Fujita and Pearson , Tecson et al. McCarthy recently updated that work and showed that the width of tornado paths tends to increase with the intensity, but there is considerable overlap between classes. If the distributions of width and length can be modeled with simple theoretical probability distributions, then the information associated with the thousands of observed tornado path lengths and widths could be summarized in two or three numbers.
This offers obvious computational ease in comparison to tables based on empirical distributions, such as would produce histograms, as well as produces continuous functions, which seem physically more plausible. Development of statistically based hazard models for tornadoes could then use the parameters of the distributions as input. Changes in the parameterized distributions with time or space and differences between different classifications could also be investigated.
Herein I will describe an attempt to model the distribution of path lengths and widths using Weibull distributions. The relationship of path length and width to damage classification will be investigated, and an estimate of the probability of a particular F scale, given the length or width of a tornado, will be developed.
Finally, the temporal robustness of the estimates and implications for interpretation of the data will be discussed. Schaefer and Edwards and McCarthy described the database and the changes that have occurred over the years, including the effects of increasing verification efforts and public awareness. Path lengths are reported in miles, widths in yards, 1 and the maximum damage as rated by the F scale. Doswell and Burgess have discussed problems with assigning F-scale ratings, but it is hoped that the relatively large sample size here will overcome random errors in assignments.
If systematic biases exist, they are extremely difficult to detect and there is nothing that can be done about them. Only those events with a reported length or width are included in the analysis. The distributions have been fit over a variety of time intervals. Sample-size limitations make interpretation of some of those time intervals for the highest values of the F scale difficult.
For example, there are only 51 F5 3 tornadoes in the record, so that interpretation of the distributions on anything less than the complete record for F5 tornadoes is questionable. On the other hand, there are approximately F2 tornadoes with path length and width information, so that short time ranges provide an adequate sample size.
Quantile—quantile q — q plots are a useful tool to assess the goodness of fit of the models qualitatively Wilks Quantile—quantile plots compare the values associated with the same quantile of an empirical observed and modeled probability distribution function.
For example, a plot of the 10th, 20th, 30th, etc. In this case, the quantiles are plotted for all values at which the empirical quantiles exist. The gaps in the plots are a result of gaps in the observational record. The fits to the length data improve with increasing F scale. The fits are not especially good at F0 or, to a lesser extent, F1, although they are better than fits assuming a normal distribution for all values.
In general, all of the modeled distributions overestimate the empirical distribution for short lengths, as indicated by the points being below the diagonal, perfect-fit line Fig.
The problems at short lengths are a result of the quantization of the observations. The F0 tornado fit departs from the observations at about 4 km, underestimating the distribution for long lengths Fig.
The underestimation of density at long path lengths decreases for F1 and F2 tornadoes and is very small by F3 tornadoes. The picture is very similar for the widths Fig. Fits improve with increasing width, and the statistical distribution tends to overestimate the density at low widths. The calculated mean path length for tornadoes increases from a little over 1 km for F0 tornadoes to over 50 km for F5 tornadoes Table 1.
The mean length roughly doubles with each value of the F scale from F1 to F4. The change from F0 to F1 is somewhat larger, and there is less change from F4 to F5. This implies that the maximum probability moves away from zero length for the high F values.
The distributions for the different F-scale values are well separated except for perhaps between F4 and F5, as illustrated by the cumulative distribution functions for the various values of F Fig. The mean width also increases with F scale Table 2 , from less than 30 m for F0 to more than m for F5.
The distributions are less distinct for the high F values, particularly at wide widths Fig. The distributions represent the probability of a path length width given that a tornado of a particular intensity occurs. It is easy to invert the problem to calculate the probability of a particular intensity given that a path length width is observed.
To do so, all that must be done is to weight the distributions given by 1 by the number of tornadoes at each F scale and then divide the result for each F scale by the sum of the weighted distributions at any given length width.
The results illustrate the potential utility and pitfalls of estimating a damage rating simply from the length or width data associated with a tornado. Length information appears to be potentially of some limited utility for setting lower bounds on the likely intensity of tornadoes.
Given the rarity of tornadoes of that length the most recent one in the record was in , this is not a strong result in a practical sense. It is also of interest to note that, because of the rarity of F5 tornadoes, they are never the most likely event at any length.
Width information potentially has more value in putting limits on the likely intensity rating Fig. Thus, one can have some confidence that a wide tornado is probably at least F2. Finer distinctions based on width are difficult to justify.
Again, because of the rarity of F5 tornadoes, they are never the most likely event at any width. Consideration of shorter time periods in the record allows for the opportunity to look at the stability of the estimates of the parameters in time and to put confidence limits on the long-term values.
The typical number of reports per year varies dramatically through time, as illustrated by the number of reports in overlapping 4- yr periods Fig. The number of weak tornadoes F0 and F1 has increased dramatically in the dataset, with the F0 increasing particularly when data from the year are first included. Part of this increase for F0 tornadoes is a result of a policy change in to assign F0 to all tornadoes that did not have rated damage D.
McCarthy, personal communication. An additional component of the increase is likely due to increasing population in the western United States and better public awareness.
The numbers of F2 and stronger tornadoes show a slightly downward trend, with an apparent step function decrease in the mids. The step function may be a result of the beginning of real-time damage surveys when the Fujita scale was adopted by the NWS.
Almost all 4-yr periods have at least F3 tornadoes and 20 F4 tornadoes in them. Thus, the sample size allows some hope of estimating the parameters of the distribution from a 4-yr period. In order to get a handle on variability, I have randomly selected 4 yr out of the record, calculated the parameters from those years, and then repeated that process times to compute distributions of the parameters. Box and whisker plots illustrate the variability of the mean values Figs. Random collections of years clearly show a distinction between the different F values, with more damaging tornadoes being longer and wider.
The estimates are not consistently robust in time, however. Most, such as the mean length of F3 tornadoes, are quite consistent in time Fig. Others, particularly associated with the weaker tornadoes, show a decrease in the early periods, as illustrated by the mean width of F0 tornadoes Fig. This could be explained by the greater ease of detecting the effects of only the largest of all weak tornadoes.
The shape of the intensity distribution becomes broader as tornado path width and length increase. Given an EF rating along with path length, path width, and whether or not there was a fatality, the model generates samples of predictive intensity Fig. The plot shows histograms based on samples from 36 tornadoes since The histograms are bounded by the wind speeds assigned to the EF category.
In some cases the histogram is flat indicating that the length and width do not provide information on tornado intensity beyond the EF rating. However there are exceptions especially for tornadoes with ratings between EF1 and EF3. Here we see cases where the distribution is positively skewed indicating that length and width suggest a lower-end intensity for the given rating. Six randomly chosen from each of six EF ratings top row lowest to highest.
The collective predictive distribution and model residuals are used to check against model adequacy Fig. The shape of the predictive distribution appears reasonable for intensity with a positive skew and a long right tail.
There is a small notch in the distribution around the cutoff between EF1 and EF2 tornadoes. This is explained by relatively few high-end EF1s and relatively many low-end EF2s predicted based on path dimensions. The model residuals are approximately normally distributed with the exception being a long right tail indicating a few unusually short-lived and narrow tornadoes relative to their high assessed EF rating.
Individual predictive distributions provide a check on model validity. The vast majority of tornadoes do not have an estimated wind speed. However, in some cases it is possible to obtain a wind speed estimate from a nearby Weather Service RadarD measurements or from a mobile radar Doppler on Wheels.
We obtain estimates from the SPC's Storm Reports for nine tornadoes during the season and compare them to samples from our intensity model Fig.
The predictive distributions are shown as histograms. In cases where the histograms are skewed, the estimated wind speed tends to be on the corresponding side of the EF range.
The exception is the Sedgwick, KS May 19th tornado. The correlation between the estimated wind speeds and the average over all predictive samples is. The location of the estimated wind speed is shown as a dot and the range of wind speeds defined by the corresponding EF category is shown as a gray horizontal bar. Model skill is estimated relative to a null model of choosing a random intensity within the wind speed ranges. Skill is assessed as the percentage increase in the coefficient of variation between path dimension and predicted intensities.
The correlation between path length and EF rating is. The correlation between length and tornado intensity using our intensity model is. The correlation between length and tornado intensity from the null model is.
Similar skill metrics are noted using path width. We perform an out-of-sample test by correlating the modeled intensities from twelve tornadoes that have corresponding wind speeds estimated from radar measurements that are independent of the damage assessment. The derived radar wind speeds result from a calibration of mobile radar Doppler on Wheels with nearby Weather Service RadarD measurements. The data and method used to obtain the radar wind speeds are described in [16].
The modeled intensities correlate with the radar wind speeds at. Finally a single predictive sample for each tornado is plotted by year as a box plot Fig. While the number of years is too few to ascertain a significant trend, there is an apparent increase in the upper quantiles of the annual intensity distributions resulting from the noted increases in damage path dimensions. Tornado intensity depends on updraft speeds within the parent thunderstorm and on increasing winds with height shear in the environment surrounding the thunderstorm [17].
Updraft speed is directly related to the available potential energy in the environment, which increases with greater low altitude heat and moisture. Upward trends in surface dew point temperature and specific humidity across the United States are coincident with upward trends in temperature especially over the tornado-prone Midwest [18]. With all else equal greater surface humidity implies greater available potential energy.
Local shear can be large, even if it decreases in the mean, when waves in the upper-level flow amplify as occurs more often when warming in the Arctic outpaces warming elsewhere [19]. Tornadoes are capable of catastrophic damage. Direct measurements of tornado intensity are difficult and dangerous to get. Surveys rate the tornado damage on the EF scale and wind speed bounds are attached to the scale. Unfortunately the categorical scale is not adequate for analyzing tornado intensity separate from tornado frequency.
Moreover, the historical database cannot directly benefit from improved surveillance technology. Here we use path length and width which are measured on a continuous scale and which are strongly correlated to the EF category to estimate tornado intensity on a continuum.
Diagnostic plots of the predictive density and residuals reveal no significant concern about model adequacy. The modeled intensity allows analyses to be done on the tornado database not possible with the categorical scale. The predicted probabilities by EF category can be calibrated to the area affected by this level of damage and an index of tornado destructiveness would then follow naturally. The modeled intensities can be used in climatology and in environmental and engineering applications but more work needs to be done to understand the reason behind the increase in path length and width.
We thank Parks Camp from the U. National Weather Service Forecast Office in Tallahassee, Florida for helping us understand the protocol associated with surveys of tornado events. The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. National Center for Biotechnology Information , U.
PLoS One. Published online Sep James B. Jagger , 1 and Ian J. Elsner 2. Thomas H. Ian J. Duccio Rocchini, Editor. Author information Article notes Copyright and License information Disclaimer. What is the smallest, largest, and average size?
Tornadoes can vary significantly in size and intensity. Thus, the easiest way to answer this question is to assess the size of the damage path. However, the term "average" can be misleading, since the majority of tornadoes are small compared to the infrequent large events.
With this said, the typical tornado damage path is about one or two miles, with a width of around 50 yards. The largest tornado path widths can exceed one mile, while the smallest widths can be less than 10 yards. Widths can even vary considerably during a single tornado, since its size can change during its lifetime. Path lengths can range from a few yards to more than miles. A key point to remember is that the size of a tornado is not necessarily an indication of its intensity. Large tornadoes can be relatively weak, while small tornadoes occasionally can be violent.
How long and fast is a tornado on the ground? Detailed statistics are not available to answer this question. Nevertheless, ground time can range from an instant to several hours, although the typical time is around 5 to perhaps 10 minutes. Supercell tornadoes tend to be longer-lived, while those pawned by squall lines and bow echoes may only last for a few minutes. Tornado movement can range from virtually stationary to more than 60 miles per hour.
A multiple-vortex tornado contains two or more small, intense sub-vortices rotating around the center of the larger tornadic circulation. Occasionally visible, these vortices may form and die within a few seconds, and can occur in all tornado sizes, from huge "wedge" tornadoes to narrow "rope" tornadoes. Sub-vortices can cause narrow, short, extreme swaths of damage that sometimes arc through tornado tracks.
More information about tornadoes can be found on-line at www. Please Contact Us. Please try another search. Multiple locations were found. Please select one of the following:.
Location Help.
0コメント