1. Introduction
U.S. severe thunderstorms (ones that produce damaging winds, large hail, and tornadoes) are currently responsible for 20%–30% of global natural catastrophe insured losses (Swiss Re Institute 2023). Although the majority of severe thunderstorm insured losses are due to hailstorms, tornadoes are especially notable because of their potential for causing extreme localized destruction and loss of life. Accounting for the role of large-scale climate signals such as El Niño–Southern Oscillation (ENSO; Cook and Schaefer 2008; Allen et al. 2015) and climate change (Diffenbaugh et al. 2013; Lepore et al. 2021) in driving tornado activity trends and low-frequency variability is important for understanding why one year may be more active than another and for developing a comprehensive view of current and future tornado risk. Trends in tornado reports have been noted in the form of increased clustering—the same annual number of tornadoes but occurring on fewer days (Brooks et al. 2014; Elsner et al. 2015; Tippett et al. 2016)—and in spatial shifts of where tornadoes are reported (Gensini and Brooks 2018). In some studies (e.g., Tippett et al. 2016; Gensini and Brooks 2018), trends in meteorological environments (e.g., measures of shear and instability) that are favorable for tornadoes, especially supercell tornadoes, have been found to be consistent with the observed trends in tornado reports. This independent line of evidence from the environments is particularly valuable because the tornado report database contains nonmeteorological features due to changes in technology and reporting practices (Verbout et al. 2006).
Synoptic weather serves as an intermediary between large-scale climate signals and severe thunderstorms with their mesoscale environments. Identifying synoptic patterns that are typical for tornado occurrence has long informed the forecast process. The first operational tornado forecast issued in 1948 was based on the similarity of synoptic conditions to those present five days earlier when a tornado had occurred (Maddox and Crisp 1999). One of the forecasters responsible for that historical forecast later defined five tornado-producing synoptic patterns based on the distribution of winds aloft, the presence of dry-air intrusions, and low-level influxes of moisture (Miller 1972). Schaefer and Doswell (1984) applied principal component analysis (also known as empirical orthogonal function analysis) to gridded radiosonde data to create composites of the meteorological conditions preceding so-called progressive tornado outbreaks (ones that advance from west to east with time). More recently, Mercer et al. (2012) compared synoptic composites of tornadic events having more than six tornadoes (outbreak) with nonoutbreak events and found that outbreak days were distinguished by features that included a strong 500-hPa trough west of the outbreak location. There are also indications that synoptic patterns associated with tornado activity can be imprinted on seasonal means. Childs et al. (2018) found that enhanced November–February tornado activity was associated with an anomalous 500-hPa trough over the western United States and warm and moist conditions over the Southeast. In general, analyzing the role of synoptic-scale variability in modulating severe convective weather is especially attractive in the extended range prediction context because it is more predictable and robustly represented in relatively coarse numerical models than mesoscale variability. These considerations motivate interest in the application of weather regimes. Such “envelopes” of daily synoptic variability (Cassou 2010) have long been recognized as effective representations of persistent and predictable circulation patterns (Lamb 1950; Rex 1951; Reinhold and Pierrehumbert 1982).
The weather regime framework classifies each day’s large-scale anomalous flow configuration into one of a few predefined patterns, aiming to capture aspects of low-frequency variability that correspond to recurrent, persistent, and quasi-stationary states (e.g., Michelangeli et al. 1995). Condensing atmospheric variability into a few recurrent patterns is of particular interest in subseasonal prediction (e.g., Vautard 1990; Robertson et al. 2020; Büeler et al. 2021; Osman et al. 2023) where the weekly time scale of regimes provides a bridge between synoptic-scale weather systems (typical of medium-range prediction) and the leading modes of climate variability (typical of seasonal prediction). The differing levels of predictability associated with different regimes may provide information about the expected skill of forecasts, as well as the physical processes that may reduce or enhance forecast skill (Ferranti et al. 2015; Matsueda and Palmer 2018). By condensing forecast information into a few patterns, the weather regime framework also facilitates the identification of so-called windows of opportunity when predictability extends beyond the usual 1–2 week limit of weather forecasts (Gensini et al. 2019; Robertson et al. 2020; Mariotti et al. 2020).
In contrast to the well-established European–Atlantic sector regimes (e.g., Vautard 1990; Michelangeli et al. 1995), relatively fewer studies have investigated North American weather regimes. Nonetheless, analysis of North American weather regimes has become increasingly common, especially for the winter/cold season when low-frequency variability is prominent (e.g., Straus et al. 2007; Vigaud et al. 2018; Robertson et al. 2020; Molina et al. 2023). However, a particular barrier to the application of regimes in studying North American severe weather has been the lack of a year-round weather regime classification. Recently, Lee et al. (2023) used a variance normalization method similar to that introduced in the year-round European–Atlantic regimes of Grams et al. (2017) to define four year-round weather regimes for the North American continent. Evidence from dynamical systems theory suggests that this classification is physically meaningful and possesses characteristics consistent with greater intrinsic predictability (Lee and Messori 2024). This novel classification of North American weather regimes therefore presents an opportunity to investigate the association between weather regimes and U.S. tornado activity in all seasons under a single framework.
The only previous study on this topic is Miller et al. (2020), which examined associations between weather regimes and U.S. tornado activity occurring during the month of May only. In that study, a five-regime classification was derived from daily 500-hPa geopotential height anomalies over a relatively restricted CONUS-focused domain (notably without the typical preprocessing steps of time filtering or principal component dimension reduction). Weather regime one (WR1)—which features a zonally elongated negative 500-hPa height anomaly extending from the northwestern United States to eastern Canada and a positive height anomaly centered over the coasts of North Carolina and Virginia—was found to be the most favorable overall for tornado activity. Miller et al. (2020) also developed a deterministic (yes/no) weekly prediction model for above-normal/below-normal tornado activity based on regime forecasts from numerical weather prediction and reported greater skill than climatology for lead times up to 3 weeks. Their results indicate that there is potential for using regimes-based diagnostics to understand and predict the large-scale circulation patterns responsible for severe weather.
In this study, we focus on two questions which have not been previously addressed:
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What is the year-round relation between U.S. tornado activity and weather regimes, and how are these relations expressed in the frequency distribution of tornado report numbers?
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ENSO is known to impact weather regime frequency (Robertson and Ghil 1999; Lee et al. 2023) as well as U.S. tornado activity (e.g., Cook and Schaefer 2008; Allen et al. 2015; Cook et al. 2017). Does the weather regime framework provide a synoptic context for explaining the influence of ENSO on U.S. tornado activity?
The remainder of the paper is laid out as follows. Section 2 summarizes the tornado report data used here, reviews the year-round weather regime classification procedure, describes a logistic regression-based index that relates tornado occurrence probability with reanalysis fields, and details the significance tests that were applied. In section 3, the modulation of tornado report numbers by weather regimes is analyzed at annual, seasonal, and monthly resolution, including its dependence on ENSO phase. The tornado index provides regional detail and a connection with convective environments. A summary and discussion is given in section 4.
2. Data and methods
a. Data
Tornado reports are taken from the NOAA Storm Prediction Center (SPC) storm report database. Consistent with previous work (e.g., Brooks et al. 2014), only tornado reports with Fujita/enhanced Fujita (F/EF) rating 1 or greater (denoted F/EF1+) are retained in the analysis. This choice serves to avoid nonstationarity present in the time series when F/EF0 tornado reports are included (e.g., Verbout et al. 2006; Tippett et al. 2015). Daily numbers of F/EF1+ tornado reports are computed for the period 1979–2022. Some analysis here uses the threshold of six or more F/EF1+ tornadoes to connect with tornado outbreak criteria of Fuhrmann et al. (2014). For the spatial representation of tornado activity, we use spatially smoothed tornado reports (also known as practically perfect probabilities; Brooks et al. 1998), which are computed with a Gaussian filter with length scale σ = 120 km on a 1° × 1° grid (Hitchens et al. 2013; Gensini et al. 2020; Sobash et al. 2020).
Weather regimes are classified at daily resolution as in Lee et al. (2023) for the period 1979–2022 using data from the fifth major global reanalysis produced by European Centre for Medium-Range Weather Forecasts (ERA5; Hersbach et al. 2020) in the region 20°–80°N, 180°–30°W at 1.5° horizontal resolution. Here, we summarize the method. First, 500-hPa geopotential height anomalies are calculated by subtracting the daily climatology (smoothed with a 60-day running mean). The anomalies are then smoothed with a 10-day low-pass Fourier filter. (The classification is fairly insensitive to this filtering step, which facilitates forecast applications.) Next, the (cosine-latitude weighted) area-averaged 500-hPa geopotential height trend (5.9 m decade−1) is removed; local trends in the circulation are retained. Then, the detrended and low-pass-filtered anomalies are normalized to remove the seasonal cycle in the total variance within the domain. The normalization factor is a function of calendar day only (i.e., for a given calendar day, it is the same scalar for all grid points in the domain). It is calculated by first computing the standard deviation of the 500-hPa geopotential height anomalies for each day of the year at each grid point and then area averaging with a cosine-latitude weighting, before applying a 60-day centered running mean. The leading 12 principal components (PCs) of the normalized, low-pass filtered, and detrended 500-hPa geopotential height anomalies then go into a k-means clustering, with k = 4. The choice of four regimes is based on the results of several statistical tests, outlined in Lee et al. (2023). The resultant regimes are named Pacific Trough, Pacific Ridge, Alaskan Ridge, and Greenland High and explain 43% of the low-pass filtered 500-hPa geopotential height anomaly variance. As a final step, days for which the Euclidean distance to climatology (i.e., the origin in PC space) is smaller than the distance to any of the cluster centroids are classified as No regime.
The mean 500-hPa geopotential height anomalies associated with each of the four regimes are shown in Fig. 1 and are overlaid with the mean 850-hPa wind anomalies as a proxy for moisture and temperature advection. The mean anomalies during No regime days are negligible (not shown). In general, because the regime structures are dominantly barotropic, the 850-hPa meridional wind anomalies are closely aligned with the anomalous 500-hPa circulation. The dominant features of the Pacific Trough regime are an anomalous trough centered over the Gulf of Alaska and accompanied by low-level anomalous cyclonic flow, a modest anomalous ridge over central Canada collocated with low-level anomalous southerly flow and easterly/northeasterly low-level anomalous flow over the eastern half of the United States. Over the Pacific, the Pacific Ridge regime (Fig. 1a) presents height and low-level flow anomalies that are similar in magnitude and location to those of Pacific Trough but opposite in sign (Fig. 1b). Additionally, there is an anomalous southerly 850-hPa flow exceeding 2 m s−1 centered over the central Plains region, which is between an anomalous trough to the west and an anomalous ridge to the east, which is reminiscent of the various tornado-favorable synoptic patterns mentioned in introduction. Prominent features of the Alaskan Ridge regime are an anomalous ridge over Alaska and an anomalous trough centered over eastern Canada with northerly 850-hPa flow extending south over the central Plains (Fig. 1c). The Greenland High regime consists of a strong high-latitude positive height anomaly, similar to the negative phase of the North Atlantic Oscillation, accompanied to the south by low-level anomalous cyclonic flow and negative height anomalies (Fig. 1d).
Composite-mean 500-hPa geopotential height anomalies for the four weather regimes (shading) and 850-hPa wind anomalies (arrows). Percentages indicate the fraction of all days in 1979–2022 in each regime (total 85.9%, remaining 14.1% classified as No regime).
Citation: Monthly Weather Review 152, 9; 10.1175/MWR-D-24-0016.1
The monthly Niño-3.4 index 1979–2022 was computed using the Extended Reconstructed Sea Surface Temperature, version 5, dataset (Huang et al. 2017). Anomalies are with respect to the monthly climatology of the full period. The monthly values were linearly interpolated to daily resolution and classified as cool, neutral, or warm based on monthly varying 25th and 75th percentiles (e.g., Hanley et al. 2003). This approach results in asymmetric thresholds that are stricter than the common ±0.5°C ones in boreal winter when Niño-3.4 variability is larger and that are more lenient in boreal spring and summer when Niño-3.4 variability is smaller (Table 1).
The 25th and 75th percentiles of Niño-3.4 monthly anomalies.
b. Statistical significance
Two-sided permutation tests were used to determine if the dependence of tornado number statistics (e.g., mean and exceedance frequency) on weather regime signals is statistically significant. To assess whether a particular weather regime has an impact on the mean number of tornado reports per day, the observed difference between the mean number on days in that regime and the mean number on all other days was computed. The total sample size is
Two-sided permutation tests with annual block sampling were used to decide if the frequency of weather regime occurrence and the number of tornado reports per day have a statistically significant dependence on ENSO phase. For a given weather regime, season, and ENSO phase (cool, warm, or neutral), the frequency of the weather regime in that season and ENSO phase is compared to its frequency in that season and all other ENSO phases. The absolute value of this observed difference is ranked relative to the absolute value of the frequency difference between days from Ny randomly selected years (without replacement) and days from the remaining
A Wilcoxon rank sum test was used to assess the statistical significance of the weather regime warm minus cool ENSO difference composites. The Wilcoxon rank sum test procedure is nonparametric and essentially compares the medians of the warm ENSO and cool ENSO composited sets. The false discovery rate (FDR) correction from Benjamini and Hochberg (1995) was used as an additional step to assess the statistical significance of the (difference) composite maps and to account for multiple testing (e.g., see Wilks 2016). In the FDR procedure, a two-sided p value is calculated at every grid point and sorted from smallest to largest. Then, the sorted p values are compared to the sequence α/S, 2α/S, 3α/S, …, where S is the number of land grid points and α is the selected FDR, which we set at 10% here. The null hypothesis is rejected for p values that are smaller than the comparison sequence.
A two-sample Kolmogorov–Smirnov test (e.g., see section 5.2.5 of Wilks 2011) was used to decide whether a particular regime has a statistically significant impact on the frequency distribution of tornado report numbers. The two samples are the days in that regime and the days not in that regime.
3. Results
a. Report numbers
On an annual basis, the number of tornado reports per day is higher during Pacific Ridge days and lower during Pacific Trough and Alaskan Ridge days (Fig. 2a). The number of tornado reports per day on Greenland High and No regime days is above the average but near the margin of sampling variability. The frequency of days with six or more tornado reports, a threshold sometimes used to classify outbreaks (e.g., Fuhrmann et al. 2014), shows the same dependence on the weather regime (Fig. 2b). Enhanced activity during Pacific Ridge days is plausible since Pacific Ridge features northward low-level transport of moisture and warmer temperatures in conjunction with a trough over the western United States and ridge over the eastern United States, which are the synoptic features that have been previously related to tornado activity (Mercer et al. 2012). Suppressed activity during Alaskan Ridge might be related to the southward low-level meridional flow over eastern North America and western ridge/eastern trough configuration, which is to some extent opposite that of Pacific Ridge. Pacific Trough also presents a configuration that lacks elements that are typically considered favorable for severe weather, such as moisture transport from the Gulf of Mexico (Molina et al. 2016).
Annual (a) number of F/EF1+ reports per day and (b) frequency of 6 or more F/EF1+ reports by weather regime. Error bars are 95% confidence intervals based on 1000 bootstrap samples. Monthly (c) number of F/EF1+ reports per day and (d) frequency of six or more F/EF1+ reports by weather regime. Solid and open squares indicate statistically significant differences at the 5% and 10% levels, respectively, based on a two-sided permutation test.
Citation: Monthly Weather Review 152, 9; 10.1175/MWR-D-24-0016.1
Seasonality might be a confounding factor in the interpretation of the annual dependence of tornado activity on the weather regime (Malloy et al. 2023). For instance, Lee et al. (2023) found that Pacific Trough was more frequent in December–February (DJF; a season with low tornado activity) than in March–May (MAM; peak tornado season), which would tend to result in lower tornado activity during Pacific Trough on an annual basis simply due to seasonality. To address this possibility and to account for seasonality, we stratified our analysis by calendar month. During the June–August period, there is little difference across regimes in either the average numbers of reports (Fig. 2c) or in the frequency of days with six or more reports (Fig. 2d), with the exception of Pacific Trough, which has the lowest reports per day and frequency of six or more reports, particularly in June. The lack of a weather regime signal during summer months is consistent with the general lack of large-scale forcing during summer (Jankov and Gallus 2004; Hart and Cohen 2016).
Pacific Ridge is the regime with the highest number of reports per day during December–June and September, and the frequency of six or more reports during Pacific Ridge is above average during September–June as well. Alaskan Ridge and Pacific Trough have below-average numbers of reports during September–December, and below-average numbers of reports continue for Alaskan Ridge during January–March. Alaskan Ridge and Pacific Trough also show statistically significant reductions in the frequency of days with six or more reports in October and November. In the peak month of May, report numbers are above average on Pacific Ridge and Greenland High days and below average on Pacific Trough and No regime days. Alaskan Ridge days have report numbers that match the climatological rate in May. During October and November, the number of reports per day is the highest during No regime days, with the number of reports per day during No regime days in November being roughly the same as the climatological rate in April. Similar indications of enhanced activity are seen in the frequency of days with six or more reports. The average of 500-hPa geopotential height anomaly fields on the 10 November No regime days that have more than 10 F/EF1+ tornado reports (Fig. 3) shows a wave train and an anomalous trough to the west of climatological November severe weather activity locations, which is generally robust across cases (Fig. S1 in the online supplemental material). The pattern in Fig. 3 is indicative of a recurrent yet transient synoptic-scale weather type, and such patterns are distinct from the persistent, large-scale regimes used herein. This finding serves to emphasize that while the anomaly fields on No regime days are closer to climatology than any of the four regimes, those anomalies are not necessarily negligible on any individual day or subset of No regime days.
Average 500-hPa geopotential height anomaly fields (unfiltered) on 10 November No regime days with more than 10 F/EF1+ tornado reports. Regions where the sign of the anomaly in all 10 cases agrees with the mean are stippled.
Citation: Monthly Weather Review 152, 9; 10.1175/MWR-D-24-0016.1
We next examined the full frequency distribution of daily F/EF1+ report numbers, stratified by season and weather regime, to see the impact of weather regimes on the spread and tail behavior of the distribution. The distributions of daily F/EF1+ report numbers show statistically significant weather regime signals in all seasons except June–August (JJA; Fig. 4). Pacific Ridge is associated with more tornado reports for a fixed exceedance probability in all seasons except JJA. The distribution of daily report numbers is shifted to higher values during Greenland High days in September–November (SON). The distributions of daily F/EF1+ report numbers on Pacific Trough and Alaska ridge days show statistically significant shifts toward lower values in SON and DJF, respectively. Steeper slopes of the exceedance curves indicate greater variance (spread) in the distribution. Increases in the mean during Pacific Ridge (all seasons except JJA) are accompanied by increases in variance. Decreases in the mean during Alaska ridge days in DJF and Pacific Trough days during SON are accompanied by decreases in variance.
Distribution of daily F/EF1+ report numbers by season and weather regime. Data values up to the 99th percentile are shown. Thick lines indicate statistically significant differences at the 10% level based on a two-sided two-sample Kolmogorov–Smirnov test.
Citation: Monthly Weather Review 152, 9; 10.1175/MWR-D-24-0016.1
b. Spatial patterns and convective environments
To see the spatial expression of the weather regime modulation of tornado activity during MAM, we constructed regime composites of smoothed reports (practically perfect probabilities), the tornado index probabilities, and the constituents of the tornado index (Fig. 5). The regime composites of smoothed report anomalies show a good correspondence with those of the tornado index, which supports using the tornado index as a diagnostic tool. Pacific Trough is associated with increased tornado activity over western Texas and eastern New Mexico and broad areas of decreased tornado activity over central Plains and Ohio River valley, with the index showing large-scale areas of statistical significance. Despite the broad areas of decreased tornado activity over central Plains and Ohio River valley, Pacific Trough does not have a statistically significant impact on the frequency distribution of tornado report numbers, although the exceedance probabilities are less than the all-regimes case (Fig. 4). Pacific Ridge is associated with increased tornado activity over Midwest and Ohio River valley, which is statistically significant in both the smoothed observations and index, along with decreased tornado activity over Florida. Both Alaskan Ridge and Greenland High are associated with a modest increase in tornado activity over Florida and decreased tornado activity over Ohio River valley.
MAM composites of (first column) anomalous smoothed tornado reports (practically perfect probabilities), (second column) tornado index probabilities, (third column) CP, (fourth column) SRH, and (fifth column) CAPE, on days classified as (a)–(e) Pacific Trough, (f)–(j) Pacific Ridge, (k)–(o) Alaskan Ridge, and (p)–(t) Greenland High. Stippling indicates the statistically significant values.
Citation: Monthly Weather Review 152, 9; 10.1175/MWR-D-24-0016.1
Since the tornado index is computed from reanalysis values of CP, SRH, and CAPE, we can, to some extent, explain weather regime-related patterns of tornado activity by examining the corresponding composite anomalies of CP, SRH, and CAPE. A caveat to this diagnostic is that the tornado index is a nonlinear function of the synchronous environmental values, which means that seasonal composites of the index differ from the index evaluated on seasonal composite values of the environments. Nonetheless, there is some reasonable correspondence between the ingredient and index composite differences. This correspondence is especially clear in the case of Pacific Ridge, which is associated with positive CP, SRH, and CAPE anomalies that overlap over the Midwest and Ohio River valley regions and where increased tornado activity is observed. Likewise, the reduced activity in Pacific Trough is consistent with below-normal SRH and to a lesser extent below-normal CAPE. Similar analysis for DJF is also effective in connecting the higher activity during Pacific Ridge days and lower activity during Alaskan Ridge days to changes in convective environments (Fig. S2).
c. Influence of ENSO
ENSO has been shown to modulate U.S. tornado activity and associated meteorological environments on seasonal time scales, with La Niña conditions being associated with overall higher activity (Cook and Schaefer 2008; Allen et al. 2015). The influence of ENSO on seasonal tornado activity might be expressed through weather regimes. For instance, ENSO might modulate the frequency of weather regimes that have an impact on tornado activity (e.g., Pacific Ridge in DJF or MAM), and in doing so modulate seasonal tornado statistics. Lee et al. (2023) found that the year-round frequency of Pacific Ridge is higher during La Niña conditions than during El Niño conditions. Alternatively, ENSO might modulate the efficacy (reports per day) of weather regimes via moisture transport (Molina et al. 2018).
To check whether ENSO modulates weather regime frequency at seasonal resolution, we examined weather regime frequency stratified by season and ENSO state and found statistically significant ENSO-related shifts in weather regime frequency in DJF (Fig. 6). In DJF, Pacific Ridge is roughly twice as frequent during cool ENSO conditions as during warm ENSO conditions. Pacific Ridge shows the same qualitative behavior in MAM (more frequent during cool conditions than during warm conditions), but the difference is not statistically significant at the 5% level. Since Pacific Ridge has more tornado reports per day, the increased frequency of Pacific Ridge during cool ENSO conditions is consistent with increased tornado activity during La Niña conditions, assuming the number of tornado reports per day during Pacific Ridge is independent of ENSO phase. Pacific Trough is more frequent during warm ENSO conditions in DJF and MAM. Pacific Trough shows a statistically significant reduced number of reports per day and reduced likelihood of six or more reports in May. Therefore, the increased frequency of Pacific Trough during warm ENSO conditions is consistent with reduced tornado activity in May during El Niño if the number of tornado reports per day during Pacific Trough is independent of ENSO phase.
Frequency of weather regimes by season and ENSO state. Cool and warm conditions are defined by the monthly varying 25th and 75th percentiles of the monthly Niño-3.4 index. Error bars are 95% confidence intervals from 1000 block (annual) bootstrap samples. Dots indicate statistically significant differences from the other two ENSO phases at the 5% level by a two-sided block permutation test. The dashed lines show the frequency of the regime in that season.
Citation: Monthly Weather Review 152, 9; 10.1175/MWR-D-24-0016.1
Whether ENSO modulates seasonal tornado statistics through changes in the frequency of Pacific Ridge days depends on whether and how the number of tornado reports per day during Pacific Ridge also depends on ENSO phase. We examined this question by stratifying the average number of tornado reports per day by season, weather regime, and ENSO state (Fig. 7). The average number of reports per day for Pacific Ridge days is higher during cool ENSO conditions in DJF and MAM (both statistically significant at the 10% level), which is consistent with more activity during La Niña conditions. In short, Pacific Ridge both occurs more often and has more reports per day during cool ENSO conditions. Outside of cool ENSO conditions, enhanced tornado activity during Pacific Ridge days in DJF and MAM is absent. Other differences between ENSO phases in the number of tornado reports per day are mostly statistically insignificant, and because of the high variability in tornado report numbers, no differences are statistically significant at the 5% level (not shown). The frequency of days with six or more reports is higher on Pacific Ridge days during cool ENSO conditions but not statistically significant at the 10% level (not shown). The number of reports per day during Alaskan Ridge and Pacific Trough days in SON is relatively insensitive to ENSO phase, and tornado activity during these two regimes is substantially reduced regardless of ENSO phase.
Average number of F/EF1+ reports per day by season, weather regime, and ENSO state. Cool and warm ENSO conditions are defined by the monthly varying 25th and 75th percentiles of the monthly Niño-3.4 index. Error bars are 90% confidence intervals from 1000 block (annual) bootstrap samples. Dots indicate statistically significant differences from the other two ENSO phases at the 10% level by a two-sided block permutation test. The dashed line in each panel shows the average number of F/EF1+ reports by season.
Citation: Monthly Weather Review 152, 9; 10.1175/MWR-D-24-0016.1
We stratified DJF and MAM Pacific Ridge days by ENSO state to see whether there are differences in the amplitude or structure of the 500-hPa geopotential height anomalies for warm and cool ENSO Pacific Ridge days. Overall, we found very few statistically significant ENSO signals in the amplitude of the projection of daily normalized Z500 anomalies onto the cluster mean (Fig. S3). DJF Pacific Ridge shows a higher ridge amplitude during cool ENSO conditions compared to during warm conditions (Fig. 8, top row), consistent with the North Pacific atmospheric response to ENSO. However, the difference map shows little statistical significance. MAM Pacific Ridge amplitudes appear roughly the same during warm and cool ENSO conditions (Fig. 8, bottom row). The warm minus cool ENSO Pacific Ridge composite in MAM shows a weaker western trough with a concomitant weaker southerly flow into the central Plains. The storm track also appears farther south, which is the understood physical mechanism for overall reduced U.S. tornado activity during El Niño conditions.
(top) DJF and (bottom) MAM detrended 500-hPa geopotential height anomalies (colors) and 850-hPa wind anomalies (arrows) on Pacific Ridge days composited by ENSO phase. Stippling in the right panels indicates statistically significant differences (annual block permutation test with an FDR of 10%).
Citation: Monthly Weather Review 152, 9; 10.1175/MWR-D-24-0016.1
The warm minus cool ENSO composite difference of smoothed reports shows reduced tornado activity on Pacific Ridge days in parts of the mid-South (Arkansas, Tennessee, Kentucky, and Missouri) during DJF (Fig. 9). During MAM, the warm minus cool ENSO composite difference of smoothed reports shows reduced tornado activity on Pacific Ridge days across most of the eastern United States, except for Wisconsin, Pennsylvania, and New York. The composite differences of smoothed reports are not statistically significant, which reflects the high variability at the gridpoint level. In the DJF index composite difference, enhanced activity in southern coastal areas is more prominent than in the smoothed reports, and reduced activity in the mid-South is more localized, which may reflect the fact that no explicit spatial smoothing is applied to the tornado index. The negative DJF mid-South composite differences are coincident with slightly negative, though spatially noisy and not statistically significant ENSO composite differences of CP, SRH, and CAPE. The lack of a strong correspondence between the index composites and the environment composites may reflect the fact that an average of the index differs from the index evaluated with the averages, which is especially relevant in DJF when there are few active days. In addition, the index composites are based on simultaneous values of the environments while that information is not included in the environment composites. The positive DJF coastal composite differences of CP, SRH, and CAPE are more consistent with the index. The MAM index composite difference shows mainly reduced probability of tornado occurrence during warm ENSO conditions, which mostly matches the smoothed reports, with the largest discrepancies in west Texas and northward into Kansas where smoothed reports show negative values. During warm ENSO conditions, Pacific Ridge environments are less favorable due to reduced SRH over the central Plains, which seems to prevail over widespread positive CAPE and CP composite differences.
Warm minus cool ENSO composite differences during Pacific Ridge days of (first column) anomalous smoothed tornado reports, (second column) tornado index probabilities, (third column) CP, (fourth column) SRH, and (fifth column) CAPE, for the (a)–(e) DJF and (f)–(j) MAM season.
Citation: Monthly Weather Review 152, 9; 10.1175/MWR-D-24-0016.1
4. Summary and discussion
In this study, we examined the dependence of daily U.S. F/EF1+ tornado report numbers on the daily weather regime for the period 1979–2022 using a recently developed year-round classification (Lee et al. 2023). The classification has four categories (Pacific Trough, Pacific Ridge, Alaskan Ridge, and Greenland High) plus a No regime category. On an annual basis, tornado activity is enhanced on Pacific Ridge days and reduced on Pacific Trough and Alaskan Ridge days. Stratifying the analysis by season and month, the enhancement during Pacific Ridge days is clearest in winter and spring, while the reduction during Pacific Trough and Alaskan Ridge days is most prominent in fall and early winter. The general trough-to-the-west, ridge-to-the-east configuration of Pacific Ridge over the United States is similar to favorable patterns noted in previous studies of synoptic patterns that are associated with tornado occurrence (e.g., Schaefer and Doswell 1984; Mercer et al. 2012).
Changes in the mean number of tornado reports per day are accompanied by corresponding changes in extremes and in spread of the frequency distribution. That is, when the mean of the frequency distribution increases so does its spread. Examination of the spatial pattern of smoothed report data (practically perfect probabilities) in March–May showed widespread positive anomalies for Pacific Ridge and negative anomalies for Pacific Trough over most of the eastern United States, with a tendency toward opposite values over the Southeast and Gulf Coasts. Similar features were present in the tornado index and its constituents: convective precipitation, convective available potential energy, and storm relative helicity.
We found two ways in which ENSO has an impact. First, Pacific Trough days are more frequent during warm ENSO conditions and Pacific Ridge days are less frequent. These frequency shifts are statistically significant in December–February and statistically insignificant in March–May. Second, the number of tornadoes per day on Pacific Ridge days is higher during cool ENSO conditions, again statistically significant in December–February and statistically insignificant in March–May. These behaviors are consistent with cool ENSO conditions having more tornado activity than warm ENSO conditions (Cook and Schaefer 2008; Allen et al. 2015; Malloy and Tippett 2024). Similar features (more tornadoes per day on Pacific Ridge days) were seen in the tornado index, but the behavior of its constituents was less uniform with SRH composites showing the most consistent indication of enhanced activity during cool ENSO conditions.
As noted in introduction, Miller et al. (2020) analyzed the dependence on F/EF1+ report numbers on the weather regime category for the month of May only. The 500-hPa geopotential height anomaly of their weather regime one (WR1), which was associated with above-normal tornado activity, bears some similarity to that of the Pacific Ridge with negative anomalies in the west that extend northward and positive anomalies to the east. Whether or not WR1 is associated with ridging over the Pacific is impossible to say since the domain in Miller et al. (2020) has a more limited longitudinal extent. Likewise, whether or not WR1 days and Pacific Ridge days coincide is impossible to say because no classification data were provided by Miller et al. (2020).
A notable difference between the results in Miller et al. (2020) and those here is that the probability shifts found here for May are substantially smaller. The probability of one or more tornadoes on WR1 days was >75% compared to the climatological frequency of 55% (a shift of ∼20 percentage points), and the probability of five or more tornadoes on WR1 days was >65% compared to the climatological frequency of 17% (a shift of ∼48 percentage points). The corresponding probability shifts found here are 64% probability of one or more tornadoes on Pacific Ridge days in May compared to the climatological frequency of 60%, and 28% probability of five or more tornadoes on Pacific Ridge days in May compared to the climatological frequency of 21% (not shown). The main methodological difference between the two studies is the weather regime classification method—both studies use F/EF1+ tornado reports, but Miller et al. (2020) uses only data from May during the shorter period 1990–2019 and a smaller spatial domain on which to define the weather regimes. Their classification could perhaps be considered closer to weather “types” or “patterns” (e.g., Neal et al. 2016), rather than the large-scale, low-frequency regimes used herein. Nevertheless, reconciling these differences by quantifying the predictability of the year-round classification would have substantial implications for subseasonal forecasting of severe weather.
A direction for future work would be to examine to what extent previously reported clustering trends (the same number of tornadoes on fewer days and more tornadoes in the most extreme outbreaks; Brooks et al. 2014; Elsner et al. 2015; Tippett et al. 2016) have an interpretation in terms of weather regimes. ENSO might also play a role because cool ENSO conditions have been common over recent decades, and cool ENSO conditions were seen here to result in more tornadoes per day on Pacific Ridge days. A related issue is whether observed ENSO trends are externally forced or not (Lee et al. 2022; Sobel et al. 2023), in addition to trends in the frequency of the regimes themselves. During March–May, there has been a slight decrease in Pacific Trough frequency, offset by an equivalent slight increase in Alaskan Ridge frequency (Lee et al. 2023). However, both these regimes suppress tornado activity similarly, suggesting no overall effect. In terms of the regimes which enhance tornado activity, no significant trends in the frequency of the Pacific Ridge regime in any season or on the annual scale were found by Lee et al. (2023); the Greenland High regime has become substantially more frequent in summer (+3.9 days decade−1), but its influence on tornado activity is minimal in that season.
Weather regimes also provide an additional perspective from which to assess the fidelity of numerical models. Future work might examine how well numerical models (free running and initialized) simulate the observed structure and frequency of year-round North American weather regimes and their associations with convective parameters, particularly at subseasonal lead times.
Acknowledgments.
The authors acknowledge the support of this research by the WTW Research Network (Grant WILLIS CU15-2366). The authors thank three anonymous reviewers for their useful comments.
Data availability statement.
Weather regime data are available on Zenodo at https://doi.org/10.5281/zenodo.8165165, based on ERA5 reanalysis available from the Copernicus Climate Data Store at https://doi.org/10.24381/cds.bd0915c6. Tornado report data are available from the Storm Prediction Center at https://www.spc.noaa.gov/wcm/#data. NCEP North American Regional Reanalysis (NARR) data are provided by the NOAA PSL, Boulder, Colorado, USA, from their website at https://psl.noaa.gov and by the Research Data Archive at the National Center for Atmospheric Research at https://rda.ucar.edu/datasets/ds608.0.
REFERENCES
Allen, J. T., M. K. Tippett, and A. H. Sobel, 2015: Influence of the El Niño/Southern Oscillation on tornado and hail frequency in the United States. Nat. Geosci., 8, 278–283, https://doi.org/10.1038/ngeo2385.
Benjamini, Y., and Y. Hochberg, 1995: Controlling the false discovery rate: A practical and powerful approach to multiple testing. J. Roy. Stat. Soc., 57B, 289–300, https://doi.org/10.1111/j.2517-6161.1995.tb02031.x.
Brooks, H. E., M. Kay, and J. Hart, 1998: Objective limits on forecasting skill of rare events. Preprints, 19th Conf. on Severe Local Storms, Minneapolis, MN, Amer. Meteor. Soc., 552–555.
Brooks, H. E., G. W. Carbin, and P. T. Marsh, 2014: Increased variability of tornado occurrence in the United States. Science, 346, 349–352, https://doi.org/10.1126/science.1257460.
Büeler, D., L. Ferranti, L. Magnusson, J. F. Quinting, and C. M. Grams, 2021: Year-round sub-seasonal forecast skill for Atlantic–European weather regimes. Quart. J. Roy. Meteor. Soc., 147, 4283–4309, https://doi.org/10.1002/qj.4178.
Cassou, C., 2010: Euro-Atlantic regimes and their teleconnections. Proc. ECMWF Seminar on Predictability in the European and Atlantic Regions, Shinfield Park, Reading, ECMWF, 1–14, https://www.ecmwf.int/en/elibrary/73944-euro-atlantic-regimes-and-their-teleconnections.
Childs, S. J., R. S. Schumacher, and J. T. Allen, 2018: Cold-season tornadoes: Climatological and meteorological insights. Wea. Forecasting, 33, 671–691, https://doi.org/10.1175/WAF-D-17-0120.1.
Cook, A. R., and J. T. Schaefer, 2008: The relation of El Niño–Southern Oscillation (ENSO) to winter tornado outbreaks. Mon. Wea. Rev., 136, 3121–3137, https://doi.org/10.1175/2007MWR2171.1.
Cook, A. R., L. M. Leslie, D. B. Parsons, and J. T. Schaefer, 2017: The impact of El Niño–Southern Oscillation (ENSO) on winter and early spring US tornado outbreaks. J. Appl. Meteor. Climatol., 56, 2455–2478, https://doi.org/10.1175/JAMC-D-16-0249.1.
Diffenbaugh, N. S., M. Scherer, and R. J. Trapp, 2013: Robust increases in severe thunderstorm environments in response to greenhouse forcing. Proc. Natl. Acad. Sci. USA, 110, 16 361–16 366, https://doi.org/10.1073/pnas.1307758110.
Elsner, J. B., S. C. Elsner, and T. H. Jagger, 2015: The increasing efficiency of tornado days in the United States. Climate Dyn., 45, 651–659, https://doi.org/10.1007/s00382-014-2277-3.
Ferranti, L., S. Corti, and M. Janousek, 2015: Flow-dependent verification of the ECMWF ensemble over the Euro-Atlantic sector. Quart. J. Roy. Meteor. Soc., 141, 916–924, https://doi.org/10.1002/qj.2411.
Fuhrmann, C. M., C. E. Konrad, M. M. Kovach, J. T. McLeod, W. G. Schmitz, and P. G. Dixon, 2014: Ranking of tornado outbreaks across the United States and their climatological characteristics. Wea. Forecasting, 29, 684–701, https://doi.org/10.1175/WAF-D-13-00128.1.
Gensini, V. A., and H. E. Brooks, 2018: Spatial trends in United States tornado frequency. npj Climate Atmos. Sci., 1, 38, https://doi.org/10.1038/s41612-018-0048-2.
Gensini, V. A., T. L. Mote, and H. E. Brooks, 2014: Severe-thunderstorm reanalysis environments and collocated radiosonde observations. J. Appl. Meteor. Climatol., 53, 742–751, https://doi.org/10.1175/JAMC-D-13-0263.1.
Gensini, V. A., D. Gold, J. T. Allen, and B. S. Barrett, 2019: Extended US tornado outbreak during late May 2019: A forecast of opportunity. Geophys. Res. Lett., 46, 10 150–10 158, https://doi.org/10.1029/2019GL084470.
Gensini, V. A., A. M. Haberlie, and P. T. Marsh, 2020: Practically perfect hindcasts of severe convective storms. Bull. Amer. Meteor. Soc., 101, E1259–E1278, https://doi.org/10.1175/BAMS-D-19-0321.1.
Grams, C. M., R. Beerli, S. Pfenninger, I. Staffell, and H. Wernli, 2017: Balancing Europe’s wind-power output through spatial deployment informed by weather regimes. Nat. Climate Change, 7, 557–562, https://doi.org/10.1038/nclimate3338.
Hanley, D. E., M. A. Bourassa, J. J. O’Brien, S. R. Smith, and E. R. Spade, 2003: A quantitative evaluation of ENSO indices. J. Climate, 16, 1249–1258, https://doi.org/10.1175/1520-0442(2003)16<1249:AQEOEI>2.0.CO;2.
Hart, J. A., and A. E. Cohen, 2016: The challenge of forecasting significant tornadoes from June to October using convective parameters. Wea. Forecasting, 31, 2075–2084, https://doi.org/10.1175/WAF-D-16-0005.1.
Hersbach, H., and Coauthors, 2020: The ERA5 global reanalysis. Quart. J. Roy. Meteor. Soc., 146, 1999–2049, https://doi.org/10.1002/qj.3803.
Hitchens, N. M., H. E. Brooks, and M. P. Kay, 2013: Objective limits on forecasting skill of rare events. Wea. Forecasting, 28, 525–534, https://doi.org/10.1175/WAF-D-12-00113.1.
Huang, B., and Coauthors, 2017: Extended Reconstructed Sea Surface Temperature, version 5 (ERSSTv5): Upgrades, validations, and intercomparisons. J. Climate, 30, 8179–8205, https://doi.org/10.1175/JCLI-D-16-0836.1.
Jankov, I., and W. A. Gallus, 2004: MCS rainfall forecast accuracy as a function of large-scale forcing. Wea. Forecasting, 19, 428–439, https://doi.org/10.1175/1520-0434(2004)019<0428:MRFAAA>2.0.CO;2.
King, A. T., and A. D. Kennedy, 2019: North American supercell environments in atmospheric reanalyses and RUC-2. J. Appl. Meteor. Climatol., 58, 71–92, https://doi.org/10.1175/JAMC-D-18-0015.1.
Lamb, H. H., 1950: Types and spells of weather around the year in the British Isles: Annual trends, seasonal structure of the year, singularities. Quart. J. Roy. Meteor. Soc., 76, 393–429, https://doi.org/10.1002/qj.49707633005.
Lee, S., M. L’Heureux, A. T. Wittenberg, R. Seager, P. A. O’Gorman, and N. C. Johnson, 2022: On the future zonal contrasts of equatorial Pacific climate: Perspectives from observations, simulations, and theories. npj Climate Atmos. Sci., 5, 82, https://doi.org/10.1038/s41612-022-00301-2.
Lee, S. H., and G. Messori, 2024: The dynamical footprint of year-round North American weather regimes. Geophys. Res. Lett., 51, e2023GL107161, https://doi.org/10.1029/2023GL107161.
Lee, S. H., M. K. Tippett, and L. M. Polvani, 2023: A new year-round weather regime classification for North America. J. Climate, 36, 7091–7108, https://doi.org/10.1175/JCLI-D-23-0214.1.
Lepore, C., R. Abernathey, N. Henderson, J. T. Allen, and M. K. Tippett, 2021: Future global convective environments in CMIP6 models. Earth’s Future, 9, e2021EF002277, https://doi.org/10.1029/2021EF002277.
Maddox, R. A., and C. A. Crisp, 1999: The tinker AFB tornadoes of March 1948. Wea. Forecasting, 14, 492–499, https://doi.org/10.1175/1520-0434(1999)014<0492:TTATOM>2.0.CO;2.
Malloy, K., and M. K. Tippett, 2024: A stochastic statistical model for US outbreak-level tornado occurrence based on the large-scale environment. Mon. Wea. Rev., 152, 1141–1161, https://doi.org/10.1175/MWR-D-23-0219.1.
Malloy, K., M. K. Tippett, and W. J. Koshak, 2023: ENSO and MJO modulation of U.S. cloud-to-ground lightning activity. Mon. Wea. Rev., 151, 3255–3274, https://doi.org/10.1175/MWR-D-23-0157.1.
Mariotti, A., and Coauthors, 2020: Windows of opportunity for skillful forecasts subseasonal to seasonal and beyond. Bull. Amer. Meteor. Soc., 101, E608–E625, https://doi.org/10.1175/BAMS-D-18-0326.1.
Matsueda, M., and T. Palmer, 2018: Estimates of flow-dependent predictability of wintertime Euro-Atlantic weather regimes in medium-range forecasts. Quart. J. Roy. Meteor. Soc., 144, 1012–1027, https://doi.org/10.1002/qj.3265.
Mercer, A. E., C. M. Shafer, C. A. Doswell, L. M. Leslie, and M. B. Richman, 2012: Synoptic composites of tornadic and nontornadic outbreaks. Mon. Wea. Rev., 140, 2590–2608, https://doi.org/10.1175/MWR-D-12-00029.1.
Michelangeli, P.-A., R. Vautard, and B. Legras, 1995: Weather regimes: Recurrence and quasi stationarity. J. Atmos. Sci., 52, 1237–1256, https://doi.org/10.1175/1520-0469(1995)052<1237:WRRAQS>2.0.CO;2.
Miller, D. E., Z. Wang, R. J. Trapp, and D. S. Harnos, 2020: Hybrid prediction of weekly tornado activity out to week 3: Utilizing weather regimes. Geophys. Res. Lett., 47, e2020GL087253, https://doi.org/10.1029/2020GL087253.
Miller, R. C., 1972: Notes on analysis and severe-storm forecasting procedures of the Air Force Global Weather Central. Air Weather Service Tech. Rep. 200, 184 pp., https://apps.dtic.mil/sti/tr/pdf/AD0744042.pdf.
Molina, M. J., R. P. Timmer, and J. T. Allen, 2016: Importance of the Gulf of Mexico as a climate driver for U.S. severe thunderstorm activity. Geophys. Res. Lett., 43, 12 295–12 304, https://doi.org/10.1002/2016GL071603.
Molina, M. J., J. T. Allen, and V. A. Gensini, 2018: The Gulf of Mexico and ENSO influence on subseasonal and seasonal CONUS winter tornado variability. J. Appl. Meteor. Climatol., 57, 2439–2463, https://doi.org/10.1175/JAMC-D-18-0046.1.
Molina, M. J., J. H. Richter, A. A. Glanville, K. Dagon, J. Berner, A. Hu, and G. A. Meehl, 2023: Subseasonal representation and predictability of North American weather regimes using cluster analysis. Artif. Intell. Earth Syst., 2, e220051, https://doi.org/10.1175/AIES-D-22-0051.1.
Neal, R., D. Fereday, R. Crocker, and R. E. Comer, 2016: A flexible approach to defining weather patterns and their application in weather forecasting over Europe. Meteor. Appl., 23, 389–400, https://doi.org/10.1002/met.1563.
Osman, M., R. Beerli, D. Büeler, and C. M. Grams, 2023: Multi-model assessment of sub-seasonal predictive skill for year-round Atlantic-European weather regimes. Quart. J. Roy. Meteor. Soc., 149, 2386–2408, https://doi.org/10.1002/qj.4512.
Reinhold, B. B., and R. T. Pierrehumbert, 1982: Dynamics of weather regimes: Quasi-stationary waves and blocking. Mon. Wea. Rev., 110, 1105–1145, https://doi.org/10.1175/1520-0493(1982)110<1105:DOWRQS>2.0.CO;2.
Rex, D. F., 1951: The effect of Atlantic blocking action upon European climate. Tellus, A3, 100–112, https://doi.org/10.3402/tellusa.v3i2.8617.
Robertson, A. W., and M. Ghil, 1999: Large-scale weather regimes and local climate over the western United States. J. Climate, 12, 1796–1813, https://doi.org/10.1175/1520-0442(1999)012<1796:LSWRAL>2.0.CO;2.
Robertson, A. W., N. Vigaud, J. Yuan, and M. K. Tippett, 2020: Towards identifying subseasonal forecasts of opportunity using North American weather regimes. Mon. Wea. Rev., 148, 1861–1875, https://doi.org/10.1175/MWR-D-19-0285.1.
Schaefer, J. T., and C. A. Doswell III, 1984: Empirical orthogonal function expansion applied to progressive tornado outbreaks. J. Meteor. Soc. Japan, 62, 929–936, https://doi.org/10.2151/jmsj1965.62.6_929.
Sobash, R. A., G. S. Romine, and C. S. Schwartz, 2020: A comparison of neural-network and surrogate-severe probabilistic convective hazard guidance derived from a convection-allowing model. Wea. Forecasting, 35, 1981–2000, https://doi.org/10.1175/WAF-D-20-0036.1.
Sobel, A. H., and Coauthors, 2023: Near-term tropical cyclone risk and coupled Earth system model biases. Proc. Natl. Acad. Sci. USA, 120, e2209631120, https://doi.org/10.1073/pnas.2209631120.
Straus, D. M., S. Corti, and F. Molteni, 2007: Circulation regimes: Chaotic variability versus SST-forced predictability. J. Climate, 20, 2251–2272, https://doi.org/10.1175/JCLI4070.1.
Swiss Re Institute, 2023: Natural catastrophes and inflation in 2022: A perfect storm. Swiss Re Institute Tech. Rep. 1, 34 pp., https://www.swissre.com/dam/jcr:1d793484-9b96-4e54-91c3-09f8fc841bde/2023-05-sigma-01-english.pdf.
Taszarek, M., N. Pilguj, J. T. Allen, V. Gensini, H. E. Brooks, and P. Szuster, 2021: Comparison of convective parameters derived from ERA5 and MERRA-2 with rawinsonde data over Europe and North America. J. Climate, 34, 3211–3237, https://doi.org/10.1175/JCLI-D-20-0484.1.
Tippett, M. K., J. T. Allen, V. A. Gensini, and H. E. Brooks, 2015: Climate and hazardous convective weather. Curr. Climate Change Rep., 1, 60–73, https://doi.org/10.1007/s40641-015-0006-6.
Tippett, M. K., C. Lepore, and J. E. Cohen, 2016: More tornadoes in the most extreme U.S. tornado outbreaks. Science, 354, 1419–1423, https://doi.org/10.1126/science.aah7393.
Vautard, R., 1990: Multiple weather regimes over the North Atlantic: Analysis of precursors and successors. Mon. Wea. Rev., 118, 2056–2081, https://doi.org/10.1175/1520-0493(1990)118<2056:MWROTN>2.0.CO;2.
Verbout, S. M., H. E. Brooks, L. M. Leslie, and D. M. Schultz, 2006: Evolution of the U.S. tornado database: 1954–2003. Wea. Forecasting, 21, 86–93, https://doi.org/10.1175/WAF910.1.
Vigaud, N., A. W. Robertson, and M. K. Tippett, 2018: Predictability of recurrent weather regimes over North America during winter from submonthly reforecasts. Mon. Wea. Rev., 146, 2559–2577, https://doi.org/10.1175/MWR-D-18-0058.1.
Wilks, D. S., 2011: Statistical Methods in the Atmospheric Sciences: An Introduction. Academic Press, 676 pp.
Wilks, D. S., 2016: “The stippling shows statistically significant grid points”: How research results are routinely overstated and overinterpreted, and what to do about it. Bull. Amer. Meteor. Soc., 97, 2263–2273, https://doi.org/10.1175/BAMS-D-15-00267.1.