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THE GEOGRAPHY of CLOUD-TO-GROUND LIGHTNING in YELLOWSTONE NATIONAL PARK By

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THE GEOGRAPHY of CLOUD-TO-GROUND LIGHTNING in YELLOWSTONE NATIONAL PARK By THE GEOGRAPHY OF CLOUD-TO-GROUND LIGHTNING IN YELLOWSTONE NATIONAL PARK by Ed Amrhein A Thesis Submitted to the Graduate Faculty of George Mason University in Partial Fulfillment of The Requirements for the Degree of Master of Science Geography and Geoinformation Science Committee: Dr. Paul Delamater, Thesis Director Dr. Timothy Leslie, Committee Member Dr. Paul Houser, Committee Member Dr. Anthony Stefanidis, Department Chair Dr. Donna M. Fox, Associate Dean, Office of Student Affairs & Special Programs, College of Science Dr. Peggy Agouris, Dean, College of Science Date: Fall Semester 2016 George Mason University Fairfax, VA The Geography of Cloud-To-Ground Lightning in Yellowstone National Park A Thesis submitted in partial fulfillment of the requirements for the degree of Master of Science at George Mason University by Ed Amrhein Master of Science Texas A&M University, 2001 Bachelor of Science Texas A&M University, 1999 Director: Paul Delamater, Professor Department of Geography and Geoinformation Science Fall Semester 2016 George Mason University Fairfax, VA This work is licensed under a creative commons attribution-noderivs 3.0 unported license. ii DEDICATION To the Spirit of Yellowstone iii ACKNOWLEDGEMENTS Very few things in life can be accomplished alone, especially a task such as a Master’s thesis. This thesis could not have been accomplished without the love, help, support and encouragement of several people. First I would like to express my deepest gratitude to my thesis advisor Dr. Paul Delamater for his willingness and eagerness in mentoring me during this process. He showed a deep and genuine interest in my research and was a great source of motivation. His leadership and extensive knowledge contributed greatly to the success of this research. I would also like to express my gratitude to my committee members Dr. Timothy Leslie and Dr. Paul Houser for their support and instrumental comments which enhanced this research. I’m also thankful for Melissa Hayes who helped me navigate the extension process and obtain the approvals for me to continue and complete my work. I am also indebted to my fellow Airman at the U.S. Air Force’s 14th Weather Squadron and to Vaisala for graciously providing the lightning data used to complete this research. I am also grateful to have an extensive team of coworkers and close friends who were extremely supportive during this process: Rita, Mike, Chris, Leanna, Jason, Beth, Neal, Tim, and Brian. Furthermore, I could not have accomplished this goal without the love and encouragement of my parents and my daughter Tara who sacrificed a lot of family time so that I may continue my studies and complete this research. Finally, I owe a special thanks to my beautiful bride Cyndy who has faithfully stood by me through 27 years of marriage that included 24 years of faithful service to our country while in the Air Force, one Bachelor’s degree, and now two Masters degrees. She’s always been extremely supportive allowing me to successfully reach my goals. iv TABLE OF CONTENTS Page List of Tables .................................................................................................................... vii List of Figures .................................................................................................................... ix List of Equations ................................................................................................................ xi List of Abbreviations ........................................................................................................ xii Abstract ............................................................................................................................ xiii 1. INTRODUCTION .......................................................................................................... 1 2. LITERATURE REVIEW ............................................................................................... 5 2.1 The Lightning Flash ................................................................................................. 5 2.2 Lightning Detection and Measurement .................................................................... 6 2.3 Lightning Studies ..................................................................................................... 7 2.4 Lightning Ignited Wildfire Studies ........................................................................ 10 2.5 GIS Applications .................................................................................................... 13 3. STUDY AREA ............................................................................................................. 18 4. DATA ........................................................................................................................... 23 4.1 Lightning Data........................................................................................................ 23 4.2 Terrain Data............................................................................................................ 27 4.3 National Land Cover Data...................................................................................... 27 5. ANALYSIS METHODOLOGY ................................................................................... 29 5.1 Visualizing the Spatial Pattern of CG Lightning Events........................................ 30 5.1.1 CG Lightning Event Maps ............................................................................... 30 5.1.2 CG Lightning Flash Density Maps .................................................................. 31 5.2 Temporal Analysis of CG Lightning Activity........................................................ 33 5.3 Testing the Spatial Pattern of CG Lightning Activity for Clusters ........................ 33 5.3.1 Nearest Neighbor and K-order Nearest Neighbor Analysis ............................ 33 5.3.2 Getis-Ord General G Statistic (High/Low Clustering) .................................... 36 5.3.3 Global Moran’s I (Spatial Autocorrelation) .................................................... 37 5.3.4 Ripley’s K (Multi-Distance Spatial Cluster Analysis) .................................... 38 * 5.3.5 Getis-Ord Gi (Hot Spot Analysis) .................................................................. 39 5.3.6 Anselin’s Local Moran’s I (Cluster and Outlier Analysis).............................. 40 v 5.4 Analyzing the CG Lightning-Topography Relationship ........................................ 42 6. RESULTS AND DISCUSSION ................................................................................... 45 6.1 Visualizing the Spatial Pattern and Analyzing for Global Clustering ................... 45 6.1.1 CG Lightning Event Maps ............................................................................... 45 6.1.2 CG Lightning Flash Density Maps .................................................................. 51 6.1.3 Global Spatial Autocorrelation ........................................................................ 59 6.2 Temporal Analysis ................................................................................................. 83 6.3 Analyzing the Spatial Pattern for Local Clustering ............................................... 86 * 6.3.1 Getis-Ord Gi (Hot Spot Analysis) .................................................................. 87 6.3.2 Anselin Local Moran’s I (Cluster and Outlier Analysis) ................................ 94 6.4 Analyzing the Relationship Between CG Lightning and Topography ................ 101 7. FUTURE RESEARCH ............................................................................................... 110 8. SUMMARY ................................................................................................................ 114 References ....................................................................................................................... 122 Biography ........................................................................................................................ 132 vi LIST OF TABLES Table Page Table 1. Table summarizing the spatial statistics used to test for global clustering of CG lightning. ........................................................................................................................... 59 Table 2. Table of Nearest Neighbor Index (NNI) values for lightning point event data collected between 1995 and 2004 and aggregated by month. Columns labeled as “Observed” and “Expected” refer to distance (m) between point events, “N” is the number of point events and “C/R/D” indicates whether the point pattern is considered as clustered, dispersed, or random. The row labeled “All” shows the results when applying nearest neighbor analysis to the entire 10-year dataset as a whole. .................................. 61 Table 3. Table of Nearest Neighbor Index (NNI) values for lightning point event data collected between 1995 and 2004 and aggregated by hour (UTC). Columns labeled as “Observed” and “Expected” refer to distance between point events, “N” is the number of point events and “C/R/D” indicates whether the point pattern is considered as clustered, dispersed, or random. The row labeled “All” shows the results when applying nearest neighbor analysis to the entire 10-year dataset as a whole. .............................................. 62 Table 4. Summary results of K-order Nearest Neighbor analysis for the monthly data. N is the total number of events. K is the Kth nearest neighbor
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