Improved Short-Term Atlantic Hurricane Intensity Forecasts Using Reconnaissance- Based Core Measurements David Andrew Murray

Florida State University Libraries

Electronic Theses, Treatises and Dissertations The Graduate School

2009 Improved Short-Term Atlantic Hurricane Intensity Forecasts Using Reconnaissance- Based Core Measurements David Andrew Murray

Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] THE FLORIDA STATE UNIVERSITY

COLLEGE OF ARTS AND SCIENCES

IMPROVED SHORT-TERM ATLANTIC HURRICANE INTENSITY

FORECASTS USING RECONNAISSANCE-BASED CORE

MEASUREMENTS

DAVID ANDREW MURRAY

A Thesis submitted to the Department of Meteorology in partial fulfillment of the requirements for the degree of Master of Science

Degree Awarded: Fall Semester, 2009

The members of the committee approve the thesis of David Andrew Murray defended on November 6, 2009.

______Robert Hart Professor Directing Thesis

______Carol Anne Clayson Committee Member

______Philip Sura Committee Member

The Graduate School has verified and approved the above-named committee members.

This thesis is dedicated to my wonderful, loving wife, Marisa Murray, for her tremendous support throughout the process of the research and the writing of the manuscript. Her acceptance of my working late hours and her support at home made completion of this work possible. My appreciation to her for all the sacrifices she made cannot be expressed in words. Thank you, Marisa.

iii

ACKNOWLEDGEMENTS

I would like to thank my committee members, both Dr. Carol Anne Clayson for her advice as well as Dr. Philip Sura for his input regarding the statistical methods involved in this research. I also would like to thank the Hart/Reasor/Ruscher lab for their support and for making days in the lab more enjoyable. Thanks are also due to my parents for their continued support throughout my education. I would also like to thank my best friend, Tim Kurtz, for helping me keep my sanity. Special recognition is due to Ben Schenkel for all the time he invested reviewing my work, offering excellent suggestions, assisting me with coding problems, and proofreading my thesis. His efforts are greatly appreciated. Finally, I would like to recognize my major professor, Dr. Robert Hart, for all of his assistance and advice over the last year and a half. He has been not only a great mentor and advisor but also a good friend, and I thank Bob for everything. This research was funded by NASA Grant #NNX09AC43G and by the Florida Catastrophic Storm Risk Management Center of the Florida State University College of Business.

TABLE OF CONTENTS

List of Tables ...... vii List of Figures ...... viii Abstract ...... xv

1. INTRODUCTION ...... 1 1.1 Datasets ...... 2 1.2 Intensity Forecast Models ...... 3 1.2.1 Climatology and Persistence (CLIPER) Models ...... 3 1.2.2 Dynamical Models ...... 4 1.2.3 Statistical-synoptic and Statistical-dynamical Models ...... 6 1.3 Eyewall Contraction and ERC Theory ...... 10 1.4 Previous TC Intensity Forecasting Studies ...... 12 1.4.1 Rapid Intensity Index ...... 12 1.4.2 Annular Hurricanes ...... 14 1.4.3 Logistic Growth Equation Model (LGEM) ...... 15 1.4.4 Secondary Eyewall Formation Probability ...... 16 1.4.5 Inner-core Studies ...... 17 1.5 Objectives ...... 18

2. DATA ...... 25 2.1 Vortex Data Messages ...... 25 2.2 NHC ATCF Archives ...... 28 2.3 Manual Corrections to ATCF Data ...... 29

3. VORTEX DATA MESSAGE CLIMATOLOGY ...... 32 3.1 Development ...... 32 3.2 Distribution of VDM Parameters ...... 34 3.2.1 Distribution of VDM Reports ...... 34 3.2.2 Distribution of Variables Reported in VDMs ...... 36

4. EYE STRUCTURE FORECAST TOOL ...... 46 4.1 Development ...... 46 4.2 Application ...... 47 4.2.1 Pattern of Climatological Intensity Change ...... 47 4.2.2 Relation to Sawyer-Eliassen Nonlinear Balance ...... 51 4.3 Hindcasting Results ...... 52

5. STATISTICAL REGRESSION FORECAST MODEL (ASPIRE) ...... 60 5.1 Development of Database for Regression ...... 60 5.2 Formulation of Forecast Equations ...... 62 5.2.1 Overview of Stepwise Multiple Regression ...... 62 5.2.2 Forecast Equation Sets ...... 63

5.3 Predictor Variables ...... 65 5.4 Interpretation of Equations ...... 68

6. ASPIRE RESULTS ...... 86 6.1 Testing of Developmental Equations on Independent Datasets .... 87 6.2 Improvement through the Use of Intensity Bins ...... 89 6.3 Comparison to SHIPS Benchmark ...... 90 6.3.1 ASPIRE Performance Stratified by Intensity ...... 90 6.3.2 ASPIRE Performance Stratified by Geography ...... 94 6.4 Implications ...... 97

7. CASE STUDIES ...... 113 7.1 Well-Hindcast Case: Hurricane Ivan (2004) ...... 114 7.1.1 Storm History ...... 114 7.1.2 Performance and Analysis of ASPIRE Hindcasts ...... 115 7.2 Poorly-Hindcast Case: Hurricane Katrina (2005) ...... 116 7.2.1 Storm History ...... 116 7.2.2 Performance and Analysis of ASPIRE Hindcasts ...... 117

8. CONCLUSIONS AND FUTURE WORK ...... 126

REFERENCES ...... 129

BIOGRAPHICAL SKETCH ...... 134

LIST OF TABLES

1.1: 2003 SHIPS model predictors from DeMaria et al. (2005) ...... 24

2.1: Explanation of Vortex Data Message along with its field location in the ATCF f-deck archives...... 30

2.2: List of manual changes made to Vortex Messages in ATCF f-deck archives. For storms with more than two reported eyewalls, only the first two are provided below. For eye shape data, 1=Circular; 2=Concentric; 3=Elliptical...... 30

3.1: Summary of differences between the VDM climatology presented in this study and that of Piech (2007)...... 45

4.1: Summary of the types of TC intensity forecast guidance...... 59

5.1: Summary of types of regression equation sets developed in the ASPIRE technique...... 83

5.2: Table of predictors chosen for stepwise regression (NSNC, NS, and TOTAL). Before regression is performed, all predictor distributions were examined for normality and transformed using natural logarithms or exponentials as necessary. Italicized predictor names denote variables which were transformed to achieve approximate normality. The number of times the predictors were selected during the NSNC, NS, and TOTAL methods using the step indicated by the stopping rules is also listed, with a maximum possible of 133 times selected (19 intensity bins by 7 forecast times)...... 83

5.3: Julian day/Calendar day equivalent...... 85

7.1: Number of VDMs by forecast hour for Hurricanes Ivan and Katrina along with the average number of VDMs per TC in the ASPIRE database from 1991-2008...... 125

vii

LIST OF FIGURES

1.1: NHC official forecast annual average track errors for 1989-2008 with least-squares trendlines superimposed, courtesy of NHC (http://www.nhc.noaa.gov/verification/verify5.shtml)...... 20

1.2: NHC official forecast annual average intensity errors for 1990-2008 with least-squares trendlines superimposed, courtesy of NHC (http://www.nhc.noaa.gov/verification/verify5.shtml)...... 20

1.3: 2007 Atlantic basin hurricane season intensity model forecast skill. Higher values denote greater skill. Note the dominance of statistical models over dynamical models. (Franklin 2008) ...... 21

1.4: Same as in Figure 1.3, except for the 2008 Atlantic basin hurricane season. (Franklin 2009)...... 21

1.5: Schematic of the primary and secondary circulations (Salby 1996)...... 22

1.6: Cross-section through a tropical cyclone core, depicting the secondary circulation (Palmen and Newton 1969). The left-hand side shows pressure (solid) and temperature (dashed) while the right-hand side shows temperature deviations from a standard atmosphere (dashed-dotted)...... 22

1.7: Schematic of a secondary circulation induced by a heat source in a balanced vortex (Elsberry 1995)...... 23

1.8: Graphical representation of the secondary circulation of a tropical cyclone with concentric eyewalls (Willoughby 1988). Note the area of subsidence between the primary and secondary eyewalls as the outer eyewall intercepts some of the inflow and prevents it from reaching the primary eyewall...... 23

3.1: Frequency distribution of VDMs in the Atlantic basin for 1991-2008. Stronger storms are located on the left side of this diagram...... 38

3.2: Frequency distribution of VDMs in the Atlantic basin for 1989-2005 (Piech 2007)...... 38

3.3: Frequency distribution for VDMs in the Atlantic basin for 1991-2008. Abscissa is maximum sustained surface wind speed. Stronger storms are located on the right...... 39

3.4: Same as in Figure 3.3, but with frequency determined by wind speed 12 h later...... 39

viii

3.5: Distribution of temperature inside the eye. Blue curve superimposed on the frequency plot shows the best fit of Gaussian distribution to the data. Middle schematic plot shows the median, 1st and 3rd quartiles, and outlier data points. Bottom plot shows 95% confidence intervals for the mean and median values. Right-hand box gives basic statistical information for the variable. All plots such as the one above are directly from Minitab. .... 40

3.6: Distribution of temperature outside the eye...... 40

3.7: Distribution of dewpoint inside the eye...... 41

3.8: The highly non-Gaussian distribution of dewpoint depression (temperature minus dewpoint) inside the eye...... 41

3.9: Distribution of initial MSLP...... 42

3.10: Distribution of initial maximum wind speed...... 42

3.11: Distribution of eye type, where 1=Circular, 2=Concentric, and 3=Elliptical...... 43

3.12: Distribution of eye diameter. For TCs with multiple eyewalls, only the inner eyewall is included in this diagram...... 43

3.13: Distribution of initial TC latitude multiplied by 100. Thus, latitude is shown in this figure with the decimal removed such that 2000 indicates a latitude of 20.00°N...... 44

3.14: Distribution of initial TC longitude multiplied by 100. Thus, longitude is shown with the decimal removed such that 8000 indicates a longitude of 80.00°W...... 44

4.1: Average hourly intensity change (kt) at 12 h for the first eyewall of TCs based on the advisory winds associated with a VDM. Image smoothed twice using a nine-point smoother...... 54

4.2: Standard error (kt) associated with Figure 4.1. Image smoothed twice using a nine-point smoother...... 54

4.3: Same as Figure 4.1, but with unsmoothed standard error contours (kt) overlaid...... 55

4.4: Same as Figure 4.1, but for the 24-h time period...... 55 4.5: Same as Figure 4.2, but at 24 h...... 56

4.6: Same as Figure 4.1, but at 36 h...... 56

4.7: Same as Figure 4.2, but at 36 h...... 57

4.8: Same as Figure 4.1, but at 48 h...... 57

4.9: Same as Figure 4.2, but at 48 h...... 58

4.10: Comparison of RMSE of climatological eye structure forecast tool (blue), SHIPS (red), and persistence (green)...... 58

5.1: Distribution of SHIPS model forecasts at 12 h used in TOTAL forecasts for the ASPIRE technique...... 71

5.2: Distribution of climatological eye structure tool forecasts at 12 h used in TOTAL and NS forecasts for the ASPIRE technique...... 71

5.3: Distribution of initial wind for 12-h forecasts...... 72

5.4: Distribution of MSLP for 12-h forecasts...... 72

5.5: Distribution of temperature inside the eye for 12-h forecasts...... 73

5.6: Distribution of change in temperature inside the eye for 12-h forecasts...... 73

5.7: Distribution of eye area multiplied by the temperature inside the eye for 12-h forecasts. Note the highly non-Gaussian distribution...... 74

5.8: Same as Figure 5.7, but transformed by raising to the power 0.15...... 74

5.9: Distribution of eye area multiplied by (1020-MSLP) for 12-h forecasts. .... 75

5.10: Same as Figure 5.9, but transformed by raising to the power 0.15...... 75

5.11: Distribution of the initial wind speed squared divided by the radius of the eye for 12-h forecasts...... 76

5.12: Same as Figure 5.11, but transformed by taking the natural logarithm...... 76

5.13: Predictor matrix for NSNC forecasts at 12 h using the ASPIRE technique while applying the stopping rules described in Section 5.2 rather than using the final step of the regression. Predictors are listed from bottom to top according to frequency of use. Dots indicate the predictors selected for a given intensity bin...... 77

5.14: Same as Figure 5.13, but for NS forecasts at 12 h using the ASPIRE technique...... 78

5.15: Same as Figure 5.13, but for TOTAL forecasts at 12 h using the ASPIRE technique...... 79

5.16: Same as Figure 5.13, but for NSNC forecasts at 36 h using the ASPIRE technique...... 80

5.17: Same as Figure 5.16, but for NS forecasts at 36 h using the ASPIRE technique...... 81

5.18: Same as Figure 5.16, but for TOTAL forecasts at 36 h using the ASPIRE technique...... 82

6.1: RMSE for TCs from 1991-2008 using the full NSNC regression equation applied to all initial intensities. Results are valid as a dependent verification. Note that the NSNC forecasts (blue) outperform SHIPS (red) and persistence (green) at all forecast lead times...... 98

6.2: Independent NSNC (blue) and SHIPS (red) forecast error results in terms of RMSE at 12 h (left) and 36 h (right) for the period 1997-2002. The ASPIRE technique outperforms SHIPS at 12 h but not at 36 h. For comparison, RMSE for the entire period 1991-2008 are provided for both the NSNC method (green) and SHIPS (purple)...... 98

6.3: Same as Figure 6.2, but for the independent period from 2005-2008. Results are similar to those seen for 1997-2002...... 99

6.4: Comparison of R2pred of SHIPS guidance from 1991-2008 applied to all intensities (red) and SHIPS guidance from 1991-2008 applied to Category 1 TCs only (blue)...... 99

6.5: 36-h dependent forecast verification comparing the RMSE resulting from the binned NSNC forecast equations (blue) to SHIPS (red), the full NSNC regression equation (green), and persistence (purple) for three separate initial intensities. Note that the binned equations outperform the full equation for every intensity bin, with a nearly 5-kt improvement for an initial intensity of 125 kt...... 100

6.6: Out-of-sample performance (R2pred) of the NSNC method in the ASPIRE model. Regression using 20-kt bins (blue) and the full regression (green) outperform SHIPS (red) at all initial intensities, with the binning yielding higher potential predictive ability than the full regression...... 100

6.7: Same as Figure 6.6, but valid at 24 h. Note the decrease in predictive ability near 105 kt and 135 kt which is likely associated with the onset of concentric eyewall cycles...... 101

6.8: Same as Figure 6.6, but valid at 36 h. Overall performance decreases substantially for all guidance, with SHIPS surpassing the ASPIRE technique at 85 kt. The notable decrease in predictive ability is likely associated with concentric eyewall cycles...... 101

6.9: Same as Figure 6.6, but valid at 48 h. Performance increases compared to 36 h shown in Figure 6.8 and may be associated with the completion of an ERC. The binned NSNC regressions through the ASPIRE technique generally outperform the full regression and SHIPS...... 102

6.10: Mean MSLP, mean eye diameter, and frequency of concentric and elliptical eyewall occurrence for the Gulf of Mexico, 1989-2005. Concentric and elliptical eyewall occurrence show a relative peak near 24 h after eye formation, and an increase in the standard deviation of the mean MSLP is seen immediately following these peaks. (Piech 2007) ...... 103

6.11: Same as Figure 6.10 but for the Caribbean Sea. A defined peak in elliptical eyewall frequency is shown at 24 h after eye formation followed by a slight increase in the standard deviation of the mean MSLP. (Piech 2007) ...... 104

6.12: Shaded plot of R2pred for the NSNC method of the ASPIRE technique using the specified stopping rules. Note the three distinct regions of decreased potential predictive ability at 70 kt, 105 kt, and 140 kt. No smoothing is applied to this image...... 105

6.13: Same as Figure 6.12 but for the NS method of the ASPIRE technique. The same general pattern seen in the NSNC plot can be seen here, with the primary difference a slightly increased predictability at 70 kt, possibly due to the inclusion of climatological eye structure tool predictors and the climatological tendency of TCs to self-organize once developing an eye. .. 106

6.14: Same as Figure 6.12 but for the TOTAL method of the ASPIRE technique. Improvement in potential predictive ability due to the inclusion of environmental predictors in the SHIPS model can be seen, particularly for TCs of Category 2 intensity...... 107

6.15: Same as Figure 6.12 but for SHIPS model guidance. Note the dramatic decrease in predictive ability compared to the ASPIRE technique. Two regions of increased performance occur from 80-100 kt and from 115-130 kt...... 108

xii

6.16: Scatter plot of binned NSNC forecast error with respect to geography (1055 VDM data points)...... 109

6.17: Same as Figure 6.16, but for SHIPS guidance at 12 h (1055 VDM data points)...... 109

6.18: Same as Figure 6.16, but for binned NSNC forecasts at 24 h (947 VDM data points)...... 110

6.19: Same as Figure 6.18, but for SHIPS guidance at 24 h (947 VDM data points)...... 110

6.20: Same as Figure 6.18, but for binned NSNC forecasts at 36 h (847 VDM data points)...... 111

6.21: Same as Figure 6.20, but for SHIPS guidance at 36 h (847 VDM data points)...... 111

6.22: Same as Figure 6.20, but for binned NSNC forecasts at 48 h (762 VDM data points)...... 112

6.23: Same as Figure 6.22, but for SHIPS guidance at 48 h (762 VDM data points)...... 112

7.1: NHC best-track positions for Hurricane Ivan, 2-24 September 2004, courtesy of the National Hurricane Center (http://www.nhc.noaa.gov/2004atlan.shtml)...... 121

7.2: RMSE (kt) for Hurricane Ivan (2004) comparing NSNC (blue), NHC OFCL (red), and SHIPS (green)...... 121

7.3: 500 hPa relative humidity (%; shaded) and MSLP (hPa; contour) for Hurricane Ivan (11.0°N, 52.5°W) at 1200 UTC 06 September 2004 from the GFS operational analysis...... 122

7.4: Same as Figure 7.3, but for 0000 UTC 15 September 2004...... 122

7.5: NHC best-track positions for Hurricane Katrina, 23-31 August 2005, courtesy of the National Hurricane Center (http://www.nhc.noaa.gov/2005atlan.shtml)...... 123

7.6: RMSE (kt) for Hurricane Katrina (2005) comparing NSNC (blue), NHC OFCL (red), and SHIPS (green)...... 123

xiii

7.7: 600 hPa relative humidity (%; shaded) and MSLP (hPa; contour) for Hurricane Katrina at 1200 UTC 28 August 2005 from the GFS operational analysis...... 124

7.8: 850 hPa-200 hPa vertical wind shear (kt; shaded) and MSLP (hPa; contour) for Hurricane Katrina at 0600 UTC 29 August 2005 from the GFS operational analysis...... 124

xiv

ABSTRACT

While tropical cyclone (TC) track forecasting has improved noticeably over the last twenty years, intensity forecasting has remained somewhat of an enigma to forecasters. Despite increased computing capabilities and more sophisticated dynamical models, statistical models, such as the Statistical Hurricane Intensity Prediction Scheme (SHIPS), still often outperform their dynamical counterparts. There has been a great deal of research focused on improving intensity forecasts of TCs during the past two decades. However, the overwhelming majority of this statistical research has focused on the impacts of the storm environment rather than the effects of the TC structure itself or inner-core measurements. More focus has been placed recently on using some of these measurements from within the TC core, such as the structure of the storm and reconnaissance flight data. Still, much work remains to be done to fully utilize the available data from the inner core of TCs. To this end, flight data from Hurricane Hunter reconnaissance missions will be exploited to the fullest extent in this study. This research seeks to develop a new statistical-climatological forecasting scheme to improve short-term intensity forecasts for well-developed TCs in the Atlantic basin. Well- developed TCs are classified in this study as having a defined eye. Using Vortex Data Messages (VDMs) gathered from the aforementioned reconnaissance flights and stored in the National Hurricane Center’s (NHC) Automated Tropical Cyclone Forecast (ATCF) archives, a VDM climatology from 1991-2008 is developed. These VDMs are collected from dropsondes and include various structural and thermodynamic parameters. This climatology includes storm- scale thermodynamic parameters to aid in TC prediction. A new climatological forecast tool is produced which gives the expected rate of intensity change for 12-48 hour periods based on an initial eye diameter and wind speed. This climatological tool also provides insight into the dynamics involved in hurricane intensity change. Other implications based on the climatological forecast tool, such as the ability to produce probabilistic intensity range forecasts, are also discussed. Finally, stepwise multiple linear regression is performed to create a SHIPS-style intensity forecast model (Atlantic-based Statistical Prediction of Hurricane Intensity using Recon, or ASPIRE). Examination of the regression equations and the change in predictors selected with

xv varying intensity and forecast length offers additional insight into the science of TC intensity forecasting. Cross-validation results show that the ASPIRE technique outperforms SHIPS at nearly every forecast time and initial intensity, indicating that a new benchmark for TC intensity forecasting may have been attained. Two dependent case studies of Hurricane Ivan and Hurricane Katrina are presented for further analysis of the ASPIRE scheme. Further work involving the utilization of satellite data to create proxy VDMs may lead to an expanded climatological database of inner-core data for TCs in the Atlantic basin as well as the capability to create similar regression schemes in the East Pacific and West Pacific basins.

xvi

CHAPTER 1

INTRODUCTION

Until the Atlantic hurricane seasons of 2007 to the present, tropical cyclone (TC) activity in the Atlantic basin had been relatively high over the last two decades. Rappaport et al. (2009) make note of the fact that this activity included the busiest season ever recorded (2005, with 28 TCs); one of the deadliest TCs (Mitch 1998); as well as the deadliest TC to strike the U.S. in nearly a century and the most costly TC in U.S. history (Katrina 2005). Many of these problems were exacerbated by rather extreme forecast challenges in which available guidance as well as operational forecasts fell short of the accuracy desired. Figure 1.1 shows the annual average track errors for the official forecasts (OFCL) from the National Hurricane Center (NHC) with least-squares trendlines superimposed. It is apparent that the average error has been at least halved for almost every forecast length, with 96-120 h forecasts being the only exceptions. These improvements are substantial, with these improvements in track forecasts due largely to advances in Numerical Weather Prediction (NWP) guidance (Rappaport et al. 2009). Figure 1.2 offers a sobering picture of the state of TC intensity forecasting, however. NHC annual average intensity forecast errors are shown for the period 1990-2008, again with least-squares trendlines superimposed. Given that NHC OFCL forecasts are issued to the nearest 5 knots (kt), it is difficult to discern a statistically significant improvement in the average error of NHC OFCL intensity forecasts. This relatively small change in forecast skill is startling, considering that much prior research has indicated that intensity forecasts should be closely tied to track forecasts. The apparent resultant dichotomy seems to indicate that the model improvements that have produced more accurate track forecasts may not translate to better intensity forecasts. This research seeks to use inner-core measurements of TCs rather than large- scale environmental factors to improve the state of TC intensity forecasting with an underlying goal of helping to save lives and reduce the cost of damages incurred from TCs. A review of the datasets and types of models currently used in TC intensity forecasting is presented first, followed by an examination of the prior research regarding forecasting TC intensity change.

1.1 Datasets

The datasets available for hurricane intensity research are in a state of constant development and improvement. The National Hurricane Center (NHC) has analyzed and archived data for several decades. One of the very first compilations was the TC data tape by Jarvinen and Caso (1978, hereafter referred to as JC78). This tape contained the dates, tracks, maximum sustained wind speed, and minimum sea level pressure (MSLP) of TCs in the Atlantic basin from 1886-1977. This collection of data came to be known as the hurricane dataset, or HURDAT (JC78). HURDAT was compiled using simple ship and land reports of TCs for earlier years in the period. In recent years, newer types of information available, including reconnaissance (hereafter, recon) and radar information, were utilized to improve HURDAT. Jarvinen et al. (1984) updated HURDAT to include crucial visible and infrared satellite data. Satellites have greatly improved detection of TCs as they are able to provide information over remote areas of ocean basins that would not have been sampled in the past. A significant addition to the available databases was the NHC best track (BT) dataset by Neumann et al. (1993). This database provides additional information beyond what is contained in HURDAT by providing statistical summaries every six hours along with the storm track data for the Atlantic basin from 1871-1992. From 1964-1992, the primary source of the data was annual summary reports of TC activity created by NHC/Tropical Prediction Center (NHC/TPC); prior to 1964, much of the data relies on information from the U.S. Weather Bureau. Additional information was added to the BT to develop the extended best track dataset (EBT) (Pennington et al. 2000; Demuth et al. 2006) which contains storm size parameters such as the radius of the outermost closed isobar and the radius of 34-, 50-, and 64-kt winds. More recently, Piech (2007) created a Vortex Data Message (VDM) database which contains information on the inner core of TCs in the Atlantic basin gathered from VDMs for the period 1989-2005. This dataset included information on temperatures inside and just outside the eye, dewpoint within the eye, MSLP, and storm location, along with eyewall characteristics. Piech (2007) manually gathered the data from the VDMs and documented the characteristics of this VDM climatology in several ways, most noticeably with extensive analyses of the frequency distributions of the various parameters. Soon after the work by Piech (2007), NHC’s Technical Support Branch updated the Automated Tropical Cyclone Forecast (ATCF) system to archive the

VDMs along with various other data and model outputs. More information on Vortex Data Messages, the NHC ATCF archives, and the climatology by Piech (2007) is provided in Chapters 2 and 3. Many intensity forecast models currently use the above described datasets, and they can be broadly divided into three groups—climatological/persistence, dynamical, and statistical. The following section discusses and compares some of these models.

1.2 Intensity Forecast Models

1.2.1 Climatology and Persistence (CLIPER) Models As indicated by their name, these models rely solely on input of climatological variables or simple persistence to produce forecasts. The first intensity model created of this type is the Statistical Hurricane Intensity Forecast, otherwise known as SHIFOR (Jarvinen and Neumann 1979, hereafter JN79). SHIFOR was developed using statistical regression techniques (JN79). As noted in Piech (2007), the predictors used in SHIFOR were derived from the Climatology and Persistence (CLIPER) track model developed by Neumann (1972), which uses climatology and persistence predictors to statistically predict TC motion. The data used in SHIFOR was gathered from HURDAT (JC78). Together, the CLIPER and SHIFOR models have traditionally provided the verification benchmarks for TC track forecasting and intensity forecasting, respectively. The intensity change prediction equations were developed through a multivariate regression analysis technique. The values for maximum surface wind speed change from 12 h through 72 h at 12-h intervals are the predictands, while the predictors included initial latitude and longitude, the initial maximum wind speed, and the change in maximum wind speed over the previous 12 h (JN79). DeMaria and Kaplan (1999) show that, for very short-range intensity forecasts (12 to 24 h), the SHIFOR model provides skill comparable to that which CLIPER does for track. However, beyond 24 h, the skillfulness of intensity forecasts from SHIFOR drops quickly compared to the skill of track forecasts from CLIPER. This result was to be expected, as JN79 concluded that climatology and persistence can only predict change in hurricane intensity with any reasonable skill out to 12 h. Still, SHIFOR is the benchmark against which other operational intensity forecast models are compared (DeMaria and Kaplan 1994a and 1999; DeMaria et al. 2005; Bender et al. 2007; Rappaport et al. 2009). For this reason, Knaff et al. (2003) undertook the task of extending

forecasts for both CLIPER and SHIFOR from 3 days to 5 days. Results showed that the error and bias characteristics of the 5-day forecasts were similar to those of the original 3-day forecasts and that the errors tended to level off beyond 3 days. The updated SHIFOR model also produced intensity change forecasts that deviated farther from their initial intensities than their 3- day counterparts. The empirical inland decay model created by Kaplan and DeMaria (1995, 2001) along with DeMaria et al. (2006) has since been applied to the SHIFOR model for cases that pass over land, and the version of SHIFOR used today as the intensity verification benchmark is the Decay-SHIFOR model. Bender et al. (2007) and Rappaport et al. (2009) discuss some more sophisticated dynamical models such as the Geophysical Fluid Dynamics Laboratory (GFDL) and Hurricane Weather Research and Forecast (HWRF) models and offer comparisons of GFDL to Decay-SHIFOR for a measure of its relative skill. An overview of these dynamical models is presented next.

1.2.2 Dynamical Models Dynamical models are fundamentally different from CLIPER-style models in that they rely on the actual physical and dynamical equations of motion which govern our atmosphere rather than simply using climatological and persistence variables as predictors for future intensity change. Several dynamical models are used operationally, including the Global Forecast System (GFS), European Centre for Medium-Range Weather Forecasts (ECMWF), U.K. Met Office (UKMET), and the Navy Operational Global Atmospheric Prediction System (NOGAPS). This section will focus on the two models mentioned in the previous section which were developed specifically for prediction of TC intensity, the GFDL and HWRF models. Bender et al. (2007) provide a detailed examination of the history of the development of the GFDL, beginning with its creation as a sophisticated research model and continuing through its transition to operational status in 1995. Specific details about the original version of the operational version from 1995, including the governing equations, grid configuration, model physics, convective schemes, and other pertinent details can be found in Kurihara et al. (1998). Bender et al. (2007) explain the various improvements and upgrades that have been applied to the GFDL model since 1995. Some of the most important additions include a transition from an uncoupled, purely atmospheric model to a coupled atmosphere-ocean model in 2001, increases in model grid resolution in both 2002 and 2005, and critical physics upgrades in 2003 and 2006.

Bender et al. (2007) show significant increases in model performance in both 2003 and 2006 due to the upgraded physics. Since 2006, the GFDL model has consistently been the best track model performer of all available dynamical guidance for the Atlantic basin (Rappaport et al. 2009). The GFDL also saw a steady reduction in intensity forecast error from 2002-2006, such that it is now skillful compared to Decay-SHIFOR. The success of the track forecasts output from GFDL along with the recent increase in skill for its intensity forecasts led the developers of HWRF to utilize most of the physics packages from the 2006 version of GFDL (Bender et al. 2007). The HWRF model became operational at NCEP for the 2007 Atlantic hurricane season. The HWRF is a coupled air-sea- land prediction model which utilizes a movable nested grid with highly advanced physics based on the GFDL for high resolution. Most importantly, like the GFDL model, HWRF is a non- hydrostatic mesoscale model, which yielded high expectations that it would provide the desired boost in accuracy desired by NHC (Rappaport et al. 2009). An in-depth analysis of the performance of HWRF has not been published at this time, but an examination of Figures 1.3 and 1.4 (intensity model error for the 2007 and 2008 Atlantic hurricane seasons) show that its intensity forecasts have not yet surpassed those of the GFDL, although model development continues. Global forecast models generally do not produce accurate intensity forecasts for TCs. Much of the reason for the lack of improvement in intensity forecasting for the global dynamical models such as the GFS can be attributed to a lack of resolution (Rappaport et al. 2009). However, the GFDL and HWRF models do have the necessary resolution to more accurately resolve the structure and physics associated with TCs. Still, both of these models have lagged behind the accuracy of intensity forecasts based on statistical models such as SHIPS/Decay- SHIPS (discussed in Section 1.2.3), and dynamical intensity prediction overall has not yet surpassed that of statistical prediction. This marked lack of improvement in dynamical intensity forecasting has led NHC to declare its top priority to be to produce more accurate guidance for TC intensity change. It is NHC’s belief that continued gains in operational NWP guidance will be the impetus for more accurate dynamical intensity guidance in the future (Rappaport et al. 2009).

1.2.3 Statistical-synoptic and Statistical-dynamical Models The third broad set of TC intensity prediction models fall under the category of statistical models. These models do not have any physical or dynamical basis in the governing equations that describe atmospheric motion. Statistical models are generally considered to be a separate branch of model from the CLIPER-type models, even though the CLIPER style also involves statistical methods. The distinguishing characteristic that sets statistical models apart is that they use additional synoptic-scale information detailing the TC environment as predictors, allowing these models to move beyond a statistical prediction method based solely on climatological and persistence inputs. Statistical-synoptic models are so named because the predictors are CLIPER-type inputs along with synoptic predictors. The synoptic variables come only from the initial-state synoptic field, meaning that there is no dynamic change of the synoptic variables with time. Obviously, not allowing the large-scale environment to change with time is a limiting factor for any model as the environmental conditions can and often do change quite rapidly. One of the first attempts to assimilate synoptic information into a statistical model was that of Merrill (1988). Predictors in this model included the HURDAT dataset (Jarvinen et al. 1984), monthly mean sea surface temperatures (SST) (Reynolds 1982), and the 200 hPa tangential flow of the environment. Despite including effects of terrain and coastlines, this model did not provide any significant improvement over SHIFOR. Merrill (1988) noted that one method that would likely improve intensity forecasts of this sort would be to identify and quantify the roles of the environmental factors along with internal convection of the TC, although he remained pessimistic that the use of synoptic variables would add significant value to forecasts. Still, Merrill (1988) concluded that TCs are driven by internal characteristics and structure but regulated overall by their oceanic and atmospheric surroundings and that weak vertical shear of the horizontal wind is necessary for intensifying TCs. Elsberry et al. (1988) created an objective technique for TC intensity forecasting in the Western North Pacific basin. Their conclusions were in direct contrast to Merrill (1988) as they found that the utilization of environmental parameters added value to TC intensity forecasts beyond that of SHIFOR provided that the data sample was stratified by initial maximum wind speed. Stratification by wind speed allows for creation of separate regression equations for different initial wind speeds.

DeMaria and Kaplan (1994a, hereafter DK94) created a statistical-synoptic model for TCs in the Atlantic basin, the Statistical Hurricane Intensity Prediction Scheme (SHIPS). This model used climatology, persistence, and synoptic predictors, along with SST data in a multiple linear regression scheme to generate TC intensity forecasts. They noted that the use of multiple linear regression was justifiable given that the dependent predictand, intensity change, showed an approximate Gaussian distribution with zero mean. The developmental data sample included all 38 storms from 1989-1992 along with 11 cases from 1982-1988. The synoptic predictors added included the eddy flux convergence (EFC) of angular momentum at 200hPa, vertical shear of the horizontal wind, and the difference between the initial maximum intensity and an estimate of its maximum potential intensity (MPI) (Emanuel 1988). The synoptic data was gathered from the initial analysis of the National Centers for Environmental Prediction (NCEP) medium-range weather forecast model (known then as the Aviation model, now known as the previously- mentioned GFS). The SHIPS model was developed solely for TCs over water, since the characteristics of overland hurricanes are different from those over water (Kaplan and DeMaria 1995, hereafter KD95). DK94 concluded that SHIPS showed a 10%-15% improvement over SHIFOR and could explain approximately 50% of the observed variability. Still, obvious limitations of the initial version of SHIPS were cited by DK94, such as the lack of change in environmental parameters with time, the inability to create forecasts for TCs crossing land, and inability to account for storm-scale processes such as concentric eyewalls (Willoughby et al. 1982; Willoughby 1990). While large-scale predictors will likely never be able to adequately include these storm-scale effects (DK94), recon information from VDMs can in fact do so. DK94 also suggested potential improvement by including real-time SST analyses rather than the climatological SST analyses. In 1996, the SHIPS model became operationally available to NHC forecasters (DeMaria and Kaplan 1999). DeMaria and Kaplan (1999, hereafter DK99) implemented upgrades to the original DK94 SHIPS model. The most important of these upgrades was the transition of SHIPS from a statistical-synoptic model to a statistical-dynamical model. This seemingly subtle difference was actually a crucial factor because the change allowed incorporation of initial-state synoptic predictors as well as predictors from forecast fields gleaned from dynamical models, implementing the suggested change by DK94 for evolution of environmental parameters with forecast time. Other changes included the use of weekly SST analyses, replacing the old

7 climatological SST analyses, as well as a larger developmental data sample. The size of the developmental data sample increases every year, as the storms from the most recent TC season are added to the developmental database and then used to create new intensity forecast equations for the upcoming TC season. Therefore, SHIPS model equations are different each year. One other change was the addition of a Laplacian filter, used to remove the storm circulation from the initial Aviation model analyses. The DK99 version of SHIPS was first implemented in 1997 for both the Atlantic and East Pacific basins. Results of forecasts from the new version of SHIPS showed that the forecasts had statistically significant skill compared to both climatology and persistence, particularly from the 36 h to 72 h time range. DK99 note that this newer version of SHIPS could still be further improved by including satellite information (Fitzpatrick 1997) and aircraft recon data. Further changes made to the SHIPS model occurred after 1999 as documented by DeMaria et al. (2005). In 2000, the effects of TC decay over land were implemented through the addition of an empirical inland decay model (KD95). This addition is applied through a post- processing technique. The SHIPS model is run, ignoring any predicted storm tracks that cross land. The empirical decay model is then applied to the portions of the tracks that were forecast to cross land. This updated version of SHIPS is called Decay-SHIPS, or D-SHIPS (DeMaria et al. 2005). For instances where the TC does not cross land during the intensity forecast period, D- SHIPS produces forecasts exactly equivalent to those of SHIPS. In 1999, NHC OFCL track forecasts replaced model forecasts from the Limited Area Sine Transform Barotropic (LBAR) model. This conversion is possible through the use of the previous 6-h OFCL track forecast, corrected to match the current storm position. Also, in 2001, SHIPS was modified to include intensity forecasts extending through 120 h. Other significant improvements included the utilization of GFS 5-day forecasts (DeMaria et al. 2005). Prior to 2001, SHIPS used a simple 10-layer dry-adiabatic model in which the TC circulation was filtered from its environment. This adiabatic model eliminated the difficulty of removing the storm circulation from the model forecast but only produced forecasts out to 48 h. Thus, when SHIPS forecasts were extended to 5 days, model fields for a longer period were required. In order to attempt to maintain continuity throughout the developmental sample, operational analyses from 1989-2000 were replaced with NCEP-National Center for Atmospheric Research (NCAR)

8 reanalyses in 2003 (Kalnay et al. 1996; Kistler et al. 2001), providing a more complete and consistent dataset. Results documented by DeMaria et al. (2005) were promising. Most importantly, for the period 1997-2003, SHIPS demonstrated statistically significant skill through 72 h. Unfortunately, that skill did not extend to 4- or 5-day forecasts. Another important finding was that D-SHIPS reduced intensity forecast errors by 10%-15% (relative to SHIPS) from 12 h to 72 h and that the improvements were statistically significant through 72 h. Beyond 72 h, the effects of D-SHIPS were neutral compared to SHIPS. DeMaria et al. (2006) documented improvements to the empirical decay model implemented in D-SHIPS that account for the fact that the decay rate is proportional to the portion of the TC that is actually over land. This method minimizes bias in the forecasts and reduced the intensity error by approximately 8% relative to the original D-SHIPS model for the period 2001-2004 for storms within 500 km of land. Another notable upgrade to the SHIPS model was the use of high-resolution SST data from NCEP 1/2°x1/2° daily global analysis (Berg et al. 2004) in which they found that intensity forecast error and bias were both reduced. Rather than give a detailed list of the year-to-year changes in the predictors used in SHIPS, Table 1.1 lists the most recent predictors used in SHIPS, as documented by DeMaria et al. (2005). Note that oceanic heat content (OHC) and brightness temperature information from Geostationary Operational Environmental Satellite (GOES) channel 4 (10.7 µm) imagery are now included (RAMMB/CIRA 2009), but no specific documentation has yet been published detailing changes in other predictors as a result of these additions. For this reason, only predictors listed in DeMaria et al. (2005) are included in Table 1.1. The GOES data is gathered from archives maintained by the Cooperative Institute for Research in the Atmosphere (CIRA), while the OHC data is gathered from European Remote Sensing Satellite-2 (ERS-2) and TOPEX/Poseidon satellite altimetry observations (DeMaria et al. 2005). Despite the promising results shown by the SHIPS model, there are still noticeable limitations such as the lack of ability to predict concentric eyewalls (DK94). These concentric eyewall cycles, often referred to as eyewall replacement cycles (ERC), can often lead to rapid intensity fluctuations within the TC. Before delving into some of the key intensity forecasting studies performed in recent years, a review of the theories associated with eyewall contraction and ERCs is provided in the next section.

1.3 Eyewall Contraction and ERC Theory

To begin a discussion on eyewall contraction, concentric eyewalls, and ERC theory, a review of the Eliassen (1951) model of secondary circulations should first be reviewed and will in large part follow the summary offered in Piech (2007). Beginning with the primary circulation (the cyclonic/anticyclonic circulation in the x-y plane), ascent and latent heat release produce a radial heating profile (Figure 1.5). The radial heating causes gradient wind balance and thermal wind balance to become violated. In order to restore gradient wind and thermal wind balance in the TC, a secondary circulation forms in the r-z plane. The secondary circulation moves radially inwards towards the center of the TC along the surface, upwards along the top of the center of the primary circulation, and then outwards at the top of the TC near the tropopause. This secondary circulation can be modified—compressed vertically and/or horizontally—depending on the magnitudes of the static and inertial stability as well as the baroclinicity (Figure 1.6). Shapiro and Willoughby (1982, hereafter SW82) developed a model based on the Eliassen (1951) model that describes the nature of these forced secondary circulations. First, a point source of heat or momentum is initiated near a tangential wind maximum. This source of heat or momentum causes isobaric heights to fall very quickly just inside the radius of maximum winds (RMW) since the vertical integral of heating is maximized inward of the RMW. Heights outside the RMW fall more slowly, resulting in a tightened height and pressure gradient. The height falls themselves produce peak intensification in the time tendency of the tangential winds. Since this peak occurs inside the RMW, the RMW itself is necessarily drawn inward as a response to the heating (SW82). The contraction of the RMW can be directly associated with the contraction of an eyewalls in a TC (SW82). To go into further detail, the warm air at the base of the eyewall rises moist adiabatically to the top of the eyewall, maintaining nearly constant angular momentum (Figure 1.7). As can be seen in Figure 1.7, the air is then either evacuated radially outward or it subsides into the eye. If the air descends into the eye, it warms dry adiabatically, thus strengthening the existing temperature gradient between the eye and eyewall. The presence of an eye in a TC may also have significant implications for TC intensity change since the subsident warming increases the temperature gradient in addition to increasing radial confinement of the heat source as the RMW

contracts. As the temperature in the eye increases, heating continues just inside the RMW due to the heat source, causing surface pressures to fall hydrostatically even faster and causing gradient wind and thermal wind balance to become further violated. The secondary circulation continues to intensify despite the attempt to restore balance, and the eyewall contracts. Recall that the temperature inside the eye is increasing while the temperature outside the eye remains relatively constant. Thus, an even stronger temperature gradient is produced, and a positive feedback process on TC intensification results. The secondary circulation continues to strengthen in an unsuccessful attempt to restore thermal wind balance. Based on the results of SW82, it is hypothesized that utilizing measurements of the difference between the temperature inside and outside the eye as well as the moisture in the eye could help produce more accurate intensity forecasts. While SW82 provided crucial insight into the mechanisms for TC eyewall contraction, it only addressed single eyewalls. Willoughby, Clos, and Shoreibah (1982, hereafter WCS82) tackled the task of describing the process of concentric eyewalls with regards to formation of a concentric eyewall structure and onset of an ERC. WCS82 used a combination of radar, wind, and eyewall data from recon flights to examine the evolution of eyewalls, secondary wind maxima, and concentric eyewalls, all viewed through the convective ring model of SW82. Figure 1.8 provides a schematic of the secondary circulations associated with concentric eyewalls. If a local maximum of the tangential wind can form outside the original, inner eyewall, a second convective ring sometimes forms as a result. The process of the formation of a secondary eyewall is still not fully understood (Kossin and Sitkowski 2009, hereafter KS09), but KS09 summarize several potential explanations put forth in the literature. Molinari and Vollaro (1989) suggest that interactions with upper-level momentum sources in the environment can trigger this phenomenon. Nong and Emanuel (2003) also argue for forcing from the external environment. Kuo et al. (2004) offer a slightly different idea in that environmental asymmetries may actually cause an axisymmetrization process. Meanwhile, Terwey and Montgomery (2006) provide an opposite viewpoint of secondary eyewall formation and pose the theory that such phenomena can be initiated in a steady, homogeneous environment without the influence of external forcing. Finally, Montgomery and Kallenbach (1997) suggest that outward propagating vortex Rossby waves initiated near the RMW lead to formation of an outer eyewall. The theory put forth by Montgomery and

Kallenbach (1997) and Terwey and Montgomery (2006) emphasize impacts of internal dynamics of TCs rather than the external environment as the driving impetus for secondary eyewall formation. Regardless of the specific mechanism that triggers these events, once the secondary eyewall has formed, it interferes with the advection of angular momentum inward towards the primary eyewall. The secondary eyewall creates a new set of primary and secondary circulations (Figure 1.8). Mechanisms associated with the outer eyewall are much like the inner eyewall, including creating subsidence inside of it. What results is a region of subsidence between the primary and secondary eyewalls, creating a region of enhanced warming, and causing surface pressures to fall farther away from the center of the TC (WCS82). Thus, the temperature and pressure gradients between the center of the TC and the second eyewall relax, while those gradients between the secondary eyewall and the outer edges of the storm strengthen. The net impact on the outer eyewall is similar to the previous description of contraction for the case of a single eyewall. The secondary eyewall begins to contract, while the inner eyewall remains relatively steady-state or slowly weakens. Eventually, the secondary eyewall “chokes off” the inner eyewall, and that primary eyewall vanishes entirely, leaving a single eyewall and thus completing the ERC. Once the inner eyewall has dissipated, the heating within the eye is forced to spread outward over a larger area, and the MSLP increases hydrostatically. The results of these theoretical findings can be confirmed through analysis of TC core data provided by VDMs, as well as through case studies of TCs with concentric eyewalls via use of satellite data. Concentric eyewall formation remains poorly understood (KS09) and poses a serious challenge to NHC forecasters. For this reason, it is important to gain a better understanding of this phenomenon, as it would likely lead to improved intensity forecasts. The next section will go into very brief detail of nine separate key studies that have direct bearing on the research presented here.

1.4 Previous TC Intensity Forecasting Studies

1.4.1 Rapid Intensity Index Recognizing the utility of the SHIPS model, Kaplan and DeMaria (2003, hereafter KD03) attempted to predict rapid intensification (RI) of TCs. Researchers have looked at the effects of

oceanic influences, inner-core processes, as well as environmental interactions when researching TC intensity change. However, most of these studies have focused on only one of these areas rather than on the interactions between all three (KD03), and very few examined RI specifically. KD03 sought to rectify this situation by limiting the scope of their study to RI cases. Using information from the HURDAT database (Jarvinen et al. 1984) and the SHIPS database (DK99), KD03 used a total of five predictors to produce a technique for estimating the probability of RI in TCs. KD03 defined the threshold for RI as the 95th percentile of all 24-h intensity changes for TCs remaining over water for the period 1989-2000, which corresponded to a 30 kt increase in maximum sustained wind for the Atlantic basin. The five predictors included in their RI scheme were the previous 12-h change in maximum sustained wind, 850-200 hPa vertical shear, SST, the difference between current intensity and the theoretical MPI (Emanuel 1988), and the 850-700 hPa relative humidity. These predictors were selected for inclusion if there was a difference between the RI and non-RI cases which was significant at the 99.9% level using a two-sided t test. Results from the dependent sample showed that the probability of RI reaches as high as 41% when all five predictor thresholds are satisfied. In 2001, the technique of KD03 was implemented in real-time at NHC. Results for the 2001 season were similar to the results based on the dependent developmental data. KD03 suggested that using new predictors such as oceanic heat content (OHC) and GOES satellite imagery might improve the RI technique even further. KD03 also stated that inner-core processes appear to be critical to understanding the problem of forecasting RI, which indicates that using recon flight data could yield better TC intensity forecasts. Kaplan et al. (2009, hereafter KDK09) expanded on the work completed by KD03 and developed a revised rapid intensification index (RII) for the Atlantic basin. This new technique uses large-scale predictors from the SHIPS model (DeMaria et al. 2005) previously described to estimate the probability of RI using linear discriminant analysis. The methodology employed is very similar to that described by KD03. The primary differences include the use of weights to account for the extent that an RI threshold is exceeded (KDK09) as well as slight changes in the predictors. All of the predictors used in KD03 are used in the current study with the exception of SST, which is replaced in the new version by OHC. Three new predictors are also added (200 hPa divergence, standard deviation of the 50-200 km GOES infrared cloud-top brightness

temperatures, and the percentage of the area from 50-200 km covered by cloud tops of temperatures -30°C or colder). The three most important predictors for RI in the Atlantic were found to be, in order, the 200 hPa divergence, previous 12-h change in maximum sustained wind, and 850-200 hPa vertical shear. Independent results from the 2006-2007 hurricane seasons showed that the revised RII had skill compared to climatology. When used in a deterministic manner, the skill of the RII method of KDK09 surpassed all other available guidance in terms of probability of detection (POD) of an RI event as well as in terms of the false alarm ratio (FAR) (Wilks 2006). However, KDK09 point out that the relatively low POD and high FAR still show that accurately predicting RI is extremely difficult, especially in the Atlantic basin. KDK09 suggest that incorporating more detailed inner-core information will likely improve the RII skill. This conclusion lends more motivation to the research presented here, as the same concept is applied to forecasting intensity change in the Atlantic basin (but applied to all developed storms rather than specifically examining the problem of RI).

1.4.2 Annular Hurricanes A special type of TC was analyzed by Knaff, Kossin, and DeMaria (2003, hereafter KKD03), and the term “annular hurricane” was coined as a result of their research. Annular hurricanes tend to have a large eye, maintain almost constant intensity, exhibit unusual symmetry, and have virtually uniform equivalent potential temperature (θE) within the eye. KKD03 theorized that these TCs are possible when they move into a favorable hurricane environment characterized by light wind shear and relatively cold 200 hPa temperatures. Annular hurricanes tend to be translating into a region of slightly lower TCs, which may serve as the limiting factor preventing these TCs from further intensification despite the favorable synoptic environment. Asymmetric mixing of eye and eyewall components involving either one or two mesovortices also appears to influence formation of annular hurricanes. These storms present another significant challenge to NHC forecasters as intensity forecasts tend to have larger-than-average errors (KKD03). This problem is due partly to the fact that the majority of Atlantic TCs tend to have a steady or rapid increase in intensity (given favorable conditions for development) as they traverse the Atlantic Ocean. Annular hurricanes typically maintain a constant intensity, even if conditions are favorable for intensification. Two methods were

14 proposed to objectively identify annular hurricanes in a real-time setting—a) using digital brightness temperatures from infrared satellite imagery; b) examining environmental conditions that appear to be necessary for annular hurricane formation (a total of eight conditions, with all eight needing to be satisfied) (KKD03). Building on the work initiated by KKD03, Knaff et al. (2008) formulated a method to objectively identify annular hurricanes in a real-time setting. Data from 1995-2003, encompassing 11 annular hurricanes, is used as the developmental dataset. One caveat noted was that annular hurricanes comprise only ~4% of all Atlantic TCs, so a special two-step algorithm had to be developed in order to achieve this goal. The first step (prescreening the data) involves the elimination of all cases that fail to meet the intensity and environmental characteristics typically associated with annular hurricanes. The second step passes the cases that satisfy step one on to a linear discriminant function which uses five factors to determine the degree to which a specific TC is annular (Knaff et al. 2008). Results showed that the algorithm developed by Knaff et al. (2008) is able to differentiate more “ordinary” TCs from annular hurricanes for TCs with initial intensities of 85 kt or greater. Their algorithm has been operational within the SHIPS model (DeMaria et al. 2005) framework since 2008 (Knaff et al. 2008).

1.4.3 Logistic Growth Equation Model (LGEM) While the SHIPS model has generally been the most accurate operational intensity guidance available to NHC forecasters (DeMaria et al. 2007), intensity forecasting is nonetheless lagging track forecasting in terms of skill. DeMaria (2009) developed a logistic growth equation model in hopes of improving upon the SHIPS model by allowing for nonlinear regression techniques. In this model, the change in maximum sustained surface wind speed is proportional to the sum of only two terms, one growth term and another term which constrains the maximum wind within an upper bound. The growth rate is a linear function of the vertical shear, a convective instability parameter, and the product of the shear and the convective instability. The shear and convective instability are both derived from global model fields. Due to the above assumptions, parameter estimation is reduced to only six constants. When applied to TC intensity prediction, DeMaria (2009) calculated individual values for the six constants through a fitting process involving forecasts for the Atlantic basin for the period 2001-2006, a total of more

than 2400 forecasts. Results indicate that LGEM fits observed intensity changes more accurately than the SHIPS scheme. More importantly, the improved accuracy involves fewer constants, reducing possible spurious variability (DeMaria 2009).

1.4.4 Secondary Eyewall Formation Probability KS09 developed an empirical model which provides the probability of imminent secondary eyewall formation. These secondary eyewall events demonstrate significant changes in both the structure and intensity of TCs. Yet, there is still no formal objective definition of what constitutes the formation of a secondary eyewall (KS09). For their study, KS09 relied on explicit statements from an aircraft VDM, NHC forecast discussions identifying two eyewalls, or subjective assessments of circular symmetry of an outer eyewall as seen in satellite microwave imagery or radar depiction. KS09 required an outer ring of convection clearly separated from the primary eyewall along with a “quasi-circular” organization in the secondary eyewall forming at least 75% of a complete, closed circle. A relatively cloud-free “moat” region between the primary and secondary eyewalls was also a necessary requirement, as such a region indicates increased subsidence and an increase in inertial stability associated with secondary wind maxima (KS09). Independently tested, the model described by KS09 performed with skill when compared to climatology. KS09 found that the environment plays a significant role in secondary eyewall formation. Another important hypothesis proposed by KS09 is that secondary eyewall formation may be a precursor to the evolution of annular hurricanes. Rather than contract closer to the size of the original eyewall, the new outer eyewall reaches a quasi-steady state at a larger radius, slowly choking off the inner eyewall and resulting in a single large eyewall, resulting in an annular hurricane. KS09 anticipate combination of their model with the annular hurricane identification technique of Knaff et al. (2008) in hopes of providing a tool to diagnose upcoming changes in TC structure. While the studies previously described all show promise in being able to help solve the TC intensity forecasting problem, none of them take sufficient advantage of available inner-core observations, focusing on environmental conditions instead. The next three studies have attempted to incorporate inner-core data from TCs rather than relying on environmental data.

1.4.5 Inner-core Studies Samsury and Rappaport (1991, hereafter SR91) conducted a study in which they used recon flight reports detailing the wind field structure of TCs to create mean profiles for use in intensity prediction. Their underlying assumption was that the intensity and structure characteristics of a TC at an initial time are related to the intensity/structure at a later time and can be used to create intensity forecasts. In addition to wind and structure data reported by the recon flights, SR91 also used NHC best track information for maximum wind data, storm track at 6-h intervals, and SSTs in the storm environment. SR91 established five distinct wind profiles—distant, broad, narrow, dual, and broad/dual—describing the most prominent feature in the radial wind profiles. Forecasts were then made based on the initial wind profile. These forecasts showed some degree of usefulness in the short-term (24 h or less), but beyond 24 h any trends disappeared. While the approach used by SR91 did incorporate recon flight data, the methodology employed was more of a climatological forecast approach. A more sophisticated approach was adopted by Law and Hobgood (2007, hereafter LH07). LH07 combined environmental, oceanic, and inner-core predictors to create a new 24-h regression model to predict RI in terms of both maximum sustained surface wind as well as MSLP. Twenty-five potential predictors were gathered from NHC’s HURDAT database, NCEP- NCAR reanalyses, and the Atlantic Oceanographic and Meteorological Laboratory (AOML). The basic premise assumed by LH07 was that different statistical models need to be applied for differing initial intensities of TCs as well as for differing stages during the TC’s life cycle. Their model used a discriminant function analysis (DFA) which allowed for selection of a prediction equation from a collection of varying 24-h regression models. The DFA utilized contained two steps. First, it examined each case in an attempt to determine if the TC had the characteristics necessary to become a major hurricane or if it would only become at most a minor hurricane. The second step classified each case according to its temporal proximity to undergoing RI (more than 48 h prior, 24 to 48 h prior, less than 24 h prior, and at the time of RI). As a result, a total of 16 possible regression equations were created—8 for predicting MSLP and 8 for predicting maximum winds—with half of the MSLP and maximum wind equations applying to major hurricane cases and the other half applying to minor hurricanes (LH07). To create the equations, LH07 used stepwise multiple regression, a linear regression technique that selects the predictors explaining the most variance while preventing highly

correlated variables from being simultaneously included in any one regression equation. More detail concerning stepwise multiple linear regression is provided in Chapter 5. Results showed that, for the most part, different predictors were selected between the separate time segments, potentially indicating that the primary factors affecting TC intensity change vary with forecast length. However, similar predictors were selected between matching forecast times for MSLP and maximum winds. When the DFA correctly selected the appropriate model (i.e., was able to correctly identify how far from the RI period the TC was), the average 24-h error was only 8.47 kt. The primary caveat noted by LH07 was the use of reanalysis data rather than real-time data, which could potentially lead to over-confident forecasts since reanalysis data corrects for any systematic biases in observational data. Regardless, the research put forth by LH07 demonstrated the usefulness of inner-core data in combination with environmental and oceanic predictors. Finally, Piech (2007) compiled a Vortex Data Message (VDM) climatology for the period 1989-2005. His climatology included information on various core parameters such as eye size, MSLP, eye temperature and dewpoint, and other data reported in the VDMs. Piech (2007) produced extensive frequency diagrams documenting the climatological inner-core characteristics based on the VDMs. Also presented were details of the composite mean eyewall cycle along with concentric eyewall cycles. An eyewall phase diagram was developed to graphically depict the evolution of a TC by using mean MSLP, eye size, and frequency of concentric or elliptical eyewalls. Piech (2007) attempted preliminary forecasts relating eye characteristics to future intensity change. Results indicated that further research needs to be performed to fully quantify the usefulness of incorporating inner-core data into forecasts of TC intensity change. More details on the work by Piech (2007) will be provided throughout this manuscript.

1.5 Objectives

Much research has been devoted to improving TC intensity change forecasts during the last few decades. However, as noted earlier, improvements in intensity forecasting still lag well behind those of track forecasting. In fact, average 24-h NHC OFCL forecast errors appear to

18 have remained virtually constant over the last 20 years (Figure 1.2), demonstrating the need for improved intensity forecasts. The research presented here expands on the preliminary research performed by Piech (2007). An updated VDM climatology is developed to encompass the time period from 1991- 2008, and a simple climatological forecasting tool based on initial eye diameter and maximum sustained surface wind speed is presented. Finally, a stepwise multiple linear regression technique (ASPIRE) is utilized to produce SHIPS-style forecasts from 12 h to 48 hr for well- developed (possessing a defined eye) TCs in the Atlantic basin. Chapter 2 provides more detail on the datasets used and methodology employed to create the VDM climatology. Comparisons to results from the climatology compiled by Piech (2007) are presented in Chapter 3. Some of the more relevant frequency distributions shown in Piech (2007) are discussed, and updated distributions from the current study are shown for visualization purposes. Chapter 4 explains the development of the simplistic climatological eye structure forecast tool. A qualitative summary in relation to Sawyer-Eliassen balance is discussed, and results of 12- to 48-h forecasts made using this tool are shown and compared to the SHIPS model and persistence. Chapters 5 and 6 describe the development and results of the multiple regression forecast method, which incorporates inner-core data from TCs gathered by recon flights. Chapter 5 focuses on the compilation of the database and formulation of the equations used in the forecasting process. A discussion of the predictors selected during the regression modeling and their relationships to the science of TC intensity forecasting is also presented in Chapter 5. Chapter 6 presents the results of this technique in terms of the out-of-sample variance explained in comparison to SHIPS and persistence, along with a breakdown of the forecast errors resulting from the technique in relation to geography and time of year. Two dependent case studies of Hurricane Ivan (2004) and Hurricane Katrina (2005) more closely examine the performance of the new model in Chapter 7. The final chapter offers a brief summary along with conclusions and recommendations for improvement of this method through future work.

Figure 1.1: NHC official forecast annual average track errors for 1989-2008 with least-squares trendlines superimposed, courtesy of NHC (http://www.nhc.noaa.gov/verification/verify5.shtml).

Figure 1.2: NHC official forecast annual average intensity errors for 1990-2008 with least- squares trendlines superimposed, courtesy of NHC (http://www.nhc.noaa.gov/verification/verify5.shtml).

Figure 1.3: 2007 Atlantic basin hurricane season intensity model forecast skill. Higher values denote greater skill. Note the dominance of statistical models over dynamical models. (Franklin 2008)

Figure 1.4: Same as in Figure 1.3, except for the 2008 Atlantic basin hurricane season. (Franklin 2009).

Figure 1.5: Schematic of the primary and secondary circulations (Salby 1996).

Figure 1.6: Cross-section through a tropical cyclone core, depicting the secondary circulation (Palmen and Newton 1969). The left-hand side shows pressure (solid) and temperature (dashed) while the right-hand side shows temperature deviations from a standard atmosphere (dashed- dotted).

Figure 1.7: Schematic of a secondary circulation induced by a heat source in a balanced vortex (Elsberry 1995).

Figure 1.8: Graphical representation of the secondary circulation of a tropical cyclone with concentric eyewalls (Willoughby 1988). Note the area of subsidence between the primary and secondary eyewalls as the outer eyewall intercepts some of the inflow and prevents it from reaching the primary eyewall.

Table 1.1: 2003 SHIPS model predictors from DeMaria et al. (2005) Predictors Description of Data Source Static or Time- Predictor dependent predictor JDAY Gaussian function of NHC Best Track Static (Julian day – peak value) VMAX Initial maximum winds NHC Best Track Static DVMX Maximum wind change NHC Best Track Static during the last 12 h VMAX * DVMX Initial max winds times NHC Best Track Static previous 12-h change SPDX Zonal component of NHC Best Track Static storm motion SLP Steering layer pressure Global Forecast Static averaged 200-800 km System (GFS) D200 200-hPa divergence GFS Static averaged 0-1000 km POT Max potential intensity GFS/NHC Best Track Time-dependent – current intensity SHR 850-200 hPa vertical GFS Time-dependent wind shear averaged 200-800 km T200 200-hPa temperature GFS Time-dependent averaged 200-800 km RHHI 500-300 hPa relative GFS Time-dependent humidity averaged 200- 800 km Z850 850-hPa relative GFS Time-dependent vorticity averaged 0- 1000 km STAB 1000-200 hPa theta-e GFS Time-dependent deviation of a lifted parcel averaged 200- 800 km LSHR Vertical shear times GFS Time-dependent sine of storm latitude POT2 POT squared GFS/NHC Best Track Time-dependent VMAX * SHR Initial intensity times GFS/NHC Best Track Time-dependent vertical shear

CHAPTER 2

DATA

This study uses data from Vortex Data Messages (VDMs), NHC Automated Tropical Cyclone Forecast (ATCF) archives, and the SHIPS model. Information on the data included in SHIPS is presented previously in Chapter 1. An explanation of the information contained in the VDMs and the ATCF archives is provided in the following three sections, along with an explanation concerning manual changes that were made to data from the ATCF archives.

2.1 Vortex Data Messages

VDMs provide information about the inner core of TCs, including initial latitude and longitude, temperatures, winds, and various other parameters. Details concerning the collection of these messages are provided by Piech (2007). VDMs have been available since the 1989 Atlantic hurricane season and are gathered by the Hurricane Hunter reconnaissance flights into TCs. The data is quality controlled initially by the flight crew itself. Additional quality control measures are then applied by the Chief Aerial Reconnaissance Coordination, All Hurricanes (CARCAH; NHC 2009). Data from dropsondes released into the eye of the TC, combined with flight level and radar data, compose the full VDM. A sample message from Hurricane Dean (2007) is provided below:

URNT12 KNHC 210702 CCA VORTEX DATA MESSAGE AL042007 A. 21/06:48:30Z B. 18 deg 36 min N 087 deg 06 min W C. 700 mb 2285 m D. 120 kt E. 171 deg 007 nm F. 268 deg 123 kt G. 171 deg 009 nm H. 907 mb I. 9 C / 3049 m J. 21 C / 3009 m K. 14 C / NA

L. CLOSED WALL M. C15 N. 12345 / 7 O. 0.02 / 2 nm P. AF306 1504A DEAN OB 13 CCA MAX FL WIND 165 KT N QUAD 06:53Z EXCELLENT RADAR PRESENTATION

Relevant sections of the VDM used in this study are sections A, B, C, H, I, J, K, L, and M. Section D lists the maximum sustained surface wind either as estimated by the flight crew or as measured by a dropsonde. This section was not used due to lower confidence in the accuracy of the wind values reported. While observed/extrapolated MSLP is reported reliably, accurate measurement of the peak wind speed is largely dependent on the success of releasing a dropsonde from flight level directly into a sloping eyewall. Even if a dropsonde is successfully released into the eyewall, there is no guarantee that the winds measured will actually be the strongest winds within the eyewall. Alternatively, a reduction factor may be applied to the maximum flight-level winds in order to estimate the maximum sustained surface wind speed. Unfortunately, it appears that reduction factors applied thus far have resulted in high biases for surface wind speed estimates (Powell et al. 2009). For this reason, an alternative method of matching the VDM to the most recent advisory wind speed is employed in this study, described in Chapter 3. Data from section E provides more information on the exact location of the maximum sustained surface wind reported in D and is therefore not relevant to this study. Sections F and G contain information on the intensity and location of the maximum sustained flight level winds measured by the Hurricane Hunter aircraft. While these flight level winds can be used to estimate surface winds through use of a reduction parameter, those estimations are not as accurate as the maximum winds listed in NHC OFCL advisories. Flight fix position and fix accuracy are provided in sections N and O. Section P is known as the remarks section. It includes a large amount of information, but none of it is necessary for this study. A breakdown of the sections used in this study, based on the above VDM, is as follows:

 A. Date and time of the fix of the center of the TC. 21/06:48:30Z means this report is from the 21st day of the month at 06:48:30 UTC.

 B. Latitude and longitude of the center of the vortex fix in degrees and minutes. The latitude of the above fix is 18 degrees 36 minutes North, while the longitude is 87 degrees 6 minutes West.  C. Flight level (mb) and minimum height of the flight at the standard level. 700 mb 2285 m indicates a flight level of 700 millibars with a minimum height of 2285 meters.  H. Minimum sea level pressure (mb). MSLP is measured either through the use of a dropsonde or through extrapolation based on aircraft instruments. MSLP for Hurricane Dean at this time is 907 mb.  I. Maximum flight level temperature (°C) and pressure altitude outside the eye. 9 C/ 3049 m indicates a temperature of 9°C and pressure altitude of 3049 m.  J. Maximum flight level temperature (°C) and pressure altitude inside the eye. 21 C/ 3009 m means a temperature of 21°C and pressure altitude of 3009 m.  K. Dewpoint temperature at the center of the TC, 14°C in this case. Note that the second part of item K is no longer used by NHC.  L. Eye character. Possible classifications of eye character are either “CLOSED WALL” for a fully defined eye, “OPEN ‘direction’” if there is a break in the eyewall, or “N/A” if there is less than 50% of a visible eyewall. Item L is not directly used in this study, but if “N/A” is reported, then Item M will also be listed as “N/A.”  M. Shape and diameter of the eye. Possible entries for the shape are either Circular (C), Concentric (CO), or Elliptical (E). Diameter is always reported in nautical miles.

Vortex messages for the period 1991-2008 are utilized in this study and are available from NHC’s ftp site. Data from 1989 and 1990 are not included for reasons discussed in Chapter 3. Since this study focuses on using well-developed TCs exhibiting an eye feature, the initial minimum criterion for a vortex message to be included was that the vortex message had to report an eye diameter. Additionally, for forecasting purposes, a homogeneous dataset is desired. The majority of recon flights into TCs with eyes occur at 700 hPa. For this reason, VDMs from other flight levels were excluded in order to maintain consistency in variables such as flight-level temperatures. Finally, a valid MSLP report was required since MSLP is used as a predictor in the statistical regression models described in Chapters 5 and 6.

2.2 NHC ATCF Archives

Since the work of Piech (2007), in which the VDMs were required to be manually entered into a climatological database due to the lack of a consistent format, NHC updated its ATCF f-deck archives to include all VDMs dating back to their inception in 1989. This upgrade constituted a significant step forward for research purposes, as every VDM is now available from 1989-present in a common format. The ATCF archives are also typically updated within about thirty minutes of real-time, allowing for immediate use of new messages as they are reported from the Hurricane Hunter recon flights. The primary advantage of the addition of the VDMs to the ATCF archives is the elimination of a subjective analysis of the vortex messages, such as the database created by Piech (2007). Rather than use the raw messages, the f-deck database is utilized in this study, minimizing the potential for typographical errors or incidental oversights since that database was created by existing software at NHC. One limitation of the f-deck database is that there are not routinely reliable measures of observed maximum sustained surface wind. The maximum winds reported within the f-decks are those listed in the VDM which are either measured with a dropsonde or visually estimated by the flight crew, as described in the previous section. The ATCF f-deck archives include all of the pertinent information from the raw vortex messages as well as SST, wall cloud thickness, and accuracy information, when available. Due to the more sporadic nature of reports of variables other than those explicitly listed in the breakdown of the vortex message in Section 2.1, these other variables are not included in this study. Those variables listed in the preceding section were gathered and used to compile an updated VDM database. Table 2.1 shows the relationship between the variables from the raw VDM and their field location within the ATCF f-deck archives. Information from the ATCF a-deck archives is also used in this study. The a-decks include all available data from NHC model runs along with the OFCL forecasts and the data used to initialize the models from the Combined Automated Response to Query (CARQ) files. Pertinent data for this study are the CARQ and SHIPS files for the period 1991 to 2008. The CARQ files are used to provide a matching wind value for each VDM rather than using the wind speed reported in the VDM, for reasons discussed previously. SHIPS files are used during

28 verification of the forecast methods presented in this study, and they also add data for the set of equations that incorporate the SHIPS model itself as a predictor.

2.3 Manual Corrections to ATCF Data

Upon inspection of the output from the code written to retrieve the desired data from the ATCF archives, some anomalies were found. The majority of these issues involved reports of concentric eyewalls with the inner eye diameter listed as being larger than the outer eyewall. For those reports exhibiting this problem, the order of the eyewall diameters was reversed such that the diameter of the inner eyewall is now listed in our database as less than that of the outer eyewall. During the process of examining the incorrect diameters from the concentric eyewall reports, it was noticed that some of the other reports were listed as concentric but had only the inner eye diameter included. A few of these discrepancies had exceedingly large diameters— greater than 50 nautical miles—for an inner eye. The raw vortex messages matching those reports in the ATCF archives were subsequently examined, and if they were found to be different, manual changes were implemented in the updated vortex message database. Table 2.2 documents the data that was updated manually.

Table 2.1: Explanation of Vortex Data Message along with its field location in the ATCF f-deck archives. Data Type Vortex Data Message ATCF Archive Field Section Location Location Date/Time of center fix A 3 Latitude of center of TC B 8 Longitude of center of TC B 9 Pressure of flight level C 34 Minimum height of flight C 35 level Minimum sea level pressure H 43 Maximum flight level I 44 temperature outside the eye Maximum flight level J 45 temperature inside the eye Dewpoint temperature inside K 46 the eye Eye shape (1=Circular; M 49 2=Concentric; 3=Elliptical) Inner eye diameter M 51 Outer eye diameter M 52

Table 2.2: List of manual changes made to Vortex Messages in ATCF f-deck archives. For storms with more than two reported eyewalls, only the first two are provided below. For eye shape data, 1=Circular; 2=Concentric; 3=Elliptical. Storm Year Month Day Time Original Original Corrected Corrected Corrected Name (UTC) Eye Eye Eye Inner Eye Outer Shape Diameter Shape Diameter Eye (nm) (nm) Diameter (nm) Andrew 1992 08 23 2045 2 8 2 8 20 Andrew 1992 08 23 2232 2 8 2 8 20 Andrew 1992 08 24 0013 2 8 2 8 20 Luis 1995 09 07 2352 2 58 2 20 58 Luis 1995 09 08 0208 2 58 2 21 58 Luis 1995 09 08 1123 2 50 2 20 50 Luis 1995 09 08 1333 2 50 2 20 50 Marilyn 1995 09 16 1211 2 15 1 15 N/A Marilyn 1995 09 16 1357 2 20 3 20 15

Table 2.2—continued Storm Year Month Day Time Original Original Corrected Corrected Corrected Name (UTC) Eye Eye Eye Inner Eye Outer Shape Diameter Shape Diameter Eye (nm) (nm) Diameter (nm) Marilyn 1995 09 16 1531 2 15 1 15 N/A Marilyn 1995 09 19 0015 2 20 2 20 40 Marilyn 1995 09 19 1137 2 14 1 14 N/A Bertha 1996 07 10 1454 2 16 2 16 60 Bertha 1996 07 11 1331 2 20 3 20 15 Edouard 1996 08 29 2049 2 15 2 15 50 Edouard 1996 08 29 2309 2 12 2 12 55 Edouard 1996 08 30 0053 2 10 2 10 50 Edouard 1996 08 30 0233 2 10 2 10 40 Edouard 1996 08 30 0421 2 10 2 10 30 Edouard 1996 08 31 1327 2 10 2 10 30 Edouard 1996 08 31 1509 2 10 2 10 30 Edouard 1996 08 31 1707 2 10 2 10 30 Erika 1997 09 07 0309 2 55 1 55 N/A Mitch 1998 10 26 0508 2 8 2 8 15 Floyd 1999 09 14 2323 2 17 2 17 50 Jose 1999 10 20 1330 2 30 3 35 20 Iris 2001 10 08 0620 2 8 2 8 22 Iris 2001 10 08 1119 2 3 2 3 9 Iris 2001 10 08 1916 2 10 2 10 30 Isidore 2002 09 21 0723 2 15 2 15 25 Isabel 2003 09 18 0117 2 25 1 25 N/A Ivan 2004 09 11 0612 2 12 2 12 40 Ivan 2004 09 11 0743 2 15 2 15 20 Ivan 2004 09 11 0916 2 12 2 12 30 Ivan 2004 09 11 1730 1 10 1 18 N/A Ivan 2004 09 11 1917 2 17 2 17 20 Ivan 2004 09 11 2044 2 17 2 17 20 Ivan 2004 09 12 0005 2 15 2 15 17 Ivan 2004 09 12 0906 2 15 2 15 30 Ivan 2004 09 12 2008 2 14 2 14 40 Ivan 2004 09 12 2359 2 17 2 17 40

CHAPTER 3

VORTEX DATA MESSAGE CLIMATOLOGY

3.1 Development

Before attempts at hindcasting or forecasting could be made, a new VDM climatology updating the prior work by Piech (2007) was necessary. The frequency of occurrence of the VDMs were grouped into bins according to the eye diameter and MSLP reported by the recon flights. As noted by Piech (2007), there is justification for splitting the bins up nonlinearly since the distribution of vortex messages is not uniform for all eye sizes. However, since the underlying goal of this study is to provide an improved intensity forecast method for TCs in the Atlantic basin, it was determined that creating nonlinear bins would prevent a sufficient number of VDMs from falling within the smaller bins, thus making statistical forecasts more difficult. Therefore, bins of equal 5 kt by 5 nautical miles (nm) size were created. Once the data were sorted into their respective bins, they were plotted in a variety of ways. The first analysis step was to attempt to replicate the general structure of the VDM frequency diagram presented in Piech (2007), while adding the most recent climatological data from the 2006-2008 Atlantic hurricane seasons. Graphs showing the number of occurrences for pertinent VDM parameters were also produced. These graphs were made for eye type, inner eye diameter, MSLP, initial maximum wind speed (as matched from the a-decks), temperature inside the eye, temperature outside the eye, dewpoint inside the eye, latitude, and longitude. The most critical step during formulation of this updated VDM climatology was the matching of recon observations to the NHC a-deck CARQ file (hereafter referred to as the advisory wind speed within this study) containing the maximum sustained wind speed preceding the VDM. Matching the VDM to the preceding advisory wind speed permits a sustained peak wind speed to be associated with every VDM, since the estimated maximum sustained surface wind speed reported in the VDMs is unreliable, as discussed in Chapter 2. Utilization of advisory winds also enables forecast verification, given that MSLP is not a forecast variable provided by NHC forecasts or statistical models such as SHIPS. The matching of the recon to

32 the preceding advisory effectively moves the time of the recon back to the time of the preceding advisory, although the VDM does contain new data not available at the time of preceding advisory. If the recon time happened to exactly match an advisory time, the matching advisory was used. This concept is crucial when applied in a forecasting setting, as it changes the respective verification times of the forecasts by up to 5 hours and 59 minutes. It is worth stressing that this process in no way introduces any future wind data into the forecast process, as would happen if best track data from the ATCF b-deck archives were used instead of the a-decks for advisory winds. Additional ramifications of this matching procedure are discussed further in Chapter 4. A brief review of the differences between the climatology presented in this study and that of Piech (2007) is warranted before examining the climatology of VDM parameters. This study encompasses the time frame from 1991-2008 rather than 1989-2005 as used by Piech (2007). The difference in the beginning of the climatology is a direct result of the change in data source used to create the climatology. As noted earlier, Piech (2007) was forced to resort to manual data entry due to a lack of a consistent, established format for archiving the VDMs. In late 2007, the NHC ATCF f-deck archives were updated to include information on all VDMs dating back to 1989 in a robust, consistent format. However, the statistical forecast model (SHIPS) used in this study for a comparison of skill was not run until 1991. Additionally, the CARQ files in the NHC ATCF a-deck archives used to match recon reports to the preceding advisory wind do not contain wind data for 1989, and the wind data for 1990 was incomplete in some instances. For these reasons, the most homogeneous dataset possible would be that which corresponded exactly with the time range of available SHIPS forecasts. Finally, the database of Piech (2007) included VDMs from all flight levels (1500 ft, 850 hPa, and 700 hPa), while the climatology presented here only contains VDMs from the 700 hPa flight level, ensuring that TCs included will be relatively well-developed. Limiting the climatology to 700 hPa flight level data only also provides a homogeneous database and represents the greatest percentage of the total VDM archive. Table 3.1 provides a summary of the differences between the data used to produce the updated climatology of this study and that used in Piech (2007). The frequency distribution of VDMs from 1991-2008 is next examined along with the distributions of relevant parameters from those reports.

3.2 Distribution of VDM Parameters

3.2.1 Distribution of VDM Reports Figure 3.1 shows the frequency distribution of all VDMs. The ordinate represents eye diameter (nm) as measured by recon flights, while the abscissa shows MSLP. TC intensity, as measured by MSLP, increases as one moves left in the plot. The lower left corner is representative of the strongest TCs possessing low MSLPs along with small eye diameters. The TC with the smallest eye and lowest pressure on record (Wilma 2005) is seen in the far lower left corner of the diagram. Similar to Piech (2007), the area of maximum occurrence is located in the region of eye diameters of 15-20 nm. Figure 3.1 provides the most direct comparison to the original VDM frequency distribution by Piech (shown in Figure 3.2) since the abscissa used in both studies is MSLP. The overall structure of the distributions is very similar, although more frequent occurrence of TCs with MSLP values greater than 960 hPa is seen in Figure 3.2. This difference is primarily due to the inclusion of VDMs at flight levels other than 700 hPa by Piech (2007), which allows for inclusion of weaker storms. While this study does not utilize flight levels other than 700 hPa, future research may wish to consider examining those flights for additional predictive potential. After matching the VDMs to the preceding or matching advisory wind speed, Figure 3.1 was reproduced with the abscissa changed to maximum sustained surface wind. Figure 3.3 illustrates this change, as it is essentially (although not exactly, given variability in pressure-wind relationships; Knaff and Zehr 2007) a mirror image of Figure 3.1. In this case, stronger storms are located on the right side with strongest TCs in the lower right corner. Hurricane Wilma appears as the sole bin with an eye diameter smaller than 3 nm. Note also that the peak frequencies between Figures 3.1 and 3.3 differ slightly, illustrating the previously mentioned lack of one-to-one correspondence of MSLP and maximum sustained wind speed. A preferential region of eye size existence is still evident between 15 and 20 nm. Larger eye sizes in the upper portion of the diagram are often associated with extratropically transitioning TCs or annular hurricanes (KKD03). Kimball and Mulekar (2004, hereafter KM04) developed a 15-year climatology of North Atlantic TC size parameters based on the NHC EBT dataset for 1988-2002. While KM04 did not explicitly study TC intensity, their findings can be used to help confirm and explain the

distribution seen in Figure 3.3. KM04 used TC structure data from a variety of sources, including recon flights. The climatology of KM04 has limited use for forecasting due to inhomogeneity of datasets used in that study. Nevertheless, the detailed climatology presented by KM04 offers insight into the typical characteristics of TC structure in the Atlantic basin. Six parameters—eyewall radius, maximum sustained surface winds, radius of gale-force winds, radius of damaging-force winds, radius of hurricane-force winds, and radius of the outermost closed isobar—were examined both spatially and seasonally. KM04 found that strong storms with small eyes, such as the lower right corner of Figure 3.3, are primarily due to intensification through eyewall contraction, as expected. Another finding is that if a tropical storm forms an eye early in its life cycle, the eye tends to remain rather small. Tropical storms have large RMWs, are typically small in size, and thus spend a larger amount of time strengthening rather than weakening. Intensification of tropical storms is a slow process due to increased time required to organize the eyewall. This result can be used to help explain some of the observed VDMs on the left side of Figure 3.3 which have relatively small eyes and maximum sustained wind speeds of only tropical storm strength. KM04 found that storms must achieve a high level of organization before an eye can develop. If this level of organization is not reached until the end of the life cycle, an eye will not have enough time to fully develop. Weakening systems also tend to have small eyes, an indication that they have reached the end of the eyewall contraction process and are more likely to decay (KM04). Along with storms experiencing self-organization early in their life cycles (Bloemer 2008), the above scenarios offer potential explanations for the high frequency of TCs of Category 2 strength or less with small eye diameters. An understanding of the climatological future intensity of a storm based on the initial eye diameter and wind speed of a TC is the foundation for the simple forecasting tool presented in Chapter 4. Therefore, after pairing the VDMs with the previous advisory winds (the 0 h advisory from the perspective of the VDM database), the subsequent advisory winds from 6, 12, 18, 24, 30, 36, 42, and 48 h in the future were added to the VDM climatology database. Figure 3.4 gives an example of this concept. While similar to Figure 3.3, the VDM frequency plotted in Figure 3.4 represents the climatological wind speed that is to be expected 12 h following the 0-h advisory wind speed based on the eye diameter reported in the first VDM of the VDM database.

3.2.2 Distribution of Variables Reported in VDMs Figures 3.5 through 3.8 show the thermodynamic characteristics of the TCs as reported in the VDMs. The temperature inside the eye can be seen in Figure 3.5. The most frequent temperatures occur between 15°C and 18°C, well above normal for 700 hPa at these locations partly because of the increased subsidence but also because 70 hPa itself is much closer to the ocean surface in a major hurricane. According to SW82, an increase in eye temperature corresponds to an increase in intensity. As viewed through the concept of Sawyer-Eliassen balance (discussed in Chapter 1), this warming of the eye—which yields an increase in intensity through hydrostatic lowering of the surface pressure and thus an increase in the pressure gradient force at the surface—also causes contraction of the eye. Figure 3.6 shows the distribution of temperature outside the eye. Comparing to Figure 3.5, the temperatures outside the eye tend to be roughly 6°C cooler than those inside the eye, although that difference increases as the TC becomes more intense, consistent with a pressure gradient force that increases. As noted in SW82, the amount of drying that occurs in the eye due to subsidence can be an indicator that surface intensity change has occurred or is imminent. Accordingly, Figure 3.7 provides the distribution of dewpoint inside the eye and illustrates the effects of subsidence since the highest frequency of occurrence of dewpoint temperature falls between 10°C and 14°C. Extremely low values of dewpoint are indicative of enhanced subsidence and are typically associated with very strong TCs. Finally, Figure 3.8 shows the dewpoint depression (temperature inside the eye minus the dewpoint inside the eye), effectively a coarse proxy for relative humidity. Based upon the relationships shown in these figures, certainly some parameters that will be tested for future intensity prediction include not only dewpoint and dewpoint depression but also recent short-term changes in those variables. Further, the non- Gaussian nature of Figure 3.8 argues that before statistical regression can be performed (Chapters 5 and 6), transforms of some variables will be necessary. Figures 3.9 and 3.10 show the distribution of MSLP as measured by VDMs from recon flights and the distribution of the advisory wind at 0 h associated with the MSLP values, respectively. Frequency of MSLP observations peaks near 955 hPa and exhibits a relatively Gaussian distribution overall. The extremely low values of MSLP below 900 hPa are associated with Hurricane Wilma (2005). The range of wind values displayed in Figure 3.10 does not show the same near-normal distribution as seen in the MSLP. A structure with three occurrence

maxima is visible, with peaks occurring near 85 kt, 100 kt, and 120 kt. Piech (2007) discovered preferential regimes for concentric eyewall development located near 920 hPa, 940 hPa, and 965 hPa. The findings of KD03 showed that 83% of major hurricanes in the Atlantic basin undergo RI. These results suggest that the distribution of wind in Figure 3.10 may be indicative of types of transition zones for storms undergoing RI or an ERC. If this is a preferred region for TCs to undergo RI or an ERC, then this region may produce more uncertainty for TC intensity forecasting. Figures 3.11 and 3.12 offer details of the distribution of eye type and eye diameters reported in the VDMs. The overwhelming majority of TCs exhibit a circular eye (79.7%), while concentric eyes are the most uncommon (5.8%). Eye diameter varies greatly, but the earlier observation of a preferred size between 15 and 20 nm is still easily detected. Relative maxima of 30, 40, 50, and 60 nm eye diameters arise as a result of apparent rounding of eye diameters as reported by the recon crew. Finally, Figures 3.13 and 3.14 show the latitude and longitude of the VDMs, respectively. It can be seen that reconnaissance flights are not often flown north of 30°N nor east of 55°W. There is also a sharp jump in frequency near 62°W. The graphs of latitude and longitude illustrate the primary limitation of using VDMs for forecasting TCs—that recon flights do not provide coverage of the entire Atlantic basin, and thus any forecast development using them would be biased toward representation of a subset of the basin as a whole. This chapter has sought to provide insight into the overall distribution of VDM parameters as measured by recon flights. The following chapter presents a method by which two of these parameters—initial eye size and maximum wind speed—can be used to produce simple climatological forecasts of future intensity change.

Figure 3.1: Frequency distribution of VDMs in the Atlantic basin for 1991-2008. Stronger storms are located on the left side of this diagram.

Figure 3.2: Frequency distribution of VDMs in the Atlantic basin for 1989-2005 (Piech 2007).

Figure 3.3: Frequency distribution for VDMs in the Atlantic basin for 1991-2008. Abscissa is maximum sustained surface wind speed. Stronger storms are located on the right.

Figure 3.4: Same as in Figure 3.3, but with frequency determined by wind speed 12 h later.

Figure 3.5: Distribution of temperature inside the eye. Blue curve superimposed on the frequency plot shows the best fit of Gaussian distribution to the data. Middle schematic plot shows the median, 1st and 3rd quartiles, and outlier data points. Bottom plot shows 95% confidence intervals for the mean and median values. Right-hand box gives basic statistical information for the variable. All plots such as the one above are directly from Minitab.

Figure 3.6: Distribution of temperature outside the eye.

Figure 3.7: Distribution of dewpoint inside the eye.

Figure 3.8: The highly non-Gaussian distribution of dewpoint depression (temperature minus dewpoint) inside the eye.

Figure 3.9: Distribution of initial MSLP.

Figure 3.10: Distribution of initial maximum wind speed.

Figure 3.11: Distribution of eye type, where 1=Circular, 2=Concentric, and 3=Elliptical.

Figure 3.12: Distribution of eye diameter. For TCs with multiple eyewalls, only the inner eyewall is included in this diagram.

Figure 3.13: Distribution of initial TC latitude multiplied by 100. Thus, latitude is shown in this figure with the decimal removed such that 2000 indicates a latitude of 20.00°N.

Figure 3.14: Distribution of initial TC longitude multiplied by 100. Thus, longitude is shown with the decimal removed such that 8000 indicates a longitude of 80.00°W.

Table 3.1: Summary of differences between the VDM climatology presented in this study and that of Piech (2007).

Murray (2009) Piech (2007) Dataset Period 1991-2008 1989-2005 Data Source NHC ATCF a-deck and f-deck Raw vortex data messages archives Flight level 700 hPa All (1500 ft, 850 hPa, and 700 hPa) Total VDMs 1929 > 2900 Number of TCs 83 92

CHAPTER 4

EYE STRUCTURE FORECAST TOOL

4.1 Development

As described in Chapter 3, each VDM containing a report of a defined eye for the period 1991-2008 was included in the VDM climatology. Frequency distributions of the various wind speeds and the initial eye diameter from the VDMs were created, and examples of these plots were shown in Figures 3.3 and 3.4. Those diagrams demonstrate the possibility of determining the expected climatological rate of intensity change, as described next. As described earlier, each VDM reporting an eyewall diameter was paired to the advisory wind preceding or (rarely) matching the VDM. Next, advisory winds from 6 h to 48 h in 6-h intervals following the 0-h advisory wind were added to the database. In order to maximize the size of the dataset, if a TC dissipated within the 48-h time frame, it was still allowed to be included in future times prior to dissipation. For example, if a TC dissipated 36 h after a VDM, that VDM was then included in the database used to create the intensity change plots from 6 h to 30 h; however, from 36 h through 48 h, that TC was removed from the database. Thus, the sample size decreases with time due to TC dissipation and interaction with land, causing a lack of a future advisory wind speed from which an intensity change can be calculated. The intensity change plots were created using the same binning technique used for the frequency distribution diagrams described in Chapter 3. The difference between the future advisory wind speed and the initial advisory wind speed matching the VDM was calculated for all VDMs within each 5 kt x5 nm bin, with the bins based on the initial eye diameter and advisory wind speed. These rate changes were then averaged within each bin and plotted as a mean hourly rate change. A nine-point smoother was applied twice to each rate change figure in order to capture the broader functionality and minimize fine-scale variability that results from sampling variability. The standard error associated with the average hourly intensity change for each time frame was also calculated to identify those intensity change values which are

significantly different from zero and thus provide a reliable forecast of intensification or weakening. One drawback of the advisory wind matching technique employed in this study is that 6-h wind change plots were rendered essentially useless because the matching process effectively moves the time of the VDM back to the preceding advisory time. Thus, the climatological intensity change forecasts are valid 6 h after the time of the advisory paired with the VDM rather than 6 h after the time of the VDM itself. This very important caveat introduces a problem, particularly when the VDM occurs more than 3 h after the most recent advisory. In the most extreme case, it is possible that a VDM could occur 5 h 59 min following the preceding advisory—in other words, 1 min before the next advisory in the a-decks. That VDM is then moved back in time nearly 6 h. When attempting to produce a 6-h forecast, the above scenario becomes highly unrealistic. While it is entirely possible to create such a 6-h forecast, it makes very little physical sense to do so, since in reality the 6-h forecast is being applied to an advisory occurring only 1 min following the VDM. For this reason, no 6-h rate changes or forecasts are shown throughout this study, although it would be possible to interpolate between the advisory time and the 12-h forecast to provide a 6-h forecast. The following section provides examples of the climatological intensity change calculations along with their standard errors. The 18-, 30-, and 42-h time frames are not shown for the sake of brevity, since their patterns resemble the shown times. In addition to a discussion of the mean intensity change patterns shown, their relationship to the known intensity change paradigm implied by the Sawyer-Eliassen nonlinear balance is presented .

4.2 Application

4.2.1 Pattern of Climatological Intensity Change Figure 4.1 shows the climatological mean hourly wind speed change from 0 to 12 h. It is worth noting that the increment size for wind speed reporting in the a-decks is 5 kt over 6 h, suggesting that any mean intensity change of less than 0.5 kt per hour is perhaps indistinguishable from zero given the observational uncertainty. For concentric eyewalls, only the first eyewall is included in the creation of this figure and other similar figures discussed in this section. An analysis focusing solely on concentric eyewalls would be ideal; unfortunately,

the small number of concentric reports (5.8% of all VDMs) precludes this possibility. Although requiring comparison to the standard error of the mean to be confident, a stark contrast between intensifying and weakening regimes is evident initially. TCs initially stronger (weaker) than 90- 95 kt will weaken (strengthen). This finding argues that the 95 kt threshold fundamentally represents a mean transition intensity in the evolution of an Atlantic recon-sampled TC and thus begs further examination. One potential explanation for the intensifying structure seen on the left side of the diagram involves the timing and location of the VDMs themselves. Recon flights are very rarely flown east of 50°W longitude. At the same time, most TCs into which recon missions are flown are still developing and intensifying as they pass west of 50°W. Thus, it is not wholly unexpected to see such a defined intensifying structure for TCs of initially weaker intensity. Another possible explanation can be inferred from prior works by KM04 and Bloemer (2008). KM04 found that a high level of organization or storm symmetry is necessary for development of an eye, while Bloemer (2008) found that as a TC approaches Category 1 intensity on the Saffir-Simpson scale, the TC begins to undergo a type of self-organization through which its natural tendency is to further intensify, consistent to Sawyer-Eliassen theory. Therefore, the intensifying regime on the left side of Figure 4.1 could be interpreted as storm- scale self-organization of the TC leading to intensification. Additionally, weaker storms are farther from their MPI (Emanuel 1988) than the more intense storms and thus, given favorable conditions for intensification, have a higher probability of strengthening. The weakening observed for TCs with advisory winds greater than 95 kt could be explained two different ways. First, stronger TCs are typically closer to their theoretical MPI. DeMaria and Kaplan (1994b) have shown that only 20% of all Atlantic TCs reach at least 80% of their MPI. An even lower percentage of those TCs actually achieve their MPI, and, on average, Atlantic TCs only reach 55% of their MPI. These results indicate that it is extremely difficult for a TC to maintain a high intensity for any significant length of time because either the underlying fuel (SST) or environment (shear, dry air entrainment, trough interaction) preclude it. Therefore, one potential explanation for the weakening regime is that those TCs are already closer to their theoretical MPI, inherently making it more difficult for them to maintain their intensities and thus more likely to weaken (Emanuel 2000). Another possible explanation relates to structural changes of the TCs. As described in Chapter 1, TCs often undergo secondary

eyewall formation and ERCs. While not immediately evident in Figure 4.1, structural changes associated with ERCs in TCs could explain the weakening observed at higher intensities. The standard error associated with the mean 12-h intensity change is shown in Figure 4.2. While this diagram indicates that there is great case-to-case variability, preventing conclusions concerning the significance of individual bins from being drawn from this figure, the overall intensifying/weakening structure is, in fact, significant. In other words, for a majority of the figure, there is a mean intensity change statistically significant from zero. It is theorized that the three areas of decreased robustness shown in Figure 4.2 are, in part, indicative of concentric eyewalls and ERCs, as proposed earlier. Piech (2007) found that there appear to be three preferred areas of concentric eyewall occurrence, in terms of MSLP: 905 hPa-925 hPa, 935 hPa- 945 hPa, and 955 hPa-975 hPa. These preferred areas of MSLP for concentric eyewalls approximately coincide with the regimes of higher standard error for the mean 12-h intensity change between 75 kt-85 kt, 100 kt-115 kt, and 135 kt-155 kt. Since Figure 4.1 was made using only the first eyewall of TCs, this theory could help explain the weakening observed on the right side of the diagram. TCs stronger than 135 kt are already much closer to their theoretical MPI than weaker storms, yielding a tendency to weaken. If a secondary eyewall event is occurring as well, the weakening trend for the inner eyewall would likely be accelerated as the outer eyewall cuts off the inflow of angular momentum towards the TC core. Similarly, TCs at wind speeds within the 100 kt-115 kt range typically weaken from a climatological viewpoint (Figure 4.1). Secondary eyewall events superimposed on this trend would also tend to accelerate the weakening of the inner eyewall, causing the higher variability observed in Figure 4.2. Finally, the region from 75 kt-85 kt with higher standard error in Figure 4.2 may be explained by the climatological tendency to strengthen being countered by weakening associated with secondary eyewall formation; alternatively, this regime may also represent a peaking TC moving over colder water. KS09 found that the average intensity during a secondary eyewall event based on a climatology from 1997-2006 was 109 kt. This finding meshes well with Figure 4.2, which shows a broad swath of higher variability between 100 kt-115 kt. One potential theory for this intensity range to be the most favorable region for formation of a secondary eyewall begins with the self-organization of TCs noted by Bloemer (2008). As a TC becomes better organized near Category 1 intensity, it can form an initial eye (KM04). Internal storm-scale dynamics continue

49 to allow further storm symmetrization and intensification. Storm symmetry is generally considered to be a necessary condition for formation of a secondary eyewall (Kuo et al. 2004; KS09). Further, KS09 found that the radial gradient of angular velocity tends to promote organization of asymmetric convection into a circular ring. They also found that more highly axisymmetric GOES infrared brightness temperatures yielded higher probabilities of secondary eyewall formation. The region of large standard error for intensities of at least 140 kt (Figure 4.2) may also be explained through a symmetrization argument. The results of KS09 showed that the climatological probability of secondary eyewall formation for Category 5 TCs is 60%. Category 5 TCs typically are highly symmetric and located in low-shear environments. Perhaps it as an inherent tendency of TCs to form a secondary eyewall when sufficiently favorable conditions for intensification exist, allowing the greater level of storm symmetry necessary for such events. No definitive explanation of the physical processes which cause secondary eyewall events has yet been proposed, and it is beyond the scope of this study to determine the specific dynamical and physical processes driving these events. It is hoped that future observational and numerical modeling studies will be able to uncover the exact mechanisms which lead to secondary eyewall events in order to provide improved warning for such rapid intensity changes. Regimes of lower variability are also apparent in Figure 4.2. One possible explanation for the decrease in standard error for TCs with large initial eye diameters could be the phenomenon of annular hurricanes. KKD03 showed that annular hurricanes tend to maintain nearly constant intensity with an average intensity of 107.6 kt. Figure 4.2 shows a decrease in standard error for TCs with wind speeds greater than 100 kt and eye diameters greater than 40 nm, indicating that annular hurricanes may indeed present a feasible theory for the increased confidence despite the fact that they account for less than 4% of all TCs (Knaff et al. 2008). Other regions of reduced error are located between the potential areas of concentric eyewall signatures. These areas are likely a result of a more predictable vortex as it contracts according to Sawyer-Eliassen theory following an ERC. The area from 65 kt-75 kt likely exhibits reduced variability due to the self-organization tendency of TCs approaching Category 1 intensity. Figure 4.3 combines the previous two diagrams by plotting the average hourly intensity change in shaded bins with standard error contours overlaid. This combination more readily elucidates the variability associated with the structure of the climatological intensity change.

The mean hourly intensity change at 24 h is shown in Figure 4.4. The most noticeable feature is the slight shift of the divide between intensifying and weakening regimes towards initially weaker TCs. This change is most likely due to the fact that it becomes increasingly difficult for TCs to maintain strong intensities over longer periods of time. Figure 4.5 shows the standard error associated with the average hourly intensity change at 24 h. Error in the center of the diagram decreases compared to the standard error at 12 h. This result may be due to the completion of an ERC, thus decreasing the variability associated with such an event. From 24 h through 48 h, the trends previously described continue, as seen in Figures 4.6 through 4.9. Figures 4.6 and 4.8 show the average hourly intensity changes at 36 h and 48 h, while the standard error associated with these means can be seen in Figures 4.7 and 4.9, respectively. The area of near-zero intensity change dividing the regions of intensifying and weakening TCs progressively shifts further towards TCs of initially weaker intensity. Additionally, the magnitudes of the average intensity changes decrease with time, as expected due to increased averaging times. The standard error also decreases with time as a result of the overall decrease in magnitude of the average intensity change. Another explanation for the observed decrease in standard error is that variability due to intensity changes on shorter time scales, such as that of a secondary eyewall event, is reduced over increased time. As a result, the general intensity trend is correctly identified by the climatological averaging technique employed here, thus reducing the error. Areas of standard error of 0.45 kt or greater appear to be statistically significant from zero at the 95% confidence interval, given that the mean intensity change associated with these regions is typically on the order of 1.0 kt. Unfortunately, to be useful from a forecasting perspective, a mean intensity change of 1.0 kt must be accompanied by a standard error of 0.25 kt or less.

4.2.2 Relation to Sawyer-Eliassen Nonlinear Balance The discussion of Sawyer-Eliassen nonlinear balance presented in Chapter 1 can be applied to Figure 4.1. KM04 found that eyewall formation is favored once a TC approaches Category 1 intensity. Subsidence induced within the eye causes an increase in warming, which leads to tightening of the pressure gradient, increasing winds, and ascent within the eyewall, thus producing a source of heating. The vertical integral of this resulting heating within the eye (including the eyewall) is maximized inward of the RMW, causing isobaric heights to fall more

51 quickly just inside the RMW than they do outside it. An increased pressure gradient forms as a result, yielding a stronger maximum wind speed. At the same time, the height falls themselves produce peak intensification in the time tendency of the tangential winds just inside the RMW. The RMW is drawn inward as a response to the heating (SW82), and a contracting eyewall is typically associated with TC intensification (SW82; Willoughby 1990). This scenario provides a feasible explanation for the climatological tendency of intensification of weaker TCs (Figure 4.1) as they begin to reach a sufficient level of organization.

4.3 Hindcasting Results

Hindcasts were created using the simple climatological eye structure tool detailed in the previous sections. In order to produce a forecast, a VDM reporting an eyewall diameter must first be available. These hindcasts were made at 6-h intervals from 12 h through 48 h into the future by multiplying the climatological average hourly intensity change by the forecast length desired. The intensity hindcasts were made using the VDM reports included in the VDM climatology described in Chapter 3; as a result, it is important to note that these “forecasts” were not made using independent data and thus should not be considered fully representative of the true accuracy and usefulness of the eye structure tool. Serial correlation likely yields additional overconfidence since VDMs are often reported multiple times within a given 6 h or 12 h period. The standard error figures shown in Section 4.2 also indicate that such climatological forecasts alone are unlikely to be sufficient to reliably forecast intensity change. These obvious limitations notwithstanding, it was nonetheless desired to examine the performance of such climatological hindcasts based solely on initial structure and intensity of a TC and to determine whether a basic, overfit tool can compete with SHIPS. As described in Chapter 1 and noted by Rappaport et al. (2009), the best-performing intensity guidance over the last decade has been statistical in nature, and the top model within the statistical guidance suite has been the SHIPS/D-SHIPS model (DeMaria et al. 2007). For this reason, the hindcasts presented here will be compared to simple persistence forecasts in which the future intensity is predicted to be identical to that of the initial intensity, as well as the benchmark intensity forecast model of SHIPS. SHIPS is chosen as the model for comparison rather than D-SHIPS since forecasts from D-SHIPS were not available prior to the 2000 Atlantic

hurricane season, while SHIPS forecasts have been archived since 1991. The extended period of SHIPS model output available allows for verification of climatological hindcasts from 1991 through 2008. The climatological prediction technique described here removes storms that passed over land from the database, unlike SHIPS. However, this apparent difference in model formulation is not detrimental towards the SHIPS model performance since the removal of overland TCs from the climatological database also removes the SHIPS forecasts involving interaction with land. To maximize consistency and fairness during verification of the climatological hindcasts, SHIPS is used rather than D-SHIPS. Table 4.1 summarizes the periods of development and types of predictors contributing to SHIPS model guidance, D-SHIPS, and the eye structure forecast tool. Figure 4.10 shows the results of the climatological intensity hindcasts in terms of the root-mean squared error (RMSE) and compares these hindcasts to the RMSE of both persistence and SHIPS. RMSE is calculated by squaring each of the individual hindcast errors which gives the squared error. The average of these squared error values is then computed, known as the mean squared error (MSE), and the square root of the MSE gives the RMSE. Figure 4.10 indicates that the climatological prediction technique outperforms both SHIPS and persistence at all forecast times, with anywhere from 4%-10% improvement noted over SHIPS. This result is rather unexpected, considering that the average hourly rate change diagrams essentially showed that storms stronger (weaker) than 90 kt-95 kt will always be forecast to weaken (strengthen). It should be pointed out that these hindcasts likely would not surpass those of SHIPS if the effects of serial correlation and the lack of an independent verification dataset were accounted for, given the marginal (4%-10%) improvement. Still, these intensity hindcasts based purely on climatological characteristics of TCs gathered from VDMs could potentially provide additional utility as a new benchmark against which to verify currently available operational intensity guidance. Future work associated with these climatological hindcasts will seek to construct confidence intervals within which the future intensity of the TC can be expected to fall with 95% certainty. The next step in research will seek to more robustly predict future intensity change using out-of-sample performance of stepwise regression on VDM measurements as well as the climatological tool just described.

Figure 4.1: Average hourly intensity change (kt) at 12 h for the first eyewall of TCs based on the advisory winds associated with a VDM. Image smoothed twice using a nine-point smoother.

Figure 4.2: Standard error (kt) associated with Figure 4.1. Image smoothed twice using a nine- point smoother.

Figure 4.3: Same as Figure 4.1, but with unsmoothed standard error contours (kt) overlaid.

Figure 4.4: Same as Figure 4.1, but for the 24-h time period.

Figure 4.5: Same as Figure 4.2, but at 24 h.

Figure 4.6: Same as Figure 4.1, but at 36 h.

Figure 4.7: Same as Figure 4.2, but at 36 h.

Figure 4.8: Same as Figure 4.1, but at 48 h.

Figure 4.9: Same as Figure 4.2, but at 48 h.

Figure 4.10: Comparison of RMSE of climatological eye structure forecast tool (blue), SHIPS (red), and persistence (green).

Table 4.1: Summary of the types of TC intensity forecast guidance. Model Period of Development Contributing Predictors SHIPS 1989-2008 Environmental and Oceanic *also includes 11 TCs from 1982-1988 D-SHIPS 1989-2008 for SHIPS Environmental and Oceanic 1967-2008 for decay model used with inland decay model applied in post-processing Eye Structure Tool 1991-2008 Eye diameter from VDMs and advisory wind speed

CHAPTER 5

STATISTICAL REGRESSION FORECAST MODEL (ASPIRE)

The existing benchmark for statistical hurricane intensity forecasting, SHIPS, primarily (but not exclusively) utilizes measurements or estimates of the synoptic environment of a hurricane, such as potential intensity, vertical wind shear, OHC, and upper-level divergence. What this benchmark lacks is observational measurements of the TC inner core, which prior research has shown are key to understanding and predicting hurricane intensity change (Holland and Merrill 1984; LH07). To address this issue, the present study seeks to incorporate these core measurements, as provided by recon flights, in order to produce an increasingly skillful benchmark for TC intensity forecasting, the Atlantic-based Statistical Prediction of Hurricane Intensity using Recon (ASPIRE). This chapter details the development of the database used in the statistical stepwise regression modeling, the predictors used within the equations, and the method behind limiting the regression process. Examples of the distributions of the predictors and their transformations are also provided, and insight is offered into the physical mechanisms that drive TC intensity change and how those processes vary with time and TC intensity.

5.1 Development of Database for Regression

The VDM climatology described in Chapter 3 provided the initial database used during the statistical regression. All of the relevant information (latitude, longitude, recon time, temperature inside the eye, temperature outside the eye, dewpoint inside the eye, MSLP, eye diameter, and eye type) reported in the VDMs were included in the database. Many linear and nonlinear combinations of predictors were calculated, such as potential temperature (θ), θE inside the eye, θE outside the eye, area of the eye, area of the eye multiplied by the previously mentioned thermodynamic parameters, dynamic measures of inertial stability such as approximate centripetal acceleration at the eyewall (V2/R), and many others. All of the variables calculated were not necessarily chosen during the regressions; only those variables which were actually chosen during the regressions will be discussed. Backward temporal differencing was

60 also utilized to calculate other parameters such as the change in temperature inside the eye, change in temperature outside the eye, change in the difference between the temperature inside and outside the eye, and change in eye diameter, leading up to the VDM report. Many of the parameters computed were chosen using existing knowledge of the Sawyer- Eliassen secondary circulation and its relationship to TC intensity change. For example, a predictor such as the area of the eye multiplied by either the potential temperature or the dewpoint depression may be used as a proxy for the strength of the mass subsidence within the eye. Subsidence within the eye can be used as one measure of the potential for a TC to intensify since increased subsidence can indicate a strengthening secondary circulation which may not have yet manifested itself. Likewise, measures of the temporal changes listed above all have direct bearing on the Sawyer-Eliassen secondary circulation model. The size of the developmental database was reduced from that used to develop the eye structure forecasts due to VDMs missing some necessary data. For example, several VDMs were missing temperature data and thus could not be included in the development dataset. Inclusion of parameters involving temporal changes further reduced the size of the developmental database, given that the first VDM report for a TC could not be used. Thus, forecasts using the ASPIRE technique cannot be created until two recon missions have been flown in which VDMs containing all of the necessary initial parameters are gathered since two VDMs were needed to calculate the parameters involving temporal changes. Finally, the distributions of all potential predictors were examined for their normality. Any predictors exhibiting a highly non-normal structure (e.g. Figure 5.7) were transformed using either exponentials or natural logarithms as necessary to more closely approach normality (Wilks 2006). These transformations increase the potential predictive power of the regression technique by reducing the skewed distribution of the residuals following each regression step while simultaneously increasing the variance explained at each step. All predictors included in the various regression equations along with any variable transformations are provided in Section 5.3.

5.2 Formulation of Forecast Equations

5.2.1 Overview of Stepwise Multiple Regression A stepwise multiple regression technique available in the Minitab software package was performed to create the equations used in the ASPIRE model. Stepwise regression is an efficient statistical method in which the predictor having the highest correlation with the predictand—in this case, the future maximum sustained surface wind speed as given by the a-decks—is first entered into the regression. All variables included in the regression must also be statistically significant at a specified threshold, set at a level of α < 0.10 for this study. The second variable entered into the regression is the one having the next highest correlation with the dependent variable while still accounting for the first variable already included in the regression. That is, the second chosen predictor must be best correlated with the residuals after the first predictor is subtracted from the predictand. At this point, the first variable may be removed from the equation if it is no longer statistically significant; otherwise, it is retained in the regression equation being developed. The Minitab software filters the predictors at each step of the regression to eliminate predictors that are highly covarying, and it will remove previously chosen predictors should the new predictor set explain more variance when prior predictors are removed. This stepwise multiple regression procedure is continued until the addition of new predictors does not explain any more of the variance (within the alpha threshold previously stated) as quantified in the raw R2, a measure which is a function of the amount of variance in the dependent data sample that can be explained by the regression equation. When developing a set of equations using stepwise multiple regression to be used in a forecasting setting, care must be taken to avoid overfitting the regression to the developmental data (Wilks 2006). For this purpose, rather than continuing the regression until the maximum R2 is achieved, the out-of-sample R2-predicted (hereafter, R2pred) value is used instead. The R2pred is calculated by removing each individual observation from the developmental dataset of size N, estimating the regression equation from the resulting N-1 data points, and evaluating how accurately the model predicts the observation that has been removed. Utilizing the R2pred rather than the R2 allows for insight into how well the equation will predict future values using new observations instead of showing how well the model fits the developmental data.

Wilks (2006) also suggests implementation of stopping rules during multiple linear regression to ensure that the regression equations are not overfit to the developmental data. In order to avoid subjectivity when selecting the point at which to stop during the regressions, specific rules for stopping the regressions were established prior to model development. Glahn (1985) found that, in forecasting practice, including more than about a dozen predictors adds little to the effectiveness of a regression equation. At the same time, Wilks (2006) notes that the exact stopping point is not usually critical as long as it is approximately correct. For these reasons, no more than 15 predictors were allowed in any one forecast equation. Additionally, an objective measure of the increase in the variance explained through the R2pred was also necessary. Wilks (2006) points out that less rigorous stopping criteria, such as an increase of 0.05% in the R2, are often employed. More stringent stopping rules were desired for this study given the larger dataset and larger size of the predictor pool; therefore, the second rule applied was the requirement of an increase of at least 0.10% in the R2pred for a new predictor to be added during the regression. The only exception to these objective stopping rules was the use of a subjective examination of each equation in which it was verified that there was not a substantial change in the value of the constant for each regression. For example, while following the imposed stopping rules, if the final step of the regression attempted to add a predictor which would change the predicted wind speed by a large amount (which typically induces a large change in the value of the constant), then the equation was subjectively chosen to stop at the first prior step satisfying this additional requirement—an earlier step than that which would otherwise be indicated by strictly adhering to the objective rules. This one deviation from the objective stopping rules was imposed solely to ensure that the equations would remain relatively stable and would not produce a drastic change in model output due to a single variable Rarely did a large change in the constant occur within the first 10 predictors.

5.2.2 Forecast Equation Sets Two different sets of forecast equations were initially developed. The first set of equations uses all data at all initial intensities for a given forecast length. Thus, there is one equation for forecast hour 12, one equation for forecast hour 18, and so on, continuing through 48 h. These forecasts represent the “full” equations in the sense that they incorporate the full initial intensity range to create a forecast equation which will be applied to any new forecast

situations, regardless of initial intensity. A second set of equations was developed using running bins of 20 kt size for the initial intensity. The size of the running bins was set at 20 kt to provide a sample size which averaged roughly 225 data points. Additionally, a 20-kt bin approximates the size of an intensity category on the Saffir-Simpson scale. For example, for a TC with an initial intensity of 100 kt, the forecast equation in this instance was developed using data spanning an intensity range from 90 kt through 110 kt. The bin size of 20 kt was chosen to approximately match the largest size of the Saffir-Simpson categories, and it also ensured that enough data points are available for each binned regression equation that it is unlikely to be overfit to the developmental data. Table 5.1 lists the differences between the three sets of regressions performed within the ASPIRE technique. The first two sets of forecast equations were developed using all available data, including SHIPS model output as well as forecasts from the climatological eye structure forecast tool described in Chapter 4, and is hereafter referred to as the “TOTAL” equation since it includes all data available for use as predictors. Note that the TOTAL equation set is different from the “full” regressions developed. The TOTAL equation set refers to the inclusion of all available data as potential predictors, including SHIPS and the eye structure forecast tool. The full regressions simply provide a distinction between the “full” equations involving the complete range of initial intensities and the binned equations developed using running bins of 20 kt. In order to avoid ambiguities and to show the extent of the usefulness of the ASPIRE technique, two additional sets of two types of forecast equations were developed. The two equations within each set follow the same methodology previously described whereby one of the regressions incorporates all intensities to formulate a single equation for all intensities, and the other type of regression utilizes a 20-kt running bin to create a suite of equations dependent on the initial intensity of a TC. One of these sets of two equations removed predictors involving SHIPS output, and is referred to as the “no SHIPS” (hereafter, NS) forecast method. The two predictors in the developmental dataset which included SHIPS were removed to demonstrate that the utilization of TC core data in a regression model is sufficient to predict TC intensity change as well as to verify that the ASPIRE technique was not beating the SHIPS model simply on the grounds of adding additional predictors to an underlying framework based on SHIPS itself. The third set of equations removed predictors from both SHIPS and the climatological eye structure forecast tool, and is referred to as the “no SHIPS, no climo” (hereafter, NSNC)

forecast method. Predictors involving the eye structure forecast tool were removed from the NSNC method due to potential bias from the inclusion of dependent data in the forecasts. As described in Chapter 4, the climatological eye structure forecast tool was created using the dependent dataset. For points with a low number of VDMs, the climatological tool may produce an over-confident forecast even though the R2pred is used rather than R2. For example, in the most extreme case, if only one VDM falls within an individual bin in the eye structure tool, then the resultant forecast produced using the climatological tool will be perfect. If the eye structure tool is then selected as a predictor in the regression equations, the eye structure tool will yield undue influence on the predicted wind speed, despite the use of the out-of-sample R2pred and removal of the individual data point from the developmental dataset. For these reasons, the majority of this study will focus on the NSNC forecasts in hopes of emphasizing the effectiveness of the ASPIRE model without influence from dependent data or the SHIPS model It is worth noting that even though the climatological eye structure tool may not be available for the NSNC regression, the individual eye size and intensity measurements are, of course, available as potential predictors.

5.3 Predictor Variables

A total of 61 potential predictors were available during each individual regression. All but one of these variables were indeed used at least once during either the TOTAL, NS, or NSNC forecast equations. Table 5.2 lists all of the variables which were actually selected as predictors in any of the TOTAL, NS, or NSNC equations. Italicized (bolded) variable names in Table 5.2 indicate that the predictors were transformed using an exponential (logarithmic) technique. A discussion of the variables follows. For the TOTAL equations, forecasts from the SHIPS model were collected and included as potential predictors. The SHIPS model outputs forecasts in intervals of 12 h. To account for the lack of a SHIPS forecast between model output times, forecasts were interpolated as necessary using an equally-weighted average of the SHIPS model output around the desired time. For example, a SHIPS forecast at 18 h was created by averaging the SHIPS forecasts at 12 h and 24 h. For forecasts at 6 h, the initial advisory wind and the SHIPS forecast at 12 h were averaged. Figure 5.1 shows the distribution of the SHIPS predictor at 12 h. The difference

between SHIPS model output and forecasts made using the climatological eye structure tool was included in the TOTAL regression as well, but not the NS or NSNC regressions. The eye structure forecast tool was used as an individual predictor in the TOTAL and NS equations, and its distribution at 12 h is provided in Figure 5.2. The normalized difference between forecasts from the eye structure tool and the initial wind was also calculated by subtracting the advisory wind speed from the eye structure forecast and then dividing by the advisory wind. The remaining predictors discussed were used in all three of the equation sets, including the NSNC forecasts. The first advisory age (1stAdvAge) of the TC was calculated by subtracting the time of the initial CARQ advisory for the TC as listed in the ATCF a-decks and the current time of the VDM as listed in the ATCF f-decks, in seconds. The first tropical storm age (1stTSAge) and first hurricane age (1stHAge) were computed in the same manner, using the time since the first listing of the TC in the CARQ advisories as a tropical storm and hurricane, respectively. The time of day of the advisory was included as a predictor in case the diurnal cycle of tropical convection impacted the intensification forecasts. This variable was calculated as the number of seconds since 0000 UTC with an additional modification which accounted for longitudinal variation due to the variability in local time across the planet. Predictors related to the location of the TC included latitude, longitude, cosine and sine of the latitude multiplied by the advisory wind, and cosine and sine of the latitude divided by MSLP. The calculations involving cosine and sine functions were included as potential predictors in an attempt to account for any possible nonlinear interactions between TC location and wind speed for those TCs located at an unusual latitude. Initial TC latitude was also multiplied by initial longitude (Lat*Lon) to create a proxy for MPI. Lat*Lon generally increases in magnitude from southeast to northwest and is maximized in the Gulf of Mexico. MPI itself was not calculated since the goal of the approach here is to determine how largely core-centric data can compete with largely environment-centric data for TC intensity prediction. Several predictors involving MSLP and advisory wind measurements were created. The most logical choice is inclusion of the initial advisory wind itself. The advisory winds from 6 h and 12 h prior to the initial wind were also included. Differences were calculated between the initial wind and the prior winds (initial wind minus wind from 12 h prior, initial wind minus wind from 6 h prior, and wind from 6 h prior minus wind from 12 h prior). Additionally, the

initial wind was multiplied by the previous 12-h change in wind speed as well as the previous 6- h change in wind speed. MSLP as reported in the ATCF f-decks was found to be an important predictor. The change in MSLP between the current VDM and the previous VDM was also calculated. Figures 5.3 and 5.4 show the distribution of the initial advisory wind and MSLP, respectively, at 12 h. Thermodynamic predictors gathered directly from the VDMs were temperature inside the eye, temperature outside the eye, dewpoint inside the eye, and the difference between the temperature inside and outside the eye. The distribution of the temperature inside the eye is provided in Figure 5.5. Several other measures were calculated, including θ inside the eye, θ outside the eye, difference between θ inside and outside the eye, θE inside the eye, and the

difference between θE and θ inside the eye. Predictors involving temporal changes in dewpoint, temperature inside the eye, temperature outside the eye, and the difference between the temperatures inside and outside the eye were also created. Figure 5.6 shows the distribution of the change in temperature inside the eye. These variables provide insight into intensity change in relation to the Sawyer-Eliassen secondary circulation. Information on eye characteristics was also utilized as predictors. The eye type (circular, concentric, or elliptical) was used rather often, despite being a non-continuous variable. Eye diameter was also chosen often, and the area of the eye was calculated using eye diameter information reported in the VDMs. The change in inner eye diameter was calculated to account for contraction of the eyewall as an indicator of intensification (SW82). The area of the eye was multiplied by the change in dewpoint and the change in temperature inside the eye to estimate

the amount of heating and drying inside the eye. Area of the eye was also multiplied by θ, θE, and temperature within the eye to be used as proxies for the mass subsidence within the eye. The Julian day was included as a predictor in order to account for the time of year in which the TC occurred, although this variable was never selected first. Table 5.3 shows the relationship between Julian day and calendar day. The absolute value of the difference between the climatological peak of the hurricane season (Julian day 253, or 10 September), and the Julian day of the recon report was also calculated as a measure of how far away a given TC is from the climatological peak of the season. This variable only rarely was selected first. Four additional variables were created involving the initial wind speed and the radius of the eye of the TC to approximate inertial stability. These variables included the initial wind

speed divided by the eye radius, initial wind speed was divided by the square of the radius of the eye, and the square of the initial advisory wind divided by the eye radius as well as the square of the eye radius. Since multiple linear regression methods generally assume a Gaussian distribution for potential predictor variables, the distributions of all the variables described above were examined for their normality. Those predictors displaying a highly non-normal distribution were transformed using exponentials or logarithms as necessary in order to more closely approach normality and reduce the unexplained variance due to residuals with structure in their distribution. Figures 5.7 through 5.12 provide three examples of variables that originally exhibited a non-normal distribution along with its transformed counterpart. Distributions of variables that vary depending on the length of the forecast, such as those involving SHIPS model output or forecasts from the climatological eye structure tool, are shown at only 12 h since there is not much change at longer forecast times other than a gradual broadening of the distribution.

5.4 Interpretation of Equations

Examination of the resultant regression equations potentially offers crucial insight into the science of TC forecasting. When performing statistical multiple regression, a physical relationship between the first variable chosen in the final equation and the predictand may be developed. However, physical relationships between the predictand and remaining predictors picked are not as easily identified due to the nature of multiple regression. After the first predictor selected, the remaining predictors explain the variance in the residuals rather than having a direct correlation with the predictand. Nonetheless, we can imply relative importance to TC intensity forecasting by examining how often certain predictors were chosen in the numerous regressions. For brevity, only the 12-h and 36-h periods will be examined in detail in order to show how the variables driving intensity change with forecast length. Accordingly, Figures 5.13 through 5.15 show predictor matrices for 12-h forecasts for the NSNC, NS, and TOTAL regressions, respectively. The abscissa represents the 20-kt intensity bin for which the various equations were created. Thus, all of the predictors selected for a given intensity bin can be found by looking vertically at each intensity bin. If a dot is plotted, then the

predictor corresponding with that horizontal line was selected for that intensity. For example, in Figure 5.13, eight predictors were selected for the 150-kt equation (not including the dot plotted for the constant). Predictors listed at the bottom of the figures are chosen most often in the regressions, and the frequency of selection decreases towards the top of the figures. Note that a higher frequency of selection shown in these matrices does not necessarily indicate that those predictors were selected early in the regression; therefore, inferences of physical relationships with the predictand based solely on these figures should be made with caution. The variables most often selected first at 12 h were MSLP and the cosine of the initial latitude multiplied by the wind or divided by the MSLP, indicating that, not surprisingly, measures related to persistence explain the majority of the variance in short-term TC intensity change. Examination of these three figures reveals that the predictor most often chosen at 12 h for each of the three equation sets is MSLP. Intuitively, this finding is expected, given the relationship between MSLP and maximum sustained wind speed. Even though the pressure- wind relationship in TCs varies with a number of factors such as storm size, MSLP is still one of the most reliable indicators of the maximum wind of a TC. Other predictors chosen frequently between each of the three equation sets include variables related to the age of the TC, Julian day, and change in temperature inside the eye. The importance of age-related variables is likely due to the increased probability for an “older” TC to be located in the warm waters of the Caribbean or the Gulf, provided that it has not recurved northward as it moves westward across the Atlantic. The TC hurricane age predictor also is selected for relatively weak hurricanes. This finding suggests that TCs that have been hurricanes for a longer period of time may be weakening while TCs with a relatively young hurricane age may be strengthening. One other predictor chosen with surprising frequency in Figure 5.13 is the natural logarithm of the square of the initial wind speed divided by the radius of the eye, suggesting that measures of the inertial stability of the TC core have partial predictive skill for TC intensification and should be accounted for during statistical modeling of TC intensity change. Of particular importance is the frequent selection of thermodynamic predictors at 12 h. Temperature inside the eye, temperature outside the eye, the difference between the temperature inside and outside the eye, and their temporal changes are all chosen often. Additionally, there is a tendency for many of the predictors, thermodynamic and otherwise, to be selected in clusters of intensity ranges rather than displaying a more random pattern. This result indicates that certain

variables should have a stronger relationship to the intensity change of a TC depending on the current stage of the life cycle of the TC. Figures 5.13 through 5.15 all indicate preferential regions for the temperature change within the eye to be chosen—from 80 kt-90 kt and from 110 kt-125 kt—indicating that the rate of change in subsidence and warming within the eye could play a significant role in RI of a TC. Figures 5.16 through 5.18 show examples of the same types of matrices for forecasts at 36 h. The most interesting detail is the less-frequent selection of thermodynamic variables at longer forecast times coupled with an increased emphasis on age-related and persistence variables. Eye type—circular, concentric, or elliptical—is also selected more frequently at 36 h. The reduced selection of thermodynamic predictors at longer forecast times implies that the impact of these variables on TC intensity change occurs on shorter time scales and also suggests that using TC core data independently of environmental factors is less effective beyond 1-2 days for statistical forecasting purposes. Figure 5.18 reveals that the SHIPS model is selected as a predictor for every intensity bin except 145 kt. This finding provides additional confidence that environmental factors play a larger role in predicting TC intensity change at longer forecast times. SHIPS was also typically selected first in the TOTAL forecast equations at 36 h. However, this finding does not necessarily indicate that environmental factors are more important than TC core parameters, given that the skill of the NSNC method (discussed further in Chapter 6) does not decrease noticeably when SHIPS model guidance is excluded as a potential predictor. It is possible that SHIPS provides a better initial start for the forecast, but the details on a case-to-case basis are determined by core parameters. The forecast equations and matrices suggest that inner-core processes may play a more dominant role in short-term TC intensity change while environmental variables are more important factors beyond 36 h. Still, measures of the TC core do provide added skill to intensity forecasts at longer forecast times, even if these measurements are not explaining the bulk of the variance. The results of the ASPIRE technique will be presented next in Chapter 6.

Figure 5.1: Distribution of SHIPS model forecasts at 12 h used in TOTAL forecasts for the ASPIRE technique.

Figure 5.2: Distribution of climatological eye structure tool forecasts at 12 h used in TOTAL and NS forecasts for the ASPIRE technique.

Figure 5.3: Distribution of initial wind for 12-h forecasts.

Figure 5.4: Distribution of MSLP for 12-h forecasts.

Figure 5.5: Distribution of temperature inside the eye for 12-h forecasts.

Figure 5.6: Distribution of change in temperature inside the eye for 12-h forecasts.

Figure 5.7: Distribution of eye area multiplied by the temperature inside the eye for 12-h forecasts. Note the highly non-Gaussian distribution.

Figure 5.8: Same as Figure 5.7, but transformed by raising to the power 0.15.

Figure 5.9: Distribution of eye area multiplied by (1020-MSLP) for 12-h forecasts.

Figure 5.10: Same as Figure 5.9, but transformed by raising to the power 0.15.

Figure 5.11: Distribution of the initial wind speed squared divided by the radius of the eye for 12-h forecasts.

Figure 5.12: Same as Figure 5.11, but transformed by taking the natural logarithm.

Figure 5.13: Predictor matrix for NSNC forecasts at 12 h using the ASPIRE technique while applying the stopping rules described in Section 5.2 rather than using the final step of the regression. Predictors are listed from bottom to top according to frequency of use. Dots indicate the predictors selected for a given intensity bin.

Figure 5.14: Same as Figure 5.13, but for NS forecasts at 12 h using the ASPIRE technique.

Figure 5.15: Same as Figure 5.13, but for TOTAL forecasts at 12 h using the ASPIRE technique.

Figure 5.16: Same as Figure 5.13, but for NSNC forecasts at 36 h using the ASPIRE technique.

Figure 5.17: Same as Figure 5.16, but for NS forecasts at 36 h using the ASPIRE technique.

Figure 5.18: Same as Figure 5.16, but for TOTAL forecasts at 36 h using the ASPIRE technique.

Table 5.1: Summary of types of regression equation sets developed in the ASPIRE technique. Equation Set Acronym Data Included TOTAL All available data, including SHIPS and eye structure forecast tool NS Same as TOTAL but with SHIPS removed NSNC Same as TOTAL but with SHIPS and eye structure forecast tool predictors removed *Note that binned equations as well as a “full” regression equation including all available intensities were developed for all 3 of the above equation sets.

Table 5.2: Table of predictors chosen for stepwise regression (NSNC, NS, and TOTAL). Before regression is performed, all predictor distributions were examined for normality and transformed using natural logarithms or exponentials as necessary. Italicized predictor names denote variables which were transformed to achieve approximate normality. The number of times the predictors were selected during the NSNC, NS, and TOTAL methods using the step indicated by the stopping rules is also listed, with a maximum possible of 133 times selected (19 intensity bins by 7 forecast times).

Predictor Abbreviation Predictor Description NSNC NS TOTAL 1stAdvAge Seconds since first advisory issued 43 43 50 (1stHAge)^0.60 Seconds since first advisory at hurricane intensity, 74 72 61 raised to the power 0.60 (Abso(253-Jday))^0.35 Absolute value of the difference between Julian 89 88 57 day 253 and the Julian day of the VDM, raised to the power 0.35 (Area*(1020- Eye area multiplied by the difference between 1020 39 41 39 MSLP))^0.15 hPa and initial MSLP, raised to the power 0.15 Area*dTd Eye area multiplied by the prior change in 2 5 4 dewpoint inside the eye Area*dTi Eye area multiplied by the prior change 11 12 8 temperature inside the eye (Area*Tdiff(K))^0.20 Eye area multiplied by the prior change in the 5 4 4 difference between temperature (K) inside the eye and temperature outside the eye, raised to the power 0.20 (Area*theta)^0.20 Eye area multiplied by the potential temperature 0 0 2 inside the eye, raised to the power 0.20 (Area*thetae)^0.15 Eye area multiplied by the equivalent potential 4 4 5 temperature inside the eye, raised to the power 0.15 ((Area*(thetae- Eye area multiplied by the difference between 5 10 6 theta))+0.01)^0.05 equivalent potential temperature and potential temperature inside the eye, raised to the power 0.05 (Area*Ti)^0.15 Eye area multiplied by the temperature inside the 23 17 12 eye, raised to the power 0.15 (Area*wind)^0.15 Eye area multiplied by advisory wind, raised to the 10 8 13 power 0.15

Table 5.2—continued Predictor Abbreviation Predictor Description NSNC NS TOTAL (Area/MSLP)^0.25 Eye area divided by VDM MSLP, raised to the 20 15 17 power 0.25 Cos(lat)*wind Cosine of latitude multiplied by advisory wind 25 17 10 Cos(lat)/MSLP Cosine of latitude divided by VDM MSLP 81 84 53 (Dewdepr+1)^0.05 Dewpoint depression inside the eye, raised to the 24 27 28 power 0.05 Dewpointchange Prior change in the dewpoint inside the eye 6 3 3 Diam1^0.40 First eye diameter, raised to the power 0.40 1 1 0 Diam1change Prior change in the first diameter of the eye 16 20 20 Diff_theta Prior change in potential temperature inside the eye 12 10 8 Difftemp Difference between temperature inside the eye and 13 13 14 temperature outside the eye Difftempchange Prior change in the difference between temperature 12 12 7 inside the eye and temperature outside the eye Dpdtprev Prior change in VDM MSLP 27 28 24 Eye_area^0.20 Eye area, raised to the power 0.20 0 1 1 Eyetempi Temperature inside the eye 14 12 20 Eyetempichange Prior temperature change inside the eye 23 27 26 Eyetempo Temperature outside the eye 14 15 15 Eyetempochange Prior temperature change outside the eye 18 15 11 Fcst Climatological eye structure forecast 0 51 20 Jday Julian day 43 47 36 Lat Latitude 19 18 14 Lat*Lon Latitude multiplied by Longitude 47 42 39 Lon Longitude 38 39 37 Ln(dt) Natural logarithm of the number of seconds between 17 19 15 VDMs Ln(v^2/r) Natural logarithm of the advisory wind squared 29 21 21 divided by eye radius MSLP Mean sea level pressure reported in VDM 50 44 45 New_Eyetype Type of eye: 1=Concentric, 2=Circular, 3=Elliptical 53 56 59 -(Normdiff+1)^-1.0 Normalized difference between eye structure tool 0 15 28 forecasts and advisory wind, raised to the power - 1.0 Prev6wind 6-hour prior advisory wind 9 7 7 Prev6diff Prior 6-hour change in advisory wind 25 23 20 Prev12wind 12-hour prior advisory wind 14 17 16 Prev12diff Prior 12-hour change in advisory wind 25 21 18 Prevp6diff Difference between 6-hour prior advisory wind and 15 15 11 12-hour prior advisory wind S-Fcst Difference between SHIPS model forecast (S) and 0 0 24 eye structure forecast SHIPS SHIPS forecast issued at or prior to advisory 0 0 113

Table 5.2—continued Predictor Abbreviation Predictor Description NSNC NS TOTAL Sin(lat)*wind Sine of latitude multiplied by advisory wind 12 16 26 Sin(lat)/MSLP Sine of latitude divided by MSLP 25 21 20 Sqrt(1stTSAge) Square root of the number of seconds since the first 64 62 54 advisory at tropical storm status Td(K)^1.50 Dewpoint temperature (K) inside the eye, raised to 11 13 9 the power 1.50 Theta Potential temperature inside the eye 9 10 11 Theta(O) Potential temperature outside the eye 10 11 9 Thetae^0.05 Equivalent potential temperature inside the eye, 14 9 7 raised to the power 0.05 Thetae-Theta Difference between equivalent potential 5 6 6 temperature and potential temperature inside the eye Time_day Local hour of the day (UTC) 28 26 24 -(V/R)^-0.20 Advisory wind divided by eye radius, raised to the 1 1 1 power -0.20 -(V/R^2)^-0.10 Advisory wind divided by eye radius squared, 4 4 4 raised to the power -0.10 -(V^2/R^2)^-0.10 Advisory wind squared divided by eye radius 2 3 1 squared, raised to the power -0.10 Wind Advisory wind at or prior to the VDM 8 6 3 Wind*Prev6diff Advisory wind multiplied by the prior 6-hour 20 17 14 change in advisory wind Wind*Prev12diff Advisory wind multiplied by the prior 12-hour 21 17 24 change in advisory wind

Table 5.3: Julian day/Calendar day equivalent. Julian Day Calendar Day (non-leap years) 191-200 10 July-19 July 201-210 20 July-29 July 211-220 30 July-8 Aug 221-230 9 Aug-18 Aug 231-240 19 Aug-28 Aug 241-250 29 Aug-7 Sept 251-260 8 Sept-17 Sept 261-270 18 Sept-27 Sept 271-280 28 Sept-7 Oct 281-290 8 Oct-17 Oct 291-300 18 Oct-27 Oct 301-310 28 Oct-6 Nov 311-320 7 Nov-16 Nov 321-330 17 Nov-26 Nov

CHAPTER 6

ASPIRE RESULTS

The performance of the NSNC, NS, and TOTAL forecast equations in the ASPIRE technique was measured using both the out-of-sample R2pred produced by the regressions and the raw forecast errors produced using the full equation that includes all initial intensities. This chapter will first examine the results of two independent data samples to verify that the ASPIRE model works outside of the dependent data sample used to create the equations. An example of the superiority of the equations produced through the use of 20-kt running bins will next be shown. Following these preliminary steps, the ASPIRE technique will be compared to the current benchmark for statistical TC intensity forecasting, the SHIPS model. It should be noted that while all of the forecast equations and R2pred values were gathered using leave-one-out cross-validation by systematically removing one VDM at a time, all of the hindcast error results shown in this chapter (with the exception of those in Section 6.1) were obtained using the same dataset used to create the equations. Thus, the verification dataset was not completely independent. The leave-one-out cross-validation technique also does not account for serial correlation which can be a substantial problem for TCs. However, serial correlation likely does not significantly reduce the accuracy of the ASPIRE technique when applied to independent data, as discussed in the following section. Figure 6.1 shows the results of the full NSNC equation applied to all forecast intensities compared to SHIPS and persistence. The full NSNC equation is shown to be superior to SHIPS at all forecast times, with the most substantial improvement noted in short-term forecasting, particularly at 12 h. While these results are encouraging, the caveats noted above must be taken into account. Thus, the ASPIRE technique was tested on independent data samples as well, as described in the following section.

6.1 Testing of Developmental Equations on Independent Datasets

When performing statistical regression to create equations that will be used in a forecasting setting, how those equations will perform when confronted with independent (future) data is of primary concern. Equations that are highly accurate when tested on the dependent developmental data yet inaccurate when applied to future data are of little use to operational forecasters and suggest overfitting. The first step required when testing the results of the ASPIRE technique was to withhold two separate subsets of the data of approximately one fourth of the size of the full dataset spanning from 1991-2008 for independent performance examination. These two periods were from 1997-2002 and 2005-2008. In this process, one of the blocks of years—for example, 1997-2002—is removed from the developmental dataset, and a single full forecast equation valid for all initial intensities is created using the remaining years (1991-1996 and 2003-2008). Forecasts are then created for the period 1997-2002, and error statistics can be calculated which provide a more robust measure of the potential accuracy when applied to future data. This process was also repeated for the period from 2005-2008, using 1991-2004 as the developmental sample. Rather than leaving only one year out of the sample and testing each year separately using the process described above, removing a larger portion of the data increases the degree of difficulty for the resulting equations since there is less data available for developing accurate equations. Figure 6.2 shows the independent verification results for 1997-2002 in terms of the RMSE of NSNC forecasts produced at 12 h and 36 h. For comparison, the performance of SHIPS during the period 1997-2002 is also shown, along with the performance of dependent forecasts using the full time range from 1991-2008 and SHIPS from 1991-2008. As expected, the accuracy of the independent forecasts for 1997-2002 decreases when compared to the period from 1991-2008; however, this decrease was only roughly 1.5 kt at 12 h and 3 kt at 36 h, indicating that the ASPIRE technique performs reasonably well when applied to independent data given the reporting of wind is 5 kt in the database. Additionally, NSNC forecasts produced using the ASPIRE method improved upon the SHIPS model at 12 h by approximately 11% in the independent verifications for both 1997-2002 and 2005-2008. Dependent verification of NSNC forecasts for the entire period from 1991-2008 showed a 21% improvement beyond SHIPS. At

36 h, the independent NSNC forecasts did not outperform SHIPS, a common result for all forecast hours beyond 24 h. Independent verification results for the period 2005-2008 are provided in Figure 6.3. It can be seen that the average forecast error in terms of RMSE from both SHIPS and the NSNC method for the period 2005-2008 increase in comparison to that of Figure 6.2, indicating that TCs from 2005-2008 were somewhat more difficult to predict. 12-h forecasts from the NSNC method are again superior to those of the SHIPS model for both the dependent and independent data samples. However, SHIPS forecasts at 36 h outperformed those of the NSNC method. The superiority of SHIPS at 36 h was not entirely unexpected, as it was found that SHIPS is able to produce intensity forecasts reasonably well when working within a full range of intensities but that it produces less accurate forecasts when applied to smaller 20-kt intensity bins. Figure 6.4 shows the R2pred for SHIPS for the period 1991-2008 applied to all intensities compared to that when applied to Category 1 TCs only. It can be seen that SHIPS guidance performs better for the complete intensity range, implying that it has more potential predictive ability to forecast a future intensity range rather than a specific intensity within that range. Additionally, as shown in the predictor matrices in Figures 5.13-5.18, there is a tendency for thermodynamic and other core predictors to be selected less often than climatological, persistence, and environmental predictors at longer forecast lead times, indicating that SHIPS should be expected to exhibit increased accuracy compared to forecasts made using the NSNC equation at longer forecast times Given that SHIPS emphasizes environmental predictors, it would be expected that SHIPS would have an edge at longer lead times while the ASPIRE technique developed, which focuses on core measures, would have an edge at shorter lead times. The minimal decrease in performance of the full NSNC forecast equation applied to fully independent data as shown in the RMSE in Figures 6.2 and 6.3 implies that serial correlation is not greatly detrimental to the predictive ability of the ASPIRE technique. If serial correlation were indeed a problem, a correspondingly larger increase in the RMSE of the NSNC forecast equations would be expected when applied to the independent datasets. The fact that the NSNC method performed reasonably well for two separate independent time periods of very different TC climatologies further argues that the ASPIRE technique utilizes robust equations that are not sensitive to oscillations occurring on longer time scales, such as the El Niño/Southern Oscillation (ENSO), which occurs on a time scale of two to seven years (CPC 2009).

6.2 Improvement through the Use of Intensity Bins

A question to be asked is if the utilization of separate equations from running intensity bins increases the performance of the ASPIRE technique. While forecast equations using a narrower range of initial intensities may allow for greater representation of the detail on a case- to-case basis, it also means that the developmental sample size for each equation decreases significantly. Whether the overall performance improves depends upon how these two factors mitigate each other. To verify that a running bin does indeed improve model performance, the RMSE resulting from the use of binned equations produced for initial intensities of 105 kt, 125 kt, and 145 kt at a forecast lead time of 36 h were compared to the RMSE of forecasts using the full equation developed for all intensities. Forecasts from the SHIPS model and persistence are also provided for comparison. These three intensity bins were selected to demonstrate the performance of the ASPIRE technique for regions of high, average, and low confidence. As will be shown in Section 6.3, the initial intensity bin of 105 kt provides a minimum for forecast confidence, which is likely associated with concentric eyewall cycles as discussed in Chapter 4, while the intensity bin of 125 kt provides a relative maximum in forecast accuracy in terms of the R2pred. The 105 kt intensity bin included 41 VDMs for 13 TCs; the 125 kt bin included 41 VDMs for 12 TCs; and the 145 kt bin included 9 VDMs for 3 TCs. It is quite clear in Figure 6.5 that the use of intensity bins increases the performance of the ASPIRE technique when compared to the full equation, although noting that this increase in performance is measured using a remove-one-VDM out-of-sample technique. Improvement for TCs with an initial intensity of 105 kt was minimal, but the forecasts improved by nearly 5 kt for storms with an initial intensity of 125 kt. In contrast to Figure 6.3 in which the SHIPS model outperformed forecasts using the full NSNC equation of the ASPIRE technique applied to all initial intensities, Figure 6.5 shows that both the full NSNC equation and the binned NSNC equations are superior to the SHIPS model. This improvement is maximized when using the binned equations. The findings presented in Figure 6.5 support the use of equations created using a 20-kt running bin.

6.3 Comparison to SHIPS Benchmark

As previously mentioned, statistical TC intensity guidance—in particular, the SHIPS/D- SHIPS model—has provided the best operational intensity forecasts over the last decade (DeMaria et al. 2007). With this in mind, forecasts created using the ASPIRE technique are here compared to SHIPS rather than using the more traditional (and less skillful) comparison to SHIFOR (JN79). This section seeks to provide evidence that a new benchmark in TC intensity forecasting has been attained through the utilization of TC core measurements in statistical regression modeling. Forecasts produced using the ASPIRE model are examined first by intensity as a function of forecast length and then by geographical location and are compared to SHIPS as well as persistence.

6.3.1 ASPIRE Performance Stratified by Intensity R2pred performance through leave-one-VDM-out measures are given in Figures 6.6 through 6.9 for 12-, 24-, 36-, and 48-h forecasts using the NSNC equations of the ASPIRE technique. The binned regression equations using initial intensity subsets (blue lines) are compared to the regression equation encompassing all initial intensities (green lines) and the SHIPS forecasts (red lines). Results from the binned stepwise regressions are shown in Figure 6.6. It can be seen that both the full regression and the binned regressions outperform SHIPS for all initial intensities, with the binned routinely outperforming the full regression. A consistently high level of performance displayed by the binned regressions is seen, as the R2pred values remain between 60% and 70% for every initial intensity except 140 kt and 145 kt. The gap in performance between the NSNC regressions and the SHIPS model is most pronounced for TCs of Category 4 to Category 5 intensity on the Saffir-Simpson scale as the SHIPS model performance rapidly trends downward, indicating that the ASPIRE technique could yield valuable societal impacts from improved forecasting. The overall performance of the NSNC models at 12 h shows that storm-scale (rather than, or in addition to, environmental) predictors are likely essential for improving statistical TC intensity forecasting, further suggesting that the incorporation of TC core measurements into statistical models such as SHIPS could further enhance the quality of intensity forecasts. Alternatively, large-scale environmental parameters could be developed and included in future versions of the ASPIRE technique.

Results for the 24-h regression equations are shown in Figure 6.7. As expected, the overall performance of all three types of guidance decreases with increased forecast lead time. The full NSNC regression is actually surpassed by the SHIPS guidance for TCs with an initial intensity of 135 kt to 140 kt. Both the full regression and SHIPS show zero skill in terms of the R2pred at 24 h for storms stronger than 140 kt, a rather startling result considering that these storms should be somewhat easier to predict given the increased difficulty for a TC to maintain a very high intensity for an extended period of time. However, the binned analyses produce at least a 10% increase in R2pred beyond that of the SHIPS model for each initial intensity. Three distinct areas of relative minima in R2pred can be seen near 70 kt, 105 kt, and 140 kt. It is theorized that these skill minima are associated with the as-yet unpredictable nature of concentric eyewalls and ERCs in TCs, although progress in prediction of these events has been made recently (KS09). Again, the ability of the NSNC regression equations to outperform SHIPS for all initial intensities at 24 h reinforces the assertion that TC core measurements are essential for improving short-term TC intensity forecasts, acknowledging the caveat that these performance measures are not purely devoid of serial correlation concerns. Both the binned and full NSNC regressions at 36 h show a noticeable decrease in performance for TCs with an initial intensity of Category 1 to Category 2 strength, with Figure 6.8 indicating nearly a 20% reduction in R2pred compared to Figure 6.7. In addition to the expected decrease due to a longer forecast time, one potential explanation for this observation is that TCs may complete the self-organization and intensification process within 24 h of reaching Category 1 intensity, reducing the inherent predictability of strengthening associated with this stage of the TC life cycle. Storms at an initial intensity within the Category 4 range become more predictable at 36 h, with the R2pred of the SHIPS guidance reaching nearly 50% and the ASPIRE technique achieving slightly over 70% at 135 kt. Figure 6.9 shows the results of the regressions at 48 h. Interestingly, overall performance of the binned NSNC regression equations appears to increase when compared with Figure 6.8. The ASPIRE technique exhibits the best results for TCs of an initially higher intensity which is likely correlated with the increased likelihood for intense TCs to weaken over a longer period of time. It should be noted that the binned NSNC equations once again surpass the predictive ability demonstrated by the SHIPS model guidance at each initial intensity.

A more detailed discussion of some of the more intriguing aspects of Figures 6.6 through 6.9 is deserved. Figure 6.7 indicates that forecasts produced using both TC core measurements in the NSNC equations and environmental predictors in the SHIPS guidance fail to accurately forecast storms with an initial intensity of 100 kt to 110 kt. It is beyond the limits of the dataset used in this study to conclusively show that this distinct decrease in performance occurs as a direct result of concentric eyewalls and ERCs, given the relative infrequence of such events even in a period of 18 years. However, results from Piech (2007) do support the theory of ERCs initiating around 24 h following the formation of an eye. Figure 6.10 shows the mean MSLP and mean eye diameter along with their standard deviations for TCs occurring in the Gulf of Mexico from 1989-2005. Also shown are the frequency of concentric eyewall occurrence and frequency of elliptical eyewall occurrence as a function of the time since eye formation. It is seen that a relative maximum in elliptical eyewall occurrence occurs just prior to 24 h after eye formation, with a peak in concentric eyewall frequency at 24 h. Figure 6.11 shows a similar plot but for the Caribbean Sea. A sharp peak in frequency of elliptical eyewall occurrence occurs at 24 h. Additionally, Piech (2007) showed that one of the preferred regimes for concentric eyewall formation is from 935-945 hPa, coinciding with a TC of Category 3-4 intensity. Together, Figures 6.10 and 6.11 lend credence to the supposition that concentric eyewall cycles and structural changes of the eye of the TC create an inherently more unpredictable storm between 100 kt and 110 kt. The decrease in predictability at 36 h may also be explained by Figure 6.10. Following the concentric eyewall formation near 24 h, the standard deviation of the mean MSLP increases dramatically during the next 24 h, demonstrating the increased variability in TC intensity and suggesting a more difficult regime for TC intensity forecasting. The overall decrease in the R2pred trend at 36 h shown in Figure 6.8 is likely tied to the concentric eyewall cycles identified by Piech (2007). Figure 6.9 shows that the NSNC regression equations explain slightly more variance than the 36-h NSNC regression equations as shown in Figure 6.8. This finding again may be a result of concentric eyewall cycles. Figure 6.10 indicates that the mean MSLP briefly becomes approximately steady-state 48 h after eye formation, just prior to another cycle of increased probability of formation of an elliptical or concentric eyewall at 48 h. Recall also that forecasts made using the ASPIRE technique are subject to the same time adjustment described in Chapter 4 in which the VDM reported by the recon flights are matched with the prior advisory

wind, effectively moving the time of the VDM back to the previous advisory. Applying this slight adjustment in time to the second maximum in the frequency of occurrence of concentric eyewall cycles discussed in Piech (2007) causes it to fall slightly beyond 48 h, thus indicating that the increased predictability apparent in Figure 6.9 may be associated with the completion of an ERC. Figure 6.12 provides a more concise summary of the performance of the ASPIRE technique using the NSNC regression method. The out-of-sample R2pred is plotted as a function of forecast length and initial intensity, with warmer colors indicating a higher percentage of variance explained in the regression. This figure quickly reveals that the predictability of future TC intensity is strongly a function of the initial intensity of the hurricane. Three minima of forecast confidence are evident at the 70 kt, 105 kt, and 140 kt intensities, coinciding with the maxima in standard error associated with the eye structure forecast tool shown in Figure 4.2. As previously discussed, it is believed that these regimes of decreased forecast confidence are likely related to the occurrence of concentric eyewall cycles. The high percentage of variance explained for Category 5 storms from 42 h to 48 h in Figure 6.12 is also intriguing. While at first glance it may be suspected that this increase in R2pred is a result of overfitting the regression equations to the developmental data, an average of only 6 predictors are used for the four regression equations at these intensities, suggesting that overfitting may not pose a significant problem given the total of 40 to 107 VDMs within the intensity bins at 140 kt, 145 kt, and 150 kt. Another potential explanation for this region of high predictability is the increased probability of a general trend towards weakening for storms of such high intensity over a two-day period. However, examination of dependent forecasts produced using these equations indicates that the NSNC regression equations are not merely picking up on the general trend of a decrease in maximum wind speed. These equations allow for a greater number of forecasts of substantial weakening or intensification of greater than 50 kt over a 48-h period, and in a select few cases actually forecast a TC of nearly the same intensity 48 h later. In contrast, SHIPS never produces a forecast of intensification greater than 40 kt. This result indicates that the TC core measurements utilized within the ASPIRE technique could provide the necessary observations to improve our understanding of rapid changes in hurricane intensity.

Figures 6.13 and 6.14 show the same type of plot as in Figure 6.12 but for the NS and TOTAL methods, respectively. The predictive ability of the SHIPS model guidance is provided in Figure 6.15. The NS method shows a nearly identical pattern to that of the NSNC method. This result was expected, considering that the added predictors involving the climatological eye structure tool exhibited high variability. Figure 6.14 indicates that the inclusion of the SHIPS model guidance as a predictor in the regression modeling greatly increases the overall predictive ability of the ASPIRE technique. Three regimes of decreased predictive ability are still evident when using the TOTAL equations, but overall performance appears to increase by anywhere from 10% to 15%, indicating that environmental factors must also be accounted for in statistical TC intensity forecasting. For comparison, the predictive ability of the SHIPS model alone is provided in Figure 6.15. It is clear that SHIPS has very limited ability for very intense TCs, which is not surprising since the SHIPS forecast equations are modeled to the entire distribution rather than a 20-kt bin focused on an initial intensity within the Category 4 or 5 range, as is done here. Figure 6.15 also supports the claim by KDK09 that detailed inner-core data is likely necessary for improved RI forecasts since SHIPS exhibits a decrease in skill in the preferred regimes for concentric eyewall formation as identified by Piech (2007). However, contrary to KDK09, SHIPS appears to have two relative maxima of variance explained between 80 kt and 100 kt and again near 120 kt. These results suggest that inner-core data may be required for increased predictability of concentric eyewall cycles while environmental data is necessary for predicting the amount of strengthening that will occur following an ERC. The variance explained by SHIPS is maximized from 42 h to 48 h, consistent with the end of an ERC as discussed previously, again suggesting that environmental factors determine the extent of intensification following an ERC.

6.3.2 ASPIRE Performance Stratified by Geography The geographical distribution of forecast error using the ASPIRE technique is important to examine in case performance is better in certain areas of the Atlantic basin. Regional model biases can also be discerned along with possible forecast degradation for near-land cases. If the ASPIRE technique exhibits consistent positive or negative biases in a specific region, these biases could potentially be accounted for by TC forecasters in a real-time forecasting setting. The most straightforward method of inspecting model performance with respect to geography is

94 through the use of a scatter plot. In order to create these scatter plots, actual forecasts first had to be run, and the resultant errors associated with the forecasts had to be computed. Creating forecasts using the binned regression equations for every VDM in the 18-year database would have been prohibitively time-intensive. Instead, the single full NSNC equation which applies to all intensities was used to create these model forecasts to get a feeling for the geographic distribution of expected forecast error. Scatter plots were made at each of the forecast intervals for the NSNC method of the ASPIRE model as well as for the SHIPS model guidance in order to provide a comparison of performance between the two models. It should be noted that the forecast results presented in this section are not produced using a fully independent dataset. While a leave-one-out cross-validation technique was employed to formulate the regression equations, the forecasts are nonetheless being run on the same storms included in the developmental data; serial correlation may also increase overconfidence in these results, although this increase is small given the prior findings discussed in this chapter. The performance of the ASPIRE technique with respect to initial intensity discussed in the previous section provides proof that utilization of the binned equations would provide additional skill in reducing the magnitude of the forecast errors shown in this section, and it is assumed that the geographic pattern of error shown in this section would remain somewhat similar when using the binned equations. Figure 6.16 shows the scatter plot of forecast error for the NSNC method at 12 h. Positive error is indicative of overforecasting, while negative error shows that the ASPIRE technique underforecasted a specific event. It can be seen that the vast majority of the forecasts resulted in a 12-h forecast error magnitude within 10 kt of the observed value. The large amount of gray and light blue or yellow shading is encouraging since it shows that many of the forecasts yielded errors within 7.5 kt of the observation—or within less than half of a Saffir-Simpson category. Three primary areas of larger forecast error magnitude are apparent in the southern Caribbean Sea, near the Yucatan Peninsula, and in the central Gulf of Mexico. The very large positive forecast errors near the Yucatan Peninsula likely result from interaction of the TC with terrain. Large negative errors in both the Caribbean Sea and the Gulf of Mexico seem to be associated with periods of RI. The Loop Current in the Gulf is typically located in the same area as the largest negative errors from the NSNC forecasts initiated in that region, suggesting that

measures of the vertically integrated energy source of the TC should aid core-based forecasts of TC intensity. The forecast error for the SHIPS model at 12 h is provided in Figure 6.17. In general, the magnitude of forecast error produced by SHIPS appears to be larger for all areas of the Atlantic basin than those shown in Figure 6.16. The most notable degradation in forecast accuracy is evident in the Caribbean Sea and the Gulf of Mexico. The worst performance for TCs is found in the Gulf of Mexico, where several forecasts produce errors with a magnitude of 20 kt or more. Given the high population density clustered along the Gulf coast along with the abundance of oil rigs in the Gulf, these rather poor forecasts have a considerable societal impact, especially when one considers that, climatologically, a TC located in the Gulf of Mexico (Caribbean Sea) has greater than 90% (80%) probability of hitting land (Hart 2009). While the ASPIRE model forecast results shown in Figure 6.16 are not valid for independent data, it appears that this new technique may provide a tremendous boost to the accuracy of TC intensity forecasts through the incorporation of TC core measurements in statistical regression modeling. Figures 6.18 and 6.19 show the scatter plots of 24-h forecast error for the NSNC and SHIPS models, respectively. The same general pattern seen at 12 h is observed, with a tendency to overforecast TCs initially located near land and forecast performance minimized in the same areas. TC tracks in the Gulf end farther away from land due to landfall occurring by 24 h, causing forecasts using the ASPIRE technique to be invalid due to land interaction; thus, those points are removed at 24 h. NSNC forecast errors at 36 h are provided in Figure 6.20, and SHIPS errors at 36 h are shown in Figure 6.21. Again, forecasts using the ASPIRE technique show increased predictive ability in both the Gulf of Mexico and the Caribbean Sea, while the SHIPS model generally exhibits larger forecast error magnitudes. Similar results are seen for 48- h forecasts, shown in Figures 6.22 and 6.23. It is interesting to note that while the NSNC forecasts of the ASPIRE model tend to produce more accurate forecasts in the Gulf of Mexico and Caribbean Sea, the SHIPS model appears to outperform the ASPIRE technique for latitudes north of 30°N over the Atlantic Ocean. This finding intuitively is reasonable, given the increased predictive ability of NWP models over land in the U.S. attributable to the denser network of upper-air observation stations. As these mid-latitude weather systems traverse the U.S. mainland and emerge over water in the Atlantic, the NWP models are still capable of producing better forecasts for storms at higher

latitudes given the better upstream observation network than what is available over Mexico and Central America. Additionally, when a TC passes north of 35°N, the ocean itself is typically ceases to be an energy source as SSTs decrease. SST thus serves as a limiting factor for TC intensity as they move north through the Atlantic Ocean. Since the SHIPS model incorporates environmental predictors from the GFS model as well as SST data, a plausible conclusion is that environmental and oceanic parameters are more important for accurate TC intensity forecasting for TCs north of 30°N, allowing SHIPS to perform comparably with the ASPIRE technique for higher-latitude storms. However, the overall performance of the NSNC forecasts of the ASPIRE model is superior to that of SHIPS for the majority of the Atlantic basin. Two case studies of specific TCs from the 1991-2008 period, Hurricane Ivan (2004) and Hurricane Katrina (2005) are provided in Chapter 7 to provide a more in-depth analysis of good and poor performance from the ASPIRE technique.

6.4 Implications

The results of the NSNC forecasts shown in Section 6.3 indicate that a new benchmark in statistical TC intensity forecasting may have been reached. In particular, the binned equations through the ASPIRE technique—whether NSNC, NS, or TOTAL—appear to provide sets of the most skillful hurricane intensity forecast equations thus far developed, providing insight into the potential of incorporation of TC core measurements in a forecasting setting. A by-product of this research is the indication that additional Hurricane Hunter recon flights could allow more accurate intensity forecasts in the future, in particular for basins that do not regularly fly them such as the Pacific. The ASPIRE technique appears to show that data from recon flights is essential to breaking through the barrier that has been limiting TC intensity forecasting thus far. Alternatively, other methods of estimating TC core data, such as the utilization of satellite imagery as a proxy for TC core parameters typically reported in VDMs from recon flights, could also be used to produce more extensive coverage of core data for use in TC intensity forecasting.

Figure 6.1: RMSE for TCs from 1991-2008 using the full NSNC regression equation applied to all initial intensities. Results are valid as a dependent verification. Note that the NSNC forecasts (blue) outperform SHIPS (red) and persistence (green) at all forecast lead times.

Figure 6.2: Independent NSNC (blue) and SHIPS (red) forecast error results in terms of RMSE at 12 h (left) and 36 h (right) for the period 1997-2002. The ASPIRE technique outperforms SHIPS at 12 h but not at 36 h. For comparison, RMSE for the entire period 1991-2008 are provided for both the NSNC method (green) and SHIPS (purple).

Figure 6.3: Same as Figure 6.2, but for the independent period from 2005-2008. Results are similar to those seen for 1997-2002.

Figure 6.4: Comparison of R2pred of SHIPS guidance from 1991-2008 applied to all intensities (red) and SHIPS guidance from 1991-2008 applied to Category 1 TCs only (blue).

Figure 6.5: 36-h dependent forecast verification comparing the RMSE resulting from the binned NSNC forecast equations (blue) to SHIPS (red), the full NSNC regression equation (green), and persistence (purple) for three separate initial intensities. Note that the binned equations outperform the full equation for every intensity bin, with a nearly 5-kt improvement for an initial intensity of 125 kt.

Figure 6.6: Out-of-sample performance (R2pred) of the NSNC method in the ASPIRE model. Regression using 20-kt bins (blue) and the full regression (green) outperform SHIPS (red) at all initial intensities, with the binning yielding higher potential predictive ability than the full regression.

100

Figure 6.7: Same as Figure 6.6, but valid at 24 h. Note the decrease in predictive ability near 105 kt and 135 kt which is likely associated with the onset of concentric eyewall cycles.

Figure 6.8: Same as Figure 6.6, but valid at 36 h. Overall performance decreases substantially for all guidance, with SHIPS surpassing the ASPIRE technique at 85 kt. The notable decrease in predictive ability is likely associated with concentric eyewall cycles.

101

Figure 6.9: Same as Figure 6.6, but valid at 48 h. Performance increases compared to 36 h shown in Figure 6.8 and may be associated with the completion of an ERC. The binned NSNC regressions through the ASPIRE technique generally outperform the full regression and SHIPS.

102

Figure 6.10: Mean MSLP, mean eye diameter, and frequency of concentric and elliptical eyewall occurrence for the Gulf of Mexico, 1989-2005. Concentric and elliptical eyewall occurrence show a relative peak near 24 h after eye formation, and an increase in the standard deviation of the mean MSLP is seen immediately following these peaks. (Piech 2007)

103

Figure 6.11: Same as Figure 6.10 but for the Caribbean Sea. A defined peak in elliptical eyewall frequency is shown at 24 h after eye formation followed by a slight increase in the standard deviation of the mean MSLP. (Piech 2007)

104

Figure 6.12: Shaded plot of R2pred for the NSNC method of the ASPIRE technique using the specified stopping rules. Note the three distinct regions of decreased potential predictive ability at 70 kt, 105 kt, and 140 kt. No smoothing is applied to this image.

105

Figure 6.13: Same as Figure 6.12 but for the NS method of the ASPIRE technique. The same general pattern seen in the NSNC plot can be seen here, with the primary difference a slightly increased predictability at 70 kt, possibly due to the inclusion of climatological eye structure tool predictors and the climatological tendency of TCs to self-organize once developing an eye.

106

Figure 6.14: Same as Figure 6.12 but for the TOTAL method of the ASPIRE technique. Improvement in potential predictive ability due to the inclusion of environmental predictors in the SHIPS model can be seen, particularly for TCs of Category 2 intensity.

107

Figure 6.15: Same as Figure 6.12 but for SHIPS model guidance. Note the dramatic decrease in predictive ability compared to the ASPIRE technique. Two regions of increased performance occur from 80-100 kt and from 115-130 kt.

108

Figure 6.16: Scatter plot of binned NSNC forecast error with respect to geography (1055 VDM data points).

Figure 6.17: Same as Figure 6.16, but for SHIPS guidance at 12 h (1055 VDM data points).

109

Figure 6.18: Same as Figure 6.16, but for binned NSNC forecasts at 24 h (947 VDM data points).

Figure 6.19: Same as Figure 6.18, but for SHIPS guidance at 24 h (947 VDM data points).

110

Figure 6.20: Same as Figure 6.18, but for binned NSNC forecasts at 36 h (847 VDM data points).

Figure 6.21: Same as Figure 6.20, but for SHIPS guidance at 36 h (847 VDM data points).

111

Figure 6.22: Same as Figure 6.20, but for binned NSNC forecasts at 48 h (762 VDM data points).

Figure 6.23: Same as Figure 6.22, but for SHIPS guidance at 48 h (762 VDM data points).

112

CHAPTER 7

CASE STUDIES

Although the prior statistical analysis gives a measure of the overall performance of the ASPIRE model, individual case studies are needed to better understand the case-to-case variability of the model and the predictive ability of ASPIRE in a variety of different prediction conditions. For this reason, examinations of Hurricane Ivan (2004) and Hurricane Katrina (2005) are provided to show the respective performance of the NSNC method of the ASPIRE technique as it applies to specific TCs. Selection of cases was determined by two factors. First, for the well-predicted case (Ivan 2004), it was desired that the ASPIRE model hindcasts consistently beat SHIPS model guidance from 12 h through 48 h and NHC OFCL forecasts at least twice from 12 h through 48 h. The case of Hurricane Ivan satisfied this criterion. For the poorly-predicted example, it was desired that the ASPIRE model produce inferior hindcasts to OFCL forecasts and SHIPS guidance, and Hurricane Katrina (2005) met this condition. The second factor determining case selection was the need for a relatively robust number of VDMs for each case. A large number of VDMs allows for analysis of performance of the ASPIRE model for a broader range of forecast situations, including changes in the internal thermodynamic and structural characteristics of the hurricane as well as other synoptic-scale forcings not accounted for in the ASPIRE technique, such as environmental shear. 90 (28) VDMs were available for creation of 12-h hindcasts for Hurricane Ivan (Hurricane Katrina) over a 9-day (2-day) period from 6-15 September (26-28 August). The chance for serial correlation should not increase since a group of 2-6 VDMs is typically reported within 6-8 h on any given recon mission. The larger number of VDMs for these two cases is merely a function of the extended period of time during which these TCs were under surveillance by recon flights. Since an average of 4 VDMs is typically reported within any given recon mission which lasts an average of 11 h (Hurricane Hunters 2009), and given that VDMs separated by more than 8-12 h are unlikely to have a strong serial correlation, additional serial correlation beyond that which has already been discussed in Chapter 6 is highly unlikely. Table 7.1 provides the number of

113

VDMs for both Ivan and Katrina for each forecast length along with the average number of VDMs per TC in the developmental sample for the ASPIRE technique. These cases provide further insight into the varying factors (both meteorological and climatological) that may determine whether a case is well-forecast or poorly-forecast by the new technique and offer a foundation upon which to improve the ASPIRE model.

7.1 Well-Hindcast Case: Hurricane Ivan (2004)

7.1.1 Storm History Hurricane Ivan was a classic, long-track Cape Verde hurricane which was anomalously strong for a TC located so far southeast of the Lesser Antilles (Stewart 2005). Ivan was classified as a tropical depression (TD) at 1800 UTC 2 September, a tropical storm (TS) at 0600 UTC 3 September, and became a hurricane at 0600 UTC 5 September. Ivan traversed a portion of the Atlantic basin and the entire length of the Caribbean Sea as a hurricane and remained so until landfall around 0700 UTC 16 September on the northern Gulf Coast just west of Gulf Shores, Alabama, with winds of 105 kt (Category 3 hurricane on the Saffir-Simpson scale). Figure 7.1 gives the NHC best track of Ivan’s path. The primary mechanisms which allowed the formation of the TD and further intensification to TS status were very favorable upper-level outflow and a low-shear environment from 2-3 September, despite the fact that few TCs typically exist south of 10°N (Stewart 2005). Immediately after reaching hurricane strength, Ivan underwent a period of RI during which Dvorak estimates from satellites indicate that the maximum sustained wind speed increased by 50 kt in 18 h on 5 September, making Ivan the southernmost major hurricane on record in the Atlantic basin (Stewart 2005). Weakening of 20 kt ensued throughout 6 September due to mid- level dry air entrainment into the center of Ivan, disrupting the structure of the eyewall. During this time, Ivan was too far east for recon missions to be tasked, leaving satellites as the primary method for estimating intensity. By 1800 UTC 6 September, recon flights reached Hurricane Ivan, and direct measurements of MSLP via dropsondes became available. Hindcasts using the ASPIRE technique were initialized after the second VDM report at 1919 UTC 6 September. Thus, the majority of the period of mid-level dry air entrainment on 6 September was not incorporated into the ASPIRE hindcasts.

114

Ivan strengthened once again from 7-9 September with two brief periods of RI. Brief weakening occurred as Ivan moved south of Jamaica on 11 September, likely due to an ERC (Stewart 2005). Throughout the concentric eyewall cycles, Ivan maintained at least Category 4 status. By 13 September, Ivan re-intensified to 140 kt and maintained Category 5 status for 30 h, likely influenced by high values of OHC (Shay 2006). By the next day, steady weakening ensued, most likely due to very strong vertical wind shear as the upper-level flow increased to 30 kt or greater. Dry air advecting around or into the core, cooler, shallower shelf waters, and additional ERCs (not directly reported in the VDMs, as they occurred between flights) all likely contributed to the weakening trend prior to landfall.

7.1.2 Performance and Analysis of ASPIRE Hindcasts Despite the forecasting challenges present during Hurricane Ivan, including multiple ERCs, two periods of dry air entrainment, increased vertical wind shear, and slight interaction with the rugged topography of Jamaica, the hindcasts produced using the NSNC method of the ASPIRE technique were comparable to OFCL forecasts and superior to the SHIPS model. This result is due in part to the lack of use of an independent regression dataset for Hurricane Ivan along with potential serial correlation, although results from Chapter 6 suggest that this bias is not substantial. Still, the hindcasts exhibited a consistent improvement on SHIPS model guidance at every forecast period. Figure 7.2 shows the RMSE for the NSNC method of the ASPIRE technique (blue), SHIPS model guidance (red), and NHC OFCL forecasts (green). At all forecast times, the ASPIRE technique outperformed SHIPS; additionally, the RMSE of ASPIRE was less than that of OFCL forecasts at both 12 h and 36 h and was within 1 kt at 24 h and 48 h. Although Stewart (2005) recognized dry air advected into the inner core of Ivan as one of several potential mechanisms for weakening on 6 September as well as from 14-15 September prior to landfall, that dry air was never readily apparent in dewpoint measurements as reported in VDMs. Since the eye is dry by nature, it is likely difficult to see the effects of dry air intrusion from measurements taken within the eye. Figures 7.3 and 7.4 show the 500 hPa relative humidity along with the MSLP of Ivan on 6 September and 15 September, respectively. While it is possible that the mid-level dry air was not able to penetrate entirely into the center of Ivan at either time, the eyewall did begin to erode in each case, as noted by NHC (Stewart 2005). The

115

NSNC hindcasts may not have been impacted as significantly by dry air in the surrounding area if the dry air indeed did not penetrate fully into Ivan’s core since the ASPIRE model only includes a dewpoint measurement from inside the eye. Regardless, the ASPIRE technique hindcast intensity during these periods of dry air entrainment relatively well, with errors typically less than 5 kt. From 11 September through the early morning hours of 13 September, Hurricane Ivan experienced a series of concentric eyewalls and ERCs. These structural changes, usually involving rapid changes in eyewall diameter, present particularly difficult forecast challenges using the ASPIRE technique—especially for the full regression equation which is valid for all intensities. It is suspected that these structural changes, which are not represented well in the full regression equation, may be better captured through the utilization of the binned equations in the NSNC method. This theory will be further expounded upon in the following section regarding Hurricane Katrina. Unfortunately, without additional extensive testing of these equations on independent data, it is impossible to quantify potential performance of these binned equations. Hindcast errors during these structural regime changes ranged from 5 kt to 15 kt at 12 h and tended to only become slightly larger at longer forecast times. A possible explanation for the relatively small increase in forecast error for longer forecast lead times is that the verification wind speeds for Hurricane Ivan were highly consistent, ranging only from 115 kt to 140 kt over the entire period of 9 days of VDMs. This constrained range of observed wind speeds also allowed the persistence variables within the ASPIRE technique to produce reliable forecasts, surpassing NHC OFCL forecasts at both 12 h and 36 h.

7.2 Poorly-Hindcast Case: Hurricane Katrina (2005)

7.2.1 Storm History Katrina was an extremely large, powerful hurricane that became the costliest TC to ever strike the U.S. (Knabb et al. 2006). The genesis of Katrina was highly complex and involved several different atmospheric phenomena. It became a TD at 1800 UTC 23 August over the Bahamas, intensified to a TS at 1200 UTC 24 August, and reached hurricane status at 2100 UTC 25 August just prior to its first landfall over the southeastern portion of the Florida peninsula. An eye first became visible on the Miami National Weather Service WSR-88D radar prior to

116 landfall, and the eye actually became more defined as it crossed the Everglades (Knabb et al. 2006). After briefly weakening during passage over the Everglades, it quickly re-intensified to hurricane status at 0600 UTC 26 August, approximately one hour after emerging back over the Gulf of Mexico. Katrina proceeded to undergo two periods of RI from 26-28 August, achieving Category 5 status on 28 August after intensifying by 50 kt within 18 h. Katrina weakened to 110 kt while approaching the northern Gulf Coast before making its second landfall near Buras, Louisiana. It briefly emerged over water once again and hit land a third time on the south-central coast of Mississippi. The NHC best track of Hurricane Katrina is shown in Figure 7.5. Katrina was able to rapidly intensify after entering the Gulf of Mexico as it became located underneath an upper-level anticyclone encompassing the entire Gulf. RI was also promoted by the especially high OHC associated with warm-core ocean eddies shed from the Loop Current in the Gulf of Mexico (Shay 2006). This anticyclone created an environment virtually devoid of wind shear and also enhanced the upper-level outflow. Two periods of RI and two ERCs accompanied by structural changes represented the most challenging aspect of forecasts for Katrina (Knabb et al. 2006). The first RI period occurred on 26 August shortly after its entrance into the Gulf of Mexico. Following this RI, a secondary eyewall developed during the day on 27 August. The first ERC ensued, causing deterioration of the inner eyewall. During the ERC, the wind speed remained virtually constant. Immediately after this ERC, the outer eyewall contracted, resulting in intensification through Sawyer-Eliassen nonlinear balance vortex arguments (Eliassen 1951; SW82; WCS82), and Katrina rapidly intensified early on 28 August to Category 5 intensity. Prior to landfall, another outer concentric eyewall began to form; however, this secondary eyewall never fully consolidated. As the inner eyewall deteriorated, the lack of a fully-formed outer eyewall allowed rapid weakening (RW) to Category 3 status before landfall.

7.2.2 Performance and Analysis of ASPIRE Hindcasts The RI period and ERCs associated with Hurricane Katrina made it a particularly difficult TC to forecast. The NSNC method of the ASPIRE technique was noticeably inferior to NHC OFCL forecasts at every time from 12 h through 48 h, and the skill of ASPIRE hindcasts surpassed SHIPS only at 12 h. Figure 7.6 shows the RMSE of the NSNC method hindcasts, NHC OFCL forecasts, and SHIPS model guidance for VDMs reported from 26-28 August.

117

The NSNC hindcasts did attempt to predict intensification of as much as 15 kt for forecasts at 12 h (technically an RI forecast), but they were simply incapable of correctly predicting an increase in wind speed of 40 kt in 12 h. In fact, the largest wind speed increase of any 12-h hindcast through the ASPIRE method for TCs from 1991-2008 was 27 kt. Nonetheless, it is intriguing that the core data alone appears capable of producing forecasts of rather large RI while having no direct knowledge of the extremely favorable environment surrounding the storm. It is quite likely that inclusion of environmental parameters such as vertical shear and divergence as well as detailed information of OHC in the ASPIRE technique would allow for increased strengthening in a situation such as this one seen in Hurricane Katrina. Also, despite the lack of knowledge of the storm environment, the ASPIRE technique produced a hindcast of at least Category 3 intensity for each VDM reported between 1800 UTC 26 August through 0000 UTC 29 August. Prediction of the RI periods occurring in Katrina worsened with increased forecast time. Beyond 18 h, the ASPIRE technique showed very little increase in maximum wind speed, and all hindcasts produced predicted wind speeds that were at least 15 kt less than observed. Examination of the full NSNC regression equation (valid for all wind speeds, not the binned equations) revealed that persistence predictors were picked earlier and more often at longer forecast lead times. Thus, the overwhelming influence of persistence precludes the full NSNC equation from correctly predicting RI. In contrast, the binned NSNC equations tend to incorporate other core predictors, such as thermodynamic variables, much more regularly. It is believed that utilization of the binned equation set may lead to greater variability in TC intensity forecasting and may allow more frequent forecasts of RI. Structural changes associated with ERCs also had a noticeable detrimental impact on ASPIRE hindcasts as well as OFCL and SHIPS forecasts. The full NSNC equation inherently is dominated by predictors associated with the most common type of TC structure reported in the VDMs—circular eyewalls. Due to the drastic under-representation of concentric eyewall structures (5.8% of all VDMs), the conditions associated with these storms are not captured in the full equation. Additionally, as shown by Piech (2007), elliptical eyewalls often precede a concentric period. Only 14.3% of all VDMs reported an elliptical eyewall. Combined, concentric and elliptical eyewalls account for roughly 20% of all eye structures in the developmental data. Therefore, accurate forecasts during these periods of rapid structural and

118 dynamical changes are believed to be virtually impossible. However, as discussed previously, since there appear to be preferred regimes for development of concentric eyewalls and ERCs, it is entirely possible that these structures may be more reliably predicted using the binned equations. Alternatively, a separate regression equation formulated from a developmental database comprised of all concentric and elliptical eyewall reports may need to be created and is proposed for future research. For the case of Hurricane Katrina, during the ERC on 27 August, the inner eyewall diameter jumped sharply from 8 nm to 40 nm after the inner eyewall dissipated. Examination of the full regression equation used to produce the hindcasts for Katrina revealed that parameters involving the area of the eye tended to have a relationship with the predicted wind speed such that a smaller eye produced greater wind speeds, as expected. For a circular eye, this correlation is supported by the Sawyer-Eliassen nonlinear balance vortex model as well as prior research on the relationship between intensity and structure—as a larger eye contracts, wind speed forecasts progressively increase. However, in some cases, for periods of significant structural changes, such as the aforementioned ERC of Katrina, the wind speed may not decrease noticeably and often remains nearly steady-state. If the TC is able to maintain a relatively constant wind speed during an ERC, it often will be followed by a period of RI as the larger, new eyewall contracts. Due to this occurrence in Katrina, the full regression equations were unable to produce accurate forecasts during the ERC. Knabb et al. (2006) also noted that dry air entrainment, gradually increasing wind shear, and slightly lower SSTs all could have contributed to the weakening of Katrina prior to landfall on 28 August. Figure 7.7 shows the GFS operational analysis of relative humidity at 600 hPa for 1200 UTC 28 August. Dry air (RH < 60-70%) to the west of Katrina is clearly visible impinging upon the storm circulation. Figure 7.8 shows the 850 hPa-200 hPa vertical wind shear analyzed by the GFS analysis at 0600 UTC 29 August. Strong shear approaching from the northwest of Katrina can also be seen, perhaps in association with the trough that is helping to turn Katrina to the north. In this case, it appears that the dry air entrainment and wind shear had detrimental impacts on hindcasts produced using the ASPIRE technique since it has no knowledge of the TC environment specific to this case. Incorporating environmental predictors into the regressions could prove crucial for improved RI forecasting, suggesting a merger of the environmental benefits of SHIPS and the core benefits of ASPIRE.

119

One final point of interest is that the climatological aspect of the statistical ASPIRE technique may actually be quite beneficial for TCs nearing landfall on the northern coast of the Gulf of Mexico. According to Knabb et al. (2006), an unpublished study conducted by NHC in 2006 found that over the last 20 years, all TCs with a MSLP of less than 973 hPa 12 h prior to landfall on the northern coast of the Gulf weakened during those last 12 hours. For both Hurricane Ivan and Hurricane Katrina, the ASPIRE technique also forecasted weakening during the final 12 h, despite having no knowledge of the progressively more hostile environment each was entering. Perhaps the ASPIRE technique will be capable of providing more accurate forecasts of TCs approaching landfall on the Gulf Coast, given these preliminary results.

120

Figure 7.1: NHC best-track positions for Hurricane Ivan, 2-24 September 2004, courtesy of the National Hurricane Center (http://www.nhc.noaa.gov/2004atlan.shtml).

Figure 7.2: RMSE (kt) for Hurricane Ivan (2004) comparing NSNC (blue), NHC OFCL (red), and SHIPS (green).

121

Figure 7.3: 500 hPa relative humidity (%; shaded) and MSLP (hPa; contour) for Hurricane Ivan (11.0°N, 52.5°W) at 1200 UTC 06 September 2004 from the GFS operational analysis.

Figure 7.4: Same as Figure 7.3, but for 0000 UTC 15 September 2004.

122

Hurricane Katrina 23-31 August 40 31 Hurricane Tropical Storm Tropical Dep. Extratropical Subtr. Storm 35 Subtr. Dep. Low / Wave 00 UTC Pos/Date 30 12 UTC Position PPP Min. press (mb) 928 mb

30 920 mb 902 mb 29 26 25 25 28 984 mb 27 24

20 -95-90-85-80-75-70

Figure 7.5: NHC best-track positions for Hurricane Katrina, 23-31 August 2005, courtesy of the National Hurricane Center (http://www.nhc.noaa.gov/2005atlan.shtml).

Figure 7.6: RMSE (kt) for Hurricane Katrina (2005) comparing NSNC (blue), NHC OFCL (red), and SHIPS (green).

123

Figure 7.7: 600 hPa relative humidity (%; shaded) and MSLP (hPa; contour) for Hurricane Katrina at 1200 UTC 28 August 2005 from the GFS operational analysis.

Figure 7.8: 850 hPa-200 hPa vertical wind shear (kt; shaded) and MSLP (hPa; contour) for Hurricane Katrina at 0600 UTC 29 August 2005 from the GFS operational analysis.

124

Table 7.1: Number of VDMs by forecast hour for Hurricanes Ivan and Katrina along with the average number of VDMs per TC in the ASPIRE database from 1991-2008.

12 hr 18 hr 24 hr 30 hr 36 hr 42 hr 48 hr Ivan 90 88 85 83 77 77 74 Katrina 28 24 20 18 15 12 9 Average 9.5 9.2 9.3 9.4 9.4 9.2 9.3

125

CHAPTER 8

CONCLUSIONS AND FUTURE WORK

Accurately forecasting hurricane intensity remains a challenge even though much progress has been made in improving TC track forecasting. Despite the increasing amount of observations from within the TC core in the Atlantic basin in particular, relatively little research focusing on improved operational intensity forecasting has been performed which utilizes this data. Instead, the majority of TC intensity forecasting studies have focused on the influence of the storm environment and its impacts on intensity change. Advances in computing power have permitted meteorological centers to develop more sophisticated dynamical models (e.g. WRF, HWRF, GFDL); yet, the skill of intensity forecasts from these high-resolution dynamical models still lags that of statistical models. The study performed here has attempted to build on the successes of the SHIPS-style regression model to create a statistical regression scheme (ASPIRE) that utilizes core measurements provided in VDMs to produce TC intensity forecasts from 12 h to 48 h. A VDM climatology from 1991-2008 was presented which included information such as eye type, eye size, eye diameter, MSLP, temperature, and dewpoint, to name a few parameters. Distributions of each parameter were examined, and their relationship to our understanding of the processes behind rapid intensity change and structural change were explored. An eye structure forecast tool was created through which the expected climatological rate of intensity change can be produced from 12 h to 48 h, given an initial eye diameter from a VDM and an advisory wind speed. These diagrams revealed that TCs with a wind speed of less than (greater than) 95 kt will strengthen (weaken), climatologically. This finding argues that the 95 kt threshold fundamentally represents a transitional intensity in the evolution of a TC. The standard error associated with the mean plots of rate of intensity change was also presented. These plots indicated that there are three intensity regimes with increased variability. The possibility that these regimes may be related to preferred areas for concentric eyewall development and ERCs was discussed. The relationship of the climatological 12-h change in intensity to Sawyer- Eliassen balance was also discussed, offering a potential explanation for the observed tendency

126 of strengthening for TCs with an intensity of less than 95 kt. Simple forecasts using the eye structure tool were created. While these intensity forecasts based solely on climatological characteristics of TCs gathered from VDMs have limited use in an operational setting, they could prove beneficial as a new verification benchmark for TCs in the Atlantic basin that have an eye. Future work involving these eye structure forecasts will seek to create confidence intervals within which the mean intensity of the TC can be expected to fall with 95% certainty. A stepwise multiple linear regression scheme to predict TC intensity change in the Atlantic basin (ASPIRE) was also developed. The ASPIRE technique utilized TC inner core measurements reported in VDMs as well as persistence variables. Other thermodynamic predictors and measures of inertial stability were computed and included as potential predictors in an attempt to take full advantage of the available data resources provided in VDMs. Three separate sets of equations were created (TOTAL, NS, and NSNC). Each of these methods had one full equation in which a single equation was used to produce forecasts for TCs of all intensities. Separately, forecast equations using running bins of 20 kt initial intensity were also developed for each of the three methods. Results of independent testing for the periods from 1997-2002 and 2005-2008 show that the NSNC method of the ASPIRE technique performs reasonably well for independent data. Comparisons of potential predictive ability as measured by the R2pred along with RMSE calculations demonstrated that the binned equations outperform their full regression equation counterparts for virtually every intensity bin at all forecast lead times. Dependent tests of the overall performance of the NSNC models at 12 h shows that storm-scale predictors are likely essential for improving statistical TC intensity forecasting and suggests that the incorporation of TC core measurements into statistical models such as SHIPS could further enhance the quality such forecasts. Regimes of decreased potential predictive ability through the ASPIRE technique—likely associated with concentric eyewalls and ERCs— were evident in Figure 6.12. This figure quickly revealed that the predictability of future TC intensity is strongly a function of the initial intensity of the hurricane, with three minima of forecast confidence evident at the 70 kt, 105 kt, and 140 kt intensities. Figure 6.15 showed that SHIPS exhibits a decrease in skill in these preferred regimes for concentric eyewall formation. At the same time, two areas of increased predictive ability from the SHIPS model located between these concentric regimes were also noted. These results suggest that inner-core data

127 may be required for increased predictability of the onset of concentric eyewall cycles while environmental data is necessary for predicting the amount of strengthening that will occur following an ERC. The performance of the ASPIRE technique indicates that a new benchmark in statistical TC intensity forecasting may have been attained for forecasts within 24 h, while combination of core predictors utilized in ASPIRE with environmental and oceanic predictors in SHIPS may improve forecasts from 24 h to 48 h. However, without extensive testing of ASPIRE on independent data, no definitive conclusions on the effectiveness of this model can be drawn as of yet. The rather inactive 2009 Atlantic hurricane season precluded independent real-time testing of the ASPIRE technique from being performed. However, preliminary independent results from Hurricane Bill (not shown) indicate that the NSNC method of the ASPIRE technique was superior to SHIPS model guidance and comparable to NHC OFCL forecasts. Future work with the ASPIRE technique will seek to expand the version detailed in this study to create a new regression scheme valid for tropical systems of weaker intensities. Rather than using 700 hPa flight level data, that work will focus on 850 hPa flight level data and will attempt to utilize core measurements of temperature and dewpoint in a new regression scheme to predict TC intensity change. A regression developed specifically for concentric and elliptical eyewalls may improve the accuracy of TC intensity forecasts for TCs undergoing ERCs. The ASPIRE technique may also see additional improvement beyond that described in this study through the inclusion of predictors such as vertical wind shear, upper-level divergence, and OHC. Finally, the ASPIRE technique may be able to be expanded to other ocean basins where recon flights are not currently flown, such as the West Pacific, through the use of satellite data to create proxy VDMs.

128

REFERENCES

Bender, M.A., I. Ginis, R. Tuleya, B. Thomas, and T. Marchok, 2007: The Operational GFDL Coupled Hurricane–Ocean Prediction System and a Summary of Its Performance. Mon. Wea. Rev., 135, 3965–3989.

Berg, R., C. Sisko, and M. DeMaria, 2004: High Resolution SST in the SHIPS Model: Improving Operational Guidance of Tropical Cyclone Intensity Forecasts. Preprints, 26th Conf. on Hurricanes and Tropical Meteorology, Miami, FL, Amer. Meteor. Soc., 536-537.

Bloemer, M., 2008: A Climatology and Analysis of the Decay of Tropical Cyclones Making Landfall in the US from the Atlantic Basin. M.S. Thesis, Florida State University, 93 pp.

CPC, cited 2009: Frequently Asked Questions about El Niño and La Niña. [Available online at http://www.cpc.ncep.noaa.gov/products/analysis_monitoring/ensostuff/ensofaq.shtml#HOWO FTEN].

DeMaria, M., and J. Kaplan, 1994: A Statistical Hurricane Intensity Prediction Scheme (SHIPS) for the Atlantic Basin. Wea. Forecasting, 9, 209–220.

------, and J. Kaplan, 1999: An Updated Statistical Hurricane Intensity Prediction Scheme (SHIPS) for the Atlantic and Eastern North Pacific Basins. Wea. Forecasting, 14, 326–337.

------, M. Mainelli, L.K. Shay, J.A. Knaff, and J. Kaplan, 2005: Further Improvements to the Statistical Hurricane Intensity Prediction Scheme (SHIPS). Wea. Forecasting, 20, 531–543.

------, J.A. Knaff, and J. Kaplan, 2006: On the Decay of Tropical Cyclone Winds Crossing Narrow Landmasses. J. Appl. Meteor. Climatol., 45, 491–499.

------, J.A. Knaff, and C.R. Sampson, 2007: Evaluation of Long-term Trends in Operational Tropical Cyclone Intensity Forecasts. Meteor. Atmos. Phys., 59, 19-28.

------, 2009: A Simplified Dynamical System for Tropical Cyclone Intensity Prediction. Mon. Wea. Rev., 137, 68–82.

Demuth, J.L., M. DeMaria, and J.A. Knaff, 2006: Improvement of Advanced Microwave Sounding Unit Tropical Cyclone Intensity and Size Estimation Algorithms. J. Appl. Meteor. Climatol., 45, 1573–1581.

Eliassen, A., 1951: Slow Thermally or Frictionally Controlled Meridional Circulation in a Circular Vortex. Astrophys. Norv., 5, 19-60.

Elsberry, R.L., E.L. Weniger, and D.H. Meanor, 1988: A Statistical Tropical Cyclone Intensity Forecast Technique Incorporating Environmental Wind and Vertical Wind Shear Information. Mon. Wea. Rev., 116, 2142–2154.

129

Elsberry, R.L., 1995: Global Perspectives on Tropical Cyclones. WMO Report TD-No. 693, Geneva, Switzerland, 289 pp.

Emanuel, K.A., 1988: The Maximum Intensity of Hurricanes. J. Atmos. Sci., 45, 1143–1155.

Emanuel, K., 2000: A Statistical Analysis of Tropical Cyclone Intensity. Mon. Wea. Rev., 128, 1139–1152.

Fitzpatrick, P.J., 1997: Understanding and Forecasting Tropical Cyclone Intensity Change with the Typhoon Intensity Prediction Scheme (TIPS). Wea. Forecasting, 12, 826–846.

Franklin, J., 2008: 2007 National Hurricane Center Forecast Verification Report. [Available online at http://www.nhc.noaa.gov/verification/pdfs/Verification_2007.pdf].

Franklin, J., 2009: 2008 National Hurricane Center Forecast Verification Report. [Available online at http://www.nhc.noaa.gov/verification/pdfs/Verification_2008.pdf].

Glahn, H.R., 1985: Statistical Weather Forecasting. In: A.H. Murphy and R.W. Katz, eds., Probability, Statistics, and Decision Making in the Atmospheric Sciences. Boulder, Westview, 289-335.

Hart, R., 2009: Historical and Current Tropical Cyclone Landfall Risk. [Available online at http://moe.met.fsu.edu/tcprob/].

Holland, G.J., and R.T. Merrill, 1984: On the Dynamics of Tropical Cyclone Structural Changes. Quart. J. Roy. Meteor. Soc., 110, 723-745.

Hurricane Hunters, 2009: Frequently Asked Questions. [Available online at http://www.hurricanehunters.com/faq.htm].

Jarvinen, B.R., and E.L. Caso, 1978: A Tropical Cyclone Data Tape for the North Atlantic Basin, 1886-1977: Contents, Limitations, and Uses. NOAA Technical Memorandum S NHC 6, Scientific Services Division, Fort Worth, Texas, 19 pp.

------, and C.J. Neumann, 1979: Statistical Forecasts of Tropical Cyclone Intensity Change. NOAA Tech. Memo. NWS NHC-10, 22 pp. [Available from the National Technical Information Service, U.S. Department of Commerce, 5285 Port Royal Rd., Springfield, VA 22151].

------, C.J. Neumann, and M.A.S. Davis, 1984: A Tropical Cyclone Data Tape for the North Atlantic Basin, 1886-1983: Contents, Limitations, and Uses. NOAA Tech. Memo. NWS NHC-22, 21 pp.

Kalnay, E., et al., 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77, 437–471.

130

Kaplan, J., and M. DeMaria, 1995: A Simple Empirical Model for Predicting the Decay of Tropical Cyclone Winds after Landfall. J. Appl. Meteor., 34, 2499–2512.

Kaplan, J., and M. DeMaria, 2001: On the Decay of Tropical Cyclone Winds after Landfall in the New England Area. J. Appl. Meteor., 40, 280–286.

Kaplan, J., and M. DeMaria, 2003: Large-Scale Characteristics of Rapidly Intensifying Tropical Cyclones in the North Atlantic Basin. Wea. Forecasting, 18, 1093–1108.

Kaplan, J., M. DeMaria, and J.A. Knaff, 2009: A Revised Tropical Cyclone Rapid Intensification Index for the Atlantic and Eastern North Pacific Basins. Weather and Forecasting: In Press.

Kimball, S.K., and M.S. Mulekar, 2004: A 15-Year Climatology of North Atlantic Tropical Cyclones. Part I: Size Parameters. J. Climate, 17, 3555–3575.

Kistler, R., et al., 2001: The NCEP–NCAR 50–Year Reanalysis: Monthly Means CD–ROM and Documentation. Bull. Amer. Meteor. Soc., 82, 247–267.

Knabb, R.D., J.R. Rhome, and D.P. Brown, 2006: Tropical Cyclone Report, Hurricane Katrina. National Hurricane Center, 43 pp. [Available online at http://www.nhc.noaa.gov/pdf/TCR- AL122005_Katrina.pdf].

Knaff, J.A., M. DeMaria, C.R. Sampson, and J.M. Gross, 2003: Statistical, 5-Day Tropical Cyclone Intensity Forecasts Derived from Climatology and Persistence. Wea. Forecasting, 18, 80–92.

------, J.P. Kossin, and M. DeMaria, 2003: Annular Hurricanes. Wea. Forecasting, 18, 204– 223.

------, and R.M. Zehr, 2007: Reexamination of Tropical Cyclone Wind–Pressure Relationships. Wea. Forecasting, 22, 71–88.

------, T.A. Cram, A.B. Schumacher, J.P. Kossin, and M. DeMaria, 2008: Objective Identification of Annular Hurricanes. Wea. Forecasting, 23, 17–28.

Kossin, J.P., and M. Sitkowski, 2009: An Objective Model for Identifying Secondary Eyewall Formation in Hurricanes. Mon. Wea. Rev., 137, 876–892.

Kuo, H.C., L.Y. Lin, C.P. Chang, and R.T. Williams, 2004: The Formation of Concentric Vorticity Structures in Typhoons. J. Atmos. Sci., 61, 2722–2734.

Kurihara, Y., R.E. Tuleya, and M.A. Bender, 1998: The GFDL Hurricane Prediction System and Its Performance in the 1995 Hurricane Season. Mon. Wea. Rev., 126, 1306–1322.

131

Law, K.T., and J.S. Hobgood, 2007: A Statistical Model to Forecast Short-Term Atlantic Hurricane Intensity. Wea. Forecasting, 22, 967–980.

Merrill, R.T., 1988: Environmental Influences on Hurricane Intensification. J. Atmos. Sci., 45, 1678–1687.

Molinari, J., and D. Vollaro, 1989: External Influences on Hurricane Intensity. Part I: Outflow Layer Eddy Angular Momentum Fluxes. J. Atmos. Sci., 46, 1093–1105.

Montgomery, M.T., and R.J. Kallenbach, 1997: A Theory for Vortex Rossby-waves and Its Application to Spiral Bands and Intensity Changes in Hurricane. Quart. J. Roy. Meteor. Soc., 123, 435-465.

Neumann, C.J., 1972: An Alternate to the HURRAN Tropical Cyclone Forecast System. NOAA Tech. Memo. NWS SR-62, 22 pp. [Available from the National Technical Information Service, U.S. Department of Commerce, 5285 Port Royal Rd., Springfield, VA 22151].

------, B.R. Jarvinen, C.J. McAdie, and J.D. Elms, 1993: Tropical Cyclones of the North Atlantic Ocean, 1871-1992, National Climatic Data Center in Cooperation with the National Hurricane Center, Coral Gables, FL, 193 pp. [NHC homepage for most recent track information: http://www.nhc.noaa.gov].

NHC, 2009: Responsibilities and Timeliness for Aircraft Reconnaissance and Surveillance Data. [Available online at http://www.nhc.noaa.gov/aboutrecon.shtml].

Nong, S., and K.A. Emanuel, 2003: A Numerical Study of the Genesis of Concentric Eyewalls in Hurricane. Quart J. Roy. Meteor. Soc., 129, 3323-3338.

Pennington, J., M. DeMaria, and K. Williams, 2000: Development of a 10-year Atlantic Basin Tropical Cyclone Wind Structure Climatology. [Available online at http://www.bbsr.edu/rpi/research/demaria/demaria4.html].

Piech, D., 2007: Atlantic Reconnaissance Vortex Message Climatology and Composites and Their Use in Characterizing Eyewall Cycles. M.S. Thesis, Florida State University, 139 pp.

Powell, M.D., E.W. Uhlhorn, and J.D. Kepert, 2009: Estimating Maximum Surface Winds from Hurricane Reconnaissance Measurements. Wea. Forecasting, 24, 868–883.

RAMMB/CIRA, 2009: Milestones in the Operational SHIPS and Related Model Development. [Available online at http://rammb.cira.colostate.edu/research/tropical_cyclones/ships/#milestones].

Rappaport, E.N., et al., 2009: Advances and Challenges at the National Hurricane Center. Wea. Forecasting, 24, 395–419.

132

Reynolds, R.W., 1982: A Monthly Averaged Climatology of Surface Temperature. NOAA Tech. Rep. NWS-31, 42 pp. [Available from the National Technical Information Service, U.S. Department of Commerce, 5285 Port Royal Rd., Springfield, VA 22151].

Samsury, C.E., and E.N. Rappaport, 1991: Predicting Atlantic Hurricane Intensity from Research and Reconnaissance Aircraft Data. Preprints, 19th Conf. on Hurricanes and Tropical Meteorology, Miami, FL, Amer. Meteor. Soc., 516-520.

Shapiro, L.J., and H.E. Willoughby, 1982: The Response of Balanced Hurricanes to Local Sources of Heat and Momentum. J. Atmos. Sci., 39, 378–394.

Shay, L.K. (Nick), 2006: Positive Feedback Regimes During Tropical Cyclone Passage. Preprints, 14th Conf. on Interaction of the Sea and Atmosphere, Atlanta, GA, Amer. Meteor. Soc.

Stewart, 2005: Tropical Cyclone Report, Hurricane Ivan. National Hurricane Center, 44 pp. [Available online at http://www.nhc.noaa.gov/pdf/TCR-AL092004_Ivan.pdf].

Terwey, W.D., and M.T. Montgomery, 2006: Modeled Secondary Eyewall and Spiral Band Dynamics. Extended Abstracts, 27th Conf. on Hurricanes and Tropical Meteorology, Monterey, CA, Amer. Meteor. Soc., 2B.3.

Wilks, D.S., 2006: Statistical Methods in the Atmospheric Sciences. 2nd ed. International Geophysics Series, Vol. 91, Academic Press, 627 pp.

Willoughby, H., J. Clos, and M. Shoreibah, 1982: Concentric Eye Walls, Secondary Wind Maxima, and The Evolution of the Hurricane vortex. J. Atmos. Sci., 39, 395–411.

Willoughby, H., 1990: Temporal Changes of the Primary Circulation in Tropical Cyclones. J. Atmos. Sci., 47, 242–264.

133

BIOGRAPHICAL SKETCH

David Andrew Murray was born March 19, 1986, in Enterprise, AL, to his parents David and Deborah. He has a younger brother, Aaron, who graduated with a B.S. in Mathematics from Troy University in 2009. Andrew is married to Marisa Pervon Murray, whom he wed on March 8, 2008, in Mobile AL. He graduated as valedictorian of his high school class in 2003 from Emmanuel Christian School in Dothan, AL, and he received his B.S. in Meteorology from the University of South Alabama in Mobile, AL, in 2007, graduating near the top of his class with a GPA of 3.93. Andrew’s passion for meteorology began through experiencing the inland effects of Hurricane Andrew, which actually knocked a tree onto his parents’ house in Columbus, Mississippi. Hurricane Andrew sparked a desire to study meteorology, and tropical cyclones in particular, inside him, leading him to continue his education at Florida State University to study tropical cyclones under Dr. Robert (Bob) Hart. Andrew aspires to have a career in education, teaching meteorology at the university level.

134