National Weather Service Office
In a recent study, DiPlacito and Kwiatkowski (1994) observed more significant (F2-F5) tornadoes had been reported in the Goodland Weather Service Office (WSO) County Warning Area (CWA) in August than in July. These authors stated that such a result was contrary to the conventional wisdom that tornado frequency decreases after a maximum in the late spring or early summer. Further, they were not certain if their observation might be explained by normal random variation of tornado frequency, or genuinely manifested an underlying phenomena. They suggested the question be put to further study. This paper describes work that indicates the reported secondary tornado maximum may in fact be more than statistical noise, and advances a physical explanation of why a secondary maximum might occur in late summer.
STATISTICAL TESTING OF THE REPORTED SECONDARY MAXIMUM
IN SIGNIFICANT TORNADO FREQUENCY
Figure 1 shows the Goodland WSO CWA. Frequency distribution by month of F2-F5 tornadoes from DiPlacito and Kwiatkowski, developed from a data base stemming from work done by Grazulis (1991), and clearly displays the "August secondary tornado maximum" in question. There were nine days in August with significant tornadoes over the 1880-1989 period of record, but only four days in July.
Figure 1. Goodland WSO County Warning Area.
To quantitatively attack the question of whether the August tornado peak could be due to chance, the question that needs to be asked is: given the size of our sample, what are the odds that an infinitely large sample would produce a similar August maximum? This question can be answered using the "Student t" test as outlined in Panofsky and Brier (1965).
The equation for the Student t is where X is the mean of a number of samples, µ is the mean from an infinitely large sample (i.e., a population mean), N is the number of samples, and s is the standard deviation determined from those samples. Here the value of t can be related to the probability that X; was determined from the same population represented by µ.
To relate this equation to the problem here, let X be the DIFFERENCE in number of significant tornadoes between July and August per decade. Table 1 gives a tabular listing of X over the period we are studying. Now take µ to be the average difference in significant tornado number between August and July per decade over an infinite number of years. If there are actually more tornadoes on average in July than August, µ will be negative. If both months have the same number of tornadoes, it will be zero. The question now becomes, given X determined from Table 1, what are the odds µ could really be zero (or greater) based on the sample of significant tornadoes gathered? To check for this, µ was assigned a value of zero when we computed our t value.
Note here that there is nothing magical about using significant tornadoes per decade as the test variable. For instance, significant tornadoes per year could also be used, but would result in counterintuitive small fractions of tornadoes. On the other hand, over-consolidating the data would reduce the value of N in the Student t equation and ultimately make statistical inferences worthless. (Taking things to extremes, it would be useless to try to do significance testing with a "significant tornadoes per century" statistic with only one century worth of data.)
The value of t obtained using the data from Table 1 was 1.34. Referring to Panofsky and Brier (1965), this value is too small to confidently state that µ as developed above is greater than or equal to zero. To reduce the chance of being wrong in making such a statement to 1 in 10 or less, µ would have to be AT LEAST 1.812. Putting it another way, from what has been observed up to this point, statistical analysis indicated it is quite possible the number of significant tornadoes in July is greater than or equal to that in August over the long term.
|Frequency distribution by decade of July and August significant tornadoes
|July||August||August - July
However, the last sentence contains a clue how to further refine the testing. Suppose one is willing to concede that July and August may indeed have the same number of significant tornadoes on average. The t test can still be used to analyze the chance that July has MORE significant tornadoes than the following month, and thus study whether the significant tornado season decreases or continues without letup into August. This is called a "one-tailed test" and is discussed in many introductory statistical textbooks, including Walpole and Meyers (1972).
For the one-tailed test, significant values of t are substantially lower than those described previously. If t is just 1.38, there is a 10 percent chance of being wrong if the number of August tornadoes is assumed to be at least equal to that of July, while the corresponding value for 15 percent is 1.10 (Neter and Wasserman 1974). Referring to the computed t statistic of 1.34, by interpolation the chance that over an infinite number of years July has MORE significant tornadoes than August is just over 10 percent. Conversely this could be stated that the probability that August averages at least as many significant tornadoes as July is nearly 90 percent.
Thus it is probable that on average August genuinely has at least as many significant tornadoes as July. It could have more--nothing we have with the one-tailed test denies this possibility--but there is not sufficient data to answer the question authoritatively. However, while it may seem impressive by the standards of the meteorological community, statisticians do not regard a 90 percent degree of confidence as particularly high. For instance, Panofsky and Brier (1965), Neter and Wasserman (1974), or Walpole and Meyers (1972). Confidence in the statistical analysis of the July vs. August tornado distribution would be increased if a physical mechanism that might explain that distribution could be found. This problem will be addressed in the next section.
PHYSICAL REASONS FOR THE FREQUENCY OF SIGNIFICANT TORNADOES IN JULY AND AUGUST
Tornadogenesis phenomena are complicated and involve many atmospheric processes (for example, Rotunno 1993 and Walko 1993). Anything approaching a complete discussion of elements that play a role in tornado formation is far beyond the scope of this work. However, relatively simple meteorological parameters can be related to assess the dynamics and provide some insight into the tornado climatology of an area tornadogensis.
As observed by Sanders and Doswell (1995), fronts have traditionally presumed to be areas where low-level temperature discontinuities are associated with middle and upper tropospheric baroclinic disturbances. In the same paper Sanders and Doswell go on to discuss the limitations of this tradition; however, it is still reasonable to assume many fronts meet the classical definition. This would make them preferred regions for tornadogenesis (Johns and Doswell 1992), and this is what is commonly observed. It stands to reason therefore, that an index of the frequency of frontal passages in a given area would give insight to tornado frequency there, all other things being equal (this "all other things being equal" is an important caveat that we shall return to later).
Such an index was developed from Table 2, which shows a distribution of day-to-day 10°F (Fahrenheit) maximum temperature drops at the Goodland (GLD) Weather Service Office (WSO) by decade for the months of July and August. Such a drop is a fairly significant event in that a 10°F temperature is about twice what a normal person can detect simply from skin sensation (Anthes et al. 1975). For the purposes of developing Table 2, a 10°F drop between June 30 and July 1 was not tabulated, a 10°F drop between July 31 and August 1 was counted in July, and a 10°F drop from August 31 to September 1 was credited to August.
While many things, such as cloud cover, could cause such a significant day-to-day drop, the passage of moderate or stronger cold fronts would certainly be one of them. Data from Table 2 can be used to gauge the RELATIVE frequency of cold front passages in the Goodland vicinity in July and August. For simplicity in wording, for the remainder of this paper the data displayed in Table 2 shall be assumed to represent cold frontal passage numbers. The reader should bear in mind the numbers actually represent temperature drops from whatever cause.
Note that situations where temperatures increase sharply from one day to the next are deliberately being ignored here. This is because, as discussed in Johns and Doswell (1992) cold fronts are more commonly associated with tornado production than warm fronts.
A visual inspection of Table 2 demonstrates that more frontal passages (according to this study's definition) occurred at Goodland in August than July over the period of record. Given the frequency of July and August frontal passages by decade at Goodland as presented in the table, the Student t equation can again be used to test for statistical significance. In this case, X would be the mean of the difference in August and July frontal passages per decade over the period of record. Again, µ would be zero, which corresponds to assuming that over a sufficiently long period there is no difference in the number of frontal passages between July and August. Given these parameters, the t test is used to examine the likelihood July and August actually have the same number of frontal passages given what has been observed during record.
Using the above definitions and the values from Table 2, yields a t statistic of 2.25. Referring to Panofsky and Brier (1965), for a sample size of 8, a t value of 1.86 indicates there is a 10 percent chance of there really being no difference in number of July and August frontal passages. A value of 2.31 would be sufficient for a 5 percent chance, so although not quite there, the computed t is considerably closer to that than the 10 percent level. Note that here the relatively strict "two-tailed" test is being used as opposed to the one-tailed test discussed earlier in this paper. The two-tailed test allows an attack on the issue of whether a sample mean and a proposed population mean are equal. The conclusion is the statement: "the number of frontal passages is greater (NOT just "greater than or equal to") in August than July" has a greater than 90 percent but not quite 95 percent chance of being right.
|Frequency distribution by decade of July and August day-to-day maximum temperature drops of 10°F or more.
|July||August||August - July
Given the above analysis, we have established the likelihood that August actually does have more day-to-day 10°F maximum temperature drops than July. This does not prove the contention frontal activity is greater in August than July, but it does support it. There is a plausible mechanism for August to have just as many, if not more, significant tornadoes than July. The cause of this mechanism will not be examined in detail, but might be from the beginnings of the southerly descent of the westerlies as summer ends.
SOME POSSIBLE OBJECTIONS
At this point, it is necessary to return to a statement earlier in the paper, namely that extra frontal passages in August would explain an extended or secondary tornado season in that month "all other things being equal". One might argue that it is unlikely all other things would be equal. In particular, it is well known that the average atmospheric lapse rate is lower in late than mid summer as solar insolation declines while the upper atmosphere has been warmed by a season of convective overturning (Anthes et al. 1975). At Goodland one of the results of this effect is that monthly average precipitation declines from 2.87 inches in July to 1.80 inches in August as moist convection becomes less frequent. This drying trend does tend to support the contention that strong day-to-day temperature changes in August are often cold front induced. As the "weather dries", the chance for temperature variation due to precipitation or differing soil moisture decreases.
However, changes in the amount of solar energy available to be converted into thermal energy and thus instabilities are more modest between July and August than later in the year. According to the Smithsonian Meteorological Tables (1971) radiation arriving at the top of the atmosphere over Goodland (approximately 39°N latitude) decreases by 11 percent from mid-July to mid-August. From mid-August to mid-September, the corresponding decrease is 17 percent, so that as the autumn equinox approaches radiation at the top of the atmosphere is less than 75 percent of that in July. Of course the energy that arrives above the atmosphere will not equal the amount received at the Earth's surface, but these figures do give an indication of the relative effects of decreasing sun angle as summer wanes. This analysis suggests that while changing amounts of solar energy, and corresponding changes in atmospheric lapse rates would certainly have an effect on the potential for tornadogenesis in July compared to August, these effects are likely to be smaller than what occurs as fall really gets underway.
Another important factor to consider is that, at least for the F2 and stronger tornadoes we have been considering, the wind shear associated with a baroclinic environment is normally required (Rotunno 1993, Johns and Doswell 1972, or Brooks et al. 1993). This gets back to the relatively high number of fronts suspected in the Goodland vicinity in August, with its further implication of a relatively high number of significantly baroclinic environments. It seems logical that any disadvantage for significant tornadoes caused by decreasing insolation from August to July is offset by the increased availability of baroclinic systems.
SUMMARY AND CONCLUSIONS
It has been said, "nothing is certain in life except death and taxes". An August secondary significant tornado season in the area served by WSO GLD is no exception to this rule. However, the preponderance of evidence indicates that either such a secondary season does in fact exist, or that August is at least as likely to see significant tornadoes as July.
Statistical analysis of July and August significant tornado frequency by decade over 100 years indicates there is nearly a 90 percent chance that August has just as many, or more, such tornadoes than July. A search for a mechanism why this should be demonstrates beyond much doubt that August sees more sharp downward day-to-day temperature changes than July. It is likely this represents a relatively high number of frontal passages through the Goodland area, which in turn would provide a basis for most significant tornadoes.
Thus, physical and statistical arguments work together to support the probability of an extended or secondary late summer significant tornado season in the central High Plains. This season is not an extremely prominent feature of the region's weather--a century's worth of data was needed to detect its signature. Even with that, the proof for its existence is not ironclad. However, the best bet is that it is there. The fact that we are dealing with strong or violent tornadoes are enough to make it potentially significant. The forecaster unaware of it might never know the difference--or could get that "once in a career shift" a lot later in the year than he or she may have thought possible.
This study also raises some issues for further research. For example, a more detailed look at seasonal factors playing a role in strong tornadogenesis would have been fascinating, as would have been an examination of the relative frequency of smaller tornadoes. Unfortunately, such studies were beyond the resources available at the time research was being done for this work. Hopefully they will be pursued later.
The author would like to thank Lynn DiPlacito, Administrative Assistant for her extensive work in gathering data. Also, both Ms. DiPlacito and Scott Mentzer, MIC NWSO Goodland, Kansas, provided their constructive review of this manuscript. Finally, thanks are given to the entire Goodland staff for providing inspiration and encouragement by their continued professionalism.
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