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MEASUREMENT, MODELING AND SIMULATION OF GROUNDLEVEL TROPICAL CYCLONE WINDS By FORREST JAMES MASTERS A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2004 Copyright 2004 by Forrest James Masters ACKNOWLEDGMENTS Kurtis Gurley, Luis Aponte, Gary Consolazio, Jennifer Jacobs, Perry Green, Lou Cattafesta, Tim Reinhold, Scott Robinette, Jon Lamb, Cos Gardener, Greg Kopp, Mark Powell, Eric Ho and Peter Vickery deeply deserve my gratitude. Only with their gracious support did this document make its way into your hands. TABLE OF CONTENTS Page A C K N O W L E D G M E N T S ......... .................................................................................... iii LIST OF TABLES ............................... ............. .................. vii LIST OF FIGURES ...................................................... ................... viii A B S T R A C T .......................................... ..................................................x iii CHAPTER 1 IN TR OD U CTION ............................................... .. ......................... .. The Hurricane W ind to Dam age Chain ............................................. ............... 1 R research U nderw ay ........................................................................... .............. ...2 Florida Coastal M monitoring Program ................................. ....................... 3 Hurricane Loss Reduction Project..................................................................... 4 Scope of Research.............................. ........5 2 HURRICANE DAMAGE MITIGATION RESEARCH ................... ................. Sources of W ind Speed D ata ......... ................. ........................................................6 Use of Permanent Instrumented Towers ..................... .......... ...... ......9 Use of Portable Instrumented Towers ......... .............. ..................... 10 Current Wind Load Design Provisions and Standards ............................................18 American Society of Civil Engineer's Minimum Design Loads for Buildings and Other Structures (A SCE 702) ...................................... ............... 18 Applicability of the Current Standard ......................... .......................20 ReliabilityBased DatabaseAssisted Design .................................. ............... 22 Sum m ary .............................. ................... .......................... 25 3 ANALYSIS AND SIMULATION TECHNIQUES FOR WIND...........................27 Characterization of GroundLevel Hurricane Winds ...............................................27 M ean V elocity P rofile .............................................................. .....................2 8 Turbulence Characteristics ............................................................................ 32 E stim ation of R oughness .......................................................... ............... 37 Correlation and Spectral Relations ....................................... ...............39 Stochastic Sim ulation M ethods ............................................................................ 42 Spectral R presentation ......................................................... ..................... 43 Random Variable Transformation.................... ..... ......................... 44 Existing Simulation Techniques................................................... ................. 46 Spectral Correction ........ ................................ ...... ..... .... ... ........ .... 53 Application of Simulation for the NIST Project: Interpolation of Existing Tim e H istories.............................................. 58 S u m m a ry ................................ ................................................................5 8 4 FULLSCALE MEASUREMENT OF TROPICAL CYLONE WINDS ...................60 Deployment History, Organization and Logistics ............... ................... ...........60 Ire n e ( 1 9 9 9 ) ................................................................................................6 1 G abrielle (2001)................................................... 62 Isid o re (2 0 0 2 ) ................................................................6 2 L ili (2 0 0 2 ) ...................................................................................................... 6 3 Isab e l (2 0 0 3 ) .................................................................................................. 6 5 Satellite Tow er System ................................................................. ......... 68 RealTime Data Acquisition ................................. .......................... ....... 71 Internet Upload Capability ................. ................................73 Continuous D ata A acquisition ................................... ...... ............... 74 Automated Processing of Data ...................................................74 Im proved Graphical Interface............................... ................... 75 Im proved Flexibility ...................................... .......... ..............................77 Outcomes of Hurricane Isabel .............................. ....... .....................77 Impact on Meteorology .................................................. 77 Impact on Emergency Management ................................80 Su m m ary ....................................................................................................... 8 1 5 ANALYSES OF TROPICAL CYCLONE WIND DATA .........................................86 E xperim ental A ssum options ................... ...................8...................7.......... Concerning the Hurricane Boundary Layer ................. ................. ....87 Concerning Experim mental Rigor ................ .................. ................ ............. 88 Concerning the Homogeneity and Flatness of Upwind Terrain ..........................88 D ata R e d u ctio n ..................................................................................................... 9 1 D ata A n aly ses ...............................92.............................. T u rbu len ce Inten sities ................................................................................... 93 Comparison to Known Gust Factor Curves...........................95 Formulation of Gust Factor Curves based on a 10Minute Wind Speed for Varying Gust Durations and Roughness Lengths .................... .................104 Integral Length Scales ................................. .......................... ....... 109 Spectral M models ......................................................... .............. .. 111 Sum m ary ............... .. ................................................................................. .....113 6 MULTIVARIATE STOCHASTIC SIMULATION OF WIND PRESSURE OVER LOW RISE STRUCTURES ...................................... ................................115 M methodology ........................................................................................... 117 v O v erv iew .......................................1...................1.........7 W ind Tunnel D ata Sets.............................................. ............................ 118 C a se s S tu d ie d ............................................................................................... 1 1 9 Interpolation Overview................................................. 120 Interpolation of the Probability Targets ...................................................120 Validation of CDF Interpolation Concept ............................... 121 Interpolation of the Spectral Targets ........................................... ......... .......124 Validation and Limitations of the Simulation Algorithm .............................126 Accuracy of the Simulation Algorithm .................................. ............... 127 R results .................................... .................................... ................. 129 Com prison of Peak A ggregate U plift .............................................................129 Su m m ary ...................................... ....................................................136 7 CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE RESEARCH.... 137 Contributions to FullScale Measurement Research ...............................................137 Recommendations for Future FullScale Measurement Research.........................139 W wireless D ata Acquisition.................................................................... 139 R oughness E stim ation ................................................ ........................... 140 Dissemination of RealTime Data.....................................................142 Contributions to Stochastic Simulation Research................................ ...............144 Recommendations for Future Stochastic Simulation Research.............................145 APPENDIX A F C M P D A T A B A SE ...................................................................... ..................... 147 B AERIAL IMAGERY OF TOWER SITES ........................................................158 C RESULTS FROM PRESSURE TAP SIMULATION OF UWO WIND TU NN EL D A TA ............................................................ .. ........ .... 169 LIST OF REFEREN CES ........................................................... .. ............... 182 BIOGRAPHICAL SKETCH ........................................................... ........189 LIST OF TABLES Table pge 31. C alculated D urst gust factors.......................................................... ............... 35 32. Longitudinal turbulence PSD models............................................................43 51. Sum m ary of data reduction results ........................................ ........................ 92 53. Turbulence intensity com parison........................................ ........................... 95 54. Standard deviate, departure standard deviations, and gust factors........................100 55. Coefficients for the proposed gust factor curve .................................................... 107 56. Longitudinal integral length scales (m) for 10minute records ..............................110 61. Sim ulation test m atrix ........................................... ....................................... 120 LIST OF FIGURES Figure pge 21. W weather stations (courtesy of NOAA) ............................................. ............... 7 22. T exas T ech W E M IT E ............................................................................... .............12 23. The FCM P instrum ented tower .............................. ..................................13 24. Location of FCMP homes instrumented to measure wind pressure........................ 16 25. FCMP instrumented homes: A) Sensor installation just before Hurricane Isabel and B) Prewiring of a south Florida home ............................. ..... ...........17 31. The decomposition of an instantaneous wind velocity profile..............................28 32. Gust factor curves as a function of gust duration t based on an hourly mean wind sp e e d T .............................................................................................................. 3 3 33 C orrelation D istortion ........................................................................ ..................47 34. Yamazaki and Shinozuka univariate stochastic simulation technique...................49 35 Grigoriu univariate stochastic simulation technique ...............................................50 36. Shinozuka and Deodatis correlated nonGaussian multivariate stochastic sim ulation technique ...................... ................ ................. ..... ...... 54 41. Deployment of instrumented towers during Tropical Storm Isidore (2002)............63 43. Deployment map for Hurricane Isabel .................. ......... ...................68 44. Tower deployment and transportation..................... .... ......................... 69 45. Satellite tow er stabilization ............................................... ............................ 70 46. Satellite tower instrumentation and safety considerations .....................................71 47. Computer enclosure for remote transmission of FCMP data..................................72 48. Configuration of Tower XP user interface to set up data collection .......................76 49. Hurricane Research Division surface wind field analysis (courtesy of NOAA).......83 410. Track of NOAA research aircraft in Coastal Mission 20030918H1 during Isabel 2003 (courtesy of N OA A)......................................................... ............... 84 411. GPS sonde splash locations during Isabel 2003 (courtesy of NOAA) ..................84 412. Wind swath map from FEMA's HAZUS program, based on the NOAA H*WIND model using FCMP data (courtesy of Applied Research A sso ciate s, In c .) .................................................................... 8 5 51. Fetch requirements to determine the roughness length in a homogenous terrain at an observation height of 10 m ................................................... ..................90 52. Convergence of the longitudinal turbulence intensity over increasing averaging tim es (FC M P database) ................................................. ............................... 94 53. Ratios of vertical turbulence intensities to longitudinal and lateral turbulence intensities .......... ..... .. .................... ......... ....... .. ..... ........... 96 54. Gust Factors based on a 10minute mean wind speed......................................101 55. Mean and 5% / 95% quantile gust factors based on a 10minute wind speed.........102 56. Gust Factors based on a 1hour mean wind speed..........................................103 57. Linear regression of gust factor vs. longitudinal turbulence intensity over a variety of gust durations ........................................................................ 106 58. Rational polynomial fits to slope a, and zintercept ao .......................................107 59. Exponential fit to beta curve......................................................... ............... 107 510. Proposed gust factor relationship based on a 10minute wind speed, roughness length and gust duration ............. .................. ................................................... 108 511. Spectral analysis of tropical cyclone data ..................... ....................113 61 Tap geometry on the building model ......... ............... ............. .. ...............119 62. PDF interpolation of 24 ft eave height for a single tap (winds parallel to the rid g e lin e ) ........................................................................ 12 2 63. PDF interpolation of 24 ft eave height for a single tap (cornering winds)............123 64. PDF interpolation of 24 ft eave height for a single tap (winds perpendicular to th e rid g elin e) ..................................................................... 12 3 65. Experim ental pressure tap data..................................................................... ..... 130 67. Comparison of the target and simulated spectral matrices for one realization of H = 24 ft and a = 180 ............................................. ................................... 132 71. Aerial imagery of the Tower T3 deployment site in Isabel................................ 141 72. Wind speed, wind direction and turbulence intensity measured by Tower T3 in H hurricane Isabel ................................... ... .. .......... .............. .. 141 A1. Velocity and turbulence intensity records from Tower TO in Hurricane Isabel at Elizabeth City, North Carolina................. ...................................148 A2. Velocity and turbulence intensity records from Tower T1 in Hurricane Isabel at W ilm ington, N orth Carolina ............................................................................ 149 A3. Velocity and turbulence intensity records from Tower T2 in Hurricane Isabel at Atlantic Beach, North Carolina.................................. ......... ........ ....... 150 A4. Velocity and turbulence intensity records from Tower T3 in Hurricane Isabel at Frisco, N north C arolina ........................................................................... 151 A5. Velocity and turbulence intensity records from Tower TO in Hurricane Lili at L afayette, Louisiana ............................................... .... .... ... ........ .. .. 152 A6. Velocity and turbulence intensity records from Tower T3 in Hurricane Lili at Lydia, L o u isian a ......... ............................................... ..................................... 15 3 A7. Velocity and turbulence intensity records from Tower TO in Tropical Storm Isidore at M ary Esther, Florida ........................................ ......................... 154 A8. Velocity and turbulence intensity records from Tower T2 in Tropical Storm Isidore at G ulf B reeze, Florida......... ................. .......................... ............... 155 A9. Velocity and turbulence intensity records from Tower T1 in Tropical Storm G abrielle at V enice B each, Florida ............................................. ............... 156 A10. Velocity and turbulence intensity records from Tower T1 in Tropical Storm Irene at M elbourne Beach, Florida................................. .......................... 157 B1. Aerial Imagery of the terrain surrounding Tower TO in Hurricane Isabel at Elizabeth City, N orth Carolina..................................... ............................ ........ 159 B2. Aerial Imagery of the terrain surrounding Tower T1 in Hurricane Isabel at W ilm ington, N orth Carolina ............................................................................ 160 B3. Aerial Imagery of the terrain surrounding Tower T2 in Hurricane Isabel at A tlantic B each, N orth C arolina.................................... ............................. ....... 161 B4. Aerial Imagery of the terrain surrounding Tower T3 in Hurricane Isabel at Frisco, N north C arolina ........................................................................... 162 B5. Aerial Imagery of the terrain surrounding Tower TO in Hurricane Lili at L afay ette, L ouisiana .................................................................. .................. 163 B6. Aerial Imagery of the terrain surrounding Tower T3 in Hurricane Lili at Lydia, L ouisiana ....................................................................... ....... ....... 164 B7. Aerial Imagery of the terrain surrounding Tower TO in Tropical Storm Isidore at M ary E sther, Florida................................................ ............................... 165 B8. Aerial Imagery of the terrain surrounding Tower T2 in Tropical Storm Isidore at G ulf B reeze, Florida ............. ..... ....... .............. ..... ...... .. ........ .... 166 B9. Aerial Imagery of the terrain surrounding Tower T1 in Tropical Storm Gabrielle at V enice B each, Florida .................................................................................. 167 B10. Aerial Imagery of the terrain surrounding Tower T1 in Tropical Storm Irene at M elbourne B each, Florida............................................. ............................. 168 C1. Comparison of direct and interpolated simulated peak aggregate uplifts to wind tunnel data and simple averaging for winds parallel to the ridgeline on a 125 X 80 ft gable end building with a 24 ft eave height ............ ...................170 C2. Comparison of direct and interpolated simulated peak aggregate uplifts to wind tunnel data and simple averaging for cornering winds on a 125 X 80 ft gable end building with a 24 ft eave height ............... .... .... ................. 171 C3. Comparison of direct and interpolated simulated peak aggregate uplifts to wind tunnel data and simple averaging for winds perpendicular to the ridgeline on a 125 X 80 ft gable end building with a 24 ft eave height ...................................172 C4. Comparison of direct and interpolated simulated peak aggregate uplifts to wind tunnel data and simple averaging for winds parallel to the ridgeline on a 125 X 80 ft gable end building with a 24 ft eave height ............ ...................173 C5. Comparison of direct and interpolated simulated peak aggregate uplifts to wind tunnel data and simple averaging for cornering winds on a 125 X 80 ft gable end building with a 24 ft eave height ............... .... .... ................. 174 C6. Comparison of direct and interpolated simulated peak aggregate uplifts to wind tunnel data and simple averaging for winds perpendicular to the ridgeline on a 125 X 80 ft gable end building with a 24 ft eave height ............ ...................175 C7. Comparison of direct and interpolated simulated peak aggregate uplifts to wind tunnel data and simple averaging for winds parallel to the ridgeline on a 125 X 80 ft gable end building with a 32 ft eave height ............ ...................176 C8. Comparison of direct and interpolated simulated peak aggregate uplifts to wind tunnel data and simple averaging for cornering winds on a 125 X 80 ft gable end building with a 32 ft eave height .......................... .. .. ............. .... 177 C9. Comparison of direct and interpolated simulated peak aggregate uplifts to wind tunnel data and simple averaging for winds perpendicular to the ridgeline on a 125 X 80 ft gable end building with a 32 ft eave height ............ ...................178 C10. Comparison of direct and interpolated simulated peak aggregate uplifts to wind tunnel data and simple averaging for winds parallel to the ridgeline on a 125 X 80 ft gable end building with a 32 ft eave height ...............................179 C11. Comparison of direct and interpolated simulated peak aggregate uplifts to wind tunnel data and simple averaging for cornering winds on a 125 X 80 ft gable end building with a 32 ft eave height ........... ..... .... ...... ......... ...............180 C12. Comparison of direct and interpolated simulated peak aggregate uplifts to wind tunnel data and simple averaging for winds perpendicular to the ridgeline on a 125 X 80 ft gable end building with a 32 ft eave height ..............................181 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy MEASUREMENT, MODELING AND SIMULATION OF GROUNDLEVEL TROPICAL CYCLONE WINDS By Forrest J. Masters August 2004 Chair: Kurtis R. Gurley Cochair: Gary R. Consolazio Major Department: Civil and Coastal Engineering Designing lowrise structures to prevail against strong winds requires a detailed understanding of the turbulence structure of the winds that impinge upon them. Knowledge of these descriptors has accumulated since the late 1800s, although most of the information was determined from data collected in winter storms and thunderstorms. Whether the turbulent behavior of tropical storms and hurricanes differ from these models remains an active subject of debate and is the focus of this dissertation. During the 19992003 Atlantic Hurricane Seasons, instrumented towers collected hundreds of hours of surfacelevel wind speed data from 29 instrumented towers in ten different named storms in Florida, North Carolina and Louisiana. From these data, the 19 records with the highest speeds were divided into 10minute segments and compiled into a database from which turbulence intensity, gust factors, integral length scales and power spectra were measured. In this dissertation, turbulence intensity ratios and longitudinal length scales are analyzed over a range of roughness regimes and wind speeds. Gust factor relationships are presented for 10minute and 1hour mean wind speeds, and a formula relating gust factors to gust duration and roughness length is developed for a 10 minute mean wind speed. From these analyses, it is shown that tropical cyclones produce gustierr" winds than extratropical data. Additionally, the use of a nonGaussian multivariate simulation algorithm to recreate aggregate pressure loading on untested building shapes is investigated. CHAPTER 1 INTRODUCTION The Hurricane Wind to Damage Chain The likelihood that another intense hurricane will strike a major population center remains high. As evidence, consider that metropolitan areas including Miami, Tampa, New Orleans and New York City will surpass their return period for hurricane landfall after 2005 (Williams 2003) and that tropical meteorologists predict that the post1994 trend of reduced wind shear and elevated ocean temperatures in the Atlantic basin will persist, increasing hurricane activity throughout the next few decades (Gray and Klotzbach 2003). In addition to increased strike probability, the rising coastal population has elevated the potential for catastrophe. Presently, over 45 million residents live in hurricane prone coastlines (Noserale 2001) and by 2010, the population of Florida is expected to grow to more than 16 million residents, which is twice its 1960 population (Hinrichsen 1999). Although the casualty rate associated with hurricane landfall has rapidly declined despite the population increase, the economic repercussion of a tropical cyclone remains staggering. According to the Insurance Information Institute, the world's most costly insurance loss from a disaster (from 19702002) occurred during Hurricane Andrew in 1992. MiamiDade County suffered an estimated $20.5 billion in insured damages (in 2002 dollars), which is commensurate to the insured losses from the terrorist attacks on the World Trade Center and the Pentagon. Eleven insurance companies emerged insolvent, and another forty withdrew or severely limited their underwriting in the state of Florida. Ten percent of the businesses in six south Florida counties closed in Andrew's aftermath (Rappaport 1993, Barnes 1998, Hartwig 2003). On a longer timeline, the destructive forces of hurricanes and other extreme wind eventsincluding tornadoes and thunderstormsis tremendous. The United States sustains an average of $6.3 billion dollars in damage from windstorms annually (Meade and Abbot 2003). Research seeking to reduce loss of life and property during extreme wind events, such as Hurricane Andrew, is conducted in the wind engineering community. Born from the Tacoma Narrows Bridge collapse in 1940, when a suspension bridge collapsed at one third of its design wind load from dynamic wind effects (Scott 2001), wind engineering has evolved from the field of industrial aerodynamics (as it was originally known in the 195060s) to a multidisciplinary research focus, working in conjunction with meteorologists, emergency managers and social scientists in addition to designers of windresistant structures, risk assessment experts and modelers of windstructure interaction. The research presented herein is a contribution to wind engineering, particularly to improve the current understanding of ground level hurricane winds and to develop the ability to simulate wind loading on lowrise structures in hurricane prone regions. This dissertation documents the measurement of tropical cyclone winds in the field during the 19992003 Atlantic hurricane seasons, presents the analyses of collected data and details computer simulation methods to recreate wind loading on lowrise structures. Research Underway Modem design of wind resistant structures relies heavily on wind tunnel testing to estimate dynamic pressure loading. The pressure loading on lowrise buildingswhich reside within the lowest 5% of the atmospheric boundary layeris deeply sensitive to the turbulence characteristics of the wind field, which in turn, is dependent on the roughness of the upwind terrain. To better understand turbulent wind fields in situ, engineering research has complemented the testing laboratory with modern techniques to measure wind fields from hurricanes and thunderstorms. Since the late 1990s, fullscale researchi.e., infield measurement to capture real environmental loading and actual structural responsehas grown significantly, providing valuable insight into surface level winds and the resultant loads on residential structures during extreme wind events. The research presented in this document is the result of two such programs involved in fullscale measurement activities: the Florida Coastal Monitoring Program (FCMP) and the National Institute of Standards and Technology (NIST) Hurricane Loss Reduction project. These projects are described below, followed by the list of original contributions discussed in detail within this dissertation. Florida Coastal Monitoring Program The FCMP, a joint venture between the University of Florida and Clemson University, focuses on fullscale experimental methods to quantify nearsurface hurricane wind behavior and the resultant loads on residential structures. Before storm landfall, portable instrumentation is deployed in the path of the cyclone. Four 10meter tower systems (capable of withstanding 90 m/s wind gusts) measure highresolution time histories of wind velocity and transmit data to a web server where meteorologists from the National Oceanic and Atmospheric Administration (NOAA) and analysts contracted by the Federal Emergency Management Agency (FEMA) ingest data into surface wind field models (H*Wind and HAZUS, respectively). Additionally, the FCMP will instrument a series of residential houses should the storm make landfall in the proximity of the 30 homes participating in the project. Collected data from an individual house include time histories of pressure at various locations on the roof, soffit, and attic as well as wind speed and direction. Chapter 2 provides greater detail concerning the tower and house experimental configurations. Chapter 4 discusses the history and logistics of FCMP deployments into tropical cyclones. Chapter 5 contains analyses of surfacelevel wind speed data collected in those deployments. Hurricane Loss Reduction Project The overarching goal of the Hurricane Loss Reduction Project is to strengthen the scientific and engineering basis for measures that reduce losses from windstorms and particularly, from hurricane events striking the United States. The consortium, composed of research teams from Clemson University (CU), Virginia Polytechnic Institute and State University, the University of Illinois at UrbanaChampaign, Johns Hopkins University and the University of Florida (UF), has established a coordinated series of research activities in four thrust areas: 1. Dependence on wind load magnitudes and distributions on wind characteristics 2. Hurricane wind loads and wind characteristics 3. Physical modeling and computer simulation of structural capacities and responses to wind loads 4. Simulation and modeling tools for databaseassisted, reliabilitybased design UF is responsible for objectives 2 and 4. The research aims of objective 2 are coincident to the goals of the FCMP, as both programs seek to characterize the ground level wind field during the landfall of tropical cyclones. Original contributions concerning objective 2 are located in Chapter 5. Contributions towards objective 4 are located in Chapter 6. Scope of Research This document provides the background of wind hazard mitigation research conducted at UF and its partnering universities. Chapter 2 documents the fullscale measurement of hurricane boundary layer winds, specifically efforts to measure surface level wind speeds and the resultant pressures on lowrise buildings during extreme wind events. The design of windresistant structures under the guidance of the American Society of Civil Engineers Minimum Design Loads for Buildings and Other Structures (ASCE 2002) and recent efforts to enhance design with reliabilitybased, database assisted design (DAD) techniques are also explored in Chapter 2. Chapter 3 covers aspects of atmospheric turbulence that are of interest to structural and wind engineers and explains the principles and methods of stochastic simulation techniques. Chapter 4 presents the history, organization and logistics of deployments and presents original contributions to fullscale measurement, namely the development of the satellite tower system and the first realtime data acquisition to transfer continuous, high frequency, digital observations to NOAA meteorologists from a U.S. landfalling hurricane. Chapter 5 presents analyses of surfacelevel wind speed data collected from the FCMP mobile instrumented towers during the 19992003 Atlantic hurricane seasons, including a new model to represent extreme departures of wind gusts from the sustained wind speed for coastal regions. Chapter 6 focuses on the use of a stochastic simulation algorithm for the generation of the pressure coefficient time histories on buildings geometrically similar to those tested in wind tunnel facilities. Finally, Chapter 7 summarizes conclusions about fullscale measurement and the application of stochastic simulation in wind engineering and presents suggestions for future research. CHAPTER 2 HURRICANE DAMAGE MITIGATION RESEARCH This chapter chronicles research efforts to measure surface level wind speeds and the resultant pressures on lowrise buildings during extreme wind events, outlines the design of windresistant structures under the guidance of the American Society of Civil Engineers Minimum Design Loads for Buildings and Other Structures (ASCE 702), and details recent efforts to enhance design practice with reliabilitybased, databaseassisted design (DAD). Sources of Wind Speed Data Meteorological data of interest to wind engineers include highresolution time histories of threedimensional (3D) wind velocities observed at ground level (<20 m) from fixed points of observation. This information allows engineers to characterize the turbulent wind fields that envelop lowrise structures in extreme wind events. A variety of weather stations collect groundlevel wind speed data in the United States (as seen in Figure 21), including * Offshore and coastal stations operated by NOAA's National Data Buoy Center (NDBC), such as moored buoys and the Coastal Marine Automated Network (CMAN) * Airport stations, such as the National Weather Service (NWS) Automated Surface Observing System (ASOS) * Regional networks of automated environmental monitoring systems with realtime data collection and dissemination capabilities. Examples include the Florida Automated Weather Network (FAWN) and the Texas MesoNet Program (B) NDBC Buoy (C) ASOS Figure 21. Weather stations (courtesy of NOAA) While these weather monitoring stations are useful for normal operationas tools for meteorological prediction, assessment of flight level conditions, air pollution studies, and climate monitoring in agrarian regionsthey are unreliable for measurement in extreme wind events. Tree branches succumbing to high winds (> 2030 m/s) commonly disrupt power service, and absence of backup power prevents further data collection. Stations also fail from debris impact and wind loadingparticularly due to damage to the structure supporting the anemometry (e.g., masts, crossarms and/or guywires). Some stations lack recording capability altogether, and the remainder sample at rates (0.32 Hz) too low to capture dynamic wind effects. In Hurricane Andrew, only 10 out of the 34 weather stations in MiamiDade County survived with a record (Powell et al. 1996). Meteorologists have issued recommendations concerning the implementation of backup power, improved archival abilities and better construction techniques to ameliorate the current observational configuration (Powell 1993), but the ability to record high A J Ti (A) CMAN resolution time histories of hurricane winds from these stations has yet to reach implementation. In addition to employing ground and oceanbased weather stations, the U.S. Air Force Reserves and the National Oceanic and Atmospheric Administration (NOAA) Hurricane Research Division (HRD) fly reconnaissance aircraft into hurricanes to measure winds at heights of 2.13.7 km. NOAA meteorologists linearly reduce typically 6390%those wind speeds measured at the cruising height of the aircraft to estimate the ground level wind speeds of interest to wind engineers. Comparison to ground observations, however, has demonstrated the potential to underestimate (Hurricane Bonnie) and overestimate (Hurricane Mitch) wind speeds (Franklin et al. 2000). From the aircraft, the research crew also drops instrument packages called Global Positioning System (GPS) sondes to measure pressure, temperature and position throughout their descent. While GPS sondes provide useful data to describe the velocity profile of the hurricane boundary layer, they do not provide a time history at a fixed position. Additionally, it is difficult to glean ground level wind speeds due to the high rate of descent (1015 m/s) before splashdown (Powell et al. 1999). While modem weather stations provide valuable insight for meteorological predication and the monitoring of decaying weather conditions during hurricane landfall, they do not meet the needs of wind engineers. They do not provide the highresolution time histories of wind speeds over a variety of different terrains needed to quantify the turbulence structure of the gusts that cause damage to lowrise structures. In order to address the need for such data sets, researchers have employed permanent and portable instrumented towers since the 1950s to collect wind speed data. Use of Permanent Instrumented Towers Towers instrumented to record highresolution time histories are scarce in hurricane prone regions. The earliest documented digital measurements in civil engineering literature occurred during Hurricanes Carol and Edna (1954), Connie (1955) and Donna (1960) by an instrumented tower at Brookhaven National Laboratory (BNL) on Long Island, New York. The 100m tower provided the time series that would form the basis of the first groundlevel wind spectral models (van der Hoven 1957, Davenport and Stagg 1962). During Hurricanes Eloise (1975) and Frederic (1975), the US Army Corps of Engineers (USACE) collected data from oil rigs in the Gulf of Mexico as part of its Ocean Current Measurement Program (Forristall 1988). The USACE has also measured waves, winds, tides, and currents from its Field Research Facility located in Duck, North Carolina, since 1977. In 1987, the USACE relocated its anemometry from the central building to a tower at the end of a 560 m pier, where it sits at 19 m above the National Geodetic Vertical Datum (NGVD). Most recently, the facility collected wind speeds from Hurricanes Bob (1991) and Isabel (2003). In Asia, typhoon wind speeds have been collected from instrumented towers in Nakagawa (Japan, 19641967), Tokyo (Japan, 1959 and 1961) and Tarama Island (Japan, 19751977) and in Hong Kong (1959 and 1961). Analyses of these data may be found in Ishizaki (1983). Data from many storms are necessary to evaluate the velocity field and its turbulence characteristics in a statistically meaningful way. To increase the likelihood of recording hurricane winds, NOAA's Hurricane Research Division (HRD) implemented the Hurricanes at Landfall Time Series Data Recorders (HALTSR) program. Before tropical cyclone landfall, research personnel augmented existing weather stations in the path of the storm with portable instrumentation packages equipped with backup power and highresolution data acquisition software. The HALTSR experiment provided digital ground observations for Hurricanes Dennis, Floyd and Irene in 1999 (personal communication with Mark Powell, January 19, 2004). The HALTSR program represents a significant transitioning point for fullscale measurement of surfacelevel tropical cyclone winds. Prior to that experiment, data collection only occurred if the path of the cyclone brought it within close proximity of an observation site. Use of Portable Instrumented Towers Engineers need wind records from a variety of terrain exposures, but a fixed observation point only provides velocity field data for the local terrain exposure. Additionally, most weather stations operate in flat expansessuch as airports and beachfrontsthat do not generate the turbulence of builtup terrains such as suburban neighborhoods. These conditions are of great interest to engineers as they reveal the turbulent wind fields that envelop lowrise structures. To collect these data, two other programs were formed to add portability and flexibility to hurricane data collection efforts. In 1998, the Federal Emergency Management Agency (through the State of Florida Department of Community Affairs) and the Idaho National Engineering and Environmental Laboratory (INEEL) funded the development of two university research programs to collect fullscale hurricane data: the Wind Engineered Mobile Tower Experiment (WEMITE) and the Florida Coastal Monitoring Program (FCMP). This dissertation is concerned in large part with contributions made to the FCMP. Wind Engineered Mobile Tower Experiment (WEMITE). Civil engineering and atmospheric science faculty at the Texas Technological University (TTU) Wind Science and Engineering Research Center jointly administer the WEMITE program. Instrument capabilities include five towers, specially equipped vehicles (mobile mesonets), and a Shared Mobile Atmospheric Research and Teaching Doppler on Wheels (SMARTDOW) used in conjunction with Oklahoma and Texas A&M Universities. Of the five towers, Texas Tech employs two towers capable of withstanding 67 m/s (150 mph) wind gusts: WEMITE I and II. WEMITE I collects data at 3.1 m, 6.1 m and 10.7 m, and the second generation tower, WEMITE II, collects data at five levels: 2.13 m, 3.96 m, 6.1 m, 10.06 m, and 15.2 m. Both systems collect temperature, barometric pressure and relative humidity and maintain stability from outrigger arms, guy wires and ground screws. Instruments and the data acquisition system receive power from a wind generator and a bank of four deepcycle batteries. Figure 22 provides pictures of WEMITE II. The remaining three towers are lightweight 10m aluminum towers that use guy wires and shear pins to remain stabile in high winds. Florida Coastal Monitoring Program. The FCMP is a unique joint ventureled by structural engineering faculty at Clemson University and the University of Florida that focuses on fullscale experimental methods to quantify nearsurface hurricane wind behavior and the resultant loads on residential structures. The aim of the project is to provide the data necessary to identify methods to costeffectively reduce hurricane wind damage to residential structures. 12 i ....... m ...... P,, Figure 22. Texas Tech WEMITE Similar to the WEMITE deployment strategy, FCMP teams remain on standby throughout the hurricane season to respond rapidly when the threat of a tropical storm arises. When a cyclone approaches, FCMP teams leave their home universities to meet the inbound hurricane with foursoon to expand to sixportable tower systems (as seen in Figure 23). Based on advisories issued by the National Hurricane Center, research personnel deploy the towers in the vicinity of anticipated landfall approximately 824 hours before impact. Figure 23. The FCMP instrumented tower Designed to capture hurricane winds in a variety of exposures and to survive a hurricane episode, the towers are highly mobile and rugged. They meet U.S. Department of Transportation (DOT) requirements for transport as a conventional trailer, and with the tow capabilities of the FCMP's fourwheel drive vehicles, the towers can be erected in a wide variety of offroad terrains. Several performance measures were implemented to simplify tower setup and to increase the window of time for research personnel to evacuate the impacted region. The tower is stable without guy wires, requires only six bolts during assembly and is hoisted into place with an electric winch in seconds. These timesaving measures allow three research personnel to erect each tower in less than 30 minutes. Designed to withstand extreme service conditions, the tower can resist a peak gust wind speed of 90 m/s (200 mph), which corresponds to a strong SaffirSimpson Category 5 hurricane (Simpson and Riehl, 1981). The main tower is built from a structural steel lattice, bolstered by structural tubing that connects the tower to its trailer. All computer, generator and battery enclosures are built from 16 gauge steel or diamondplated aluminum. Wiring for power and data cables are encased in conduit for protection. The towers resist sliding and overturning from impinging wind loads through its 2700 kg of self weight, an outrigger system which places supports 6 m from the tower base, and earth screws (similar to those used in manufactured housing), which are augured into the ground and attach to the end of the outriggers. The natural frequencies of the tower 5.66 Hz and 6.45 Hz perpendicular and parallel to the axles of the trailer, respectively render dynamic effects negligible as the practical upper frequency limit of ground level hurricane wind spectra is approximately 12 Hz. Three levels of sensors outfit the tower at 3, 5 and 10 m. The data acquisition system measures 3D wind speed and direction at the top two levels and collects temperature, rainfall, barometric pressure, and relative humidity data at the tower's base. Two RM Young anemometry systemsa wind monitor and a custom array of three gill propellerscollect data at the 10m level, which the World Meteorological Organization deems as the standard wind speed observation height. A second array of gill propellers collects wind speed data at the 5m level to measure winds at the approximate eave height of a singlestory home. Dynamic characteristics of the anemometer's fourblade polypropylene helicoid propellers include a 2.7 m 63% recovery distance constant and a damped natural wavelength of 7.4 m. The wind monitor 50% recovery vane delay distance is 1.3 m and is rated for a 100 m/s gust survival. A contractorgrade gasoline generator powers a linked uninterruptible power supply system, which in turn powers the onboard computer and instrumentation. The equipment can operate for up to 2436 hours before research personnel must refuel the generator. All data are stored in digital form on two hard disks in the tower's computer system. Customized C++ data acquisition software samples at a rate of 100 Hz, which provides excellent resolution of highspeed wind field dynamics (Poss 2000). The FCMP has produced data sets from the portable towers for Tropical Cyclones Georges (1998), Dennis (1999), Floyd (1999), Irene (1999), Gordon (2000), Gabrielle (2001), Michelle (2001), Isidore (2002), Lili (2002) and Isabel (2003). In addition to the mobile tower experiments, the FCMP conducts fullscale measurement of wind pressures on lowrise structures during hurricane landfall. The following section explains this program. FCMP House Experiments: The purpose of the house component of the FCMP is to collect uplift pressure data on the roofs of real residential homes during landfalling hurricanes. Together, the towers and houses provide critical data to engineers developing windresistant designs in hurricane prone regions by tying together ground level wind speeds and the resultant pressure forces that impinge upon lowrise structures. To date, the project has funded the instrumentation of 30 homes (Figure 24) along the Southeastern and Panhandle coasts of Florida. Private homeowners agree to participate in the program in exchange for retrofits to their homes to increase wind resistance. These retrofits can include a new roof, braced garage door, hurricane shutters, gableend bracing, and other measures. An inspection of the home determines the individual measures taken for each home. Before any data collection work is done on a house, the promised retrofits are performed on the participant's home. In the event that a hurricane impacts one or more of the homes, the FCMP will compare damage between the retrofitted houses and neighboring structures to assess the effectiveness of the retrofits. Figure 24. Location of FCMP homes instrumented to measure wind pressure Microswitch pressure transducers housed in 30.5 cm diameter aluminum pans collect data on the roof. Each pan anchors to three stainless steel brackets permanently attached to the roof. A shielded cable connects the transducer to wiring encased in CPVC piping discretely located under the eave. In addition to the pan sensors, an anemometer and a pressure sensor located in the attic tie into the conduit. The CPVC pipes terminate at a disconnect box, where each instrument is separately fused in the event debris severs a cable and disrupts the electronics. Weatherproof flexible conduit extends from the disconnect box to the data acquisition system, which, along with its backup power, is located inside a rugged steel enclosure. Sequential 15minute data records are recorded at a sampling rate of 100 Hz. Left alone, the system can operate up to 12 hours after a power outage. Figure 25 illustrates the experimental setup. A Figure 25. FCMP instrumented homes: A) Sensor installation just before Hurricane Isabel and B) Prewiring of a south Florida home To date, the home instrumentation systems have not collected data from hurricane force winds but did succeed in capturing the outer bands of Floyd, Michelle, Isidore and Isabel. Recently, Clemson University conducted wind tunnel studies of models of two instrumented homes that collected data in Tropical Storm Isidore (Dearheart 2003). The portable tower and house components of the FCMP operate independently, while providing complementary data sets to quantify wind field and structural load behavior. A portion of this dissertation focuses on the portable tower component, while the house data system is not a subject directly addressed. Current Wind Load Design Provisions and Standards Currently, engineers seeking guidelines to design modem lowrise buildings resistant to wind loads usually turn to the American Society of Civil Engineers Minimum Design Loads for Buildings and Other Structures (ASCE 702) for guidance. ASCE 702 is referenced by most major building codes, including the International Building Code (BC 2003) and the Florida Building Code (FBC 2003). American Society of Civil Engineer's Minimum Design Loads for Buildings and Other Structures (ASCE 702) The provisions offer three sets of guidelines for design: simplified, analytical and wind tunnel. The simplified and analytical methods are applicable to buildings without unusual geometric irregularities and response characteristics making it subject to aeroelastic vibrations such as flutter, vortex shedding, etc. Application of the simplified method is further restricted to buildings not subject to topographic effects with * A mean roof height that does not exceed 60 ft * An approximately symmetrical building cross section in each direction * An angle of plane of roof from horizontal 0 < 450 for a gableend roof or 0< 270 for a hip roof * A natural frequency > 1 Hz In the simplified case, wind pressures are extracted from a table. For the analytical case, the provisions hinge upon the calculation of the dynamic velocity pressure (in psf), q,= 0.00256 KKKdV2I (b/ft2) (1) (ASCE 702 Eq 615) where Kz = a terrain exposure coefficient, Kt = a topographic effect factor to account for wind speed up over hills, Kd = a directionality factor, V= the design wind speed dependent on location of the structure (mph), and I = the building importance factor, which ranges from 0.87 (e.g., agricultural structures) to 1.15 (e.g., hospitals). For the design of lowrise buildings, design pressures p are calculated by the following equations: 1. Main WindForce Resisting Systemthe structural system that provides support and stability to the overall structure. Examples include roof and floor diaphragms, rigid and braced frames, shear walls and truss anchorages ASCE 702 p = qh [GCf) (GC,)] (2) Eq. 618 where qh = the velocity pressure evaluated at the mean roof height GCpf= external pressure coefficient (See ASCE 702 Figure 610) GC,, = internal pressure coefficient (See ASCE 702 Figure 65 2. Components and Claddingelements that transfer wind loading to the MWFRS. Examples include curtain walls, sheathing, trusses and exterior windows and doors ASCE 702 p = qh [(GCp) (GCp,)] (3) Eq. 622 where qh = the velocity pressure evaluated at the mean roof height GCp = external pressure coefficient (See ASCE 702 Figures 611 through 616) GCp, = internal pressure coefficient (See ASCE 702 Figure 65) The dimensionless pressure coefficients Cp provide the empirically determined relationship between upstream wind velocity and the pressure on the building in different regions. For example, the coefficients on the windward wall will be positive (inward pressure), while the coefficients on a flat roof may be strongly negative (suction). Pressure coefficients are calculated from the following equation C PPo (4) p 1/2pV2 where p po = the pressure difference between the local and far upstream pressure po, p = the density of air, V= the mean value of the velocity (taken from far upstream or point above the boundary layer) and 1/2 pV2 is the mean dynamic pressure of the far upstream wind or the freestream wind at a point out of the boundary layer (Simiu and Scanlan 1996). In terms of application of the standard, the most likely extreme wind speed in a 50 year period (dependent on building location and found in the ASCE 702's wind map) is used as the design wind speed in combination with the pressure coefficient Cp and the gust effect factor G to envelope dynamic effects to formulate design pressures acting on the exterior of the structure.. The gust effect factors accounts for gust load effect and dynamic structural response (which is negligible for a rigid structure). Applicability of the Current Standard The framework of ASCE 702 relies on tables and figures to extract parameters for equations that determine the design loads. The wind tunnel studies used to create the pressure coefficient information were only performed on a few very simple shapes over a range of directions. From this information, a worstcase scenario approach was used to determine pressure coefficient values for the provisions using an enveloping approach. Loading on structures or buildings with reentrant corners, geometrical asymmetries and/or distinguishing architectural treatments are approximated based on the handful of building shapes offered in the provisions. The conservative nature of the enveloping procedure is intended to account for these limitations (Rigato et al. 2001). Additionally, ASCE 702 does not explicitly account for directional effects on cladding and components and the main windload resisting system, even though the worstcase scenarios for both cases may occur at different incident wind angles. Rather than explicitly account for directional issues, ASCE 702 relies on the directionality reduction factor coefficient Kd (which for lowrise buildings = 0.85) that places the design load at 85% of the worst possible enveloped value. Simiu and Heckert (1998) and Rigato et al. (2001) have shown that the reduction factor may underestimate loads since Kd is not dependent upon the mean recurrence interval of landfalling hurricanes. The study also indicated that the same building that is overdesigned in some areas of the structure is underdesigned in other areas. While overdesign (within reason) is the intent of the ASCE prescriptive approach, the simultaneous occurrence of underdesigned regions was an unintended (and unacceptable) consequence of this simplified approach to account for a very complex phenomenon. The methodology of ASCE 702 draws upon three series of tests to provide an assessment of wind forces on a lowrise building: * Irminger's 1894 aerodynamic tests * Flachsbart's 1932 boundary layer wind tunnel experiments * The University of Western Ontario's (UWO) tests sponsored by the Metal Building Manufacturers Association (MBMA) in the 1970s and early 1980s Clearly, the investigators could not avail themselves to the benefits of modern technology, particularly the digital computer and today's high resolution data acquisition systems. Only the latter study employed computing hardware to record and store data. This statement does not imply that the original tests are inaccurate but instead recognizes that the resolution gains (e.g., denser clusters of pressure tap arrays) and greater data storage capabilities offered by modern data acquisition systems can provide a more complete view of the complex phenomenon of windstructure interaction. Recent highresolution wind tunnel tests performed by UWO in 1997 and 2001 2004 have called the adequacy of the ASCE 7 pressure coefficient values into question. While stateoftheart computer based models can calculate bending moments, shear forces and axial forces to within a 5% deviation from experimental results, the models used to develop ASCE 7 can result in wind pressure load deviations as high as 50% (Rigato et al. 2001). ReliabilityBased DatabaseAssisted Design One concept to modernize wind load provisions envisions the use of an online database containing the wind load time histories over a building surface for a huge variety of structural shapes. These time histories will be comprised of wind tunnel tests and computer generated simulations. Advanced (and proven) analysis methods that have been developed since the creation of the existing pseudostatic design procedure can then be applied to determine the maximum critical stresses in a statistically reliable sense. As a result, engineers can rationally create a uniformly conservative design based on a detailed analysis of structural response to wind loads created for that building shape. Whalen et al. (1998) and Rigato et al. (2001) established the foundations for databaseassisted design (DAD) concept for wind loads in hurricane prone regions: 1. The development of technology for recording and storing simultaneous wind tunnel or fullscale pressure time histories over the external and internal surfaces of building models 2. The development of climatological databases containing large numbers of simulated hurricane wind speed data 3. Computational capabilities allowing the use of pressure and climatological databases for the calculation of bending moments, shear forces and axial forces in windresistant structures Item 2 above is supported in part by Objective 4 set forth by the Hurricane Loss Reduction Project introduced in Chapter 1. Computer simulation of these pressure coefficients using multivariate stochastic simulation techniques is a component of the successful implementation of this procedure and is addressed in Chapter 6. DAD is intended as a natural extension to analytical design, providing more accurate loads for a wide variety of building types. The development of electronic standards for wind load provisions has elicited the interest of many private, government and educational institutions including the UWO, Purdue University, Texas Technological University (TTU), Colorado State University, Ceco Building Systems, MBMA, Clemson University, University of Notre Dame, Virginia Polytechnic Institute and State University, Johns Hopkins University, the University of Illinois at UrbanaChampaign, and the University of Florida. Additionally, industry professionals developing vulnerability models for insurance and reinsurance companies have taken an interest, because the DAD concept will provide considerably more building shapes than the set of building geometries currently found in ASCE7. Several paths of research have manifested to further DAD aims. Efforts have been made to determine internal force peaks from stochastic simulation methods (Sadek and Simiu 2002) and to quantify the resultant sampling errors (Sadek et al. 2002). Additionally, the analysis of wind tunnel data collected at the Wind Load Test Facility at Clemson University has been used to characterize the probabilistic content and correlation structure of pressure coefficients on the roof of lowrise buildings (Cope and Gurley 2001). Chapter 6 addresses methods to generate time histories of loads on untested buildings based on interpolation of load time histories between building shapes tested in the wind tunnels. The problem statement under consideration is: Given the wind tunnel measured time histories of pressure coefficients at multiple roof taps on two similar but not identical buildings, develop methods to accurately represent the pressure coefficient time histories of a building whose geometry lies between the two measured buildings. For example, consider three buildings identical in all respects other than roof pitch. If wind tunnel studies are conducted on models with 3 on 12 and 8 on 12 roof pitches, one can infer appropriate time histories for the roof taps on a 5 on 12 roof pitch building. The resulting aggregate loads in the structural members should be statistically similar to the actual loads in terms of mean, rms, and peak values. The highly nonGaussian and strongly correlated nature of uplift on lowrise roofs renders this a challenging problem. A viable solution to the problem statement will serve to increase the applicability of the intended online DAD database by making a wider array of lowrise building geometries available. Recently, UWO researchers have addressed this issue through rescaling of the measured pressure time histories of tested buildings. Using the example above, the time histories from the 3 on 12 roof pitch building are translated and dilated to adjust the mean and rms values, with the resultant serving as the inferred time histories for the unmeasured 5 on 12 roof pitch building. The translation and dilation parameters are determined using neural network training of a handful of tested buildings of similar shape (Chen, Kopp and Surry, 2003a). Another approach reconstructed the resultant aggregate loads using linear stochastic estimation (Chen, Kopp and Surry 2003b). In both studies the added complexity of direct simulation of the time histories was avoided in order to explore the efficacy of simpler methodologies. The tradeoff is the inability to capture differences in higher order statistics between time histories on different geometries, potentially influencing the ability to reproduce accurate peak value magnitudes and rates of occurrence. Chapter 6 presents the use of a stochastic simulation algorithm for the generation of the pressure coefficient time histories on a building similar to tested geometries. This method goes beyond the translation and dilation of time histories of tested buildings, potentially improving the accuracy of the load time histories. The use of simulation preserves the spectral content, correlation, and the nonGaussian probability distribution, thereby maintaining higher moments and accurate fluctuating peak values. The spectral and probabilistic models used as input to the stochastic simulation algorithm are derived from interpolation of models fitted to data from similar buildings. Background on simulation methods is provided in Chapter 3, and the development and results of this interpolation simulation methodology are presented in Chapter 6. Summary This chapter has introduced two avenues of hurricane damage mitigation research including fullscale ground level wind velocity and structural load data collection, and new concepts for providing structural wind loading for design via Database Assisted Design. The research in this dissertation focuses on contributions to both these avenues of research. Chapter 3 will present the background necessary to provide a proper context for the original contributions in Chapters 4 through 6. Chapter 4 discusses the data collection efforts of the FCMP. Chapter 5 presents the results of detailed analyses of the FCMP datasets, including new models of turbulent gust behavior for coastal regions. 26 Chapter 6 presents the development of computational simulation algorithms combined with interpolation schemes using existing wind tunnel data sets to expand the utility of the DAD concept for prescriptive structural wind loading. CHAPTER 3 ANALYSIS AND SIMULATION TECHNIQUES FOR WIND This chapter provides a brief description of the aspects of atmospheric turbulence that are of interest to structural and wind engineers and explains the principles and methods of stochastic simulation techniques required to computationally simulate wind loading. This is necessary background material for the research presented in Chapters 4 through 6. Of principal interest to structural engineers are winds in the surface layer region of the atmospheric boundary layer (ABL), where surface friction primarily influences wind structure. Wind speeds and pressure loading vary with time inside the ABL, and require probabilistic and spectral analyses to characterize their turbulent nature. In addition to characterizing surface level wind fields, these analyses also yield the target statistical models required to recreate wind loading in Monte Carlo simulation techniques. Characterization of GroundLevel Hurricane Winds Data collected by the portable towers are processed to quantify the data in terms of steady and fluctuating components, and their relationship to terrain roughness. The wind velocity is observed at a fixed point (x,y,z) in a righthanded Cartesian coordinate system over the time duration T. The longitudinal or alongwind (u), lateral or acrosswind (v), and vertical (w) components decompose into the superposition of its steady state or mean velocity and its fluctuating or turbulent components. Assuming stationary, horizontally homogeneous and neutrally stratified flow, the velocity field reduces to a twodimensional instantaneous vertical velocity profile u(z) and constituents u(z) and u '(z) (shown in Figure 31). P I Height z O(z) Mean Wind Velocity u'(z,t) u(z,t) Turbulence Instantaneous Component Wind Velocity Figure 31. The decomposition of an instantaneous wind velocity profile Mean Velocity Profile Many velocity profiles exist to describe the variation in mean wind speed with height. The two most widely used profiles are presented in this section. The first profile (and also one of the earliest profiles proposed) is the power law, z Ug Z 1g zb uz O Z> Zg which relates a gradient wind speed ug at height Zg to velocity over a range of heights z with knowledge of the nondimensional surface roughness parameter a. Typical values of a range from 0.10 in open terrain to 0.33 in metropolitan exposures. Its mathematical simplicity has made it a popular choice for many building codes and standards, including ASCE 7, Eurocode, AS 1170.2 (Standards Australia) and the RLB (Architectural Institute of Japan). ASCE 7 uses the following form u(z) = UoE(z)= Uob(z/l 0) (6) where the mean velocity is a function of the mean wind speed U0 and the wind exposure category E(z), which is determined from the observation height z (units of meters) and the terrain dependent constants a and b (Zhou and Kareem 2002). The second profile, proposed by Sverdrup (1934), is based on flatplate boundary layer theory of Prandtl and von Karman. The logarithmic law is valid from several meters off of the ground to 50100 m depending on the surface roughness and the wind speed (Wieringa 1993), k zO and defines the mean velocity ui(z) as a function of von Karman's constant (observed experimentally to be k 0.40 + 0.01), the shear velocity u,, the observation height z, and the roughness length zo. Like the coefficient a in the power law, the roughness length provides a mathematical description of the degree of roughness in the upwind terrain. Physically, it represents the size of the characteristic eddy size that is formed from the friction between the air and the ground surface (Dyrbye and Hansen 1999), and mathematically, it is equivalent to the zintercept of the logarithmic profile. Extensive effort has been undertaken to produce reliable estimates of a and zo for varying roughness conditions, but considerable variability exists in the literature, possibly due to the assumptions about the flow field (e.g., adiabatic equilibrium) or the upwind terrain (e.g., that sufficient homogeneous fetch exists to develop a boundary layer fully). Counihan (1972) and Wieringa (1993) provide the most complete review and analysis of available data. The shear velocity, U, (8) is dependent on the turbulent shear stress To and the density of air p. The shear stress can be calculated directly using a drag plate (or floatingelement skin friction balance), which typically consists of a 12 m representative ground sample mounted on a sensitive balance mechanism buried beneath the ground, by measuring the tangential force of the wind (Kaimal 1994). More commonly, the shear velocity is calculated from measured eddy fluxes in the constant shear stress region close to the surface. At least four definitions of u, exist in the literature. Some authors use the length of the horizontal Reynolds stress vector in the direction of the mean wind vector, u = (E[u'w']2 + E[v'w'2 4 (9) where E] = the expectation operator or in this case, the covariance of the turbulence components. Others employ the absolute value of the horizontal Reynolds stress vector to define friction velocity, u1I = E[u'] (10) For complex terrain, Zemann and Jensen (1987) suggested a coordinate transformation of the turbulence components to align the longitudinal axis with the 3D mean wind vector such that the mean vertical and lateral components equal zero. From the new longitudinal (uD) and vertical (w3D) components, the friction velocity is calculated as ~ = iE VU3 (11) Finally, McMillen (1988) modified Eq. 11 to account for rotation about the longitudinal axis (i.e., instrument tilts relative to the vertical axis). In cases where the rotation angle < 100, he suggests rotating the coordinate system to reduce the lateral vertical covariance to zero (i.e., E[v'w'] = 0). Weber (1998) performed leastsquare fits of the logarithmic profile to wind speed data collected on a 70m instrumented tower and compared results to four methods. He determined that Eq. 9 yielded the lowest mean square error in fitted profile. Based on his conclusion, the research presented in Chapter 5 relies on that estimation technique. Important to note, however, is the significant amount of scatter and error associated with zo estimation using eddy fluxes. Wind tunnel studies (e.g., Iyengar and Farell 2001) have shown that Reynolds stress measurements can be off by more than 15% (using hotwire anemometry), which produce substantial deviations in zo. Fullscale measurement, devoid of the idealness of a laboratory, is considerably more problematic. Turbulence Characteristics Turbulence Intensity. A simple measure of the fluctuating component of the wind is turbulence intensity (TI), which is a ratio of the root mean square (rms) of the turbulence component to the mean wind speed f. In practice, decomposition of the measured wind speed and direction removes the mean from the turbulence component u', so the rms value is a standard deviation o. Assuming negligible influence of rotational and convective effectswhich implies that u, = u =0 only the longitudinal, lateral and vertical TI components remain, TI = TI = TI = (12) Su u u Gust Factors. The gust factor GF relates the peak gust wind speed Um,a to the mean wind speed f over the selected gust duration t and record length T Umax (t) GF(t,T) t < T (13) u(T) Choice of gust duration varies in the literature, but meteorologists and engineers commonly use t = 2 and 3second gusts, respectively, over T= 10minute to 1hour durations. Structural design of lowrise structures, in particular, typically references peak gusts to an hourly mean wind speed. Three hourly mean wind speed gust factor modelsDurst (1960), Cook (1985) and Krayer and Marshall (1992)are presented in this study (shown in Figure 32). The Durst and Cook models are similar in that: (1) their models were not developed from observations in the hurricane boundary layer, and (2) these gust factor models provide the reference wind speed for structural design (ASCE 7 and Eurocode, respectively). Krayer and Marshall (1992) developed a gustier model from tropical cyclone data for the design of lowrise structures in hurricane prone regions predicated on the methodology (and assumptions) of Durst. The model replaced the Durst curve in the 1995 edition of ASCE7 but was replaced by its predecessor in the 1998 edition. A new gust factor model has been developed based on the FCMP database and is presented in Chapter 5. Its development required a complete reanalysis of Durst (1960). Details concerning these studies follow. E r'"  Krayerviarsnall 2 " 1.6 1.5 02 3 10 100 1000 3600 1.4 CU 0 1 2 3 10 100 1000 3600 Gust Duration (sec) Figure 32. Gust factor curves as a function of gust duration t based on an hourly mean wind speed T The first gust model, proposed in Durst (1960), was generated from wind speed records obtained from Dines pressure tube recorders in an open countryside at Cardington, England (detailed in Giblett 1932). From these data, Durst divided T= 10 minute records into Ngust tduration segments, Ngust = T/t (14) and averaged each segment to calculate the shortduration gust ugst(e.g., from a 10 minute record, he calculated 120 fivesecond ugst values). Next, he calculated the population standard deviation of the gust sequence gust with its mean wind speed u removed, _ I (N ))2 (15) C (t)= gu (t) l2 gusts and divided the results of Eq. 15 by the mean wind speed i before averaging the values to produce the first row of values in Table 31. The ratio of oto u represents the standard deviation of the gust departures of duration t (sec) from the mean wind speed over interval T(sec), for which subsequent literature has adopted the notation SD(t,T). In order to produce gust factor estimates for a one hour time frame rather than the 10 minutes used in the measurements, the values in row one of Table 3.1 must be manipulated as detailed next. Transforming SD(t, 600) into an hourly mean wind speed gust factor relationship required three additional steps. First, Durst transformed the experimental SD(t, 600) values to an hourly mean wind speed basis SD(t, 3600) through a Gaussian translation of variance, which assumes that the mean square of the instantaneous tsecond average velocity ut may be decomposed by the following relationship, Eu,2]=2u +E[u(t,)]+ EuE,(t,,t, )] (16) 1=2. where E[] = the expectation operator, u, = the gust departure sequence inside of the duration T,_1, T = the duration of the record and n = the number of points in the gust. Since the terms in Eq. 16 have a common mean, it may be reduced further and rearranged into the form employed by Durst (1960, pg. 185) to calculate Table 31. Calculated Durst gust factors Period in seconds (t) 5 10 15 20 25 30 40 50 60 SD(t,600)= o/ 0.145 0.135 0.128 0.124 0.120 0.115 0.107 0.098 0.095 SD(t,3600) 0.159 0.150 0.144 0.140 0.137 0.132 0.125 0.118 0.115 SU(t,3600) 2.99 2.77 2.64 2.54 2.46 2.39 2.29 2.20 2.13 GF(t,3600) 1.48 1.42 1.38 1.36 1.34 1.32 1.29 1.26 1.24 Note: SD(t,600) can be found in Table II ofDurst (1960) SD(t,3600)= /SD2 (600,3600)+ SD2 (t,600) (17) Three anemograms available from the Cardington site indicated that SD(600,3600) equaled 0.055, 0.065 and 0.075 at a 50 ft observation height. Durst chose the median value of 0.065 to estimate SD(t,3600) from row one of Table 31 and Eq. 17. Next, the standardized normal deviate SU(t,T)i.e., the number of standard deviations from zero in a standardized normal cumulative distribution function CDF was calculated for the gust duration t inside of the record interval T su(t, T) = CDF (1 t/T) (18) Finally, the gust factor was calculated from Eq. 19. Values of SD(t,3600), SU(t,3600) and GF(t,3600) are provided in Table 31. GF(t,T)= 1+ SU(t, T). SD(t,T) The second model, proposed in Krayer and Marshall (1992), resulted from an analysis of stripchart data from several postdisaster investigations of wind damage by Hurricanes Frederic (1979), Alicia (1983), Elena (1985) and Hugo (1989). Records with wind speed anomalies generated from the presence of structures and trees near the anemometry were eliminated. The remaining 13 records were divided into 10minute sequential segments, and 2second peak gusts were extracted from spikes in the pen trace. Following Durst (1960), the observed GF(2,600) were transformed into estimates of GF(2,3600). Subsequent analysis supported an upward adjustment of the gust factors estimated from extratropical storms. The third model, proposed in Cook (1995), simplified an empirical curve offered by Wieringa (1973) that assumes a linear dependence on the longitudinal turbulence intensity and a logarithmic dependence on the gust duration t. GF(t, T = Ihour)= 1 + 0.42TI, ln(3600/t) (20) The large volume of high fidelity wind velocity data recorded by the FCMP during tropical storms and hurricanes provides a significant database for the characterization of turbulent wind behavior in coastal areas. As coastal structures are typically most vulnerable to the worst of the damage associated with high winds during storm landfall, a gust factor model was developed exclusively from wind records collected near the coast. The development of this new coastal hurricane gust factor model is presented in Chapter 5, and contrasted with the three models shown in Figure 32. Estimation of Roughness Methods to estimate the roughness length zo commonly employ the logarithmic law. Neutral stability, horizontal homogeneity and stationary imply that the statistical properties of the vertical velocity profile changes only with height z. Accordingly, given enough observations, zo can be estimated by fitting the observed vertical wind profile to Eq. 7. To calculate a roughness length within a factor of two, Wieringa (1993) suggests at least three profile levels over rough terrain (zo z 1 m), four profile levels over moderately rough terrain (zo z 0.1 m) and five profile levels over smooth terrain (zo 0.01 m). The longitudinal TI is useful to estimate an associated roughness length of the approach terrain (Wieringa 1993). Assuming that the variance of the longitudinal turbulence component o' is linearly proportional to the shear velocity squared by a factor p, 2 = /7(u)2 (21) and further that von Karman's constant k and P share the relationship, kY = 1 (22) The logarithmic law can be rearranged to solve for the roughness length zo in terms of the longitudinal turbulence intensity TIu z0 = exp[ln(z) (z)/l (z)] (23) zo = exp[ln(z) 1/TI (z)] Strictly speaking, application of Eq. 24 is limited to homogeneous, flat terrains (where p= 6.25) because the calculation of zo in a heterogeneous terrain will cause its overestimation. In heterogeneous terrain, the upwind fetch must be divided into homogeneous patches for assessment of surface roughness, before an "effective" zo value can be calculated from the area (Claussen 1991). Counihan (1975) hypothesized that the TIbased roughness estimation is only valid for values ofzo < 0.10 m and suggested a downward adjustment for values beyond that limit. Gust factors can also be used to estimate zo. Wieringa (1993) presented the following equation, z0 =z. ex[ A[1.42 + 0.31n( 4000/U)] (25) (JUmax/U) 1+A fA where (Umax/U) = the median gust factor taken from at least 15 gust observations, A = the attenuation factor (0.9) of the anemometry,fr = a factor which is unity for 10minute averaging periods and increases to 1.1 for hourly averages and Ut = the average wavelength of maximum gusts observed by the anemometerrecorder (usually varying between 50 and 100). Finally, zo can be estimated directly from a rearrangement of Eq. 7, = z exp ki(z) (26) u] with the knowledge of a mean longitudinal wind speed u(z) and the shear velocity u,. Since the momentum fluxes are assumed to be independent of height in the surface layer, 3D turbulence measurements at the 10m observation height can be used to estimate the shear velocity from Eq. 9. This methodology is the basis of the roughnessdependent turbulence analyses presented in Chapter 5. Correlation and Spectral Relations Integral Length Scales. Quantifying the length and width of an average gust in an extreme wind event is of special interest to design engineers because a gust's dimensions and velocity determine the pressure loading a structure experiences. To quantify the average length of a gust in a stationary wind record, engineers calculate the autocorrelation function Rxx(r) of the longitudinal turbulence component u' over a range of time lag values r. Noting that u'is meanremoved, Rxx(r) equals the covariance function Cov(r) Cov(r) = R (r, u' = 0) = E[u'(t)' (t + r)] (27) The covariance function is scaled by the variance and integrated to produce the time scale T, which equals the average gust duration, T =1 Cov(r)dT (28) ou' 0 In practice, the upper limit of integration is reduced to the lag value where Cov(r) dips below zero. To calculate the average gust length L, the time scale is multiplied by the mean velocity (Simiu and Scanlan 1996). Lx = T u In all there are nine integral length scales L' corresponding to the direction i (x,y,z) and the turbulence components (u,v,w). The notation in Eq. 29 corresponds to the size of the fluctuation in the direction x with respect to the longitudinal component of the wind. Below 200300 m elevations, the integral length scale grows as the surface roughness decreases and the elevation increases. Counihan (1975) compiled and analyzed data from 18801972 to propose one such empirical relationship, LX = Czm (30) where C and m are obtained graphically (the figure is available in Simiu and Scanlan 1996) from the roughness length zo. Assuming that C = 145 and m = 0.13 for zo = 0.01 m and C= 90 and m = 0.19 for zo= 0.03 m, Eq. 30 estimates L' to be 196 m and 139 m, respectively. Dyrbe and Hansen (1996) have proposed a conservative relationship between longitudinal length scale and roughness for structural design, L=LL10' 10m where zo = 10 m and Lo = 100 m are independent of surface roughness. Chapter 5 will present the results of a length scale analysis of tropical storm and hurricane level winds collected by the FCMP that demonstrate a dependence of length scale not only on roughness, but on mean wind speed as well. Power Spectra. Accurate prediction of structural response to pressure loading requires an understanding of the distribution of wind energy with respect to frequency. In wind, larger or lowfrequency eddies generate turbulent energy and smaller or high frequency eddies dissipate it through viscous effects. This phenomenon is referred to as the energy cascade, which consists of three major spectral regions. In the lower frequency range, energy is produced by buoyancy and shear. In the highest frequency range, kinetic energy is converted into internal energy (viscous dissipation). In the intermediate or inertial subrange, energy is neither produced nor dissipated if the flow is horizontally homogenous and neutrally stratified (Kaimal 1994). Power spectral density functions (PSD) of turbulent wind energy employed for structural design purposes include those found in von Karman (1948), Davenport (1961), Kaimal et al. (1972) and Harris (1990). More recently, Tieleman (1995) proposed unified spectral models for threecomponent velocity fluctuations at all frequencies in two different exposures: (1) flat, smooth and uniform and (2) complex or perturbed terrain. Equations for these models are presented in Table 32. PSD ordinates are normalized by the variance of the longitudinal turbulence component and multiplied by the frequency. To invoke similarity, wind PSD ordinates are plotted against reduced frequency or the nondimensional quantityfknown as the Monin coordinate, f = n (32) where n =frequency (Hz), z = the observation height and u = the mean wind speed. For engineering purposes, the Monin coordinate is valid forf> 0.2 (Simiu and Scanlan 1996). Chapter 5 will present the results of a PSD study of the FCMP wind velocity database, and compare the resulting empirical estimates with several of the models in Table 32. Stochastic Simulation Methods Chapter 6 presents the development and results of a study to enhance the database of wind tunnel tested building shapes through interpolation of existing data sets and application of stochastic simulation algorithms to digitally create loading time histories on untested building shapes. This section presents background material for the simulation work presented in Chapter 6. Reliabilitybased structural design and analysis often rely on the Monte Carlo approach to quantify the probability of occurrence of various failure modes. The accuracy of such techniques depends on both appropriate system modeling and the proper representation of stochastic loads. To characterize the pressure fields acting on bluff bodies immersed in a turbulent flow field, engineers draw from model testing in the wind tunnel, fullscale experimental data and computational fluid dynamics (CFD). Testing requires time, money and research personnel to conduct the experiment, and CFD requires significant computational resources. Preferably, structural engineers would like to have an efficient means to produce an unlimited number of loading inputs for their models. For this reason, stochastic simulation techniques emerged as an alternative to enhance existing methods. Considerable work has been done in the simulation of Gaussian processes (Shinozuka and Jan 1972, Borgman 1990, Shinozuka and Deodatis 1991, Grigoriu 1993, Shinozuka and Deodatis 1996) and elements of these methods as well as new techniques have been applied to the simulation of nonGaussian sample functions (Cai and Lin 1996, Gurley et al. 1997, Popescu et al. 1998, Masters and Gurley 2003), nonstationary sample functions (Priestly 1967, Vanmarcke and Fenton 1991, Zhang and Deodatis 1996, Li and Kareem 1997), nonGaussian and nonstationary sample functions (Phoon et al. 2002, Sakamoto and Ghanem 2002, Sakamoto and Ghanem 2002) and conditional nonGaussian sample functions (Elishakoff et al. 1994, Gurley and Kareem 1998, Hoshiya et al. 1998). Table 32. Longitudinal turbulence PSD models Name Equation Parameters Reference nS(z,n)_ 0.33/yf nL von Karman von Karman 2 /6 f ) S(1+ 70.8f2) u(z) (1948) nS(z,n)_ 0.33x2 1200n Davenport (34) Davenport 2 x (9 6 S (1+50x2)4 u (0m) (1961) nS(z,n)_ 33.33f nz Kaimal et al. 3 Kaimal 2 = (35) SKa(1+50 f)2/3 (z) (1972) nS(z,n) 0.33x2 1800n Harris Harris x=2 (36)/ S (2 +x2)6 u(10m) (1990) Flat, Smooth and Uniform nS(z, n) 20.53f nz Tieleman (37) (FSU) a0 1+475.1f5/3 (z) (1995) Terrain Perturbed nS(z, n) 40.42f nz Tieleman Teri f (38) Terrain 2 (1 + 60.62f)53 u(z) (1995) The majority of these methods rely on two numerical techniques to infuse prescribed spectral and probabilistic contents into each random signal or field: the Spectral Representation method and the random variable transformation. Spectral Representation Simulation of uplift pressure on roofs of lowrise structures requires multivariate, nonGaussian algorithm capability in order to properly capture the peak and aggregate loading experienced in separation zones. The simulations will be based on empirical models of turbulent wind behavior, including both probabilistic and spectral models. Spectral representationbased methods are therefore used in the Chapter 6 simulation work. The use of the fast Fourier transform (FFT) to impart the desired distribution of energy with respect to frequency is known as the spectral representation method of simulation. Comprehensive descriptions of the spectral representation method exist in many works (Shinozuka and Jan 1972, Shinozuka and Deodatis 1991). Shinozuka and Jan (1972) present the principal formulation of the spectral representation method for a ID process M1 y(jAt) = 2Z SkAo)A e e(kAco)(JAt) (39) k=0 where Syy = twosided power spectral density (PSD) of the sample function y, M= index of the highest contributing frequency, and 0 = phase angles. If 0 is uniformly and independently distributed over [0 ... 2ir], the probability content ofy will be Gaussian as M gets large, and the statistical properties measured over multiple realizations at a given time instant will be invariant to the time instant chosen. Random Variable Transformation Fitting a probabilistic model to a nonGaussian random process in practical engineering application (e.g., wind pressure in the separation zones of a residential structure) typically involves matching moments measured from the time history with those integrated from the distribution being fitted. This implies the need to match moments beyond second order to describe the manner of deviation from Gaussian statistics. Since the spectral representation method produces a Gaussian signal from a prescribed PSD and a uniformly and independently distributed random phase, additional methods must be employed to infuse a prescribed nonGaussian content into the signal. For realvalued stationary random variables, a reliable technique is a class of memoryless translations that transform the probability content of a random variable into a prescribed probability density function (PDF). Three typical random variable transformations are given below: 1. Analytical Filter. When available, a deterministic nonlinear equation is an efficient approach to altering the probability content of a stochastic sample function 2. Empirical or Analytical Gaussian to nonGaussian Mapping (Translation Process). (Grigoriu 1984) used the following relationship to map a Gaussian signal u(t) into a prescribed nonGaussian signal x(t) through their respective cumulative distribution (CDF) functions: x(t) = F1 (cu [u(t)D (40) where the prescribed nonGaussian cumulative distribution function is Fx and the Gaussian cumulative distribution function is Ou. This translation can either take the form of an analytical relation or an empirical mapping scheme. 3. Empirical nonGaussian Mapping. Deodatis and Micaletti (2001) expanded the Gaussian to nonGaussian CDF mapping (translation) concept by generalizing it to an empirically based nonGaussian to nonGaussian CDF mapping x(t) =F (F, (t)) (41) where the arbitrary nonGaussian sample function x is mapped through its CDF F; into the target cumulative distribution F, to create a sample function x with the desired marginal PDF. A refinement to this procedure was recently developed by Masters and Gurley (2003). Existing Simulation Techniques NonGaussian spectral representationbased methods may be sorted into two categories of simulation ideology: Correlation Distortion and Spectral Correction. Both are designed to simultaneously satisfy the spectral and probabilistic target information. Correlation Distortion The goal of Correlation Distortion is the simultaneous imparting of a desired power spectral density function (PSD) and a nonGaussian probability content to a sample function (simulated time history). Correlation Distortion methods seek to identify a PSD to assign to the initial Gaussian sample function. This underlying PSD differs from the target PSD desired for the final nonGaussian sample function. This "underlying Gaussian" PSD is chosen such that the nonlinear transformation to nonGaussian probability distorts the spectral content of the Gaussian sample function into the target PSD without sacrificing an accurate representation of the target PDF. Figure 33 illustrates this process. First, the underlying PSD S,, and a uniformly distributed random phase q! are combined, and a Gaussian process u is generated using the Spectral Representation Method (SRM). Second, the Gaussian process u is passed through a random variable transformation to produce a nonGaussian process x that possesses the target probability and spectral contents. Spectral Gaussian Random NonGaussian Representation Random Variable Random Method Process, u Transformation Process, x A :::: Replacement PSD I Target PSD Sm  Correct PDF S P7 Correct PSD Figure 33. Correlation Distortion Yamazaki and Shinozuka (1988) presented a Correlation Distortion simulation algorithm that iteratively alters the PSD associated with the Gaussian sample function before transformation (see Figure 34). During each iteration, a Gaussian sample function u is generated from the current S, and passed through a Gaussian to non Gaussian CDF Map. If the resultant PSD S, matches the target ST as measured by the chosen error quantification, the simulation is successful and the algorithm exits. If S, is deemed an unacceptable match of ST, an updated version of S,, is produced via the following equation, T Sn S '+l = S (42) where i = iteration index. Generally, the first underlying Gaussian PSD S, is seeded with the target SI for simplicity. The resultant underlying Gaussian PSD is unique to the individual sample function, and cannot be reused to generate multiple sample functions. For faster convergence and greater robustness, Deodatis and Micaletti (2001) suggested a modification to Eq. 42: Suu+l Suu (43) where the /factor is included to attenuate the iterative modification to the underlying Gaussian PSD. For most applications, / may be set to 0.3 (as determined by trial and error to optimize convergence). Grigoriu (1995, 1998) offered another Correlation Distortion method that utilizes the relationship between the scaled covariance function T of the target process and a Gaussian image <,, (see Figure 35). For a process with a variance of unity the scaled covariance function is o (r) = f (g(y) )(g(z) p)4y, z, po (r)]dy dz (44) where g is a monotonic translation (CDF mapping function) and q(y,z,po(r)) is the density function of a standard bivariate Gaussian distribution with Gaussian variables of integration and z and the corresponding Gaussian correlation coefficient po (which is bounded by + unity). o is the corresponding correlation between the nonGaussian variables g(y) and g(z). Eq. 44 is used to map the relationship between the target non Gaussian scaled covariance function 'jT and the underlying Gaussian scaled covariance function 5,, corresponding to o and po respectively. The underlying Gaussian PSD Su, is then identified from ,u, via the WienerKhintchine relationship. For multivariate simulation, Eq. 44 is modified to map between pairs of variates as: (r) = U (g (y) X)(g (z) 2) y, z, p, (r)]y dz (45) where gi and g2 are the CDF mapping functions for the two random variables with potentially different marginal PDFs imparted by the operators gi and g2. Eq. 45 is required to calculate the offdiagonal terms in the underlying scaled covariance matrix (Grigoriu 1995, 1998). Figure 34. Yamazaki and Shinozuka univariate stochastic simulation technique For largescale Monte Carlo simulation, Grigoriu's method holds one major advantage. Since the underlying Gaussian spectrum is a function of the target PSD and END not the PSD of an individual sample function, it may be reused for each new simulation. Convergence to the target PSD can be shown in the ensemble sense, although any individual sample function will contain variance ordinatee) error in the PSD. Figure 35 Grigoriu univariate stochastic simulation technique Shinozuka and Deodatis (1996) presented an efficient algorithm to simulate ergodic Gaussian multivariate stochastic processes, and Gioffre et al. (2001) utilized a modified algorithm using Eq. 45 that is suitable for the simulation of stationary nonGaussian random variables. An outline of this methodology (illustrated in Figure 36) is presented below: Steps 16. Calibration: Random Variable Prescription and Correction for Non Gaussian The following steps need only be performed once for each set ofprobabilistic, spectral and crossspectral targets. 1. For each random variable X1...XN (where N = number of correlated random variables under simulation), prescribe the following: marginal PDFfx (with mean /.x = 0 and variance cr =1) PSD S (a))appropriately discretized N1 S k coherence functions y7, (ao,, P2,... ,pM)for each pair of ith and jth k=l variates 2. Create an NX Ntarget PSD matrix STx S S ... S' X1X1 1X2 lN S' S' ... S1 S T X2X1 2X2 (46) S' ... S' NXX1 N2 NN where the diagonal terms are the autoPSDs (S,,), and the offdiagonal terms are calculated from the coherence function and the respective autoPSDs between the ith and th variates: S,, (o)= S,,()Sjj(m)r,(cu,pl,p,...pM) (47) 3. Using the WienerKhinchine Relationship, calcue te t t = c 0,varae f n ma=)=Slate the t (ro)eo () calculate the target scaled covariance function matrix e from the cross PSD Sx^ T T xNx1 xxN2 e r_ >, x >xx T T ] x2xN ... XVXV 4. Create the underlying Gaussian scaled covariance function u. by mapping the diagonal terms of Eq. 49 through Eq. 44 and the offdiagonal terms of Eq. 49 through Eq. 45 5. Using the WienerKhinchine Relationship, S,(g)= 1 jC (r)e ""d 2;r convert ,. into the underlying PSD S,, SU, SU1U2 Su,, Su2U2 SU UUl U2U2 ... SU1UN ... S2U ... U NUN 6. Perform a Cholesky decomposition of Su, at each frequency point S21(C0) Ns(I(O=) s(^ (S) s2 () S22 () SN2(() H 11(w) 0 0 H'1() H21,(w) H,22() 0 H*21(Co) HNI(a) ( 2() H,, () Hi()_ HN (0) .................................*....*.* e ** ee* *ee H(o)H* ()' 0 H*22(W) H 2 (C) T 0 0 * HNN (0) Steps 710. Simulation of Correlated Random Variables The following procedure isperformedfor each set of unique realizations. 7. Generate a complex white noise vector = r + gi from two independent Gaussian white noise vectors q and with means and variances E[]= E[C]= 0 (53) E[72] E[ 2]= A (54) 8. Multiply the cholesky decomposition H(o) and q to get the underlying correlated Gaussian PSDs U(o) U,(o3) H~I(W) 0 ... 0 (3) U2) H21 ) H22( 0 02()) (55) U (o)) H,, (o) H ()() ... HN2()_ (o)_ 9. Inverse Fourier transform each U(o) into its correlated Gaussian time series u(t) 10. CDF Map the correlated normal random variables through their respective target nonGaussian probability distributions through Eq. 40. The underlying Gaussian PSD and crossPSD will then distort to the final desired targets Spectral Correction Recent publications have presented alternatives to the Correlation Distortion methods to simulate univariate (Gurley et al. 1997, Masters and Gurley 2003) and multivariate (Gurley and Kareem 1998) nonGaussian sample functions using a technique known as spectral correction. This method does not seek an underlying Gaussian PSD for the initial sample function and thus is not properly classified as a Correlation Distortion method. Rather, Spectral Correction iteratively applies corrective transformations to the probability and spectral content of the signal in the time and frequency domain, respectively, until the signal converges to the PDF and PSD targets. For Each RV For Each Pair of RVs Prescribe Target CDF Prescribe Coherence Functions Prescribe Target PSD Build CrossPSDs IFFT Build Target Scaled Covariance Matrix 0 Create (p) Map for each pair of Scaled Covariance Functions Map Target Covariance Functions through the Map into the underlying Covariance Functions Convert underlying Covariance Functions into underlying PSDs Simulate Correlated Gaussian RVs from underlying PSDs CDF Map Correlated Gaussian RVs into Correlated nonGaussian RVs Figure 36. Shinozuka and Deodatis correlated nonGaussian multivariate stochastic simulation technique Two Spectral Correction methods are available for univariate simulation, and they differ by technique of random variable transformation. The original method by Gurley and Kareem (1997) relies on a Hermitebased probability filter to correct the statistical content of the simulated random process. Fourparameter models like the modified Hermite polynomial (i.e., PDF models that require knowledge of the mean, variance, skewness and kurtosis to generate the parameters that affect the shape of the distribution) have been used with excellent results in a variety of applications where traditional models fail to properly represent the time series under consideration. The third order Hermite polynomial is one such fourparameter model that has been used in civil engineering applications. The coefficients in the polynomial are selected based on the desired first four moments (Winterstein 1995). x = fUX + K [u + c3 (u1)2 1) + 4 (3 3u)] (56) K= 1+2C32 +6c,2)0 (57) where the normalized Gaussian sample function u is translated to the nonGaussian sample function x. The parameters c3 and c4 are dependent upon the desired third and fourth central moments skewnesss y3 and kurtosis y ): c Y3 13 (58) 6 1+0.2( 3) 4 4 1 l4 (23T 10 01(yT )I8 c 40 1i 1.43( 11.254 3)1 (59) 74 3 c40 10 Eqs. 58 and 59 provide an approximate solution to identifying the parameters c3 and c4. For higher accuracy, an optimization routine (using c3 and c4 as initial guesses) is employed to determine the parameters needed to provide a sample function with the desired moments (Gurley and Kareem 1997). Limitations The stochastic simulation methods outlined in the previous sections work well for many engineering applications, including the generation of environmental loads in the analysis of structural response, but are subject to limits concerning the choice of target probabilistic and spectral content. This section details those limitations. Four Parameter Hermite Polynomial Transformation. Unlike the Correlation Distortion methods that utilize the CDF mapping concept, Hermitebased Spectral Correction uses only the first four moments to define the desired probability. The resulting PDF in the sample function is always described by a fourparameter thirdorder Hermite polynomial PDF model (Gurley and Kareem 1997, 1998a). The probability correction requires an optimization routine to identify the Hermite polynomial coefficients needed for an accurate transformation to the desired moments. This presents two limitations to the Spectral Correction method. The first is the computational expense of the simulation due to the embedded optimization. The second is a limit in the range of probability contents that can be simulated. Since the Hermite PDF (with its domain of + 00) has unbounded tails, it may not accurately recreate a PDF that is bounded. Additionally, the absence of higher order moments (i.e., > 4th order, such as hyper skewness and hyperkurtosis) as inputs to the polynomial affects the tails and peaks adversely for some families of probability distribution functions. A solution to these limitations replaces the Hermite polynomial transform with a modified CDF mapping technique to impart the desired probability to the realization (Masters and Gurley 2003). This improves numerical efficiency by eliminating the embedded Hermite optimization, and expands the range of probability content to any desired PDF model. Spectral and Probabilistic Incompatibilities. The methods presented by Grigoriu (1998) perform well for symmetrically nonGaussian and/or widebanded systems, but incompatibilities will arise for certain combinations of highlyskewed and/or narrow banded processes. This observation made by Grigoriu (1998) was addressed in several works (Deodatis and Micaletti 2001, Gioffre et al. 2001) by presenting two forms of incompatibility that arise during the translation of a Gaussian process u into a non Gaussian process x: 1. Successfully mapping the target scaled covariance function 'Tj through the mapping scheme is only possible if every ordinate of 'x lies between <* and 1, where equals the evaluation of the double integral at p = 1. If any value of T, falls outside this range (i.e., the additional constraint that the map is bounded above (p = 1) as well as below (p = 1) 2. The underlying autocorrelation function C,, as determined through the application ofEqs. 44 and. 45 can be nonpositive definite, producing an underlying Gaussian power spectral density S,, with values < 0. This is a physically unrealizable condition The Efficacy of LargeScale Simulation. In addition to the abovementioned mathematical obstacles associated with the algorithm, largescale multivariate simulation also carries storage limit issues. The use of crossspectral matrices inherently requires tremendous data storage and handling capacity. For example, multivariate simulation via the method offered by Grigoriu requires 12(N2 +N) integration of Eqs. 44 and 45, where Nis the number of random variables under simulation. One collaborator in the NIST project, Massimiliano Gioffre of the University of Perugia, reported extreme difficulty in simulating more than 8 correlated random variables at one time at the expense /2(82 + 8) = 36 integration. The practical bottleneck is the solution of the Cholesky decomposition of the spectral matrix. The spectral matrix associated with N> 8 strongly correlated variables leads to illconditioned spectral matrices, and the decomposition fails. While this can be numerically avoided using an ad hoc adjustment procedure, eventually enough frequencies are affected that the resultant simulations diverge from the intended crossspectral targets. Application of Simulation for the NIST Project: Interpolation of Existing Time Histories As presented in Chapter 2, the specific application of stochastic simulation in this research is to digitally create uplift loading on the roofs of lowrise structural shapes that were not tested in wind tunnel studies. The spectral and probabilistic targets for the simulations are derived by interpolating models from time histories of tested buildings of similar shape. Given the restrictions in the number of variables that may be simulated, efforts focus on simulation of aggregate loads over large sections of the roof. Evaluating the efficacy of deriving appropriate models using interpolation schemes is a major contribution to the NIST project. The direct interpolation of peak loads from measured time histories was also found to be valid, thus deemphasizing the need to rely on full simulation algorithms to characterize key load parameters on untested buildings. Details of the study are found in Chapter 6. Summary This chapter presented the background material for the original contributions to be discussed in Chapters 4 through 6. The statistical characterization of hurricane winds has been discussed, and will be applied in Chapter 5 to the analysis ofFCMP datasets collected since 1999. NonGaussian stochastic simulation has also been discussed, including the limitations which partially determined the direction of the research 59 presented in Chapter 6. The next chapter presents the FCMP data collection efforts, and the impact of the program on meteorological and emergency management interests. CHAPTER 4 FULLSCALE MEASUREMENT OF TROPICAL CYLONE WINDS During the 19982003 Atlantic hurricane seasons, the FCMP deployed instrumented towers for ten named stormsGeorges, Dennis, Floyd, Irene, Gordon, Gabrielle, Michelle, Isidore, Lili and Isabeland collected 29 data records at locations throughout Florida, Lousiana and North Carolina. Twenty one of these records were selected for analysis in Chapter 5. This chapter addresses four aspects of the experimental process. First, the history, organization and logistics of deployments for selected storms are discussed. Second, the satellite tower system employed during Isabel (2003) to calculate lateral integral length scales is presented. Third, this chapter details the development and implementation of the first mobile realtime data acquisition system to transmit detailed coastal tower wind data to National Oceanic and Atmospheric Administration (NOAA) meteorologists during a landfalling hurricane. Finally, outcomes of the realtime data acquisition system are addressed, specifically the response from meteorological and emergency management interests. Deployment History, Organization and Logistics This section provides a brief narrative of the events that occurred during four storm deployments and details the involvement of research teams at the University of Florida (UF) and Clemson University (CU). Synoptic history and track data for each cyclone were taken from the National Hurricane Center Tropical Cyclone Report archives, available at the agency's website: www.nhc.noaa.gov. Pictures of the deployment sites are located in Appendix B and may also be found at the project website: www.ce.ufl.edu/fcmp. Irene (1999) At 1200 UTC on October 13, 1999, Irene reached tropical storm status in the northwestern Caribbean Sea and kept a general northward track before slowing down and curving to the northnortheast southwest of the Isle of Youth, Cuba. The center of the storm crossed the Havana and Ciudad Havana provinces on the 14th. Irene reached hurricane status over the Florida Straits before its center moved over Key West and made landfall near Cape Sable, Florida as a tropical storm. The cyclone trekked across southeast Florida, eventually reemerging back over water in northern Palm Beach County near Jupiter at approximately 0000 UTC on the 16t UF and CU teams arrived in Melbourne Beach prior to the storm's arrival on the evening of the 15th, where colleagues from Florida Institute of Technology and local authorities assisted in the location of deployment sites. With their assistance, teams were able to begin acquiring data by 1100 UTC. During the night, Irene regained hurricane strength and began a northward track paralleling the Florida east coast heading for the Carolinas. An upperlevel trough, sweeping eastward across the eastern United States, sped its progress. On the morning of the 16th, teams collected the towers and caravanned up the 195 corridor to intercept the storm. Within a few hours, the convoy was traveling parallel to Irene, where buffeting winds and unavailability of fuel (gasoline pumps require power to operate) significantly impeded the team's progress. At 0100 UTC on the 17th, twentyfive hours after the departure from Melbourne Beach, teams arrived in Wilmington, NC, where two towers were deployed. Residential and shoreline exposure were chosenthe shoreline site would be later reused by Tower Tl in Hurricane Isabel. The FCMP only succeeded in capturing the outer bands of Irene in North Carolina because the cyclone veered away from the mainland and brushed the Outer Banks before moving out to sea. Gabrielle (2001) The shortest deployment in FCMP history occurred during Gabrielle, which made landfall in Venice, Florida around 1200 UTC on September 14, 2001. The cyclone moved in a small counterclockwise loop over the southeastern Gulf of Mexico for two and a half days before reaching tropical storm strength on the 13th. At that time, Gabrielle was located 325 km southwest of the landfall site. One UF team with tower T1 in tow left Gainesville around 2200 UTC on the 12th to intercept the storm and arrived in Venice Beach immediately prior to landfall. Data collection continued into the early afternoon, and the team returned to the University of Florida by late evening. Isidore (2002) Isidore became a hurricane at 1800 UTC on September 19, 2002 as it tracked west northwest across the Cayman Islands. As the cyclone neared the southwest coast of the Isle of Youth, Cuba, the FCMP deployed one UF team to monitor the storm from Key West, Florida. Isidore moved westerly, however, and the team only succeeded in capturing the outermost bands of the cyclone. Isidore moved west and southwestward toward the Yucatan Peninsula, reaching its maximum intensity of 56.6 m/s (126.7 mph) at 1800 UTC on the 21st. The cyclone remained nearly stationary for 24 to 36 hours over northern Yucatan and weakened to a minimal tropical storm, before it moved northward over the Gulf of Mexico. Figure 41 contains a map of the deployment region. 63 *83a 495' 67 3(1 Alabama / Mississippi I Florida Loulsiana : TO V ) TZ' 2610600 UTC S 15 3'0 0 Miles *9C 45' ? 30' Figure 41. Deployment of instrumented towers during Tropical Storm Isidore (2002) UF and CU FCMP teams remained on standby as the cyclone moved northward into the Gulf of Mexico, anticipating the possibility that Isidore might strike somewhere in the array of instrumented homes located on the west end of the panhandle of Florida (shown in Figure 24). On the 24th, UF met CU in Gulf Breeze, Florida, to ready three instrumented homes and set up three towers (TO, T and T2) in close proximity. Isidore made landfall with winds of 28.3 m/s (63.4 mph) with a minimum pressure of 984 mb just west of Grand Isle, Louisiana at 0600 UTC on the 26th. Although it weakened to a minimal tropical storm in the Gulf of Mexico, its circulation expanded which provided significant wind (as high as 26.9 m/s) approximately 350 km away. Lili (2002) As the center of Hurricane Lili trekked past the southwest tip of the Isle of Youth over western mainland Cuba on October 1st, FCMP teams from CU and UF traveled to Mobile, Alabama. On the morning of the 2nd (while the cyclone turned northward through the Gulf of Mexico), FCMP personnel and equipment caravanned to Baton Rouge, Louisiana and set up base camp. In the afternoon, the team split into two deployment groups. The first team traveled west along I10 inserting towers in Lafayette (TO) and Baton Rouge (T1). The second team traveled south placing towers in Donaldsonville (T2) and Lydia (T3). With nine personnel working, the four towers went operational over a 7hour period (between 2/2303 and 3/0616 UTC). Figure 42 illustrates the tower locations with respect to the path of the cyclone. o03 1800 rc Louisiana *1 *TO T2 *T3 _ . 03 .1200 UTC ' 03 1 200 UTC .Kim.. 03B60UTC 12.5 25 P is Figure 42. Deployment of instrumented towers during Hurricane Lili (2002) Between Cuba and Louisiana, Lili intensified to 64.4 m/s (144 mph) early on the 3rd over the northcentral Gulf of Mexico and then rapidly weakened during the 13 hours until landfall. Lili made landfall on the Louisiana coast with an estimated 41.2 m/s (92.2 mph) maximum wind speed. Isabel (2003) Isabel captured the attention of the FCMP during the second week of September 2003. Initially, it appeared that the storm's path would bring in within striking distance of Florida's Atlantic coastline as it emerged from the Greater Antilles. Uncertainty in the forecast beyond that point, namely the influence of troughs/ridges that would eventually steer the storm, brought great trepidation to communities in hurricane prone regions along the Atlantic coast. At its peak intensity, the hurricane, with SaffirSimpson Category 5 winds and a 90 km eye, represented a potential major threat to lives and property. By the end of the week, meteorologists at NOAA's Tropical Prediction Center had narrowed the projected path of the storm to landfall somewhere in or above the Carolinas. On the 13th, FCMP teams were put on standby, anticipating deployment to that region. Final testing of the new "internetcapable" data acquisition system was completed earlier in the week, and for the first time, the FCMP mobile towers were synchronized with forecasters at the Hurricane Research Division of NOAA to transmit realtime high resolution data every 15 minutes from the field. Equipped with this new technology, the team from the University of Florida left Monday with towers T1 and T2 and arrived in Morehead City, NC early Tuesday. The optimal location for a tower (to capture the highest winds) is north of the predicted landfall for a hurricane striking the Atlantic coast. To achieve this end required tower deployment around the Outer Banks, a great challenge for the FCMP. First, traveling on barrier islands required that the team arrive well in advance of the closures of inbound traffic lanes. Secondly, potential tower sites were limited by the storm surge potential for that area. After coordinating with the Clemson University FCMP team and researchers from Texas Tech University, the UF team decided to deploy T2 in the vicinity of Morehead City (north of the latest forecasted landfall). With the help of South Carolina Sea Grant, the team contacted the North Carolina Department of Environment and Natural Resources and received permission to erect at Tower at Fort Macon State Park. T2 went operational at 1530 UTC, and afterwards, the team secured lodging in Morehead City. For the remainder of the afternoon, the team scouted Craven and Pamlico counties to locate a site amenable to the new satellite tower system, which required an open 60 m swath of land to erect the three towers. As nightfall approached, it became apparent that the majority of the coastline was unacceptable for deployment, given the reach of the estuary system and its favorable environment for flooding and storm surge. The team backtracked its survey and received permission to deploy the towers on a horse ranch in Oriental, a small town five miles inland. Meanwhile, the Clemson FCMP team arrived in Wilmington to begin instrumentation of a home the following day. Early Wednesday morning, the UF team traveled from Morehead City to Wilmington to reorganize teams. The first (southern) team remained in Wilmington to instrument the home, and the second (northern) team pulled the remaining towers northward to deploy in Elizabeth City (TO) and Cape Hatteras (T3), two population centers with established local contacts and potential for higher ground. As the northern team split off, 36 hours remained until the expected landfall of Isabel. The TO Team secured a site at the Elizabeth City Coast Guard Airstation. Bordering Pamlico Sound, the flat expanse of terrain afforded by the airport provided a significant amount of upwind open exposure. After some modifications to the new software were made, TO went operational at 0541 UTC. The team secured lodging for the entire northern team nearby. The T3 team traveled through Manteo to reach the outer banks. After conferring with locals, the team decided to deploy the tower at Billy Mitchell Airport, purportedly the highest ground in Cape Hatteras. T3 went operational at 0214 UTC on the 18th, and afterwards, the team drove to Elizabeth City to join up with the remainder of the northern team. Meanwhile, the southern team had split, allowing one group to complete the home instrumentation and the other to refill the onboard generator on T1 in Oriental. New information concerning flooding at the existing site, however, prompted the team to relocate T1. With the preparations to instrument the home in Wilmington nearing completion, the team decided to relocate T1 to capture the wind field in the vicinity of the house. The teams recombined and erected the tower system at a nearby boat ramp. T1 restarted at 0420 UTC on the 18th After the storm passed, the priority of all teams involved became retrieval of instrumentation. For TO, T1 and T2, this was a relatively straightforward operation, but extracting T3 from Cape Hatteras required significantly more effort than inserting it. Multiple roadblocks separated the team from the tower, each progressively more difficult to negotiate. After acquiring the proper permit, the team stopped in Kill Devil Hills to perform damage surveys. The imposed mandatory curfew throughout the Outer Banks forced the team to continue south to collect the remaining tower, however. The storm surge that impacted the strip of land between Nags Head and Rodanthe rendered US 12 impassable in some areas, leaving up to 2 m of aerated sand across the roadway. Using 4wheel drive and bypassing the road via the beach, the team inched their way down the coastline, arriving in Cape Hatteras in the early afternoon. A map of the impacted region and the location of FCMP instrumentation is provided in Figure 43. Florida Coastal Monitoring Program i INiPam 0 ASOS Deployment for Hurricane Isabel FCMP Towes BUOY Septfmber 1619, 2003 A FCMP Houses CMAN For more Informailon, visit our web page at htp://www.ce.ufR.edu/rcmp WE.MITE METAR Figure 43. Deployment map for Hurricane Isabel Satellite Tower System Studies of the correlation structure and integral length scales of lateral turbulence have been conducted since the 1920s. The earliest experiments were conducted to study the strength of wind loading on electric power lines in winter storms (Sherlock and Stout 1937). Through 19601972, extensive threedimensional turbulence data were obtained (Counihan 1975), and relationships between the longitudinal and lateral components were developed (Shiotani 1967, Harris 1971, Deacon 1971). In the summer of 2003, two of the four instrumented towers were outfitted with additional towers to conduct similar experiments, but in a wider range of exposures and in tropical cyclone winds. Lightweight (<37 kg) and highly portable, the 5m aluminum towers may be erected up to 37 m (120 ft) from the main tower. In practice, the satellite towers are separated from the main tower by 15.2 m (50 ft) and 30.5 m (100 ft). This asymmetric configuration allows the FCMP teams to investigate correlations of wind speeds of lateral separation distances < 45.7 m (150 ft). The left picture in Figure 44 illustrates the deployment geometry and orientation (as configured for testing in Tropical Storm Henri) A team of three people can assemble one tower in less than 30 minutes. The main tower is erected with the tongue of the trailer facing the direction of anticipated maximum winds (into the path of the storm at landfall). Next, the team removes the satellite towers from the main tower (shown in the right picture in Figure 44) and places them on opposite sides of the main tower. (a) Tower array (b) Transportation Figure 44. Tower deployment and transportation The satellite towers employ two measures to resist the wind: four shear pins are driven with a sledgehammer to resist sliding (shown in the left picture in Figure 45) and three guy wires attach the top of the tower to earth screws to provide lateral stability (shown in the right picture of Figure 45). Once the guy wires are attached at the top of the tower, research personnel augur the earth screws into the ground and attach RM Young threeaxis gill anemometers to the same assembly hub found on the larger towers. Then, the tower is raised and the guy wires are connected to the earth screws. The turnbuckles are tightened to remove slack and to level the tower. Finally, safety ribbons are tied to the guy wires for visibility, and a shielded cable is connected from the main tower's computer enclosure to the satellite tower. Figure 46 illustrates this process. (a) Shear Pins (b) Earth Screws and Guy Wires Figure 45. Satellite tower stabilization During Isabel, the satellite tower system was tested successfully at the Wilmington and Frisco, North Carolina sites. Preliminary results of length scale analysis, site details and suggestions for future deployments may be found in Aponte (2003). (a) Anemometry (b) Safety measures Figure 46. Satellite tower instrumentation and safety considerations As the goal of this research is the estimation of lateral and longitudinal length scales in different roughness lengths, many additional experiments will have to be performed to produce statistically meaningful results. For this reason, the FCMP will construct six additional lightweight 5m towers for the 2004 season. The 5m tower design has been modified for the construction of two 10m lightweight tower systems. The 10m towers will operate independently of the main towerdata collection will be performed on a notebook computer encased at the base of the tower. These systems will also be internet capable, the subject of the next section. RealTime Data Acquisition Recognizing that realtime access to surface level wind speeds during hurricane landfall would aid: * meteorological institutions forecasting the hurricane's path and local news affiliates providing weather updates to the public * federal, state and local agencies conducting emergency management operations including both evacuation and assignment of limited recovery resources post disaster * utility companies assessing potential damage and estimating a time of safe entry to begin restoration of power, water, telephones, etc. * the FCMP teams, which need to respond quickly to any problem that might occur during data acquisition, the FCMP team enhanced its existing hardware and software on its mobile tower system to disseminate real time data over the internet. Each of the four 10meter towers is now equipped with new hardware and software that orchestrate collection, postprocessing and internet connectivity on National Instrument's LabVIEW platform. The new software, dubbed Tower XP, was developed at the University of Florida and represents an original contribution to FCMP research efforts. For redundancy, the FCMP team used the original tower computer system (detailed in Chapter 2) in conjunction with the new hardware/software. Additional storage space was needed and new computer enclosures were constructed to house the laptops, cellular modem and CDMA antenna (shown in Figure 47). (a) Enclosure Fabrication (b) Mounted Enclosure Figure 47. Computer enclosure for remote transmission of FCMP data The Tower XP software retained all of the capabilities of the original software (used since 1998) and received five major enhancements: realtime data transfer to the internet, continuous data acquisition, automatic data processing, an improved graphical interface and the flexibility to make changes to the software in the field if necessary. Internet Upload Capability Given the number of available coverage plans and technologies available to implement the realtime data acquisition system, a study was carried out to determine the optimum plan for the FCMP's needs. Four of the major cellular technologies in the United States were considered: Global System for Mobile Communications (GSM), Iden/Nextel, Time Division Multiple Access (TDMA) and Code Division Multiple Access (CDMA). TDMA and CDMA dominate the American markets, with GSM gaining in popularity but still lacking in coverage. CDMA is considered the more advanced digital technology and generally has better performance than TDMA because it separates channels by giving each user a unique code that is used to identify his or her conversation. For this project, a CDMA dual mode digital cell phone that works in the 850 MHz band was chosen to transmit data from the tower to remote network servers every 15 minutes. Verizon's wireless data service plan was chosen from the subset of companies offering this service because it carries the largest area of coverage in the southeastern United States. With this plan, the laptop dials into one of two services depending on availability. In larger cities, the modem connects to Verizon's Express Network (CDMA2000 IX) and transfers data at speeds up to 144 Kbps (averaging 4060 Kbps). Otherwise, the modem dials into Verizon's Quick 2 Net service on regular CDMA with speeds up to 14 Kbps. Either way, the modem dials directly into an internet service provider (ISP), making file transfers out of LabVIEW possible. The modem is connected to the notebook by a serial port connection, and TCP/IP connections are managed by Microsoft Windows' builtin command window dialup capabilities (rasdial.exe). Once the notebook connects to Verizon's internet service, files are transferred through execution of customized file transfer protocol (FTP) scripts. If the transfer is successful, the modem disconnects and the software waits until the next transfer request. If the transfer fails, Tower XP tries connecting once more with the high speed connection before attempting a final connection with the slower service. The software also supports the option to use either an ethernet or a phone line to connect to the internet and can be configured to disable its upload capability if required. Continuous Data Acquisition The original system collected data and paused 24 seconds to store it to the hard drive after every 15 minutes of operation, which left gaps in the data. In Tower XP, data are stored at 10 Hz in a circular memory buffer on the data acquisition card, which allows for seamless acquisition and storage. Automated Processing of Data The original software (prior to summer 2003) did not process data during acquisition and required considerable effort to extract the data. Raw voltages were written to binary data files and reloaded into the program poststorm to retrieve the data. Voltages were scaled into engineering units, and records from gill anemometry were converted from the nonorthogonal experimental configuration into wind speed, wind direction and the vertical fluctuation. As the system did not possess batch processing capabilities, research personnel were required to spend three to four hours extracting the individual files. Additionally, corrections for the tower orientation and time gaps had to be made in postanalysis. All of these procedures had to occur before analysis (turbulence intensities, gust factors, length scales and spectra) could begin. Tower XP was designed to obviate these issues. The software calculates turbulence intensities, peak gusts, roughness length estimates, and averages of temperature, humidity, rainfall and barometric pressure information every 15 minutes and writes a summary text file for transfer to the internet through its builtin upload feature. After the storm, research personnel activate a subprogram that batch processes the data into text files, which are formatted to be read into several analysis programs (including Matlab, Mathcad and Excel). Wind direction records are automatically adjusted with regard to the orientation of the tower, and each instantaneous data point is uniquely time stamped. For 2004, a new module is under development to write (serialize) data directly to Matlab binary files to improve processing times. Improved Graphical Interface This interface allows users to input considerably more information about the deployment site and its terrain than the original software. Figure 48 illustrates the configuration of the user interface of the data acquisition software developed for Tower XP. After the program is started, the user activates the configuration algorithm (user interface), which consists of five components (dialog boxes). First, the sampling rate and the number of scans the data acquisition card are set. Based on the number of channels, the size of the binary files is estimated. Second, information about the storm and the location and orientation of the tower is input. This information is written to a text file that can be sent to the web server if desired. Third, easytoread gauges and digital readouts provide 1 Hz measurements from all of the instrument channels to assist research personnel during the system checkout. Fourth, descriptions of the upwind fetch are entered into the program. If the user has captured digital photos of the site, a dialog box can be activated to load the picture into the program for uploading to the web server. This feature can only be used with the high speed cellular or ethernet connections. Finally, the user selects the connection type and initiates a test of the software's upload capability. DATA ACQUISITION INPUT: Sampling Rate, Number of Scans, Memory Buffer Size and Channels DISPLAY: Estimated File Size DEPLOYMENT I INPUT: Stor Name, Towe Number, Phys Location, GP Coordinates Azimuth to No Team Members Misc. Notes INSTRUMENTATION INTERNET CONNECTIVITY DISPLAY: Readings INPUT: Choice of of Voltages or connection: Low or Engineering Units High Speed Cell, from Instruments of Phone, Ethernet or Raw Channels None and Orthogonal Components ACTION: Upload file with site information NFO TERRAIN DESCRIPTION m INPUT: ?r Description and ical pictures of the 'S upwind exposure , in the N, NE, E, BEGIN DA rth, SE, S, SW, Wand ACQUISI and NW directions Figure 48. Configuration of Tower XP user interface to set up data collection Tower XP's graphical interface is updated every time data are stored to the hard drive. Research personnel can view 3second and 1minute time histories of wind velocity data recorded in the previous 15minute segment. ATA TION Improved Flexibility Tower XP is a flexible program that can easily be reconfigured to collect data over any length interval. Unlike the original software, the LabVIEW platform is an interpreted, graphical language that does not require recompilation of the source code if a change is made. The capability to record data from the satellite tower system was added to the program's functionality. In a future version, this feature will be activated. Outcomes of Hurricane Isabel The FCMP intended Hurricane Isabel to be the proving grounds to test the prototype realtime data acquisition system. Within 24 hours of the first upload, however, its role in a research experiment shifted to that of an operational tool for meteorologists and hazard loss estimators. Each of the four tower systems reliably transmitted data to web servers even while a number of METAR and CMAN weather stations lost communication with their network. This section addresses the importance of continuing synergistic research in the wind engineering community, specifically through the efforts of the FCMP to meet the needs of forecasters and emergency managers during Hurricane Isabel. The feedback from the various users of the realtime data systems deployed during Isabel indicates a strong need for continuation of this program and the further development of its capabilities. Impact on Meteorology The concept of developing a realtime data acquisition capable of transferring summary files to the internet was borne from the recognition that meteorologists and FCMP researchers could equally benefit from a remote monitoring capability. During its development, considerable interaction occurred with scientists at the Hurricane Research Division (HRD). HRD is the unit of NOAA dedicated to advancing the basic physical understanding of hurricanes and to improving the forecasts of tropical meteorological systems. Based on their recommendations, the summary format and transmission scheme were developed. During Isabel, the collected data were ingested into HRD's realtime hurricane wind analysis system, H*Wind, and utilized to validate measurements from reconnaissance aircraft. Additionally, observations at the northern sites were used to monitor decaying weather conditions. H*Wind. Since 1996, the Hurricane Research Division has operated the H*Wind Project to integrate wind data in and around a hurricane into a single surfacelevel wind analysis for use by hurricane specialists at the National Hurricane Center. Continual development over this period was intended to evolve H*Wind from a hindcasting to a nowcasting model of overland surface level hurricane winds. Data sources include ships, buoys, coastal platforms, surface aviation reports and reconnaissance aircraft data. The evolution to nowcasting is dependent upon the availability of data in nearreal time rather than post storm recovery of wind velocity data. During Isabel, FCMP data were ingested into eight runs of the H*Wind model over September 17th and 18th. Figure 49 contains a map of the 1minute maximum gusts at 1630 UTC as determined by the H*Wind software. Note at the top of the figure the reference to TOWERLD_TO as a source of data for this analysis. These analyses were also used by the National Hurricane Center as a part of the Joint Hurricane Testbed, a consortium between NASA, NOAA and the U.S. Navy seeking to expedite the transfer of technology from the United States Weather Research Program (USWRP) to operational meteorologists. Aircraft Reconnaissance. Meteorologists at NOAA's Hurricane Research Division conduct aircraft experiments to support multiple ongoing research activities at the center. Research aircraft deploy expendable instrument packages called Global Positioning System (GPS) sondes to measure pressure, temperature and position throughout their descent, which is retarded by a parachute. During Isabel (Mission 20030918H1), research aircraft deployed numerous sondes near the Diamond Shoals area specifically for comparison with realtime data reported by Tower T3 at Cape Hatteras. The track of the aircraft through North Carolina is shown in Figure 410, and shows the reliance of the path upon the location of the FCMP tower. Sonde splashdown locations are shown in Figure 411, showing significant and intentional clustering near FCMP tower locations. Data from several other sensors were compared to the incoming data from the instrumented towers, including emissivity records from the stepped frequency microwave radiometer and surface wind speed estimates from flightlevel data. Forecasting. The observations made by the Frisco, NC tower (Tower T3) constitute the highest ground level wind speeds recorded during Isabel and are also the highest wind speeds for which continuous, high frequency, digital observations have been recorded in a U.S. landfalling hurricane. The reaction from meteorologists was encouraging. On October 19th (the day proceeding landfall), Peter Black, Director of the Coupled Boundary Layers/AirSea Transfer (CBLAST) project, contacted the FCMP in regards to the realtime transmission. An excerpt from his email follows: "The placing of your towers appeared just about optimal and the reliability of your real time reports while I was doing the HWIND analysis at NHC on Wed night was fantastic. The CMAN sites went down for a time due to communications problems at Wallops and your data were the only wind reports from the coast that were coming in. I was able to relay the reports to the NHC forecasters and keep them abreast of the rate of wind increase at the coast as Isabel approached. Your effort is a terrific example of how a research project can make a valuable contribution to operations while at the same time gather a research data set that will be studied for years. ... Not only did it make the HWIND product invaluable to forecasters but gave them a sense for how quickly conditions on the coast were deteriorating." Impact on Emergency Management The towers were in close proximity to the Atlantic Ocean, which meant that they provided some of the first inland wind speed observations in the impacted region. They also provided these data four times an hour, a considerably higher frequency than existing weather stations. Unknown to FCMP research personnel during Isabel, these two characteristics prompted hazard loss estimators contracted by the Federal Emergency Management Agency (FEMA) and several major (re)insurance companies to use the real time data to monitor decaying weather conditions. Modelers at several internationally recognized consultant firms, including Applied Research Associates (ARA) and Risk Management Services (RMS), conducted loss estimates throughout the storm's landfall (personal correspondence with Auguste Boissonnade, RMS, April 4, 2004). Once discovered, this fact explained why the FCMP project websiteinitiated one week earlier and known only to project personnel and collaborators at NOAAreceived almost 4000 hits in the 24 hours preceding the storm's landfall. The largest of these models is FEMA's hurricane riskassessment software (HAZUSMH), which estimates the physical damage, economic loss and social impact from a hurricane impact. In the weeks preceding Isabel's arrival, contractors at the National Institute of Building Science and ARA were beta testing the latest release. FEMA decided to implement the program to produce its official damage estimates through the storm. Wind swath data generated from the H*Wind software was ingested into the model (shown in Figure 412), and wind speed estimates were validated against FCMP realtime data. According to presentations at the 2004 National Hurricane Conference (NHC) in Orlando, the developers of the FEMA HAZUSMH model were able to project damages within 20% of the final actual tallies. Specific credit was given to the FCMP realtime data systems for providing accurate wind speed information. The potential impact of a forecasting / nowcasting model of hurricane wind damage lies in the ability of emergency management personnel to allocate recovery resources better in the immediate aftermath of a storm and to make more informed decisions regarding evacuation. The FCMP personnel presented the details of the realtime data system at the 2004 NHC, and received immediate commitments from emergency managers for special assistance with logistics for future deployments, including special access to restricted areas and identification of ideal deployment locations. Such feedback and cooperation underscores the potential impact of this research in the eyes of both federal and local emergency managers. Summary This chapter details the FCMP deployment histories for those storms that are used for the analyses to be presented in Chapter 5. The development of new hardware and software implemented during the 2003 season is also presented. The significance of these contributions is documented in terms of their impact upon the hurricane meteorology and emergency management communities. Beyond providing nearly instantaneous information on peak winds and roughness estimates, the data collected from the FCMP towers also serves engineers seeking to 82 better characterize the localized groundlevel behavior of landfalling hurricane winds and their interaction with structures. The detailed analysis of these wind records from the perspective of wind and structural engineers is presented in Chapter 5. 5 I Hurricane Isabel 1630 UTC 18 Sep 2003 Max I min sustained surface winds (kt for marine exposure Analysis based on GOES from 1802 1602 ; TOWERLD TO froua 1724 1500 z MOOREDBUOY from 1609 1429 z; GPSSONDESFC from 1706 1429 zE SFMR from 1721 I500 o; AFRES fr 171Z 1415z; CMAN from l705 1428a GPSSONDE WLISO fErnn 1706 1429 z; 180 z position Interpolated from 1544 Vortels msr p 957.0 ab 78 76 74 :11 .1 ir M M t 50 78 76 74 Obse rd Ma Surface W&lbd91 kls,47 nm NEofcener basedon 1706 zAFRES scn man n mena Analyzed Ma Wlnd: S I kta, 460a NE of center Experimental research product of: Figure 49. Hurricane Research Division surface wind field analysis (courtesy of NOAA) Figure 410. Track of NOAA research aircraft in Isabel 2003 (courtesy of NOAA) Coastal Mission 20030918H1 during 80 79 78 77 76 75 74 2530 5 43 030918H GPS sodxes # Sonde UTC 4 1024125007 1419 2024125010 1421 3023555110 1423 36 4023555108 1439N" 36 5 024125005 1440 6023555011 1443 7 023555016 1446 8023555104 1504 9023555012 1504 10 023555120 1507 11023555105 1518 12023555017 1531 13023555013 1548 35 14 023555112 1549 35 KMI, I. 1 , *' s21 1, m .11 1b 34 .Lt;'. 1'. KLTX 3 St78 76 75 74 Figure 411. GPS sonde splash locations during Isabel 2003 (courtesy of NOAA) 79 78 77 76 75 74 TO .. K% X , SR1 , .R2 85 35 35 KMHX.i : flLr... .... 34 .~T ~b J34 79 78 77 76 75 74 Study Region: Isabel_NC_VA Current Scenario: User defined; Name: ARABestTrack Legend StormTrlkARA BestTrack StonmTrack ARA BestTrac Wd Speeds eak Gf s (ph) < 50 275 65 1e so 95110 1. 125 140 140 155 M 155 170 S170 185 I 185 200 II >200 Census Tract Reg on Boundary Region Boundary CountyBoundares ] County Boundaries 275 137 5 0 275 Kilometers W r E4 I I 19972003 FEMA Figure 412. Wind swath map from FEMA's HAZUS program, based on the NOAA H*WIND model using FCMP data (courtesy of Applied Research Associates, Inc.) CHAPTER 5 ANALYSES OF TROPICAL CYCLONE WIND DATA This chapter presents analyses of velocity data records from tropical cyclone collected from the FCMP mobile instrumented towers during the 19992003 Atlantic Hurricane Seasons. The goal of the project is to characterize overland turbulent wind behavior by quantifying the statistical descriptions of interest to structural designers. In particular, these data will provide wind tunnel modelers with turbulence information to validate that the model flow field is similar to actual conditions in a landfalling tropical cyclone. Analyses of turbulence intensity, gust factors (ratios of peak shortduration gusts to mean wind speeds of longer durations), integral length scales (statistical estimates of the physical dimensions of turbulent eddies) and power spectra (the distribution of energy with respect to frequency) are presented herein. Knowledge of these descriptors has accumulated since the late 1800s, although most were derived empirically from data sets collected from winter storms and thunderstorms (Counihan, 1975). Whether the turbulent behavior of tropical storms and hurricanes differ from these models remains an active subject of debate (Krayer and Marshall, 1992). This chapter is divided into three sections. The first section outlines the experimental assumptions that guided data reduction and are the basis of analysis. The second section explains the data reduction algorithm employed to evaluate segments for admission to the FCMP storm database and summarizes the quantities of segments by roughness length and mean wind speed. In the final section, results from turbulence intensity (TI), gust factor (GF), integral length scale and power spectral density (PSD) 