1. Introduction
Since 2003, engineers and scientists at the National Oceanic and Atmospheric Administration’s (NOAA) National Severe Storms Laboratory (NSSL) have been actively working on the applications for phased-array radar (PAR) technology, a potential replacement candidate for the current operational Weather Surveillance Radar-1988 Doppler (WSR-88D) network across the United States (Weber et al. 2007; Zrnić et al. 2007; Heinselman and Torres 2011; Curtis and Torres 2011). An experimental S-band PAR research radar is located at the National Weather Radar Testbed (NWRT) in Norman, Oklahoma (Forsyth et al. 2005), and has been used to explore the feasibility of this technology for severe weather applications. There are several significant differences between the NWRT PAR and WSR-88D technology. While the WSR-88D collects data over a 360° azimuthal sector with a fixed 0.95° beamwidth, the NWRT PAR, containing only a single panel at this time, scans only up to a 90°-wide sector and the beamwidth varies with azimuth (from 1.6° at boresight to 2.3° at ±45° off boresight). Thus, the WSR-88D observations have a larger spatial coverage area and higher spatial resolution compared with the PAR observations. However, one unique feature of PAR technology that makes it very attractive to the field of meteorology is its electronic steering ability, which enables it to scan one complete volume of observations in less than a minute (Heinselman and Torres 2011). In contrast, the WSR-88D takes about 4.5 min to scan one complete volume of observations because of its mechanically steered beam.
Several studies during the past decade have demonstrated the advantages of high-temporal-resolution NWRT PAR observations in better understanding rapidly evolving complex features of a variety of severe convective systems ranging from microbursts, hailstorms with associated lightning activity (Heinselman et al. 2008; Emersic et al. 2011), quasi-linear convective systems (Newman and Heinselman 2012), and tornadic supercell storms (Tanamachi et al. 2015). In addition, the Phased Array Radar Innovative Sensing Experiments (PARISE) conducted at NSSL over the past several years show that the rapid volumetric PAR observations of ongoing convection more closely match the NWS forecasters’ conceptual models of storm evolution compared with 4–5-min volumetric updates provided by the operational WSR-88Ds (Heinselman et al. 2012, 2015; Bowden et al. 2015). The rapid-scan PAR observations also increase the forecasters’ situational awareness, resulting in longer tornado warning lead times compared with the traditional WSR-88D radar updates (Heinselman et al. 2012, 2015; Kuster et al. 2015). While the rapid-scan PAR observations have already shown promise toward improved understanding of convective weather and longer severe weather warning lead times, there is also considerable interest in evaluating the impact of the rapid-scan capability of PAR in storm-scale numerical weather prediction (NWP) as compared with the WSR-88Ds. This evaluation is particularly important within the context of NOAA’s Warn-on-Forecast (WoF; Stensrud et al. 2009, 2013) program, which envisions incorporating storm-scale NWP models into the severe weather warning-decision process of NWS operational forecasting.
One advanced data assimilation (DA) approach for storm-scale NWP is the ensemble Kalman filter (EnKF; Evensen 1994), with the ensemble square root filter (EnSRF; Whitaker and Hamill 2002) being one of the most popular variants. Results from studies during the past decade show that assimilating WSR-88D observations using EnSRF in both homogeneous, single-sounding idealized frameworks (e.g., Snyder and Zhang 2003; Dowell et al. 2004; Tong and Xue 2005; Xue et al. 2006; Aksoy et al. 2009, 2010; Yussouf and Stensrud 2010, 2012; Dowell et al. 2011; Dawson et al. 2012) and heterogeneous mesoscale environments (e.g., Lei et al. 2009; Dowell et al. 2010; Snook et al. 2011, 2012; Jung et al. 2012; Yussouf et al. 2013; Putnam et al. 2014; Wheatley et al. 2014; Snook et al. 2015; Yussouf et al. 2015) creates a good representation of convection in both analyses and forecasts. However, the impact of assimilating high-temporal-resolution PAR observations in NWP models for severe weather forecasting is not clear. Yussouf and Stensrud (2010) conducted several observing system simulation experiments (OSSEs) using an EnSRF data assimilation technique and demonstrated that, with only a short 15-min data assimilation period, assimilating high-temporal-frequency PAR observations yields significantly better analyses and ensemble forecasts than those produced using WSR-88D observations. The findings of Yussouf and Stensrud (2010) are consistent with the findings of Xue et al. (2006), who also found that simulated radar scan volumes at 1-min intervals significantly shorten the time needed to obtain good analyses of a convective storm.
However, the OSSEs conducted in both of the above studies are based on a perfect model assumption in which model error does not play a role. Given the idealized nature of such OSSE studies, their results may be too optimistic, although they do provide an upper-limit estimate of the benefit of rapid-scan PAR in NWP. Demonstrating similar impacts using real PAR observations in a realistic atmospheric environment is more challenging, where model errors are inevitable and can arise from inaccuracies in model physics parameterizations, insufficient resolution, numerical approximations, errors in initial and boundary conditions, etc. (Aksoy et al. 2009, 2010; Potvin and Wicker 2013). Moreover, assimilating such high-temporal-frequency PAR observations using the three-dimensional (3D) EnSRF technique involves shorter assimilation cycles of 1 min or less, which are computationally very expensive. In addition, the frequent stopping and restarting of the model with a very short assimilation frequency can potentially introduce imbalances and can generate noise in the prediction system every time a new analysis is performed (S. Wang et al. 2013; Lange and Craig 2014). On the other hand, using longer assimilation cycles (10 min or more) can save computational cost and avoid imbalances due to frequent model updates. But using longer assimilation cycles with a 3D EnKF algorithm can introduce data timing errors when the observations taken at different times within the assimilation windows are assumed to be valid at the analysis time. If observations away from the analysis time are discarded, important features associated with the evolving storms may be missed, leading to poorer analyses and forecasts.
To counteract these problems with 3D EnKF, Sakov et al. (2010) proposed a generic asynchronous or four-dimensional (4D) EnKF called AEnKF that allows for the assimilation of observations distributed over time. The algorithm involves calculating updates using observations from the time of actual observation rather than from the time of analysis, as in the traditional 3D EnKF. Therefore, the AEnKF technique is able to utilize more observations collected over time with fewer analysis cycles, reducing the frequent model stopping and restarting.
Recently, S. Wang et al. (2013) developed a 4D asynchronous implementation of the EnSRF (which they called 4DEnSRF) that is most commonly used for storm-scale radar DA. They tested the 4DEnSRF technique for radar DA using OSSEs with assimilation cycle lengths ranging from 1 to 20 min. The results indicate that 4DEnSRF outperforms the traditional 3D EnSRF when the assimilation cycle frequency is longer than 1 min (S. Wang et al. 2013). The 4DEnSRF technique assimilates high-frequency observations distributed over a specified time interval using a single update, thereby reducing the number of analysis cycles, which is desirable for reducing the computational cost and potential noise generation. This advantage of the 4DEnSRF technique in handling high-temporal-frequency observations is attractive for PAR DA.
To evaluate and compare the impact of assimilating rapid-scan PAR and the traditional WSR-88D observations in storm-scale severe weather forecasting, several 4DEnSRF DA and forecast experiments are conducted using WSR-88D, rapid-scan PAR, and PAR observations subsampled at a WSR-88D-like temporal resolution. The study is conducted within a heterogeneous mesoscale environment using the 22 May 2011 Ada, Oklahoma, tornadic supercell event. The radar observations are assimilated every 5 min for a 45-min-long assimilation period prior to tornadogenesis, and 1-h ensemble forecasts are launched after 15, 30, and 45 min of radar DA. The goal is to see if the findings from the OSSE study of Yussouf and Stensrud (2010) hold true in a realistic mesoscale environment using real radar observations.
The rest of this paper is organized as follows. A brief description of the supercell event is documented in section 2. Section 3 describes the experiment design and the radar observations used in the DA and forecast experiments. Section 4 presents the results and discussions, followed by a summary in section 5.
2. Overview of the 22 May 2011 Ada, Oklahoma, tornadic supercell event
The 22 May 2011 Ada, Oklahoma, tornadic supercell was a weakly tornadic event with a tornado rating of EF0 on the enhanced Fujita (EF) scale. The tornadoes started at ~0119 UTC and ended at ~0141 UTC (based on tornado reports; Table 1). Several operational WSR-88D radars and the NWRT PAR documented the life cycle of this supercell storm. During the late afternoon and evening of 21 May 2011, a dryline extended from the Big Bend area of Texas (southwest Texas) through central Oklahoma and into south-central Kansas where it intersected the Pacific front. A midlevel jet rotating through the base of an upper low increased the effective shear. The bulk wind difference through 0–6 km AGL in the 0000 UTC 22 May 2011 Norman, Oklahoma, sounding was 43 kt (22.1 m s−1); values greater than 40 kt (20.6 m s−1) favor supercell storms. Convection initiated along the dryline in south-central Oklahoma, and by 0000 UTC on 22 May, a storm (storm A) evolved into a supercell in south-central Oklahoma (Fig. 1a). Several smaller cells developed north of storm A (Figs. 1a–c), and the one (storm B) closest to storm A matured into a supercell with a hook echo feature by 0045 UTC (Fig. 1d). There was one tornado report associated with storm A at 0040 UTC in Murray County, Oklahoma (SPC storm report database). During the next 30 min, storm B grew stronger, and storm A quickly dissipated when it encountered storm B (Figs. 1e–h). There were four tornado reports (Table 1) associated with storm B, all of which were rated as 0 on the EF scale. The first tornado report was at 0119 UTC and located 3.2 km northwest of Vanoss, Oklahoma. The supercell continued east toward Ada. The last tornado report from storm B was at 0141 UTC, located 6.44 km west-northwest of Ada. There is no damage track available for this event. The storm starts to dissipate after 0200 UTC (Figs. 1i–k). The storms were sampled by both WRD-88D radars and NWRT PAR. The observations from both radar platforms are assimilated separately into a storm-scale ensemble forecast system in order to compare the ability of the radars in forecasting the storm and its associated low-level mesocyclone.
Tornado reports associated with storm B on 22 May 2011 obtained from the Storm Prediction Center (http://www.spc.noaa.gov/climo/reports/110521_rpts.html).
Observed reflectivity (dBZ, from the NSSL NMQ system) at 2 km MSL at (a) 0000, (b) 0025, (c) 0030, (d) 0045, (e) 0100, (f) 0115, (g) 0130, (h) 0145, (i) 0200, (j) 0215, and (k) 0215 UTC 22 May 2011 over the area of interest. The black circle indicates the location of Vanoss and the black star indicates the location of Ada. (l) The black triangles are the four tornado reports from storm B (Table 1).
Citation: Weather and Forecasting 32, 4; 10.1175/WAF-D-16-0159.1
3. Data, model, and experiment design
a. The WSR-88D (KTLX) observations
The storm associated with the Ada tornado was ~80 km away from the operational WSR-88D radar at Twin Lakes, Oklahoma (KTLX). The WSR-88D radar sampled the storm at ~4.2-min intervals with a volume coverage pattern that consisted of 14 tilts (elevation angles) ranging from 0.46° to 19.45° (Table 2). The level II reflectivity and radial velocity observations from the WSR-88D at KTLX are quality controlled using an automatic procedure within the Advanced Regional Prediction System (ARPS) package to eliminate noise and ground clutter from the reflectivity observations and to unfold the aliased radial velocity observations (Brewster et al. 2005). The quality controlled reflectivity and radial velocity observations from both radars are interpolated onto the model grid horizontally, but remain on the radar elevation levels vertically; this procedure is used in many real-data studies with the ARPS EnKF DA system (e.g., Jung et al. 2012; Snook et al. 2012).
Physics options for the 40-member ARPS mesoscale and storm-scale ensemble system.
b. The NWRT PAR observations
The NWRT PAR sampled the evolution of the Ada supercell with a 90° sector at a rapid ~50 s for volume updates. The volume coverage pattern spanned tilts from 0.5° to 60° with a higher number of tilts at lower levels of the atmosphere. In this study, the lowest 14 elevation angles from 0.5° to 19.5° are assimilated (Table 3) into the model during the 45-min DA period. However, because of mechanical failures, several volume scans of NWRT PAR observations are missing between 0045 and 0108 UTC (listed in Table 3) and therefore are not assimilated in the experiments. The NWRT PAR observations are quality controlled using the same ARPS quality control package and interpolated in the same manner as the WSR-88D observations.
List of experiments conducted and the number of volume scans of radar observations assimilated during the 45-min DA period from 0030 through 0115 UTC 22 May 2011.
There are a few caveats to using the PAR data. The first is that the scan sector is free to change between volume scans; this occurs twice for this case. The first and most substantial change occurs between the 0045 and 0050 UTC analyses, when the sector shifts approximately 21° counterclockwise. The second sector change is between the 0050 and 0055 UTC analyses; the scan sector shifts a further 2° counterclockwise. The effect of a sector change is that storms that were outside of the radar coverage area are now observed by the radar, which affects the observation space statistics. This will be discussed in more detail in later sections. In addition, because the PAR scans over a limited sector in azimuth, there is no way to suppress spurious convection outside the scan sector from the PAR. This can result in spurious convection interacting with the assimilated storms and degrading the quality of the forecast. To mitigate this, the zero-reflectivity observations from the most recent KTLX volume are used outside the PAR scan sector in the following manner. If the composite reflectivity from KTLX is less than or equal to 0 dBZ, the corresponding column of PAR observations is set to 0 dBZ. Otherwise, the entire column of PAR observations is set to “missing.”
c. The mesoscale ensemble DA and forecast
The storm-scale radar DA experiments are performed on a grid with 2-km grid spacing, nested within a mesoscale grid of 18-km grid spacing that covers the continental United States (CONUS; Fig. 2a). ARPS (Xue et al. 2000, 2001, 2003) is used as the prediction model for the DA and forecast experiments while the EnSRF system developed for the ARPS system (Xue et al. 2006; Jung et al. 2012; Snook et al. 2012, 2015; Y. Wang et al. 2013; Putnam et al. 2014) and extended to the 4DEnSRF algorithm (S. Wang et al. 2013) is used for the ensemble DA.
(a) The mesoscale domain (d01) covering the CONUS and the nested storm-scale domain (d02). (b) The timeline of the mesoscale DA experiments. (c) The storm-scale domain with county borders (d02, enlarged) and locations of WSR-88D (KTLX, blue triangle), PAR (blue triangle), and Ada (black square). (d) The timeline of the storm-scale DA and forecast experiments.
Citation: Weather and Forecasting 32, 4; 10.1175/WAF-D-16-0159.1
The mesoscale domain contains 243 × 163 × 51 grid points over the continental United States (Fig. 2a). The vertical grids are stretched with a vertical spacing of 50 m near the surface and 900 m at the model top. The model top is at 25 km with a Rayleigh damping layer above 12 km. A 40-member mesoscale ensemble is initialized from the 20-member National Centers for Environmental Prediction (NCEP) Short-Range Ensemble Forecasting (SREF; Du et al. 2006) analyses (at 40-km horizontal grid spacing) at 2100 UTC 21 May 2011, but using two sets of physics parameterizations (Table 2). The schemes used in the first set of 20 ensemble members are the Betts––Miller–Janjić cumulus parameterization scheme (Betts 1973) and the Sun and Chang TKE-based planetary boundary layer (PBL; Sun and Chang 1986; Xue et al. 1996) scheme. The remaining 20 ensemble members use the Kain–Fritsch cumulus parameterization scheme (Kain and Fritsch 1990, 1993) and the Yonsei University (YSU) PBL scheme (Hong and Pan 1996). In addition, the single-moment Lin (Lin et al. 1983) microphysics scheme, stability-dependent surface-layer physics, a two-layer soil model initialized from NCEP’s Eta Model analysis, and the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC) (Chou 1990, 1992; Chou and Suarez 1994) long- and shortwave radiation schemes are used in all 40 ensemble members except for differences in the transmission functions used. The transmission function in the radiation scheme is computed using the k-distribution method for the first 20 members and using a lookup table for the remaining 20 ensemble members. The physics diversity in the mesoscale ensemble is used to represent model error in the ensemble system and to help account for ensemble underdispersion in the assimilation system (Yussouf and Stensrud 2012; Snook et al. 2012). This mesoscale ensemble is used to provide initial and boundary conditions for the one-way nested storm-scale ensemble system.
Routinely available surface (i.e., horizontal u and υ wind components, temperature T, and dewpoint Td), wind profiler (u and υ), and radiosondes (u, υ, potential temperature θ and Td; only available at 0000 UTC 22 May 2011) observations are assimilated into the mesoscale domain every 1 h starting from 2200 UTC 21 May 2011 out to 0000 UTC 22 May 2011 (Fig. 2b) using the ARPS EnSRF (Xue et al. 2006; Y. Wang et al. 2013) system. Radar data are not assimilated onto the mesoscale grid. The covariance localization function is based on the fifth-order correlation function from Gaspari and Cohn (1999) with a horizontal cutoff radius of 300 km and 800 km used for the surface and upper-air (both wind profiler and radiosonde) observations, respectively. A 6-km cutoff radius in the vertical is used for all observations (Snook et al. 2015). To help maintain the ensemble spread, multiplicative inflation (Anderson 2001) with a factor of 5% is applied everywhere in the model domain to all model state variables. The mesoscale ensemble analyses at 0000 UTC are used to create the initial conditions for the storm-scale ensemble. Meanwhile, 2-h ensemble forecasts are generated from the mesoscale ensemble analyses at 0000 UTC 22 May 2011 out to 0200 UTC 22 May 2011 to provide ensemble boundary conditions for the storm-scale ensemble.
d. Storm-scale ensemble DA and forecast
The physics packages used by the ARPS on the 2-km nested grid are the same as the first 20 members of the mesoscale ensemble, except that the double-moment Milbrandt and Yau (2006a,b, hereafter MY) microphysics scheme and the YSU PBL scheme are used, while the cumulus parameterization scheme is turned off (Table 2).
A 40-member 2-km storm-scale ensemble is downscaled from the mesoscale ensemble analyses at 0000 UTC 22 May 2011 in a one-way nested configuration. The domain is centered on Ada and covers most of Oklahoma and the northern part of Texas with 203 × 163 × 51 grid points (Fig. 2c). To introduce smaller-scale perturbations into the convective-scale ensemble, samples from a Gaussian distribution with zero mean are drawn at each grid point in the domain. Then, a two-dimensional recursive filter (Jung et al. 2012) with a decorrelation length scale of 6 km is applied to these samples horizontally, and a homogeneous Gaussian filter with a decorrelation length scale of 4 km is applied vertically. This generates smoothed, spatially correlated perturbations, and these are added to the interpolated mesoscale ensemble at 0000 UTC. The smoothed perturbations have zero mean and standard deviations of 2 m s−1 for the horizontal velocity components u and υ and 1 K for potential temperature θ over the entire domain. The perturbation standard deviations of the mixing ratios for water vapor qυ, cloud water qc, rainwater qr, ice qi, snow qs, hail qh, and graupel qg are set to 10% of their values at each grid point where the observed reflectivity is larger than 10 dBZ. Only positive perturbations are retained for θ, qυ, qc, qr, qi, qs, qh, and qg. The effect of the recursive filter is similar to but computationally more efficient than that used by Tong and Xue (2008).
Oklahoma Mesonet (Brock et al. 1995; McPherson et al. 2007) observations (i.e., 10-m u, υ; 2-m temperature T; and relative humidity rh) are assimilated every 5 min into the storm-scale ensemble starting from 0005 UTC and ending at 0020 UTC using 3D EnSRF (Fig. 2d) DA. A cutoff radius of 50 km is used in the horizontal and 6 km in the vertical for covariance localization [as in Snook et al. (2015), similar to Sobash and Stensrud (2015)]. A 15% multiplicative inflation factor and relaxation-to-prior spread (RTPS; Whitaker and Hamill 2012) with a relaxation factor of 0.85 are applied over the whole domain to all model variables to help maintain ensemble spread during the period of mesonet data assimilation. These values are selected based on several sensitivity studies (not shown).
The radar reflectivity and radial velocity observations from the WSR-88D or PAR are assimilated into the storm-scale ensemble starting at 0030 UTC using the 4DEnSRF (Fig. 2d), and the assimilation continues until 0115 UTC with a 5-min assimilation window. To show the effect of the radar data assimilation without the effect of other observation types, Oklahoma Mesonet data are not assimilated during this period.
Both the PAR and WSR-88D radar observation times are reassigned into 1-min batches, as in a traditional EnSRF approach. For example, a ~50-s complete volume scan of PAR observations is reassigned to the nearest minute and the ~4.2-min volume scan WSR-88D observations, which consist of 14 elevation angles, are separated into single-elevation angles and regrouped at 1-min intervals based on the times of the tilts. Therefore, these 1-min data batches contain between two and three tilts for WSR-88D observations rather than full volume scans that are often treated as being collected simultaneously in 3D EnSRF (S. Wang et al. 2013; Yussouf and Stensrud 2010). The 4DEnSRF scheme precalculates the observation prior H(x) for all these observations every 1 min to perform an analysis every 5 min (S. Wang et al. 2013). Specifically, to produce an analysis valid at time t, the 4DEnSRF uses five batches of data and their priors at t − 2 min, t − 1 min, t, t + 1 min, and t + 2 min, with each batch consisting of observations within 30 s of the batch time.
The standard deviations of the WSR-88D reflectivity and radial velocity observation errors are assumed to be 5 dBZ and 3 m s−1, respectively, following Putnam et al. (2014). After several sensitivity experiments, the same observation error standard deviations as those for the WSR-88D dataset are used for the PAR dataset as well. The cutoff radius used in covariance localization for the storm-scale ensemble is 6 km in both the horizontal and vertical, the same as those used in Jung et al. (2012), while the time localization is assumed to be 5 min, following S. Wang et al. (2013). To help maintain ensemble spread, RTPS with a relaxation factor of 0.9 is applied over the entire region, and multiplicative inflation of 20% is applied to the prior ensemble in regions directly influenced by the radar data during the period of radar data assimilation. These values are selected based on several sensitivity studies and the guidance of earlier studies.
Three DA and forecast experiments are conducted (Table 3) on the 2-km grid, forced by the same mesoscale ensemble at the lateral boundaries. The first experiment assimilates the KTLX WSR-88D radar observations only (referred to as the WSR-88D experiment hereafter), while the second experiment assimilates the full-volume PAR observations (referred to as the PAR experiment hereafter). The third experiment assimilates PAR observations but uses only those tilts that closely match the times of the tilts of the WSR-88D observations (referred to as the PAR-reducedtilts experiment hereafter). Four to five volume scans of PAR observations are needed to reproduce one volume scan of PAR-reducedtilts observations that has the same temporal frequency as in WSR-88D. An example radar observation dataset that is assimilated in the WSR-88D, PAR, and PAR-reducedtilts experiments during a 5-min DA window is shown in Table 4. As mentioned earlier, while the PAR observations have higher temporal resolution than the WSR-88D observations, the PAR observations have a slightly coarser spatial resolution than the WSR-88D observations. Therefore, while experiments WSR-88D and PAR-reducedtilts have similar temporal resolutions, the latter has a coarser spatial resolution. The differences between the PAR and PAR-reducedtilts results will reveal the impact of the higher temporal frequency of the PAR observations. Additional information regarding the experiments is found in Table 2. Finally, 1-h deterministic forecasts are initialized from the ensemble mean analyses and three sets of 1-h ensemble forecasts are initialized from the ensemble analyses for all three experiments after 15-, 30-, and 45-min of ensemble radar DA (Fig. 2d). The analyses and forecasts are used to investigate how quickly and accurately the rapid-scan PAR observations initialize and forecast the storm.
An example list of tilts of PAR observations that are assimilated in the PAR-reducedtilts experiment. Listed are the tilts and corresponding times of observation used in the WSR-88D, PAR, and PAR-reducedtilts experiments from 0028 to 0031 UTC.
4. Results and discussions
a. Innovation statistics during the DA period
Observation-space diagnostic statistics. (a) Forecast and (b) analysis RMSI. (c),(d) As in (a),(b), but for TES. (e),(f) As in (a),(b), but for mean innovation (positive values denote that the observations are larger than the ensemble mean). (g) Forecast consistency ratio for reflectivity (dBZ) from the three data assimilation and forecast experiments. Calculations are limited to locations where observed and/or ensemble mean reflectivity exceeds 15 dBZ.
Citation: Weather and Forecasting 32, 4; 10.1175/WAF-D-16-0159.1
All three experiments start with an analysis RMSI of ~15 dBZ (Fig. 3b); by the end of the assimilation period, the analysis RMSI is reduced to ~5–7 dBZ. The forecast and analysis RMSI values from the PAR experiment are generally less than those from the other experiments. Additionally, the effect of the missing PAR volumes between 0045 and 0055 UTC (see Table 3) is apparent in the increased RMSI near 0055 UTC in both the analyses and forecasts in the PAR-reducedtilts experiment. However, by the 0115 UTC cycle, the RMSI is stabilized (Fig. 3a), which suggests that the missing PAR observations have minimal effect by the end of the assimilation period.
Furthermore, the TES (Figs. 3c,d) is similar for all experiments in either the forecasts or the analyses, suggesting the ensembles are fairly configured. The consistency ratios are also comparable in magnitude between the experiments, with values between 0.1 and 0.4 (Fig. 3g). These values are well below 1, suggesting underdisperson in the ensemble, which is commonly seen in storm-scale real-data ensemble DA studies (e.g., Jung et al. 2012; Yussouf et al. 2013, and references therein). Despite the spread deficiency, the filter shows no sign of divergence during the 1-h assimilation period, indicating the reasonable robustness of the DA system.
The mean innovation (Figs. 3e,f) is largely positive, indicating that the model reflectivity is lower than the observed reflectivity. The underprediction of reflectivity in the model during the assimilation period is also seen in other studies (Dawson et al. 2012; Yussouf et al. 2015). As expected, the forecast and analysis mean innovation results generally decrease with time as more data are assimilated. There are some apparent oscillations in the forecast mean innovation in the early part of the assimilation period that are the result of the overprediction of spurious echoes and the underprediction of the geographical extent of storms before the forecast is sufficiently improved. The intensity of the storms is underpredicted at 0035 UTC, while the spatial coverage of the reflectivity is overpredicted, leading to a small mean innovation. Radar DA at this time is too aggressive at removing reflectivity, resulting in a large positive mean innovation and large RMSI at 0040 UTC. Both spurious echoes and the underprediction of storm intensity are improved at 0045 UTC, as more data are assimilated at 0040 UTC, leading to a smaller mean innovation. The main reason for the large positive mean innovation at 0050 UTC is different. As mentioned earlier, the PAR scan sector shifts approximately 21° counterclockwise at 0050 UTC, meaning the PAR is observing storms that were previously not in the PAR coverage area. Those storms have yet to spin up in the model, leading to underprediction and a large positive mean innovation (Figs. 3e,f) during the 0050 UTC assimilation. After 0055 UTC, both mean innovation and RMSI continue to decrease, indicating that the filter is stable.
b. Analyzed near-surface cold pool and vertical vorticity
Studies by Dawson et al. (2010) and Putnam et al. (2014) have shown the importance of the analyzed and predicted cold pool in convective storms on their dynamics and evolution. To evaluate the analyzed cold pools and associated low-level mesocyclones, the ensemble mean analyses of equivalent potential temperature θe, horizontal winds, and vertical vorticity at the first model level or about 25 m above ground from the three experiments after 15 (valid 0045 UTC), 30 (valid 0100 UTC), and 45 min (valid 0115 UTC) of DA cycles are shown in Fig. 4.
The ensemble mean analyses of vertical vorticity (black contours at intervals of 100 × 10−5 s−1; maximum vorticity is shown in each panel with unit ×10−5 s−1), horizontal wind vectors and θe (colored; in 4-K increments; minimum is shown in each panel) after 15 (valid 0045 UTC), 30 (valid 0100 UTC), and 45 (valid 0115 UTC) min of DA from (a)–(c) WSR-88D, (d)–(f) PAR, and (g)–(i) PAR-reducedtilts experiments at the first model grid level (~25 m) above ground. Green contours represent 35-dBZ reflectivity analyses.
Citation: Weather and Forecasting 32, 4; 10.1175/WAF-D-16-0159.1
After 15 min of DA, the cold pool in storm B in the PAR experiment is the coldest out of all three experiments (minimum θe of 319 K in Fig. 4d). Assimilating more reflectivity observations in the PAR experiment leads to a stronger cold pool, likely because of the negative correlation between reflectivity and temperature in the cold pool (Dowell et al. 2011). The low-level mesocyclones are also relatively weak in all experiments, though the WSR-88D experiment has the strongest examples (1.9 × 10−3 s−1), followed by the PAR experiment (1.7 × 10−3 s−1), and then by the PAR-reducedtilts experiment (1.4 × 10−3 s−1). As 4DEnSRF uses a 5-min assimilation window, the missing PAR observations during the last assimilation cycle from the initial 15 min of the DA period (Table 3) directly impact the analysis and may be partly responsible for weaker low-level mesocyclone PAR-reducedtilts.
After 30 min of DA, the PAR (Fig. 4e) experiment has stronger cold pools than the other two experiments, in general, in storm A and storm B. Additionally, the PAR experiment has the strongest low-level mesocyclone for both storms A and B. The peak of 5.4 × 10−3 s−1 is in storm A. By this time, 8, 26, and 6 volume scans of observations are assimilated into the WSR-88D, PAR, and PAR-reducedtilts experiments, respectively (Table 3), leading to the weakest mesocyclone being found in the PAR-reducedtilts experiment.
After an additional 15-min of DA (valid 0115 UTC), the PAR experiment continues to have the strongest vorticity values associated with storm B, with the maximum vertical vorticity reaching 6.6 × 10−3 s−1 (Fig. 4f) while the other two experiments produce much smaller maximum values (Figs. 4c,i). In addition, the minimum θe for both the WSR-88D and PAR experiments are in the cold pool for storm A; the minimum θe values are similar between these two experiments. For storm B, the cold pool has approximately the same minimum θe in all three experiments. However, approximating the outline of the cold pool as the 336-K contour, the PAR experiment has a slightly more widespread cold pool.
c. Analyses and forecasts of reflectivity
To evaluate the impacts of DA on the forecasts, the observed National Mosaic and Multi-Sensor QPE (NMQ) 3D radar reflectivity mosaic product (Zhang et al. 2011) reflectivity is compared with the analyses and 15-min forecasts from the ensemble member closest to the mean (Figs. 5 and 6). This member is chosen in a similar way to that in Yussouf et al. (2013). It is defined as the member with the smallest normalized root-mean-square difference from the mean in potential temperature and u and υ wind components. The reflectivity analyses at 2 km MSL valid at 0045 UTC (after 15 min of DA or three assimilation cycles) are able to capture both storms A and B in all three experiments, though storm A in particular has lower reflectivity in the analyses than the observations (Figs. 5a,d,g,j). Because the PAR does not observe the cells to the north of storm B until 0050 UTC, they are not well represented at this time in the PAR and PAR-reducedtilts experiments (Figs. 5g,j). In particular, both experiments have one intense storm instead of two weaker storms.
(a)–(c) The NMQ reflectivity observations (colored, in 5-dBZ increments) and analyses from the member closest to the mean at (left) 0045, (center) 0100, and (right) 0115 UTC from the (d)–(f) WSR-88D, (g)–(i) PAR, and (j)–(l) PAR-reducedtilts experiments. Reflectivity at 2 km AGL is color filled. The 0.004 s−1 vertical vorticity contours are given in solid black. The verification domain for the skill scores in Figs. 8 and 9 are shown by the black box. The portion of the domain shown here is over southeast OK.
Citation: Weather and Forecasting 32, 4; 10.1175/WAF-D-16-0159.1
As in Fig. 5, but for 15-min deterministic forecasts initialized from the ensemble member closest to the mean. Note that the verification domain for the skill scores is omitted.
Citation: Weather and Forecasting 32, 4; 10.1175/WAF-D-16-0159.1
As PAR observations of the two cells to the north of storm B start when the scan sector changes at 0050 UTC, the reduction in intensity of these cells induced by the PAR observations is apparent in the PAR experiment at 0100 UTC (Fig. 5h). While seven full volumes are assimilated in the PAR experiment, only two partial volumes are assimilated in the PAR-reducedtilts experiment because of the missing data discussed earlier. As a result, those storms are still poorly resolved at 0100 UTC (Fig. 5k). Otherwise, only minor structural differences are evident between the experiments. By the 0115 UTC analyses, all three experiments show similar storm structures, suggesting sufficient observations are assimilated by this time (Figs. 5f,i,l).
The 15-min forecast from the member closest to the ensemble mean is examined in Fig. 6. In the forecasts initialized at 0045 UTC, the intensity and structure of storm A in the PAR experiment matches the observations more closely (Figs. 6a,d,g,j). However, storm B, which is located near the boundary of the PAR coverage area, is merging with a spurious supercell outside of the PAR coverage area. In the forecasts initialized at 0100 UTC, the overall structure of storm B in the WSR-88D and PAR-reduced tilts experiments is more realistic than the corresponding initialization (see Figs. 5e,k). Additionally, the ensemble member closest to the mean happens to develop much less spurious cells to the east of storms A and B in the PAR and PAR-reducedtilts experiments compared with the WSR-88D experiment. All other ensemble members (not shown) show similar results, and this is consistent with our observation that northern storms outside of the PAR coverage area are underpredicted in the PAR and PAR-reducedtilts experiments, producing less convection.
Additionally, the reflectivity in storm A is much more intense in all three experiments than in the observations, and the simulated storms continue to display hook echoes, whereas the observed storm does not. In fact, storm A does not dissipate through the end of the 1-h forecast in any of the experiments (not shown). Thus, the reflectivity forecasts from 15 min through the end of the run are considered poor. Furthermore, the 15-min forecasts initialized at 0115 UTC (Figs. 6f,i,l) are largely similar, except that the PAR experiment and, to a lesser extent, the PAR-reducedtilts experiment develop a spurious vorticity maximum in the northeastern quadrant of storm B. Also, storm A in the 0115 UTC forecasts is still much stronger than was observed, though it does begin to dissipate near the end of the run.
One problem seen in all three experiments is the faster propagation of supercells to the north and east compared with the observations. Similar problems have been seen in many prior storm-scale radar DA studies (e.g., Dawson et al. 2012, 2015; Xue et al. 2014; Yussouf et al. 2015, 2016; Stensrud and Gao 2010, to name a few). Stensrud and Gao (2010) suggest that this may be because the model is unable to develop midlevel pressure perturbations that lead to deviant motion in supercells. Xue et al. (2014) speculate that this may be due to errors in analyzing the storm environment, which leads to incorrect steering winds in the model. Fiori et al. (2010) found that the storm motion depends on the turbulence closure model and grid spacing. Reducing errors associated with supercell motion in storm-scale NWP is worthy of further investigation, however addressing it is beyond the scope of this paper.
d. Forecast probability of low-level vorticity
The 2-km model horizontal grid spacing used in this study is far too coarse to explicitly resolve tornadoes and is barely capable of resolving mesocyclone-scale features of the supercell. To infer the amount of low-level rotation from the three experiments, the ensemble forecast probability of low-level vorticity is compared with the surface–2 km MSL mesocyclone circulations generated by the Warning Decision Support System–Integrated Information (WDSS-II; Lakshmanan et al. 2007) (Miller et al. 2013) from KTLX radar observations (Stensrud and Gao 2010; Dawson et al. 2012; Yussouf et al. 2013, 2015; Xu et al. 2015). The vorticity probabilities are calculated at the first model level above ground level (~25 m AGL) during the 0–1-h forecast period. The forecast output (which is written out at 5-min intervals) from each ensemble member initialized from a certain analyses time is checked to see whether the vorticity exceeds a threshold value within a radius of 4 km in the horizontal direction around each horizontal grid point at any output time during the 1-h forecast period, and the vorticity probabilities are calculated from the number of members exceeding the threshold values. A threshold of 0.0015 s−1 is used for vertical vorticity. The 1-h forecast probability of vorticity is examined every 15 min from after 15, 30, and 45 min (valid 0045, 0100, and 0115 UTC initialization times) of radar DA and is compared with the WDSS-II rotation track (Fig. 7).
The 1-h forecast neighborhood ensemble probability of vertical vorticity exceeding a threshold of 0.0015 s−1 at the first model level above ground from (a)–(c) WSR-88D, (d)–(f) PAR, and (g)–(i) PAR-reducedtilts experiments initialized after (left) 15 min (valid 0045 UTC), (center) 30 min (valid 0100 UTC), and (right) 45 min (valid 0115 UTC) of DA. The black contours overlaid are the WDSS-II-generated KTLX low-level mesocyclone rotation exceeding 0.01 s−1 vorticity during the 0–1-h forecast periods.
Citation: Weather and Forecasting 32, 4; 10.1175/WAF-D-16-0159.1
The 1-h forecast probability of low-level vorticity exceeding 0.0015 s−1 initialized at 0045 UTC shows largely low (<40%) probabilities of vorticity (Figs. 7a,d,g). The PAR experiment (Fig. 7d) has the largest overlap between the forecast vorticity swath and the WDSS-II rotation track. The WSR-88D experiment (Fig. 7a) shows the highest probability values (~50%) displaced well to the north and west of the WDSS-II track, and the PAR-reducedtilts experiment shows only weak probabilities overlapping the WDSS-II track.
The forecast probabilities of strong low-level rotation increase with an additional 15 min of DA (Figs. 7b,e,h), and the forecast vorticity swaths are aligned better with the observed WDSS-II track compared with the 0045 UTC forecasts. The WSR-88D experiment (Fig. 7b) has very low probability over the beginning part of the observed strong rotation track but increases to high probabilities over the later part of the track. The PAR-reducedtilts experiment (Fig. 7h) has coverage of midrange probabilities (40%–60%) over the first part of the track, but the probabilities never increase above ~60%. On the other hand, the PAR experiment (Fig. 7e) has coverage of high probabilities over the first part of the observed rotation track and at least midrange probabilities over the rest of the track. Thus, the assimilation of the higher temporal frequency PAR observations clearly produces more reasonable probabilistic forecasts of vorticity with only 30 min of DA compared to the assimilation of WSR-88D data.
The forecast of low-level vorticity initialized after 45 min of DA generates relatively large areas with probability > 90% in all three experiments (Figs. 7c,f,i). These areas are displaced slightly south of the WDSS-II track in all experiments. As in the forecasts initialized at 0115 UTC, the PAR experiment (Fig. 7f) has better coverage in the early part of the track as compared to the WSR-88D and PAR-reducedtilts experiments (Figs. 7c,i). Additionally, the spurious vorticity maximum seen in the 2 km MSL vorticity from the PAR and PAR-reduced tilts experiments (see Figs. 6i,l) does not extend down to the surface. However, aside from the coverage in the early part of the rotation track, few differences are apparent between experiments in the forecasts initialized at 0115 UTC.
Though the above analysis has primarily focused on storm B, the forecasts for storm A show similar results. In particular, in the forecasts initialized at 0100 UTC, the PAR experiment shows higher probabilities of vorticity for storm A than the WSR-88D and PAR-reducedtilts in the early part of the swath, where there is observed rotation from the WDSS-II track. Additionally, the probabilities of vorticity for storm A increase with eastward extent in the WSR-88D and PAR-reducedtilts experiments, which is not reflected in the WDSS-II rotation track. In contrast, the vorticity probabilities in the PAR experiment remain approximately the same with a slight reduction in value with eastward extent. This is consistent with storm A being underpredicted during early DA cycles in the WSR-88D and PAR-reducedtilts experiments and dissipating much later than the observations. However, the PAR experiment was able to retrieve the intensity and the spatial coverage much better during early cycles although dissipation was delayed as in the other two experiments.
e. Skill scores of ensemble reflectivity forecasts
ETSs vs forecast times (UTC) for reflectivity thresholds of (top) 25 and (bottom) 40 dBZ from the three experiments. Forecasts are initialized after (a),(d) 15 min (valid 0045 UTC), (b),(e) 30 min (valid 0100 UTC), and (c),(f) 45 min (valid 0115 UTC) of DA. Calculations are performed over a small subdomain (see text for details).
Citation: Weather and Forecasting 32, 4; 10.1175/WAF-D-16-0159.1
The ETSs are found largely to increase with decreasing forecast lead time as expected in all three experiments, declining to near or below 0 by the end of the forecast periods. In general, the PAR experiment has a higher ETS for both the 25- and 40-dBZ thresholds than the WSR-88D experiment for the forecasts (Fig. 8) despite the missing observations and lower spatial resolution. We suspect that those limitations are responsible for a similar or slightly higher ETS in the WSR-88D experiment in general compared with the PAR-reducedtilts experiment. The differences between the WSR-88D and PAR experiments are evident only for the first 30 min of the forecasts initialized at 0045 UTC (Figs. 8a,d), while differences are noticeable almost to the end of the 1-h forecast period for forecasts initialized at 0100 and 0115 UTC (Figs. 8b,c,e,f). The ETS of the PAR-reducedtilts experiment remains lower than that of the PAR experiment for the duration of all 1-h forecasts, indicating the benefit of high-temporal-frequency observations.
The area under the relative operating characteristic (ROC; Mason 1982) curve (AUC) is calculated for a range of reflectivity thresholds (10–50 dBZ), and results are shown in Fig. 9 for the analyses and forecasts. As discussed in Snook et al. (2012), ROC measures hit and false alarm rates at varying probability thresholds (Mason and Graham 1999); it therefore provides information on the ability of a probabilistic forecast system to correctly discriminate between events and nonevents. A forecast with perfect skill has an AUC of 1.0 and 0.5 means zero skill.
AUC results from the (left) analyses after 15, 30, and 45 min of DA; (center) 30-min forecasts; and (right) 1-h forecasts for reflectivity thresholds ranging from 10 to 50 dBZ. Calculations are performed over a small subdomain (see text for details).
Citation: Weather and Forecasting 32, 4; 10.1175/WAF-D-16-0159.1
All three experiments have high AUCs in the analyses (Figs. 9a,d,g) and the value decreases as the forecast lead times increases (cf. Figs. 9b,e,h and 9c,f,i). The 30-min forecasts after 15 min of DA are just below the skillful range (AUC > 0.7), and the 60-min forecasts have very small AUCs, indicating no ability to discriminate (AUC < 0.5). The 30-min forecasts after 30 and 45 min of DA increase the AUCs to above 0.7 for most thresholds for the PAR experiment, suggesting that at least eight radar volume scans (~30 min of DA) are needed to produce operationally useful forecasts.
The reasons for the improved ETS scores and AUCs can be seen in Fig. 10, which shows the 10-min forecast from the 0100 UTC initialization of the number of hits, misses, and false alarms at the 25-dBZ threshold at each grid point, summed over all members of the ensemble. All three experiments have large numbers of hits where the observed storms overlap with the storms in the ensemble. The majority of the misses in all three experiments occur to the south and west of storms A and B (Figs. 10d,e,f), and the majority of false alarms occur to the northeast of storms A and B (Figs. 10g,h,i), likely as a result of the faster propagation of storms in the model, as noted earlier. The three experiments are largely similar, except the PAR experiment better captures the southern extent of both storms A and B, resulting in fewer misses and more hits in those regions. This directly increases the ETS score and also results in larger AUCs because of the higher probability of detection, which is used in computing the ROC curve.
The 10-min forecast from the 0100 UTC initialization of the number of (top) hits, (middle) misses, and (bottom) false alarms at the 25-dBZ threshold at each grid point, summed over all ensemble members, at 2 km MSL.
Citation: Weather and Forecasting 32, 4; 10.1175/WAF-D-16-0159.1
Overall, the PAR experiment generates the highest AUCs and the PAR-reducedtilts experiment the lowest AUCs during the 1-h forecast period. In the analyses, these differences are largest after 15 min of DA and decrease as more data are assimilated. However, the largest differences in the 30-min forecasts are after 30 min of DA, and in the 60-min forecasts, the AUCs are largely the same between experiments. These results suggest that the PAR data are most useful in DA windows that are ~30 min long.
5. Summary and discussions
To evaluate the impact of high-temporal-resolution PAR observations compared with the current operational WSR-88D observations on convective storm prediction, three DA and forecast experiments are conducted for the 22 May 2011 Ada, Oklahoma, tornadic supercell event using radial velocity and reflectivity observations from both rapid-scan NWRT PAR and WSR-88D KTLX. The experiments are conducted with the ARPS model and its 4DEnSRF DA system using a heterogeneous mesoscale environment. The first experiment assimilates traditional WSR-88D radar observations, the second experiment assimilates observations from the NWRT PAR, and the third experiment assimilates PAR observations with WSR-88D-like temporal frequency (PAR-reducedtilts experiment). The WSR-88D and PAR experiments are designed to compare the accuracy of the forecasts due to two different temporal resolutions from the different radar platforms. The PAR-reducedtilts experiment picks a subset of elevations from the rapid-scan PAR observations from the observation dataset to mimic the WSR-88D-like coarser-temporal-resolution observations (even though spatial resolution differences exist between PAR and WSR-88D observations) and is designed to examine the differences in the analyses and forecasts due to high-temporal-resolution PAR observations. All three experiments assimilate radar observations for a continuous 45-min DA period at every 5-min assimilation frequency. There are some missing PAR volume scans during this period. Finally, 1-h forecasts are launched at the end of the 15-, 30-, and 45-min assimilation periods, respectively. The goal is to evaluate how quickly and accurately the rapid-scan PAR observations can initialize and forecast the tornadic supercell storm.
The observation-space diagnostic statistics compared against the assimilated observations reveal that the filter shows no sign of forecast divergence during the 45-min assimilation period. All three experiments are able to analyze reflectivity structures that are similar to the observations even after a short 15-min DA period. The 15-min forecasts from the member closest to the ensemble mean largely captured the storm evolution, though storm A was too strong in the 0100 and 0115 UTC initializations. The 1-h forecast probabilities of low-level vorticity after 15, 30, and 45 min of DA from all three experiments indicate that the placement and alignment of the swath of high probabilities from the PAR experiment more closely match the WDSS-II-derived rotation track, particularly from the forecast initialized after only 30 min of DA. For this forecast, the low-level rotation from the WSR-88D does not cover the initial part of the WDSS-II rotation track, and the probability values from the PAR-reducedtilts experiment are comparatively low. The ETS score and the AUC also indicate that the PAR experiment forecasts showed improved skill compared with the WSR-88D and PAR-reducedtilts experiments, particularly over 15- and 30-min-long assimilation periods. The improved skill in the PAR experiment is the result of better capturing the southern extent of the reflectivity coverage in both storms A and B.
The overall results indicate that the WSR-88D and PAR-reducedtilts experiments perform most similarly to each other, and the PAR experiment performs better than those two experiments. From this, we conclude that the assimilation of high-frequency PAR observations results in improved accuracy over traditional WSR-88D observations. Furthermore, we conclude that this improvement in accuracy is the result of the increased data volume from the PAR. The improved accuracy is more pronounced with a short or moderately long (15–30 min) assimilation period. The positive impact of the higher temporal resolution of the PAR observations decreases for a longer assimilation period (45 min in this study). This is similar to the findings of the OSSE studies of Xue et al. (2006) and Yussouf and Stensrud (2010).
The ultimate goal of storm-scale radar DA and forecasts is to extend severe weather warning lead times (Stensrud et al. 2009). Within the context of the WoF paradigm, the overall results obtained from this study provide reasons for cautious optimism. A hypothetical real-time prediction system would require at least 12 volume scans, or about 45 min of operational WSR-88D data, to produce a reasonably good forecast. In contrast, the length of the NWRT PAR data assimilation period could be reduced to as little as 15 min, potentially increasing severe weather forecast lead times. These rapid-scan observations would be particularly beneficial in a rapidly evolving severe weather situation. The results from this study are consistent with the findings from the OSSE study in Yussouf and Stensrud (2010). However, the case we used for this study involves only two supercell storms. To lay a foundation for the value of the next-generation PAR technology beyond the current WSR-88D network in storm-scale modeling, more rigorous testing on how to best assimilate PAR observations in a variety of severe weather systems (e.g., quasi-linear convective systems, microbursts, hailstorms, nontornadic as well as tornadic supercell storms, etc.) is still needed. Additionally, the impact of the unique flexible adaptive scanning capability from NWRT PAR [e.g., dense vertical scanning and elevation prioritized scanning strategies; Heinselman and Torres (2011)], particularly when the storm is close to or far away from the radar, on the model analyses and forecasts also needs to be investigated. Moreover, errors in storm motion in storm-scale modeling warrant further investigation. Accurate forecasts of storm position are necessary for the skillful prediction of storm-associated hazards, a primary research goal of WoF.
Acknowledgments
The computing for this project was performed at the University of Oklahoma (OU) Supercomputing Center for Education and Research (OSCER). Thanks to Pamela Heinselman for providing the PAR observations, Chris Karstens for helping with the radar QC, and Carrie Langston for the NMQ reflectivity data. Thanks to Louis Wicker for providing very helpful suggestions and Pamela Heinselman for reviewing the paper. The constructive comments of three anonymous reviewers greatly improved the manuscript. Local computer assistance is provided by Brett Morrow, Steven Fletcher, and Robert Coggins. Partial funding for this research was provided by NOAA/Office of Oceanic and Atmospheric Research under NOAA–University of Oklahoma Cooperative Agreement NA11OAR4320072, U.S. Department of Commerce. TAS, YJ, and MX were also supported by the NOAA Warn-on-Forecast project under Grant DOC-NOAA NA080AR4320904 and by NSF Grant AGS-1261776.
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