1. Introduction
The upgrade of the Weather Surveillance Radar-1988 Doppler (WSR-88D) with polarimetric capabilities continues to fuel a resurgence in microphysical studies of precipitating systems. The transmission/reception of orthogonally polarized waves by these radars has provided a wealth of new information regarding the characteristics of hydrometeors within precipitating systems. In turn, forecasters have access to improved radar-based hydrometeor classification (e.g., Park et al. 2009) and quantitative precipitation estimation (e.g., Giangrande and Ryzhkov 2008) algorithms. For a detailed overview and discussion regarding commonly used polarimetric radar variables, including radar reflectivity factor at horizontal polarization ZH, copolar cross-correlation coefficient ρhv, specific differential phase KDP, and differential reflectivity ZDR, the reader is referred to Doviak and Zrnić (1993), Bringi and Chandrasekar (2001), and Kumjian (2013a,b,c).
Perhaps more importantly, this new information can highlight microphysical processes that reveal critical details about the evolution of precipitating systems such as thunderstorms. Polarimetric radar data can be used to identify changes in the hydrometeor distribution within various parts of a storm, potentially signaling imminent convective growth or decay. For example, polarimetric radar can distinguish between drops of different sizes—most notably via ZDR (Seliga and Bringi 1976)—providing the ability to investigate microphysical processes in greater detail. ZDR is proportional to the aspect ratio of hydrometeors that are small relative to the radar wavelength. Moreover, the magnitude of ZDR increases with increasing dielectric constant for a given particle size and shape. However, pure raindrops have a steady dielectric constant, and their axis ratio increases monotonically (i.e., they become more oblate) as their size increases (e.g., Pruppacher and Beard 1970; Brandes et al. 2002). Therefore, operational ZDR data have great utility for analyzing estimates of bulk drop size distributions when used in conjunction with other radar variables.
Owing to their spherical shape, small drops tend to be characterized by ZDR near 0 dB. At S band (WSR-88D wavelength; approximately 10–11 cm), ZDR can increase to near 5 dB for the largest drops (around 8 mm in diameter). For hydrometeors that are large relative to the radar wavelength, ZDR can fluctuate wildly and may no longer be proportional to the hydrometeor aspect ratio, due to resonance scattering (Trömel et al. 2013). In turn, characterizing hydrometeor shape via ZDR is considerably more difficult when resonance scattering is present. However, even the largest raindrops can be considered sufficiently small relative to the radar wavelength when using S-band data. The work presented herein focuses purely on S-band radar data, such that ZDR is utilized heavily to analyze raindrop sizes in a bulk sense.
a. Size sorting
Raindrop size sorting is a ubiquitous feature of precipitating systems. Generally, as raindrops increase in size, so does their terminal fall speed. As a result, raindrops with different sizes can take considerably different trajectories, which are sensitive to the airflow patterns within a precipitating system (Marshall 1953; Gunn and Marshall 1955; Kumjian and Ryzhkov 2012; Dawson et al. 2015). In the simplest form of size sorting, the onset of precipitation occurs when cloud droplets grow large enough to fall toward the ground, while smaller droplets remain suspended. Extending this concept further, large drops reach the surface prior to small drops beneath a nascent precipitating cloud, due to the greater terminal velocity of the large drops. A common anecdote related to such sorting is the initial “splat” of big drops often observed underneath a growing cumuliform cloud. Figure 1 offers an example (via a radar cross section) of this initial differential sedimentation in developing cells.
(left) Cross sections and (right) associated 1.8° elevation scans of (a) ZH and (b) ZDR. Note the higher values of ZDR annotated in double black lines at the bottom of the developing precipitation core. These values represent initial sedimentation of larger drops—a common size sorting occurrence. The 40- and 50-dBZ contours are overlaid on ZDR for reference.
Citation: Weather and Forecasting 33, 5; 10.1175/WAF-D-18-0025.1
Such a signature is fairly transient and vanishes once smaller drops begin to reach the surface. In general, this size sorting signature due to initial differential sedimentation lasts no more than 5–10 min, with ZDR decreasing as more smaller drops contribute to the total backscattered signal at lower-elevation radar scans (Kumjian and Ryzhkov 2012). However, the polarimetric signature of size sorting can be sustained for much longer periods of time via the presence of strong upward motion, such as a convective updraft. Only large drops with terminal velocities exceeding that of the updraft speed descend toward the ground, while smaller drops can be suspended, lifted upward, or detrained from the updraft. The resultant drop size distribution (DSD) at low to midlevels (from the surface to several kilometers aloft) is then skewed toward larger raindrops, with fewer small drops present. Thus, a sustained size sorting signature can serve as a proxy for maturing updraft location, potentially portending near-term cell propagation and intensification. Such information has large implications for the operational convective warning process.
Perhaps the most notable and documented polarimetric signature of updraft-induced size sorting is the ZDR column (e.g., Illingworth et al. 1987; Caylor and Illingworth 1987; Wakimoto and Bringi 1988; Bringi et al. 1991; Conway and Zrnić 1993; Brandes et al. 1995; Jameson et al. 1996; Hubbert et al. 1998; Smith et al. 1999; Kennedy et al. 2001; Loney et al. 2002; Kumjian and Ryzhkov 2008; Kumjian et al. 2012, 2014; Snyder et al. 2015). A ZDR column is the by-product of large drops being lofted by an updraft above the environmental freezing level [see Kumjian et al. (2014) for a summary of the mechanisms driving drop growth]. Stronger updrafts can result in a columnar layer of positive ZDR extending several kilometers beyond the 0°C level (Kumjian and Ryzhkov 2008). As a result, the ZDR column can be used as a proxy for updraft location and perhaps strength (with taller/broader columns potentially suggesting a more robust updraft), making it a favorable tool for convective nowcasting. These signatures are often observed emanating upward from a “foundation” of anomalously high ZDR (for the associated range gate value of ZH) beneath the 0°C level, which is the lower-level size sorting signature described in the previous paragraph. Figure 2 presents an example of a ZDR column signature extending upward from a zone of high ZDR beneath the 0°C level.
(left) Cross sections and (right) associated 4.0° elevation scans of (a) ZH and (b) ZDR. Note the higher values of ZDR extending above the 0°C level represent the ZDR column, which is the result of liquid drops and liquid-coated ice particles lofted by an updraft.
Citation: Weather and Forecasting 33, 5; 10.1175/WAF-D-18-0025.1
Strong horizontal flow can also sustain size sorting of hydrometeors (Kumjian and Ryzhkov 2012; Dawson et al. 2014). Nonzero storm-relative flow horizontally advects raindrops away from the parent cloud. Since larger drops descend more rapidly than smaller drops, there is less time for downstream advection by the storm-relative wind. Therefore, a stronger storm-relative wind field (over the depth of the sorting layer) will cause a more apparent radar size sorting signature.
In the case of a storm-relative wind field that changes direction with height, size sorting may manifest via the ZDR arc signature (Kumjian and Ryzhkov 2009, 2012), which appears on the forward-flank reflectivity gradient along the inflow region of a supercell. Here, the drop size distribution can be characterized by a relatively low number of larger drops (and water-coated ice particles) and a lack of smaller drops (which have been advected farther downstream in the forward-flank region). In turn, the signature is characterized by significant, positive ZDR values (generally greater than 2–3 dB) collocated with low to moderate reflectivity (around 30–40 dBZ or less).
Dawson et al. (2014) found that this signature is related to the mean storm-relative wind vector over the depth of the precipitation shaft above the layer containing the signature. Thus, as the magnitude and shape of the signature are correlated with the strength and direction of the storm-relative wind field, this signature can reveal critical information regarding the near-storm environment—specifically, the likely presence of storm-relative helicity favorable for low-level mesocyclogenesis. While such a capability does not offer explicit prediction of tornadogenesis, it can signal a near-storm environment favorable for tornadogenesis. Robust automated detection of this signature would likely benefit operations considerably.
b. Operational application
Recent numerical simulations incorporating either bin or bulk microphysical schemes have illustrated the diagnostic potential of these polarimetric size sorting signatures (Kumjian and Ryzhkov 2009; Jung et al. 2010; Kumjian and Ryzhkov 2012; Dawson et al. 2014; Kumjian et al. 2014; Dawson et al. 2015; Snyder et al. 2015), highlighting the need for their incorporation into operational radar analysis procedures. Moreover, observational studies have confirmed the operational applicability implied by these simulations. For example, ZDR columns have exhibited a positive lagged correlation with reflectivity-based metrics (e.g., the ratio of the 60-dBZ volume to the 40-dBZ volume; Picca et al. 2010; Kumjian et al. 2014). Such work suggests that ongoing warning operations research should focus on the creation and implementation of algorithms that capitalize on the microphysical clues offered by polarimetric radar.
Snyder et al. (2015) developed an automated ZDR column algorithm that detects these signatures and outputs a maximum height for each detection, providing a diagnostic tool for assessing updraft evolution. At closer ranges from radar, the algorithm has exhibited skill in assessing updraft strength with more robust, organized cells. Such next-generation radar algorithms can enable more operational meteorologists to utilize the powerful diagnostic capabilities of polarimetric radar. These algorithms lessen the “data overload” of several new variables by synthesizing polarimetric data into one clear output—in this instance, a ZDR column height that serves as a proxy for updraft location and strength.
However, at farther distances and with weaker, less organized convection, the zone of lofted drops above the 0°C level becomes small relative to the radar’s effective beamwidth, resulting in a backscattered signal that can easily be masked by other hydrometeors in the range bin. Therefore, ZDR columns can become quite subtle or even nonexistent, such that their utility often decreases with more distant and/or shallower convection. Future work may be able to quantify the decrease in skill via objective verification of ZDR columns across a wide distribution of ranges from radar.
Updraft-related size sorting does not only occur above the 0°C level, as previously described. Raindrop sorting also occurs within and near updrafts at lower elevations. Thus, radar signatures of low-level size sorting can supplement ZDR columns by offering valuable information regarding convective evolution at altitudes where improved spatiotemporal radar coverage typically exists. Figure 3 exhibits the utility of the low-level size sorting signature in terms of nowcasting convective evolution.
The 0.5° PPIs from the Goodland, KS (KGLD), radar of (a) ZH and (b) ZDR at 0133 UTC and (c) ZH at 0138 UTC 8 Aug 2015. Note the high values of ZDR (>3 dB) associated with ZH around 25–35 dBZ in (a) and (b). Five minutes later, there is a dramatic increase in ZH.
Citation: Weather and Forecasting 33, 5; 10.1175/WAF-D-18-0025.1
Despite this capability, the low-level signature can be more difficult to identify (relative to the ZDR column), as ZDR is generally higher everywhere beneath the melting layer (due to the dominance of liquid scatterers, biota, and so on with intrinsic positive ZDR) than it is above the melting layer. Whereas there is often high contrast between a ZDR column and the ambient background ZDR, the contrast between a low-level size sorting signature and its background ZDR tends to be much lower. Considering the nowcasting utility of this low-level signature, we are motivated to develop an algorithm that highlights all zones of hydrometeor size sorting (both low-level and ZDR columns) and provides some quantitative detail regarding the magnitude of sorting. Such an algorithm would likely reduce the analysis load on radar operators while simultaneously enhancing their ability to synthesize polarimetric data with more conventional datasets (e.g., reflectivity, velocity). Subsequently, it would supplement radar operators’ ability to nowcast convective evolution.
Paramount to this improvement would be the algorithm’s capability to highlight imminent cell propagation and intensification trends (on the order of 0–10 min). Forecasters frequently encounter convective situations in which they must rapidly construct a downstream warning area (e.g., polygon) to alert the public or clients in a timely manner. In turn, a warning forecaster must quickly assess cell evolution and synthesize radar and mesoscale data to predict near-term storm motion. A key component of this motion is cell propagation (e.g., deviant movement in supercells, upshear/downshear MCS propagation), and such trends are not always clear in conventional datasets. With improved visualization of these trends, forecasters could better anticipate overall storm motion and more appropriately tailor the size and shape of short-fused storm-based warnings. Additionally, decision support meteorologists could offer even greater detail on the forecast timing and location of convective impacts.
2. Algorithm overview
The size sorting identification algorithm described in this paper utilizes polarimetric data from operational WSR-88D sites to estimate the magnitude of size sorting via a rapidly updating product (on the order of 2 min), which will be described later in this work. Hereafter, this algorithm is referred to as the Thunderstorm Risk Estimation from Nowcasting Development via Size Sorting (TRENDSS). The TRENDSS algorithm and its preprocessing routines are managed within the Warning Decision Support System–Integrated Information (WDSS–II; Lakshmanan et al. 2007) software framework.
a. Preprocessing
First, Level-II radar data are ingested into WDSS–II to generate Level-III polarimetric data that are equivalent to radar fields produced by the WSR-88D radar product generator. This produces smoothed ZDR and ρhv fields and estimates the heights of the melting layer top and bottom from the melting layer detection algorithm (MLDA; Giangrande et al. 2008). By smoothing the original Level-II data (from 0.5° to 1° azimuthal resolution via a linear combination), the reduction in variance within these radar fields makes them more suitable for algorithm processing. After this step, the ZH data are quality controlled using a reflectivity quality control algorithm (Lakshmanan et al. 2007, 2010) to remove returns from nonhydrometeors (e.g., filter clutter, biota). The smoothed ZDR, ρhv, MLDA, and quality controlled ZH fields are the four radar inputs into the TRENDSS algorithm. As a backup to the MLDA and to provide the TRENDSS algorithm with a first-guess field of the melting level and a ceiling to stop data collection, the environmental 0° and −10°C levels are derived from the 13-km Rapid Refresh (RAP; Benjamin et al. 2016) model, serving as the fifth and final algorithm input.
b. Algorithm core
Fundamentally, the TRENDSS algorithm aims to identify radar gates representative of raindrop size sorting signatures. As previously discussed, such signatures are characterized by ZDR that is anomalously high for the corresponding value of ZH in a range gate. Thus, some ZH–ZDR relationship must be constructed to identify anomalously high ZDR values. To do so, TRENDSS first filters range gates that may be dominated by scatterers deemed unsuitable for analysis. Various ZH, ZDR, and ρhv thresholds are utilized, with the specific values dependent upon the position of the gate relative to the melting layer (determination of microphysical layers and resultant algorithm “stages” discussed later in this section). Table 1 offers specifics regarding these thresholds.
Various thresholds for different radar variables and microphysical layers are presented. Range gates passing these criteria are retained for analysis by the TRENDSS algorithm.
All thresholds were determined via a heuristic process in which numerous cases from a diverse set of regions and seasons were analyzed (Table 2). For all gates, regardless of height, only ZDR <6 dB is considered suitable for analysis. While ZDR values above this threshold could be associated with meteorological scatterers (and potential size sorting), the possibility of nonmeteorological contamination (insects, birds, etc.) increases considerably with such high values (e.g., Wilson et al. 1994). Below the melting layer, a ≥15-dBZ ZH threshold was chosen to further reduce contamination from biota and other weak returns with potentially questionable data quality. Additionally, a ≥0.9 ρhv threshold was utilized, which serves to filter nonmeteorological scatterers and non-Rayleigh scatterers (e.g., larger melting hailstones), which may have a wildly fluctuating ZDR.
Events analyzed to define the TRENDSS radar parameter thresholds. The four events used to validate the TRENDSS algorithm are marked with an asterisk (*).
Within and above the melting layer, the ZH threshold is increased to 25 dBZ to reduce contributions from ice crystals, which can exhibit high ZDR and modest ZH, yet are not necessarily indicative of storm intensification. The ρhv threshold is also further tightened within and above the melting layer, where the lower bound increases to 0.98 and 0.97, respectively, to mask ice crystal contamination. The threshold is slightly higher within the melting layer, as isolated gates characterized by very high ZDR (likely composed of initially melting snow) still exhibited ρhv values around 0.95–0.97 during subjective case analysis. Consistent with ice crystal gates, we do not wish to highlight these gates, owing to the low probability they are associated with size sorting.
There of course remains considerable uncertainty regarding hydrometeor distributions and the corresponding observed polarimetric values within range gates. As such, these filtering values may at times under- or overcensor data; however, prior literature and analysis of TRENDSS output from numerous cases suggests these current values are suitable for operational use. Additionally, future iterations of the algorithm could use dynamic threshold values that more appropriately filter bins unsuitable for analysis. For example, these values could be sensitive to the estimated precipitation regime (e.g., tropical, continental).
With the remaining gates now deemed suitable for processing, TRENDSS approximates up to three ZH–ZDR relationships for each elevation scan. These three relationships consist of one below the melting layer (stage 1), one within the melting layer (stage 2), and one above the melting layer (stage 3). Radar range gates are classified into one of these stages based upon output from the MLDA with the RAP serving as a backup. These three stages are distinct from one another such that the estimated ZH–ZDR relationships are at least modestly tailored to the layer being analyzed. For example, ZDR within stage 3 is less likely to increase with increasing ZH due to the predominance of frozen scatterers. Meanwhile, ZDR typically exhibits a monotonic increase with increasing ZH in stage 1. Blending data from these stages would result in an estimated relationship that is less representative of the precipitation regimes of all range gates.
At all three stages, we are confident that the majority of TRENDSS detections will be associated with size sorting. The well-established nature of the ZH–ZDR relationship below the melting layer, combined with the filtering thresholds described above, ensures that low-level detections are very likely from updraft-enhanced sorting, differential sedimentation, or strong storm-relative flow. Our motivation to extend the TRENDSS domain to colder temperatures (i.e., within/above the melting layer) is based in our desire to extend ZDR anomalies to the problem of ZDR column identification. Thus, future iterations of the algorithm could potentially predict cell intensification via an integrated height product. For the current iteration, we still retain the three-stage approach. Although this does open the algorithm to false detections from, for example, ice crystals (discussed in further detail in section 4), the filtering thresholds within/above the melting layer are quite strict and were shown to reduce false detections considerably in heuristic testing. Moreover, increasing the domain’s vertical coverage increases the likelihood that size sorting will be identified in regions with poor radar coverage and that these identifications will be maintained during smoothing/postprocessing.
Within stage 3, expected ZDR is set to 0 dB, as most frozen Rayleigh scatterers have intrinsic ZDR near this value. Additionally, for all stages and bins, the default standard deviation is set to 0.5 dB, which was found to be sufficiently representative for most continental convection in our subjective analysis of over 20 cases (Table 2). Indeed, this value differs only slightly from the expected standard deviation of 0.2–0.3 dB theorized by Ryzhkov et al. (2005). Similar to concerns on a singular ZH–ZDR equation, these values are not optimized for all situations, but in the brief instances of very isolated, developing convection (in which only a few samples are available), they provide some framework for identifying anomalously high ZDR.
Following the initial relationship approximation, TRENDSS then enters an application step, in which a ZDR anomaly value is calculated for each valid range gate (thresholds in Table 1). This value is simply the difference between the range gate ZDR and the expected ZDR, which is a function of the ZH bin. TRENDSS normalizes this anomaly by 1σ (also a function of the ZH bin). For example, the solid line in Fig. 4 represents 3σ above the expected ZDR (the dashed line). Higher values suggest a greater likelihood that the range gate is characterized by ongoing size sorting, potentially signaling the presence of an updraft and/or ZDR arc signature. Thus, this normalized anomaly value is the fundamental output of TRENDSS. Figure 5 is an example of ZH, ZDR, and resultant normalized anomaly data from one elevation scan.
A hexbin plot representing filtered ZH and ZDR data from a 5.0° elevation scan by the Sterling, VA (KLWX), radar at 0331 UTC 1 Jul 2015. The frequency of ZH–ZDR points falling in each hexagon is represented by its corresponding color. The dashed green and solid blue lines indicate the expected/mean ZDR and three standard deviations above the mean, respectively, for each 5-dB bin. Note the points above the blue line—TRENDSS considers these to be size sorting gates.
Citation: Weather and Forecasting 33, 5; 10.1175/WAF-D-18-0025.1
The 23 Jun 2015 0.5° scans from the Sterling, VA (KLWX), radar of (a) ZH, (b) ZDR, and (c) standardized ZDR anomalies. Note the higher anomaly values along the leading edge of convection. These are stronger indications of size sorting.
Citation: Weather and Forecasting 33, 5; 10.1175/WAF-D-18-0025.1
While there is no clear anomaly threshold that can isolate size sorting gates across an array of precipitation regimes, analysis of over 20 cases (Table 2) across diverse geographic regions, seasons, and precipitating regimes suggests a threshold value around 3σ has the greatest utility in highlighting size sorting gates. To further solidify this conclusion, our objective verification discussion below (section 3) includes analysis of values starting at 1σ.
To minimize false detections (potential causes discussed in section 4), a median filter is implemented on each elevation scan to reduce the presence of noisy data as well as to smooth and emphasize zones of legitimate size sorting. Range gates beyond 20 km from a WSR-88D were smoothed with a three-by-three median filter window (i.e., replacing the central range gate with the median value of its adjacent eight gates). At ranges closer than 20 km where radar gate widths are smaller, the window size is increased to five-by-five (25 total gates) to boost the magnitude of smoothing. This aids in mitigating noisy data and false detections (e.g., initially unfiltered clutter, biota) that are more prevalent closer to the WSR-88D in nonmountainous regions (e.g., Hubbert et al. 2009).
c. Multiradar design
With TRENDSS operating on all elevation angles of a volume scan, the wealth of additional data can be considerably difficult to integrate into established radar analysis and warning-decision processes of various users (National Weather Service offices, TV meteorologists, air traffic control, etc.). Therefore, TRENDSS incorporates data from multiple radars to produce one primary product (discussed below) that can reduce workload on users. The algorithm core operates uniquely on each elevation scan of every WSR-88D within a specified domain. In this manner, ZH–ZDR relationship data are not blended among different radars, which would likely hinder the algorithm’s ability to identify size sorting. For example, if all ZH–ZDR pairs are blended into only a few relationships, varying ZDR biases among different radars would produce large standard deviation values (for each ZH bin), precluding the algorithm from highlighting anomalously high ZDR values. Section 4 expands on TRENDSS’s immunity to ZDR miscalibration.
Each valid range gate within the specified domain contains spatial information attributes, such that a three-dimensional volume of ZDR anomaly data is available across the entire domain. For consistency with the approximate volume scan time of a single WSR-88D (when it is operating in a standard convective precipitation mode), TRENDSS maintains data points within this volume if its associated elevation scan timestamp is no more than 5 min old. Thereafter, the data are discarded. Those data within 5 min of the current time are composited onto a Cartesian grid of 0.01° latitude × 0.01° longitude spacing at 2-min intervals. In other words, the maximum value in a vertical column above each grid box is mapped to a single planar view every 2 min. These composited data compose the primary TRENDSS product tested below. Figure 6 offers an example of the mosaicked product from 23 June 2015 in the Mid-Atlantic (one of the four cases chosen for objective verification below).
The 23 Jun 2015 (a) composite reflectivity at 2227 UTC, (b) composite reflectivity and TRENDSS at 2227 UTC, and (c) composite reflectivity at 2248 UTC. Note the TRENDSS identifications near the gap in reflectivity in (b), followed by the expansion of reflectivity in this area shown in (c).
Citation: Weather and Forecasting 33, 5; 10.1175/WAF-D-18-0025.1
3. Objective verification and case examples
In addition to the subjective analysis performed on cases in Table 2, four cases were chosen for more rigorous objective testing. We selected these cases to test TRENDSS’s performance across a diverse range of regions, convective regimes, and cell modes to collect insight regarding the algorithm’s ability to predict convective trends on warning/nowcast time scales. Subsequently, this insight can mold best practices for potential operational implementation within the National Weather Service and other members of the weather enterprise.
We chose the 23 May 2015 southern Great Plains case for its large areal coverage and diverse convective modes. Additionally, the regime was considerably more tropical in nature than is typical for the region, with the 0000 UTC 24 May 2015 Norman, Oklahoma, sounding sampling 44.48 mm of precipitable water. According to SPC sounding climatology (Rogers et al. 2014), this value is the record maximum for the date. The 23 June 2015 Mid-Atlantic case was selected to test a high-impact convective system along the East Coast (NOAA/NCEI 2015), while the 8 August 2015 High Plains case was chosen for both its diversity in convective modes and its aviation implications—a Delta Air Lines flight encountered a rapidly developing updraft over Nebraska and experienced significant hail damage, necessitating an emergency landing in Denver (NTSB 2015). Last, the 8 September 2015 California case was chosen for its unique geographic region and terrain influence.
For each case, we used the closest hourly 13-km RAP analysis grid to calculate the mean wind field across the cloud-layer depth by averaging the U and V components at all available levels between the lifted condensation level (LCL) and equilibrium level (EL; Fig. 7a). At each 2-min time interval, three sets of TRENDSS objects were identified by region growing (Jain 1989) contiguous areas starting from a seed grid cell with a minimum TRENDSS value of 1, 2, or 3σ (Fig. 7b). A 10-min forecast plume polygon was created by advecting the TRENDSS object downstream along the mean wind direction vector (Fig. 7c). The Multi-Radar Multi-Sensor (MRMS; Smith et al. 2016) reflectivity at lowest altitude (RALA) product was used to define thunderstorm intensity. It is defined as the closest reflectivity value to Earth’s surface that is not terrain blocked and is used by forecasters to diagnose precipitation intensity near the ground. RALA values at t = 0 min were collected to quantify the initial state of each plume (Fig. 7d). The final state of each plume was determined by spatially accumulating the maximum RALA measured in each grid cell over the next 10 min (Fig. 7e). By comparing these two states, we can quantify the relationship between TRENDSS objects exceeding certain σ thresholds and patterns in convective development.
An automated workflow to verify the TRENDSS algorithm. The (a) mean wind field over the cloud-layer depth and (b) TRENDSS objects exceeding 1, 2, or 3σ (shown here) are used to create 10-min polygons of forecasted storm location. A comparison of the (d) RALA values at t = 0 min to the (e) spatially accumulated RALA values at t = 10 min allows for an evaluation of the effectiveness of different TRENDSS sigma levels at nowcasting downstream convective maintenance and intensity.
Citation: Weather and Forecasting 33, 5; 10.1175/WAF-D-18-0025.1
Objective analysis
Despite being chosen from diverse geographical regions and over a span of several months, TRENDSS objects of at least 3σ exhibited skill in all four cases tested. These four cases encompassed 32 292 individual cell objects, from which RALA plumes were generated 10 min downstream. In 30 977 of these cases (~95.9% of total), the median RALA within a 10-min plume was equal to or higher than the initial median RALA. Additionally, 16 614 objects (~51.4%) exhibited an increase in median RALA by at least 5 dBZ. Figure 8 displays this bulk signal, suggesting that TRENDSS objects can be a reliable predictor for nowcasting downstream maintenance and/or intensification of reflectivity.
Scatterplots and related histograms where each data point represents a single TRENDSS object and related downstream plume (characterized by a maximum TRENDSS value and the change in median RALA over 10 min). Points to the right of the dashed black line in each plot correspond to objects with a maximum TRENDSS value exceeding 3σ. The cases are (a) 23/24 May, (b) 23 Jun, (c) 8 Aug, and (d) 8 Sep 2015. For more details on these cases, see Table 2.
Citation: Weather and Forecasting 33, 5; 10.1175/WAF-D-18-0025.1
Lowering the threshold to 1σ produced an additional 47 904 objects, of which 43 975 (~91.8%) also preceded a change in median RALA of at least 0 dBZ. Initially, these statistics might suggest lowering the threshold to improve algorithm performance. However, only 12 566 of these objects (~26.2%) preceded an increase of at least 5 dBZ. Figure 8 shows clustering of sub-3σ objects around lower values of median RALA difference. Meanwhile, higher values exhibit a slightly greater likelihood of convective maintenance and/or intensification. Therefore, lower-σ objects appear to lack a worthwhile signal for downstream propagation/intensification, especially considering the large increase in data that forecasters would have to consider if the threshold is lowered.
Of note, the fourth case (Fig. 8d) represents orographically enhanced convection over Southern California. Convective cells and their associated TRENDSS objects remained somewhat sparser than they were with the other three cases, resulting in a reduction of data points and making any relationship between maximum values and reflectivity changes more difficult to ascertain. Furthermore, we acknowledge that changes of approximately 5–10 dBZ do not seem noteworthy; however, considering the large number of objects for each case (on the order of thousands), even a modest increase in median value suggests a consistent signal for intensification.
To further investigate this relationship, maximum TRENDSS values were binned to produce univariate kernel density estimate (KDE) plots of the changes in median RALA value (Fig. 9). The KDE plots utilized a Gaussian kernel and Scott’s method (Scott 1992) for determining bandwidth size. In the first three cases (Figs. 9a–c), the peak of each curve moves from near 0 dBZ to approximately 5 dBZ, once again highlighting a modest positive correlation between TRENDSS values and the downstream evolution of reflectivity. Meanwhile, the fourth case (Fig. 9d) exhibits only a very weak relationship, which is likely caused by fewer samples increasing uncertainty with the density estimates, especially at higher maximum TRENDSS values.
Kernel density estimates of the 10-min change in median RALA, binned by maximum TRENDSS value, for (a) 23/24 May, (b) 23 Jun, (c) 8 Aug, and (d) 8 Sep 2015. The probabilities range from 0 to approximately 0.15. For more details on these cases, see Table 2.
Citation: Weather and Forecasting 33, 5; 10.1175/WAF-D-18-0025.1
Overall, TRENDSS appears to be a reliable identifier of size sorting and the propagation component of storm motion. Our testing methods considered the advection component of storm motion (via the 10-min plume based on mean convective layer wind), such that the addition of the propagation component (via the actual TRENDSS object) offers a robust estimate of total storm motion. Indeed, these results lend confidence in the algorithm’s ability to assist in the nowcasting of storm motion. Regarding prediction of cell intensification, our verification methods imply that compositing size sorting identification (in the manner of TRENDSS) possesses some skill in forecasting very near-term strengthening. Nonetheless, future observational/model analyses comparing the estimated magnitude of sorting with updraft velocities are needed to further elucidate this relationship. Furthermore, size sorting from processes other than updrafts, while much less common, will be highlighted by TRENDSS. For example, size sorting within a ZDR arc signature will frequently be identified, and this signature is not indicative of cell propagation/intensification (although it can signal increasing storm-relative helicity, which influences propagation). Benefits of such identification are discussed in section 4.
We acknowledge that uncertainty exists in this analysis, as some cases may be impacted by unrelated convection moving through the downstream plume of the original object. Thus, we constrained the plume to only 10 min downstream, with a buffer of 1 km to focus on very near-term cell propagation. By constraining the plume to 10 min, we also reduce the potential for persistent, deviant propagation to undermine our verification methods. In other words, the 10-min plume is testing propagation predicted by the specific TRENDSS object identified at t = 0. A longer plume would likely require more sophisticated object tracking (and more dynamic plume generation) to maintain robust verification methods. While we did not perform such an analysis, future work could investigate the temporal continuity of TRENDSS objects, perhaps offering new avenues for storm motion prediction. Finally, we aimed to avoid “cherry picking” by automating the identification of TRENDSS objects and downstream plume creation.
Another consideration is that our verification methods do not account for missed events (i.e., we do not identify storms without TRENDSS objects). Although we are certain that some storms do intensify without radar identification of size sorting (e.g., due to masking of sorting gates), our subjective analysis of the cases in Table 2 indicates that cells are not as likely to maintain or increase intensity if their corresponding standardized ZDR anomalies remain below 3σ. However, future analysis of the performance of TRENDSS should more formally investigate cells that lack size sorting signals.
4. Algorithm strengths and weaknesses
The primary motivation behind TRENDSS is the automated detection of size sorting via the synthesis of three polarimetric fields—ZH, ZDR, and ρhv. The goal of this algorithm is to reduce analysis workload on forecasters, while simultaneously leveraging the microphysical information of polarimetric radar for improved near-term prediction of convective trends. We understand that the integration of such automation into established radar analysis routines can prove difficult if an algorithm proves too complex (i.e., difficult to understand) and/or is fraught with conditions or exceptions for its proper use. Therefore, we designed TRENDSS in a manner that minimizes some issues that can plague other algorithms.
a. Strengths
1) Immunity to ZDR bias
While National Weather Service meteorologists and technicians strive to maintain proper ZDR calibration of the WSR-88D fleet, calibration within ±0.1 dB (the precision required for accurate quantitative precipitation estimation algorithms; Ryzhkov et al. 2005) has proven challenging. Therefore, forecasters and other users occasionally are forced to interpret biased ZDR data, hindering radar analysis during potentially fast-paced warning operations. This drawback must be considered when designing or using an algorithm incorporating ZDR data. A benefit of TRENDSS is its utilization of ZDR anomaly data based on an expected value calculated from local data. By doing so, it incorporates any ZDR bias that may exist, rendering the algorithm immune to miscalibration. For example, if a radar is plagued by a positive 0.5-dB ZDR bias, the expected (mean) ZDR values for each bin will accordingly increase 0.5 dB, and the standardized anomalies will remain unchanged. Therefore, unlike many other polarimetric-based algorithms, TRENDSS data are not degraded by poor ZDR calibration.
2) Mosaicking/multiradar design
Developed within the WDSS–II/MRMS paradigm, TRENDSS incorporates polarimetric data from multiple radars, thereby offering improved spatiotemporal coverage. Moreover, while the viewing angle of one radar may be impacted by differential attenuation or nonuniform beam filling (NBF), another radar may have an unobstructed view of the storm cell of interest. The second radar, thus, can provide meaningful input to the TRENDSS algorithm. Also, during the compositing process, it is unlikely that local TRENDSS data impacted by differential attenuation or NBF from the first radar would mask more accurate data from the second radar. Except in rare instances of anisotropic blockage by trees, towers, and other thin objects, differential attenuation would produce negatively biased radials of ZDR data, leading to negative anomalies in TRENDSS. Because of their negative values, these data points would be overridden by the second radar’s data in the compositing process. Meanwhile, gates characterized by excessive NBF (and an attendant reduction of data quality down radial) would likely be filtered by ρhv thresholds within the initial TRENDSS preprocessing steps. As such, most radar artifacts are unlikely to contaminate or mask legitimate size sorting detections by a second radar.
3) Automated ZDR arc detection
Although the original motivation for TRENDSS is based in cell motion prediction, automated ZDR arc identification presents a noteworthy operational opportunity. Manual identification of ZDR arcs within the fast-paced convective warning environment can prove challenging. Therefore, TRENDSS’s ability to highlight this feature is a considerable achievement. Figure 10 illustrates this ability with a supercell south of Dallas, Texas, at 2358 UTC 26 December 2015. The algorithm highlights a ZDR arc in Fig. 10c, suggesting the near-storm environment was characterized by ample storm-relative flow (and likely helicity). Three minutes after this radar image, a tornado developed in Midlothian, Texas, eventually producing EF-3 damage (NOAA/NCEI 2015). Although we stress that ZDR arcs do not explicitly predict tornadogenesis, they can signal near-storm environments favorable for stronger low-level mesocyclones, which can increase the probability of tornadogenesis.
The 26 Dec 2015 0.5° scans from the Dallas/Fort Worth, TX (KFWS), radar of (a) ZH, (b) ZDR, and (c) TRENDSS overlaid on ZH at 2358 UTC for a supercell south of Dallas, TX. The southwest–northeast-oriented corridor of high TRENDSS values along the forward-flank reflectivity gradient of the supercell indicates the presence of a ZDR arc.
Citation: Weather and Forecasting 33, 5; 10.1175/WAF-D-18-0025.1
b. Weaknesses
1) Radials of NBF or differential attenuation
The algorithm utilizes ρhv to filter data from melting hydrometeors, diverse ice crystal habits, non-Rayleigh scattering, low signal-to-noise ratio, NBF, and so on. These occurrences can make size sorting detection quite difficult, and thus gates characterized by these features are masked. However, radially oriented zones of low ρhv due to NBF may mask downstream zones of size sorting if downstream ρhv is reduced below algorithm thresholds (Table 1). If no other radar data are available, then detection of this size sorting will be impossible. Similarly, differential attenuation can also render down-radial detection impossible. Excessive attenuation of power within the horizontal channel will negatively bias ZDR measurements down radial. If the attenuation is great enough, size sorting gates will be represented by ZDR values near/below the expected value from the local relationship, thereby rendering detection of size sorting impossible if there are no additional radar data. In turn, users of TRENDSS data should be aware of the potential for missed identifications in areas of sparse radar coverage. Figure 11a illustrates both differential attenuation and NBF down radial of a heavy precipitation core.
Examples of radar and meteorological features that can be challenging for the TRENDSS algorithm. This includes (a) nonuniform beam filling (region annotated in black) from the Hastings, NE (KUEX), radar at 0227 UTC 17 Jun 2017, (b) ice crystal contamination from the Upton, NY (KOKX), radar at 1100 UTC 13 Aug 2014, and (c) differential sedimentation (region annotated in black) from the Sterling, VA (KLWX), radar at 0441 UTC 1 Jul 2017.
Citation: Weather and Forecasting 33, 5; 10.1175/WAF-D-18-0025.1
These issues will be magnified for users implementing only a single-radar composite of ZDR anomaly data. At closer ranges, radar analysis benefits from improved spatial resolution and lower potential for gates to be impacted by differential attenuation and/or NBF. With increasing range, single-radar ZDR anomaly data will suffer from the same issues (e.g., beam broadening, increasing altitude) that impact other radar data. Therefore, radar operators should be especially aware of the decreasing performance of single-radar ZDR anomaly algorithms at more distant ranges from radar.
2) Ice crystal contamination
Often, ice crystals exhibit reduced ρhv and ZH values, due to their diverse shapes and smaller sizes. Therefore, gates dominated by these scatterers are typically filtered and not passed downstream to the algorithm core. On infrequent occasion, however, the defined filters are not strict enough to remove all range gates dominated by ice crystals. These instances present a challenge, in that pristine crystals can exhibit high ZDR values (due to their oblate alignment during descent), which TRENDSS interprets as anomalously high. In turn, crystals can masquerade as detections of impending convective propagation and/or intensification. Note the TRENDSS identifications along the fringes of stratiform precipitation in Fig. 11b. Analysis of this case suggested little to no convectively enhanced size sorting.
While further tightening of filter thresholds would be an intuitive step to alleviate this issue, testing on cases in Table 2 suggests tightening beyond current thresholds causes excessive masking of legitimate size sorting signatures. Therefore, the current thresholds appear to offer a reasonable compromise to filter as many ice crystal gates as possible, while maintaining legitimate size sorting. Moreover, any remaining contamination is further reduced by median filtering. Any residual false alarms are often transient and relegated to the edges of stratiform precipitation shields, such that they should be relatively easy for a forecaster to identify manually. Users of TRENDSS data should factor in the longevity, magnitude, and relative location of size sorting detections to ensure greater accuracy in near-term prediction of convective trends.
3) Differential sedimentation
In nascent precipitating cells, initial size sorting distributions are a by-product of differential sedimentation, as larger raindrops descend more rapidly than smaller ones do. TRENDSS is designed to capture all size sorting; therefore, differential sedimentation is often identified in new cells. Figure 11c gives an example of such an instance. These cells may not have much potential for intensification, but transient ZDR anomalies over 3σ may be realized for 5–10 min at lower elevations. Nonetheless, if a sustained, vigorous updraft is present, TRENDSS should maintain higher anomalies (both in composite and height) for a longer duration. Therefore, users should place the greatest probability of intensification on cells with persistent, high anomalies (on the order of tens of minutes).
5. Conclusions
Forecast and thunderstorm warning operations are becoming increasingly nuanced in the weather enterprise, owing to a greater focus on decision support services, impacts-based forecasting, and probabilistic warnings (e.g., Rothfusz et al. 2018). In turn, forecast products must continually leverage the greater detail offered by the latest observational and model data. The TRENDSS algorithm aims to do so by capitalizing on hydrometeor shape information provided by ZDR. By dynamically estimating ZH–ZDR relationships and identifying areas of anomalously high ZDR, the algorithm can highlight ongoing raindrop size sorting, often portending downstream convective evolution. Moreover, the local nature of the relationships renders the algorithm immune to ZDR miscalibration.
Initial subjective and objective analysis indicates that the algorithm performs reliably in emphasizing areas of new updrafts, related directions of propagation, and potential for near-term intensification. In numerous cases, cells would develop (based on various reflectivity metrics) in the direction of TRENDSS identifications. We believe such information can be useful for warning operations and decision support services by empowering forecasters to make decisions such as the shape of warning polygons with more confidence. Critical to this utility, TRENDSS serves as a new visualization of potential updraft location, which forecasters can use to diagnose deviant motion, forward acceleration, and so on.
The algorithm is not without needs for future development. While it does attempt to tailor ZH–ZDR relationships to local data (i.e., unique relationships for each stage on every elevation angle), this method can still combine varying precipitation regimes into one relationship, rendering anomaly detection less effective. Therefore, future iterations of the algorithm could include relationships tailored to various sectors discriminated by precipitation regime, such as using the MRMS surface precipitation type product (Qi et al. 2013; Zhang et al. 2016).
Another target of opportunity is the incorporation of height information into the algorithm. While the current iteration can struggle to differentiate updrafts from ZDR arcs (by compositing data), vertical consistency checks for “columns” of size sorting, similar to the manner of the ZDR column algorithm (Snyder et al. 2015), could output a maximum height of sorting for each grid box. In turn, the algorithm would potentially discriminate between deeper updrafts and lower-level ZDR arc signatures. Moreover, such discrimination would solidify automated ZDR arc detection, further enhancing support for warning forecasters and mesoscale analysts.
More intensive observational and modeling examinations that compare ZDR anomalies and vertical velocity are also needed to establish the robustness of the relationship between TRENDSS and updraft location. Modeling updrafts and their related polarimetric signatures (followed by a TRENDSS-like analysis of the simulated polarimetric field) would offer insight regarding these anomalies and vertical motion, perhaps guiding further refinement of the algorithm. Indeed, a merging of the current technique with a vertical integration such as that of the ZDR column algorithm may yield a comprehensive, automated updraft detection and visualization scheme that could benefit the weather enterprise considerably.
Acknowledgments
We wish to thank many National Weather Service forecasters for their assistance and feedback with the TRENDSS algorithm development and testing, especially Todd Lindley, David Stark, Matthew Tauber, Jeffrey Tongue, Melissa DiSpigna, Joe Dellicarpini, Stephanie Dunten, Benjamin Sipprell, Frank Nocera, and Fred Burtz. Furthermore, we acknowledge Dr. Michael French (SUNY Stony Brook) and Dr. Alexander Ryzhkov (CIMMS/NSSL) for their ample feedback in the design process. Funding was provided by the NOAA/Office of Oceanic and Atmospheric Research under NOAA–University of Oklahoma Cooperative Agreement NA11OAR4320072, U.S. Department of Commerce, and a 2016 Cooperative Institute for Mesoscale Meteorological Studies Director’s Directed Research Fund grant. The views expressed in this paper are those of the authors and do not necessarily represent those of the NOAA, NSSL, or CIMMS.
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