\documentclass[letter,12pt,dissertation]{OUdissertation6} %for Ph.D. disseration style
%\documentclass[letter,12pt,thesis]{OUdissertation5} %for M.S. thesis style
\usepackage{graphicx} %allows .eps and .epsi graphics to be inserted
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\usepackage{losymbol}
%\usepackage{loacronym}
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\usepackage[titletoc,title]{appendix}
% Brian added this on July 15 2006 from suggestion of Di Jin:
\usepackage[centerfoot]{pageno}

%\usepackage{harvard} %use with agsm.bst, see near end
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\newcommand{\zdr}{$Z_{DR}$~}
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\newcommand{\zdrns}{$Z_{DR}$}
\newcommand{\zhh}{$Z_{HH}$~}
\newcommand{\zvv}{$Z_{VV}$~}
\newcommand{\ldr}{$L_{DR}$~}
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\newcommand{\cdr}{$CDR$~}
\newcommand{\cdrns}{$CDR$}
\newcommand{\zhhns}{$Z_{HH}$}
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\newcommand{\zdrts}{$\hat{Z}_{DR}$}
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\begin{document}
\title{POLARIMETRIC RADAR OBSERVATIONS AND NUMERICAL SIMULATIONS OF TORNADIC DEBRIS}
\author{DAVID JOSEPH BODINE}
\depositdate{2014}
\majorfield{SCHOOL OF METEOROLOGY}
\memberone{Dr. Robert D. Palmer}
\membertwo{Dr. Michael I. Biggerstaff}
\memberthree{Dr. Howard B. Bluestein}
%next two members are used in dissertation
\memberfour{Dr. Pamela L. Heinselman}
\memberfive{Dr. Mark B. Yeary}
%another member is possible, but you must hack OUdissertation.cls
%\membersix{Dr. Spock}
%%%%
\begin{preface}
%\prefacesection{Dedication} %Dedication must be without a pagenumber, see end of this file.
\prefacesectionX{Dedication}
This dissertation is dedicated to my late grandparents, Walt Bodine and Warren Hannon, for being great role models, instilling a strong work ethic in me, encouraging my interest in meteorology, and leaving an indelible impression on my life.  
%\prefacesectionX{Dedication}
%This dissertation is dedicated to Donald Knuth and Linus Torvalds.
%
%A dedication page is optional in the OU dissertation.  
%This section is not allowed to have a printed pagenumber, nor is it allowed to
%increment the page number counter. This is why we use the hacked \verb+\prefacesectionX+ for
%the Dedication, rather \verb+\prefacesection+.
\prefacesection{Acknowledgements}
%Thank my committee
\hspace{0.5cm} I would like to thank my Ph.D. advisor, Dr. Robert Palmer, for his excellent mentoring and advice, and the opportunities he gave me throughout my graduate education.  I appreciate the freedom he gave me to pursue research topics which interested me, and the opportunities to participate in interesting projects ranging from building a unique phased array radar to leading field projects.  Dr. Palmer encouraged me to pursue a cross-disciplinary education in meteorology and engineering, which helped me cultivate a valuable skill set and a deeper appreciation for the engineering underlying weather radar systems.  Finally, he encouraged me to pursue a research experience in Japan that was very rewarding intellectually and personally.  I look forward to continuing our collaboration throughout my career.

I am grateful to my doctoral committee members, Dr. Michael Biggerstaff, Dr. Howard Bluestein, Dr. Pamela Heinselman, and Dr. Mark Yeary, for their excellent guidance and feedback.  I enjoyed long conversations with Dr. Biggerstaff and appreciate his advice about research, teaching and scientific funding.  I also enjoyed the opportunities to work with him during VORTEX-2 and the Hurricane Irene deployment, both of which were quite memorable.  Dr. Bluestein provided a great foundation for my education, serving as an instructor in four different courses (perhaps setting a record).  Watching videos of Dr. Bluestein's research groups collecting radar data also motivated my interest in radar and mesoscale studies.  I am grateful to Dr. Pamela Heinselman for her mentoring, and her willingness to provide career advice and insight.  I benefited greatly from working with her during my Master's degree, and continued to enjoy our collaborations and discussions throughout the Ph.D.  I have enjoyed sharing an office corridor with Dr. Mark Yeary.  He has always given useful advice for research or career-related questions, for which I am grateful.  

The SoM faculty provided a great undergraduate and graduate education, and I would like to thank the SoM staff for their hard work.  I am grateful to Dr. Petra Klein for giving me an opportunity to conduct research with her as an undergraduate, which helped cultivate my research skills and accelerate my progress as a graduate student.  Dr. Alan Shapiro has been a great resource for advice, an excellent instructor, and a terrific liaison and advocate for the students.  Dr. Mark Laufersweiler was a great resource for both computing help and interesting discussions on a variety of topics.  I would like to thank Celia Jones, Marcia Pallutto, Becky Steely, Nancy Campbell, and Christie Upchurch for their assistance throughout my time at OU, and for many enjoyable conversations.  

I would like to thank several ARRC scientists, engineers and staff for their efforts, which have facilitated the research activities conducted in this Dissertation.  Dr. Boon Leng Cheong has been a great resource throughout my graduate education for helpful discussions about polarimetric radar, numerical simulations and computing issues.  Redmond Kelley and John Meier are thanked for their tremendous efforts in maintaining the ARRC radars, allowing us to collect great data sets with OU-PRIME and the AIR.  Finally, I appreciate the assistance of ARRC staff, Krysta Bruehl, Jo Ann Mehl, and Lauren White, for their great effort and patience, which has made life as an ARRC student much easier.  

I would like to thank Dr. Takashi Maruyama for supervising my six-month stay at Kyoto University, and enabling a great educational, professional, and personal experience.  I appreciate his effort in helping me understand the numerical simulation process for LES, and the time he devoted to making arrangements for my stay.  I also enjoyed the lunches and dinners with Professor Maruyama, his insights into Japanese culture, and the lab trip to Kyushu.  I enjoyed getting to know the Japanese students in Professor Maruyama's lab, Junya Okazaki, Mayuko Hanatani, and Naoko Tamura.  I am grateful for the opportunity to meet several international students as well.  I look forward to continuing my collaborations with Professor Maruyama in the future. 

Discussions with Jim Kurdzo, Chris Schwarz, Dr. Matt Kumjian, Dr. Brad Isom, Feng Nai, Dr. Qing Cao, Gabe Garfield, Dan Betten, Dr. Jeff Snyder, Dr. Robin Tanamachi, and many others have been helpful and enjoyable.  In particular, I have enjoyed sharing an office with Jim Kurdzo and having an excellent scientist with whom I can discuss various science and engineering topics.  Discussions with Dr. Kim Elmore on statistics and Dr. Alexander Ryzhkov on polarimetric radar were helpful and enlightening.  

Funding for this research was provided by NSF grants ATM-0750790, AGS-1303685, and IIA-1209444.  OU-PRIME was maintained by Redmond Kelley, John Meier, Dr. Boon Leng Cheong, and several other engineers, whose efforts contributed to providing high-quality data.  The National Weather Service Weather Forecast Office is also thanked (Doug Speheger and Greg Stumpf, in particular) for providing high-resolution damage surveys which were critical to many analyses herein.

I thank my roommates Pat, Darrel and Boomer for putting up with me for four years, and for many great late-night ice cream trips to Braum's.  I also thank my girlfriend, Christina Tippy, for her support and understanding throughout the Dissertation writing process.  Bruce Thomas has been a great mentor and friend, and provided an internship in high school that was a turning point for my education and career path.     

Finally, I am grateful to my family for their support over the past decade.  They enabled me pursue my dream of studying meteorology at OU and obtain a Ph.D., and rarely complained about me watching the Weather Channel too much as a child.  I thank my parents, Tom and Ellen Bodine, for their endless love, support and encouragement, and for being the best parents anyone could hope to have.  

\tableofcontents
\listoftables
\listoffigures
\prefacesection{Abstract}
\hspace{0.5cm} Tornadic debris are critical aspects of tornado studies because airborne debris pose significant threats to life and property, and debris often dominate backscattered radar signals, causing biased Doppler velocity measurements.  Polarimetric radar offers new research opportunities because debris produce a unique polarimetric radar signature called the tornadic debris signature (TDS).  In this study, new applications of TDSs are examined using Transmission (T) matrix calculations, polarimetric radar observations, and numerical simulations.  To illuminate electromagnetic scattering characteristics of different debris types, T-matrix calculations are presented.  While most TDS studies have focused on tornado detection, this study conducts a detailed analysis of 14 TDS cases to determine relationships between TDS parameters and EF-rating.  As tornado EF-rating increases, 90th percentile radar reflectivity factor, TDS height, and TDS volume increase, and 10th percentile co-polar cross-correlation coefficient and differential reflectivity decrease.  While the TDS parameter analysis focuses on a single radar frequency, debris scattering characteristics vary depending on radar frequency, and thus multiple frequency polarimetric radar observations may provide new information about debris.  In a statistical analysis of dual-wavelength TDSs, higher radar reflectivity factor and lower co-polar cross-correlation coefficient are observed at S band compared to C band, and negative differential reflectivity is sometimes observed simultaneously at both frequencies.  

Multiple frequency radar observations have additional utility in determining debris concentrations to assess debris loading impacts.  To simulate polarimetric radar signatures, tornado vortices are simulated in a Large-Eddy Simulation (LES) model with a drag force coupling parameterization based on debris trajectories, enabling momentum exchange between air and debris.   As debris loading increases, simulations reveal decreasing near-surface radial, tangential and vertical velocities in the lowest grid cell.  Further increases in debris loading cause greater reductions in near-surface velocities and reduced tornado core tangential and vertical velocities.  Using T-matrix calculations and LES model runs, equivalent radar reflectivity factor and two-way attenuation rates are calculated to determine if equivalent radar reflectivity factor or attenuation provide useful upper-bounds on debris loading.  These simulations reveal that if sufficient amounts of debris loading are present to affect tornado dynamics, significant attenuation will occur at W band, in many cases fully attenuating the transmitted radar signal.  

\end{preface}
\chapter{Introduction}
\label{intro}
\input{intro}
\chapter{Background}
\label{back}
\input{background}
\chapter{Tornado Damage Estimation Using Polarimetric Radar}
\label{tds_param}
\input{tds_parameters}
\chapter{Dual-Wavelength Observations of Tornadic Debris Signatures}
\label{dualwave}
\input{dual_wave}
%\chapter{Dual-Doppler Analysis of 10 May 2010 Supercells}
%\label{dualDop}
%\input{dual_Dop}
\chapter{Numerical Simulations of Tornadic Debris Using A Large-Eddy Simulation Model}
\label{model}
\input{LES}
\chapter{Conclusions and Recommendations For Future Work}
\label{conc}
\input{conclusions}
%
%\references{agsm}{myreferences}

\newpage
\references{ametsoc}{bodine}
%comment out the next four lines if you don't have an appendix
%\appendix
%\chapter{A Long Proof}
%\OUdoublespace
%\input{appex}

\appendix
\chapter{Large-Eddy Simulation}
\label{LES_overview}
\OUdoublespace
\input{LES_overview}
%\chapter{Symbols}
%\label{symbols}
%\OUdoublespace
%\input{symbols_new}
%\listofsymbols
%\listofacronym
\chapter{List of Acronyms}
\label{acronyms}
\OUdoublespace
\input{acronyms}

\newpage
\chapter{List of Symbols} %\addcontentsline{toc}{chapter}{Appendix C}
\listofsymbols

\newpage    % Need this to get the page number correct in the TOC
\addcontentsline{toc}{chapter}{{\indexname}}
\printindex

\end{document}
