Topography and Land-Cover Effects on Tornado Intensity using Rapid-Scan Mobile. Radar Observations and Geographic Information Systems

Transcription

1 Topography and Land-Cover Effects on Tornado Intensity using Rapid-Scan Mobile Radar Observations and Geographic Information Systems A thesis presented to the faculty of the College of Arts and Sciences of Ohio University In partial fulfillment of the requirements for the degree Master of Science Nathaniel L. McGinnis December Nathaniel L. McGinnis. All Rights Reserved.

2 2 This thesis titled Topography and Land-Cover Effects on Tornado Intensity using Rapid-Scan Mobile Radar Observations and Geographic Information Systems by NATHANIEL L. MCGINNIS has been approved for the Department of Geography and the College of Arts and Sciences by Jana L. Houser Assistant Professor of Geography Robert Frank Dean, College of Arts and Sciences

3 3 ABSTRACT MCGINNIS, NATHANIEL L., M.S., December 2016, Geography Topography and Land-Cover Effects on Tornado Intensity using Rapid-Scan Mobile Radar Observations and Geographic Information Systems Director of Thesis: Jana L. Houser High spatio-temporal datasets collected by two rapid-scan, mobile, Doppler radars (the University of Oklahoma s rapid-scan, X-band, polarimetric (RaXPol) radar and the Naval Post-Graduate School s Mobile Weather Radar 2005 X-Band Phased Array (MWR-05XP)) are used to investigate the relationships between tornado intensity and land cover type. Through the application of Geographic Information System techniques, elevation, slope, and aspect values are derived using the United States Geological Survey s Digital Elevation Model. Additionally, surface roughness values are extracted using land-cover data from the USGS National Land-Cover Database and surface roughness values from the Environmental Protection Agency AERSURFACE User s Guide. The extracted topographic and surface roughness values are then compared to the intensity values ( Vmax) obtained through radar analysis. Linear correlations, comparison of means, and multiple linear regression techniques are used to test the significance of the data in order to determine the possible relationships between tornado intensity and topography/land-cover. While significant statistical relationships are found using these techniques, the relationships do not favor a specific direction and often reversed between cases. However, based upon the results from the multiple linear regression it is hypothesized that the radar beam height was a strong predictor of tornado intensity for

4 4 these particular cases, which implies that over all of the topographic and land-cover variables, the tornado intensity observed was significantly influenced by the location of the radar s lowest-level beam height. Nevertheless, several unique topography/land-cover features did appear to affect tornado intensity, encouraging the continued investigation of the potential relationships, despite the contradicting statistical relationships found here.

5 5 ACKNOWLEDGMENTS Over the last two years, I have had the greatest privilege serving the Scalia Lab as Associate Director while completing my master s degree. The journey was long, and there are many people that assisted me along the way. Firstly, to Dr. Ryan Fogt, thank you for allowing me the opportunity to serve the Scalia Lab. It truly was a great honor to carry that role, and I will never forget the many things holding that position as taught me. Additionally, your passion as an instructor and an advisor creates an environment where the program can thrive. I look forward to seeing the future growth of the program! To Dr. James Lein, thank you for your challenging insight and sincere investment into the furthering of my education. Your classes encouraged creativity which allowed me to develop and strengthen skills that will contribute to my future career. To Dr. Jana Houser, your expertise and passion for severe weather motivates every student you come into contact with. I am extremely grateful for the opportunities you provided to me over the last two years for which many had been lifelong dreams. I would also like to thank you for your inspiration regarding this thesis. As an advisor, you were always there to provide knowledge and ideas. I appreciate the many hours you spent assisting me with this project. It has and will continue to be an honor working with you. To my friends, Doug, Chad, Megan, and Hallie, the laughter during all of our adventures provided an escape from the stresses of graduate school. I can t imagine what the journey would have been like without you all.

6 6 To my family, your love and encouragement pushed me through one of the biggest hurdles in my life. Through my moments of doubt, your words and prayers inspired me to continue on. Lastly, to my girlfriend Toni, these simple words do not cover the patience you graced me with over the last two years. Your love has been steadfast through all of my personal endeavors, and I can t thank you enough.

7 7 TABLE OF CONTENTS Page Abstract 3 Acknowledgments 5 List of Tables...9 List of Figures 14 Chapter 1: Introduction and Motivation Introduction Motivation 21 Chapter 2: Literature Review Tornado Structure Elevation and Land-Cover Effects Elevation Land-Cover Storm Mechanisms..45 Chapter 3: Instrumentation and Methodology Instrumentation Methodology Radar Analysis GIS Analysis Statistical Analysis Case Studies Goshen County, Wyoming- 5 June Lookeba, Oklahoma- 24 May El Reno/Piedmont, Oklahoma- 24 May Carney, Oklahoma- 19 May Shawnee, Oklahoma- 19 May Instrumentation and Methodology Limitations...83 Chapter 4: Results..89

8 8 4.1 Individual Cases Goshen County, Wyoming- 5 June Lookeba, Oklahoma- 24 May El Reno/Piedmont, Oklahoma- 24 May Carney, Oklahoma- 19 May Shawnee, Oklahoma- 19 May Cumulative Review 181 Chapter 5: Discussion..191 Chapter 6: Conclusion..199 References 205

9 9 LIST OF TABLES Page Table 3.1: Basic information regarding the differences between the WSR-88D (Crum and Alberty 1993) and the two mobile radars, RaXPol (Pazmany et al. 2013) and MWR- 05XP (Bluestein et al. 2010) Table 3.2: Surface roughness lengths from EPA s AERSURFACE User s Guide organized according to the 2011 land-cover data from NLCD Table 3.3: Information summary regarding the time periods analyzed for the Goshen tornado. Tornadogenesis or Tornado Dissipation categories with N/A indicate that those processes were not associated with those periods Table 3.4: As in Table 3.3, but the Lookeba tornado Table 3.5: As in Table 3.3, but for the data collected by RaXPol during the El Reno tornado Table 3.6: As in Table 3.3, but for the data collected by the MWR-05XP during the El Reno tornado Table 3.7: As in Table 3.3, but for the Carney tornado Table 3.8: As in Table 3.3, but for the Shawnee tornado Table 4.1: A summary of basic information for the second period of the Goshen County, WY case Table 4.2: A summary of correlations and the associated probabilities for the topographic parameter, elevation, slope, and aspect. Bolded values are significant (p < 0.05 for a twotailed t-test) Table 4.3: Unstandardized coefficient summary from the multiple linear regression output containing the coefficient value, standard error, t-value, and probability for each variable used in test 1 (all predictors available are used). Probability values that are significant at the 95% confidence interval (p < 0.05) are bolded Table 4.4: As in test 1, but excluding beam height (test 2) Table 4.5: As in Table 4.1, but for the third observational period

10 Table 4.6: As in Table 4.2, but for the second period of the Goshen case Table 4.7: As in Table 4.3, but for time period Table 4.8: As in Table 4.4 but for time period Table 4.9: As in Table 4.1, but for the Lookeba, OK tornado Table 4.10: As in Table 4.2, but for Lookeba, OK tornado Table 4.11: As in Table 4.2, but for the surface roughness parameters of the Lookeba tornado Table 4.12: As in Table 4.3, but for the Lookeba tornado Table 4.13: As in Table 4.4, but for Lookeba, OK tornado Table 4.14: As in Table 4.1, but for the first period of the El Reno, OK tornado Table 4.15: As in Table 4.2, but for first period of the El Reno, OK tornado Table 4.16: As in Table 4.11, but for the first period of the El Reno, OK tornado Table 4.17: As in Table 4.3, but for the first period of the El Reno, OK tornado Table 4.18: As in Table 4.4, but for the first period of the El Reno, OK tornado Table 4.19: As in Table 4.1, but for the second period of the El Reno, OK tornado Table 4.20: As in Table 4.2, but for the second period of the El Reno, OK tornado Table 4.21: As in Table 4.11, but for the second period of the El Reno, OK tornado Table 4.22: As in Table 4.3, but for the second period of the El Reno, OK tornado Table 4.23: As in Table 4.11, but for the second period of the El Reno, OK tornado Table 4.24: As in Table 4.1, but for the third period of the El Reno, OK tornado Table 4.25: As in Table 4.2, but for the third period of the El Reno, OK tornado

11 11 Table 4.26: As in Table 4.11, but for the third period of the El Reno, OK tornado Table 4.27: As in Table 4.3, but for the third period of the El Reno, OK tornado Table 4.28: As in Table 4.4, but for the third period of the El Reno, OK tornado Table 4.29: As in Table 4.1, but for the fourth period of the El Reno, OK tornado Table 4.30: As in Table 4.2, but for the fourth period of the El Reno, OK tornado Table 4.31: As in Table 4.11, but for the fourth period of the El Reno, OK tornado Table 4.32: As in Table 4.3, but for the fourth period of the El Reno, OK tornado Table 4.33: As in Table 4.4, but for the fourth period of the El Reno, OK tornado Table 4.34: As in Table 4.1, but for the fifth period of the El Reno, OK tornado Table 4.35: As in Table 4.2, but for the fifth period of the El Reno, OK tornado Table 4.36: As in Table 4.11, but for the fifth period of the El Reno, OK tornado Table 4.37: As in Table 4.3, but for the fifth period of the El Reno, OK tornado Table 4.38: As in Table 4.4, but for the fifth period of the El Reno, OK tornado Table 4.39: As in Table 4.1, but for the Carney, OK tornado Table 4.40: As in Table 4.2, but for the Carney, OK tornado Table 4.41: As in Table 4.11, but for the Carney, OK tornado Table 4.42: As in Table 4.3, but for the Carney, OK tornado Table 4.43: As in Table 4.4, but for the Carney, OK tornado Table 4.44: As in Table 4.1, but for the first period of the Shawnee, OK tornado Table 4.45: As in Table 4.2, but for the first period of the Shawnee, OK tornado Table 4.46: As in Table 4.11, but for the first period of the Shawnee, OK tornado

12 Table 4.47: As in Table 4.3, but for the first period of the Shawnee, OK tornado Table 4.48: As in Table 4.4, but for the first period of the Shawnee, OK tornado Table 4.49: As in Table 4.1, but for the third period of the Shawnee, OK tornado Table 4.50: As in Table 4.2, but for the third period of the Shawnee, OK tornado Table 4.51: As in Table 4.11, but for the third period of the Shawnee, OK tornado Table 4.52: As in Table 4.3, but for the third period of the Shawnee, OK tornado Table 4.53: As in Table 4.4, but for the third period of the Shawnee, OK tornado Table 4.54: Summary of the results for the unsmoothed correlations between tornado intensity ( Vmax) and the topographic parameters: elevation, slope, and aspect for each time period. Positive correlations are green and negative correlations are red. Bold correlations are significant. Significance is quantified by a probability that is lower than the critical p-value of p < for a two-tailed t-test Table 4.55: As in Table 4.54, but for the derivative value ( Vmax / zelev), elevation change Table 4.56: As in Table 4.54, but for the surface roughness parameters, area mean, weighted mean, and weighted trimean Table 4.57:As in Table 4.56, but the derivative values ( Vmax / zrough) of all three surface roughness parameters, area mean change, weighted mean change, and weighted trimean change Table 4.58: Summary for the comparison of means test of the topographic parameters: elevation, slope, and aspect. The probabilities represent the likelihood that the means between the two intensity categories are equal. Bold probabilities are significant (p < 0.025) Table 4.59: As in Table 4.58, but for the derivative: change in intensity over elevation change ( Vmax / zelev) Table 4.60: As in Table 4.58, but for the surface roughness parameters, area mean, weighted mean, and weighted trimean

13 Table 4.61: As in Table 4.60, but the derivative values ( Vmax / zrough) of all three surface roughness parameters, area mean change, weighted mean change, and weighted trimean change Table 4.62: Summary of significant predictors of intensity from the linear regression technique for each period. Test 1 involved all predictors, and Test 2 excluded beam height. Probability values represent the likelihood of the coefficient equaling zero (b = 0). A significant threshold of p < 0.05 was applied. Cases that did not evaluate significant predictors are labeled N/A for not applicable Table 5.1: Summary of key information for each time period. Scan interval indicates how quickly the radar was scanning one volume. Beam height depicts how high with the tornado intensity ( Vmax) was derived. Elevation range specifies the magnitude of topography, and surface roughness range (area mean only) range throughout the tornado track

14 14 LIST OF FIGURES Page Figure 2.1: Idealized structure of a tornado with specific flow features divided into regions. Region 1 is the outer flow, region 2 is the boundary layer with 2a as the inertial layer and 2b as the friction layer, region 3 is the corner flow, and region 4 is the core. The corner radius or where the flow (brown streamlines) turns the corner is indicated by rc (Bluestein 2013, Figure 6.41) Figure 2.2: Force-diagram illustrating the transition from tangential flow to radial flow (curved dashed arrow) due to friction. Due to the decreasing tangential velocities, the pressure gradient force (PGF) dominates the magnitude of the centrifugal force as illustrated by the larger solid arrow (Bluestein 2013, Figure 6.42) Figure 2.3: Balance of forces within the friction layer. As the flow of air interacts with surface roughness, the flow is slowed, resulting in an outward oriented force as indicated by the friction arrow (Bluestein 2013, Figure 6.43) Figure 2.4: Idealized illustration of vorticity stretching. As a column of vorticity moves upslope, the column is forced to compress reducing vorticity. As the compressed column moves downslope, the column stretches, increasing vorticity (Prociv 2012, Figure 3.13) Figure 2.5: The transition of a vortex from one-cell to two-cell kinematic structure as swirl increases. At low swirl, the vortex consists of a central updraft along the axis. As swirl increases, a downward-directed vertical pressure gradient force produces a downdraft which splits the updraft. Eventually, the downdraft overwhelms the updraft, producing a two-celled vortex. At maximum swirl, the downdraft is surrounded by annulus updraft which produces multiple vortices (Bluestein 2013, Figure 6.55). Based on Davies-Jones (1986) Figure 2.6: Results from a numerical simulation illustrating the impacts differing levels of swirl can have on a tornado-like vortex. The shades of blue represent pressure. Darker blues indicate low pressure which is correlated to intensity (Lewellen 2014, Figure 5).. 43 Figure 2.7: Idealized supercell with archetypal storm-scale features: rear-flank downdraft (RFD), rotating updraft (UD), and forward-flank downdraft (FFD). The green area represents the expected radar echo. Typical tornado location is on the north side of the hook echo marked by the red triangle. Purple arrows are streamlines. Blue lines indicate boundaries (forward flank gust front and rear flank gust front) where horizontal vorticity is generated (Doswell 2011, Figure 2). Adapted from Lemon and Doswell (1979)

15 Figure 2.8: An illustration of tornado demise due to the advancement of the RFD through time. The RFD separates the tornado from the intersection of the RFGF, FFGF, and updraft, resulting in a weakening tornado (Marquis et al. 2012, Figure 1) Figure 2.9: Three-dimensional view of a DRC descending prior to tornado formation over the span of 15 minutes: a) 0042, b) 0047, c) 0052, and d) 0057 (Rasmussen et al. 2006, Figure 1) Figure 3.1: Dual-polarization illustration of hydrometeor identification using the horizontal (blue sinusoid) and vertical (maroon sinusoid) pulse planes (NOAA, online source 1) Figure 3.2: The 2011 land-cover legend provided by NLCD (Homer et al. 2015) Figure 3.3: A diagram illustrating the radial profile of tangential velocities associated with an idealized Rankine Vortex. Normalized radial distance is represented by R/Rx, where R is the radial distance from the vortex center and Rx is the radius at which the tangential velocity maximum Vx occurs (Wood and Brown 2011, Figure 2) Figure 3.4: An example showing the various radii, full radius (black), ¾ radius (dark grey, ½ radius (light grey), ¼ radius (black with white fill) plotted as buffers and the associated land-cover within each circle around the tornado center Figure 3.5: Designated path by National Weather Service based on damage survey for the Lookeba tornado (dark red shaded area). Yellow rectangle indicates estimated radar observed sector for time period 1 (Adapted from NOAA, online source 1) Figure 3.6: Designated path by National Weather Service based on damage survey for the El Reno/Piedmont tornado (dark red shaded area). Tornado B3 is identifying the location of a short-lived satellite tornado that was associated with the main tornado B2. The rectangles represent the estimated radar observed sectors for the five different periods: 1 st period (red), 2 nd period (orange), 3 rd period (yellow), 4 th period (green), and 5 th period (blue) (Adapted from NOAA, online source 1) Figure 3.7: Damage Assessment Toolkit analysis of Carney tornado. The shaded areas are estimated intensity ratings based on the Enhanced Fujita Scale, light blue (EF-1), yellow (EF-2), orange (EF-3). The red rectangle represents the estimated portion of the path that the radar observed for time period 1 (Adapted from NOAA, online source 2)

16 Figure 3.8: Damage Assessment Toolkit analysis of Shawnee tornado. The different colored triangles represent damage reports. The shaded areas are estimated intensity ratings based on the Enhanced Fujita Scale, light blue (EF-0), green (EF-1), yellow (EF- 2), orange (EF-3), red (EF-4). The yellow-orange rectangle is the estimated radar observed area during time period 1. The red rectangle is the estimated observed area during time period 3 (Adapted from NOAA, online source 2) Figure 3.9: An illustration depicting how the beam height changes with increased distance from the target. The RaXPol radar is mobile, while the WSR-88D is stationary. A mobile radar can approach the target from a much closer range Figure 4.1: GIS maps illustrating a) land-cover and b) elevation over the path of the tornado. For 4.1a, the center of the tornado for each scan (green dots) is overlain onto the 2011 Land Cover dataset, which for this case is primarily Grassland/Herbaceous (see legend). The grey circles represent the full radius derived from radar analysis. 4.1b consists of the same tornado path, however, the path is now overlain on the elevation dataset. Higher elevation is indicated by the dark orange and lower elevation is indicated by the dark blue Figure 4.2: Graphical representation of the relationship between elevation and intensity throughout the time period. For 20a, the unsmoothed intensity (blue line) values (left y- axis) are combined with the elevation (brown area) values (right y-axis) according to the scan number (x-axis). 20b is similar to 20a; however, a 5-scan running mean has been applied to the raw data Figure 4.3: As in Fig. 4.1, but for the third period of the Goshen County case Figure 4.4: As in Fig.4.2, except for the third observation period Figure 4.5: As in Fig. 4.1 except for the Lookeba, OK tornado. For 4.5a, circles around the tornado center (yellow dots) represent the four radii used to derive surface roughness values, full radius (black), ¾ radius (dark gray), ½ radius (light gray), and ¼ radius (white) Figure 4.6: As in Fig. 4.2, but for the Lookeba, OK tornado. For 4.6b, 3-scan running mean instead of

17 Figure 4.7: Graphical representation of the correlation between surface roughness and intensity throughout the Lookeba, OK tornado: a) unadjusted data (upper left), b) 3-scan running mean (upper right), and c) the surface roughness change vs. intensity change. For 4.7a, b, the intensity ( Vmax) is represented by the blue line, the area mean is represented by the red line, the weighted mean is represented by the gray line, and the weighted trimean is represented by the yellow line. For 4.7c, the blue line represents intensity change, the red line, area mean change, the gray line, weighted mean change, and the yellow line, weighted trimean change Figure 4.8: As in Fig. 4.5 but for the first period of the El Reno, OK tornado Figure 4.9: As in Fig. 4.6, but the first period of the El Reno, OK tornado Figure 4.10: As in Fig. 4.7, but for the first period of the El Reno, OK tornado Figure 4.11: As in Fig. 4.5, but for the second period of the El Reno, OK tornado Figure 4.12: As in Fig. 4.2, but for the second period of the El Reno, OK tornado Figure 4.13: As in Fig. 4.7, but for the period of the El Reno, OK tornado Figure 4.14: As in Fig. 4.5, but for the third period of the El Reno, OK tornado Figure 4.15: As in Fig. 4.6, but for the third period of the El Reno, OK tornado Figure 4.16: As in Fig. 4.7, but for the third period of the El Reno, OK tornado Figure 4.17: As in Fig. 4.5, but for the fourth period of the El Reno, OK tornado Figure 4.18: As in Fig. 4.6, but for the fourth period of the El Reno, OK tornado Figure 4.19: As in Fig. 4.7, but for the fourth period of the El Reno, OK tornado Figure 4.20: As in Fig. 4.5, but for the fifth period of the El Reno, OK tornado Figure 4.21: As in Fig. 4.6, but for the fifth period of the El Reno, OK tornado Figure 4.22: As in Fig. 4.7, but for the fifth period of the El Reno, OK tornado Figure 4.23: As in Fig. 4.5, but for the Carney, OK tornado

18 18 Figure 4.24: As in Fig. 4.6, but for the Carney, OK tornado Figure 4.25: As in Fig. 4.7, but for the Carney, OK tornado Figure 4.26: As in Fig. 4.5, but for the first period of the Shawnee, OK tornado Figure 4.27: As in Fig. 4.6, but for the first period of the Shawnee, OK tornado Figure 4.28: As in Fig. 4.7, but for the first period of the Shawnee, OK tornado Figure 4.29: As in Fig. 4.5, but for the third period of the Shawnee, OK tornado Figure 4.30: As in Fig.4.6, but for the third period of the Shawnee, OK tornado Figure 4.31: As in Fig. 4.7, but for the third period of the Shawnee, OK tornado

19 19 CHAPTER 1: INTRODUCTION AND MOTIVATION 1.1 Introduction As one of the most powerful forces of nature, tornadoes have caused devastating disasters, mangling trees, flattening crops, and forcing entire communities to rebuild from nothing. Therefore, the persistent threat to life and property, coupled with the lack of complete understanding regarding tornadoes, demands the need for research. While a majority of past research has focused on the storm mechanisms that form and maintain tornadoes, a small amount of research has associated topography and land-cover to tornado intensity changes. One of the first to recognize such changes through the observations of tornado damage was Dr. Theodore Fujita. Fujita, developer of the original tornado intensity rating scale now known as the Enhanced-Fujita scale, revolutionized the study of tornadoes by contributing new ideas and in-depth analyses. Fujita was one of the first to provide a thorough investigation of a strong tornado (F-4) that occurred over mountainous terrain at the continental divide in Wyoming (Fujita, 1989). The extensive damage path analysis provided a glimpse into how topography could impact tornado intensity. Since then, additional observational studies have linked changing elevation to changing tornado intensity (Forbes 1998, Bluestein 2000, Homar et al. 2003, Seimon and Bosart 2004, Bosart et al. 2006, Schneider 2009, Lyza and Knupp 2014). The use of radar data, coupled with damage surveys, has provided multiple instances where topography seemed to have an influence on tornado intensity. One of the overarching conclusions found from these works is that tornado intensity increases with decreasing elevation and

20 20 vice versa. With the modern day increase in computing power, these observational studies have encouraged techniques utilizing numerical simulation (Lewellen 2012) to investigate the possible relationship as well. Lewellen s (2012) simulation results reveal that while there seems to be an effect on tornado intensity due to changing elevation, the pattern of tornado intensity changes is not always the same. A considerable shortcoming with the majority of the radar observation studies (Homar et al. 2003, Schneider 2009, Lyza and Knupp 2014) is that they used data collected by the Weather Surveillance Radar 1988 Doppler (WSR-88D) radar network, which is the main radar network for the U.S. The use of radar, coupled with damage surveys accounts, have provided multiple instances where topography seemed to have an influence on tornado intensity. It has also been hypothesized that land-cover also seems to have an impact on tornado intensity (Church and Snow 1993, Kellner and Niyogi 2014). Primarily through the use of vortex chambers and numerical simulations, land-cover, more specifically, surface roughness has been linked to tornado intensity change. Dessens (1972), Ward (1972), and Leslie (1977) were some of the first to experiment with surface roughness within laboratory controlled vortex chambers, which were designed to imitate the structure and behavior of an atmospheric tornado vortex. Early indications suggested that increasing surface roughness resulted in weakened tangential velocities and strengthened vertical velocities. Church and Snow (1993), Lewellen et al. (1997, 2008), and Natarajan and Hangan (2009) all concluded that while the earlier experiments contained some deficiencies (i.e. non-realistic surface roughness), similar relationships were found in

21 21 these more modern studies. Modern numerical simulations studies (Lewellen 2014), continue to investigate the impacts of surface roughness on tornado intensity. Although recent studies, specifically ones which utilize numerical simulations and WSR-88D radar data, continue to investigate the possible role of topography and landcover on tornado intensity, a gap remains regarding high temporal resolution radar observations. WSR-88D radar provides an additional resource for estimating tornado intensity outside the use of damage indicators, however, the data refresh rate is too slow (4.5 min). Ultimately, the slow refresh rate results in poor temporal resolution (i.e. tornado travels large distances between scans), which could lead to the loss of potentially important topography or land-cover features. It is with this foundation that additional research is warranted, motivating the study presented in this thesis. 1.2 Motivation Over the past couple of decades, advances in radar technology have allowed for the study of supercells to advance, specifically regarding the structure, dynamics, and kinematics of rapidly changing features like tornadoes associated with such convective systems. Additionally, mobile radars have provided the opportunity to examine such features from close range, which leads to improved observations. In many of the previously mentioned radar observational studies examining topography and land-cover impacts on tornado intensity, the WSR-88D radar are the primary radar instruments used. These radars, while vast in coverage, can only complete one volume scan every four and a half minutes. In the case for a tornado, such a large time span between observations can result in large distances traveled between volume scans. For example, if a tornado is

22 22 moving 15 meters per second (~33 mph), it will have traveled over 4000 meters (~2.5 miles) between consecutive observation scans. Many topography/land-cover changes could possibly occur throughout that distance. As a result, a faster scan rate is desired. Advancement in radar technology and computational efficiency have promoted the construction of rapid-scanning mobile radars. Available for this thesis are two radars: the rapid-scanning, X-band, polarimetric (RaXPol) radar and the Mobile Weather Radar 2005 X-Band Phased Array (MWR-05XP) radar. Both of these instruments have obtained data from several tornadic supercells (RaXPol-4, MWR-05XP-2), which will make up the sample analyzed herein. Over all of the cases observed and analyzed herein, the slowest scan rate over which data are collected at the lowest elevation angle is 52 seconds, which is over four times faster than the WSR-88D. The fastest scan rate is 2 seconds. The fast scan rates available in the datasets utilized for this study will ensure additional topography and land-cover changes that could have been missed by the WRS-88D radar, are now observed more appropriately. To date, these relationships have not been explored using rapid-scan mobile radar. Four of the five cases observed by the radars occurred in Oklahoma, while the other occurred in Wyoming. When reviewing the literature, it will be shown that the majority of the research exploring these relationships had been completed while examining rugged, sometimes mountainous terrain (western Pennsylvania, Tennessee, Alabama). While Oklahoma s topography is lower relief, conclusions from (Lyza and Knupp 2014) found that elevation changes even as small as 20 meters were seen to have an impact on tornado intensity ( Vmax). For the purposes herein, Vmax, represents the

23 23 difference between the maximum inbound and maximum outbound velocity magnitudes and is used as a proxy for intensity. With the current lack of rapid-scan mobile radar observations over lower relief topography motivates this research. Additionally, the lack of radar observations, especially rapid-scan mobile radar, observations regarding landcover change and its impacts on tornado intensity further motivates the research. With this motivation, the following questions will be addressed: Are there statistically significant relationships between topography and/or land-cover and tornado intensity ( Vmax)? Are there statistically significant relationships between topography and/or land-cover change and tornado intensity ( Vmax) change? Are conclusions found using WSR-88D data (e.g. upslope weakening/downslope strengthening, terrain influenced environments, specific tornado behavioral conditions due to terrain influences) applicable when using rapid-scan mobile radar? Are conclusions made from numerical simulations (increased friction resulting in a stronger tornado, upslope strengthening/downslope weakening, altering tornado path as a result of terrain influences) applicable when rapid-scan mobile radar observations and varying groundcover are used as a proxy for friction? With the combination of Geographic Information Systems and radar analysis, this thesis seeks to provide additional contributions to the past research discussed in Chapter 2.

24 24 CHAPTER 2: LITERATURE REVIEW 2.1 Tornado Structure Since the late 1950s and early 1960s, atmospheric scientists have attempted to establish an understanding of tornado structure and development. Initially, observations were made with in situ measurements, photographs, conventional radar, and photogrammetric analysis. The introduction of more powerful computers and laboratory experiments during the 1970s and 1980s provided new techniques. Vortex chamber experiments allowed researchers to study vortex dynamics in a controlled environment (Bluestein 2013). With a chamber design that allowed variables to be systematically changed, it was determined from early experiments that the texture of the surface had a direct impact on the structure of the vortex (Dessens 1972, Lewellen 1976, Leslie 1977). Regarding the effects of surface roughness and tornado structure, a literature review completed by Church and Snow (1993) states that through several investigations, it is clear that the nature of the surface over which vortices form has a significant impact on their flow structure and intensity. In a more recent summary about tornado structure, Bluestein (2013) states, the degree of smoothness underneath the vortex can play a role in the nature of the flow. As is apparent from the above discussion, it is important to analyze the idealized structure of a tornado in greater depth; specifically, how changing topographic elevation and surface roughness can affect the structure and therefore the intensity of tornadoes. In a literature review consisting of multiple studies (e.g. Dessens 1972, Ward 1972, Davies-Jones 1973, Church et al. 1977, Lewellen 1976, Rotunno 1977, Gall 1983,

25 25 Davies-Jones 1986, Fiedler and Rotunno 1986, Wilson and Rotunno 1986), Lewellen (1993) defined four main flow regions associated with a tornado: the core, the surface boundary layer, the corner flow, and the upper flow. Twenty years later, Bluestein (2013) updated the conceptual model proposed by Lewellen (1993), incorporating additional results from more modern research (Church and Snow 1993, Grasso and Cotton 1995, Lewellen et al. 1997, Bluestein 2000, Lewellen et al. 2000, Trapp 2000, Wurman 2002, Bluestein 2004, Bosart et al. 2006, Bluestein 2007, Lewellen 2007ab, Fiedler 2009, Alexander 2010, Rotunno 2013) (Fig. 2.1). Figure 2.1: Idealized structure of a tornado with specific flow features divided into regions. Region 1 is the outer flow, region 2 is the boundary layer with 2a as the inertial layer and 2b as the friction layer, region 3 is the corner flow, and region 4 is the core. The corner radius or where the flow (brown streamlines) turns the corner is indicated by rc (Bluestein 2013, Figure 6.41).

26 26 The update separated the surface boundary layer into two sections: the friction layer and the inertial layer, and it introduced a new region, the outer flow. While not heavily focused on, the upper flow regime is briefly updated as well. The core region (4, Fig. 2.1), which extends from the central axis of the tornado vortex to the radius of maximum winds, above the ground-influenced layer (discussed later) and below the top layer (also discussed later), is characterized by a velocity field that is primarily in cyclostrophic balance. Cyclostrophic balance is a force balance between the outward-directed centrifugal acceleration of air due to rotation and the inward-directed pressure gradient force (i.e. a pressure force causing an acceleration directed from high to low pressure) due to the formation of lower pressure within the rotating tornado vortex. As a result of the stability achieved by this balance, the core region of a tornado often appears non-turbulent or laminar (smooth) in photographs. Additionally, the flow is primarily tangential (i.e. no radial inward or outward directed wind flow), although the core also contains upward and downward vertical flow. Due to the convergence of the flow below the core region, upward directed axial flow initially dominates the core. As the tornado progresses and the vorticity strengthens at the surface, a downward-directed pressure perturbation gradient force develops due to decreasing vorticity with height. Because of this dynamically-induced process, the core can contain both upward and downward motion simultaneously at different heights along the central axis. The process is reproduced in vortex chambers and numerical simulations, but it is difficult to capture visually because the central axis of the tornado is often visually blocked by the condensation funnel (Fiedler and Rotunno 1986, Lewellen 1993,

27 27 Bluestein 2013). Additional information regarding this process will be provided in the review on the corner flow. Lewellen (1993) also concludes that the core region is defined as the region that contains the maximum horizontal velocities, which are typically found near the bottom of the core, just above the influence of the surface. The flow in the second region, the surface boundary layer (2a, 2b), is more complex due to the interactions with the surface that occur there. Unlike the core region, the surface boundary layer is comprised of primarily radial flow (i.e. toward or away from the axis of rotation). Due to the presence of friction associated with surface features, the flow near the surface is slowed, causing a disruption in the cyclostrophic balance. Because centrifugal force is directly proportional to the velocity of the flow, the centrifugal force is also therefore reduced, causing the pressure gradient force to become the dominating force (Fig. 2.2). This force configuration results in an inward directed component of flow. Figure 2.2: Force-diagram illustrating the transition from tangential flow to radial flow (curved dashed arrow) due to friction. Due to the decreasing tangential velocities, the pressure gradient force (PGF) dominates the magnitude of the centrifugal force as illustrated by the larger solid arrow (Bluestein 2013, Figure 6.42).

28 28 Complexities arise when the initial momentum of the flow varies and when surface roughness (e.g. flat grassland verses forested hills) changes. Such factors result in a turbulent and complex region within the surface boundary layer (Lewellen 1993). Because of these complexities, Bluestein (2013) divided the surface boundary layer region into two separate parts, the inertial layer (region 2a, Fig. 2.1) and friction layer (region 2b, Fig. 2.1). While the Bluestein (2013) model is consistent with Lewellen (1993) in that the flow is dominated by the radial component within the entire surface boundary layer, the division of the layer arises due to the resistance on the radial flow by the surface features such that the drag is sufficient enough to impede the radial flow within the friction layer. As a result, the force of friction is directed radially outward, balancing with the radially inward directed pressure gradient force (Fig. 2.3). The rougher the surface features are (e.g. grassland, forest, urban), the deeper the friction layer is. Figure 2.3: Balance of forces within the friction layer. As the flow of air interacts with surface roughness, the flow is slowed, resulting in an outward oriented force as indicated by the friction arrow (Bluestein 2013, Figure 6.43).

29 29 Despite the outward directed frictional force, the flow in the friction layer still remains primarily radial. The depth of the friction layer based on vortex chamber experiments is approximately 10 meters (Bluestein 2013); however, the friction layer decreases in height toward the central axis of the tornado. (Fig. 2.1). This behavior occurs because the flow changes from horizontal to vertical, which reduces the magnitude of tangential flow and the subsequent force balances. Directly above the frictional layer is the inertial layer. While still within the surface boundary layer as Lewellen (1993) reviewed, Bluestein (2013) further explains that the disruption of the cyclostrophic balance (i.e. sub-cyclostrophic flow) decreases with height within the inertial region until the flow reaches cyclostrophic balance at the top. Based on experiments that were similar to those that estimated the height of the friction layer, the height of the inertial layer is approximately 100 meters above the ground (Bluestein 2013). The third region, the corner flow (3, Fig. 2.1), is an even more complex flow regime in comparison to the surface boundary layer. The corner flow is defined as the region of the tornado in which the radially inbound air from the surface boundary layer converges toward the center of the tornado and is suddenly forced vertically, or turns the corner from horizontal to vertical motion. The radius (relative to the center of the tornado) at which the turn occurs depends upon the swirl ratio of the air entering the tornado (Lewellen 1993). The swirl ratio is defined according to the equation: S = (r o C)/2Q = (v o /w o ) Equation 2.1

30 30 where C is the circulation at radius r o from the axis of rotation, and Q is the mass flux through the tornado. The swirl ratio is also equal to the tangential (rotational) velocity, v o, divided by the vertical velocity, w o. Conceptually, S is the ratio of tangential velocities (rotation) to the updraft strength, which is a function of the amount of air converging at the low-levels. Qualitatively, a smaller swirl ratio will be associated with a tornado having a dominating updraft and strong low-level convergence while a larger swirl ratio is associated with large values of angular velocities and relatively weak convergence within the corner region. When S is large (>1), centrifuging (i.e. outward acceleration of air) exceeds convergence, rotation dominates the flow, and multiple vortices occur (i.e. small vortices develop around the periphery of the main circulation, often rotating around the central axis). The swirl ratio is commonly used to investigate and alter tornado structure in numerical simulations and laboratory vortex chambers because the quantities that comprise S (namely C and Q) can be manually and numerically adjusted and controlled (Dessens 1972, Ward 1972, Leslie 1977, Church and Snow 1993, Lewellen et al. 1997, 2008, and Natarajan and Hangan 2009). However, it is difficult to quantify S in the real atmosphere because frequently, the contributing parameters are unknown or are immeasurable, and are constantly changing. Although radar technology can assist in viewing the kinematic structure of a tornado, exact swirl ratio numbers cannot be calculated without a three dimensional reconstruction of the wind field, which is frequently impossible to attain. An important consequence of an environment having large swirl on tornado flow is that the dynamically induced central downdraft (forced by the downward-directed perturbation pressure gradient force) is able

31 31 to penetrate to the surface because the central convergence is not able to overcome the high angular velocity of the air. Therefore, a two-celled vortex forms in which the tornado flow has a downdraft at the center encompassed by an annulus of updraft. In section 2.2.2, a more in-depth review of the swirl ratio and how changing surface roughness alters the structure (e.g. by having an effect similar to changing the swirl ratio) of the tornado can be found. Lewellen (1993) lastly includes a fourth region in the description of tornado structure: the upper flow. Of the four regions, the properties, behavior, and dynamics of the upper flow are the most uncertain because the region is located within the parent storm and many numerical simulations poorly resolve the interface between the tornado and the storm above. Due to simulation constraints associated with grid resolution, the upper flow within the parent storm generally cannot be quantified along with the tornado because the tornado is a very small feature requiring extremely high spatial resolution. The storm above is too large to represent on such a fine spatial scale due to computational limitations and is therefore represented by a larger grid. Thus, there is often a disconnect between the tornado vortex and the parent storm when both are being numerically represented. Additionally, vortex chambers are only capable of producing and manipulating a tornado-like vortex, not an entire storm. With the two primary techniques for studying tornado vortices unable to provide details about the upper flow, radar observations of dynamical processes can assist in theorizing where the strong upward motion ends in the parent storm.

32 32 Lewellen (1993) hypothesized that since air with a large angular momentum is brought into the vortex at the surface, there is flow along the axis of rotation that diverges outward at a higher height. He also argued that at the top of the tornado, there is a net accumulation of mass as air from the updraft becomes concentrated in this region. Consequently, there is a net reduction of mass near the surface as air is evacuated into the updraft and as rotation at the surface exceeds rotation aloft as a result of the strong surface convergence. The combination of these effects induces a downdraft which descends along the axis of rotation due to the vertical pressure gradient force responding to the relative lower pressures near the surface. These processes occur inside the cloud, above the tornado and as a result, visual observations to support the dynamical theory are lacking. Additionally, these processes frequently occur on spatial scales that are typically unresolvable by radar observations and it is logistically challenging to collect data in a manner that is conducive for the generation of the 3-D wind field analysis required to quantify vertical motion. In the absence of radar observations, Fujita et al. (2004) depicts sinking cloud tops associated with tornadoes during the 20 March 1976 tornado outbreak, which supports the discussion by Lewellen (1993). In a brief discussion of the upper flow, Bluestein (2013) confirms these dynamical theories should exist, but that processes occurring at the surface are the primary forces governing the dynamics of a tornado. Bluestein (2013) also includes another region, the outer flow (1, Fig. 2.1). The outer flow is above the surface boundary layer, and outside the core. Therefore, the air flow within this region is considered potential flow since it could potentially enter the

33 33 core region. The dynamics of this region in correlation to the tornado are dependent upon the structure and dynamics of the parent storm and the conditions within the surrounding atmosphere (Bluestein 2013). Similar to the upper flow described by Lewellen (1993), the outer flow has little direct consequence to changing elevation or surface roughness. Perhaps the only time the outer flow could be influenced by topography is if the topography is large enough to change the environment associated with the parent storm, and therefore the outer flow becomes altered as well. In summary, with the development of vortex chambers and numerical simulations, coupled with visual observations, radar technology, and photography, the understanding of the complex structure of tornadoes has improved over the last 50 years. It is clear now, that even though tornadoes of different structure and intensity can exist as a result of characteristics of the parent storm, the surface in which they develop and translate upon, can alter their structure and their intensity. Because vortex structure is linked to tornado intensity, further investigations are needed concerning how elevation and surface roughness could impact the tornado structure and intensity. 2.2 Elevation and Land-Cover Effects When isolated from the parent storm (for example in a vortex chamber or numerical simulation), the structure of the tornado is strongly correlated with the intensity of the tornado. Geographic characteristics (e.g. topography and land-cover) will alter the surface flow conditions and could consequently alter the tornado s structure. It is therefore important to understand the role such characteristics may have on tornadoes.

34 Elevation One of the most commonly used explanations for tornado intensity changes associated with topography is the relationship between changes in elevation and vorticity stretching and contracting (Lewellen 2012, Prociv 2012, Knupp and Lyza 2014, Knupp et al. 2014). Another explanation is that significant topography (e.g. a mountain) favorably alters the nearby environment such that the tornado would not have occurred if the topography did not exist (Forbes 1998, Bluestein 2000, Homar et al. 2003, Seimon and Bosart 2004, Bosart et al. 2006, Schneider 2009, Markowski and Dotzek 2011). The final theory for how changing elevation can alter tornado intensity is that the configuration of the near-surface flow transforms the structure of the tornado. (Lewellen 2012). In order to evaluate the implications of these three processes on tornado intensity, previous studies have utilized both numerical simulations and field observations. The majority of research that has focused on topography s impact on tornadoes are associated with landforms that are hundreds to thousands of meters in height (Fujita 1989, Forbes 1998, Bluestein 2000, Homar et al. 2003, Seimon and Bosart 2004, Bosart et al. 2006, Schneider 2009, Lyza and Knupp 2014). Some studies (Markowski and Dotzek 2011, Prociv 2012) primarily focused on the impacts of topography on the parent supercell storm. A large number of the observationally-based studies focused on individual cases because the event was rare or unique to the specific region. Markowski and Dotzek (2011) concluded that since the evolution of a supercell is governed by the surrounding environment, the terrain must be significant enough (greater than 500 meters) to alter the environment in order to affect the supercell. Homar et al. (2003),

35 35 examined a case study in Spain and attempt to replicate the scenario using a model verification technique in order to examine the potential impacts of topographic influences the parent storm. They concluded that the model simulated a storm similar to the one in their study, and that terrain influences of 2-5 km in height could potentially strengthen low-level vorticity and vertical updrafts. Additional observational studies (Bluestein 2000, Homar et al. 2003, Prociv 2012) concluded that the orientation of topographic features (e.g. south-southeasterly) promoted a configuration where the low-level winds increased through a valley allowing for a more favorable environment and a stronger inflow. Increased shear at the surface, oriented in a favorable direction, creates additional vorticity and may ultimately assist in producing or maintaining a tornado. For example, Bosart et al. (2006) examined a case where a tornado developed rapidly as it entered the north-south orientated Hudson Valley in Massachusetts. They concluded that the topographically driven inflow increased the low-level wind shear near the surface. Along with increased inflow, a rear-flank downdraft descended down the slope and into the valley. Additional vorticity developed along the boundary of the rear flank downdraft, and in combination with the enhanced inflow, the supercell produced a destructive tornado. Schneider (2009) found similar occurrences with tornadoes in the Tennessee Valley. Prociv (2012) concluded that the translation direction of the storm, coupled with the orientation of the valleys and ridges, could potentially lead to a favorable tornadic environment where otherwise it would not exist. However, even though the conclusion that orientation of the terrain could provide a more conducive environment for tornado

36 development, all three cases also state that these conclusions were made with uncertainty, partially because the only radar data available for these case studies was the WSR-88D data. With a volumetric scan rate of four minutes and thirty seconds, tornado processes were not observed with the appropriate temporal resolution to analyze the details of the relationship between the storm and the topography. As a tornado moves across the ground, it is forced to translate over the terrain at the surface. The conservation of potential vorticity associated with a column of air as it passes over different levels of elevation may therefore impact the tornado. The equation for absolute potential vorticity is: ( d + f ) (ζ dt h ) = 0 36 Equation 2.2 where the absolute change through time, ( d ) of the absolute vorticity of a column (ζ+f ) dt h where ζ is relative vorticity, f is the Coriolis force, and h is column depth, is equal to 0. If latitude (and therefore f) and the mass of the column are held constant, then the relative vorticity within the column will respond to a change in column depth. For example, as a rotating column of air moves over an area of higher terrain, the column becomes compressed between the tropopause and the terrain, h decreases, and the relative vorticity also decreases. However, when that same column of air moves back over an area of decreasing elevation, h increases, the column stretches, and the relative vorticity increases, as illustrated in Fig. 2.4.

37 37 Figure 2.4: Idealized illustration of vorticity stretching. As a column of vorticity moves upslope, the column is forced to compress reducing vorticity. As the compressed column moves downslope, the column stretches, increasing vorticity (Prociv 2012, Figure 3.13). Although this process is widely used to explain intensification and weakening of mid-latitude cyclones in the presence of terrain (OHandley and Bosart 1996), several observational and numerical studies attribute this relationship to changing intensity of supercells and tornadoes when approaching or retreating from topographic features (Lewellen 2012, Prociv 2012, Knupp and Lyza 2014, Knupp et al. 2014). After observing tornado damage from the historic tornado outbreak of 1974, Fujita (1974) hypothesized that tornadoes intensify on downslopes and weaken on upslopes, consistent with the theory of conservation of potential vorticity. Forbes (1998) continued the discussion for tornadoes that occurred in western Pennsylvania, observing the contraction and intensification of the damage path on downward slopes and weakening intensity on upward slopes. These observations agree well with the notion of vorticity stretching and contraction. Knupp et al. (2014) studied the 27 April 2011 outbreak in the southeast U.S. and arrived at similar conclusions, finding several

38 38 occasions where tornadoes formed and intensified on downslopes and weakened or dissipated on up-slopes repeatedly for the same parent storm. In this study, the tornado damage was also coupled with mobile radar observations. The addition of radar data improves temporal resolution and provides a secondary method to quantifying tornado intensity without depending on tornado damage, which is not always representative of the actual tornado wind intensity (e.g. lack of damage indicators, structure integrity, etc.). Inspiration from the tornadoes that occurred during the outbreak encouraged further research across other parts of the southeast from past events. Lyza and Knupp (2014) attributed changing elevation impacts to 75 additional tornadoes using WSR-88D archived radar data and developed a series of commonly observed behaviors that were associated with topographical influences on the tornadoes. Each case contained one or more of these four conditions: 1) the strengthening (weakening) of the tornado as it moved through downslope (upslope) terrain; 2) the strengthening (weakening) as the tornado moved atop a plateau (moved over a valley); 3) the deviation of tornado tracks that seemed to follow the valleys; 4) the tendency for tornadoes to follow ridge lines. Another overarching conclusion was that an increase in temporal resolution was desired in order to increase confidence for these conditions. A final conclusion from Lyza and Knupp (2014) was that the elevation change required for these conditions to occur was between meters; however, changes as small as 20 meters were seen to have an impact on tornado intensity. With observational studies continuing to suggest that vorticity stretching may have a significant role in a tornado s intensity even over minor elevation changes, it is

39 39 important to discuss the conclusions found using other techniques. Lewellen (2012) utilized numerical simulations to investigate the possibility of vorticity stretching over a wide range of elevation (i.e. 100 meters or less) landforms (e.g. hills, valleys, ridges, etc.). Lewellen conducted over 250 numerical simulations of tornadoes within a closed domain that varied the tornado translation speed, inflow swirl ratio, and topographic configurations in order to evaluate how such changes affect tornado intensity. The study concluded that the types of behavioral responses (upslope weakening and downslope strengthening) noted in Forbes (1998) are also found across the wide range of simulations; however, some simulations strayed from the theorized response. These deviate simulations produced strengthening on uphill slopes and weakening on downhill slopes. Lewellen states that this occurs because tornadoes are not purely swirling flows. Purely swirling flows strengthen and weaken according to the conservation of potential vorticity; however, the tornado s structure, especially close to the surface, can deviate from the potential vorticity theory. He concluded that the topography altered the near-surface inflow into the tornado. For example, during an uphill climb, the inflow was deflected into the central axis of rotation, therefore increasing convergence toward the center. Increased convergence results in a stronger vertical velocity and an intensification of the tornado. Additionally, observations by Forbes (1998) and Fujita (1989), noted swirl spots both on and after a tornado crossed downslope terrain. Lewellen (2012) also discovered swirl spots both on and after a tornado crossed downslope terrain with the numerical simulations. Given the similarities with observational case studies and the number of simulations conducted, it was clear that changing elevation even moderately

40 40 (around 100 meters), can impact the structure of the tornado and therefore the intensity of the tornado. From the review of the studies presented above, it is clear that topography can impact supercells and tornadoes. High relief topography (hundreds to thousands of meters in height) has the potential to alter the environment which can change the intensity of the parent storm or tornado. Even when simulated in isolation, without a parent storm, moderate elevation change (100 meters or less) has been shown to impact the nearsurface intensity of the tornado. As a result, it is important to investigate if similar observations are detectable through the use of rapid-scan mobile radar Land-Cover During the 1970s, when vortex chambers and numerical simulations started becoming possible, it was determined that surface roughness was a key requirement in developing a tornado-like vortex. As a result, the impacts of surface roughness on the tornado-like vortex were examined in depth. Dessens (1972), Ward (1972), and Leslie (1977) were some of the first to study tornado-like vortex interaction with the surface using vortex chambers and numerical simulations, and they found that increased surface roughness resulted in a disruption of cyclostrophic balance. In the simulations, surface roughness and swirl ratio were adjusted separately in order to isolate the possible impacts of each on the vortex. When surface roughness was held constant and swirl ratio was increased, the change in structure was visible as an axial downdraft descended within the vortex (Fig. 2.5).

41 41 Figure 2.5: The transition of a vortex from one-cell to two-cell kinematic structure as swirl increases. At low swirl, the vortex consists of a central updraft along the axis. As swirl increases, a downward-directed vertical pressure gradient force produces a downdraft which splits the updraft. Eventually, the downdraft overwhelms the updraft, producing a two-celled vortex. At maximum swirl, the downdraft is surrounded by annulus updraft which produces multiple vortices (Bluestein 2013, Figure 6.55). Based on Davies-Jones (1986). Low swirl flows produce tornado-like vortices with a central updraft along the axis of rotation. As the swirl continues to increase, vertical vorticity becomes stronger. Eventually, the near-surface rotation becomes so strong that the downward-directed, dynamically-induced vertical pressure gradient force overwhelms the buoyantly/kinematcially driven updraft. The dynamically-induced perturbation downdraft continues to move toward the surface as low-level rotation increases, and the updraft is

42 42 forced to ascend around the downward propagating air, resulting in an annulus updraft around the central downdraft. At the interface where the updraft meets the downdraft, a dynamical condition exists called vortex breakdown, which marks a transition in the flow regime from stable below to unstable above. As the swirl ratio continues to increase within the vortex chamber, the height at which breakdown occurs moves progressively closer to the surface. Eventually, the central downdraft reaches the surface and the center of the vortex is dominated by downward motion. As the swirl ratio is increased further, multiple vortices form around the broad circulation. Church and Snow (1993) speculate that a tornado structure with a vortex breakdown close to the surface could be as violent as one with multiple vortices. As mentioned earlier, increasing the surface roughness results in stronger radial flow within the corner region, leading to a stronger axial updraft. Dessens (1972), Ward (1972), and Leslie (1977) concluded that within vortex chambers, increasing friction behaves similarly to lowering the swirl ratio (i.e. it required larger swirl to force the vortex breakdown to the surface). Later research investigated the applicability of the results from vortex chambers to real-world surface roughness. Experiments by Church and Snow (1993), Lewellen et al. (1997, 2008), and Natarajan and Hangan (2009) addressed deficiencies (e.g. the surface techniques that were unrealistic) within the earlier vortex chamber experiments. Ultimately, the later studies concluded similar results with more reliable simulations. Although the surface roughness values were confirmed reliable in controlled environments, applications of swirl ratio values outside of vortex chambers are complicated. In one observational case, Church (1993) suggested that as a tornado

43 43 moved from urban to an open field, the tornado encountered a change in swirl (low to high) due to the change in surface roughness. The change in swirl potentially changed the structure of the tornado and resulted in increased damage within the open field. Church (1993) further concluded that the tornado encountered higher swirl air as it entered the field (increased angular momentum at the near surface due to the lack of surface friction) resulting in the lowering of the vortex breakdown close to the surface (Fig. 2.5) which caused a maximum of intensity in that localized area. Results from Lewellen (2014) support Church s conclusions by demonstrating how a tornado vortex can change intensity when passing through tall buildings ( meters in height). As the tornado translates over the buildings (Fig. 2.6), low swirl weakens the tornado, but as it exits, the tornado is impacted by high swirl outside the buildings and intensifies. Figure 2.6: Results from a numerical simulation illustrating the impacts differing levels of swirl can have on a tornado-like vortex. The shades of blue represent pressure. Darker blues indicate low pressure which is correlated to intensity (Lewellen 2014, Figure 5).

44 44 Lewellen et al. (2008) also suggest that sudden changes in surface roughness for even lesser amounts of surface roughness could alter characteristics of the flow resulting in variable intensities throughout the path. In comparison to elevation, very little research has been done concerning the impact of surface roughness on tornadoes, especially observationally. Although numerical modeling and vortex chambers provide an initial understanding of the relationship between surface roughness and tornado intensity, observational studies, which are crucial in verifying the laboratory and numerical theory, are essentially missing. Since a tornado s intensity is typically estimated from the damage it inflicts, the majority of the observational studies investigating surface roughness relationships are tornado damage related. Wilkens et al. (1975) and Dessens and Snow (1989) observed a transition to lower swirl (i.e. narrowing damage path indicating a strong central updraft) when a tornado entered an area with increased surface roughness, which agrees with the conclusions from the numerical simulations. Baker (1981) and Dessens and Snow (1989) concluded that damage increased with further penetration by the tornado into forested areas. Monji and Wang (1989), on the other hand, found that a tornado produced only light damage in an urban area before producing major damage in an open field, which would agree with the conclusions of Church (1993) and Lewellen (2014). Even fewer studies have investigated the relationship between surface roughness and tornado intensity utilizing radar observations as a proxy for intensity. Kellner and Niyogi (2014) did a climatological study (years ) of tornado touchdowns (the

45 45 location where the damage path began) across the state of Indiana using GIS and tornado touch-down points provided by the National Climatic Data Center. Using tornadogenesis locations and 2005 land-cover data from the U.S. Geological Survey, they found that tornado touchdowns increased with increased surface roughness (forest, urban) and decreased with decreased surface roughness (pasture land, agriculture). They hypothesize that tornadogenesis is more likely to occur in areas of increased surface roughness as a result of promoting a favorable near-surface flow pattern that increases convergence, producing a stretched vortex. Despite the discrepancies in the results, numerical simulations and damage observations have shown that surface roughness, specifically changes in surface roughness, can cause the structure and therefore the intensity of the tornado to change. While topographic features and surface roughness have been shown to be linked to tornado intensity, the parent storm and the internal mechanisms which drive and sustain tornadoes are not negligible and must be discussed. 2.3 Storm Mechanisms Tornadoes can form from parent storms having various convective modes including supercells, quasi-linear convective systems, and even ordinary convection. However, only tornadoes spawned by supercells will be analyzed for this thesis. Supercells are thunderstorms that have a deep, sustained, rotating updraft known as a mesocyclone, and are long-lived (> 1 h) with a quasi-steady structure (Bluestein 2013). As depicted in (Fig. 2.7), the primary storm-scale vertical airflow regimes found in a

46 46 supercell include the rear flank downdraft (RFD), updraft (UD), and forward flank downdraft (FFD). The red triangle is the location at which a tornado is commonly seen. Figure 2.7: Idealized supercell with archetypal storm-scale features: rear-flank downdraft (RFD), rotating updraft (UD), and forward-flank downdraft (FFD). The green area represents the expected radar echo. Typical tornado location is on the north side of the hook echo marked by the red triangle. Purple arrows are streamlines. Blue lines indicate boundaries (forward flank gust front and rear flank gust front) where horizontal vorticity is generated (Doswell 2011, Figure 2). Adapted from Lemon and Doswell (1979). A supercell also contains two surface boundaries associated with converging air: the forward flank gust front (FFGF) and the rear flank gust front (RFGF) (blue lines, Fig. 2.7). The converging air, as manifest by the purple streamlines, is collocated with

47 47 baroclinically-generated horizontal vorticity along the interface between the storm-cooled air and the warm environmental air. Horizontal vorticity generated along the FFGF wraps around the updraft and encounters the RFGF, which tilts it into the vertical, promoting tornadogenesis approximately where the red triangle is located (Dowell 2011). The lifecycle and evolution of a tornado is extremely sensitive to the characteristics and evolution of storm-scale features. In certain instances, the same feature can act favorably at one point during the evolution, and unfavorably at another point, or can have opposite effects in the different storms. For example, the features that assist in the development of the tornado, like the RFD, can also result in its dissipation (e.g. Marquis et al. 2012). Therefore, it is important to discuss the features or phenomena that can intensify or weaken a tornado. Three processes that have been proven to be important to tornadogenesis, maintenance and/or decay will be discussed here: the rearflank downdraft occlusion (Marquis et al. 2012), the secondary rear-flank downdraft (or internal momentum) surge (Marquis et al. 2008, Skinner et al. 2014), and the descending reflectivity core (Rasmussen et al. 2006, Byko et al. 2009). The rear-flank gust front occlusion frequently occurs just before tornado development, but can occur afterwards in some cases. For clarity, the RFD is associated with regions of subsiding dry air which develop on the rear side (i.e. typically the north side) of a supercell. The descending air contacts the surface and spreads outward. As stated earlier, the RFGF is understood to contribute to tornadogenesis by the tilting of horizontal vorticity originating along the FFGF, therefore, the location and progress of the RFGF has important implications on tornado production. For example, if the RFGF

48 48 advances too quickly, the tornado may not have the time to develop. If a tornado does form, the maintenance of the tornado could suffer due to the quickly advancing RFGF which results in the occlusion of the tornado by cool, relatively stable air, separating it from the source of buoyant inflow (Fig. 2.8). Figure 2.8: An illustration of tornado demise due to the advancement of the RFD through time. The RFD separates the tornado from the intersection of the RFGF, FFGF, and updraft, resulting in a weakening tornado (Marquis et al. 2012, Figure 1). Ultimately, the processes and features that assisted in tornado formation are no longer in the ideal locations, which leads to a weakening tornado. The sensitive nature of the occluding rear-flank downdraft could lead to tornadogenesis or tornado demise depending on the atmospheric scenario. Although it has been shown that downdraft occlusions can result in a lack of tornado maintenance, another feature, the secondary rear-flank downdraft surge, has been proven to maintain the tornado, despite the occlusion (Marquis et al. 2008). Behind the initial RFGF, another surge of subsiding air can result in the maintenance or intensification of the pre-existing tornado. This is known as a secondary rear-flank downdraft surge.

49 49 The last storm mechanism discussed here is the descending reflectivity core (DRC). According to Rasmussen et al. (2006), The DRC is a blob-like precipitation protuberance that forms within the rear-flank of a supercell, similar in location to the rear-flank downdraft, and is approximately 2-3 km in horizontal length (Fig. 2.9). In one of the first broad studies regarding the DRC, Rasmussen et al. (2006) found that the DRC precluded tornadogenesis in all five of their cases; however, it is also admitted that the sample size is small. Figure 2.9: Three-dimensional view of a DRC descending prior to tornado formation over the span of 15 minutes: a) 0042, b) 0047, c) 0052, and d) 0057 (Rasmussen et al. 2006, Figure 1). A more thorough statistical study done by Kennedy et al. (2007) analyzed 64 supercell cases (33 tornadic, 31 non-tornadic) and discovered that 23 of the 33 tornadic

50 50 supercells contained a DRC. However, 16 of the 31 non-tornadic supercells also contained a DRC. So, it appears that while DRCs are quality indicators of potential tornadogenesis, they are not always associated with tornadic supercells. In regards to the atmospheric mechanisms that are potentially creating a favorable environment for tornadoes, Byko et al. (2009) concluded that in some cases, the DRC results in a strong cyclonic vorticity maximum along the RFGF shortly after arrival to the surface. The importance of vorticity along the RFGF is relatable to tornadogenesis/maintenance as described by the previously explained processes. With an additional process providing enhanced vorticity, tornado probability increases. These three mechanisms only represent a small part of the complex process of creating and maintaining a tornado. However, due to time limitations, their roles in the cases within this study are not addressed.

51 51 CHAPTER 3: INSTRUMENTATION AND METHODOLOGY 3.1 Instrumentation In order to acquire quantitative, reliable, semi-continuous data about tornado intensity, this thesis will utilize mobile radar data from the University of Oklahoma s rapid-scanning, X-band, polarimetric (RaXPol) and the Naval Post Graduate School s Mobile Weather Radar 2005 X-Band Phased Array (MWR-05XP) radar. This section will explain the details of the mobile radars and how these instruments differ from the National Weather Service s network of WSR-88Ds, and from each other. Table 3.1 provides an overview of the specifications for all three instruments. Table 3.1: Basic information regarding the differences between the WSR-88D (Crum and Alberty 1993) and the two mobile radars, RaXPol (Pazmany et al. 2013) and MWR- 05XP (Bluestein et al. 2010). RADAR WSR-88D RaXPol MWR-05XP Antenna Type Parabolic (8.5 m) Parabolic (2.4 m) Phased Array (diameter) Wavelength (band) 10cm (S-band) 3cm (X-band) 3cm (X-band) Peak Power 750 kw 20 kw 15kW Maximum Range 460 km 90km 30-60km Azimuthal Beam Width Range Resolution 250 m m 150 m Scanning Strategies Only 360 Only and sectors by 90 Scan Rate (full volumetric scan) 4.5 min 20s 24s (360 ) 6s (90 ) The WSR-88D instruments were upgraded from the WSR-57 in order to improve the coverage across the United States as well as to improve the quality of the data received by adding Doppler velocities. The WSR-88D is an S-band radar (10 cm

52 52 wavelength) with an 8.5-m-diameter parabolic antenna. A full volumetric scan covers 360 azimuthally, over 11 elevation angles and takes four and a half minutes to complete when scanning in precipitation mode. The slower scan rate is required to allow for decorrelation of hydrometeors to occur between pulses in order to obtain 33 independent samples at each point where data are quantized. The range resolution (the radial distance traveled between each radar pulse pair) is 250 m, and the azimuthal beam width is With a peak power of 750 kw, the radar has a maximum unambiguous range of 460 km (Crum and Alberty 1993). Dual-polarization of the transmitted pulses allows the radar to transmit in both horizontal and vertical planes (Fig. 3.1). Figure 3.1: Dual-polarization illustration of hydrometeor identification using the horizontal (blue sinusoid) and vertical (maroon sinusoid) pulse planes (NOAA, online source 1). Dual-polarization allows for characteristics of the scatterers (e.g. size, shape, type) to be acquired, providing additional information about the nature of the scatterers within the radar volume.

53 53 RaXPol also has a parabolic antenna and polarimetric capabilities, but operates at X-band (3 cm wavelength) and has a 2.4-m diameter antenna. A full 360 volumetric scan (10 elevation angles) can be completed in approximately 20 seconds. The rapid-scan technique is possible through the process of frequency hopping. Frequency hopping is a technique that shifts the transmitted frequency of the wave multiple times during the ~5 millisecond sampling interval. For each pulse pair within the sampling interval, the shift must be by at least the pulse bandwidth after each pulse pair in order to gather an adequate amount of independent samples (Pazmany et al. 2013). The range resolution can also be adjusted from 15 m to 150 m. The radar azimuthal beam width is 1. With a peak power of 20 kw, the maximum unambiguous range is 90 km. The MWR-05XP was transformed from an Army tactical radar into a mobile meteorological instrument. The MWR-05XP radar (wavelength of 3 cm, X-band) is different from the WSR-88D and RaXPol radars because it is a partial phased-array radar. Through a series of phase shifters, the radar completes a full 10-step elevation scan (2 vertical beam-width each) in one azimuthal scan. The radar consists of a flat antenna that has two modes of data collection: sector (90 azimuth) and full (360 azimuth). Depending on the scanning method, a full scan can be completed between 6 and 24 seconds. The range resolution is 150 m, and with a peak power of 15 kw, the maximum unambiguous range is 60 km. A limitation to the MWR, in comparison to the other radars, is that the azimuthal beam width is 1.8, which is nearly twice as large as the WSR-88D and RaXPol. As a result, a decrease in spatial resolution (less detailed) is observed. (Bluestein et al. 2010).

54 Methodology In order to investigate the relationships between topography/land-cover and tornado intensity using observations, two analysis techniques have to be combined; radar analysis using Solo3, which was developed by the National Center for Atmospheric Research (NCAR) and geographical information analysis using ArcMap10.3.1, which is maintained by the Environmental Systems Research Institute (ESRI). Although the combination of these two methods has not been explored extensively, methodology adapted from Prociv (2012) is used to formulate the methodology utilized here Radar Analysis The lowest elevation scans for each of the datasets are obtained and analyzed in Solo3. The lowest scans are used because the strongest winds associated with tornadoes are typically found near the surface or above the surface features (Monji and Wang, 1989) and, the impacts of surface roughness on tornadoes are believed to be the greatest in the lowest part of the tornado, so the lowest possible scan is desired. Five specific parameters were documented: the latitude and longitude for the center of the tornado, the tornado radius using 35 ms -1 as the proxy for the periphery of the tornado, and the maximum inbound and maximum outbound radial velocities. The center of the tornado is estimated by a change in radial velocity sign observed by the radar that is perpendicular to the radar beam. Also, for large tornadoes, an area of low to zero velocity often separates the change because flow perpendicular to the beam is observed as velocity equals zero. Due to the rapidly changing wind direction associated

55 55 with the circulation of a tornado, the point selected as the center typically has a low velocity. All of the radar data obtained for the radar analysis are collected by a user evaluating each individual low-level velocity scan. The data are selected using the understanding of radar imagery. With a point and click method, a specific radar quantity (e.g. radar pixel) is selected by the user, and the data (e.g. velocity values, latitude and longitude, beam height, scan time stamp) associated with the specific pixel are made available through the examine feature in Solo3. These data are then organized by observation time, deployment time period, and case study in Microsoft Excel. The radius of the tornado is also obtained by the point and click technique; however, it requires a calculation. The distance formula: Distance = sqrt((x 2 X 1 ) 2 + (Y 2 Y 1 ) 2 ) Equation 3.1 where X1 and Y1 are the east-west, north-south Cartesian coordinates obtained for the center of the tornado (with respect to the radar location) X2 and Y2 are the coordinates obtained at the periphery the tornado where velocity is ~35 ms -1. The same errors associated with deriving the center of the tornado are possible when selecting the edge of the tornado. Additionally, the radius of the tornado is a function of height. With height, the radius increases until a certain point, where it subsequently decreases. The radial velocities observed by the radar and extracted from Solo3 are used to calculate the estimated intensity ( Vmax) of the tornado according to the following equation:

56 56 Vmax = Vmax(outbound) Vmax(inbound) Equation 3.2 Throughout the remainder of this thesis, the term intensity is referring to values derived from Vmax (i.e. intensity = Vmax). Additionally, intensity is not representing the damage-based intensity of the tornado, which is often done through the use of the Enhanced Fujita Scale. For a couple cases, missing observations within the time period do occur. To amend the data gaps, which are few, a linear interpolation consisting of averaging the adjacent scans is applied. While there is error associated with this process, the short scan intervals prevent significant errors (e.g. missing an entire valley or hill). For each time period that contains missing observations, there is no more than one consecutive scan for which data are not available. This means that interpolated values are not being used to average another missing scan GIS Analysis Recently released in May 2015, the 2011 land cover analysis of the United States was published by the National Land Cover Database (NLCD) through the U.S. Geological Survey (Homer et al. 2015). The data are made available online through the National Map at the Seamless Data website maintained by the USGS ( At 30 m resolution, the land cover product provides a 16-class land cover classification (Fig. 3.2). For elevation, the digital elevation model (DEM) data are also available through the USGS site. Four DEM (1/3 arc-second) maps were downloaded to cover the specific regions where the selected tornadoes

57 57 occurred. These data are then imported into ArcMap, a geospatial program designed by ESRI for the use of mapping and gathering geographic information. In ArcMap, all of the data were given the Geographic Coordinate System North American 1983 (GCS_NA_1983) with the North American Equidistant Conic as the projected coordinate system, and then projected using the Equidistant Conic projection. Figure 3.2: The 2011 land-cover legend provided by NLCD (Homer et al. 2015). Using the latitude and longitude obtained in Solo3, each data point for the cases are added to ArcMap using the Add XY Data function. Once the points for each case are mapped, elevation is extracted using the Extract Values to Points tool in the Spatial Analyst Toolbox. The Spatial Analyst Toolbox is also used in calculating and creating the

58 58 slope and aspect values from the DEM data. The slope, or the incline/steepness of the land, is extracted using the Extract Values to Points tool. Aspect, or the direction in which the slope lies, is extracted in the same manner. In ArcMap, the values for aspect are defined in compass degrees and are as follows, North ( and ), Northeast ( ), East ( ), Southeast ( ), South ( ), Southwest ( ), West ( ), and Northwest ( ). The values are added to the attribute table in ArcMap, which are then exported to Excel. Obtaining surface roughness data requires several additional steps. The first step involves reclassifying the land-cover data. The reclassification is necessary because the land-cover data are provided as a raster map (i.e. qualitative categories as pixels which are given a specific value). The raster map contains values for each pixel ranging from 11 to 95; however, there are only 16 primary qualitative land-cover classes. In order to organize the pixel values into their proper qualitative categories, a reclassification technique is completed. The reclassification process allows the user to organize the value ranges provided by the NLCD for each category. For example, the land-cover pasture/hay, which is one qualitative category is given the quantitative pixel values Reclassifying the range of pixels into one category allows the user to gather and map qualitative information. Each range of pixels is reclassified into their proper qualitative name (e.g. Grassland, Deciduous Forest). Once the reclassification process is complete, land-cover information (e.g. surface area) is able to be extracted by the proper qualitative categories.

59 59 For quantifying surface roughness, the reclassified land-cover categories needed numerical values. The surface roughness values organized and derived by the Environmental Protection Agency s AERSURFACE User s Guide (EPA, 2008) are applied. The AERSURFACE tool is designed to assist users of the software AERMOD, a modeling processer created to provide state-of-the-art modeling for EPA s air quality models. The models and software are not utilized here; however, the surface roughness lengths organized by the designers, and employed in the model are (Table 3.2). Table 3.2: Surface roughness lengths from EPA s AERSURFACE User s Guide organized according to the 2011 land-cover data from NLCD. Land-Cover Roughness Roughness Land-Cover Type Type Length, zo, meters Length, zo, meters Open Water Evergreen Forest 1.3 Ice/Snow Mixed Forest 1.1 Developed-Open Shrub/Scrub 0.3 Developed-Low 0.52 Grassland/Herbaceous 0.05 Developed- Medium 0.8 Cultivated Crops 0.05 Developed-High 1.0 Pasture/Hay 0.03 Barren Land 0.05 Woody Wetlands 0.7 Deciduous Forest 1.0 Emergent Herbaceous Wetlands 0.2 The tornado size (i.e. radius obtained from radar analysis) is contrived in ArcMap by using the Buffer tool within the Geoprocessing toolbox. The Buffer tool allows the user to place a boundary of a specified distance around a desired feature. Here, the radius

60 60 obtained from the radar analysis is the specified distance, and the feature is the center of the tornado. Prociv (2012), while primarily investigating mesocyclone intensity changes, used a 1.6 km radius buffer for each center point. A similar methodology is applied here; however, since tornado structure is a priority, several additions to the Prociv (2012) method are utilized. In total, three separate means (area mean, weighted mean, weighted trimean) for deriving surface roughness are used. Three values are needed because there have been no previous works utilizing this type of methodology, therefore, it is unknown which method is most appropriate. By describing three separate parameters, errors specifically involving this methodology are assumed to be limited. The area mean is a single circle of maximum radius at a specified distance from the center point. The radius derived in the radar analysis is used to define the first and coarsest mean (in comparison to the other two). Once the radius buffer is applied, all land-cover types within the circle are given the same weight of effect on the tornado. The second method, weighted mean, is more complex. It is designed to more accurately illustrate a tornado and the effect surface roughness will have on its structure. Due to the complex structure associated with tornadoes, multiple radii (1/4r, 1/2r, 3/4r, and the full radius) are used in order to approximate the influence of surface roughness. The four radii are based on the Rankine vortex (Rankine 1882) velocity structure (Fig. 3.3) commonly used for atmospheric vortices (e.g. a tornado), where the tangential velocities increase linearly from zero at the center of the tornado to approximately 1/2r (the core radius). The velocity then decreases with increasing radius (Fig. 3.3). The inner

61 core (1/4r) is associated with mainly vertical motion so it is assumed that the influences of roughness are limited. 61 Figure 3.3: A diagram illustrating the radial profile of tangential velocities associated with an idealized Rankine Vortex. Normalized radial distance is represented by R/Rx, where R is the radial distance from the vortex center and Rx is the radius at which the tangential velocity maximum Vx occurs (Wood and Brown 2011, Figure 2). As a result, a weighted mean surface roughness equation was developed: Weighted Mean = ((full radius(r) 0.25) + ( 3 r 0.3) + 4 ( 1 2 r 0.35) + (1 r 0.1)) 4 Equation 3.3 where r is the roughness value quantified for each radius. The equation was designed around the Rankine vortex; however, due to unknown errors associated with the selection of the radius and the center of the tornado, the center of the tornado is given 0.1 weight. At the core radius, where the velocities are expected to have the maximum influence by

62 62 the surface roughness, a weight of 0.35 is assigned. The weight then decreases outward from the core radius similar to that of the Rankine vortex. Once the various radii are calculated from the maximum radius, they are plotted as buffers in ArcMap (Fig. 3.4). Figure 3.4: An example showing the various radii, full radius (black), ¾ radius (dark grey, ½ radius (light grey), ¼ radius (black with white fill) plotted as buffers and the associated land-cover within each circle around the tornado center. Finally, a third parameter, weighted trimean, is similar to the weighted mean; however, a trimean equation is applied to the values within each radius. The trimean equation is as follows: TM = Q 1 + 2Q 2 + Q 3 4 Equation 3.4 where Q1 is the 25 th percentile of the total area, Q2 is the 50 th percentile of the total area, and Q3 is the 75 th percentile of the area. The surface areas for each scan are organized

63 63 from least rough to roughest. The surface areas within each scan are summed. Whichever land-cover type crosses the percentile thresholds set by the trimean equation, the associated surface roughness value is filled in for Q1, Q2, and Q3. As a result, the trimean prioritizes the land-cover type based on their percentage of area within the total area. The trimean technique is applied to each of the four radii. Then, equation 3.3 is applied to create the weighted trimean parameter. All three parameters: area mean, weighted mean, and weighted trimean, are then used to derive different surface roughness values within the area of the tornado. After each radius is created in ArcMap, extracting land-cover information from within the circles and quantifying surface roughness requires the use of the Tabulate Area tool, in ArcMap, from the Spatial Analyst Tools Prociv (2012). This tool allows the user to extract the amount of surface area per land-cover type within a desired shape (e.g. the buffer). However, when applied here, the tool does not appropriately extract the information due to overlapping circles between each radar scan (Fig for example). For small scan intervals, the displacement of the tornado does not provide enough distance between each scan to make the radii spatially independent, so overlapping circles occur. To amend the issues, ESRI designed a supplemental toolbox to fix the errors associated with tools found in the Spatial Analyst toolbox. The updated tool, Tabulate Area 2, appropriately extracts area within each circle to an attribute table, which is exported into Excel. Once all the areas of each radius are available in Excel, then surface roughness values representative of the tornado s impact with the surface are calculated for area

64 64 mean, weighted mean, and weighted trimean. At the conclusion of the GIS and radar analyses, beam height, intensity, elevation, aspect, slope, and surface roughness values (e.g. area mean, weighted mean, and weighted trimean) are available for every scan Statistical Analysis In order to investigate the potential relationship between tornado intensity ( Vmax) and topographic/land-cover features, and the significance of the relationship if any, statistical methods are utilized. For each variable ( Vmax, elevation, slope, aspect, surface roughness), it is assumed that there is a normal distribution centered around the mean. The values extracted or the raw data are examined for statistically significant relationships; however, since there is also an interest in how the change in topography/land-cover may affect intensity, a derivative function is utilized to compare the change of intensity with the change of elevation and surface roughness. For the purposes here, only an approximate derivative of intensity, elevation, and the three surface roughness parameters are calculated. The equation used to calculate the derivative from the data is as follows: d V dt = ( V 3 V 1 ) 2(t scan ) where d V is the change of Vmax from the first to the third scan and dt is the scan interval times two. The same equation is applied to elevation (dz elev ) and surface roughness (dz rough ). Equation 3.5 Correlations are used to investigate relationships between intensity and each individual variable separately. The correlation, r is found using the following equation:

65 65 r = n i=1 (x i x )(y i y ) n i=1(x i=1 x ) 2 n i=1(y i y ) 2 Equation 3.6 where r is the correlation coefficient, xi and yi are each variable in the selected case (e.g. intensity and elevation, intensity and area mean, etc.), x and y are the means of each variable, and n is the number of samples. All topographic/land-cover variables are given a correlation to intensity for each time period associated with each tornado. Once the correlations are found, the significance of the correlations is calculated using a t-test. The t-test has a null hypothesis (H0) that r = 0, or that intensity and some topography/landcover variable are not linearly related. The alternative hypothesis (HA) is that r 0. Since it is unknown whether or not any correlations are positive or negative, a two-tailed t-test is required. The first step of the t-test is to find the t-value which is then applied to a statistical table for probability of significance. The t-value equation is as follows: t n 2 r ( N 2 1 r 2) Equation 3.7 where t is the t-value with (n-2) degrees of freedom, N is the number of samples, and r is the correlation coefficient. Once the t-value is found, the probability, p, is found using a statistical table and the degrees of freedom, which is the number of samples within each time period minus two (n -2), The probability is the likelihood that the null hypothesis is true. Here, a two-tailed t-test is computed in Microsoft Excel, which corrects for the double sided tails, and thus, probability values of p < 0.05 are considered significant. The value of 0.05 is the mark where the null hypothesis of no relationship is rejected, and the

66 66 alternative hypothesis of a relationship in the positive or negative direction, is accepted. Relationships that are significant will assist in determining the impact of topography and land-cover on tornado intensity. The correlations with the lowest values of p are considered the most significant. A composite analysis technique through a comparison of means is applied to each time period as well. The comparison of means analysis allows the data to be tested according to the individual means associated with the variables. First, the anomaly (i.e. difference from the mean) is found using the following equation: x anom = x i x period Equation 3.8 where xanom is the anomalous difference of the variable, xi, from the mean of that particular variable for that specific time period, x period. Once the anomalies are found, they are grouped by 75 th and 25 th percentiles of intensity anomalies, and the associated values of the other variables are isolated. By doing this, the means of the values for topographic/land-cover variables associated with those groups are tested for significance. For example, if it can be discovered that the difference between the means of elevation within those two groups are large (e.g. higher elevation in top 25 th percentile intensity group and lower elevation in the bottom 25 th percentile intensity group), a significant relationship with intensity may be produced. A two-sample t-test is used, and the equation is as follows:

67 67 t n 2 = x 1 x 2 S p 1 n n 2 Equation 3.9 where x 1 and x 2 are the sample means of the percentile groups and n is the number of samples. Since both percentile groups are included in the test, the degrees of freedom are described by (n-2). S p is the sample pooled variance and is quantified by: S p 2 = (n 1 1)S (n 2 1)S 2 2 n 1 + n 2 2 Equation 3.10 where S 1 2 and S 2 2 are the sampled variance for the categories. For the comparison of means technique and two-sample t-test the critical significance level, α = 0.05 is used. Therefore, if the probability is below the threshold (p < 0.05 for a two-tailed t-test), the null hypothesis of x 1 = x 2 is rejected, and the alternative hypothesis of x 1 x 2 is accepted. The first two methods, correlation and composite analysis, provide the opportunity to examine the individual topography/land-cover variables with intensity; however, these methods assume isolation from the other variables (i.e. there are no interactions between the various topographic variables). In order to acquire a better sense of how the various parameters may be interrelated, linear regression techniques are used. Linear regression provides the opportunity to investigate how well one value (e.g. elevation) can predict another value (e.g. intensity) in the presence of all the other parameters. For linear regression, one independent value is used to predict one dependent value; however, in order to investigate which variables provide the strongest

68 68 contributions to predicting intensity, multiple regression is used. SPSS Statistics software is used to calculate the multiple regression outputs for each time period within each case. Two separate tests are used. The first (referred to as test 1) includes all independent variables available (beam height, elevation, slope, aspect, area mean, weighted mean, weighted trimean). The second (referred to as test 2) removes the only value that is not topographic/land-cover derived, beam height. With beam height removed, the more influential variables concerning topographic/land-cover interactions only, are distinguished. For each test, several components are analyzed and used in the results section. The regression correlation, R, indicates how correlated the model predicted intensity and the actual intensity are. The percentage of variance explained by the model, R 2, reveals how close the data are to the model-predicted regression line. For the predictors, unstandardized coefficients are calculated. The coefficients represent the slope of the linear trend line, b. The coefficients are given a standard error value or the error of the slope produced by the model. The slope is quantified by: b = n i=1 n i=1 (x i x )(y i y ) (x i x ) 2 Equation 3.11 where, x i is the independent variable (elevation) and y i is the dependent variable (intensity) and x and y are the sample averages. Also provided are the t-value and probability. With a critical significance value of α = 0.05, probability values of less than 0.05 results in a rejection of the null hypothesis (Ho) of slope, b = 0, and the acceptance

69 69 of the alternative hypothesis (HA) of b 0, which implies that there is a relationship between the variables. 3.3 Case Studies One of the main criteria for deciding the cases for study is that the duration of the tornado must be long enough to assume the initial tornadogenesis mechanisms are no longer the primary factor governing intensity change. The same logic is applied to the dissipation of the tornado as well. The individual time periods within the cases may result in some exceptions. Examination of specific topography or land-cover characteristics is not proposed. For example, the first case study described in section has nearly homogeneous land-cover (surface roughness), however, it is still analyzed for possible elevation influences Goshen County, Wyoming-5 June 2009 On 5 June 2009, a supercell developed in southeast Wyoming. As it tracked eastward across Goshen County, a tornado formed and progressed through a relatively rural area with the nearest city, La Grange, about six miles away. The data set, collected by the MWR-05XP, is unique because it captured the entire lifecycle of the tornado with rapid temporal data acquisition (French et al. 2014). Data were collected in four increments over the duration of the event; however, only the second and third time periods are analyzed (Table 3.3). During the first increment, 2143: :19 (time in UTC throughout), data were collected prior to and during tornadogenesis (which occurred at 2152); however, the tornado did not maintain a persistent strength until later. The second and longest increment, 2200: :07, began as the tornado developed and

70 70 visual contact of the condensation funnel with the ground occurred. Data from this period contains 156 scans of the lowest elevation angle, each scan collected at six-second intervals. Topographic elevations ranged from m above sea level (ASL), and the lowest level beam height ranged from 114 to 225m above ground level (AGL). The land-cover throughout this time frame consisted of mainly grassland. The only exceptions were a road that the tornado crossed, and scattered areas of cultivated crops and barren land. Due to the nearly homogeneous nature of the landscape, the surface roughness only deviated from 0.08 to 0.1 m throughout the second increment. After a brief lull in operation to adjust the sector over which data were being collected, the radar began scanning again for the third time at 2217:11 and continued until 2220:34. During this period, the volumetric data collection rate continued at six seconds resulting in an additional 30 scans. Initially, ΔVmax was 110 ms -1 but it rapidly decreased to 49 ms -1 by the conclusion of data collection in this increment. Topographic elevations ranged from m, and the lowest beam height ranged from 96 to 107 m. Compared to the second increment, the land cover over the third period of data collection was even more homogeneous (0.1 m); grassland was the only type of ground cover. The first and fourth periods of data collection did not maintain a persistent tornado and predominately contained the formation and dissipation of the tornado and were therefore omitted from the analysis. Since the land-cover was primarily homogeneous, the Goshen County tornado is not included in the surface roughness analysis. However, statistical tests investigating relationships with change in elevation, aspect, and slope are completed.

71 Table 3.3: Information summary regarding the time periods analyzed for the Goshen tornado. Tornadogenesis or Tornado Dissipation categories with N/A indicate that those processes were not associated with those periods. Case (period) Goshen (2) Goshen (3) Collection Time (UTC) 2200: : : :34 Scan Interval (seconds) ~ 6 ~ 6 Beam Height (meters AGL) Elevation Range (meters) Surface Roughness Range (meters) Vmax Range (ms -1 ) Tornadogenesis 2152 N/A Tornado Dissipation N/A Lookeba, Oklahoma-24 May 2011 On 24 May 2011, a supercell produced a strong EF-3 tornado southwest of Oklahoma City, Oklahoma near the town of Lookeba (Fig. 3.5). According to the damage survey (NOAA, online source 2), the tornado had already been on the ground for six minutes ( ) by the time RaXPol began scanning in rapid scan mode (2037:18); however, the Vmax values were still around 50 ms -1 at the onset of the deployment (Table 3.4).

72 72 Figure 3.5: Designated path by National Weather Service based on damage survey for the Lookeba tornado (dark red shaded area). Yellow rectangle indicates estimated radar observed sector for time period 1 (Adapted from NOAA, online source 2). The observation period continued through the time when the tornado dissipated at With a scan interval of 17 seconds, 33 scans were available for analysis at the lowest elevation angle. Values of ΔVmax ranged from ms -1, and the beam height range for the lowest level scans were m above ground level. The surface roughness ranged from m, and the topographic elevation ranged from m. Even with the relatively high beam height, the change in surface roughness throughout the track provides an opportunity to examine surface roughness change and tornado intensity. At the onset of the observation period, the tornado moved into a

73 73 wooded area. The tornado then moved into an area of cultivated crops/grassland and intensified. The intensification continued as the tornado crossed state highway 281. The dissipation of the tornado began shortly after crossing the highway. The supercell that resulted in the Lookeba, Oklahoma tornado eventually also produced the El Reno/Piedmont, Oklahoma tornado, which will be examined hereafter. Table 3.4: As in Table 3.3, but the Lookeba tornado. Case (period) Lookeba Collection Time (UTC) 2037: :20 Scan Interval (seconds) ~ 17 Beam Height (meters AGL) Elevation Range (meters) Surface Roughness Range (meters) Vmax Range (ms -1 ) Tornadogenesis 2031 Tornado Dissipation El Reno/Piedmont, Oklahoma-24 May 2011 As the supercell that produced the Lookeba tornado moved northeastward, another tornado formed at 2050, only three miles from and four minutes after the dissipation of the previous tornado (Fig. 3.6). According to the final damage survey, this second tornado was on the ground for an hour and forty-five minutes and traversed 63 miles (NOAA, online source 2).

74 74 Figure 3.6: Designated path by National Weather Service based on damage survey for the El Reno/Piedmont tornado (dark red shaded area). Tornado B3 is identifying the location of a short-lived satellite tornado that was associated with the main tornado B2. The rectangles represent the estimated radar observed sectors for the five different periods: 1 st period (red), 2 nd period (orange), 3 rd period (yellow), 4 th period (green), and 5 th period (blue) (Adapted from NOAA, online source 2). Due to the longevity of the tornado, five different time periods and data from two radars were examined (Table 3.5, Table 3.6). RaXPol observations are utilized for three of the five time periods (periods 1, 2 and 3). Tornadogenesis and intensification of the tornado were observed as it moved toward the city of El Reno. The MWR-05XP radar resumed the observations after the tornado passed to the northwest of El Reno and headed toward the city of Piedmont (periods 4 and 5). After the conclusion of the observations, the tornado continued north for an additional forty-five minutes. The first time period only lasted for three and a half minutes (2051: :50), and with volumetric scan rates of 17 seconds, this equated to 12 scans for analysis.

75 75 During this period, the remnant circulation from the Lookeba tornado dissipated and a new area of strong low-level rotation developed, which went on to produce the El Reno tornado (Houser et al. 2015). The intensity started at 58 ms -1 and increased to 104 ms -1. The surface roughness ranged from m as the tornado moved through a wooded area near the end of the time period. Lowest level beam heights ranged from m, and elevation started at 497 m and dropped to 419 m. Data collection was briefly interrupted at this point in time to change the scanning strategy. Over the next six minutes (2055: :38), data were collected only at 1 beam elevation every two seconds, equating to over 200 frames. The magnitude of intensity ranged from 103 ms -1 to 192 ms -1. Topographic elevation dropped from 450 m to 408 m within the flood plain of the Canadian River before increasing back to 467 m during the second half of the time period. The lowest beam heights throughout the entire study (55-84 m AGL) were associated with this time period. Although the majority of the dataset contained mainly lower surface roughness (0.03 m), there were periods when the tornado moved through deciduous forest that where associated with moderately higher values (0.43 m). The third scanning strategy returned to the 17 second scanning strategy which was used during the first time period. The observations continued for an additional 14 minutes (2102: :50). At the onset of the third time period, the tornado began to move in a more easterly direction. During the first two time periods, the tornado was moving from southwest to northeast; however, around 2102, it made a definitive switch to a more eastnortheast direction (Fig 3.6). During the third observation period, the tornado nearly

76 76 paralleled interstate 40, before crossing the highway at the conclusion of the period. Due to the slower scanning method, 54 scans were available for analysis. The intensity values ranged from 188 ms -1 at the onset of the period to 89 ms -1 at its conclusion. Although the majority of the land cover was grassland, there were a few areas of deciduous forest resulting in a surface roughness range (area mean) from m. The height of the lowest level scan was between 89 and 302 m AGL, and the topographic elevation started near 482 m and dropped to 425 m near the end of the time period. Table 3.5: As in Table 3.3, but for the data collected by RaXPol during the El Reno tornado. Case (period) El Reno (1) El Reno (2) El Reno (3) Collection Time (UTC) Scan Interval (seconds) Beam Height (meters AGL) Elevation Range (meters) Surface Roughness Range (meters) 2051: : : : : :50 ~ 17 ~ 2 ~ Vmax Range (ms -1 ) Tornadogenesis 2050 N/A N/A Tornado Dissipation N/A N/A N/A The third time period concluded the observations collected by the RaXPol radar, however, the tornado continued to move northeast toward Piedmont, Oklahoma. The

77 77 MWR-05XP radar observed an additional 16 minutes with a two-minute pause as the radar changed sectors (Table 3.6). The fourth time period began at 2133:43, creating a 17-minute gap between the third and fourth time periods. With an 11 second scanning strategy, the MWR-05XP observed 38 scans at the lowest elevation angle during the fourth time period. The intensity ranged from ms -1, and the lowest level beam height started at 207 m and ended at 307 m AGL. The topographic elevation varied from 372 m to 418 m due to the presence of small river valleys, and the surface roughness ranged from m. The fifth and final observational time period for the El Reno/Piedmont tornado lasted seven minutes (2142: :43). The 11 second scanning strategy remained from the fourth time period so 42 scans were observed. The intensity ranged from ms -1, and the lowest level beam height increased from 337 m to 409 m AGL by the end of the observation period. Similar to time period four, there were minor changes in elevation (range, m) associated with small river valleys. The surface roughness change was of less magnitude when compared to the previous time period, with values ranging from m. The tornado continued moving northeast for an additional 45 minutes after the conclusion of the final time period.

78 78 Table 3.6: As in Table 3.3, but for the data collected by the MWR-05XP during the El Reno tornado. Case (period) El Reno (4) El Reno (5) Collection Time (UTC) 2133: : : :43 Scan Interval (seconds) ~ 11 ~ 11 Beam Height (meters AGL) Elevation Range (meters) Surface Roughness Range (meters) Vmax Range (ms -1 ) Tornadogenesis N/A N/A Tornado Dissipation N/A N/A Carney, Oklahoma-19 May 2013 On 19 May 2013, two tornadoes were observed by RaXPol. The first of the two tornadoes was the Carney tornado. According to the damage survey (NOAA, online source 3), the tornado was on the ground from , and was given an intensity rating of EF-3 within the city of Carney (Fig 3.7).

79 79 Figure 3.7: Damage Assessment Toolkit analysis of Carney tornado. The shaded areas are estimated intensity ratings based on the Enhanced Fujita Scale, light blue (EF-1), yellow (EF-2), orange (EF-3). The red rectangle represents the estimated portion of the path that the radar observed for time period 1 (Adapted from NOAA, online source 3). The observation period (2149: :36) does not contain the portion of the track that impacted the city. As the observation period with the longest scanning rate, 52 seconds, the 17 minutes of observation only equated to 21 scans (Table 3.7). The intensity ranged from ms -1, and the lowest level beam height started at 271 m and decreased to 158 m AGL before observations ceased. The topographic elevation ranged from 266 m to 328 m, and the surface roughness ranged from 0.13 to 0.87 m, which is the highest range across all datasets analyzed. Large shifts in the surface roughness occurred due to dense areas of deciduous forest along the path.

80 80 Table 3.7: As in Table 3.3, but for the Carney tornado. Case (period) Carney Collection Time (UTC) 2149: :36 Scan Interval (seconds) ~ 52 Beam Height (meters AGL) Elevation Range (meters) Surface Roughness Range (meters) Vmax Range (ms -1 ) Tornadogenesis 2141 Tornado Dissipation Shawnee, Oklahoma- 19 May 2013 The second tornado occurred a little over 30 minutes after the Carney tornado ended ( ). RaXPol made three different deployments; however, the second only consisted of five frames and was therefore removed from the analysis. The first time period began shortly after the tornado crossed Lake Thunderbird, which is southwest of Shawnee, OK (Fig. 3.8).

81 81 Figure 3.8: Damage Assessment Toolkit analysis of Shawnee tornado. The different colored triangles represent damage reports. The shaded areas are estimated intensity ratings based on the Enhanced Fujita Scale, light blue (EF-0), green (EF-1), yellow (EF- 2), orange (EF-3), red (EF-4). The yellow-orange rectangle is the estimated radar observed area during time period 1. The red rectangle is the estimated observed area during time period 3 (Adapted from NOAA, online source 3). With a 33 second volumetric scan rate, the observation period, 2313: :52, equated to 15 scans at the lowest elevation angle. The intensity ranged from 94 to 141 ms -1 and the lowest level beam height started at 215 m and decreased to 150 m AGL as the tornado moved toward the radar. The topographic elevation ranged from 330 m to 370 m, and surface roughness values ranged from m, which is the highest weighted mean average across all of the datasets. Due to the tornado s location and heading, RaXPol s crew stopped collecting data to move to a safer location. At the new

82 82 location, the radar started scanning, but ground features blocked the propagation of the radar beam into the storm, so data collection again stopped and the instrument was moved to another location. Throughout these events, the tornado crossed the Shawnee Reservoir to the west of Shawnee and caused EF-4 damage immediately after exiting the reservoir (NOAA, online source 3). Unfortunately, these events occurred during times when the radar was not collecting data. After finding a sufficient deployment location, the third deployment began 21 minutes after the first deployment ended (Table 3.8). The observations continued for nine minutes (2341: :27) as the tornado crossed interstate 40 and caused EF-3 damage to a neighborhood north of I-40. The 33 second volumetric scan rate continued so 15 additional scans at the lowest elevation angle were added to the analysis with intensity ranging from ms -1. The lowest level beam height started at 145 m and increased to 215 m AGL by the end of the deployment, and the elevation ranged from 320 m to 345 m. The surface roughness values ranged from m.

83 83 Table 3.8: As in Table 3.3, but for the Shawnee tornado. Case (period) Shawnee (1) Shawnee (3) Collection Time (UTC) 2313: : : :27 Scan Interval (seconds) ~ 33 ~ 33 Beam Height (meters AGL) Elevation Range (meters) Surface Roughness Range (meters) Vmax Range (ms -1 ) 94 to Tornadogenesis 2300 N/A Tornado Dissipation N/A Instrumentation and Methodology Limitations Although radar technology provides the capability of observing tornado behavior, the radars and the data collected are not without limitations. Since the intensity of the tornado is the primary focus, only the limitations associated with the gathering of velocity data are discussed. The first limitation arises because radars do not measure the actual velocity of the wind. Radars gather information by sending out pulses of electromagnetic radiation. The radar measures the speed of scatterers (e.g. dust, insects, rain, debris, etc.) in the atmosphere because scatterers are needed for the absorption and subsequent reemission of electromagnetic radiation that is then returned to the radar. Based on the amplitude of the returned wave and the phase change between two consecutive wave pulses, information about the size/density of the targets (reflectivity) and the speed of the targets (velocity), respectively is quantized during post-processing. In order for the velocity data

84 84 to be non-zero, a target must be in motion and must have a component of motion that is parallel to the transmitted wave. For example, two wave pulses are transmitted by the radar in a sine wave configuration. When the first wave encounters a moving target, the return wave arrives at a particular point along the sine wave. The second wave encounters the same target, however, at a lesser (or greater) distance than the first wave owing to the motion that has occurred between the transmission of the two pulses. Due to this change in distance, the return wave arrives at a different phase along the sine wave. The difference in phase along the sine wave is correlated to an actual physical distance, which is then used to calculate the velocity of the target, as the time between the transmission of the two pulses is known. Another limitation arises because tornado intensity is derived (i.e. for radar analysis) from the comparison of the maximum inbound winds versus the maximum outbound winds. Two key factors are associated with this specific limitation. The first is that radar can only detect the motion directly toward or away from the orientation of the radar beam (i.e. the radial component of motion). Additionally, the ever changing distance between the tornado and the radar results in varying heights of measurement within the tornado (Fig. 3.9).

85 85 Figure 3.9: An illustration depicting how the beam height changes with increased distance from the target. The RaXPol radar is mobile, while the WSR-88D is stationary. A mobile radar can approach the target from a much closer range. The beam height increases with distance from the radar for two reasons, the initial elevation angle of the lowest-level radar beam and the curvature of the earth. If the distance between the radar and the tornado is changing, then the height of a measurement at a specific point in the tornado is also changing. As a result, the velocity values that are used to derive an intensity value for the tornado are acquired at a varying heights throughout the observation time periods. For this study, velocity values at 250 meters above the ground are assumed to be similar to velocity acquired at 100 meters above the ground; however, this is probably not true. Changing beam heights will certainly result in error for particular cases with large changes in beam height. Another limitation arises with how the data velocity data are quantified in the presence of strongly rotating motion. As tornadoes move along the ground, debris (e.g.

86 dust, insects, trees, man-made structures) are often introduced into the circulation of the tornado. As stated previously, radars detect properties of scatterers (objects such as dust, insects, precipitation, birds, large debris, etc.). Doppler velocity is a power-weighted parameter, meaning that the higher the amplitude of the return, the more it contributes to the estimate of velocity estimate. Therefore, the introduction of debris, especially large debris, will bias the estimate of air velocity in comparison to the estimate of air velocity of smaller debris and this debris will have the same velocity as the air surrounding it as a result of differences in inertia. Additionally, when debris, which has a greater mass than hydrometeors, enters the tornado vortex, the centrifugal force increases according to the equation: CF = mv2 r 86 Equation 3.12 where the centrifugal force, CF equal the mass, m times velocity squared, V 2 divided by radius, r (Dowell et al. 2005). Mass and velocity are proportional to the magnitude of the centrifugal force, while radius is inversely proportional. As a result of centrifuging, debris scatterers cause error within the radar-derived wind speeds as a result of debris diverging away from the axis of rotation (Dowell et al. 2005, Wurman and Alexander 2005, Wurman et al. 2013). Dowell et al. (2005) conclude that debris availability (e.g. only rain drops and insects versus trees and urban areas) will impact radar estimated wind speeds differently due to the different magnitudes of power returned and centrifuging. A type of displacement error can also occur. The center of the tornado as derived by radar data may not represent the true center of the tornado at the ground because

87 87 tornadoes can tilt vertically in the atmosphere. The biggest errors will potentially be associated with higher low-level beam heights, because the tornado may be tilted below the beam. Since data are extracted primarily using the center of the tornado, any tilt would result in a possible incorrect location for the exact center, therefore, a misrepresentation of the values extracted while using the center is possible. Conclusions found using cases where the lowest beam height is further from the surface will contain an unknown amount of error because the tilt of the tornado between the radar and the ground is unknown. Since the mapping techniques utilize the radar analysis data to extract geographic information, limitations associated with the location selection could result in error. The center of the tornado is used to extract elevation, slope, and aspect values. Therefore, any unknown errors that occurred during the radar analysis, would impact the values extracted using the GIS methods described. Additionally, the methods used for evaluating the surface roughness are dependent on the locations of the center and full radius of the tornado. Since tornadoes are rapidly evolving systems which form due to sensitive storm mechanisms and atmospheric conditions, the chosen statistical analysis may also contribute additional errors. These statistical tests analyze the time periods as a whole which may diminish specific events that are related to topography and land-cover effects. When analyzing these statistical tests it is assumed that there is a normal distribution across all of the variables investigated, which may not be entirely true, especially for cases with a small number of samples. For this reason, three different statistical methods

88 88 are used. Additionally, graphics created in Microsoft Excel will assist in noticing any unique or significant changes that can be investigated outside the statistical methodology. The final limitation in regards to the statistical analysis is associated with the assumption that the effects of land-cover and topography are acting independently of one another. Lastly, the number of case studies (five tornadoes divided into eleven time periods) discussed limits the overall dataset. From different low-level beam heights, to varying intensity, there are very few similarities across the five tornadoes so comparisons between cases will carry limitations as well. Four of the five tornadoes occur in Oklahoma, which has minor relief in topography and abundant low roughness land-cover. The lack of robust changes with respect to these variables may decrease the potential in verifying the effects found in studies with larger topographic features. Despite all of these limitations, the research completed here is unique and may assist in benefiting future research regarding topographic and land-cover effects on tornado intensity.

89 89 CHAPTER 4: RESULTS 4.1 Individual Cases Goshen County, Wyoming- 5 June 2009 The initial intensification phase of the tornado ended just prior to the second period of data collection, which occurred from 2200: :07 (Table 4.1). Because surface roughness did not change (Fig. 4.1a) across the path of the tornado, a relationship between surface roughness and intensity with this particular tornado is not investigated; however, topographic elevation (Fig. 4.1b) did change. At the start of the second period, the tornado was nearly stationary, as illustrated by the collection of green dots in the upper left portion of Fig. 4.1b. The tornado advanced eastward, into a valley of ~30 m in depth (Fig. 4.2a), decreasing in intensity ( Vmax) ~15 ms -1. The tornado then ascended the other side of the valley, decreasing another ~20 ms -1. Once atop the ridge, the tornado gradually intensified ~20 ms -1. The tornado descended into another valley, continuing to intensify to ~90 ms -1. Near the end of the time period, the tornado maintained similar intensity until the last scan, where the velocity reached over 100 ms -1.

90 Table 4.1: A summary of basic information for the second period of the Goshen County, WY case. Number of scans, Intensity ( Vmax) Case (period) Time frame scan rate range in ms (seconds) -1 Goshen County (2) 2200: :07 156, Low-level beam height range (m) Elevation range (m) Area mean surface roughness range (m) Number of interpolated scans Note: The information specifies the case study location (Goshen County, Wyoming) and chronologically-based subset of data collection within the deployment (Period 2); the time (UTC) over which data were collected within that period (2200: :07); the number of scans observed (156 scans) along with the scan interval (6 seconds); the intensity range ( Vmax) derived from radar analysis ( ms -1 ); the lowest-level beam height range in meters above ground level ( m); the topographic elevation range in meters about sea level ( m); the area mean surface roughness range in meters ( m); and the number of missing scans interpolated for within the time period. 90

91 Figure 4.1: GIS maps illustrating a) land-cover and b) elevation over the path of the tornado. For 4.1a, the center of the tornado for each scan (green dots) is overlain onto the 2011 Land Cover dataset, which for this case is primarily Grassland/Herbaceous (see legend). The grey circles represent the full radius derived from radar analysis. 4.1b consists of the same tornado path, however, the path is now overlain on the elevation dataset. Higher elevation is indicated by the dark orange and lower elevation is indicated by the dark blue. 91

92 Figure 4.2: Graphical representation of the relationship between elevation and intensity throughout the time period. For 20a, the unsmoothed intensity (blue line) values (left y- axis) are combined with the elevation (brown area) values (right y-axis) according to the scan number (x-axis). 20b is similar to 20a; however, a 5-scan running mean has been applied to the raw data. 92

93 93 Topographic elevation is negatively correlated with intensity (Table 4.2), having a correlation coefficient of , suggesting that higher elevation is associated with lower intensity ( Vmax). The correlation is statistically significant with a probability of p < 0.001, where the null hypothesis of no relationship is rejected, and the alternative hypothesis of a relationship is accepted. Thus, for this case, there is a statistically significant correlation between elevation and intensity such that the tornado was weaker when located on higher topography. Slope is positively correlated with intensity, having a correlation coefficient of 0.152, which is just above the criteria for a statistically significant value, having a probability p < The correlation coefficient for aspect (0.010, p < 0.902) is near 0, indicating no relationship between intensity and aspect. Table 4.2: A summary of correlations and the associated probabilities for the topographic parameter, elevation, slope, and aspect. Bolded values are significant (p < 0.05 for a twotailed t-test). Correlation Correlation Correlation Method Prob. Prob. Prob. (elevation) (slope) (aspect) Unsmoothed < Smoothed < Derivative Despite the overall correlation present between elevation and intensity, several exceptions to the correlation can be determined within shorter time periods using a smoothed version of Fig. 4.2a (Fig. 4.2b). The smoothed data yields a correlation of , which slightly improves the negative correlation coefficient found with the

94 94 unsmoothed data. During the initial part of the period, 2200: :09 (scans 1-13), tornado intensity increases over increasing elevation; however, as stated before, the collection of green dots suggests that the circulation was relatively stationary for several scans, so very little credence is given to the possible effects of elevation on this portion of the tornado path. The increasing elevation during that time may have been caused by the manually selected placement for the center of circulation. With the lowest level beam height approximately 225 meters above ground level, the exact location of the tornado at the surface may not be perfectly represented here either, introducing error to the results. Based on Fig 4.2b, an important conclusion is that the tornado intensified on top of the hill or ridge before moving eastward into the valley. Two additional exceptions to the negative correlation are found in time frames 2201: :19 (scans 13-41) and 2210: :37 (scans ). Here it is found that decreasing intensity occurred over decreasing elevation. The derivative: Vmax / zelev specifies the change of elevation verses the change of intensity, and this parameter is also investigated. The correlation coefficient remains negative (-0.139) meaning that as the tornado moved from higher to lower elevations, the intensity increased. The statistical probability of p < reveals that this particular relationship is nearly significant; however, since the probability failed to reach the p < 0.05 threshold, the null hypothesis is not rejected. For the composite analysis, the intensity anomalies are quantified as given in eq. 3.8 and the top 25 th (i.e. 75 th ) and bottom 25 th intensity anomaly percentiles are split into two groups. The means of elevation, aspect and slope between the two groups are

95 95 compared and tested for significance. The probability of the means for elevation being equal between the two groups is p < Therefore, it is appropriate to reject the null hypothesis and accept the alternative hypothesis that the means between the two categories are, in fact, different. The difference indicates that topographic elevation values were greater for higher intensity and lower for lower intensity. Slope is nearly significant with a probability of p < Similar to the correlation coefficient, aspect reveals no significance with a probability of p < The same method is applied to the derivative value of elevation. The comparison of means returns a non-significant probability of p <0.436, indicating a lack of large differences between the means. In order to examine the predictability of intensity with respect to all of the variables available in the dataset, (beam height, elevation, aspect, slope), linear regression tests were performed. The first test (test 1) utilizes all of the variables available while the second test (test 2) removes beam height because it is not a geographic derived variable and it is known that the intensity of a tornado vortex is a function of beam height. Several components to the model are of interest here, the regression correlation, R and the percentage of variance explained by the model, R-squared. Additionally, each independent variable (i.e. predictor) is provided a coefficient (or slope) with a standard error. The standard error represents the precision of the estimated slope. Predictors with large correlation values indicate a possible relationship with intensity; however, the standard error must remain small, relative to the coefficient, in order for the relationship to possibly be significant. The significance is provided by a t-value and the resulting probability.

96 96 The first test produced an overall regression correlation, R = with an R 2 = When the beam height was removed, the second test produced a regression correlation, R= with an R 2 = 0.381, implying that only 38.1% of the model variance is explained by elevation, slope, and aspect. With the removal of beam height, the model maintains the regression correlation and percentage of variance explained. The justification for the lack of large change between the different model output is discovered through the interpretation of the predictor significance (Table 4.3, Table 4.4). For test 1, slope and elevation carry the highest negative coefficient values, and respectively; however, slope contains a larger standard error. The standard error represents the average distance of the observations away from the regression line. The larger the error, the more uncertain the slope. Ultimately for test 1, the influence of beam height (p < 0.001) and elevation (p < 0.001) is significant, therefore the null hypothesis of b = 0 is rejected, and the alternative hypothesis of b 0 is accepted. This result implies that beam height and elevation were strongly associated with intensity. With beam height removed in test 2, elevation is the only variable that is significant. Overall, for this particular case, beam height and elevation are considered important predictors of intensity, therefore implying a relationship.

97 Table 4.3: Unstandardized coefficient summary from the multiple linear regression output containing the coefficient value, standard error, t-value, and probability for each variable used in test 1 (all predictors available are used). Probability values that are significant at the 95% confidence interval (p < 0.05) are bolded. 97 Goshen 2 Test 1 Coefficient Standard Error t-value Probability Beam Height Elevation <0.001 Slope Aspect Table 4.4: As in test 1, but excluding beam height (test 2). Goshen 2 Test 2 Coefficient Standard Error t-value Probability Elevation <0.001 Slope Aspect Throughout the application of the three statistical methods, three results are determined from the second time period of the Goshen County tornado, 1) a significant negative correlation exists between intensity ( Vmax) and elevation, 2) elevation means within the composite analysis are significant, and 3) elevation and beam height are significant predictors of intensity in test 1, and elevation remains significant in test 2. In comparison to the second observational period, the third time period, 2217: :34, is much shorter. Only 31 scans were observed during the increment of time. The surface roughness is still homogeneous (Fig. 4.3a) so it will not be included in the

98 98 analysis (Table 4.5). The beam height continued to decrease throughout the period as the tornado moved closer to the radar, initially starting at 107 m, dropping to 96 m by scan 16, and slowly increasing to 103 m by the end of the period. At the onset of the observations, intensity ( Vmax) started at ~110 ms -1 and consistently decreased in intensity to ~49 ms -1 by the end of the period (Fig. 4.4a), most likely as a result of stormrelated processes (the tornado dissipated at 2231). The 5-scan running mean (Fig. 4.4b) also clearly indicates decreasing intensity with decreasing elevation. The only deviation from the steady decrease in elevation throughout the time period (Fig. 4.4a) occurred between 2217: :51 (scans 3-7) as the tornado moved out of a valley and onto the north side of a ridge. The elevation increased by ~20 m, and the intensity decreased by ~20 ms -1. Table 4.5: As in Table 4.1, but for the third observational period. Number of scans, Intensity ( Vmax) Case (period) Time frame scan rate range in ms (seconds) -1 Goshen County (2) 2217: :34 31, Low-level beam height range (m) Elevation range (m) Surface roughness range (m) Number of interpolated scans

99 Figure 4.3: As in Fig. 4.1, but for the third period of the Goshen County case. 99

100 Figure 4.4: As in Fig. 4.2, except for the third observation period. 100

101 101 Throughout the time period, correlations revealed an opposite relationship in comparison to time period 2. Elevation still had the strongest correlation coefficient (0.687); however, the correlation was now positive, indicating that lower (higher) elevation was correlated with weaker (stronger) intensity (Table 4.6). The correlation is supported by the statistically significant probability of p < 0.001, resulting in the rejection of the null hypothesis of no correlation. Slope (0.264, p < 0.151) contained a statistically non-significant positive correlation and aspect (-0.03, p < 0.872) revealed no correlation. Despite the lack of large fluctuations in the data, the 5-scan running mean technique was applied to the raw data. With the fluctuations removed, the correlation between intensity and elevation became more positive (0.807), increasing confidence in the relationship between these two parameters. Table 4.6: As in Table 4.2, but for the second period of the Goshen case. Correlation Correlation Correlation Method Prob. Prob. (elevation) (slope) (aspect) Prob. Unsmoothed < Smoothed < Derivative The correlation coefficient between the change of intensity and the change of elevation ( Vmax / zelev) is not nearly as impressive (0.092, p < 0.622), suggesting that it is likely that no correlation exists between these two variables in either observation period.

102 102 For the composite analysis, the top 25 th and bottom 25 th intensity anomaly percentiles are split into two groups. The means of elevation, aspect and slope between the two groups are compared and tested for significance. The composite analysis through the comparison of elevation means between the two intensity categories yields a probability of p < Therefore, the null hypothesis that the means are equal can be rejected, implying that the means between the two categories are significantly different. Slope (p < 0.255) and aspect (p < 0.628) both are non-significant. Despite the significant result between elevation and intensity, the derivative test produces an insignificant probability of p < Linear regression techniques were also applied to the third time period in order to determine the strongest variables in predicting intensity. With all four variables (beam height, elevation, slope, and aspect) included, test 1 produced a regression correlation, R = 0.876, and an R 2 = That means that the linear regression model explains nearly 77% of the variance. With beam height removed, the second test produced a regression correlation, R = 0.835, and an R 2 = Similarly, to the second time period, the removal of the beam height variable did not have a large impact on the model. When examining the coefficients for test 1 (Table 4.7), positive coefficients (slope) are associated with beam height, elevation, and slope, which indicates a positive correlation. Additionally, all three of these values carry significant probabilities less than the 0.05 threshold. Elevation contains the smallest standard error, therefore, it is produces a low probability of p < Beam height, elevation and slope all contain significant probabilities of being predictive variables and thus the null hypothesis of b = 0 can be

103 103 rejected. For test 2 (Table 4.8), elevation and slope are both significant with aspect continuing to provide minimal contribution to the model. Table 4.7: As in Table 4.3, but for time period 3. Goshen 3 Test 1 Coefficient Standard Error t-value Probability Beam Height Elevation <0.001 Slope Aspect Table 4.8: As in Table 4.4, but for time period 3. Goshen 3 Test 2 Coefficient Standard Error t-value Probability Elevation <0.001 Slope <0.001 Aspect By analyzing the data above, four conclusions of the third period are: 1) a significant positive correlation between tornado intensity ( Vmax) and elevation exists, 2) elevation means within the composite analysis are significant, 3) elevation, beam height, and slope are significant predictors in linear regression test 1, and 4) slope and elevation are significant predictors in both tests Lookeba, Oklahoma 24 May 2011 At the onset of the observational period (2037: :20), the tornado was located in an area classified as evergreen forest (Fig. 4.5a) with a Vmax of ~50 ms -1. The

104 104 time period started and concluded with the highest elevation (480 m) observed with this particular case (Fig. 4.6a). The tornado then moved into a valley (420 m) (Fig. 4.5b) of primarily cultivated crops and grassland (lower surface roughness) and increased in intensity ( Vmax) to ~110 ms -1. Continuing to move east-northeastward, the tornado climbed a ridge (460 m) and crossed a road. The Vmax value dropped over 40 ms -1. The final scans captured the dissipation of the tornado (2046 UTC) as in entered a valley (440 m) and then ascended upslope on the opposing side of the valley (480 m). With the tornado over 17 km away at the start of the observations and a relatively high beam angle (4 ), the lowest level beam height started at 1668 m. Then beam height decreased to 974 m by the end of the period. This range of beam height for this case was hundreds of meters higher than any of the other cases. Consequently, any result is shadowed by this limitation. Despite the limitation, a full analysis is completed for all of the data available (Table 4.9). Since frictional impacts are expected near the surface, the results found here can be used to compare to cases with lower beam height. Table 4.9: As in Table 4.1, but for the Lookeba, OK tornado. Number of scans, Intensity ( Vmax) Case (period) Time frame scan rate range in ms (seconds) -1 Lookeba, OK (1) 2037: :20 33, Low-level beam height range (m) Elevation range (m) Surface roughness range (m) Number of interpolated scans

105 105 Figure 4.5: As in Fig. 4.1 except for the Lookeba, OK tornado. For 4.5a, circles around the tornado center (yellow dots) represent the four radii used to derive surface roughness values, full radius (black), ¾ radius (dark gray), ½ radius (light gray), and ¼ radius (white). In line with the observation, a strong negative correlation coefficient between the intensity ( Vmax) and elevation of is found (Table 4.10). The correlation is

106 106 statistically significant with a p value of < This means that the null hypothesis of no correlation is rejected, and the alternative hypothesis is accepted, implying that it is statistically likely that intensity decreases (increases) with increasing (decreasing) elevation. Slope (-0.208, p < 0.244) has a non-significant negative correlation and aspect (0.142, p < 0.432) has a non-significant positive correlation. When a 3-scan running mean 1 is applied to the data (Fig. 4.6b), the correlation coefficient for elevation remained negative and strengthened to Additionally, the correlation coefficient for slope ( ) strengthened and became significant with a probability p < 0.021, which indicates that while slope is decreasing, intensity ( Vmax) is increasing. No change is found with respect to aspect. The correlation between the change in intensity and the change in elevation ( Vmax / zelev) is also negative. However, with a correlation of and p < 0.312, the relationship is not significant. 1 Since the scan interval is 17 seconds, only a 3-scan running mean is applied.

107 Figure 4.6: As in Fig. 4.2, but for the Lookeba, OK tornado. For 4.6b, 3-scan running mean instead of

108 Table 4.10: As in Table 4.2, but for Lookeba, OK tornado. Correlation Correlation Method Prob. Prob. (elevation) (slope) Correlation (aspect) Prob. 108 Unsmoothed < Smoothed < Derivative For the composite analysis, the top 25 th and bottom 25 th intensity anomaly percentiles are split into two groups. The means of elevation, aspect and slope between the two groups are compared and tested for significance. The comparison of means method for elevation provides a statistically significant probability p < 0.001, which argues for the rejection of the null hypothesis that the means between the two categories are zero. With the rejection of the null hypothesis, it can be declared that the elevation values between the two intensity categories are significantly different. Slope (p < 0.253) and aspect (p < 0.456) are found to be non-significant for this particular test. This result does not reject the null hypothesis, suggesting the means of slope and aspect associated with the intensity categories are not significantly different. In regards to the composite analysis for the derivative, the top 25 th and bottom 25 th intensity change anomalies are split into two groups. Then the means of the elevation change are compared for significant differences. For this particular case, the comparison of means test returned a probability p < 0.186, which is not significant, which implies the changes in elevation associated with the two intensity change categories are not significantly different. As described previously, it is expected that changes in the surface roughness will likely influence the strength of the tornado. Intensity was greatest over low surface

109 109 roughness areas from 2039: :16 (Fig. 4.7a, scans 8-22). Intensity decreased as higher surface roughness values associated with wooded areas were encountered between 2043: :03 (scans 24-32). Figure 4.7: Graphical representation of the correlation between surface roughness and intensity throughout the Lookeba, OK tornado: a) unadjusted data (upper left), b) 3-scan running mean (upper right), and c) the surface roughness change vs. intensity change. For 4.7a, b, the intensity ( Vmax) is represented by the blue line, the area mean is represented by the red line, the weighted mean is represented by the gray line, and the weighted trimean is represented by the yellow line. For 4.7c, the blue line represents intensity change, the red line, area mean change, the gray line, weighted mean change, and the yellow line, weighted trimean change. The correlation between intensity and surface roughness is negative, which means that with rougher land-cover, the intensity is lower with this particular case. The area

110 110 mean, which is simply the mean surface roughness within the full radius, has the strongest correlation coefficient (-0.462), and is supported by a significant probability value of p < (Table 4.11). The weighted mean, which weights the surface roughness according to the defined radii (equation 3.4), has a correlation of (-0.418), and is also supported by a significant probability value of p < The weighted trimean parameter, which has the greatest variability in surface roughness values, still has a negative correlation of , and the probability value of p < is significant. Table 4.11: As in Table 4.2, but for the surface roughness parameters of the Lookeba tornado. Method Correlation (area Prob. Correlation (weighted Prob. Correlation (weighted Prob. mean) mean) trimean) Unsmoothed Smoothed < < < Derivative The 3-scan running mean that was previously applied to the elevation analysis, is also applied to surface roughness (Fig. 4.7b). The correlations for area mean (-0.640), weighted mean (-0.619), and weighted trimean (-0.633) are all strengthened; moreover, all correlations are significant with a probability of p < The cause for the lower correlation in the raw data, with respect to the weighted trimean, is lessened, which ultimately leads to a stronger correlation that is significant. As was done with the analysis of elevation, the derivative values ( Vmax / zrough) are calculated for the surface

111 111 roughness parameters (Fig. 4.7c). Investigating the influence of surface roughness using the derivative values reveals an opposite relationship in comparison to the raw values. The three parameters: area mean change (0.205), weighted mean change (0.259), and weighted trimean change (0.278), all have a positive correlation to intensity change. The weighted trimean change has the lowest probability of p < 0.110, which is not significant. Nevertheless, the positive correlation contradicting the negative correlation found using the unsmoothed data makes for an interesting result, which could be associated with errors during the extraction of surface roughness. For the composite analysis, the top 25 th and bottom 25 th intensity anomaly percentiles are split into two groups. The means of area mean, weighted mean, and weighted trimean between the two groups are compared and tested for significance. The surface roughness parameters, area mean, weighted mean, and weighted trimean, evaluate to probabilities p < 0.004, p < 0.025, and p < using a two-tailed t-test. Area mean and weighted mean meet the significant threshold, therefore, rejecting the null hypothesis that the means between the two intensity categories are the same. The weighted trimean does not meet the significance threshold. For the derivative values, p-values for area mean (p < 0.354), weighted mean (p < 0.223), and weighted trimean (p < 0.110) all evaluate to non-significant probabilities. Interestingly, while the probability for the coefficients increases from area mean to weighted trimean, the probability decreases for the derivative values, which could indicate important differences between the three surface roughness parameters.

112 112 Unlike the Goshen County case, the Lookeba case contains three more variables associate with surface roughness: area mean, weighted mean, and weighted trimean. With the introduction of these variables, additional support for the model is provided. For test 1, which includes all geographic variables (elevation, aspect, slope, area mean, weighted mean, and weighted trimean) and beam height, the regression correlation and R-squared values, R = and the R 2 = 0.546, reveal that the predictors do reasonably well at predicting intensity, and that 54.6% of the response variable (intensity) variance is explained by the model. For test 2, the removal of beam height affected the output very little (R = 0.735, R 2 = 0.540), which indicates the contribution of beam height is low for this particular case. Examining the statistics of each parameter (Table 4.12), the probability value p < of beam height indicates the contribution is not significant, which explains why there is little change in the model performance in Test 2. Test 1 also reveals that topographic elevation is once again a strong predictor. It has a coefficient of and is statistically significant with a probability p < The standard error value of indicates a precise estimate of the predictor. Table 4.13 enforces the results from test 1, with elevation remaining the only significant predictor. The large coefficients associated with the surface roughness parameters indicate a slope, b 0. However, the standard error, or the precision of the estimate, is also large, indicating uncertainty with relationship.

113 113 Table 4.12: As in Table 4.3, but for the Lookeba tornado. Lookeba Test 1 Coefficient Standard Error t-value Probability Beam Height Elevation < Slope Aspect Area Mean Weighted Mean Weighted Trimean Table 4.13: As in Table 4.4, but for Lookeba, OK tornado. Lookeba Test 2 Coefficient Standard Error t-value Probability Elevation < Slope Aspect Area Mean Weighted Mean Weighted Trimean The Lookeba case provides an opportunity to analyze the possible relationship between surface roughness/elevation and intensity with beam height measurements around 1000 m above the ground (the upper flow of the tornado). The height of the

114 114 observations may be a limitation, especially for surface roughness, in regards to the significance and application of this particular case in comparison to the rest of the results. Despite the possible introduction of differences in this case as a result of high beam height, four conclusions are: 1) elevation and intensity ( Vmax) are negatively correlated (significant), 2) intensity and surface roughness are negatively correlated (significant), 3) the comparison of means test indicates elevation and surface roughness are significant with intensity events, and 4) topographic elevation is the most significant predictor for both tests El Reno/Piedmont, Oklahoma 24 May 2011 After the Lookeba, Oklahoma tornado dissipated (2046), the supercell that was associated with that tornado went on to produce the El Reno/Piedmont tornado (referred to as simply El Reno throughout the section). The first time period (2051: :50) was short lived. This period contains the rapid development of the tornado from a small funnel to a rapidly intensifying tornado (Houser et al. 2015). This could therefore be a limitation regarding the results for this particular time period since it is likely that storm mechanisms were a significant factor in the development of the tornado. The tornado developed over areas of cultivated crops and grassland (Fig. 4.8a) and moved downhill (Fig. 4.8b) as it approached the Canadian River. Throughout the period, low-level beam height decreased from 588 m to 342 m as the tornado advanced northeastward (Table 4.14).

115 Table 4.14: As in Table 4.1, but for the first period of the El Reno, OK tornado. Number of scans, Intensity ( Vmax) Case (period) Time frame scan rate range in ms (seconds) -1 El Reno (1) 2051: :50 13, Low-level beam height range (m) Elevation range (m) Surface roughness range (m) Number of interpolated scans Figure 4.8: As in Fig. 4.5 but for the first period of the El Reno, OK tornado.

116 116 Throughout the time period, elevation decreased and intensity ( Vmax) increased leading to a correlation of , which is statistically significant, having a probability value of p < and a consequent rejection of the null hypothesis (Table 4.15). The exception to the relationship is at the end of the time period 2054:50 (scan 13), where intensity decreases ~15 ms -1 with decreasing elevation (Fig. 4.9a). Slope (0.257, p < 0.394) has a positive correlation, but the relationship is not significant. Aspect (0.027, p < 0.544), with a correlation near 0, accepts the null hypothesis of no correlation. By smoothing the data with a 3-scan running mean (Fig. 4.9b), the correlation with elevation becomes stronger (-0.806) and the probability (p < 0.001) is therefore more significant. Slope and aspect remain non-significant, despite the smoothed data. The correlation between the change in Vmax and topographic elevation ( zelev) resulted in a nearly significant (p < 0.077) positive correlation of

117 Figure 4.9: As in Fig. 4.6, but the first period of the El Reno, OK tornado. 117

118 118 Table 4.15: As in Table 4.2, but for first period of the El Reno, OK tornado. Correlation Correlation Correlation Method Prob. Prob. (elevation) (slope) (aspect) Prob. Unsmoothed Smoothed < Derivative For the composite analysis, the top 25 th and bottom 25 th intensity anomaly percentiles are split into two groups. The means of elevation, aspect and slope between the two groups are compared and tested for significance. The composite analysis produced similar findings, possibly due to the small number of samples. Elevation had a probability p < 0.032, which is considered significant (p < 0.05) for a two-tailed t-test. Slope and aspect are also not significant with probability values of p < and p < respectively. The composite analysis also returned non-significant (p < 0.343) for the derivate values of elevation. These non-significant results therefore cannot reject the null hypothesis that the means of the two categories are equal. With the limited number of scans, the surface roughness analysis centered on one specific change in surface roughness between 2052: :44 (Fig. 4.10ab, scan 4-9). During the period of higher surface roughness, tornado intensity is increasing resulting in a positive correlation across all surface roughness parameters: area mean (0.694), weighted mean (0.631), and weighted trimean (0.231). Additionally, two of the three: area mean (p < 0.007) and weighted mean (p < 0.018) are supported by significant probabilities, and therefore a rejection of the null hypothesis, which means that there is a

119 119 relationship between surface roughness and intensity for this particular case. The weighted trimean (p < 0.102) is not significant (Table 4.16). A three-scan mean (Fig. 4.10b) of the data retain the positive correlations for all three parameters (area mean, 0.688, weighted mean, 0.633, weighted trimean, 0.366), and again, the results are statistically significant for area mean (p < 0.008) and weighted mean (p < 0.018). Since the weighted trimean method is strongly reflective of the dominating land-cover type within each radius, low values of surface roughness are being quantified due to the coverage of grassland and cultivated crops. This is the explanation for the differences in the correlations in comparison to the area mean and weighted mean parameters. Investigating the derivative ( Vmax / zrough) of the data (Fig. 4.10c) produces similar results for area mean (0.589, p < 0.031) and weighted mean (0.518, p < 0.066), but only one of these relationships are now below the critical significance value. The weighted trimean (-0.018, p < 0.953) changes the most with no relationship found.

120 120 Figure 4.10: As in Fig. 4.7, but for the first period of the El Reno, OK tornado. Table 4.16: As in Table 4.11, but for the first period of the El Reno, OK tornado. Method Correlation (area Prob. Correlation (weighted Prob. Correlation (weighted Prob. mean) mean) trimean) Unsmoothed Smoothed Derivative For the composite analysis, the top 25 th and bottom 25 th intensity anomaly percentiles are again split into two groups. The means of area mean, weighted mean, and

121 121 weighted trimean between the two groups are compared and tested for significance. For the unsmoothed values, two of three surface roughness parameters returned significant results, area mean (p < 0.007) and weighted mean (p < 0.011). The probability of the weighted trimean (p < 0.102) is non-significant. The conclusion here is that the area mean and weighted mean parameters reject the null hypothesis that the means are equal. However, the comparison of means for the derivative data did not produce similar results. Area mean (p < 0.178), weighted mean (p < 0.222), and weighted trimean (p < 0.772) all produced non-significant results. With the variables available (beam height, elevation, aspect, slope, area mean, weighted mean, weighted trimean), the linear regression test provides an opportunity to examine the predictability of intensity for this particular case. Test 1 (Table 4.17), and test 2 (Table 4.18) both contain strong regression correlations, R = 0.984, R = respectively. These strong correlations are supported by R-squared values of R 2 = and R 2 = 0.924, which implies that the predictors available for the model were satisfactory predictors of intensity. Although beam height, elevation, and slope are strong predictors in test 1, beam height is the only predictor to be supported by a significant probability value (p < 0.045); however, slope is nearly significant (p < 0.054). With beam height removed (test 2), the area mean surface roughness parameter becomes the strongest predictor and is supported by a probability value of p < 0.033, therefore the null hypothesis of b = 0 is rejected, which for this particular case implies that surface roughness (area mean) is a strong predictor, when beam height is not included. The other

122 two surface roughness parameters, along with elevation, were also strong predictors in test 2, but did have significant probabilities. 122 Table 4.17: As in Table 4.3, but for the first period of the El Reno, OK tornado. El Reno 1 Test 1 Coefficient Standard Error t-value Probability Beam Height Elevation Slope Aspect Area Mean Weighted Mean Weighted Trimean Table 4.18: As in Table 4.4, but for the first period of the El Reno, OK tornado. El Reno 1 Test 2 Coefficient Standard Error t-value Probability Elevation Slope Aspect Area Mean Weighted Mean Weighted Trimean

123 123 With only 13 frames available for analysis during the development of the tornado, the relationships discovered are only associated with intensity over a short time frame. Nevertheless, five distinct results from the time period are, 1) elevation is negatively correlated (significant) with intensity ( Vmax), 2) surface roughness is positively correlated (significant) with intensity, 3) comparison mean tests for area mean and weighted mean are significant 4) beam height is a significant predictor (test 1), and 5) surface roughness (area mean) is a significant predictor (test 2). At the conclusion of the first period, data collection was briefly interrupted in order to change the scanning strategy. Over the next six minutes (2055: :38, Table 4.19), data were collected at an elevation angle of 1 every two seconds, yielding in 205 scans. The data resumed with the tornado entering the Canadian River flood plain (Fig. 4.11ab). The low-level beam height started at 75 m, dropped to 54 m by 2057:35, and continued roughly at that height until 2059:08. The beam height rose to 84 m by the end of the period. As the tornado moved into the Canadian River flood plain between 2056: :03 (Fig. 4.12a, scans 26-86), elevation decreased ~40 m, and intensity ( Vmax) increased ~60 ms -1 from 130 ms -1 to 190 ms -1 by 2056:35 (scan 38). Intensity then decreased ~50 ms -1 shortly after the rapid intensification.

124 Table 4.19: As in Table 4.1, but for the second period of the El Reno, OK tornado. Number of scans, Intensity ( Vmax) Case (period) Time frame scan rate range in ms (seconds) -1 El Reno (2) 2055: :38 205, Low-level beam height range (m) Elevation range (m) Surface roughness range (m) Number of interpolated scans The 5-scan running mean (Fig. 4.12b) suggests the intensity remained fairly steady the remainder of time within the flood plain. As the tornado ascended the other side of the flood plain, there are a few deviations in intensity, increasing in some instances while decreasing in others, from 2058: :32 (scans 106 to 136). The only other topographic feature the tornado crossed over was a slight depression ~20 m in depth from 2059: :53 (scans ). Intensity increased on the downslope and subsequently decreased on the upslope of this feature.

125 Figure 4.11: As in Fig. 4.5, but for the second period of the El Reno, OK tornado. 125

126 Figure 4.12: As in Fig. 4.2, but for the second period of the El Reno, OK tornado. 126

127 127 Throughout the course of the entire period, elevation has a positive correlation with intensity (0.242) and is statistically significant with a probability p < (Table 4.20). Aspect (0.161, p< 0.021) also has a positive correlation that is statistically significant, which means increasing intensity with more westward facing slopes. Slope (0.035, p < 0.615) is not strongly correlated with intensity for this case. A 5-scan running mean for elevation evaluated slightly more positive with a correlation value of and a p < The significance means that the null hypothesis of no correlation is rejected and the alternative hypothesis (positive correlation) is accepted, which implies increased intensity with higher elevation for this particular case. The smoothed data also increased the correlation for aspect (0.277) and lowered the probability to p < Slope remained non-significant. The derivative ( Vmax / zelev) reveals an opposite correlation (-0.101, p < 0.150); however, the probability is not significant. Table 4.20: As in Table 4.2, but for the second period of the El Reno, OK tornado. Correlation Correlation Correlation Method Prob. Prob. Prob. (elevation) (slope) (aspect) Unsmoothed < Smoothed < < Derivative For the composite analysis, the top 25 th and bottom 25 th intensity anomaly percentiles are split into two groups. The means of elevation, aspect and slope between the two groups are compared and tested for significance. The composite analysis of the

128 128 means produces similar results to the correlations. Elevation has a probability p < Aspect is also significant with a probability p < These significant results imply that the null hypothesis that the mean between the two intensity categories are equal can be rejected. The rejection of the null hypothesis for elevation and aspect indicates the values associated with lower intensity versus higher intensity are significantly different. Slope, in agreement with the correlation, is not significant with a probability value of (p < 0.322). The derivative ( Vmax / zelev) comparison is not significant (p < 0.337). With the Canadian River flood plain (low surface roughness, ~ m) covering a large section of the analysis, there are only two areas of higher surface roughness noted between 2055: :39 and 2059: :13 (Fig. 4.13a, scans and respectively). The first area, which is associated with deciduous forecast along the river bank, contains an area of increasing intensity ( Vmax); however, the peak intensity occurs after the maximum in surface roughness. The second region is associated with scattered areas of deciduous forest within the valley and contains varying intensity changes.

129 Figure 4.13: As in Fig. 4.7, but for the period of the El Reno, OK tornado. 129

130 130 The correlations between surface roughness and intensity are negative (area mean, , weighted mean, , weighted trimean, ), which would suggest lower surface roughness is associated with higher intensity (Table 4.21). The correlations however, are not supported by statistically significant probabilities (area mean, p < 0.063, weighted mean, p < 0.451, weighted trimean, p < 0.649). The 5-scan mean (Fig. 4.13b) removes a degree of variability associated with the 2 second scan rate, which provides a more fluid analysis. As a result, the correlations between surface roughness and intensity for the smoothed data increase across all three parameters. The correlation for area mean (-0.157) is now supported by a statistically significant probability p < The weighted mean (-0.082, p < 0.295) and weighted trimean (-0.050, p < 0.474) are negatively correlated; however, the probability values do not reach the critical significant value (p < 0.05). Unlike the unsmoothed correlations, the derivative ( Vmax / zrough) (Fig. 4.13c) surface roughness correlations for all three surface roughness parameters are non-significant. Table 4.21: As in Table 4.11, but for the second period of the El Reno, OK tornado. Method Correlation (area Prob. Correlation (weighted Prob. Correlation (weighted Prob. mean) mean) trimean) Unsmoothed Smoothed Derivative

131 131 For the composite analysis, the top 25 th and bottom 25 th intensity anomaly percentiles are split into two groups. The means of area mean, weighted mean, and weighted trimean between the two groups are compared and tested for significance. When comparing the means between the two intensity events, a similar relationship is found. Area mean (0.942) is the variable nearest to a significant value with a probability p < Weighted mean (p < 0.955) and weighted trimean (p < 0.688) are also not significant and rather suggest that there is little differentiation in the means of the two quartiles. The derivative ( Vmax / zrough) values for area mean (1.160, p < 0.249), weighted mean (0.391, p < 0.697) and weighted trimean (0.159, p < 0.874) also indicate a positive relationship with elevation, but are also not significant. Linear regression tests for period two of El Reno produced low regression correlations; however, more predictors are depicted as significant predictors. The regression correlation including all variables (test 1) (Table 4.22) is R = 0.488, and R 2 = 0.238, which indicates a lack of performance by the model. Beam height, elevation, weighted mean, and weighted trimean are all significant predictors for test 1, therefore the null hypothesis of the correlation being near zero is rejected, and these four predictors are found to be important to the model for predicting intensity. When beam height is removed for test 2 (Table 4.23), the correlation decreases to R = and the variance explained by the model drops to R 2 = 0.142, which indicates decreasing performance without beam height included. The low performance is likely associated with the large and rapid swings in intensity from scan to scan. In regards to the predictors, all three

132 surface roughness parameters are significant, which means the null hypothesis can still be rejected. 132 Table 4.22: As in Table 4.3, but for the second period of the El Reno, OK tornado. El Reno 2 Test 1 Coefficient Standard Error t-value Probability Beam Height < Elevation Slope Aspect Area Mean Weighted Mean < Weighted Trimean < Table 4.23: As in Table 4.11, but for the second period of the El Reno, OK tornado. El Reno 2 Test 2 Coefficient Standard Error t-value Probability Elevation Slope Aspect Area Mean Weighted Mean Weighted Trimean

133 133 With a scanning strategy of 2 seconds, period 2 of the El Reno tornado provides a unique opportunity to analyze tornado intensity ( Vmax) and elevation/surface roughness at very small timescales. Six main points can be taken away from the El Reno period 2 dataset: 1) elevation is positively correlated (significant) with intensity, 2) aspect is positively correlated (significant) with intensity, 3) the smoothed raw data produced a significant negative correlation with one surface roughness parameter, area mean, 4) comparison of means test produced significant probabilities for elevation and aspect, 5) as predictors, beam height, elevation, weighted mean, and weighted trimean are all significant in test 1, and 6) in test 2 (beam height removed) all three surface roughness parameters are significant in predicting the intensity of the tornado. For time period 3 (2102: :50), the El Reno tornado shifted from a northeastward track to a more easterly track (Fig 4.14ab). The scanning strategy of the RaXPol radar also changed from 2 seconds to 17 seconds. The beam height was at 89 m and gradually rose to 302 m by the end of the observation period (Table 4.24). Starting on top of a ridge of ~480 m, the tornado moved eastward through a valley ~30 m in depth (Fig 4.14b), slowly decreasing in intensity ( Vmax) from ~190 ms -1 to 140 ms -1. The tornado then moved through a valley of ~440 m and over a hill of ~470 m before descending to an elevation of ~430 m into an area of primarily agricultural flat land (Fig. 4.14a). The tornado paralleled interstate 40 throughout the majority of the time period before crossing it near the end. The intensity varied between 130 ms -1 and 150 ms -1 while the tornado moved across a ridge between 2107: :07 (Fig. 4.15ab, scans 18-33)

134 before descending ~40 m into a valley. Intensity decreased ~60 ms -1 to ~90 ms -1 by the end of the period. 134 Table 4.24: As in Table 4.1, but for the third period of the El Reno, OK tornado. Number of scans, Intensity ( Vmax) Case (period) Time frame scan rate range in ms (seconds) -1 El Reno (3) 2102: :50 54, Low-level beam height range (m) Elevation range (m) Surface roughness range (m) Number of interpolated scans Figure 4.14: As in Fig. 4.5, but for the third period of the El Reno, OK tornado.

135 Figure 4.15: As in Fig. 4.6, but for the third period of the El Reno, OK tornado. 135

136 136 It is discovered that for this particular case, elevation has a positive correlation of with intensity (Table 4.25). The correlation is significant at a probability of p < This result rejects the null hypothesis implying that there is a relationship, positive in this case, between elevation and intensity. Slope (0.489, p < 0.001) is also positively correlated and supported by a significant probability. Aspect (-0.022, p < 0.892) is not significant. A 3-scan running mean (Fig. 4.15b), increases the correlation for elevation and slope to and respectively, further increasing the significance. Aspect (p < 0.434) remains non-significant. When specifically addressing the change of elevation and the change of intensity, the derivative ( Vmax / zelev) correlation and probability ( , p < 0.485) accepts the null hypothesis of no correlation. Table 4.25: As in Table 4.2, but for the third period of the El Reno, OK tornado. Correlation Correlation Correlation Method Prob. Prob. Prob. (elevation) (slope) (aspect) Unsmoothed < < Smoothed < < Derivative For the composite analysis, the top 25 th and bottom 25 th intensity anomaly percentiles are again split into two groups. The means of elevation, aspect and slope between the two groups are compared and tested for significance. Both elevation and slope are significant with a probability of p < for elevation and p < for slope. This suggests that the means between the two intensity categories are not equal. Aspect

137 137 remains non-significant (p < 0.890). The derivative ( Vmax / zelev) also remains nonsignificant (p < 0.506). Higher surface roughness between 2102: :23 (Fig. 4.16ab, scans 1-34) are associated with higher intensity ( Vmax), which results in a positive correlation for all three surface roughness parameters (Table 4.26), area mean (0.640, p < 0.001), weighted mean (0.522, p < 0.001), and weighted trimean (0.265, p < 0.052). The correlations are significant for area mean and weighted mean, therefore, the null hypothesis is rejected; however, weighted trimean is again outside the significant threshold. The 3-scan running mean increases all three correlations, pushing the probability (p < 0.004) for the weighted trimean passed the significant threshold. The derivative ( Vmax / zrough) (Fig. 4.16c) method did not evaluate as strongly as the unsmoothed data. Area mean (0.030, p < 0.816), weighted mean (0.059, p < 0.670), and weighted trimean (0.053, p < 0.705) were all found to have non-significant correlations.

138 Figure 4.16: As in Fig. 4.7, but for the third period of the El Reno, OK tornado. 138

139 139 Table 4.26: As in Table 4.11, but for the third period of the El Reno, OK tornado. Correlation Correlation Correlation Method Prob. (weighted Prob. (weighted Prob. (area mean) mean) trimean) Unsmoothed < < Smoothed < < Derivative For the composite analysis, the top 25 th and bottom 25 th intensity anomaly percentiles are split into two groups. The means of area mean, weighted mean, and weighted trimean between the two groups are compared and tested for significance. Area mean and weighted mean have significant probabilities of p < for both parameters, suggesting the surface roughness between the highest and lowest intensity categories are significantly different. The weighted trimean is not significant (p < 0.079). This would indicate that once again, the weighted trimean derives surface roughness slightly different, which alters the results in comparison to the other two surface roughness parameters. When examining the derivative values ( Vmax / zrough), the comparison of means reveal lower probabilities (area mean, p < 0.396, weighted mean, p < 0.089, weighted trimean, p < 0.206) in comparison to the derivative correlation discussed previously. This means that while the correlations between intensity change and surface roughness change are not significant, the mean surface roughness change between the two categories of intensity change did show some differences; however, the differences are not statistically significant.

140 140 Linear regression techniques with all variables included (test 1, Table 4.27) produce a regression correlation and R-squared values of R = and an R 2 = respectively. The only significant predictor in test 1 is beam height with a probability value of p < 0.001, therefore the null hypothesis of no correlation between beam height and intensity can be rejected. This would indicate beam height is a significant contributor to predicting intensity. With beam height removed (test 2, Table 4.28), the regression correlation is R = and the R-squared value is R 2 = 0.662, which do decrease in comparison to test 1. Despite the drop in model performance with beam height removed, elevation (p < 0.001) and slope (p < 0.031) become significant predictors for the model. So while beam height is important to predicting intensity in test 1, the contribution of elevation and slope maintain the performance of the model. Table 4.27: As in Table 4.3, but for the third period of the El Reno, OK tornado. El Reno 3 Test 1 Coefficient Standard Error t-value Probability Beam Height < Elevation Slope Aspect Area Mean Weighted Mean Weighted Trimean

141 141 Table 4.28: As in Table 4.4, but for the third period of the El Reno, OK tornado. El Reno 3 Test 2 Coefficient Standard Error t-value Probability Elevation < Slope Aspect Area Mean Weighted Mean Weighted Trimean For period 3, four results were found, 1) elevation and slope were both positively correlated (significantly) to intensity, 2) area mean, weighted mean, and weighted trimean (only for smoothed data) were positively correlated (significantly) to intensity, 3) beam height is a significant predictor in test 1, and 4) topographic elevation and slope are significant predictors in test 2. At the conclusion of period 3, the MWR-05XP radar resumed observations of the El Reno tornado (period 4: 2133: :22) 17 minutes later. With an 11 second volumetric scanning strategy, 38 additional scans were acquired. The lowest-level beam height started at 207 m and ended at 307 m (Table 4.29). Initially located on top of a ridge of ~420 m (Fig. 4.17b), the tornado moved eastward before turning northeastward for the remainder of the period (Fig. 4.17a). As the tornado moved along the northwest side of a ridge, only subtle elevation changes (between 10 to 30 m) associated with three tributary valleys occurred, 2134: :32 (scans 7-11), 2137: :35 (scans 20-

142 142 23), and 2138: :17 (Fig. 4.18ab) where areas of increasing intensity ( Vmax) occur. Table 4.29: As in Table 4.1, but for the fourth period of the El Reno, OK tornado. Number of scans, Intensity ( Vmax) Case (period) Time frame scan rate range in ms (seconds) -1 El Reno (4) 2133: :22 38, Low-level beam height range (m) Elevation range (m) Surface roughness range (m) Number of missing radar scans Figure 4.17: As in Fig. 4.5, but for the fourth period of the El Reno, OK tornado.

143 Figure 4.18: As in Fig. 4.6, but for the fourth period of the El Reno, OK tornado. 143

144 144 Elevation has a negative correlation (-0.730) with intensity ( Vmax), and is supported by a statistically significant probability value p < 0.001, therefore the null hypothesis is rejected and it is concluded that for this case, elevation increased as velocity decreased, and vice versa (Table 4.30). Additionally, slope (-0.407, p < 0.011) is negatively correlated, and is also significant. Aspect (0.237, p < 0.152) is positively correlated, but is not significant. Applying a 3-scan running mean increases all three topographic correlations, elevation (-0.832), slope (-0.490), and aspect (0.498). The only change in regards to the significance of these correlations is that the correlation for aspect is now significant (p < 0.001). The derivative ( Vmax / zelev) values reveal a similar negative relationship with a correlation of ; however, at a probability value of p < 0.243, the relationship is not significant. Table 4.30: As in Table 4.2, but for the fourth period of the El Reno, OK tornado. Correlation Correlation Correlation Method Prob. Prob. Prob. (elevation) (slope) (aspect) Unsmoothed < Smoothed < Derivative For the composite analysis, the top 25 th and bottom 25 th intensity anomaly percentiles are split into two groups. The means of elevation, aspect and slope between the two groups are compared and tested for significance. Probability values for elevation (p < 0.001) and slope (p < 0.020), are both significant events, therefore rejecting the null

145 145 hypothesis of the means being equal, indicating the means between the two intensity categories are different for this particular case. Aspect (p < 0.155) is not significant. For the derivative ( Vmax / zelev), elevation change versus changes in intensity are not statistically significant (p < 0.693) for the comparison of means test, indicating the elevation change means are not significantly different between the two intensity change categories. With the highest surface roughness for the period at the onset of data collection (Fig. 4.19ab, scans 1-14) when intensity ( Vmax) is lowest throughout the period, a strong negative correlation exists for: area mean, , weighted mean, , and weighted trimean, (Table 4.31). All three surface roughness parameters are supported by significant probability values of p < Therefore, the null hypothesis of no correlation is rejected, and the alternative hypothesis of a correlation is accepted, indicating a strong relationship between surface roughness and intensity. The 3-scan running mean causes all three correlations to become even more negative. The derivative ( Vmax / zrough) (Fig. 4.19c) correlations are also negative and two are significant (area mean change, (p < 0.010), weighted mean change, (p < 0.009), weighted trimean change, (p< 0.116)). This result suggests that decreasing surface roughness is associated with increasing intensity in this case.

146 Figure 4.19: As in Fig. 4.7, but for the fourth period of the El Reno, OK tornado. 146

147 147 Table 4.31: As in Table 4.11, but for the fourth period of the El Reno, OK tornado. Method Correlation (area Prob. Correlation (weighted Prob. Correlation (weighted Prob. mean) mean) trimean) Unsmoothed < < <0.001 Smoothed < < <0.001 Derivative For the composite analysis, the roughness data corresponding with the top 25 th and bottom 25 th intensity anomaly percentiles are split into two groups. The means of area mean, weighted mean, and weighted trimean between the two groups are compared and tested for significance. The comparison of means test once again produces similar results to the correlations. All three surface roughness parameters: area mean (p < 0.001), weighted mean (p < 0.001), and weighted trimean (p < 0.019) are statistically significant. Therefore, it is understood that the surface roughness means between the two intensity categories are significantly different, resulting in a rejection of the null hypothesis. This would indicate higher and lower intensity values are associated with different types of surface roughness. The derivative ( Vmax / zrough) values did not evaluate to the same degree of significance (area mean change, p < 0.176), weighted mean change, p < 0.393, and weighted trimean change, p < 0.995). Once again, a linear regression model is evaluated. For test 1 (all variables used), the predictors (Table 4.32) produced a regression correlation of R = and an R- squared value of R 2 = The strongest predictor is beam height, but the probability is outside the significant, p < With the removal of beam height for the second test

148 148 (Table 4.33), the regression correlation and R-squared values decrease slightly to R = and R 2 = Since beam height is not a significant predictor in test 1, the slight reduction is expected. As is the case in test 1, there are no significant predictors in test 2. Table 4.32: As in Table 4.3, but for the fourth period of the El Reno, OK tornado. El Reno 4 Test 1 Coefficient Standard Error t-value Probability Beam Height Elevation Slope Aspect Area Mean Weighted Mean Weighted Trimean Table 4.33: As in Table 4.4, but for the fourth period of the El Reno, OK tornado. El Reno 4 Test 2 Coefficient Standard Error t-value Probability Elevation Slope Aspect Area Mean Weighted Mean Weighted Trimean

149 149 For El Reno time period 4, there are six conclusive results, 1) elevation and slope are negatively correlated (significantly) with intensity, and 2) all three surface roughness parameters are negatively correlated (significantly) with intensity, 3) two of the three surface roughness parameters: area mean and weighted mean, are negatively correlated (significantly) with intensity change, 4) mean comparison of the intensities for the upper and lower 25 th percentiles are significant for elevation and slope, 5) mean comparison for all three surface roughness parameter are significant, and 6) neither linear regression test produced a significant predictor. The final period of observations (2142: :43, Table 4.34) for the El Reno tornado is the second dataset from the MWR-05XP. The lowest-level beam height started at 337 m and gradually increased to 448 m by the end of the period. The most significant topographical feature with this particular case is a hill that the tornado crossed during the middle of the period (Fig. 4.20b). The surface roughness throughout the case was the lowest of all the datasets ( m), containing mostly cultivated crops and grassland (Fig. 4.20a). Throughout the first 17 scans (2142: :09), the tornado maintained an intensity ( Vmax) between 130 ms -1 and 150 ms -1 as it ascended ~30 m to the top of a hill (Fig. 4.21ab). While traversing the hill, intensity ( Vmax) varied by ~ ±20 ms -1 through 2147:10 (scan 28). As the tornado descended ~20 m into the valley, the intensity gradually decreased until the end of the period. While there is some variation in intensity, the period ended with a similar intensity as the beginning.

150 Table 4.34: As in Table 4.1, but for the fifth period of the El Reno, OK tornado. Number of scans, Intensity ( Vmax) Case (period) Time frame scan rate range in ms (seconds) -1 El Reno (5) 2142: :43 42, Low-level beam height range (m) Elevation range (m) Surface roughness range (m) Number of interpolated scans Figure 4.20: As in Fig. 4.5, but for the fifth period of the El Reno, OK tornado.

151 151 Figure 4.21: As in Fig. 4.6, but for the fifth period of the El Reno, OK tornado. The correlation of suggests a positive relationship between elevation and intensity. A statistically significant probability value of p < supports the relationship by rejecting the null hypothesis of no correlation. Slope (-0.152, p < 0.335)

152 152 and aspect (-0.253, p < 0.106) are not significantly correlated with intensity for this time period (Table 4.35). The 3-scan running mean (Fig. 4.21b) increases the elevation correlation to 0.613, and decreases the probability to p < Slope (p < 0.104) and aspect (p < 0.060) probabilities also decrease, but they do not quite reach the significant threshold, therefore the null hypothesis is not rejected and it cannot be said that either parameter is likely correlated with intensity. The derivative ( Vmax / zelev) correlation (0.123, p < 0.436) suggests a similar positive relationship; however, it is not supported by a probability value of significance. Table 4.35: As in Table 4.2, but for the fifth period of the El Reno, OK tornado. Correlation Correlation Correlation Method Prob. Prob. Prob. (elevation) (slope) (aspect) Unsmoothed Smoothed < Derivative For the composite analysis, the top 25 th and bottom 25 th intensity anomaly percentiles are split into two groups. The corresponding means of elevation, aspect and slope between the two groups are compared and tested for significance. The composite analysis repeats similar results to the correlation results. With a probability of p < 0.003, the rejection of the null hypothesis implies the elevation means between the two categories is significantly different. The difference in means between slope (p < 0.245),

153 153 and aspect (p < 0.376) are not statistically significant. The derivative ( Vmax / zelev) also returned a non-significant result with a probability of p < Isolated pockets of deciduous forest contribute to an initial surface roughness value higher than that of the rest of the period (Fig. 4.22a). As the tornado encountered lower surface roughness between 2145: :32 (scans 18-30) intensity increased, although the intensification is not persistent. The period ends with another small increase of surface roughness between 2147: :26 (32-36); however, the change is very small and is not recognized by all of the surface roughness parameters. Overall, a negative correlation is found between intensity and surface roughness. The correlations and probability values for the three surface roughness parameters: area mean (-0.302, p < 0.051), weighted mean (-0.259, p < 0.097), and weighted trimean (-0.174, p < 0.270), indicate negative correlations that do not quite reach the significant threshold (Table 4.36). When the 3-scan running mean is applied (Fig. 4.22), the significance is met for two of three parameters: area mean (p < 0.010) and weighted mean (p < 0.020). The derivative ( Vmax / zrough) values (Fig. 4.22c) revealed no significant relationships. The only parameter to reflect similarly to the unsmoothed correlation is the area mean with a correlation of and a statistical probability of p < 0.182, which, as stated previously is not significant.

154 Figure 4.22: As in Fig. 4.7, but for the fifth period of the El Reno, OK tornado. 154

155 155 Table 4.36: As in Table 4.11, but for the fifth period of the El Reno, OK tornado. Method Correlation (area Prob. Correlation (weighted Prob. Correlation (weighted Prob. mean) mean) trimean) Unsmoothed Smoothed Derivative For the composite analysis, the means of area mean, weighted mean, and weighted trimean between the top and bottom 25 th percentile groups are compared and tested for significance. The composite analysis comparing the means for the two intensity categories, reveals similar results to the correlations. Area mean (p < 0.089), weighted mean (p < 0.081), and weighted trimean (p < 0.172) all evaluated to probabilities close to the significant threshold. The derivative ( Vmax / zrough) values were not significantly different either, with area mean change (p < 0.278), weighted mean change (p < 0.515), and weighted trimean change (p < 0.546). Since the criteria for significance are not satisfied, the null hypothesis is not rejected, and it can be concluded that the means between the two categories are not significantly different. The linear regression calculations for test 1 (Table 4.37) produced a regression correlation of R = and an R-squared value R 2 = These values would imply that although the regression correlation is modest, the variance explained by the model is only ~28%, which means the predictors are not strong predictors of intensity. All predictors are found to be non-significant, with area mean having the lowest probability p < When beam height is removed (test 2, Table 4.38), the correlation decreases to

156 156 R = and the R-squared value decreases to R 2 = Very small changes are expected because beam height is not a significant predictor in test 1. When beam height is removed, elevation becomes a significant predictor with a probability value of p < The coefficient increases and the standard error decreases. As a result, the t-value increases the probability becomes significant. Table 4.37: As in Table 4.3, but for the fifth period of the El Reno, OK tornado. El Reno 5 Test 1 Coefficient Standard Error t-value Probability Beam Height Elevation Slope Aspect Area Mean Weighted Mean Weighted Trimean

157 157 Table 4.38: As in Table 4.4, but for the fifth period of the El Reno, OK tornado. El Reno 5 Test 2 Coefficient Standard Error t-value Probability Elevation Slope Aspect Area Mean Weighted Mean Weighted Trimean The final period involving the El Reno tornado can be summarized by four conclusions: 1) elevation and intensity are positively correlated (significant), 2) surface roughness for area mean and weighted mean and intensity are negatively correlated (significant) when examining the smoothed running mean data, 3) the comparison of means test for elevation is significant, and 4) elevation is a significant predictor of intensity with the absence of beam height in test Carney, Oklahoma 19 May 2013 With the longest scanning strategy (52 seconds) out of the entire dataset, the Carney, Oklahoma tornado was observed for approximately 17 minutes, moving through areas of deciduous forest and grassland (Fig. 4.23a). The observation period began in a valley of ~270 m in elevation. Initially the tornado intensity ( Vmax) increased between 2150: :37 (Fig. 4.24a, scans 2-6) as it ascended the first hill (Fig. 4.23b). Then, as it entered the valley, descending ~40 m, the intensity remained fairly steady between

158 2154: :57 (Fig. 4.24b, scans 7-11). However, as it ascended the second hill of ~60 m, the intensity increased by ~25 ms Table 4.39: As in Table 4.1, but for the Carney, OK tornado. Number of scans, Case (period) Time frame scan rate (seconds) Intensity ( Vmax) range in ms -1 Carney (1) 2149: :36 21, Low-level beam height range (m) Elevation range (m) Surface roughness range (m) Number of interpolated scans Figure 4.23: As in Fig. 4.5, but for the Carney, OK tornado.

159 159 Figure 4.24: As in Fig. 4.6, but for the Carney, OK tornado. Elevation has a positive correlation of 0.590, and is statistically significant with a probability value of p < Aspect (0.308, p < 0.173) is positively correlated, but is

160 160 not supported by a significant probability (Table 4.40). Slope (0.073, p < 0.753) is also positively correlated, but is not significant. The 3-scan mean improves the positive correlation between elevation and intensity to 0.677, decreasing the probability to p < 0.001; however, slope and aspect remain non-significant with probability of p < and p < respectively. A non-significant (p < 0.681) positive correlation of is produced when examining the derivative ( Vmax / zelev). Table 4.40: As in Table 4.2, but for the Carney, OK tornado. Correlation Correlation Method Prob. Prob. (elevation) (slope) Correlation (aspect) Prob. Unsmoothed Smoothed < Derivative For the composite analysis, the means of elevation, aspect and slope corresponding with the upper and lower quartile of intensity values are compared and tested for significance. The comparison of means method describes a similar scenario to the correlation coefficients. The comparison regarding topographic elevation equates to a statistically significant probability p < 0.019, which means the null hypothesis of the being equal is rejected, which implies the elevation means between the two categories are significantly different. Slope (p < 0.932) and aspect (p < 0.063) are not significant and therefore the null hypothesis cannot be rejected. For the derivative ( Vmax / zelev), a

161 161 probability of p < does not reject the null hypothesis, which implies that the elevation change means within the categories are likely not statistically different. When examining the intensity of the tornado with a surface roughness analysis, Fig. 4.25a, does not indicate any strong relationship. Ultimately, area mean (0.117), weighted mean (0.164), and weighted trimean (0.152) attribute a weak positive correlation with intensity; moreover, the relationships are not statistically significant (Table 4.41). The 3-scan running mean (Fig. 4.25b) reveals basically no relationship with correlations near zero, area mean (-0.103), weighted mean (-0.003), and weighted trimean (0.028). Despite the absence of a significant relationship in the raw correlation, a nearly significant relationship is found when applying the derivative function ( Vmax / zrough) to the raw data (Fig. 4.25c). The positive correlations: area mean change (0.478), weighted mean change (0.495), and weighted trimean change (0.514) produce probability values of p < 0.051, p < 0.112, and p < respectively. Although not significant, a positive correlation between surface roughness change and intensity change exists nonetheless.

162 Figure 4.25: As in Fig. 4.7, but for the Carney, OK tornado. 162

163 163 Table 4.41: As in Table 4.11, but for the Carney, OK tornado. Method Correlation (area mean) Prob. Correlation (weighted mean) Prob. Correlation (weighted trimean) Prob. Unsmoothed Smoothed Derivative For the composite analysis, the top 25 th and bottom 25 th intensity anomaly percentiles are split into two groups. The means of area mean, weighted mean, weighted trimean between the two groups are compared and tested for significance. The comparison of means tests produces similar results to the raw correlations. Area mean (p < 0.453), weighted mean (p < 0.630), and weighted trimean (p < 0.664) do not indicate any strong differences between the means; however, the derivative ( Vmax / zrough) values, area mean change (p < 0.053), weighted mean change (p < 0.115), and weighted trimean change (p < 0.172) indicate once again, the nearly significant result. The linear regression model for test 1 computed a regression correlation and R- squared value of R = and R 2 = respectively, which means the variables predict the intensity well. The beam height, slope, aspect, and area mean are all strong predictors; however, beam height is the only variable that is supported by a statistically significant probability of p < (Table 4.42). For test 2, the skill of the model decreases (R = 0.599, R 2 = 0.358) considerably. The amount of variance explained decreases from ~90% to ~36%, acknowledging the significance of beam height in test 1. When examining the model output with the significant variable removed (Table 4.43),

164 164 elevation is the strongest predictor, which is supported by a probability value of p < All other variables are poor predictors. Table 4.42: As in Table 4.3, but for the Carney, OK tornado. Carney Test 1 Coefficient Standard Error t-value Probability Beam Height < Elevation Slope Aspect Area Mean Weighted Mean Weighted Trimean Table 4.43: As in Table 4.4, but for the Carney, OK tornado. Carney Test 2 Coefficient Standard Error t-value Probability Elevation Slope Aspect Area Mean Weighted Mean Weighted Trimean With the longer scanning strategy and robust surface roughness changes, four primary conclusions are drawn from the Carney case: 1) elevation is positively correlated

165 165 (significant) with intensity ( Vmax), 2) surface roughness change is positively correlated with intensity change (not significant), 3) beam height is a significant predictor for test 1, and 4) when beam height is removed (test 2), elevation is a significant predictor Shawnee, Oklahoma 19 May 2013 Despite the multiple deployments by the RaXPol, two sections of data are examined. The first started as the tornado crossed a hill (Fig. 4.26a) of deciduous forest (Fig. 4.26b) and entered a valley, As the tornado descended the ~40 m valley between 2313: :33 (Fig. 4.27a, scans 1-7), tornado intensity ( Vmax) decreased slightly (~15 ms -1 ). At the base of the valley and into the following ~20 m hill, tornado intensity increased ~40 ms -1. Throughout the remainder of the period (2317: :52), the intensity in the smoothed data (Fig. 4.27b, scans 9-15) levels out before increasing near the end as the data concludes. Throughout the 15 scans, the tornado increased in intensity ( Vmax) as the beam height lowered from 215 m to 154 m (Table 4.44). Table 4.44: As in Table 4.1, but for the first period of the Shawnee, OK tornado. Number of scans, Intensity ( Vmax) Case (period) Time frame scan rate range in ms (seconds) -1 Shawnee (1) 2313: :52 15, Low-level beam height range (m) Elevation range (m) Surface roughness range (m) Number of interpolated scans

166 Figure 4.26: As in Fig. 4.5, but for the first period of the Shawnee, OK tornado. 166

167 Figure 4.27: As in Fig. 4.6, but for the first period of the Shawnee, OK tornado. 167

168 168 Despite the occasions where the intensity increased with increasing height, the correlation (-0.048) indicates a lack of relationship between intensity and elevation (Table 4.45). The lack of a correlation is supported by the probability value p < Slope (-0.111, p < 0.693) and aspect (0.174, p < 0.533) are found to not have a significant relationship with intensity as well. However, with the application of the 3-scan running mean, aspect gains a positive correlation with intensity of 0.653, and it supported by a probability of p < This result indicate higher intensity is associated with higher aspect for this particular case. Elevation (-0.194, p < 0.488) and slope (-0.400, p < 0.136) remain non-significant with the running mean. The derivative values ( Vmax / zelev), indicate a positive correlation of and a probability value p < 0.157, but the positive correlation is not significant. Table 4.45: As in Table 4.2, but for the first period of the Shawnee, OK tornado. Correlation Correlation Correlation Method Prob. Prob. Prob. (elevation) (slope) (aspect) Unsmoothed Smoothed Derivative For the composite analysis, the top 25 th and bottom 25 th intensity anomaly percentiles are split into two groups and the correlating means of elevation, aspect and slope between the two groups are compared and tested for significance. For the composite analysis, all three geographical parameters, elevation (p < 0.781), slope (p <

169 ), and aspect (p < 0.788), are non-significant. Despite the poor correlations with data, the derivative ( Vmax / zelev), produces a probability of p < While not significant, the low probability indicates that the difference between the means of elevation change within the two intensity change categories is modest. When examining the unsmoothed data (Fig. 4.28ab), two distinct patterns emerge, the intensity ( Vmax) becomes nearly constant over areas of higher surface roughness between 2313: :00 and 2317: :47 (scans 1-6, 9-13), while the intensity increases in areas between 2316: :38 and 2319: :52 of lower surface roughness (scans 6-9, 13-15). As a result, area mean (-0.524, p < 0.042), weighted mean (-0.550, p < 0.031), and weighted trimean (-0.506, p < 0.052) all support a statistically significant negative correlation where tornado intensity increases with decreasing surface roughness (Table 4.46). When the 3-scan running mean is applied, all three parameters, area mean (p < 0.011), weighted mean (p < 0.002), and weighted trimean (p < 0.016), are a statistically significant, which suggests high (low) intensity is associated with low (high) surface roughness. The derivative method ( Vmax / zrough) (Fig. 4.28c) produces a negative correlation (values ranging from to ); however, these negative correlations are not significant.

170 Figure 4.28: As in Fig. 4.7, but for the first period of the Shawnee, OK tornado. 170

171 171 Table 4.46: As in Table 4.11, but for the first period of the Shawnee, OK tornado. Method Correlation (area Prob. Correlation (weighted Prob. Correlation (weighted Prob. mean) mean) trimean) Unsmoothed Smoothed Derivative The composite analysis comparing the means of area mean, weighted mean, and weighted trimean to their corresponding values of the upper and lower intensity quartiles produces significant results where the raw correlations did not. Area mean (p < 0.024), weighted mean (p < 0.003), and weighted trimean (p < 0.006) all reject the null hypothesis that the means between the two intensity categories are equal indicating that there is a difference in surface roughness when comparing the maximum and minimum anomalies of intensity. The results for the derivative values ( Vmax / zrough) returned similar results to the correlation coefficients. Although the composite analysis depicted some relationships between elevation/surface roughness and intensity, linear regression output for test 1 and test 2 do not indicate such strong relationships. The parameters for Test 1 (Table 4.47), resulted in a regression correlation of R = and a R 2 =0.761 meaning that 76% of the variance is explained by the model. The only significant predictor is beam height with a probability value of p < The significance of the beam height predictor for the model is verified in test 2 (Table 4.48). The regression correlation (R = 0.588) and R- squared (R 2 = 0.346) values decrease and none of the predictors are significant.

172 172 Table 4.47: As in Table 4.3, but for the first period of the Shawnee, OK tornado. Shawnee 1 Test 1 Coefficient Standard Error t-value Probability Beam Height Elevation Slope Aspect Area Mean Weighted Mean Weighted Trimean Table 4.48: As in Table 4.4, but for the first period of the Shawnee, OK tornado. Shawnee 1 Test 2 Coefficient Standard Error t-value Probability Elevation Slope Aspect Area Mean Weighted Mean Weighted Trimean Even with only 15 scans available, the first Shawnee time period provides four results, 1) aspect is positively correlated (significant) with intensity when the 3-scan

173 173 mean is applied, 2) surface roughness is negatively correlated to intensity (significant when the running mean is applied), 3) comparison of means significant for all three surface roughness parameters, and 4) beam height was the only predictor to show a strong and significant result with the regression output. After the first time period, and a second deployment that only obtained five scans, a third deployment provided a third observational period 2341: :27 (Table 4.49). At the onset of observations, the tornado was crossing an interstate overpass (Fig. 4.29a), which is situated on the western side of a ridge (Fig. 4.29b). As the tornado crossed the highway, it ascended a ~10 m high ridge, intensifying ( Vmax) ~15 ms -1. While on the ridge, the tornado intensity decreased (Fig. 4.30a, b), and it continued to decrease to ~60 ms -1 from ~100 ms -1 by scan 10. A brief period of intensification of ~20 ms -1 occurred between 2346:40 and 2348:50 (scans 10-14). The temporary intensification was immediately followed by a decrease in intensity as the tornado moved into a valley at the conclusion of the observation period. Table 4.49: As in Table 4.1, but for the third period of the Shawnee, OK tornado. Number of scans, Intensity ( Vmax) Case (period) Time frame scan rate range in ms (seconds) -1 Shawnee (3) 2341: :27 17, Low-level beam height range (m) Elevation range (m) Surface roughness range (m) Number of interpolated scans

174 Figure 4.29: As in Fig. 4.5, but for the third period of the Shawnee, OK tornado. 174

175 Figure 4.30: As in Fig. 4.6, but for the third period of the Shawnee, OK tornado. 175

176 176 A correlation analysis revealed that elevation (0.515, p < 0.033) is positively correlated with intensity and is supported by a significant probability value, which indicates stronger intensity is associated with higher topographic elevation (Table 4.50). Slope (-0.042, p < 0.873) did not have a relationship to intensity in this particular case. Aspect (0.454, p < 0.065) indicated a positive correlation, but the correlation is not significant. The 3-scan mean for topographic elevation maintains the positive correlation at and decreases the probability slightly to p < 0.031, which is statistically significant. The correlation and associated probability for slope (-0.257, p < 0.330) improves with the smoothed data. For aspect, the correlation improves to and produces a probability p < 0.005, which now suggests that the relationship is statistically significant, or that higher intensity is associated with westward facing slopes. The derivative ( Vmax / zelev) correlation between the change in Vmax and the change in elevation is 0.038, which is a significant correlation. Table 4.50: As in Table 4.2, but for the third period of the Shawnee, OK tornado. Correlation Correlation Correlation Method Prob. Prob. Prob. (elevation) (slope) (aspect) Unsmoothed Smoothed Derivative The elevation mean comparison between the two intensity categories in the composite analysis produces a significant probability p < This means that the null

177 177 hypothesis can be rejected, which indicates that the elevation means are significantly different between the two intensity categories. Slope (p < 0.558) and aspect (p < 0.112) do not indicate any significant results. The derivative ( Vmax / zelev) of elevation (p < 0.565) for the comparison of means test was also found to be not significant. Over the highway overpass, the surface roughness began in a modest range from (Fig. 4.31ab), with an intensity ( Vmax) around 45 ms -1. As the tornado continued to move northeastward between 2344:30 and 2346:40, it traversed into areas of low surface roughness (open water and cultivated crops) and decreased in intensity (Fig. 4.31ab, scans 6-10). However, after entering an area with deciduous forest between 2347: :12, surface roughness increased along with intensity (scans 11-14). The brief period of intensification was quickly followed by a decrease of intensification as the tornado entered an area of lower surface roughness. In accordance with the events explained above, all three surface roughness parameters: area mean (0.397, p < 0.112), weighted mean (0.467, p < 0.057), weighted trimean (0.422, p < 0.089), returned positive correlations; however, none of these correlations are considered statistically significant (Table 4.51). When applying the 3-scan running mean, not much change occurs in the correlations or probabilities. In fact, the probabilities increase for each parameter. Despite the lack of significance, the positive correlation emphasizes a relationship where high surface roughness is associated with stronger tornado intensity. Additionally, the derivative ( Vmax / zrough) method (Fig. 4.31c) also returned non-significant positive correlations for area mean change (0.439, p < 0.076), weighted mean change (0.489, p <

178 0.044), weighted trimean change (0.438, p < 0.076), reinforcing the idea of increasing surface roughness change leading to increasing intensity. 178 Figure 4.31: As in Fig. 4.7, but for the third period of the Shawnee, OK tornado.

179 179 Table 4.51: As in Table 4.11, but for the third period of the Shawnee, OK tornado. Method Correlation (area Prob. Correlation (weighted Prob. Correlation (weighted Prob. mean) mean) trimean) Unsmoothed Smoothed Derivative The comparison of means technique for the composite analysis leads to similar results for both the intensity data and the derivative values. For the surface roughness data, the area mean (p < 0.240), weighted mean (p < 0.133), and weighted trimean (p < 0.057) evaluate outside the critical significance values when comparing the means between the upper and lower quartile intensity data. For the derivative values ( Vmax / zrough), area mean change (p < 0.274), weighted mean change (p < 0.138), and weighted trimean change (p < 0.159), all suggest a separation in the means; however, it is not large enough to be significant. Although the raw and derivative data indicated a few relationships, linear regression tests reveal no significantly strong predictors. With the lack of influence from a strong predictor in beam height, both tests predicted intensity similarly. Test 1 (Table 4.52) produced a regression correlation, R = 0.869, and an R 2 = 0.755, meaning that the model explains nearly 76% of the variance. Test 2 (Table 4.53) produced similar results with the regression correlation decreasing slightly to R = 0.858, and the R-squared value decreasing slightly to R 2 = The overall conclusion with this particular case is that beam height was not a strong predictor, therefore, the model maintained its performance

180 180 with the influence of beam height removed. Perhaps the explanation for the strong model performance between both tests is that all of the predictors were important to the model; however, none were statistically significant for this particular case. Table 4.52: As in Table 4.3, but for the third period of the Shawnee, OK tornado. Shawnee 3 Test 1 Coefficient Standard Error t-value Probability Beam Height Elevation Slope Aspect Area Mean Weighted Mean Weighted Trimean Table 4.53: As in Table 4.4, but for the third period of the Shawnee, OK tornado. Shawnee 3 Test 2 Coefficient Standard Error t-value Probability Elevation Slope Aspect Area Mean Weighted Mean Weighted Trimean

181 181 The third observation period for the Shawnee tornado provides three conclusions: 1) aspect is positively correlated (significant for smoothed data) with intensity ( Vmax), 2) while not significant, increasing surface roughness is associated with increasing intensity for both raw and derivative methods, 3) comparison of means significant for elevation, and 4) linear regression tests performed well; however, no specific predictors are significant in either test. 4.2 Cumulative Review Due to the extensive list of results for each case across the different statistical methods, it is important to synthesize these results into a cumulative review. The correlations for the topography parameters (Table 4.54), provides a summary of the possible relationships associated with topography and tornado intensity ( Vmax). For elevation, five cases are negatively correlated while six are positively correlated. Only two of the correlations, Shawnee periods 1 and 3, are not significant. Due to the opposite significant correlations throughout the eleven cases, no immediate conclusions are made here in this section except to say that there does appear to be a relationship between topographic elevation and tornado intensity, but the relationship is not consistent. The derivative values of elevation change (Table 4.55) also reveal contrasting correlations; moreover, none are significant, indicating a lack of strong relationship between intensity change and elevation change. The slope parameter correlations also do not suggest a relationship with intensity. Two of the correlations: El Reno periods 3 and 4, are significant; however, the correlations have opposite signs. For eight of the cases, aspect is positively correlated, but only one case has a significant (El Reno 2) correlation. The

182 182 majority of cases have a positive correlation between aspect and tornado intensity; however, several cases: Goshen 2, Goshen 3, and El Reno 1, have correlations near 0. As a result, the relationship between aspect and intensity resists generalization. Table 4.54: Summary of the results for the unsmoothed correlations between tornado intensity ( Vmax) and the topographic parameters: elevation, slope, and aspect for each time period. Positive correlations are green and negative correlations are red. Bold correlations are significant. Significance is quantified by a probability that is lower than the critical p-value of p < for a two-tailed t-test. Case (period) Sample Size Correlation (elevation) Prob. Correlation (slope) Prob. Correlation (aspect) Prob. Goshen (2) < Goshen (3) < Lookeba (1) < El Reno (1) El Reno (2) < El Reno (3) < < El Reno (4) < El Reno (5) Carney (1) Shawnee (1) Shawnee (3)

183 183 Table 4.55: As in Table 4.54, but for the derivative value ( Vmax / zelev), elevation change. Case (period) Sample Size Correlation Probability Goshen (2) Goshen (3) Lookeba (1) El Reno (1) El Reno (2) El Reno (3) El Reno (4) El Reno (5) Carney (1) Shawnee (1) Shawnee (3) For the surface roughness parameters, area mean, weighted mean, and weighted trimean, the signs of the correlations (Table 4.56) are split nearly equally, with five cases indicating a positive correlation with intensity and four indicating a negative correlation with intensity. There are two significant correlations for area mean and weighted mean, but they have opposite sign. The weighted trimean only reveals one significant period: El Reno 4, in the negative direction, which would indicate lower surface roughness is correlated with higher intensity ( Vmax) for that case. Out of all the correlations between the derivative values ( Vmax / zrough), area mean change for El Reno 4 is the only case with a significant value (Table 4.57). The negative correlation indicates that with decreasing surface roughness, intensity is increasing.

184 184 Table 4.56: As in Table 4.54, but for the surface roughness parameters, area mean, weighted mean, and weighted trimean. Case Sample (period) Size Correlation Correlation Correlation (area Prob. (weighted Prob. (weighted Prob. mean) mean) trimean) Lookeba (1) El Reno (1) El Reno (2) El Reno (3) El Reno (4) El Reno (5) < < < < < Carney (1) Shawnee (1) Shawnee (3)

185 Table 4.57:As in Table 4.56, but the derivative values ( Vmax / zrough) of all three surface roughness parameters, area mean change, weighted mean change, and weighted trimean change. Case (period) Lookeba (1) Sample Size Correlation (area mean change) Prob. Correlation (weighted mean change) Prob. Correlation (weighted trimean change) Prob El Reno (1) El Reno (2) El Reno (3) El Reno (4) El Reno (5) Carney (1) Shawnee (1) Shawnee (3) Composite analysis using the comparison of means test provides a second opportunity for analyzing the possible relationships associated with topography/landcover and intensity. By comparing the means of either elevation or surface roughness associated with the top 25 th and bottom 25 th percentiles of intensity anomalies, significance regarding the relationships between these parameters are discovered (Table 4.58). For elevation, all but two periods (El Reno 1 and Shawnee 1) are significant, which indicates there is a 95% confidence that the means between the two categories are not

186 186 equal. This results in the rejection of the null hypothesis of the means being equal, which indicates a significant difference between the means. For the derivative values (Table 4.59), no tests returned significant results, therefore indicating the means for the elevation change between the two intensity categories are not significantly different. Slope has two periods: El Reno 2 and 3, that return significant differences between the means. These are the same periods that returned significant results for the raw correlations, strengthening the possibility that a relationship exists. Only one significant result is found associated with aspect. El Reno 2, which is the only raw correlation that is significant for aspect, is also significant for the comparison of means test. For this particular case, the results would imply aspect was associated with intensity. Table 4.58: Summary for the comparison of means test of the topographic parameters: elevation, slope, and aspect. The probabilities represent the likelihood that the means between the two intensity categories are equal. Bold probabilities are significant (p < 0.05). Case (period) Probability (elevation) Probability (slope) Probability (aspect) Goshen (2) < Goshen (3) < Lookeba (1) El Reno (1) El Reno (2) < El Reno (3) < El Reno (4) < El Reno (5) Carney (1) Shawnee (1) Shawnee (3)

187 Table 4.59: As in Table 4.58, but for the derivative: change in intensity over elevation change ( Vmax / zelev). Case (period) Probability Goshen (2) Goshen (3) Lookeba (1) El Reno (1) El Reno (2) El Reno (3) El Reno (4) El Reno (5) Carney (1) Shawnee (1) Shawnee (3) The comparison of means for the surface roughness parameters provides the opportunity to evaluate the relationship between intensity and surface roughness with respect to the two intensity categories (top and bottom 25 th intensity anomalies). As is the case for the correlations, area mean and weighted mean have the same significant cases (Table 4.60). The weighted trimean parameter only has two significant results in comparison to the six that area mean and weighted mean have. Similar to the elevation derivative values, the surface roughness derivative values have zero cases that are significant (Table 4.61). This lack of significance would indicate a lack of large differences in the means between the two intensity categories.

188 188 Table 4.60: As in Table 4.58, but for the surface roughness parameters, area mean, weighted mean, and weighted trimean. Probability Probability Probability Case (period) (area mean) (weighted mean) (weighted trimean) Lookeba (1) El Reno (1) El Reno (2) El Reno (3) < < El Reno (4) < < El Reno (5) Carney (1) Shawnee (1) Shawnee (3) Table 4.61: As in Table 4.60, but the derivative values ( Vmax / zrough) of all three surface roughness parameters, area mean change, weighted mean change, and weighted trimean change. Probability Probability Probability Case (period) (area mean change) (weighted mean change) (weighted trimean change) Lookeba (1) El Reno (1) El Reno (2) El Reno (3) El Reno (4) El Reno (5) Carney (1) Shawnee (1) Shawnee (3)

189 189 Linear regressions provide the opportunity to examine the contribution of the specified variables: beam height, elevation, slope, aspect, area mean, weighted mean, and weighted trimean, in predicting intensity through regression modeling. Table 4.62 is a summary of all predictors that were found to provide significant contributions in predicting intensity over the eleven cases. Two separate tests, or models, are evaluated. Test 1 includes all the available parameters, while test 2 excludes beam height, which is the only non-geographically derived parameter. For test 1, beam height is a significant parameter for seven of the eleven cases, which indicates the beam height is strongly correlated to intensity for those cases. Additionally, when the cases that did not result in any significant predictors are removed, only one case, Lookeba 1, does not indicate beam height as a strong predictor, therefore implying that beam height has a strong influence on intensity observations. The second important predictor for test 1, topographic elevation, is found to be a significant predictor for four of the eight cases that contain significant predictors, indicating that elevation is also a strong contributor to predicting intensity within the model. Slope, weighted mean, and weighted trimean are each significant in only one period, indicating that in comparison to elevation and beam height, these variables are much weaker contributors through all the cases. With beam height excluded for test 2, elevation becomes the dominating predictor. Six of the eleven cases have significant contributions to tornado intensity from elevation. Slope is significant in two cases, and weighted mean/trimean are significant for the same case as test 1: El Reno 2. With beam height removed, the area mean parameter

190 is the only significant predictor for El Reno 1. It is also significant for El Reno 2. Aspect is not a significant predictor for any case across the two tests. 190 Table 4.62: Summary of significant predictors of intensity from the linear regression technique for each period. Test 1 involved all predictors, and Test 2 excluded beam height. Probability values represent the likelihood of the coefficient equaling zero (b = 0). A significant threshold of p < 0.05 was applied. Cases that did not evaluate significant predictors are labeled N/A for not applicable. Case (period) Test 1 Probability Test 2 Probability Goshen (2) Goshen (3) Beam Height Elevation < Elevation < Beam Height Elevation < Elevation < Slope Slope < Lookeba (1) Elevation < Elevation < El Reno (1) Beam Height Area Mean El Reno (2) Beam Height < Area Mean Elevation Weighted Mean Weighted Trimean < < El Reno (3) Beam Height < Weighted Mean Weighted Trimean Elevation < Slope <0.031 El Reno (4) N/A N/A N/A N/A El Reno (5) N/A N/A Elevation Carney (1) Beam Height < Elevation Shawnee (1) Beam Height N/A N/A Shawnee (3) N/A N/A N/A N/A

191 191 CHAPTER 5: DISCUSSION Three different statistical techniques were applied to the extracted data in order to investigate potential relationships between topography/land-cover and tornado intensity. Additionally, the results found here are compared to previous studies examining these relationships through numerical simulations and WSR-88D data. For elevation, the culmination of all three statistical tests reveals five cases that are significant with a positive correlation with intensity: Goshen 3, El Reno 2, El Reno 3, El Reno 5, and Carney 1. In contrast, only two cases: Goshen 2 and Lookeba 1, show significance through all three statistical tests with a negative correlation. However, examining the cases using the observation information (Table 5.1) and test 1 results for the linear regression may assist in creating some exceptions to the statistical findings. Goshen 3 consisted of a dissipating tornado. This persistent weakening, along with the demise of the tornado shortly after the end of the period, makes the results from Goshen 3 subject to limitations. The strong correlations are likely associated with storm mechanisms rather than topographic influence. Although El Reno 2 returned a significant positive correlation with elevation, an obvious increase in intensity as the tornado entered the Canadian River floodplain challenges the positive correlation since intensity increased as elevation decreased, which would indicate possible vorticity stretching as the vortex entered the valley. So, despite the overall positive correlation, this specific event raises suspicion regarding its validity and must be considered as an effect of elevation change. An explanation for the

192 192 significant result is likely based on the later part of the period when intensity is strong over higher elevation. The results for El Reno 3 appear justified. The tornado decreased in intensity as it moved downhill, then maintained intensity while on a ridge, before decreasing in intensity again on the next downslope. However, the large change in beam height may be important. The beam height started at 89 m and increased to 302 m by the end of the period. A beam height that is increasing would suggest a potential bias toward lower intensity since higher velocities are expected to be closer to the surface. For test 1 in the linear regression, beam height was a very strong predictor of tornado intensity, further increasing confidence about this limitation. The significance for El Reno 5 also seems justified. Beam height (Table 5.1) remains fairly steady throughout and intensity increases on upslope and decreases on downslope. Interestingly, the elevation range was one of the lowest relief (34 m difference between the lowest and highest elevation throughout the case) out of the entire dataset. The last significant case with a positive correlation between topographic elevation and tornado intensity was Carney 1. Even with the longest scan time out of the entire dataset, the elevation was observed appropriately (e.g. no major features missed). Similar to El Reno 3, beam height was a strong predictor for test 1. Here, the beam height was decreasing from 271m to 158 m as tornado intensity was increasing. Although there was an ~50 m drop in topographic elevation during the first half of the case, overall elevation increased. With beam height decreasing, elevation increasing, tornado intensity

193 193 increasing, and no pronounced intensity changes associated with significant elevation changes, the statistical result of higher intensity associated with higher elevation stands. However, the application of this result contains limitations, specifically associated with the beam height. After initially having five time periods where intensity and elevation were positively correlated and contained significance through all three statistical measures, only one, El Reno 5, did not have any obvious limitations that diminished the result; however, it is important to note the low relief associated with El Reno 5. For the Goshen 2 and Lookeba 1 cases which were significantly negatively correlated across all three statistical methods, Lookeba 1 is the only case that would indicate a possible response to vorticity stretching. The beam height is a limitation for surface roughness; however, for vorticity stretching, it assumes the entire column or tornado would increase in vorticity with decreasing elevation. The highest intensity was associated with the lowest elevation; therefore, the significant result stands. The Goshen 2 case presents several limitations. There are several sections within the data that contradict the negative correlation, for instance the weakening of intensity through the first valley. While on the ridge, tornado intensity steadily increases, which has been noted to occur in other observational and numerical simulation studies (Forbes 1998, Lewellen 2012). Near the end of the time period, there is a period of increased intensity as the tornado moves downslope, possibly indicating vorticity stretching. Despite this, throughout all of the case, beam height was decreasing from 225 m to 114 m while tornado intensity was increasing. So, the test 1 result indicating beam height as an

194 194 important contributor verifies. Ultimately, both cases contain limitations (e.g. high beam height for Lookeba 1 and decreasing beam height with Goshen 2) that diminish the statistical findings. For elevation alone, it appears that statistical analyses may always be contradicted by specific sections of the case, which could be a limitation for this type of analysis. For the derivative values, neither comparisons of means nor correlations returned a significant result, suggesting that the change in elevation and the change of intensity do not have a strong enough correlation throughout the entire period. These results also suggest that the derivative values themselves, may not be the best way to represent elevation change. Since the derivative is the change in intensity with time versus the change of elevation with time, every minor change in either variable is included into the final calculation. For example, the signs of the correlations are compared between the correlation and the derivative correlation. For four of the eleven cases, the sign of the correlation switched from positive (negative) to negative (positive). While an overwhelming conclusion is unknown, it is suggested that the limitation described above may be producing too high of a spatial resolution. The other two topographic parameters, slope and aspect, provided very few significant results. It is possible that there may indeed be no relationship between intensity and these parameters. However, it is also possible that with the point extraction from the GIS methods, slope and aspect were likely not represented appropriately. Both were extracted using the location for the center of the tornado. Since aspect is derived by the angle of the topography, point values likely resulted in errors. Additionally, due to the

195 195 low relief topography, various values of aspect were likely associated within the estimated tornado radius. Multiple ways of quantifying slope and aspect, along with higher relief topography will allow for more detailed information, and could ultimately lead to more meaningful results. Table 5.1: Summary of key information for each time period. Scan interval indicates how quickly the radar was scanning one volume. Beam height depicts how high with the tornado intensity ( Vmax) was derived. Elevation range specifies the magnitude of topography, and surface roughness range (area mean only) range throughout the tornado track. Surface Case (period) Scan Interval (seconds) Beam Height (meters) Elevation Change Range (meters) Roughness Change Range (meters) Goshen (2) Goshen (3) Lookeba (1) El Reno (1) El Reno (2) El Reno (3) El Reno (4) El Reno (5) Carney (1) Shawnee (1) Shawnee (3) For the three surface roughness parameters, area mean, weighted mean, and weighted trimean, significant correlations were not as frequent as topographic elevation.

196 196 Of the nine cases, five were positively correlated, with only two of those being significant correlations: El Reno 1, and El Reno 3. Of the remaining four that were negatively correlated, two were associated with significant correlations, Lookeba 1 and El Reno 4. For the positively correlated cases, El Reno 1, which only consisted of 13 observation scans, was at the onset of a long-lived, destructive tornado. As a result, uncertainty associated with possible storm mechanisms exists, therefore, it is unclear how influential the statistically significant result is for this particular case. For the second case, El Reno 3, it has already been discussed that beam height change throughout the case likely contributed to a bias in tornado intensity. Since higher surface roughness was present during the first half of the case, when the tornado was strongest, a positive correlation is justified; however, confidence that surface roughness contributed to the intensity is low. The beam height once again overwhelms the significance of the statistical results. The negative significant correlations for El Reno 4 and Lookeba 1 also contain limitations. El Reno 4 had very little ( ) roughness change (Table 5.1). In fact, it had the second lowest magnitude of roughness change across the nine datasets. The significant correlation arose due to the weaker intensity at the onset of the case, when surface roughness was roughest, and stronger intensity associated with the rest of time period which had very low roughness. So, while the significant result is justified based on the data, the application to the surface roughness verses intensity question seems unwarranted. For Lookeba 1, the high beam height (over 900 m throughout), is a clear

197 197 limitation to this significant result since the literature review suggests that surface roughness has its strongest impacts on the near-surface intensity. With limitations surfacing for all statistically significant cases, a specific discussion outside the statistical techniques might indicate some weight for the argument that surface roughness may alter tornado intensity to the point that it is observed through radar analysis. For instance, a case that had larger changes (Table 5.1, Carney 1) with respect to surface roughness could indicate a relationship between tornado intensity and surface roughness. Carney 1, which did not return a significant result for correlation, seemed to indicate a positive correlation with the derivative values or the change in surface roughness versus the change of intensity. The limitation of decreasing beam height throughout the case does diminish this result; however, since the derivative value is specifically targeting the change of intensity, the actual magnitude of the velocity does not necessarily apply. So, for the purposes of identifying a specific result, the Carney 1 case indicated that increasing surface roughness change leads to increasing tornado intensity change. Another interesting case is the El Reno second time period. In regards to a discussion concerning the surface roughness impacts only, the Canadian River provided a unique feature that did not occur in any other case. As the tornado entered the Canadian River Valley (low surface roughness), the tornado intensified very quickly. As was mentioned in the literature review, specific transitions between surface roughness features (e.g. urban to open field (Church 1993, Lewellen 2014) or deciduous forest to grassland/barren land in this case) could result in a change in tornado intensity. So it is

198 198 suggested here that as the tornado entered the Canadian River floodplain, the vortex encountered an environment of higher swirl due to the lack of surface roughness in the flat floodplain, which resulted in an increase of intensity. The lowest beam height (55 to 84 m) in comparison to all of the case studies may have provided the ideal observations for concluding this result. The overall limitation to this argument is that, storm mechanisms, decreasing elevation, and the lack of surface roughness could have all played a role in the intensification of the tornado for this particular case. Additional cases where large river floodplains are encountered along the path could provide support to this argument. The final discussion regarding surface roughness and intensity is associated with the three parameters used to quantify surface roughness. The area mean and weighted mean behaved fairly similar (e.g. cases had the same correlation and significance), while the weighted trimean reversed the correlations for two cases and only had two significant correlations overall in contrast to the six indicated by the area mean and weighted mean. Based on these results, the area mean could be eliminated since it s the simplest of the three parameters, and the results for surface roughness would remain the same. The weighted trimean was found to be useful because it enhanced the change of intensity more frequently than the weighted mean. With additional cases, more opportunities for encountering large changes in surface roughness may arise, perhaps leading to a more statistically justified result.

199 199 CHAPTER 6: CONCLUSION This thesis work used rapid-scan mobile radar observations to fill the void that exists in the study of tornado intensity and topography/land-cover features by providing high temporal and spatial resolution data to investigate this relationship. By utilizing these observations, it was anticipated that an increase in temporal and spatial resolution would improve the potential for examining the changes in intensity associated with these features. While this was the case, the statistical techniques employed did not reveal any overwhelmingly conclusive relationships. However, individual cases, specifically El Reno 2 and Carney 1, provided unique results that moved beyond the statistical analysis, therefore, motivating further improvements regarding the analysis, along with the addition of more cases. Multiple cases which provide topographic features that result in robust changes in elevation (e.g. river valley) and surface roughness (e.g. grassland to deciduous forest) would allow for a comparison between these events, which could strengthen the results found within these two specific cases. Previously it was discussed that a series of questions would be addressed regarding the investigations between topography/land-cover and tornado intensity. Those questions are as follows: Are there statistically significant relationships between topography and/or land-cover and tornado intensity ( Vmax)? Are there statistically significant relationships between topography and/or land-cover change and tornado intensity ( Vmax) change?

200 200 Are conclusions found using WSR-88D data (e.g. upslope weakening/downslope strengthening, terrain influenced environments, specific tornado behavioral conditions due to terrain influences) applicable when using rapid-scan mobile radar? Are conclusions made from numerical simulations (increased friction resulting in a stronger tornado, upslope strengthening/downslope weakening, altering tornado path as a result of terrain influences) applicable when rapid-scan mobile radar observations and varying groundcover as a proxy for friction are used? For the first question, statistical relationships were found across several of the cases for both elevation and surface roughness; however, the significant correlations switched signs between the time periods, resulting in a lack of confidence as to which direction the actual relationship was oriented. A deeper investigation into why these significant results were occurring revealed that the relationships found were dependent on where the intensity was extracted within the vertical height of the tornado during that particular time period. For the regression analysis, it was found the topographic elevation was a significant predictor in several cases; however, the radar beam height was a significant predictor of intensity for many of the cases. If radar beam height is an important element in deriving tornado intensity, it is therefore unknown what the exact statistical relationship between topography/land-cover and intensity is based on these initial conclusions. Additionally, the autocorrelation associated with the intensity values likely enhanced the correlations since the samples are within the same period. Future

201 201 research can diminish the significance of beam height using several techniques. The addition of more cases would expand the sample size, which would limit the noise. Additionally, instead of using the lowest-level beam height, deriving intensity from the same vertical height within the tornado would nearly eliminate this limitation. Lastly, cases with minor changes in low-level beam height would provide higher confidence in the results. The autocorrelation issue needs addressed as well. Statistical techniques that provide more independent samples or eliminate autocorrelation in the analysis should be prioritized. In regards to the second question, the change of topography/land-cover versus the change of intensity revealed a general lack of significant results with the unsmoothed data. Similar to the previous discussion, the derivative correlation often switched sign form one-time period to another. It is therefore hypothesized that the calculation of the derivative may have been negatively impacted by the high resolution of the data. Small deviations in the elevation or surface roughness throughout the entirety of the case could result in error across a much broader relationship temporally and spatially. It is also suggested that examining the derivative over the entire time period prevents a significant relationship from being identified. For this study, the Carney 1 case, was the single case that revealed a strong, but non-significant, relationship between the change of surface roughness and the change of intensity. Unfortunately, changing beam height throughout the time period introduces limitations which prevents increased confidence in the relationship as an overwhelming conclusion.

202 202 The third and fourth questions were investigated in order to relate previous conclusions in other studies to the ones found here. As discussed previously, many of the observational studies and even the numerical studies were focused on unique events rather than statistical evidence. Eventually, if enough unique events are found, the significance of those relationships becomes more profound. Perhaps the most influential topography case was associated with the Canadian River during the second time period of the El Reno tornado. Despite the significant positive correlation found through statistical analysis over the entire time period, the very low beam height observed a strong intensity increase as the tornado entered the Canadian River floodplain. It is hypothesized that several factors could have facilitated the increase in intensity. First, storm mechanisms could have played a role since the tornado had recently developed. Second, the drop in elevation could have contributed to vorticity stretching, which was manifest by the rapid intensification followed by a subsequent decrease in intensity has the stretching forces were reduced. The third and final hypothesis is that as the tornado entered the floodplain, an area of high swirl due to the lack of surface roughness associated with the river resulted in the rapid increase in intensity. This potential relationship reflects comments from Church (1993); however, with the lack of additional features, the analysis can only be justified with additional cases. The second period of the El Reno tornado encourages several motivational statements. The first is that more cases associated with robust topographic features may help increase confidence in regards to the potential relationships associated with topography and land-cover change. Additionally, while more cases would be ideal, cases

203 203 particularly with low radar beam heights would increase the confidence with respect to surface roughness changes. Finally, as evidence of this study, the increased temporal and spatial resolution do provide unique opportunities to investigate specific features like the one seen here. Without these observations, there could be no definitive investigation because the data would lack the proper resolution. For example, the second period of the El Reno case, would only contain two WSR-88D radar scans during the six-minute time period; however, 205 were analyzed using the RaXPol. Depending on the location of the tornado during the two radar scans, the river valley may have been missed by the WSR- 88D data. Analysis of additional case studies with similar spatio-temporal resolution would increase the confidence of the relationship on a statistical level. Although the improvements in observations with the rapid-scan mobile radar data provided a detailed investigation into the potential relationships between topography/land-cover, the general lack of robust changes in topography and land-cover, limited the extent of this study. Additionally, the strong relationship associated with beam height and tornado intensity over these cases reduced the number of periods where very little limitations existed. The best way to combat these limitations would be to eliminate beam height as a strong predictor. This could be done through the inclusion of more beam levels to derive intensity, as well as, introducing more cases to the overall study. The results found here are associated with a unique methodology that has not been utilized before. With time and additional cases, the methodology could be improved, and it would be expected that the results would improve too.

204 204 While maintaining the appropriate spatio-temporal resolution, additional cases would provide the opportunity to compare similar topographic features within different cases. Eliminating the strong influence of radar beam height by deriving intensity throughout the same vertical height of the tornado would eliminate the strong contribution toward predicting tornado intensity within the linear regression techniques. Since it was found that the three surface roughness parameters quantified surface roughness similarly, prioritizing the results made using one specific surface roughness value would simplify the results associated with surface roughness. The statistically significant results found with this study warrant additional study, and with the improvements described above, clarification on the application of these results could be discovered. Clarification of these results would ultimately provide another portion to the overall knowledge and understanding of tornadoes.

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