1. Introduction
Mesoscale snowbands are commonly observed embedded within the stratiform precipitation shield of extratropical cyclones (Novak et al. 2004; Baxter and Schumacher 2017). These narrow bands are associated with heightened snowfall rates, leading to significant and highly heterogeneous snowfall accumulations and reduced visibility. Furthermore, the small scale of these bands can result in rapid and oftentimes unexpected onsets, causing major traffic disruptions and other societal impacts. Though not specific to snowbands, Tobin et al. (2019) found that snow was occurring during 14% of precipitation-related motor vehicle fatalities and increases crash rates by 84% (Qiu and Nixon 2008).
Several robust climatologies of mesoscale snowbands in the United States have been developed using slightly differing methods for different regions, including Novak et al. (2004), Baxter and Schumacher (2017), Ganetis et al. (2018), and Radford et al. (2019). The definition of the “single” mesoscale snowband varies slightly between these studies, but is generally accepted to be an intense reflectivity feature persisting for at least two hours, with a length of at least 250 km and an aspect ratio of 3:1 (length:width). Bands are most frequently observed in the northeastern United States and the central United States with similar synoptic ingredients but differing cyclone-relative locations (Novak et al. 2004; Baxter and Schumacher 2017).
Single bands are generally associated with intensifying cyclones when air on the warm side of a front meets colder air, leading to a deformation zone and midlevel frontogenesis (Thorpe and Emanuel 1985; Sanders and Bosart 1985). Strong frontogenesis disrupts thermal wind balance, leading to an ageostrophic, thermally direct circulation, with rising air in the warm sector parallel to the warm front and sinking air ahead of the warm front. Vertical motion can be strengthened by the presence of reduced stability just above the midlevel frontogenesis due to the dry tongue overlapping warmer, moister air (Nicosia and Grumm 1999). In short, the key mesoscale components to the formation of most mesoscale snowbands are strong midlevel frontogenesis and reduced midlevel stability leading to strong ascent (Nicosia and Grumm 1999; Novak et al. 2004, 2008; Baxter and Schumacher 2017).
With widths between 20 and 100 km, and the updrafts potentially even smaller, mesoscale snowbands present a challenge to numerical weather prediction (NWP) models (Novak et al. 2004; Novak and Colle 2012; Radford et al. 2019). Novak et al. (2006) advocated for an ingredients-based forecasting approach, but also noted the potential value of a probabilistic forecasting approach. Along those lines, Novak and Colle (2012) used a 12-km ensemble to investigate three banding cases, finding large timing and location uncertainty, most likely associated with initial condition error. Novak and Colle (2012) suggested convection-allowing models could be an avenue for improved forecast accuracy.
Theoretically, high-resolution models such as the members of the High-Resolution Ensemble Forecast (HREF; Roberts et al. 2019) system should be able to represent these features. Connelly and Colle (2019) investigated even smaller, multiband features, and found that a 2-km ensemble could resolve most snowbands, but systematically underpredicts the number of multibands. Radford et al. (2019) found limited predictive skill for single bands with the High-Resolution Rapid Refresh (HRRR) model and noted frequent timing and displacement error. However, performance was substantially improved by the application of fuzzy verification, allowing for small time discrepancies between forecasts and observations. Radford et al. (2019) also showed large variance in HRRR forecast skill between snowband events using object-oriented verification but stopped short of evaluating the commonalities between well-forecast events and poorly forecast events. Radford et al. (2019) suggested that an ensemble forecasting approach would likely produce superior forecasts compared to deterministic approaches.
The identification of distinct snowband environments that may exhibit differing predictive skill is a challenge that may be solved using clustering methods, such as self-organizing maps (SOMs), a type of unsupervised artificial neural network (Kohonen 1982). The primary advantage of SOMs over other clustering techniques is in their treatment of topology. SOMs preserve the topology of the input data, clustering data into grids of “nodes” while at the same time organizing the nodes into coherent gradients. In other words, similar clusters are placed close to one another. This works by matching an input vector to a node, after which the weight vector of the matching node and nodes within a user-defined radius are adjusted toward the feature. This radius gradually decreases and the SOM converges to a final estimate of the weight vectors (Kohonen 2013). SOMs have been successfully applied in several studies classifying synoptic (Hewitson and Crane 2002; Cassano et al. 2006; Mechem et al. 2018) and mesoscale (Nowotarski and Jones 2018; Hua and Anderson-Frey 2022) environments.
Our work has two unique scientific goals. First, we wish to extend Radford et al.’s (2019) work and investigate the variables contributing to variance in snowband predictive skill within convection-allowing models. Second, we seek to determine whether patterns in variables more explicitly tied to snowbands (e.g., vertical motion and reflectivity) or more implicitly related variables (e.g., trough- and cyclone-relative locations, frontogenesis, stability) are better indicators of snowband predictability. These goals are accomplished by objectively ranking the HREF forecast skill for snowband events over a 5-yr period using object-oriented verification, after which we apply SOMs to cluster banding events based upon synoptic environmental patterns, such as 500-hPa geopotential height anomalies and mean sea level pressure (MSLP), and mesoscale variables, such as frontogenesis, vertical motion, and saturation equivalent potential vorticity (SEPV). This analysis yields clusters of synoptic and mesoscale patterns representative of the most prominent mesoscale snowband modes, along with corresponding HREF predictive skill. Skill differences between snowband modes can then help to identify scenarios where we might expect the HREF to struggle with the forecast or otherwise perform adequately and provide forecasters with a greater understanding of NWP band forecast limitations, as well as assist model developers to improve the underlying physics of high-resolution models.
2. Data and methods
a. HREF verification
Our observational snowband verification dataset is CONUS-wide and spans from 2017 to 2022 between 1 November and 31 March, with the exception of March 2022. Following Novak et al. (2004), Baxter and Schumacher (2017), and Radford et al. (2019), this dataset will be based upon features identified in base radar reflectivities. The Iowa Environmental Mesonet (IEM) produces CONUS-wide base reflectivity mosaics, from which we identify snowband occurrences at hourly intervals. The IEM mosaics have a native grid spacing of ∼0.5 km but are bilinearly interpolated to match the 3-km HREF grid. The use of radar reflectivity to identify snowbands means that areas of sparse radar coverage may not be well-represented in our dataset. This is generally of little consequence to our study, as we are only comparing HREF forecast features to observed bands, but means that we may underrepresent bands in the mountain west and other radar-sparse regions of the United States. Each reflectivity mosaic is then paired with categorical precipitation-type data from the corresponding HRRR analysis for precipitation type estimation, requiring snow to be the predominant precipitation type along ≥50% of the feature’s axis. Ikeda et al. (2013) showed that HRRR categorical precipitation type is quite accurate for snow and rain, making it suitable for our purposes.
The forecast snowband dataset is also CONUS-wide and spans from 2017 to 2022 between 1 November and 31 March, excluding March 2022 as analysis began prior to March 2022 data availability. Forecast reflectivity features are identified from the HREF members’ simulated 1000-m reflectivities and forecast categorical precipitation type. The evaluated HREF forecast leads were between 3 and 15 h (time-lagged member leads between 15 and 27 h out). HREF output is provided by the National Centers for Environmental Prediction (NCEP) and has been made publicly available through an archive maintained by the National Severe Storms Laboratory (NSSL). The HREF has changed twice over the period of this study. HREFv1 consisted of the Advanced Research version of the Weather Research and Forecasting (ARW-WRF) Model, the Nonhydrostatic Multiscale (NMMB-WRF) model, the National Severe Storms Laboratory (NSSL-WRF) model, the North American Mesoscale (NAM) Nest model, and their 12-h time-lagged counterparts. In 2019 (HREFv2) the HRRR and its 6-h time-lagged counterpart were added to the HREF, and in 2021 (HREFv2.1) the NMMB model was replaced by the Finite-Volume Cubed (FV3) model. Our evaluation handles these changes by evaluating both individual member forecast performances and overall HREF forecast performance (computed as the simple arithmetic mean of member performances). The member configurations are shown in Table 1.
HREF member physics configurations. Acronyms: Advanced Research Weather Research and Forecasting (ARW), Nonhydrostatic Multiscale Weather Research and Forecasting (NMMB), National Severe Storms Laboratory Weather Research and Forecasting (NSSL), North American Mesoscale Nest (NAM), High-Resolution Rapid Refresh (HRRR), Finite-Volume Cubed (FV3), Time-lagged (TL), Rapid Refresh (RAP), Global Forecast System (GFS), WRF single-moment 6-class (WSM6), Geophysical Fluid Dynamics Laboratory (GFDL), Yonsei University (YSU), Mellor–Yamada–Janjić (MYJ), Mellor–Yamada–Nakanishi–Niino (MYNN), and eddy-diffusivity mass-flux (EDMF).
Bands are identified from the observed reflectivity field in an automated procedure closely following Radford et al. (2019) with three modifications. First, HRRR categorical “p-type” is used for precipitation-type determination in lieu of 2-m temperature. Second, in order to reduce the number of “borderline” bands that may muddy cluster signals, the minimum length criterion was increased from 250 to 300 km. Third, a 15-dBZ minimum average intensity was implemented to filter out features that are intense relative to their surroundings but likely inconsequential in terms of precipitation rate. The reflectivity distribution-based threshold approach applied by Radford et al. (2019) helps to level the playing field between different ensemble members that use different microphysics schemes and reflectivity calculations. Bands identified using this method were then manually grouped into band “events” to increase the independence of the cases. Bands that were more than six hours removed from a previous band identification or less than six hours removed but more than 500 km away from a previous band constituted new events. At this stage we also removed transient bands (bands with only one hour duration), bright bands (highly linear reflectivities in excess of 40 dBZ), and lake-effect bands (those parallel to the shores of the Great Lakes with a length nearly equal to the length of the coastline).
We then apply an object-oriented verification procedure to compare forecast and observed features. We identify embedded intense precipitation objects in the HREF dataset at the forecast hour corresponding to the observed band and compare the characteristics of this intense precipitation object to the observed snowband using a custom scoring function. This function compares the centroid locations, minimum contour distance, areas, area intersection, orientation angles, and aspect ratios of the two features to produce a bulk “interest” score between zero and one, with zero indicating there is no intense precipitation feature in the forecast within 500 km of the observed band, and one indicating that the forecast and observed objects are identical. These chosen parameters are similar to other object-oriented verification studies, such as Johnson and Wang (2013) and Ji et al. (2020), which used centroid distances, area ratios, aspect ratios, and orientation angle differences. Centroid distance, minimum contour distance, and area intersection are generally different measures of location, area is a measure of size, and orientation angle and aspect ratio are measures of shape. The functions used for this scoring are shown in Fig. 1 and the equations are described in Table 2. To give the models the best possible chance for success, we used the maximum interest score from the hour prior to the observed band to the hour after the observed band, and from slightly lower (mean + 1.10 std; std = standard deviation) and higher (mean + 1.40 std) intensity thresholds. This small tolerance helped ensure temporal consistency between band identifications if the intensity of the precipitation had slight fluctuations from hour to hour. Finally, these interest scores are averaged over the lifetime of a banding event to calculate an overall forecast skill for the duration of the band for each member and compared.
Scoring functions used for object-oriented snowband verification including centroid distance, minimum contour distance, area ratio, area intersection, aspect ratio, and orientation difference. These individual functions are averaged to compute an overall interest score.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0004.1
Functions to calculate object-oriented interest scores for each component. These six components are averaged to calculate the overall score. CEf = forecast centroid, CEo = observed centroid, COfi = forecast contour points, Cooj = observed contour points, Af = forecast area, Ao = observed area, Aint = intersection area, Rf = forecast aspect ratio, Ro = observed aspect ratio, ∅f = forecast orientation angle, and ∅o = observed orientation angle.
The interest scoring functions presented here are unintuitive, so we provide additional explanation here. For parameters with a “best” and “worst” case scenario, such as orientation angle difference (where best case would be 0° difference and worst case would be 90° difference), the function is linear between these two points. For parameters with a best case but no clear worst case, such as centroid distance (where best case is a 0-km difference and the worst case goes to infinity), minimum contour distance, area ratio, and aspect ratio, the scoring is a decay function. Note that these parameters are not independent. For example, centroid distance, minimum contour distance, and area intersection are all some measure of feature location and are thus highly correlated. This amounts to the overall interest score representing a sort of weighted average. This could be viewed as a limitation of the interest score, but we contend that some parameters, particularly location, are more important than others and should be weighted more heavily. However, we caution that not all aspects of a precipitation feature are equally represented in the average interest score.
Our verification and SOM analyses are “observation oriented,” meaning they are composited entirely from the observational band dataset. A drawback to this type of analysis is that false-alarm cases, in which the HREF forecasts a band and none is observed, are not factored into predictive skill estimations. For contingency table statistics, this bias could result in favoritism toward over-forecasting as we attempt to increase probability of detection with no knowledge of false alarm ratio. This is less of a problem with object-oriented verification but means that we are not able to make any conclusions on environments or estimates of similarity when bands are forecast but no bands are observed. Analysis of environments associated with false alarms would require “model-oriented” SOMs, in which all HREF-forecast band objects are identified and composited and then compared to observed precipitation features. Such an exercise is an avenue for future work, but would require significantly more computation, since all banding objects in every HREF member at every forecast hour would need to be identified and matched before compositing and comparison to observed precipitation features could occur.
b. SOM analysis
The SOM analysis incorporates the hourly ERA5 reanalysis dataset (Hersbach et al. 2023) for the same 2017–22 period. From this reanalysis, we collected and/or calculated 500-hPa heights, 500-hPa height anomalies, and MSLP, and vertical velocities, frontogenesis, and SEPV on pressure levels between 200 and 1000 hPa at 50-hPa increments.
SOMs have previously been successfully applied to classification of mesoscale environments for other phenomena (Nowotarski and Jensen 2013; Nowotarski and Jones 2018; Hua and Anderson-Frey 2022), but the noise can make extraction of consistent patterns more difficult and can lead to cancellation when compositing events. We test SOM classification for both synoptic snowband environments and mesoscale snowband environments using the Python package MiniSOM (Vettigli 2019). The primary difference in treatment of synoptic-scale and mesoscale categorizations is the domain size. Domains for both are relative to the snowband centroids, but to capture the relevant synoptic wave pattern the domain needs to be larger. We choose a domain of 20° latitude × 20° longitude, similar to the 20° latitude × 25° longitude used by Wang et al. (2022). In contrast, we are more likely to capture consistent mesoscale signals if we limit the domain to the near-band environment. Thus, the domain for mesoscale fields is 12.5° × 12.5°. Mesoscale fields are also smoothed with a one-sigma Gaussian filter prior to SOM training to extract more coherent patterns. SOMs are developed using environmental variables at the observed temporal midpoints of banding events to capture the conditions at band maturity, when we would expect the frontogenetical signal to be greatest, rather than development or dissipation. Repeating our analysis for band initiation or dissipation would be a valuable exercise for future work and may help to elucidate whether there are differences in predictability of band formation compared to band maintenance. Rather than clustering on one variable for all SOMs, we cluster on each variable independently. Thus, nodes in each SOM figure generally do not align with the other SOMs presented unless otherwise specified. We suspect that the banding ingredients are localized enough that clustering on one field, such as 500-hPa height anomalies, would not result in clear signals in mesoscale features. Clustering on multiple variables together or a subset of variables in a multivariate SOM would be valuable future work.
As Schuenemann et al. (2009), Mechem et al. (2018), and Wang et al. (2022) note, the choice of the number of SOM nodes is the most important user-defined parameter of the SOM. Following Tibshirani et al. (2001) and Schuenemann et al. (2009), we apply the “elbow criterion” to choose the number of SOM nodes. This is accomplished through investigation of the trade-off between quantization error and topographic error. Quantization error is the average distance between each input sample and its best matching node and generally decreases with addition of nodes. Topographic error is the proportion of samples for which the best matching node and second-best matching node are not adjacent and generally increases with more nodes (Kohonen 2001). Examples of these trade-offs applied to 500-hPa height anomalies and 650-hPa vertical velocity are shown in Fig. 2 using constant values for the neighborhood function, learning rate, sigma, and number of iterations (Gaussian, 0.05, 1.5, and 250 000, respectively). For 500-hPa height anomalies, there is a clear acceleration in topographic error and a diminishing return for quantization error after 5 × 5 nodes. For vertical velocity the topographic error begins to increase after 4 × 5 nodes and quantization error decreases at a nearly constant rate. The ideal number of nodes differs based upon the variable under investigation but was generally between 4 × 4 nodes and 5 × 5 nodes for our purposes. Given these findings, we have chosen to use a 5 × 5 grid for all variables. A sigma of 1.5 was used for sensitivity tests for consistency because sigma must be less than the smaller of the number of SOM rows but was increased to 3.5 for the SOMs shown throughout this paper. All other parameters remained the same.
The quantization and topographic errors for (left) the 500-hPa height anomaly SOM and (right) the vertical velocity SOM. A size of 5 × 5 was chosen based on the trade-off between decreasing quantization error and increasing topographic error. Neighborhood function, sigma, learning rate, and number of iterations were fixed at Gaussian, 1.5, 0.05, and 250 000, respectively.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0004.1
Within each SOM node the average interest scores and associated distributions are calculated to find the overall predictability of the node. If different SOM nodes exhibit different predictabilities, this indicates that the variable is important to snowband prediction and may be useful to forecasters when quantifying snowband forecast confidence and for model developers in making physics or other model improvements. In addition to the overall interest score, we also investigate the variability of the individual HREF members and the components of the interest score to reveal more specifically the manner in which the forecast was deficient by node.
An alternative SOM analysis strategy for discerning patterns in high- and low-predictive skill banding events was also explored, in which events are first sorted based upon forecast quality, after which a set of SOMs are developed for the upper tercile of events and lower tercile of events. SOMs for these events are 3 × 3 with a sigma of 2.5 in order to account for the smaller set of cases (101 banding events in each tercile). The average location of events in the upper tercile was (42.0°, −87.3°), compared to (41.3°, −89.3°) for the lower tercile. This approach generally reaffirmed the results of the primary analysis, thus, in the interest of brevity, we will only discuss this alternative approach when additional insights were gained.
3. Results
a. HREF verification
Following removal of transient bands, bright bands, and lake-effect bands, the band identification algorithm identified 1608 h with banding, which were manually grouped into 305 banding events for the 5-yr period. The average band had a length of 421 km and width of 99 km at onset, 445 and 101 km at its temporal median, and 414 and 94 km before dissipation. The geographic climatology of these events is extremely similar to that shown in Radford et al. (2019; Fig. 3) with most bands occurring in the Northeast and central United States, though there are a few (<10) banding events in our dataset in the western CONUS, which was not included in that climatology.
First, we attempt to contextualize the following interest scores for the reader. Subjectively, we view an interest score of below 0.65 as poor, 0.65 as fair, 0.75 as good, and 0.85 as excellent. Figure 3 demonstrates an example of a forecast scored at 0.78, or a “good” forecast. Overall forecast performance is similar between members (Table 3), with the time-lagged ARW member performing the worst with an average event interest score of 0.70 and the HRRR performing the best with an average event interest score of 0.76. The addition of the HRRR to the HREF in 2019 marginally improved the ensemble’s average performance, while the replacement of the NMMB with the FV3 in 2021 has had little impact on HREF snowband forecast quality. The HRRR received slightly higher scores across all components, but received the greatest boost from positional parameters, including the centroid offset and area intersection. 12-h time-lagged members consistently performed 0.03 points worse than their counterparts, a slightly different result from Radford et al. (2019), which found no skill variance by forecast lead for the HRRR and may be attributable to our improved interest functions and object matching. Further investigation will not stratify by forecast lead, given that this would substantially reduce the sample sizes. Instead, we evaluate band forecasts at forecast leads of between three hours and 15 h (and between 15 and 27 h for time-lagged members). We acknowledge that this is a limitation of our analysis but feel that it is an acceptable sacrifice given the short forecast leads under evaluation and the relatively small effect of forecast lead on predictive skill.
An example of the interest score calculation for forecast precipitation feature (ARW initialized at 1200 UTC 3 Nov 2017 16-h forecast) contoured in purple, compared to an observed snowband (valid at 0400 UTC 4 Nov 2017) contoured in red. Both are overlaid onto the simulated 1000-m radar reflectivity. The average interest score for this pair was 0.78, roughly indicative of a “good” forecast. The main score detraction was a result of low area intersection.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0004.1
Average interest scores, standard deviations, and p values for differences between not time-lagged and time-lagged members across all 305 banding events for each HREF member.
The largest overall contributor to forecast error for all members came from the “area intersection” parameter, for which the average event score was 0.51 (Table 4). The area intersection parameter is primarily an alternative measure of positional error and indicates that only half of the area of the forecast and observed features overlap, on average. The average area ratio and centroid distance scores are also on the lower end, with an average area ratio of 0.61 and an average centroid distance score of 0.65, indicative of an average centroid offset of about 100 km. On the other end of the spectrum, the average minimum contour distance score is 0.98, meaning almost all forecast features are overlapping the observed band contour at some point. The average aspect ratio score is 0.71 and the average orientation score is 0.84, indicating that precipitation features were generally similar in shape and orientation to observed bands.
Interest scores for each HREF member broken down by component.
Though the average interest scores for area ratio were similar between members, we investigated each member’s area forecasts individually to determine whether there were any systematic biases in area forecasts. The median forecast areas for the ARW, NSSL, FV3, and their time-lagged counterparts were all approximately 15% lower than the observed band areas, indicating that these members are consistently underforecasting band area. In contrast, the NMMB, NAM and their time-lagged counterparts’ median areas fell between just 0% and 7% greater than the observed median. The time-lagged HRRR median was 11% greater than the observed median, but this reduced to −2% for the HRRR at the shorter forecast lead. The NMMB, NAM, and HRRR models may still exhibit large area errors (hence similar interest scores), but there is no obvious pattern in over- or underforecasting band areas.
All members exhibited relatively high variance in interest scores across the set of events. Standard deviations for the members fell between 0.08 and 0.14, which represents a significant range in forecast quality. This is consistent with Radford et al. (2019) and our expectations for widely varying predictive skill for individual banding events and reaffirms the need for investigation into environmental parameters that may be associated with these differences.
b. SOM synoptic regimes
Most mesoscale snowbands are associated with a strong surface cyclone downstream of a 500-hPa trough in a southwesterly flow regime (Novak et al. 2004; Baxter and Schumacher 2017). However, a notable portion (17%) of bands were found to form in west-northwesterly flow (Baxter and Schumacher 2017). 55% of central U.S. snowbands were found in the northeast quadrant of the surface cyclone, compared to 30% in the northwest quadrant (Baxter and Schumacher 2017). This is in contrast to Northeast U.S. snowbands, which occurred in the northwest quadrant 81% of the time (Novak et al. 2004). These findings serve as a sanity check for the patterns we expect to see in our synoptic-scale SOMs.
We first applied a SOM analysis to 500-hPa geopotential height anomalies and calculate the mean 500-hPa height anomaly (filled contours) and mean 500-hPa heights (unfilled contours) for each node in Fig. 4. Height anomalies were computed based on the ERA5 reanalysis monthly averaged 500-hPa heights. The length and orientation of the bands associated with each node are overlaid with colored lines. First, we acknowledge that even though a particular pattern is evident in a node composite, there is likely significant variability among the individual events within each node. As an example of intranode variability, we list the average anomaly correlation coefficients (ACC) per node in Fig. 4. Values of negative one would indicate anticorrelation, zero would be no correlation, and one would be perfectly correlated. In general, the cases are well-correlated with the node composites, but some nodes, such as the top-left node with an r of 0.56, demonstrate greater variability than others. This caveat in mind, the composites shown in Fig. 4 corroborate the findings of Novak et al. (2004) and Baxter and Schumacher (2017). Most composites depict the band centroid downstream of a negative 500-hPa height anomaly and a trough axis, associated with southwesterly flow over the band. The exceptions are the nodes on the left side of the SOM, which tend to show bands closer to a positive anomaly and ridge and exhibit more zonal flow. We pay particular attention to the trends on the diagonals of the SOM: From top left to bottom right, the band’s position shifts immediately upstream of a relatively strong positive anomaly and ridge to downstream of a strong negative anomaly and trough. From bottom left to top right, the magnitudes of the anomalies increase and the band shifts from a location of more zonal or northwesterly flow to a position in more southerly flow. If 500-hPa height anomalies are correlated with band predictive skill, we would expect the differences to be most evident between these sets of nodes on opposite corners of the SOM.
ERA5 500-hPa height anomalies SOM with a domain of 20° lat × 20° lon. Orientations and lengths of bands at the observed temporal midpoints of snowband events assigned to the node are overlaid. Sample sizes comprising each node are in the top-right corners. Average anomaly correlation coefficients between cases and node averages are shown in the bottom-right corner of each node.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0004.1
Because sample sizes tend to be small for individual nodes, we compare the predictive skill of clusters of nodes rather than individual nodes. In this case, we cluster the four nodes in the top left of the SOM (strong positive anomalies) and the four nodes in the bottom right of the SOM (strong negative anomalies). The median interest score for the negative anomaly nodes is 0.71, somewhat less than the median of 0.75 for the positive anomaly node, but the 95% confidence intervals of the medians overlap (not shown). Furthermore, no individual HREF member demonstrated a difference beyond the confidence intervals or a consistent signal between a member and its time-lagged counterpart. The predictive skill of the four bottom-left nodes (n = 52), which show bands in more northwesterly flow, and the four top-right nodes (n = 54), which show bands in more southerly flow have a similar difference in medians of 0.05. However, while there was no consistent pattern among HREF members for positive and negative anomaly predictive skill, there is more consistency for flow direction. The ARW, NMMB, NSSL, and NAM members all demonstrate a difference in medians of between 0.03 and 0.06 points. However, only the NAM’s medians exhibit distinct 95% confidence intervals. Thus, predictive skill is more likely to be linked to 500-hPa flow direction than to 500-hPa anomaly sign and strength, but both relationships are weak relative to the variance of scores.
We next produced a SOM trained with mean sea level pressure (Fig. 5). Nearly all of the bands were found in either the northwest or northeast quadrant of the surface cyclones. In total, 117 of the 305 events were clearly located to the northwest of the composite surface low center, 132 were in the northeast quadrant, and the remainder were either ambiguous or south of the surface low. This proportion falls squarely in-between Novak et al.’s (2004) study of Northeast U.S. snowbands, which found predominantly northwest quadrant bands, and Baxter and Schumacher’s (2017) study of central U.S. snowbands, which found predominantly northeast quadrant bands. The average location of northeast quadrant bands was (41.1°, −89.6°) slightly farther west and south than the average location of (42.3°, −86.8°) for northwest quadrant bands.
ERA5 MSLP SOM with a domain of 20° lat × 20° lon. Orientations and lengths of bands at the observed temporal midpoints of snowband events assigned to the node are overlaid. Sample sizes comprising each node are in the top-right corners.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0004.1
The most highly populated nodes are the top-left node (n = 27), which demonstrates a weak surface cyclone southwest of the band centroids, and the bottom right node (n = 24), which demonstrates bands immediately northwest of a strong surface cyclone. The top-right node (n = 13) and bottom-left node (n = 11) show low pressure systems with similar strength, west of the band centroids in the former and east of the band centroids in the latter. We again group the four nodes in each corner of the SOM before comparing skill. In the case of MSLP, this produces a top-left cluster (n = 62), comprised of bands northeast of a weak surface low and a bottom right cluster (n = 54), comprised of bands northwest of a strong surface low. We can also cluster the bottom-left (n = 48) and top-right (n = 39) corner nodes, producing clusters of predominantly west quadrant bands versus predominantly east quadrant bands. The strong low cases (n = 54) exhibit slightly higher skill than the weak low cases (n = 62), with median interest scores of 0.75 and 0.73, respectively, consistent among most HREF members. The differences all fall within the 95% confidence intervals, however, meaning there is unlikely to be a strong relationship between MSLP magnitude and snowband predictive skill. There is similarly little preference in skill for east quadrant or west quadrant bands.
c. SOM mesoscale organization
The key mesoscale ingredients contributing to snowband development are midlevel frontogenesis and reduced midlevel stability, which combine to produce strong vertical motion. The 700-hPa level is often chosen as a representative level to view midlevel frontogenesis and typically shows a narrow strip of enhanced frontogenesis northeast of the surface cyclone (Novak et al. 2004, Fig. 15). A snowband cross-sectional analysis typically shows enhanced frontogenesis sloping upward toward colder air (Novak et al. 2004, Fig. 16). Vertical motion is strongest when this frontogenetical region is located just below a bullseye of reduced stability at about 650 hPa (Nicosia and Grumm 1999; Novak et al. 2004; Baxter and Schumacher 2017). As in Baxter and Schumacher (2017), saturation equivalent potential vorticity (SEPV) is used here as a proxy for moist symmetric stability. Our mesoscale analysis investigates frontogenesis at the 700-hPa level, and SEPV and vertical motion at the 650-hPa level, in addition to frontogenesis and vertical motion cross sections.
We begin this section by analyzing the 650-hPa pressure vertical motion (omega) SOM (Fig. 6). Note that all variables are composited based on ERA5 reanalysis data, which parameterizes convection and may be missing vertical motion associated with upright or slantwise convection. All nodes are associated with locally enhanced upward motion at the 650-hPa level. The top-right node (n = 18) demonstrates strong upward motion with a northwest–southeast orientation, while the bottom left (n = 28) shows weak, disorganized vertical motion. The bottom right node (n = 20) shows comparably intense upward motion to the top right, but with a southwest to northeast orientation. The top-left node (n = 30) shows modest upward motion without clear organization. The 700-hPa frontogenesis associated with each of the 650-hPa vertical velocity nodes is shown in Fig. 7. Note that while Fig. 7 shows 700-hPa frontogenesis, it has been clustered on 650-hPa vertical velocity as depicted in Fig. 6 so that relationships between the two can be evaluated. All of the enhanced vertical motion regions are associated with at least some degree of substantial frontogenesis, though we again note that there may be significant intranode variability and other forcing mechanisms likely contribute to vertical motion.
The 650-hPa vertical velocity SOM with a domain of 12.5° lat × 12.5° lon. Orientations and lengths of bands at the observed temporal midpoints of snowband events assigned to the node are overlaid. Sample sizes comprising each node are in the top-right corners.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0004.1
The 700-hPa frontogenesis associated with the 650-hPa vertical velocity SOM nodes (Fig. 6). Orientations and lengths of bands at the observed temporal midpoints of snowband events assigned to the node are overlaid. Sample sizes comprising each node are in the top-right corners.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0004.1
Figure 8 compares the predictive skill of the four top-right nodes (n = 38), representing strong vertical motion with a northwest to southeast or nearly zonal orientation, to the four bottom left nodes (n = 62), representing weak vertical motion. Events with strong upward motion are associated with higher predictive skill compared to weak upward motion events, with medians of 0.75 and 0.69, respectively. There is no overlap between confidence intervals for the two medians, and the two-tailed p value is less than 0.005.
Predictive skill boxplots (corresponding to Fig. 6) for the four nodes in the bottom-left corner (n = 62) exhibiting weak upward motion and the four nodes in the top-right corner (n = 38) exhibiting strong upward motion with a northwest–southeast orientation. Notches correspond to the 95% confidence interval of the median.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0004.1
We next trained a SOM with band vertical velocity cross sections and oriented each of them with colder column-averaged temperatures to the left to see if patterns were evident in the vertical velocity profiles and whether these patterns influenced skill. Cross sections were taken at the temporal midpoint of each of the banding events to capture the mature band stage. Each cross section was 10° long centered on the band centroid and were 90° offset from the band orientation. The vertical velocity cross-sectional SOM is shown in Fig. 9. There is a bullseye of enhanced vertical velocity between approximately 700 and 550 hPa in all nodes, consistent with previous work (Baxter and Schumacher 2017). These regions tilt toward the colder air with increasing height. In the top-left corner (n = 14) there is a bimodal pattern, with greatest upward motion toward the warm sector and a secondary maximum tilted up toward the cold air. In the bottom-right corner (n = 22) there is a more well-defined upward maximum collocated with the band axis. From bottom left (n = 28) to top right (n = 19) there is a very distinct gradient from weak upward motion to strong upward motion with consistent tilt toward the cold air. This top-right maximum is similar in magnitude to the bottom-right node, but deeper through the column and more expansive toward the warm air.
A 10° band cross-sectional ERA5 vertical velocity SOM. Colder column-averaged air is on the left in each node. Sample sizes comprising each node are in the top-right corners.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0004.1
The predictive skill for the four weak vertical motion cross-section nodes (bottom left; n = 72) is compared to the four strong vertical motion nodes (top right; n = 36) in Fig. 10. The contrast in skill for these two cross-sectional nodes is even clearer than the contrast at the 650-hPa level, with a difference in median interest scores of 0.07 (0.77 versus 0.70), clearly distinct 95% confidence intervals, and a two-tailed p value < 0.0005. All members show greater interest scores for stronger vertical motion events [Table 5, median distance column], though the sample sizes are considerably smaller for the HRRR and FV3 (HRRR strong n = 14 and weak n = 37; FV3 strong n = 5 weak n = 6) due to their shorter operational periods. The interest score spread is also larger for the weak vertical motion compared to strong vertical motion [Table 5, IQR distance column].
Predictive skill boxplots (corresponding to Fig. 9) for the four nodes in the bottom-left corner (n = 72) exhibiting weak upward motion and the four nodes in the top-right (n = 36) corner exhibiting strong upward motion.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0004.1
Median average interest and area ratio scores along with interquartile ranges (IQRs) for strong upward motion and weak upward motion events for each HREF member and the associated differences between the medians and the interquartile ranges (IQRs) for the strong and weak upward motions.
The opposite diagonal demonstrates a similar discrepancy in interest scores, with the four nodes in the bottom right (n = 44) receiving interest scores 0.07 points higher than the four nodes in the top left (n = 31). This suggests that a more cohesive, singular region of vertical motion leads to greater band predictive skill than more disorganized or bimodal regions of enhanced vertical motion of similar magnitude. All members demonstrated a difference of similar magnitude, primarily driven by differences in the area intersection parameter. The NSSL also has relatively large error in the area ratio parameter.
Considering the vertical motion for most single bands is frontogenetically driven, one could reasonably expect to see 700-hPa frontogenesis demonstrate the same relationship as vertical motion, with stronger frontogenesis correlating with greater skill. The SOM for 700-hPa frontogenesis is shown in Fig. 11. Narrow regions of strong frontogenesis are evident in most of the nodes and range from a west-northwest–east-southeast orientation to a southwest–northeast orientation. These regions are not necessarily collocated with the band centroids, perhaps due to the frontal slope or to hydrometeor lofting and advection (Lackmann and Thompson 2019). Magnitude of frontogenesis increases from top to bottom and orientation shifts clockwise from left to right. Most nodes in Fig. 6 exhibited at least some upward motion but a number of frontogenesis SOM nodes exhibit no enhanced frontogenesis at 700 hPa (top right).
ERA5 700-hPa frontogenesis SOM with a domain of 12.5° lat × 12.5° lon. Orientations and lengths of bands at the observed temporal midpoints of snowband events assigned to the node are overlaid. Sample sizes comprising each node are in the top-right corners.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0004.1
The predictive skill for the four top-right corner nodes with no 700-hPa frontogenesis (n = 72) and the four bottom-left corner nodes (n = 32) with strong 700-hPa frontogenesis are shown in Fig. 12. While strong 700-hPa frontogenesis cases demonstrate higher predictability (median = 0.76) than no frontogenesis cases (median = 0.73), the difference is modest compared to the difference for 650-hPa vertical motion and there is significant overlap between 95% confidence intervals. This small difference is relatively consistent between all HREF members.
Predictive skill boxplots (corresponding to Fig. 11) for the four nodes in the bottom-left corner exhibiting strong frontogenesis and the four nodes in the top-right corner exhibiting weak frontogenesis.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0004.1
The average 650-hPa vertical motion for each 700-hPa frontogenesis SOM node is shown in Fig. 13. Note that while Fig. 13 shows 650-hPa vertical velocity, it has been clustered on 700-hPa frontogenesis as depicted in Fig. 11 so that relationships between the two can be evaluated. While frontogenesis and vertical motion are strongly correlated, modestly enhanced upward motion is evident in the top-right node even in the absence of frontogenesis at this level, suggesting that there may be other forcing mechanisms for these bands, such as orography, convective processes, or that frontogenesis is present at a different level (or a combination of these factors). Ganetis et al. (2018) showed that single bands were sometimes associated with weak frontogenesis, and suggested investigation of gravity waves or vertical shear instability as possible forcing mechanisms.
ERA5 650-hPa vertical velocity associated with the 700-hPa frontogenesis SOM nodes (Fig. 11). Orientations and lengths of bands at the observed temporal midpoints of snowband events assigned to the node are overlaid. Sample sizes comprising each node are in the top-right corners.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0004.1
Figure 14 shows the cross-sectional SOM for frontogenesis. Elongated regions of enhanced frontogenesis sloping up toward the colder air beneath the levels of maximum vertical motion are apparent in most nodes. The magnitude of frontogenesis increases on the diagonal and is weakest in the top-right node (n = 23) and strongest in the bottom left node (n = 20). The bottom right corner (n = 19) has slightly greater frontogenesis than the top-left corner (n = 15), more clearly defined frontal slopes, and significantly stronger frontolysis just behind the frontogenetical region. This frontogenesis and frontolysis couplet below may be related to the couplets identified by Han et al. (2007), which were found to be a result of diabatic processes and contributed to greater ascent. All nodes exhibit similar predictabilities except for those in the top-left quadrant, which have lower predictability (not shown). The fact that predictability is lower even than nodes with little to no frontogenesis indicates that the organization of frontogenesis, rather than the magnitude, is the contributing factor and may be related either to the displaced frontogenesis maximum or the shallower frontal slope.
A 10° ERA5 cross-sectional frontogenesis SOM. Sample sizes comprising each node are in the top-right corners.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0004.1
Developing SOMs for upper and lower forecast quality terciles further elucidates frontogenetical differences (Fig. 15). Magnitudes of frontogenesis are not substantially different between SOM nodes for the two terciles, but the upper tercile exhibits more nodes with enhanced low-level frontogenesis. Among events with strong and deep frontogenesis, the low-level frontogenesis is collocated with the band centroid and slightly more upright for the upper tercile, while it is offset toward the warmer air with a shallower slope for the lower tercile. These differing slopes, combined with the above analysis of Fig. 14, suggest that events with shallower sloping frontogenesis offset toward warmer air at lower levels may be more difficult to predict than more upright frontogenesis. Both terciles show nodes with regions of frontolysis behind the frontogenetical region but the signal is strongest for the upper tercile.
(a) 10° ERA5 band cross-sectional frontogenesis SOM for the upper tercile of events sorted by forecast quality and (b) 10° ERA5 band cross-sectional frontogenesis SOM for the lower tercile of events sorted by forecast quality. Sample sizes comprising each node are in the top-right corners.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0004.1
ERA5 650-hPa SEPV SOM with a domain of 12.5° lat × 12.5° lon. Orientations and lengths of bands at the observed temporal midpoints of snowband events assigned to the node are overlaid. Sample sizes comprising each node are in the top-right corners.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0004.1
4. Conclusions
We investigated variations in predictive skill of mesoscale snowbands by HREF members over a period of five winter seasons using object-oriented verification. HREF simulated reflectivity forecasts were verified by comparing forecast and observed feature centroids, minimum contour distances, area ratios, area intersections, aspect ratios, and orientations. HREF members performed comparably, with member average interest scores falling between 0.70 and 0.76 on a scale of 0 (worst forecast) to 1 (best forecast). There was a small skill dependence on forecast lead, as time-lagged members performed about 0.03 points worse than their counterparts. Positional errors, including the centroid displacement and area intersection, were the greatest contributors to forecast error, though area differences also played an important role. The ARW and NSSL members systematically under-forecast the areas of observed snowbands.
To determine the causes for predictability variance, we used SOMs to identify patterns in environmental parameters associated with observed snowbands that may lead to better or worse snowband forecasts. These parameters included synoptic settings, including 500-hPa height anomalies and MSLP, and mesoscale environments, including frontogenesis, SEPV, and vertical motion. Our SOMs clustered banding events by these parameters, after which we compared the predictive skill of events within contrasting patterns to determine if skill varied across SOM nodes. A caveat to our results is that the intranode variability of the SOMs may be large at times, as demonstrated by ACC values in the geopotential height anomaly SOM and the variability in band orientations within SOM nodes. Thus, individual events may differ from the nodal average, even when the signal is strong.
The 500-hPa SOM reaffirmed the most common snowband flow patterns found by Novak et al. (2004) and Baxter and Schumacher (2017) using a robust, objective compositing procedure. That is, most bands were observed downstream of a negative 500-hPa anomaly and trough in southwesterly flow, with a smaller set of bands found near a positive anomaly and weak northwesterly or westerly flow. Nodes with band centroids near strong positive anomalies and ridges demonstrated slightly higher skill than nodes with band centroids near strong negative anomalies and troughs, driven by differences in the ARW, NMMB, and NSSL members, though the uncertainties are relatively high. The MSLP SOM reaffirmed previous findings of Novak et al. (2004) and Baxter and Schumacher (2017), with bands nearly evenly split between the northeast and northwest cyclone quadrants. Nodes organized based upon both the band-relative position of the cyclone and the strength of the cyclone, but neither appeared to be correlated with predictive skill.
Strong midlevel vertical motion is commonly associated with snowbands, and our SOM nodes reflected this relationship, with most nodes exhibiting some degree of enhanced upward motion. At the 650-hPa level, magnitude of upward motion was correlated with snowband predictive skill, with the strongest vertical motion events having a median interest score 0.06 points greater than the weakest vertical motion events. A SOM of cross-sectional vertical motion revealed a difference of 0.07 points between strong and weak vertical motion cases. Differences were primarily the result of positional error in all members, but the ARW and NSSL demonstrated the largest errors due to significant under-forecasting of precipitation areas in weak vertical motion events. The cross-sectional analysis also revealed that events with a single, organized region of upward motion have greater skill than events with disorganized or bimodal regions of upward motion, influenced by greater positional errors in the disorganized nodes.
The 700-hPa frontogenesis SOM showed at least some enhanced frontogenesis associated with most nodes. However, there was a set of nodes that demonstrated no frontogenesis or weak frontolysis and these nodes received comparable interest scores to the nodes with strong frontogenesis. Vertical motion without frontogenesis may be associated with other forcing mechanisms, such as convective processes, orography, or shear instability, frontogenesis at a level other than 700 hPa, the result of cancellation when averaging regions of frontogenesis and frontolysis, or a combination of these factors. Nodes with shallower frontal slopes and greater low-level frontogenesis displacement toward warm air were less well-predicted than nodes with more upright frontogenesis. An analysis of 650-hPa SEPV indicated that events with greater midlevel stability have slightly greater predictive skill than events with reduced midlevel stability, but the signal was not particularly robust.
The dependence of band predictive skill on vertical motion is not necessarily a surprising result, as it seems logical that the more tractable forcing signal would be easier for models to capture, but the large magnitude of skill variance by vertical velocity could help forecasters to modulate their forecast confidence in potential banding scenarios. Our results reaffirmed the primary ingredients present in mesoscale snowband formation but emphasize that examination of the vertical velocity signature should be a key step in snowband forecasting. These results could also serve as a starting point for model developers to refine HREF members for snowband events based on the interest score parameters.
The lack of dependence of snowband predictability on most synoptic and mesoscale variables, such as 500-hPa heights, MSLP, magnitude of frontogenesis, and SEPV suggests that the variability in verification scores may largely be driven by case-to-case differences. In particular, differences may be associated with initial condition or model physics errors, corroborating results of Novak and Colle (2012), which found large ensemble uncertainty primarily due to differences in initial conditions. Analysis of initial condition errors associated with the identified snowband cases could shed more light on this possibility.
Additional future work may involve testing multivariate SOMs, which could reveal interactions of variables that contribute even more to band predictive skill. For example, while the band-relative position of the surface cyclone may not relate to forecast skill, the intersection of band-relative position of the surface cyclone and flow regime still may correlate with skill. We also seek to apply these results to improve probabilistic snowband forecasts through other means, such as machine learning. This would also help to clarify the relative value of an ingredients-based forecasting approach using frontogenesis and stability, versus a more explicit forecasting approach using vertical motion and simulated-reflectivity, and whether there is additional utility in applying both.
Acknowledgments.
Support for this research was provided by NOAA Grant NA19NWS4680001, awarded to North Carolina State University. Dr. Maria Molina of the University of Maryland and the National Center for Atmospheric Research (NCAR) provided an invaluable SOM script framework for us to follow, greatly expediting this work. We would also like to thank the National Severe Storms Laboratory, Dr. Adam Clark, and Dr. Brett Roberts for making an archive of HREF system data available. Finally, we thank three anonymous reviewers for their insightful comments and suggestions.
Data availability statement.
HREF data are available through the National Severe Storms Laboratory at https://data.nssl.noaa.gov/thredds/catalog/FRDD/HREF.html, ERA5 data are available through the European Centre for Medium-Range Weather Forecasts (ECMWF) at https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5, and base reflectivity mosaics are available through the Iowa Environmental Mesonet (IEM) at https://mesonet.agron.iastate.edu/docs/nexrad_mosaic/.
REFERENCES
Baxter, M. A., and P. N. Schumacher, 2017: Distribution of single-banded snowfall in central U.S. cyclones. Wea. Forecasting, 32, 533–554, https://doi.org/10.1175/WAF-D-16-0154.1.
Bluestein, H., 1993: Synoptic-Dynamic Meteorology in Midlatitudes. Vol. II, Observations and Theory of Weather Systems. Oxford University Press, 594 pp.
Cassano, E. N., A. H. Lynch, J. J. Cassano, and M. R. Koslow, 2006: Classification of synoptic patterns in the western Arctic associated with extreme events at Barrow, Alaska, USA. Climate Res., 30, 83–97, https://doi.org/10.3354/cr030083.
Connelly, R., and B. A. Colle, 2019: Validation of snow multibands in the comma head of an extratropical cyclone using a 40-member ensemble. Wea. Forecasting, 34, 1343–1363, https://doi.org/10.1175/WAF-D-18-0182.1.
Ganetis, S. A., B. A. Colle, S. E. Yuter, and N. P. Hoban, 2018: Environmental conditions associated with observed snowband structures within Northeast U.S. winter storms. Mon. Wea. Rev., 146, 3675–3690, https://doi.org/10.1175/MWR-D-18-0054.1.
Han, M., R. M. Rauber, M. K. Ramamurthy, B. F. Jewett, and J. A. Grim, 2007: Mesoscale dynamics of the trowal and warm-frontal regions of two continental winter cyclones. Mon. Wea. Rev., 135, 1647–1670, https://doi.org/10.1175/MWR3377.1.
Hersbach, H., and Coauthors, 2023: ERA5 hourly data on single levels from 1940 to present. Copernicus Climate Change Service (C3S) Climate Data Store (CDS), accessed 1 December 2021, https://doi.org/10.24381/cds.adbb2d47.
Hewitson, B., and R. G. Crane, 2002: Self-organizing maps: Applications to synoptic climatology. Climate Res., 22, 13–26, https://doi.org/10.3354/cr022013.
Hua, Z., and A. K. Anderson-Frey, 2022: Self-organizing maps for the classification of spatial and temporal variability of tornado-favorable parameters. Mon. Wea. Rev., 150, 393–407, https://doi.org/10.1175/MWR-D-21-0168.1.
Ikeda, K., M. Steiner, J. Pinto, and C. Alexander, 2013: Evaluation of cold-season precipitation forecasts generated by the hourly updating High-Resolution Rapid Refresh model. Wea. Forecasting, 28, 921–939, https://doi.org/10.1175/WAF-D-12-00085.1.
Ji, L., X. Zhi, C. Simmer, S. Zhu, and Y. Ji, 2020: Multimodel ensemble forecasts of precipitation based on an object-based diagnostic evaluation. Mon. Wea. Rev., 148, 2591–2606, https://doi.org/10.1175/MWR-D-19-0266.1.
Johnson, A., and X. Wang, 2013: Object-based evaluation of a storm-scale ensemble during the 2009 NOAA Hazardous Weather Testbed Spring Experiment. Mon. Wea. Rev., 141, 1079–1098, https://doi.org/10.1175/MWR-D-12-00140.1.
Kohonen, T., 1982: Self-organized formation of topologically correct feature maps. Biol. Cybern., 43, 59–69, https://doi.org/10.1007/BF00337288.
Kohonen, T., 2001: Self-Organizing Maps. 3rd ed. Springer-Verlag, 501 pp.
Kohonen, T., 2013: Essentials of the self-organizing map. Neural Networks, 37, 52–65, https://doi.org/10.1016/j.neunet.2012.09.018.
Lackmann, G. M., and G. Thompson, 2019: Hydrometeor lofting and mesoscale snowbands. Mon. Wea. Rev., 147, 3879–3899, https://doi.org/10.1175/MWR-D-19-0036.1.
May, R. M., and Coauthors, 2022: MetPy: A python package for meteorological data. Unidata, accessed 14 December 2021, https://github.com/Unidata/MetPy.
Mechem, D. B., C. S. Wittman, M. A. Miller, S. E. Yuter, and S. P. de Szoeke, 2018: Joint synoptic and cloud variability over the Northeast Atlantic near the Azores. J. Appl. Meteor. Climatol., 57, 1273–1290, https://doi.org/10.1175/JAMC-D-17-0211.1.
Nicosia, D. J., and R. H. Grumm, 1999: Mesoscale band formation in three major Northeastern U.S. snowstorms. Wea. Forecasting, 14, 346–368, https://doi.org/10.1175/1520-0434(1999)014<0346:MBFITM>2.0.CO;2.
Novak, D. R., and B. A. Colle, 2012: Diagnosing snowband predictability using a multimodel ensemble system. Wea. Forecasting, 27, 565–585, https://doi.org/10.1175/WAF-D-11-00047.1.
Novak, D. R., L. F. Bosart, D. Keyser, and J. S. Waldstreicher, 2004: An observational study of cold season–banded precipitation in Northeast U.S. cyclones. Wea. Forecasting, 19, 993–1010, https://doi.org/10.1175/815.1.
Novak, D. R., J. S. Waldstreicher, D. Keyser, and L. F. Bosart, 2006: A forecast strategy for anticipating cold season mesoscale band formation within eastern U.S. cyclones. Wea. Forecasting, 21, 3–23, https://doi.org/10.1175/WAF907.1.
Novak, D. R., D. R. Bright, and M. J. Brennan, 2008: Operational forecaster uncertainty needs and future roles. Wea. Forecasting, 23, 1069–1084, https://doi.org/10.1175/2008WAF2222142.1.
Nowotarski, C. J., and A. Jensen, 2013: Classifying proximity soundings with self-organizing maps toward improving supercell and tornado forecasting. Wea. Forecasting, 28, 783–801, https://doi.org/10.1175/WAF-D-12-00125.1.
Nowotarski, C. J., and E. A. Jones, 2018: Multivariate self-organizing map approach to classifying supercell tornado environments using near-storm, low-level wind and thermodynamic profiles. Wea. Forecasting, 33, 661–670, https://doi.org/10.1175/WAF-D-17-0189.1.
Qiu, L., and W. Nixon, 2008: Effects of adverse weather on traffic crashes: Systematic review and meta-analysis. Transp. Res. Rec., 2055, 139–146, https://doi.org/10.3141/2055-16.
Radford, J. T., G. M. Lackmann, and M. A. Baxter, 2019: An evaluation of snowband predictability in the High-Resolution Rapid Refresh. Wea. Forecasting, 34, 1477–1494, https://doi.org/10.1175/WAF-D-19-0089.1.
Roberts, B., B. T. Gallo, I. L. Jirak, and A. J. Clark, 2019: The High Resolution Ensemble Forecast (HREF) system: Applications and performance for forecasting convective storms. 2019 Fall Meeting, San Francisco, CA, Amer. Geophys. Union, Abstract A31O-2797.
Sanders, F., and L. F. Bosart, 1985: Mesoscale structure in the megalopolitan snowstorm of 11–12 February 1983. Part I: Frontogenetical forcing and symmetric instability. J. Atmos. Sci., 42, 1050–1061, https://doi.org/10.1175/1520-0469(1985)042<1050:MSITMS>2.0.CO;2.
Schuenemann, K. C., J. J. Cassano, and J. Finnis, 2009: Synoptic forcing of precipitation over Greenland: Climatology for 1961–99. J. Hydrometeor., 10, 60–78, https://doi.org/10.1175/2008JHM1014.1.
Thorpe, A. J., and K. A. Emanuel, 1985: Frontogenesis in the presence of small stability to slantwise convection. J. Atmos. Sci., 42, 1809–1824, https://doi.org/10.1175/1520-0469(1985)042<1809:FITPOS>2.0.CO;2.
Tibshirani, G., G. Walther, and T. Hastie, 2001: Estimating the number of clusters in a data set via the gap statistic. J. Roy. Stat. Soc., 63, 411–423, https://doi.org/10.1111/1467-9868.00293.
Tobin, D. M., M. R. Kumjian, and A. W. Black, 2019: Characteristics of recent vehicle-related fatalities during active precipitation in the United States. Wea. Climate Soc., 11, 935–952, https://doi.org/10.1175/WCAS-D-18-0110.1.
Vettigli, G., 2019: MiniSom: Minimalistic and NumPy based implementation of the self organizing map, Release 2.1.5. Accessed 14 December 2021, http://github.com/JustGlowing/minisom.
Wang, D., and Coauthors, 2022: Linking synoptic patterns to cloud properties and local circulations over southeastern Texas. J. Geophys. Res. Atmos., 127, e2021JD035920, https://doi.org/10.1029/2021JD035920.
