1. Introduction
Numerous climatological studies have examined the connections between sounding-derived severe weather parameters and severe storm and tornadic ratings. Early diagnoses of near-storm soundings (e.g., Fawbush et al. 1951; Fawbush and Miller 1952, 1954; Beebe 1958; Maddox 1976) indicated that environments of tornadic thunderstorms are marked by large CAPE and strong midlevel wind speeds (3–6 km AGL). Subsequent studies revealed that mid- and low-level (1–3 km AGL) shear and thermodynamic properties are skillful in distinguishing between tornadic and nontornadic thunderstorms as well as in forecasting tornado damage rating (Davies-Jones et al. 1990; Colquhoun and Riley 1996). Recent studies have stressed that characteristics of the lowest 1 km AGL, especially kinematic quantities, are essential in determining supercellular strength and tornadic potential (Markowski et al. 2003; Rasmussen 2003; Markowski et al. 2003; Rasmussen 2003; Thompson et al. 2003, hereafter T03; Craven et al. 2004; Davies 2004; Grams et al. 2012; Thompson et al. 2012; Nowotarski and Jensen 2013).
These investigations provide a general framework for using sounding-derived parameters to forecast supercells and tornadoes. However, their conclusions may not be applicable in all regimes. In particular, the sounding databases used in these studies were weighted toward, if not exclusively composed of, daytime cases. Environments that support daytime tornadoes typically have high CAPE. However, many nocturnal environments are characterized by decreased near-surface temperatures and a low-level inversion, leading to less surface-based instability and greater CIN. Logically, these conditions would be expected to inhibit strong tornadogenesis in some cases (Leslie and Smith 1978; Nowotarski et al. 2011).
Recent research has sought to describe the characteristics of environments in which nocturnal tornadoes form. For example, Davies and Fischer (2009) compared nighttime to daytime “significantly tornadic” [F2 on the Fujita scale; Fujita (1971)] supercell soundings and found that low-level static stability shows skill in discriminating between significantly tornadic and nontornadic environments. Also, Mead and Thompson (2011) considered model-derived soundings for significant nocturnal tornadoes in the central and southern Great Plains associated with a certain similar synoptic pattern. They found, as did Davies and Fischer (2009), that nocturnal tornadoes generally occur with less instability, but much larger values of storm-relative helicity (SRH; Davies-Jones et al. 1990) than during the day, and that CIN can be a limiting factor for tornadoes at night. Kis and Straka (2010) provided the most comprehensive climatology of significant nocturnal tornadoes to date. They found that environments deemed inhospitable for late afternoon/evening tornadoes (those with marginal convective instability and stable boundary layers) were, in fact, conducive to nocturnal tornadogenesis. Given this finding, their conclusion was that guidance from existing tornado climatologies, obtained primarily from daytime conditions, can be inadequate and even misleading for forecasting nocturnal tornadoes.
Taking into account these differences when forecasting tornadoes is important as nocturnal tornadoes, though less common than their daytime counterparts, pose a disproportionate threat to human life. From 1985 to 2005, nocturnal tornadoes accounted for only 26% of all tornadoes but were responsible for over 42% of all tornado fatalities (Ashley 2007). While this increased vulnerability to nocturnal tornadoes can be largely attributed to decreased situational awareness as well as geographic and socioeconomic factors (Ashley et al. 2008), it also highlights an area of scientific uncertainty.
In this study, Rapid Update Cycle (RUC-2; Benjamin et al. 2004a,b) model output was utilized to compile a database of tornado proximity soundings that span the diurnal cycle. Abandoning radiosonde observations in favor of model data provides access to a larger number of tornado proximity environments and mitigates the timing and location issues often associated with defining a suitable proximity sounding (Beebe 1958; Potvin et al. 2010). However, the process of using simulated instead of observed soundings is not without caveats. Several studies have found that RUC-2 environments have biases when compared with observations, especially in the boundary layer. For example, RUC-2 has a tendency to overestimate near-surface wind speeds and underestimate boundary layer depths (Schwartz and Brundage 2004; Nowotarski and Jensen 2013). To alleviate systematic errors in this sounding database (Doswell 1991), model analyses were used whenever possible, and it is assumed that these profiles offer an accurate representation of the environment. Indeed, previous studies (e.g., T03) have found RUC-2 soundings to be suitable proxies for radiosonde observations, and they are frequently used in severe storm climatologies.
Analysis of these soundings seeks to identify differences between nighttime and daytime near-storm tornadic environments, as well as to find parameters that show the greatest skill in forecasting tornado ratings in both regimes. To investigate the nocturnal tornado environment, this study employed a selection of 33 parameters previously found relevant for forecasting tornadoes (Table 1) as calculated from 194 RUC-2 proximity soundings associated with recent (2003–12) lengthy (≥10-km track length) ≥ EF1 [on the enhanced Fujita scale; Doswell et al. (2009)] tornadoes. Note that EF0 tornadoes were not considered because of the difficulty associated with discriminating between strong nontornadic winds and EF0 tornado damage. This database contains more nocturnal tornado soundings and examines a broader array of severe parameters than those used by Davies and Fischer (2009), Kis and Straka (2010), and Mead and Thompson (2011). Identifying diurnal changes in tornado proximity environments will facilitate a comparison of these results with findings from previous studies that used datasets dominated by daytime cases. Hence, we formed sets of approximately equal numbers of nighttime and daytime cases, as well as comparable numbers of weak (EF1–EF2) and strong (≥EF3) tornadoes (Table 2). We analyzed parameter value distributions and forecast skill in order to investigate differences in sounding-derived tornado forecast parameters between these collections, a method that previous studies of nocturnal tornado proximity soundings have not used. A description of the data and the methods are presented next, followed by the results in section 3, and a discussion and general conclusions in sections 4 and 5, respectively.
References and equations for the severe parameters calculated for this study. Here, T denotes a temperature (°C), with a subscript indicating the pressure level (hPa) where this value was taken; α denotes the specific volume and a subscript lp denotes a value associated with a lifted parcel; LFC stands for a lifted parcel’s level of free convection; and EL stands for its equilibrium level. For SRH, C denotes the storm motion vector. In the text or figures, the two integers following VS or SRH represent 
Breakdown of tornado cases by time of day and by EF-scale rating.
2. Data and methods
a. Case selection and data retrieval
The dataset used for this analysis is composed of soundings for 194 tornadic storms, spanning the 10-yr period from 2003 to 2012. Nontornadic storms were not included. All storms occurred east of the Rocky Mountains and were largely confined to the central and southeastern United States (Fig. 1). All tornadoes had a damage path of at least 10 km. In addition, all tornadoes occurred at least 300 km away from, or at least 2 h before or after, any other tornado in the dataset. The goal of these constraints was to prevent oversampling of similar environments. The National Center for Environmental Information’s Storm Data information, accessed via the National Oceanic and Atmospheric Administration/Storm Prediction Center’s actual tornado database, was used to obtain the rating, start and end times, pathlength, and exact path start location of each tornado.
Distribution of tornado cases by state as compiled from RUC-2 analyses.
Citation: Weather and Forecasting 32, 2; 10.1175/WAF-D-16-0029.1
The F scale is subject to intrinsic errors (Doswell and Burgess 1988; Grazulis 1993). It is a damage-based scale, meaning that rating a tornado is possible only if it causes damage. Even if a tornado does cause damage, rating a tornado based on damage alone is difficult given the dependence of destruction upon a structure’s constructional quality and material composition. This problem was specifically addressed with the implementation of the EF scale (Edwards et al. 2013); however, rating errors still exist. Hence, it is possible that some tornadoes in this dataset are miscategorized.
To ensure that each sounding was representative of the environment proximate to the storm, sounding locations within the RUC model output were selected carefully. To be considered in proximity to a tornado, each sounding was
taken from a RUC analysis ≤ 2 h from tornadogenesis,
located ≤80 km from the tornado start, and
free of contamination from precipitation (i.e., saturated and/or moist-adiabatic profiles over the depth of the troposphere).
Strong nocturnal tornadoes, climatologically, are the least frequent category considered in this analysis. Hence, to form the current dataset, we acquired all soundings associated with nocturnal ≥EF3 tornadoes that adhere to these restrictions, which yielded 47 cases. From there, cases were selected randomly from the remaining categories (nocturnal weak, daytime weak, and daytime strong) until each dataset was composed of approximately 47 cases from each category (Table 2).
Model analyses were available every hour, with forecasts available every 1 h out to 12 h at each analysis time. Model fields were available at every 50 hPa in the vertical and on a 40-km horizontal grid for all cases from 2003 through 2004, at every 50 hPa and on a 20-km horizontal grid from 2005 through 15 April 2007, and at every 25 hPa on a 13-km grid afterward.
b. Parameter computation
Each sounding was used to calculate 33 severe storm parameters that have been used to diagnose severe potential in previous sounding studies (Table 1). Storm-relative parameters were calculated using the Bunkers et al. (2000) storm motion vector. All thermodynamic variables (e.g., CAPE and CIN), unless otherwise noted, were calculated using the 100-hPa mixed layer as suggested by Craven et al. (2002), and will henceforth be referred to without the mixed layer (ML) designation. Also, the virtual temperature correction (Doswell and Rasmussen 1994) was applied for thermodynamic computations.
c. Analysis techniques
Several graphical and statistical techniques were employed to examine the computed parameters. In addition to traditional statistical measures, such as mean, interquartile range, variance, bias, and standard deviation, the Heidke skill score (HSS; Heidke 1926), a statistical estimate of skill, was used to determine whether or not a parameter has skill in forecasting the tornado rating (Doswell et al. 1990). In addition to traditional graphing techniques such as x–y scatterplots, Gaussian kernel density estimation (GKDE; Scott 1992) was utilized for two-dimensional probability analysis.
1) HSS
Illustration of one- and two-parameter HSS methods. Each plot shows the same scatter of weak (light blue) and strong (dark blue) 0–1-km shear (VS01) vs 3–9-km shear (VS39). (a) A one-parameter illustration, where gray shading shows the region containing points that would be associated with a forecast of a strong tornado based on a threshold of VS01 ≥ 16.2 m s−1. (b) A two-parameter illustration, where the points that would be associated with a strong tornado, shaded in gray, are those with VS01 ≥ 16.4 m s−1 and VS39 ≥ 10.4 m s−1. The highest HSSs for the one- and two-parameter methods are 0.50 and 0.56, respectively.
Citation: Weather and Forecasting 32, 2; 10.1175/WAF-D-16-0029.1
2) Gaussian kernel density estimation
This study also used kernel density estimation (KDE), a nonparametric method for estimating the multivariate probability density function of two random variables. In GKDE employed here, a Gaussian curve (i.e., the kernel) is used to smooth point density estimates, whereby information can be gathered about the distribution at points where no observed data exist. Similar methods have been used to create continuous probabilistic fields of significant severe storm report locations (Smith et al. 2012) and tornadic near-storm environmental characteristics (Thompson et al. 2013) by the convective mode. This study will employ GKDE to evaluate the clustering of tornado environments in two-dimensional spaces of severe weather sounding parameters.
3. Results
Analyses presented here include examinations of the distribution of parameter values as well as parameter forecasting skill. The initial focus will be on comparing distributions of each parameter for nocturnal and daytime cases, as well as for weak and strong tornadoes. The differences noted in this evaluation will then guide an assessment of the skill that each parameter, or combination of parameters, has in discriminating between weak and strong tornadic environments.
a. Parameter distributions
First, we present distributions of actual parameter values and how these distributions vary diurnally and by tornado damage category. Parameters are grouped as either thermodynamic or shear based, and are then presented alongside similarly categorized variables. See the appendix for parameter distribution means for the various groups analyzed here. As a general rule of thumb, separation between the upper or lower quartile of one box plot and the median of another indicates that the distributions are likely different (Tukey 1977; Krzywinski and Altman 2014). For convenience, this separation will be used herein to denote “significant” separation.
Lower near-surface temperatures typical of the nocturnal boundary layer result in generally higher nighttime LFCs (Fig. 3b) and correspondingly lower surface-based CAPE (SBCAPE) and most unstable CAPE (MUCAPE) values and higher CIN (Fig. 3a). However, the difference between the nighttime and daytime distributions is not significant. Lower LFCs (Fig. 3f) and higher SBCAPE and MUCAPE values (Fig. 3e) are associated with strongly tornadic daytime environments, but these differences are not as evident in the nocturnal soundings (Figs. 3d,c). In fact, the only significant difference in the thermodynamic environments of weak and strong nocturnal tornadoes is found in the MUH (Fig. 3d), which is higher for strong rather than weak nocturnal tornadoes. Environments of weakly tornadic storms, both at night and during the day, occupy a larger CIN and smaller CAPE, SBCAPE, and MUCAPE parameter spaces than those of strongly tornadic storms (Figs. 3c,e). As there are equal numbers of weak and strong tornadoes, this spread is not attributable to differences in nighttime and daytime sample sizes.
(a) Violin and box-and-whisker plots for all cases of CAPE, SBCAPE, and MUCAPE plotted along the left axis, and CIN and 0–3-km CAPE are plotted along the right axis. The color-filled bars for each nighttime (blue) and daytime (red) violin plot represent a smoothed histogram of the data. Data above (below) the 95th (5th) percentile were not used in the histograms. In the box plot, the white circle corresponds to the data median; the top and bottom black box edges identify Q3 (75th percentile) and Q1 (25th percentile), respectively; and the top and bottom whisker ends correspond to the 10th and 90th percentiles, respectively. Outliers, or points outside the whiskers, are not plotted. (b) Violin and box-and-whisker plots for all cases of LCL, LFC, MUH, and 
Citation: Weather and Forecasting 32, 2; 10.1175/WAF-D-16-0029.1
Overall, shear parameters show more significant separation among the various groups than do thermodynamic variables. Decreased near-surface wind speeds are associated with the decoupling of the nocturnal boundary layer from the atmosphere above. This phenomenon likely contributes to higher nocturnal SRH (Fig. 4a) and vector shear (Fig. 4b) throughout the troposphere compared with daytime cases. This increase in wind shear at night is particularly evident in the distributions of 0–1- and 0–3-km SRH and shear. However, this increase in low-level shear could also be a result of the boundary layer wind maximum, or low-level jet (LLJ; Bonner 1968), often seen in the plains at night. Similarly, shear parameters computed over all surface-based levels, as well as the effective-layer SRH (ESRH; Fig. 4c) and bulk-wind difference (EBWD; Fig. 4d), are significantly higher for strong versus weak nocturnal cases. Comparable results can be seen for daytime cases (Figs. 4e,f), though the separation between the distributions of weak and strong daytime tornadoes is only significant for EBWD as well as 0–1- and 0–3-km shears.
As in Fig. 3, but for (a),(c),(e) SRH01, SRH03, SRH06, and ESRH plotted along the left axis and EBS plotted along the right axis; and (b),(d),(f) VS01, VS03, VS06, VS09, VS13, VS16, VS19, VS36, VS39, and EBWD.
Citation: Weather and Forecasting 32, 2; 10.1175/WAF-D-16-0029.1
Given a relatively large number of possible parameters from which to draw conclusions, it is convenient to eliminate some of the parameters to simplify the analysis. To accomplish this, permutation tests (Pitman 1938) were conducted. The significance of the test statistic p represents the probability that the difference between the means of any two samples could arise by pure chance, given no assumptions about the distribution of the larger population. Three pairs of tornado categories (representing six samples) were used for analysis: all nighttime versus all daytime cases, weak versus strong nighttime cases, and weak versus strong daytime tornadoes. For each group comparison, permutation tests of the group means were carried out on each severe parameter (Table 3). A significance level of p = 5% was used to determine if a test statistic was considered statistically significant. These permutation tests only analyzed differences in distribution means; hence, they do not take the parameter spread or distribution skew in to account. However, for brevity, further analyses will only include those parameters for which any test resulted in a significant test statistic value. Removing the parameters with p ≥ 0.05 from consideration is not an indication that a parameter is unimportant for tornadic storms, only that it fails to distinguish, statistically, between weak and strong, or daytime and nighttime, tornadoes.
Results from permutation of means testing and difference between group means for all three pairs of comparison groups. The difference values shown are the result of subtracting the nighttime (weak) tornado mean from the daytime (strong) tornado mean in the case of nighttime vs daytime (weak vs strong) comparison. Permutation test statistics are given (in %). Variables for which no test resulted in a significant test statistic are not shown.
For comparisons of all weak and strong tornadic environments (Table 3), nearly all parameters were retained after permutation testing. When considering the differences between strong and weak tornadoes during the day, only surface-based and effective-layer shear parameters, and most thermodynamic parameters, were kept. However, for nocturnal tornadoes, nearly all shear parameters were kept, while MUH and CAPE were the only thermodynamic parameters retained. These results suggest that, while thermodynamic quantities vary more frequently between weak and strong daytime tornadoes than shear-based variables, the greatest differences present between weakly and strongly tornadic nocturnal soundings are kinematic parameter values.
b. Single-parameter forecast applicability
Although single-parameter statistics, in the form of box plots, are useful for comparing distributions of parameters, they provide less information about a parameter’s forecast applicability. Some measure of the skill for each parameter is desirable to provide a more robust analysis about its usefulness in forecasting. Toward this end, the HSS was employed to determine each parameter’s suitability for predicting the tornado rating category (i.e., weak or strong). Any HSS greater than 0.24 denotes meaningful forecast skill. Five hundred different values within the range of each parameter were tested for skill, and only the parameter value corresponding to the most skilled forecast is reported. Thus, these values provide only an approximate threshold value (±0.02%).
Only shear parameters, MUH, and LFC display significant skill at night, with 0–1- and 0–3-km shears and MUH having the highest skill values (Table 4). Although 0–1-km shear also displays significant skill for the forecasting of the daytime tornado rating, its HSS value is smaller than at night, and the optimal threshold speed is ~5.4 m s−1 slower. In addition, 0–3-km shear has the highest forecasting skill during the day, with a forecasting skill similar to that of night. Thus, more shear parameters are skillful in predicting tornado ratings at night than during the day, in agreement with the distributions of the shear parameters in Fig. 4. Additionally, the optimal MUH threshold at night is only 20 m, but the nocturnal HSS for MUH remains relatively high (0.39) if we allow the threshold to be 0 m (i.e., the same as the daytime optimal threshold). This observation, combined with higher (lower) MUH values for strong compared with weak nocturnal (daytime) tornadoes (Fig. 3 and Table A1), indicates that while a surface-based most unstable parcel is favored for stronger tornadoes during the day, elevated maximum instability is favored at night. Furthermore, CIN, SBCAPE, and MUCAPE display significant forecasting skill during the day, though they do not at night. This also coincides with the results in section 3a. Together, these findings suggest that, while many shear parameters have skill in forecasting the tornado rating for this dataset, both at night and during the day, their relative importance varies between the two forecasting regimes.
Highest HSS values and their associated optimal statistical thresholds for all single-parameter skill score tests. The biases, defined as (false alarms/misses), are also shown for each parameter. Parameters and values set in boldface were those with HSS ≥ 0.24 and were therefore considered to have significant skill vs the no-skill forecast.
While the values in Table 4 are useful for analyzing how well the parameters forecast tornadic ratings within the current sample, these values do not indicate how well a parameter performs when used to forecast tornadic damage rating for a different population (e.g., a climatologically representative sample with ~10% tornadoes of magnitude ≥ EF3 and ~25% nocturnal tornadoes). To investigate how the highest-skilled parameter thresholds might perform when used with different samples, the optimal thresholds listed in Table 4 were used to calculate the HSS for each of 5000 random permutations (with replacement, i.e., statistical bootstrapping) of the current 194-sounding dataset. Analyzing parameter skill for forecasting in each of these resampled datasets removes the dependency on the sample distribution that is inherent in the skill scores in Table 4, thus allowing broader applicability.
All parameters found to have significant skill when used to forecast for the current dataset distribution also are the only parameters to have a median resampled HSS value above the critical line denoted by HSS ≥ 0.24 (Figs. 5 and 6). The height of the most unstable parcel and the LFC are the only thermodynamic parameters tested that have median nighttime resampled HSS values that exceeded 0.24 (Fig. 5), confirming that, regardless of sample configuration, thermodynamics are generally poor at forecasting the nocturnal tornado rating group. This result is generally true for daytime cases, although daytime LFC, CIN, SBCAPE, and MUCAPE have median resampled HSS values ≥ 0.24, with much of the daytime distributions of the latter three displaced above the corresponding nighttime distribution. While more daytime thermodynamic parameters display significant forecasting skill than at night, the daytime HSS distribution of MUH is displaced significantly below the corresponding nighttime distribution. This difference suggests that, although nighttime thermodynamic quantities may not have significant skill in forecasting tornadic intensities in general, they have the potential to be more skillful than during the day.
Resampled HSS values for all thermodynamic parameters remaining after permutation testing. Nighttime (blue) and daytime (red) resampled skill scores are plotted for each parameter. The black triangle corresponds to the data median; the top and bottom box edges identify Q3 (75th percentile) and Q1 (25th percentile), respectively, and the top and bottom whisker ends correspond to the 10th and 90th percentiles, respectively. Outliers, or points outside the whiskers, were not plotted. Note that the horizontal black solid line represents the line for significant skill (0.24).
Citation: Weather and Forecasting 32, 2; 10.1175/WAF-D-16-0029.1
As in Fig. 5, but for all shear parameters remaining after permutation testing.
Citation: Weather and Forecasting 32, 2; 10.1175/WAF-D-16-0029.1
Irrespective of the time of day, shear parameters show more skill in discriminating between tornado damage ratings than do thermodynamic variables (Fig. 6). However, for 9 out of the 13 shear parameters, the nocturnal HSS distribution is significantly higher than during the day. All shear parameters, save 
While the median value of all nighttime SRH quantities, along with most daytime and all nighttime vector shear distributions, exceed 0.24, none of the daytime SRH HSS distributions surpasses this threshold. This difference in daytime forecasting skill is large enough such that the shear over the 0–1-, 0–3-, and 0–6-km layers displays significantly greater skill during the day than SRH computed over the same layer. Additionally, nocturnal HSS distributions for shear computed over shallow depths (e.g., the 0–1- and 0–3-km layers) are greater than those for nocturnal SRH calculated over the same depth. These differences suggest that the vector shear may be more useful for forecasting the tornado rating than SRH, especially during the day.
c. Combined parameter forecasting applicability
Although the distributions of the single parameters and their forecasting ability prove insightful, it is possible that a multiparameter forecasting method could have higher skill. Therefore, pairs of candidate parameters were considered. For this evaluation, parameters that had the highest single-parameter forecasting skill (0–1-, 0–3-, and 0–6-km shears and effective bulk wind difference) were combined with other parameters in an attempt to improve upon the resampled HSS distribution of the original parameter. The optimal thresholds for the two-parameter HSS resampling were not necessarily the same as those in the single-parameter HSS resampling technique.
Assessing thermodynamic parameters in addition to daytime shear parameters (Fig. 7) results in significantly higher daytime tornadic forecasting skill for more combinations than at night. Of the 31 distributions, 17 (5) improve significantly on the single-parameter forecasting skill during the day (at night), resulting in a mean increase in median skill of 0.07 (0.02). Of all thermodynamic parameters, CIN, MUCAPE, and SBCAPE add the most skill for forecasting daytime tornadic rating, especially when combined with 0–1-km shear (Fig. 7a) and MUH (Fig. 7d). Combining CIN with MUH also results in an increase in its nocturnal forecasting skill, but CIN does not improve on the skill of the other three shear parameters tested. Traditional severe storm forecasting considers both kinematic and thermodynamic parameter analyses, but these results indicate that this approach for forecasting the nocturnal tornado rating may not be useful as only CIN, LFC, and MUH infrequently add value to the forecasting skill of the shear parameters at night. Overall, the combinations that produce the highest daytime increase over the original parameters skill scores are 0–1-km shear with MUCAPE and MUH with LFC. During the nighttime, the most significant improvements result from combining the effective bulk wind difference and LFC with MUH.
Resampled HSS values for (a) 0–1-, (b) 0–3-, and (c) 0–6-km shears, and (d) the effective-layer shear combined with thermodynamic parameters. Nighttime (blue) and daytime (red) resampled skill scores are plotted for each parameter/combination. Pink (blue) horizontal lines indicate the median of the distribution of each single-parameter HSS values for daytime (nighttime) cases.
Citation: Weather and Forecasting 32, 2; 10.1175/WAF-D-16-0029.1
The addition of other kinematic parameters to the 0–1-, 0–3-, and 0–6-km shears, and effective bulk wind difference results in more modest overall improvements over single-parameter skill for daytime tornado rating forecasts, but more substantial skill improvements at night (Fig. 8). Significant increases over the single-parameter forecasting skill occurred for 19 (12) of the 53 combinations at night (during the day), providing a mean increase in median skill of 0.05 (0.04). Combining low-level shear, or 0–1-km (Fig. 8a) and 0–3-km (Fig. 8b) shears with the deeper-layer shear (e.g., 0–6-, 0–9-, and 1–6-km shears) results in significant skill improvements at night, but not during the day. In fact, the combination of 0–1-km shear with deep-layer shear at night results in HSS distributions that are significantly greater than those during the day. No combination of 0–1 or 0–3 km shear with other shear parameters significantly improves their skill during the day, aside from combining them with each other. However, as these parameters are mutually dependent (r ~ 0.73), combining them provides little insight. The greatest combined HSS for nighttime forecasting came from the combinations of 0–1-km shear with the 3–9-km and effective-layer shear, suggesting that considering both shallow- and deep-layer shears provide utility in forecasting nocturnal tornado ratings. For forecasting daytime tornado rating groupings with combinations of kinematic parameters, considering effective bulk shear and 
As in Fig. 7, but for combinations with kinematic parameters.
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The HSS values and optimal thresholds for these significant combinations, as well as the most significant kinematic–thermodynamic parameter combinations discussed previously, are shown in Table 5. Although the optimal thresholds for these two-parameter forecasts were not forced to be the same as their optimal one-parameter thresholds, the majority remained unchanged. However, this was not the case for the effective bulk wind difference and CIN, whose optimal values changed when combined with each other. The optimal nocturnal CIN threshold increased from −46.5 to −77.8 J kg−1 when combined with the effective bulk wind difference, whose optimal threshold decreased from 28.1 to 23.6 m s−1. Thus, the effective bulk shear and CIN pose a problem for practical tornado rating forecasting: the use of a parameter by itself leads to one optimal threshold, whereas combining that same parameter with another variable leads to a different optimal threshold.
HSS values and their associated optimal thresholds for the most significant two-parameter skill score tests. For each combination, 
d. Two-parameter-space analysis
The maximum HSS values and their distributions for resampled populations are useful for objective analyses of which parameter or combination of parameters provides the greatest forecasting skill. However, these distributions do not offer insight into how an HSS value would change if the threshold lines were subjectively modified. To provide information on how an HSS value would change with shifted thresholds, scatterplots in two-parameter space were used. For this analysis, the only parameter combinations considered were 0–1-km shear with 3–9-km shear (the highest performing parameter combination for nighttime tornado environments; Fig. 9) and MUCAPE with 0–3-km shear (the most highly skilled combination of parameters for daytime cases; Fig. 10).
(a) Scatterplot of 0–1- vs 3–9-km shear for all nocturnal tornadoes, with the GKDE contours overlaid. Values for weak and strong nighttime tornadoes are plotted as light blue circles and dark blue triangles, respectively. The GKDE contours encompassing the top 25% and 75% densest points are plotted, in solid and dashed lines, respectively, for each scatter group in the corresponding color. Vertical and horizontal lines are plotted for the optimal two-parameter HSS values of VS01 and VS03, respectively. (b) As in (a), but for daytime tornadoes. Values for weak and strong daytime tornadoes are plotted as orange circles and dark red triangles, respectively.
Citation: Weather and Forecasting 32, 2; 10.1175/WAF-D-16-0029.1
As in Fig. 9, but for 0–3-km shear vs MUCAPE.
Citation: Weather and Forecasting 32, 2; 10.1175/WAF-D-16-0029.1
For nighttime tornado environments, the most concentrated area of points (i.e., the 25% density contour) for strong tornado environments tend to be extended diagonally from weak tornado environments toward larger values of both 3–9-km shear (rightward) and 0–1-km shear (upward) shear (Fig. 9a). This displacement supports the conclusion that combining 0–1-km shear with 3–9-km shear adds skill to both parameters compared with considering them individually (Tables 4 and 5). During the day (Fig. 9b), though the 25% contour for strong tornadoes is displaced toward lower 3–9-km shear than that for weak tornadoes, the general distributions for both weak and strong daytime tornadoes (represented by the 75% contours) occupy a similar 3–9-km parameter space; hence, this combination is less skillful than during the night (Table 5). In addition to separation within daytime and nighttime intensities, separation also exists between daytime and nighttime groupings. The 25% contour of nighttime strong tornado cases is displaced from that of daytime strong tornadoes toward higher 3–9-km shear, but even farther toward higher 0–1-km shear.
Both the 75% and the 25% contours for daytime strong tornado combinations of MUCAPE and 0–3-km shear (Fig. 10b) are displaced toward greater MUCAPE and 0–3-km shear compared with those of weak tornadoes, with part of the strong 25% contour lying outside of the weak 75% contour. This indicates that strong and weak daytime tornadoes tend to occupy different 0–3-km shear-MUCAPE parameter spaces. This tendency is also evident in the skill increase over the single-parameter skill values (Table 4) of both MUCAPE (0.29) and 0–3-km shear (0.44) when the two are combined together (0.55). However, the 25% contour for strong nocturnal tornadoes (Fig. 10a) is displaced toward smaller values of MUCAPE compared to that of weak nocturnal tornadoes, while the 75% contour extends toward increased MUCAPE values. This concentration of cases toward smaller values of MUCAPE, but with a long tail of cases toward greater values of MUCAPE, is also evident in the violin plot of nocturnal MUCAPE values (Fig. 3c). The result of these competing elements is that the addition of MUCAPE to 0–3-km shear at night does not improve upon the skill of the 0–3-km shear alone.
4. Discussion
Few thermodynamic parameters are skillful in forecasting tornadic rating, especially at night, though MUCAPE, but not CAPE, discriminates well between weak and strong tornado environments during the day, especially when combined with 0–3-km shear. The latter result agrees with those of Rasmussen and Blanchard (1998), Edwards and Thompson (2000), Craven et al. (2002), and T03, whose findings suggest that CAPE has little operational use when attempting to discriminate between adjacent groups (e.g., severe and nonsevere or weakly and nontornadic), though the former result suggests that MUCAPE may have some use in discriminating between weak and strong daytime tornado environments.
However, our results indicate that these conclusions may be inappropriate when applied to forecasting for tornado rating group at night. All nocturnal CAPE parameters (i.e., CAPE, MUCAPE, and SBCAPE) were nearly uniform across tornadic intensities, resulting in poor forecasting skill. Though the distributions of LCL for weak and strong nocturnal tornado environments were not significantly different, LCL did have some skill in discriminating between tornado ratings at night. Furthermore, though the distributions of CIN for nocturnal weak and strong tornadoes were similar, CIN distributions at night were quite different than during the day, with values extending toward lesser (more negative) values at night, especially for weak tornadoes. This resulted in a mean nighttime CIN that was significantly lower than during the day. These findings suggest that CIN is an important limiting factor to strong nocturnal tornado occurrence, which agrees with the findings of Davies and Fischer (2009) and Mead and Thompson (2011). However, a more detailed study including null tornado cases should be undertaken to verify this result.
The height of the most unstable parcel was significantly higher for strong compared with weak nocturnal tornadoes, opposite the relationship during the day, though the distributions of SBCAPE are quite similar for both strong and weak nocturnal tornado cases. These results suggest that, though all nocturnal tornadoes in this study occur in environments with similar surface-based instability, elevated instability may favor stronger tornadoes, perhaps by providing unstable parcels above the nocturnal surface inversion that could be lifted more readily by an updraft. However, these results were derived from model soundings that have, at most, 250-m vertical spacing near the ground. In many cases, this may not be sufficient to resolve a shallow inversion. Future investigations should focus on acquiring modeled soundings with greater near-surface resolution, or observed soundings in the vicinity of nocturnal supercells, to determine if strong nocturnal tornadoes do favor elevated instability.
Shear parameters, especially 0–1- and 0–3-km shears, were found to be skillful in discriminating among tornadic rating groups, both at night and during the day. Other studies (e.g., T03; Craven et al. 2004) came to similar conclusions regarding low-level shear parameters in forecasting for significant (F2–F5) tornadoes versus nontornadic supercells and nonsupercellular storms. However, none of those studies arrived at skill scores as high as those found in this study. This skill discrepancy is perhaps a result of their choice to not separate cases by time of day, as it was found in this study that there were large differences in shear values and distributions between night and day. When comparing the skill scores in this study to those from other works, it also is important to note the differences in the dataset configurations. T03, who used RUC-2 soundings, and Craven et al. (2004), who utilized 0000 UTC radiosondes, both use very large climatology databases; hence, the ratios of EF3–EF5 tornadoes to EF1–EF2 tornadoes in their datasets are much smaller than the ratio in this study.
Also, nighttime vertical wind shear magnitudes throughout the troposphere were higher than those during the day. This result might be attributable to the LLJ and the corresponding decrease in near-surface wind speeds. Though the LLJ can be very important for nocturnal severe weather (Coniglio et al. 2010; Coffer and Parker 2015), it is not unique to severe weather environments. Hence, future studies should examine how the low-level shear distributions shown here compare to the average plains nocturnal environment.
The most significant finding from the single-parameter analysis was that 0–1-km shear had higher skill than 0–3-km shear in forecasting tornado ratings at night, but the opposite was true during the day. To investigate the possibility that this shift toward an increasing depth over which shear was most important could be due to an increase in boundary layer depth, the vector shear between the surface and the LCL and that between the surface and the LFC were computed and compared (not shown). The distributions of both shear parameters are nearly identical to that of 0–1-km shear and, hence, cannot explain the drastic increase in the skill of 0–3-km shear from nighttime to daytime.
Both the distributions of HSS and the two-parameter-space scatters showed that combining parameters can improve on the skill of individual parameters. In particular, combining 0–1-km with 3–9-km shear resulted in the highest HSS value for the forecasting tornado rating at night, while 0–3-km shear combined with MUCAPE was the most skillful combination during the day. The latter agrees with similar findings by Rasmussen (2003) and Craven et al. (2004). An analysis not considered in this study is the comparison of the differences between nighttime and daytime cases to the dissimilarities seen for these groups climatologically. Perhaps some of the variations in parameter values not only are functions of tornado rating, but are also dependent on the mean parameter values that occur for each group. While a possibility, it is beyond the scope of this research and, hence, is purely speculative.
The most important caveat to these findings is that they are based on model-derived soundings. While RUC-2 soundings are generally considered to be accurate representations of the actual environment, they still are prone to biases and errors, especially in their near-surface characteristics. The model soundings used here are also severely limited in their vertical spacing when compared with radiosonde data. This limitation is especially important when examining parameters in the lowest 1 km of the atmosphere, as they are based on as few as two model levels. Furthermore, RUC-2 was replaced operationally by the Rapid Refresh model (RAP; Benjamin et al. 2016) on 1 May 2012. RAP has not yet been tested for tornado-forecasting performance in the same manner as RUC was here and in other studies, and it uses a very different data assimilation scheme and dynamical core than does RUC. While operational experience indicates that the models share enough similarities to render conclusions from RUC-based studies valid for RAP, further research should be performed to investigate how findings derived from RUC sounding climatologies should be applied to using the RAP model.
Furthermore, each sounding is separated in time and space from the tornado that it represents by different amounts (Fig. 11). Whereas some soundings may be as much as 2 h before and 80 km from tornado start, others are within just a few minutes or 500 m. In environments that are rapidly changing, such as those in which severe weather often occurs, significant changes can occur within this time–space window. Additionally, some soundings are technically located northwest, northeast, or southwest of the tornado start location (Fig. 11a), which would put it outside of the typical inflow region (and typical proximity radiosonde/model sounding location) of a supercell, although this only happened when that was the grid location closest to the tornado start location. Finally, all soundings were hand analyzed for lingering effects of convective feedback (e.g., sounding saturation). Hence, some soundings are more likely to be representative of the actual tornado environment than others. This issue concerns the blurred line between precedent and proximity soundings first addressed by Beebe (1958).
(a) Polar plot of the locations of all nighttime (blue circles) and daytime (red triangles) tornado proximity soundings relative to tornado start location (center of the polar plot). (b) Bar graph of time (min) before tornadogenesis for which all proximity soundings were taken.
Citation: Weather and Forecasting 32, 2; 10.1175/WAF-D-16-0029.1
Finally, although forecasting skill was discussed, a study that builds upon the dataset used in this study by adding null cases would be more directly applicable to operational forecasting. Findings from this work could be successfully applied to a dataset designed for prognostic applications following the guidelines laid out in Doswell and Schultz (2006). Furthermore, the thresholds used to obtain the skill scores discussed here are purely statistical thresholds derived from a sample of events that do not necessarily represent the entire range of atmospheric probabilities. These statistical thresholds do not constitute true forecasting thresholds and as such should not be applied directly for forecasting tornado ratings.
5. Summary and conclusions
A total of 194 RUC-2 proximity soundings of lengthy (≥10-km track) EF1+ tornadoes were examined, 92 of which were during the nighttime, while the other 102 cases were during the daytime. Each time-of-day grouping was divided approximately equally between soundings from weak and strong tornado environments. From each sounding, 33 severe storm parameters were calculated, most of which were used for analysis. All parameters were examined with box-and-whisker plots of parameter values, HSS forecasting analysis, distributions of resampled one- and two-parameter HSSs, and scatterplots with GKDE contours. In summary, the most important outcomes of this study were the following:
Thermodynamic parameters were found to vary only slightly between weak and strong tornado environments during the nighttime. However, MUCAPE, SBCAPE, LCL, and CIN values were lower for daytime strong compared with daytime weak tornado environments. In general, thermodynamic parameters such as CAPE, 0–3-km CAPE, and SBCAPE were larger during the daytime than during the nighttime, while CIN was lower during the daytime.
Kinematic properties of weakly and strongly tornadic soundings showed much greater differences than thermodynamic variables. All shear parameters tested were larger at night than during the daytime. Strong tornado environments, both at night and during the day, were also characterized by greater shear than weak tornado environments. The single parameter that displayed the most skill in forecasting tornadic ratings during the daytime (nighttime) was the 0–3-km (0–1 km) shear.
Combining various parameters provided improved forecast skill compared with single-parameter skill. The combination that best discriminated between tornado ratings at night (during the day) was 0–1-km shear with 3–9-km shear (0–3-km shear with MUCAPE) The two-parameter space scatter and GKDE plots confirmed these skill values and also provided means of assessing the skill of a suboptimal choice of parameter thresholds.
Future studies should consider the differing roles of low-level shear in producing more damaging tornadoes, and how these roles change throughout the day. In addition, the inclusion of null cases in future analyses of nocturnal tornadoes would provide better operational forecasting applicability than the current study. Furthermore, it also would be useful to classify tornadoes not just as nighttime or daytime, but instead by their solar hour (Ashley 2007; Ashley et al. 2008). This could prove valuable because the nocturnal boundary layer is known to change quickly during the early nighttime, but more slowly throughout the rest of the night (Stull 1988). This kind of analysis would provide a better understanding of how near-surface thermodynamic and kinematic characteristics affect the association of different sounding parameters with tornadogenesis.
Acknowledgments
This work was supported in part by NSF Grant AGS-1036237, and I would like to acknowledge Dr. Chungu Lu as the program director of this grant. Special thanks go to Dr. Jerry Straka for initial research motivation and ideas and for providing guidance during much of this work. Thanks go to Drs. Charles Doswell III, Lance Leslie, Michael Richman, and Harold Brooks for serving on my thesis committee and offering a great deal of their time toward improving this work. I would also like to acknowledge Dr. David Parsons for providing suggestions for improving the final manuscript. In addition, I thank Kiel Ortega for sharing his storm motion estimation code and Ryan Lagerquist for providing code for obtaining model data files. Finally, I would like to thank Jimmy Correia for (inadvertently) providing the inspiration for the use of violin plots in this manuscript.
APPENDIX
Parameter Mean Values
Our analysis of parameter values involved examining box and violin plots of variables modified so that they could be viewed on the same axis. While these distributions allowed for easier comparison of separation between groups among the various parameters, it masked the actual parameter values. For completeness, the mean for each parameter μ among the six groups analyzed in this study is provided in Table A1.
Mean parameter values μ for the six diurnal and tornado rating groupings considered in this study.
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