DEVELOPMENT AND CALIBRATION OF CENTRAL PRESSURE FILLING RATE MODELS FOR HURRICANE SIMULATION A Thesis Presented to the Graduate School of Clemson University In Partial Fulfillment of the Requirements for the Degree Master of Science Civil Engineering by Fangqian Liu May 2012 Accepted by: WeiChiang Pang, Committee Chair Scott Schiff Bryant Nielson ABSTRACT This study presents the development of a new central pressure filling rate model to characterize the rate at which hurricanes or tropical storms decay after landfall. It has been shown that the post landfall decay rate of hurricanes is closely related to the time after landfall, the size of hurricane and proximity of the hurricane eye to the coastline. In addition, it has been observed that the decay rates of hurricanes are geographically dependent. Based on these observations, a set of simple empirical models expressed in terms of exponential and linear equations are utilized to characterize the decay rate of hurricanes after landfall. The filling rate model, which consists of a set of empirical equations, is organized according to the geographic region, the storm heading direction and proximity of the hurricane eye to the coastline. To account for the influence of the land terrain on the decay rate of hurricanes, the North American continent is divided into seven regions: Gulf Coast, Florida, East Coast and Northeast Coast, Great Lakes, Inland and Mexico area. A new along-shore hurricane decay model is introduced to account for the decay rate of hurricanes traveling along the coastline and with the hurricane eye relatively close to the coastline. In the new filling rate model, modeling parameters are determined through regression analysis using the hurricane database (HURDAT) maintained by the National Hurricane Center for hurricane records from 1975 to 2011 (HRD 2012a). Based on the results of the regression analysis, it has been shown that the modeling uncertainty (or error term), which is defined as the difference between the model predicted and the ii actual observed decay rates, can be characterized using the unbounded Johnson distribution. The new model is benchmarked against two current state-of-the-art models by comparing the simulated central pressures for historical hurricane events to that of the actual observations in HURDAT. The benchmark study has shown that the simulated results using the new decay model are generally more accurate and match reasonably well with the actual central pressures of historical storm events. The new decay model has been coded into a Matlab program and the codes are provided herein with this manuscript. The new decay model and the computer codes can be implemented into a stochastic hurricane simulation framework for long-term hurricane risk assessment or hurricane hazard mapping. iii DEDICATION I would like to dedicate this study to my parents, Mr. Honglin Liu and Mrs. Fang Sun. iv ACKNOWLEDGMENTS I would like to attribute my accomplishment of this study to my advisor Dr. Weichiang Pang for his instructions, patience and professional spirit that encourage me to be a graduate student. Also, I appreciate the help from my committee members Dr. Scott Schiff and Dr. Bryant Nielson, not only for their work on this thesis but also for everything they did in research and coursework through my two and half year in Clemson University. Since the great patience and care that they have given to Chinese students like me, it did not take long for me to conquer the first few of months in U.S. and start the regular graduate student life. I would like to thank my dear friends and colleagues Masood Hassanzadeh, Michael Grayson Bin Pei and Mengyu Yang for their helps on my research and courses. The communications among us keep encourage me to bravely face the difficulties in my studies. Finally, I would like to present special thanks to Dr. Hui Wu from Beijing Institute of Architecture and Civil Engineering who encouraged me to study in U.S, for his trust and devotion on his students. v SPONSOR This manuscript was prepared in part as a result of work sponsored by the S.C. Sea Grant Consortium with NOAA financial assistance award NA10OAR4170073. The statements, findings, conclusions, and recommendations are those of the author and do not necessarily reflect the views of the South Carolina Sea Grant Consortium, or NOAA. vi TABLE OF CONTENTS Page TITLE PAGE .................................................................................................................... i ABSTRACT ..................................................................................................................... ii DEDICATION ................................................................................................................ iv ACKNOWLEDGMENTS ............................................................................................... v LIST OF TABLES .......................................................................................................... ix LIST OF FIGURES ......................................................................................................... x CHAPTER I. INTRODUCTION ......................................................................................... 1 II. BACKGROUND ........................................................................................... 4 Hurricane Characteristics ......................................................................... 4 Stochastic Hurricane Model ..................................................................... 9 Previous Studies of Central Pressure Deficit Decay Models ........................................................................ 21 III. MODEL FORMULATION ......................................................................... 28 Model Outline ........................................................................................ 29 Division of Coastal and Inland Regions ................................................ 30 Landfalling Model for Gulf Coast, East Coast, Northeast Coast and Mexico .............................................................. 31 Least-square Fitting of Filling Rate for Each Storm (ai) ....................... 33 Least-square Fitting of Regional Decay Rate (ao) ................................. 36 Filling Rate Modeling Error................................................................... 42 Parameters Estimation for Johnson System Distribution .............................................................. 47 Exiting Model ........................................................................................ 49 Florida Model......................................................................................... 56 Along-shore Model ................................................................................ 60 Inland Model .......................................................................................... 64 Great Lakes Model ................................................................................. 69 vii Table of Contents (Continued) Page Summary of New Filling Rate Model ................................................... 72 IV. MODEL BENCHMARKING ...................................................................... 75 Pc Errors of Coastal Regions .................................................................. 77 Pc Errors of Inland and Great Lakes Regions ........................................ 89 Pc Errors of Along-shore and Exiting Storms ........................................ 94 Summary of Model Benchmark Results ................................................ 99 V. CONCLUSION AND RECOMMENDATIONS ...................................... 102 Summary and Conclusion .................................................................... 102 Recommendations for Future Work..................................................... 103 APPENDICES ............................................................................................................. 104 A: Flow-chart of application procedure for multi-region and scenario Pc decay model ....................................... 105 B: Storms landfall information used in derivation of regions and scenarios models ...................................................... 106 C: Hurricane central pressure simulation Matlab code ........................ 115 REFERENCES ............................................................................................................ 126 viii LIST OF TABLES Table Page 1 Saffir-Simpson hurricane scale. ..................................................................... 5 2 Parameters for event-based hurricane model (Huang et al. 2001). ............................................................................... 13 3 Decay constant a and regression parameters (Vickery 2005). ...................................................................................... 27 4 Summary of current central pressure deficit decay models. ........................ 28 5 Outline of the new hurricane central pressure deficit decay model...................................................................................................... 29 6 Classification of decay model. ..................................................................... 72 7 Formulation and filling rate parameters of new decay models. ................................................................................................... 73 8 Distribution parameters for decay rate error. ............................................... 74 9 Summary of central pressure