Figure 1. The three regions of the U.S., and the four zones of the Pacific.
Caren Marzban
NSSL/CIMMS and OU Dept. of Physics
1. INTRODUCTION
Possible relationships between El Niño/La Niña and the occurrence of tornadoes in the contiguous United States have been the topic of several recent papers. The conclusions have been quite varied. Bove (1998), compared the annual number of reported tornadoes in 1.25o latitude/longitude squares across the eastern United States to the existence during the previous autumn of an El Niño/La Niña as determined by the JMA index. His analysis indicated that during the period February through July, El Niño years show a large decrease in the number of tornadoes in ``Tornado Alley ", Arkansas, Louisiana, and Iowa. However, the Ohio and Tennessee River Valleys experience a large increase during La Niña. The Florida peninsula shows that tornado activity is decreased during both El Niño and La Niña years. Similar findings for northwest Missouri were noted by Browning (1998) who counted the number of tornadoes, hail storms and wind storms each year in Northwest Missouri, and compared them to the list of El Niño/La Niña years kept by the CDC. He noted that Northwest Missouri typically had more tornadoes in La Niña years than in El Niño years. In contrast, he found that hail storms, and wind storms are more prevalent in El Niño than La Niña.
Somewhat different results were found by Agee and Zurn-Birkhimer (1998). They examined the ratio of the number of tornadoes in strong El Niño years to the number of tornadoes in La Niña years on a state-by-state basis. Their analysis indicated that Texas, Oklahoma, Missouri, Colorado, and New Mexico receive more tornadoes during strong El Niño years. However, as in the first study noted above, they found that the area from Iowa through the Carolinas, and Tennessee through Ohio has the most tornadoes during La Niña years. A study of Florida tornadoes indicated that strong El Niño's of the magnitude of 1983 and 1998 increase the chance of strong and violent weather in Florida (Hagemeyer, 1998).
Schaefer and Tatom (1998) looked at the mean Sea Surface Temperature (SST) in the strip 5o N to 5o S and 180o W to 150o W. A Kruskal-Wallis H test was then used to see if any difference in different tornado measures exists between El Niño, La Niña and neutral years. Also the entire contiguous U. S., and three sub-areas were considered. All six of these combinations failed to have significance at the 99% level. One could not state with confidence that El Niño/La Niña had any effect on tornado or strong tornado activity.
2. METHODOLOGY
These differing results reflect the imprecise definition of the terms El Niño and La Niña. There are ambiguities due to 1) different behavior of the sea surface temperature in different regions of the Pacific Ocean, 2) different methods of assessing and identifying an unusually warm or cold season, and 3) the possibility that the duration of a cold or warm phase does not coincide with the length of a year.
To attend to the first ambiguity, the mean monthly SST over four different zones in the Pacific is considered. The zones (Figure 1) are:
Figure 1. The three regions of the U.S., and the four zones of the Pacific.
The second ambiguity simply cannot be eliminated. To examine “unusually” warm or cold events requires one to define “usual. " This is unknown and can only be inferred from a statistical model. Different models of the “usual " lead to different notions of the anomalous. Any conclusions based on SST anomalies are contingent on the underlying assumptions. In this paper, it is assumed that the “usual " component of the SSTs (and the tornadic activity) is one that can be filtered out by “Seasonal Differencing” (see Section 3). Therefore, the anomalies examined in this paper are specific to this filter (or model).
Finally, to attend to the third ambiguity, the time unit of analysis is the calendar month. The data spans the 588 months from January, 1950, to December, 1998. Two metrics of tornadic activity are employed - the number of tornadoes per month, and the number of tornado days per month.
Given the effect of El Niño and La Niña on the position of the jet stream (Hoerling et al., 1997), it is conceivable that SST can have a different effect on tornadic activity in different geographic regions. Consequently, in addition to examining the correlation between SST and the nationwide tornadic activity, that of three distinct regions of the U.S. are also considered (Figure 1):
Region 1 corresponds to classic “tornado alley.” Region 2 runs from Kentucky and Virginia northward and includes the Ohio Valley (i.e., Northeast). Region 3 is the Southeast, running from Tennessee and North Carolina southward. These regions are large enough so that monthly tornado counts are typically non-zero, but small enough to show the sub-regional variability.
Because of the SST-jet stream relationship one can envision how the correlation between SST and tornadic activity could be a function of tornado strength. By helping position the jet stream, SST's could contribute to producing conditions favorable for the development of strong and violent tornadoes. Thus, in addition to tornadoes of all strengths, the correlation between SST and F2 or greater tornadoes (strong and violent tornadoes) is analyzed.
The analysis is in the context of statistical hypothesis testing. Every correlation between SST and tornadic activity is subjected to the test that it is in fact zero (the null hypothesis). To do this, a statistical test is performed to assess the confidence in any evidence to the contrary. A nonparametric measure, Kendall's tau, is used (Press et al. 1986). Kendall's tau is a measure of the monotonic relation between a pair of variables. It is based on the notion of concordant and discordant pairs. Concordant (discordant) pairs of data (x,y) are those for which a larger x is associated with a larger (smaller) y. Kendall's tau is the difference between the proportion of pairs that are concordant and the number of pairs that are discordant. With n being the sample size, the total number of pairs is n(n-1)/2 and Kendall's tau is
The value of tau ranges between plus and minus 1, with tau = 0 denoting no correlation at all. The percent of concordant pairs (%con) can be approximated by
Thus tau = 0.1 means that only 55% of the pairs are concordant and 45% are discordant.
For any quantity computed from a sample, it is important to compute a statistic that gauges whether the computed value can be generalized to the population, and with what level of confidence. Here, the null hypothesis is tau = 0, and the appropriate statistic for the test is
where 
The statistic z follows the standard normal distribution.
If |z| > z 1- "/2 one can reject the null hypothesis; otherwise the data provides insufficient evidence for rejecting the possibility that tau is nonzero at the alpha= 0.01 level. It means that only 1% of the time the null hypothesis will be incorrectly rejected (Type I error). A few other conventional probabilities are the 95% probability, corresponding to a z-value of 1.960 ( alpha = 0.05), and 90% probability corresponding to z = 1.645 ( alpha = 0.1). Usually any value of |z| less than 1.645 (i.e., less than 90% confidence) is considered insufficient for rejecting the null hypothesis.
3. PRE-PROCESSING
Testing the correlation between two variables that have a non-trivial dependence on time, requires preprocessing the data. Otherwise, trends can dominate the time series and obfuscate any underlying function of interest. Periodicity often causes large correlations between two variables that are simply a consequence of the periodic nature of the variables rather than of a true correlation.
An appropriate method for filtering time series data is seasonal differencing (Masters 1995, p. 261). The method is straight forward; one simply subtracts from each observation the value exactly one cycle earlier. For instance, the number of tornadoes in January, 1950 is subtracted from the number of tornadoes in January, 1951, and the number of tornadoes in February, 1950 is subtracted from that of February, 1951, etc. This technique eliminates the fundamental, all harmonics, and any linear trend.
To illustrate how using data containing a seasonal dependence can be misleading, Table 1 shows the values of Kendall's tau and the corresponding z statistic for the correlation between the number of strong and violent tornadoes with the SSTs. According to the z-values, almost all the results are highly statistically significant - recall that a |z|>2.575 is statistically significant at the 99% level ( alpha=0.01). The extreme values (tau, Z) = (0.21,7.69) and (tau, Z) = (-0.07,-2.39) correspond to the most significant positive and negative correlations, respectively. This suggests that the correlation between the number of strong and violent tornadoes in Region 3 (the Southeast) and SST1 is positive, relatively strong, and significant, while its correlation with SST3 is negative and significant, but weak. This implies an El Niño and La Niña effect, respectively. However, the periodic nature of the two variables being correlated makes these results unreliable at best.
It is enlightening to examine the pre-processing steps. Figure 2a illustrates the periodic nature of SST1 (top) and how the application of seasonal differencing removes it (bottom). Although it is not immediately obvious from the graph, the trend too has been removed. Figures 2b and 2c show the number and seasonally differenced values of strong and violent tornadoes, respectively.
Figure 2. a) SST1 (top) and the seasonally differenced values thereof (bottom), and b) the number of strong and violent tornadoes, and c) the seasonally differenced number of strong and violent tornadoes.
4. RESULTS AND DISCUSSION
The calculation of (tau, Z) - pairs and their interpretation for the other correlations follows the example in Section 3. Table 2a shows the (tau, Z) - pairs for the correlation between filtered SST and the number of all tornadoes, and Table 2b shows the correlation between SST and the number of tornado days. Table 3a and 3b are similar, but for strong and violent tornadoes. The values in Tables 2 and 3 suggest a rich and complex interaction between the four zones in the Pacific and the various regions in the U.S. Comparison to the values in Table 1 (i.e., before filtering), shows that the z-values have dropped dramatically. No longer are “large " correlations (|tau|) up to 0.21) with high significance (|z| up to 7.69) present. We concentrate on z-values ( significance), because they indicate the confidence in the tau -values (correlation). A tau , no matter how large, accompanied by a |z| of say 0.001, is dubious.
In Tables 2 and 3 the correlations are generally too weak to have any forecast value. Since every |tau| #0.08, there is nearly an even split in concordant/ discordant pairs (about 54 to 46).
For tornadoes of any strength, when the measure of activity is the number of tornadoes (Table 2a), the most significant (confident) of the correlations has a |z|=2.10, insufficiently large to be considered significant at the 99% ( alpha = 0.01) level, but sufficiently large to be statistically significant at the 96%. When the measure of activity is tornado days (Table 2b), the most confident correlation (|z|=2.91) is significant at the 99% level.
For strong and violent tornadoes (Table 3), and with the number of tornadoes as the measure of activity, the most significant result has |z|=2.56, almost large enough to be significant at the 99% level. When the measure of activity is tornadic days, the most significant correlation has a |z| of 2.68, which is significant at the 99% level.
Each of these z-values is accompanied by the largest tau - values in their respective tables. Thus, Region 2 (the Northeast) has the largest and most significant correlation. However for tornadoes of all strengths, the best correlation is with SST2 (the Eastern Equatorial Pacific). While for strong and violent tornadoes it is with SST3 (the East-central Equatorial Pacific).
In general, Table 2 suggests that correlations between the SST’s and U.S. tornadic activity are mostly not significant. As such, the corresponding tau - values are statistically indistinguishable from zero. Region 2 (the Northeast) generally has the most significant correlations with any of the SST areas, while Regions 1 and 3 are generally uncorrelated with any of the SSTs.
None of the four sea surface temperature areas in the Pacific consistently have the most significant correlations with general tornado activity. For instance, SST3 is the ocean area with the most significance when correlated with all tornadoes in Region 3 and tornado days in Regions 1 and 3. But it also has the least significance when correlated with the tornado count in Regions 1 and 2, and tornado days in Region 2.
A general pattern that emerges for strong and violent tornadoes (Table 3) is higher significance levels are found when activity is gauged in terms of their number (this is in contrast to the results for tornadoes of any strength). Another pattern is that these storms in Region 3 (the Southeast) are generally uncorrelated with any of the SSTs. Region 1 shows some correlation with SST1 and SST2 when activity is measured with the number of tornadoes, but no correlation when activity is gauged with the number of tornado days. However, tornado days in this Region are somewhat correlated with SST3. The ocean area that typically has the most significant correlations when either strong and violent tornadoes or strong and violent tornado days are considered is SST3.
With few exceptions, tau - values are negative. A positive tau would suggest a positive correlation with El Niño (or a negative correlation with La Niña), while a negative value would suggest a negative correlation with El Niño (or a positive correlation with La Niña). Exceptions have z-values too small for statistical significance. Thus, according to the data, El Niño seems to have no positive correlation with the tornadic activity occurring anywhere in the U.S. (except possibly for very small regions). Even the strongest of the correlations are so weak that they have little prognostic value. For instance, while over the long term more strong and violent tornadoes will occur in the Northeast U.S. during La Niña months than during El Niño months, for a specific month there is less than a 53% chance that this will occur.
5. REFERENCES
Agee, E., and S. Zurn-Birkhimer, 1998: Variations in USA tornado occurrences during El Nino and La Nina. Preprints, 19th Conference on Severe Local Storms, Minneapolis, MN., Amer. Meteor. Soc., 287-290.
Bove, M.C., 1998: Impacts of ENSO on United States tornado activity. Preprints, 9th Symposium on Global Change Studies, Phoenix, AZ. Amer. Meteor. Soc., 199-202.
Browning, P., 1998: ENSO related severe thunderstorm climatology of Northwest Missouri. Preprints, 19th Conference on Severe Local Storms, Minneapolis, MN., Amer. Meteor. Soc., 291-292.
Hagemeyer, B.C., 1998: Significant extratropical tornado occurrences in florida during strong El Nino and strong La Nina events. Preprints, 19th Conference on Severe Local Storms, Minneapolis, MN., Amer. Meteor. Soc., 412-415.
Masters, T., 1995: Neural, Novel & Hybrid Algorithms for Time Series Prediction. John Wiley & Sons, Inc., 514 pp.
Press, W. H., B. P. Flannery, S. A., Teukolsky, and W. T. Vetterling, 1986: Numerical Recipes; The Art of Scientific Computing, Cambridge University Press, New York, 818 pp.
Schaefer, J.T., and F.B. Tatom, 1998: The relationship between El Nino, La Nina, and United States tornadoes. Preprints, 19th Conference on Severe Local Storms, Minneapolis, MN., Amer. Meteor. Soc., 416-419.