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Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6* x 9* black arxf white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. Bell & Howell Information and Learning 300 North Zfteb Road, Ann Arbor, Ml 48106-1346 USA UMI 800-521-0600 UNIVERSITY OF OKLAHOMA GRADUATE COLLEGE A PSEUDO-DUAL-DOPPLER ANALYSIS OF CYCLIC TORNADOGENESIS A Dissertation SUBMITTED TO THE GRADUATE FACULTY in partial fulfillment of the requirements for the degree of Doctor of Philosophy By DAVID C. DOWELL Norman, Oklahoma 2000 UMI Number 9956999 UMI UMI Microform9956999 Copyright 2000 by Bell & Howell Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. Bell & Howell Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 A PSEUDO-DUAL-DOPPLER ANALYSIS OF CYCLIC TORNADOGENESIS A Dissertation APPROVED FOR THE SCHOOL OF METEOROLOGY BY — n r ? # : / g r r . U l © Copyright by DAVID C. DOWELL 2000 All Rights Reserved. ACKNOWLEDGMENTS Many helpful comments on this research were provided by my doctoral committee: John Albert, Howie Bluestein, David Jorgensen, Doug Lilly, Alan Shapiro, and Morris Weisman. Most of all, I would like to thank Howie for his input and support throughout my graduate program. This research was funded by National Science Foundation grant ATM-9612674. Contributions from many others also made this study possible. I am grateful to the following individuals; Wen-Chau Lee for providing the ELDORA data and answering many questions about airborne radar, Susan Stringer (and Wen-Chau Lee) for providing the GRJD2PS graphics software, Michelle Case and Dick Oye for answering questions about the REORDER objective analysis software, Erik Rasmussen for leading the VORTEX field program and motivating careful analysis of the data that were collected, Roger Wakimoto for directing the aircraft operations. Josh Wurman for leading the Doppler on Wheels project, Jerry Straka and Erik Rasmussen for designing and coordinating the mobile mesonets, all other VORTEX participants for their efforts during the project, Mike Magsig for providing WSR-88D data and adding insightful comments on the 8 June 1995 case, Frank Gallagher for scanning images, John Mewes for providing comments on dual-Doppler analysis methods, Ed Adlerman for offering helpful comments on cyclic tomadogenesis, Bruce Haynie for contributing video and photographic documentation of the McLean storm, and Herb Stein, Cristina Kauftnan, Tim Marshall, Dave Ewoldt, and Scott Richardson for providing other documentation of the storm. This work would not have been possible without the computer assistance of Tom Condo and Mark Laufersweiler at OU. For the test-case numerical simulations, the National Center for Atmospheric Research (NCAR) provided computer time on a Cray. NCAR is sponsored by the National Science Foundation. Last but not least, I want to thank Mom, Dad, Don, and Darren for their support throughout my days as a graduate student. IV TABLE OF CONTENTS Page Abstract vii 1. INTRODUCTION 1 2. PSEUDO-DUAL-DOPPLER ANALYSIS METHDOLOGY 6 2.1 Background 6 2.2 Test Cases 16 2.3 Strong Constraint Dual-Doppler Analysis Scheme 20 2.3.1 Formulation 20 2.3.2 Tests 28 2.4 Weak Constraint Dual-Doppler Analysis Scheme 30 2.4.1 Formulation 30 2.4.2 Tests 36 2.5 Reference Frame 38 2.5.1 Formulation for Moving Radars 38 2.5.2 Non-uniform Moving Reference Frame 43 2.5.3 Tests 44 2.6 Incorporation of Time Derivatives 47 2.6.1 Formulation 47 2.6.2 Tests 52 2.7 Application of Analysis Methodology to Real Data 53 3. McLEAN, TEXAS STORM 58 3.1 Reflectivity Features 58 3.2 Tornado Formation, Maintenance, and Dissipation 60 3.2.1 Background 60 3.2.2 Pre-Tomadic and Tomadic Stages 70 3.2.3 Steady Phase (Tornado #4) 81 3.2.4 Tornado Dissipation 83 3.3 Cyclic Tomadogenesis 85 3.3.1 Background 85 3.3.2 Hypothesis for the Cyclic Process 91 4. CONCLUSIONS 99 4.1 Summary 99 4.2 Future Work 102 REFERENCES 105 APPENDIX A. Processing of Raw ELDORA Data 116 APPENDIX B. Stability of an Iterative Dual-Doppler Analysis 119 APPENDIX C. Relationship between Reflectivity and Fall Speed 125 APPENDIX D. Least Squares Interpolator 128 APPENDIX E. Limitations of Doppler Observations of Tornadoes 130 TABLES 134 FIGURES 147 VI ABSTRACT Several tomadic storms formed in the Texas Panhandle on 8 June 1995, the date of the last mission of VORTEX (Verification of the Origins of Rotation in Tornadoes Experiment). The southernmost storm in this severe weather outbreak produced a family of at least five tornadoes near the town of McLean. Airborne Doppler radar scans of this storm by the ELDORA (ELectra DOppler RAdar) offer the most detailed look to date at a storm producing a family of tornadoes. The goals of this study were twofold. The first was to determine a pseudo-dual- Doppler wind synthesis method in Cartesian coordinates appropriate for the analysis of the ELDORA data. Unique aspects of this part of the study include a comparison of wind synthesis methods based on variational formulations and the use of a non-uniform moving reference frame for the syntheses. A dual-Doppler formulation in which the radial velocity and continuity equations are all satisfied as weak constraints (Gamache 1997, Shapiro and Mewes 1999) yields a more accurate wind field than traditional (and variational) methods in which the radial velocity equations are satisfied exactly. The second goal of this study was to diagnose both the cyclic process and the formation of individual tornadoes. The McLean storm produced three large tornadoes at 18 min intervals. The last of these then lasted much longer (over one hour) and was stronger than the previous tornadoes. New pre-tomadic vortices formed on the east side of the updrafi by tilting of strong environmental low-level horizontal vorticity into the vertical and then stretching of the vertical vorticity within the updrafi. The vortices did not mature at low levels until they migrated to the west side of the updrafi. Indirect evidence indicates that both baroclinie generation of horizontal vorticity and the rear downdraft may have played roles in tornado formation at this stage. The tomadic potential of a storm appears to be related to the relative strength of low-level storm outflow and inflow beneath the west side of updrafi. Cyclic tomadogenesis modes may be possible both when the inflow slightly dominates and when the outflow slightly dominates. The description of an inflow-dominated cyclic mode like that observed in the McLean storm is original. Intemal cell interactions within VII the McLean storm appear to have helped the transition from the cyclic phase to a more steady phase. VIII 1. INTRODUCTION An individual supercell thunderstorm that is capable of producing a tornado is often capable of producing a series of tornadoes. This is especially true during tornado outbreaks, in which the tornadoes tend to be organized into famililes of many tornadoes produced by individual storms (Fujita et al. 1970, Fujita 1974) (Figure 1 .1). Doswell and Burgess (1988) argue that some of the very long swaths of tornado damage thought originally to have been produced by single long-track tornadoes were more likely the result of tornado families. Individual tornadoes within a family often overlap in lifetime with the previous tornado (e.g.. Fig. 1.2) such that damage may be continuous in time and nearly continuous in space along the surface. Previous documentation of cyclic tomadogenesis (that is, the formation of a succession of tornadoes in a single storm) is mostly in the form of single-Doppler observations (Burgess et al. 1982) and visual observations (photographs, videos, and surveys of tornado tracks) (e.g., Fujita et al. 1970, Rasmussen et al. 1982, Jensen et al. 1983, Davies et al. 1994). Multiple-Doppler observations capable of resolving the 3D wind field in cyclic storms have been very limited. Perhaps the best case was the Fort Cobb, Oklahoma storm o f 20 May 1977 (Johnson et al. 1987). In this case, however, the tornadoes were -60 km from one of the two radars, and there was a gap of 20 min between dual-Doppler volumes during the most critical stage (Ray et al. 1981, Johnson et al. 1987). The quality of Doppler observations of cyclic tomadogenesis improved dramatically in 1995 with the use o f airbome Doppler radar in a tomado field program. One of the primary motivations for the development of airbome Doppler radar was the study of hurricanes (Marks and Houze 1984, 1987; Jorgensen and Marks 1984). Since hurricanes and other tropical precipitating systems are often far away from land- based radars along coastlines, the advantage of the moving airbome platform is obvious.