1. Introduction
Tornadoes pose a great risk to society. In particular, tornado outbreaks—when multiple tornadoes occur in a relatively short time period—often result in significant loss of life and property. Approximately 85% of tornadoes rated 4+ on the Fujita/enhanced Fujita (F/EF) scale as well as 80% of tornado-related fatalities occur in tornado outbreaks (Fuhrmann et al. 2014). As a result, there are ongoing efforts to better quantify risk from severe convective storm (SCS) activity and advance its long-range prediction (Vitart et al. 2019; Gensini et al. 2019; Gensini and Tippett 2019; Gensini et al. 2020a).
A major challenge is that dynamical weather and climate models do not resolve individual tornadoes or thunderstorms. In addition, tornadoes are rare and sporadic, and the long-term observational record of tornado reports is inhomogeneous in time and space. These limitations make it difficult to directly detect robust climate signals in observations and to make observation-based estimates of risk. For instance, if a location has not recorded a tornado, it does not mean that the risk at that location is zero. A common strategy for assessing risk from rare, high-impact natural hazards is to generate a large number of synthetic events which are consistent with the observed data, thus increasing the number of samples—and hence, increasing event diversity—to more accurately estimate risk (Bloemendaal et al. 2020; Emanuel et al. 2006; Lee et al. 2018; Davies 2019; Fan and Pang 2019; Guillaume et al. 2019; Quinn et al. 2019; Hatzis et al. 2020; Wing et al. 2020; Welker et al. 2021). Synthetic events are generated by introducing a stochastic component in purely statistical or hybrid dynamical–statistical models.
Pioneering studies, such as Brooks et al. (1994, 2003), showed that the favorability of tornadic events has a clear association with local, contemporaneous environmental variables. This framework provided a basis for relating anomalous tornado activity to the temporal evolution and spatial distributions of environmental variables which are independent of possible limitations of the storm report data. Understanding favorable environmental conditions for tornado activity is useful for long-lead prediction because large-scale environmental variables can be forecast or measured in dynamical models (Tippett et al. 2012, 2014, 2015; Carbin et al. 2016). In addition, this framework can be useful for detecting climate signals and quantifying present-day and future SCS risk.
To inform the forecast process, convective parameters, such as the energy helicity index (EHI; Davies 1993), the supercell composite parameter (SCP; Thompson et al. 2003), and the significant tornado parameter (STP; Thompson et al. 2003) have been developed to interpret observations and model output. These parameters are typically a single unitless number that combines the thermodynamic and dynamic atmospheric ingredients to determine the favorability of the environment for supercell formation or tornadogenesis. These parameters are a practical summary of multiple factors and generally show ability to discriminate between significant tornado, weak tornado, and nontornadic storms. Gensini and Tippett (2019) used SCP in Global Ensemble Forecast System to evaluate skill in deterministic forecasts of tornado and hail events, finding that tornado forecasts were skillful in the medium range. However, the format of these parameters does not directly provide probabilistic information or expected number of tornadoes for an event.
Alternatively, the tornado environment index (TEI) was designed to match the monthly number of U.S. tornadoes from monthly averaged convective precipitation (CP) and storm relative helicity (SRH), and it captures much of the seasonality, spatial distribution, and interannual variability of tornado activity (Tippett et al. 2012, 2014; Lepore et al. 2018). This approach, with the inclusion of convective available potential energy (CAPE) as an additional predictor, was also used to develop an index that predicts the monthly number of U.S. hail events (Allen et al. 2015). While TEI has some utility for describing monthly tornado activity, the use of monthly averages makes it unsuited for tornado outbreaks and submonthly activity. Additionally, probabilistic information about the range of possible outcomes is needed. For instance, the Additive Regressive Convective Hazard Model (AR-CHaMo) was developed to predict the 6-hourly probability of lightning, large hail, and damaging wind over most of Europe given instability, humidity, and shear conditions (Rädler et al. 2018). AR-CHaMo is currently used for short-term severe weather guidance at the European Severe Storms Laboratory. It can reproduce the spatial distribution and seasonal cycles of the convective hazards. However, it has not been applied to tornado prediction or to investigate modulation from natural climate variability. Similarly, the Statistical Severe Convective Risk Assessment Model (SSCRAM) was developed to predict probabilities of severe storm hazard—including tornadoes—from lightning activity and environments (Hart and Cohen 2016b). Hill et al. (2020) used random forest models to forecast daily probabilities of tornado, hail, and severe wind using atmospheric fields, e.g., CAPE, convective inhibition (CIN), and wind shear, as predictor variables. These frameworks, while effective at providing probability maps, do not provide an estimate of the number of hazards or their intensity. Daneshvaran and Morden (2007) and Strader et al. (2016) estimated tornado risk in terms of both occurrence and number/intensity, though these studies use a Monte Carlo approach rather than modeling activity via the large-scale environment. Cheng et al. (2015, 2016) also related tornado occurrence and/or intensity to large-scale environments using a Bayesian modeling approach, but, similar to the TEI method, it only provides predictions of activity on monthly or seasonal time scales.
Schroder and Elsner (2021) found that the number of outbreak tornadoes in a cluster is related to averaged environmental conditions in the cluster region, finding that deep layer bulk shear and CAPE are particularly important. However, the empirical model from Schroder and Elsner (2021) is designed to predict number of outbreak given that a tornado is known to have occurred. Consequently, the models are trained on the environments in the vicinity of SPC report locations and excludes the environments of “nonevents.” This framework is not suited for applications (e.g., prediction) where the occurrence is unknown.
Following that the climatology and variability of tornado activity is a function of the large-scale environment; its statistics may be modulated by predictable climate signals. The ingredient-based approach provides physical factors for explaining modulation from climate, e.g., shifts in spatial distribution or long-term trends (Murugavel et al. 2012; Rädler et al. 2018, 2019; Koch et al. 2021). For instance, La Niña is linked to increased tornado and hail activity over the Tennessee River Valley in late winter into spring (Allen et al. 2015; Lepore et al. 2017, 2018; Tippett and Lepore 2021), and ENSO is a source of prediction skill for tornado activity (Lepore et al. 2018; Tippett and Lepore 2021). This can be explained by constructive interference of La Niña–related CAPE and SRH over this region (Koch et al. 2021). ENSO has also been linked to tornado outbreak activity (Cook and Schaefer 2008; Lee et al. 2013, 2016), though studies typically use short data records with limited number of ENSO and tornado outbreak events. A tornado outbreak index would provide spatially and temporally smooth fields of tornado outbreak activity that could be reconstructed from environmental predictors in reanalysis or climate (forecast) models, which could be used to clarify links between tornado outbreak activity and large-scale climate variability, including ENSO and trends.
The main objective of this study is to develop a procedure that estimates or downscales tornado outbreak activity from the large-scale environment provided by reanalysis or climate (forecast) models. The procedure should have some stochastic component so that a range of potential outcomes can be generated (e.g., synthetic events), a feature notably missing from current tornado modeling approaches. We accomplish this by constructing a two-part submonthly tornado outbreak index which predicts 1) a map of CONUS probabilities for outbreak tornadoes and 2) the expected number and probability distribution of total CONUS outbreak tornadoes. In section 2, data and methods are described, including the construction of the outbreak tornado index. In section 3, results are delivered as follows: first, the outbreak tornado index is evaluated against SPC report data, and skill is assessed. Then, smoothed observations and the outbreak index are used to describe the seasonal cycle and interannual variability of tornado outbreak activity. This includes assessing how ENSO modulates tornado outbreak activity. Trends in 1979–2021 tornado outbreak activity are also reported. Finally, we demonstrate use of this index to generate synthetic events for three case study examples. In section 4, a summary of results is given as well as a discussion of the broader context of this work and prospects for future work.
2. Data and methods
a. Data
Environmental variables of instantaneous 0–3-km SRH (m2 s−2) and instantaneous mixed-layer CAPE (J kg−1) are taken for the 1979–2021 period from the North American Regional Reanalysis (NARR), which provides 3-hourly data on a 32-km native grid. We also take accumulated convective precipitation (CP; mm day−1) from NARR, which NARR utilizes convective adjustment type scheme and directly assimilates precipitation observations (Bukovsky and Karoly 2007). We interpolate NARR data to a 6-hourly temporal resolution, such that we resample as a 6-hourly sum for CP and 6-hourly average for SRH and CAPE, and we perform a bilinear interpolation of variables to a 1° × 1° spatial resolution. This matches the resolution of many weather and climate (forecast) models, and this resolution emphasizes large-scale environmental conditions. Mixed-layer CAPE in NARR is calculated by looking at the lowest 180 hPa above ground and taking the 30-hPa layer with the highest mean equivalent potential temperature, using the mean properties from that layer as the parcel Gensini and Ashley (2011). Although reanalyses present CAPE biases (Gensini et al. 2014), the biases are smaller in NARR compared to other reanalyses (King and Kennedy 2019).
Tornado reports for the 1979–2021 period are taken from the NOAA Storm Prediction Center (SPC) Severe Weather Database, which provides information on each tornado report, including time of occurrence, start and end locations, and damage classification on the F/EF scale from 0 to 5. While the SPC report database serves as the official observational record of U.S. tornado activity, there are sources of error (Verbout et al. 2006; Edwards et al. 2021). The changes in data collection practices and advancements in observational technology, e.g., switch from Fujita to enhanced Fujita scale, increased resolution and improved scanning methodologies of Doppler radar, introduction of dual-polarization radar, over time has led to an increase of reports, especially for weak (F/EF0) tornadoes and tornadoes from quasi-linear convective systems (Thompson 2023), which may produce an artificial trend in tornado counts between 1979 and 2021. However, the annual number of tornado reports with intensity F/EF1 or greater have remained stable overall. For this study, we exclude F/EF0 tornadoes. A tornado outbreak is defined here as a sequence of six or more tornadoes that occur with no more than 6 h between consecutive tornadoes, following the definition used in Fuhrmann et al. (2014). We do not consider a geographic constraint when labeling outbreak tornadoes (Doswell et al. 2006). Using these criteria, we identified 930 tornado outbreak events between 1979 and 2021 with an average duration of 9 h. After labeling the tornado outbreaks, the SPC report data are aggregated to a 6-hourly (0000, 0600, 1200, 1800 UTC) and 1° × 1° resolution. We also use report observations that are spatially smoothed using 2D convolution with a Gaussian kernel with σ = 120 km (Hitchens et al. 2013; Gensini et al. 2020b; Sobash et al. 2020), similar to “practically perfect” probability hindcasts. The main advantage of using the smoothed observations for assessing regional performance is that it is consistent with the probabilities from our model (lies between 0 and 1) and takes into account uncertainty of the location of sporadic tornado events. However, we acknowledge limitations of the smoothed observations. For instance, greater probabilities arise when multiple adjacent grid points have outbreak tornadoes, and it is possible that the grid point of maximum probability might not correspond to where an outbreak tornado occurred.
We define ENSO by the Climate Prediction Center (CPC) oceanic Niño index (ONI), which is calculated by averaging the SST anomalies over the Niño-3.4 region (5°N–5°S, 120°–170°W) and applying a 3-month running mean.
b. Logistic regression for probability maps
We tested various environmental variables related to SCS activity as predictors in the LR model: CP, total accumulated precipitation, SRH, CAPE, convective inhibition (CIN), 2-m dewpoint temperature, 2-m specific humidity, and surface pressure. We used deviance to determine goodness of fit, with a smaller deviance indicating a better fit. Consistent with previous work (e.g., Brooks et al. 2003; Tippett et al. 2012), we take the logarithms of the variables to better fit the data. We tested each variable individually in the LR model, choosing the first predictor as the one that results in the smallest deviance. Here, log(CP) is the first predictor as it resulted in the single-predictor model with smallest deviance. Then, we calculated the deviance as well as the 95% CI of the deviance when adding each of the other predictors separately. Including log(SRH) and then log(CAPE) resulted in a statistically significant reduction in deviance; therefore, they were added as predictors. Including more than these three predictors did not result in a statistically significant reduction in deviance.
Applying the LR to NARR data produces CONUS map of P(Outbreak) with 6-hourly resolution. We aggregate this to daily resolution by taking the maximum P(Outbreak) at every grid point during a 24-h period. Here, we take the maximum between 1200 UTC of a given day and 1200 UTC of the following day, matching the SPC convective day. Two probability map characteristics are the map sum of P(Outbreak) values, denoted sum(PCONUS), and the maximum value of P(Outbreak), denoted max(PCONUS). The probability maps and their characteristics are used to describe the seasonal cycle, case examples, and interannual variability of tornado outbreak activity. For the ENSO analysis, we also calculate the rank correlation between the 3-month running average of P(Outbreak) anomalies and ONI centered around the same month (e.g., March–April–May tornado activity with March–April–May ONI). Trend analysis uses the 6-month period December–March.
c. Negative binomial regression for number of outbreak tornadoes
d. Statistical significance
To assess the statistical significance of the ENSO-related rank correlation maps, we include an additional step of applying the false discovery rate (FDR) procedure from Benjamini and Hochberg (1995). The two-sided p value is calculated at every land grid point and sorted from smallest to largest. Then, the sorted p values are compared to the sequence γ/S, 2γ/S, 3γ/S, …, where S is the number of land grid points (S = 860) and γ is the selected FDR. We set γ = 0.1 here.
e. Performance metrics
To evaluate index calibration for P(Tornado) and P(Outbreak), we consider reliability diagrams, which assesses the extent to which the index probability matches the observed frequency from the unsmoothed report data. To evaluate calibration for the index number of tornadoes, we assess the conditional bias, or how well the index number of outbreak tornadoes matches the observed number of outbreak tornadoes conditional on the forecast value. The error bars for the reliability diagrams are the 95% CI of the estimate based on the standard error for probabilities:
3. Results
a. Outbreak index description and performance
Observed (shaded) and LR modeled (thick gray contours) log-odds, i.e.,
Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-23-0219.1
Next, we compare the observed dependence of tornado and outbreak occurrence on the environmental predictors with that of the indices. In Fig. 1, we show the bivariate dependence of the observed log-odds for tornadoes (shaded) on binned logarithm values of CP and SRH (Fig. 1a), CAPE and CP (Fig. 1c), and CAPE and SRH (Fig. 1e), i.e., each bivariate histogram shows the log-odds conditional on two of the predictors and averaged over values of the third predictor. If the two predictors in the bivariate histogram have a systematic dependence on the third predictor, the isolines in the bivariate histogram can show sensitivities that differ from those in Eqs. (5) and (6). Moreover, while the dependence of the log-odds on the predictors is linear, if the dependence of the two predictors in the bivariate histogram have a nonlinear dependence on the third, the isolines will show curvature. Including a third predictor to model such curvature is an alternative to Rädler et al. (2018) who introduced curvature in a two-predictor model using thin-plate regression splines. The log-odds for tornado occurrence increases with increasing CP and SRH (Fig. 1a), with observed contours mostly straight for log(SRH) less than 5 but showing curvature for values of log(SRH) greater than 5. Therefore, tornado occurrence is modeled by a linear combination of log(CP) and log(SRH) for log(SRH) values less than 5 but is more sensitive to log(CP) for log(SRH) values greater than 5. The log-odds increases with increasing CP and CAPE for log(CP) greater than 2 (Fig. 1c), yet log-odds remains relatively high (≥−7) for low-CAPE environments when log(CP) is between 0.5 and 2. The log-odds increases with increasing SRH and CAPE (Fig. 1e), though log-odds remains relatively high (≥−7) for log(SRH) greater than 5, even for low-CAPE environments.
In general, the LR modeled log-odds for tornadoes (gray contours) matches well with the observed log-odds. For instance, the modeled isolines of log-odds follows the departure away from strict power-law dependence on log(CP) and log(SRH) for high values of log(SRH) (Fig. 1a). This indicates that the greater sensitivity of tornado occurrence to log(CP) for large values of log(SRH) is explained by dependence on the other predictor, log(CAPE), in the model. Some details in the dependence of log-odds on environmental predictors are less well captured, such as the relatively high log-odds for low-CP and low-CAPE environments (Fig. 1c).
The log-odds for observed outbreak tornado occurrence is lower than the log-odds for (any) tornado occurrence, especially for environments with low values in CP, SRH, and CAPE (Figs. 1b,d,f, shaded), which reflects the rarity of outbreak tornado events in low-CP, low-CAPE, and low-SRH environments. The closer contours in Figs. 1b and 1f compared to those in Figs. 1a and 1c reflect the greater sensitivity of outbreak tornado frequency/probability to SRH. Yet similar behavior in the dependence of log-odds on the environment is seen, such as the curvature in the log-odds contours for log(SRH) greater than 5 in Fig. 1b, indicating greater sensitivity of outbreak tornado occurrence to log(CP), and relatively high log-odds for low-CAPE environments with log(SRH) greater than 5 in Fig. 1f. As with modeling tornado occurrence, the LR model is generally able to represent the observed dependence of outbreak tornado occurrence on the environment.
We show the reliability diagrams for all the data (Fig. 2a) as well as stratified by season (Figs. 2b–e). A perfectly calibrated model or index will have a reliability curve along the 1:1 line (labeled “perfect” in Fig. 2a). Models with positive skill scores have reliability curves within the gray shaded region, and models that have negative skill will have reliability curves that fall below the diagonal line between observed climatological frequency and the perfect line (labeled “no skill” in Fig. 2a). When considering the full year of data, the tornado index has virtually perfect reliability for index probabilities less than 8%, and its reliability curve stays close to the perfect 1:1 line for probabilities less than 18% (with the error bars mostly including the 1:1 line). The outbreak index has virtually perfect reliability for index probabilities less than 6% but more quickly falls below the perfect 1:1 line for greater index probabilities. This indicates that the index generally overforecasts outbreak tornado events, e.g., when index probabilities are 20%, outbreak tornadoes may occur only ∼12% of the time). Yet the outbreak index reliability curves stay above the no skill line, indicating that it can still outperform climatological forecasts.
Reliability diagrams for tornado index probabilities (red) and outbreak index probabilities (blue) verified against occurrence data (not smoothed) during (a) full year, (b) DJF, (c) MAM, (d) JJA, and (e) SON. The inset in (a) shows the sharpness diagram for full year data. The “perfect” reliability line and “no skill” lines are displayed as dashed and are labeled in (a). Light gray shading indicates where forecasts positively contribute to skill scores. Error bars are the 95% confidence interval of the estimate.
Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-23-0219.1
The indices are fairly well calibrated during March–April–May (MAM) and September–October–November (SON) seasons. However, the indices generally underpredict during December–January–February (DJF) and overforecasts outbreak events during June–July–August (JJA). In fact, the JJA index reliability curves fall below the no-skill line. We focus on the outbreak index, P(Outbreak), for the remainder of the study.
We evaluate regional skill by assessing maps of MSESS, shown in Fig. 3. Skill is highest in regions where tornado outbreaks occur most frequently climatologically. During DJF (Fig. 3a), skill is relatively high over the Midwest and Tennessee River Valley. During MAM (Fig. 3b), skill is relatively high over most of eastern CONUS, especially over the Plains, Tennessee River Valley, and Southeast United States. During JJA (Fig. 3c), skill is relatively low compared to other seasons, but there is some skill over the Southeast United States. During SON (Fig. 3d), skill is relatively high over the Tennessee River Valley and Gulf Coast.
Map of mean squared error skill score (MSESS) for outbreak index probabilities, P(Outbreak), for (a) DJF, (b) MAM, (c) JJA, and (d) SON. The reference MSE (MSEref), which is proportional to the variance of outbreak tornado frequency, is overlaid in black contours. Grid points are masked gray where the climatological probability is less than 0.005%.
Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-23-0219.1
(a) Observed (shaded) and modeled (gray contours) daily number of outbreak tornadoes dependent on logarithm of summed outbreak index probability map [sum(PCONUS)], and max value on outbreak index probability map [max(PCONUS)]. The 95% confidence interval for the predictor coefficients is shown at top left. (b) Mean squared error score for outbreak index probabilities dependent on logarithm of sum(PCONUS) and max(PCONUS) values. The 6-tornado contour line from (a) is overlaid.
Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-23-0219.1
In Fig. 4a, we show how the observed number of tornadoes (shaded) depends on binned values of the logarithm of sum(PCONUS) and max(PCONUS). In general, the NBR modeled expected number of tornadoes (μ, gray contours) and its dependence on binned log[sum(PCONUS)] and log[max(PCONUS)] matches well with the observed dependence on log[sum(PCONUS)] and log[max(PCONUS)]. The observed number of outbreak tornadoes tends to decrease as the log[max(PCONUS)] increases for fixed log[sum(PCONUS)]. In particular, there is a clear distinction between outbreak events and nonoutbreak events in this index space, differentiated by the 6-tornado contour in observations (shading) and NBR model (gray contour).
The skill of the index P(Outbreak) is related to these event characteristics of sum(PCONUS) and max(PCONUS). In Fig. 4b, the MSESS is calculated and binned from events defined by values of log[sum(PCONUS)] and log[max(PCONUS)]. Events with higher sum(PCONUS) and higher max(PCONUS) have greater skill. The 6-tornado contour line from Fig. 4a is overlaid here, signifying the boundary between nonoutbreak and outbreak environments. This contour also separates between index values with low or negative skill and positive skill. For a given log[P(Outbreak)max] bin, there is a sharp gradient between index values with no skill and index values with high skill depending on the value of log[sum(PCONUS)], especially for high values of max(PCONUS). For instance, for the bin from −1.9 to −1.5 log[max(PCONUS)], there is no or negative skill for log[sum(PCONUS)] values less than 0.8 and high, positive skill for log[sum(PCONUS)] values greater than 0.8. For fixed log[sum(PCONUS)], skill generally decreases with increasing log[max(PCONUS)]. This demonstrates lower index skill or higher uncertainty for events with environments that fall on the left side or along the 6-contour isoline.
Figure 5 shows the conditional bias in the NBR modeled number of outbreak tornadoes. For the full year of data (Fig. 5a), the index estimation of number of tornadoes is well calibrated, meaning that on average the observed number is equal to the modeled number. The uncertainty (error bars) increases with increasing index number of tornadoes due to the decreasing sample sizes. We also display the PIT histogram on the bottom-right corner of the panels. The PIT histogram for the full year of data are nearly uniform, indicating that the observations are consistent with being drawn from the index distribution.
Calibration for NBR modeled number of outbreak tornadoes during (a) full year, (b) DJF, (c) MAM, (d) JJA, and (e) SON. The top-left inset in (a) shows the number of samples for full year data. The bottom-right inset shows the probability integral transform histogram (see text for details). The “perfect” line is displayed as dashed and is labeled in (a). Error bars are the 95% confidence interval of the estimate.
Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-23-0219.1
We separate the data by season to assess seasonal calibration (Figs. 5b–e). During MAM and SON, the index number of outbreak tornadoes is generally well calibrated. However, the PIT histogram for MAM suggests that observed number of outbreak tornadoes are often higher than the index. The index generally underpredicts the number of outbreak tornadoes during DJF and overpredicts outbreak events during JJA, generally consistent with the reliability diagrams from Fig. 2. This is also corroborated with the PIT histograms: the right bins containing more observed values than the left bins during DJF indicates a systematic bias in the model to underpredict tornado numbers during winter, and the left bins containing more observed values than the right bins during JJA indicates a systematic bias in the model to overpredict tornado numbers during summer.
Last, we calculated the rank correlation between both the observed and NBR modeled number of tornadoes (over CONUS) to evaluate performance in representing variability in tornado outbreak activity, as shown in Table 1. Data are grouped by season (DJF, MAM, JJA, and SON), and both the daily number of tornadoes (first row) as well as the summed total of tornadoes over the season (second row) is shown to assess the representation of both daily and seasonal/interannual variability of tornado outbreak activity by the index. Seasonal correlations are higher than daily correlations, suggesting that temporal aggregation of the tornado counts improves representation of its variability. DJF and MAM seasonal correlations (0.84 and 0.61, respectively) are highest, and JJA and SON daily correlations (0.26 and 0.34, respectively) are lowest.
Rank correlations between observed and NBR modeled tornadoes by season. All correlations are considered significant at the 5% level based on bootstrapping.
In brief, the outbreak index is valuable because it captures the general dependence of tornado outbreak activity on the large-scale environment. This dependence includes probabilistic maps as well as the expected number (μ) of U.S. outbreak tornadoes and a corresponding probability distribution. The probability distribution adds an element of uncertainty or spread to the outbreak tornado totals, making it possible to generate a range of scenarios. The probability maps were evaluated using reliability and MSESS, and the NBR modeled number of outbreak tornadoes were evaluated using conditional bias, PIT histograms, and rank correlation. Overall, the index performs well in MAM and SON, underpredicts tornado outbreak activity in DJF and overpredicts tornado outbreak activity in JJA. The next set of results uses sum(PCONUS) and max(PCONUS) to represent the seasonal cycle, interannual variability, and trends of tornado outbreak activity.
b. Evaluation of seasonal cycle, interannual variability, and trends
In observations, the seasonal cycle of tornado outbreak activity over CONUS can be depicted by the movement in monthly averaged sum(PCONUS) and max(PCONUS) in Figs. 6a and 6b solid lines. DJF is characterized by low monthly averaged sum(PCONUS) and max(PCONUS) values, or climatologically low tornado outbreak activity. From March through May, tornado outbreak activity elevates, as seen by the monthly averaged sum(PCONUS) and max(PCONUS) values increasing. sum(PCONUS) and max(PCONUS) also increase at the same rate, signifying an increase in both the monthly averaged accumulated and gridpoint maximum tornado outbreak risk. During June, tornado outbreak activity is reduced, as seen by the monthly averaged sum(PCONUS) and max(PCONUS) values that decrease. July–October experiences climatologically low tornado outbreak activity, as seen by the low monthly averaged sum(PCONUS) and max(PCONUS) values. A small secondary peak in tornado outbreak activity is observed during November.
Comparison of seasonal cycles between smoothed observations (solid) and index (dashed) for (a) sum(PCONUS) and (b) max(PCONUS). Climatological frequency via smoothed observations in (c) DJF, (f) MAM, (i) JJA, and (l) SON. (d),(g),(j),(m) As in (c), (f), (i), and (j), but calculated with index probabilities. (e),(h),(k),(n) Difference between index and smoothed observations.
Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-23-0219.1
Similarities as well as biases in the seasonal cycle of the index are seen in Figs. 6a and 6b dashed lines. The index well simulates the low tornado outbreak activity in DJF and the increasing tornado outbreak activity throughout March, April, and May. However, tornado outbreak probabilities remain high in June and values of sum(PCONUS) and max(PCONUS) decrease more slowly in July–September. In addition, there is no elevated tornado outbreak risk in November as in the smoothed observations. In general, the values of sum(PCONUS) and max(PCONUS) are lower in the index versus observations.
The spatial representation of the seasonal cycle can be found in Figs. 6c, 6e, 6g, and 6i, which indicates the climatological frequency of outbreak tornadoes via the smoothed observations during DJF, MAM, JJA, and SON, respectively. DJF tornado outbreak activity is highest over the Gulf States and Tennessee River Valley (Fig. 6c). The increase in MAM tornado outbreak activity occurs over most of the eastern side of the Rockies, with the most frequent outbreak tornadoes occurring over Oklahoma–Arkansas–Louisiana as well as Tennessee River Valley (Fig. 6e). Tornado outbreak activity decreases in JJA, with highest frequency over the Midwest (Fig. 6g). SON tornado outbreak activity is highest over Mississippi (Fig. 6i). The November increase in activity from Fig. 6a is not as apparent in the regional climatological frequency likely because it is filtered from the averaging over the SON season here.
The spatial representation of the index outbreak probabilities also shows some strengths and weaknesses (Figs. 6d,f,h,j). The index indicates relatively low tornado outbreak activity during DJF and SON (Figs. 6d,j) and high tornado outbreak activity during MAM (Fig. 6f). However, the region with highest probability of outbreak tornadoes during DJF (SON) is over the Louisiana Gulf Coast (Oklahoma), and index climatological probabilities in MAM are higher over the Southern Plains and lower over the Tennessee River Valley compared to observations. The JJA index climatological probabilities of outbreak tornadoes are too high, as seen by probabilities as high as during the MAM season over the Plains and Midwest regions (Fig. 6h). The underestimated index climatological probabilities during DJF and overestimated climatological probabilities during JJA are consistent with the results from the reliability diagrams (cf. Figs. 2b,d, respectively).
The influence of ENSO on the interannual variability of tornado outbreak activity is shown in Fig. 7. We focus particularly on January–February–March (JFM) activity as this season is close to the peak of ENSO SST anomalies and February–March tornado activity is especially known to be affected by ENSO variability (Tippett and Lepore 2021). Individual years of above-median tornado outbreak activity are seen in observations (Fig. 7a), including 2008, 2012, 2017, and 2020. These years of above-median tornado outbreak activity are captured with the index (Fig. 7b). The index can capture extremes of tornado outbreak activity well; for instance, the index correctly models 75% of the years as above-median sum(PCONUS) and max(PCONUS) and 67% of the years as below-median sum(PCONUS) and max(PCONUS). ENSO state from the year is indicated by red (El Niño) or blue (La Niña) text color, and marginal probability density shifts in sum(PCONUS) and max(PCONUS) depending on ENSO state are shown above and beside the joint distribution, respectively. During La Niña, there is a shift in the probability of experiencing above-median sum(PCONUS) and max(PCONUS) as well as a shift in the median sum(PCONUS) and max(PCONUS), suggesting La Niña increases tornado outbreak activity. The index captures this behavior, demonstrating that the index can represent ENSO variability in CONUS tornado outbreak activity. Similar observed shifts in the median of sum(PCONUS) were shown for February–April (FMA) but not MAM (Figs. 7c,d), indicating ENSO influence might not be as robust after April (Tippett and Lepore 2021).
ENSO influence on mean daily tornado outbreak probability: (a) JFM joint PDFs with smoothed observations from SPC report data dependent on sum(PCONUS) and max(PCONUS). Thin black contours indicate joint PDFs for all data, with individual years overlaid as neutral ENSO (black text), El Niño (red text), or La Niña (blue text) years. Marginal PDFs for sum(PCONUS) and max(PCONUS) during El Niño (red) and La Niña (blue) are also displayed, with median value marked by “X.” (b) As in (a), but with index probabilities. (c) Observed marginal PDF for sum(PCONUS) for FMA and MAM during El Niño (red) and La Niña (blue), with median value marked by “X.” (d) As in (c), but with index probabilities. Values are normalized by the maximum value in observations/index.
Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-23-0219.1
Rank correlation maps in Fig. 8 between P(Outbreak) anomaly and ONI reveal the regional influence of ENSO on tornado outbreak activity. La Niña is related to an observed increased probability/frequency of outbreak tornadoes over the Ohio River Valley and Tennessee River Valley (Figs. 8a,c,e). These changes in probability are statistically significant during JFM (Fig. 8a). The index is able to capture the patterns in the relationship between ENSO and tornado outbreak activity during the winter and spring (Figs. 8b,d,f), including the statistically significant correlations only during JFM (Fig. 8b). The index also suggests increased probability of outbreak tornadoes over Florida in JFM.
Rank correlation between anomalous probability of outbreak tornado and ONI during (a),(b) JFM; (c),(d) FMA; and (e),(f) MAM, with the (left) smoothed observations and (right) index. Black stippling indicates statistically significant values. Grid points are masked where no observed outbreak tornadoes occurred and average (smoothed) observed probability < 0.01%.
Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-23-0219.1
In Fig. 9, we examine how the environmental predictors behind the index are modulated by ENSO. La Niña is associated with increased CP, SRH, and CAPE over the Ohio River Valley and Tennessee River Valley regions, especially during JFM (Figs. 9a–c), though this increase is only statistically significant for SRH. The consistent La Niña–related increases in SRH help explain why tornado outbreak activity would be expected to increase over these regions during La Niña years.
Rank correlation between ONI and anomalous (left) convective precipitation (CP), (center) storm relative helicity (SRH), or (right) convective available potential energy (CAPE) during (a)–(c) JFM, (d)–(f) FMA, and (g)–(i) MAM. Black stippling indicates statistically significant values.
Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-23-0219.1
Finally, we examine 1979–2021 trends in December–May (DJFMAM) tornado outbreak activity in Fig. 10. These months exhibited a robust trend signal compared to summer and autumn (not shown). The smoothed observations indicate a positive, upward trend in P(Outbreak) up to ∼0.15 percentage points per decade (monthly climatological frequency ∼0.2%–1%) for the Tennessee River Valley and southeastern U.S. coast excluding Florida and a negative trend for the Plains (Fig. 10a). This may indicate a shift in tornado outbreak activity from the Plains eastward as found in Gensini and Brooks (2018). The index also exhibits an increasing trend in P(Outbreak) for the Tennessee River Valley and southeastern U.S. coast (Fig. 10b). However, it shows an increasing trend for much of the Plains region as well, which is dissimilar to the negative trend in observations, and the observations show a negative trend in Florida that the index does not show.
1979–2021 trends during the December–March (DJFMAM) season: P(Outbreak) trends (percentage points per decade) detected with (a) smoothed observations, (b) index, and (c) time series of the 50th (blue lines), 80th (green lines), and 95th (red lines) percentile of the daily sum(PCONUS) over DJFMAM season for smoothed observations (solid) and index (dashed). Observed trends of (d) convective precipitation (CP), (e) storm relative helicity (SRH), and (f) convective available potential energy (CAPE) also shown.
Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-23-0219.1
We also consider the trends in sum(PCONUS) since it represents daily accumulated U.S. tornado outbreak risk. Figure 10c shows the 50th (blue lines), 80th (green lines), and 95th (red lines) percentiles of the daily sum(PCONUS) for tornado outbreak days for every DJFMAM season, for the smoothed observations (solid) and index (dashed). The observations and outbreak index are well correlated for their time series of the 50th, 80th, and 95th percentiles of daily sum(PCONUS), with a statistically significant correlation of 0.38, 0.5, and 0.58, respectively. The increasing trend in accumulated U.S. tornado outbreak risk is most apparent for the strongest storms, with a trend of +10.3% (i.e., daily summed percentage points) per decade (significant at 99% confidence level) for the 95th percentile daily sum(PCONUS) versus the +4.5% per decade and +1.5% per decade trends in the 80th and 50th percentile daily sum(PCONUS), respectively.
The spatial pattern of the trends in tornado outbreak activity can be explained by the spatial pattern in the trends in CP, SRH, and CAPE (Figs. 10d–f). An increasing trend in CP and CAPE is found for the eastern United States, and an increasing trend in SRH is found for much of CONUS. This suggests that the environment is becoming more favorable for tornado outbreaks over much of the eastern United States, especially where these trends in CP, SRH, and CAPE are greatest and where they overlap, such as over the Gulf States and Tennessee River Valley. The environment trends, however, do not provide a clear explanation for the eastward shift. In addition, the spatial pattern of the trends for the environments resemble the ENSO patterns for the environments, which raises whether these trends are solely a result of more La Niña events in more recent decades.
c. Example use cases
Figure 11 illustrates how the index represents three high-impact tornado outbreak cases and corresponding synthetic events. First, the tornado outbreak on 12 May 2010 (1200 UTC 12 May–1200 UTC 13 May) is shown (Figs. 10a–c). A mesoscale convective complex was organized that evening, producing 11 F/EF1+ tornadoes over northeast Oklahoma, southeast Kansas, and northwest Arkansas. The SPC issued a day 1 tornado outlook with 10% as the highest tornado probability contour centered over the border of Kansas and Missouri (Fig. 11a, faint shaded contours). The outbreak index is shown in Fig. 11b, including the map of P(Outbreak) for the 24-h period (shaded) and the location of this event in sum(PCONUS)–max(PCONUS) space (red “X” in bottom-left subpanel). The outbreak index well describes the risk of outbreak tornadoes. Relatively high outbreak index probabilities are located where tornadoes were observed. With these values of sum(PCONUS) and max(PCONUS), the index expected value for total number of tornadoes (μ) is 6. We simulate 1000 event total tornadoes to generate a PDF of possible tornado totals (bottom subpanel in Fig. 11b). The observed total of 11 is well within the range of possible scenarios generated by the index.
Case examples of tornado outbreak events: (a)–(c) 1200 UTC 12 May 2010–1200 UTC 13 May 2010. The observed event, including SPC day 1 tornado outlook categories (shaded colors), grid points with at least one tornado (gray), and the number of tornadoes at a grid point (blue shaded circles) are shown in (a). The total number of reported F/EF1 + tornadoes is displayed at bottom right. The index for the event, including (shaded) probability of at least one tornado is shown in (b). The bottom-left subpanel displays the event’s location in sum(PCONUS)–max(PCONUS) space with a red “X.” The bottom-right subpanel shows the event’s PDF (black curve) for number of tornadoes, its expected value μ (solid gray line), the 10th–90th percentile (gray shading), and observed value (solid red line). The set of nine simulated events (i.e., tornado locations randomly generated) is shown in (c), based on the total number percentiles labeled at the top left, with tornado locations (blue shaded circles) and the total number indicated at the bottom right of the subpanels. (d)–(f),(g)–(i) As in (a)–(c), but for 27 Apr 2011 and 7 Feb 2017 events, respectively.
Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-23-0219.1
Figure 11c shows nine simulated events generated by drawing a value of total number of tornadoes from the index PDF and then generating the locations of these tornadoes based on the map of P(Outbreak). The nine events correspond to total numbers equal to the 10th, 20th, 30th, …, up to the 90th percentile of the index PDF. For each CONUS grid point, the P(Outbreak) is used to randomly determine if an outbreak tornado occurs (+1) or not (+0). This is performed iteratively—i.e., one iteration is complete after computing over all CONUS grid points—until the total across CONUS is equal to or greater than the total number value. The number of tornadoes and their locations in the simulated event are statistically consistent with the environment (shaded circles). For this event, the simulated tornado locations well describe the potential risk in the Plains and Midwest.
Next, we consider the day of 27 April 2011, which was part of a major, violent tornado outbreak that lasted 4 days (25–28 April) and killed over 300 people. There was widespread supercell activity that day, including a mesoscale convective system that evolved into a quasi-linear convective system over northern Alabama (Knupp et al. 2014). The SPC issued a day 1 tornado outlook with 30% as the highest tornado probability contour centered over northern Alabama (Fig. 11a, faint shaded contours). The total number of reported F/EF1 + tornadoes for this 24-h period was 115. The environment of this day is markedly conducive to outbreak tornadoes, with maximum gridpoint probabilities above 20%. With these high values of sum(PCONUS) and max(PCONUS), the index expected value for total number of tornadoes (μ) is 26. We simulate 1000 event total tornadoes to generate a probability density function (PDF) of possible tornado totals (bottom subpanel in Fig. 11b). The observed total of 115 is considered extreme by the index (∼99th percentile value), but within the range of possible events. The P(Outbreak) and set of simulated events captures the regions of high tornado activity, though the index underestimates the expected number of outbreak tornadoes and cannot resolve the extreme numbers of tornadoes at individual grid points (e.g., northern Alabama). However, the index effectively describes the tornado outbreak risk in regards to severity and forecast confidence via its location in sum(PCONUS)–max(PCONUS) coordinate space, and regional-scale details are resolved, e.g., highest probability of outbreak tornadoes over Alabama/Tennessee.
Finally, we show the event of 7 February 2017 (Figs. 11g–i). The SPC issued a day 1 tornado outlook with the highest tornado probability contour being 5% centered over Alabama and Mississippi (Fig. 11g). Despite a forecast with relatively low tornado probabilities, a shortwave trough and strong midlevel winds helped produce 10 F/EF1 + tornadoes in that 24-h period. The outbreak index captures similar regions of tornado risk as SPC day 1 outlook. The location of the event in sum(PCONUS)–max(PCONUS) coordinate space is just left of the outbreak versus nonoutbreak line, suggesting high uncertainty/low confidence that this day will produce a tornado outbreak. The index expected total number of tornadoes is 4. However, the event PDF suggests that the observed value is within the 10th–90th percentile range of possibility (∼87th percentile), and simulated events further capture potential risk in regions affected by the observed event. Considering the model’s conditional bias to underpredict DJF totals (cf. Fig. 5b) by a factor of 2–3, a postcalibrated model expected value and PDF would further improve the representation of this observed event.
4. Summary and discussion
Due to the adverse impacts of tornado outbreaks, there is an increasing effort to understand modulation of tornado activity on long-range time scales and accurately model risk. More specifically, there is a need for a stochastic submonthly tornado outbreak index to more easily evaluate influences from large-scale climate variability and that can generate synthetic events for risk assessment. In this study, we developed a 6-hourly tornado outbreak index that predicts 1) the probability of outbreak tornado occurrence given collocated environmental conditions of CP, SRH, and CAPE, and 2) expected total number of tornadoes and a probability distribution given the probability map from 1. This two-part index combines approaches from previous work, resulting in a more complete assessment of tornado outbreak risk.
In the first part of the index, the frequency or probability of outbreak tornado occurrence—P(Outbreak)—is related to the CP, SRH, and CAPE environment. We found that P(Outbreak) is more sensitive to SRH changes than CP or CAPE changes and that increased sensitivity to SRH is the main distinction compared to the probability/frequency of any (outbreak or nonoutbreak) tornado occurrence (Fig. 1). The increased sensitivity of outbreak tornadoes to SRH changes is consistent with previous work. Lepore et al. (2018) found that tornadoes with higher F/EF rating were more sensitive to SRH changes. SRH as a dynamical variable contributes to supercell formation and maintenance (Droegemeier et al. 1993; Colquhoun and Riley 1996; Coffer et al. 2019), resulting in an organized environment conducive to producing many tornadoes. The outbreak index probabilities are well calibrated for spring and fall but generally underpredict (overpredict) outbreak probabilities for winter (summer) (Fig. 2). In general, the MSESS for the index probabilities are highest over regions where outbreak tornadoes occur often climatologically (Fig. 3), which corresponds with other studies that evaluated skill of probabilistic forecasts (Herman et al. 2018; Hill et al. 2020). The MSESS is lowest over regions where the index climatological frequency is high while observed climatological frequency is low, e.g., over the Plains during JJA (cf. Fig. 3c versus Figs. 6g,h), likely because climatological CP and CAPE remains relatively high (not shown; Tippett et al. 2014). This overprediction during summer is consistent with results from (Hart and Cohen 2016a) study, which suggested that convective modes during summer are dissimilar to convective modes in other seasons (Smith et al. 2012).
The expected total number of outbreak tornadoes is related to the sum and maximum value of the P(Outbreak) map (Fig. 4a). For fixed max(PCONUS), increasing sum(PCONUS) increases the total number of tornadoes, while for fixed sum(PCONUS), increasing max(PCONUS) decreases the total number of tornadoes. The tornado outbreak events with high sum(PCONUS) and max(PCONUS) generally have higher skill (Fig. 4b). This may have implications for the predictability of tornado outbreak events; events with P(Outbreak) maps that fall along or left of the 6-contour line might have greater uncertainty. In addition, the P(Outbreak) map characteristics might be related to the spatial scale of the drivers of the tornado outbreak risk. Events with larger sum(PCONUS) are associated with favorable thermodynamic (CP and CAPE) and dynamic (SRH) environmental conditions over a larger spatial area. Hence, these events are more likely driven by synoptic-scale systems. In contrast, events with smaller sum(PCONUS) are associated with favorable environmental conditions that overlap over a smaller spatial area and/or have more concentrated regions of risk, especially if it is associated with a relatively high max(PCONUS). These events are likely to be driven more by mesoscale features and are generally less predictable on the medium- to long-range time scale (Carbin et al. 2016; Sobash et al. 2016). The index expected number of total tornadoes is well calibrated when considering the full set of data and spring (Fig. 5), but presents seasonal biases including overestimation of total tornadoes during summer.
The seasonal cycle and interannual variability of tornado outbreak activity can be described well with the outbreak index (Figs. 6–9). The index captures the increasing tornado outbreak activity from winter to spring. However, the index does not sharply decrease in summer as in observations, and the observed increase in tornado outbreak activity during November is not well represented. Regional patterns in the frequency biases might be explained by the seasonal cycles in the environments. For instance, the general underestimation of tornado outbreak activity by the index during DJF and SON coincides with climatologically low values of CP and CAPE during these seasons, and general overestimation of tornado outbreak activity by the index during JJA coincides with climatologically high values of CP and CAPE. It is also possible there are missing relevant predictors in the model that would better account for this seasonality.
It is possible that outbreak tornado activity related to landfalling tropical cyclones (TCs) has a different signature in the large-scale environment than outbreak tornado activity related to midlatitude weather systems. For example, TC tornadic events generally have lower CAPE and higher SRH values than non-TC tornadic events (Edwards and Mosier 2022; Edwards 2012; Edwards et al. 2012; Davies 2006). However, most TC tornadoes are typically weak (EF0) and do meet outbreak criteria. Using the Edwards and Mosier (2022) dataset for the 1995–2021 period, we found that only 3% of outbreak tornadoes in JJA were related to TCs, and 7% of outbreak tornadoes in SON were related to TCs. Ultimately, TC outbreak tornadoes are a small fraction of the total outbreak tornadoes, but they are important to consider on an event-by-event basis and when modeling TC risk. They serve as an example of correlated perils (TCs and tornado outbreaks) which are often overlooked.
Tornado outbreak activity increases during La Niña years in the JFM season and over the Ohio River Valley and Tennessee River Valley regions, as seen in observations and the outbreak index (Figs. 7a,b and 8a,b). Tornado outbreak activity is also greater during La Niña years in FMA in both observations and index, but this link is weaker (Figs. 7c,d and 8c,d). These links can be explained by La Niña–related increases in SRH especially (Fig. 9). These results are consistent with previous studies that found a relationship between ENSO and tornado activity (Cook and Schaefer 2008; Allen et al. 2015; Lepore et al. 2017, 2018), including the peak in ENSO influence in late winter and early spring (Tippett and Lepore 2021). We defined ENSO with ONI value centered on the same month (e.g., JFM tornado activity and JFM ONI); different descriptions/indices of the ENSO state and/or other SST patterns could also be important to understand climate influences on tornado outbreak activity (Lee et al. 2013, 2016; Molina et al. 2018; Chu et al. 2019). In addition, while we focused on each environmental variable’s independent relationship with ENSO, tornado outbreak activity does depend on the covariation of instability (e.g., CAPE) and shear (e.g., SRH). Future work should address the influence of other predictable climate signals. The Madden–Julian oscillation might modulate tornado activity on subseasonal time scales (Baggett et al. 2018; Gensini et al. 2019; Kim et al. 2020; Miller et al. 2022), though the robustness of this link is less clear (Tippett 2018). The phase of the Arctic Oscillation, a prominent mode of variability in the winter and early spring, can mask ENSO-related signals in tornado outbreak activity (Tippett et al. 2022). Weather regimes, which describe recurrent, persistent circulation patterns, might also modulate tornado outbreak activity (Miller et al. 2020).
Seasonality is not explicitly included in the tornado outbreak index and is only introduced through seasonality of the environmental predictors. While beyond the scope of this study, the addition of explicit seasonal dependence to the index may be a way to improve its performance during seasons when there are systematic deficiencies. For instance, index probabilities could be calibrated from the reliability diagrams, i.e., index probabilities of 8% during DJF would be converted to ∼16% based on a fitted line through the blue curve in Fig. 2b. Another solution is to introduce seasonality in the model coefficients and allowing them to vary by season.
Observed trends to date and projected trends for the future in tornado activity are still not fully documented nor understood. The outbreak index developed here might be a useful tool for diagnosing trends and shifts in the spatial distribution of tornado outbreak activity. Because the outbreak index is spatially and temporally smooth, and it can provide environmental context for any trend projections found in climate models in future work. We found an increasing trend in tornado outbreak activity between 1979 and 2021, especially over the Tennessee River Valley and for the most extreme events (Figs. 10a–c). Tippett et al. (2016) also found that only the more extreme events (outbreaks) were becoming more extreme over time. The model’s ability to capture the trends depends on its ability to capture trends in the environments. These trends can be explained by the increasing trend in the environmental ingredients of tornadoes (CP, SRH, CAPE) over the eastern United States (Figs. 10d–f), similar to results from other studies (Koch et al. 2021).
Whether these trends are due to anthropogenic climate change is unclear since not all the environmental trends match those expected in a warming climate. A confounding factor is the fact that recent decades generally have had more La Niña years, and observed trends might reflect low-frequency SST variability rather than a forced response. In fact, the trend pattern in SRH resembles the ENSO-related pattern for SRH (Figs. 9b,e,h), and there is not a clear dynamical understanding for why SRH would increase in a warming climate. In contrast, the ENSO signal is weaker for CP and CAPE, and there is greater evidence and greater thermodynamic understanding for CP and CAPE increases in a warming climate (e.g., Clausius–Clapeyron relation; Trenberth et al. 2003; Trapp et al. 2009; Diffenbaugh et al. 2013; Brooks 2013; Lepore et al. 2021). While beyond the scope of this study, more work is needed to disentangle the influences of SST variability and anthropogenic climate change on tornado and tornado outbreak activity, which will help diagnose present climate risk and estimate future climate risk from tornado activity.
We demonstrated the use of the index with three case examples: 12 May 2010, 27 April 2011, and 7 February 2017 (Fig. 11). A novel use of this index is the generation of simulated events that are statistically consistent the environmental factors. Simulating events might be a useful method in assessing risk as has been done for tropical cyclones and other natural hazards (Bloemendaal et al. 2020; Emanuel et al. 2006; Lee et al. 2018; Davies 2019; Fan and Pang 2019; Guillaume et al. 2019; Quinn et al. 2019; Hatzis et al. 2020; Wing et al. 2020; Welker et al. 2021). Each realization is a statistically possible event that is consistent with the observed large-scale environment and a collection of many simulations could help to estimate a range of potential impacts, such as human lives at risk and/or property losses. Future work should assess how the index performs in representing extreme event risk.
Acknowledgments.
The authors acknowledge the support of this research by the WTW Research Network (Grant WILLIS CU15-2366). The authors would also like to acknowledge the editor, Thomas Galarneau, and three anonymous reviewers for their helpful feedback that improved the paper.
Data availability statement.
NARR data are provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, from their website https://psl.noaa.gov/data/gridded/data.narr.html. Mixed-layer CAPE data are provided by NCAR Research Data Archive from https://rda.ucar.edu/datasets/ds608.0/. Storm report observations are provided by NOAA/SPC at https://www.spc.noaa.gov/wcm/#data. ONI data are provided by NOAA/CPC at https://origin.cpc.ncep.noaa.gov/products/analysis_monitoring/ensostuff/ONI_v5.php.
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