Mark C. Bove

3. Methodology

Using tornado statistic data from Grazulis (1991), an empirical analysis of the results of Knowles and Pielke’s unpublished work was possible. Using the statistical data, the two main findings of Knowles and Pielke are tested. First, whether large tornadic outbreaks are more common during La Niña events, and second whether La Niña events produce stronger tornadoes.

The area of study within the contiguous United States is the region bounded by 25°N and 50°N and 75°W and 110°W. This region covers most of the eastern two-thirds of the United States, which is home to the greatest concentration of tornadoes on the planet (Grazulis 1991). The western United States are omitted, due to less frequent tornadic activity.

The region is divided into a grid for statistical significance checks. Since tornadoes are microscale phenomena primarily caused by mesoscale systems, we choose to focus on grids with bins that reflect the size scales of tornadoes and their parent storms. Thus, bin sizes of 2.5° by 2.5° and 1.25° by 1.25° are implemented. These bins are used for examining ENSO related impacts of tornadic activity (Figure 2). Only 2.5° bins are shown in this paper for brevity, but the results using each size bin are equivalent.

Tornado data containing year, month and location of tornado touchdown are extracted from the data provided by the NSSFC. The tornado events are then categorized as occurring during one of three ENSO phases.

The data is used to create seasonal totals. The seasonal totals are from a running three-month total of tornado occurrences in each bin. The result is 10 3-month ENSO seasons, starting from October-November-December (OND) and running through July-August-September (JAS). This partitioning allows seasonal changes in the tornadic activity to be highlighted. Since most tornado events occurs during late winter into spring, the seasons JFM through AMJ are emphasized (Table 2).

Four different methods are used to analyze the binned data. First, the number of tornadoes in a bin during El Niño (La Niña) is differenced from the amount of tornadoes in the same bin during neutral ENSO conditions. This allows a simple comparison of changes in tornadic activity. Second, the number of tornado days (the number of days that the bin sees at last one tornado) in each bin during extreme events is differenced from the number of tornado days during neutral ENSO conditions. Using tornado day differences instead of tornado event differences can remove potential biases from large tornado outbreaks.

Next, the amount of tornadoes during El Niño (La Niña) in each bin is compared against its neutral counterpart to check for statistically significant differences between them. Finally, a resampling technique known as the ‘bootstrap’ is used to help determine the underlying distribution of seasonal tornado occurrences. Both these methods are discussed below.

By using key characteristics of tornadic distributions, the difference between the means of two tornado populations can be determined. Since a single tornado is assumed to be an independent event, the number of tornado occurrences during an ENSO year, X, is considered a discrete random variable. Sampled over time, these discrete random variables create a population with Poisson distribution. For each grid box, annual and monthly populations of tornado events are compiled for each ENSO phase. By comparing these Poisson populations, it can be determined whether they are statistically distinguishable from each other.

If the distribution of a discrete random variable, X, is distributed as a Poisson random variable with parameter l, the mean amount of events expected in a population, is:

(1) k= 0,1,2,...

(Taylor 1982). Also, if X1, X2, . . . , Xn is a sample of size n from a Poisson distribution with parameter l, then has a Poisson distribution with parameter nl (Lehmann 1986).

We assume that the distribution of tornado events totals for an extreme year (warm or cold) to be a Poisson random variable with parameter lx, where lx is the rate of tornado occurrence for the extreme year. Likewise, we assume the number of tornado events for a neutral year is also a Poisson random variable with parameter ly, representing the rate of tornado occurrences for a neutral year (Lehmann 1986).

With these two arguments, we can formulate the following hypothesis test:

(2) Ho : lx = ly vs. H1 : lx > ly

The Null hypothesis, Ho, states that we assume the two Poisson populations, represented by lx and ly, are statistically indistinguishable. The alternative hypothesis, H1, assumes that there is a significant difference between the two Poisson tornado populations.

The following notation is used to perform the statistical analysis with the two Poisson populations. Within any region, x is the number of tornadoes that occurred during n extreme event years. Likewise, y is the number of tornadoes that occurred during m neutral event years. The sum of all tornado events in both neutral and extreme events is denoted by t (t = x + y).

A Z-statistic can be used to compare the mean of the two populations. Since the means of the Poisson distribution have a binomial distribution, i.e. x has a binomial distribution with parameters t and . Thus, under he null hypothesis that Ho : lx = ly:

(4) k = 0,1,2,...,t

With a sample size of at least 25, the Z statistic is:

(5)

Rejection of Ho occurs when Z > 1.645 at a confidence of 95% (confidence coefficient a = 0.05), Z > 1.287 at a confidence of 90% (a = 0.1), and Z > 0.845 at a confidence of 80% (a = 0.2), showing significant statistical change in the amount of tornado events in extreme years than in neutral years (Lehmann 1986).

2) Bootstrap Method

The number of years in each ENSO category is insufficient to determine the actual underlying statistical distribution of seasonal tornadic activity. For instance, there are only 10 years of tornado data for cold events. Therefore, the resampling technique based on the bootstrap method of Draconis and Efron (1983) is implemented for generating a representative probability distribution function. In the bootstrap method, monthly tornado event data is considered independent.

The bootstrap is implemented to create 3-month ENSO seasonal composites by repeated sampling of the available data with instant replacement. Each individual month in a composite ENSO season is chosen randomly from a list of same months that occurred during the same ENSO phase. For example, a seasonal composite for MJJ in the cold phase could consist of the sum of the number of tornadoes in May 1988, June 1970, and July 1955. The three randomly selected months then create one composite season (Green 1996). This procedure is repeated 10,000 times. Then, the sum of all tornadic activity during the composite seasons is taken, producing a total amount of tornadoes for a particular season. This resampled data is used to construct histograms showing the frequency and distribution of tornadic activity in fixed locations during different parts of the ENSO cycle.

There are some limitations to the bootstrap. While the mean of a bootstrap sample is the same as the original sample, the variance in the bootstrap sample is conservative. Therefore, the actual range of tornadic activity shown by the bootstrap is not as broad as the distribution is in nature.

Another limitation of the bootstrap is that it regards individual months as independent. With respect to tornadoes, this assumption can be invalid if a tornado outbreak associated with one synoptic system occurs on the last day of a month and continues into the first day of the new month. The events on each day are then not independent of each other, but are treated as such in the bootstrap.

4. Results

The first conclusion of Knowles and Pielke was that there is a greater chance of large tornado outbreaks (40 or more tornadoes caused by one synoptic system) during La Niña than other phases of the ENSO cycle. A list of top fifteen tornadic outbreaks with at least 40 tornadoes is obtained from Grazulis (1991). The date of each outbreak is used to determine the ENSO phase at the time.

The results, shown in Table 3, reveal that only one outbreak out of the top 15 occurred during an El Niño event. Six of the top 15, including two of the top three, occurred during a La Niña event, while the remaining eight occurred during neutral ENSO years. This reveals that large outbreaks are indeed very scarce during El Niño events, and more common during non-El Niño years. Further, if you consider the fact that there are roughly twice as many neutral years than La Niña years, outbreaks during La Niña are also more common than in neutral years.

The second finding of Knowles and Pielke was that tornadoes during La Niña events were typically stronger than their non-La Niña counterparts. To test this result, annual F4 and F5 tornado data from 1950-1988 are taken from Grazulis (1991) and sorted by ENSO year. The results are listed in Table 4. La Niña years see an average of 16.2 F4 and F5 tornadoes. Meanwhile, neutral and El Niño years only see 8.42 and 8.2 F4 and F5 tornadoes, respectively. The data show that there is almost a doubling of the amount of devastating tornadoes during La Niña as compared to other years.

To summarize, it does appear that the conclusions of Knowles and Pielke were well founded. La Niña years shows a large increase in large tornadic outbreaks as well as an increase in the number of devastating tornadoes, while El Niño years show a significant decrease in devastating tornadoes and less potential to create large outbreaks.

The vast majority of the region studied in this paper showed that ENSO causes no significant change in tornadic activity. However, there are two areas in which tornadic activity exhibits a response to ENSO: the southern plains during El Niño, and the Ohio Valley and Deep South during La Niña. Thus, the following results are discussed with respect these two geographical areas (Figure 3).

Seasonal differences of tornado events in the southern plains over late winter and spring show that there is a reduction in tornado occurrences in the warm phase as compared to neutral conditions. Changes during JFM, if any, are minimal (Figure 4a). Most of the region sees no changes in the number of tornado events, but areas of eastern Oklahoma and Kansas see 2 fewer tornadoes per El Niño year during this season.

As spring approaches, the total area seeing fewer tornadoes increases. Meanwhile, the difference in the number of tornado event increases (Figures b-d). The FMA season shows the area seeing a reduction in tornadoes has more than doubled, covering areas east of central Texas, Oklahoma, and Kansas. The differences in some regions have also increased, with northeast Oklahoma seeing 4 fewer tornadoes in this El Niño season. MAM sees the area of reduced tornado activity shift westward. By this time, all of Oklahoma is witnessing a reduction of tornado events, as well as the majority on north Texas and Kansas. Further, large regions of northeast Texas, Oklahoma, and east Kansas see three to four fewer tornadoes during this El Niño season. By AMJ, the signal continues to shift west, with the western half of the plain states seeing the reductions in tornado events. Southeast areas of the region still show some reduced activity, but the northeast quadrant shows the signal disappearing.

Differences in Tornado days follow much the same pattern. During JFM (Figure 5a), there is little in the way of a continuous pattern. In fact, an increase in El Niño seasonal Tornado days near the Louisiana-Texas border seems to be the most coherent signal, while there are spotty decreases and increases elsewhere in the region.

The reduction of tornado days becomes more apparent during FMA, however, and increases through AMJ (Figures 5b-d). During FMA, bins south of Oklahoma start showing 2-6 fewer tornado days per 10 El Niño seasons, a slight decrease in activity. A few bins show a stronger decrease, but there are still spotty areas of increases, indicating the possibility that some of these reductions and increases are simply white noise. The MAM season, however, shows a clear reduction of tornado days. From east Texas to southern Nebraska, a large region of reduced El Niño tornado days develops. The largest decreases are in central Texas and Oklahoma, with over 10 fewer tornado days per 10 El Niño seasons. The reduction of tornado days continues to expand in area and deepen into AMJ, with area of southern Nebraska also seeing over 14 fewer tornado days per 10 El Niño seasons.

The statistically significant changes in tornadic activity closely parallel the results of the previous two binning experiments. The JFM season (Figure 6a) shows that the 20+ tornado differences in eastern Oklahoma and Kansas as seen in figure 4a are significant at the 95% level. This region expands dramatically into FMA (6b), with most of the eastern half of the region showing 95% confidence in reduced tornadic activity. Central Kansas, Oklahoma, and Texas also show a reduction in tornadoes, though only at 80% confidence. The region expands westward during MAM (6c), where most of north Texas, Oklahoma, and Kansas see reduced tornadic activity at the 95% confidence level. Confidence in Missouri, however, begins to wane, and approach noise as we enter AMJ (6d). The southern and western regions, however, still maintain 95% confidence of reduced tornadic activity.

Histograms can further demonstrate decreases in tornadic activity that occur during ENSO warm phase springs in the southern plains. Around Dallas, Texas (Figure 7a), for example, there is a 45% probability that 3 or more tornadoes will occur in this region during MAM neutral seasons, but that probability is reduced to 22% during MAM El Niño seasons. The probability of four of more tornadoes is 30% during MAM neutral seasons, but only 7.5% during MAM El Niño season, a four-fold decrease. The histogram also shows no El Niño MAM seasons in the Dallas area have produced more than 6 tornadoes. During a neutral MAM, however, there is still over a 10% chance that there will be more than 6 tornadoes during this time period.

The results at Shreveport, Louisiana are similar to Dallas (Figure 7b). The probability of five or more tornadoes in the Shreveport area during a neutral MAM season is 30%, but the probability is reduced to 2.5% during El Niño MAM seasons, a ten-fold decrease. Also like Dallas, the histogram around Shreveport showed that El Niño MAM seasons have produced no more than six tornadoes in the region. However, the chances of 6 or more tornadoes during a neutral MAM in Shreveport are more than 20%.

2) Ohio Valley and Deep South — La Niña

Conversely, seasonal differences of tornado events in the Ohio and Deep South over late winter and spring show that there is an increase in tornado occurrences during warm phase as compared to neutral conditions. The changes in activity are already apparent during JFM (Figure 8a). A line of increased activity can be seen extending from Louisiana northeast into Indiana and Michigan. The greatest increases appear in Louisiana and Mississippi, with another maximum in Indiana.

As spring approaches, the total area seeing more tornadoes spreads eastward while the number of La Niña seasonal tornado event increases (Figures 8b-d). The area seeing an increase in tornadoes during FMA has more than doubled, completely enveloping Mississippi, Tennessee, Kentucky, and Indiana and large sections of surrounding states. The region of maximum increase (upwards of 4 more tornadoes per La Niña season) shifts northeast, centered in Indiana, Kentucky, and Tennessee.

MAM sees the area of increased tornado activity decline in the western areas, such as Louisiana, Arkansas and Illinois. The maximum centered along the Ohio River remains, while increase move southward into Florida. The region of maximum increase of tornadic activity shifts southward during AMJ, into eastern Tennessee. Georgia and the Carolinas see an increase in tornadic activity, upwards of 3 more per La Niña season.

Differences in Tornado days show the same pattern, but is more apparent in the early seasons. During JFM (Figure 9a), the southwest-northeast patter is discernable, but the increases in tornado days also spread along the Gulf of Mexico coast. The largest increases are also along the Gulf coast, with the largest change in Louisiana.

The increase of tornado days becomes more apparent during FMA, but begins to weaken during MAM and into AMJ (Figures 9b-d). FMA sees a large continuous area of increased tornado days from Louisiana north through Michigan. The largest change is in Tennessee, and coincides with the maxima of tornado event differences as seen in Figure 8b. Overall, most of a region from Louisiana to Indiana sees at least one more tornado day per La Niña year. The MAM season shows a reduction in increased tornado days in the southwest area of the region. However, the number of tornado days starts increasing in north Florida and Georgia during the same time. The maxima continues to occur in Tennessee. The increase tornado days continues to weaken in area and intensity into AMJ, with area of Ohio, Indiana, and Illinois returning to normal. The increases in the Deep South continue to hold on through this season.

The statistically significant changes in tornadic activity once again parallel the results of the previous two analyses. The JFM season (Figure 10a) shows more tornadoes at the 95% significance level over Louisiana and Arkansas, as well as Indiana and central Kentucky and Tennessee. A weaker band of 80% significance extends over the Gulf Coast. Regions of 95% confidence expands dramatically into FMA (10b), stretching from Arkansas to North Carolina, and extending northward into Michigan. The region shrinks slightly and moves eastward during MAM (10c), with areas of Georgia and the Carolinas now witnessing more tornadic activity at the 95% confidence level. Confidence levels west of the Mississippi River, however, begins to wane, and continues as we enter AMJ (10d). The southern and central regions, however, still maintain 95% confidence of reduced tornadic activity.

The histograms further show the increases of tornadic activity within the Ohio and Tennessee River valleys. Around Nashville, Tennessee (Figure 11a), the probability of 3 or more tornadoes during a neutral MAM season is 12.5%, but the probability increases to 37.5% for La Niña MAM, a three-fold increase. Towards the tail of the curve, the histogram shows that the probability of a neutral MAM season around Nashville producing nine or more tornadoes is 2%. However, the chance of a La Niña MAM producing 9 or more tornadoes around Nashville is 12%, a six-fold increase.

The changes around Indianapolis, Indiana (Figure 11b) are even more dramatic than those at Nashville. The probability of four or more tornadoes during neutral MAM in Indianapolis is 16%, but increases to 51% for La Niña MAM, over a three-fold increase. Five or more tornadoes during neutral MAM has a probability of 6%, but increases to 40% for La Niña MAM seasons, over a six-fold increase.

The largest differences in Indianapolis, though, are the chances for large outbreaks of tornadic activity during La Niña MAM compared to neutral MAM. The probability of six or more tornadoes in the Indianapolis area during neutral MAM is 3%. Meanwhile, the chance of six or more tornadoes during La Niña MAM around Indianapolis is 38%, an increase of over 1300%. For seven or more tornadoes, neutral MAM seasons are at 2%, while La Niña MAM seasons are at 30%, a 1500% increase.

Further, no recorded neutral MAM has produces more than 7 tornadoes in the Indianapolis area during MAM. However, the region still have a 25% chance of seeing 8 or more tornadoes during a La Niña MAM.

There are significant changes in tornadic activity associated with ENSO events in the eastern two-thirds of the United States. Most noticeable changes in tornadic activity take place during the spring, when tornadic activity is most frequent in the Untied States (JFM-AMJ). During this period, southern plains shows statistically significant decreases in activity during El Niño, and this area of decreased activity stretches as far as Louisiana, Arkansas, and Iowa. The Ohio River Valley and Deep South see a region of statistically significant increased tornadic activity during La Niña.

Please recall that the tornado events in this study are assumed to be independent. Tornadoes, however, can be related to each other in large outbreaks. Certain synoptic scale systems can produce families of tornadoes over the course of a day, and a supercell can spawn several tornadoes during its existence. Whether all these types of tornadic events are truly independent from one another can not be readily determined from the data available.

The results of this study support the findings of Knowles and Pielke (1993), who found that El Niño events tend to produce weaker tornadoes with shorter damage paths, and produce few major outbreaks of tornadoes. They further found that La Niñas are associated with stronger tornadoes that remain on the surface longer, and tend to create more families of 40 or more tornadoes due to one synoptic system.

The physical mechanisms and dynamics that may bring about these changes in tornadic activity have been identified in other works. A northward displacement of the subtropical jet stream during cold events brings stronger dynamical forcing to the Tennessee River valley (Ropelewski and Halpert 1989). Inversely, warm phase shifts the subtropical jet stream southward, removing its dynamical forcing from the United States. Also, the work of Smith et al. (1998) implies that directional shear is more pronounced between 850 and 500 hPa over the Deep South during the cold phase. Shear is one key ingredient for tornado development (Fawbush and Miller 1954). During warm phase, the 850 and 500 hPa winds fields are parallel to each other, which is not conducive to tornadic development.

Tornado development also requires certain climatological features. Tornadoes commonly develop in spring due to a large difference in the cold dry air masses pushing southward from Canada and the warm, moist air flowing north from the Gulf of Mexico. Ropelewski and Halpert (1986) note that the PNA and reverse PNA patterns associated with ENSO warm and cold events, respectively, cause changes in regional temperatures. Warm events tend to decrease the temperature gradient between the gulf coast and Great Plains, which is less conducive for tornadic activity. However, cold phase tends to increase the temperature gradient between these two areas, making an environment more conducive to tornadic development.

The predictability of tornadic activity with respect to ENSO events is of great importance to the scientific community. With this knowledge, scientist can better pinpoint where tornadic activity is more likely, dependent on the ENSO season, and improve the chances of observing and studying tornadoes as they occur, and cut down on storm chases that end in failure. This in turn will improve knowledge of this destructive cyclone.

Research in this area is also of importance to the public as well. Knowing that there is a greater chance of tornadic activity during some years than other, there is a chance for better prediction of these storms, and can possibly save lives and property damage. This information can further be used to aid insurance agencies and governmental offices like the Federal Emergency Management Agency (FEMA) in preparing financially for these events and to get response teams on site more quickly. This could save these companies millions of dollars as well.

Acknowledgements. COAPS receives its base funding from the Physical Oceanography Section of the Office of Naval research. Additional funding for this research was provided by the National Science Foundation. The author gratefully acknowledges Dr. James J. O’Brien and Dr. Peter S. Ray for proposing this research, Dr. Xufeng Niu for help with statistical analysis, and Mrs. Jiraporn Whalley for producing figures. Further thanks are extended to Mr. Shawn Smith and Mr. James Stricherz for technical assistance. The original form of this paper was the recipient of the 1998 AMS Father James B. Macelwane Award in meteorology.

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