The Effects of Land Cover Type on Tornado Intensity in the Southeastern U.S

The Effects of Land Cover Type on Tornado Intensity in the Southeastern U.S.

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

Kelly M. Butler

August 2017

This thesis titled

The Effects of Land Cover Type on Tornado Intensity in the Southeastern U. S.

KELLY M. BUTLER

has been approved for

the Department of Geography

and the College of Arts and Sciences by

Jana B. Houser

Assistant Professor of Geography

Robert Frank

Dean, College of Arts and Sciences

ABSTRACT

BUTLER, KELLY M., M.S., August 2017, Geography

The Effects of Land Cover Type on Tornado Intensity in the Southeastern U.S.

Director of Thesis: Jana B. Houser

While storm-scale mechanisms are known to be associated with changes in tornado intensity, tornadoes also intensify and weaken without direct correlation to a known storm- or tornado-scale feature. One non-storm mechanism that could influence the intensity of a tornado is the land cover over which the vortex is traversing. In theory, friction disrupts the cyclostrophic balance achieved between the pressure gradient force and the centrifugal force. While conserving angular momentum, a new balance must be achieved which ultimately alters the rotational velocities. The purpose of this research is to determine if there are statistical relationships between land cover (a proxy for friction) and tornado intensity (as quantified by the difference between the maximum inbound and the maximum outbound Doppler velocities, ΔVmax).

Historical storm report data and level II WSR-88D radar data are acquired from archival resources for 30 tornadic storms within the domain and land cover data are extracted from the National Land Cover Database. Tornado locations are approximated from radar observations and a radius of influence extends out from the central point of the tornado, representing area directly affecting the tornadic flow field. Tornado intensity is spatially analyzed against land cover types within the tornadic flow fields using a GIS framework, and only at locations along the tornado path where radar data are observed.

Linear and non-parametric statistics are utilized in this preliminary study. Conclusions

4 reveal there are statistical relationships between land cover and tornado intensity. It is found that both the magnitude and direction of surface roughness change are associated with unique changes in tornado intensities.

DEDICATION

This work is dedicated to my loving mother, Doreen Butler. Thank you for always pushing me to follow my dreams and for always believing in me, even on the days I did

not believe in myself. “Believe it, and you will achieve it”.

ACKNOWLEDGMENTS

Primarily, I would like to thank my academic advisor, Dr. Jana Houser. Jana, you are the reason I specifically sought out Ohio University to obtain my Master of Science degree. You have inspired me in many different capacities. Your depth of knowledge on severe storms and tornadoes is unparalleled, as is your ability to effectively communicate the science. Thank you for your patience, your advice, and your willingness to listen during the many meetings that we had; and especially for the countless hours that were spent reading drafts of this thesis. Thank you for being a great female role model personally and professionally. I appreciate all the real-world wisdom and life lessons that you have passed on to me.

To my other committee members Dr. Ryan Fogt and Dr. Gaurav Sinha, thank you for your professional critiques of this thesis. I would also like to thank you both for the invaluable lessons that were taught in your classes.

Chad Goergens, thank you for the motivation and the distractions. You are one of the hardest workers I know and inspired me many of times to be productive on days when

I felt doing like anything but thesis work. You were always there to lighten the mood whenever the stress load was high. Even if destressing meant making fun of an imaginary chicken, Clarence. While we are going separate ways, I hope that we can keep in touch, and I wish you and your wife the best of luck on your future endeavors.

I would like to say thank you to Nate McGinnis for the numerous conversations that we had discussing our theses and for pioneering some of the methods used herein.

Also I would like to thank Dr. Kevin Farrell for all the slight nudges I needed to apply for graduate school after taking time off from school.

To Kayla Flynn, thank you for helping me with Matlab and for your generosity in helping me make my code run efficiently and working through the bugs in my script. I can’t forget to thank you for saving my thesis document when all my equations decided to turn into question marks and I thought my life was over. You always were the calm and collected one out of the two of us! Thank you for your continued encouragement and motivation, and most of all, for being the best friend a woman could ask for.

Finally, I need to thank my mother, Doreen Butler. You have shown me more love and support than anyone else these last couple of years. You were always there for a quick video chat to tell me to keep smiling and were always replacing my doubt with hope. You have always taught me to work hard for things in life, so I hope you can see that I have continued to do so.

TABLE OF CONTENTS

Page

Abstract ...... 3 Dedication ...... 5 Acknowledgments...... 6 List of Tables ...... 10 List of Figures ...... 11 Chapter 1: Introduction and Motivation ...... 14 1.1 Introduction ...... 14 1.2 Motivation ...... 16 Chapter 2: Literature Review ...... 19 2.1 Understanding Supercells ...... 19 2.2 Tornadogenesis ...... 19 2.2.1 Stages of Genesis ...... 20 2.2.2 Genesis Failure...... 24 2.3 Storm Scale Mechanisms ...... 25 2.3.1 The Rear Flank Downdraft and its Internal Momentum Surge ...... 26 2.3.2 Descending Reflectivity Cores ...... 28 2.3.3 Summary ...... 30 2.4 Friction (Surface Roughness) ...... 30 2.4.1 Numerical and Lab Simulations...... 30 2.4.2 Observational Studies ...... 37 Chapter 3: Data and Methods ...... 39 3.1 Event Acquisition...... 39 3.3 Radar Interpretation and Analysis ...... 43 3.4 GIS Analysis ...... 46 3.5 Statistical Analyses ...... 56 3.5.1 Parametric Analysis ...... 56 3.5.2 Non-Parametric Analysis Theory ...... 59 3.5.3 Non-Parametric Analysis Applications...... 62 Chapter 4: Results ...... 67 4.1 Parametric Results ...... 67

4.2 Non-Parametric Results ...... 73 4.2.1 Results of Zw and ΔV at Lag 0 ...... 73 4.2.2 Results of Zw and ΔV at Lag 1 ...... 82 4.2.3 Results of dZw and dΔV at Lag 0 ...... 87 4.2.4 Results of dZw and dΔV at Lag 1 ...... 94 Chapter 5: Discussion and Conclusions ...... 101 5.1 Discussion ...... 101 5.2 Conclusions ...... 108 5.3 Future Work ...... 111 References ...... 113

LIST OF TABLES

Page

Table 3.1: List of all tornado events used in this study including EF rating, date, and the radar which recorded event...... 41 Table 3.2: List of Doppler radar sites utilized in this study. Radar ID, location and responsible weather forecast office (WFO) is listed...... 42 Table 3.3: Land surface roughness lengths adapted from AERSURFACE User’s Guide (EPA 2008) for the months DJF and MAM...... 48 Table 4.1: List of individual tornado events with their respective statistical correlation coefficient (SCC) values, r, at lag 0 and at lag 1 and associated p-values. The number of Zw - ∆V raw data pairs for each tornado event is indicated and p-values meeting the 5% significance level are in bold...... 70 Table 4.2: List of CSs, including the Zw constraint for the CS, and statistical difference (1), marginal statistical difference (1*), near statistical difference (0^), or no statistical difference (0) of associated ΔV at lag 0. The relative tornado intensity is listed as weaker, stronger, and no value if there is no intensity preference. The number of ΔVs in each sub-s and sub-r are indicated...... 74 Table 4.3: As in Table 4.2, except at lag 1...... 83 Table 4.4: List of CSs, including the dZw constraint for the CS, and statistical difference (1), marginal statistical difference (1*), near statistical difference (0^), or no statistical difference (0) of associated ΔV at lag 1. The relative tornado intensity is listed as weaker, stronger, and no value if there is no intensity preference. The number of ΔVs in each sub-s and sub-r are indicated...... 89 Table 4.5: As in Table 4.4, except associated dΔVs are at lag 1...... 95 Table 5.1: A suggested order of time (from longest to shortest amount of time) taken for a tornado to adjust to changes in weighted surface roughness...... 106

LIST OF FIGURES

Page

Figure 1.1: Image of all United States tornadoes from 1950-2015. Study area outlined in black contour...... 17 Figure 1.2: Satellite image of land cover around Little Rock, AR. Showing several types of land coverage over a short distance. Image from Google...... 18 Figure 2.1: Vertical vorticity contributing to the supercellular mesocyclone from tilting horizontal vorticity. Figure extracted from Markowski and Richardson (2009)...... 20 Figure 2.2: A schematic of wind shear developing into mid-level vertical vorticity (red) and low level baroclinically generated horizontal vorticity developing into low level vertical vorticity (blue). Figure extracted from Markowski and Richardson (2009)...... 22 Figure 2.3: Effect of tornado flow structure with swirl ratio increasing from a to f. Extracted from Davies-Jones et al. (2001)...... 36 Figure 3.1: Example of radar representation of a tornado. The dashed white circle indicates the approximate location of the tornado. a: Reflectivity (dBZ), b: Radial Velocity (ms-1). Location of maximum inbound (yellow arrow) and outbound (blue arrow) velocities and the approximate vortex center (white arrow)...... 45 Figure 3.2: Example of radar representation of a tornado. a: Reflectivity (dBZ), b: Radial Velocity (ms-1). Location of maximum inbound (yellow arrow) and outbound (blue arrow) velocities and the approximate vortex center (white arrow). Radius of maximum winds (solid circle) and full radius of influence (dashed circle)...... 46 Figure 3.3: Legend of NCLD qualitative land cover categories...... 47 Figure 3.4: Radar locations utilized herein are indicated by a star and labeled by Radar ID and the 60 km range from each radar is indicated by the yellow shaded circle. These features are overlaid on the NLCD layer. States are outlined in grey. Legend of NCLD qualitative land cover categories shown in lower box...... 49 Figure 3.5: Tornado path (black dots) and relative intensity (graduated pink triangles) of a tornado (event 3) throughout its lifecycle overlaid on the NLCD layer. Legend of NCLD qualitative land cover categories shown in lower box...... 51 Figure 3.6: Tornado paths (pink triangles) of all tornado events within a 60 km radius (yellow) of a radar station (star)...... 52 Figure 3.7: Regions of influence shown in progressively dark shades of black from QR, HF, QR3, to the outer most region, FRI. These areas are centered about the tornado center (black dot) and are overlaid on the NLCD layer. Legend of NCLD qualitative land cover categories shown in lower box...... 55 Figure 3.8: Scatter plot of Zw and ΔVmax. The data pairs (blue dots) and trend line (red) are shown...... 56

Figure 3.9: Schematic adapted from Efron and Tibshirani’s (1993) Figure 2.1 to show the bootstrap process where X is the data sample, X* = (X*1, X*2, X*3,…, X*B) is the set of bootstrapped samples of X, and 휃̂∗= (s(X*1), s(X*2),…, s(X*B)) is the set of bootstrap replications of statistic, s (in this study the statistic in question is the mean)...... 60 Figure 3.10: Histogram of sub-s of CS 4 post bootstrapping. The histogram shows the frequency of the bootstrap replicate means of the 15,000 bootstrap replicates and it shows an approximately normal distribution...... 63 Figure 4.1: Lag 0 time series of individual tornado events, 3,7, and 8, in subplot a, b, and c, respectively. Time (UTC) along the ordinate, Zw along the primary (left) abscissa, and ΔV along the secondary (right) abscissa. Zw (ΔV) plotted in orange (grey). SCC for each plot is given in plot title...... 71 Figure 4.2: As in Figure 4.1 except ΔV is plotted at lag 1 for individual tornado events, 13, 25, and 26, in subplot a, b, and c, respectively. Time step along the ordinate is Zw (ΔV) at lag 0 (lag 1)...... 72 Figure 4.3: Conceptual diagram of the variables weighted surface roughness (Zw) and tornado intensity at lag 0 (ΔV) as they relate with time. Time moves left to right along the horizontal arrow with each time step (t) indicated by a vertical bar with the time step label immediately to the right. Variables which are functions of a given time step are labeled at either end of the vertical bar...... 74 Figure 4.4: Pseudo plots of CSs 5, 6, and 7 are in panels a, b, and c, respectively. Subsample sub-s (sub-r) is on the left (right) with 휃̂∗푀 indicated by the red dashed line (for sub-s) and blue asterisk (for both subsets, respectively). The inter-quartile range (range from 25th and 75th percentile) is indicated by a blue box for each subset, end lines indicate the upper and lower ΔV values of the 95% bca CI for each subset, respectively. Note these are not box and whisker plots. The dashed red line references 휃̂∗푀 of sub-s such that if the line falls outside (inside) of the bca CI of sub-r, the CS is (not) statistically different...... 76 Figure 4.5: As in Fig. 4.4 except for CSs 14, 15, and 16 are in subplots a, b, and c, respectively...... 78 Figure 4.6: As in Fig. 4.4 except for CSs 1, 9, and 2 are in panels a, b, and c, respectively...... 81 Figure 4.7: As in Fig. 4.4 except for CSs 10 and 11 are in panels a and b, respectively. 81 Figure 4.8: As in Fig. 4.4 except for tornado intensity at lag 1 (LΔV)...... 83 Figure 4.9: As in Fig. 4.4 except CSs 18, 19, and 20 are in panels a, b, and c, and CSs 22, 23, and 24 are in panels d, e, and f. CSs in panels a, b, and c (d, e, and f) are associated with small (large) weighted surface roughness lengths...... 85 Figure 4.10: As in Fig. 4.4 except for CSs 32 and 33 are in panels a and b, respectively...... 86

Figure 4.11: As in Fig. 4.4 except the change of Zw (dZw) and change of ΔV at lag 0 (dΔV) are indicated above the orange and below the blue braces, respectively. The braces indicate which two variables and two time steps contribute to each dZw and dΔV...... 88 Figure 4.12: As in Fig. 4.4 except for CSs 34, 35, and 37 are in panels a, b, and c, respectively...... 90 Figure 4.13: As in Fig. 4.4 except for CSs 38, and 39 are in panels a, and b, respectively...... 91 Figure 4.14: As in Fig. 4.4 except for CSs 40, 41, 44, and 43 are in subplots a, b, c, and d, respectively...... 93 Figure 4.15: As in Fig. 4.11 except the for change of ΔV at lag 1 (LdΔV) is displayed. 95 Figure 4.16: As in Fig. 4.4 except for CSs 45, 46, 47, and 48 are in panels a, b, c, and d, respectively...... 96 Figure 4.17: As in Fig. 4.4 except for CSs 49, 50, 51, and 52 are in panels a, b, c, and d, respectively...... 98 Figure 4.18: As in Fig. 4.4 except for CSs 55 and 57 are in panels a and b, respectively...... 100

CHAPTER 1: INTRODUCTION AND MOTIVATION

1.1 Introduction

Every year, tornadoes result in billions of dollars in damage to homes, businesses, and crops. In some unfortunate cases, fatalities occur. With more than 1,000 tornadoes occurring on average each year (ncdc.noaa.gov), it is important that the scientific community fully understand these destructive and deadly natural phenomena. Currently, there is a gap in the literature of what causes a tornado to intensify or weaken. Ongoing and past research on storm-scale and tornado-scale mechanisms can account for some instances of strengthening or weakening, but in other cases, tornadoes intensify and weaken without any apparent link to storm or tornado-scale features or processes.

According to the basic dynamics governing rotational flow fields (i.e. tornadic wind field), friction disrupts the cyclostrophic balance achieved between the pressure gradient force (PGF) and the centrifugal force (CF). This disruption allows for rotating winds to converge closer to the axis of rotation, by causing the inward-directed PGF to exceed the outward-directed CF, ultimately resulting in increased rotational velocities, per the conservations of angular momentum which state: when a rotating fluid is brought closer to the axis of rotation, its tangential velocity will increase.1

Based on this theory, a tangential velocity about a tornado should increase

(decrease) with increasing (decreasing) friction. Since frictional values differ with land cover type, studies must be done to understand vortex behavior as it traverses across a surface with heterogeneous land cover. Multiple laboratory studies (Dessens 1972;

1 Conservation of angular momentum is only purely conserved in frictionless flow.

Leslie 1977), numerical simulations (Lewellen 2008; Natarajan and Hangan 2012;

Lewellen 2014) and an observational study (Kellner and Niyogi 2014) have found possible relationships between tornadogenesis, maintenance, and decay, with land surface heterogeneity.

In laboratory simulations, increasing surface roughness (a proxy for the magnitude of surface friction) was found to increase vertical velocity (Dessens 1972), and Leslie (1977) suggested decreasing surface roughness could trigger a transition from a single cell to multi-vortex tornado. In both laboratory and numerical simulations performed by Church and Snow (1993) and Natarajan and Hangan (2012), introducing surface roughness was found to reduce the tangential velocity of the vortex, which is contradictory to what is expected in theory based on the disruption of cyclostrophic balance. A modern numerical simulation found roughness elements, such as buildings, could either significantly strengthen or weaken the tornado depending upon the size of the element and its range from the vortex (Lewellen 2014). Finally, a study confined to the state of Indiana suggested the number of tornadoes that touched down within 1 km of a unique land cover type decreased with decreasing surface roughness lengths2 (Kellner and Niyogi 2014). Based upon results from both numerical simulations and observational studies, it appears likely that tornado characteristics and behavior are impacted by land cover type, a proxy for friction.

2 A surface roughness length is the height at which the wind velocity is zero; based on a logarithmic wind profile (American Meteorological Society 2017b).

1.2 Motivation

Based upon the studies mentioned above, it is hypothesized that land cover type impacts tornado characteristics and behavior. For example, a tornado moving from forested land to grasslands or from agricultural to urban land cover, might be expected to exhibit changes in intensity. The nature of the relationship between surface friction and tornado characteristics has been poor due to limited capabilities of simulations and observational data (Markowski and Richardson 2014). The potential relationships between tornadoes and land-cover type is momentous since there is currently no capability or guidance available to predict tornado maintenance (e.g. current intensity, future intensity, or duration) (Markowski and Richardson 2014).

The purpose of this research is to determine if frictional changes across land cover can be correlated with changes in tornado intensity. The problem herein is approached in a novel way, utilizing a geographic information system (GIS), which few meteorological studies have employed to research tornadoes. Use of the GIS framework enables a comprehensive understanding of the spatial relationship between land surface cover and tornado characteristics. Relevant data including land cover, storm tracks, and radar data are displayed together overlaid in a common spatial reference system. The powerful built-in analysis and statistical tools of GIS enables a robust analysis of the relationships between the mentioned datasets.

The geographic domain of the analysis is the Southeastern region of the United

States (Alabama, Arkansas, Georgia, Louisiana, Mississippi, South Carolina, and

Tennessee). The chosen study area ensures many tornado events are available, as seen by

17 the tornado tracks in Fig. 1.1. This area, importantly, has a multitude of land cover types over relatively small geographic areas. For instance, land cover around Little Rock, AR is shown in Fig. 1.2 and (from west to east) consists of forest, residential and urban, agricultural, and grasslands. Multiple land cover types are important because if a tornado does not traverse over varying land cover types then the applied methods and results of spatial analyses would not be meaningful.

Figure 1.1: Image of all United States tornadoes from 1950-2015. Study area outlined in black contour.

It is hypothesized herein that frictional changes across land cover types are related to changes in tornado intensity. The fundamental questions to be investigated in this study are as follows:

1) Are tornadoes more (less) intense when located over surfaces which have land

cover types with relatively high (low) values of friction?

2) Will a tornado intensify or weaken if it traverses from land cover types with lower

friction to ones with higher friction, and vise-versa?

By answering these research questions, this work will provide insight on the relationships between tornadoes and land surface cover and perhaps advance our understanding of how and why tornadoes intensity.

5 km

Figure 1.2: Satellite image of land cover around Little Rock, AR. Showing several types of land coverage over a short distance. Image from Google.

CHAPTER 2: LITERATURE REVIEW

2.1 Understanding Supercells

Most damaging and violent tornadoes are spawned by supercell thunderstorms

(Markowski and Richardson 2014; Davies-Jones 2015). Supercells usually have cyclonic rotation, generally produce cyclonic tornadoes (Markowski and Richardson 2014) and tend to propagate to the right side of the environmental-wind hodograph curve in the

Northern Hemisphere (Bluestein 2013). What sets these highly-organized supercells apart from other storm modes is the presence of deep, persistent rotating updrafts, or mesocyclones (Fig. 2.1). Mesocyclones typically are 5-10 km wide and several km deep, with vertical vorticity on the order of 10-2s-1 (Doswell and Burgess 1993; Davies-Jones

2015). Tornadoes in supercells are hypothesized to form from horizontal vorticity created by the storm that becomes tilted in the vertical direction by a downdraft (Rotunno and

Klemp 1985; Markowski and Richardson 2009).

2.2 Tornadogenesis

Before an investigation begins on how surface roughness can change tornado characteristics, it is important to understand the mechanisms that govern how tornadoes form or fail to form. In most cases, in order for a tornado to occur in a supercell, three processes must occur. First, mid-level rotation develops, then low-level rotation is generated, and finally, the low-level rotation contracts into a tornado.

Figure 2.1: Vertical vorticity contributing to the supercellular mesocyclone from tilting horizontal vorticity. Figure extracted from Markowski and Richardson (2009).

2.2.1 Stages of Genesis

Mesocyclones are known to form as a result of shear-driven environmental horizontal vorticity that is tilted into the vertical by an updraft (Rotunno and Klemp

1985). Assuming no friction or temperature gradients, the vertical vorticity equation can be simplified such that:

휕휁′ = −푣 ∙ ∇ 휁′ + 푆×∇ 휔′, 휕푡 ℎ ℎ

휕휁′ −푣 ∙ ∇ 휁′ where 휕푡 is the local change in vertical vorticity over time, ℎ is the vertical vorticity advection by the horizontal wind and the remaining term is the tilting term

(Markowski and Richardson 2010), which is responsible for the generation of the mid-

21 level mesocyclone. Conceptually, tilting occurs when the environmental vertical wind shear induces horizontal vorticity which gets tilted (pulled up) by an updraft, thus reorienting the horizontal vorticity into vertical vorticity. This tilting by an updraft creates a cyclonic/anticyclonic vorticity couplet that straddles the updraft. The orientation of the storm-relative wind will determine which (if either) of the vortices will become dominant. When the storm relative wind is more streamwise than crosswise to the shear induced vorticity vector, advection moves the vorticity couplet across the updraft where the cyclonic member becomes centered near the updraft maximum. The updraft then gains net cyclonic rotation and the mesocyclone forms. The mid-level mesocyclone forms by dynamically different processes than the low-level mesocyclone.

Prior to the formation of a tornado, a strong low-level (< 1 km above the ground) mesocyclone usually is present. It is well understood that parcels ascending due to tilting will not produce near-ground rotation, nor will they produce a tornado (Markowski and

Richardson 2014; Davies-Jones 2015) because parcels must rise hundreds of meters before their rotation is that of mesocyclone strength (Markowski and Richardson 2014).

Hence, other mechanisms must be in place to create the low-level mesocyclone.

The full vertical vorticity equation is defined by

′ ′ 휕휁 휕휁 휕휔 휕푣 휕휔 휕푢 휕휔 휕퐹푦 휕퐹푥 = −푣 ∙ ∇ 휁′ − 휔 − [ − ] + 휁 + [ − ], 휕푡 ℎ 휕푝 휕푥 휕푝 휕푦 휕푝 휕푝 휕푥 휕푦 where the left-hand side is the local change in vorticity over time and the terms on the right-hand side (from left to right) are: the horizontal vorticity advection, the vertical vorticity advection, the tilting, the stretching, and the differential friction terms

(Lackmann 2012). One mechanism that both numerical and field observations suggest

22 aids in the formation of low-level rotation stems from buoyancy gradients. This mechanism is commonly referred to as the baroclinic generation of vorticity. A large downdraft area exists downshear from the updraft (called the forward flank downdraft, or

FFD) of the supercell as a result of falling precipitation in this area. The air parcels in the

FFD area are largely negatively buoyant, due to cool temperatures resulting from evaporation. The downdraft extends to lower altitudes as precipitation evaporates and cools the air at progressively lower levels. The resultant buoyancy gradient between the evaporatively-cooled FFD and the warmer ambient environment create horizontal vorticity (Markowski and Richardson 2014) which then gets tilted by the vertical velocity gradient between the updraft and the rear-flank downdraft, providing the basis of the low- level vertical vorticity (Fig. 2.2) (Markowski and Richardson 2014; Davies-Jones 2015).

Figure 2.2: A schematic of wind shear developing into mid-level vertical vorticity (red) and low level baroclinically generated horizontal vorticity developing into low level vertical vorticity (blue). Figure extracted from Markowski and Richardson (2009).

The last process to occur is the intensification of the near-ground vortex associated with the incipient tornado. This occurs by way of the conservation of angular momentum as rotating air converges toward the center of rotation (Markowski and

Richardson 2014). According to this law, as air converges near the surface it must also move upward. However, since parcels have relatively low buoyancy, from cooling in the

RFD, work is required to accelerate them back upward. To overcome the stability of the relatively low-buoyancy parcels, an upward-directed vertical perturbation pressure gradient force is required. In supercells, this force is generated when a rotation- dominated wind field (such as the mesocyclone aloft) induces low perturbation pressure.

Perturbation pressure 푝′ is of the form:

′ ̅̅̅̅ ′ ̅̅̅̅ 2 1 휕푤 휕푢 휕푤 휕푣 휕퐵 푝′ ∝ 푒′ − |휔′|2 + 2 ( + ) − , 푖푗 2 휕푥 휕푧 휕푦 휕푧 휕푧

1 푒′2 − |휔′|2 where the terms 푖푗 and 2 are the non-linear dynamic pressure perturbation

휕푤′ 휕푢̅̅̅̅ 휕푤′ 휕푣̅̅̅̅ 휕퐵 2 ( + ) − terms, 휕푥 휕푧 휕푦 휕푧 is the linear dynamic pressure perturbation term, and 휕푧 is the buoyancy perturbation pressure term. The first non-linear term is the deformation perturbation due to spatial variations of the velocity field, also known as the ‘splat’ term; where high pressure perturbations exist anywhere there is horizontal deformation. The second non-linear term is the vorticity perturbation, known as the spin term. The linear perturbation term can be rewritten in terms of the shear vector of the form 2푆 ∙ ∇ℎ푤′ which implies a high-pressure perturbation on the upshear side of the updraft and a low perturbation pressure, on the downshear side (Markowski and Richardson 2010).

The interest here is in the second non-linear term, where any amount of rotational vorticity is going to contribute to a lower pressure perturbation (Markowski and

Richardson 2010). Thus, if rotation aloft intensifies, the upward directed PGF will intensify, radial inflow will increase, and convergence will therefore increase as well.

These processes help stretch the vertical vorticity to tornadic strength.

2.2.2 Genesis Failure

Tornadogenesis is sensitive to many variables. For instance nearly 80% of supercells that generate low-level mesocyclones never produce a tornado (Trapp et al.

2005). In referring back to the negatively buoyant air, if it is too negative, it could be disadvantageous because the perturbation pressure gradient force would not be strong enough to accelerate the parcel upward (Markowski et al. 2002). Conversely, if the air is less negatively buoyant, it could be advantageous because the perturbation pressure gradient force would be strong enough to accelerate the parcel upward. In cases where tornadic rotation first develops aloft (Trapp and Davies-Jones 1997), tornadogenesis failure could occur if the vertical stability of the convective boundary layer is very large.

In such a case, the nascent tornado would be limited to hovering above the ground (Trapp

1999).

Naylor and Gilmore (2014) found tornadogenesis was sensitive to vorticity production in descending parcels from aloft. In their simulations, tornadogenesis failure was caused by weak overall vorticity production compared to cases resulting in tornadogenesis. Additionally, Ward’s (1972) laboratory model found that a tornado will not form if the updraft does not contain sufficient rotation. Here, the flow field was

25 largely dominated by convergence and the resulting accumulation of mass which was not removed as quickly as it came in. Thus, high pressure developed in the area near the central axis of rotation which results in an opposing PGF directed away from the central axis of rotation. The tornadogenesis failure was due to the boundary layer separating before air reached the axis of rotation (Ward 1972). The separation of the boundary layer is referring to the fact that inward directed air and outward directed acceleration meet and are then forced upward; thus, the incoming air does not make it to the central axis of rotation at the surface. Tornadogenesis and/or failure could also be sensitive to its surrounding surface roughness or other storm scale mechanisms.

2.3 Storm Scale Mechanisms

Unfortunately, there are still many unknowns in the science, like why a supercell is not always tornadic. Furthermore, in an ongoing tornadic event, even less is known about the forcing and triggers that play roles in tornado maintenance. Forecasters have no ability to predict the details regarding intensification, weakening, decay, or duration.

Research is now focusing on specific mechanisms that may contribute to tornadogenesis, as well as understanding processes that contribute to tornado maintenance and intensification (Markowski and Richardson 2014; Davies-Jones 2015; Naylor and

Gilmore 2014). While the research herein will investigate how surface roughness may affect tornado properties, it is important to acknowledge storm-scale mechanisms that may also affect tornado properties, including rear flank downdraft internal surges and descending reflectivity cores.

2.3.1 The Rear Flank Downdraft and its Internal Momentum Surge

One storm-scale feature that has been observed to be important in tornado processes is the rear-flank downdraft (RFD) (Markowski et al. 2002). One potentially important process associated with the RFD is the process of “recycling” into a tornadic updraft, first developed by Fujita (1975). He hypothesized that the descending air from the RFD will be pulled into the updraft at the surface, and while it converges into the vortex, maintaining its angular momentum, tangential acceleration will occur. Thus, the

RFD became a mechanism of interest in tornadogenesis and intensification (Fujita 1975) thereafter.

Since the Fujita (1975) study, it has been shown that air with large angular momentum transported to the surface can indeed be ‘ingested’ into the updraft, creating the essential low-level rotation through vertical stretching, required for tornadogenesis

(Davies-Jones 2008; Markowski et al. 2003). This genesis, however, appears to be dependent, again, on the relative buoyancy of the RFD air. An RFD with large negative buoyancy could weaken a tornadic updraft and thereby result in tornadogenesis failure, or potentially weaken an ongoing event. Markowski et al. (2002) found that most significant tornadoes (F2+) have less negatively buoyant air along with smaller changes in equivalent potential temperature in the RFD region compared to non-tornadic supercells.

Markowski et al. (2002) hypothesized that the likelihood of a tornado, its intensity and longevity, increase with increasing surface buoyancy, convective available potential energy, and equivalent potential temperature in the RFD. Markowski et al. (2002) mentions that these conditions are not sufficient alone for tornadogenesis and comments

27 on additional factors that are “almost certainly” important. Specifically, they mention surface roughness, along with angular momentum distributions within the descending

RFD.

In investigating RFDs, many recent studies have focused on periodic events where stronger winds (augmented horizontal momentum) are observed behind the main boundary between the RFD and the environmental air (Skinner et al. 2015). These events are known as RFD internal surges (RFDIS) (Skinner et al. 2014). RFDISs represent a discrete acceleration of the outflow within an existing RFD behind its leading edge.

RFDISs have been identified as being important to tornadogenesis (Mashiko et al. 2009;

Kosiba et al. 2013, Schenkman 2016), maintenance (Marquis et al. 2012; Kosiba et al.

2013; Kurdzo et al. 2015), and decay (Marquis et al. 2012; Lee et al. 2012; Kurdzo et al.

2015). They have been studied using portable in situ instruments (e.g. Skinner et al. 2011;

Lee et al. 2012), high spatial resolution remote sensing (e.g. Marquis et al. 2008; Marquis et al. 2012; Kosiba et al. 2013; Bluestein et al. 2014; Skinner et al. 2014), and numerical simulations (e.g. Mashiko et al. 2009, Schenkman 2016).

Marquis et al. (2012) studied four supercells and found that tornadoes were maintained when located near (or partially embedded in) the convergence zone along the

RFDIS. They hypothesized the aid in tornado maintenance is due to transportation of angular momentum inward to the low-level mesocyclone (Marquis et al. 2012).

Therefore, the RFDIS would also be a source of increased vertical vorticity for an undeveloped tornadic circulation thereby aiding in genesis as well (Kosiba et al. 2013).

Kurdzo et al. (2015) identified an apparent relationship with RFDISs and the tornado track. In the case of the 2013 Moore, OK tornado, most RFDISs that occurred while the tornado was on the ground resulted in a shift in the tornado track direction.

Each shift occurred either simultaneously, or just after, the RFDIS. Kurdzo identified an occlusion-forcing RFDIS, which shifted the tornado track north and was closely followed by another RFDIS which seemed to restore the tornado to its prior steady state and easterly track (Kurdzo et al. 2015). Thus, the timing and frequency of RFDISs might be of immense importance. Finally, an RFDIS can induce tornado dissipation if the surge were to wrap completely around the tornado vortex (Marquis et al. 2012; Lee et al. 2012).

Essentially, this process results in changes to the low-level rotation and displaces the parent updraft away from the tornado, destroying the maintenance mechanism of the tornado.

2.3.2 Descending Reflectivity Cores

Another separate mechanism, a descending reflectivity core (DRC), also has impacts on the low-level rotation. A reflectivity core is a 3D reflectivity maximum phenomenon which is located above the weak-echo region of a supercell (Rasmussen et al. 2006). Rasmussen et al. (2006) hypothesized that DRCs may influence tornadogenesis. In their study, a DRC occurred prior to tornadogenesis in all four cases they studied. Their conclusions generated subsequent research in this area (Kennedy et al. 2007; Byko et al. 2009).

In a study of 64 supercells (tornadic and non-tornadic), Kennedy et al. (2007) found, in the majority (65%) of cases, the DRC influenced the velocities in the

29 supercell’s rear flank region but did not enhance the flow in every case. When the flow was enhanced, the acceleration was associated with counter-rotating vortices on either side of the acceleration; consistent with that found by Rasmussen et al. (2006). However, only in some of the cases was the cyclonic vortex related to an incipient tornado

(Kennedy et al. 2007). Connections between DRCs and tornadogenesis seem likely as they precede tornadogenesis in most cases, but the current spatial and temporal resolution of Weather Surveillance Radar-1988 Doppler (WSR-88D) cannot currently separate a tornadic versus non-tornadic DRC appendage (Kennedy et al. 2007).

Byko et al. (2009) used mobile radars and high–resolution numerical simulations to analyze DRCs. The numerical simulation yielded three different mechanisms by which a DRC was produced. One type was from the stagnation of midlevel flow, another from supercell cycling, and lastly from the intensification of low-level rotation. The

DRC that formed by stagnation of the midlevel flow (type I per Byko et al. (2009)), was the only DRC which had subsequent rapid low-level vorticity amplification such as those in identified in Kennedy et al. (2007) and Rasmussen et al. (2006). Unlike Kennedy et al.

(2007) and Rasmussen et al. (2006), Byko et al. (2009) found it unlikely that a type I

DRC directly contributed to the rapid intensification of a vortex. No concrete relationship could be determined between DRCs and the low-level wind field using mobile radar observations or using numerical simulations. The outcomes of the mentioned studies have produced diverse results on whether a DRC can be used to forecast low-level rotation intensification and incipient tornadogenesis.

2.3.3 Summary

While mechanisms such as RFDISs and DRCs are known to be associated with changes in tornadic rotation, the temporal resolution of this study limits looking at these variables. However, there are still many unknowns regarding tornadic systems.

Tornadoes also intensify and weaken with no specific known storm-scale or tornado- scale feature responsible. Thus, it is plausible that non-storm-related features could be affecting the system. One possible avenue of investigation is the surface over which the system is traversing: it is possible for surface roughness to potentially contribute to weakening or intensification of tornadoes.

2.4 Friction (Surface Roughness)

The effect of friction on tornadogenesis, maintenance, and decay has been investigated in a small number of studies. Most these studies have been through numerical or lab simulations, although a few are observational. Numerical and lab simulations offer many benefits, such as the ability to control variations in certain parameters (Lewellen 2012) and most importantly, have the ability to isolate certain parameters and physical processes one at a time (Markowski and Richardson 2014). The observational studies have tried to validate hypotheses of the numerical simulations, but more must be done with an increased number of tornado cases and in different study areas.

2.4.1 Numerical and Lab Simulations

It has been found that tornado simulations which include friction behave very differently from simulations that do not include friction (Davies-Jones 2015). A

31 contracting vortex will try to achieve cyclostrophic balance. When friction is not included, the outward-directed centrifugal force (CF) increases as a result of increasing tangential velocities until it achieves balance with the inward PGF (Davies-Jones 2015).

This balance will then inhibit any further contraction of the vortex. Furthermore, assuming a frictionless surface, the balance would be uniform down to the surface if the winds in the tornado vortex were constant with height (Davies-Jones 2015). Therefore, based upon cyclostrophic and hydrostatic balances, the winds must have a maximum achievable limit. This limit is known as the thermodynamic speed limit3 (Davies-Jones

2015). Without including friction, this configuration of the flow field would only produce a broad, weak tornado at best.

When friction is allowed in the simulation, the result is drastically different

(Davies-Jones 2015; Lewellen 2014) in that the friction will intensify the vortex (Davies-

Jones 2015). In a model simulation of tornadogenesis with and without surface friction performed by Davies-Jones (2008), contraction of the low level vortex into a tornado occurred only in the presence of friction. Boundary layer parcels lose their angular momentum due to ground frictional torque (Davies-Jones 2008; Lewellen et al. 2000).

As this occurs, the hypothetical cyclostrophic balance which would be achieved over a frictionless surface is upset such that the inward PGF becomes stronger than the outward

CF (which is now reduced due to the direct, exponential relation between tangential velocity and CF, such that

3 The thermodynamic speed limit of a tornado may be expressed as: 1 푤 = 푉푚 = (2 ∗ 퐶퐴푃퐸)2 where CAPE is the convective available potential energy of a parcel, 푤 is the vertical maximum speed, and 푉푚 is the tangential maximum speed (American Meteorological Society 2017).

푣2 퐶퐹 = , 푟 where v is the tangential velocity and r is radius) thereby promoting much stronger radial inflow (Davies-Jones 2015), and exceeding the expected thermodynamic speed limit.

Of worth, Davies-Jones (2015) mentions that due to vortex dynamics, the maximum vertical velocity can be very close to the surface rather than near the tropopause. Vertical accelerations are generally maximized at low levels because the vertical pressure perturbation force and buoyancy force are both directed upward.

Compared to a typical convective storm where the buoyancy force is accelerating all the way to the top of the troposphere, the vertical pressure perturbation force can reverse aloft in a rotating supercell, opposing the buoyancy force. This reversal occurs because rotation generates a low pressure around the mid-level mesocyclone as a result of rotationally-induced pressure perturbation, thus generating a downward directed vertical

PGF.

Surface friction can cause maximum winds in quasi-steady tornadoes to exceed the thermodynamic speed limit by 3-4 times in the vertical component, twice in tangential velocity, and 1.5 times in the radial inflow (Davies-Jones 2015). Most notably, surface friction amplifies the maximum pressure deficits by 9 times the hydrostatic-deficit4 value

(Davies-Jones 2015). Hence, it would seem likely that land cover (a proxy for surface friction) would have impacts on tornadogenesis, intensity, and decay. Additionally,

Lewellen (2012) states that properties of near-surface inflow are likely critical to both the

4 Hydrostatic-deficit is the maximum pressure drop supported by hydrostatic balance.

33 structure and intensity of a tornado, and inflow properties will be influenced by land cover (i.e. its surface roughness). Therefore, land cover may significantly impact tornado behavior as the tornadic wind field interacts with the surface. Yet, there are few observational studies that specifically address the influence of friction, even though numerical simulations have already begun to suggest its importance (Lewellen 2014;

Lewellen 2012; Lewellen et al. 2008; Lewellen and Lewellen 2007; Lewellen et al.

2000;).

Dessens’ (1972) study was one of the first to explore the effects of surface roughness on lab simulated tornado-like vortices. In his simulation, he found that adding surface roughness both increased the radius of maximum velocity and decreased the maximum magnitude of velocity. The overall findings of the study concluded that roughness increased the difference between the PGF and centrifugal force in the boundary layer. Furthermore, the larger difference led to stronger convergence of the corner flow diameter and subsequent increase in the vortex core diameter with a visual appearance that was much more turbulent (Dessens 1972).

In a numerical study, Lewellen (2012) executed over 250 tornado simulations varying parameters including the initial swirl ratio (defined in next paragraph), translation speed, topography shape, length, surface roughness, and more. Lewellen found that the dominant topographic mechanisms affecting the vortex intensity and structure were due to changes related to the near-surface inflow, which directly affects the corner flow swirl ratio, where corner flow is the region where the flow turns upward, from a horizontal direction to a primarily vertical direction (Lewellen 2012). Generally, a decrease in corner flow swirl ratio will increase vortex intensity if the corner swirl ratio is above the critical low-swirl peak, and will lower intensity otherwise (Lewellen 2012).

Swirl ratio (S) is a measure of angular momentum to radial momentum, with S being defined as:

푟0퐶 푣0 푆 = = , 2푄 푤0 where C is the circulation at radius r0 about the central axis, “Q is the rate of volume flow through the top of the tornado chamber, v0 is the tangential [rotational] velocity at r0, and w0 is the mean vertical velocity at the top of the chamber” (Markowski and Richardson

2010). In other words, it is a ratio of tangential velocity at the updraft edge divided by the mean updraft velocity. The mean updraft velocity is also a function of horizontal convergence and divergence via the mass conservation equation. Small swirl ratios will exhibit flow dominated by convergence and updraft rather than rotation. As swirl ratio increases (Fig. 2.3), the structure of the vortex will change from one cell (Fig. 2.3b) to

35 two cell (Fig. 2.3e) to multiple vortices (Fig. 2.3f), depending on the value of S

(relatively low, medium, or high) (Markowski and Richardson 2010). The one cell vortex structure circulation has convergence at the bottom, rising motion in the middle, and divergence aloft as pictured in Fig. 2.3b. In the two-cell structure, the circulation is much different, such that there is downward motion along the central axis which constitutes divergence at the surface. The surface divergence meets inward directed branches of air which dominate the outer circulation. Their surface convergence then leads to upward motion and divergence aloft as in Fig. 2.3e.

A study by Natarajan and Hangan (2012) clarified the influence of roughness on translating tornadic circulations at varying degrees of swirl ratios. By introducing roughness to their simulations, they found the mean tangential velocity about the vortex was reduced across all swirl ratios. Another result of the simulation was that roughness causes an effect similar to that of a reduction in swirl ratio. They argued that increasing roughness directly affects frictional dissipation near the surface boundary layer and results in changeover to a lower swirl ratio arrangement (Natarajan and Hangan 2012).

These conclusions support other previously completed numerical studies (Dessens 1972;

Leslie 1977) but are in direct opposition to what is suggested from theory.

Figure 2.3: Effect of tornado flow structure with swirl ratio increasing from a to f. Extracted from Davies-Jones et al. (2001).

Tornadic debris could also affect the swirl ratio. Lewellen et al. (2008) essentially acknowledge that debris may be responsible for significant changes in the near surface wind field, which in turn can significantly alter the corner flow. Therefore, the availability and type of debris must be important. Thus, the translation of a tornado through different land surface types could lead to significant increases or decreases in intensification (Lewellen et al. 2008), but for a different reason than from frictional changes.

2.4.2 Observational Studies

Kellner and Niyogi (2014) used the climatologic tornado record from 1950-2012 along with land surface cover data (from 2005) and GIS to study tornado touchdown locations (start of tornado path) across the state of Indiana. They found that for all strong tornadoes (classified EF2 or greater), 64% touched down within 1 km of urban land and

42% of all strong tornadoes touched down in forested land (multiple land cover boundaries could exist within 1 km of the tornadogenesis location; thus, total percentages are over 100%). Interestingly, these two land use types both have high surface roughness. Kellner and Niyogi (2014) found much fewer touchdowns within 1 km of land surface types with lower surface roughness values. They hypothesized that surface roughness would contribute to tornadogenesis due to the generation of local vorticity boundaries.

A few observational case studies of tornadoes interacting with different land cover types have been documented such as those by Baker (1981) and Dessens and Snow

(1989). In both cases, as the tornado moved further into a grove of trees the tornado

38 intensity and damage increased. Opposing these case studies and theory based on the disruption of cyclostrophic theory, is another observational case study by Monji and

Wang (1989) who observed a tornado increasing its damage and path width as it moved from high surface roughness (urban) to low surface roughness (grasslands). The opposition between these case studies shows the complexity of potential relationships between surface roughness and tornado intensity. From the results of the previous studies, it is noted that there are a variety of effects that friction and surface roughness appear to have on tornadoes. Most of these studies are numerical and therefore more observational studies need to be completed to validate the hypotheses of numerical and laboratory simulations.

CHAPTER 3: DATA AND METHODS

In this observational study, in order to ensure that an assortment of land cover types is represented for a significant number of tornado events, specific tornadic storms occurring in the Southeastern U.S. (black contoured region in Fig. 1.1) will be identified.

The storms are identified using historical tornado storm data reports and radar data which are acquired from various archival sources. These data are recorded in a GIS framework where tornado location and intensity are spatially analyzed against surrounding land cover types. Statistical tests are applied to determine any relationships between tornado intensity, tornado intensity change, and land cover type.

3.1 Event Acquisition

Tornado events are selected from the National Center for Environmental

Information (NCEI) Storm Data Reports (Table 3.1). The NCEI reports are publicly available online and free to download. The reports contain information about tornado start/end times and locations, the tornado rating, and the economic cost of the event. In order for a tornado event to be included in this dataset, the following criteria were applied: (i) must be with in the study area5; (ii) must have an exact latitude and longitude

(lat/lon) location recorded for the start and end locations; (iii) must be within 60 km of a

WSR-88D site, due to limitations of radar data at large distances; (iv) must be verified by radar via the presence of a Doppler velocity tornado vortex signature (TVS); (vi) must be of magnitude EF 2 or greater; (vii) must have occurred since 2007 (the reasons why tornado events are being limited to those which occur after 2006 is due to the

5 Event 22 interacts with the Texas-Louisiana border.

40 implementation of the EF scale as well as a change in the preciseness of the lat/lons of start and end locations of tornadoes in the storm report data). The tornado must also exist long enough to be sampled by the radar at a minimum of 4 times. Only significant (EF 2 or greater) tornadoes are studied since less significant tornadoes (EF 0 or EF 1) usually are not long lived and thus may not traverse over different land covers and/ or may not exist long enough to be sampled by 4 consecutive radar volumes.

Latitude and longitude information from the NCEI storm data are used to initially view the start and end locations of the tornadoes. The NCEI data are known to often misrepresent the genesis and dissipation locations. Thus, the NCEI lat/lons are crosschecked with the radar data to make sure they are in the proximity of the TVS or rotation on the radar data, but ultimately, the lat/lons from the center of radar vorticity couplets are used herein as the approximate center locations of the tornadoes. The storm data reports are crosschecked by requiring a TVS within 10 minutes of the start time, which is within 20 km of the reported lat/lon; otherwise the event is not used.

While several tornado events were possible to study, these criteria limit the number of useable tornado events to 30. By adhering to these criteria, errors in the manual placement of tornado locations are minimized. Additionally, by limiting the range of the tornado from the radar, the spatial resolution is acceptable for manual estimation of the intensity of the winds associated within the tornado. This process is discussed in the next section.

Table 3.1: List of all tornado events used in this study including EF rating, date, and the radar which recorded event. Event Rating Date Radar 1 EF 3 04/28/2014 KHTX 2 EF 3 04/28/2014 KGWX 3 EF 4 04/27/2014 KLZK 4 EF 2 03/18/2013 KFFC 5 EF 3 03/02/2012 KHTX 6 EF 3 01/23/2012 KBMX 7 EF 2 01/23/2012 KBMX 8 EF 2 01/23/2012 KBMX 9 EF 4 05/24/2011 KSRX 10 EF 5 04/27/2011 KGWX 11 EF 4 04/27/2011 KHTX 12 EF 4 04/27/2011 KBMX 13 EF 3 04/27/2011 KFFC 14 EF 3 04/27/2011 KBMX 15 EF 3 04/27/2011 KFFC 16 EF 2 04/27/2011 KFFC 17 EF 2 04/25/2011 KLZK 18 EF 3 04/15/2011 KDGX 19 EF 1 03/05/2011 KLIX 20 EF 2 04/30/2010 KLZK 21 EF 2 04/30/2010 KLZK 22 EF 3 01/20/2010 KSHV 23 EF 4 04/10/2009 KOHX 24 EF 3 04/10/2009 KHTX 25 EF 2 02/18/2009 KFFC 26 EF 3 05/02/2008 KNQA 27 EF 2 05/02/2008 KLZK 28 EF 2 03/15/2008 KCLX 29 EF 2 02/05/2008 KNQA 30 EF 3 01/10/2008 KGWX

Data from various WSR-88D radars within and around the study area are utilized, see Table 3.2. WSR-88D’s have sampled thousands of supercells (Wurman et al. 2013).

However, there are some limitations in using the WSR-88D data, particularly in comparison to using mobile radar data. These limitations largely revolve around the

42 temporal and spatial resolution of the radar. A full volume scan takes the WSR-88D ~4.2 minutes to complete. Such poor temporal resolution is less than ideal when studying tornadoes since a tornado can develop, traverse 1.6 km, and produce EF 3 and EF 4 in just 4 minutes, as in the event of the 2013 Moore, Oklahoma tornado (Atkins et al. 2014).

Using WSR-88Ds imposes spatial limitations as well, since the radar locations are fixed.

In general, the tornadoes will be much farther away from the radar than those found in studies using mobile radar data, and thus the WSR-88D’s will not capture the same amount of detail as a mobile radar can. While WSR-88D’s temporal resolution is much more course than mobile radar units, the network of WSR-88Ds provides a large coverage area and thus captures more storms than a mobile radar unit. Additionally, most mobile radar studies and deployment strategies limit the geographical domain to the central U.S., where land cover is not nearly as variable.

Table 3.2: List of Doppler radar sites utilized in this study. Radar ID, location and responsible weather forecast office (WFO) is listed. Radar ID Site Location WFO KSHV Shreveport, LA Shreveport, LA KBMX Alabaster, AL Birmingham, AL KCLX Grays, SC Charleston, SC KDGX Brandon, MS Jackson, MS KFFC Peachtree City, GA Atlanta, GA KGWX Columbus AFB, MS Jackson, MS KHTX Hytop, AL Huntsville, AL KLIX Slidell, LA New Orleans, LA KLZK North Little Rock, AR Little Rock, AR KNQA Millington, TN Memphis, TN KOHX Old Hickory, TN Nashville, TN KSRX Chaffee Ridge, AR Tulsa, OK

All archived radar data used for this research are previously recorded and are stored in an online database which was downloaded for free from the NCEI. The specific type of radar data that are extracted from the database are archived level 2 radar data.

These data are first used to verify the convective storm mode of the storm report given in the Storm Data archives. Since different convective modes can produce tornados through different dynamical processes (Trapp and Davies-Jones 1997), this study limits tornado events to those formed by supercells. To visualize the archived radar data, the GR2

Analyst software produced by Gibson Ridge LLC was utilized. GR2 Analyst imports the radar data, graphically displays the radar returns, and easily allows the user to query information about the location of a radar echo including lat/lon, beam elevation above ground level, and distance from radar.

3.3 Radar Interpretation and Analysis

The Doppler velocity parameter (Vr) from the WSR-88D dataset is used to manually track the location and intensity of rotation of each tornado via its tornado vortex signature (TVS), coined by Brown et al. (1978). A TVS is essentially a gate-to-gate shear signature in Doppler velocities which has been shown to represent tornado-scale rotation. The lowest elevation radar scans (recorded with a tilt of 0.5) are used to extract

Vr because they would likely best reflect any change due to surface roughness owing to the physical proximity between the ground and the vortex. Furthermore, herein, a TVS is required to have a gate-to-gate absolute minimum difference of 20ms-1 and isolated max/min values separated by 2 km or less, as used by French (2014).

The difference between maximum inbound (velocity directed toward the radar) and the maximum outbound (velocity directed away from the radar) velocities (∆Vmax) is used as a proxy for tornado intensity (as in French et al. 2013 and Houser et al. 2015); and, these variables are manually identified. Finally, the approximate center location

(lat/lon) of the TVS is also manually identified based upon an estimation of the azimuthal and radial center of the velocity couplet, and is defined as the center of the tornado vortex.

For an example of the WSR-88D radar representation of a tornado and the analysis completed on each usable radar scan, see Fig. 3.1. The reflectivity field in Fig.

3.1a, shows exceptionally high reflectivity (measured in dBZ) in the vicinity of the hook echo which, when collocated with a confirmed tornado, very likely represents debris lofted by the tornado. The TVS is usually located within or very near this debris ball.

The rotation of the tornado is manifest by the TVS, as inbound velocities are located immediately azimuthally adjacent to outbound velocities, implying motion toward the radar right next to motion away from the radar. Note for Fig 3.1, the radar scanning location is located to the northwest of the image. As illustrated in Fig. 3.1b, the maxima, inbound (-40 ms-1) and outbound (48 ms-1) velocities are identified. The difference

-1 between the two velocity maxima or the ∆Vmax is 88 ms and is recorded as the tornado’s intensity. Furthermore, the approximate lat/lon center of the tornado (white arrow) is also recorded and indicated in Fig. 3.1b.

In some situations, radar scans are missing data in the location of the expected

TVS, or data from one of the volume scans was absent. For scans that are missing data

45 along only one azimuth, data from the adjacent radials are used to obtain information about ∆Vmax and a best guess center is chosen. If there are multiple radials with missing data, then the scan is deemed unusable and the event is either truncated or thrown out

(depending on the number of usable continuous scans), again limiting the number of events in this study.

a. WSR-88D 0.5° 4/28/11 04:54:23 UTC b. R V -1 -40 ms

Center -1 48 ms

-1 70 20 dBZ +40 0 ms -35

Figure 3.1: Example of radar representation of a tornado. The dashed white circle indicates the approximate location of the tornado. a: Reflectivity (dBZ), b: Radial Velocity (ms-1). Location of maximum inbound (yellow arrow) and outbound (blue arrow) velocities and the approximate vortex center (white arrow).

A final set of data are acquired to estimate the region of the tornadic flow field which is immediately associated with the tornado. This region extends past the TVS center over a distance equal to two times the radius of maximum winds (rmax) on either side of the TVS. The rmax region is depicted in Fig. 3.2b as a green circle. The distance from the tornado center to 2*rmax, from here on defined as the full radius of influence

(FRI) is also shown in Fig 3.2b as a dashed green circle and again, denotes the approximate flow field associated with the tornado.

The quantification of the FRI is somewhat subjective and represents a cut-off point of the assumed near-surface tornado flow field. For this research, areas within the

FRI are assumed to have influence on the tornado flow field and the kinematics associated with the immediate tornado vortex; areas outside are assumed not to affect the vortex. All of the radar associated variables are identified for each radar scan associated with a TVS which meets the 60 km radius threshold.

a. WSR-88D 0.5° 4/28/11 04:54:23 UTC b. R UTC V -1 -40 ms

Center -1 48 ms

-1 70 20 dBZ +40 0 ms -35 - Figure 3.2: Example of radar representation of a tornado. a: Reflectivity (dBZ), b: Radial Velocity (ms-1). Location of maximum inbound (yellow arrow) and outbound (blue arrow) velocities and the approximate vortex center (white arrow). Radius of maximum winds (solid circle) and full radius of influence (dashed circle).

3.4 GIS Analysis

In addition to meteorological datasets, geographic information datasets are utilized. The most recent land cover data are extracted from the National Land Cover

Database (NLCD) (Homer et al. 2015), which is free to download online. ArcMap 10.4.1 is used to view the NLCD. The NLCD uses the North American Datum 1983, Global

Coordinate System coordinate system North American 1983, and the data frame is projected to Conic Equal Area so that accurate area measurements are made. Natively, the NLCD land cover categories have a numerical classification code. Here, these coded values are reclassified such that each unique coded value is assigned a unique qualitative description per the NLCD 2011 metadata (i.e. the raster value 41 is reclassified as deciduous forest). There are 16 unique land cover categories in the data set which are displayed in Fig. 3.3. The land cover type of ‘perennial ice/snow’ was removed from the display since the land cover type does not exist in the study area.

Figure 3.3: Legend of NCLD qualitative land cover categories.

Additionally, surface roughness lengths are acquired from the Environmental

Protection Agency (EPA, EPA 2008) and are assigned to each land cover type. The roughness lengths were taken from the EPA since the categories were already well aligned with land cover categories of the NLCD. The specific roughness length is

48 dependent on month of year as foliage coverage varies seasonally. Since all events herein are between 10 Jan and 24 May, only the December-February (DJF) and March-

May (MAM) roughness’ are indicated in Table 3.3.

Fig. 3.4 depicts the locations (star) of all radars as well as the 60 km radii of radar sites utilized herein, thus all radar scans used fall within the yellow shaded circles in the illustration. There are many partial tornado events included in this study such that the tornado begins within the 60 km radius but leaves the radius before the end of its lifecycle. Likewise, there are some events which begin outside of the 60 km radius but enter and remain in the 60 km radius until their demise. For all events, a minimum of four radar scans are required to be completed while the tornado was within the 60 km radius.

Table 3.3: Land surface roughness lengths adapted from AERSURFACE User’s Guide (EPA 2008) for the months DJF and MAM. Land Cover Months DJF Months MAM Open Water 0.001 m 0.001 m Perennial Ice/Snow 0.002 m 0.002 m Developed Open Space 0.01 m 0.015 m Developed Low Intensity 0.5 m 0.52 m Developed Med Intensity 0.83 m 0.83 m Developed High Intensity 1 m 1 m Barren Land 0.05 m 0.05 m Deciduous Forest 0.6 m 1 m Evergreen Forest 1.3 m 1.3 m Mixed Forest 0.9 m 1.1 m Shrub/Scrub 0.3 m 0.3 m Grassland/Herbaceous 0.01 m 0.05 m Pasture/Hay 0.02 m 0.03 m Cultivated Crops 0.02 m 0.03 m Woody Wetlands 0.3 m 0.7 m Emergent Herbaceous Wetlands 0.1 m 0.2 m

Figure 3.4: Radar locations utilized herein are indicated by a star and labeled by Radar ID and the 60 km range from each radar is indicated by the yellow shaded circle. These features are overlaid on the NLCD layer. States are outlined in grey. Legend of NCLD qualitative land cover categories shown in lower box.

Next, all tornado locations (lat/lons) recorded from radar data are imported into the GIS as XY data under the North American Datum 1983. The tornado locations are then projected automatically to Conic Equal Area as they overlay the land cover data

50 layer. Imported along with tornado locations were the associated information collected in the radar analyses (i.e. the ∆Vmax, rmax, and radius of the FRI). The path and relative change in ∆Vmax of a tornado over its lifecycle is quickly depicted in the GIS. This is done simply, as illustrated in Fig. 3.5, by viewing the tornado center locations (x, y data) for a tornado event and using graduated symbology to represent the associated ∆Vmax at each location. To see the spread of tornado events utilized in this study, all 30 tornado events are shown together in Fig. 3.6.

Since the tornado is not a singular point event, areas within the FRI are assumed to have influence on the tornado flow field and the kinematics associated with the immediate tornado vortex. Thus, it is important to quantify the range of land cover types that are within the FRI for each tornado center location. Since each tornado location is associated with a unique FRI radius, the buffer analysis tool is used to create the FRI at each location. The buffer analysis tool creates a polygon (circle) around an input

(tornado center) using the FRI radius (2rmax).

Figure 3.5: Tornado path (black dots) and relative intensity (graduated pink triangles) of a tornado (event 3) throughout its lifecycle overlaid on the NLCD layer. Legend of NCLD qualitative land cover categories shown in lower box.

Figure 3.6: Tornado paths (pink triangles) of all tornado events within a 60 km radius (yellow) of a radar station (star).

Rather than using one region of influence (the FRI) to define the contribution of land cover on tornado inflow, multiple radii of influence are developed to mimic the

Rankine Vortex structure. The Rankine structure is often used to model an atmospheric vortex (Wood and Brown 2011). The analytical model suggests that the tangential velocity of a vortex increases linearly from zero outward from its center, maximizes at the rmax, and decreases exponentially thereafter (Wood and Brown 2011). Thus, the land cover within the core radius should have more influence on the tornado flow field than say the outer radius. A total of three additional regions of influence are constructed from the FRI to mimic the Rankine structure, and will be used to create a weighted contribution of the surface roughness within the FRI.

The decision to create a weighted surface roughness parameter using the Rankine vortex model is based on methods used by McGinnis (2016). McGinnis (2016) studied the sensitivity to different weighted surface roughness methods (i.e. area mean, weighted

Rankine mean, and weighted tri-mean) and found there are minimal impacts on the calculations. The method which appears most relatable to this study is the method utilizing the Rankine vortex model. Therefore, buffer analysis is used again to create the regions of radii ¾ FRI (QR3), ½ FRI (HF), and ¼ FRI (QR), respectively, as seen in Fig.

3.7. The new regions are then used to weight the influence of land cover on the tornado’s low-level wind field.

To begin quantifying this data set, the spatial analyst tool, tabulate area, was used in GIS to identify the area of each land cover type (e.g., forest, agricultural, water, residential, urban) within each radius of influence for each documented tornado location, respectively. The result of this tool is a table which outputs the total area occupied by each land cover category for every influence region (FIR, QR3, HF, QR) for each TVS location. The table is imported into Microsoft Excel for further evaluation. To get the total areas of land cover unique (indicated by subscript U) to each region, subtraction is used such that:

FRIU = FRI areas – QR3 areas,

QR3U = GR3 areas – HF areas,

HFU = HF areas – QR areas, and

QRU = QR areas.

Surface roughness lengths (ZL) derived by the EPA (Table 3.3) are assigned to the extracted land cover categories. To further quantify this dataset, the area for each land surface category contained within the unique regions is multiplied by its associated ZL. A mean surface roughness parameter (Z0) is calculated for each unique region, of the four regions (FRIU, QR3U, HFU, and QRU) contributing to the full circle contained by the FRI.

The Z0 values are then used to calculate a total weighted surface roughness (Zw) representing the approximate roughness length contributing to the tornado wind field within the FRI.

The contribution of surface roughness is weighted such that different radii from the tornado center contribute differently to Zw where Zw is constructed to mimic the

Rankine Vortex model giving locations with stronger velocities greater weights such that:

Zw = 0.25 (FRIU Z0) + 0.3 (QR3U Z0) + 0.35 (HFU Z0) + 0.1 (QRU Z0).

This process results in, one Zw value and one ∆Vmax associated with each TVS location, thereby making it possible to derive a quantitative method to statistically evaluate the relationship between the two parameters.

Figure 3.7: Regions of influence shown in progressively dark shades of black from QR, HF, QR3, to the outer most region, FRI. These areas are centered about the tornado center (black dot) and are overlaid on the NLCD layer. Legend of NCLD qualitative land cover categories shown in lower box.

3.5 Statistical Analyses

3.5.1 Parametric Analysis

Figure 3.8 is a simple scatter plot displaying the raw Zw and ΔVmax data for all tornado events which are being analyzed in this study. The red linear regression line in

Fig. 3.8 indicates a slight positive trend in the data suggesting that there may be a relationship between the two data sets. Initially, traditional statistics are used to investigate the nature of this relationship.

ΔVmax vs. Weighted Surface Roughness 140

120

100

60 Vmax Vmax (m/s) Δ

0 0 0.2 0.4 0.6 0.8 1 1.2 Weighted Surface Roughness (m)

Figure 3.8: Scatter plot of Zw and ΔVmax. The data pairs (blue dots) and trend line (red) are shown.

Statistical correlation coefficients (SCCs) are calculated based on Zw and the associated ∆Vmax for each tornado event, and for the entire sample. The acronym

57 chosen for statistical correlation coefficient is defined here as SCC rather than the conventional acronym of CC in order to avoid confusion with the radar variable of co- polar cross-correlation coefficient, which is also abbreviated as CC in meteorological literature. The SCC variable, r, is defined by

푛 ∑푖=1(푥푖 − 푥̅) (푦푖 − 푦̅) 푟 = , 푛 2 푛 2 √∑푖=1(푥푖 − 푥̅) √∑푖=1(푦푖 − 푦̅) where n is the sample size, 푥푖 and 푦푖 are each data pair in the weighted surface roughness and ΔVmax variables, and 푥̅ and 푦̅ are the sample means of each variable, respectively.

An r value of 1 (-1) indicates a perfect positive (negative) linear correlation and a value of 0 indicates no linear correlation. SCCs are also calculated such that Zw at time t = i is associated with ∆Vmax at the next volume time: i+1 (lag 1) since it is possible that a tornado takes time to adjust to the surface roughness change that it encounters (note lag 0 is then defined such that Zw at time t = i is associated with ∆Vmax at t = i).

The SCCs are tested for significance using a two-tailed t-test since the sign of the correlations is unknown. The t-value is defined by

푟√푛 − 2 푡푛−2 = , √1 − 푟2 where r is the SCC, n is the sample size, and t is the t-value with n-2 degrees of freedom.

The t-value is then used with the degrees of freedom to determine the probability (p) using a t-distribution table where values of p < 0.05 are considered significant. The p- value is the probability of the null hypothesis that weighted surface roughness and

ΔVmax are not linearly correlated. For p < 0.05, the null hypothesis can be rejected.

As the parametric statistics were being calculated, the validity of the assumptions made about samples used for such statistics became unclear, particularly whether the data are of Gaussian distribution. Thus, statistical tests were completed in Matlab to test for normality.

One such test is the Jarque-Bera (JB) test where the null hypothesis is that a vector comes from a normal distribution where the mean and variance are unknown.

This test is defined by

푛 (푘 − 3)2 퐽퐵 = (푠2 + ), 6 4 where n is the sample size, s is the skewness of the sample, and k is the kurtosis or a measure of the distribution of the tails of the data (mathworks.com). When running the

JB tests, the null hypothesis that the data are normal is rejected at the 5% significance level for both the ΔVmax and Zw datasets with p-values of 0.001 and 0.03, respectively.

A similar test for normality is the Chi-Square Goodness of Fit Test, which is defined as

푛 2 ∑푖=1(푂푖 − 퐸푖) 푋2 = , 퐸푖 where Oi and Ei are the observed and expected frequency of values present in the sample based on the hypothesized distribution, respectively. For this test, the null hypothesis that the vector comes from a normal distribution with a mean and variance estimate from the vector is rejected at the 5% significance level for the ΔVmax dataset (p-value of 0.015), but not rejected for the Zw dataset (p-value of 0.30). The acceptance of the null hypothesis for the Zw dataset is most likely an arbitrary coincidence, since land cover is, to a large degree, random. The third and final test was the Lilliefors test which rejects the

59 null hypothesis at the 5% significance level for both the ΔVmax and Zw datasets with p- values of 0.039 and 0.002, respectively. Details about this test can be viewed online at mathworks.com.

3.5.2 Non-Parametric Analysis Theory

Since a normal distribution cannot be assumed, traditional parametric tests which assume normality cannot be used and deemed statistically viable. Instead, a bootstrapping method is used since no assumptions are made about the underlying distribution of the data. The bootstrapping process essentially resamples the raw data and creates B resampled data sets. Here, B is 15,000 bootstrap samples of the data set, X. To illustrate this idea, consider an original sample dataset for variable X such that X = (x1, x2, x3,…, xn). In the bootstrap process, as shown in Fig. 3.9, many (B) bootstrap samples

(X*) = (X*1, X*2, X*3,…, X*B) are generated. Each independent bootstrap sample (e.g.

X*1) is generated by randomly selecting data from X, allowing for replacement, n times to create a new dataset with the same number of samples (n) as the original. By selecting

1 ( ) data from X allowing replacement, all values in X have the same probability, 푛 , of being selected each time a value contributing to the sample X*1 (e.g.) is randomly selected. Thus, individual datum from X can be used multiple times in any given bootstrap sample in X*. Note X and all bootstrap samples in X* are of length, n (Fig.

3.9).

1 For example, if n=5, and X = (x1, x2, x3, x4, x5) one bootstrap sample may be X*

= (x3, x2, x4, x3, x1), where x3 happens to be used twice and x5 is not used at all. A statistic, s, is then calculated for each bootstrap sample in X*, yielding a bootstrap

60 replication of the statistic, 휃̂∗= (s(X*1), s(X*2),…, s(X*B)) (Efron and Tibshirani 1993).

The statistic in question, s, for this thesis is the mean; thus, s(X*B) is the mean of bootstrap sample, B. The mean of all the bootstrap replications (휃̂∗푀) is then used to determine the spread of the means in 휃̂∗ to construct a confidence interval (CI).

All bootstrapping and 95% CI computations are completed using Matlab software. There are five different CIs built in with the bootci (bootstrap CI) function in

Matlab. Here, only one CI, the bias corrected and accelerated percentile (bca) CI, is chosen to discuss further. See mathworks.com for information regarding the remaining

CIs. According to Efron and Tibshirani (1993, p.141, 184-185), the bca CI can be defined as

( ) ( ) ∗ 훼1 ∗ 훼2 (휃̂푙표, 휃̂푢푝) = (휃̂ , 휃̂ ),

61 where 휃̂푙표 and 휃̂푢푝 are the lower and upper endpoints of the estimated bca CI,

(훼 ) (훼 ) respectively, and 휃̂∗ 1 and 휃̂∗ 2 are the “100 ∗ 훼th percentiles of the bootstrap

∗ ∗ ∗ replications 휃̂(1), 휃̂(2), … , , 휃̂(퐵)”, where α1 and α2 are

(훼) 푧0̂ + 푧 훼1 = Φ (푧0̂ + (훼) ), 1 − 훼̂(푧0̂ + 푧 ) and

(1−훼) 푧0̂ + 푧 훼2 = Φ (푧0̂ + (1−훼) ), 1 − 훼̂(푧0̂ + 푧 ) respectively (Efron and Tibshirani 1993).

In the above equations Φ is the standard normal cumulative distribution function

(훼) [CDF], 푧 is the 100 ∗ 훼푡ℎ percentile point of a standard normal distribution”, 푧0̂ is the bias correction, and 훼̂ is the acceleration, respectively (Efron and Tibshirani 1993).

Efron and Tibshirani (1993) describe the bias correction 푧0̂ , as a measure of the median bias of 휃̂∗ and is defined as

#{휃̂∗ < 휃̂} 푧̂ = Φ−1 ( ), 0 퐵 where Φ−1 is the inverse CDF, the numerator is the number of values (#) in 휃̂∗ which are less than 휃̂, and B are the number of bootstraps. The acceleration (훼̂) “refers to the rate of change of the standard error of 휃̂” (Efron and Tibshirani 1993), and is defined as

푛 ̂ ̂ 3 ∑푖=1(휃(∙) − 휃(푖)) 훼̂ = , 3⁄ 푛 ̂ ̂ 2 2 6 {∑푖=1(휃(∙) − 휃(푖)) } where 훼̂ is in terms of the jackknife values of 휃̂ such that

푛 휃̂(푖) 휃̂(∙) = ∑ , 푖=1 푛 and

휃̂(푖) = 푠(푋푗(푖)).

Here, 휃̂(푖) is the mean of the ith jackknife sample xj(i). The jackknife leaves out one observation at a time, such that the ith jackknife sample is of the form xj(i) = (x1, x2, x3,…, x(i-1), x(i+1),…, xn). It is important to note that when 푧0̂ and 훼̂ are zero, 훼1becomes

훼 and 훼2 becomes (1 − 훼) which would essentially give intervals that are the same as the

( ) ( ) ∗ 훼 ∗ 1−훼 regular percentile intervals, (휃̂ , 휃̂ ). Only when 푧̂0 and 훼̂ are non-zero do the interval endpoints change (Efron and Tibshirani 1993).

An oversimplified summary of the bca CI, as adapted to this research study, is that the final row of data from fig. 3.8, or the bootstrap replications of the mean (휃̂∗=

(s(X*1), s(X*2),…, s(X*B), will be used to find the approximate 95% CI where, α is

0.025, but in doing so, the interval will be corrected for any bias and acceleration, as previously defined, ultimately resulting in the 95% bca CI. Let it be noted that a limitation that comes with bootstrapping data is that if data are of inferior quality prior to bootstrapping, meaningful results will not be gained from testing the bootstrapped data.

3.5.3 Non-Parametric Analysis Applications

In order to evaluate differences in surface roughness, the data will be broken apart such that there is an initial subsample which is constrained around Zw. From there, all

Zw values in the initial subsample are matched with their corresponding ΔVmax values.

A second subsample will house any remaining ΔVmax values which are not utilized in

63 the first. Next, the bootstrapping process is applied to each and then the means of the two bootstrapped subsamples (휃̂∗푀), which are now approximately of normal distribution, are compared. For example, Fig. 3.10 shows the approximately normal distribution of sub-s from CS 4 after the subset had been bootstrapped. Then, through a comparison of the means, it is possible to determine if there is a statistical difference in the velocities values contained in these different subsamples.

Figure 3.10: Histogram of sub-s of CS 4 post bootstrapping. The histogram shows the frequency of the bootstrap replicate means of the 15,000 bootstrap replicates and it shows an approximately normal distribution.

Call to mind, constraints on Zw are used to determine the subsamples of ΔVmax

(here forward ΔV). A sample constraint is Zw > 0.9 m. Thus, all ΔV values associated with a Zw greater than 0.9 m make up the subsample sub-s. The chosen constraints on

Zw are largely based objectively around natural breaks in the data such that sub-s never has less than 10 values. All the remaining ΔV values not associated with Zw > 0.9 m make up the subsample sub-r. Thus, the combination of sub-s and sub-r for a given constraint is the original population. Each sample constraint (case study, CS, from here on) is recorded as a different CS number.

In addition to using Zw and ΔV, the change of the variables between time steps

(i.e. consecutive radar scans) is also tested. The time spacing is even between all derivatives (within seconds) thus the derivatives are calculated in a consistent way. Let dZw be the change in weighted surface roughness and dΔV be the change in the associated ΔV values with time (i), respectively, such that

푑푍푤(푖) = ((푍푤2 − 푍푤1), (푍푤3 − 푍푤2), … (푍푤푖+1 − 푍푤푖)), and

푑ΔV(i) = ((ΔV2 − ΔV1), (ΔV3 − ΔV2), … (ΔV푖+1 − ΔV푖)). Equation 3.1

Consider a constraint example where the change in Zw between two consecutive data points is greater than or equal to 0.2 m but less than or equal to 3 m. The constraint is used to populate subsample sub-s and will be referred to using the notation: 0.2 m <= dZw <= 0.3 m. Again, values that fall outside of the constraint will occupy the remaining subsample sub-r. A variety of ranges in the constraints placed on dZw are used to create unique subsamples, sub-s, and sub-r, for each CS (to be presented in Chapter 4).

Each subset in a given CS is bootstrapped as previously described. Then, the means (휃̂푀s) for each sub-s and sub-r in a CS are compared and evaluated using 95% bca

CIs. A CS is considered statistically different if 휃̂∗푀 of sub-s is outside the 95% bca CI of sub-r. All five confidence intervals for each sub-r are calculated to see how unanimously different or indifferent the CSs are. For the clear majority of the CSs, whether sub-s is statistically different is unanimous regardless of the specific method used in calculating the CIs.

The visual results for the bootstrapped data are displayed by a series of pseudo- boxplots (from here forward pseudo plots). The pseudo plots show the interquartile ranges (IQR) of the subplots as well as upper and lower end lines extending outward from the IQR. These end lines are showing the ΔV values of the 95% bca CI; thus, the end lines are not showing the full distribution of the data (nor the maximums/minimum values). For each pseudo plot, 휃̂∗푀 for each subset is plotted as a blue asterisk.

Additionally, 휃̂∗푀 of sub-s is also shown as a red dashed line to help examine its relative location to 휃̂∗푀 of sub-r.

Through a comparison of the means it is possible to determine if there is a statistical difference in the mean velocity values contained in these different subsamples which are now approximately normally distributed. A statistical difference is represented in data tables as 1, marginally different is marked as 1*, nearly statistically different is marked as 0^, and a non-statistical difference result is marked with a 0. Here, a marginally different result occurs when the result is statistically different in most CIs, but not the bca CI, which is chosen as the CI truth. A near statistical difference result occurs

66 when the result falls just short of being classified as statistically different. Note that

Zw(i) and ΔV(i) are always a function of the same time step at lag 0.

The statistical difference is inferred by examining the location of the sub-s 휃̂∗푀 line in the pseudo plots. When the sub-s 휃̂∗푀 line falls outside of the 95% bca CI of sub- r, (the end lines of the upper and lower extensions of the pseudo plot), the result is statistically different. If instead the sub-s 휃̂∗푀 line falls inside the 95% bca CI of sub-r, the result is not statistically different.

CHAPTER 4: RESULTS

4.1 Parametric Results

Parametric statistics are used first in this study, but after determining the non-

Gaussian distribution of the data, the study continues by switching to non-parametric statistics. Thus, results come in the form of two separate statistical methods, both which are presented herein. The first set of results is derived from parametric statistics and the latter from non-parametric statistics. Statistical correlation coefficients (SCCs) are calculated based on Zw and the associated ∆V for each tornado event, and for the entire sample (see Table 4.1). As can be seen from Table 4.1, the SCC for the entire data set is close to zero, and slightly positive with an r value of 0.091. The near-zero value for SCC indicates that the data are likely not correlated and thus are perhaps independent data sets.

Instead of using the dataset in its entirety, SCCs are calculated for each tornado event individually. Note that for individual events the sample sizes vary from 4 to 12 samples.

By breaking up the data by event, a very different picture is painted. When evaluating the tornado events individually, there does appear to be some correlation between the data sets (Table 4.1).

Events which had the strongest correlations, such as events 18 and 29 which had

SCC values of 0.85 (p = 0.15) and -0.98 (p = 0.02) respectively, also had the fewest number of data values to represent the event. For this brief discussion, the events with only four Zw - ∆V raw data pairs in the dataset are neglected. The focus is then on events where the tornado lasted longer thus there are more data pairs to evaluate. While there does seem like there is a week signal in the data, the signal is very unclear due to

68 the mixed SCC results. There are SCC values that are both moderately negative (event

3), moderately positive (event 7), and about zero (event 8), see Fig 4.1. Even without the

SCCs in Fig. 4.1, visually there does appear to be some sort of relationship between the two datasets. However, the correlation of the entire dataset at lag 0, is minimally positively correlated, such that r = 0.091 (p = 0.21).

Since it is possible that it takes time for the wind field of a tornado to adjust to the surface roughness change that it encounters, the SCCs are also calculated at lag 1 and can be seen in Table 4.1 (this technique uses Zw at time t = i and ΔV at time i + 1). The

SCCs at lag 1 are just as mixed as they are at lag 0, such that there are again moderately positive (event 13) and negative results (event 26), as well as a about zero (event 25, see

Fig. 4.2). Interestingly, by excluding the events with few (4) raw data pairs, two-thirds of the remaining events have lag 1 SCCs which are negative. Negative SCCs could suggest that the tornado intensity is increasing when surface roughness weakens and the tornado intensity is weakening when surface roughness increases. This negative SCC relationship is opposite of what is expected, based on the disruption of cyclostrophic balance. From the events with only 4 data pairs, there are 4 which are significant with p < 0.05 in which

2 show strong negative correlations and 2 show strong positive correlations. However, including all events, roughly half have some form of (weak, moderate, or strong) positive correlation and the other half, negative correlations (Table 4.1). The SCC of the entire dataset at lag 1 again shows only a very weak positive correlation of 0.181 with p = 0.01, which implies statistical significance despite a relatively poor linear fit.

The SCC of the entire data set at lag 0 gives no indication of a relationship between the two parameters Zw and ΔV. However, the statistically significant slight positive trend in the entire data set at lag 1, suggests the data are perhaps dependent on each other. Correlating on an event by event method, we see there are instances where there are weak, moderate, and strong correlations between the two data sets, both at lag 0 and lag 1. However, based on sample size, some of these correlations may not be particularly reliable. Given such a spread of the SCCs over the dataset and between specific tornado events, the underlying distribution of the data was analyzed. At this point in time, the datasets were tested for normality, as previously mentioned, and they failed. For this reason, non-parametric methods are used hereafter in place of traditional parametric statistical methods.

Table 4.1: List of individual tornado events with their respective statistical correlation coefficient (SCC) values, r, at lag 0 and at lag 1 and associated p-values. The number of Zw - ∆V raw data pairs for each tornado event is indicated and p-values meeting the 5% significance level are in bold. Tornado r p-value r p-value Raw Data Events (Lag 0) (Lag 0) (Lag 1) (Lag 1) Pairs 1 -0.28 0.72 0.96 0.04 4 2 -0.24 0.65 -0.52 0.29 6 3 -0.63 0.03 -0.54 0.07 12 4 -0.09 0.88 -0.55 0.34 5 5 0.36 0.38 -0.04 0.93 8 6 -0.33 0.67 0.68 0.32 4 7 0.59 0.22 0.45 0.37 6 8 0.01 0.98 0.78 0.12 5 9 -0.70 0.30 0.97 0.03 4 10 0.09 0.80 0.35 0.33 10 11 -0.03 0.95 -0.25 0.52 9 12 0.29 0.39 -0.11 0.76 11 13 -0.33 0.52 0.50 0.31 6 14 -0.57 0.43 -0.99 0.01 4 15 -0.53 0.14 -0.68 0.04 9 16 0.30 0.62 -0.58 0.30 5 17 -0.31 0.32 -0.40 0.20 12 18 0.85 0.15 -1.00 0.00003 4 19 0.03 0.97 -0.55 0.45 4 20 0.54 0.34 -0.74 0.15 5 21 0.33 0.43 0.05 0.90 8 22 0.05 0.95 1.00 0.0003 4 23 0.41 0.36 -0.23 0.61 7 24 0.51 0.49 0.87 0.13 4 25 -0.47 0.34 0.01 0.99 6 26 -0.21 0.73 -0.82 0.09 5 27 0.11 0.73 0.13 0.68 12 28 0.15 0.81 -0.40 0.50 5 29 -0.98 0.02 0.03 0.97 4 30 -0.86 0.14 -0.13 0.87 4 Entire Dataset 0.091 0.21 0.181 0.01 192

a. Event 3 (SCC, -0.63) 100 1 80 0.8 ) 1 - 60 0.6 40 0.4 Zw Zw (m) ΔV ΔV (ms 20 0.2 0 0

Time (UTC)

b. Event 7 (SCC, +0.59) 80 1.2 70 1 60 ) 1 - 50 0.8 40 0.6

30 Zw (m) ΔV ΔV (ms 0.4 20 10 0.2 0 0 104705 105140 105614 110523 110959 111433 Time (UTC)

c. Event 8 (SCC, 0.01) 70 1.2 60 1

) 50 1

- 0.8 40 0.6 30 Zw Zw (m) ΔV ΔV (ms 20 0.4 10 0.2 0 0 90830 91304 91739 92214 92648 Time (UTC)

Figure 4.1: Lag 0 time series of individual tornado events, 3,7, and 8, in subplot a, b, and c, respectively. Time (UTC) along the ordinate, Zw along the primary (left) abscissa, and ΔV along the secondary (right) abscissa. Zw (ΔV) plotted in orange (grey). SCC for each plot is given in plot title.

a. Case 26 (SCC, -0.82) 80 0.2 70 60 0.15 50 ) at lag 1 1

- 40 0.1

30 Zw (m) 20 0.05 ΔV ΔV (ms 10 0 0 1 2 3 4 Time Step (every ~4.5 mins)

b. Event 13 (SCC, +0.5) 80 1.2 70 1 60 50 0.8 ) at lag 1 1

- 40 0.6

30 0.4 Zw (m) 20 ΔV ΔV (ms 10 0.2 0 0 1 2 3 4 5 Time Step (every ~4.5 mins)

c. Event 25 (SCC, 0.1) 60 1

50 0.8 40 0.6 ) at lag 1

1 30 - 0.4 20 Zw (m) 0.2 ΔV ΔV (ms 10 0 0 1 2 3 4 5 Time Step (every ~4.5 mins)

Figure 4.2: As in Figure 4.1 except ΔV is plotted at lag 1 for individual tornado events, 13, 25, and 26, in subplot a, b, and c, respectively. Time step along the ordinate is Zw (ΔV) at lag 0 (lag 1).

4.2 Non-Parametric Results

Since the datasets failed tests of normality, traditional parametric statistics are not used to draw conclusions about the relationships between weighted surface roughness length and mean tornado intensity. Instead, non-parametric methods are used to assess the relationships. The method chosen herein is bootstrapping the data, which requires no assumptions to be made about the data or its underlying distribution and the data are evaluated through a comparison of subset means.

4.2.1 Results of Zw and ΔV at Lag 0

Constraints on Zw are used to determine the subsamples of ΔV (sub-s and sub-r) which are bootstrapped for each CS. When CSs are constrained on Zw and the subsets contain ΔVs at lag 0, there does appear to be relationships between the two datasets. A visual diagram of how the datasets are aligned with time is shown in Fig. 4.3; note that

Zw(i) and ΔV(i) are always a function of the same time step (different time steps shown by vertical lines). Through a comparison of the means, statistical differences in the mean velocity values contained in the different subsamples are determined and shown in

Table 4.2. However, at the first glance of Table 4.2, the CSs which are statistically different do not seem to tell a specific story. However, some justification for certain results are made.

Figure 4.3: Conceptual diagram of the variables weighted surface roughness (Zw) and tornado intensity at lag 0 (ΔV) as they relate with time. Time moves left to right along the horizontal arrow with each time step (t) indicated by a vertical bar with the time step label immediately to the right. Variables which are functions of a given time step are labeled at either end of the vertical bar.

Table 4.2: List of CSs, including the Zw constraint for the CS, and statistical difference (1), marginal statistical difference (1*), near statistical difference (0^), or no statistical difference (0) of associated ΔV at lag 0. The relative tornado intensity is listed as weaker, stronger, and no value if there is no intensity preference. The number of ΔVs in each sub-s and sub-r are indicated. Constraint on Zw Statistical Tornado Size of Size of CS (m) Difference Intensity Sub-s Sub-r 1 Zw <= 0.1 1 weaker 11 181 2 Zw <= 0.2 0 22 170

3 Zw <= 0.3 0 weaker 46 146 4 Zw >= 0.5 0^ stronger 110 82 5 Zw >= 0.6 1 stronger 86 106 6 Zw >= 0.7 0 stronger 66 126 7 Zw >= 0.8 1 stronger 46 146 8 Zw >= 1 1 stronger 14 178 9 0.1 <= Zw <= 0.2 1 stronger 11 181 10 0.2 <= Zw <= 0.3 0 weaker 24 168 11 0.3 <= Zw <= 0.4 1 weaker 18 174 12 0.4 <= Zw <= 0.5 0^ weaker 18 174 13 0.5 <= Zw <= 0.6 0 weaker 24 168 14 0.6 <= Zw <= 0.7 1 stronger 20 172 15 0.7 <= Zw <= 0.8 0 weaker 20 172 16 0.8 <= Zw <= 0.9 1 stronger 23 169 17 0.9 <= Zw <= 1.15 0^ stronger 23 169

Beginning with CS 5 (Zw >= 0.6 m), the first statistically different relationship between tornado intensity and weighted surface roughness length is seen in Fig. 4.4a.

This difference is inferred by examining the location of the sub-s 휃̂∗푀 line (red dashed line) in the figure. In Fig. 4.4a, the sub-s 휃̂∗푀 line falls outside of the 95% bca CI of sub- r, (the end lines of the upper and lower extensions of the pseudo plot), which indicates that the result of CS 5 is statistically different. Thus, the mean ΔVs associated with Zws

>= 0.6 m are statistically different from the mean ΔVs associated with Zws < 0.6 m. It is also inferred from Fig. 4.4a that the weighted surface roughness lengths constraining CS

5 are associated with stronger mean ΔVs since 휃̂∗푀 of sub-s lies above 휃̂∗푀 of sub-r.

Recall, ΔV is a proxy for tornado intensity; thus, it can be said that weighted surface roughness values greater than 0.6 m are associated with mean tornado intensities that are both statistically different and more intense (stronger ΔVs) than the mean tornado intensities associated with weighted surface roughness values outside of the constraint.

Notice that Table 4.2 shows CS 5 has 86 (out of 192) ΔVs in its sub-s. However, as the constraint focuses on only higher weighted surface roughness’, the number of ΔVs in sub-s decreases, as in CS 6 (Zw >= 0.7 m) where there are only 66 (out of 192) ΔVs.

Interestingly, the result of CS 6 as illustrated in Fig. 4.4b, is not statistically different, indicated by the sub-s 휃̂∗푀 line being present inside the bca CI bounds of sub-r.

However, the sub-s 휃̂∗푀 line does fall well above the 휃̂∗푀 of sub-r which suggests that the mean tornado intensities tend to be more intense when associated with the weighted surface roughness’ defining CS 6 than the mean tornado intensities outside of the constraint, but the result is not statistically different. The reason CS 6 is not statistically different is not clear, since CS 5 is not statistically different and includes all the ΔVs constrained in CS 6.

Figure 4.4: Pseudo plots of CSs 5, 6, and 7 are in panels a, b, and c, respectively. Subsample sub-s (sub-r) is on the left (right) with 휃̂∗푀 indicated by the red dashed line (for sub-s) and blue asterisk (for both subsets, respectively). The inter-quartile range (range from 25th and 75th percentile) is indicated by a blue box for each subset, end lines indicate the upper and lower ΔV values of the 95% bca CI for each subset, respectively. Note these are not box and whisker plots. The dashed red line references 휃̂∗푀 of sub-s such that if the line falls outside (inside) of the bca CI of sub-r, the CS is (not) statistically different.

Unlike what is described in CS 6, the mean ΔVs for CS 7 (Zw >= 0.8 m) are statistically different and stronger than mean ΔVs outside of the constraint, shown in Fig

4.4c. The statistical difference implies that mean tornado intensities are stronger when associated with CS 7 than outside of the CS 7 constraint. As the weighted surface roughness constraints get higher, the statically different results are not uniform. There is

77 however, a general tendency such that CSs 5, 6, and 7 all suggest higher roughness values are associated with stronger mean tornado intensities.

It may be useful to try and understand why CS 6 (Zw >= 0.7 m) did not produce a statistically different result. In doing so, case studies use tighter constraints as in CS 14

(0.6 m <= Zw <= 0.7 m) and with tighter constraints also come smaller sub-s subsample sizes. For CS 14 there are now just 20 ΔVs in subsample sub-s. Regardless of the size of the subsample, Fig. 4.5a illustrates a CS 14 sub-s 휃̂∗푀 line which rises above the upper limit of the bca CI of sub-r. In the same manner, Fig 4.5c depicts CS 16 (0.8 m <= Zw

<= 0.9 m) which resembles that of Fig 4.5a. Thus CS 14 and CS 16 are statistically different such that the weighted surface roughness values defining each CS are associated with stronger mean tornado intensities than mean tornado intensities which are outside of the constraints.

Notice that CS 15 (0.7 m <= Zw <= 0.8 m) represents the weighted surface roughness’ between CS 14 and CS 16. Interestingly, in CS 15 the sub-s 휃̂∗푀 line not only falls inside of the bca CI of sub-r in Fig. 4.5b, but also falls below 휃̂∗푀 of sub-r (right blue asterisk). From Fig. 4.5b, it is implied that the weighted surface roughness lengths defined in CS 15 are associated with weaker mean tornado intensities than mean tornado intensities outside of the constraint. That said, 휃̂∗푀 of sub-s is only slightly less than 휃̂∗푀 sub-r, and with there being no statistical difference in the case, no conclusive statements can be made regarding CS 15. However, it is possible that the lack of statistical difference, coupled with slightly weaker tornado intensity associations, contribute to the lack of a statistically different result in CS 6 (Zw >= 0.7 m).

Figure 4.5: As in Fig. 4.4 except for CSs 14, 15, and 16 are in subplots a, b, and c, respectively.

It appears a threshold exists at approximately Zw >= 0.6 m, where the weighted surface roughness values tend to be associated with stronger mean tornado intensities than other mean tornado intensities which are associated with Zws < 0.6 m. Here, we assume that the lack of statistical difference for CS 6 is a function of the slightly weaker result of CS 15. Thus, a notable conclusion from these data are that large weighted surface roughness lengths are associated with relatively strong mean tornado intensities at lag0.

Upon further inspection, the results also suggest that very small weighted surface roughness lengths have unique mean tornado intensities at lag 0. For instance, Fig 4.6a indicates that CS 1 (Zw <= 0.1 m) is associated with mean ΔVs which are less than mean

ΔVs associated with Zw values > 0.1 m. In Fig 4.6a, 휃̂∗푀 of sub-s is clearly outside the bca CI of sub-r, warranting CS 1’s statistical difference. Additionally, the mean line of sub-s falling below the mean of sub-r indicates weaker mean ΔVs. Thus, weighted surface roughness values less than or equal to 0.1 m, are associated with mean tornado intensities which are weaker than mean tornado intensities associated with weighted surface roughness lengths outside of CS 1, at lag 0.

Interestingly, opposing the CS 1 results are results from CS 9 (0.1 m <= Zw <=

0.2 m). As illustrated in Fig. 4.6b, the sub-s 휃̂∗푀 line is present both outside the bca CI bounds of sub-r and above the mean of sub-r, again opposing what it shown and described for Fig. 4.6a. Consequently, opposing CS 1, with statistical difference, the weighted surface roughness’ defining CS 9 are associated with stronger mean tornado intensities than intensities associated with weighted surface roughness values which are outside of the CS 9 constraint.

The result from CS 9 is contrary to what is expected. It makes sense that CS 9 would perhaps exhibit slightly stronger mean tornado intensities than CS 1 due to increased roughness lengths, but it would have been expected that CS 9 still show a result which indicates weaker mean tornado intensities. Thus, it is no surprise why the result of

CS 2 (Zw <= 0.2), a combination of CSs 1 and 9, is not statistically different. Results of

CS 2 are illustrated in Fig. 4.6c. Here, it appears the mean ΔVs of each subsample are

80 approximately equivalent and thus the line indicating 휃̂∗푀 of sub-s is inside the bca CI bounds, and additionally shows no preference of stronger or weaker mean ΔVs. The result for CS 2 supports the notion that combining CSs 1 and 9 results in a mean of sub-s which is approximately equivalent to that of sub-r, visually seen in Fig. 4.6. It is almost as if the magnitude of stronger mean ΔVs in CS 1 (Fig 4.6a) are added to weaker mean

ΔVs (Fig. 4.6b) in CS 9 of approximately equal magnitude, resulting in CS 2 where the mean ΔVs in sub-s and sub-r appear equivalent.

As slightly higher weighted surface roughness lengths are examined, the results seem to align with the results in CS 1. As in Figs. 4.7a and b, CS 10 (0.2 m <= Zw <=

0.3 m) and CS 11 (0.3 m <= Zw <= 0.4 m) each exhibit a 휃̂∗푀 sub-s line which lies below each 휃̂∗푀 sub-r associating weaker mean ΔVs than mean ΔVs not associated with the

CSs, respectively. However, CS 10 and 11 do differ, in that CS 10 is not quite statistically different, and CS 11 is statistically different. The statistical difference in CS

11 is indicated in Fig. 4.7b where the red 휃̂∗푀 sub-s line is outside of bca CI pseudo plot bounds of sub-r. In the same manner, Fig. 4.7a shows the 휃̂∗푀 sub-s line within the bca

CI bounds of sub-r, indicating no statistical difference. Although Fig. 4.7a indicates no statistical difference of weaker mean ΔVs, notice the 휃̂∗푀 sub-s line is below the sub-r interquartile range (blue box which indicates the range from the 25th and 75th percentiles) and is closer to the lower bound of the bca CI of sub-r. Thus, it is close to being statistically different.

Figure 4.6: As in Fig. 4.4 except for CSs 1, 9, and 2 are in panels a, b, and c, respectively.

Figure 4.7: As in Fig. 4.4 except for CSs 10 and 11 are in panels a and b, respectively.

CS 3 (Zw < 0.3 m) has a non-statistically different result associated with weak mean tornado intensities (not shown). It is possible that the result of CS 3 is simply a

82 combination of the results of CS 9 (0.1 m <= Zw <= 0.2 m; statistically different and stronger, CS1 (Zw < 0.1 m; statistically different and weaker) and CS10 (0.2 m <= Zw <=

0.3 m; non-statistically different and weaker). Notice CS 1, CS 9 and CS 10 essentially make up CS 3. Furthermore, there is support for weak mean tornado intensities being associated with small weighted surface roughness lengths since CS 11 (0.3 m <= Zw <=

0.4 m), previously described, is another statistically different result pertaining to weak mean tornado intensities associated with small weighted surface roughness lengths. So, apart from CS 9, it can be said that lower weighted surface roughness lengths are again, associated with relatively weak mean tornado intensity.

4.2.2 Results of Zw and ΔV at Lag 1

This study also permits an analysis of the role time might play on the mean tornado intensities by considering if the tornado takes time to adjust to the weighted surface roughness with which it interacts. Additional CSs are tested using the associated

ΔVs at lag 1 (LΔV from here on). Recall the technique of lag 1 uses Zw at time t = i and

ΔV at time t = i + 1. This technique is illustrated as a diagram in Fig. 4.8. Notice that

Zw(i) and LΔV(i) are never functions of the same time steps. Remarkably, Table 4.3 indicates most CSs which are tested at lag 1, are statistically different. There is only one

CS which is marginally statistically different, and there are three CSs which are not statistically different.

Figure 4.8: As in Fig. 4.4 except for tornado intensity at lag 1 (LΔV).

Table 4.3: As in Table 4.2, except at lag 1. Constraint on Zw Statistical Tornado Size of Size of CS (m) Difference Intensity Sub-s Sub-r 18 Zw <= 0.1 1 weaker 10 152 19 Zw <= 0.2 1 weaker 18 144 20 Zw <= 0.3 1 weaker 37 125 21 Zw >= 0.5 1 stronger 92 70 22 Zw >= 0.6 1 stronger 72 90 23 Zw >= 0.7 1 stronger 55 107 24 Zw >= 0.8 1 stronger 38 124 25 0.1 <= Zw <= 0.2 1 weaker 8 154 26 0.2 <= Zw <= 0.3 1 weaker 19 143 27 0.3 <= Zw <= 0.4 0 stronger 17 145 28 0.4 <= Zw <= 0.5 0^ stronger 16 146 29 0.5 <= Zw <= 0.6 0 weaker 20 142 30 0.6 <= Zw <= 0.7 1 stronger 17 145 31 0.7 <= Zw <= 0.8 1 weaker 17 145 32 0.8 <= Zw <= 0.9 1* stronger 22 140 33 0.9 <= Zw <= 1.15 1 stronger 16 146

Again, call to mind that statistical difference is determined by examining the location of the sub-s 휃̂∗푀 line (red dashed line). The first group of CSs consist of CSs 18

(Zw <= 0.1 m), 19 (Zw <= 0.2 m), and 20 (Zw <= 0.3 m), which generally cover all small weighted surface roughness’. These CSs are displayed in Figs. 4.9a-c. Generally, the three figures show that each CS is associated with weaker mean LΔVs than the mean

LΔVs associated with weighted surface roughness’ outside of the constraints in each CS,

84 respectively. This interpretation is made by examining the sub-s 휃̂∗푀 lines in Figs. 4.9a-c and recognizing they all fall below the 휃̂∗푀of sub-r in each CS. Additionally, in Figs.

4.9a-c, statistical difference is inferred in all three CSs since the sub-s 휃̂∗푀 line falls outside the bca CI bound in CSs 18, 19, 20. Thus, for small weighted surface roughness values the mean tornado intensities at lag 1 are weaker than mean tornado intensities associated with weighted surface roughness values outside the constraints of CSs 18, 19, and 20, respectively.

The second group consists of CSs 22 (Zw >= 0.6 m), 23 (Zw >= 0.7 m), and 24

(Zw >= 0.8 m), which generally cover all large weighted surface roughness’. CSs 22, 23, and 24, are displayed in Figs. 4.9d-f. Within Figs. 4.9d-f, statistical difference is again implied in all CSs, as the sub-r 휃̂∗푀 line exists outside the bca CI of sub-r. Additionally,

휃̂∗푀 of sub-s is greater than 휃̂∗푀 of sub-r indicating stronger mean LΔVs are associated with the constraints in CSs 22, 23, and 24. The illustration of the results in Figs. 4.9d-f suggest that large weighted surface roughness’ are associated with stronger mean tornado intensities at lag 1 than mean tornado intensities at lag 1 at outside of the constraints in

CSs 22, 23 and 24, respectively.

Figure 4.9: As in Fig. 4.4 except CSs 18, 19, and 20 are in panels a, b, and c, and CSs 22, 23, and 24 are in panels d, e, and f. CSs in panels a, b, and c (d, e, and f) are associated with small (large) weighted surface roughness lengths.

The final group consists of CSs 32 (0.8 m <= Zw <= 0.9 m) and CS 33 (0.9 m <=

Zw <= 1.15 m) which cover only the largest weighted surface roughness’. CS 32 is shown in Fig. 4.10a and here, the sub-s 휃̂∗푀 line falls exactly on the upper boundary of the bca CI of sub-r. Here the 95% bca CI bounds are the upper and lower end lines in the pseudo plot. Although it is not clearly identifiable in Fig. 4.10a, CS 32 is not statistically different according to the 95% bca CI (thus the sub-s 휃̂∗푀 line must fall just barely below

86 the sub-r bca CI upper bound). In the other four CIs, which are not discussed herein, CS

32 is in fact statistically different. For this reason, CS 32 is labeled as marginally statistically different, indicated by 1* in Table 4.3. Regardless of difference, the sub-s

휃̂∗푀 line in Fig. 4.10a lies above 휃̂∗푀of sub-r indicating stronger mean LΔVs. The same occurs in Fig. 4.10b for CS 33 (0.9 m <= Zw <= 1.15 m); the 휃̂∗푀 line sub-s is above the

휃̂∗푀 of sub-r (right blue asterisk). In contrast to CS 32, the placement of 휃̂∗푀 line sub-s relative to the bca CI in sub-r in CS 33 is indicative of a statistically different result at lag

1, seen in Fig. 4.10b.

Figure 4.10: As in Fig. 4.4 except for CSs 32 and 33 are in panels a and b, respectively.

In summary, there are multiple statistically different results, in agreement, that indicate small weighted surface roughness lengths are associated with weak mean ΔVs at lag 1. Additionally, there are multiple statistically different results which indicate that large weighted surface roughness lengths are associated with strong6 LΔVs. Finally, the mid-range weighted surface roughness lengths (approximately 0.3 m < Zw < 0.6 m) have

6 CS 32 is marginally statistically different and CS 31 indicated weaker LΔVs.

87 non-statistically different results, none of which sharply favor strong nor weak mean

LΔVs. Perhaps, the mid-range weighted surface roughness lengths are representing a transition zone between the weighted surface roughness lengths which strongly associate themselves with either strong or weak mean LΔVs, but the mid-range weighted surface roughness lengths themselves have no preference. Therefore, land cover types such as shrub, grasslands, pasture, and wetlands would be associated with weak mean tornado intensities downstream and land cover types with high weighted surface roughness such as medium and highly developed land and forests, would be associated with strong mean tornado intensities downstream.

4.2.3 Results of dZw and dΔV at Lag 0

Not only is it possible that the weighted surface roughness length itself be influencing the tornado intensity, but it is also possible that there are relationships between changes in the weighted surface roughness lengths with time (i.e. the weighted surface roughness length is increasing or decreasing) and changes in tornado intensity

(i.e. the tornado intensity is strengthening or weakening) with time. By inspecting the change of the variables with time, i.e. dZw and dΔV (defined in Equation 3.1), more information is learned about the relationships between weighted surface roughness and tornado intensity. First, the results from CSs which examine the change of the variables at lag 0 will be discussed and the results from CSs which examine the change of the variables at lag 1 will follow. Fig. 4.11 is built from Fig. 4.3 to visualize the change of variables Zw and ΔV, as indicated by the braces. Notice that each brace making up dZw

88 and dΔV are functions of two times steps. Specifically, for this section, dZw(i) and dΔV(i) are always functions of the same two time steps.

The CSs which are examined in this section are listed in Table 4.4. The first CSs discussed are those which have the smallest magnitudes of dZw: CS 34 (-0.06 m >= dZw

>= 0 m) and CS 35 (0 m <= dZw <= 0.06 m). From Figs. 4.12a and b, the relationship between dZw and dΔV is seen to be statistically different for CSs 34 and 35, respectively.

This result is construed by examining the relative positions of the red sub-s 휃̂∗푀 line and the bounds of the 95% bca CI of sub-r. In Figs. 4.12a and b, the sub-s 휃̂∗푀 line is positioned outside of the bca CI of sub-r. The only difference in the figures is the position of the sub-s 휃̂∗푀 line with respect to 휃̂∗푀 of sub-r (indicated by the right blue

89 asterisk). As seen in Fig. 4.12a, the sub-s 휃̂∗푀 line is below the 휃̂∗푀 of sub-r indicating weakening mean ΔVs whereas in Fig. 4.12b, the line is well above 휃̂∗푀 of sub-r indicating strengthening mean ΔVs than mean dΔVs associated with dZws outside each

CS, respectively. Similarly, CS 37 (0 m <= dZw <= 0.1 m) has the same statistically different result as in CS 35, which is identified by examining Fig. 4.12c.

Table 4.4: List of CSs, including the dZw constraint for the CS, and statistical difference (1), marginal statistical difference (1*), near statistical difference (0^), or no statistical difference (0) of associated ΔV at lag 1. The relative tornado intensity is listed as weaker, stronger, and no value if there is no intensity preference. The number of ΔVs in each sub-s and sub-r are indicated. Constraint on Statistical Tornado Size of Size of CS dZw (m) Difference Intensity Change Sub-s Sub-r 34 -0.06 >= dZw >= 0 1 weakening 16 146 35 0 <= dZw <= 0.06 1 strengthening 18 144 36 -0.1 >= dZw >= 0 0 strengthening 23 139 37 0 <= dZw <= 0.1 1 strengthening 26 136 38 -0.2 >= dZw >= -0.1 0^ strengthening 15 147 39 0.1 <= dZw <= 0.2 1 weakening 19 143 40 -0.3 >= dZw >= -0.2 1 weakening 24 138 41 0.2 <= dZw <= 0.3 1 weakening 14 148 42 dZw <= -0.2 0 strengthening 43 119 43 dZw >= 0.2 1 weakening 36 126 44 dZw <= -0.3 1 strengthening 19 143

Accordingly, the statistically different result in CS 34 suggests that the small decreases in weighted surface roughness lengths defining CS 34 are associated with weakening mean tornado intensities at lag 0. Additionally, CSs 35 and 37 are also statistically different which suggests small increases in weighted surface roughness are associated with strengthening mean tornado intensities at lag 0. This result implies that a

90 tornado that is traversing from herbaceous wetlands (ZL = 0.1 m) over to grasslands (ZL =

0.2 m) would perhaps be expected to increase in intensity. The results here may also suggest that when changes in Zw are small, the tornado experiencing the change does not take very long to adjust itself to the roughness change. This is inferred since the expected results based on theory are observed ‘quickly’ (at lag 0).

Figure 4.12: As in Fig. 4.4 except for CSs 34, 35, and 37 are in panels a, b, and c, respectively.

As the magnitude of dZw increases, the associated dΔVs seem to have a very different result than what is described for small magnitudes of dZw. When the dZws surpass a magnitude of 0.1 m, such that the constraints are those of CSs 38 (-0.2 m >= dZw >= -0.1 m) and 39 (0.1 m <= dZw <= 0.2 m), the associated dΔVs no longer directly

91 follow what is expected based on the disruption of cyclostrophic balance (this discrepancy may be justified, however, as discussed later). Results for CSs 38 and 39 are presented in Figs. 4.13a and b, respectively. In Fig. 4.13a, the sub-s 휃̂∗푀 line is located above 휃̂∗푀 of sub-r indicating strengthening ΔVs; however, the 휃̂∗푀 line is also located inside the bca CI boundaries of sub-r thus indicating the result is not statistically different. It should be noted, though, that the 휃̂∗푀 line just barely fails to be statistically different, as indicated by the sub-s 휃̂∗푀 line’s proximity to the upper bca CI boundary of sub-r.

Figure 4.13: As in Fig. 4.4 except for CSs 38, and 39 are in panels a, and b, respectively.

On the contrary, Fig. 4.13b shows the sub-s 휃̂∗푀 line clearly outside on the bca CI bounds of sub-r, demonstrating the statistical difference of CS 39. Here the sub-s 휃̂∗푀 line is opposite of what is seen in Fig. 4.13a, and falls below the 휃̂∗푀 of sub-r, thus representing ΔVs which are weakening. These results of CS 38 and 39 indicate with nearly statistical difference and statistical difference that medium (approximately 0.1 m to 0.2 m) weighted surface roughness changes are inversely related to changes in mean

92 tornado intensities. Specifically, medium increases in weighted surface roughness’ seem to be associated with decreases in mean tornado intensities at lag 0 and medium decreases in weighted surface roughness’ seem to be associated with increases in mean tornado intensities at lag 0. For example, a tornado moving from barren land (Zw = 0.05 m) to emergent herbaceous wetlands (Zw = 0.2 m), dZw is increasing 0.15 m and the tornado would be expected lose intensity according to the result of CS 39.

The opposite relationship between the change in weighted surface roughness and change in mean tornado intensities continue even as the magnitude of dZw gets quite large. Figs. 4.14c and d show results of CSs 44 (dZw <= -0.3 m) and 43 (dZw >= 0.2 m), respectively. First, in Fig. 4.14c, the statistical difference of CS 44 is inferred due to the sub-s 휃̂∗푀 line’s position being outside of the bca CI boundaries of sub-r. The same inference is made for CS 43 in Fig. 4.14d. In these figures, 휃̂∗푀 of sub-s is above 휃̂∗푀 of sub-r for CS 44 but below 휃̂∗푀 of sub-r for CS 43. Based on CS 44 and CS 43 it appears that large negative changes in Zw are associated with weakening ΔVs, and large positive changes in Zw are associated with strengthening ΔVs. CS 41 (0.2 m <= dZw <= 0.3 m), by definition, is included in the results of CS 43 (dZw >= 0.2 m) and thus is expected to support the statistically different result from CS 43. As displayed in Fig. 4.14b, CS 41 is indeed statistically different and associated with weakening ΔVs.

Figure 4.14: As in Fig. 4.4 except for CSs 40, 41, 44, and 43 are in subplots a, b, c, and d, respectively.

What is not shown in Fig. 4.14, is CS 42 (Zw <= -0.2 m). The results of CS 42 also indicate large negative changes in Zw are associated with strengthening ΔVs, but the result is not statistically different. The probable cause of the result in CS 42 is likely associated with the result of CS 40. The result of CS 40 (-0.3 m >= dZw >= -0.2 m) does not follow the same relationship between the change in weighted surface roughness and change in mean tornado intensities. Fig. 4.14a illustrates CS 40. In the figure, sub-s 휃̂∗푀 line is below 휃̂∗푀 of sub-r as well as outside the bca CI of sub-r in which signals a statistically different result of weakening ΔVs. Perhaps the there is a reason CS 40 has a statistically different result which is inconsistent with the other large magnitude change

CS but the temporal resolution of this study is not adequate to resolve said reason. Thus,

94 apart from CS 40, it appears that large increases in weighted surface roughness are associated with decreases in mean tornado intensities at lag 0 and large decreases in weighted surface roughness are associated with increases in mean tornado intensities at lag 0. Possible reasons for the ‘switch’ in the way the mean tornado intensities changed with increasing weighted surface roughness change will be discussed further in Chapter

4.2.4 Results of dZw and dΔV at Lag 1

Finally, results from CSs which examine dZw and dΔV at lag 1 (from here on

LdΔV) are discussed and can be viewed in Table 4.5. Fig 4.15 is a conceptual diagram like Fig. 4.11, except here the diagram displays LdΔV. The major difference to note is in

Fig. 4.15, where dZw(i) and LdΔV(i) are never functions of the same two time steps. In this section, there appears to be evidence that small dZw and large dZw have opposite associations with mean LdΔVs. Beginning again with CSs which have the smallest magnitude of dZw, CSs 45 (-0.06 m >= dZw >= 0 m) and 46 (0 m <= dZw <= 0.06 m) are illustrated in Figs. 4.16a and b, respectively. Remember, here 휃̂∗푀 is the mean LdΔV of all the bootstrap replications in the dataset 휃̂∗, and is calculated for each subsample sub-s and sub-r. In Fig. 4.16a the red dashed line represents 휃̂∗푀 of sub-s and its location relative to 휃̂∗푀 of sub-r (right blue asterisk) establishes that strengthening mean LdΔVs are associated with small decreases in Zw since 휃̂∗푀 of sub-s is situated above 휃̂∗푀 of sub-r..

Table 4.5: As in Table 4.4, except associated dΔVs are at lag 1. Constraint on Statistical Tornado Size of Size of CS dZw (m) Difference Intensity Change Sub-s Sub-r 45 -0.06 >= dZw >= 0 1 strengthening 11 121 46 0 <= dZw <= 0.06 1 weakening 17 115 47 -0.1 >= dZw >= 0 1 strengthening 17 115 48 0 <= dZw <= 0.1 0 weakening 24 108 49 -0.2 >= dZw >= -0.1 1 weakening 13 119 50 0.1 <= dZw <= 0.2 0 16 116

51 -0.3 >= dZw >= -0.2 1 weakening 16 116 52 0.2 <= dZw <= 0.3 1 strengthening 11 121 53 -0.2 >= dZw >= 0 0 30 102

54 0 <= dZw <= 0.2 0 weakening 40 92 55 dZw <= -0.2 0 weakening 31 101 56 dZw <= -0.3 0 strengthening 15 117 57 dZw >= 0.2 1 strengthening 31 101 58 dZw >= 0.3 0 strengthening 20 112

Figure 4.15: As in Fig. 4.11 except the for change of ΔV at lag 1 (LdΔV) is displayed.

Since 휃̂∗푀 of sub-s is located outside of the bca CI for sub-r in Fig. 4.16a, CS 45 is considered statistically different. Notice the placement of 휃̂∗푀 of sub-s is outside the bca CI of sub-r in Fig. 4.16b as well. However, in Fig. 4.16b, 휃̂∗푀 of sub-s is below 휃̂∗푀

96 of sub-r indicating statistically different weakening mean LdΔVs are associated with small increases in Zw (CS 46). These results suggest that small decreases in weighted surface roughness (i.e. moving from cultivated crop land to open developed space) are associated with strengthening mean tornado intensities downstream and that small increases in weighted surface roughness are associated with weakening mean tornado intensities downstream.

Figure 4.16: As in Fig. 4.4 except for CSs 45, 46, 47, and 48 are in panels a, b, c, and d, respectively.

Similar results occur for CSs 47 (-0.1 m >= dZw >= 0 m) and 48 (0 m <= dZw <=

0.1 m) such that the location of 휃̂∗푀 of sub-r with respect to the bca CI of sub-r in Figs.

4.16c and d, are indicative of the CSs being associated with strengthening and weakening

97 mean LdΔVs, respectively. However, for CSs 47 and 48, only the CS which is constrained to negative changes in Zw (CS 47) is statistically different. As displayed in

Fig. 4.16d, 휃̂∗푀 of sub-s is located inside of the bca CI for sub-r, and is just shy of being statistically different. Thus again, small decreases in weighted surface roughness (e.g. tornado is moving from grasslands to hay pasture) are associated with strengthening mean tornado intensities downstream and small positive changes in weighted surface roughness are associated with weakening mean tornado intensities downstream.

As the magnitude of change in Zw increases, and in particular surpasses a threshold change of 0.1 m, there is again this ‘switch’ of direction seen amongst the associated mean LdΔVs. Take CS 49 (-0.2 m >= dZw >= -0.1 m), this CS is displayed in

Fig. 4.17a. In the figure, the 휃̂∗푀 of sub-s line is below 휃̂∗푀 of sub-r indicating an association with weakening mean LdΔVs. The 휃̂∗푀 of sub-s line is also outside of the bca CI of sub-r, signifying CS 49 is statistically different. The same results are seen in

Fig. 4.17c for CS 51 (-0.3 m >= dZw >= -0.2 m). Notice that here, medium decreases in dZw (-0.3 m <= dZw <= -0.1 m) are associated with weakening mean LdΔVs which is opposite of what was found for small decreases in Zw (ex. CS 45 was associated with strengthening mean LdΔVs).

On the contrary, medium increases in dZw are the constraints for CSs 50 (0.1 m<= dZw <= 0.2 m) and 52 (0.2 m <= dZw <= 0.3 m). A similar switch occurs for CS

52 as shown in Fig. 4.17d. From the figure, an association with strengthening mean

LdΔVs is inferred since the 휃̂∗푀 of sub-s line is above 휃̂∗푀 of sub-r. Since the 휃̂∗푀 line of sub-s is also placed outside of the bca CI of sub-r, statistical difference is assumed as

98 well. Here, the results inferred from Fig. 4.17d suggest that medium increases in Zw are associated with strengthening mean LdΔVs which is opposite of the result found for small increases (ex. CS 46 was associated with weakening mean LdΔVs).

Figure 4.17: As in Fig. 4.4 except for CSs 49, 50, 51, and 52 are in panels a, b, c, and d, respectively.

CS 50 has an unusual result than what may be expected after viewing the results of CSs 49, 51, and 52. Rather, CS 50 (0.1 m<= dZw <= 0.2 m) exhibits a non- statistically different and neutral result. This result is very clearly displayed in Fig.

4.17b. In the figure, 휃̂∗푀 of sub-s and 휃̂∗푀 of sub-r are positioned approximately at the same location, thus, 휃̂∗푀 of sub-s is within the bca CI of sub-r. The non-statistically different result here, which is not associated with mean LdΔVs changing in one specific

99 direction (neither weakening nor strengthening), may be justified by the original data sampled in this study.

Most raw data values in the CS 50 sub-s, correspond to raw dZw values which are close to the lower constraint of CS 50 (0.1 m). Thus, the range of the dZw constraint may not be well represented in the raw dataset. In summary, apart from CS 50, medium increases in weighted surface roughness, such as low intensity developed land to medium intensity developed land, are associated with strengthening mean tornado intensities downstream. Likewise, medium decreases in weighted surface roughness, i.e. medium intensity developed land to low intensity developed land, are associated with weakening mean tornado intensities downstream.

Larger magnitude changes in Zw, as in CSs 55 (dZw <= -0.2 m) and 57 (dZw >=

0.2 m) have similar results to medium magnitude changes in Zw. CS 55 is shown in Fig.

4.18a where statistical difference is not achieved due to the 휃̂∗푀 of sub-s line being located within the bounds of the bca CI of sub-r. Additionally, the line is located below

휃̂∗푀 of sub-r (right blue asterisk) which together indicates a non-statistically different association with weakening mean LdΔVs. However, the positive change in Zw, CS 57, implies a statistically different result which is associated with strengthening mean

LdΔVs. The result of CS 57 is inferred from the 휃̂∗푀 of sub-s line being positioned above the 휃̂∗푀 of sub-r asterisk and outside the bounds of the bca CI of sub-r. While only CS 57 is statistically different, the results for CS 55 and 57 largely mimic the results described in the medium magnitude changes in Zw listed in the previous paragraph.

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Figure 4.18: As in Fig. 4.4 except for CSs 55 and 57 are in panels a and b, respectively.

Finally, the largest changes in Zw, as in CSs 56 (dZw <= -0.3 m) and 58 (dZw >=

0.3 m), each result in non-statistically different associations of strengthening mean

LdΔVs (not shown). While it was nearly expected to find strengthening mean LdΔVs with the largest increases in dZw (CS 58), it is unexpected to find strengthening mean

LdΔVs associated with the largest decreases in dZw (CS 56) (keep in mind the results here are not statistically different). One possible reason for strengthening mean LdΔVs in CS 56 might be that such extremely large changes in dZw (such as dZw > 0.6 m or >

0.7 m) are associated with mean LdΔVs which differ from mean LdΔVs associated with moderately large changes in dZw (i.e. dZw > 0.3 m or > 0.4 m). It may also be that the tornadoes represented in this study did not truly undergo such extreme changes in weighted surface roughness, and that the changes are more gradual in nature (thus, a function of the resolution of the study). It is also possible that tornadoes take different amounts of time to adjust to the changing weighted surface roughness’ which are represented here.

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CHAPTER 5: DISCUSSION AND CONCLUSIONS

5.1 Discussion

In summary, SCCs of Zw and ΔV indicate some relationship between the two data sets when testing the data pairs recorded for each tornado event separately. The individual tornado events had SCCs at lag 0 and at lag 1 ranging from strong negative correlations, correlations around zero and strong positive correlations. However, there appears to be some discernable relationship seen visually. The entire dataset had an SCC of about zero at both lag 0 and at lag 1. This result would indicate that surface roughness and tornado intensity have no generalizable relationship.

However, since the datasets failed tests of normality, non-parametric bootstrapped means are calculated for a variety of sample subsets of the entire dataset. In general, there are many cases which have a statistically different result using the non-parametric methods. The non-parametric method suggests that there is a relationship between weighted surface roughness and tornado intensity, and the nature of the relationship varies depending upon the data being tested. Statically different results are found when relating the change in surface roughness to the corresponding change in tornado intensities. It is found that tornado intensity behaves differently when associated with small and large changes in surface roughness, and also depends on the direction of the surface roughness change (i.e. low roughness to high roughness vs. high roughness to low roughness.) Had non-parametric statistics not been applied, it is possible that these relationships could have been overlooked as well, given dim results of the SCCs for the entire dataset.

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The most basic relationships that are found between Zw and ΔV are that large weighted surface roughness lengths are associated with relatively strong mean tornado intensities at lag 0. Additionally, small weighted surface roughness lengths are associated with weak mean tornado intensities at lag 0. The same general relationships found at lag 0 also occur at lag 1 such that small Zws and large Zws are associated with weak and strong mean ΔVs, respectively. Statistical differences of mean ΔVs at lag 1 support the idea of surface roughness perhaps affecting tornado intensities with time.

These results suggest that land cover with large surface roughness lengths (i.e. highly developed land or forest) correspond to higher tornado intensities than tornado intensities which correspond to land cover with low surface roughness lengths (i.e. grasslands or wetlands).

These results match well with the theory based hypothesis of this study.

However, the results are in opposition to what is found in the literature; where introducing surface roughness in numerical simulations found reductions in tornado intensity (Dessens 1972; Natarajan and Hangan 2012). However, keep in mind that the simulations are of a tornado-like vortex and do not truly represent tornadic flow forced by a parent supercell. Additionally, the numerical simulations are looking at winds almost directly in contact with the ground whereas radar data are collected several hundred meters above the ground. The observational data in this study are utilized to analyze how the change in surface roughness corresponds with changes seen in tornado intensities.

Based on results found between Zw and ΔV, one would expect as a tornado encounters a

103 greater (lesser) surface roughness (i.e. a change of surface roughness) it would also result in increased (decreased) tornado intensities as well.

While some general statements could be made about changes in Zw and ΔV (i.e. dZw and dΔV) looking at lag 0 and lag 1 separately, a better understanding can be made when comparing the results between those at lag 0 and at lag 1. From this relationship, it appears that there is the possibility (depending on the magnitude of dZw) that tornado intensity does not instantaneously adjust to changes in surface roughness; but rather, there is some amount of time needed for the tornado to adjust to changing surface roughness.

For instance, comparing CSs 41 and 52 for medium large increases (0.2 m <= dZw <= 0.3 m), at lag 0 there is weakening of ΔV (CS 41), but between the following two observations (i.e. at lag 1) there is strengthening of ΔV (CS 52). In these cases, the tornado is moving from lower roughness to higher roughness (such as from emergent herbaceous wetlands to an area of shrubs) and in doing so, the tangential velocities must slow, at least initially, in response to the increased friction. In so doing, the cyclostrophic balance is disturbed. When the balance is disturbed in this manner, the weakening of tangential velocities allows the inward-directed pressure gradient force to overpower the outward-directed centrifugal force. This process will contract the vortex, and by conserving angular momentum, will increase ΔV (or tornado intensity) with time, which is perhaps the reason we see the expected ‘end’ result of this change several minutes later, at lag 1, rather than at lag 0. CSs 41 and 52 both have statistically different results

(refer to Fig. 4.14 b and 4.17 d, respectively for reference).

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Again, there seems to be a threshold around weighted surface roughness changes of 0.1 m such that for changes (positive or negative) that are less than magnitude 0.1 m, the tornado likely adjusts very quickly and thus the expected change in tornado intensity is seen at lag 0 for small roughness changes. But, as those changes exceed magnitude 0.1 m, perhaps a longer time is required for the tornado to adjust to the surface roughness change. Thus, the change in intensity occurs later in time, at lag 1. For samples on the latter half of the threshold (i.e. dZw > |0.1 m|) it seems we may be sampling the initial

(lag 0) and final (lag 1) changes to the tornado’s intensity as the tornado adjusts to large surface roughness changes. As the tornado initially encounters a positive change in surface roughness moving into an area with increased Zw, a decrease in tornado intensity occurs as the increase in roughness slows the tangential velocities and the cyclostrophic balance of the tornado is disturbed. As the PGF becomes greater than CF, the tornado adjusts and comes to a new balance; and, with momentum conserved, the tangential velocities increase and result in an intensified tornado which is recorded at lag 1.

Another possibility, is that not only does the magnitude of a surface roughness change affect the time a tornado takes to adjust its balance, but so may the direction of which the surface roughness is changing. For example, a tornado may take more time to adjust to decreasing surface roughness changes and less time adjusting to increasing surface roughness changes. By coupling the tornado intensity adjustment time due to magnitude and direction of surface roughness change, it is possible that further information can be inferred.

If the generalizations being suggested by the data here are indeed valid such that

105

• A tornado adjusts to small surface roughness changes faster than it adjusts to

large surface roughness changes.

• A tornado adjusts to surface roughness increases faster than it adjusts to

surface roughness decreases.

• Tornado adjustment time depends more on the magnitude of surface

roughness change than the direction of change.

Then it is possible to order combinations of surface roughness change according to the relative amount of time it should take for the tornado intensity to adjust to the change in surface roughness. Such an order is listed in Table 5.1. In context, if the magnitude and direction of surface roughness change suggest a longer time is needed for the tornado intensity to adjust, then the expected resultant outcome on tornado intensity will be seen in the lag 1 data; whereas, in the shorter adjustment category, the expected result should be seen in the lag 0 data. When Table 5.1 is applied to the CSs in this study there is evidence that this order is somewhat followed. However, there are also cases where it appears that the tornado adjusted either more quickly, or more slowly than what is suggested by the table.

An example of CSs which appear to follow Table 5.2 are CSs 41 and 52 which were discussed earlier in this section. These CSs have a constraint of 0.2 m <= dZw <=

0.3 m which is considered a medium-large magnitude change in the positive direction, and thus would fall under a longer adjustment time. CS 41 indicates decreasing tornado intensities at lag 0, and CS 52 indicates strengthening tornado intensities at lag 1. So, the

106 expected result (of increased tornado intensities) took longer to occur since the expected result is seen in lag 1 rather than lag 0.

Table 5.1: A suggested order of time (from longest to shortest amount of time) taken for a tornado to adjust to changes in weighted surface roughness. Time needed Magnitude and Direction of Surface Roughness Change to Adjust Magnitude of change is large and surface roughness is decreasing. Longest (Tornado moving from large roughness to smaller roughness.)

Magnitude of change is large and roughness is increasing. (Tornado moving from smaller roughness to larger roughness.)

Magnitude of change is small and roughness is decreasing. (Tornado moving from large roughness to smaller roughness.)

Magnitude of change is small and roughness is increasing Shortest (Tornado moving from smaller roughness to larger roughness.)

Another example is for a change of Zw less than -0.3 m, which would be considered a large magnitude change in the negative direction and would fall under the longest adjustment time. The expected result of decreasing tornado intensities would then be expected to be seen at lag 1. In CS 44, it is seen that the constraint is indicating strengthening tornado intensities at lag 0, which would be expected. However, the constraint still indicates strengthening tornado intensities at lag 1 for CS 56. So, a possible explanation for this result is that the tornado is still adjusting to the change and perhaps needed a bit more time before the expected result of weakening tornado intensities could be recorded, or perhaps the temporal resolution is insufficient to identify the true nature of the changes.

107

If, perhaps, passing of time is not the solution for the result of CS 56 (and others), it could be that the change in surface roughness is not discrete from one landcover type to another when the magnitude of dZw is 0.3 m or more. Rather, the tornado moves from a surface with a Zw of 0.6 m to one with a Zw of 0.8 m, to one with a Zw of 0.9 m over the

~4.2 minute scanning time. Not only is possible that the changes in surface roughness are more gradual in nature, but it is also possible for the tornado to traverse over one land cover type then back to the original land cover type all within the span of one volume.

Thus, due to the temporal resolution of the WSR-88D radar, the data in this study do not account for any gradual undulations or extreme changes in surface roughness that the tornado may or may not encounter while traversing between time steps. Additionally, the data in this study also do not account for other known storm scale mechanisms which may be affecting the tornado such as RFDISs or DRCs due to temporal resolution limitations.

It is also entirely possible that different surface roughness’ affect a tornado differently depending on how strong the tornado is initially. For instance, a very small change in surface roughness (i.e. 0.6 m) might be enough to significantly alter the intensity of an already weak tornado. Or, it could be that only very large changes in surface roughness significantly alter a particularly strong tornado, and lesser changes in surface roughness would not seem to alter the tornado at all.

Likewise, if a tornado begins in an area of relatively high surface roughness such as medium developed land and moves into a mixed forest, where roughness increases by a small amount (0.1 m), it is possible the dΔVs would react differently than for a situation

108 with the same change in roughness occurring, but lower on the surface roughness spectrum. For instance, the tornado moving from open water (least roughness) to pasture land is also a change of 0.1 m but could result in different changes to the tornado intensity than the transition from medium developed land to mixed forest (also a change of ~0.1 m).

The results of this study suggest that land cover as represented by surface roughness is important to the near surface wind field of tornadoes and their intensity which agrees with previous studies (i.e. Davies-Jones (2015), Dessens (1972), Lewellen

(2014), Lewellen (2012), Lewellen et al. (2008), Lewellen and Lewellen (2007),

Lewellen et al. (2000), Natarajan and Hangan (2012), Leslie (1977), and Ward (1972)).

5.2 Conclusions

This study begins to address the current deficiency in the peer-reviewed literature regarding the relationships between tornadoes and land cover features and advances our understanding of how and why tornados intensify, a process currently minimally understood. The research has been approached in a novel way, utilizing the robust capabilities of GIS, which few tornado studies have employed. The research questions of this study are:

1) Are tornadoes more (less) intense when located over surfaces which have land

cover types with relatively high (low) values of friction?

2) Will a tornado intensify or weaken if it traverses from land cover types with lower

friction to ones with higher friction, and vise-versa?

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Weighted surface roughness and tornado intensity cannot simply be analyzed using parametric statistical tests. To explicitly answer research question 1, the SCCs of the entire dataset at lag 0 and lag 1 are near zero, suggesting no relationship between surface roughness and tornado intensity. Additionally, there is no clear or consistent

SCC in the data for the individual tornado events. However, by using non-parametric methods, statistical relationships between the weighted surface roughness and tornado intensities can be made.

Certain weighted surface roughness constraints are associated with mean tornado intensities that are statistically different than the mean tornado intensities associated with surface roughness values outside of the constraints. Generalizations of the relationships between these parameters are as follows:

• Large weighted surface roughness lengths (Zw >= 0.6 m) are associated with

relatively strong tornado intensities at lag 0 and at lag 1.

• Small weighted surface roughness lengths are associated with relatively weak

tornado intensities at lag 0 (Zw < 0.4 m) and at lag 1 (Zw < 0.3 m).

Similarly, changes in weighted surface roughness and the mean changes in tornado intensity are examined. To explicitly answer research question 2, both small and large changes in surface roughness as well as positive and negative changes in surface roughness length are associated with changes in tornado intensity that are statistically different. The generalizations of the relationships between these parameters are as follows:

110

• Small decreases in weighted surface roughness lengths (-0.1 m > dZw > 0 m)

are associated with weakening mean tornado intensities at lag 0.

• Small increases in weighted surface roughness lengths (0 m < dZw < 0.1 m)

are associated with strengthening mean tornado intensity at lag 0.

• Medium and large decreases in weighted surface roughness (dZw < -0.1 m)

are associated with strengthening mean tornado intensities at lag 0.

• Medium and large increases in weighted surface roughness lengths (dZw > 0.1

m) are associated with weakening mean tornado intensities7 at lag 0.

• Small decreases in weighted surface roughness lengths (0 m < dZw < -0.1 m)

are associated with strengthening mean tornado intensities at lag 1.

• Small increases in weighted surface roughness lengths (0 m < dZw < 0.1 m)

are associated with weakening mean tornado intensities at lag 1.

• Medium decreases in weighted surface roughness lengths (-0.1 m < dZw < -

0.3 m) are associated with weakening mean tornado intensities at lag 1.

• Medium increases in weighted surface roughness lengths (0.1 m < dZw < 0.3

m) are associated with strengthening mean tornado intensities at lag 1.

These concluding remarks indicate the hypothesis of the study was valid, and indicate that surface roughness must be an important part of how and why tornadoes intensify and should not be simply overlooked. Based on this discussion and conclusion, other possible, (yet not as strong), relationships between surface roughness and tornado intensities may be:

7 Except where 0.2 m < dZw < 0.3 m.

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• A tornado adjusts more quickly to small changes in surface roughness than

large changes in surface roughness.

• A tornado adjusts to increasing surface roughness change faster than it adjusts

to decreasing surface roughness changes.

Perhaps data with improved temporal resolution data could provide a clearer sense of the temporal nature of tornado intensity adjustments.

In conclusion, there are statistical relationships between land cover and tornado intensity and these relationships should most definitely be explored further using non- parametric methods. However, the nature of these relationships is complex and not entirely understood. Ultimately, this research finds that land cover is influencing tornado intensity in southeastern USA and provides a foundation for future, more in depth, studies.

5.3 Future Work

In order to determine the statistical significance of the differences between the means that were described herein future work will include execution of permutation tests.

Additionally, while it not thoroughly discussed here, radar beam height fundamentally plays a major role in the interpretation of this data, since the velocity signal is dependent on how high the radar beam is sampling. Future work could include interpolating the radar data onto a 3D grid to record tornado intensity at a uniform height across all events.

It might also be beneficial to compare the changes seen through the vertical column. For instance, the behavior of the TVS below 100-200 m can be compared to the behavior of

112 the TVS at say, 800 m. This could give some indication on how change (if any) due to surface roughness translates in the tornado.

Future work should also look further into tornadogenesis and decay locations to analyze surface roughness lengths around these locations. It could be possible that a study focusing on intensity change may not capture the instance in which surface roughness (or change thereof) is so profound that the tornado decays completely. A study of this nature would likely need to include radar data with higher temporal resolution than the WSR-88D, utilized in this study.

Other studies might also incorporate elevation changes to get a sense of how the tornado is changing as it either increases or decreases its elevation, or perhaps even shifts the tornado tracks. It would also be useful if this study were repeated in other regions of sufficient land cover change, and add to the number of events which were examined.

This and other studies will help fill the gap in current literature in regards to how and why tornadoes intensify.

113

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