DOC. C 55.13: NWS38 <*»* , ° ,r «v ^irts o« * NOAA Technical Report NWS 38 Hurricane Climatology for the Atlantic and Gulf Coasts of the United States Silver Spring, MD April 1987 The %? ***. *h Q Study completed under agreement EMW-84-E-1589 for FEDERAL EMERGENCY MANAGEMENT AGENCY U.S. DEPARTMENT OF COMMERCE National Oceanic and Atmospheric Administration National Weather Service NOAA TECHNICAL REPORTS National Weather Service Series The National Weather Service (NWS) observes and measures atmospheric phenomena; develops and distrib- utes forecasts of weather conditions and warnings of adverse weather; collects and disseminates weather information to meet the needs of the public and specialized users. The NWS develops the national meteorological service system and improves procedures, techniques, and dissemination for weather and hydrologic measurements, and forecasts. NWS series of NOAA Technical Reports is a continuation of the former series, ESSA Technical Report Weather Bureau (WB). Reports listed below are available from the National Technical Information Service, U.S. Depart- ment of Commerce, Sills Bldg. , 5285 Port Royal Road, Springfield, VA 22161. Prices vary. Order by accession number (given in parentheses). ESSA Technical Reports WB 1 Monthly Mean 100-, 50-, 30-, and 10-Millibar Charts January 1964 through December 1965 of the IQSY Period. Staff, Upper Air Branch, National Meteorological Center, February 1967, 7 p, 96 charts. (AD 651 101) WB 2 Weekly Synoptic Analyses, 5-, 2-, and 0.4-Mb Surfaces for 1964 (based on observations of the Meteorological Rocket Network during the IQSY). Staff, Upper Air Branch, National Meteorologi- cal Center, April 1967, 16 p, 160 charts. (AD 652 696) WB 3 Weekly Synoptic Analyses, 5-, 2-, and 0.4-Mb Surfaces for 1965 (based on observations of the Meteorological Rocket Network during the IQSY). Staff, Upper Air Branch, National Meteorologi- cal Center, August 1967, 173 p. (AD 662 053) WB '+ The March-May 1965 Floods in the Upper Mississippi, Missouri, and Red River of the North Basins. J. L. H. Paulhus and E. R. Nelson, Office of Hydrology, August 1967, 100 p. WB 5 Climato logical Probabilities of Precipitation for the Conterminous United States. Donald L. Jorgensen, Techniques Development Laboratory, December 1967, 60 p. WB 6 Climatology of Atlantic Tropical Storms and Hurricanes. M. A. Alaka , Techniques Development Laboratory, May 1968, 18 p. WB 7 Frequency and Areal Distributions of Tropical Storm Rainfall in the United States Coastal Region on the Gulf of Mexico. Hugo V. Goodyear, Office of Hydrology, July 1968, 33 p. WB 8 Critical Fire Weather Patterns in the Conterminous United States. Mark J. Schroeder, Weather Bureau, January 1969, 31 p. WB 9 Weekly Synoptic Analyses, 5-, 2-, and 0.4-Mb Surfaces for 1966 (based on meteorological rocket- sonde and high-level rawinsonde observations). Staff, Upper Air Branch, National Meteorological Center, January 1969, 169 p. WB 10 Hemispheric Tele connect ions of Mean Circulation Anomalies at 700 Millibars. James F. O'Connor, National Meteorological Center, February 1969, 103 p. WB 11 Monthly Mean 100- , 50-, 30-, and 10-Millibar Charts and Standard Deviation Maps, 1966-1967. Staff, Upper Air Branch, National Meteorological Center, April 1969, 124 p. WB 12 Weekly Synoptic Analyses, 5-, 2-, and 0.4-Millibar Surfaces for 1967. Staff, Upper Air Branch, National Meteorological Center, January 1970, 169 p. NOAA Technical Reports NWS 13 The March-April 1969 Snowmelt Floods in the Red River of the North, Upper Mississippi, and Mis- souri Basins. Joseph L. H. Paulhus, Office of Hydrology, October 1970, 92 p. (COM-71-50269) NWS 14 Weekly Synoptic Analyses, 5-, 2-, and 0.4-Millibar Surfaces for 1968. Staff, Upper Air Branch, National Meteorological Center, May 1971, 169 p. (COM-71-50383) NWS 15 Some Climato logical Characteristics of Hurricanes and Tropical Storms, Gulf and East Coasts of the United States. Francis P. Ho, Richard W. Schwerdt, and Hugo V. Goodyear, May 1975, 87 p. (C0M-7 5-1 1088) (Continued on inside back cover) '.Vhix'oliY OF •- «i013 LIBKAKY ■'■■■JA-CHAMPAIGN STACKS NOAA Technical Report NWS 38 Hurricane Climatology for the Atlantic and Gulf Coasts of the United States Francis P. Ho, James C. Su, Karen L. Hanevich, Rebecca J. Smith and Frank P. Richards Silver Spring, MD April 1987 Government Document Book Stacks Study completed under agreement EMW-84-E-1589 for FEDERAL EMERGENCY MANAGEMENT AGENCY U.S. DEPARTMENT OF COMMERCE Malcolm Baldrige, Secretary National Oceanic and Atmospheric Administration Anthony J. Calio. Under Secretary National Weather Service Richard E. Hallgren, Acting Assistant Administrator Digitized by the Internet Archive in 2012 with funding from University of Illinois Urbana-Champaign http://archive.org/details/hurricaneclimatoOOhofr TABLE OF CONTENTS Page Abs tract 1 1 . Introduction I 1 .1 Authorization. 1 1.2 Purpose 2 1.3 Scope of report 2 1.4 Relation to flood insurance studies 4 1.5 Previous studies. 5 2. Data 5 2.1 Introduction 5 2.2 Sources of data 6 2.3 Hurricane central pressure (P Q ) data 23 2.3.1 Central pressure criteria based on balanced wind model 2 4 2.3.2 Central pressure adjustments 2 4 2.3.3 Revised central pressure from previous studies 2 5 2.4 Hurricane radius of maximum winds (R) data 2 5 2.4.1 Source of radius of maximum winds 2 6 2.4.1.1 Radius of maximum winds from aerial reconnaissance 26 2.4.1.2 Radius of maximum winds from wind records 2 7 2.4.1.3 Radius of maximum winds from eye radius. 28 2.4.1.4 Radius of maximum winds from pressure fit...... 2 8 2.4.1.5 Radius of maximum winds from Monthly Weather Review 28 2.5 Speed and (T) direction (9) of forward motion 2 8 2.5.1 Source of T and 9 data 28 2.5.2 T and 9 data used in probability distributions 30 3. Meteorological parameters and their interrelations......... 30 3.1 Introduction. 30 3.1.1 Overview of the statistical study... 30 3.1.2 Scope of the chapter 3 1 3.2 Considerations of data samples for statistical tests 31 3.2.1 Forward speed 32 3.2.2 Forward direction 34 3.3 Homogeneity of the hurricane data samples.. 3 4 3.3.1 Methods for testing the homogeneity of storm parameters 3 5 3.3.2 Comparison of results from different homogeneity tests 3 7 3.3.2.1 Meteorological method 37 3.3.2.2 Cluster analysis 38 3.3.2.3 Discriminant analysis 38 3.3.2.4 Principal component analysis 39 3.3.3 Selection of hurricane groups for independence testing 40 3.3.3.1 Gulf coast 42 3.3.3.2 Florida coast 42 3.3.3.3 Atlantic coast 43 Page 3.4 Interrelations between hurricane parameters 43 3.4.1 Brief review of previous studies 43 3.4.2 Methods for testing the interrelations between hurricane parameters 44 3.4.2.1 Contingency table with Chi-square test 44 3.4.2.2 Spearman test 44 3.4.3 Comparison of results from different independence tests 45 3 .5 Discussion 45 4. The joint probability question: Central pressure versus radius of maximum winds 50 4 .1 Introduction 50 4.2 Central pressure versus radius of maximum winds 50 4.3 Meteorological analysis 52 4.4 Discussion of analysis 55 4 .5 Conclusions 59 5. Other joint probability questions 59 5 . 1 Introduction 59 5.2 Forward speed versus direction of storm motion 60 5.3 Central pressure versus direction of storm motion 61 5.3.1 Gulf coast 61 5.3.2 Atlantic coast.. 64 5.3.2.1 Atlantic coast, south of 33 ,5°N 64 5.3.2.2 North Atlantic coast 66 5.4 Cape Hatteras area 66 5.4.1 Parameters for landfalling hurricanes from northeast quadrant.. 66 5.4.2 Parameters for landfalling hurricanes from southeast quadrant 67 5.4.3 Landfalling track frequency 67 6. Frequency of hurricane and tropical storm occurrences 67 6.1 Classification of hurricanes and data 67 6.2 Frequency of landfalling tropical cyclones..... 72 6.2.1 Direct-count method........ 72 6.2.1.1 Objective smoothing procedure 75 6.2.1.2 Evaluation of procedure 7 5 6.2.2 Discussion of results 7: 6.2.2.1 Areas of high entry frequencies 7 6.2.2.1 (a) Northwest Florida 77 6.2.2.1 (b) South Florida 77 6.2.2.1 (c) Upper Texas coast 78 6.2.2.1 (d) Cape Hatteras 78 6.2.2.2 Areas of low entry frequencies 78 6.2.2.2 (a) East coast 78 6.2.2.2 (b) Gulf coast 78 6.3 Frequency of exiting tropical cyclones 78 6. 3.1 Analysis * 78 6.3.2 Results and discussion 6.3.2.1 Gulf coast 79 iv Page 6.3.2.2 Atlantic coast 79 6.3.2.3 Application in tide-frequency analysis 79 6.4 Frequency of alongshore tropical cyclones 81 6.4.1 Analysis 81 6.4.2 Results and discussion 85 7. Central pressure 85 7 .1 Introduction 85 7 .2 Analysis 86 7.3 Results 89 7.3.1 Pressure minima 89 7.3.1.1 South Florida minimum..... 89 7.3.1.2 South Texas minimum 92 7.3.1.3 Carolinas and southern New England minima 92 7.3.1.4 Mississippi Delta minimum 92 7.3.2 Pressure maxima 92 7.3.2.1 Cross City, Florida, maximum 92 7.3.2.2 Delaware Bay maximum 93 7.3.2.3 Jacksonville maximum.... 93 7.3.2.4 Northern New England coastal maximum 93 8. Radius of maximum winds 94 8.1 Analysis 94 8.1.1 Gulf of Mexico 95 8.1.2 Atlantic coast 95 8.2 Evaluation of the analysis 95 8.2.1 Gulf coast 95 8.2.1.1 Florida and Mexico minima 95 8.2.1.2 Mississippi-Florida panhandle maximum..... 95 8.2.2 Atlantic coast 95 8.3 Radius of maximum winds for intense hurricanes 98 9. Speed and direction of storm motion 98 9.1 Speed of storm motion 98 9.1.1 Forward speed of landf ailing tropical cyclones 98 9.1.1.1 Analysis 98 9.1.1.2 Results and discussion 98 9.1.2 Forward speed of bypassing tropical cyclones 102 9.2 Direction of storm motion 102 9.2.1 Direction of storm motion for landfalling tropical eye lones 102 9.2 .1.1 Analysis 102 9.2.1.2 Results and discussion 103 9.2.1.2 (a) Gulf coast 106 9.2.1.2 (b) East coast, south of Cape Hatteras 107 9.2.1.2 (c) East coast, north of Cape Hatteras 107 9.2.1.3 Areas of discontinuous direction profile 107 9.2.2 Direction of storm motion for bypassing tropical cyclones... 107 10. Adjustment of hurricane intensity for filling overland 108 10.1 Introduction 108 10.2 Index for overland filling 108 Page 10.3 Previous observational studies .. 109 10.4 Analysis of data 109 10.5 Filling rates by region 110 10.6 Results 121 11. Application of hurricane parameters 123 11.1 Introduction 123 11.2 Landfall point 123 11.3 Peripheral pressure 124 11.4 Probability distributions of hurricane parameters and frequency of occurrence 12 4 11.5 Applications of profiles of probability distributions for hurricane parameters. 12 7 11.6 Exiting tropical cyclones 13 6 12. Summary and discussion... 136 12.1 Frequency of tropical cyclone occurrences 13 7 12.2 Probability distribution of storm parameters 138 12.3 Independence of parameters.... 138 Acknowledgments 139 References 140 Appendix A Detailed analysis of selected storms 147 A.l Introduction 147 A.2 Hurricane Alicia, August 15-21, 1983 147 A .2 .1 Introduction. 147 A.2 .2 Previous reports 147 A.2 .3 Sources of data 148 A.2 .4 General meteorological situation 149 A.2 .5 Detailed meteorological analysis... 149 A.2. 5.1 Storm track 149 A.2 .5.2 Forward speed... 150 A.2 .5.3 Central pressure 152 A.2. 5. 4 Wind analysis 154 A.2. 5. 5 Radius of maximum winds 156 A.2 .6 Discussion 159 A.3 Hurricane David, September 2-5, 1979 160 A. 3 .1 Introduction 160 A.3 .2 Previous studies * 162 A.3 .3 Aircraft data..... 163 A.3. 4 Central pressure 164 A.3 .4.1 P from aerial reconnaissance. 164 A.3 .4.2 P from land station observations 164 A. 3. 4.3 Pressure fit at the coast 164 A.3. 4. 4 Time variation of P 164 A.3 .5 Radius of maximum winds 170 A.3. 5.1 R from aerial reconnaissance...... 170 A. 3. 5.2 R from land station observations 170 A.3 .5.3 Time variation of radius of R 174 A. 4 Hurricane Allen, August 2-10, 1980 174 A. 4.1 Introduction . 174 A. 4.2 Previous reports 176 A. 4. 3 Reconnaissance flight data.. 177 Page A. 4. 4 Central pressure analvsis 177 A. 4. 5 Wind analvsis 177 A. 4. 6 Time variation of central pressure and radius of maximum winds ' 1 82 A. 4. 7 Relation of P Q and R in Hurricane Allen 182 Appendix B Statistical methods for tests of homogeneitv and independence 185 B .1 Introduction 18 5 B .2 Methods for the test of homogeneity 185 B.2.1 Cluster analysis 185 B.2.1.1 Description of the method 185 B.2.1. 2 Rationale for choice 186 B.2.1. 3 Limitations of the method 187 B.2.1. 4 Interpretation of the results 187 B.2.2 Discriminant analysis 187 B.2.2.1 Description of the method 187 B.2.2 .2 Rationale for choice 187 B.2.2 .3 Limitations of the method 187 B.2.2. 4 Interpretation of the results 188 B.2.3 Principal component analysis 188 3.2.3.1 Description of the method 188 B.2.3 .2 Rationale for choice 188 B.2.3 .3 Limitations of the method 188 B.2.3 .4 Interpretation of the results 188 B.2.4 Mann-Whitney test 189 B.2.4.1 Description of the method 189 B.2.4.2 Rationale for choice 190 B.2.4.3 Limitations of the method 190 B.2.4.4 Interpretation of the results 190 B.3 Methods for the test of independence 190 B.3.1 Spearman test 191 B.3. 1.1 Description of the method..... 191 B.3. 1.2 Rationale for choice. 191 B.3. 1.3 Limitations of the method 191 B.3. 1.4 Interpretation of the results 191 B.3. 2 Contingency table with Chi-square test 192 B.3 .2.1 Description of the method 192 B.3 .2 .2 Rationale for choice 192 B.3. 2.3 Limitations of the method 192 B.3 .2 .4 Interpretation of the results 192 Appendix C Plotting position formula 192 C .1 Introduction 192 C.2 Criteria for evaluation 192 C.3 Evaluation of plotting position formulae 194 C.4 Comparison of formulae 194 LIST OF FIGURES Number Page 1 Locator map with coastal distance intervals marked (nmi) 3 2 Hourly observations of wind speed and direction, and distance of Allen's center from Brownsville, Texas 27 3 Radius of maximum winds versus inner radar eye radius 2 9 4 Difference between the radius of maximum winds and the inner radar eye radius versus maximum wind speed 2 9 5 Forward speed of landfalling hurricanes and tropical storms versus milepost (a) along the Gulf coast of Florida, and (b) along the Atlantic coast 33 6 Possible homogeneous regions for landfalling hurricane parameters * 36 7 Plot of the second principal component versus the first principal component 40 8 Central pressure of landfalling hurricanes versus milepost 41 9 Interrelations between parameters of landfalling hurricanes for the Gulf and Atlantic coasts of the United States 46 10 Landfalling hurricane parameters versus milepost for the Atlantic coast. 48 11 Location and minimum central pressure of extreme hurricanes 54 12 Tracks of extreme hurricanes 56 13 Same as Figure 12 57 14 Plot of P versus R for extreme hurricanes listed in Table 16 58 15 Scatter diagram of direction versus speed of forward motion for hurricanes landfalling on the Atlantic coast 60 16 Probability distribution of forward speed of (a) landfalling, and (b) alongshore hurricanes in the vicinity of Charleston, South Carolina, for the period 1886-1973 62 17 Plot of forward direction versus milepost for the landfalling hurricanes on the Gulf coast of the United States 63 18 Variation with latitude of direction of forward motion for hurricanes landfalling on the Atlantic coast... 63 vi i i Number Page 19 Histogram for direction of storm motion for the 2.5° latitude and longitude block centered about Key West, Florida 65 20 Track, of tropical storms and hurricanes showing motion from northeast 68 2 1 Cumulative probability curve of central pressure for landf ailing tropical cyclones near Wright Monument, North Carolina 69 22 Cumulative probability curve of speed of storm motion adapted for landfalling tropical cyclones near Wright Monument, North Carolina. 69 23 Frequency of landfalling hurricanes and tropical storms 70 24 Smoothed coastline obtained by applying the objective smoothing function 71 2 5 Map showing extensions of west coast of Florida and the Atlantic coast through the Florida Keys..... 73 2 6 Count of landfalling tropical storms and hurricanes (1871-1984) by 50-nmi segments of a smoothed coastline 74 27 Frequency of landfalling tropical cyclones (1871-1984) for the Gulf and Atlantic coasts of the United States.. 76 28 Frequency of exiting hurricanes and tropical storms (1871-1974).... 80 2 9 Tide frequencies at Wright Monument, North Carolina, for several classes of storms 81 3 Accumulative count of hurricane and tropical storm tracks passing the coast at sea (1871-1984) 82 3 1 Cumulative frequency of tropical cyclones bypassing the Gulf coast at selected distances offshore (1871-1984) 83 32 Cumulative frequency of tropical cyclones bypassing the Atlantic coast at selected distances offshore (1871-1984) 84 33 Cumulative probability curve of central pressure of hurricanes landfalling within (a) 250 nmi of milepost 250, near Corpus Christi, Texas, and (b) 200 nmi of milepost 1600 near Vero Beach Florida a 88 3 4 Probability distribution of central pressure for hurricanes landfalling on the Gulf coast (1900-84) 90 35 Same as Figure 34, but for Atlantic coast hurricanes... 91 Number Page 36 Cumulative probability curve of radius of maximum winds for hurricanes landf ailing within (a) 2 50 nmi of milepost 2 50, near Corpus Christi, Texas, and (b) 200 nmi of milepost 1600, near Vero Beach, Florida 94 37 Probability distribution of radius of maximum winds for hurricanes landf ailing on the Gulf coast (1900-84) 96 38 Same as Figure 37, but for Atlantic coast hurricanes 97 3 9 Cumulative probability curve of forward speed of tropical cyclones landfalling within (a) 250 nmi of milepost 250, near Corpus Christi, Texas, and (b) 200 nmi of milepost 1600, near Vero Beach, Florida 99 40 Probability distribution of forward speed for tropical cyclones landfalling on the Gulf coast (1900-84) 100 41 Same as Figure 40, but for Atlantic coast tropical cyclones........ 101 42 Cumulative probability curve of direction of storm motion of tropical cyclones landfalling within (a) 100 nmi of milepost 2 50, near Corpus Christi, Texas, and (b) 100 nmi of milepost 1600, near Vero Beach, Florida 103 43 Probability distribution for direction of storm motion for tropical cyclones landfalling on the Gulf coast (1900-84) 104 44 Same as Figure 43, but for the Atlantic coast south of Cape Hatteras 105 45 Same as Figure 43 , but for the Atlantic coast north of Cape Hatteras 106 46 Pressure profiles after landfall for (a) hurricane Frederick September 1979 and (b) Hurricane Alicia, August 1983 HI 47 Map showing geographical regions used to study filling rates 112 48a Variation with time after landfall of filling rate of hurricanes listed in region A of Table 19 114 48b Same as Figure 48a 115 49 Filling rates for hurricanes of various intensities for region A (Gulf coast, west of Apalachicola, Florida) 116 50 Comparison of filling rates for various hurricanes crossing the Florida peninsula and Che filling curve for region B from Schwerdt et al. (1979) 118 Number Page 51 Filling rates for hurricanes of various intensities for region B (southern Florida) 119 52 Variation with time after landfall of filling rates for Hurricanes Hazel (1954), Gracie (1959), and David (1979) 120 53 Variation with time of filling rates for New England hurricanes.... 12 1 54 Filling rate for hurricanes in region C (Atlantic coast, north of Georgia ) 12 2 55 Plot of cumulative counts of alongshore storms versus distance from coast for Vero Beach, Florida (milepost 1600) 12 6 56 Cumulative probability curves of P Q for designated locations....... 133 57 Cumulative probability curve for pressure deficit at Vero Beach, Florida 13 5 A.l Hurricane track for Alicia, 0000 CST August 16 through 1200 CST August 18, 1983 150 A.2 Hurricane eye position obtained from radar, aircraft reconnaissance penetration fixes, and satellite observations 151 A. 3 Minimum pressure recorded at land stations and by aircraft reconnaissance during Hurricane Alicia 152 A. 4 Variation of minimum central pressure estimates for Hurricane Alicia 153 A. 5 Hourly observations of sea-level pressure and surface wind speed recorded at Houston Intercontinental Airport, Texas 155 A. 6 Same as Figure A. 5, but for Baytown, Texas 156 A. 7 Composite isotach analysis for Hurricane Alicia, centered at 2240 GMT, August 17, 1983 157 A. 8 Streamline and 10-m isotach analysis for Hurricane Alicia, 0730 GMT, August 18, 1983.. 158 A. 9 Flight-level winds recorded along radials through the center of Hurricane Alicia, 1352-1433 GMT, August 17, 1983 159 A. 10 Radius of primary and secondary wind maxima in Hurricane Alicia, August 17-18, 1983 160 A.ll Track with central pressures for Hurricane David, September 2-5, 1979. 161 xi Number Page A. 12 Reconnaissance flight pattern, designated as star pattern used in Hurricanes David and Allen 163 A. 13 Sea-level pressure observed during passage of Hurricane David, (September 1979) at (a) Shuttle Airport, Florida, and (b) Savannah (Municipal Airport), Georgia 165 A. 14 Pressure-profile curve during Hurricane David (a) for Florida coast at 2100 GMT, September 3, 1979, (b) Georgia coast at 1800 GMT, September 4, 1979 166 A. 15 Central pressure (sea-level) for Hurricane David, September 3-5, 1979 167 A. 16 Flight-level winds recorded along radials through the center of Hurricane David, (a) 2308-2356 GMT, September 2, (b) 0644- 0748 GMT, September 4, and (c) 1751-1841 GMT, September 4, 1979.. 169 A. 17a Wind speed and direction at Shuttle Airport, Florida, during the passage of Hurricane David, September 2-4, 1979.. 171 A. 17b Wind speed and direction at Savannah, Georgia, during the passage of Hurricane David, September 3-5 , 1979 172 A. 18 Radial distances (from eye center) of wind maxima in Hurricane David, September 2-5, 1979 173 A. 19 Track of Hurricane Allen, August 2-11, 1980 175 A.20 Reconnaissance flight patterns used in Hurricane Allen... 179 A.2 1 Central pressure for Hurricane Allen, (a) August 3-7, and (b) August 7-10, 1980 180 A.22 Flight-level winds recorded along radials through the center of Hurricane Allen, 1535-1627 GMT, August 5, 1980 181 A.23 Flight-level winds recorded along radials through the center of Hurricane Allen, 1844-1945 GMT, August 7, 1980 181 A. 2 4 Composite map of flight-level winds recorded between 02 00 and 0400 GMT, August 9, 1980 ' 182 A.2 5 Central pressure and radial distances (from eye center) of wind maxima in Hurricane Allen, August 3-10, 1980 183 A.2 6 Concurrent observations of central pressure and radius of maximum winds for Hurricane Allen, August 3-9, 1980 184 B.l Levels two through nine of the hierarchical clustering of la ndf ailing hurricanes. 186 C.l Comparison of plotting position formulae for N = 10 195 LIST OF TABLES Number Page 1 Hurricanes with central pressure < 982 mb, ranked in chronological order from 1900-84. Gulf coast United States 7 2 Hurricanes with central pressure < 982 mb ranked in chronological order from 1900-84. East coast United States 14 3 Miscellaneous Florida hurricanes with central pressure < 982 mb ranked in chronological order from 1900-1984 20 4 Hurricanes with revised central pressure 2 6 5 Forward speed of hurricanes and tropical storms for selected portions of the coast 32 6 Initially selected coastal segments.. 35 Results of Mann-Whitney test for a priori selection of coastal segments in the Gulf of Mexico.. 3 7 8 Results of Mann-Whitney test for modified segments of the Gulf coast 38 9 Percentages of variance accounted for by principal components...... 39 10 Loading of hurricane parameters in the principal components which account for more than 12 percent of variance.... 39 11 Coastal segments that include homogeneous hurricane parameters for the test of independence 41 12 Breakpoint values for contingency tables 44 13 Sample sizes of paired parameters of landfalling hurricanes for coastal segments 45 14 An example of a general two-by-two contingency table 51 15 Frequency of occurrence of different storm radii in two different class intervals of hurricane intensity observed in the Gulf of Mexico , 1900-84 52 16 Severe hurricanes since 1900 with P Q < 93 mb 53 17 Comparison of speeds of landfalling and alongshore storms for the vicinity of Charleston, South Carolina 61 18 Partition of P q and for landfalling hurricanes striking the Atlantic coast south of 33.5°N , 64 x i i i Number Page 19 Selected landfalling hurricanes (1928-1983) used to estimate overland filling rates 113 2 Changes in hurricane pressure deficits due to overland filling 117 2 1 Summary sheet of information needed from this report for surge-frequency computations 12 8 22a Summary sheet for Vero Beach, Florida 130 22b Summary sheet' for 50 nmi north of Vero Beach, Florida 13 1 22c Summary sheet for 50 miles south of Vero Beach, Florida 132 23 Tropical cyclone parameters Vero Beach, Florida 13 4 2 4 Data used in this report for probability analyses 137 A.l Time, flight pattern, and flight level of NOAA/RFC missions into Hurricane David, September 1979 162 A.2 Time, flight pattern, and flight level of NOAA/RFC missions into Hurricane Allen, August 1980 178 C.l List of plotting position formulae 193 C .2 List of plotting position formulae in the descending order of their p *s 194 r m HURRICANE CLIMATOLOGY FOR THE ATLANTIC AND GULF COASTS OF THE UNITED STATES Francis P. Ho, James C. Su, Karen L. Hanevich, Rebecca J. Smith and Frank Richards Water Management Information Division Office of Hydrology National Weather Service National Oceanic and Atmospheric Administration ABSTRACT A climatology of hurricane factors important to storm-surge modeling is presented for the Atlantic and Gulf coasts of the United States. A smoothed frequency of hurricanes and tropical storms entering, exiting, and passing within 150 nmi of the coast during the period 1871-1984 is given. The central pressure and radius of maximum winds for hurricanes occurring during the 85-year period, 1900-84, were obtained from analysis of available hurricane data. Direction and speed of storm motion for hurricanes and tropical storms at the time they crossed the coast were also analyzed for the same 85-year period. The cumulative probability curves of each factor were plotted and analyzed for each 50-nmi interval along the coast. Selected probability levels of each distribution were summarized, and smoothed variations along the coast were obtained. Statistical independence of hurricane parameters has also been examined and interrelations of central pressure and radius of maximum winds investigated. 1 . INTRODUCTION 1.1 Authorization The National Flood Insurance Act of 1968, Title XIII, Public Law 90-448, enacted August 1, 1968, authorized and provides for a National Flood Insurance Program to insure residences and small businesses against hazard of damage or destruction by flood. The Federal Insurance Administration (FIA), a part of the Federal Emergency Management Agency (FEMA), is the executive agency for the National Flood Insurance Program. In July 1982 , a Joint Technical Assistance Work Plan was signed between FEMA and the National Oceanic and Atmospheric Administration (NOAA). The plan, among other things, allows for the National Weather Service (NWS), NOAA, to provide technical support Co FEMA upon request. Authorization for this particular study is Project No. 53967 under agreement No. EMW-84-E-1589 between the FIA, FEMA and the NWS, NOAA, dated March 15, 1984 and duly signed April 2 5, 1984. 1 .2 Purpose The Federal Insurance Administration, FEMA, requested the NWS, NOAA, to develop a comprehensive and authoritative set of hurricane clima tological statistics for the Atlantic and Gulf Coasts of the United States. These statistics are prerequisites in tidal flood-frequency analyses which are essential to establish flood insurance criteria for a given community. Coastal tidal inundations on the Gulf and Atlantic coasts of the United States are primarily caused by hurricanes. Therefore, the characteristics of these storms are the beginning point in making tidal flood-frequency analyses. The present study is a climatological assessment of the central pressure, radius of maximum winds, and other characteristics of hurricanes along the U.S. Atlantic and Gulf coasts in a manner suitable for determining the frequency of storm surge levels. It includes only the atmospheric characteristics of hurricanes and does not include surge levels that are the subject of other reports. The present study is an update and revision of an earlier study published as NOAA Technical Report NWS-15 (Ho et al 197 5), which will hereafter be referred to as TR 15. TR 1 5 presented a climatology of hurricane parameters important to storm-surge modeling along the U.S. Gulf and Atlantic Coasts. This climatology was an analysis of available hurricane data, with storm tracks from 1871 through 1973, and also included data for other meteorological variables since 1900. TR 15 included the cumulative probability distributions of each hurricane factor analyzed at 50-nmi intervals along the coast, and smoothed variations of each factor at selected probability levels along the coast were presented. A smoothed frequency of tropical storms and hurricanes entering and exiting the coast as well as those storms passing within 150 nmi of the coast was also given in TR 15. The question of joint probability among the various factors was discussed qualitatively, but formal statistical tests were not considered in TR 15. The National Research Council of the National Academy of Sciences (NAS) reported on an evaluation of the FEMA Model for estimating potential coastal flooding from hurricanes (National Academy of Sciences 1983). This NAS report concluded that the basic approach used by FEMA is sound and appropriate for estimating 100-yr flood elevations in communities where severe flooding is caused by hurricane storm surges. However, the Advisory Committee of the NAS made several recommendations regarding the way in which coastal flood studies are conducted. The committee recommended, among other things, that the selection of storm samples and the adoption of appropriate interdependency assumptions should be carried out in a centralized way by an organization with the necessary expertise in hurricane climatology. The committee concluded that inter- dependencies among storm parameters, particularly among storm intensity, size, and direction, should be determined by that organization on a regional basis and an appropriate method for handling these interdependencies when applying the probability procedure to coastal flood elevations should be developed. 1.3 Scope of Report The geographical region covered by the report is the U.S. Gulf and Atlantic coasts from Texas to Maine (fig. 1). The first objective was to define, clima- tologically, the frequency of hurricanes and tropical storms influencing each coastal segment. This was done for three classes of storms — those entering the coast from the sea (entering or landf ailing) , those having entered the coast and then proceeding from land to sea (exiting), and those moving parallel to the v^ino'dS"* 1 , ,»vi* 3000 * -2900 SfcT'N Iaiyestoh . 500 / \ 400 ^ U 600 700 -# 300 -200 J00_ 1200 -— • -r,So G U| L O f Figure 1« — Locator map with coastal distance intervals marked (max). 3 coast, with the center remaining at sea, but within 150 nmi of the point under consideration (alongshore or bypassing). These frequencies are presented in Chapter 6. The second objective was to develop cumulative probability distributions for four hurricane parameters: (1) central pressure (P Q ), an index of storm inten- sity, (2) the radius of maximum winds (R), an index of storm size, (3) forward speed of the storm (T), and (4) direction of storm motion (9). Each of these factors influences the capability of the storm to produce storm tides. Chapter 2 discusses in detail the data sources and analyses from which the hurricane characteristics were obtained. Probability distributions and their along-coast variations for each parameter are presented in Chapters 7 through 9 of this report. The statistical independence of hurricane parameters is considered in Chapter 3. The homogeneity of each parameter along the Gulf and Atlantic coasts was tested separately. Interrelations between pairs of parameters have been examined in Chapter 3. Non-linear relations between central pressure (P ) and radius of maximum winds (R) are discussed both dynamically and statistically in Chapter 4. For this purpose, the data base for P q and R was extended to include extreme hurricanes in the Caribbean and the Gulf of Mexico. Chapter 5 considers other conditional probability questions that are important to the currently used joint probability approach for tide-frequency analysis. Chapter 10 examines changes in the wind and pressure fields due to the filling of hurricanes overland. Finally, Chapter 11 discusses application of the results of this study to flood insurance studies. 1.4 Relation to Flood Insurance Studies Meteorological parameters P R, 9 and T can be used together with other conditions as input to storm-surge models. Other conditions include boundary conditions such as bathymetry, orientation of the coastline, etc. A storm-surge model can be used to compute the surge heights at the coast. The storm surge generated by a hurricane is the increase of the sea water surface elevation due to two physical processes. One process is the water surface elevation increase in the core region of a hurricane where the atmospheric pressure is extremely low. This is the so-called "inverse barometer effect." The other process is the convergence of the sea water, driven by the surface wind from the deeper ocean to the shallower coastal regions. This is related to surface wind stress and bathymetry. The atmospheric pressure gradient in a hurricane is the difference between the central pressure and a peripheral pressure. The surface wind stress in a hurricane is parameterized on the basis of the wind field near the water surface. Using appropriate meteorological assumptions, a wind field can be derived from knowledge of the pressure gradient, the radius of maximum wind speed, and the forward direction and speed of the hurricane. The joint probability approach, as currently used in storm-surge frequency studies, assumes that each meteorological parameter used as input to the hydrodynamical model is independent. Development of storm-surge probabilities involves making computations for a range of meteorological parameters. The probability of occurrence of a given simulation is assumed to be the product of the probabilities represented by each input (meteorological) parameter. However, if the meteorological parameters are interrelated, a simple product of the individual probabilities is not appropriate. Hence, the need to evaluate the possibility of interdependence among the factors that are the focus of this study. With this specific application in mind, there were a number of decisions made during the course of our analysis that ensured that the results would be tailored to the needs of the hydrodynamic modeling application. Some examples include the selection of the radius of maximum winds at the time of minimum pressure, and the assumption that the parameters represented steady-state storms. But these decisions also mean that the "climatology" described in this report may not be appropriate for other more general meteorological applications. 1.5 Previous Studies One of the first systematic compilations of the characteristics of hurricanes affecting the United States coast was Tropical Cyclones (Cline 192 6). Table 1 in Hydrometeorological Report No. 32 (Myers 1954) provided the first compilation of all hurricane central pressures and radii of maximum winds from 1900 to 1949. The National Hurricane Research Project Report No. 33 (Graham and Nunn 1959), hereafter referred to as NHRP 33, updated Myers' list and systematized the geographical distribution of the factors. Technical Paper No. 55 (Cry 1965) described all the hurricane tracks from 1871 to 1963, and cited the earlier works of this kind. HUR 7-97, Interim Report - Meteorological Characteristics of the Probable Maximum Hurricane, Atlantic and Gulf Coasts of the United States (Weather Bureau 1968) updated and revised the data in NHRP 33 and gave the geographical distribution of the characteristics of hypothetical hurricanes that had combinations of factors that made them the most severe hurricanes that can probably occur at a particular coastal location. NOAA Technical Report NWS 23 (Schwerdt, et al 1979) revised and updated the previous studies on meteorological criteria for engineering design hurricanes. Neumann et al. (1981) extended the period covered in Cry's hurricane tracks and prepared revised tracks where additional data indicated that they were necessary. This provided a firm climatological base describing tropical cyclones on the synoptic scale. 2 . DATA 2.1 Introduction Observations from hurricanes occurring near the United States Gulf and Atlantic coasts were used in this study to determine probability distributions of various parameters. Data presented in this chapter are used in later chapters of this report. If additional data were required for a specific purpose, it is discussed in the chapter where required. The amount of observed data available from past hurricanes varies greatly and almost all of it required further analysis and interpretation before it could be of use for storm-surge computation. The amount of data available for any single storm also varies during different portions of the storm's life, from various geographic regions, and from different sections of the hurricane. These data are subject to numerous uncertainties in interpretation. We have attempted to bring this information together to make a comprehensive analysis, to develop accurate storm tracks from which speed and direction of storm motion are determined and to present an authoritative determination of central pressures and radius of maximum winds. Examples of detailed meteorological analyses are given in Appendix A. Tables 1 through 3, for hurricanes during the years 1900-84, list most of the information used throughout this report. Parameter values in the tables are given for storms with P Q less than or equal to 982 mb (2 9.00 in.) occurring within 150 nmi of the Gulf and Atlantic coasts. The data are our update, revision and extension of Tables 1 and 2 in TR 15. There were a few changes made to the previously published data. In particular, to address the question of interdependence among parameters, available data were reviewed to ascertain their time of occurrence and to provide concurrent values of P and R where necessary. Tables 1 through 3 give the date at which a hurricane entered, exited or came closest to the coast. The point along the coast where the hurricane parameters may be applied is indicated in the tables as the coastal reference point. The tables list parameters for the 85-yr period, 1900-84. The year 1900 was chosen to initiate estimation of the parameters by weighing the inaccuracies that would result from the sparse data of earlier years against the desirability of a longer period. Each of the P and R values listed in the tables is followed by a superscript letter or letters that refer to a legend at the end of the tables giving the source of the data value. The storm direction, measured from the north, denotes the track direction from which the hurricane crossed or bypassed the coast. Tables 1 and 2 list a storm twice only if it crosses the coastline a second time (or if a bypassing storm makes another approach to the coast) after it has traveled a distance of 400 nmi (500 nmi along the Gulf Coast). An exception to this is Hurricane David: it was listed twice within 400 nmi, but only the second entry was included in the statistical computations discussed below. These dupli- cate storms are identified by a section mark (§) in the two tables. Hurricanes whose centers passed through the Florida Keys are listed in both the Gulf and Atlantic coast tables for the convenience of the user. The information on hurricanes which crossed the Florida Keys and eventually entered the west coast of Florida (within 500 nmi of its initial crossing), are listed separately in Table 3A. If a hurricane crossed the coast on one side of the Florida peninsula, with a P less than or equal to 982 mb (29.00 in.) and weakened in intensity to P greater than 982 mb when it was more than 50 nmi from the opposite coast, it was listed for only the initial coastline it crossed (table 1 or 2). Those exiting storms, still of hurricane intensity at, or within 50 nmi of, the coast of exit, are included in Tables 1 and 2. Hurricanes which entered the Florida coasts and moved northward over land maintaining hurricane intensity within 50 nmi of the opposite coast are listed separately in Table 3B. They may be considered as bypassing hurricanes moving inland parallel to the coast. 2.2 Sources of Data Original sources of hurricane data are barograph traces from land stations and ships, wind records from NWS and military stations, aircraft reconnaissance flight data, radar data, satellite data, miscellaneous pressure and wind reports and textual descriptions in the scientific literature. These descriptions have appeared in the Monthly Weather Review (published since June 1872), Clima tological Data, National Summary (since 1950), National Hurricane Research Project Report No. 39 (Graham and Hudson 1960), NOAA Technical Memorandum NWS SR-56 (Sugg et al. 1971), the book Tropical Cyclones (Cline 192 6), and a few other sources (e.g., data sources listed in append. A). C S "O c O k II O C O t. u -H 4J O C en c uj to Shut: O HU u o 3 3 T3 Z 3 r- o Z 3 f~ o Z 3 03 o M U U TO 3 3 c u m a o to .a e to >■> rtTJU [i, > ffl 4) TO B.H u - 01 BO 1- O O -H X- S 01 H S J *j 2 I 2 3 O CD u a. c en Z 01 00 o o in o r-^ en — -i — x in O iJ > O. (0 — O r^ cm cm oo u"» vo cr* r-~ 2 3 to co m co cm — co co to to . . O o O o ir\ — . 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CM CfN ON 2 3 Z 3 ■* — l«- O vO O -3- — Z 3 vD C^ Z 3 vO CD Z 3 o o 14 a. ** — i > a a <-> -a a. u = u o a a th a u, c -rt o £ O :-l£ o 4J -- O o >, o 3 = 3 i>- o os as — — OS as OS o o o o OS — i OS 15 1 .- 3 = — 1 TJ <-> = a js C w 3] -J) CO <0 o l-> C-M *- o o 1) U u- -J 3 O en <-> (0 > -a bo TO c t: o ao 0> 3> c u c ai to u > u o e u a. u c a> o o c oo o o> ■j~. iz. en 16 Hi. 3 3 3 3 ■0 X O u 2 3 Z 3 ON — 1 -H (N i/^ O in ifl u c : c *H -H •h j= z -I O C Z 3 2 3 -3- m a- — 00 oc o o jj w bO-w 17 CO S ei a e 1 1 ■o o C ft. -J _ c H -* 3 3 ■*" m ■o 0) z CD CO > vo to u in 3 1) m z C as -a <3> CU o 2 OS CU as = CD o m c m ■o 01 CD 3 u (DO) c c c o. .C o o o O o o CU OS ei os ^ o o © ft. B cjn a\ evi ~3- d cr\ av on ? S Z ? Z 3 T3 © en on m CU cu 03 -. en -t O 00 C-J 00 to a > a TO "7 %) CU ^ c O c^ m 00 00 a. ^ o O o B O". er\ cr\ cJn. On B • u u. o -. m o C u *a ON ■* C/5 ~ rg v >, O u U 43 J3 J2 o. co u -» O o. o m NO < O s 5 CD 00 00 lTI ON ON on - CU on >-, t— c CD 0) CO CD. CO MQ •u X B0--> 3 ^ a.--' < CU «cfi ■" en u a. o o in u 2 3 Z 3 00 = O u U 3 a " JO • g to u Hi II 3 -VI - CiJ m OOE 3 CU -o -* O S 3 o (03 3U > .3 co o .c cu -< :> O co ouu-u^rj O'-J'-mu < « H _] JJ u o s C CO o c 21 S 1 O O E •u JJ c c to —I OJ , C o h ii.a m V Q. 4J O !- <4- fc. K o bo 73 J= 00 O - !0 -J -H a. a u (0 4J 3 to jC -I > C U a 4-i •* a; u a «j ao o 3 22 Tropical cyclone track information was used to determine the frequency of entering, exiting, and alongshore tropical storms and hurricanes, direction of forward motion and in some cases speed of motion. Smoothed best tracks have been given in several NOAA publications and periodicals previously cited. Cry (1965) combined data from available sources into a comprehensive report showing the most accurate and consistent locations of all tropical cyclones for the period 1871-1963. These tracks were designed to provide a smoothed track for all storms. Neumann et al. (1981) have extended the period covered and prepared revised tracks where additional data have indicated they were necessary. In addition, Jarvinen et al. (1984) have prepared a computer file of North Atlantic tropical cyclones (commonly referred to as the HURDAT tape). This file contains dates, tracks, windspeeds, and central pressure values (if available) for all tropical cyclones that occurred during the period 1886-1983. This file is maintained by the National Hurricane Center (NHC), NOAA, in Miami, Florida and is updated annually. This data file contains storm positions and wind speed information at 6-hourly intervals. They are subject to some degree of uncertainty, especially for the earlier years. It should be noted that linear interpolation of the data within 6-hourly intervals could lead to inaccurate instaneous storm track and wind speed information. 2.3 Hurricane Central Pressure (P Q ) Data The most important factor in storm surge modeling is the* intensity of the hurricane, which is directly related to its central pressure. Harris (1959) demonstrated that storm surge height is approximately proportional to the central pressure depression, other factors being constant. The specific pressure values in Tables 1 through 3 are the lowest pressures, generally determined from actual observations by either a barometer or dropsonde. For hurricanes of recent years, minimum pressure observed in penetrations of the hurricane eye by reconnaissance aircraft near the coast provided the central pressure in most cases. For earlier hurricanes, P values were estimated from observations taken at land stations. Observed pressures, P , were extrapolated inward to P (since P were rarely observed at the storm center) by using visually-fitted radial pressure profiles based on the formula (Schloemer 1954): P " - exp(-R/r) (1) P - P n o where P is the pressure at radius r, P is the pressure at some large distance from the center at which the profile is asymptotic, and R is the radius at which the windspeed is greatest. Schwerdt et al. (1979) computed pressure profiles for 19 past hurricanes using equation (1) and nine other pressure profile formulas and compared the results with observed data at radial distances of 40 and 80 nmi. They concluded that equation (1) gives a reasonably representative sea-level hurricane pressure profile. They also concluded that further refinements would not improve the reliability of the formula at this time because of the rather large scatter of pressure data around most hurricane profiles. 23 2.3.1 Central Pressure Criteria Based on Balanced Wind Model Tables 1 through 3 also list the lowest pressure observed at a station (P_), the observing station and a geographical reference to which P pertains (either at the coast or as far as 150 nmi offshore). The criterion used to select storm data for inclusion in Tables 1 through 3 ( P <_ 982 mb) was based on consideration of the windspeed computed from a balanced wind model (after Myers 1954): where, V Q = cyclostrophic windspeed, at which the centrifugal force exactly balances the horizontal pressure gradient force at radius, r, p = density of air, P = asymptotic pressure (same as defined in eq. 1), R = radius of maximum winds. At the radius of maximum winds (R=r), with a central pressure of 982 mb (29.00 in.) and an asymptotic pressure of 1015.9 mb (30.00 in.), the cyclostrophic windspeed is 73 mph, or about the windspeed required for classification as a hurricane. The asymptotic pressure used by Myers is different from the peripheral pressure suggested in Chapter 11. Both pressures are intended to be representative of the environment removed from the dynamics of the tropical cyclone; Myers' pressure is that value to which an exponential pressure profile defined by equation 1 is asymptotic. It is a parameter for defining the intensity of the pressure gradient and does not actually have a physical counterpart in the pressure field. The peripheral pressure used in this report is the surface pressure at the outer limit of a hurricane where the cyclonic circulation ends and, therefore, has a physical meaning. The 982-mb criterion was used to put a specific bound on the data sample. We realize that there have been storms with hurricane-force winds and central pressures higher than 982 mb south of 3 5°N. It is not intended to be used as a forecasting criterion to distinguish hurricanes from tropical storms. 2 .3 .2 Central Pressure Adjustments In some areas, barometric pressures could not be obtained near the coast. The central pressures were determined at the location nearest the coast where reliable observations could be obtained and adjusted downward to a coastal value. This was done for those central pressures for which the lowest observed pressure was from a station inland or at a coastal station when the storm was emerging from land to sea. These adjustments were made for 13 hurricanes and were carried over from TR 15 and earlier reports, including NHRP 33. Recomputations using filling rates given in Chapter 10 did not show significant differences; P values for 3 of 13 hurricanes were revised. 24 Questions have been raised about the minimum central pressure of Hurricane Camille which struck the northern Gulf coast in 1969. The best obtainable value is needed because Camille had the lowest central pressure on the mainland coast since record keeping began during the later part of the last century, and stronglv influences the lower end of the probability distribution of central pressure. A minimum pressure of 905 mb was measured by an Air Force reconnaissance aircraft at 0016 GMT on August 17, 1969 near 25.2°N, 87.2°W, or 250 mi southeast of the mouth of the Mississippi River. Eighteen hours later, and only a few hours before the center made landfall, another reconnaissance aircraft penetrated the hurricane, and reported an even lower central pressure of 901 mb. A post-audit of the dropsonde computation at the National Climatic Center adjusted this to 908 mb. This value, which is quoted by Bradbury (1971), is the value in Table 1. The eye passed over Bay St. Louis, Mississippi, at landfall and an aneroid barometer a few blocks from the west end of the Bay St. Louis-Pass Christian bridge read 2 6.85 in. (909.4 mb) . This barometer was later checked and found to be accurate by the New Orleans NWS Office (DeAngelis and Nelson 1969). One may assume then that Camille remained in a near steady state during its last 25 hours at sea. 2.3.3 Revised Central Pressure from Previous Studies A virtual absence of pressure data made it necessary to omit the Louisiana hur- ricane of August 6, 1918, in which the closest recorded pressure was some 90 nmi from the path of the storm center. An estimate of P from such a distance would be highly questionable. Two hurricanes listed in NHRP 33 are not included in Tables 1 through 3. Upon reanalysis of the data, it was decided that both had weakened' to tropical storm strength before they reached a point 50 nmi from where they exited the Florida coast. They are the storms of September 11, 1903 (Gulf coast) and October 20, 192 4 (Atlantic coast). On the basis of additional data discovered since the 1975 study, we revised the central pressure for several hurricanes. The most significant change involved the storm of September 20, 1909. The revision was based on a reconsideration of records available from the Weather Service Forecast Office in New Orleans. A few other changes of central pressures were made in hurricanes whose radius of maximum winds were revised. A recomputation using the pressure profile formula with the revised R values dictated these revisions. The dates of these hurricanes, and their previous and revised central pressure values are listed in Table 4. 2.4 Hurricane Radius of Maximum Winds (R) Data Values of R for hurricanes were derived from various sources for the Gulf and Atlantic coasts of the United States. In TR 1 5 the values of R were for arbitrary locations and times. In this study, we reviewed all available data and determined concurrent values of P and R. The R values listed in Tables 1 through 3 are derived near the location and time where P applies. With aerial reconnaissance data, the R values are obtained from wind data recorded during the same traverse of the storm center in which the minimum P was observed. In a few cases, R could not be obtained by any reliable method. Storms with R's in this category are represented in Tables 1 through 3 by the abbreviation MSG (missing). 25 Table 4. — Hurricanes with revised central pressure Gulf Previous Revised Date P o P o (mb) (mb) Oct. 18, 1906 976.6 966.8 Sept. 20, 1909 980.0 965.1 July 5, 1916 961.1 950.2 Nov. 5, 193 5 972.9 977.0 Oct. 5, 1948 977.0 962.7 Sept. 10, 1960 (Donna) 933.0 93 0.0 Sept. 15, 1960 (Ethel) 972.0 976.0 Date Atlantic Previous Revised ( 3 (mb) (ml O Sept. 17, 1906 981.4 976 .6 Sept. 18, 1926 93 4.3 93 1 .0 Aug. 23, 1933 969.5 966 .5 Sept. 21, 1938 939.7 943 .0 Sept. 15, 1944 958.7 955 .3 Sept. 17, 1947 940.1 946 .8 Aug. 28, 1958 (Daisy) 957.0 949 .0 Sept. 12, 1960 (Donna) 961.1 959 .0 Sept. 10, 1964 (Dora) 965.8 961 .0 2.4.1 Source of Radius of Maximum Winds The values of R in the tables were developed from several sources: 1) windspeed records from aerial reconnaissance (for hurricanes since 1947), 2) windspeed records from land stations, whenever applicable, 3) approximations of eye radii deduced from airborne or land-based radar, 4) computations from an estimate of the pressure profile, or 5) on the basis of narrative or tabular data in the Monthly Weather Review. 2.4.1.1 Radius of Maximum Winds from Aerial Reconnaissance. Maximum flight- level winds and estimated maximum surface winds are usually included in flight reports from reconnaissance aircraft. Flight-level winds, recorded at one-second intervals by N0AA research aircraft flown into hurricanes have also been available since 1953. Recorded flight-level winds were processed and 10-second averages are stored on microfilm for data prior to 1973 and on magnetic tapes for recent years. Wind and pressure data on microfilm were tabulated, plotted, and analyzed for hurricanes affecting the U.S. coasts. From magnetic tape records since 1973, composite maps of flight-level winds relative to the storm center at given intervals and winds at various radial distances from the storm center recorded in a traverse through the eye were plotted by computer and made available to us by the Hurricane Research Division (HRD) of the Atlantic Oceanographic and Meteorological Laboratory (AOML) of NOAA. Analyses of these maps yielded another measure of the radius of maximum winds. Examples of these analyses are given in Appendix A. It is generally accepted that, above the boundary layer, there is little vertical shear in a hurricane windfield in the lower troposphere (below about 600 mb). Miller (1958) developed a 3-dimensional description of the windfield in a tropical cyclone. Shea and Gray (1972) found that only the weaker storms exhibit a tendency for a slope of the radius of maximum winds with height; more intense storms do not. Willoughby et al. (1982) analyzed multi-level (1,500, 5,000 and 10,000 ft) flight data in Hurricane Allen (1980) and showed that 26 50 45 40 35 ^ - 30 '"' o LkJ RS ■jA .n 20 2 3 15 10 OBSERVED WIND SPEED 3 00 OS i 2 00 00 TIME CGMT5 7igure 2. — Hourly observations of wind speed and direction, and distance of Allen's center from Brownsville, Texas for period 1300 GMT on August 8 through 0600 GMT on August 11, 1980. the magnitudes of the maximum winds at different flight levels were generally quite similar. We concluded that flight-level wind data recorded at altitudes below the 600-mb level can be used to determine the surface value of R in hurricanes of moderate or greater than average intensity. Examples of this method of obtaining R are given in the data analysis in Appendix A. 2.4.1.2 Radius of Maximum Winds from Wind Records. Observed maximum winds are determined by noting the time when a wind-reporting station experienced the highest windspeed prior to the wind slackening in the hurricane's eye. From a knowledge of the location of the storm center at that time, one can deduce a value of R. Similar results can be obtained from various types of wind recorders. The windspeeds read off anemometer records were plotted on a time scale and a smooth curve drawn. A curve of distance from the storm center, as measured from the best track, was constructed on the same time scale. The two curves are shown for Hurricane Allen (1980) in Figure 2. The two peaks in the wind graph indicated that the storm's track took the center closer to the station than the radius of maximum winds. The 'observed' radius of maximum winds would 27 be the distance from the wind center at the time of these peaks. If the track had kept the storm center beyond R, there would have been only one peak in the wind profile. In this case, it was established that the radius of maximum winds was less than the distance of station from the storm track. 2.4.1.3 Radius of Maximum Winds from Eye Radius. In their work, The Structure and Dynamics of the Hurricane's Inner Core Region , Shea and Gray (1972) stated that, in the mean, the radius of maximum winds occurs at radii 5 to 6 nmi outside the inner radar eye radius (IRR) - assumed synonymous with the inner cloud wall. The IRR may be obtained from land-based radar, ships at sea, or aircraft. Figure 3, taken from Shea and Gray, shows the position of R relative to the IRR for 2 1 Atlantic Ocean and Gulf of Mexico hurricanes. Figure 4, also from Shea and Gray, shows the difference between R and IRR versus the maximum windspeed for radial flight legs. Note that the more intense the wind the better the agreement between R and IRR. 2.4.1.4 Radius of Maximum Winds from Pressure Fit. Computed R's can be estimated by fitting an exponential pressure profile to the data from a given hurricane. By their nature, computed values of R are more subject to error than observed R's. The procedure was used in previous studies to derive estimates that were carried over into the present study and was discussed by Myers (1954). 2.4.1.5 Radius of Maximum Winds from Monthly Weather Review . Reports of radii of maximum winds extracted from storm analyses in the Monthly Weather Review usually consist of estimates of the diameters from the measured time interval between the slackening and resumption of hurricane-force winds over some point near or along the coast. In other instances, researchers have reported their findings in the Monthly Weather Review , and these results (including estimates of the radius of maximum winds) have been accepted by the authors of this study. 2.5 Speed (T) and Direction (9) of Forward Motion The translation speed and direction of hurricane motion are, among others, important factors for determination of storm surges along the open coast. Forward speed and direction were determined primarily from analysis of hourly hurricane positions when they were available. Generally, the analyses of meteorological data are weighted toward synoptic-scale motions. The hurricane track, thus obtained, is a best estimate of the large-scale storm motion and not a precise location of the eye at discrete time intervals. In this report, direction of storm motion is measured clockwise from north and denotes the direction from which the storm crossed or bypassed the coast. 2.5.1 Source of T and 8 Data The T and 9 information in Tables 1 through 3 were extracted from storm track charts. Hurricane tracks compiled by Cry (1965) and the charts for recent years published by the NHC, NOAA, in Miami, Florida (Neumann et al. 1981, and Jarvinen et al. 1984) were used. The speeds were derived mostly from detailed track charts, depicting hourly or bi-hourly positions in the vicinity of the coast, such as: Myers (1954), Graham and Hudson (1960), and Ho and Miller (1982, 1983). The listed T and 8 pertain to the time of landfall, exit, or closest approach to the coast. In Tables 1 through 3, both the T and 9 data prior to 1973 were carried forward from Tables 1 and 2 of TR 15. 28 Figure 3. — Radius of maximum winds (R) versus inner radar eye radius (IRR). Points falling on the 45° line are Chose where the R and IRR coincide- The curved line indicates the best fit curve (from Shea and Gray 1972). a: ic- S I ' • - 1 • - 1 • < • • • i*i • _ 5 ••• • • • • a • ~ 3 • • : • • • — d • • • • • _ UJ • 9 • • £; •• •••••• • • • _ a • • .•!•: •* $ • ••• • •/) • • • • • _ z • v* •^^_^ • * ••• • •• • • / •• • 2 • • • X • • • • — * • . ..37f>4c ^ m*t — • _ . -1 ( %'" •1 :"•%*•. •*** «f ^**><*f^ • - NO DIFFERENCE ...,:« # •. '.'jVV h » r 1 ■ L« * ••••••••• t 3 • • •"* • •' IRR _ - • • • • • . • 30 SO ICC MAXIMUM WIND SPEED ! Figure 4. — Difference between the radius of maximum winds (R) and the inner radar eye radius (IRR) versus maximum wind speed. The best fit curve is indicated by the heavy line (from Shea and Gray 1972). 29 2.5.2 T and 9 Data Used in Probability Distributions In our present study, cumulative probability curves for T and 9 were plotted for tropical cyclones since 1900. In TR 15, T data for hurricanes since 1886 were used in the plots. We made similar analyses using hurricane data from 1900- 84 and found little difference in the results. To expand our data sample for speed of forward motion, we utilized T data from all tropical cyclones landfalling on the Gulf and Atlantic coasts. In addition to the T data for landfalling hurricanes listed in Tables 1 through 3, average speeds for weaker storms were estimated from 6-hourly positions given on the HURDAT tape (Jarvinen et al. 1984). We chose the average speed, computed at synoptic hours, closest to the time of landfall as an approximation for landfalling tropical storms. Directions of landfalling tropical cyclones were determined at the times they crossed the coast. In TR 15, the sample of 9 included values from hurricanes and tropical storms since 1871. In the present study, 9 data came from tropical cyclones that occurred during the 85-year period, 1900-84. 3. METEOROLOGICAL PARAMETERS AND THEIR INTERRELATIONS 3.1 In t r oduc t ion Meteorological parameters used in the hurricane climatology analysis are central pressure (P Q )> radius of maximum winds (R) , forward speed (T) and direction (9) of storm motion. Since the computation of storm-surge frequencies using the joint probability approach assumes independence among the parameters, any interdependencies must be identified and taken into account. In addition to the basic hurricane parameters, location parameters include a coastal reference milepost (m), the latitude (0) and the longitude (X). The mileposts are assigned such that m = at the Mexican border and increases along the Gulf coast toward Florida, reaching a value of 1415 at the southern tip of Florida. The value of m further increases northward along the Atlantic coast to m = 3100 at the Canadian border (see fig. 1). 3.1.1 Overview of the Statistical Study The ultimate purpose of the statistical tests was to find interrelations between the hurricane parameters, if any, so that those parameters could be properly accounted for in the storm-surge frequency computations. Because of large natural variability, our data sample did not provide a sufficient number of storms to estimate the underlying populations over coastal segments short enough to allow homogeneity to be assumed a priori. This made it desirable to pool data over as large an area as possible, to increase reliability of population estimation and hypothesis testing. However, the pooled data could only include coastal segments that were both statistically and meteorologically homogeneous. While determination of meteorologically homogeneous coastal segments was, of necessity, somewhat subjective, we complemented our judgments with consideration of statistical homogeneity. We felt that the variability in the data and limited sample sizes precluded a purely statistical determination of homogeneous regions. 30 The statistical methods used in this chapter are outlined in Appendix B, wherein the rationale for their choice, their limitations, and the interpretation of the results are discussed. We used two methods to delineate regions in which the hurricane parameters might be considered homogeneous: a meteorologically based method and a statistical method (based on cluster analysis). For the meteorological method, hurricanes that struck a coastal segment that had relatively uniform orientation were grouped together. We then performed tests to determine whether the statistical characteristics of hurricane parameters among the various groupings were similar. The groups with no significant differences in statistical characteristics were considered for combination into a larger group. These pooled groups provided larger sample sizes for tests of interrelations between hurricane parameters. We also performed a cluster analysis on the parameters of all hurricanes located along Gulf and Atlantic coasts; the hurricanes were separated into clusters (groups) based upon the characteristics of the sample data. The groups of hurricanes so obtained were then examined using principal component analysis and discriminant analysis to determine whether significant differences existed between the groups. The results were compared with those of the meteorological method. 3.1.2 Scope of the Chapter In Section 3.2, a comparison of the statistical characteristics of forward speed of hurricanes and tropical storms Is discussed. Practical problems with the treatment of the direction of motion of landf ailing hurricanes and tropical storms is also discussed in this section. The homogeneity of hurricane parameters from different geographical regions is discussed in Section 3.3. The results of homogeneity test were used as guidelines for pooling the data samples used in the independence tests. In Section 3.4, interrelations between hurricane parameters are examined. In Section 3.5, the interdependence between hurricane parameters is discussed, and our conclusions are presented. 3.2 Considerations of Data Samples for Statistical Tests Tropical storm data included forward direction and speed for the Gulf and Atlantic coasts of the United States. Central pressure and radius of maximum winds for individual tropical storms could not be adequately specified. However, central pressures of all tropical storms are, by our definition (see sec. 2.3.1), greater than 982 mb. Only landfalling tropical storm data were considered. The landfalling tropical storm data were separated into two groups: one for the Gulf coast and the other for the Atlantic coast. For comparison, the landfalling hurricane data were also separated in the same manner. To examine whether the distributions of landfalling hurricanes and tropical storms should be considered separately, we set up the following data subsets: GH: landfalling hurricanes on the Gulf coast, GT: landfalling tropical storms on the Gulf coast, AH: landfalling hurricanes on the Atlantic coast, and AT: landfalling tropical storms on the Atlantic coast. 31 Table 5. — Forward speed of hurricanes and tropical storms for selected portions of the coast Type of Sample Average Speed ~ Standard Deviation Storms "Size (kn) (kn) ___ West coast of Florida (1050 <_m <1415 nmi) — Hurricanes 13 10.5 " 3.6 Tropical storms 28 15.8 7.6 Northern Atlantic coast (m > 2 400 nmi) Hurricanes 7 34.7 7.8 Tropical storms 12 22.8 6.7 We performed the (1) Mann-Whitney test, (2) Wilcoxon two-sample test with normal approximation, and (3) Kruskal-Wallis test with Chi-square approximation on the data set pairs GH and GT, and AH and AT. Part of the Mann-Whitney test, and all of the Wilcoxon and Kruskal-Wallis tests were conducted using SAS procedures. 3.2.1 Forward Speed The results of the three tests show no significant difference between the distributions of landfalling hurricanes and landfalling tropical storms for either the Gulf or Atlantic coasts. We also inspected scatter diagrams of forward speed vs. railepost for landfalling hurricanes and landfalling tropical storms. Figures 5a and 5b show that the distribution of forward speed of landfalling hurricanes and tropical storms for the west coast of Florida (m = 1050-1415) differs from that for mileposts greater than. 2400. The latter is located north of Chesapeake Bay. Table 5 shows that tropical storms that struck land, on average, moved faster than did hurricanes along the west coast of Florida, but moved more slowly than hurricanes for the northern portion of the Atlantic coast. The variation along the Florida coast appears to be reasonable, and is explained by the fact that storms that recurve tend to move faster as they become embedded in stronger westerly flow. Strong westerlies also tend to disrupt the delicate thermal circulation necessary to support intense storms. Therefore, storms that recurve tend to be weaker (tropical storms) and move more rapidly. We concluded that hurricanes and tropical storms in this area represented complementary portions of the same distribution, not separate distributions. Clearly, the observations north of milepost 2 400 cannot be explained this way. While we have no fully satisfactory explanation for what the data indicate, we note that the sample size is rather small, and for the hurricanes, the variability is considerably higher than the Florida sample (see table 5). Furthermore, most storms, whether hurricanes or tropical storms, that reach SAS is the Statistical Analysis System. Mention of a commercial product does not constitute endorsement by the Federal Government. 32 050 1100 1200 1300 I 400 "500 MILEPOST Cnmi) * Hurricanes • Tropical Storms 30 - — r # > i i r- T" " r 1 1 1 (b) 40 * * - 30 - • * * • • a LU Q. 20 10 " • * • • • • • • • 2400 2500 ^ Hurrfeanvt • Trojteal 3torm« 2600 2700 2800 2900 MILEPOST Cnmi) 3000 3100 3200 Figure 5. — Forward speed of landfalling hurricanes and tropical storms versus adlepost (a) along the Gulf coast of Florida, and (b) along the Atlantic coast. 33 these northern latitudes are moving quite rapidly. They appear to have been transformed into systems whose circulations have extratropical characteristics. The fastest moving storms are probably propagating as waves along a baroclinic zone. Because of the small sample size, the generally large variability and the indication that the dynamics of the storms north of milepost 2400 appear to be quite unlike classical tropical cyclones, we exercised judgment in our analysis of these data. We felt that the best estimate of the underlying population could be achieved by consideration of the forward speed of both hurricanes and tropical storms. Based upon the test results and on our judgment, we treated the speed of motion for tropical storms the same as for hurricanes for both the Gulf and Atlantic coasts. 3.2 .2 Forward Direction. The data only include landf ailing storms. In our data sample, landf ailing hurricanes outnumber hurricanes in the other categories (bypassing and exiting) by a large amount. The sample sizes in the bypassing and exiting categories are so small that it would not be possible to make meaningful inferences based on statistical analysis. Landfalling tropical cyclones are defined as those that strike the coast, hence their range of forward directions is limited by the coastal orientation. The range of directions can vary greatly as the coastal orientation changes over short distances. This variation can limit the range of directions in the category of landfalling storms in a way totally unrelated to real meteorological variability. For this reason, we decided that it was not appropriate to treat direction of motion as a random variable for the purposes of hypothesis testing, and in particular, for examination of interrelations with other parameters. Possible interrelations between 9 and the other hurricane parameters will be considered further in Chapter 5. 3.3 Homogeneity of the Hurricane Data Samples For the purposes of this study, homogeneity for a given coastal segment means that parameter estimates from a sample of storms for one location appear to be drawn from the same population as the parameter estimates for any other location in the segment. We separated the storms into groups so that each group consisted of the storms that made landfall on a coastal segment that had relatively uniform orienta- tion. Presumably, if the segment was properly selected, the data would be meteorologically homogeneous. We then performed statistical tests to determine whether the frequency distribution of the parameters from one group appeared to be the same as other groups. The groups which appeared to show no significant difference in their distributions were considered for combination into a larger group. Cluster analysis of the parameters provided another method to separate the hurricanes into groups based on the characteristics of the data sample. The groups of storms so obtained were tested using principal component analysis and discriminant analysis to determine whether they appeared to be reasonable partitions. The results were then compared with those of the meteorological method (based on coastal orientation). 34 Table 6. — Initially selected coastal segments Segment Number Number of Milepost Range Hurricanes (smoothed coastline) Description 23 0-400 Gulf coast from Mexican border to Galveston, Texas 400-700 700-1100 Gulf coast from Galveston, Texas to Mississippi delta Gulf coast from Mississippi delta to Suwannee Sound, Florida 12 1100-1415 Gulf coast from Suwannee Sound, Florida to the southern tip of Florida peninsula 1415-1800 1800-2200 Whole Atlantic coast of Florida Atlantic coast from Georgia to Cape Hatteras 22 00-2 700 2 700-3100 Atlantic coast from Cape Hatteras to Rhode Island Atlantic coast from Rhode Island to Canadian border 3.3.1 Methods for Testing the Homogeneity of Storm Parameters In the meteorological method, we first selected eight segments along the Gulf and Atlantic coasts of the United States. These eight segments were located in the milepost ranges shown in Table 6 and are shown schematically in Figure 6 (see also fig. 1). The number of landf ailing hurricanes in each segment is also listed in Table 6. There were four segments on the Gulf coast and another four segments on the Atlantic coast. Milepost 1415 is located at the southern tip of Florida. Along each segment, the orientation of the coastline is relatively uniform, except for the two most northern segments along the Atlantic coast. For the first six segments we used the Mann-Whitney test to examine the relation of P , R, and T among pairs of segments. Segments 7 and 8 were not included in the testing because of the small numbers of observations. The test was used to determine whether the distribution functions of a given parameter appeared to be significantly different between two segments of the coastline. If no difference in distribution functions for two segments was detected for all parameters, those two segments could be combined if the meteorological conditions in each segment were deemed to be similar enough. The seven parameters used in the cluster analysis were P , R, 0, T, the milepost value (m), the latitude (0), and longitude (A) of the landfalling point. For each grouping, principal component analysis and discriminant analysis 35 1 I I 1 [ 1 I I 1 I 1 1 I I GULF COAST I I I | J I I I ATLANTIC COAST Ml! 12 3 4 5 6 7 8 COASTAL SEGMENTS SELECTED INITIALLY RESULT OF MAM-WHITNEY TEST 1 4 | 2 3 |lllll 5 illiij !*: : t$ &**>**&:'] RESULT OF CLUSTER ANALYSIS (? , R, 9 , T , n, , k ) o ' > 1 \ \ LOCATIONS OF FREQUENCY MINIMA GLF C ATL A COASTAL SEGMENTS SELECTED FOR INDEPENDENCE TESTING GULF COAST | ATLANTIC COAST t I 1 I I I I 1 I I 1 1 1 I 1 1 1 1 1 I I I 1 I I 1 1 I I 5 10 15 20 25 20 MILEPOST (100 nmi) Figure 6, — Possible homogeneous regions for landf ailing hurricane parameters. Shaded areas have Insufficient or no data. 36 Table 7. — Results of Mann-Whitney test for a priori selection of coastal segments in the Gulf of Mexico Segment Segment Number Number 12 3 Segment Number 1 2 3 Segment Number 1 2 3 * * * * * Segments as given in Table 6 * indicates segments with similar distributions indicates segments with different distributions were used to examine the similarity between the groups. The most distinctively separated groups were selected and the parameters within each group were examined for possible interrelations. 3.3.2 Comparison of Results from Different Homogeneity Tests 3.3.2.1 Meteorological Method. After the coastal segments were selected (table 6), the Mann-Whitney test (Conover 1971) was performed to compare pairs of segments. Adjacent segments with no significant difference in distribution functions were considered for combination. The results for the Gulf coast are shown in Table 7. In all cases, adjacent segments appeared to have similar distributions. However, for P and T, some segments that were separated by one or two segments appeared to come from different distributions. For instance, for both parameters, segments 1 and 3 had different distributions, even though they both had distributions similar to that of segment 2. To explore the variation along the Gulf coast further, we divided the data sample into different segments. An example is shown in Table 8, where only 3 segments were used. Again, all segments appeared to have similar distributions of R, but different distributions of P and T. Our analysis of shifting the segment boundaries led us to conclude that the data appear to be Table 8. — Results of Mann-Whitney test for modified segments of the Gulf coast Segment Number P o Segment Number 1 2 R Segment Number 1 2 T Segment Number 1 2 Milepos t Range 1 2 3 * * * * * * 0-500 500-1000 1000-1415 * indicates segments with similar distributions indicates segments with different distributions 37 "locally homogeneous." It appears that there may be variations along the smoothed coastline in the Gulf that could result in samples that would not be homogeneous if the segments were too large. However, it is not clear what "too large" is. By that, we mean that the variation appears continuous and that there are no obvious breakpoints between homogeneous regions. Therefore, the data can be considered homogeneous locally. In Section 3.3.3, we combine this with an evaluation of the statistically based cluster analysis to specify homogeneous segments for the independence testing. The concept of local homogeneity was also assumed to apply for the Atlantic coast. As indicated in Table 6, the number of storms beyond milepost 2200 was too small to consider formal statistical testing. The results of the Mann- Whitney test for the region south of milepost 2200 were variable, depending on the segments chosen. However, the results were not inconsistent with the concept of local homogeneity. This Is reasonable, considering the known variation of the hurricane parameters with latitude. 3.3.2.2 Cluster Analysis. The results of the cluster analysis were generally consistent with the results of the meteorological method. In application of the cluster analysis procedure, the number of clusters was assigned a priori, and the cluster boundaries were then determined. Analyses for two through nine clusters were conducted. When five clusters were selected, the partitioning was most similar to that determined by the meteorological method. The cluster analysis technique assigns each storm to a particular cluster and assigns it an identification (ID) number. These ID numbers are shown in the schematic in Figure-6. Somewhat surprisingly, each of the clusters included storms that struck land over a continuous extent of the coast. That is, milepost alone could be used to totally delineate which storms were included within each cluster. This is consistent with our judgment used in specifying regions by the meteorological approach (sec. 3.3.2.1). The cluster boundaries for the five-cluster partition were generally located in regions of storm-frequency minima (see fig. 27). Because of this, the last storm in one cluster (largest milepost value) could be at a considerable distance (40 nmi or more) from the first storm in the adjacent cluster. With this in mind, a cluster boundary in Figure 6 should be considered a point somewhere in the transition region - cluster boundaries are not precise delineations. 3.3.2.3 Discriminant Analysis. To determine how well the clusters of hurricanes were separated, discriminant analysis was performed on them. In addition to providing the seven parameters mentioned in Section 3.1 (P , R, T, 9, m, 4>, A), a cluster identification number (as shown in fig. 6, for a 5-cluster partition) was also used as input to the procedure. The results showed that hurricanes were not distinctively separated by the cluster analysis for 3 through 9 clusters. For example, in the case of five clusters, Hurricane Hazel of 1954, which made landfall at milepost 2 077, was put in cluster 3 by the cluster analysis but classified into cluster 1 by the discriminant analysis. In this case, cluster 1 includes hurricanes which made landfall in the milepost range 1-500 and cluster 3 includes those in the milepost range 1752-2294. The discriminant analysis and the cluster analysis agree only on classifying all landfalling hurricanes into two clusters: one Includes those in the milepost range 1-1201 and the other in the milepost range 12 92-2 750, with missing data outside of these ranges. However, 38 Table 9. — Percentages of variance accounted for by principal components Cumulative Principal Percentage Percentage Component of Variance of Variance 1 44.6 44.6 2 15.2 59.8 3 14.3 74.1 4 12.2 86.3 5 9.0 95.3 6 4.5 99.8 7 0.2 100.0 examining these milepost ranges, we felt that these two clusters cannot be meteorologically homogeneous, especially the second cluster, because it includes hurricanes which are generally larger in size and faster in forward motion as compared to hurricanes in the lower latitudes. 3.3.2.4 Principal Component Analysis. Principal component analyses were conducted to examine the relative importance of the parameters. The percentage of variance that each principal component accounted for is shown in Table 9. The first principal component accounts for almost 45 percent of the total variance, and each of the next three principal components account for more than 12 percent of the total variance. "Loadings" provide a measure of the contribution of the parameters to each component. The loading of the hurricane parameters in the four most significant principal components is shown in Table 10. Each column in the table is an eigenvector normalized to have a unit length. This means that the square root of the sum of squares of numbers in each column is unity. Table 10 shows high positive loadings on the milepost (m) and landfalling latitude (0) and high negative loading on the landfalling longitude (A) in the first principal component, and high positive loading on central pressure (P.) in the second principal component. The loading and importance of the first component confirms our meteorological judgment that location is an important factor in delineating homogeneous regions. Table 10. — Loading of hurricane parameters in the principal components which account for more than 12 percent of variance Principal Component Parameter 12 3 4 " F 07l3 0787 =0TT4 -0.16 R 0.31 0.33 0.11 0.60 9 0.20 0.13 0.73 -0.57 T 0.39 -0.28 0.39 0.26 -0.2 1 0.25 0.34 0.13 0.87 -0.14 0.31 0.33 0.11 0.20 0.13 0.73 0.39 -0.2 8 0.39 0.50 -0.14 -0.38 0.47 0.01 0.11 •0.48 0.14 0.3 6 39 ■ I . 2 ■3 * t ii , ! 1 1 * radius of maximum winds (R) , forward speed (T), and direction of motion (9) along the Atlantic and Gulf coasts. In calculating frequency distributions of hurricane-induced surges on the coast it is necessary to combine the probabilities from the individual distributions. In such applications, the question of statistical independence among the individual probability distributions has to be addressed. For example, of all the hurri- canes affecting a given coastal stretch over a long period of time, what fraction of the storms are in both the upper 10 percent in intensity (P ) and size (R)? If P and R are independent, the probabilities can be multiplied. In this case, there would be a 1-percent chance of their joint occurrence. If P and R are positively correlated, there would be more than a 1-percent chance of the simul- taneous occurrence of a storm both this intense and this large. Similarly, if P and R are negatively correlated, the joint probability is less than 1 percent. Statistical tests may be inappropriately biased toward acceptance of indepen- dence if the significance level chosen for the test is too low, especially considering the high variability and relatively small sample sizes available for this study. Dependencies which are meteorologically based may be present, but may not lead to rejection of the null hypothesis of independence. Another point that must be considered is whether or not certain interdependencies are expected to extend across the entire spectrum of a given parameter or whether such relations might be important only within some limited range of values. 4.2 Central Pressure Versus Radius of Maximum Winds A significant joint probability question is whether hurricane size (R) and intensity (P ) are independent. A storm that is both large and intense would have enormous destructive power. Hurricanes with very large R's (in excess of 4 5 nmi) are generally found to be of moderate or weak intensity. In hurricanes that have undergone recurvature and are moving northward in the Atlantic, often becoming ext ratropical , the radius of maximum winds tends to become larger and more ill-defined, and the central pressure rises. Extremely intense hurricanes (low P ) and those with small radii of maximum winds tend to occur together because, if angular momentum is conserved, a vortex contracts in size as it increases its rotational speed. If we examine the data for P and R for the Gulf coast (table 1), it is not surprising that the calculated correlation coefficient was only 0.16. A correlation coefficient this low indicates that the linear relation between P q and R is not likely to be significant. However, a low correlation could occur if a nonlinear relation existed between these two variables. It is also possible that a relation between P Q and R could be masked by the high degree of natural variability inherent in hurricane observations. If such a relation exists, it is likely to be most prominent for intense storms where the dynamics that couple the variation of both P and R are stongest and less susceptible to the masking dependence of P and R, we choose to employ non-parametric statistics. A non- parametric test does not require specification of the form of the distribution, 50 Table 14. — An example of a general two— by— two contingency table Condition 1 Condition 2 Total Group 1 a b a + b Group 2 c d c + d Total a + c b + d n thus, Che statistical test avoids the assumption of linearity. It can also provide insight into behavior of the extreme portion of the distribution by judicious selection of the P Q and R groupings. (See below.) The test of interdependence of P Q and R involves comparing the two samples of observations to see if the populations appear co be related. In other words, to determine if a given P Q value is more likely to be associated with a limited range of R values (interdependence), or whether any R from the complete spectrum of values has the same probability as the distribution specified for R for every ? value (independence). We set up a contingency table, the form of the tabulation is displayed conventionally in Table 14. The letters a, b, c, and d 3 re the count of occurrences in each group for a given condition. We used Fisher's exact probability test (Conover 1971) to compare our groupings. Fisher's test assumes that the marginal totals of Table 14 are fixed (that is, the number of observations in each group and for each condition are fixed), and tests whether the partitioning of frequencies (a, b, c, d) could have arisen by chance. The probability of such an occurrence is calculated as, a + c ( b ; d ) n a + b where ! "' '" j is a binominal coefficient ; — ; — - , hence = (a + b)! (c + d)! (a + c)! (b + d) P ~~ n! a! b! c! d! 51 Table 15. — Frequency of occurrence of different storm radii in two different class intervals of hurricane intensity observed in the Gulf of Mexico, 1900-84 R < 15 nmi R > 15 nmi Total P Q > 93 mb 16 47 63 P Q <_ 93 mb 3 3 Total 19 Ul 66 Table 15 sbows tbe number of occurrences of burricanes making landfall on the Gulf coast, within different categories of central pressure and storm size. We formed a null hypothesis, H Q , that there was no significant difference between R associated with group 1 (P Q > 930 mb) and group 2 ( P Q < 93 mb). Fisher's test gives a probability of occurrence by chance a value of 0.02. At the 5-percent level we rejected H and concluded that there was a significant difference between the two groups of hurricanes, in terms of occurrence of the specified hurricane radius. A similar test was applied to the parameters, P Q and R, for hurricanes landfalling on the Atlantic coast. With a small sample size and a much larger degree of scatter, the formal statistical test could not detect any significant interdependence of these two parameters for Atlantic coast hurricanes. While it is clear that a relation appears to be reasonable for the extremely intense hurricanes, natural variability seems to overwhelm this effect for most of the other (weaker) storms. Furthermore, it requires a much larger sample of data to establish the functional form of the joint probability of two parameters with a degree of reliability, as compared to specifying a single probabilitv distribution. The hurricanes listed in Tables 1 and 2 are insufficient to auantify anv joint probabilitv relation that might exist over the full range of P and R. The data must be supplemented by a measure of deduction and meteorological judgment. Before reaching a conclusion, we supplemented our data base by including extremelv intense hurricanes that occurred outside our main area of interest (within 150 nmi of the Gulf and Atlantic coasts). 4.3 Meteorological Analysis The basic observations used in our analysis of extremely intense hurricanes (P<93 mb) were based primarily on wind and pressure data recorded by recon- naissance aircraft. In some cases, central pressures were also obtained from a search of other sources, including studies of individual hurricanes in the liter- ature. Table 16 gives a list of hurricanes with P Q less than or equal to 93 mb recorded during the period 1900-85, together with the radius of maximum winds taken at the time of minimum central pressure. The R values for Hurricane Janet of 1955 could not be determined because of a lack of wind data. Janet was a very compact storm with winds reaching hurricane force only about 2 hr before the arrival of the eye (Dunn et al. 1955). Estimated maximum winds of 2 00 mph were reported just about 30 min prior to the passage of the eye over Swan Island. The table also lists locations where the P and R data were observed. In all cases, 52 3 3 3 3 be 3 O 00 o 00 o CO in co v£> O 2 00 2 CO 2 2 oo 2 O 2 en 2 O^ H >< CNI o> 00 in CN) CO ^O (U 3 <3 a O o o o o CO O o o fa-i CJ 2 2 a 2 2 2 2 M c 3 •H < -a ^ co s • CO 2 CD •U 73 CO 0) s „ , 1—1 >-, CO CU £ N< 3 U J3 O — i \0 vD — H CTi C^ O r-» o CTi 00 — i a> a a a a CD 01 0) 0) CO CO en CO ,_| 4-J CO 0) •H CO ,—1 CU CO T3 c O CU C JS 4-J N s J-J •H cij 1-4 3 C 4J ■U 0) 3 s M •H > i— i CO co o cn CO 3 0> CO CO 3 CO , — 1 u T) a W S3 H pa CJ U ^ — ' r ! UkMOPAkUNO HURMIOUMS J / a L • •/ - 03 " /l 2 • / ' | - •--¥ ■» - i» I /• & « •!/ _ Z -J o / ♦ x L lil 1 • a. a i £ 945 mb Total 9 >_ 95° 3 15 18 9 < 95° 4 4 Total 3 19 22 separately show no evidence of interrelations between the parameters. However, this conclusion must be interpreted narrowly: independence is with respect to landfalling storms. Because of the variation of the coastline, this should also be considered locally independent, in the same sense as described in Section 3.5. It should not be extended to the underlying populations that contain the full range of possible values without more detailed and extensive analysis. 5.3.2 Atlantic Coast On the Atlantic coast, the interrelations of P Q and 9 are masked by their correlations with latitude. Figure 18 shows the variation with latitude of the direction of motion for hurricanes landfalling on the Atlantic coast. The plot suggests two groups of storm track directions. These two groups appear to be separated by a forward direction of about 170° (vertical line on fig. 18). From a meteorological standpoint, the data sample suggests the existence of two distinct groups: (1) landfalling hurricanes crossing the Atlantic coast from easterly directions (20-170°), which are westward moving hurricanes embedded in the basic easterly current, and (2) landfalling hurricanes coming from 170-220°, which are hurricanes moving northeastward after recurvature. There is also a stretch of the coast, from 33.5-3 7°N, which apparently includes hurricanes from both groups (dashed horizontal lines in fig. 18). Statistical tests of homogeneity, using contingency tables and the Mann-Whitney test, indicate that storm track data north of 37°N are significantly different from similar data Co the south. These results also suggest that there are two distinct groups of storm-track directions for landfalling hurricanes along the Atlantic coast. Since the data along the entire Atlantic coast cannot be considered homogeneous, it is inappropriate to consider the interdependence of P and 9 for these data without separating the sample into separate groups. 5.3.2.1 Atlantic Coast, South of 33.5°N. We considered the data sample of landfalling hurricanes for the Atlantic coast, south of 33.5°N, in the form of a 2X2 contingency table. We estimated the probability that specific partitionings of the frequencies arose by chance. One partition of the data can be made as shown in Table 18. This contingency table shows the number of occurrences (frequencies) of hurricanes within different categories of P Q and 9. We then formed a null hypothesis that the noted distribution of observations (frequencies) arose by chance, that is, there was no significant difference between 9 _> 95° and 9 < 95°. The Fisher exact probability test gives a 0.53 probability of occurrence by chance. This indicates that we cannot reject the null hypothesis at the 5-percent level. We further tested for different groupings by changing the dividing line for both track directions and central pressures. These tests also yielded results which did not allow us to reject the 64 145 £30 215 200 185 170 155 140 DIRECTION (deg) 10 95 Figure 19. — Histogram for direction of storm motion for the 2.5' longitude block centered about Key West, Florida. latitude and null hypothesis. We concluded that, at the 5-percent level, there is no significant difference between the two groups of hurricanes, in terras of occurrence of the specified direction of storm motion. In other words, there is no detectable relation between P and 9. o This conclusion is based on the total data sample. However, there may be localized areas that could exhibit characteristics different from this general conclusion. The data sample is inadequate to detect such situations. For instance, an interrelation between P and might occur locally near the southern tip of the Florida peninsula and the Florida Keys. Figure 19 shows a histogram for direction of storm motion for a 2.5 degrees latitude and longitude block centered about Key West. This histogram indicates a bimodal distribution for direction of storm motion with storms traversing the 2.5 degree block both from the southeast and the southwest. It is generally observed that storms coming from an easterly direction are more intense than those coming from a westerly direction. These localized interrelations between P , 9, and possibly between other parameters need further scrutiny. It is left to the user of this report to look at conditions at specific locations more closely. The treatment of storms affecting the Cape Hatteras area that follows in Section 5.4 may be used as a guide. 65 5.3.2.2 North Atlantic Coast. Examination of Figure 10a showing the latitudinal variation of pressure suggests no noticeable variation with milepost for the northern Atlantic coast. Meteorological conditions associated with the increase in central pressure with increasing latitude are discussed in Chapter 7. This feature is not obvious from Figure 10a. Consideration of Figure 10c for storm direction shows a variation due in part to variations in coastal orientation, but primarily due to synoptic-scale meteorological conditions. A large scale high pressure system (the Azores-Bermuda high) usually is centered off the coast creating a clockwise flow around it during the hurricane season. In association with this high pressure system, storm direction tends to turn clockwise as the storms move northward. This is the main explanation for the variation shown in Figure 10c. In the absence of adequate data to test for interrelations independent of latitude, it is our judgment that the concept of local independence is appropriate for the northern part of the Atlantic coast. 5.4 Cape Hatteras Area There are a number of coastal locations that, because of geographical features, are probably not well represented by the generalized results presented in this report. Such areas include protrusions, such as the Mississippi delta, the southern part of Florida, Cape Hatteras and Cape Cod. It also includes major bays and partially enclosed bodies of water, such as Chesapeake Bay, Delaware Bay and the New York Bight. The paucity of storms affecting any one of these areas makes generalized analysis such as done in this report impossible. They must be examined on an individual basis. To illustrate some factors that might be considered in such an analysis, we studied the area around Cape Hatteras. What follows includes consideration of the more important factors for this particular location. Some aspects of the approach might not be equally appropriate for other locations. One reason for selecting Cape Hatteras was based on consideration of Figure 18. It appears that between 33.5 to 37.0°N, the storms may include different types of hurricanes. For the coastal region from Cape Hatteras, North Carolina to Virginia Beach, Virginia on the Atlantic coast, hurricanes landfalling from the southeast quadrant cover the full range of intensities from severe to weak. Occasionally, a hurricane meanders and strikes this stretch of the coast from the northeast quadrant; observations indicate that these storms have been weaker than those coming from the southeast. They have been weakened either by unfavorable conditions in the troposphere or by the reduction of energy supply while drifting over cold water. These storms, which typically move at less than 15 kn, generally have slower speeds of translation than storms entering the coast from the southeast quadrant. Therefore, a separation of P and T, as well as P and Q, between landfalling storms from the southeast and northeast quadrant was considered. The data for all landfalling hurricanes do not suggest that R differs much depending on 9. Therefore, the R probability distribution as given in Chapter 8 is recommended for both storm categories. Portions of the statistical treatments used below were formulated by Ho and Tracey (1975). 5.4.1 Parameters for Landfalling Hurricanes from Northeast Quadrant A special analysis was made of tropical cyclones landfalling from the northeast quadrant. Hurricane Doria (1967), which was a tropical storm at landfall, was used from Table 2, and, to expand the sample, data from other tropical cyclones 66 (1886 to 1984) moving from a northeasterly direction within an area west of 70°W and north of 32 °N were also used. Tracks for Doria and these seven additional storms are shown in Figure 2 0. These eight central pressure values were used in the estimation of the cumulative probability curve shown in Figure 2 1 (curve A). The speeds of forward motion for the same storms were measured from storm track maps (Neumann et al« 1981), and were used to help establish the probability distribution shown in Figure 22 (curve A). 5.4.2 Parameters for Landf ailing Hurricanes from Southeast Quadrant To obtain the probability distribution of central pressure for storms landfalling from the southeast quadrant, the probabilities for northeast quadrant tropical cyclones were subtracted from the overall probability for all landfalling storms. The probability distribution thus obtained was also checked against a direct sample of storm data. The resultant distribution for the southeast storms (fig. 2 1, curve B) differs only slightly from that of all landfalling storms. Speed of forward motion probabilities were evaluated in a similar manner (fig. 22, curve B). 5.4.3 Landfalling Track Frequency A discontinuity of track directions at Cape Hatteras can be seen between the curves in Figures 44 and 45. The frequency of storms landfalling from the sector 91-160° is approximately the same immediately north and south of the Cape. Landfalling storms from the other possible directions - 160-240° south of the Cape and from the northeast quadrant north of the Cape - are not of equal frequency. The overall frequency of landfalling storms (fig. 27), which was averaged along the coast by using a smoothing function, was adjusted to define this discontinuity. A track count of storms from the northeast quadrant and the 91-160° sector crossing overlapping two-degree latitude and longitude squares was examined separately. The sum of these frequencies was checked against the frequencies of all landfalling tropical cyclones. Figure 23 shows the resulting frequencies with which hurricanes and tropical storms entered the coast from different sections both north and south of the Cape. The plotted points show the frequencies of all tropical cyclones at 50-nrai intervals (determined from fig. 27). 6. FREQUENCY OF HURRICANE AND TROPICAL STORM OCCURRENCES 6.1 Classification of Hurricanes and Data The frequency with which a coastal area has experienced tropical storms and hurricanes during the period 1871-1984 is analyzed in this chapter. The data have been divided into three categories of storms that affect the coast in dif- ferent ways: 1) landfalling storms, 2) exiting storms, and 3) alongshore storms. The frequency of storm occurrences is defined as the number of tracks of each category of storms per year per nautical mile along a smoothed coast. The term "smoothed coastline" is discussed further in Section 6.2.1.2 and a smoothed coastline, defined objectively, is shown in Figure 24. The statistics on the frequency of hurricane and tropical storm occurrences are based on the yearly storm track charts by Neumann et al. (1981) from 1871-1980, and from their annual updates between 1981-1984 (published in Monthly Weather Review ). Following the criteria used in the track charts, tropical storms are 67 + JUL. 1934 + 4- OCT. JUL. I 897 I 90 I SEPT. 1889 / SEPT. 1967 SEPT. 972 + OCT. 913 NOV. I 935 Figure 2 0. — Track of tropical storms and hurricanes showing motion from northeast (from Ho and Tracey 1975). 68 RETURN PERIOD (yr) .001 1. 1 I.I -i i-t- 1.5 2 3 4 5 'l' I I I 'l ' I 25 50 1 ■ ■■ ' ■ i ■ 100 500 1000 'I rnvl i 'r ■ I ■!■ NE LANDFALLING (A), "SE LANDFALLING, WRIGHT MONUMENT, N.C. '(B) 920L-LL . I .5 1.0 5 10 20 30 40 50 SO 70 80 30 95 96 97 98 CUMULATIVE PROBABILITY I I I I I I l I I I l I 99 99.5 99.7 99.8 99.: Figure 21.— Cumulative probability curve of central pressure for landf ailing tropical cyclones adapted for Wright Monument, North Carolina. RETURN PERIOO (yr) 3 4 5 'I ' I 2 5 50 100 t— I — i' " i : i ' i ' i ' i i ' ; n ' ! i 500 1 000 SE LANDFALLING STORMS NE LANDFALLING STORMS WRIGHT MONUMENT, N.C. i i i i i i i i i i i i • 1 .5 1.0 5 10 20 30 40 50 60 70 30 90 95 96 97 38 99 99.3 99.7 99.8 99.9 CUMULATIVE PROBABILITY Figure 22.— Cumulative probability curve of speed of storm notion adapted for Wright Monument, North Carolina. 69 1 1 1 1 1 1 Hovia i VINOHIA 1 i 1 1 i - 9 - - ■eA-'O'N - 1N3WPNOW 1H9IHAA - OA1VS O / ° / * e - c X UJ — Q cc NOAV d ~~ - 2 — 5 _ o X li. UJ _ U 2 < 40 — 3dVO 131NI J sxoovaoo o 1 > -1 - i ' ! i i inoxocn — 3dVO • L .L _ - 1 I 1 ! 1 1, .1 . 1 ! ! i , ! Ciujuoi/JAQoi/SWaOlS) A0N3nO3Hd waois ONmvdQNxn 70 Figure 24. — Smoothed coastline obtained by applying the objective smoothing function. 71 defined as storms with maximum winds 34 to 63 kn, and hurricanes as storms with winds 64 kn or greater. The track charts also show extratropical stages of the cyclone tracks when the tropical circulation was modified as the cyclone moved into a nontropical environment. Beginning in 1972, the term subtropical was adopted as official terminology to describe such storms. Satellite imagery and other observational evidence enabled Hebert and Poteat (1975) to reexamine the official Atlantic hurricane tracks and to identify subtropical portions of the cyclone tracks since 1968. We included, in our frequency counts, subtropical storms and extratropical storms which have intensity equal to or greater than that of a tropical storm. For conciseness we use the term "tropical cyclone" in this report to include all four classifications. Storms classified as "tropical depressions" and "subtropical depressions" (maximum winds less than 34 kn) are not included in the statistics. 6.2 Frequency of Landfalling Tropical Cyclones Determination of the frequency of landfalling storms in a given area would be relatively simple if a sufficiently large sample were available. However, data are available for only 114 years, from 1871-1984. Inspection of this sample reveals variations within short coastal strips which are likely to be chance occurrences due to the relatively small sample size. A goal of this report was to smooth out such variations, and to portray the characteristics of the population , not the variability of the samples. Special effort was made to take into account the effect of coastal orientation on the frequency of storms. 6.2.1 Direct-Count Method The most direct method of assessing the frequency of landfalling tropical cyclones is to count the number of storms striking the coast. The number of entries was totaled for each 50-nmi segment along the smoothed coastline from a point some 2 50 nmi south of the Texas-Mexico border to the Maine-Canada border (see fig. 24). We created extensions of the Gulf and Atlantic coastlines at the tip of Florida. We "extended" the Gulf coast from Cape Sable to the Keys, stopping at its intersection with 81 °W longitude, as shown in Figure 2 5. We "began" the Atlantic coastline at approximately 82.5°W, and continued it eastward along the Florida Kevs to the mainland (see fig. 2 5). A storm could only be counted once on each "coast." The extensions were used for estimation of the probability distributions of storm frequency, P and R. We did not use the coastal extensions for T and 9, since these data sets included both hurricanes and tropical storms; we felt that the data were adequate to resolve the variation of T and 6 along this part of the coast. The Gulf coast analysis stopped, and the Atlantic coast analysis began at coastal reference point 1415. For the period 1871-1984, 307 tropical cyclones entered the Gulf coast, and 193 entered the Atlantic coast, not including storms passing the Florida Keys west of 81 °W. The 50-nmi segment counts were smoothed by using the smoothing function described in Section 6.2.1.1. Figure 2 6 shows the frequency plot of these discrete storm entry values at 50-nmi intervals (points joined by a dashed line) and the smoothing obtained as described in the next section. These frequencies depict tracks of storm centers, but do not take into consideration the lateral extent of coast affected by an individual hurricane. The damage swath from a major hurricane can cover more than 100 nmi of coastline. The frequencies of occurrences given in terms of storms per 100 yr per 10 nmi of the coast (vertical scale in fig. 2 6) represent long-term averages of tropical cyclones which include 72 / it Petersburg SOUThf, • Parish _ I "auchula 2 NW '•II -TS- w Mountain „.iie. I - L .aw I Bartow .^ J 3absoa Park w -0- | Oasia Fisnin* Lodge X--! -<> Avon Park -3-1 yr>ro 3radenton Exp 3ta w j | "V f" Fort Drum 3 NW ^V O- ■ ~ort Green 12 WSW Cte Soto City 4 SW • O Q Comwell 4 X* j l J Lake Placid 2 SW "^ j Myakka-Sivr it Park'" > O^echobee 9 V | > " — ■ it - CENTRAL '^ * ' Longboat Key_. ^-O- Sarasota .enice Arcadia ' Okeechobee Hrcn Gate Venus 3 SE I Port Mayaca S L Canal • I-f^A/FR Moore Haven^L l' Canal ?olnt Gate 5 ^ -. . „ v >. I My Canal Point USDA» ! Ortona.2^^ J+ g^gy -7-O-— Clewi s tonOtkJ iell ( , e w Glade HrC:l Gt - 4 ' ?aira 3eaci1 La 3elle r-, Ti^- iW Loxahatchee 1 _-0 1 ue Clewiston US En? ■ -&■ £jVf: 3elle Glade Exp Sta V" .„ „ , ^ ' ' J Felda. _Q. 1 j * ?ala 3eac!i WB AP % -Q- \J^-?£/ ^ • Oevils Garden Tower • . <>■ ,?t Myers #B AP I 1 I N Sew River Canal 1 Hypoluxo I ~\ O 1 Lake Trafford .V Mew River Canal Miles City Tower '. *»pies EVERGLADES'-, Lauderdale Exp sta ^o" j Pennsuco 4 SW -Soma ' ~f* ■_. J 3oca Sat on 5 * ;— '-' I PomDano Beach 9" I Ft. Lauderdale 3ahia-Mar Fort Lauderdale -O- Everglades lani *B AP ami Canil Hialeah , _ ■ _ 1 Miami WB City ami 3each „"9~ ykxsm-L 3ay Fror Miami 3 * CT^ndall 2 £ ANq j Tamiami T 40 Mi 3d -<^- Coconut Grove 7 5 -O- 30 AST C$ASt I Exp ST:a«f 83 32 Figure 2 5. — Map showing expansions of west coast of Florida and the Atlantic coast through the Florida Keys. Numerals are ndlepost between 1395 and 1500 (see fig. 1). 73 — EA3TPCRT. ME. ■•-BOSTON. MASS. — NEW YCRK, N.Y ;ape HATTERAS. N.C. — CHARLESTON, S.C OAYTCNA 3EACH, FLA. — MiAMI, FLA. FT. MYERS. FLA. — 3T. MARKS, r LA •°ENSACCLA, -LA — 3IL0XI, MISS. 0=T LAKE CHARLES, LA ■GALVESTON, TEX. •PORT ISABEL. TEX o t- a isvoo do iujuoj./sav3A ooi./s3iaiN3 do aaswrm D W ?0 U CB 4-t 3 o -a 74 storms ranging in intensity from weak tropical storms to intense hurricanes. In a probabilistic sense, one storm per 100 years should be interpreted as that event which has a 1-percent chance of occurrence per year over a 10-nmi coastal segment. 6.2. 1.1. Objective Smoothing Procedure. The 50-nmi segment counts were smoothed by weighted averaging over 11 data points. We used a weight function in the same manner as in low-pass filtering in time series analysis. The adopted function has the following assigned weights (after Craddock 1969): W n = 0.300, 0.252, 0.140, 0.028, -0.040, -0.030; for n = 0, ±1, ±2 , ±3, ±4, ±5, respectively. An alternative smoothing procedure sometimes applied in climatological analyses uses a running-mean [W = 1/(2N+1)]. The results thus obtained may have distortions in phase angle variation (shifting of maximum or minimum positions). The weighting function adopted here is designed to maintain the average frequencies and phase angles of the original input series. These weights were applied to all successive discrete values from south of Texas to the southern portion of Florida, and from Key West to Maine. The end of the input series was extended as a mirror image of the original series. Thus, smoothed frequency estimates of landf ailing tropical cyclones for each 50-nmi interval were obtained along the smoothed coastline, from Texas all the way to the Canadian border. The two series were then connected to give a continuous smoothed curve of frequency of landfalling tropical cyclones (solid curve of fig. 2 6). Figure 27 shows the final frequency curve including an extension at the southern tip of Florida depicting the frequencies for the Florida Keys (upper portion of the curve). 6.2.1.2 Evaluation of Procedure. The direct count method derives its data from a count of tropical cyclones at the coast and not out over the water. It gives the best estimate of the variation along a smooth coastline of the frequency of landfalling storms. However, it tends to obscure variations due to coastal shape. A stretch of the coast that turns sharply in a direction almost parallel to that of the predominant storm motion is less exposed than adjacent coastal segments more nearly normal to the track direction. We have implicitly smoothed sampling variability associated with small scale variations of the coast. To identify areas where the implied smooth coastal direction differs significantly from the actual coastline, a smoothed coastline was constructed. Coastal locations at 50-nmi intervals along the Gulf coast and Atlantic coast were smoothed using the smoothing function described in Section 6.2.1.1. These points were plotted and a continuous line joining these points was drawn for both the Gulf and Atlantic coastlines (fig. 24). This diagram reveals that this smooth line cuts across the actual coastline at several places — most significantly, across the Mississippi Delta, along the west coast of Florida and across Cape Cod. For the most part, the smoothed coastline approximates quite well the orientation of the actual coast. Areas where a smoothed coastal direction differs substantially from the actual direction may be detected in Figure 24. These areas may either be sheltered from or exposed to the prevailing direction of storm motion more than the smoothed coastal direction would suggest. Differences between these coastal directions on 75 — EASTPCRT. ME. ' ' i i 1 r— -7-i ~ V — - x. - ^80ST0N, MASS. J- - ^^^^ - ~NEW YORK. N.Y. ^ - " ^■•^^ — ^s- - ^^^■^ - »CAPE HATTERAS. N.C. ^*^~~*~~~ - . r — CHARLESTON, S.C. S, - - \ — x^^ - ^•OAYTONA 3EACH, FLA. ^N — ^^s - S- MIAMI, FLA. ^^^^* — ■"■* — J{^ — •-FT. MYERS, FLA. / ^*-«»^ >< ^ - — ^ - S** ^ - — 3T. MARKS. FLA. ( — V _ — PENSACOLA, FLA. \ — 3IL0XI. MISS. \ — \ - — \ - i- LAKE CHARLES. LA. J - •■GALVESTON, TEX. f v^^ - — — PORT ISABEL. TEX. 1 J 1 1 1 U 1 1 J 01 O 111 < et aa «\i oJ oi *■ *- d o" isvoo jo iuiuoi./sav3A o. intensities due to limited overland reduction as they move across the relatively narrow Florida peninsula.' For estimating exiting storm intensities, the reader is referred to Chapter 10 for consideration of overland tilling; rates and Chapter 11 for application procedures. 6.4 Frequency of Alongshore Tropical Cyclones 6.4.1 Analysis The frequency estimates for tropical cyclones that bypassed the coast were based on the same maps and data period used above. A count was made of storms intersecting 5-nmi intervals along lines drawn perpendicular to a smoothed coastline centered at each of the coastal locations (A to Z) in Figure 30. The same storm may have been counted several times as it moved parallel to the coast. The cumulative track counts along each of the 2 6 lines normal to the coast were plotted against the distance from the coast. A smooth curve was then fit to the data on each of these freauencv Dlots. Figure 30. — Accumulative count of hurricane and tropical storm tracks passing tbe coast at sea (1871-1984). Based on counts along heavy dashed lines shown projected normal to coast. 32 The frequency distributions were smoothed subjectively both along the coast and perpendicularly outward. These results are shown on Figure 30 by isolines of accumulated number of storm tracks bypassing the coast at sea for the period 1871-1984. We then read from the map accumulated track counts at discrete distances of 10, 20, 30, 50, 75 and 100 nmi from the coast and plotted them as alongshore profiles. Additional track counts and frequency plots were made at close intervals near areas where the alongshore profiles fluctuated greatly because of either a geographic protrusion or a concave coastline. Analysis was then undertaken to obtain a set of smooth frequency curves for the Atlantic and Gulf coasts. The resultant curves are shown in Figures 31 and 32 depicting the accumulated storm track counts in storms per 100 years at selected distances off the Gulf and Atlantic coasts, respectively. 6.4.2 Results and Discussion Figure 30 reveals that the maximum concentration of alongshore storms occurred off Cape Hatteras, North Carolina. Fewer than five tropical cyclones bypassed within 50 to 80 nmi off the coasts of northwest Florida, Alabama, and Mississippi and within some 100 nmi of the Texas coast. The higher values off the Mississippi Delta may be caused by geographic protrusion. There is a high frequency of bypassing storms off the coast of Cape Hatteras for the same reason that there is a high frequency of landfalling storms south of Cape Hatteras. The gradient at a distance of 100-150 nmi off the Atlantic coast indicates that storms frequently traverse at some greater distances off the coast rather than bypassing near the coast. This may be explained by the existence of the semi -permanent high pressure system (the Bermuda High) in the Atlantic and the location of the Gulf Stream off the coast. Atlantic hurricanes approaching these latitudes tend to recurve along the western edge of the high pressure cell. The higher track counts between 100 to 150 nmi off the coast seem to be associated with the mean position of the Gulf Stream. Because of the steep gradient of bypassing storm frequencies at some distance off the coast, caution should be used in determining a representative frequency over finite distance intervals from the coast. Figure 31 shows a higher number of storms bypassing the Mississippi Delta and the southern tip of the Florida peninsula in the Gulf of Mexico. An analysis of storm track counts passing through two and a half degree latitude and longitude blocks in the Gulf yielded maximum concentration of storm tracks in an area extending from south of the Mississippi Delta to western Cuba (diagram not shown). This explains the high values shown in Figure 31. The minimum values occurred off the Texas coast and the Apalachee Bay area because of the concave coastline in those areas which minimized the count of bypassing storms near the coast. Figure 32 shows similar peaks and troughs in the alongshore profile of bypassing storm frequencies off the Atlantic coast. These extreme values also appear to be associated with geographic features of the coastline. 7. CENTRAL PRESSURE 7.1 Introduction Central pressure (P ) is a commonly used index of hurricane intensity. Harris (1959) demonstrated that storm surge height is approximately proportional to the central pressure deficit (AP = P - P ), other factors being constant. This chapter develops probability distributions of central pressure for tropical cyclones along the coast. 83 13SVSI IHOd J 1 Li O U5 -* CO CM t- 0) CO N (O Uf ^ m ..... (ja ocu/swaois ONissvdAa) siNnoo a3J.vinwnoov 84 o o o CO CM T" \ \ \ CM - O u * 5 C 3 i a o o o lO ^ CO > O SO t CO CM i- I 1- (jx ooi/swaois ONissvdAa) siNnoo a3ivnnwnoov 85 is I a) "3 The data on which we developed the P Q probability distributions for the Atlantic and Gulf coasts of the United States have been collected in Tables 1 through 3. Original sources of data are described in Section 2.2. Revisions were made in P data from TR 15 where we verified suspect data not accepted in previous reports and, in a very few cases, as an analysis judgment after reviewing all the data. A description of the data analyses was included in Section 2.3, and revised hurricane central pressures were listed in Table 4. Tables 1 through 3 list parameters of all storms with a central pressure less than 982 mb (29.00 in.) that crossed the Atlantic and Gulf coasts or passed within 150 nmi on the seaward side of the coast. The criterion that central pressure be less than 982 mb was based on the consideration that the computed magnitude of cyclostrophic wind using this pressure value (as described in sec. 2.3.1) is approximately the wind speed required for classification as a hurricane . With central pressure available for an average of less than one hurricane per year for the period of record for each coast (Gulf and Atlantic), the data in Tables 1 through 3 form a limited sample. 7.2 Analysis Cumulative probabilities of hurricane P were determined from tabulated values listed in Tables 1 through 3 for overlapping zones, generally centered 50 nmi apart along the coast (see fig. 1). The lateral extent of the zone over which the data were pooled was 400 nmi along the Atlantic coast, and 500 nmi on the Gulf coast. We used a shorter distance along the Atlantic coast because latitudinal variations were more important than along the Gulf coast. The 50-nmi criterion was modified in areas where the data were sparse. On the Atlantic coast, between the mouth of Chesapeake Bay and eastern Long Island, the overlapping 400-nmi zones were separated by 100 nmi, and a single zone was used from Long Island to the Canadian border. Near the southern tip of Florida, hurricanes that passed near Dry Tortugas, and those that crossed the Florida Keys, together with Atlantic coast hurricanes were used to determine the probability distributions of P at locations on the Florida Keys. The cumulative probability curves, thus obtained, were used in the extension of the Atlantic coast along the Florida Keys (see fig. 2 5). In southern Florida, along the Gulf coast, the overlapping 500-nmi zones were centered 100 nmi apart (instead of 50 nmi). Hurricanes that pass the Florida Keys and make landfall in western Florida usually become weaker as they approach the coast. Parameters for hurricanes passing the Florida Keys are listed in Following the criteria used by NHC, hurricanes are defined as tropical storms with winds 64 kn or greater. We realize that there have been storms with hurricane-force winds and central pressures as high as 990 mb south of 3 5°N. The 982-mb criterion was used to put definite bounds on the data sample. In our statistical analysis, cumulative probability curves for central pressure are extended to cover the full range of hurricanes and tropical storms. 86 Table 1 and their characteristics near the time of landfall are given in Table 3a. As discussed in Section 7.3.2.1, P Q values tend to be higher north of Cape Sable. Treatment of the data near the southern tip of Florida was handled differently because of the break at milepost 1415 (see sec. 6.2.1 and fig. 2 5). In determining the cumulative probabilities for P Q at coastal reference points 1350 and 1400 (near Cape Sable), we used P values for 6 hurricanes observed near Dry Tortugas instead of the weaker intensities measured near landfall points at some distance north of the points of interest. This was done to minimize the biasing influence of the large number of generally weaker storms to the north. Tables 1 through 3 include only hurricanes with P below 982 mb. However, the track count on which the storm frequency (chapt. 6) is based includes tropical cyclones of both hurricane and tropical storm intensities. In the application of hurricane climatology, frequency of a representative, clima tologically specified hurricane of given characteristics is the product of the frequency of all storms and the probability of a storm having those particular characteristics. In order to ensure a higher leveJL of consistency in our analysis, we expanded the central pressure probability distribution to include weaker hurricanes and tropical storms, in the manner described below. The first step in the analysis of central pressure data was to construct cumulative probability curves for each 400- or 500-mile zone. The magnitude of central pressure versus probability of occurrence was plotted. Determining the probability to be assigned to a data point is commonly referred to as determining the plotting position. A plotting position may be expressed as a percent from 0-100. Probability plotting of hydrologic or meteorologic data requires that individual observations or data points be independent of each other and that the sample data be representative of the population. Gumbel (1958) proposed five criteria for plotting position relationships. Several plotting relationships have been presented by Chow (1964). Benson (1962) in a comparative study of several plotting position relationships found, on the basis of theoretical sampling from extreme value and normal distributions, that the Weibull relationship provided estimates that were consistent with experience. The Weibull plotting position formula meets all five of the criteria proposed by Gumbel. An evaluation of plotting position formulae is included in Appendix C. All of the relationships give similar values near the center of the distribution, but they vary in the tails. In TR 15, the Hazen plotting position formula was used to assess the probabilities. One objection to the Hazen plotting position is that the return period for the largest event is twice the record length. In the present studv, the Weibull relationship was used in assessing the probabilities of all parameters. This plotting position relationship can be expressed as: X 100 where p is the probability expressed as a percent of the total number of storms, n, and m is the rank from lowest to highest. To get n for all tropical cyclones, the count of central pressures (up to 982 mb) was adjusted similar to TR 15, using the ratio of hurricanes to the total number of tropical cyclones based on a direct count of storm tracks. The upper part of the curve for each graph is ex- tended smoothly to 1003 mb at the 100-percent level to arbitrarily represent CENTRAL PRESSURE Cm»> Figure 33.--Cuaulative probability carve of central pressure of hurricanes landfalling within (a) 250 ami of mi 1 epos t 250, near Corpus Christi, Texas, and (b) 200 ami of milepost 1600, near Vero Beach, Florida- tropical cyclones with central pressure greater than or eaual Co 982 mb. Examples of cumulative frequency curves for two coastal zones are shown in Figures 33a and 33b. The first is centered near Corpus Christi, Texas and Che second near Vero 3each, Florida. It should be noted chad the best fit cumulative probability curves were not always the most consistent solution for successive 50-nmi increments. The Question of how to deal with an outlier in an extreme value distribution analysis is always debatable. The central pressure determined for engineering design hurricanes (called standard project hurricanes) along the Atlantic and Gulf coasts by Schwerdt et al. (1979) was used extensively as a guide in analyzing the lower end of the cumulative probability curves for central pressure (see fig. 2.1 of Schwerdt 's report). In the example given in Figure 33b, central pressure data which was used in plotting; the cumulative probabilitv curve for milepost 1600 near Vero Beach, Florida included value of 892 mb from the 193 5 hurricane, Earlier studies (e.g., Schwerdt et al. 1979) indicated that a hurricane with such a low P would have approached the intensity of a "probable maximum hurricane" with a probability of occurrence as much as an order of magnitude less than 0.1 percent. Undoubtedlv, this ? value would be considered o an outlier for the purposes of our analyses. In treating this outlier, more weight was given to this storm in the analysis for the Florida Keys, where the hurricane made landfall, than at Vero Beach, Florida. The decrease in intensity of a "standard project hurricane" from the Florida Keys to Vero Beach was 3lso used as a guide in the analvsis. 88 Using the smoothed set of cumulative probability curves of minimum central pressure, we read off the 1-, 5-, 15-, 30-, 50-, 70, and 90-percentile points for each increment and plotted then as alongshore profiles. Analysis was then under- taken to obtain a set of curves representing a consistent view of the probability distribution of P for the Atlantic and Gulf coasts. The resultant central pressure values at selected percentiles for each increment were smoothed using the same weighting function employed in Chapter 6 (see sec. 6.2.1.1). The relative infreauency of hurricanes near the Canadian border and of P data near the Mexican border forced us to subjectively adjust the results of the objective smoothing in these end areas. A discontinuity in the analysis with re- spect to all but the uppermost class interval was found to exist between the chain of Florida Keys and Cape Sable. This was a result of the geographical features associated with the tip of the Florida peninsula. Gulf storms striking the southern tip of Florida are generally weaker than those moving from the east and striking the Atlantic coast of southern Florida and the Keys. Treatment of this area was discussed in Section 6.2.1. 7.3 Results An inspection of Figures 34 and 35 reveals that there is an overall increase in central pressure from south to north, a well-known fact, caused, in part, by decreasing water temperature toward the north. Distinct minima ranked in order from lowest pressure at the 5-percent level are found on 1) the tip of the Florida peninsula, 2 ) at the Texas-Mexico border, 3) near Louisiana's Mississippi Delta, 4) at the South Carolina-North Carolina state line, and 5) over the southern New England coast. The primary maximum occurs near the (until recently) sparsely populated coastal area west of Cross City, Florida (mile 1,100 in fig. 34). Secondary maxima lie near the mouth of Delaware Bay (mile 2,400 in fig. 3 5), and near Jacksonville, Florida (mile 1,800 in fig. 3 5). The Jacksonville maximum exceeds the Delaware Bay maximum for the higher percentile levels. Pressures also rise northward along the upper New England coast. Reasons for the increase in central pressure from south to north include the entrance of colder and drier air at low levels, which destroys the upward slope of the isotherms from outside to inside the circulation and decreases the amount of energy available to the storm. According to Riehl (1954), jet streams at high levels which are detrimental to tropical cyclones are stronger and more common in temperate latitudes. Riehl states that "the arrival of the equatorward margin of a westerly jet stream at high levels will destroy a [tropical cyclone] circulation rapidly since it favors upper convergence, entrance of cold air aloft, subsidence, and drying." 7.3.1 Pressure Minima 7.3.1.1 South Florida Minimum. The lowest accepted sea-level barometer reading (892.3 mb) , not including tornadoes, in the Western Hemisphere occurred at Long Key, Florida, in the hurricane of September 2, 1935. This contributed to the south Florida minimum. 89 3c±3AVTJJ — sxawris - nOOVSN3d - ixoia 3n=W0 2W^ >ClS3AlW TSVSIldua 3 e •J u C -( n cq « 3 2 o — S- u a SO ° 5 « a aa - (0 -J U 3 C 4) V y y « 1) 3 *J o o CD c qui ) 3^nss2ad ja a s U, 35 "3 T 8 «■ — I o 3J O _ m 3> e 3 — — 80*-/ 3 yj 90 iao O 96 — 8OST0N. MASS >>—£ASTPORT. ME. —NEW YORK, ,N.Y. — CHARLESTON. S.C. GAPE HATTSRAS, N.C. t— OAYTONA 3EACH, FLA. 2 1 X I? QWU ) 3GNIM wnwixvw jo smcva 97 Hatteras area. It is in these latitudes that hurricanes most often pass from a tropical to a temperate environment, and it is in this region where one would expect R to show its greatest increase for the reasons discussed in Section 8.3. The slope of the lower probabilities curves change less between Georgia and Cape Hatteras because there are a few storms with small R in the data sample. 8.3 Radius of Maximum Winds for Intense Hurricanes Observations indicate that hurricanes with very large R's are of moderate or weak intensity. In hurricanes moving northward in the Atlantic and becoming extratropical, R tends to become larger and more diffuse and P generally rises. Data from intense hurricanes of record (see table 16 and fig. 14) indicate that the most extreme hurricanes (P less than 92 mb) tend to have small R's. The question of interdependence of P and R was discussed in Chapter 4. We recommend that an R value of 13 nmi be used for hurricanes with P in the range of 908-92 mb, and R = 9 nmi be used with P rt less than 908 mb. 9. SPEED AND DIRECTION OF STORM MOTION 9.1 Speed of Storm Motion Data for the speed of storm motion is discussed in Section 2.5. Included in these data are a few subtropical storms. We chose to include them since they also have the ability to produce storm surges. 9.1.1 Forward Speed of Landf ailing Tropical Cyclones 9.1.1.1 Analysis. Cumulative frequencies of forward speed for landf ailing tropical cyclones were determined for the same overlapping zones used for both P (sec. 7.2) and R (sec. 8.1). As indicated in Section 2.5, both T and 9 could be reliably determined for tropical storms as well as hurricanes, thus increasing the sample size. Cumulative probability curves of forward speeds were determined using Weibul's plotting position formula (see sec. 7.2). Figure 39 shows examples of the cumulative frequency analysis of raw data at two points along the coast (near Corpus Christi, Texas and Vero Beach, Florida). Percentage values at each 50-nmi location were determined from analyses such as Figure 39 for 5-, 20-, 40-, 60-, 80- and 95-percent levels. The values were then analyzed to ensure consistency along the coast. The resulting curves are shown in Figures 40 and 41. 9.1.1.2 Results and Discussion. Figures 40 and 41 show that tropical cyclone speed generally increases with northward progression of each storm, especially after recurvature to a northerly or northeasterly direction. The upper 50 percent of forward speeds increases from 11-17 kn near Daytona Beach, Florida, to 35-53 kn at the northern extent of the United States' Aclantic coastline. Overall, there was a marked increase in values of T along the west coast of Florida as compared with the variation shown in values of TR 15. In this study, we omitted hurricanes prior to 1900 that had been used in TR 15. This was done to ensure a consistent sampling period for all parameters (P , R, T and 9). Before finalizing this decision, however, we examined the effect of omitting storms prior to the turn of the century. We found that there were no significant 98 - 60- 10 1S 20 25 ?0RWA*D SPEED (kn) FORWAP.0 SPEED (kn) Figure 39.-- Cumulative probability curve of forward speed of tropical cyclones landf ailing within (a) 2 50 ™i of ailepost 250, near Corpus Christi, Texas, and (b) 2 00 nmi of milepost 1600, near Vero Beach, Florida. differences in the probability distribution of speed for hurricanes by this truncation of the period of record. TR. 1 5 had based its speed distribution on hurricanes only. To provide a sample that was consistent with the storms used for Che direction distributions, and to increase the sample size, the speeds of tropical storms were used in determining the speed distribution. The substantial increase in the speeds in the higher percentile levels along the west coast of Florida (see fig. 40) was due, not to the change in period of record, but to the addition of tropical storms. Between coastal reference points 900 to 1300, 12 storms with speeds greater than 2 kn were added to the data sample. All were less than hurricane intensity. Storms that exceed 2 kn at these latitudes generally have become embedded in a broader-scale circulation that usually leads to these higher translation speeds. These same oe teorological conditions involve recurvature, usually into an environment associated with horizontal temperature gradients that create conditions that are not favorable to the thermal circulation associated with strong hurricanes (see discussion in sec. 7.3.2.1). Therefore, the faster translation speeds appear to be associated with weaker storms. However, the small number of storms and high degree of 99 -^u *navs 3dvo •"U *SH3AW "li Id "YIOCIWO' — ^i^TOCVSHBd — sw 1x011a •VI 'S31HVH0 3XV1 •XI 'N01S3A1V9 —XX H39VSI IdOd _ ^r _o o 1) NOHOW IflUOlS JO Q33dS "3° a ** — ^ ? *" c to is * J ab w to 100 -*-vw 'Noisoa U-AN 'XHOA M3N —OS 'N01S3iyVHO i-ON 'SVU311VH 3dVO CM o O ~4-ld *H0V38 VNOIAVQ -•-"Id llNVIW (U>j) NOHOW WdOlS JO d33dS 101 variability from storm to storm precluded us from establishing whether a joint probability relation actually exists, let alone what form the relation might take. Inclusion of these tropical storms also leads to discontinuities in the speed distributions between the west and east coasts of southern Florida for all but the lowest percentiles. 9.1.2 Forward Speed of Bypassing Tropical Cyclones Observations of bypassing storms are more limited than for those storms striking the coast, especially for storms from earlier years. Additionally, the frequency of occurrence of bypassing storms, subject to the criteria in this study, is lower than for landfalling storms. Given the high degree of natural variability of tropical cyclones and the limitations just mentioned, we felt it would be unlikely that we could develop an adequate probability distribution for the speed of bypassing storms. Consideration of meteorological factors affecting the speed of storm motion suggests that there is likely to be little difference in the speed distribution between landfalling and bypassing tropical cyclones. The speed is primarily dependent on conditions of the larger-scale meteorological environment. In general, the controlling circulation patterns that affect the speed are not sensitive to coastal orientation, the factor that leads to the segregation of landfalling and bypassing storms. We recommend using the speed distribution for landfalling storms as a reasonable approximation for bypassing storms* 9.2 Direction of Storm Motion 9.2.1 Direction of Storm Motion for Landfalling Tropical Cyclones 9.2.1.1 Analysis. Tropical cyclone tracks compiled by Cry (1965) and updated track charts (Neumann et al. 1981) were used in summarizing the directions of storm motion. Directions of landfalling tropical cyclones were measured at the time they crossed the coast. Cumulative frequencies of the entry direction for overlapping 200-nmi zones (100 nmi either side of the central point) were used in plotting cumulative probability curves at 50-nmi intervals along the Atlantic and Gulf coasts. In TR 15, cumulative frequencies were counted for overlapping zones of 75 nmi on each side. In both cases the zones along the coast were smaller than those used for the other three parameters (P , R and T) because the landfall directions are totally dependent on coastal orientation which can change significantly over relatively short intervals. The smaller zones minimized pooling inconsistent directions. We used storm data since 1900 in the present study instead of the longer period used in TR 15. We believe the decrease in sample size due to a shorter observational period is partially compensated by the increased number of storms taken from a somewhat larger sampling area. In areas where the coastal orientation changes significantly within 100 nmi of the point of interest, the direction of entry with reference to the coast was taken into consideration. For example, a storm that crossed the coast from 2 50° near Key West would not be counted as a landfalling storm for another point on the Florida Keys, some distance to the east. In areas where the coastline turns abruptly, frequency counts were taken over shorter distances. Because of insufficient data north of Cape Hatteras, analyses there were made over larger distance increments. 102 105 125 145 195 DIRECTION (dog. Tom north) 35 105 125 145 1 95 195 DIRECTION (dog. Tom north) direction of aotion of tropical Figure 42.— Cumulative probability curve of cyclones landf ailing within (a) 100 nmi of milepost 250, near Corpus Chris ti Texas, and (b) 100 nmi of milepost 1600, near Vero Beach, Florida. Cumulative probability curves for direction of storm motion for landfalling tropical cyclones were constructed using the Weibul plotting position formula given in Section 7.2. Figure 42 shows examples of these curves for two coastal locations near Corpus Christi, Texas, and Vero Beach, Florida. Each of the cumulative probability curves was divided into class intervals, and the values at selected percentiles were analyzed for three sections along the coast: the Gulf coast (fig. 43), and the Atlantic coast south (fig. 44) and north (fig. 45) of Cape Hatteras. 9.2.1.2 Results and Discussion. The direction of landfalling storm motion is closely related to the coastal orientation curve because the definition of landfalling restricts the storm direction data selection, exiting and alongshore storm motions being excluded. Under the influence of the easterly circulation of the lower latitudes (the Azores-Bermuda high) the tracks of most storms in the tropics is westward. There is a tendency for these low latitude storms to drift slowly northward at the western end of the high pressure system. As the storms drift toward higher latitude, they come under the influence of westerly winds and recurve northeastward. 103 1 i i r i — i — i — r t — i — r •Id '319VS 3dV0 'Id '3d3AW *ld •id *s> LU 965 < LU 955 jT • PRESSURE - OISTANCE PROFILES STATION PRESSURE 945 C 1 ' 1 (a) i i i 9 12 TIME fhr) 15 13 1000 1 990 980 970 960 - - ! 1 1 1 I 1 ■„.**% - ^S* - / - • PRESSURE-DISTANCE PROFILES & RECONNAISSANCE AIRCRAFT STATION PRESSURE (b) ! i 1 1 i 1 12 TIME Chr) Figure 46. — Pressure profiles after landfall for (a September, 1979 and (b) Hurricane Alicia, August, 1983. 1 3 Hurricane Frederick. Ill Figure 47. — Map showing geographical regions used Co study filling rates. L 12 Table 19. — Selected landf ailing hurricanes (192 8-1983) used to estimate overland filling rates. No. of Storms Hurricane State of Landfall Region 11 Aud rey Carla ( Betsy ( Camille Celia ( #Edith ( •/Carmen #Eloise //Frederi #Allen ( //Alicia (1957) 1961) 1965) (1969) 1970) 1971) (1974) (1975) ck (1979) 1980) (1983) Louisiana Texas Louisiana Mississippi Texas Louisiana Louisiana NW Florida Mississippi-Alabama S. Texas Texas (Gulf coast from Apalachicola, FL westward) Sept. 17, 1928 Sept. 15, 1945 Aug. 27, 1949 Donna (1960) S. Florida S. Florida S. Florida S. Florida (Florida south of 29°N) Sept. 21, 193 8 Sept. 15, 1944 Carol (1954) Hazel (1954) Gracie (1959) Donna (1960) //Belle (197 6) #David (1979) New York New York New York North Carolina South Carolina New York New York Georgia (Atlantic coast from South Carolin, northward) # Indicates storms since 1971 rates for other hurricanes prior to 1971 determined by Schwerdt et al. were checked for consistency by using observed minimum pressure data as previously discussed. Minor changes were made whenever warranted. The filling rates at selected time intervals for the 11 hurricanes listed in Table 19 for region A were averaged to develop a filling rate for hurricanes of lesser intensity. Separate filling rates for more intense hurricanes were estimated by taking into consideration this average filling rate and the extreme filling rate associated with Camille. Intense hurricanes were arbitrarily defined as storms with AP greater than 85 mb, which have approximately the same intensity as category 5 hurricanes according to the Saf fir/Simpson scale (Saffir 1977) Figure 49 shows the filling rate curves for hurricanes with AP. less than or equal to 85 mb, AP equal to 100 mb, and AP equal to 110 mb. These curves have been used to develop the pressure deficits in part (a) of Table 20. Linear interpolation between values in Table 20 should be used instead of recourse to Figure 49 to assure a higher degree of accuracy and consistency. 113 11 CD & \ Tx \ A V x* \ \ \\ x. X \ \ \ x \ *V x X \ \\ ^ x " x \\ x \ x\\ \\ - Xv X >\ \\ \ \ 1 I'll! X i- XV5i ! 1^ - cvJ -co -CO CM rO lO CD CO CD *dv OliVd 115 22. oiiva U -j •x - s i "o u — - 2 116 Table 20. — Changes in hurricane pressure deficits due to overland filling Time After Landfall (hr) Pressure Deficit (mb) (a) Gulf hurricanes, west of Apalachicola, Florida 40 60 80 85 90 95 100 105 110 2 34 51 68 72 76 78 80 81 82 4 30 44 59 63 66 67 68 69 70 6 26 40 53 56 58 59 60 61 62 8 22 34 45 48 50 51 52 53 54 10 20 30 40 42 44 45 46 47 47 12 18 27 36 38 39 40 41 41 42 14 16 24 32 34 35 36 36 36 36 16 14 21 28 30 31 32 32 32 32 18 12 19 25 26 27 28 28 28 28 (b) Florida hurricanes, south of 29°N 40 60 80 85 90 95 100 105 110 38 57 75 80 85 88 90 91 92 36 54 70 75 79 81 82 83 84 6 34 51 67 71 75 76 77 78 79 8 32 48 63 67 71 72 73 74 75 10 30 45 59 63 67 68 69 70 71 12 28 42 56 60 63 64 65 66 67 14 26 40 53 56 59 60 61 62 63 16 25 37 50 53 55 56 57 58 59 18 24 35 47 50 52 53 53 54 55 (c) Atlantic hurricanes, north of Georgi a-Sou th Carolina state line 40 60 80 85 90 95 100 105 110 2 36 54 72 76 81 86 90 94 99 4 32 49 65 68 73 77 81 85 89 6 28 44 58 61 65 68 72 76 79 8 25 39 51 54 57 60 64 67 70 10 22 34 44 47 50 53 56 59 61 12 19 29 38 41 43 46 48 51 53 14 17 25 34 36 38 40 42 44 46 16 15 22 30 31 33 35 37 39 ' 40 18 13 19 26 27 29 30 32 34 35 117 <]|<3 ' 6 Figure 50, — Comparison of filling rates for various hurricanes crossing the Florida peninsula and Che filling curve for region B from Schwerdt ec al. (1979). There were no additional storms that affected region B since 1971. The average filling rate curve determined by Schwerdt et al. (1979) was adonted after checking for consistency by comparing A? t /A? ratios for several hurricanes. Mo attempt was made to obtain separate filling rate curves for each of these hurricanes because data was scanty. Figure 50 shows a plot of these ratios at various times after landfall and the filling rate curve for region B from Schwerdt et al. It is again recommended that filling rates be obtained from the values in Table 20b by linear interpolation. Figure 51 shows filling rate curves for selected oressure deficit levels in region B. Figure 52 shows the filling rate at various times after landfall for Hurricane Hazel (1954) and Gracie (1959). These two hurricanes entered the Atlantic coast, crossed the Carolinas, and recurved towards the north. Filling rates for a 12-hr period after landfall are shown in the figure because both hurricanes became extratropical soon after that period of time. The changes in intensity during their extratropical stage would not be representative of hurricanes. Only the rate of weakening for the first 12-hr period, as indicated by the solid line, was used in this analysis. Figure 52 also shows the rate of weakening for Hurricane David (1979) after entering the coast just south of Savannah, Georgia. The obvious difference between the curves reveals that David had a much slower 113 119 Ol<3 - 6 Figure 52. — Variation with tine after landfall of filling rates for Hurricanes Hazel (1954), Gracie (1959), and David (1979). filling rate than those of Hazel and Gracie. This can be partially explained by che fact that David traveled inland, parallel Co the coast, with half of the cyclonic circulation of che storm remaining over water. The heat supply from the underlying sea acted to minimize the filling process. For this reason, David was not used in obtaining an average filling rate for Atlantic coast hurricanes. Figure 53 shows a plot of filling rate versus time after landfall for hurricanes which crossed the shores of Long Island, New York and the New England states. Data obtained during the first 12-hr period after landfall were used in Che analysis because Chese hurricanes were fast moving storms. In a 12-hr period after landfall, they would have either moved across the United States border into Canada or become extratropical. The average filling rates for these hurricanes agree fairly well with the filling curve for Hurricanes Hazel and Gracie (fig. 52). Combining both sets of data, we obtained the average filling curve as shown in Figure 54. Since region C has not experienced any extreme hurricanes, this curve was adopted to represent the filling rates of landfalling hurricanes of all intensities in this region. Again, linear interpolation from Table 20 should be used to determine pressure deficits. 120 <3l<3 < 1.0 6 8 TIME Chr) Figure 53. — Variation with tiae of filling races for New England hurricanes. 10.6 Results The lower filling rate curves for regions A and 3 in Figures 49 and 51 ara applicable to hurricanes with pressure deficits less Chan or equal to 85 mb at the time of landfall. For hurricanes with pressure deficits greater than 35 mb, filling rates may be obtained from interpolation of pressure deficit values given in Tables 20a and 20b for regions A and B, respectively. There is no separate filling rate determined for hurricanes of the most intense category in region C. 12 1 122 The filling rate for region C, shown in Figure 54, was extended to depict filling up to 18 hr after landfall, for consistency. One should realize that the degree of accuracy decays with increasing time after landfall. The curve for region C is also applicable to areas north of Long Island, New York in order to include the entire coastline. Assuming that the rate of filling is linear for the first 10-hr period after landfall, we can draw a straight line joining the point indicating the filling rate at 10 hr after landfall and the point of origin for each of the three regions. We obtained slopes of .051, .075, and .056 for regions A, B, and C, respectively. Linear interpolation of the slopes may be used as an aid to develop intermediate curves in estimating appropriate filling rates for areas lying between designated regions. 11. APPLICATION OF HURRICANE PARAMETERS 11.1 Introduction An objective of this report has been to define climatological probability distributions of hurricane central pressure (P Q ), radius of maximum winds (R), forward speed (T), and direction of motion (9) along the Atlantic or Gulf coasts of the United States. In some applications of these data — for example, in flood insurance studies — it would be necessary to calculate frequency distributions of hurricane-induced surges on the coast by combining the analysis of hurricane climatology with the application of a numerical storm-surge model. Also needed in such application is the overall frequency with which hurricanes enter the coast in terms of strikes per mile per year, or some equivalent unit, within certain discrete distances. The landfall point of a hurricane is another parameter needed in a surge-frequency analysis. If storm track is parallel to the coast, then distance from the coast is needed instead of direction. This chapter outlines procedures to be followed in selecting hurricane parameters, their corresponding probabilities, and the representative storm tracks and frequencies for surge-frequency analyses as currently adopted in flood insurance studies. 11.2 Landfall Point The cyclonic wind field of a hurricane usually increases from the edge of the storm to the highest value at the radius of maximum winds (R) then rapidly decreases to low values near the center. There is usually some asymmetry to the approximately circular pattern, with the highest winds on the right side as the storm moves forward. From the geometry of the hurricane wind field pattern, the maximum shoreward component is experienced at a given coastal site when the hurricane center landfalls approximately at distance R to the left. On a straight coast with uniform bathymetry, the highest surge along the coast will be experienced at this point of highest wind. Variable bathymetry can modify this location somewhat. Similarly, a bay experiences the strongest winds from a hurricane of given intensity and lateral extent when the storm track is about at distance R to the left of the center of the bay, as viewed from the sea. In addition to the inverse barometer effect and the convergence of wind affecting surge levels near a storm's center, the major driving force for coastal surges is the stress of the wind on the water, roughly proportional to the square of the wind speed. Average wind profiles show that surface winds of a hurricane 123 at a distance five times the radius of maximum winds (5R) from the storm center are less than half of its maximum magnitude (Schwerdt et al. (1979), chapt. 13) and the magnitude of the corresponding peak surge heights are only about 2 5 percent of the peak. Except for the most intense storms, hurricane-induced surges of any significant level would not affect the coast if the hurricane made landfall at a distance exceeding 5R to the left of the point of interest or at a distance of more than 3R to the right. The distance 3R is chosen because coastal surge heights drop off much more rapidly to the left of the landfall point. 11.3 Peripheral Pressure The linkage between the climatologically-def ined hurricane central pressure (P Q ) and the pressure deficit (AP) used in a storm-surge model is the peripheral pressure (P n )« p n is used to compute the pressure deficit (AP = P - P ), which is a measure of the intensity of a hurricane. P is frequently considered the average pressure around the hurricane where the isobars change from cyclonic to anticyclonic curvature. This pressure occurs at a distance from the storm center near where storm inflow begins and, therefore, has physical meaning. In this study, P is used in conjunction with clima tologically determined hurricanes. The use of a climatological mean value for P is considered adequate for this purpose. Schwerdt et al. (1979) described several techniques for evaluating P and indicated that there is no significant variation of P with latitude. They compiled peripheral pressures for Gulf and Atlantic coast hurricanes with P less than 982 mb since 1900. The average value of these given peripheral pressures is 1013 mb. We recommend that this climatological mean value be adopted as a representative peripheral pressure to compute pressure deficits in storm-surge frequency analysis. 11.4 Probability Distributions of Hurricane Parameters and Frequency of Occurrence This chapter describes the application of hurricane parameters needed to calculate storm surge levels on the coast. The assessment of probability distributions of these parameters assumes a steady-state hurricane moving on a constant course during the time period required for storm-surge computations. The averaging process along the Gulf and Atlantic coasts assures a smooth continuous variation of individual parameters along the coast. Exceptions to these basic assumptions and specific treatment of discontinuities have been discussed in preceding chapters. These include frequencies of landfalling tropical cyclones for the Florida Keys (sec. 6.2), refinements in alongshore hurricane track counts and probability distributions of landfalling storms for the North Carolina coast (sec. 5.4), frequencies of exiting storms (sec. 6.3), and filling of storms as they pass overland (chapt. 10). The procedure to estimate probability distribu- tions of hurricane parameters for exiting storms will be discussed further in subsequent paragraphs. The probability distribution of P is determined for landfalling tropical cyclones (sec. 7.3). There is no reason to believe that the pressure distribution of alongshore storms would be different from that of landfalling storms because both classes of storms experience an area with climatologically similar atmos- pheric and sea-surface conditions. Hence, this probability distribution of P can also be applied to alongshore storms. The probability distribution of R is 124 assumed to be the same for the landf ailing, bvpassing and exiting categories of storms. Probability distributions for direction and speed of storm motion for landfalling storms are given in Chapter 9. For alongshore storms, the direction is, by definition, assumed to be parallel to the coast and the probability distribution of forward speed is assumed to be the same as for landfalling hurricanes. The frequency of tropical cyclone occurrence is defined as the number of tracks per year per nautical mile of a smoothed coast for each of the landfalling and exiting categories of storms (chapt. 6). Figure 27 depicts variation of frequencies of landfalling tropical cyclones along a smooth coastline. We have implicitly smoothed out the coast while smoothing out the accidental landfalling points of storms. A stretch of the coast that turns sharply in a direction almost parallel to that of the predominant storm motion is less exposed than adjacent coastal segments more normal to the track direction. For areas where the coast turns abruptly, such as the Mississippi Delta, Apalachee Bay, and the tip of Florida, special consideration must be given in using the generalized results in this report. An example of the treatment of a discontinuity in land- falling storm frequencies at Cape Hatteras, North Carolina, is discussed in Section 5.4. In areas where variations of frequencies along the coast are large, the effects of the steep gradient of hurricane frequencies along the coast on resultant coastal surge frequencies must be considered (see examples given in the following section). For alongshore hurricanes, the bypassing distance is a significant parameter instead of the landfalling point discussed in Section 11.2. The frequency of an alongshore hurricane event is treated in the same way as the landfalling storms, except that the frequency is defined as the number of storms per year passing through a given distance interval along the line perpendicular to the coast. It is the counterpart of the frequency per year for landfalling storms multiplied by the length of coastal segment, determined by the spacing of storm tracks for computations. The application of this is further discussed in the following section. Figures 3 1 and 32 depict the variation along the Gulf and Atlantic coasts of tropical cyclone tracks bypassing the coast at sea. These figures give accumulated track count at selected intervals from the coast. With this information, plots of the cumulative count of tracks versus distance from the coast can be constructed for any coastal point. Figure 55 is an example of the accumulated track count plotted against distance from the coast for Vero Beach, Florida. The difference in accumulated track count between two points read off the graph gives the number of storms, per 100 years, crossing the given distance interval. It is advisable to use small distance intervals near the coast, using the selected R values for landfalling storms as a guide. This would ensure that the effect of maximum winds on coastal waters would maximize generated surge levels. The frequency of tropical cyclones bypassing the coast overland is not treated as such in this report. First, these storms tend to weaken after traversing over land and the surge frequencies resulting from these storms are usually not significant (see for example fig. 29). Second, the contribution of this class of storms to surge frequencies varies greatly in different localities. Coastal surges of significant levels can be produced by such storms in areas near the Outer Banks of North Carolina and in the southern portion of the Florida peninsula. For the treatment of this class of storms in North Carolina, the reader is referred to the report by Ho and Tracey (1975). The North Carolina 12 5 40 60 80 DISTANCE FROM COAST (nmi) Figure 55. — Plot of cumulative count of alongshore storms versus distance from coast for Vero Beach, Florida {milepost 1600). 12 6 study mav be used as a .guide for the Florida peninsula area. A good example of these storms in Florida is the hurricane of October 1950 which entered the coast of south Miami and moved north-northwestward over the entire length of the peninsula. Its intensity weakened to that of a tropical storm after passing near Orlando, Florida. Another hurricane that entered the southern tip of Florida and weakened rapidly while moving northward is the hurricane of 193 5. It was the most intense Atlantic hurricane ever recorded (P = 892 mb while crossing the Florida Keys). It weakened to minimal hurricane intensity (P = 960 mb) by the time it crossed the northern Florida coast, near 30°N. Hurricanes that move northward over the Florida Peninsula seem to fill faster than hurricanes that cross the peninsula in a east-west duration. It should be noted that the filling rate in Chapter 10 for Florida should not be applied to this class of northward moving hurricanes. The treatment of such tropical cyclones passing the coast inland needs further investigation. 11.5 Applications of Profiles of Probability Distributions for Hurricane Parameters Hurricane parameters for storm-surge frequency computations can be obtained by constructing cumulative probability curves for each of the hurricane parameters from smoothed alongshore graphs. Table 2 1 itemizes the information needed by the user. Items 1-4 are information to be listed for identification. Item 5 lists the meteorological information needed for surge-frequency computations and where it can be found in this report. Numerical values to be filled in (5a through 5 j ) are hurricane parameter values for designated percentiles and frequencies read from the appropriate figures for the location (milepost) listed in Item 4. Using these values for the designated percentiles, the full range of individual parameters of clima tologically possible hurricanes that can make landfall at the point of interest can be determined. The cumulative probability curve, thus obtained, is then divided into class intervals that can be used in frequency computations. In storm-surge frequency analysis, landfall points should be selected by taking into consideration the lateral extent of the coast affected by an individual hurricane. Based on the geometry of the hurricane wind field, as discussed in Section 11.2, we recommend that the coastal area of influence for the purpose of surge computations be limited to a distance 5R to the left and 3R to the right of the point of interest. Hurricane tracks crossing landf ailing points at 10-2 5 nmi intervals should be considered in estimating overall surge levels. The computed peak surge at the point of interest for a given storm passing along each of the selected hurricane tracks is assumed to be representative of a "surge event" that could occur within the distance interval (10-2 5 nmi) between two landf ailing points. Hence, the selection of track spacing should be guided by (1) the alongshore gradient of the bathemetry, (2) the storm size and (3) the configuration of coastal areas. For example, tracks spaced at larger distance intervals may be specified for a straight coastline with uniform bathymetry while computation for storms crossing landf ailing points at close intervals would be needed to produce representative surge levels on the shorelines of bays and estuaries. To obtain the frequency of this "surge event" multiply the frequency of landfalling storms (storms/nmi/yr, given in item 5h of table 2 1) by the selected distance interval between landfalling points. 127 Table 21 — Summary sheet of information needed from this report for surge- frequency computations 1. Geographic location 2. Latitude 3. Longitude 4. Milepost [fig. 1] 5. Hurricane parameters Central pressure (P ) [fig. 35] Pressure deficit (1013-P Q ) Forward speed (T) [fig. 41] Direction (9) [fig. 44] Coastal orientation Angle of approach (d-e) Radius of maximum winds (R) [fig. 38] Percentile 1 5 15 30 50 70 90 Percentile 5 1 20 40 60 80 95 1 Percentile 5 16.67 50 83.33 95 h. Frequency of landfalling storms [fig. 27] i. Frequency of exiting storms [fig. 28] storms/10 nmi/100 yr, or storms/nmi/yr storms/10 nmi/100 yr, or storms/nmi/yr j. Frequency of alongshore storms (accumulative counts) [fig. 32] Distance from coast (nrai) Frequency (storms/100 yr) Frequency (storm/yr) Frequency within distance interval 10 20 30 50 75 100 128 After completing the appropriate number of forms for the coastal area of interest, the information can be used to reconstruct cumulative probability curves for the parameters that describe the clima tologically possible hurricanes for each of the selected locations. Intermediate cumulative probability curves, if required, may be estimated using linear interpolation. The reconstructed cumulative probability curves will provide values for any selected percentile within the full range of individual parameters. Intermediate curves will insure a smooth transition from one location to the next. Table 22a is an example of a completed computation form for storm-surge frequency analysis at Vero Beach, Florida (milepost 1600). Tables 22b and 22c contain similar information for locations located 50 nmi to the north and south of Vero Beach, respectively. Figure 56 shows a plot of cumulative probability curves of P for the three locations. Curves for intermediate locations can be determined by linear interpolation. It should be noted that the lowest 1 percent of P for Vero Beach and the lowest 2 percent of P for the location 50 nmi to the south (fig. 56) fall into the intense hurricane category. As discussed in Section 4.5, these hurricanes should have an assigned R of 13 nmi. Similarly, cumulative probability curves can be plotted for the other parameters. Figure 55 shows a plot of cumulative frequency of bypassing hurricane tracks versus distance from the coast for Vero Beach. The accumulated track counts for selected distances from the coast are taken from Item 5j of Table 22a. A smooth line was then drawn by eye joining the data points. From this curve, the frequency of bypassing storms within the first 10 nmi of the coast is 0.0170 storms/yr, the number of storms passing the distance interval of 10-30 nmi is (0.0575-0.0170) 0.0405 storms/yr and the track count for the distance interval of 30-75 nmi is (0.1600-0.0575) 0.1025 storms/yr. Similarly, frequencies within other distance intervals may be obtained (e.g., table 23). The next step in determining hurricane probabilities requires that the hurri- cane parameters be divided into class intervals for the landfalling storms and that the mid-point value of each class interval be determined. The size and number of intervals cannot be specified a priori, but must involve judgment that considers factors that can vary from site to site; an example for P is given in Figure 57. It should be noted that Figure 57 shows only the fraction of all hurricanes with intensities below certain levels and makes no reference to frequency in terms of events per year. For storm-tide frequency computation, this continuous distribution could be divided into five class intervals, each represented by the pressure deficits at the mid-point of the class interval. This computational probability distribution is indicated by the dashed line on Figure 57. For computation purposes, the hurricanes are treated as if the most severe 1 percent all had pressure deficits of 95 mb, the next 6 percent had a deficit of 84 mb, the next 12 percent a deficit of 70 mb, the next 40 percent a deficit of 45 mb and the last 41 percent a deficit of 19 mb. These class intervals are representative values and their corresponding probabilities are listed in Table 23. It is of interest to note that these class intervals are not equally spaced. Closer intervals are used for parameters associated with intense hurricanes. Higher surge levels produced by the intense hurricanes contribute to the 100-yr or higher tide frequencies. Similarly, cumulative probability curves for other parameters can be divided into class intervals, and values for designated percentiles are listed in Table 23. 129 Table 22a — Summary sheet for Vero Beach, Florida 27° 39» N 80° 27' w 1600 1. Geographic location 2. Latitude 3 . Longi tude 4. Milepost [fig. 1] 5. Hurricane parameters Central pressure (P ) [fig. 35] Pressure deficit (1013-P ) Forward speed (T) [fig. 41] Direction (9) [fig. 44] Coastal orientation Angle of approach (d-e) Radius of maximum winds (R) [fig. 3< Vero Beach, Florida Percentile 1 5 15 30 50 70 90 921 93 1 94 5 958 977 990 997 92 82 68 55 36 23 16 Percentile 5 20 40 | 60 80 95 3.5 6.5 8.5 10.6 13.0 16.3 Percentile 5 16.67 50 83.3 3 95 055 087 118 13 5 153 020 020 020 02 020 03 5 067 098 115 133 5.5 11.0 18.0 28.0 37.0 h. Frequency of landf ailing storms [fig. 27] i. Freemen cy of exiting storms [fig. 23] 0.76 storms/10 nmi/100 yr, or 0.00076 storms /nmi/yr 1 .2 storms/10 nmi/100 yr, or 0.0012 storms/nmi/vr j. Frequency of alongshore storms (accumulative counts) [fig. 32 Distance from coast (nmi) Frequency (storms/100 yr) Frequency (storm/vr) Frequency within distance interval 10 1.70 0.0170 0.0170 (0 - 10 nmi) 20 3 .3 0.033 0.0160 (10- 20 nmi) 30 5.75 0.0575 0.0245 (2 0- 30 nmi) 50 10.00 0.1000 0.042 5 (3 0- 50 nmi) 75 16.00 0.1600 0.0600 (50- 75 nmi) 100 2 4.00 0.2 400 0.0800 (75-100 nmi) 130 Table 22b — Summary sheet for 50 nmi north of Vero Beach, Florida 1. Geographic location 2 . Latitude 3 . Longi tude 4. Milepost [fig. 1] 5. Hurricane parameters Central pressure (P ) [fig. 35] Pressure deficit (1013-P Q ) c. Forward speed (T) [fig. 41] d. Direction (0) [fig. 44] e. Coastal orientation f. Angle of approach (d-e) g. Radius of maximum winds (R) [fig. 38] Vero Beach + 50 nmi 28° 30* N 80° 42' W 1650 Percentile 1 5 15 30 50 70 90 92 5 93 5 949 963 981 991 997 88 78 64 50 32 22 16 Percentile 5 20 40 60 80 95 3.8 6.8 8.8 11.0 13.2 16.5 Percentile 5 16.67 50 83.33 95 044 076 115 131 153 000 000 000 000 000 044 076 115 • 131 153 6.3 11.5 19.0 28.8 37.5 h. Frequency of landfalling storms 0.74 storms/10 nmi/100 yr, or [fig. 27] 0.00074 storms /nmi/yr 1.65 storms/10 nmi/100 vr, or i. Frequency of exiting storms _ _ [fig. 28] 0.00165 storms /nmi/yr j. Frequency of alongshore storms (accumulative counts) [fig. 32] Distance from coast (nmi) Frequency (storms/100 yr) Frequency (storm/yr) Frequency within distance interval 10 1.3 6 0.0136 0.013 6 (0 - 10 nmi) 20 2.41 0.02 41 0.0105 (10- 20 nmi) 30 4.32 0.0432 0.0191 (20- 30 nmi) 50 8.2 5 0.082 5 0.0393 (3 0- 50 nmi) 75 14.10 0.1410 0.0585 (50- 75 nmi) 100 22 .60 0.2260 0.0850 (75-100 nmi) 131 Table 22c — Summary sheet for 50 miles south of Vero Beach, Florida 1. Geographic location 2 . Latitude 3 . Longi tude 4. Milepost [fig. 1] 5. Hurricane parameters Vero Beach 50 26° 54' N 80° 11» W 1550 Percentile Central pressure (P ) [fig. 3 5' Pressure deficit (1013-P ) Forward speed (T) [fig. 41] Direction (9) [fig. 44] Coastal orientation Angle of approach (d-e) Radius of maximum winds (R) [fig. 3. 1 5 15 30 50 70 90 916 92 7 941 955 974 989 996 97 86 72 58 39 24 17 Percentile 5 20 40 60 1 80 95 3.4 6.4 8.5 10.5 1 12 .8 16.2 Percentile 5 16.67 50 83.33 95 059 093 12 142 155 020 020 02 020 02 039 073 100 122 13 5 5.0 10.0 17.5 28.0 37.0 h. Frequency of landfalling storms [fig. 27] i. Frequency of exiting storms [fig. 28] 0.97 torms/10 nmi/100 yr, or 0.00097 storms /nmi/yr 0.90 storms/10 nmi/100 yr, or 0.00090 storms /nmi/yr j. Frequency of alongshore storms (accumulative counts) [fig. 32] Distance from coast (nmi) Frequency (storms/100 yr) Frequency (storm/yr) Frequency within distance interval 10 2 .34 0.0234 0.023 4 (0 - 10 nmi) 20 4.02 0.0402 0.0168 (10- 2 nmi) 30 7.10 0.0710 0.0308 (20- 30 nmi) 50 12.50 0.1250 0.0540 (3 0- 50 nmi) 75 18.50 0.1850 0.0600 (50- 75 nmi) 100 25.80 0.2580 0.0730 (75-100 nmi) 132 10 ._ — '* - 20 ■ 30 - - s~\ '// -a ;/' ° 40 u-,^-^ U L F ' ^~Jr \0600 "S w r J^^ Op >-* \ # "^\ >^^ MEXICO \ /^^GALVESTON + FRECPORT J^""^ +■ 4- +29' -^ 964(»0000CST/I8t» Aw,. ^S 30 j LEGENO 990 CENTRAL PRESSURE (mb) 35 RAORJS OF MAX. WNOS ~ 1200 998^*^ 20 >«. ^^0600 + . , -f. ^"soooocsi/ieto 95' 94* 93* !< JP| S, 9' 96" Figure A-l. — Hurricane track for Alicia, 0000 CST August 16 through 1200 CST August 18, 1983. Hurricane eye positions based on radar observations reported from Galveston, Texas, and Lake Charles, Louisiana, are shown as solid dots. Aircraft reconnaissance penetration fixes are shown by triangles. Locations of the hurricane's center determined from satellite observations are given by diamonds. The data from radar fixes and aircraft penetrations were the primary sources used in determining the track and speed of the hurricane over the open ocean. However, information obtained from satellite observations and from ships and oil rigs operating in the area was considered in determining the final track and speed of motion. A.2.5.2 Forward Speed. The translation speed of the hurricane is an important factor in determination of the surge along the open coast and in bays and estuaries. Hourly positions were the basic data used to determine the forward speed. Speeds between successive hours from positions along the best track were first determined and plotted on a time scale and smoothed. Then smooth curves drawn from these data were used to adjust the hourly locations. The new locations were examined with regard to the observed data and, if necessary, some further adjustments were made. This process was continued in an iterative fashion until the best combination between smooth forward speeds and observed eye 150 <•> £f 28°N + 95 °W • • •*• Q LAKE CHARLES • • • Figure A. 2. — Hurricane eye position obtained froa radar (•), aircraft reconnaissance penetration fixes (A), and satellite observations (). 151 Figure A.3 • — Minimus pressure recorded at land stations and by reconnaissance during Hurricane Alicia (1800 CST August 16 - August 18, 1983). aircraft 1200 CST positions was obtained. This process helped to obtain the best possible estimate of forward speed and hourly locations. A.2.5.3 Central Pressure. The most important meteorological input to storm- surge models is the intensity of the hurricane which can be parameterized in terms of its central pressure. Minimum pressures observed at stations and during reconnaissance aircraft penetrations are presented in Figure A.3. These observations were not all obtained at the same time. Since the track of the eye did not cross any land station location, none of the values reported at land stations are equal Co the 'minimum central pressure in the storm. Figure A. 4 shows our analysis of pressure data from land stations and aircraft reconnaissance flights used to obtain a cime history of Alicia's central pressure. A smooth curve was fit to the data by eye. Alicia deepened gradually 152 o o O o en 03 o 05 05 /-j M/'- 90 30 50 30 10 -10 -30 STORM DISTANCE (km) Figure A.. 9. — Flight-level (1500 a) vind3 recorded along radials through the center of Hurricane Alicia, 1352-1433 GMT August 17, 1983. A«2 .6 Discussion The value of R is one of the important factors Co be prescribed in a numerical computation of hurricane surges at the coast as well as in bays and estuaries. The R value, together with a precisely determined storm track specify the location of maximum winds along the coast. This, in turn, influences the water level produced by surface wind stress in a storm-surge model. It is important for surge modelers, as well as users of hurricane surge models, to have precise meteorological information in order to calibrate or verify a numerical surge model. The radius of maximum winds for Alicia shifted from 15 nmi (2 7.8 km) to 3 nmi (58.6 km) near the time of landfall. The transformation of storm size for Alicia took several hours to complete. The high winds near the inner core caused severe damages to downtown Houston, Texas. However, high-water levels in Galveston 3ay (close to 11 ft above MSL at Baytown, Texas) were generated by the winds within the region of highest winds. After examining all available data, we concluded that R for Alicia shifted from 15 nmi (27.8 km) to 30 nmi (55.6 km) just before the hurricane made landfall and that the larger R should be applied to surge computations for the Galveston Bay area. Hurricane data of recent years have shown large variabilities in hurricane parameters at various stages of a hurricane's life cycle. After a hurricane moves over land, its characteristics often change abruptly, due to larger surface friction and modifications to the heat and energy supply. Such changes in the characteristics of the hurricane would result in a departure from the standardized wind profile of the storm-surge model. Hurricane parameters, especially the index R, given in Tables 1 through 3 may not be the best values 159 2 X 40 O 1 1 1 RADIAL DISTANCE OF WIND MAXIMA HURRICANE ALICIA, AUGUST I 983 - RECON. DATA 7 LAND STATIONS TIME (GMT) Figure A. 10. — Radius of primary (solid line) and secondary (dashed line) wind maxima in Hurricane Alicia, August 17-18, 1983. for replicating observed surges with a standardized wind profile. The variation in R near landfall might have to be examined on a case-by-case basis before a suitable value can be determined for the calibration of a numerical surge model. In the calibration process, the computed model winds, in addition to the computed high-water level, should be verified using observed data to ensure the adequacy of the wind model used in the numerical surge computation. A.3 Hurricane David, September 2-5, 1979 A.3.1 Introduction Hurricane David emerged from the central Caribbean on September 2 after devastating the Dominican Republic and rapidly weakening to tropical storm strength over the mountains of Hispanola. David was the strongest hurricane to hit Santo Domingo, Dominican Republic since 1930 (Hebert 1980). Once over water north of Cuba, David began to reintensify as it moved northwestward and approached Andros Island in the western Bahamas with winds of 61-69 kn (DeAngelis 1979). As the center crossed the island late in the afternoon on September 2, it appeared to be heading toward the Miami area (fig. A. 11). A turn to the north-northwest, however, brought the slowly strengthening hurricane about 50 nrai (92.6 km) east of Miami on Labor Day, September 3. Winds of 50 kn were reported buffeting Miami 3each by 0800 GMT September 3. David continued moving north-northwestward and passed within 2 5 nmi (46.3) of West Palm 3each with a minimum central pressure of 973 mb at 1445 GMT September 3. Winds of 50 kn were experienced at West Palm Beach shortly before David's nearest approach. At 1730 GMT on September 3, the storm center made landfall just south of Stuart, Florida, with a central pressure of 968 mb. Winds of 60 kn were recorded 160 Figure A.ll. — Track with central pressures (mb) for Hurricane David, September 2-5, 1979. 161 Table A.l. — Time, flight pattern, and flight level of NOAA/RFC missions into Hurricane David, September 1979 Mission Time period (GMT) Pattern Flight level(s) (ft) 790902F 7909021 7 90902H 02/0145-092 5 02/1130-1853 02/2002-03/0454 east-west race track star Recon. 5,000 variable variable 790903F 7909031 03/0504-1240 star (see fig. A. 12) 5,000 03/2312-04/0641 along FL coast variable 790904H 04/1723-05/0128 modified star (eye partly onshore) variable The missions are designated by an identification code, YYMODAAC where: YY = year (F = NOAA/RFC C130B aircraft 41 MO = month AC = aircraft (H = NOAA/RFC WP-3D aircraft 42 DA = day of the month (i = NOAA/RFC WP-3D aircraft 43 at Stuart at 1600 GMT. David remained close to the Florida east coast for the next 11 hours as it moved north-northwestward over land. By 0600 GMT September 4, the storm center had moved back over open water north of Cape Canaveral. David was the first hurricane to strike the Cape Canaveral area since 192 6 (Hebert 1980). Central pressures in David remained steady as it made its way north toward Georgia. Landfall occurred for a second time in the United States at 1822 GMT September 4 north of Brunswick, Georgia, with a minimum central pressure of 968 mb. David continued on a northerly track and passed just west of Savannah, Georgia, at 2346 GMT September 4. A .3 .2 Previous Studies Hebert (1980) prepared a detailed description of Hurricane David and included meteorological data from land stations as far south as the Lesser Antilles, and as far north as Mt. Washington, New Hampshire. He compiled meteorological data from regularly reporting stations, as well as various unofficial sources which were used in the analysis of the variation of central pressure with time (shown in fig. A. 15). The National Hurricane Center published an annual verification and data tabulation for Atlantic tropical cyclones of 1979 which included Hurricane David (Hebert and Staff 1980). The compiled data tabulations give David's center-fix positions obtained by aerial reconnaissance penetrations, satellite images, and land-based radar. Central pressures, maximum winds and other data observed by aerial reconnaissance were also included for Hurricane David. 162 DIRECTION OF STORM MOVEMENT Optiona 80 NM leg Figure A. 12. — Reconnaissance flight pattern, designated as star pattern, Hurricanes David and Allen (refer to Friedman et al. 1982). used in Howell at al. (1982) provided a report of tide data during; the passage of Hurricane David at Miami Beach, Palm Beach, and Vero Beach, Florida. Storm surges at Palm Beach and Vero Beach were computed by Howell et al. using a numerical storm-surge model and compared with observed values. A.3.3 Aircraft Data NOAA research aircraft flew six missions into Hurricane David during the period September 2-5. Table A.l summarizes the flight patterns, flight levels and the time periods for which meteorological and flight data were recorded. The flight patterns flown in these missions included a 'star' type (fig. A. 12) and a 'Recon' type. The 'Racon' flight pattern was a deviation from typical flight patterns. In this case, the actual pattern completed was designed to optimize both the determination of the storm center location and collection of research data. A 163 detailed inventory of airborne research meteorological data is described by Friedman et al. (1982). This set of NOAA flight data was supplemented by Air Force reconnaissance flight data recorded on the morning of September 4. A.3 .4 Central Pressure A.3 .4.1 P From Aerial Reconnaissance. Minimum central pressures were recorded nearly continuously from September 2-4 by NOAA and Air Force reconnaissance air- craft when Hurricane David was moving over open water. Pressure values were obtained from Hebert et al. (1980). These pressure values were used in Figure A. 15. When Hurricane David moved over land, reconnaissance aircraft did not penetrate the eye to obtain a pressure reading because of increased turbulence over land. A.3 .4.2 P Q From Land Station Observations. Once Hurricane David was over land, station reports of hourly weather observations and barograph traces were used to determine minimum pressures. If the center of the hurricane eye passed directly over a land station, then the minimum pressure could be readily determined. Hurricane David, however, did not pass directly over any land stations. Since several stations were very close to the track, their minimum pressures were used to estimate the storm's minimum pressure. Figure A. 13a shows the time variation of minimum pressures recorded at Shuttle Airport, Florida every 3 hours. From this plot, the lowest pressure observed during the passage of David, 974 mb, occurred at about 0300 GMT September 4, when the storm's eye was located only about 5 nmi (9.3 km) to the west of the station. This estimate was plotted in Figure A. 15. Another example of (hourly) station pressure data is shown in Figure A. 13b for Savannah Municipal Airport, Georgia. A minimum pressure of 970 mb was experienced at 2300 GMT September 4 when David was about 7 nmi (13 km) to the west. This estimate was also used in the analysis shown in Figure A. 15. A.3 .4.3 Pressure Fit at the Coast. Minimum pressures determined at the Florida and Georgia coasts were not based on any single source. Observed pressures were extrapolated inward to P using visually-fitted radial pressure profiles based on equation 1. Figure A. 14a shows a subjectively fit pressure profile curve at the Florida coast, near the time of landfall, at 2100 GMT September 3. Pressure observations from several land stations were plotted against distance from storm center at 2100 GMT. Then a curve was drawn to fit the data. Figure A. 14b is another example of the pressure profile curve except at 1800 GMT September 4, at the Georgia coast. In both cases, a minimum central pressure of 968 mb was estimated. In the case of the Georgia coast, a NOAA research aircraft measured a minimum 700 mb height of 2 82 m at 1822 GMT September 4. Using a nomogram for estimating surface pressure in the eye of tropical cyclones (Jordan 1957), a central pressure of 968 mb was also estimated. A.3 .4.4 Time Variation of P . Hurricane David was most intense (central pressure of 92 4 mb) while still located in the Caribbean Sea, south of Puerto Rico. The analysis for this period was used in Chapter 4. As David emerged from the central Caribbean Sea, however, central pressures moderated considerably (see fig. A.ll). Figure A. 15 shows the time variation of central pressure in David for the period of September 3-5. Minimum pressures recorded by reconnaissance aircraft and land stations at various times were used to obtain a time history of David's central pressure. The line drawn is a curve fit to the data by eye. 164 1020 1010 — 1 1 T 1 1 ! r ...... , j ^ -3 £ bJ 1000 K ZD 00 oO 111 a. 990 \ / ~ -j uj > LU -J 980 \ / < LU CO 970 (a) - 96C 1., , ! . 1 -L— L_ L 1 1 1 3/00 06 4/00 06 TIME (GMT) 020 1 1 1 1 I ! 1 1 r- i 010 - 000 Nl j* 990 - \ / 980 X i 970 -i (b) 1 I II 06 4/00 06 5/00 TIME (GMT) Figure A. 13. — Sea-level pressure observed during passage of hurricane David (September 1979) at (a) Shuttle Airport, Florida, and (b) Savannah (Municipal Airport) , Georgia. 165 250 300 350 DISTANCE FROM STORM CENTER C rani) 100 150 200 250 300 350 400 DISTANCE FROM STORM CENTER Cnmi) Figure A. 14. — Pressure—profile curve during Hurricane David for (a) Florida coast at 2100 GMT, September 3, 1979, (b) Georgia coast at 1800 GMT, September 4, 1979. 166 o — © 311IAN0SX0Vr 2 J cw 3^nss3dd 167 168 STORM DISTANCE (km) Figure A.16. — Flight-level ri?As recorded along radlals through the center of Hurricane David, (a) 2308-2356 QfT, September 2 , (b) 0644-0748 GHT, September 3, and (c) 1751-1341 GMT, September 4, 1979. Reconnaissance aircraft reported a minimum pressure of 96 5 mb at 0051 GMT September 3 just as David crossed Andros Island, about 120 nmi (222 km) southeast of Miami, Florida. A central pressure of 966 mb was recorded by aerial reconnaissance at 0302 GMT. By 0531 GMT September 3, another mission reported a central pressure of 981 mb. The pressure difference in these 2 .5 hours was 15 mb. This large pressure rise seems to be inconsistent with Che other data as Figure A. 15 shows and no explanation can be given. Hurricane David approached the southeast coast of Florida at a speed of about 10 kn, and a central pressure of 968 mb was determined at landfall at about 1730 GMT September 3. This value is the pressure recorded in Table 2. As David moved northwestward over land along the Florida coast (fig. A.ll), central pressures increased very gradually until the storm exited the coast and moved over water again. A central pressure of 975 mb was consistently reported by Air Force reconnaissance aircraft from 1142-1515 GMT September 4. During this time, David was moving over water north of Cape Canaveral at about 12 kn. As the hurricane approached the Georgia coast, pressures dropped at about 2 mb/hr from 1515 GMT until a low pressure of 968 mb was determined at landfall (see sec. A.3.4.3), about 1822 GMT September 4. David moved inland at about 10 kn and weakened slowly. Savannah, Georgia experienced a minimum pressure of 970 mb when the center of David was only about 7 nmi (13 km) to the west and 40 nmi (74 km) inland. 169 A*3 .5 Radius of Maximum Winds A.3.5.1 R From Aerial Reconnaissance. Figure A. 16a shows a wind profile constructed from flight-level wind data recorded between 2 308-2 3 56 GMT September 2. The winds were recorded during a north-south traverse through the eye and are plotted against radial distance from the storm center. The figure indicates that a wind maximum is located to the north of the center at a radial distance of about 35 km (18.9 nmi). This value was plotted in Figure A. 18 at 2332 GMT September 2. Figure A. 16b is another wind profile for Hurricane David constructed from flight-level winds recorded between 0644-0748 GMT September 3 . At this time, the storm center was located over open water about 68 nmi (12 6 km) east-southeast of Miami, Florida (see fig. A.ll). Flight-level winds were recorded during a northeast-southwest traverse through the eye. The wind profile indicates that maximum winds occurred at a radial distance of about 45 km (24 nmi) northeast of center. This value was plotted in Figure A. 18 at 0716 GMT September 3. Figure A. 16c shows another wind profile constructed from data recorded between 1750-1841 GMT September 4. At this time, the storm center was over water north of Cape Canaveral and approaching landfall on the Georgia coast. The winds were recorded during an east-west traverse through David's eye. Figure A. 16c indicates a maximum wind at a radial distance of about 20 km (10.8 nmi) west of center. This value is plotted at about 1815 GMT September 4 in Figure A. 18. Figures A. 16a through A. 16c suggest the existence of secondary maxima (indicated by solid dots in fig. A. 18) which were relatively short- lived. Analysis of composite maps (diagrams not shown) revealed that these secondary maxima were scattered and quite disorganized. They were not considered relevant in the specification of the parameters that are the focus of this study. A.3.5.2 R From Land Station Observations. Once the storm moved inland, land stations were the primary source of data. Data from these stations were obtained from the NCDC in Asheville, North Carolina, where all raw data from station observations are stored. Figure A. 17a shows a time variation of windspeed and wind direction for Shuttle Airport, Florida from 1200 GMT September 2, to 0000 GMT September 5. This plot consists of hourly wind observations as Hurricane David passed just west of the station (0300-0400 GMT September 4). Note the shift in wind direction as the storm center passed. Winds veered from the east to east-southeast then south indicating the path of the storm center was to the west of the station. A maximum wind of about 3 7-3 8 kn (19-2 m/s) was experienced at Shuttle Airport at 053 GMT September 4 when the storm center was located approximately 2 nmi (3 7 km) away from Shuttle Airport (see hurricane track on Fig. A.ll). Figure A. 17a also shows the distance of the storm from Shuttle Airport (dashed line). Using this information, a radial distance of 2 nmi (3 7 km) was determined for the wind maxima and was plotted in Figure A. 18 at 0530 GMT September 4. Figure A. 17b shows another plot of hourly windspeed and direction against time for Savannah Municipal Airport, Georgia from 0600 GMT September 3 to 1700 GMT September 5. The wind direction at Savannah as David's center passed nearby shifted from the east to east-southeast then south and finally south-southwest. This indicates that the hurricane passed to the west of the station (fig. A.ll). A maximum wind of about 37 kn (19 m/s) occurred at Savannah at 2230 GMT September 4. The track in figure A.ll indicates that the hurricane center was only about 10 nmi (18.5 km) away from Savannah at 2230 GMT September 4. 170 ©-^ t 0-- -o~ -0- ^0~- t ! --ex®" § z as to NCI103dia GNIM _ OJ .2 O 3 & M U ~ 3 2 LU 3 "3 1 t « 4J 5 s _ Q y si ~ 3 3J a. 3 3 ? > f8 flj •< u ( U >D (333dS (3NIM 171 (quo 3dnSS3dd ~I3A3~! V3S o o o o O o 0) co I s - en 05 cr> 3 C U NOIl03yiQ GNIM (UM) a33dS GNIM 1 'J3 J '- V 'J 3 -C l-i •X - i 172 1 4 , " in • v- • 4 T 03 s • jj A - 1 / CJ I / so a. 4 (0 ~ • s |l o • - * <3 j . - • • 31 c * h <] o ■;af 3 a 9 •3 r s ■B — • C U5 2 < < * ■- 3 -.- - 2 z ? < § <3 < u 5 - S* 3 (0 O 2 < C £ < O 2 • 5 - 5 S < / / / ^ / i 5 10 ^ 15 20 RAOIAL DISTANCE (nmi) Figure A.2 6. — Concurrent observations of central pressure and radius of maximum winds for Hurricane Allen, August 3-9, 1980. and pressure data were recorded in a traverse of the hurricane center. Some of the data points (with no concurrent observations of P and R) shown in previous diagrams were not included in this plot. During the period of observation (August 3-9), Allen traveled from the Caribbean through the Yucatan Channel into the Gulf of Mexico. It covered a distance of about 2 ,000 nmi (3704 km) from latitude 14°N through 27°N. Except for a few instances of larse R observed in the weakening stages, Allen's maximum winds stayed within 15 nmi (27.8 km) of the center. Allen was essentially characterized by small R's before it reached the Texas coast. However, the R values in Allen, as well as in other intense Atlantic hurricanes, tend to be small and a non-linear relation may exist between P and R. o 184 APPENDIX B Statistical Methods for Tests of Homogeneity and Independence B.l Introduction The statistical methods used in this report to test the homogeneity of hurricane parameters and interrelations between them are discussed in this appendix. The methods used to test for homogeneity include cluster analysis, discriminant analysis, principal component analysis, and the Mann-Whitney test; those for the test of independence include the Spearman test and contingency table analysis using the Chi-square test. For these methods, this appendix describes assumptions, and where appropriate, the null hypotheses, the confidence levels, and decision rules. We also briefly discuss the rationale for choosing a method, its limitations, and the guidelines for interpreting the test results. B.2 Methods for the Test of Homogeneity Among the methods for the test of homogeneity, cluster analysis, discriminant analysis and principal component analysis each consider several parameters, whereas the Mann-Whitney test is based on only a single parameter. B«2.1 Cluster Analysis B.2. 1.1 Description of the Method. In cluster analysis, objects are assigned to groups or clusters suggested by the data sample, not by any grouping defined a priori. In this study, a hurricane was considered an object for the purpose of statistical analysis. That is, all parameters associated with a given storm were used to characterize the hurricane. There are many clustering methods (e.g., SAS 1982); we chose the centroid method for this study. The actual computation was performed using the CLUSTER procedure in the SAS system. The procedure computes the Euclidean distances between objects and assigns those objects that are close to each other to the same cluster. In this study, the Euclidean distance was computed using coordinates represented by P , R, 9, T, m, (b and A. In the centroid method, the distance between two clusters is defined as the Euclidean distance between their centroids (vector means). The procedure provided a cluster hierarchy from level one to level N, where N is the number of objects in the data sample. In this study, N is the number of hurricanes; if any hurricane parameter was missing, that hurricane was omitted. In the cluster hierarchy, there is only one cluster at level one and there are N clusters at level N. The cluster at level one contains all the objects in the data sample, and every cluster at level N contains only one object. As shown in Figure B.l, every cluster at a given level is completely contained in a cluster at the preceding level. For example, a cluster at level four may contain Mention of a particular commercial product should not be considered an endorsement by the federal government. 185 MILEPOST NUMBER OF CLUSTERS RANGE 2 3 4 5 6 7 8 9 11-243 © © © © © © © 296-500 o © 560-671 © © © © © © 718-904 966-1201 © © © © 1292-1584 © © © © © © © © 1752-1945 © © © © © © © 2043-2294 © © © 2532-2750 © © © © © © Figure B.l. — Levels two through nine of the hierarchical clusters of landf ailing hurricanes, based on parameters P , R, 9, T, m, d> and \ . The circled numbers are the cluster identification numbers. exactly the same objects of one cluster at level five (cluster 2 in fig. B.l), or it may' contain exactly the same objects of two clusters at level five (cluster 1 at level 4, and clusters 1 and 4 at level 5 in fig. B.l). The user must determine the most appropriate number of clusters. When the number of clusters is chosen, the parent cluster of each object (hurricane) can be identified using the TREE procedure of the SAS system. B.2.1.2 Rationale for Choice. Some clustering methods recuire that the sample data be normally discributed. The hurricane data sample has large natural variability, and' the normality of our data could not be reliably tested. We chose to use the SAS CLUSTER Drocedure since it did not reauire that the data sample be normal. 186 B.2.1.3 Limitations of the Method. No satisfactory method has heen developed to determine the appropriate number of clusters. This is dependent on the data sample and nature of the phenomena being considered. B.2.1.4 Interpretation of the Results. Conclusions drawn from cluster analysis are dependent on the selection of the number of clusters and must be interpreted cautiously. Scatter diagrams of the original parameters were helpful for the determination of the optimum number of clusters. Other methods, both nonstatistical and statistical, were also considered to help interpret the results of cluster analysis. In this study, we relied heavily on meteorological judgment; in addition we used discriminant analysis and principal component analysis to help evaluate the results of the cluster analysis. B.2.2 Discriminant Analysis B.2.2.1 Description of the Method. Discriminant analysis uses one classification variable and several continuous quantitative variables to assign each object to a class corresponding to a value of the classification variable using the information contained in the continuous variables. In this study, hurricanes were the objects to be classified, the cluster identification number obtained from the cluster analysis was the classification variable, and hurricane parameters were the continuous variables. There are several types of discriminant analysis, some are based on the assumption that each class can be considered normally distributed while others use non-parametric methods and do not require the assumption of normality. In this study, we used the "k-neares t-neighbor" discriminant analysis, where k was chosen to be seven, equal to the number of parameters (P , R, 9, T, m, 4> and A) used in the analysis. Considering each hurricane as an object represented by a vector of seven components (P R, 9, T, m, and A), the method computes the distance between two objects based on the total-sample covariance matrix (Mahalanobis distance), and, for each object, it saves the distances of the seven nearest objects (because k = 7). Based on these distances, it computes the probability that an object would fall into the class with the selected nucleus object. If the probability exceeds a specified threshold, the associated object is classified into that class. The actual computation was performed using the NEIGHBOR procedure of the SAS system. More details of the method are given in the SAS User's Guide (SAS 1982). B.2.2 .2 Rationale for Choice. The k-nearest-neighbor approach was non- parametric and did not require the assumption of normality. It allowed us to evaluate the results of the cluster analysis and to determine a number of clusters that could be characterized as homogeneous for testing the independence of the various hurricane parameters. B.2.2 .3 Limitations of the Method. The variables, except for the classification variable, must be continuous, so that the computation of distances can be performed. The classification variable can be either categorical or numerical, but there can only be one classification variable. It is recommended that the classification variable be limited to a finite number of values, so that the classes can be kept to a manageable number. 187 3.2.2.4 Interpretation of the Results. The discriminant analysis gives the classification of each object and probabilities of its membership in all the classes in which it could have been placed. By comparing the class that the object was placed in and the class assigned a priori, misclassif ied objects can be identified. The probability of membership in a particular class can be used to judge whether the classification of the object was appropriate. The threshold probability for the classification is user specified. In this study, the threshold probability was not assigned and objects were classified into the class which was associated with the largest membership probability. 3.2.3 Principal Component Analysis 3.2.3.1 Description of the Method. Given N numerical characteristics that describe a set of objects, the principal component analysis procedure computes N principal components; each principal component is a linear combination of the original characteristics (variables). The coefficients of this linear combination are the elements of an eigenvector of the correlation or covariance matrix of the original variables. The eigenvectors are normalized to have unit length (unit norm). The eigenvalues are the variances of the associated principal components. The first principal component has the largest eigenvalue and the N-th principal component has the smallest. The eigenvectors are orthonormal, i.e., they represent perpendicular directions in the space of original characteristic variables. In this study, the original characteristic variables were P , R, 9, T, m, and A be available for each hurricane. Storms with missing values had to be excluded from the analysis. B.2.3.4 Interpretation of the Results. As explained above, the results of the principal component analysis can be used to explain the relative importance of the original variables for the grouping of hurricanes. By investigating the percentage of variance accounted for by each principal component, we were able to 188 select Che more important principal components. Then, by examining the eigenvectors associated with these principal components, we found the original variables that were most important in defining these principal components. Although the results of the principal component analysis can be used to explain some linear relations between the hurricane parameters, interpretation of these relations was not always clear. Sometimes scatter diagrams of the original variables were used for additional .guidance in understanding the results. B.2.4 Mann-Whitney Test B.2.4.1 Description of the Method. The Mann-Whitney test is a rank test (non-parametric). In this study, we divided the hurricanes into several a priori groupings based on location along the coast. For each test, we selected two groups of hurricanes: one group had N hurricanes and the other had M hurricanes. Assuming that each group was a random sample drawn from its respective population and two groups were mutually independent, we performed the Mann-Whi tney test on each of the hurricane parameters P , R and T. The test was performed in the following manner: We first combined the group of N hurricanes (group 1) with the group of M hurricanes (group 2). To test whether parameter P , for example, has the same distribution function in groups 1 and 2 , we first arranged the P Q in the mixed sample from the smallest to the largest value and assigned rank values from 1 to N+M to these P values. For tied values of P , an averaged rank value was assigned to each of them as shown in the following example (note rank 6.5 for P 961.7) Example Rank Group Origin 943.0 947.2 955.3 956.7 959.0 961.7 961.7 966.5 975.0 979.0 981.0 1 2 2 2 3 2 4 1 5 2 6.5 2 6.5 1 8 1 9 1 10 2 11 1 Then, the sums of ranks (S) were computed separately for groups 1 and 2. In the 38.5 and S = 27.5, The corresponding test statistics of the Mann-Whitney test were computed using the formulae: This example is for illustration only, not to be confused with any actual grouping in this study. 189 W x = S 1 - \ N (N + 1), » 2 -S' 2 - 2 -M(M+l) respectively for groups 1 and 2. In the example, N = 5 and M = 6, and W2 = 6.5. For given sample sizes N and M, percentiles of the Mann-Whitney test statistic can be computed (see Conover, 1971, table 8). We used a two-tailed test at 5-percent significance level and the null hypothesis that P Q had the same distribution function in both groups of hurricanes. For N = 5 and M = 6 in the example, the 0.025-th percentile was 4 and the 0.975-th percentile was 26. Comparing the test statistics Wj and W 2 with these percentiles, we found that W, and W 2 were within the range between 4 and 2 6 (respectively, 0.025-th and 0.975-th percentiles), and we accepted the null hypothesis for the above example. The test was repeated for R and T for every selected pair of groups of hurricanes in this study. For more details of the Mann-Whitney test, see Conover (1971). 3.2.4.2 Rationale for Choice. The limited sample size and large natural variability of our hurricane data sample prevented us from reliably estimating the distribution functions of hurricane parameters for formal hypothesis testing. Since the Mann-Whitney test is a non-parametric test, it does not require a priori assumptions about the distribution function of the data sample and is suitable for our hurricane data. B.2.4.3 Limitations of the Method. The basic assumption for the Mann-Whitney test is that both groups are drawn as random samples. For the reasons discussed in Section 3.2.1.2, we did not consider it appropriate to use direction of landf ailing hurricanes as a random variable, and this parameter was excluded from the Mann-Whitney test. Another assumption of the Mann-Whitney test is that two samples must be mutually independent. There was no evidence that our hurricane data samples for the selected coastal segments violated this assumption. B.2.4.4 Interpretation of the Results. The Mann-Whitney test examines the similarity of two distributions of rankings, but not the distributions of the actual values of the hurricane parameters. For this reason, the results must be interpreted with caution, and any conclusions drawn from the test results must recognize that the distributions of rankings may not fully correspond to the distributions of the actual values. B.3 Methods for the Test of Independence To test independence among hurricane parameters, we used two methods: the Spearman test and contingency tables with the Chi-square test. The Spearman test is a rank test while the contingency tables with the Chi-square test is for categorical data. 190 B.3.1 Spearman Test B.3.1.1 Description of the Method. As an example, consider the Spearman test for P and R for a group of hurricanes. P Q was ranked from the smallest to the largest value and rank numbers were assigned to each value; for tied values of P , an average rank value was assigned to each of them as was done in the Mann-Whitney test (see sec. B.2.4.1). For the same group of hurricanes, R's were also ranked and assigned a rank number. Then the Spearman correlation was computed using the following formula: P = 1 - 6W N 2 N (IT-1) where W = V" [r(P Q ) - r(R.)] 2 The parameter N is the sample size of the group of hurricanes, and r is the rank value of parameters P Q or R. Spearman's correlation can be used as a test statistic. Given the sample size, N, and the probability of a percentile, this percentile can be computed. There are three ways to test the Spearman correlation. The null hypothesis for all three tests is that P and R are mutually independent, that is, the correlation coefficient is not significantly different from zero. The alternate hypothesis for the first test is that P and R are positively correlated, for the second, that P and R are negatively correlated, and for the third, that P and R are correlated (either positively or negatively). In this study, when the probability associated with a specific estimate of P was greater than 95th percentile, we rejected the null hypothesis of the first test, when p was less than 5th percentile, we rejected the null hypothesis of the second test, and when p was either less than 2.5 percent or greater than 97.5 percent, we rejected the null hypothesis of the third test. The significance level for all the tests was 5 percent. For more details, see Conover (1971). B.3.1. 2 Rationale for Choice. We chose Spearman test for the hurricane parameters because it offered the possibility of detecting the nature of interrelations, if they existed. B.3.1. 3 Limitations of the Method. As with many non-parametric tests, weak relations between two parameters may not be detected. B.3.1. 4 Interpretation of the Results. The Spearman test detects the correlation of ranks of random variables instead of the actual values of the variables. The interpretation of these correlations should be limited to the correlations of ranks only; independence between ranks of random variables may imply independence of the random variables. 191 B.3.2 Contingency Table with Chi-square Test B.3.2.1 Description of the Method. The contingency table with a Chi-square test was used at the 0.05 level and is described in detail in Section 4.2 of this report. Additional details may be found in Conover (1971). B.3.2 .2 Rationale for Choice. There was no requirement that the sample meet conditions other than it be a random sample of sufficient size. This made it suitable for use with our data sample. B.3.2 .3 Limitations of the Method. The contingency table with the Chi-square test was designed for categorical data samples, thus, we had to choose specific values to partition the parameters into categories to establish the cell frequencies in the contingency table. There cannot be more than 2 percent of cells which have expected frequency less than 5 in each of them. This limitation is to ensure that the Chi-square approximation is valid for the test. B.3.2 .4 Interpretation of the Results. The results of this test were sensitive to the values selected to partition the data into categories. A small change of the dividing value sometimes caused the result to change from not significant to significant, or vice versa. Therefore, we had to be careful in interpreting the results using this approach. APPENDIX C Plotting Position Formula C.l Introduction A plotting position formula was used to determine the location along the abscissa of ranked data in the cumulative frequency curves for the hurricane parameters. A plotting position formula was selected for this purpose from eight existing formulae based upon five evaluation criteria. Existing plotting position formulae are listed in Table C.l. The symbols used in the formulae are explained in the note underneath the table. In each line, the name of the formula is given in the left column, and the year in which the formula was introduced is given in the right column. This table does not include all existing formulae. The Beard (1943) formula is not included because it only applies to m = 1, and the Samsioe formula (see Reinius 1949, p. 51) is not included because its computation involves solving a N-th power equation and it is not easy to use. For convenience of computation, only easy-to-use formulae were considered. C.2 Criteria for Evaluation The plotting position formula listed in Table C.l were evaluated according to the criteria listed below. 1. The plotting position must be such that all the observed data can be plotted on probability paper. 192 Table C.l. — List of plotting position formulae Name Formula ' Year California P„, = -£- 1923 m N Hazen P„, = 2 ?~ 1 193 m ZN Wei bull P m = t~ 193 9 m N+l Chegodayev P„ = g~j 1955 Blora P = *.',, 1958 m N+0.4 m-3/8 m N+l/4 3m-l m 3N+1 m-0.44 m N+0.12 > — m-0.3 7 Tukey P = ";" t 1962 J m 3N+1 m -0 .44 Gringorten P m = „, n ,_ 1963 Reinius P = !" " '" 4 1982 m N+0 .2 6 P = probability; Til N = total number of items; m = rank of an item m < N. 2. Tbe plotting position sbould lie between the observed frequencies (m-l)/N and m/N. (For the explanation of m and N, see the footnote of Table C.l.) 3. The return period of a value equal to, or larger than, the largest observed value should converge towards N. 4. The observed values should be equally spaced on the frequency scale. 5. The plotting position should have an intuitive meaning, be analytically simple, and be easy to use. 193 Table C.2. — List of plotting position formulae in the descending order of their p * s. (See table C-l for the meanings of symbols.) m = 1 m = N California California Wei bull Haze n Chegodayev Gringorten Tukey Blora Reinius Reinius Bl om Tukey Gringorten Chegodayev Hazen Wei bull C.3 Evaluation of Plotting Position Formulae All formulae in Table C.l meet criteria 4 and 5. All except tbe California formula meet criteria 1 and 2. Only the California and Weibull formulae meet criterion 3. The most important problem with the California formula is that it gives p ffl = 100 percent for m = N, and this p can not be plotted on a probability paper. The most important advantage of Weibull formula is that tbe return period for m = 1 converges towards N as N * oo. Among formulae listed in Table C.l, only the Weibull formula meets all tbe criteria listed above. Thus, the Weibull formula was the choice used in this study. C.4 Comparison of Formulae To reveal more about the characteristics of the various formulae, we compared them for the special cases: m = 1, m = N, and N » oo. For m = 1 and N, the names of formulae are listed in Table C.2 in the descending order of their values of p . The order of names for m = N is exactly the reverse of that for m = 1, except for California formula. For N » oo, the values of p computed using all the formulae in Table C.l approach m/N. Since the sample size of hurricane clima tological data is usually small, we choose N = 10 for an example to compare values of p of the formulae in Table C.l. These values are plotted in Figure C.l. The Weibull formula gave the largest p for m = 1 and the smallest p for m = N. Except for the California formula, the largest difference in p between different formulae was less than 5 percent. For m = 1, the p of the Weibull formula is approximately two times that of the Hazen formula. For m = N, the p of the Weibull formula is close to ' r m that of the Hazen formula: approximately 91 percent compared to 95 percent. 194 3 7 6 m s 4 3 2 CALIFORNIA HAZEN WEIBULL CHEGODAYEV 1 0.1 0.2 0.5 I 2 5 10 m 90 95 99 99.6 99. 9< Figure C.l .--Comparison of plotting position formulae for N = 10. (See Cable C.l for the meanings of symbols.) 95 (Continued from inside front cover) NWS 16 Storm Tide Frequencies on the South Carolina Coast. Vance A. Myers, June 1975, 79 p. (C0M-75- 11335) NWS 17 Estimation of Hurricane Storm Surge in Apalachicola Bay, Florida. James E. Overland, June 1975. 66 p. (COM-75-11332) NWS 18 Joint Probability Method of Tide Frequency Analysis Applied to Apalachicola Bay and St. George Sound, Florida. Francis P. Ho and Vance A. Myers, November 1975, 43 p. (PB-251123) NWS 19 A Point Energy and Mass Balance Model of a Snow Cover. Eric A. Anderson, February 1976, 150 p. (PB-254653) NWS 20 Precipitable Water Over the United States, Volume 1: Monthly Means. George A. Lott, November 1976, 173 p. (PB-264219) NWS 20 Precipitable Water Over the United States, Volume II: Semimonthly Maxima. Francis P. Ho and John T. Riedel, July 1979, 359 p. (PB-300870) NWS 21 Interduration Precipitation Relations for Storms - Southeast States. Ralph H. Frederick, March 1979, 66 p. (PB-297192) NWS 22 The Nested Grid Model. Norman A. Phillips, April 1979, 89 p. (PB-299046) NWS 23 Meteorological Criteria for Standard Project Hurricane and Probable Maximum Hurricane and Probable Maximum Hurricane Windf ields , Gulf and East Coasts of the United States. Richard W. Schwerdt, Francis P. Ho, and Roger R. Watkins , September 1979, 348 p. (PB-80 117997) NWS 24 A Methodology for Point-to-Area Rainfall Frequency Ratios. Vance A. Myers and Raymond M. Zehr, February 1980, 180 p. (PB80 180102) NWS 25 Comparison of Generalized Estimates of Probable Maximum Precipitation With Greatest Observed Rainfalls. John T. Riedel and Louis C. Schreiner, March 1980, 75 p. (PB80 191463) NWS 26 Frequency and Motion of Atlantic Tropical Cyclones. Charles J. Neumann and Michael J. Pryslak, March 1981, 64 p. (PB81 247256) NWS 27 Interduration Precipitation Relations for Storms — Western United States. Ralph H. Frederick, John F. Miller, Francis P. Richards, and Richard W. Schwerdt, September 1981, 158 p. (PB82 230517) NWS 28 GEM: A Statistical Weather Forecasting Procedure. Robert G. Miller, November 1981, 103 p. NWS 29 Analyses of Elements of the Marine Environment for the Atlantic Remote Sensing Land Ocean Experiment (ARSLOE) — An Atlas for October 22 Through October 27, 1980. Lawrence D. Burroughs, May 1982, 116 p. (PB82 251281) NWS 30 The NMC Spectral Model. Joseph G. Sela, May 1982, 38 p. (PB83 115113) NWS 31 A Monthly Averaged Climatology of Sea Surface Temperature. Richard W. Reynolds, June 1982, 37 p. (PB83 115469) NWS 32 Pertinent Meteorological and Hurricane Tide Data for Hurricane Carla. Francis P. Ho and John F. Miller, August 1982, 111 p. (PB83 118240) NWS 33 Evaporation Atlas for the Contiguous 48 United States. Richard K. Farnsworth, Edwin S. Thompson, and Eugene L. Peck, June 1982, 26 p. NWS 34 Mean Monthly, Seasonal, and Annual Pan Evaporation for the United States. Richard K. Farnsworth and Edwin S. Thompson, December 1982, 85 p. (PB83 161729) NWS 35 Pertinent Meteorological Data for Hurricane Allen of 1980. Frances P. Ho and John F. Miller September 1983, 73 p. (PB 272 112) NWS 36 Water Available for Runoff for 1 to 15 Days Duration and Return Periods of 2 to 100 Years for Selected Agricultural Regions in the Northwest United States. Frank P. Richards, John F. Miller, Edward A. Zurndorfer, and Norma S. Foat, April 1983, 59 p. (PB84 120591) NWS 37 The National Weather Service Hurricane Probability Program. Robert C. 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