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  • View in gallery

    Work flow and data inputs for the real-time 3DVAR system.

  • View in gallery

    The 3DVAR analysis domain on 16 May 2010. The outer box shows the area of influence for radars that are used as input into the analysis grid, which is the inner box. The circles are the 230-km-range ring from each of the listed radar sites.

  • View in gallery

    The tracks of 218 supercell thunderstorms sampled in real time during spring 2010–12.

  • View in gallery

    (a) The number of times a storm was sampled in each range band from the radar closest to the storm. Each vertical bar represents the number of storm centroids in each 10-km band. (b) Distribution of the number of radars used for the analysis of each storm cell at each time increment.

  • View in gallery

    (a) Box-and-whiskers plot of the distribution of maximum 3–6-km vertical vorticity in 10-km range bands. The dark line indicates the median, the box the interquartile range (IQR), and the whiskers 1.5 times the IQR with individually plotted outliers. (b) As in (a), but for maximum 3–7-km AGL azimuthal shear.

  • View in gallery

    (left) The 3DVAR maximum 0–2 km AGL azimuthal shear (s−1) derived from KTLX Doppler velocity and (right) the maximum 3DVAR 0–3 km MSL vorticity (s−1) accumulated over the period from 2130 to 2300 UTC 10 May 2010 in central OK. The dark blue lines indicate tornado damage paths as determined by the Norman, OK, NWS Forecast Office.

  • View in gallery

    (a) Maximum 3DVAR vorticity (3–7 km MSL) and MR–MS azimuthal shear (3–6 km AGL) for a tornado-producing storm on 19 May 2010. Vorticity (filled circles) and azimuthal shear (open circles) represent the raw data, while the lines represent the trend after smoothing with a LOESS filter. (b) As in (a), but for a supercell on 26 May 2011.

  • View in gallery

    Box-and-whiskers plot of the distribution of maximum updraft speed W in 10-km-range bands. The dark line indicates the median, the box the IQR, and the whiskers 1.5 times the IQR with individually plotted outliers.

  • View in gallery

    (left) Radar-estimated maximum hail size swath (nm) and (right) accumulated maximum updraft intensity (m s−1) for the 16 May 2010 central OK hailstorm. Data are for the 4-h period from 1900 to 2300 UTC.

  • View in gallery

    (a) Maximum updraft strength and MESH for the $500 million hailstorm that occurred on 16 May 2010 (see domain in Fig. 9). MESH (filled circles) and W (open circles) represent the raw data, while the lines represent the trend after smoothing with a LOESS filter. (b) As in (a), but for a far-range storm in SD on 16 Jun 2010.

  • View in gallery

    (left) The synthesized 3DVAR reflectivity and (right) KTLX observed reflectivity (dBZ): For each panel: (top left) vertical cross section, (bottom left) reflectivity at 4 km MSL, and (right) the near-surface reflectivity (lowest height or elevation angle) showing the location of the vertical cross section.

  • View in gallery

    (a) The UH for the entire life cycle of all storms and (b) for the tornado-producing segments of tornadic storms in the analysis. Each segment includes data 5 min prior to the Storm Data tornado start time and ends 5 min after the reported end time of the tornado to account for inaccuracies in the storm report database.

  • View in gallery

    The percentage of storm analysis time increments with updraft helicity values in each range that were associated with a tornado report. The value above each bar indicates the number of time increments for each range of updraft helicity values.

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Examination of a Real-Time 3DVAR Analysis System in the Hazardous Weather Testbed

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  • 1 * Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, and NOAA/National Severe Storms Laboratory, Norman, Oklahoma
  • | 2 NOAA/National Severe Storms Laboratory, Norman, Oklahoma
  • | 3 Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, Norman, Oklahoma
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Abstract

Forecasters and research meteorologists tested a real-time three-dimensional variational data assimilation (3DVAR) system in the Hazardous Weather Testbed during the springs of 2010–12 to determine its capabilities to assist in the warning process for severe storms. This storm-scale system updates a dynamically consistent three-dimensional wind field every 5 min, with horizontal and average vertical grid spacings of 1 km and 400 m, respectively. The system analyzed the life cycles of 218 supercell thunderstorms on 27 event days during these experiments, producing multiple products such as vertical velocity, vertical vorticity, and updraft helicity. These data are compared to multiradar–multisensor data from the Warning Decision Support System–Integrated Information to document the performance characteristics of the system, such as how vertical vorticity values compare to azimuthal shear fields calculated directly from Doppler radial velocity. Data are stratified by range from the nearest radar, as well as by the number of radars entering into the analysis of a particular storm. The 3DVAR system shows physically realistic trends of updraft speed and vertical vorticity for a majority of cases. Improvements are needed to better estimate the near-surface winds when no radar is nearby and to improve the timeliness of the input data. However, the 3DVAR wind field information provides an integrated look at storm structure that may be of more use to forecasters than traditional radar-based proxies used to infer severe weather potential.

Corresponding author address: Travis Smith, NSSL/WRDD, 120 David L. Boren Blvd., Norman, OK 73069. E-mail: travis.smith@noaa.gov

Abstract

Forecasters and research meteorologists tested a real-time three-dimensional variational data assimilation (3DVAR) system in the Hazardous Weather Testbed during the springs of 2010–12 to determine its capabilities to assist in the warning process for severe storms. This storm-scale system updates a dynamically consistent three-dimensional wind field every 5 min, with horizontal and average vertical grid spacings of 1 km and 400 m, respectively. The system analyzed the life cycles of 218 supercell thunderstorms on 27 event days during these experiments, producing multiple products such as vertical velocity, vertical vorticity, and updraft helicity. These data are compared to multiradar–multisensor data from the Warning Decision Support System–Integrated Information to document the performance characteristics of the system, such as how vertical vorticity values compare to azimuthal shear fields calculated directly from Doppler radial velocity. Data are stratified by range from the nearest radar, as well as by the number of radars entering into the analysis of a particular storm. The 3DVAR system shows physically realistic trends of updraft speed and vertical vorticity for a majority of cases. Improvements are needed to better estimate the near-surface winds when no radar is nearby and to improve the timeliness of the input data. However, the 3DVAR wind field information provides an integrated look at storm structure that may be of more use to forecasters than traditional radar-based proxies used to infer severe weather potential.

Corresponding author address: Travis Smith, NSSL/WRDD, 120 David L. Boren Blvd., Norman, OK 73069. E-mail: travis.smith@noaa.gov

1. Introduction

Radar is a fundamental tool for severe storm monitoring and nowcasting activities. Forecasters examine real-time Weather Surveillance Radar-1988 Doppler (WSR-88D) observations from multiple radars, other remote sensing tools, and severe weather detection algorithms, and also use their considerable experience and situational awareness to issue severe storm warnings. Escalating data flow rates from new sensors and applications, however, will challenge forecasters to make the best use of all the available data in warning operations unless the data are merged into a single analysis. For example, the dual-polarization upgrade to the WSR-88D network (Istok et al. 2009), completed in 2013, doubled the amount of real-time data flowing from each radar, while the Geostationary Operational Environmental Satellite-R (GOES-R) series will provide raw data at a rate 30 times that of GOES-N (Krimchansky 2010) when it goes online in the late 2010s.

Lakshmanan et al. (2007) developed a series of applications to blend data from multiple sources for use in severe weather warning operations. These multiradar–multisensor (MR–MS) algorithms and displays provide a cohesive frame of reference for observational data, such as combining reflectivity or azimuthal shear fields from multiple radar views of the same storm into one image. However, the MR–MS system does not attempt to quantify the total view of storm dynamics, such as the three-dimensional wind field, temperature, and water vapor information. We investigate the use of a real-time, weather-adaptive three-dimensional variational data assimilation (3DVAR; Gao et al. 2004, 2013) system that incorporates all available radar observations and National Centers for Environmental Prediction (NCEP) North American Mesoscale Model (NAM; Janjić 2003) products to create a dynamically consistent storm-scale analysis. In addition to helping forecasters manage an overwhelming data load, the 3DVAR systems can provide initial conditions for storm-scale numerical model forecasts.

The objective of this study is to show that it is possible to run a 3D storm-scale data assimilation in real time and to explore the value of the 3D wind analysis in a quasi-operational setting in the Hazardous Weather Testbed (HWT). The system, described in detail in Gao et al. (2013), became operational in the HWT’s Experimental Warning Program (EWP) in spring 2010, and was the subject of detailed use by forecasters during the spring 2011 and 2012 EWP sessions. During these sessions, the 3DVAR system diagnosed over 200 supercell thunderstorms throughout the United States with about 425 h of storm lifetime.

The 3DVAR real-time analysis is compared to MR–MS system output as it is widely used in the National Weather Service (NWS), in academia, and by private-sector meteorologists. Additionally, the MR–MS system will officially become operational in the National Weather Service in 2015. Rapidly updating, real-time data assimilation is the first step toward the “warn on forecast” concept proposed by Stensrud et al. (2009). NWS forecaster use and feedback on the system’s performance in the HWT is the subject of a future manuscript.

Herein, we describe the setup, functionality, and initial performance characteristics of the real-time 3DVAR system. Section 2 explains the system data flow for the assimilation and display of products in the HWT. Section 3 describes the data collected during real-time events from spring 2010–12. Experiment results are discussed in section 4. We conclude in section 5 with a summary and outlook for future work.

2. A brief description of the 3DVAR system setup

The real-time 3DVAR analysis system used in this study is described in detail in Gao et al. (2013) but is summarized here. The 3DVAR was designed especially for the storm-scale assimilation of radial wind observations from multiple radars for input into the Advanced Regional Prediction System (ARPS; Xue et al. 2000, 2001, 2003). It uses a recursive filter (Purser et al. 2003), with a mass continuity equation and other constraints incorporated into a cost function, yielding physically consistent three-dimensional analyses of the wind components and other model variables. However, because model forecasts are not involved in this study, the ARPS model itself is not used. The NAM model is used to provide the background field for the analysis, thereby incorporating environmental information within the analysis. Two analysis passes are used that have different spatial influence scales to accurately represent intermittent convective storms.

The initial setup of the real-time system included an automated control technique to select storms for analysis and tracking, as well as a user interface for manual control of the domain location. Table 1 shows the general running specifications for the real-time procedures. To coincide with the operational hours of the HWT and time restrictions caused by sharing a computation platform with other projects, the 3DVAR process ran from 1200 to 2100 central daylight time (CDT) during the 2010–12 experiments. There were four analysis domains, each of which could be controlled and recentered by an automated process or overridden by users via a web map interface. Each domain consisted of a 200 × 200 grid at 1-km horizontal grid spacing, with 31 vertical, terrain-following levels defined from nonlinear stretching via a hyperbolic tangent function, yielding an average vertical grid spacing of 400 m. The number, size, and grid spacing of the domains were selected based on available computing power. The analysis updated every 5 min, corresponding to the typical update rate of the input WSR-88D data, and processed in 3–5 min. In this initial implementation, only data from completed WSR-88D volume scans were used as input to each analysis. This added between 0 and 10 min of data latency to the computational latency. Both of these latencies may be substantially reduced with additional computing power and by adopting a virtual volume (Lynn and Lakshmanan 2002) data input technique.

Table 1.

Operational characteristics of the real-time 3DVAR system.

Table 1.

Figure 1 shows the process for creating the 3DVAR datasets. Domains were defined in one of two ways. The first method is to identify the maximum reflectivity in a two-dimensional composite reflectivity field produced by the National Severe Storms Laboratory’s (NSSL) Warning Decision Support System–Integrated Information (WDSS-II; Lakshmanan et al. 2007) for the conterminous United States (CONUS). To ensure that the four analysis domains had little overlap, the selection of the second largest value of reflectivity was required to be at least 100 km away from the location of the first largest value of reflectivity; the same requirement was then applied successively in the selection of the other domains, such that all identified locations are at least 100 km from one another (Gao et al. 2013). If desired, the area for selecting domains could be restricted to smaller than CONUS scale. The automated domains were reevaluated and recentered every 30 min. The second, preferred method to select domains was to choose them manually via a web map interface. In this case, the domains remained stationary until moved again by an operator. If there was no manual intervention after 2 h, the automated system, described in method one above, would resume control.

Fig. 1.
Fig. 1.

Work flow and data inputs for the real-time 3DVAR system.

Citation: Weather and Forecasting 29, 1; 10.1175/WAF-D-13-00044.1

Once the domain was defined, we interpolated the terrain data to the analysis grid and the NCEP operational NAM (12-km grid spacing) analysis and forecast products were interpolated onto the analysis grid in both space and time using software within the ARPS program. The terrain and NAM forecast fields provided the needed lower boundary and three-dimensional background information, respectively, for input to the 3DVAR analysis.

The next step was to determine how many operational WSR-88Ds were present within the selected domain, obtain the WSR-88D data in real time, perform quality control on the radar observations, and thin and interpolate the radar data onto the analysis grid. Figure 2 shows an example of a 3DVAR analysis domain. The 200 km × 200 km inner box is the domain to be analyzed, while the outer box is 400 km × 400 km and encompasses all of the radars used in the assimilation.

Fig. 2.
Fig. 2.

The 3DVAR analysis domain on 16 May 2010. The outer box shows the area of influence for radars that are used as input into the analysis grid, which is the inner box. The circles are the 230-km-range ring from each of the listed radar sites.

Citation: Weather and Forecasting 29, 1; 10.1175/WAF-D-13-00044.1

The 3DVAR analysis then is performed using these input data. Thus, the 3DVAR only used WSR-88D radial velocity data as input observations. Reflectivity data are not used directly in the current ARPS 3DVAR data assimilation system. Reflectivity observations instead are interpolated to the analysis grid from the observed radar reflectivity using a method similar to Zhang et al. (2005). For real-time NWP applications, the ARPS 3DVAR has often been used together with a cloud analysis scheme to analyze the hydrometeor variables and adjust in-cloud temperature and moisture fields (Hu et al. 2006). The cloud analysis is not necessary for the current application because our focus is on the internal circulation structures, including updrafts within thunderstorms. Any additional available real-time data, such as surface observations data, could also be used within this analysis with little additional computational cost but were neglected for simplicity in this initial study. In the event that radar data are missing for a given vertical analysis level, the assimilation largely defaults to the NAM forecast valid at this level (subject to modifications due to the mass continuity constraint).

The final step was the postprocessing of the resulting analyses, including identification of the position of supercells, vorticity centers, regions of upward and downward vertical velocity, and production of other products that could be effectively used by the forecasters who issue severe weather warnings. These data were provided to forecasters in the Hazardous Weather Testbed via the NWS Advanced Weather Interactive Processing System (AWIPS) software (Kingfield et al. 2013), NSSL’s WDSS-II display, and both static and dynamic imagery on a web page. In the analyses that follow, we examine these 3D wind fields and derived variables such as vertical velocity and vorticity.

3. Data and methods

The initial focus of this data collection was on the observation of the full life cycles of supercell thunderstorms. Most data used in the analysis were collected in real time, although some cases were reprocessed to account for real-time data archival errors that should not affect the 3DVAR output. A total of 218 supercell events were observed on 27 days during 2010–12 (Table 2). To be included in our dataset, a storm had to be sampled for at least 1 h in the 3DVAR domain and reached a maximum vertical vorticity of at least 0.01 s−1 in the 3–7-km above mean sea level (MSL) layer sometime during its life cycle. This threshold value was chosen as a reasonable value to identify midlevel mesocyclones. These could be associated with discrete cells or embedded in a squall line. Anticyclonic mesocyclones were not included in this dataset, but may be analyzed in a future study. The supercell storms included in the study come from a number of regions including the central and southern plains as well as the Midwest and southeast United States, ranging as far northwest as Montana and southeast as Georgia (Fig. 3). Of the storms sampled, 80% had reported severe weather in the form of a tornado, large hail, or damaging wind during the collection period. The mean storm lifetime was 117 min, with the median lifetime being 110 min with an interquartile range from 75 to 170 min. Storm analyses were captured at 5094 time increments of 5 min.

Table 2.

Twenty-seven event days for which supercell thunderstorms occurred in a real-time 3DVAR domain during spring 2010–12. The numbers of supercells, tornadic supercells, and supercells with reports of any severe weather (tornado, hail, damaging wind) are shown.

Table 2.
Fig. 3.
Fig. 3.

The tracks of 218 supercell thunderstorms sampled in real time during spring 2010–12.

Citation: Weather and Forecasting 29, 1; 10.1175/WAF-D-13-00044.1

We chose to focus on two metrics for closer examination: storm updraft strength, which is not measured by traditional single-Doppler radar analysis, and vertical vorticity, which can be indirectly estimated from a single-Doppler radar analysis. Table 3 shows a selection of several derived fields from both the 3DVAR assimilation and established WDSS-II MR–MS algorithms available for comparison (Lakshmanan et al. 2007). There should be a high correlation of 3DVAR vertical vorticity that is derived from the three-dimensional wind field to radar-based azimuthal shear (Smith and Elmore 2004) derived from single-Doppler radial velocity fields although they use slightly different vertical layers in the products: MSL, interpolated from terrain-following sigma coordinates, for 3DVAR analysis fields, and above ground level (AGL) for WDSS-II azimuthal shear fields. In addition, large vertical velocities in storm updrafts are required for the formation of large hail (Knight and Knight 2001), so we hypothesize a relationship between the 3DVAR updraft strength and the radar-estimated maximum expected size of hail (MESH; Witt et al. 1998a; Lakshmanan et al. 2007; Cintineo et al. 2012), which is essentially the vertically integrated reflectivity above the 0°C isotherm. Finally, a synthesized reflectivity field is created by a weighted blending process of nearby data from multiple WSR-88Ds using the method similar to Zhang et al. (2005), and may be compared to the MR–MS reflectivity field. NWS severe weather reports are obtained from Storm Data and matched to the supercell events via the time window method suggested by Witt et al. (1998b), with a specified window of 10 min prior to and 20 min after the report time to account for storm movement and late reports.

Table 3.

A selection of assimilated and MR–MS data fields available for real-time comparisons.

Table 3.

To make these comparisons, storm cells were identified and tracked using the w2segmotion program documented in Lakshmanan et al. (2003) and Lakshmanan and Smith (2009), postevent. Variables such as MESH, maximum reflectivity from WSR-88Ds, or the various 3DVAR products were associated with each tracked storm and extracted for the analysis. The cells were identified with a minimum w2segmotion cluster size (Lakshmanan et al. 2009) of 50 pixels (approximately 50 km2) on the synthesized reflectivity field at 5 km MSL—an elevation and cluster size at which individual cells are usually identifiable. Clusters are automatically determined from local maxima and grow outward until they reach the specified pixel size. Tracking utilized the “overlap/cost method (Han et al. 2009; Lakshmanan and Smith 2010) with a size factor of 1 and a distance threshold of 15, which performed sufficiently well on these 218 supercell storms such that no manual corrections to the tracking were needed. We use a dilation filter at the 98th percentile, with an expansion radius of 8 km on the vorticity and azimuthal shear fields to ensure overlap with the identified storm cluster, as the areas of strongest circulation were frequently located outside of the high-reflectivity areas. The maximum values within the identified cluster were recorded at each storm analysis time increment for each of the variables listed in Table 3. This process created time series of these data for the entire lifetime of each storm.

4. Results and discussion

To describe the performance characteristics of the 3DVAR system, we first compare the 3DVAR-derived products against MR–MS datasets from the WDSS-II system. Weather forecasters have used WDSS-II MR–MS products in operations at various NWS forecast offices since 2002, as well as at the Storm Prediction Center since 2006, making it a good baseline for comparison. Some representative samples of the analyses that demonstrate performance and capabilities are described below, as well as a broad assessment of the entire dataset. Results are stratified by range from the nearest radar and also by how many radars contribute to each analysis to quantify the 3DVAR performance. Finally, the time series data for each storm cell are smoothed using a LOESS filter (Cohen 1999) with a span of 35% (of the total points in the time series) to reduce noise in trends of vorticity, azimuthal shear, updraft speed, and hail size estimates.

a. 3DVAR vertical vorticity–single-Doppler azimuthal shear

Because the 3DVAR vertical vorticity and the WDSS-II single-radar azimuthal shear field [essentially an estimate of half the true vorticity; Smith and Elmore (2004)] both estimate storm rotation based on the radial Doppler wind field, they should be highly correlated for each storm. We compute Pearson’s correlation coefficient R for the 5094 storm analyses in the dataset, and use a bootstrap method (Efron and Tibshirani 1993) to determine the median and confidence interval. Calculations using the entire dataset of the 3DVAR 3–7-km MSL maximum vorticity and the WDSS-II 3–6-km AGL maximum azimuthal shear yield R = 0.66 with a 95% confidence interval of ±0.02. For the low-level rotational fields, the 3DVAR 0–3-km MSL maximum vorticity and the WDSS-II 0–2-km AGL maximum azimuthal shear calculations yield R = 0.75 with a 95% confidence interval of ±0.02. These results confirm the suspected good relationship between the two parameters.

To gain insight into how the 3DVAR vorticity values may be affected by radar-sampling issues such as beam broadening, propagation, and blockage, we split the dataset by range from the nearest radar (Fig. 4a) as well as the number of radars that were included in each of the 5094 storm analyses (Fig. 4b). Nearly all of the storm cells were within 150 km of one or more of the WSR-88Ds, and the majority of the analyses contained data from three to five radars. On the whole, there was little variation in maximum 3–7-km vorticity values between 0- and 150-km range to the nearest radar (Fig. 5a). Beyond 150 km, the number or samples was insufficient to draw any firm conclusions. This result indicates the stability of the vorticity estimates from the 3DVAR, which are clearly not greatly influenced by radar range effects. In contrast, the 3–6-km maximum azimuthal shear (Fig. 5b) showed some range dependency, especially between 0- and 60-km range to the nearest radar, although this is corrected in recent versions of the azimuthal shear algorithm (Newman et al. 2013). In general, the value of vorticity is twice the value of azimuthal shear, as indicated by theory.

Fig. 4.
Fig. 4.

(a) The number of times a storm was sampled in each range band from the radar closest to the storm. Each vertical bar represents the number of storm centroids in each 10-km band. (b) Distribution of the number of radars used for the analysis of each storm cell at each time increment.

Citation: Weather and Forecasting 29, 1; 10.1175/WAF-D-13-00044.1

Fig. 5.
Fig. 5.

(a) Box-and-whiskers plot of the distribution of maximum 3–6-km vertical vorticity in 10-km range bands. The dark line indicates the median, the box the interquartile range (IQR), and the whiskers 1.5 times the IQR with individually plotted outliers. (b) As in (a), but for maximum 3–7-km AGL azimuthal shear.

Citation: Weather and Forecasting 29, 1; 10.1175/WAF-D-13-00044.1

An individual event, the tornadic outbreak over central Oklahoma on 10 May 2010, was examined in greater detail to analyze specific differences between the 3DVAR vorticity field and the azimuthal shear field from the Oklahoma City, Oklahoma (KTLX), radar (Fig. 6). The KTLX data have a horizontal resolution of 0.5° × 250 m, so the tracks of smaller-scale circulations appear in those data while not being resolved in the 3DVAR field. Visual comparison indicates that the 3DVAR analysis filters out some bad data caused by radar radial velocity dealiasing failures (Fig. 6, top right). Because the grid spacing of the 3DVAR analysis in this case is 4 times lower than the resolution of the radar data due to the close proximity to the nearest radar, the circulation paths are much broader than for the azimuthal shear field, but the overall tracks from the 3DVAR match those from the azimuthal shear. In addition, the 3DVAR tracks are much easier to identify and appear to have less noise due to the additional smoothing inherent in the 3DVAR data processing. Although the radar-derived azimuthal shear values should, in theory, be approximately one-half the true value of the vorticity in the storm, the 3DVAR data show maximum values that are smaller than expected due to the larger grid spacing than the radar data. At this 1-km scale, the 3DVAR analysis cannot resolve a tornado, but the parent mesocyclone is identifiable. A 250-m grid-spacing 3DVAR analysis is needed, in this case, to do a direct comparison of values with the radar algorithm.

Fig. 6.
Fig. 6.

(left) The 3DVAR maximum 0–2 km AGL azimuthal shear (s−1) derived from KTLX Doppler velocity and (right) the maximum 3DVAR 0–3 km MSL vorticity (s−1) accumulated over the period from 2130 to 2300 UTC 10 May 2010 in central OK. The dark blue lines indicate tornado damage paths as determined by the Norman, OK, NWS Forecast Office.

Citation: Weather and Forecasting 29, 1; 10.1175/WAF-D-13-00044.1

Figure 6 also shows reported tornado tracks for this event. The larger-scale 3DVAR vorticity tracks match up well with the tracks of mesocyclones that occurred during the event; however, a small, shallow circulation pattern that produced a tornado rated as a category 0 event on the enhanced Fujita scale (EF0) in the NW part of the image is not well detected, possibly due to the larger grid spacing (~1 km horizontal) relative to the radar’s azimuthal sampling at near range. Again, the overall performance of the 3DVAR matches well with the tornado and mesocyclone tracks.

Although the relationship between azimuthal shear and 3DVAR vorticity was very strong overall, there was some variability from storm to storm in how well they are correlated. For instance, a well-sampled cell near the Vance Air Force Base (KVNX) radar in northwest Oklahoma from 19 May 2010 (Fig. 7a) shows similar trends for both variables (R = 0.91 with ±0.08 95% confidence interval), while a storm at far ranges (120–180 km) from several radars [Springfield, Missouri (KSGF); Paducah, Kentucky (KPAH); St. Louis, Missouri (KLSX)] in southeast Missouri on 26 May 2011 (Fig. 7b) does not have correlations as high (R = 0.02 with ±0.32 95% confidence interval). Reasons for this and other low correlating storms are uncertain, but likely are due to a number of factors. One factor is that the azimuthal shear has a distinct range dependency, whereas the 3DVAR does not. Another factor is that the 3DVAR data latency sometimes is relatively high (4–5 min) while the WDSS-II latency is low, causing the data to go out of phase. WDSS-II azimuthal shear is calculated using the latest 5-min period of data from any tilt from any radar, while the 3DVAR vorticity uses only completed volume scans. Therefore, 3DVAR data could be up to 4–5 min older than the MR–MS data for the same time stamp. Finally, storms that are at a far distance (>150 km) from any radar generally cause a lower dynamic range for both data fields, and any errors in their values result in a lower correlation. Future versions of the real-time 3DVAR system will attempt to address these issues.

Fig. 7.
Fig. 7.

(a) Maximum 3DVAR vorticity (3–7 km MSL) and MR–MS azimuthal shear (3–6 km AGL) for a tornado-producing storm on 19 May 2010. Vorticity (filled circles) and azimuthal shear (open circles) represent the raw data, while the lines represent the trend after smoothing with a LOESS filter. (b) As in (a), but for a supercell on 26 May 2011.

Citation: Weather and Forecasting 29, 1; 10.1175/WAF-D-13-00044.1

b. Updraft speed–MESH

Vertical velocity estimates from 3DVAR analyses are extremely difficult to validate given the absence of a large dataset of in situ measurements of the airflow within thunderstorms and the scarcity of multi-Doppler wind measurements. However, Nelson (1983) suggests that a broad region of moderate updraft is required to support hail growth. Updraft cross-section information was not easily accessible in this study; however, when hail is present we hypothesize that there should be at least a weak-to-moderate correlation between updraft speed (vertical component of the wind vector) and MESH if the 3DVAR vertical velocity values are reasonable estimates—or at least of the correct sign and order of magnitude.

We compare the updraft speed to the WDSS-II MESH hail size estimates to determine if this hypothesized relationship, although indirect, exists by computing Pearson’s correlation coefficient R for all analysis times. Radar-based MESH is preferable to use over NWS hail reports to give consistency and objectivity to the hail size estimates (Ortega et al. 2009). We also calculate a time-lagged value of R for both 5- and 10-min differences because hail takes time to grow after the updraft intensifies, and again we use a bootstrap method to determine median and confidence intervals. For all storm analysis time increments for maximum W and MESH, R = 0.39 with a 95% confidence interval of ±0.05, with similar performance for the 5- and 10- minute time-lagged data (R = 0.38 and 0.35, respectively), supporting some relationship between the two parameters. Values of maximum W are reasonably consistent when distributed by range from the nearest radar (Fig. 8).

Fig. 8.
Fig. 8.

Box-and-whiskers plot of the distribution of maximum updraft speed W in 10-km-range bands. The dark line indicates the median, the box the IQR, and the whiskers 1.5 times the IQR with individually plotted outliers.

Citation: Weather and Forecasting 29, 1; 10.1175/WAF-D-13-00044.1

Maximum MESH for a supercell storm over central Oklahoma for the 4-h period from 1900 to 2300 UTC on 16 May 2010 is compared to the 3DVAR maximum updraft speed for the same time period (Fig. 9). In this case, strong pulses of high vertical velocity values are coincident with MESH estimates of larger hail sizes aloft. The trends of MESH and updraft speed (Fig. 10a) are correlated at 0.78 after using a LOESS filter on the data for this case, agreeing with early research by Nelson and Young (1979). They found that supercells were prolific producers of large hail; hail was hypothesized to be related to both very strong updrafts located in the supercells and to recycling of water substance in and out of updrafts.

Fig. 9.
Fig. 9.

(left) Radar-estimated maximum hail size swath (nm) and (right) accumulated maximum updraft intensity (m s−1) for the 16 May 2010 central OK hailstorm. Data are for the 4-h period from 1900 to 2300 UTC.

Citation: Weather and Forecasting 29, 1; 10.1175/WAF-D-13-00044.1

Fig. 10.
Fig. 10.

(a) Maximum updraft strength and MESH for the $500 million hailstorm that occurred on 16 May 2010 (see domain in Fig. 9). MESH (filled circles) and W (open circles) represent the raw data, while the lines represent the trend after smoothing with a LOESS filter. (b) As in (a), but for a far-range storm in SD on 16 Jun 2010.

Citation: Weather and Forecasting 29, 1; 10.1175/WAF-D-13-00044.1

A contrasting case is a hail- and tornado-producing storm on 16 June 2010 over northwest South Dakota (Fig. 10b). The storm’s nearest approach to the closest WSR-88D radar (Rapid City, South Dakota, KUDX) was about 125 km, and the updraft speed estimated by the 3DVAR assimilation was fairly constant over the life cycle of the cell. This was in contrast to the results of MESH, which varies with the vertical reflectivity profile of the storm and shows changes in anticipated hail size. In this case, the near-surface wind field is not measured by the radar as the center of the lowest elevation angle is more than 2 km above the surface at the storm’s closest approach to radar. Thus, the 3DVAR system defaults to using the NAM forecast for the near-surface wind vector.

c. Simulated reflectivity–single-Doppler reflectivity

The focus for the initial implementation of the real-time 3DVAR system is on providing a useful three-dimensional analysis of the wind field. However, to enable visualization of where the storm is located in the assimilated grid, the reflectivity field is obtained by synthesizing and interpolating reflectivity observations from nearby WSR-88Ds using a method similar to that of Zhang et al. (2005). Figure 11 shows this synthesized reflectivity (left) alongside the observed radar reflectivity from the KTLX radar (right) for the 16 May 2010 event. At this time, the storm produced 2-in. (>50 mm) hailstones on the ground and, shortly thereafter, produced 4.25-in. (>110 mm) hail.

Fig. 11.
Fig. 11.

(left) The synthesized 3DVAR reflectivity and (right) KTLX observed reflectivity (dBZ): For each panel: (top left) vertical cross section, (bottom left) reflectivity at 4 km MSL, and (right) the near-surface reflectivity (lowest height or elevation angle) showing the location of the vertical cross section.

Citation: Weather and Forecasting 29, 1; 10.1175/WAF-D-13-00044.1

There are several differences between the modeled storm structure as diagnosed from the synthesized reflectivity and from the single-radar reflectivity observations. Because the 3DVAR assimilation occurs in near–real time and can take up to 4 min to process, there is a slight lag in storm position; for the southeastward-moving storm, the 3DVAR analysis is slightly behind the radar observation. The vertical structure shows a broader updraft core, likely due to the merging of data from multiple nearby WSR-88Ds that are not time synchronized and the 1-km grid spacing of the 3DVAR analysis. Finally, the extremely high reflectivity values that appear in the radar observations are much lower in the assimilated cloud analysis as the analysis blends data from multiple sources and is smoothed due to the lower resolution.

d. Updraft helicity

Updraft helicity (UH; Kain et al. 2008) was added to the suite of real-time products available to forecasters in the HWT for the spring 2012 experiment after several forecasters expressed interest in creating such a field during the spring 2011 experiment. UH has primarily been used for the identification of supercell thunderstorms in model forecasts. UH is the vertical vorticity multiplied by the vertical velocity and integrated over a predefined depth [e.g., 2–5 km AGL in Kain et al. (2008)]. For analysis purposes, the 2010 and 2011 data were reprocessed to include this parameter as well. Figure 12a shows the UH for the life cycle of all cells, whereas Fig. 12b contains only the tornadic portion of each cell ±5 min. Notably, the track points showing low values of updraft helicity (<100 m2 s−2) are much reduced for the tornadic cases, suggesting that supercells with higher values of UH may be more likely to produce tornadoes. Figure 13 depicts the distribution of the percentage of UH values in each range that were associated with a report of a tornado. At the top of each bar in the graph is the number of storm analyses, out of the 5094 storm analysis time increments of 5 min in the dataset, that fall within each range. As UH values increase, so does the percentage of times associated with a tornado occurrence.

Fig. 12.
Fig. 12.

(a) The UH for the entire life cycle of all storms and (b) for the tornado-producing segments of tornadic storms in the analysis. Each segment includes data 5 min prior to the Storm Data tornado start time and ends 5 min after the reported end time of the tornado to account for inaccuracies in the storm report database.

Citation: Weather and Forecasting 29, 1; 10.1175/WAF-D-13-00044.1

Fig. 13.
Fig. 13.

The percentage of storm analysis time increments with updraft helicity values in each range that were associated with a tornado report. The value above each bar indicates the number of time increments for each range of updraft helicity values.

Citation: Weather and Forecasting 29, 1; 10.1175/WAF-D-13-00044.1

These findings match well with other studies that have examined mesocyclone path lengths and the percentage of the pathlength that produce tornados. Clark et al. (2013) used a 10 m2 s−2 threshold with a requirement that at least one pixel in the area meet a 60 m2 s−2 UH threshold to identify possible mesocyclones in a 1.25-km grid-spacing 3DVAR dataset from 27–28 April 2011. In their data, 26% of track lengths of this intensity were associated with tornado reports. Although there is some overlap between the Clark et al. dataset and the one used here (this dataset contains approximately 10 times as many storm analysis time increments) and the use of different methods to identify supercells, the percentage of time increments exceeding 100 m2 s−2 in these data producing a tornado was also 26%. Yet another study using a different technique, an analysis by Trapp et al. (2005) using the WSR-88D Mesocyclone Detection Algorithm (Stumpf et al. 1998), also suggests that 26% of mesocyclone detections produce tornadoes. Mesocyclone algorithm detections can be equated to pathlength since they each represent a 5-min radar volume scan and the distance the storm moved in that time. The exact value of 26% is coincidental between these studies; however, the relationship warrants further investigation.

5. Summary and future work

The experimental real-time 3DVAR assimilation system provides a continuously updating, dynamically consistent estimate of the three-dimensional wind field in and near severe thunderstorms—something that is not currently available to operational forecasters. In addition to providing observational guidance to forecasters, the assimilated data fields can be used to initialize storm-scale forecast models, as proposed for the warn-on-forecast project (Stensrud et al. 2009).

Analyses of the 3DVAR updraft strength and vorticity for a dataset of 5094 analyses collected between 2010 and 2012 show that the 3DVAR vorticity value trends compare well with the azimuthal shear, with vorticity values typically twice as large as azimuthal shear as expected from theory. Mesocyclone tracks from the 3DVAR also correspond well to mesocyclone tracks from azimuthal shear, with the 3DVAR tracks being less noisy and easier to visually identify. This initial examination indicates that mesocyclones are typically observed well by the 3DVAR for nearly all ranges. Close to the radar, the 3DVAR vertical velocity is related to estimated hail size from MESH. However, poor radar resolution may result in weaker-than-expected vertical velocity values when a storm is located at long range from all radars, as the assimilation defaults to the NAM forecast when radar data are missing for a given vertical analysis level. Calculations of updraft helicity indicate that this parameter may be useful for assessing tornadic potential of individual supercells, although additional study is needed. The addition of surface observations and cycling the model—using a 5-min storm-scale forecast for the next model assimilation background conditions instead of the NAM—should improve the wind estimates at longer ranges from radar and enable reliable estimates of the thermodynamic properties of storms such as vertical temperature and moisture profiles. Cycling allows for the development of low-level outflow from the predicted storm, potentially leading to improvements in storm conditions below the lowest radar elevation angle.

Because radar coverage is inconsistent within the WSR-88D network, the analysis may not perform equally well in all areas of the United States. These performance differences should be quantified to show how the radar coverage affects the quality of the assimilated data fields. Although our initial focus is on quantifying the behavior of supercell events, we hope to expand the scope of future studies to include other severe-weather-producing storms as well, such as short-lived convective cells and mesoscale convective systems.

Finally, and importantly, NWS forecasters, alongside severe storm researchers tested the system during simulated warning operations in NOAA’s Hazardous Weather Testbed during 2011 and 2012. The feedback they provided will be used to improve the selection of products available from the model, and to help evolve the warning decision-making process from one that relies on the ability of forecasters to rapidly mentally blend data from many sources into one that provides an integrated view of storm dynamics and thermodynamics.

Acknowledgments

Funding was provided by NOAA/Office of Oceanic and Atmospheric Research under NOAA-University of Oklahoma Cooperative Agreement NA11OAR4320072, U.S. Department of Commerce. We thank the anonymous reviewers for their thoughtful comments. Special thanks go to Karen Cooper and Jeff Brogden for their assistance with real-time data processing, and to Brett Morrow and Steve Fletcher for system support.

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