulting from the wind-profile perturbations can help im- turbations (e.g., Fig. 3 of Dowell and Wicker 2009) prove prior and posterior fits of the ensemble mean to added every 5 min to each ensemble member’s u (west- the Doppler-velocity observations. Here, a realization erly wind component), y (southerly wind component), of random, Gaussian noise with mean 0 and standard 21 u (potential temperature), and qy (water vapor) fields, in deviation 2.0 m s (magnitude chosen through ex- and near where reflectivity observations indicated pre- perimentation) was added to the base-state u and y cipitation. The horizontal and vertical length scales in the wind components at each grid level in each ensemble smoothing function in the additive-noise algorithm were member. 4 and 2 km, respectively (Caya et al. 2005). Dowell et al. The EnKF method we used to assimilate observations into the NCOMMAS ensemble is commonly called an ensemble square root filter (EnSRF; Whitaker and 2 The interpolation to grid levels 500 m apart, beginning at Hamill 2002; cf. Dowell and Wicker 2009 and Dowell 250 m AGL, results in a different near-surface hodograph shape in et al. 2004b). A primary focus of this study is to compare the model’s base-state wind profile than in the raw wind profile. Specifically, the raw low-level hodograph (Fig. 3 of Romine et al. an experiment with Doppler-velocity and reflectivity ob- 2008) has an ‘‘L’’ shape. (Wind speed increases from 7 m s21 at servations assimilated together (Vr and ZdB in Table 1) to 10 m AGL to 17 m s21 at 250 m AGL. Above 250 m AGL, winds a reference experiment with only Doppler velocity as- of roughly constant speed veer with height.) The vertical in- similated (Vr only). Every 60 s from 2046 to 2210 UTC, terpolation to the 500-m grid eliminates the ‘‘L’’ shape (Fig. 2). Doppler-velocity observations from scans (elevation an- Evidence in numerical simulations suggests that such hodograph differences can greatly affect the development of low-level storm gles) close to the current model time were assimilated rotation (Wicker 1996). Since our focus is on other aspects of into the NCOMMAS ensemble. Since KOUN obtained storm-scale modeling, we do not use a fine vertical grid here. complete radar volumes every 6 min, approximately

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TABLE 1. Summary of radar-data-assimilation experiments. Here Vr and ZdB refer to Doppler velocity and reﬂectivity, respectively.

Expt name Assimilated obs Comments

Vr and ZdB Vr and ZdB Vr only Vr 21 Less additive Vr and ZdB As in Vr and ZdB, but the standard deviation of random noise, before smoothing, is 0.1 m s , 21 noise 0.1 m s , 0.1 K, and 0.1 K after 2100 UTC for u, y, u, and Td, respectively. 21 More additive Vr and ZdB As in Vr and ZdB, but the standard deviation of random noise, before smoothing, is 0.5 m s , 21 noise 0.5 m s , 0.5 K, and 0.5 K after 2100 UTC for u, y, u, and Td, respectively. 5-dBZ obs error Vr and ZdB As in Vr and ZdB, but the reflectivity observation error is assumed to be 5 instead of 2 dBZ. No u update Vr and ZdB As in Vr and ZdB, but u is not updated when a reflectivity observation is assimilated. Update qr, qs, qh Vr and ZdB As in Vr and ZdB, but only qr, qs, and qh are updated when a reflectivity observation is assimilated.

one-sixth of a data volume was assimilated at a time. In and ice-crystal distributions in the model are mono- most experiments, reflectivity observations were also dispersed, whereas the rain, snow, and hail–graupel cat- assimilated into the model. Observation-error standard egories have inverse exponential distributions (Marshall deviations were assumed to be 2 m s21 and 2 dBZ for and Palmer 1948). Single-moment schemes like the one Doppler velocity and reflectivity, respectively (Dowell used here are employed in the current generation of et al. 2004b; Dowell and Wicker 2009; Aksoy et al. 2009; high-resolution, real-time models that produce convec- Yussouf and Stensrud 2010). Unless otherwise noted, all tive storms explicitly (e.g., Kain et al. 2008). model variables except the Exner function and the mixing The appendix describes how reflectivity correspond- coefficient (Dowell and Wicker 2009) were updated when ing to model fields, on the customary logarithmic scale each observation was assimilated. We used trilinear in- (dBZ), was computed. A minimum threshold of 0 dBZ terpolation to compute point estimates of model fields at was used when mapping model fields to reflectivity and observation locations. The transformation from model also applied to the reflectivity observations themselves. fields to reflectivity is described later. Reflectivity observations both within and outside pre- The EnKF employs covariance localization follow- cipitation regions were assimilated in the same manner, ing Houtekamer and Mitchell (2001) and Hamill et al. as in Tong and Xue (2005). (In contrast, Aksoy et al. (2001). The influence of each observation on the model 2009 used different localization radii for reflectivity state was restricted to a sphere with a radius of 6 km observations in precipitation and no-precipitation ob- around the observation. The functional form for this servations.) Most of the no-precipitation KOUN re- localization was taken from the compactly supported flectivity observations in our case are in the lowest fifth-order correlation function in Eq. (4.10) of Gaspari 1–2 km AGL within 30 km of the radar (Fig. 1 of Dowell and Cohn (1999). The localization radius used here is and Wicker 2009). Reflectivity observations below the in the range used in previous studies for ensembles of radar’s noise threshold are not used in this study, even 50–100 members (Dowell et al. 2004b; Caya et al. 2005; though they proved to be useful in the study by Aksoy Tong and Xue 2005; Aksoy et al. 2009; Dowell and et al. 2009. Wicker 2009). Although storm-scale analysis sensitivity to localization radius for radar observations has been 3. Differences between observed and simulated investigated in previous studies (e.g., Dowell et al. 2004b; reflectivity Caya et al. 2005), we suggest that there is still room for improving the data-assimilation algorithm through more Our first objective in presenting the results of radar-data rigorous and/or adaptive methods for determining local- assimilation experiments for the 8 May 2003 Oklahoma ization radii for Doppler-velocity observations, reflec- City supercell is to illustrate differences between the sim- tivity observations in precipitation, and no-precipitation ulated and observed reflectivity fields, as a function of lo- observations. cation and time. The reference experiment is the Vr-only For the representation of cloud processes in experiment (Table 1; Figs. 3a,c,e,g; Fig. 4a; Figs. 5a–d), in NCOMMAS, we selected the Gilmore et al. (2004a) ver- which Doppler-velocity observations are assimilated and sion of the Lin et al. (1983) precipitation-microphysics reflectivity observations are used only to select regions for scheme, which is a single-moment bulk scheme for cloud additive noise. The Doppler-velocity observations strongly modeling. This scheme includes two liquid and three ice constrain the kinematic fields in the storm, whereas these categories: qc (cloud droplets), qr (rain), qi (cloud ice crys- observations weakly constrain the hydrometeor fields tals), qs (snow), and qh (hail–graupel). The cloud-droplet (and thus reflectivity) through covariances that develop

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FIG. 3. Ensemble mean reﬂectivity (20- and 40-dBZ contours) at 4.25 km AGL in the

(left) Vr-only experiment and (right) Vr and ZdB experiment at two times: (a)–(d) 2118 and (e)–(h) 2202 UTC. In (a), (b), (e), and (f), observed (KOUN) reﬂectivity is shown (20- and 40-dBZ shading). In (c), (d), (g), and (h), ensemble-mean vertical velocity (shading at intervals of 4 m s21) is shown. Horizontal coordinates (km) are relative to KOUN.

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FIG. 4. Prior-ensemble-mean minus observed reﬂectivity [contours and shading at intervals of 2 dBZ; red (blue) colors indicate overprediction (underprediction) by the model] as a function of time and height for two experiments

(cf. Table 1): (a) Vr only and (b) Vr and ZdB. The statistics are computed only where observed reﬂectivity is .15 dBZ, and they are binned by height (km AGL, at intervals of 0.5 km) and radar volume (beginning time of radar volume indicated in UTC on 8 May 2003). with Doppler velocity (cf. Snyder and Zhang 2003; d 5 yo H(x f )oryo H(xa), (3.1) Dowell et al. 2004b; Tong and Xue 2005; W. Deierling and D. Dowell 2010, unpublished manuscript). By illus- trating analyses at midlevels early (38 min after the model where yo is the observation; H is the observation oper- initialization) and late (82 min after the model initial- ator, which maps the model state to the observation ization) in the assimilation window, Fig. 3 provides an location and type (cf. the appendix); x represents the en- overall sense of how the storms were simulated. At tire model state; superscript f indicates a forecast (prior)

2118 UTC, the Vr-only experiment had two large con- state; a indicates an analysis (posterior) state; and an vective storms (Fig. 3a). Whereas the precipitation overbar indicates an ensemble mean. In this section, region in the southern storm actually had shrunk hor- H is the reﬂectivity observation operator; in section 4, izontally (Figs. 1 and 3a), the analysis shows a large H is either the reﬂectivity or the Doppler-velocity ob- precipitation region. Farther north at 2118 UTC, the Vr- servation operator. The opposite of d (i.e., forecast mi- only experiment had storms in the vicinity of the de- nus observation instead of observation minus forecast) veloping Oklahoma City storm cluster, but the largest is plotted as a function of time and height (Fig. 4) and precipitation echo (near X 5235, Y 5 10 in Fig. 3a) horizontal location for a particular time and radar ele- was too far northeast, and only weak updrafts had de- vation angle (Fig. 5). In Fig. 6, innovation statistics are veloped within the southwestern part of the storm cluster plotted as a function of time (radar volume). (from X 5250, Y 5210 to X 5240, Y 5 0inFig.3c). Figure 4 focuses on the maturing and tornadogenesis Later, at 2202 UTC, there was better agreement between periods of storm evolution (Romine et al. 2008), start- the observations and the Vr-only analysis. On the broad ing 46 min after the NCOMMAS ensembles had been scale, there was good correspondence between the ob- initialized, when the storm had a well-developed pre- served and simulated locations of the main 40-dBZ core cipitation core both in the model and observations.

(Fig. 3e), and a strong updraft was present in the analysis Throughout the analysis period in the Vr-only experi- (near X 5212.5, Y 5 10 in Fig. 3g) in the tornadic region ment (Fig. 4a), the ensemble mean on average under- of the Oklahoma City storm. However, there was some predicted reflectivity below 3 km AGL by as much as 8 noticeable discrepancy between the observed and simu- to 14 dBZ. lated reflectivity in the downshear region (northern part To further illustrate spatial characteristics of how the of Fig. 3e). predicted and observed reflectivity agree and disagree, Many of the plots discussed in this section are of the we show results in observation space, at a low elevation innovation d: angle (1.58), and at a time representative of the mature

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FIG. 5. Reﬂectivity (dBZ) at 1.58 elevation angle at 2202 UTC 8 May 2003: (a) observed by KOUN; (b) prior ensemble mean in the Vr-only experiment; (c) prior ensemble mean minus observation, with observed 20- and 40-dBZ contours also shown; (d) posterior ensemble mean minus prior ensemble mean;

and (e)–(h) as in (a)–(d), but for the Vr and ZdB experiment. The KOUN radar location is indicated by a black square.

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suggest that single-moment bulk microphysics schemes such as the one used in this study poorly represent the areal extent and reflectivity distribution within downshear anvils at low levels in supercells (Dawson et al. 2010). Second, since the patterns in 2d vary spatially and have large magnitudes that are both positive and negative, we cannot explain the patterns simply through a uniform observation bias (e.g., radar miscalibration). Third, since the precipitation in the downshear anvil at low levels is rain, for which there is less uncertainty in the reflectivity calculation than for ice–mixed-phase precipitation (cf. the appendix), we suggest that other error sources—specifically, errors in the predictions of hydrometeor fields—are more significant. Figure 5c indicates overprediction of reflectivity (red colors) both on the southwest side of the Oklahoma City storm (along roughly X 5215) and in the northernmost cell on the left flank (along roughly Y 5 50). This overprediction can be explained in at least three ways. First, it appears the rainfall is concentrated too close to the updraft; the ‘‘blob’’ of high reflectivity near X 5

215, Y 5 15 in Fig. 5b is associated with qr of nearly 15 g kg21 beneath a midlevel core of heavy rain and hail–graupel (not shown). Other studies have noted that single-moment bulk microphysics schemes often produce precipitation that is too heavy close to the updraft (Gilmore et al. 2004b). Second, the simulated storm could be moving too slowly toward the northeast; red colors on the southwest side of the precipitation core and blue colors on the northeast side in Fig. 5c would be consistent with such a phase difference between simulated and observed storm locations. Higher up, the dif- FIG. 6. Observation-space diagnostics for two experiments (cf. ferences in the simulated and observed reflectivity Table 1): Vr and ZdB and Vr-only. Solid (dashed) lines indicate patterns on the southwest side of the core (near X 5 root-mean-square innovation (ensemble standard deviation) for 21 2 5 (a) KOUN reflectivity (dBZ), (b) KOUN Doppler velocity (m s ), 15, Y 10 in Fig. 3e) would also be consistent with this and (c) KTLX Doppler velocity (m s21). The statistics are computed slower movement. Third, in the simulations of this case, only where observed reflectivity is .15 dBZ and are binned by radar we have noticed a tendency for the model to be too slow volume (beginning time of radar volume indicated in UTC time on to weaken cells on the left flank. 8 May 2003). Both forecast and analysis statistics are plotted, hence, At midlevels—roughly between 3 and 8 km AGL— the sawtooth pattern. there is better agreement between observed and predicted reflectivity (Fig. 4a). At upper levels—roughly storm phase (Figs. 5a,b). Some aspects of the observed between 8 and 12 km AGL—the interpretation is com- reflectivity structure are predicted well, including the plicated because both model and/or observation-operator curved shape of the main (southernmost) high-reflectivity errors and changes in radar-data coverage seem to be cell (from roughly X 5220, Y 5 10 to X 5 10, Y 5 25) important factors. After 2140 UTC, the high-reflectivity and the locations of two left-flank cells (from X 5220, top of the Oklahoma City storm moves into the KOUN Y 5 30 to X 5 5, Y 5 35 and from X 5210, Y 5 50 to radar’s cone of silence, while the downshear anvil moves X 5 10, Y 5 55). The underprediction that dominates out of the cone of silence (not shown). The following the statistics in Fig. 4a occurs in the downshear anvil of differences between simulated and observed reflectivity the Oklahoma City storm (approximately 0 , X , 30 at upper levels contribute to the patterns seen in Fig. 4: and 15 , Y , 40 in Fig. 5c). For the following reasons, the maximum reflectivity values in storm tops, both in the we believe this underprediction is a symptom of model main cell and in the left-flank cell, are generally over- error more than other error sources. First, other studies predicted; the model is too slow to decrease the core

Unauthenticated | Downloaded 09/26/21 11:15 PM UTC JANUARY 2011 D O W E L L E T A L . 283 reflectivity at the top of the left-flank cell; the areal cover- assimilation at low levels attempts to compensate. As age of the upshear anvil of the main cell is underpredicted, discussed in the following section, recurring spatial and the magnitude of reflectivity in the downshear anvil patterns in analysis increments such as those identified is generally overpredicted (not shown). here can be indicators of model or observation biases Before examining the influences that reflectivity-data (Dee 2005). assimilation has on the storm-scale analyses in more detail in the following section, we briefly comment here on how the reflectivity innovations change when reflec- 4. Influences of reflectivity-data assimilation on tivity observations are assimilated together with Doppler- storm-scale analyses velocity observations (i.e., Vr and ZdB experiment; cf. a. Observation-space diagnostics for the Table 1). Relative to the V -only experiment, the V r r Vr-only and Vr and ZdB experiments and ZdB experiment (Figs. 4b and 6a) has generally closer prior and posterior fits of the ensemble mean to We reveal the influences that reflectivity-data assimi- the reflectivity observations, as expected. For example, lation is having on the storm-scale analyses by examining the shape of the high-reflectivity core of the main cell observation- and model-space fields and by comparing and the extent of its downshear anvil are better repre- multiple experiments. First, we use observation-space diagnostics (Dowell et al. 2004b; Dowell and Wicker sented in the Vr and ZdB experiment (cf. Figs. 3f and 3e; cf. Figs. 5f and 5e,b). Earlier in the assimilation window, 2009) to compare the Vr-only and Vr and ZdB experiments. One diagnostic is the root-mean-square of the the Vr and ZdB experiment (Fig. 3b) better represented the shape of the main northern storm cluster and the innovations: smaller extent of the southern storm than did the Vr-only qffiffiffiffiffiffiffiffiffi experiment (Fig. 3a). On average, each assimilation RMSI 5 hd2i, (4.1) cycle produced much larger changes to the reflectivity field when both reflectivity and Doppler-velocity ob- where hi indicates an average over all observations in servations were assimilated (Figs. 5h and 6a) than when a radar volume (a period of roughly 6 min). Another just Doppler-velocity observations were assimilated diagnostic is the ensemble spread (standard deviation): (Figs. 5d and 6a). This result supports the notion that vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u*+ hydrometeor fields are weakly constrained by Doppler- u N velocity observations and strongly constrained by re- t 1 2 spread 5 å [H(xn) H(x)] , (4.2) flectivity observations. N 1 n51 Some of the patterns seen before in the reflectivity innovations for the Vr-only experiment (Fig. 4a) remain where N is the number of ensemble members (50 in in the Vr and ZdB experiment (Fig. 4b), but with reduced these experiments), n is an index that identifies a par- magnitudes. The ensemble mean underpredicts re- ticular ensemble member, and H is either the reflectivity flectivity at low levels throughout experiment. Although or the Doppler-velocity observation operator. RMSI there is significant spatial variability, the reflectivity-data and spread statistics are shown for prior and posterior assimilation increases the ensemble-mean reflectivity at ensembles in Figs. 6 and 7. low levels at many more locations than it decreases the Not surprisingly, assimilating reflectivity and Doppler- reflectivity (e.g., Fig. 5h). As indicated in plots at the same velocity observations together reduces both the prior and elevation angle at other times (not shown), and as would posterior RMSI for reflectivity, typically by 5–10 dBZ, be inferred from Figs. 4a,b, the reflectivity-data assimi- relative to assimilating only velocity observations (Fig. 6a). lation is repeatedly increasing the reflectivity at low levels At the same time, assimilating both observation types during each cycle. The need to do so at low levels is increases the prior and posterior RMSI (i.e., results in perhaps increased by the reflectivity-data assimilation worse prior and posterior fits) for both the assimilated itself at midlevels. Between roughly 3 and 8 km AGL, KOUN and not-assimilated (verification) KTLX Doppler- increasing the fit to the reflectivity observations in the Vr velocity observations (Figs. 6b,c). This result is some- and ZdB experiment, relative to the Vr-only experiment, what surprising because the ensemble is being provided results in a net loss of hydrometeors and thus reflectivity more information in the Vr and ZdB than in the Vr-only over the layer (i.e., decrease in coverage of red colors experiment. and increase in coverage of blue colors in Fig. 4b relative We suggest four possible reasons for worse fits to the to Fig. 4a). Thus, the amount of precipitation falling into velocity observations. One possibility is that assimi- the lowest levels is less in the Vr and ZdB experiment lating both reflectivity and velocity observations de- than in the Vr-only experiment, and the reflectivity-data creases the ensemble spread too much, simply because

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precipitation (cf. the appendix), and a fourth possibility is biased reflectivity observations (e.g., Ulbrich and Lee 1999). Figure 4 indicates that the mean innovation for reflectivity is nonzero (i.e., blue colors dominate over red colors), and diagnostics averaged over entire radar volumes confirm that hdi is 2–8 dBZ in magnitude during the mature storm phase (not shown), suggesting bias in the model, observation operator, and/or observations. Bias in the reflectivity observations, particularly bias associated with radar-calibration errors, could possibly be significant (Sun and Crook 1997, 1998) but will not be addressed further here, since there seems to be insufficient information available to quantify a bias. Thus, the remaining discussion on errors in the assimilation will focus on evidence of bias in the model and/or reflectivity observation operator. In the analysis of differences between the predicted and observed reflectivity at low levels (section 3), we have already shown evidence of model errors that have regular patterns in a storm-relative sense. Such model-bias errors would lead to inconsistency between ensemble statistics and forecast errors, and thus the data assimilation would be expected to be suboptimal (Dee 2005). It is unclear exactly how reflectivity-data assimilation in the presence of model- and/or observation- bias errors leads to worse velocity analyses in our experiments, but the explanations could involve both how the velocity fields are affected directly by the reflectivity- data assimilation through the ensemble covariances and how errors in thermodynamic analyses resulting from the reflectivity-data assimilation project into the dynamics during the model integration. FIG. 7. As in Fig. 6, but for the following two experiments An encouraging sign in Fig. 6c is that assimilating (cf. Table 1): 5-dBZ obs error and update qr, qs, qh. KOUN observations—whether just Doppler velocity or both velocity and reflectivity—results in a better pos- more (and perhaps also because different) observations terior than prior fit to the independent KTLX velocity are being assimilated than in the Vr-only experiment. observations; that is, analysis RMSI is less than forecast Reduced prior ensemble spread during each assimilation RMSI. RMSI changes between the forecasts and analyses cycle implies that observations have less influence on the are slight at some times, significant at other times. [Note: posterior ensemble mean, all else being equal. However, Storm evolution, changing radar viewing angles, and results from another experiment (‘‘more additive noise’’; inconsistent overlap of data volumes from each radar Table 1), described in more detail later, suggest that the (collected at different sampling frequencies) probably reduced ensemble spread is not the most significant rea- all contribute to the erratic nature of the RMSI curves in son for worse fits to the velocity observations. In this Fig. 6c.] The KOUN and KTLX radars viewed the up- more additive noise experiment, in which both velocity draft and mesocyclone region with between-beam an- and reflectivity observations are assimilated, the ensem- gles increasing toward 908 as the storm approached the ble spread is greater than in the Vr and ZdB experiment radars (Fig. 1), meaning that the KTLX radar was in- and comparable to that in the Vr-only experiment, but the creasingly observing a component of the wind field that prior fits to the velocity observations are even worse than was unobserved by the KOUN radar. in the V and Z and V -only experiments (not shown). r dB r b. Analysis sensitivities to observation errors and A second reason why the reflectivity-data assimilation limited updates of model fields might make the velocity analysis worse is model bias errors (Dee 2005). A third possibility is a biased reflectivity To further reveal the influences that reflectivity-data observation operator, particularly for ice and mixed-phase assimilation has on the storm-scale analyses, we compare

Unauthenticated | Downloaded 09/26/21 11:15 PM UTC JANUARY 2011 D O W E L L E T A L . 285 the results of assimilation-sensitivity experiments. The The statistics of the update qr, qs, qh experiment (Fig. first sensitivity experiment (‘‘5-dBZ obs error’’; Table 1) 7) differ from those of the Vr and ZdB experiment (Fig. is the same as Vr and ZdB experiment, but that the as- 6) as follows: the prior RMSI (spread) in KOUN re- sumed standard deviation of reflectivity-observation flectivity is increased by 4% (increased by 17%), the errors is 5 dBZ instead of 2 dBZ.Thatis,thefittothe prior RMSI (spread) in KOUN velocity is decreased by reflectivity observations is weaker. One motivation for 12% (increased by 16%), and the prior RMSI (spread) this sensitivity experiment is to increase ensemble in KTLX velocity is decreased by 11% (increased by spread, thus allowing the velocity observations to have 20%). The update qr, qs, qh experiment also has slightly more influence on the analyses than in the Vr and ZdB lower prior RMSI for velocity observations (2% lower experiment. Another motivation is to reduce the influ- for KOUN and 3% lower for KTLX) and similar en- ences of the possible error sources related to reflectivity semble spread (within 2%) relative to the Vr-only ex- that were mentioned previously: model error, biased periment. According to these measures, we consider the observations, and/or a biased observation operator. update qr, qs, qh experiment the ‘‘best’’ that was pro- Dowell et al. (2004a) assumed reflectivity-observation duced in this study. Further supporting this claim, evi- errors were 5 dBZ for their earlier experiments with the dence will be provided shortly that the update qr, qs, qh 8 May 2003 supercell, for the reasons just provided. experiment results in a better analysis near the surface

Tong and Xue (2005) also assumed 5-dBZ observation than does the Vr and ZdB experiment. errors for their perfect-model experiments with a sim- c. Model-space diagnostics for the V -only, V and ulated supercell, although no explanation was provided r r Z , and update q ,q,q experiments for using such a large error magnitude. dB r s h The observation-space statistics of the 5-dBZ obser- We now evaluate results in model space (Fig. 8) for vation error experiment (Fig. 7) differ from those of the quantities integrated over the entire model domain: to-

Vr and ZdB experiment (Fig. 6) as follows: the prior tal masses of qc, qr, qs, qh, and qi; and total volume of RMSI (spread) in KOUN reﬂectivity is increased by 8% updraft for a threshold w $ 5ms21. For the three prog-

(increased by 17%), the prior RMSI (spread) in KOUN nostic variables in the reflectivity observation operator—qr velocity is decreased by 9% (increased by 6%), and the (Fig. 8b), qh (Fig. 8c), and qs (Fig. 8d)—it is not surprising prior RMSI (spread) in KTLX velocity is decreased by that the Vr and ZdB and update qr, qs, qh experiments, in 6% (increased by 4%). As expected, increasing the which reflectivity observations are assimilated, have trends KOUN reflectivity observation error from 2 to 5 dBZ in the domain totals that are more similar to each other increases the observation-space ensemble spread. How- than to the trends for the Vr-only experiment, in which ever, given the opposite trends of roughly the same per- reflectivity observations are not assimilated. Relative centage for RMSI in reflectivity and velocity, it is unclear to the Vr-only experiment, the Vr and ZdB and update whether the 5-dBZ observation error experiment would qr, qs, qh experiments generally increase the amount of be considered more successful than the Vr and ZdB ex- cloud droplets, decrease the amount of rain, decrease periment. Without further experimentation, it is difficult the amount of hail–graupel, and slightly decrease the to determine if the increased fit to the velocity observa- amount of snow. Late in section 3, it was noted that on tions in the 5-dBZ observation error experiment is mainly average, reflectivity-data assimilation decreases the reflec- a result of more ensemble spread, or if reduced influences tivity between 3 and 8 km AGL and increases the re- of errors in the model, observations, and/or observation flectivity below 3 km AGL (Fig. 4). The changes in rain operator are also significant. and hail–graupel at midlevels resulting from the reflectivity-

A second sensitivity experiment (update qr, qs, qh; data assimilation dominate the domain-total statistics in Table 1) is the same as the Vr and ZdB experiment, but Figs. 8b,c relative to the changes at low levels. that when a reflectivity observation is assimilated, only Before 2130 UTC, the Vr and ZdB experiment de- the qr, qs, and qh fields are updated; qr, qs, and qh are velops high updraft volume much more quickly than the the three prognostic variables in the reflectivity obser- other experiments (Fig. 8f); consistent with this result, vation operator [cf. (A.4)–(A.7)]. One possible benefit of the Vr and ZdB experiment also generally has more this approach is reducing the influence of model error; cloud (Fig. 8a). Figure 3 provides an example of these disregarding covariances between reflectivity observa- significant differences, showing much stronger updrafts tions and model fields not directly related to reflectivity in the developing Oklahoma City storm cluster (from would prevent model biases in qr, qs, and qh from pro- X 5250, Y 5210 to X 5240, Y 5 0) in the Vr and ZdB jecting into these other fields during the data assimi- experiment (Fig. 3d) than in the Vr-only experiment lation. Another possible benefit is increased ensemble (Fig. 3c). During this time in the storm’s history, the spread. updraft was relatively far from the radar—roughly

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FIG. 8. Domain-integrated quantities for three experiments (cf. Table 1): Vr and ZdB, Vr only, and update qr,qs, qh. Prior ensemble means are summed over the entire model domain every 2 min for (a) cloud water (kg), (b) rain (kg), (c) hail–graupel (kg), (d) snow (kg), (e) cloud ice (kg), and (f) volume (m3) where w $ 5ms21.

50 km away. We speculate that the relative contribu- d. Cold-pool analyses tions of reflectivity- and velocity-data assimilation to the analyses could be range dependent. When a storm is The remaining discussion in this section about how close to a radar, the Doppler-velocity observations re- reflectivity-data assimilation affects storm-scale analy- solve convergent, divergent, and rotational properties ses focuses on the analyzed pools of cold air near the of the updraft, whereas when a storm is far from a radar, surface. Cold pools in supercell thunderstorms develop the velocity observations could be too coarse to resolve from the evaporation, melting, and sublimation of pre- the updraft. Therefore, at far ranges, where the Doppler- cipitation. Dowell et al. (2004b) discuss the importance velocity observations provide less information, the co- of these cold pools for storm evolution and the diffi- variances between reflectivity and unobserved fields, culties in analyzing them from Doppler radar observa- such as w and qc, could contribute proportionally more tions. In the current study, cold-pool analyses are very to the retrieval of the updraft and cloud. Further support sensitive to some aspects of the data-assimilation system. of this speculation comes from discussions with our col- Given the limited surface observations available for this leagues (particularly M. Coniglio 2009, personal commu- case study, we cannot determine definitively which anal- nication) about data-assimilation results for other cases ysis is best, but we can rely on surface observations in (not shown) in which the convective storms were ;100 km the cold pool from one site—KOKC (Figs. 1 and 9a)—for from the radar. For these cases, adding reflectivity-data model verification. assimilation to the velocity-data assimilation also helped Temperature analyses at 250 m AGL at 2210 UTC in produce strong storms in the model more quickly. For 6 different experiments (Fig. 9) illustrate how reflectivity- three-dimensional variational data assimilation (3DVar) data assimilation affects the cold pool and, when reflec- of Doppler-velocity observations and ‘‘cloud analysis’’ tivity data are assimilated, how the analyses depend on based on reflectivity observations for convective storms ensemble spread. Both reflectivity and Doppler-velocity that were roughly 50–200 km from the radar, Hu et al. observations are assimilated into NCOMMAS in five of (2006) also found that reflectivity observations were very the six experiments (Figs. 9a–e), but only Doppler ve- important for supporting the development of strong storms locity is assimilated in the sixth (Fig. 9f). The six experi- during the data assimilation. ments produce a considerable variety of temperature

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FIG. 9. Ensemble-mean analyses of perturbation temperature (shading and thin contours at intervals of 2 K; negative values indicated by dashed contours) and reflectivity (thick contours for 20 and 40 dBZ) at 0.25 km AGL at 2210 UTC 8 May 2003 for six different experiments (cf. Table 1): (a) Vr and ZdB, (b) less additive noise, (c) more additive noise, (d) no u update, (e) update qr, qs, qh, and (f) Vr only. The location of KOKC, where surface observations are available, is indicated by a black dot. The arrow indicates a location in the storm’s forward flank where the cold-pool characteristics are particularly sensitive to how the analysis is produced. analyses, indicating that reflectivity-data assimilation can potential temperature is dominated by negative values indeed have a significant influence on the low-level cold (Fig. 10a), likely related to cooling by evaporation of pool. Relative to the Vr-only experiment, experiments in rain. More rain implies higher reflectivity, and more which reflectivity observations are also assimilated have rain also implies more evaporative cooling. Thus, a significantly different magnitudes of temperature per- negative correlation between reflectivity and temper- turbations in the cold pool (e.g., Figs. 9c vs. 9f), different ature develops at low levels. Higher up in the storm storm-relative locations and horizontal extents of the cold (e.g., at 8.25 km AGL in Fig. 10b), the situation is more air (e.g., Figs. 9a,d vs 9f), and different horizontal scales complicated. Large areas of both positive and negative of structures in the cold pool (small-scale features in correlations develop, likely related to both heating and Figs. 9a–c vs smoother features in 9f). cooling by moist processes and strong vertical motions

A comparison of the Vr and ZdB experiment and a (heating by compression in downdrafts and cooling by ‘‘no-u update’’ sensitivity experiment (Table 1) dem- expansion in updrafts). onstrates how reflectivity-data assimilation contributes At low levels, ensemble-mean reflectivity is on aver- significantly to the cold-pool analysis through covari- age too low throughout the assimilation period (Fig. 4). ances between reflectivity and temperature. When re- Therefore, on average, reflectivity-data assimilation re-

flectivity observations are assimilated, all model fields peatedly produces positive increments in qr and qh (and are updated in the Vr and ZdB experiment, whereas all corresponding positive increments in the associated re- model fields except potential temperature are updated flectivity) at low levels. At the same time, since the in the no u update experiment. The Vr and ZdB exper- correlation with temperature is negative (Fig. 10a), the iment (Fig. 9a) produces a much larger and stronger reflectivity-data assimilation repeatedly produces nega- cold pool than the no-u update experiment (Fig. 9d). At tive increments in temperature at low levels. Thus, much low levels, the correlation field between reflectivity and stronger and more widespread cold pools develop in the

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FIG. 10. Correlation [shading at intervals of 0.1; positive (negative) values indicated by red (blue) colors] between

reflectivity and potential temperature (ensemble-mean analyses) in the Vr and ZdB experiment at 2210 UTC 8 May 2003: (a) 0.25 and (b) 8.25 km AGL. Also shown is ensemble-mean reflectivity (thick black contours for 20 and 40 dBZ). Correlation is plotted only where the ensemble-mean reflectivity .15 dBZ. experiments in which reflectivity observations are as- Figs. 5c,g, 0 , X , 30 and 15 , Y , 40). Thus, reflectivity- similated and in which potential temperature is updated data assimilation repeatedly introduces positive rain and during this data assimilation (Figs. 9a–c) than in the negative temperature increments in the downshear anvil other experiments (Figs. 9d–f). The analyses are ex- near the surface. Since greater ensemble spread results trapolating, through the ensemble covariances, the bias in in larger increments, the experiment with the greatest reflectivity into systematic changes in temperature. While ensemble spread (more additive noise) has the strongest the reflectivity-temperature covariances are physically and most widespread cold pool (Fig. 9c). plausible, there is no reason to expect them to account for For ensemble forecasting and radar-data assimilation relations of bias in these model variables. for real supercells, it is not clear what the ideal amounts Experiments with different magnitudes of ensemble of ensemble spread are for temperature and other var- spread (Table 1), controlled by the specified magnitudes iables. We do not have widespread temperature obser- of additive noise, further reveal how reflectivity-data vations available for verification and must instead rely assimilation affects the low-level cold pools. In most on the radar observations to evaluate consistency be- experiments, including Vr and ZdB, the standard devia- tween ensemble spread and forecast errors. Relative to tions of additive gridpoint noise, before smoothing, were the Vr and ZdB experiment, the less additive noise and 1.0 (0.25) m s21, 1.0 (0.25) m s21, 1.0 (0.25) K, and 1.0 more additive noise experiments changed the prior ensem-

(0.25) K before (after) 2100 UTC for u, y, u, and Td, ble spread in reﬂectivity (velocity) by as much as 224% respectively (cf. Dowell and Wicker 2009). In a ‘‘less and 147% (229% and 149%), respectively (Fig. 11). additive noise’’ sensitivity experiment, the standard One could argue that the more additive noise experiment deviations were decreased to 0.1 m s21, 0.1 m s21, is best, since it results in prior consistency ratios, as de-

0.1 K, and 0.1 K after 2100 UTC for u, y, u, and Td, re- fined by Dowell and Wicker (2009), closest to the desired spectively, and in a ‘‘more additive noise’’ experiment, value of 1.0 for KOUN and KTLX velocity (not shown). 21 21 the standard deviations were 0.5 m s , 0.5 m s , One could also argue that the Vr and ZdB and less addi- 0.5 K, and 0.5 K after 2100 UTC. The strength and tive noise experiments are better than the more additive coverage of the cold pool (Figs. 9a–c) depends greatly on noise experiment because they have lower values of prior the ensemble spread (Fig. 11) associated with these RMSI for KOUN and KTLX velocity (not shown). Thus, different magnitudes of additive noise. A region in which the range of ensemble spread in these experiments seems the cold pool is particularly sensitive to the amount of well within the range of plausible uncertainty, but this ensemble spread is the forward flank (downshear anvil) at variation in ensemble spread yielded large differences low levels, roughly in the location indicated by the arrow in ensemble-mean temperature (Figs. 9a–c). An analysis in Fig. 9. As noted earlier, the model was generally un- that depends so much on ensemble spread could be viewed derpredicting reflectivity in this region (blue colors in as nonrobust, that is, not to be trusted.

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introduced through random perturbations to the base- state wind proﬁles and local random perturbations added

to the u, y, u,andqy fields where the observations indicated precipitation. A number of simplifications were employed for the simulations: an initial environment that was horizontally homogeneous, with profiles obtained from a National Weather Service sounding near the storm; a flat lower boundary; no surface fluxes; no radiative transfer; and a single-moment bulk (Lin–Gilmore) microphysics scheme. In a reference experiment, only KOUN Doppler- velocity observations were assimilated into the NCOMMAS ensemble. Then, KOUN reflectivity observations together with velocity observations were assimilated in all other experiments. Sensitivity experiments were conducted to reveal how the reflectivity observations affected the storm-scale analyses, including experiments with different specified values of observation error, different amounts of ensemble spread (additive noise), and different choices for what model variables are updated by the EnKF when reflectivity observations are assimilated. Doppler-velocity observations from a WSR-88D (KTLX) FIG. 11. Ensemble standard deviation in (a) KOUN reflectivity (dBZ) and (b) KOUN Doppler velocity (m s21) for three experi- were used for verification, in addition to the KOUN ve- ments (Table 1): Vr and ZdB (solid black), less additive noise (solid locity and reflectivity observations. Results from all data- gray), and more additive noise (dashed black). The statistics are assimilation experiments were encouraging in that 1) computed only where observed reflectivity is .15 dBZ and are realistic storm-scale structures were obtained in the binned by radar volume (beginning time of radar volume indicated analyses and 2) assimilating KOUN observations— in UTC time on 8 May 2003). Both forecast and analysis statistics are plotted, hence, the sawtooth pattern. either just Doppler velocity or both Doppler velocity and reflectivity—resulted in a better posterior than prior fit to independent KTLX observations. As mentioned previously, with the few available ob- Issues associated with reflectivity-data assimilation servations we cannot determine which analysis of the were explored for only one real-data case. Nevertheless, cold pool in the 8 May 2003 Oklahoma City supercell is many of these issues should be relevant for any attempts the best. Nevertheless, a comparison of the KOKC ob- to use ensemble Kalman filters to assimilate reflectivity servations and the ensemble-mean analyses at the same observations of convective storms directly into numerical location could suggest that the strong cold pool in the cloud models. Not surprisingly, assimilating reflectivity forward flank in the Vr and ZdB experiment (Fig. 9a) is observations significantly affected the analyses of the hy- erroneous (Fig. 12a, which shows that the ensemble- drometeor variables in the reflectivity observation opera- mean temperature is too low at 2152 and 2159 UTC). tor: rain, snow, and hail–graupel. Assimilating reflectivity

In contrast, the update qr, qs, qh (Fig. 12b) and Vr-only observations also significantly affected the analyses of (Fig. 12c) experiments more correctly capture the grad- unobserved variables, including temperature, cloud, and ual cooling at the KOKC site before 2200 UTC as the vertical velocity. Large updraft volume developed more storm approaches. Based on the limited observations from quickly in the experiments in which reflectivity and KOKC, we might conclude that the cold pool analyses in Doppler-velocity observations were assimilated together the no-u update, update qr, qs, qh,andVr-only experiments rather than just Doppler velocity, presumably through (Figs. 9d–f) are the most plausible. ensemble covariances between reflectivity and unobserved variables such as cloud and vertical velocity. We speculate that reflectivity observations are particularly useful for 5. Summary and discussion producing mature storms quickly in an ensemble when the An ensemble Kalman filter was used to assimilate radar storms are far from the radar, when Doppler-velocity ob- observations of the 8 May 2003 Oklahoma City tornadic servations are too coarse to resolve the updrafts. supercell thunderstorm into a 50-member NCOMMAS Differences between simulated (ensemble mean) and ensemble. Variability among the ensemble members was observed reflectivity had regular patterns in a storm-relative

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FIG. 12. Observed (black line) and simulated (gray line indicates prior ensemble mean and shading spans values within 1 ensemble standard deviation) potential temperature (K) at KOKC (cf. Figs. 1 and 9) for three experiments: (a) Vr and ZdB, (b) update qr, qs, qh, and (c) Vr only. sense throughout the assimilation period. Biases in the we would conclude that the forward-flank cold pools reflectivity observations, the reflectivity observation op- that developed in these experiments were too strong. In erator, and the model hydrometeor predictions are can- general, the operational observing network does not didate explanations for these patterns. We are unable provide cold-pool observations on the scale of individual to assess whether there are any biases in the reflectivity convective storms. Thus, since we cannot verify cold- observations associated with radar miscalibration, but pool analyses, we propose instead that robustness is since the KOUN radar is a 10-cm radar, we expect that a more practical quality measure for storm-scale analy- errors associated with attenuation should be small, much ses obtained by radar-data assimilation. If storm-scale less than for research radars with shorter wavelengths temperature analyses were robust, then ensemble-mean (e.g., 5 or 3 cm). Since there is considerable uncertainty in cold-pool analyses would vary only slightly over the plau- how to calculate reflectivity from model hydrometeor sible range of ensemble spread. Unfortunately, for the case fields, particularly for ice and mixed-phase precipitation, shown, when reflectivity data are assimilated, the temper- bias errors in the reflectivity observation operator are a ature analyses depend greatly on ensemble spread, and plausible error source in these experiments. Other re- thus the temperature analyses are not robust. flectivity observation operators that have been proposed Bias errors in the hydrometeor predictions appear to for the Lin–Gilmore microphysics scheme (Jung et al. be a major error source in these experiments. An option 2008a) would be worth trying in future work with this that was presented for reflectivity-data assimilation in case. Model error is also a very likely error source in the this situation was only updating a subset of model vari- current experiments. One noteworthy discrepancy be- ables, so that errors in the hydrometeor forecasts do not tween the predicted and observed reflectivity occurred in project directly into other variables during the data as- the downshear anvil at low levels, where reflectivity was similation. An experiment in which only qr, qs, and qh consistently underpredicted by as much as 20 dBZ.Since were updated by the EnKF during the reflectivity-data rain was the precipitation type in this region, and since assimilation resulted in the best verification scores for errors in the reflectivity observation operator are be- the experiment set in this study. A drawback was that lieved to be relatively small for rain, we suggest that er- not updating all model variables resulted in slower storm rors in the model’s qr predictions and/or the associated growth in the model (Fig. 8f), presumably because some drop-size distributions were responsible for the under- useful covariances were being ignored. predicted reflectivity. A more attractive approach that could be explored for Throughout the data-assimilation period, reflectivity- future work would be to improve the hydrometeor fore- data assimilation repeatedly added rain in the downshear casts, with a more sophisticated microphysics scheme be- anvil at low levels, where reflectivity was underpredicted. ing one possible option. Double- and triple-moment Simultaneously, through negative correlations with tem- schemes (Seifert and Beheng 2001; Milbrandt and Yau perature, reflectivity-data assimilation repeatedly intro- 2005; Morrison and Grabowski 2008) could mitigate some duced negative increments in temperature in the same of the model errors that affect our results. Another pos- region. Based on the limited available surface observations, sible approach is parameter estimation (Tong and Xue

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2008a,b), that is, using the observations to optimize a small for improving the manuscript. Mary Haley provided valu- number of parameters in the microphysics scheme. This able assistance with NCL graphics. approach could offer some benefit for real-data cases, but for this particular case, analyzed differences between predicted and observed reflectivity showed considerable APPENDIX spatial variability, suggesting that different parts of the storm could have significantly different optimal micro- Reflectivity Estimation from Model Fields physics parameters. When the Rayleigh approximation (radar wavelength Although beyond the scope of the current study, de- particle diameter) is valid, the reflectivity factor for spher- veloping methods to satisfy better the conditions for EnKF ical raindrops is optimality could be a worthwhile endeavor in future stud- ð ies of radar-data assimilation for convective storms. For ‘ 6 example, the observation operator for reflectivity is non- Z [ nr(D)D dD, (A.1) 0 linear (Tong and Xue 2005 and the appendix of the current paper) because the application of (A.8) results in a loga- where D is the raindrop diameter and nr(D) is the rain- rithmic relationship between ZdB and individual hydro- drop number concentration per unit diameter (Doviak meteor mixing ratios. Lorenc (2003) shows an example of and Zrnic 1993). For reflectivity associated with non- how posterior distributions are suboptimal after an ob- spherical raindrops, ice particles of any shape, and/or servation that is nonlinearly related to the model state is mixtures of particle types, the term ‘‘equivalent reflec- assimilated. We believe we see evidence of related tivity factor’’ (Ze) is used instead. Specifically, Ze is the problems in our results (not shown). One possible ap- reflectivity factor of a hypothetical target of spherical proach that could be considered for future studies would raindrops that would produce the same amount of back- be to use an iterative method (Annan et al. 2005) to scattering as the observed target. To obtain the equivalent improve the posterior mean and variance when reflec- reflectivity factor for simulated storms, we sum the contri- tivity observations are assimilated. Other suggestions butions from three hydrometeor categories: for future work include 1) developing more rigorous and/or adaptive methods for choosing localization radii Ze 5 Zr 1 Zs 1 Zh, (A.2) for reflectivity observations in precipitation and ‘‘no precipitation’’ observations; 2) including a more realistic where Zr, Zs,andZh are the equivalent reflectivity fac- mesoscale environment in the model, so that multi-hour tors associated with rain, snow, and hail–graupel, respec- forecasts after the data-assimilation window can provide tively. The reflectivity values associated with the other an additional basis for evaluating experiments; 3) re- two categories—cloud droplets and cloud-ice crystals—are peating experiments like those in the current study for considered negligible and thus not included in (A.2). other cases with a variety of storm modes; and 4) choosing The Lin–Gilmore bulk microphysics scheme assumes cases that have more detailed observations, particularly that raindrops have an inverse exponential size distri- thermodynamic observations, available for verification. bution (Gilmore et al. 2004a; Kessler 1969; Smith et al. 1975): Acknowledgments. D. Dowell’s work on this project "# was supported by the National Science Foundation un- pr n 0.25 n D 5 n D r 0r der Grant ATM-0333872 at the Cooperative Institute r( ) 0r exp , (A.3) rqr for Mesoscale Meteorological Studies and by the Na- tional Center for Atmospheric Research. C. Snyder’s where n (m24) is the intercept parameter, r is the air work on this project was supported by the National 0r density (kg m23), r is the density of water (1000 kg m23), Science Foundation under Grant ATM-0205655. Matt r and q and all other mixing ratios in this section are in Gilmore developed the precipitation-microphysics scheme r units of kilograms per kilogram. This equation for the used in these experiments and answered questions about size distribution, together with the definition of the re- the code. Mike Coniglio, Ted Mansell, and Glen Romine flectivity factor in (A.1), leads to the following relation- contributed to the data-assimilation code development. ship between the model fields and the reflectivity factor Kevin Scharfenberg and Gordon Carrie provided the associated with rain: radar observations of the 8 May 2003 Oklahoma City supercell. Discussions with Altug Aksoy, Glen Romine, 7.2 3 1020(rq )1.75 Ted Mansell, and Don Burgess were quite beneficial. Z 5 r , (A.4) r 1.75 0.75 1.75 Three anonymous reviewers provided helpful suggestions p n0r rr

Unauthenticated | Downloaded 09/26/21 11:15 PM UTC 292 MONTHLY WEATHER REVIEW VOLUME 139 where Z and all other equivalent reflectivity factors in r2 r h 3 20 r 1.75 6 23 0.23 2 7.2 10 ( qh) this section are in mm m . For the intercept parame- rr 6 24 Z 5 , (A.7) ter used in the current experiments (n0r 5 8 3 10 m ; h 1.75 0.75 1.75 p n0h rh Lin et al. 1983; Gilmore et al. 2004a), Zr 5 3.63 3 9 1.75 10 (rqr) . r Since ice hydrometeors have various shapes, orienta- where h and n0h are the density and intercept param- tions, and degrees of surface wetness, the relationship eters of hail–graupel, respectively. We use the default between reflectivity and ice is more uncertain than it is Lin et al. (1983) and Gilmore et al. (2004a) parameters: r 5 23 5 3 4 24 for rain (Smith et al. 1975; Smith 1984). As is the case for h 900 kg m and n0h 4 10 m . In this case, 5 3 10 r 1.75 rain, snow in the Lin–Gilmore bulk scheme has an in- (A.7) becomes Zh 4.33 10 ( qh) . Although our verse exponential size distribution, with the diameter D reflectivity observation operators for rain and snow are in this case referring to the size of the resulting water very similar to those in Tong and Xue (2005), our ob- drop if the snowflake were to melt. In our experiments servation operator for hail–graupel is different from (and also in the experiments of Tong and Xue 2005), we theirs. Tong and Xue (2005) used the wet-hail form of assume that when the temperature is above (below) the observation operator, and thus, all else being equal, freezing, snow has a wet (dry) surface. Thus, following they would obtain larger reflectivity values from hail– Smith et al. (1975) and Smith (1984), the relationship graupel. between reflectivity and the mixing ratio of snow is The final step in computing reflectivity is to convert to the customary logarithmic scale: 2 rs 1.75 0.23 7.2 3 1020(rq ) Z [ 10 log Z , (A.8) r2 s dB 10 e Z 5 r , T # 08C (dry snow), s 1.75 0.75 1.75 p n0s rs (A.5) where the units of ZdB are dBZ. The logarithmic scale is convenient not only for graphical displays of the wide 7.2 3 1020(rq )1.75 range of reflectivity values in observed precipitation, but Z 5 s , T . 08C (wet snow), (A.6) also for representing random errors in reflectivity, which s p1.75n0.75r1.75 0s s are commonly assumed to have a uniform error variance in dB (e.g., Wilson and Brandes 1979; Doviak and Zrnic where the coefficient 0.23 in (A.5) is the square of the 1993). A threshold for a minimum ZdB value has to be dielectric constant for ice divided by the square of the specified when mapping model hydrometeor fields to dielectric constant for water (0.21/0.93 5 0.23; Smith reflectivity because ZdB in (A.8) is undefined at loca- 1984), rs is the density of snow, and n0s is the intercept tions where the hydrometeor mixing ratios are all zero. parameter for snow. For the chosen values n0s 5 3 3 After some experimentation, we chose a minimum Z 6 24 23 dB 10 m and rs 5 100 kg m (Lin et al. 1983; Gilmore threshold of 0 dBZ for our experiments, as did Tong et al. 2004a), Eq. (A.5) and (A.6) become Zs 5 9.80 3 and Xue (2005). 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