Tornado Risk Analysis Is Dixie Alley an Extension of Tornado Alley?

Transcription

1 Tornado Risk Analysis Is Dixie Alley an Extension of Tornado Alley? by P. Grady Dixon, Andrew E. Mercer, Jinmu Choi, and Jared S. Allen Spatial analysis of tornado paths shows no areas of elevated tornado risk statistically separate from Tornado Alley, but some parts of the Southeast are identified as the most tornado prone in the nation. T he term Tornado Alley is understood by most scientists and weather hobbyists to be a gross approximation of the most tornado-prone region in the United States. Depending on the exact variables and calculation methods, Tornado Alley can shift dramatically across the space between the Rocky and Appalachian Mountains. There is some evidence that multiple alleys of peak tornado activity exist across the country (Broyles and Crosbie 2004; Passe-Smith 2006), and at least one of these proposed areas, known as Dixie Alley, has become somewhat widely known despite very little formal research on the subject. Therefore, the purpose of this study is to assess the spatial tornado risk of the entire country and use the results to determine whether there is a significant region of elevated tornado risk in the southeastern United States, or any other area, that is distinctly separate from the traditional Tornado Alley of the Great Plains. This work is not meant to identify a Tornado Alley that is better or truer than previous work. There are numerous different criteria for defining such an area, and the chosen priorities of a particular method can certainly result in an area that is different from other studies. Any method meant to define Tornado Alley will require some subjective decision making by the researchers, and that is acceptable so long as the decisions are well reasoned and justified. Brooks et al. (2003) suggest that the total threat of tornado touchdown may be the most basic and important quantity to be derived from tornado climate data, and it can be further argued that the most important quantity is the ultimate risk of being impacted by a tornado path. This research is motivated by A map of tornado events from over the middle part of the United States.

2 the benefits of identifying the most tornado-prone locations in the United States, regardless of intensity, time of day, seasonality, among others. BACKGROUND. While no formal origin of the term is known, Fawbush and Miller (issuers of the first successful tornado forecast, in 1948) reportedly began a severe weather study of the western Great Plains in 1952, which they called Tornado Alley (Gagan et al. 2010). Similarly, the term Dixie Alley was supposedly coined by Alan Pearson of the National Severe Storms Forecast Center in response to a 1971 tornado outbreak across the Delta region of Arkansas and Mississippi that resulted in 121 fatalities and more than 1500 injuries (Gagan et al. 2010). Other than the recent paper by Gagan et al. (2010), research literature addressing Dixie Alley has been limited to a few conference proceedings and informal publications (Broyles and Crosbie 2011; Gerard et al. 2011; Passe-Smith 2006). Gagan et al. (2010) detail some important statistical differences and similarities between Dixie Alley and the traditional Tornado Alley as they formally introduce the region into the research literature. Likewise, Ashley s (2007) analysis of tornado fatalities across the United States yielded a widely-publicized map of killer tornadoes that has drawn attention to a clear maximum stretching from northeast Arkansas through southwest Tennessee, northern Mississippi, and northwest Alabama. There have been many tornado climatology studies dating back more than a century (Finley 1884, 6 16; Emery 1900), but Kelly et al. (1978) were one of the first to use a dataset that had been thoroughly reviewed for accuracy. Kelly et al. (1978) also separated their frequency maps by F scale and path length, which showed that spatial tornado distributions can AFFILIATIONS: Di x o n Department of Geosciences, Mississippi State University, Mississippi State, Mississippi; Mercer Northern Gulf Institute, Mississippi State University, Mississippi State, Mississippi; Cho i Department of Geography, Sangmyung University, Seoul, South Korea; Alle n NOAA/National Weather Service, Jackson, Mississippi CORRESPONDING AUTHOR: P. Grady Dixon, Department of Geosciences, Mississippi State University, P.O. Box 5448, Mississippi State, MS grady.dixon@msstate.edu The abstract for this article can be found in this issue, following the table of contents. DOI: /2010BAMS In final form 1 November American Meteorological Society vary dramatically depending on the selection criteria. Schaefer et al. (1986), implementing the concept proposed by Thom (1963), used tornado path length and width to calculate the ratio of the mean annual area covered by tornado paths to that of the study area (squares outlined every 1 of latitude and longitude). The greatest annual probabilities of tornadoes stretched from the western portions of Texas and Kansas to the western edge of the Appalachians and from the Gulf of Mexico to northern Minnesota. In an effort to minimize some of the inherent inconsistencies of tornado data, Concannon et al. (2000) analyzed the spatial distribution of tornado days rather than all tornado events. Their results show the greatest tornado frequencies in central Oklahoma and stretching to the east through Alabama and to the northeast through Iowa. Likewise, Brooks et al. (2003) calculated the spatial and temporal probability of tornado days, and they found an irregular semicircle of elevated risk that encompasses much of the Great Plains along with large portions of Iowa, Illinois, Louisiana, and Mississippi. Further, the two regions of tornado-day maxima were located in Colorado and Florida (Brooks et al. 2003). After limiting the risk areas to those with predictable, or consistently occurring, tornado seasons, Brooks et al. (2003) produced a risk area stretching from northern Texas through most of North Dakota that conspicuously excludes the southeastern United States. This is simply because the Southeast experiences a comparatively low but consistent tornado risk throughout the year, while much of the Great Plains sees an acute peak in tornado frequency in late spring (Brooks et al. 2003). These results are important to the research literature and the fundamental understanding of tornado risks, but there could be some confusion by nonexperts when they see the often-cited maps of Tornado Alley (Brooks et al. 2003) and tornado fatalities (Ashley 2007). It is important that these different studies are publicized so that researchers, emergency managers, and the general public are able to assess the overall risk, and preparedness needs, for their respective regions. DATA AND METHODS. Tornado data for the years , the complete available record, were obtained from the National Weather Service Storm Prediction Center (SPC) as compiled for the National Climatic Data Center (NCDC) s publication Storm Data. Previous research has documented the compilation methods and history of this database (Schaefer and Edwards 1999; McCarthy 2003). The data include date and time of each tornado event, latitude and 434 april 2011

3 locations remote from any events (Fig. 1). It is possible to conduct an analysis of the ideal kernel radius, but such work is typically reserved for geospatia l research methods and journals. In practice, the kernel size is best determined by using a size consistent with that of the primary variable(s) of the study, which is tornado risk (O Sullivan and Unwin 2003). Fig. 1. Example of KDE using (left) a 100-mi and (right) a 10-mi kernel diamin this study, a kernel eter. Plotted data are tornado events for radius of 25 mi (40.25 km) was used to be consistent longitude of the genesis and dissipation locations with the SPC s forecasts of tornado risk within (when available), and other information not used in 25 miles of a point (Kay and Brooks 2000) and a this study. There are undoubtedly several concerns 5-km output grid size is used to provide maps that with this dataset, especially regarding the classifica- appear smooth at a national scale. Therefore, each tion of F scale, the likely confusion of some series of tornado event (either point touchdowns or line paths) short-path tornadoes into very long path lengths, and is surrounded by a 25-mi buffer (i.e., the kernel), the clearly increasing trend in the number of recorded and the KDE method employs the Epanechnikov tornado events through time (Doswell and Burgess quadratic probability density function as described 1988; Brooks et al. 2003; Brooks 2004). Our study does by Silverman (1986) and de Smith et al. (2007): not separate tornadoes by F scale, and our method is meant to remove the emphasis from tornado event counts in favor of tornado path density. (1) Kernel density estimation (KDE) was used to observe tornado patterns by producing a surface of interpolated tornado and tornado-day frequency. KDE is an interpolation method based on the idea that spa- where h is the kernel radius (i.e., bandwidth) and dij tial patterns have densities at any given location rather is the distance from a tornado path. than solely at places where events have been recorded (O Sullivan and Unwin 2003). This is one of the most commonly used tools in spatial analysis, and it provides an efficient way of estimating and visualizing the local intensity of any spatial process. For KDE, the output grid size and the kernel size must be predetermined (Silverman 1986). The output grid size determines only the resolution of the output; smaller grids produce smoother graphics and are essentially cosmetic. The kernel size, or bandwidth, is much more important for density calculations, as it determines the size of the surrounding area that will influence the value at any given point. Therefore, the kernel size significantly affects the resulting estimated density surface (O Sullivan and Unwin 2003; Poulos 2010). If the kernel size is large, then estimated densities will be similar Fig. 2. Example density calculations for 5-km grids everywhere. If the kernel size is small, then the surface using a km kernel. Shading represents tornado pattern will be strongly focused on individual events density or probability. Gray lines represent tornado and will yield many isolated clusters and/or zero in paths. AMERICAN METEOROLOGICAL SOCIETY april

4 Fig. 3. Sample of process to identify representative tornado-day paths. The Epanechnikov kernel assigns higher density values to locations nearer to the tornado event in question and decreasing values at distances farther from the event in question, eventually reaching zero along the outside edge of the kernel diameter. Hence, calculated densities will be greater near the middle of a tornado track than near the beginning or end, and it is possible for a location to have a high calculated tornado density (also interpreted as probability) despite never being directly affected by a tornado simply because many nearby tornadoes result in the accumulation of lower density values (Gibin et al. 2007; Fig. 2). This method was chosen because it is often considered to be the optimal or most efficient kernel, as it minimizes the asymptotic mean integrated squared error associated with other kernel functions (Gaussian, triangular, uniform, among others), but previous research has shown that the kernel function is much less important than the kernel radius (Silverman 1986; Schabenberger and Gotway 2005; de Smith et al. 2007; Xie and Yan 2008; Poulos 2010). The density calculation used in this study yields a probability of tornado occurrence per square kilometer for the study period, which is always a very small number. A much more useful value is the probability or density of tornado occurrence within 25 mi of a point (consistent with SPC forecasts), so the initial probabilities from all 5-km output grid cells within a 25-mi radius are summed to determine the expected tornado density within 25 mi of that particular grid cell. This final step results in a smoothing of risk over space by allowing the density of locations to be affected by tornado events up to 50 mi (80 km) away. Density values can then be divided by the number of study years (58) to determine the annual risk for each point. The density calculations described above were applied to all tornado events and to tornado days. Previous calculations of tornado days have relied upon predefined areas (states, counties, grid cells, among others), and a tornado day would be counted any time a tornado occurred within the predefined area (Concannon et al. 2000; Brooks et al. 2003; Raddatz and Cummine 2003; Trapp et al. 2005). Shortcomings of such methods include dependence upon the placement of the grid and the reduction of all tornado days down to a common numerical value (i.e., a long-track tornado day may be equivalent to a single brief tornado touchdown day within any given area). In this study, a 25-mi buffer was applied to all tornado events. For every day of the study period, tornado paths were removed if they fell within the buffer of a longer path on the same day (Fig. 3). This method counts only one tornado within the localized area of the buffer while maintaining the important variable of path length, and it reduced the total number of tornado events from 50,348 to 36,632 (a reduction of 27.2%). Kernel density estimations were computed for many different decades within the total 58-yr period (given in Table 1). Each decade had individual gridcell densities of tornado occurrence, leading to a temporal distribution of decadal tornado densities for each grid cell. To quantify statistical significance Ta b l e 1. Number of tornadoes per decade investigated. Data clearly show a trend toward an increase in tornado number per decade, likely a result of increased population and improved reporting methods. Decade Tornadoes , , , , , , , , , , , april 2011

5 of the computed densities spatially, a bootstrap resampling of these gridcell decadal densities was employed (Efron and Tibshirani 1998). The resulting bootstrap replicates were used to generate a bias-corrected and accelerated (BC a ; Efron and Tibshirani 1998) bootstrap confidence interval (CI) for tornado density at each grid cell. A CI of 95% is employed, which yields upper bounds of and lower bounds of This method contrasts the classic percentile-based confidence interval in that it is based on an acceleration parameter â and a biascorrection factor z 0. The parameter â represents the rate of change of the bootstrap statistic s standard error with respect to the true mean of the distribution. This acceleration is useful in that classic standard normal approximation assumes that the standard error of the bootstrap statistic is the same for all values of the true statistic. This is obviously not always true, so the acceleration corrects for this difference. The bias-correction factor is computed as the proportion of bootstrap replications that are less than the original data estimate (i.e., the original mean tornado density for the current study). If this bias correction was exactly 0, then exactly half of the replicates were less than or equal to the original estimate. Using these factors, the lower (α 1 ) and upper (α 2 ) quantiles associated with the BC a CI are given as (Efron and Tibshirani 1998) and (2) (3) where α represents the confidence level for the CI, Φ represents the standard normal cumulative distribution function, and z represents the quantile of the standard normal distribution that is equal to 100α. The BC a method yields confidence intervals that are second-order accurate, meaning the standard errors of the BC a CIs go to zero at a rate faster than for Fig. 4. Density calculations of average annual tornadoes within 25 mi of any point. Regional maxima values include 1.48 in Smith County, MS; 1.37 in Lonoke County, AR; 1.28 in Hall County, NE; and 1.27 in Oklahoma County, OK. the percentile method, which is first-order accurate. One drawback to the use of the BC a is the requirement of a large number of bootstrap replicates to reduce the Monte Carlo sampling error associated with the bootstrap, thereby reducing error on the BC a CI estimation. For the current study, 10,000 bootstrap replicates were created at each grid point in the spatial domain, yielding a BC a CI at each grid point. One of the fundamental goals of this work is to determine if a regional maximum in tornado density in the southeastern United States (Dixie Alley) is indeed geographically separate from the classic maximum of tornado density in the Great Plains, known as Tornado Alley. The BC a CIs allow this spatial relationship to be tested, since the bootstrap, by definition, is not dependent upon the underlying distribution of the data. As such, regions with a lower BC a CI limit density value that was higher than the median BC a density value in other spatial regions could be identified as having a statistically significantly larger number of tornadoes. In effect, this spatial representation allows the reader to reject the null hypothesis that the tornado densities in the two alleys are the same through visual inspection. These comparisons will be considered in more detail in the next section. AMERICAN METEOROLOGICAL SOCIETY april

6 Fig. 5. Density calculations of average annual days experiencing a tornado within 25 mi of any point. Regional maxima values include 1.38 in Smith County, MS; 1.04 in Hall County, NE; 1.02 in Oklahoma County, OK; and 0.97 in both Lonoke and Pulaski Counties, AR. RESULTS. Density maps based on all tornado events (Fig. 4) and on tornado days (Fig. 5) differ as one would expect, with similar spatial patterns but higher values for total tornado density. Three notable areas with much higher tornado densities than tornado-day densities are observed, but the most pronounced lies between Dodge City and Great Bend, Kansas, where tornado-day density is 45% less (71 tornado days versus 129 tornadoes) than total tornado density. Fifty-one of those days each experienced only 1 tornado, and no more than 10 tornadoes occurred on any given day. Nevertheless, five days (7%) account for 41 tornadoes (32%). Three counties (Cleburne, Faulkner, and White) northeast of Little Rock, Arkansas, and two counties (Bailey and Lamb) northwest of Lubbock, Texas, display notable (30% 40%) decreases in tornado-day densities from total tornado densities. It is beyond the scope of this study to determine whether these differences are primarily due to population distributions, a few extreme events, or some unexpected factors. The remaining discussion will refer to tornado-day densities (i.e., Fig. 5). The spatial distributions and areas of greatest density (Figs. 4 and 5) seem to resemble most the 438 april 2011 results of previous work by Schaefer et al. (1986) and Broyles and Crosbie (2011). This is expected, as those previous efforts considered tornado path length in their calculations, and the density estimation method described herein also favors longer paths. Additionally, the presented spatial density pattern (Figs. 4 and 5) shows maxima stretching from the Deep South westward and northward through the Great Plains and then back east and south, in a nearcircuitous fashion, through the Ohio Valley, a result consistent with studies that did not emphasize path length (Concannon et al. 2000; Brooks et al. 2003; Ashley 2007). Most areas of the country do not show up in the results (Figs. 4 and 5) because of very low density values. In contrast to the results of Brooks et al. (2003), northeastern Colorado and central Florida do not appear on the risk maps, despite experiencing many tornadoes, simply because they rarely experience tornadoes with significant path lengths. Hence, the chance of being impacted by a tornado in these regions is rather small. While the overall pattern is not surprising, some may question why there are regional maxima with densities greater than any locations in the state of Oklahoma, the state previously thought to be the maximum for tornado activity (Schaefer et al. 1986; Brooks et al. 2003; Broyles and Crosbie 2011). This discrepancy results from the emphasis on path length as opposed to tornado frequency. To illustrate this point, we compare the area of greatest density (Smith County, Mississippi) with an area commonly associated with maximum tornado frequency (Oklahoma County, Oklahoma). Figure 6 shows that Oklahoma County experienced 53 tornadoes (7.5 tornado events per 100 mi 2 ), while Smith County saw only 33 tornadoes (5.2 tornado events per 100 mi 2 ). However, the Smith County tornadoes, on average, had considerably longer path lengths, resulting in an estimated kernel density for Smith County (1.38 tornado days per year within 25 mi of a point) that is 35% greater than that of Oklahoma County (1.02 tornado days per year within 25 mi of a point). Areas experiencing at least one tornado day every four years (density of at least 0.25) include most of

7 Fig. 6. Tornado paths representing unique local tornado days for (a) Oklahoma County, OK, and (b) Smith County, MS. the central Great Plains, the Corn Belt, and the Deep South. Areas experiencing at least one tornado day every two years (density of at least 0.50) are relatively sparsely located across numerous states in the characteristic semicircle around Missouri. While the traditional Tornado Alley states of Oklahoma, Kansas, Nebraska, Iowa, and Texas possess the greatest area (223,932 km 2 ) with densities of at least 0.50, the largest single coterminous area with such values is located almost entirely in Mississippi and northern Louisiana (96,225 km 2 ). The fourth-largest area with similar densities is located in northeastern Arkansas, and the sixth-largest area is located in northern Alabama. The regional density maxima in Mississippi, Arkansas, Alabama, and Louisiana provide some support for the idea of a separate Dixie Alley, as some of the most tornado-prone areas of the country are located in the Southeast. The results of the bootstrap resampled BC a confidence intervals of tornado-day density allow for further study into the spatial separation in the two alleys. The BC a CIs include a median and upper and lower bound (α = 0.05) mean densities for each grid cell. If the particular cell s median BC a value lies outside the BC a CI of a surrounding grid cell or area, tornadoday densities in those locations are statistically significantly different (α = 0.05). Additionally, the CIs provide insight into the relative tornado-day density magnitude of Dixie Alley versus Tornado Alley, though no such difference in relative magnitude was observed from the BC a (not shown). If Dixie Alley is a physically separate region from Tornado Alley, the BC a CIs should show a statistically significantly different area of separation between the two regions. Initial analysis of the high-value lower BC a CI contours (i.e., density greater than 0.50) reveal numerous small hot spots that do not resemble alleys. These discontinuous hot spots are not useful for discerning separation between the alleys, so a lower CI bound plot for densities greater than 0.25 (annual tornado days within 25 mi of a point) was obtained (i.e., Fig. 7). This contour level reveals two discrete large areas that could be considered as Tornado Alley and Dixie Alley. However, the hypothesized statistically significantly different region of separation between the two alleys is not present. Instead, the primary separating factor between the two alleys is central Missouri and northwestern Arkansas, likely due to the Ozark and Ouachita Mountains. CONCLUSIONS. Like most tornado climatology research, this study suffers from shortcomings associated with the tornado database. By avoiding Fig. 7. Red shading represents areas with bootstrap lower BC a confidence intervals greater than 0.25 tornado days per year. Nonshaded (white) areas represent those with bootstrap BC a median values less than 0.25 tornado days per year. Hence, the gray shaded areas represent transition regions that are not statistically different from the other two regions. Dark red lines show intervals (0.25 tornado days per year) of increasing density. AMERICAN METEOROLOGICAL SOCIETY april

8 separation by F scale and by using local tornado days rather than raw tornado events, most major potential problems with the dataset have been avoided. The KDE method provides a robust assessment of tornado threat in a particular area, but the calculations are limited by the quality of the recorded tornado paths. It is assumed that the employed kernel radius (40.25 km) is sufficient to mask any rounding or spatial errors associated with event coordinates, but some events that traveled significant distances might have been reported as single-point touchdowns. Additionally, the increased numbers of tornadoes in later years is a concern, and future research might be able to account for this through spatial resampling procedures meant to minimize population bias. Despite the identification of a few Southeastern locations with unexpectedly high tornado-day densities, including the most tornado-prone area in the country (Smith County, Mississippi) and the largest region experiencing at least two tornado days per year (across Mississippi and northern Louisiana), it does not appear as though Dixie Alley is its own distinct region. Statistical analysis shows that regions with similar tornado-day densities are located throughout the Great Plains, the Corn Belt, and the Deep South without areas of statistically significant differences separating them. There are a few discontinuous patches of significantly reduced tornado-day density stretching from northeastern Missouri down through western Arkansas and southeastern Oklahoma. The result is merely a somewhat circular region of elevated risk with maxima located in places such as Mississippi, Arkansas, Oklahoma, Nebraska, and Illinois. This circular pattern is most likely due to the relative lack of events over the relatively complex, elevated terrain of the Ozark and Ouachita Mountains. It is possible that this line of relatively little tornado activity is partially responsible for the emergence of Dixie Alley as a separate region. Hence, if there were no mountains in Missouri, Arkansas, and southeastern Oklahoma, it is likely that Tornado Alley would be a continuous region of increased tornado frequency stretching from the Great Plains through the Corn Belt and Deep South. There are at least a couple areas that stand out from the overall pattern (e.g., northern Illinois, north-central Missouri), and these might be explained a few different ways. Perhaps these locations see fewer tornado reports because of lower population densities or simply because of chance over the relatively short record of events. It is certainly worth studying such areas further to determine whether there are physical processes responsible for the differences in tornado risk. It is likely that many people will continue to refer to the subjectively defined region of the southeastern United States as Dixie Alley, with respect to tornado activity. This is acceptable, though the results presented herein demonstrate the lack of separation between the two alleys when considering total tornado risk. Seasonal analyses of the United States will likely yield areas that are statistically different from the composites shown here, and perhaps it would be more appropriate to name those regions for the time of year they occur rather than the ambiguous names currently employed. Brooks et al. (2003) perform seasonal analyses of tornado frequency and show some insightful spatial patterns that vary dramatically with season, and they make the argument that seasonal repeatability is a key component of defining the phrase Tornado Alley. Our study focused more on historically consistent spatial patterns rather than temporal patterns. However, it is undoubtedly better for public preparedness if residents can reliably expect more tornadoes during certain parts of the year, so future studies should use statistical and density analyses of tornado paths to distinguish between tornado seasons across the country. Future research is also needed on the different environmental conditions commonly associated with tornado formation in the Great Plains and the Southeast. Specifically, some future efforts should focus more on the factors contributing to longer average path lengths in parts of the Southeast, which are largely to blame for the tornado risk maxima in the southeastern United States. REFERENCES Ashley, W. S., 2007: Spatial and temporal analysis of tornado fatalities in the United States: Wea. Forecasting, 22, Brooks, H. E., 2004: On the relationship of tornado path length and width to intensity. Wea. Forecasting, 19, , C. A. Doswell, and M. P. Kay, 2003: Climatological estimates of local daily tornado probability for the United States. Wea. Forecasting, 18, Broyles, J. C., and K. C. Crosbie, cited 2011: Evidence of smaller tornado alleys across the United States based on a long track F3-F5 tornado climatology study from [Available online at ams.confex.com/ams/11aram22sls/techprogram/ paper_81872.htm.] Concannon, P. R., H. E. Brooks, and C. A. Doswell III, 2000: Climatological risk of strong and violent tornadoes in the United States. 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9 on Environmental Applications, Long Beach, CA, Amer. Meteor. Soc., 9.4. [Available online at ams.confex.com/ams/annual2000/techprogram/ paper_6471.htm.] de Smith, M. J., M. F. Goodchild, and P. A. Longley, 2007: Geospatial Analysis: A Comprehensive Guide to Principles, Techniques and Software Tools. 3rd ed. Troubador Publishing, 516 pp. Doswell, C. A., III, and D. W. Burgess, 1988: On some issues of United States tornado climatology. Mon. Wea. Rev., 116, Efron, B., and R. Tibshirani, 1998: The problem of regions. Ann. Stat., 26, Emery, S. C., 1900: Tornadoes in Tennessee, Mississippi, and Arkansas. Mon. Wea. Rev., 28, Finley, J. P., 1884: Character of Six Hundred Tornadoes. U.S. Signal Service Professional Paper 7, 16 pp. Gagan, J. P., A. Gerard, and J. Gordon, 2010: A historical and statistical comparison of Tornado Alley to Dixie Alley. Natl. Wea. Dig., 34, Gerard, A. E., J. Gordon, and J. Gagan, cited 2011: A comparison of tornado statistics from tornado alley and Dixie alley. 30th Annual Meeting, St. Louis, MO, National Weather Association. [Available online at DixieAlley_17Oct2005pm.ppt.] Gibin, M., P. Longley, and P. Atkinson, 2007: Kernel density estimation and percent volume contours in general practice catchment area analysis in urban areas. Proc. Geographical Information Science Research UK (GISRUK) Conf., Maynooth, Ireland, National Centre for Geocomputation and National Institute for Regional and Spatial Analysis, 7 pp. Kay, M. P., and H. E. Brooks, 2000: Verification of probabilistic severe storm forecasts at the SPC. Preprints, 20th Conf. on Severe Local Storms, Orlando, FL, Amer. Meteor. Soc., 9.3. [Available online at ams.confex.com/ams/sept2000/techprogram/ paper_15921.htm.] Kelly, D. L., J. T. Schaefer, R. P. McNulty, C. A. Doswell III, and R. F. Abbey, 1978: An augmented tornado climatology. Mon. Wea. Rev., 106, McCarthy, D., 2003: NWS tornado surveys and the impact on the National Tornado Database. Preprints, Symp. on the F-Scale and Severe-Weather Damage Assessment, Long Beach, CA, Amer. Meteor. Soc., 3.2. [Available online at annual2003/techprogram/paper_55718.htm.] O Sullivan, D., and D. J. Unwin, 2003: Geographic Information Analysis. John Wiley & Sons, Inc., 436 pp. Passe-Smith, M. S., 2006: Exploring local tornado alleys for predictive environmental parameters. Proc ESRI Int. User Conf., San Diego, CA, ESRI. [Available online at userconf/proc06/papers/papers/pap_1339.pdf.] Poulos, H., 2010: Spatially explicit mapping of hurricane risk in New England, USA using ArcGIS. Nat. Hazards, 54, Raddatz, R. L., and J. D. Cummine, 2003: Inter-annual variability of moisture flux from the prairie agroecosystem: Impact of crop phenology on the seasonal pattern of tornado days. Bound.-Layer Meteor., 106, Schabenberger, O., and C. A. Gotway, 2005: Statistical Methods for Spatial Data Analysis. Chapman and Hall/CRC, 488 pp. Schaefer, J. T., and R. Edwards, 1999: The SPC tornado/ severe thunderstorm database. Preprints, 11th Conf. on Applied Climatology, Dallas, TX, Amer. Meteor. Soc., , D. L. Kelly, and R. F. Abbey, 1986: A minimum assumption tornado-hazard probability model. J. Climate Appl. Meteor., 25, Silverman, B. W., 1986: Density Estimation for Statistics and Data Analysis. Chapman and Hall, 175 pp. Thom, H. C. S., 1963: Tornado probabilities. Mon. Wea. Rev., 91, Trapp, R. J., S. A. Tessendorf, E. S. Godfrey, and H. E. Brooks, 2005: Tornadoes from squall lines and bow echoes. Part I: Climatological distribution. Wea. Forecasting, 20, Xie, Z., and J. Yan, 2008: Kernel density estimation of traffic accidents in a network space. Comput. Environ. Urban Syst., 32, AMERICAN METEOROLOGICAL SOCIETY april

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