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  • View in gallery

    The study region (blue box) and the 483 tornado reports (red dots) used in deriving statistical relationships.

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    Fourier function used to reconstruct the azimuth data. The azimuth data are binned, with the magnitude of the Fourier function corresponding to the likelihood of at least one tornado in each bin. Values closer to 1 indicate a greater tornado potential.

  • View in gallery

    ROC curve for the six predictors along with the 0.5-area diagonal reference line (light blue) that denotes the null hypothesis.

  • View in gallery

    Time series of TCTP 6-h forecast periods for Hurricane Ike (2008) from (a) 1200 UTC 12 Sep to (f) 1800 UTC 13 Sep 2008. Each 6-h forecast period is centered on 12 h after the analysis time (i.e., ±3 h from the valid time displayed). Red dots represent locations of tornado reports from 3 h before to 3 h after each forecast time, while the purple star indicates the position of Ike. The units of TCTP are the percentage probability of a tornado within 25 mi during a 6-h period.

  • View in gallery

    SPC tornado probability forecast issued at 1610 UTC 13 Sep 2008. The tan line outlines regions with at least a 5% probability of tornadoes within 25 mi, while the green line outlines regions of 2%–5% risk. The forecast is valid from 1630 UTC 13 Sep to 1200 UTC 14 Sep 2008.

  • View in gallery

    Time series of TCTP 6-h forecast periods during Tropical Storm Hermine (2010) from (a) 1800 UTC 7 Sep to (f) 0000 UTC 9 Sep 2010. Each 6-h forecast period is centered on 12 h after the analysis time (i.e., ±3 h from the valid time displayed). Red dots represent locations of tornado reports from 3 h before to 3 h after each forecast time, and the purple stars indicate the position of Hermine. The units of TCTP are the percentage probability of a tornado within 25 mi during a 6-h period.

  • View in gallery

    SPC tornado probability forecast issued at 1200 UTC 8 Sep 2010. The green line outlines regions of 2%–5% risk. The forecast is valid from 1200 UTC 8 Sep to 1200 UTC 9 Sep 2010.

  • View in gallery

    Time series of TCTP 6-h forecast periods during Tropical Storm Lee (2011) from (a) 0600 UTC 4 Sep to (f) 1200 UTC 5 Sep 2011. Each 6-h forecast period is centered on 12 h after the analysis time (i.e., ±3 h from the valid time displayed). Red dots represent locations of tornado reports from 3 h before to 3 h after each forecast time, and the purple stars indicate the position of Lee. The units of TCTP are the percentage probability of a tornado within 25 mi during a 6-h period.

  • View in gallery

    SPC tornado probability forecast issued at 1200 UTC 4 Sep 2011. The green area contains regions of 2%–5% risk, while the brown area contains regions of 5%–10%. The forecast is valid from 1200 UTC 4 Sep to 1200 UTC 5 Sep 2011.

  • View in gallery

    Time series of TCTP 6-h forecast periods during Tropical Storm Debby (2012) from (a) 0600 UTC 24 Jun to (f) 1200 UTC 25 Jun 2012. Each 6-h forecast period is centered on 12 h after the analysis time (i.e., ±3 h from the valid time displayed). Red dots represent locations of tornado reports from 3 h before to 3 h after each forecast time, and the purple stars indicate the position of Debby. The units of TCTP are the percentage probability of a tornado within 25 mi during a 6-h period.

  • View in gallery

    SPC tornado probability forecast issued at 1200 UTC 24 Jun 2012. The green area contains regions of 2%–5% risk, while the brown area contains regions of 5%–10%. The forecast is valid from 1200 UTC 24 Jun to 1200 UTC 25 Jun 2012.

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A Parameter for Forecasting Tornadoes Associated with Landfalling Tropical Cyclones

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  • 1 Department of Meteorology, Florida State University, Tallahassee, Florida
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Abstract

The authors develop a statistical guidance product, the tropical cyclone tornado parameter (TCTP), for forecasting the probability of one or more tornadoes during a 6-h period that are associated with landfalling tropical cyclones affecting the coastal Gulf of Mexico and the southern Atlantic coast. TCTP is designed to aid forecasters in a time-limited environment. TCTP provides a “quick look” at regions where forecasters can then conduct detailed analyses. The pool of potential predictors included tornado reports and tropical cyclone data between 2000 and 2008, as well as storm environmental parameters. The original pool of 28 potential predictors is reduced to six using stepwise regression and logistic regression. These six predictors are 0–3-km wind shear, 0–3-km storm relative helicity, azimuth angle of the tornado report from the tropical cyclone, distance from the cyclone’s center, time of day, and 950–1000-hPa convective available potential energy. Mean Brier scores and Brier skill scores are computed for the entire TCTP-dependent dataset and for corresponding forecasts produced by the Storm Prediction Center (SPC). TCTP then is applied to four individual cyclone cases to qualitatively and quantitatively assess the parameter and compare its performance with SPC forecasts. Results show that TCTP has skill at identifying regions of tornado potential. However, tornadoes in some tropical systems are overpredicted, but underpredicted in others. TCTP 6-h forecast periods provide slightly poorer statistical performance than the 1-day tornado probability forecasts from SPC, probably because the SPC product includes forecaster guidance and because their forecasts are valid for longer periods (24 h).

Corresponding author address: Henry E. Fuelberg, Department of Meteorology, Florida State University, 1017 Academic Way, Tallahassee, FL 32306-4520. E-mail: hfuelberg@fsu.edu

Abstract

The authors develop a statistical guidance product, the tropical cyclone tornado parameter (TCTP), for forecasting the probability of one or more tornadoes during a 6-h period that are associated with landfalling tropical cyclones affecting the coastal Gulf of Mexico and the southern Atlantic coast. TCTP is designed to aid forecasters in a time-limited environment. TCTP provides a “quick look” at regions where forecasters can then conduct detailed analyses. The pool of potential predictors included tornado reports and tropical cyclone data between 2000 and 2008, as well as storm environmental parameters. The original pool of 28 potential predictors is reduced to six using stepwise regression and logistic regression. These six predictors are 0–3-km wind shear, 0–3-km storm relative helicity, azimuth angle of the tornado report from the tropical cyclone, distance from the cyclone’s center, time of day, and 950–1000-hPa convective available potential energy. Mean Brier scores and Brier skill scores are computed for the entire TCTP-dependent dataset and for corresponding forecasts produced by the Storm Prediction Center (SPC). TCTP then is applied to four individual cyclone cases to qualitatively and quantitatively assess the parameter and compare its performance with SPC forecasts. Results show that TCTP has skill at identifying regions of tornado potential. However, tornadoes in some tropical systems are overpredicted, but underpredicted in others. TCTP 6-h forecast periods provide slightly poorer statistical performance than the 1-day tornado probability forecasts from SPC, probably because the SPC product includes forecaster guidance and because their forecasts are valid for longer periods (24 h).

Corresponding author address: Henry E. Fuelberg, Department of Meteorology, Florida State University, 1017 Academic Way, Tallahassee, FL 32306-4520. E-mail: hfuelberg@fsu.edu

1. Introduction

Fifty-three tropical cyclones (TCs) have affected the southeastern United States between 2000 and 2012, including 29 that impacted the state of Florida. While the effects of TC winds near the storm center are widely known, the most damage at more distant locations often is due to severe local storms in the outer rainbands (Schultz and Cecil 2009). These include tornadoes or high-wind events such as downbursts that can lead to damage hundreds of kilometers from the cyclone’s center of circulation. For example, the rainband in Hurricane Ivan (2004) that produced widespread tornadoes during Ivan’s landfall over southwestern Alabama was located between 250 and 450 km from the storm’s center (Baker et al. 2009). Although TC-related tornadoes have comprised only about 3.4% of the total number of reported tornadoes since 1950, they contributed approximately 5% of all U.S. tornado monetary damage (~$1.4 billion) (Schultz and Cecil 2009).

Schultz and Cecil (2009) noted that a greater number of tornadoes occur farther from the TC’s center with increasing time after landfall. They also showed that the threat for severe local storms may last as long as 3 days after landfall, and as far as 500 km from the cyclone’s center. TC intensity also has been related to tornado production. Specifically, strong TCs generally yield the most tornadoes (Novlan and Gray 1974; McCaul 1991), although there have been notable exceptions such as Tropical Storm Beryl (1994), which produced 37 tornadoes (Vescio et al. 1996). Numerous studies have found a strong preference for tornadoes to occur in the right-front quadrant relative to storm motion or relative to true north (these two quadrants often are similar) (Sadowski 1962; Smith 1965; Pearson and Sadowski 1965; Hill et al. 1966; Novlan and Gray 1974; Gentry 1983; McCaul 1991; Verbout et al. 2007; Schultz and Cecil 2009).

When attempting to forecast TC-related severe local storms, McCaul (1991) suggested that the “consideration of the totality of factors…hurricane size, intensity and forward speed, hodograph helicity and shear, presence of at least some buoyancy, location and timing of landfall—may yield improved forecasts” (p. 1977). These parameters vary from storm to storm, and considerable differences can occur in different quadrants of the same storm.

The environmental conditions in which tornadoes develop near TCs differ from the very unstable and highly sheared tornado environments of the Great Plains (e.g., McCaul 1991; Edwards 2008). Although wind shear and instability are crucial to tornado development in either environment, TCs typically exhibit highly sheared wind profiles but only modest instability (Novlan and Gray 1974; McCaul 1991; Bogner et al. 2000; Baker et al. 2009). Although measures of instability such as convective available potential energy (CAPE) typically are relatively small in TCs, supercells appear to be the most common mode of deep convection for tornadogenesis (e.g., McCaul 1987; Spratt et al. 1997; Suzuki et al. 2000; McCaul et al. 2004; Edwards 2008). However, these TC-related supercells often are shallower and smaller than their midlatitude counterparts (McCaul and Weisman 1996). These differences must be considered when forecasting TC-related tornadoes.

The magnitude of instability (e.g., CAPE) appears to be less important in TC-related tornadoes than in midlatitude scenarios. Indeed CAPE typically is observed to be considerably smaller for TC tornadoes (Edwards et al. 2012). Not only may CAPE be less critical to TC tornadogenesis, but different techniques may be needed to properly calculate it in the TC environment. Low-level mean-layer CAPE (e.g., 1000–950 hPa) may be a more accurate way of defining the instability in TCs that is available for developing thunderstorms because of the well-mixed nature of the TC boundary layer (Davies 2006).

The timing of TC landfall is relevant to tornado occurrence (McCaul 1991; Schultz and Cecil 2009). Schultz and Cecil (2009) point out that 84% of TC-related tornadoes occur in the time period from 12 h prior to landfall until 48 h after landfall with a peak during the period 0–12 h after landfall. Although the timing of landfall is not physically related to tornado occurrence, it may represent a proxy for physical relationships that are not yet fully understood.

The National Weather Service (NWS) Storm Prediction Center (SPC) in Norman, Oklahoma, employs an in-depth ingredients-based forecasting method to analyze the various parameters that are related to severe storm occurrence. This approach has evolved from climatology and pattern recognition. SPC also utilizes composite parameters such as the energy–helicity index (EHI; Hart and Korotky 1991; Rasmussen 2003) and the significant tornado parameter (STP; Thompson et al. 2004). Although these parameters were not developed for TC-related severe local storms, the STP composite index correctly indicated the potential for an outbreak of strong supercells and tornadoes during the landfalls of Ivan (2004) and Jeanne (2004) (Baker et al. 2009). These easy to compute indices provide insight into the probability of tornado occurrence. This is important since forecasters often have little time to make important decisions about the probability of severe weather occurrence (Doswell and Schultz 2006). Although multi-input parameters can highlight regions that require detailed examination, they certainly should not be a forecaster’s sole reference since they can lead to large forecast errors and a failure to understand the atmospheric conditions leading to tornadoes (Doswell and Schultz 2006).

Related to the forecasting problem is the public’s perception of risk during a tropical cyclone event. Forecasters often are faced with the quandary of forecasting what they believe will occur versus what will generate the appropriate response from the public. TC-related severe local storms, especially tornadoes, pose a unique threat to the public since they often occur at large distances from where the main TC damage occurs. Peacock et al. (2005) noted that “hurricane risk perception has been found to be an important predictor of storm preparation, evacuation, and hazard adjustment undertaken by households” (p. 120). While the effects of high winds generally are understood by the public, the risk of severe local storms at large radii may be less recognized. This problem is compounded by the fact that typical TC-related tornado watches typically cover large areas of the TC’s northeast quadrant and may last for extended periods of time (Edwards 2008).

The objective of this study is to develop a statistical guidance product that specifically forecasts the likelihood of tornadoes in landfalling tropical cyclones. We call this product the tropical cyclone tornado parameter (TCTP). We hypothesize that a useful composite parameter similar to those derived for forecasting tornadoes in the middle latitudes can be developed specifically for the TC environment. Stepwise multiple linear regression and logistic regression are used to develop the composite parameter because of their ability to determine those variables most indicative of TC tornadogenesis. We believe that the selection of these variables and the resulting guidance product will assist forecasters in preparing improved forecasts and lead to greater physical insights into the processes that influence TC tornado development.

2. Data and methodology

a. Predictands

The first input to our predictand included information from SPC’s tornado reports. SPC’s initial reports are highly prone to error and multiple reports of the same tornado (e.g., Doswell and Burgess 1988). Therefore, SPC and the National Climate Data Center (NCDC) perform a postanalysis to produce a more accurate dataset. Called Storm Data, the revised dataset contains information about each tornado’s path length, enhanced Fujita (EF)-scale rating, starting and ending location, etc. However, even with the quality control measures, Storm Data still contains errors and limitations. For example, damage from tornadoes that form in isolated regions may not be witnessed. In addition, Doswell and Burgess (1988) and Wikle and Anderson (2003) noted that tornado reports often are submitted by untrained observers who may not be able to distinguish between damage due to a tornado versus some other phenomenon. Although we assume that all Storm Data tornado reports represent tornado occurrences, this almost certainly is not the case.

A specific issue with tornado reports during TCs is discriminating between tornadic damage and damage due to the TC’s own winds. Schultz and Cecil (2009) defined tornadoes occurring inside a 200-km radius as “core tornadoes” and noted that approximately 25% of TC tornadoes occur inside this range. Other issues are the limited observer network that is available during TC conditions and that the tornadoes may be obscured by rolling terrain and heavy rainfall (Schultz and Cecil 2009). A final important consideration is the absence of tornado reports over the ocean. Radar data may suggest the existence of supercells capable of producing offshore tornadoes during TCs, but direct observation of the tornadoes is nearly impossible (Baker et al. 2009; Eastin and Link 2009; Schultz and Cecil 2009; Spratt et al. 1997). This produces large uncertainties in TC tornado statistics, particularly for variables such as tornado time relative to the time of TC landfall. Given these limitations, information about tornado occurrence must be considered estimates.

The second input to our predictand was the National Hurricane Center’s (NHC’s) best-track data (Jarvinen et al. 1984). This dataset is based on a postanalysis of all available information over the North Atlantic, including data from satellites, ships, and coastal observations.

The actual predictand was a combination of the best track and Storm Data. The best-track data were linearly interpolated to 1-h intervals to better indicate the time of TC landfall. The study region was defined as the area within 24.1°–35.6°N, 79.1°–101.4°W, encompassing all of the northern Gulf of Mexico, eastern coast of Florida, and coastal Georgia and South Carolina (Fig. 1). This region was chosen so that midlatitude baroclinicity (particularly during extratropical transition) would play only a small role in affecting the TC environments that produced tornadoes. The aim was to focus primarily on tornadoes being generated mainly by the TC circulation. All tornadoes within 750 km of TC centers in the study region were identified. The 750-km value, also used by Schultz and Cecil (2009), helped alleviate the uncertainty of whether a tornado report outside this range was due to the TC. We added a binary variable to the predictor pool to indicate whether the TC was over land or water.

Fig. 1.
Fig. 1.

The study region (blue box) and the 483 tornado reports (red dots) used in deriving statistical relationships.

Citation: Weather and Forecasting 29, 5; 10.1175/WAF-D-13-00086.1

Some tornadoes occurred in the study area although the parent TC already had exited the region. They were not included in the final dataset. However, since most TCs in the region during our study period generally moved northward, and most tornadoes occur in the front-right quadrant of a TC, this situation seldom occurred. Conversely, some tornadoes occurred outside the study region although the TC remained within. These reports also were deleted from the final dataset. Less than 10% of the total number of TC tornadoes in the study region were deleted from the final dataset. Table 1 lists the TCs, their total number of tornadoes, the number of EF0, EF1, EF2, and EF3 tornadoes, and the number of hours between the first and last tornado report associated with each TC.

Table 1.

Tropical cyclones used in this study and their tornado statistics.

Table 1.

A total of 29 TCs entered the study region when adequate Rapid Update Cycle (RUC) data were available, producing 483 tornado reports that met the selection criteria described above. The mean number of tornadoes per TC was 16.7, with a maximum of 78 during Hurricane Frances (2004) and a minimum of 1 (7 different TCs).

b. Potential predictors

The pool of potential predictors consisted of TC and tornado data, as well as environmental parameters. We used the best-track information and Storm Data, as well as RUC model data (Benjamin et al. 1994, 2002) from the National Centers for Environmental Predictions (NCEP). The potential predictors included geographic variables such as distance from the TC’s center and azimuth angle with respect to the TC’s forward motion. In addition, RUC-derived atmospheric variables (Benjamin et al. 1994, 2002) were determined at the location of each tornado report. These predictors are described in detail in the following paragraphs. The study period extended from 2000 through 2008 (9 yr), during which RUC underwent several changes. From 2000 through April 2002, it was run at 40-km horizontal resolution with 40 vertical levels. Afterward, it was upgraded to 20-km horizontal resolution and 50 vertical levels. Additional modifications made during April 2002 included improved moist physics, assimilation of additional satellite data, improved land surface physics, etc. (Benjamin et al. 2002). Further modifications were implemented during the later years of the study period including an upgrade to 13-km horizontal resolution in 2005. To test the impact of these changes the data were split into two approximately equally sized portions: one containing the years 2000–04 and the other consisting of years 2005–09. All coefficients and their corresponding verification statistics derived from either portion of the dataset changed very little when compared to those derived from the full dataset. This lends confidence in our ability to use RUC-derived variables throughout a period when the model underwent change.

All tornado reports and RUC data were regridded over the study region before statistical analysis was performed. Three-hourly RUC analyses were used so each tornado report was paired with the nearest RUC analysis time (which could be as much as 1.5 h different). We examined two grid spacings to encompass the study region. An 80 × 80 km2 grid mesh and a 160 × 160 km2 grid mesh were tested to see which yielded the highest correlations between the predictors and tornado occurrence. In each case, data at all RUC grid points within each larger grid box were averaged to produce a single value for each 160 × 160 km2 and 80 × 80 km2 grid cell. The 160 × 160 km2 grid provided slightly higher correlations with tornado occurrence and thus was used to derive the final relationships described later. The coarser grid most likely provided higher correlations because there typically were more tornado reports per grid cell. The finer grid (80 × 80 km2) often contained grid cells with a favorable environment for tornadoes but no tornado reports.

Our initial pool of 28 potential predictors was chosen based on their physical relevance to TC-related tornado occurrence. Each parameter is described in the paragraphs below, and Table 2 shows their correlations with tornado occurrence. The correlations were derived using standard multivariate linear regression. We concede that all possible variables related to TC tornadoes likely were not considered. For example, the inclusion of upper-level parameters (e.g., divergence) to the predictor pool may improve TCTP in future derivations.

Table 2.

Correlation coefficients (derived from multiple linear regression) between the number of tornado reports per 160 × 160 km2 grid box during a 6-h interval and each of the indicated geographic and atmospheric parameters.

Table 2.

Several independent variables describe the location and timing of the TC and tornado report including time of day relative to 1200 UTC (variable 1 is the number of hours before or after 1200 UTC), hours from landfall, and distance from the TC’s center to the tornado report. We found that most tornadoes occurred between 1200 and 2100 LST, with a peak between 1300 and 1700 LST, consistent with the results of Schultz and Cecil (2009). This afternoon peak most likely is related to decreased atmospheric stability during these hours, although the value of low-level CAPE (described in detail below) peaks slightly later, at approximately 2000 LST.

Variable 2 was the time of the tornado report relative to the time of TC landfall (McCaul 1991; Schultz and Cecil 2009). The best-track data were linearly interpolated to 1-h intervals to obtain a more specific time of landfall. Each tornado report then was compared to the best-track landfall data, and the nearest landfall time was assigned. If two TCs were located simultaneously in the study region, we were careful to ensure that tornado reports were assigned to the correct TC. This care was necessary since landfall times for some nonparent TCs were closer to a tornado report than the actual parent TC’s landfall, particularly if the parent TC’s motion paralleled the coastline.

The third predictor was distance from the tornado report to the TC center. The distance from each grid point in the study domain to each best-track point was calculated and then considered for its correlation with tornado occurrence.

The fourth variable was the azimuth angle between the tornado report and the TC (described above). The literature indicates two methods by which this angle can be calculated. Hill et al. (1966), Novlan and Gray (1974), and Weiss (1987) showed that tornadoes are most likely in the northeast quadrant of a TC relative to true north. An alternate way to describe TC tornado azimuth is relative to the TC’s forward motion (e.g., McCaul 1991). While both methods generally have yielded similar results (partly because many TCs considered in past climatologies generally have moved northward), azimuths relative to true north appear to correlate somewhat better with tornado occurrence than those relative to storm motion (Gentry 1983; Schultz and Cecil 2009). We tested both methods and found that the north-relative azimuths produced slightly better correlations with our TCs (0.48 vs 0.47). Therefore, that approach was used here.

Variable 5 described the intensity of the parent TC. Relatively strong TCs generally have been found to yield greater numbers of tornadoes than weaker TCs (Novlan and Gray 1974; McCaul 1991). While minimum central pressure and accumulated cyclone energy (ACE; Bell et al. 2000) have been used to define TC intensity, we chose maximum sustained wind as used in NHC advisories. Specifically, we defined the TC intensity associated with each tornado report as the maximum sustained wind of the parent TC in time and space.

The remaining 22 potential predictors in Table 2 were calculated from RUC analyses. It is important to note that model-derived data such as RUC generally do not adequately resolve the smaller-scale features of TCs. For example, RUC often produces errors in minimum central pressure that in extreme cases may be 20 hPa (W. Ramstrom 2007, unpublished manuscript). Improperly representing the dry-air intrusion that has been related to TC tornado occurrence is another example of model limitations (Hill et al. 1966; Novlan and Gray 1974; McCaul 1987; Curtis 2004; Baker et al. 2009). Although this inadequacy hinders our ability to understand and forecast TC-related tornadogenesis, we believe that RUC does contain information that can be used to provide statistical guidance regarding the probability of tornado occurrence (Davies 2006).

CAPE was defined using three different surface-based layers: RUC-defined, 1000–950 hPa, and 1000–900 hPa. RUC-defined CAPE (Benjamin et al. 2002; Hamill and Church 2000) is the energy available to the most buoyant parcel within 300 hPa of the surface. The two other layers considered parcels whose characteristics had been linearly averaged between 1000 and 950 or 900 hPa. Of the three versions of CAPE tested, CAPE between 1000 and 950 hPa produced slightly better correlation (0.17) with the tornado reports (TREPS; Table 2), that is, a weak positive correlation with tornado occurrence. This suggests that instability very near the surface is most crucial for TC-related tornadoes. Deeper layers (such as the 1000–900-hPa layer) may contain instability in the upper portion of the layer and not near the surface. This situation appears to be less supportive of tornadoes.

Vector wind shear over three layers, 0–1, 0–3, and 0–6 km AGL, was calculated. Although 0–6-km shear often is a good measure of supercell potential in the middle latitudes (e.g., STP uses 0–6-km shear), we hypothesized that lower-level shear might correlate better with TC tornado occurrence. The results (Table 2) indeed show that 0–3-km shear correlates slightly better with TREPS (0.51) than its 0–6-km counterpart (0.48), which correlates slightly better than 0–1-km shear (0.47).

Storm-relative helicity (SRH) was included in the predictor pool. We assumed that supercells in a TC environment will deviate less from the mean wind than in midlatitude cases (i.e., less than the often assumed 30° to the right of the mean wind). Therefore, we calculated SRH using the Bunkers method (Bunkers et al. 2000) for estimating the motion of supercells. SRH is given by
e1
where , and , represent the u and υ wind components at the bottom (the surface) and the top (either 1 or 3 km) of the layer, respectively. Also, and are the u and υ components of storm motion defined as
e2
e3
where and are the mean 0–6-km u and υ wind components, represents the shear over a depth from 0 to Z km, and () represents the difference between u (υ) at 10 m and Z km. SRH between 0 and 3 km (SRH03) was found to give slightly better results (0.50 vs 0.49; Table 2).

Midlevel temperature and relative humidity also were considered. RUC-derived temperature (K) and relative humidity (%) were averaged over 50-hPa layers between 800 and 500 hPa for each grid cell. The temperatures were found to correlate poorly (Table 2) with tornado occurrence (correlation coefficients of approximately 0.015), perhaps because of their small range of values. For example, all tornadoes occurred with 700-hPa temperatures between 277 and 286 K. Results showed that RUC-derived midlevel relative humidity correlated slightly better, ranging from 0.04 (800 hPa) to 0.08 (500 hPa). Previous studies (e.g., McCaul and Weisman 1996; Davies 2006) focused on shallower layers, as did we; however, future derivations of TCTP may benefit from consideration of upper-level parameters.

c. Statistical methods

We used a combination of multiple linear regression and logistic regression to develop the TC tornado probability guidance product. The dependent variable was binary, indicating if at least one tornado was reported in each 160 × 160 km2 grid box during a 6-h period (1 for yes or 0 for no). The 6-h period was centered on the forecast time (i.e., from 3 h before to 3 h after). This choice assumes that tornadoes during the 6-h period are related to conditions at the forecast time (the center of the 6-h interval). Each reported tornado that met these criteria and was located within 750 km of the TC’s center was used.

Before using the regression technique, we computed cross correlations (not shown) between the potential predictors to ensure that the final equation would not be overfit to the data. The goodness of a regression equation can be increased by accepting as many predictors as possible until all or most of the variance is explained. Although this improves the fit to the dependent data, it may not add predictive skill when applied to independent data and may actually reduce the skill (Wilks 2006). Therefore, “duplicate” predictors were not allowed (e.g., temperature at two different levels). However, several exceptions were made for specific reasons. For example, 0–3-km shear and 0–3-km SRH had a cross-correlation coefficient of 0.725. Both were retained because of their large correlation with TREPS and their physical relevance to tornado occurrence. The cross correlation between SRH03 and the tornado azimuth (AZIM) was 0.567, probably because SRH typically is maximized in the northeast quadrant. Both terms were retained because SRH is not always greatest in the northeast quadrant, and the potential for tornadoes can be greatest in other quadrants (see the Hermine case in the results section). All remaining cross-correlation coefficients were less than 0.5. The relatively small cross correlation between TC variables such as TC intensity (maximum sustained winds) and the RUC-derived variables (e.g., shear and SRH) was an early concern because the magnitudes of shear parameters should be related to the intensity of TCs. Since the cross-correlation coefficient between TC intensity and TREPS was found to be small (0.107), TC intensity was not selected as a predictor. Finally, we scrutinized each potential predictor to ensure that it had physical relevance and a correlation sign (positive vs negative) that was appropriate. After performing these tests, six predictors remained (Table 3).

Table 3.

The final predictors, their correlations with TREPS, coefficients for the multinomial linear regression [see Eq. (4)], and each predictor’s maximum, minimum, mean, and standard deviation.

Table 3.

Stepwise multiple linear regression (Wilks 2006) is a powerful statistical technique for deriving relationships between a set of independent variables and the dependent variable. We chose this approach because of its ability to identify the relative importance of our potential predictors. By evaluating each predictor with tornado occurrence (dependent variable), the variable with the strongest relationship is selected as the first predictor, with each remaining variable then evaluated for its additional contribution to explaining variance in the dependent variable. Because three variables (azimuth, distance from TC center, and time of day) were found to have nonlinear relationships with tornado occurrence, these variables were reconstructed before using multiple linear regression. Distance was redefined as the absolute value of the distance away from the optimal distance, which was found to be 300 km. The optimal distance was determined by binning all the distances from TC centers to tornado reports. The bin distribution peaked at 300 km. Azimuth and time of day were fit to Fourier functions using MATLAB’s Fourier fit function. Figure 2 shows the distribution of azimuth angle and the corresponding Fourier function. By reconstructing the azimuth data, the magnitude of the Fourier function now varies linearly with the likelihood of at least one tornado (i.e., larger magnitude corresponds to greater likelihood of a tornado).

Fig. 2.
Fig. 2.

Fourier function used to reconstruct the azimuth data. The azimuth data are binned, with the magnitude of the Fourier function corresponding to the likelihood of at least one tornado in each bin. Values closer to 1 indicate a greater tornado potential.

Citation: Weather and Forecasting 29, 5; 10.1175/WAF-D-13-00086.1

Logistic regression has been used widely in situations when the predictor is binary (e.g., Wilks 2009; Shafer and Fuelberg 2006; Crosby et al. 1995) Once the six variables most correlated with TREPS were identified using stepwise multiple linear regression, they were passed to the binary logistic scheme to generate a relationship between the predictors and the probability of one or more tornadoes in a grid box during a 6-h period. Multinomial logistic regression is defined as
e4
where [ represents the correlation coefficients for (k = 6 in this study because there are six predictors)], and is the probability of at least one tornado in a grid box. The values for are listed in the coefficient column of Table 3. Equation (4) represents the “final product” and is used to generate the forecasts shown later (see Figs. 4, 6, 8, and 10).

We wanted to compare results from our newly developed TCTP equation with those from SPC tornado probability forecasts. SPC generates tornado probability forecasts within 25 mi (40.2 km) of each location in the United States five times daily. Therefore, we calculated similar forecasts (using logistic regression) by converting the percentage chance of a tornado in our 160 × 160 km2 grid cells (9884 mi2) to the probability within 25 mi (1963 mi2). Once calculated, the major remaining difference between the two forecasts is that TCTP probabilities cover 6-h periods while SPC forecasts are for longer periods (typically between 6 and 24 h). Although it is possible to combine the probabilities from four 6-h TCTP forecasts into one 24-h product, this would not directly compare to SPC 24-h products because RUC [now Rapid Refresh (RAP) model] forecasts only extend to 12 (now 18) h. However the 6-h TCTP forecast periods provide forecasters with some insight into specifically which time periods may yield the highest likelihood of tornadoes. Some additional discussion about the implications for verification is provided in the results section. Average Brier scores and Brier skill scores (Wilks 2006) for the SPC and TCTP forecasts were calculated to determine their relative forecast accuracies. The climatologies needed to calculate Brier skill scores were defined as the average number of tornadoes occurring in a grid cell during a 6-h period during a landfalling TC (0.0125 tornadoes). This average was calculated using all grid cells during the 9-yr study period.

3. Results

a. Statistical summary

Table 3 statistically describes the terms of the TCTP formulation, showing the six predictors along with their correlations with TREPS (repeated from Table 2), their coefficients in the TCTP multinomial regression equation, and their maxima, minima, means, and standard deviations. In decreasing order of correlation with tornado occurrence, the predictors are 0–3-km shear (SHEAR03), 0–3-km SRH (SRH03), reconstructed azimuth angle (Fig. 2), reconstructed distance from the TC’s center, reconstructed hour relative to 1200 UTC, and 950–1000-hPa CAPE. Since SHEAR03 and SRH03 have the greatest correlation with TREPS, they are the most influential in the final TCTP equation. The importance of wind shear to TC-related tornado development is consistent with the findings of McCaul (1987, 1991).

Receiver operator characteristics (ROC; e.g., Harvey et al. 1992) were calculated for each of the six predictors (Fig. 3). The area below each ROC curve, along with its asymptotic significance, also was determined. The 0.5-area reference line (light blue diagonal line in Fig. 3) represents the null hypothesis. Confidence in statistical significance increases as the predictor lines depart from (above or below) the 0.5 reference line. The ROC analysis shows that the six predictors selected by logistic regression vary considerably from the 0.5-area null hypothesis, with the possible exception of 950–1000-hPa CAPE. Table 4 shows the area under the ROC curve for each of the final predictors along with each predictor’s ROC significance statistics. Areas for hours relative to 1200 UTC and 950–1000-hPa CAPE are closest to the area of 0.5, with 950–1000-hPa CAPE yielding an asymptotic significance greater than 0.05 (0.377). While this suggests that 950–1000-hPa CAPE is less statistically significant, it was retained in the logistic regression scheme because it passed significance tests performed as part of the multiple linear regression.

Fig. 3.
Fig. 3.

ROC curve for the six predictors along with the 0.5-area diagonal reference line (light blue) that denotes the null hypothesis.

Citation: Weather and Forecasting 29, 5; 10.1175/WAF-D-13-00086.1

Table 4.

Area under the ROC curve statistics. The standard error denotes the nonparametric assumption, whereas the asymptotic significance represents a case in which the null hypothesis is true.

Table 4.

Mean Brier scores and Brier skill scores (Wilks 2006) for the SPC and TCTP tornado probability forecasts for the dependent dataset are shown in Table 5. The Brier score is a very useful metric when considering forecasts with binary outcomes (e.g., tornado versus no tornado). The Brier scores are based on 29 tropical cyclones, which yielded 240 grid cells in which a tornado occurred. The SPC forecasts exhibit slightly better Brier scores than TCTP (0.0016 vs 0.0048). An important reason for our somewhat poorer scores is that SPC forecasters add skill to their guidance products when preparing the final forecasts, whereas TCTP has not been modified by forecasters. Another reason is that the SPC forecasts cover longer time periods than TCTP. There is a greater chance that a tornado will occur during a longer time period (SPC 24-h verification period) than a shorter one (TCTP 6-h verification period), making probability forecasting easier for the longer period.

Table 5.

Mean Brier score and Brier skill score for TCTP and SPC forecasts.

Table 5.

Four cases now are examined in detail: Hurricane Ike (2008) from the dependent dataset and Tropical Storms Hermine (2010), Lee (2011), and Debby (2012) from independent data beyond the 2000–08 study period. It is important to test TCTP on independent data; however, our choice of these cases was limited because there have been few landfalling TCs in the study area since 2008. The four cases represent different TC types, with Ike being a large hurricane and Hermine, Lee, and Debby being modestly strong tropical storms. The number of tornadoes contributed by each storm is shown in the figures that follow, along with the number of strong tornadoes (EF2 or stronger).

b. Case 1—Ike (2008)

Hurricane Ike began as a depression in the tropical Atlantic on 2 September 2008. After passing through the Caribbean, it emerged into the Gulf of Mexico before making landfall along the northeastern coast of Texas on 13 September. Ike was a large, annular hurricane as it passed through the Gulf and at landfall, allowing the effects of the system to extend outward to large radii. After making landfall, Ike turned northward and passed east of Dallas, Texas, before weakening and becoming extratropical over northern Arkansas. During the morning hours of 14 September, Ike gradually was absorbed into a trough that extended southwestward from the Great Lakes. Instability remained small in regions of the tornadoes, with CAPE less than 700 J kg−1. However, SHEAR03 was about 60 knots (kt; ~30.9 m s−1) in the northeast quadrant at the time of landfall, decreasing to about 50 kt (~25.7 m s−1) by early on 14 September. SRH03 in the northeast quadrant of Ike ranged from about 240 to 400 m2 s−2 at landfall, decreasing to 150–250 m2 s−2 by 0000 UTC 14 September.

Ike contributed 32 of the 483 tornadoes to our study, including one EF2 tornado. The first tornado associated with Ike was near Key Largo, Florida, at approximately 1100 UTC 9 September as the storm passed over western Cuba. The last reported tornado was at 1900 UTC 13 September near Gansville, Louisiana. Thus, 29 of the 32 tornadoes occurred between landfall (0600 UTC) and 1900 UTC 13 September. NHC reported that Ike contained maximum sustained winds of 95 kt (48.9 m s−1) about 6 h prior to landfall at 0000 UTC 13 September. These winds decreased to 35 kt (18.0 m s−1) by 0000 UTC 14 September as Ike neared the border of Texas and Arkansas.

The time series of TCTP 6-h forecast periods in Fig. 4 are valid 12 h after the analyses. For example, when considering Fig. 4a, a 12-h forecast from the 0000 UTC model cycle yields the 6-h forecast period which is valid between 0900 and 1500 UTC (centered on 1200 UTC). Tornado reports from each 6-h period are overlaid (red dots) as is Ike’s position (purple star). TCTP forecasts a large region of greater than 10% probability of a tornado within 25 mi (Fig. 4f) at 1800 UTC 13 September (period of peak tornado production) when Ike was approximately 100 km southeast of Dallas, Texas. During this period, 21 tornadoes were observed in Ike’s northeast quadrant. The forecasts generally show good spatial agreement with observed tornado locations. TCTP is greatest over northern Louisiana and southern Arkansas, in Ike’s northeast quadrant, where tornado reports climatologically are most common. Thus, in the case of Hurricane Ike, the RUC-based TCTP appears to accurately forecast the maximum region of tornadic potential.

Fig. 4.
Fig. 4.

Time series of TCTP 6-h forecast periods for Hurricane Ike (2008) from (a) 1200 UTC 12 Sep to (f) 1800 UTC 13 Sep 2008. Each 6-h forecast period is centered on 12 h after the analysis time (i.e., ±3 h from the valid time displayed). Red dots represent locations of tornado reports from 3 h before to 3 h after each forecast time, while the purple star indicates the position of Ike. The units of TCTP are the percentage probability of a tornado within 25 mi during a 6-h period.

Citation: Weather and Forecasting 29, 5; 10.1175/WAF-D-13-00086.1

The forecasts, extending from 1200 UTC 12 September to 1800 UTC 13 September, exhibit good spatial continuity, with gradually increasing probabilities during the period. TCTP slightly overforecasts the number of tornadoes near the time of landfall (0600 UTC 13 September; Fig. 4d). Specifically, a 5% tornado probability is forecast for much of Louisiana where no tornadoes are observed. However, it is possible that weak tornadoes did occur between the overnight hours of 0300 and 0900 UTC 13 September. Radar data from this time period (not shown) indicate several strong storm cells moving through central Louisiana in an outer band that exhibited radial velocity couplets, indicating mesocyclones that could have produced unreported, probably weak tornadoes. The area of greatest tornado expectation moves slowly northward, consistent with Ike’s forward motion and remaining in the climatologically favored right-front quadrant. The maximum forecast value at 1200 UTC 12 September is between 5% and 10%, which increases to 10%–15% at 1800 UTC 13 September, although the general trend appears to be a slight overforecast of the number of tornadoes (e.g., 10%–15% at 1800 UTC 12 September when two are observed and 5%–10% at 0600 UTC 13 September when none are observed). The forecast at 1800 UTC 13 September correctly indicates values in the 10%–15% range when 21 tornadoes are observed. TCTP is greatest over land areas where shear is greatest, even when Ike is offshore (not shown). These enhanced TCTP values are attributed to low-level shear, which is greater over land than water due to increased boundary layer friction, consistent with the results of Knupp et al. (2006) and Green et al. (2011).

The SPC tornado probability forecasts also are quite good during Ike. Figure 5 shows the SPC tornado probability forecast issued at 1610 UTC 13 September (valid from 1630 UTC 13 September to 1200 UTC 14 September). A large area of at least 5% tornado probability is forecast for the northeast quadrant of Ike where 23 tornadoes were reported during the advisory period covered by the 1610 UTC issuance.

Fig. 5.
Fig. 5.

SPC tornado probability forecast issued at 1610 UTC 13 Sep 2008. The tan line outlines regions with at least a 5% probability of tornadoes within 25 mi, while the green line outlines regions of 2%–5% risk. The forecast is valid from 1630 UTC 13 Sep to 1200 UTC 14 Sep 2008.

Citation: Weather and Forecasting 29, 5; 10.1175/WAF-D-13-00086.1

c. Case 2—Hermine (2010)

Hermine developed into a depression in the western Bay of Campeche during the afternoon of 5 September 2010. It moved north-northwestward and gradually intensified into a tropical storm before making landfall in far northeastern Mexico with a peak intensity of about 60 kt (~30.9 m s−1) at 0200 UTC 7 September. Hermine was unusual in that most of its tornadoes occurred far from the coast and over 24 h after landfall. Hermine spawned 3 tornadoes on 7 September and 11 tornadoes on 8 September, including one EF2 on 8 September. Figure 6 shows a time series of TCTP 6 h forecast periods with tornado reports overlaid. TCTP generally well forecasts regions of tornadic potential, with the exception of a large region of overforecast probability at 0000 UTC 8 September. Three tornadoes occur in regions of less than 2% during Hermine; however, each was rated EF0. Particularly interesting are the forecasts valid at 1800 UTC 8 September and 0000 UTC 9 September (Figs. 6e,f) when TCTP forecasts the greatest probabilities east-southeast of Hermine’s center (i.e., outside the most common front-right quadrant). However, this is indeed where the tornadoes were reported during the 6-h periods encompassing these forecast times.

Fig. 6.
Fig. 6.

Time series of TCTP 6-h forecast periods during Tropical Storm Hermine (2010) from (a) 1800 UTC 7 Sep to (f) 0000 UTC 9 Sep 2010. Each 6-h forecast period is centered on 12 h after the analysis time (i.e., ±3 h from the valid time displayed). Red dots represent locations of tornado reports from 3 h before to 3 h after each forecast time, and the purple stars indicate the position of Hermine. The units of TCTP are the percentage probability of a tornado within 25 mi during a 6-h period.

Citation: Weather and Forecasting 29, 5; 10.1175/WAF-D-13-00086.1

Figure 7 shows the SPC tornado probability forecast issued at 1200 UTC 8 September 2010 (valid from 1200 UTC 8 September to 1200 UTC 9 September 2010), the same time as the TCTP forecast valid at 0000 UTC 9 September (Fig. 6f). Unlike the SPC forecast, TCTP does not overforecast the probability of tornadoes in northern Oklahoma. This is a good example of when TCTP may have served as a useful guide for locating regions requiring extra forecaster scrutiny. Results from Hermine suggest that TCTP forecasts retain value even more than 24 h after TC landfall.

Fig. 7.
Fig. 7.

SPC tornado probability forecast issued at 1200 UTC 8 Sep 2010. The green line outlines regions of 2%–5% risk. The forecast is valid from 1200 UTC 8 Sep to 1200 UTC 9 Sep 2010.

Citation: Weather and Forecasting 29, 5; 10.1175/WAF-D-13-00086.1

d. Case 3—Lee (2011)

Lee formed from a depression approximately 350 km southwest of the mouth of the Mississippi River at 0000 UTC 2 September. Lee moved north-northeastward over the next 2 days and reached a maximum intensity of 50 kt (25.7 m s−1) despite encountering westerly shear of about 20 kt (~10.3 m s−1). By 1200 UTC 3 September, NHC determined that Lee was best classified as a subtropical storm. Lee made landfall as a subtropical storm with a maximum wind speed of 40 kt (20.6 m s−1) early on 4 September along the southern coast of Louisiana about 18 km south-southeast of Intracoastal City, Louisiana. The storm then became quasi-stationary over south-central Louisiana late on 4 September and weakened slightly, although retaining an area of 35 kt (18.0 m s−1) winds over the northern Gulf of Mexico. Lee merged with a cold front early on 5 September and became extratropical by 0600 UTC 5 September (Brown 2011). Seventeen tornadoes were reported in association with Subtropical Storm Lee including eight EF1 and nine EF0 tornadoes. No strong tornadoes were reported.

Figure 8 is a time series of TCTP 6-h forecast periods with tornado reports overlaid. TCTP produces reasonably accurate forecasts for three of the six periods shown. It underforecasts tornado potential at 1200 UTC 4 September when Lee produces four tornadoes (three EF0, one EF1) during the typically quiet morning hours. These tornadoes occur primarily near the coast in regions that may be less impacted by nocturnal stability. However, as was the case in Hermine, the three tornadoes that fall outside of at least 2% probability were all rated EF0. This underforecast during the overnight and early morning hours may be an example of a limitation of TCTP forecasts. TCTP forecasts the peak in tornado potential at 0000 UTC 5 September in southern Mississippi (Fig. 8d). Tornadoes then are overforecast during the early morning hours of 5 September when no tornadoes are reported. Lee demonstrates the ability of TCTP to produce reasonably accurate forecasts even as a TC undergoes transition from a tropical storm to a subtropical storm and then becomes extratropical. Figure 9 shows the SPC tornado percentage forecast issued at 1200 UTC 4 September 2011 (valid from 1200 UTC 4 September to 1200 UTC 5 September 2011: concurrent with Figs. 8b–f). The SPC forecast broadly captures the regions in which tornadoes occur.

Fig. 8.
Fig. 8.

Time series of TCTP 6-h forecast periods during Tropical Storm Lee (2011) from (a) 0600 UTC 4 Sep to (f) 1200 UTC 5 Sep 2011. Each 6-h forecast period is centered on 12 h after the analysis time (i.e., ±3 h from the valid time displayed). Red dots represent locations of tornado reports from 3 h before to 3 h after each forecast time, and the purple stars indicate the position of Lee. The units of TCTP are the percentage probability of a tornado within 25 mi during a 6-h period.

Citation: Weather and Forecasting 29, 5; 10.1175/WAF-D-13-00086.1

Fig. 9.
Fig. 9.

SPC tornado probability forecast issued at 1200 UTC 4 Sep 2011. The green area contains regions of 2%–5% risk, while the brown area contains regions of 5%–10%. The forecast is valid from 1200 UTC 4 Sep to 1200 UTC 5 Sep 2011.

Citation: Weather and Forecasting 29, 5; 10.1175/WAF-D-13-00086.1

e. Case 4—Debby (2012)

Debby was designated a tropical storm with winds of 35 kt (18.0 m s−1) when located about 260 km south of the mouth of Mississippi River at 1200 UTC 23 June 2012. Like Lee, Debby was inhibited by modest westerly shear as it gradually intensified to a peak intensity of 55 kt (28.3 m s−1) on 24 June. A combination of dry air, increasing westerly shear, and upwelling of cold shelf waters weakened Debby on 25 June before making landfall at 2100 UTC 26 June near Steinhatchee, Florida, with maximum sustained winds of 35 kt (18.0 m s−1) (Kimberlain 2013). Debby was a large system that produced tornadoes far from its center while over the eastern Gulf of Mexico. Debby’s most active tornadic period was centered on 1800 UTC 24 June while located 360 km west of Tampa, Florida. A total of 25 tornadoes were produced (all in Florida), including 1 EF2 and 5 EF1 tornadoes.

Figure 10 is a time series of TCTP 6-h forecast periods with tornado reports overlaid. The time series begins with a forecast valid at 0600 UTC 24 June and ends at 1200 UTC 25 June. TCTP forecasts are quite good during Debby since they do not overforecast tornado potential prior to or after the storm’s most prolific period. There is a slight underforecast at 1200 UTC 24 June when three tornadoes occur in areas where less than 2% is forecast. However, like the previous cases, all of Debby’s tornadoes that are outside of at least 2% probability were rated EF0. Tornadoes are particularly well forecasted during the remaining periods from 1800 UTC 24 to 1200 UTC 25 June. Seven of the 11 tornadoes between 1500 and 2100 UTC 24 June occur in areas where TCTP forecasts at least 2% probability. At 0000 UTC 25 June, all eight tornadoes occur within at least 5% probability, and seven of the eight occur in areas of at least 10% probability. TCTP then forecasts diminished probabilities that correspond to the abrupt absence of tornadoes after 0300 UTC 25 June. Figure 11 shows the SPC tornado percentage forecast issued at 1200 UTC 24 June 2012 (valid from 1200 UTC 24 June to 1200 UTC 25 June 2012: concurrent with Figs. 10b–f). TCTP forecasts are superior to the SPC forecast during this period. It should be noted that SPC did upgrade much of the Florida Peninsula to at least 5% with its 1630 UTC 24 June 2012 update to reflect the reports of ongoing tornadoes.

Fig. 10.
Fig. 10.

Time series of TCTP 6-h forecast periods during Tropical Storm Debby (2012) from (a) 0600 UTC 24 Jun to (f) 1200 UTC 25 Jun 2012. Each 6-h forecast period is centered on 12 h after the analysis time (i.e., ±3 h from the valid time displayed). Red dots represent locations of tornado reports from 3 h before to 3 h after each forecast time, and the purple stars indicate the position of Debby. The units of TCTP are the percentage probability of a tornado within 25 mi during a 6-h period.

Citation: Weather and Forecasting 29, 5; 10.1175/WAF-D-13-00086.1

Fig. 11.
Fig. 11.

SPC tornado probability forecast issued at 1200 UTC 24 Jun 2012. The green area contains regions of 2%–5% risk, while the brown area contains regions of 5%–10%. The forecast is valid from 1200 UTC 24 Jun to 1200 UTC 25 Jun 2012.

Citation: Weather and Forecasting 29, 5; 10.1175/WAF-D-13-00086.1

4. Summary and conclusions

We have developed a statistical parameter to use as guidance for forecasting the likelihood of tornadoes in the environments of landfalling tropical cyclones along the Gulf Coast, the eastern coast of Florida, and the coasts of Georgia and South Carolina. We hypothesized that a composite index tuned specifically to the TC environment would assist in forecasting TC-related tornadoes and would add insight into the physical processes governing their development. A total of 483 TC-related tornado reports from 29 storms occurring between 2000 and 2008 were used to derive the tropical cyclone tornado parameter (TCTP). Both geographic and TC environmental parameters were used to develop the guidance product. Geographic parameters described the locations and timing of the tornadoes with respect to the parent TC. The pool of potential TC environment parameters was obtained from RUC model analyses. They included measures of temperature, humidity, stability, and wind shear. Stepwise multiple linear regression then was used to isolate six parameters that were best related to tornado occurrence. The resulting equation comprised the TCTP. ROC analysis showed that five of the six predictors differed significantly from the 0.5-area null hypothesis, lending confidence to the relevance of each predictor. Although 950–1000-hPa CAPE did not pass the null hypothesis test in the ROC analysis, it was selected by the regression techniques used to derive TCTP.

TCTP first was tested on the dependent cases from which it was derived. Brier scores and Brier skill scores showed that SPC forecasts are somewhat more accurate than TCTP forecasts. However, this likely is due in part to SPC forecasts covering longer time periods and because human skill is incorporated into their preparation.

TCTP then was applied to four tropical cyclones that differed in size, intensity, and the number of tornadoes that they produced. These storms were Hurricane Ike (2008), Tropical Storm Hermine (2010), Tropical Storm Lee (2011), and Tropical Storm Debby (2012). The latter three storms occurred after our study period. Forecast tornado probabilities were compared with the number of tornadoes that actually occurred and with Storm Prediction Center tornado probability forecasts.

The four TC cases along with the statistical results suggest several general findings.

  • The shear terms in TCTP (SHEAR03 and SRH03) were most correlated with tornado occurrence. Instability (CAPE) was weakly positively correlated with tornado occurrence, contrary to McCaul (1991) but consistent with Davies (2006).
  • Values of RUC-derived shear and helicity were greatest over land areas during TC landfall, leading to somewhat greater probabilities of tornadogenesis. Boundary layer friction over land is much greater than over water, leading to greater low-level shear.
  • TCTP generally exhibited good continuity between 6-h periods, increasing during times when tornado occurrence increases and decreasing otherwise.
  • TCTP recognized the northeast quadrant of TCs as the most common region of tornado potential, agreeing with previous climatologies (Sadowski 1962; Smith 1965; Pearson and Sadowski 1965; Hill et al. 1966; Novlan and Gray 1974; Gentry 1983; McCaul 1991; Verbout et al. 2007; Schultz and Cecil 2009).
  • In Hermine (2010), when tornadoes occurred primarily in the southeast quadrant, TCTP correctly identified that region as having the maximum potential to produce tornadoes.
  • A notable diurnal signal exists in TCTP forecasts in agreement with the tornado reports, which peak during afternoon hours. TCTP appears to underforecast tornado potential in coastal locations during the overnight and early morning hours, most likely because these locations experience greater stability during these hours.
  • No tornadoes rated stronger than EF0 occurred in regions of TCTP forecast probability less than 2% during the four case studies. This suggests that strong tornadoes are unlikely when TCTP forecasts less than a 2% chance of at least one tornado.

The goal of this study was to provide forecasters with a product that could improve their ability to quickly identify regions of tornadic potential in a time-limited forecast environment. Although SPC forecasts yield better Brier scores and Brier skill scores than TCTP on the dependent dataset, we believe that forecasters who would use TCTP would quickly learn its strengths and weaknesses and thereby add human skill to the TCTP guidance. A composite index of this nature certainly cannot replace the value of detailed human forecasting. Instead, TCTP is intended to forecast an envelope of tornado potential, within which detailed analysis can be performed.

Future research will be needed to determine if TCTP is useful in areas north of the current study domain since TCs are increasingly likely to have extratropical characteristics the farther north they are located. Furthermore, since most of the present study evaluated TCTP on the dataset from which it was derived (2000–08), the utility of TCTP needs much additional study with independent data. The scarcity of landfalling storms in the study area since 2008 greatly limited our ability to perform this type of investigation. Thus, the present results should be considered tentative.

Acknowledgments

The authors appreciate the helpful comments and discussions with Steven Weiss, Irv Watson, Roger Edwards, and Daniel Cecil that substantially improved the study. The anonymous reviewers provided useful comments that clarified the original manuscript. This research was supported by the Florida Catastrophic Storm Risk Management Center at Florida State University that was created by the Florida Legislature.

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