A Climatology of Tropical Cyclone Size in the Western North Pacific Using an Alternative Metric Thomas B

Home , Climatology, Radius of maximum wind, Typhoon Francisco (2013), Typhoon Francisco (2019), Typhoon Halong (2002), Typhoon Halong (2014)

Florida State University Libraries

Electronic Theses, Treatises and Dissertations The Graduate School

2017 A Climatology of Tropical Cyclone Size in the Western North Pacific Using an Alternative Metric Thomas B. (Thomas Brian) McKenzie III

Follow this and additional works at the DigiNole: FSU's Digital Repository. For more information, please contact [email protected] FLORIDA STATE UNIVERSITY

COLLEGE OF ARTS AND SCIENCES

A CLIMATOLOGY OF TROPICAL CYCLONE SIZE

IN THE WESTERN NORTH PACIFIC USING AN ALTERNATIVE METRIC

THOMAS B. MCKENZIE III

A Thesis submitted to the Department of Earth, Ocean and Atmospheric Science in partial fulﬁllment of the requirements for the degree of Master of Science

2017

Robert E. Hart Professor Directing Thesis

Vasubandhu Misra Committee Member

Jeffrey M. Chagnon Committee Member

The Graduate School has veriﬁed and approved the above-named committee members, and certiﬁes that the thesis has been approved in accordance with university requirements.

ii To Mom and Dad, for all that you’ve done for me.

iii ACKNOWLEDGMENTS

I extend my sincere appreciation to Dr. Robert E. Hart for his mentorship and guidance as my graduate advisor, as well as for initially enlisting me as his graduate student. It was a true honor working under his supervision. I would also like to thank my committee members, Dr. Vasubandhu Misra and Dr. Jeffrey L. Chagnon, for their collaboration and as representatives of the thesis process. Additionally, I thank the Civilian Institution Programs at the Air Force Institute of Technology for the opportunity to earn my Master of Science degree at Florida State University, and to the USAF’s 17th Operational Weather Squadron at Joint Base Pearl Harbor-Hickam, HI for sponsoring my graduate program and providing helpful feedback on the research. I would also like to thank the Department of Earth, Ocean and Atmospheric Science for providing the opportunity to receive a graduate education at Florida State University. Furthermore, I appreciate the help from my colleagues within the Department who have provided support and guidance on my graduate work; in particular, I extend a special thanks to Levi Cowan and Kyle Ahern for assistance with the computer programming, as I had very little experience on the matter before enrollment. Finally, I owe my deepest gratitude to my family for their love and support, especially to my parents for always encouraging me to achieve my dreams, and my wife for motivating me through the challenging and difﬁcult nature of graduate school.

iv TABLE OF CONTENTS

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

1 Introduction 1

2 Prior Research 6 2.1 Current Metrics of Tropical Cyclone Size ...... 6 2.1.1 Critical Wind Radii ...... 6 2.1.2 Radius of Outermost Closed Isobar ...... 9 2.1.3 Research-Based Parameters ...... 11 2.2 Advantages and Limitations with Current Metrics ...... 13 2.2.1 Advantages ...... 13 2.2.2 Limitations ...... 16 2.3 Existing Climatologies of Tropical Cyclone Size ...... 19 2.4 Factors of Initial Size and Size Change ...... 25 2.4.1 Initial Tropical Cyclone Size ...... 25 2.4.2 Changes in Tropical Cyclone Size ...... 27 2.5 Parametric Models for Tropical Cyclone Wind Fields ...... 31 2.6 Summary of Prior Research ...... 35

3 Data, Definitions, and Methods 38 3.1 Data ...... 38 3.2 Definitions ...... 39 3.2.1 Derivation of Holland (1980) ...... 40 3.2.2 Defining the Outermost Closed Isobar ...... 43 3.3 Methods ...... 45 3.3.1 Size Calculations with Gridded Data ...... 45 3.3.2 Method of Statistical Analysis ...... 51 3.4 Summary of Data, Definitions, and Methods ...... 54

4 Results 56 4.1 Case Scenarios ...... 56 4.1.1 “Complete Storm Life Cycle” Case: Tropical Storm Warren (1984) . . . . 57 4.1.2 “Partial Storm Life Cycle” Case: Tropical Depression 12W (1989) . . . . . 57 4.1.3 “Expected Storm Life Cycle” Case: Typhoon Omar (1992) ...... 58 4.1.4 “Contrasting Storm Life Cycle” Case: Typhoon Ian (1987) ...... 58 4.1.5 Summary of Storm Life Cycle Cases ...... 61 4.2 Climatology ...... 62

v 4.2.1 Frequency Distribution of TC Size ...... 62 4.2.2 Size vs. Central Pressure ...... 65 4.2.3 Size vs. Age ...... 66 4.2.4 Monthly Climatology of Size ...... 67 4.2.5 Yearly Climatology of Size ...... 68 4.2.6 Size vs. Location ...... 69 4.2.7 Summary of Size Climatology ...... 71 4.3 Comparison with Prior Research ...... 74 4.4 Size Life Cycles and Environmental Inﬂuences ...... 78 4.4.1 Subcomposites of TCs at Formation ...... 79 4.4.2 Subcomposites by Month ...... 81 4.4.3 Case Studies ...... 81 4.4.4 Re-examination of Size vs. Latitude ...... 84 4.4.5 Summary of Environmental Inﬂuences ...... 84 4.5 Summary of Results ...... 86

5 Concluding Summary 87 5.1 Discussion ...... 87 5.2 Conclusions ...... 88 5.3 Future Work ...... 91

Appendix A Size Measurements with ERA-I and CFSR 93

References ...... 98 Biographical Sketch ...... 107

vi LIST OF TABLES

3.1 Comparisons between reanalysis data sets. Columns are separated by name, organization of development, horizontal grid-spacing in degrees latitude (∆X), equal-angle vertical grid-spacing in degrees latitude (∆Y), and time period used in this study. The three databases all have a temporal resolution of 6 h...... 39

3.2 Calculated values of R for the approximate full range of relevant parameters in (3.8) and (3.9). For brevity, P∞ is assumed to be 1015 hPa in all cases. Changing P∞ by 5 hPa in either direction does not meaningfully change R except when the central pressure is weak...... 42

3.3 Size measurements for Typhoon Halong at 1800 UTC on 7 August 2014. Each column represents the radius of the largest circle containing the respective isobar, the area of the isobar, the number of grid points contained within the isobar, the true area ratio, the analytical area ratio, and the ∆R based upon the previous isobar. The bolded value represents the last isobar before the ∆R threshold is met, and is therefore deﬁned as the OCI. Isobars that do not meet the grid point threshold (deﬁned here as 115 grid points) are excluded from the table...... 49

3.4 TC size categories assigned by JTWC over the WNP. Units are in degrees latitude. [Chan and Chan 2012] ...... 53

4.1 Statistical results of size for all accepted calculations with respect to each reanalysis data set, including average size (µ), standard deviation (σ), and median size. All values have been converted to a one-dimensional radius in equivalent degrees latitude. 64

vii LIST OF FIGURES

1.1 Surface wind ﬁeld plots of Hurricanes (a) Sandy on 28 October 2012 at 0900 UTC and (b) Danny on 22 August 2015 at 1500 UTC. The maximum sustained surface winds were estimated at 80 kt for both TCs at these respective times. [NHC 2017b] . 2

1.2 Infrared satellite imagery of (a) Hurricane Bertha at 1800 UTC on 12 July 1996, and (b) Hurricane Bret at 2100 UTC on 22 August 1999. The domain size is identical for both images. Imagery were extracted from NCDC GridSat-B1 dataset. [Knapp et al. 2011] ...... 2

2.1 An example of a wind radii forecast for an unspeciﬁc TC. The outer ring represents the R17, the middle ring deﬁnes the R26, and the innermost ring denotes the R33. [JTWC 2017] ...... 8

2.2 MERRA-based TC size metrics for Typhoon Tip at 1800 UTC on 16 October 1979. The blue contour highlights the R17, the R26 is outlined in green, R33 in red, RMW in purple, and ROCI in black. The gray dot represents the TC center...... 10

2.3 (a) Example of a ROCI measurement as defined by M84, and (b) as modified by Cocks and Gray (2002) for highly asymmetric profiles. [Merrill 1984; Cocks and Gray 2002; ©American Meteorological Society. Used with permission.] ...... 11

2.4 Surface wind radii observations for Hurricane Katrina, valid 0900 UTC on 29 Au- gust 2005. Radius of hurricane force winds, or R33, is highlighted in burgundy, while the radius of tropical storm force winds, or R17, is highlighted in orange. [NHC 2017b] ...... 14

2.5 M84-based OCI calculations (in hPa) using MERRA data for TC Chanchu on (a) 11 May 2006 at 0600 UTC (central SLP = 1002.81 hPa; OCI = 1007 hPa), and (b) 15 May 2006 at 1800 UTC (central SLP = 985.53 hPa; OCI = 1008 hPa). The black contour denotes the OCI, the red dot identiﬁes the TC center with respect to SLP in the reanalysis, and the red cross highlights the radii needed for ROCI calculations as noted in Figure 2.3...... 19

2.6 Monthly mean R17 for TCs in (a) the WNP and (b) NATL between 1999 – 2009. Vertical bars denote the 95% conﬁdence interval in the t distribution, while numbers above each month identify the number of cases in the respective month. [Chan and Chan 2012; ©American Meteorological Society. Used with permission.] ...... 22

2.7 The locations of the largest and smallest (top) minor hurricanes and (bottom) major hurricanes between 1978 – 2011 in accordinance with R5. Red dots indicate the largest 25% of TCs at its maximum intensiﬁcation, while blue dots depict the

viii smallest 25% of TCs at maximum intensiﬁcation. [Knaff et al. 2014; ©American Meteorological Society. Used with permission.] ...... 24

2.8 Composite 850 hPa winds (in m s−1; dashed lines) and streamlines for 13 different WNP TC cases within (a) the monsoon-gyre pattern (b) the late-season synoptic pattern. The TC center is highlighted by the typhoon symbol in the center of each subﬁgure. [Liu and Chan 2002; ©American Meteorological Society. Used with permission.] ...... 26

2.9 Mean TC size and intensity for 12 NATL hurricanes, deﬁned as the OCI (circles) and as the maximum winds in m s−1 and central SLP in mb (hPa). Time steps are identiﬁed by the number of days since TC formation. [Merrill 1984; ©American Meteorological Society. Used with permission.] ...... 28

2.10 Wind profiles with respect to radius of three TCs using the modified Rankine vortex model (Depperman 1947). The RMW for each TC is defined as 8 km (green), 10 km (blue), and 12 km (red); the maximum wind is held constant for all three profiles at 75 m s−1 (approximately 146 kt)...... 32

3.1 Flowchart describing the process of calculating the OCI per each storm ﬁx with respect to best-track data...... 44

3.2 Example of concentric circles plotted over Typhoon Omar at 1800 UTC on 26 Au- gust 1992, for calculating area and area ratio measurements of the TC’s SLP ﬁeld. . 47

3.3 (top) MERRA SLP ﬁeld for Typhoon Halong at 1800 UTC on 7 August 2014, with NCDC GridSat-B1 imagery underlaid for reference. The maximum extent of area calculations is highlighted by the green isobar, while the purple isobar is the OCI calculated by the area ratio procedure. (middle) Area calculations with respect to isobar value. (bottom) Area ratio calculations with respect to isobar value. The purple curve denotes the true area ratio, while the gray curve denotes the analytical area ratio from (3.9)...... 48

3.4 As in Figure 3.3, except for Tropical Storm Warren at 0000 UTC on 25 October 1984. (top) The purple contour outlines the OCI when the grid point threshold is reduced to 50, while the black contour highlights the correct OCI when the threshold is set to 115. Typhoon Vanessa can be seen directly to the east of Tropical Storm Warren...... 52

4.1 Time-series of OCI calculations (in hPa; top), area calculations with respect to OCI (× 106 km2; middle), and area ratio calculations with respect to both OCI and area (bottom) for (a) Tropical Storm Warren (1984), and (b) Tropical Depression 12W (1989)...... 59

4.2 As in Figure 4.1, but with (a) Typhoon Omar (1992) and (b) Typhoon Ian (1987). . . 60

ix 4.3 Relative frequency distributions for all accepted TC area calculations with respect to (a) MERRA data, (b) ERA-I reanalysis, (c) CFSR data, and (d) the aggregate of all three data sets. Numbers above vertical bars represent the number of cases within each respective bin...... 63

6 2 4.4 Mean TC area (× 10 km ) versus Pc (in hPa) with respect to (a) the individual reanalysis data sets, and (b) the JTWC EBT Pc values...... 66 4.5 (a) Mean TC area (× 106 km2) versus time since development (in h), and (b) ratio of mean TC area at the respective time since development over the mean TC area at initial formation...... 67

4.6 Mean TC area (× 106 km2) versus (a) month and (b) year for the entire database of accepted calculations...... 68

4.7 Mean TC area (× 106 km2) versus latitude in degrees North...... 69

4.8 Compilation of all accepted storm ﬁxes (MERRA) with respect to geographical location. TC size is converted from area to an approximate radius (in degrees) to classify storms in accordance with JTWC size categories...... 70

4.9 As in Figure 4.8, but with only (a) small (2 – 3◦) and (b) very large (> 8◦) storm ﬁxes. 72

4.10 As in Figure 4.8, but with only (a) the first storm fix and (b) the last storm fix per TC within the database...... 73

4.11 (a) As in Figure 4.3d, but using a bin size of 1◦, and (b) the relative frequency distribution of size for all TCs in the WNP between 1961 – 1969. [Merrill 1984; ©American Meteorological Society. Used with permission.] ...... 75

4.12 (a) As in Figure 4.6a, but with area values converted to approximate ROCI values, and (b) monthly distribution of size of typhoon occurrences in the WNP between 1945 – 1968. [Brand 1972] ...... 77

4.13 Mean formation location and mean SLP ﬁeld at formation within the MERRA database for (a) small TCs (including very small TCs; < 3◦ latitude), and (b) very large TCs (> 8◦ latitude). Shaded contours highlight the mean SLP, black contours display the standard deviation of the SLP, the black circle notes the mean formation location of TCs, and the white square depicts the formation location within the 95% conﬁdence interval...... 80

4.14 As in Figure 4.13, but with all initial storm ﬁxes (regardless of size) in (a) July, and (b) October...... 82

4.15 As in Figure 4.10a, but with only (a) small (including very small) and (b) very large TCs...... 85

x A.1 As in Figure 4.8, but with (a) ERA-I data, and (b) CFSR data (from 1979 – 2010). . 93

A.2 As in Figure 4.9a, but with (a) ERA-I data, and (b) CFSR data (from 1979 – 2010). . 94

A.3 As in Figure 4.9b, but with (a) ERA-I data, and (b) CFSR data (from 1979 – 2010). . 95

A.4 As in Figure 4.10a, but with (a) ERA-I data, and (b) CFSR data (from 1979 – 2010). 96

A.5 As in Figure 4.10b, but with (a) ERA-I data, and (b) CFSR data (from 1979 – 2010). 97

xi ABSTRACT

The size of a tropical cyclone (TC) is a critical structure parameter that influences the greatest extent of societal impacts, and can be estimated by several different metrics. In this study, a revised method of quantifying the size of a TC is introduced. This method expands upon the work of Merrill (1984) to present an alternative TC size parameter that objectively uses the sea level pressure field and the area enclosed by it. This new approach is made possible by higher resolution and more accurate gridded meteorological data. The revised method calculates the area enclosed by an isobar around a tropical cyclone, and then computes the area ratio of adjacent isobars. These calculations are then compared with an analytically-derived area ratio using the Holland (1980) radial pressure formulation. The outermost closed isobar (OCI) is generally determined to be the most outward isobar whose calculated area ratio does not significantly depart from the analytical ratio derived from Holland (1980). The algorithm is applied to a 36-year Western North Pacific (WNP) TC data set (1979 – 2014), and the results are analyzed statistically and physically. This derived climatology utilized three reanalysis data sets: NASA’s Modern-Era Retrospective Reanalysis data set (MERRA), ECMWF’s ERA-Interim reanalysis (ERA-I), and NCEP’s Climate Forecast System Reanalysis database (CFSR). On average, the algorithm was able to successfully determine an OCI for 75 – 80% of the roughly 30,000 six hour JTWC Best-Track records. The primary reason for the inability of the algorithm to determine an OCI was poor representation of the TC in the gridded reanalysis, especially at and soon after formation. The statistical analysis reveals that TC size calculations using the alternative metric are generally in agreement with existing climatologies. These results include a maximum mean TC size in October, a positive relationship between size and age of a TC, interannual variability of size, and an apparent maximum size near 25◦N. When the small TCs at formation were compared to the large TCs at formation, it was found that there was a statistically significant difference in the geographic distribution of these two groups. The size and position of the monsoon trough generally influences

xii the size of a forming TC in the WNP. The study includes an examination of several case studies representative of the analysis presented above.

xiii CHAPTER 1

INTRODUCTION

A tropical cyclone (TC) is a powerful barotropic system that typically forms over a large body of water. When in close proximity to land, its high winds and heavy rain can cause major destruc- tion to property. Appropriately, researchers and forecasters are largely concerned with where and how a TC progresses, especially in regards to its projected track, intensity, and size. In relation to track and intensity, very little research exists to account for the size of a TC. The relative size of a TC can be described by a variety of variables, such as wind (Figure 1.1), sea level pressure (SLP), relative vorticity (ζ), or cloud top temperature (Figure 1.2). With respect to operational meteorology, the size of a TC directly affects how forecasters issue watches and warnings for the general public. For example, Hurricane Bertha (1996; Pasch and Avila 1999) was a relatively large TC that prompted NOAA’s National Hurricane Center (NHC) forecasters to issue a hurricane warning along the Atlantic Coast of the U. S., which spanned approximately 1,600 km in length and affected nearly 750,000 individuals. Hurricane Bret (1999; Lawrence et al. 2001), on the other hand, was a relatively small hurricane that prompted forecasters to issue a hurricane warning area of about 700 km along the U. S. and Mexican coastline. Although a category 4 hurricane on the Saffir-Simpson Scale (Saffir and Simpson 1971), Bret only caused approximately $60 million in damage (compared with about $250 million in damage caused by Hurricane Bertha) thanks to its relatively small size, as well as the sparse population and minimal resources along the U. S. and Mexican coast (Kimball and Mulekar 2004). Forecasters may also be interested in how the size of a TC promotes or hinders changes in intensity. Although there is little to no correlation between TC size and intensity (Merrill 1984; Chavas and Emanuel 2010; Chan and Chan 2012), the rate of intensification or weakening depends heavily on the size of the TC (Carrasco et al. 2014). This is possibly due to the increase (decrease) of inertial stability as the size of a TC expands (contracts), which opposes (favors) intensification (Smith et al. 2011; Chan and Chan 2013). As an example, relatively small TCs are more likely

1 (a) (b)

Figure 1.1: Surface wind ﬁeld plots of Hurricanes (a) Sandy on 28 October 2012 at 0900 UTC and (b) Danny on 22 August 2015 at 1500 UTC. The maximum sustained surface winds were estimated at 80 kt for both TCs at these respective times. [NHC 2017b]

(a) (b)

Figure 1.2: Infrared satellite imagery of (a) Hurricane Bertha at 1800 UTC on 12 July 1996, and (b) Hurricane Bret at 2100 UTC on 22 August 1999. The domain size is identical for both images. Imagery were extracted from NCDC GridSat-B1 dataset. [Knapp et al. 2011]

2 to undergo rapid intensification (RI) than larger TCs, which can in turn affect how forecasters issue or adjust advisories to account for the possible intensification (Carrasco et al. 2014). When defining RI in accordance with Kaplan and DeMaria (2003), Carrasco et al. (2014) found that the probability of a small TC to undergo RI is three to five times greater than a large TC. This research is based upon a 21-yr climatology using an azimuthal average of gale force winds as a measure of TC size. This can possibly cause problems for decision-makers such as emergency management officials, as a rapidly intensifying TC near landfall could greatly reduce the response time needed for preparation and possible evacuation. Of particular interest to forecasters in the western North Pacific (WNP) is the very small TC, or “midget TC” (Arakawa 1952). Very small TCs are easily missed in synoptic analyses, and their intensities are not well-represented in satellite imagery because the methods of intensity estimation are based on more typical-sized storms (Brand 1972). Velden et al. (2006) even notes this challenge in their derivation of the original Dvorak technique (Dvorak 1975), which is used to estimate the intensity of a TC by analyzing satellite imagery. When reconnaissance aircraft is unavailable to directly calculate the intensity of a TC, the Dvorak technique or the Advanced Dvorak Technique (ADT; Velden et al. 1998; Olander and Velden 2007) is used as a “best-guess” estimate (Velden et al. 2006). If this estimate is unreliable due to the size of the TC, forecasts may potentially be degraded, and people and property can therefore be negatively impacted without proper notice. The influence of size on the track of the TC is a third major consideration for forecasters, because the size of the TC determines the scale over which a steering current directs its movement. Additionally, as the TC grows or intensifies, it can modify the surrounding environment. For example, the motion of a relatively large TC may be awkward to forecast, as its own circulation may cause its track to deviate away from the steering flow created by the synoptic environment (Carr and Elsberry 1997; Liu and Chan 2002). If a TC is considerably large and its horizontal length scale is comparable to nearby environmental influences, then these surrounding features will play a lesser role in the steering of the TC in comparison to their effects on a much smaller TC (Elsberry 1995). On the other hand, a smaller TC must be closer to these synoptic-scale features in order to alter its steering flow. This idea also applies to adjacent TCs that may aid in the steering flow through binary interaction (Fujiwhara 1923). Furthermore, the advection of planetary

3 vorticity (beta effect) can affect the propagation of a storm differently depending on the storm size. Larger storms will notice a greater consequence of the beta effect than smaller storms at similar latitudes, which may in turn impact the storm’s track away from the steering flow (Elsberry 1995). Thus, the beta drift becomes a greater contributor to the storm motion. As a result, forecasters can utilize knowledge of the general size of a TC to predict its future track, which may determine the timeliness and location of watches and warnings for the public. Thanks to several recent climatologies and model simulations (e.g., Weatherford and Gray 1988a,b; Cocks and Gray 2002; Kimball and Mulekar 2004; Willoughby and Rahn 2004; Knaff and Zehr 2007), researchers are now beginning to understand important details in regards to the size of a TC, such as seasonal and large-scale atmospheric preferences for various-sized storms. In the WNP, smaller TCs are typically associated with a strong subtropical ridge and a monsoon trough, and their tracks are heavily influenced by environmental or topographical features (Carr and Elsberry 1994; Lander 1994; Harr et al. 1996). Larger TCs, on the other hand, frequently form within a southwesterly surge or late-season synoptic pattern. These large storms intensify more slowly than smaller TCs, since more relative angular momentum (RAM) is needed to balance the increased frictional dissipation of larger storms (Merrill 1984; Liu and Chan 2002). Smaller TCs can instead utilize this RAM for intensification, since less RAM is needed for maintenance of the storm. The formation of very large and very small TCs is typically linked with a strong monsoon gyre (Lander 1994). A very small TC generally forms between the gyre and a subtropical ridge, as with Typhoon Nathan (Harr et al. 1996); the formation of a very large TC, however, may follow from the monsoon circulation itself, such as the case with Typhoon Tip (Dunnavan and Diercks 1980). In addition to synoptic preferences, seasonal preferences for various-sized storms have also been observed by researchers. Brand (1972) and Merrill (1984) observed the largest mean TC size in the WNP occurring in October, with the smallest mean TC size occurring in August, or midsummer in accordance with Merrill (1984). These observations may provide decision-makers some suggestions on when and where TCs may form, which can be especially beneficial if these storms form near civilization. Although progress has been made on the research of TC size, further investigation is needed to address this important concept. In order for researchers to advance on this work, however, a new

4 TC size metric may be necessary. This metric should be a robust definition of the boundary between a TC and its surrounding environment, which can be calculated rather easily using gridded analysis data. By analyzing and estimating this boundary, researchers and forecasters can better understand the interaction between the TC and its surroundings, such as the role of environmental steering, intensity change, and size change (Elsberry 1995). Understanding this interaction will promote better forecasts, which in turn will assist other decision-makers such as emergency managers and utility workers in planning and preparing for an approaching TC. Current TC size metrics either do not illustrate the full circulation of a TC, or they are very difficult to compute with direct observations. Appropriately, the goal of this research is to define a new TC size metric that is both simple and accurate, and to produce a climatology utilizing this new metric. By doing so, several questions in regards to the influences of TC size may be answered.

5 CHAPTER 2

PRIOR RESEARCH

2.1 Current Metrics of Tropical Cyclone Size

Throughout the course of TC research, and especially since the introduction of the satellite era, several metrics have been deﬁned that estimate the size of a TC; however, there is no universal deﬁnition of size documented by meteorological agencies. Three of the most well-known methods recorded in best-track and extended best-track (EBT) data by the NHC and the Joint Typhoon Warning Center (JTWC) include the critical wind radii, the radius of maximum winds (RMW), and the radius of the outermost closed isobar (ROCI; Pennington et al. 2000; Chu et al. 2002). These parameters can usually be calculated directly or estimated from available satellite data. For example, the RMW is typically found at the radius of the critical brightness temperature value from infrared satellite imagery (Olander and Velden 2007). Other metrics such as the radius of vanishing cyclonic winds (Carr and Elsberry 1997; Dean et al. 2009) and the estimated radius of 5 m s−1 wind speeds (Knaff et al. 2014), among others, are primarily used for research and will be discussed at the end of this section.

2.1.1 Critical Wind Radii

Perhaps the most recognized parameter of TC size transcribed by agencies is the R17, which represents the maximum radial extent of 17.5 m s−1 (34 kt) sustained surface winds in compass quadrants around the TC center (Sampson and Knaff 2015). Values are documented to the nearest 5 n mi. This parameter may alternatively be considered the radius of tropical storm force winds, as the minimum wind speed threshold for a tropical storm is also 17.5 m s−1 (NHC 2017a). Measure- ments of R17 can be taken as long as the TC is categorized as at least a tropical storm (see Figure 2.2). It should be noted that the R17 parameter is sometimes represented as R34 instead of R17 (i.e.: Knaff et al. 2007), which simply translates to the radius of 34 kt wind speeds and is identical

6 to R17. Some agencies, such as the Japan Meteorological Agency (JMA), record the radius of 30 kt wind speeds as opposed to R17 (JMA 2016). Additionally, JTWC records the radius of 35 kt winds instead of R17. As such, the radius under these modified definitions is distinct from the R17, though these respective radii measurements are generally in close proximity and are therefore comparable. These modified parameters have also been used in research studies such as Frank and Gray (1980), Weatherford and Gray (1988a,b), and Lee et al. (2010), among others. If the maximum 1-min sustained wind speed of a TC (10 m above the surface) is at least 25.7 m s−1 (50 kt), observers may also measure the R26, or approximately the radius of storm force winds (see Figure 2.2). The minimum threshold for a “storm,” in accordance with the Beaufort wind force scale, is officially 48 kt (World Meteorological Organization 1970); this threshold can cause considerable damage to vessels in maritime environments and may have adverse effects to property near coastal areas. Accordingly, some may be more interested in the maximum radial extent of storm force winds. If R26 exists for a particular storm, agencies will record both R26 and R17, considering that R17 must also be available. Valid measurements of R26 will always be found closer to the TC center than the R17 in any radial direction, given that wind speeds exponentially decay outward from the radius of maximum winds (Depperman 1947). Weatherford and Gray (1988a,b) and Cocks and Gray (2002) have used R25 instead of R26, which is distinct from the R26 recorded by agencies, although the R25 is approximately the same value as R26 and is therefore comparable. A third critical wind radius exists and is reserved for TCs of hurricane (or typhoon) strength. This radius of hurricane force winds, or R33, defines the maximum radial extent of 32.9 m s−1 (64 kt) wind speeds (see Figure 2.2). Values of R26 and R17 must once again be available if R33 can be recorded, and values of R33 will always be calculated inward from R26 and R17. The JTWC will officially record the radius of 65 kt winds as opposed to R33; while this still approximates to hurricane force winds, this critical wind radius can slightly vary depending on the agency or researcher, although values are comparable. For this research, R33 is considered the radius of 32.9 m s−1 (64 kt) wind speeds. Although seldom observed, the radius of 51.4 m s−1 (100 kt) winds is the last fixed wind parameter recorded by some agencies. The purpose of this metric is to identify the approximate

7 Figure 2.1: An example of a wind radii forecast for an unspecific TC. The outer ring represents the R17, the middle ring defines the R26, and the innermost ring denotes the R33. [JTWC 2017] radius of major hurricane force winds (96 kt; Hurricane Research Division 2014). Since a TC is rarely categorized as a major hurricane (or equivalent in other basins, with about 20.5% of all named Atlantic TCs reaching major hurricane status; Hurricane Research Division 2014), this metric only applies to a very small number of TCs. The NHC and the JMA do not include this metric in their respective best-track data. The combination of R17, R26, and R33 are known to meteorologists as “critical wind radii”, which are used to approximate the wind structure of a TC. In order to measure critical wind radii, surface winds must be directly estimated by in-situ observations, such as through aircraft reconnaissance or weather buoys, or derived from information dispatched by remote sensing systems like the Advanced Scatterometer (ASCAT; Figa-Saldaña et al. 2002) or the Special Sensor Mi- crowave Imager (SSM/I; Goodberlet et al. 1989). Critical wind radii are documented in compass quadrants around the TC center starting with a designated position by the recording agency, with succeeding measurements recorded moving clockwise around the starting position. Whenever in- sufficient data are available to measure wind radii in four quadrants, agencies will document wind radii in two semicircles around the TC center, or will use one measurement for the entire TC if taking two measurements for each side of the storm is not feasible (see Figure 2.1). The AR17, AR26, and AR33, or azimuthally averaged radius of gale force winds, storm force winds, and hurricane force winds, are typically used for climatological purposes and other research.

8 When used for statistical purposes, scientists will normally assume a symmetrical storm with equal wind radii values in each quadrant. Although this assumption is usually a rough estimate of the true wind radii values in each quadrant, it allows researchers to perform statistical analyses of tropical cyclone size with relative ease. Depending on the availability of wind data, critical wind radii can be measured regularly throughout the TC’s life cycle, assuming that the TC is categorized as at least a tropical storm. By using the most recent wind radii values, meteorologists are able to forecast wind radii through 72 h (Sampson and Knaff 2015). Agencies archive wind radii values every 6 h in EBT data, and are available through NHC for North Atlantic (NATL) and Eastern Pacific (EPAC) storms (Pennington et al. 2000), or through JTWC for Western Pacific or Indian Ocean storms (Chu et al. 2002). The RMW is another common wind-based TC size parameter that is defined as the distance from the TC center to the location of the maximum winds (see Figure 2.2); as such, this parameter is not fixed and is entirely dependent on the TC intensity. In a mature TC, the RMW is usually found near the inner eyewall (NHC 2017a). This metric is popularly used by researchers to define the size of a TC’s inner core, or the largest extent of the most devastating winds.

2.1.2 Radius of Outermost Closed Isobar

Brand (1972) defined the size of a TC as the ROCI to produce a TC size climatology of WNP TCs (see Figure 2.2); the method of calculating the ROCI was later described by Merrill (1984; hereafter M84) to produce a climatology of NATL TCs. The outermost closed isobar (OCI) of a TC, in accordance with M84, can be easily discovered on a surface pressure chart as the last common isobar enclosing the TC (approximated to the nearest hPa). The ROCI is then measured by averaging the radii from the TC center to the OCI in the four cardinal directions (see Figure 2.3a). If the OCI is highly distorted or elongated due to environmental or topographical features, one can instead select an adjacent pressure contour inward from the OCI. Alternatively, one may truncate the asymmetric portion of the OCI so that the TC displays a near-axisymmetric profile (Figure 2.3b; Cocks and Gray 2002). These two simple solutions combat the problem of distorted or elongated TC profiles, but they are not objective methods of doing so, since there is not a clear threshold for a “symmetric” contour.

9 Figure 2.2: MERRA-based TC size metrics for Typhoon Tip at 1800 UTC on 16 October 1979. The blue contour highlights the R17, the R26 is outlined in green, R33 in red, RMW in purple, and ROCI in black. The gray dot represents the TC center.

Since the development of M84, several researchers have used the ROCI as a primary metric of TC size to advance the understanding of TCs, as it is generally accepted to define the TC’s outer structure. ROCI calculations have also been recorded by many agencies in their respective best-track records, such as the JTWC in their EBT database (Chu et al. 2002). From a dynamical standpoint, this is a base-level parameter that is more stable than other TC size metrics, since SLP (by definition) is a vertical integral of an atmospheric column. Not only does the ROCI parameter serve as a more fundamental representation of the full TC structure, but as observations become more dense, it will also become a more accurate method to define the true TC size.

10 (a) (b)

Figure 2.3: (a) Example of a ROCI measurement as defined by M84, and (b) as modified by Cocks and Gray (2002) for highly asymmetric profiles. [Merrill 1984; Cocks and Gray 2002; ©American Meteorological Society. Used with permission.]

The wind-based and SLP-based TC size calculations mentioned above are commonly recorded by agencies, and are widely incorporated into research studies. Wind radii measurements, in particular, directly pertain to operations and can be estimated by means of satellite-derived observations. The ROCI parameter, on the other hand, is a base-level metric that is more stable than other metrics, and it generally describes the full structure of a TC. However, several other parameters have previously been documented that are primarily used for climatological research or numerical modeling. The next subsection will brieﬂy discuss several of these additional TC size parameters.

2.1.3 Research-Based Parameters

Other examples primarily used for research purposes but are not recorded in best-track or EBT data include calculating the average radius of ζ = 1.5 × 10−5 s−1 (hereafter ζ15; Liu and Chan 1999, 2002); the average radius of vanishing cyclonic winds, or where surface wind perturbations directly associated with the storm reduce to zero (R0; Carr and Elsberry 1997; Dean et al. 2009; Chavas and Emanuel 2010); the integrated kinetic energy (IKE) contained within a selected radius

11 from the TC center (Powell and Reinhold 2007; Musgrave et al. 2012; Misra et al. 2013; Kozar and Misra 2014); and the azimuthally-averaged brightness temperature anomaly (captured from IR satellite imagery) 14◦ latitude from the TC center (Frank 1977; Kidder et al. 1978). The ζ15 is fairly simple to compute (although rather noisy), as this parameter is derived from the TC wind field. To compute this value, researchers must first obtain the full TC wind field in both zonal and meridional directions, followed by calculating the curl of the TC wind vectors. The radius of vanishing storm winds is calculated in the same manner in that the relative vorticity of R0 must be zero (Dean et al. 2009). Theoretically, the R0 is the same parameter as the ROCI, in that a reversal of the pressure gradient outward from the TC center (at the OCI) results in a change of wind direction from cyclonic to anticyclonic. Because the ROCI depends upon the pressure increment within the surface analysis, as well as the pressure distribution outside the TC, the R0 typically must be estimated from other known parameters (such as R17) using a wind-pressure relationship (WPR). Despite that R0 must be empirically estimated, Dean et al. (2009) argues that R0 varies the least with respect to TC age, and is therefore a suitable parameter for analysis of size distribution. Although the ζ15 and R0 parameters are useful in TC research, they are difficult to compute with direct observations, and an empirical wind-pressure model is typically employed to aid in these calculations. Other mathematically-based parameters like the IKE metric (Powell and Rein- hold 2007) are relatively new (e.g., Musgrave et al. 2012; Misra et al. 2013; Kozar and Misra 2014), and they have not yet been applied for operational forecasting. Some of these alternative TC size parameters, such as the satellite-based metric proposed by Frank (1977), have not been tested as a reliable measure of TC size, and therefore will not be discussed throughout the remainder of this work. Some researchers have used modified versions of the critical wind radii parameters mentioned above, such as the radius of 12 m s−1 winds (R12; Chavas and Emanuel 2010; Chavas et al. 2016), the radius of the extent of 20 m s−1 winds (R20; Chavas et al. 2015), and the radius of 5 m s−1 winds (R5; Knaff et al. 2014; Chavas et al. 2015). These alternative parameters were generally chosen to account for the limitations of the respective observing platform. The R12, for example, was defined by Chavas and Emanuel (2010) because of the the low bias in satellite-derived winds

12 between 10 – 15 m s−1. The deﬁnitions of these parameters are identical to the critical wind radii parameters with the exception of the differing wind thresholds.

2.2 Advantages and Limitations with Current Metrics

A fundamental reason why several distinct TC size parameters have been proposed is because each metric, in general, represents a different component of the storm. As such, researchers and forecasters may utilize a specific parameter depending on the range of interest. For example, one may be interested in the structure and dynamics of a TC’s inner core and would therefore utilize the RMW, while the ROCI or R17 may not provide much benefit in this case. On the other hand, the RMW may not disclose much information about the TC’s full structure and environmental influences. A second and perhaps most extensive reason why several metrics have been developed is because each parameter may have several limitations, especially with regards to data availability. Accordingly, this section will discuss the advantages and limitations of each metric and the importance behind understanding these circumstances.

2.2.1 Advantages

A primary benefit of measuring the three critical wind radii (R17, R26, and R33) are that they directly aid in TC forecasting and decision-making for watches and warnings (see Figure 2.4). Since R17 is alternatively defined as the maximum extent of tropical storm force winds, forecasters may issue or modify a tropical storm advisory based primarily on the R17. Likewise, forecasters may do the same for a hurricane advisory based upon the R33, or maximum extent of hurricane force winds. Furthermore, these parameters assist forecasters in the development of other products like storm surge and wind speed probabilities (DeMaria et al. 2013; NHC 2015; Sampson and Knaff 2015). Critical wind radii measurements are especially favorable when analyzing changes in TC size. Considering that critical wind radii are fixed parameters, with the radius itself being the only variable, many researchers have been able to develop climatologies highlighting the theories of TC size change. As such, this information has been well-documented and will be discussed later

13 Figure 2.4: Surface wind radii observations for Hurricane Katrina, valid 0900 UTC on 29 August 2005. Radius of hurricane force winds, or R33, is highlighted in burgundy, while the radius of tropical storm force winds, or R17, is highlighted in orange. [NHC 2017b] in this chapter. Alongside the factors of TC size change is the relationship between size, strength, and intensity of a TC, which can be analyzed using the critical wind radii as the primary variables. A third advantage of using critical wind radii to analyze TC size is that measurements can be obtained by multiple observation systems. Direct measurements of critical wind radii can be re- trieved through aircraft reconnaissance, assuming that the aircraft analyzes the TC wind ﬁeld out to the radius of interest. Polar orbiting remote sensing systems are also very effective in estimating critical wind radii, especially R17. This method has been utilized in studies such as Liu and Chan (1999), Demuth et al. (2004), and Chan and Chan (2012) for climatological research. Infrared imagery can also be utilize to approximate critical wind radii, especially with additional information

14 (i.e.: maximum wind speed). A rather convenient asset of the RMW parameter is that, due to the advancement of TC research with satellite observations, estimating this radius is not complex and can be done quickly. As stated in the previous section, the RMW is commonly found within the inner eyewall, which can be resolved with infrared satellite imagery as long as the TC eye is visible (Olander and Velden 2007; Kossin et al. 2007a; Lajoie and Walsh 2008). This is especially valuable on the temporal scale since imagery can be obtained several times every hour. The RMW can also be employed by forecasters to predict the maximum intensity of a TC (Shen 2006), or by coastal scientists to calculate significant wave height (Hsu and Yan 1998). According to Shen (2006), the maximum intensity of a TC is very sensitive to the size of the TC’s eye, which is closely related to the eyewall size and thus the RMW (as mentioned in the previous paragraph). Significant wave height is highly dependent on RMW (Hsu and Yan 1998); therefore, calculating RMW can assist in wave height forecasts for vessels and other resources, both onshore and offshore. The ROCI parameter is unique in that it depends entirely on the SLP field instead of the TC wind field, although these two variables are loosely related from a dynamical perspective. Con- veniently, direct observations of SLP are generally more accurate and vary less quickly within the TC circulation than wind observations (Torn and Snyder 2012; Landsea and Franklin 2013), especially when aircraft reconnaissance or dropsonde data are present (Holland 1980; Courtney and Knaff 2009). Estimates of OCI and ROCI values can also be used in WPR models such as the Holland WPR (Holland 1980; hereafter H80) and the Knaff and Zehr WPR (Knaff and Zehr 2007). M84 found that the ROCI of a TC is physically meaningful in defining the TC’s outer structure, as the SLP gradient reverses outside of the ROCI. Therefore, using ROCI as the approximate boundary between a TC and its surrounding environment is a justifiable metric to define the full TC circulation. In other words, since this parameter is a dynamic threshold (unlike the critical wind radii), one can assess the outer structure of a TC at any time throughout the TC’s life cycle with a fair amount of confidence, assuming that the SLP observations are accurate. One should keep in mind, however, that atmospheric tides will affect the ROCI of a TC by modifying the sea surface height, and in turn, the SLP field (Chapman and Lindzen 1970; Dai and Wang 1999).

15 A simple advantage for the research-based size parameters mentioned in the previous section is that they describe aspects of the TC structure beyond those that are conventional or operationally relevant. An example is highlighted in Dean et al. (2009), which uses a theoretical R0 measurement based on R17. Dean et al. (2009) argues that R0 is the most accountable wind-based metric for size distribution analysis, and an alternative TC size climatology is created accordingly. As mentioned in Section 2.1.3, R0 is theoretically the same as the ROCI; however, ROCI-based size calculations typically vary over time (depending on the pressure increment within the surface analysis and the distribution of the SLP outside the TC). Although R0 must be empirically estimated, Dean et al. (2009) argues that R0 is less variable over a TC’s life cycle. Several of these research-based parameters have been created in response to the advancement of data acquisition and observation systems. Liu and Chan (1999), for instance, use the ζ15 as a TC size metric, which was achievable using high-resolution satellite-derived wind information from the European Remote-Sensing Satellites 1 and 2. In these studies, ζ15 is chosen instead of ζ = 0 s−1, since the ζ = 0 contour may include the environmental ﬂow surrounding the TC. This metric permitted a TC size climatology featuring the identiﬁcation of TC size change.

2.2.2 Limitations

Each metric discussed above has certain limitations that are largely based upon the data or observation system utilized. In particular, direct observations over open water are scarce in relation to observations over land. Therefore, the size parameters deﬁned by these data may not be easily obtained through direct observations, or they may not be easily estimated by other means such as remote sensing platforms. Ideally, this problem could be alleviated by adding more observing systems such as moored buoys over open water. This task, however, would require plenty of human resources, which may not offset the improved resource protection. An indisputable limitation of the critical wind radii is that they cannot be employed on TCs with intensities less than the respective wind threshold. For instance, R17 can only apply to tropical storms or hurricanes (alternatively typhoons or cyclones); otherwise, the R17 is undeﬁned because gale force winds do not exist within the circulation. Similarly, R33 may only apply to hurricanes, or TCs with maximum wind speeds of at least 32.9 m s−1.

16 Because the critical wind radii are fixed parameters, they do not assist in defining the full circulation of a TC. Even though the R17 is the outermost critical wind radius of a TC, the TC wind field obviously extends further outward. This limitation directly resulted in the development of climatologies using non-traditional parameters like R0 by Carr and Elsberry (1997) and Dean et al. (2009), and ζ15 by Liu and Chan (1999, 2002). Furthermore, critical wind radii cannot be adjusted to accommodate the asymmetric profiles of some TCs. This consequence does not adversely affect operations, although it may impact other tasks such as climate research. This is largely in part because critical wind radii are often simplified as an azimuthal average when a large number of TCs are sampled, which may misrepresent TCs with asymmetric profiles. If no aircraft reconnaissance is available to directly record the TC wind field, scientists must primarily rely on wind data derived from satellite imagery (Velden et al. 1992). If geostationary satellites are used, the relatively coarse spatial resolution of imagery (i.e.: 4 km resolution of IR imagery from GOES-15; NOAA 2010) will degrade the quality of wind products and may result in inaccurate or incomplete wind radii measurements. Additionally, the poor temporal resolution of imagery from polar orbiting satellites (up to 12 h between images) can also impair products, despite the fact that this imagery has a much better spatial resolution than from geostationary satellites (assuming ample swath coverage). Of course, a combination of both geostationary and polar satellite systems may be used in these cases. Furthermore, critical wind radii (especially R33 and, to a lesser extent, R26) may occasionally be corrupted due to rain contamination in satellite- derived wind imagery (Chavas and Emanuel 2010; Chan and Chan 2012). The RMW metric has many of the same limitations as with the critical wind radii, especially with regards to satellite-derived data. Rain contamination can severely impact RMW measurements, as heavy rain typically coincides with high winds in a TC. Because the RMW is generally found within the inner eyewall, the relatively coarse resolution of imagery from geostationary satellites may not be able to capture the eyewall in detail, and the RMW may be miscalculated as a result (Olander and Velden 2007). Furthermore, if no eye is visible through satellite imagery, the RMW may be severely miscalculated. Estimating TC size with the ROCI may introduce problems for small or weak TCs. If using the SLP field from gridded reanalysis data, for example, the ROCI may be poorly resolved whenever

17 the ROCI is comparable to the length of the grid-spacing from the reanalysis data. The advancement of finer-grid reanalysis data in recent years, such as the Modern-Era Retrospective Analysis for Research and Applications (MERRA) data set (Rienecker et al. 2011), has alleviated this issue due to its relatively fine grid-spacing (e.g. ∆X = 0.667◦; ∆Y = 0.5◦ with MERRA). Weaker tropical disturbances, especially invests, may not yet have a closed circuluation and therefore may not have a closed isobar surrounding its center. Moreover, TCs resolved within reanalysis data are often weaker than they are in reality, and thus their SLP field may be poorly resolved (Manning and Hart 2007; Schenkel and Hart 2012). As such, calculating the ROCI may not be possible in these cases. These problems will be discussed further in Chapter 3. Cocks and Gray (2002) point out that a TC’s surface pressure field and the pressure field of its surrounding environment are both dynamic, and therefore OCI values needed to calculate ROCI can change instantaneously. This statement suggests that evaluating temporal changes in TC size is not useful with the ROCI. Correlating ROCI with other TC size parameters can also be difficult for this reason, as shown by Cocks and Gray (2002). Recall, however, that SLP is vertically integrated (from a dynamical perspective), and thus should not change as quickly as other variables. Some subjectivity exists on defining the ROCI of a TC that has caused some debate about its accuracy; M84 states that if the calculated OCI is distorted or elongated (usually due to topographical or environmental features), the next highest isobar can be used as the OCI. As previously mentioned in Section 1 of this chapter, Cocks and Gray (2002) provide an alternate definition of the OCI in cases when the last closed isobar is elongated (refer to Figure 2.3b above). In either case, however, there is no objective measure or threshold of an elongated isobar. This makes au- tomatic calculations of ROCI extremely difficult by the M84 definition (see Figure 2.5). Another alternative action is to take the azimuthal average ROCI using the true closed isobar as the OCI. This process, however, completely disregards M84’s justification of removing unnecessary isobars and may include features that are not part of the TC circulation. In regards to the non-traditional or research-based parameters, an obvious limitation is that these metrics are not commonly recorded by agencies, and are therefore harder to retrieve. Some of these outer structure metrics, such as R0 and ζ15, are physically meaningful in that they theoretically capture the entire TC wind field, but are very hard to measure directly and usually must

18 (a) (b)

Figure 2.5: M84-based OCI calculations (in hPa) using MERRA data for TC Chanchu on (a) 11 May 2006 at 0600 UTC (central SLP = 1002.81 hPa; OCI = 1007 hPa), and (b) 15 May 2006 at 1800 UTC (central SLP = 985.53 hPa; OCI = 1008 hPa). The black contour denotes the OCI, the red dot identifies the TC center with respect to SLP in the reanalysis, and the red cross highlights the radii needed for ROCI calculations as noted in Figure 2.3. be estimated using a model, as in Dean et al. (2009). This is especially a problem when trying to calculate TC size in real-time using available data. Other fixed wind radii parameters have the same limitations of the critical wind radii, including the constraint that they do not fully capture the TC wind field.

2.3 Existing Climatologies of Tropical Cyclone Size

Scientists have produced several climatologies of TC size using the metrics mentioned above to analyze seasonal, geographical, and environmental preferences of various-sized storms. These climatologies are based upon the parameter used to deﬁne the size of a TC, the method by which

19 the data were obtained, the basin of interest, and the time period. This section will highlight the basic findings of each analysis, followed by factors of initial size and changes of size in the next section. Frank and Gray (1980) created the first statistical analysis of TC size based upon R15. This work extracted rawinsonde data from 8,500 soundings in the WNP and the West Indies from 1961 – 1974 (sounding data from the WNP after 1970 were not included). They found that the probability of locating winds greater than 15 m s−1 at any radius from the TC center expands as both the central wind speed and the ROCI increase. Cocks and Gray (2002) expand upon Frank and Gray (1980) by using aircraft reconnaissance data for 50 typhoons between 1980 – 1987, and including both R25 and R33 as TC size metrics in addition to R15. Reconnaissance data were reinforced with synoptic and scatterometer data, when available. Research discovered that about 40% of TCs increase in size by more than 50 km day−1 within 36 h preceding maximum intensity. Additionally, TCs that initially develop as larger storms tend to remain large throughout their life cycle until the mature stage, in contrast to TCs of smaller size. Large storms, including “gyre” systems, maintain the greatest R15 values when the TC is west of 135◦E, while smaller TCs commonly maximize their R15 values east of this longitude. Environmental preferences of these various-sized storms, as discussed by Cocks and Gray (2002), are reviewed in the following section. Yuan et al. (2007) expanded upon Frank and Gray (1980) and Cocks and Gray (2002) by developing a statistical analysis of WNP TCs between 1977 – 2004, using R15 and R26 as size parameters. This study used the NCEP/NCAR reanalysis (Kalnay et al. 1996) and the Extended Reconstructed Sea Surface Temperature data set (Smith and Reynolds 2003). Results show that R15 and R26 are generally larger for intense TCs in the WNP than they are in the NATL, and both parameters have a maximum in October. An additional finding is that larger R15 and R26 values are contained within TCs between Taiwan and the Philippines. Finally, the annual mean of R15 increases by 52.7 km from 1977 to 2004, while the annual mean of R26 for TCs stays relatively constant. The work of Chan and Yip (2003) investigated the interannual variations of TC size (defined as the R15) by analyzing QuikSCAT wind data of WNP TCs between 1999 – 2002. The research

20 concluded that the average TC size increased from 1999 to 2002, with TCs in 2001 and 2002 being much larger than TCs in the previous two years. The TCs in 1999 and 2000 possibly owed their smaller size with a La Niña event, while the larger TCs in the following two years may have related to the El Niño event of 2002. As such, Chan and Yip (2003) discovered environmental influences of TC size corresponding to the El Niño Southern Oscillation (ENSO); this will be revisited in the next section. Weatherford and Gray (1988a) derived an “outer core strength” (OCS) parameter from R15, which is defined as the mean tangential wind speed between 1 – 2.5◦ from the TC center. This parameter was used with aircraft reconnaissance data to analyze 66 WNP TCs between 1980 – 1982. This study revealed that TC intensification did not translate to strengthening of the outer core, and as such, changes in a TC’s outer core are independent from inner core changes. This conclusion is once again in concurrence with previous studies. Chan and Chan (2012) produced a comprehensive statistical climatology of size (defined as AR17) and strength (defined as the OCS; Weatherford and Gray 1988a) for WNP and NATL TCs between 1999 – 2009 by utilizing QuikSCAT data. Results showed that the mean AR17 in the WNP is 2.13◦ latitude and is 0.3◦ latitude larger than the NATL mean TC size. Although results showed a strong correlation between size and strength in both basins, the correlation between size and intensity is weak. The WNP mean TC size is significantly larger in July and October than in other months, whereas the mean TC size in the NATL is largest in September (see Figure 2.6). Moreover, the frequency of large TCs may vary spatially and seasonally, and the interannual variation of size correlates well with ENSO. This climatology was followed-up by Chan and Chan (2015a) using the same TC size metric (AR17) to include the EPAC, South Indian Ocean, and South Pacific basins. Research confirmed that, on average, TCs in the WNP are globally the largest and have the most variance. This additional research shows that the size of a TC does not inevitably increase with latitude, but instead has an apparent maximum size between approximately 15 – 25◦ from the equator. Brand (1972) and M84 created the first ROCI-based TC size climatologies. Brand (1972) examined WNP typhoons between 1945 – 1968, while M84 surveyed TCs from both the WNP and NATL from 1957 – 1977. Using historical data from the National Weather Records Center

21 (a) (b)

Figure 2.6: Monthly mean R17 for TCs in (a) the WNP and (b) NATL between 1999 – 2009. Vertical bars denote the 95% conﬁdence interval in the t distribution, while numbers above each month identify the number of cases in the respective month. [Chan and Chan 2012; ©American Meteorological Society. Used with permission.]

(Hodge and McKay 1970), Brand (1972) found that the average TC size gradually increases from June through October, followed by a general decrease through December. Seasonal and geographic preferences were also noted with regards to very large and very small typhoons. By utilizing NHC’s operational surface analyses, M84 discovered that the average size of WNP TCs is twice as large as the average size of NATL TCs, and differences in lower-tropospheric winds between various-sized TCs are statistically significant. The study also confirms the results of Brand (1972) in that the size of a TC varies seasonally and geographically. Furthermore, M84’s results revealed that larger TCs have much more RAM than smaller TCs of similar intensity, which must be maintained against frictional dissipation in order for the TC to persist. M84 concludes that, in partial agreement with other studies, TC size only weakly correlates with intensity. Liu and Chan (1999) aggregated the sizes of TCs in the WNP and NATL between 1991 – 1996 using scatterometer data from the European Remote-Sensing Satellites 1 and 2. By defining the size of a TC as ζ15, the study verified that the mean TC size of WNP and NATL storms are 3.7◦ and 3.0◦ latitude, respectively. Seasonal variations of TC size were also reported using this modified size parameter. The work of Chavas and Emanuel (2010) included a global climatology of TC size, defined as

22 the R0 derived from the R12 using the Emanuel (2004) WPR. Data were obtained from QuikSCAT and included TCs between 1999 – 2008. Both R12 and R0 generally increased early in a TC’s life cycle, followed by a period of near constant size throughout maturity and decay. This research was expanded by Chavas et al. (2016) using an improved version of the Emanuel (2004) analytical WPR (Chavas et al. 2015), as well as a revised QuikSCAT database. In Chavas et al. (2016), the global median R12 and R0 values were found to be 303 km and 881 km, respectively. A TC size climatology using R0 was also developed by Dean et al. (2009); their work compiled the data sets of Demuth et al. (2006) and Kossin et al. (2007a) to estimate the R0 of 12,348 storm fixes using the Emanuel (2004) WPR. The distribution of the normalized outer radius for all storm fixes is near log-normal; results show that the outer radius of TCs, defined as R0, remains somewhat constant throughout the lifetime of a TC (Frank 1977). No clear explanation was given in these studies on why the R0 remains steady. Knaff et al. (2014) developed a statistical analysis of TC size using storm-centered IR imagery from 1978 – 2011. This work employed R5 as the TC size metric, which was empirically calculated by analyzing a much smaller IR imagery database and then applied to all TCs within the larger global data set. In this study, EPAC storms were found to have the smallest size distribution, while WNP had the largest distribution. Smaller (larger) TCs were generally located at lower (higher) latitudes and associated with westward (poleward) steering flow (see Figure 2.7). This research also includes influence of initial size and size change, which will be discussed in the next section. Kimball and Mulekar (2004) formed a climatology of NATL TCs using six different size parameters: the radius of the TC’s eye, RMW, R17, R26, R33, and ROCI. Data were extracted from the EBT data set and included all NATL TCs from 1988 – 2002. Kimball and Mulekar (2004) discovered that the critical wind radii of TCs generally increase as storms move poleward and westward, which may be due to increased angular momentum imports in response to changes in the synoptic environment (M84). However, the R33 and R26 of TCs north of 40◦N decrease as a result of weakening after recurvature. The study also found that TCs located in the Gulf of Mexico have larger ROCIs and smaller eyes and critical wind radii than NATL TCs between 50◦W and 80◦W, and most of these storms form within the Gulf rather than transit from the NATL. Finally, seasonal preferences are also detected, with late-season storms larger than early-season storms.

23 Figure 2.7: The locations of the largest and smallest (top) minor hurricanes and (bottom) major hurricanes between 1978 – 2011 in accordinance with R5. Red dots indicate the largest 25% of TCs at its maximum intensiﬁcation, while blue dots depict the smallest 25% of TCs at maximum intensiﬁcation. [Knaff et al. 2014; ©American Meteorological Society. Used with permission.]

However, Kimball and Mulekar (2004) theorize that this may be a consequence of TC intensity, since late-season storms are generally more intense, and thus their critical wind radii are typically larger. The ﬁnal climatology discussed in this work is by Carrasco et al. (2014), which studied the relationship between TC size and the potential to undergo RI. The research includes data from the North Atlantic hurricane database second generation (HURDAT2) and from the EBT for NATL TCs between 1990 – 2010, and uses RMW, AR17, and ROCI as TC size metrics. A negative correlation was found between the RMW (and AR17) and intensity change, along with a maximum RMW and AR17, in which RI is unlikely beyond these thresholds. However, no correlation was

24 identiﬁed between ROCI and intensiﬁcation.

2.4 Factors of Initial Size and Size Change

As discussed in Chapter 1, scientists have made signiﬁcant progress in understanding the concept of TC size. By analyzing the climatologies above or by producing numerical simulations, researchers have hypothesized several factors to explain the initial size of TCs, or to understand reasons for changes in a TC’s size. This section will highlight several recent studies that discuss these potential factors.

2.4.1 Initial Tropical Cyclone Size

Lander (1994) theorized that the large-scale monsoon circulation in the WNP (known colloqui- ally as a “monsoon gyre”) may promote the formation of small and “midget” TCs (Arakawa 1952). These smaller TCs usually form from the buildup of mesoscale vortices in a concentrated area of high absolute vorticity, which is typically found between the peripheral circulation of the gyre and a subtropical ridge to the east (Harr et al. 1996). This was the case with the genesis of six different TCs in August 1991. An alternate mode exists in which the monsoon circulation itself may eventually form into a very large TC, prompting researchers to agree upon two distinct modes of tropical cyclongenesis associated with the monsoon gyre in the WNP. The work of Lander (1994) was later verified by Harr et al. (1996) in their study of TC formation associated with a monsoon gyre. Cocks and Gray (2002) concluded that the synoptic environment influences the size of a TC; however, special considerations must be applied when a monsoon gyre is developing. They observed that the surface pressure field around a large TC and a developing gyre was significantly different than the surface pressure field of a TC in an environment without a monsoon gyre. Liu and Chan (2002) compares closely with Cocks and Gray (2002), as the study discovered that differing synoptic environments at 850 hPa results in various-sized TCs. Furthermore, it was observed that initially small TCs are generally associated with a dominant ridge and a monsoon gyre, while large TCs are related to late-season synoptic patterns or a southwesterly surge (Figure 2.8).

25 (a) (b)

Figure 2.8: Composite 850 hPa winds (in m s−1; dashed lines) and streamlines for 13 different WNP TC cases within (a) the monsoon-gyre pattern (b) the late-season synoptic pattern. The TC center is highlighted by the typhoon symbol in the center of each subﬁgure. [Liu and Chan 2002; ©American Meteorological Society. Used with permission.]

Lee et al. (2010) alternatively observed that most small TCs in the WNP, defined by R15 using the QuikSCAT database, form from an easterly wave synoptic setup, while medium to large TCs are associated with a monsoon trough. Additionally, research found that the low-level synoptic environment in the WNP influences the size of a TC during the early stages of the TC’s life cycle. Larger TCs typically exhibit south-southwesterly winds in its southern component of the outer core, which allows the storm to maintain its size. Smaller TCs, on the other hand, are generally influenced by a subtropical high during its intensification and promotes the TC to preserve its smaller structure. Researchers understand that different synoptic environments exist in each TC basin, and as such, the initial size of a TC can be largely dependent on where the TC forms. Kimball and Mulekar (2004) found that a TC forming in the Gulf of Mexico may be influenced by a tropical upper

26 tropospheric trough (TUTT) cell or a monsoon trough from the EPAC instead of by easterly waves from Africa. Knaff et al. (2014) expanded upon TC size research in the NATL and concluded that small (large) TCs are generally located in areas where environmental low-level vorticity is weak (strong). Using guidance from Rotunno and Emanuel (1987) and from Emanuel (1989), Dean et al. (2009) theorized that the size of a TC may be a function of the geometry of the initial disturbance instead of the large-scale environment surrounding the disturbance. However, no connection has been made between the large-scale environment and the geometry of the initial disturbance. The theory proposed by Dean et al. (2009) is certainly worthy of future work; therefore, this may be later revisited using the research presented in this document. The work of Hill and Lackmann (2009) explained the relationship between TC size and environmental relative humidity (RH), or the RH far from the TC center. They argue that the size of a TC is closely related to the size and strength of its associated cyclonic potential vorticity (PV) anomalies, which in turn correlates with RH due to latent heat release in outer rainbands (where the intensity and coverage of precipitation of these outer rainbands is very sensitive to the environmental RH). Model simulations showed that a TC in a relatively dry environment has a smaller PV distribution, a smaller wind field in the outer core, and less precipitation outside the TC core in comparison to a storm with similar intensity in an environment with enhanced RH. The research of Lin et al. (2015) is consistent with Hill and Lackmann (2009) in that the TC size, defined by Emanuel et al. (1994) as the TC rainfall area, is controlled by the environmental sea surface temperature (SST) relative to the mean SST. In other words, a TC is larger in areas of higher environmental SST in comparison to a TC in areas of lower SST. Chavas et al. (2016) verified the work of Lin et al. (2015) by showing that the mean size of a TC increases with higher relative SST.

2.4.2 Changes in Tropical Cyclone Size

One of the ﬁrst studies on TC size change was produced by M84, who stated that NATL TCs generally grow in size as they move poleward (see Figure 2.9); in other words, there is a positive relationship between TC size and latitude. In Global Perspectives on Tropical Cyclones, Willoughby

27 (1995) explains, “The angular momentum required for growth [of a TC] is about the same as that required to balance friction, but signiﬁcantly less than required to balance the Coriolis torque that converts [RAM] to absolute angular momentum over the volume of a TC moving poleward at a climatological speed.” Therefore, TCs with a poleward track are much more likely to grow as opposed to those with a westward track.

Figure 2.9: Mean TC size and intensity for 12 NATL hurricanes, deﬁned as the OCI (circles) and as the maximum winds in m s−1 and central SLP in mb (hPa). Time steps are identiﬁed by the number of days since TC formation. [Merrill 1984; ©American Meteorological Society. Used with permission.]

As theorized by Holland and Merrill (1984), changes in the size of a TC are also controlled by interactions with the environment surrounding the TC. The work of M84 is consistent with this approach by stating that enhanced convergence of angular momentum by the synoptic environment may promote the growth of a TC. Weatherford and Gray (1988a,b) agree with Holland and Merrill (1984), as well as M84, in that changes in the size of a TC (defined as the derived OCS parameter) relates to changes in the lower tropospheric environmental flow surrounding the TC. Liu and Chan (2002) confirm these results in their example of Typhoon Bart, which increased in size after transitioning from a dominant ridge synoptic setup to a southwesterly surge pattern.

28 Chan and Chan (2012, 2013) reached several conclusions in regards to changes in TC size. The first is that the life cycle of a TC is a potential factor that affects size, as well as seasonal subtropical ridge activities (Chan and Chan 2012). In agreement with M84 and Willoughby (1995), Chan and Chan (2013) state that changes in angular momentum transport in the lower troposphere are appar- ently a necessary factor in TC growth or contraction. Their work also concurs with M84, Holland and Merrill (1984), and Weatherford and Gray (1988a,b) in that changes in the synoptic flow near a TC are important in determining changes in TC size. For example, a weakening subtropical high to the southeast of a TC generally allows for contraction, while a strengthening of the high promotes growth. Additionally, northward moving TCs tend to grow in size if the low-tropospheric westerlies to the west of the TC increase, which aids in strengthening the cyclonic flow of the TC. Finally, the growth of a TC may be caused by an acceleration of the TC’s northward component of the track; this once again agrees well with the concept of angular momentum transport. Preliminary work by Chan and Yip (2003) further verify the research noted above by concluding that changes in the size of a TC relates to the changes in the environmental flow along the TC’s track. The research also includes details in relation to ENSO in that TCs are generally smaller (larger) under a La Niña (El Niño) regime, as they form more westward (eastward) and therefore have a lesser (greater) chance of recurvature. As stated by Knaff et al. (2014), the size of a TC grows in areas with enhanced baroclinity and with recurvature; TCs that do not increase in size are commonly associated with landfall near maximum intensity, have a westward track with no recurvature, or their track is erratic. Smith et al. (2011) states that a positive relationship exists between the change of a TC’s size and a change in its intensity; as a TC intensifies (characterized by an increase in maximum winds), its R17 will generally increase. Chavas et al. (2016) alternatively explains that a TC’s size may

depend on the central SLP (Pc), such that an increase (decrease) in pressure will usually result in a larger (smaller) storm (in terms of R0). This agrees well with Knaff and Zehr (2007), which states that the Pc can be empirically estimated from gradient wind balance. Xu and Wang (2015) note, however, that the rate of intensiﬁcation is negatively correlated with storm size (in terms of RMW and AR17).

29 According to Chan and Chan (2014), the initial size of a TC, as well as the planetary vorticity based upon latitude, are both important in determining the size of a TC. As an example, a large TC in the initial stages of its life cycle will commonly have a larger overall size later in its development. This is because a larger TC contains higher angular momentum in the lower troposphere, allowing the TC to grow through angular momentum transport in the outer core. Chan and Chan (2014), however, note that a TC at a higher latitude may not necessarily be larger, as previous researchers have stated, as changes of size can also be controlled by the lower-tropospheric inertial stability associated with a TC. Finally, Chan and Chan (2014) note a general maximum TC size with respect to latitude at approximately 25◦N globally. The study by Wu et al. (2015) reveals that the size of a TC in the WNP, characterized by R17, generally increases as the TC intensifies; however, a maximum size of R17 = 2.5◦ latitude appears when the maximum winds approach 53 m s−1. After the TC reaches this threshold, the mean TC size decreases if the TC continues to intensify. The final major piece of research in regards to changes in TC size is by Chan and Chan (2015b). This work states that the initial intensity of a TC may influence the growth rate of the TC throughout the developing phase of the TC’s life cycle. However, when the TC approaches the mature stage or begins to decay, the initial intensity does not appear to be a significant factor in size change. In addition, size change is much more sensitive to the dynamics of the TC’s outer core (i.e.: initial size) than inner-core dynamics (initial intensity). As such, more angular momentum outside the R17 results in higher angular momentum transport toward the TC center, which can promote the growth of the respective TC. The first three sections of this chapter introduced several different TC size metrics, as well as their respective advantages and limitations. These metrics have been used by several researchers to advance the understanding of TCs, especially with regards to initial size and size change. It is evident that each of these metrics only measure one component of a TC, and none are effective in displaying the full TC structure (e.g., the R17 alone cannot reveal any information in regards to the

RMW). However, it is possible to estimate other TC size parameters, the Pc, or maximum winds using known values of TC size (or vice versa). Accordingly, researchers have developed empirical methods to estimate the full circulation of any TC. This topic will be discussed in the next section.

30 2.5 Parametric Models for Tropical Cyclone Wind Fields

As stated in Section 2 of this chapter, direct observations of SLP in a TC are generally more reliable than wind observations (Torn and Snyder 2012; Landsea and Franklin 2013). However, information on a TC’s wind field may be more beneficial to decision-makers than the SLP field, as the damage potential directly relates to the TC’s maximum winds and not its minimum SLP (Knaff and Zehr 2007). When aircraft reconnaissance is unavailable, a WPR can be utilized to estimate the maximum winds of a TC. This section will discuss several different WPRs that have been developed by scientists, which can be used to estimate the wind field of a TC with respect to its surface pressure profile, or vice versa. Some of these WPRs are relatively simple, requiring only 2 – 4 parameters, while others are very complex by depending upon multiple variables. The latter classification, however, is usually more accurate in describing the wind and pressure profile of a TC. The model by Depperman (1947) is perhaps the most fundamental model used in explaining the general structure of a TC. This model is commonly referred to as the “modified Rankine vortex” by scientists, otherwise regarded as an approximate Rankine vortex, where

Vr−1 = constant (2.1) between the TC center and the RMW, and

Vrx = constant (2.2) beyond the RMW, where x < 1 to account for the decay of winds with radius (see Figure 2.10). This allows for angular momentum to be conserved outside the RMW in agreement with the research noted in Section 4 of this chapter. In other words, winds must decrease outward from the RMW in order for angular momentum to be conserved. Despite its simplicity, this model requires a precise RMW value to estimate the maximum winds of a TC, and therefore extreme caution should be made when using this WPR (H80). By compiling the observed pressure proﬁles of several hurricanes over Lake Okeechobee, Schloemer (1954; hereafter S54) provided an empirical WPR based upon how the mean SLP ﬁeld varies in a TC as a function of radius, using a negative exponential relation. This study

31 Figure 2.10: Wind profiles with respect to radius of three TCs using the modified Rankine vortex model (Depperman 1947). The RMW for each TC is defined as 8 km (green), 10 km (blue), and 12 km (red); the maximum wind is held constant for all three profiles at 75 m s−1 (approximately 146 kt). was achieved in part by the high spatial coverage of observations in and around the lake, which allowed for an accurate representation of the full pressure profile of TCs. Considering that the size of Lake Okeechobee is very large in comparison to most landlocked bodies of water (allowing for TC maintenance over the lake due to low frictional dissipation), the SLP profiles documented in S54 were considered representative of NATL TCs over water. Results suggested a best fit model for the observed SLP profiles of all TC cases within the observing period:

RMW P = P +(P∞ − P )exp − (2.3) c c r where P is the SLP at a given radius r, the SLP at the center of the TC is deﬁned as Pc, P∞ is the estimated environmental pressure well outside the TC, and RMW is the radius of maximum wind. This relationship allows one to estimate the full TC structure using the more accurate pressure observations as opposed to direct wind observations. However, this model will commonly underestimate the maximum winds of most hurricanes (H80).

32 The WPR by S54 was generalized by H80 to develop a universal model for all TCs, and has resulted in a better estimate of the maximum winds. The H80 model is expressed as

a P = P +(P∞ − P )exp − (2.4) c c rb where RMW is replaced by the scaling parameter a, and S54’s r is modiﬁed with a second scaling parameter b (set between 1.5 and 2.5 by H80), which controls the radial width of the maximium wind. This allows the RMW to be entirely dependent on the scaling parameters, where RMW becomes RMW = a1/b (2.5) which can be applied to (2.4) in order to solve for the maximum wind speed

1/2 Vmax = C(P∞ − Pc) (2.6) where C =(b/ρe)1/2 (2.7) and ρ is the air density set to 1.15 kg m−3, while e is defined as the base of natural logarithms. This revised model allows for more accurate hurricane profiles, with only two major deficiencies: 1) supergradient winds and 2) very strong pressure gradients over short distances will likely be unresolved. Consequently, the maximum winds may still be underestimated by the H80 model if direct wind observations are not obtained. A revised version of the H80 model by Holland et al. (2010) incorporates readily available information from historical records or from TC advisory information. This revised model reduces the sensitivity to data errors, and is therefore more accurate. According to Kepert (2010), the H80 model continues to be the most widely used WPR by forecasters and researchers due to its balance of relative simplicity and its somewhat accurate representation of a TC’s true profile. Recent models appear to be more complex, but are nevertheless more accurate in general to describe the structure of a TC. One of these is the Willoughby et al. (2006) parametric profile. The Willoughby et al. (2006) relationship is defined in terms of wind,

33 which can be integrated to find the pressure profile; this differs from the H80 model, which is written in terms of pressure and must be differentiated to solve for the wind profile. The Willoughby et al. (2006) WPR is written as

r n1 v (r)=(v + v ) (2.8) 1 m1 m2 RMW inside the RMW, RMW − r RMW − r v (r)= v exp + v exp (2.9) 2 m1 L m2 L 1 2 outside the RMW, and

v(r)=(1 − α(r))v1(r)+ α(r)v2(r) (2.10)

at the RMW. In the above equations, v1 and v2 are the wind proﬁles within the eye and outside the

eye, respectively (at radius r), vm1 and vm2 are amplitudes inside and outside the RMW (where vm1

+ vm2 equals the maximum winds at the RMW), L1 and L2 are the respective length scales for the

inner and outer profiles, n1 is the shape of the eye profile where n1 < 2, and α(r) is a weighting function. Although complicated, the Willoughby et al. (2006) WPR appears to be more effective than the H80 profile when describing the structure of a TC, especially when real-time observations such as aircraft data are used (Willoughby and Rahn 2004; Willoughby et al. 2006).

Knaff and Zehr (2007) developed a WPR to estimate the Pc of a TC, deﬁned as the following equation: Vsrm1 2 Pc = 23.286 − 0.483V − − 12.587S − 0.483Φ + P∞ (2.11) srm1 24.254 where Φ is latitude, P∞ is the environmental pressure, Pc is the central SLP, and Vsrm1 is the one- minute mean maximum winds in knots conﬁgured for storm motion:

0.63 Vsrm1 ≈ Vmax1 − 1.5C (2.12) where Vmax1 is the one-minute mean maximum wind in knots, and C is the storm motion in knots. The approximate storm size S is deﬁned as a function of latitude and maximum wind, and is expressed as V500 S = (2.13) V500c

34 where V500 is the tangential wind at approximately 500 km from the TC center in knots, and V500c is the climatological tangential wind 500 km from the TC center in knots. This WPR provides one of the most complete relationships available by accounting for multiple parameters responsible for the structure of a TC (Courtney and Knaff 2009). This WPR can be altered so that it is expressed in terms of R17 and OCI. However, only the Pc can be calculated from the Knaff and Zehr (2007) WPR; therefore, the two-dimensional TC structure cannot be computed using today’s observations. A recently developed WPR by Chavas et al. (2016) combines two theoretical solutions into a full radial wind profile of a TC at the top of the boundary layer. The first part of the model, by Emanuel and Rotunno (2011), describes the inner profile of a TC within the RMW. The second characterizes a TC’s outer wind profile (Emanuel 2004). This WPR is relatively uncomplicated, yet exhibits the full TC wind profile more accurately than other models of comparable simplicity such as H80. According to Knaff and Zehr (2007), no universal WPR is used by operational TC centers. In fact, five WPRs are currently in use by agencies, including Atkinson and Holliday (1977), Koba et al. (1990), Love and Murphy (1985), Harper (2002), and Dvorak (1975). The WPR of Atkinson and Holliday (1977) is tailored for use in the WNP, while the Love and Murphy (1985) and Harper (2002) WPRs are modified for the Australian region. The Dvorak (1975) WPR, as well as the Koba et al. (1990) WPR derived from Dvorak (1975), are largely based upon satellite imagery. These models are all relatively simple parameters that can estimate the structure of a TC with a fair amount of confidence, but utilizing a particular WPR for climatological purposes or for other statistical analyses should be used with caution.

2.6 Summary of Prior Research

The purpose of this chapter was to outline prior research in regards to TC size. The first section discussed the many TC size metrics known throughout the tropical meteorology community and recorded by agencies, which included parameters with respect to both the wind field and pressure field of a TC. Examples of metrics documented regularly by agencies include the R17, R26, R33, RMW, and ROCI. Other examples are research-based or integrated parameters such as IKE, ζ15,

35 and R0, among others. The second section listed the major advantages and limitations of each metric, especially highlighting the problems with spatial and temporal resolutions in observations and how they impact the various metrics. Section 2.3 reviewed several TC size climatologies produced by researchers using the various metrics described above. Many of these prior studies noted a positive correlation between TC size and age (e.g., Cocks and Gray 2002; Chavas and Emanuel 2010), seasonal and geographical preferences (Brand 1972; Yuan et al. 2007; Chan and Chan 2012), and interannual varations of size (Chan and Yip 2003; Chan and Chan 2012). Section 2.4 outlined the different factors of initial TC size and size change as theorized by researchers after statistical analysis or model simulations. Some of these factors driving TC size at formation include environmental relative humidity (Hill and Lackmann 2009), sea surface temperature (Lin et al. 2015), and the concentration of absolute vorticity (Lander 1994). In regards to size change, the environmental flow surrounding a TC may modify TC size (Holland and Merrill 1984; Chan and Yip 2003). Finally, Section 2.5 reviewed some of the more popular WPRs that can be used in the absence of certain observations, or to aid in TC forecasting. Some of these models, such as the H80 model, are widely used by agencies due to their relative simplicity and accuracy. Many of the physical and dynamical processes responsible for the initial size of a TC and the subsequent changes in size are still relatively unclear, despite the advancement of wind observations to study the structure of a TC. To address these uncertainties, researchers may elect to study the pressure field of a TC and use ROCI as a size parameter. Although ROCI is still recorded by most TC agencies in their respective EBT databases, many researchers have deviated away from ROCI as a TC size parameter in favor of the wind-based size metrics (due to the rapid advancement of satellite-derived wind observations). Because wind measurements are more meaningful than pressure measurements to decision-makers, and because the accuracy of wind estimates has significantly improved over the past several years, wind-based TC size research has accelerated quickly in relation to SLP-based research. Instead of disposing ROCI in favor of wind-based TC size measurements, an improvement of M84’s original definition of ROCI may be prescribed, especially as observations have become dense and analysis (and reanalysis) resolution higher. Recall M84’s definition of the ROCI pa-

36 rameter, which states that one may disregard an asymmetric or elongated OCI. This order alone produces subjectivity that can manipulate TC size measurements through ROCI. Furthermore, the change in pressure between isobars on surface analysis charts produces additional subjectivity, such that the true OCI may fall between two isobars if the contour interval is too large. As such, the OCI is commonly a poor representation of TC size; researchers may expect and be more interested in an isobar inward from the M84 OCI that is objective in nature. This raises the more fundamental question of how researchers should expect the SLP field of a TC to change outward from the center, or if researchers should expect the area enclosed by a given isobar to change at a specific rate as one moves to the next isobar. Can a sudden increase in the area, either compared to the prior isobar, or compared to an “expected” area, be used for determining SLP-based TC size? Theoretically, a WPR can be used to estimate the OCI with relative accuracy; however, every WPR that has been developed relies on at least one wind parameter. A primary goal of this research is to propose a new TC pressure relationship (TCPR) that does not include any dependence on wind measurements. This new TCPR, derived from H80, will be used to develop a new TC size metric, which will more accurately describe the outer boundary of a TC. By comparing the actual SLP field of a TC with its analytical SLP field (calculated by the TCPR), researchers can better estimate the OCI of a TC, which in turn can result in a more objective measurement of TC size. This new metric is expected to be more robust by accounting for additional pressure measurements, and is intended to be a more stable metric with respect to the temporal consistency of size. The next chapter will introduce this new TCPR and will describe the methodology to calculate this new TC size metric.

37 CHAPTER 3

DATA, DEFINITIONS, AND METHODS

This study will begin by introducing an alternative TC size metric based upon a new TCPR (derived from the H80 WPR), which attempts to encapsulate the two-dimensional pressure field of a TC. In turn, a new climatology of TC size will be documented by comparing the observed pressure profiles of TCs with their analytical pressure profiles (based upon the new TCPR). By examining discrepancies between the true profiles and their analytical counterparts, an objective OCI can be found in order to improve the ROCI-based TC size measurements. Therefore, because this OCI can be objectively determined, the climatology based upon it will be more robust. The sensitivity of this metric to the data set chosen will be compared with TC size metrics from previous research. This chapter will 1) discuss the data extracted for this research; 2) define a new metric for size by reworking M84’s definition of the OCI parameter; and 3) demonstrate the methods necessary to complete this research, namely, the procedure for locating the OCI of a TC and the steps to perform a statistical analysis with this revised metric.

3.1 Data

An objective size climatology of all WNP TCs between 1979 – 2014 will be developed in this study. This research utilizes SLP data from three independent reanalysis data sets: the MERRA database (Rienecker et al. 2011), the ECMWF’s ERA-Interim data set (ERA-I; Dee et al. 2011), and NCEP’s Climate Forecast System Reanalysis data set (CFSR; Saha et al. 2010). Reanalysis data are preferred over operational analysis data in this study, as reanalysis data are homogeneous with respect to time. Thus, the statistical analysis will not be negatively impacted by the improvement of operational data over time. Because CFSR discontinued in 2011, the analysis will only use MERRA and ERA-I after 2010. Comparisons between reanalysis data sets are presented in Table 3.1. Additionally, GridSat-B1 data from NOAA’s National Climatic Data Center (NCDC; Knapp et al. 2011) are examined for quality control purposes, and to manually verify the TC position and

38 size within the reanalysis. However, GridSat-B1 data are not used directly in the algorithm. The imagery is extracted from the Climate Data Record’s 11 µm infrared window (IRWIN_CDR), and has an equal-angle grid-spacing of 0.07◦ latitude. JTWC Best-Track and EBT data sets are used to locate each storm ﬁx per every 6 h throughout the lifetime of a TC.

Table 3.1: Comparisons between reanalysis data sets. Columns are separated by name, organization of development, horizontal grid-spacing in degrees latitude (∆X), equal-angle vertical grid- spacing in degrees latitude (∆Y), and time period used in this study. The three databases all have a temporal resolution of 6 h.

Database Organization ∆X ∆Y Time Period

MERRA NASA 0.667 0.5 1979 – 2014 ERA-I ECMWF 0.7 0.7 1979 – 2014 CFSR NCEP 0.5 0.5 1979 – 2010

3.2 Deﬁnitions

To characterize the two-dimensional size of a TC, the SLP field of the storm is analyzed for this work. Studying a TC’s pressure field is especially convenient because the SLP field is continuous, pressure contours can never overlap one another, and pressure must increase outward from the TC center (given that a TC is a barotropic low). A primary question, however, is how fast this pressure should increase outward from the center. At some radius, the pressure gradient will eventually reverse due to the environmental features surrounding the TC, and the TC circulation will no longer be evident. As such, can a physically sound, empirical relationship be developed on how fast the pressure should change outward from the TC center? Furthermore, can the change in area enclosed by the pressure contours of a TC be predicted based upon the empirical relationship? The purpose of this section is to introduce a derivation of a well-known WPR previously discussed in Chapter 2, as well as to provide an alternative definition of a TC’s OCI that partially incorporates this derivation. As previously stated, no single TCPR exists that is solely based on the

39 pressure field of a TC. In order to better define the size of a TC in accordance with its OCI, a new TCPR must be developed. Due to its popularity, relative simplicity, and reliable accuracy, the H80 model was chosen as the starting foundation for this work, which of course is a generalized form of the S54 model. After deriving H80, a refined definition of the OCI by M84 will be discussed in the following section.

3.2.1 Derivation of Holland (1980)

As mentioned in Chapter 2, S54 provided one of the ﬁrst empirical functions for how the SLP ﬁeld varies in a TC as a function of radius:

RMW P = P +(P∞ − P )exp − (3.1) c c r where P is the SLP at a given radius r, Pc is the SLP at the center of the TC, P∞ is the estimated environmental pressure well outside the TC, and RMW is the radius of maximum wind. Note that

P∞ is not the same as the OCI value. The estimated environmental pressure must be sufﬁciently high in relation to the TC so that there is no interaction between the respective TC and any given location with this SLP value. The S54 relationship was extended by H80 to develop a universal model for various-sized TCs. This model included parameters a and b, which were the RMW and 1, respectively, in S54:

a P = P +(P∞ − P )exp − (3.2) c c rb H80 extended S54 to develop a universal model for TCs of various sizes, which was found to be more accurate. Given the absence of any associated two or three dimensional wind or thermal ﬁelds (explicitly) in the above equations, it is important to note that the relationships in (3.1) and (3.2) assume no atmospheric balance in the horizontal (e.g., geostrophic, gradient, or cyclostrophic) or the vertical (thermal wind). Since a primary goal of this research is to quantify how the area inside a given isobar changes with the isobar itself, the radius in (3.2) must be solved:

P − P b r = a−1 ln c (3.3) P∞ − Pc

40 Assuming the isobars are perfectly circular, which both (3.1) and (3.2) argue must be the case, given their formulation, the area inside a given isobar from (3.3) is:

P − P 2b A = π a−1 ln c (3.4) P∞ − Pc Of particular interest is how this area changes as one moves radially outward in the circulation of the TC, or more precisely, how the area changes as the pressure radially increases. Accordingly,

∂A −2πa2/b = 2 (3.5) ∂P b +1 b(P − P ) ln P−Pc c P∞−Pc If the derivative above is approximated by ﬁnite differences in area and pressure, one can solve for the change in area from two isobars separated by ∆P: − ∆ 2/b ∆ 2 Pπa A = 2 (3.6) b +1 b(P − P ) ln P−Pc c P∞−Pc Note that in (3.6) there is no reason ∆P must be an integer, and thus the use of the word “isobar” here does not necessarily imply an integer of pressure, but simply two contours of SLP separated by ∆P. Deﬁning a ratio R of the area at the current isobar compared to the prior isobar,

A ∆A −1 R = = 1 − (3.7) A − ∆A A Combining (3.4), (3.6), and (3.7):

−1 2∆P R = 1 + (3.8) " b(P − P )ln P−Pc # c P∞−Pc It is worthwhile to note here that the ratio in (3.8) does not have the a parameter; recall that this is the RMW in S54. Thus, even when using H80’s version, the wind ﬁeld is not needed. This provides a major advantage to this work, as measurements depend solely on the more stable and reliable SLP observations. In turn, the methodology results in fewer degrees of freedom, and therefore reduces error overall. While (3.8) nicely provides a ratio against which real-time TCs can be compared, the values obtained by (3.8) will likely be biased too high. Since the derivative in (3.5) is evaluated at P, the

41 value of (3.6) will be too large. Essentially, (3.8) is based on a centered ﬁnite difference implied by (3.5) that is applied in a backward ﬁnite difference sense. The bias can be removed by explicitly taking the ratios of two different areas using (3.4) for two different isobars, and bypassing (3.5):

P−P −∆P 2 ln c b P∞−Pc R = (3.9) " ln P−Pc # P∞−Pc As in (3.8), the parameter a is eliminated from the ratio R in (3.9).

There is certainly considerable sensitivity to R in the value of Pc, given that its observed value on the earth ranges from 870 hPa (Dunnavan and Diercks 1980) to about 1010 hPa. However,

the sensitivity of R to the value of P∞ clearly must be far smaller given that environmental pres- sures well removed from TCs have a much smaller pressure range of 1010 hPa to 1020 hPa. The sensitivity to b is not small, since H80 ﬁnds that values of b can often range from 0.5 to 1.5.

Table 3.2: Calculated values of R for the approximate full range of relevant parameters in (3.8) and (3.9). For brevity, P∞ is assumed to be 1015 hPa in all cases. Changing P∞ by 5 hPa in either direction does not meaningfully change R except when the central pressure is weak.

R using (3.8) for R using (3.9) for

Pc P b ∆P = 1.0 hPa (0.5 hPa) ∆P = 1.0 hPa (0.5 hPa) 900 975 0.5 1.14 (1.07) 1.13 (1.06) 925 975 1.0 1.07 (1.04) 1.07 (1.03) 950 975 1.5 1.06 (1.03) 1.06 (1.03) 900 1000 0.5 1.40 (1.17) 1.32 (1.15) 925 1000 1.0 1.17 (1.08) 1.15 (1.07) 950 1000 1.0 1.18 (1.08) 1.16 (1.08) 975 1000 1.5 1.13 (1.06) 1.12 (1.06) 1000 1005 1.0 1.57 (1.22) 1.45 (1.20) 1000 1005 1.5 1.32 (1.14) 1.28 (1.13)

42 The values of R in Table 3.2 suggest that by using (3.1), the area enclosed by a given isobar increases on average by approximately 15–25% (5–10%) if the isobar increment is 1 (0.5) hPa. Given that (3.1) is an empirical solution that contains several degrees of freedom, the expected ratio determined by (3.9) will not entirely match the observed ratio obtained from the reanalysis data. Furthermore, (3.1) does not imply any storm-scale balance of the TC, although observed values generally exhibit gradient wind balance. Thus, it is clear that the expected ratio given by (3.9) cannot and should not be used as a strict threshold against which real data should be compared to define the size of a TC. Nonetheless, (3.9), combined with other new metrics defined in the next section, can be used to give a more robust estimate of the TC size as a function of the two-dimensional SLP field.

3.2.2 Deﬁning the Outermost Closed Isobar

This subsection begins by reviewing M84’s definition of the OCI and ROCI parameters. M84 explains that the OCI is simply the last closed isobar encompassing a TC. As previously discussed in Chapter 2, the OCI can be found quickly and easily using a surface pressure analysis chart. The ROCI, in turn, is calculated by averaging the radii from the TC center to the OCI in four directions: north, south, east, and west of the center. A highly asymmetric or elongated OCI can be disregarded by selecting the last “symmetric” closed isobar in place of the true last closed isobar. This produces excessive subjectivity that has been addressed by Cocks and Gray (2002), which states that the last closed isobar can instead be truncated to fit a symmetric profile. Although this procedure increases the objectivity originated by the M84 definition, it may not be practical in approximating the TC’s outer structure by overestimating the expected OCI per M84. Due to the subjectivity of M84’s definition, automating the OCI calculation is extremely difficult, as demonstrated in the previous chapter. A solution to these problems is to revise the M84 definition of the OCI parameter, allowing measurements to be objective and making automation through software possible. Appropriately, the remainder of this subsection will provide this revision through the use of gridded data. The first subsection will discuss the process of automatically calculating the OCI per each storm fix with respect to best-track data.

43 Figure 3.1: Flowchart describing the process of calculating the OCI per each storm ﬁx with respect to best-track data.

The first step of the procedure is to identify the last closed isobar encompassing the TC center (step 1 in Figure 3.1). Outside the last closed isobar, the pressure gradient reverses, and the TC’s SLP field is no longer apparent. At this point, the last closed isobar is defined in the same manner as M84 without the considerations M84 suggests to account for an elongated or asymmetric OCI. In order to calculate the size of a TC with respect to its SLP field, the area of each closed isobar surrounding the TC center must be measured (step 2 in Figure 3.1). This differs from M84’s method of calculation where the size is measured as a radius outward from the TC center. It is obvious that the area of each closed isobar outward from the storm center will be greater than the previous isobar, as isobars cannot cross one another. The next procedure of the algorithm is to calculate the area ratio of each isobar with respect to the previous (inward) isobar (step 3a in Figure 3.1). This can be accomplished in an efficient manner, since area measurements needed to calculate the area ratio were already taken in the previous step. The area ratio, or R in the analytical area ratio defined in the previous subsection, essentially quantifies the pressure gradient outward from the TC center. Simultaneously, the analytical area ratio may be calculated alongside the true area ratio (step 3b in Figure 3.1). This method initializes the derivation of the H80 model using the required SLP values from (3.9), specifically, the Pc and

44 P variables within the selected reanalysis data set and the pre-defined P∞ and b variables set by the user. The result computes the analytical area ratio of each isobar. The true area ratio (results from step 3a in Figure 3.1), or the area ratio with respect to the selected data, is then compared to the analytical area ratio calculated by (3.9) (step 3b in Figure 3.1). The change in R, or ∆R, is computed for each isobar to find the innermost large ∆R that deviates from the analytical area ratio (step 4 in Figure 3.1). The last isobar that compares with the analytical area ratio before this sharp increase in ∆R is now defined as the OCI (step 5a in Figure 3.1). Typically, this OCI is identified closer to the TC center than the OCI in accordance with M84. However, there are many instances when the OCI by the M84 definition is also identified as the OCI using the area ratio calculation, especially for symmetric TCs. In this case, the ∆R threshold has not been met, and the OCI is thus defined as the last closed isobar encompassing the TC (step 5b in Figure 3.1). Nevertheless, this method provides a more objective OCI measurement than the modification suggested by M84, as evidenced by the derivation of H80.

3.3 Methods

The purpose of this section is to discuss the specific procedures of measuring TC size with gridded data through an automated algorithm, as well as to highlight the methods of the statistical analysis for producing a new climatology. These tasks can now be achieved using the definitions presented in Section 3.2. The three gridded reanalysis data sets mentioned in Section 3.1 are the primary data sources for TC size calculations and to develop a statistical analysis. The high spatial resolution of the data allow for a pressure contour interval (∆P in (3.9)) of 0.5 hPa, resulting in more precise measurements. This is especially important in measuring the OCI of a TC, as the pressure gradient becomes weak as the radius from the TC center increases. Additionally, the reanalysis data sets have been quality controlled to accurately represent the earth’s SLP field, and is therefore a reliable foundation for this study.

3.3.1 Size Calculations with Gridded Data

The first step of calculating the size of a TC is to utilize the JTWC Best-Track data in order to obtain a first guess location of each storm fix. This can be done in 6-h intervals throughout

45 the TC’s entire life cycle, which is assumed as the period between the first measurement and the last measurement in its respective best-track file. Once a first guess location is established, the TC center is re-calibrated inside the respective reanalysis database by finding the lowest SLP within a 6◦ by 6◦ latitude square around the first guess center. This square is large enough to correct any discrepancies between the best-track TC center and the TC center defined within the reanalysis data, but small enough to avoid a lower SLP outside the TC center (i.e.: an adjacent TC that may have a lower Pc). Schenkel and Hart (2012) states that the mean TC position difference between reanalysis and Best-Track data is largest with MERRA, with a maximum value of 2.92∆x (± 0.06), or about 2◦ latitude. Since this is a maximum mean value, a 6◦ by 6◦ latitude square (or 3◦ latitude from the first guess center to the edge of the square) is sufficient to correct discrepancies in TC position.

After locating the TC center, or the Pc within the reanalysis, the algorithm creates concentric circles around the TC center; the first has a radius of 50 km from the TC center, while each successive circle has a radius 50 km larger than the previous circle. No circle has a radius larger than 5,000 km, as it is assumed that no SLP field of any TC will expand beyond this radius, therefore truncating the process. The algorithm then determines the smallest circle that completely contains each isobar (i.e.: the area inside the isobar does not increase with a larger circle). This procedure continues until the first “open” isobar is found, that is, the first isobar that cannot be contained within any size circle around the TC (see Figure 3.2). Each isobar is then mapped to the smallest circle that encompasses it, which allows to determine the area of each closed isobar around the TC center. To measure the area of each isobar, all data outside the circle completely enclosing the isobar is masked out to prevent calculating outside the respective isobar (e.g., an isobar with the same value encompassing an adjacent midlatitude low). The area measurements are then documented for use in the area ratio calculations. Data are recorded by isobar value, area of the respective isobar, and the number of grid points enclosed by the isobar (see Table 3.3). These grid point values are needed to account for the resolution of each data set, and are used for approximating the OCI (explained later in this section). The Pc of the TC is also recorded for use in (3.9). Area ratio values are then computed from the area measurements using the method introduced in the previous section, and a ∆R value is recorded for each isobar

46 Figure 3.2: Example of concentric circles plotted over Typhoon Omar at 1800 UTC on 26 August 1992, for calculating area and area ratio measurements of the TC’s SLP ﬁeld. with respect to the previous isobar. The analytical area ratio is also computed using (3.9), with

Pc equaling the central SLP within the reanalysis, P∞ = 1013 hPa, and b = 1. The true area ratio, analytical area ratio, and ∆R values are then appended to the respective isobar measurements (see Table 3.3). The final step in the procedure is to find the innermost ∆R that deviates from the analytical area ratio, as mentioned in the previous section. Although an explicit comparison between the true area ratio and the analytical area ratio is warranted, fixed ∆R thresholds are used for each reanalysis data set for consistency. Without comparing the observed ratio with the analytical ratio, however,

47 Figure 3.3: (top) MERRA SLP ﬁeld for Typhoon Halong at 1800 UTC on 7 August 2014, with NCDC GridSat-B1 imagery underlaid for reference. The maximum extent of area calculations is highlighted by the green isobar, while the purple isobar is the OCI calculated by the area ratio procedure. (middle) Area calculations with respect to isobar value. (bottom) Area ratio calculations with respect to isobar value. The purple curve denotes the true area ratio, while the gray curve denotes the analytical area ratio from (3.9).

48 Table 3.3: Size measurements for Typhoon Halong at 1800 UTC on 7 August 2014. Each column represents the radius of the largest circle containing the respective isobar, the area of the isobar, the number of grid points contained within the isobar, the true area ratio, the analytical area ratio, and the ∆R based upon the previous isobar. The bolded value represents the last isobar before the ∆R threshold is met, and is therefore deﬁned as the OCI. Isobars that do not meet the grid point threshold (deﬁned here as 115 grid points) are excluded from the table.

Isobar Radius of Area of isobar True ∆R based (in hPa) Circle (km) (× 106 km2) Grid points Area Ratio R from (3.9) on true 994.5 500 0.442 120 1.091 1.081 0.054 995.0 550 0.475 129 1.075 1.082 -0.016 995.5 550 0.512 139 1.077 1.083 0.002 996.0 550 0.552 150 1.079 1.084 0.002 996.5 600 0.578 157 1.047 1.085 -0.032 997.0 650 0.636 173 1.101 1.087 0.054 997.5 650 0.662 180 1.041 1.089 -0.061 998.0 700 0.717 195 1.083 1.090 0.042 998.5 700 0.780 212 1.087 1.092 0.004 999.0 750 0.846 230 1.085 1.095 -0.002 999.5 800 0.908 247 1.074 1.097 -0.011 1000.0 850 1.004 273 1.105 1.100 0.032 1000.5 900 1.089 296 1.084 1.103 -0.021 1001.0 950 1.202 327 1.104 1.106 0.02 1001.5 1800 1.718 467 1.429 1.109 0.325 1002.0 1950 2.035 553 1.184 1.113 -0.245

a ﬁxed ∆R threshold is largely arbitrary and not physically meaningful. Thus, agreement between the observed and theoretical area ratios justify using a speciﬁc ∆R threshold for each reanalysis data set. Since the resolution of each reanalysis data set varies, and because the initialization scheme used to characterize a TC differs between data sets, different ∆R thresholds are used for each data set. After preliminary tests, a ∆R threshold of 0.099 is suggested for use with MERRA, ∆R =

49 0.108 for CFSR, and ∆R = 0.132 for ERA-I. The last isobar with a ∆R value less than the selected threshold is defined as the new OCI for TC size calculations (see Figure 3.3). In return, the ROCI can be found using the respective area of the OCI, or by solving in the manner recommended by M84. It is suggested that the new OCI area values can be used as an alternative TC size parameter altogether, as this is an accurate representation of the isobar fully enclosing the two-dimensional pressure field of a TC. For any given TC, a certain number of grid points is needed to adequately resolve a single closed pressure contour, depending upon the grid-spacing of the respective data set. Because OCI calculations require more than one pressure contour encompassing a TC, this minimum threshold must be even larger. Accordingly, any high ∆R measurements are excluded from the size calculation if the number of grid points contained within the respective isobar does not exceed this minimum threshold. After further testing, an optimal threshold of 115 grid points (126 grid points for calculations with CFSR) is specified within the algorithm, or about 10 × 10 grid points with a radius of 5 grid points (see Figure 3.4). Although this grid point threshold may modify the size of very small TCs, it considerably improves the accuracy of the algorithm overall by decreasing the sensitivity of the small ∆R threshold. Note that an OCI failing to meet or exceed the grid point threshold can still be valid if no other closed isobars are found outside of it. To identify and remove unrealistic OCI values that were passed through the algorithm, two additional thresholds are defined. First, the difference between Pc and the respective OCI must be at least 3 hPa in order for the OCI to be considered a reliable measurement. This is to prevent including TCs that are either too weak and do not have a well-defined SLP field, or to remove calculations where the TC was not resolved in the data set. The second is to remove any storm that has an OCI area larger than 5.25 × 106 km2. Although these are technically successful calculations by the algorithm, these are much too large to be considered reliable. For example, Typhoon Tip’s maximum OCI area with respect to all three reanalysis data sets was measured at 5.099 × 106 km2; since Tip was the largest storm on record (Dunnavan and Diercks 1980), any measurements larger than Tip’s maximum size is obviously erroneous. These erroneous measurements typically occur when the TC was unresolved within the data set (where no closed isobars were found near the

50 TC center), and the algorithm instead measures a closed contour of a synoptic- or planetary-scale feature encompassing the TC. A case study on three WNP TCs was recently executed to test the detection rate of the algorithm, or the percentage of cases that were deemed realistic for statistical analysis. The algorithm’s performance is calculated by subtracting the number of “failed” cases (those in which an OCI could not be calculated by the algorithm) and “unreliable” cases (those that returned an OCI calculation, but did not pass the filtering procedure described above) from the total number of cases. The ratio of all “accepted” cases versus total number of cases is multiplied by 100 to determine the detection rate of the algorithm. Rejected cases are defined hereafter as the aggregate of failed and unreliable cases. It is also noted that each case is referred to as a “storm fix” throughout the remainder of this study, otherwise known as a single OCI calculation for one point in time of a particular TC. A very large TC (Typhoon Tip; 1979), a medium-sized TC (Typhoon Robyn; 1993), and a small TC (Ed; 1993) were used for the case study. Results showed high performance of the algorithm, with a detection rate of 87.7% with MERRA, or 135 out of 154 accepted measurements; an 85% detection rate with CFSR (129 out of 152 accepted calculations); and an 81.2% detection rate for ERA-I (125 out of 154 accepted calculations). The rejected calculations generally occurred when a TC was too weak within the data set (and therefore not enough isobars encompassed the TC), or the pressure gradient was too tight between the SLP field of the TC and the SLP field of the surrounding environment (where the ∆R threshold was eventually met well outside the TC circulation). Thus, departures from a 100% detection rate are primarily not the fault of the algorithm, but of the representation of the TC’s SLP field within the respective data set.

3.3.2 Method of Statistical Analysis

A statistical analysis is performed to develop a climatology of all WNP TCs between 1979 – 2015. The data acquired from the methods described above are compiled together to produce the new database of TC size. Area, Pc, and OCI values are all preserved for the analysis, while grid point, area ratio, and ∆R values can be discarded since these were only needed to ﬁnd OCI values. Each storm ﬁx is regarded as a single data point in the analysis that is independent of a TC’s life cycle, geographical location, and time of year.

51 Figure 3.4: As in Figure 3.3, except for Tropical Storm Warren at 0000 UTC on 25 October 1984. (top) The purple contour outlines the OCI when the grid point threshold is reduced to 50, while the black contour highlights the correct OCI when the threshold is set to 115. Typhoon Vanessa can be seen directly to the east of Tropical Storm Warren.

52 One objective of this statistical analysis is to produce a histogram of relative size measurements, which will show the relationship between TC size and relative frequency for that respective size. This histogram is categorized into the number of cases per size category versus the relative TC size. Storm ﬁxes are placed into one of 24 separate bins, classiﬁed by every 0.5◦ latitude of radius (converted from units of km2 in area measurements, assuming a perfectly circular OCI) between 0◦ and 12◦ in area. This conversion is done to compare with prior research (e.g., M84; Liu and Chan 1999), as well as to relate to TC size categories assigned by JTWC (Table 3.4).

Table 3.4: TC size categories assigned by JTWC over the WNP. Units are in degrees latitude. [Chan and Chan 2012]

Size Category Radius

Very small < 2 Small 2 – 3 Medium 3 – 6 Large 6 – 8 Very large > 8

Another primary goal of this task is to ﬁnd a relationship between Pc and TC size (with respect to OCI) to match with prior research. A histogram of Pc (from the respective reanalysis data set) versus mean storm size is created using all acceptable data points; data are also examined using the 95% conﬁdence interval (CI) for each bin, which is produced from the mean size and standard error of each respective bin. One histogram is created per reanalysis data set (three total plots).

Ideally, the histogram will reveal a negative relationship between Pc and size; in other words, a stronger TC (one with a lower Pc) should generally be larger than a weaker TC. Additionally, TC size from reanalysis data is compared with Pc data from JTWC EBT, although this is expected to show considerable variance due to the difference between the central pressure recorded by JTWC and the corresponding central pressure within the reanalysis data.

53 Further analysis includes studying the relationship between TC size and age, a monthly climatology, and yearly trend of TC size since 1979. It is expected that the general size of TCs within this analysis should expand throughout their life cycle, since prior research generally states that TCs typically either expand or maintain their initial size. The monthly climatology should reveal similar results as those by Brand (1972) and M84. The main purpose of producing a TC size climatology with respect to year is to analyze long-term trends of size, although this task will also aid in identifying interannual variations of size. The final objective of the statistical analysis is to analyze the general size of TCs as a function of geographical location, which will considerably aid in the identification of environmental influences for storms of different sizes. Once again, this task will be compared with prior research for verification.

3.4 Summary of Data, Deﬁnitions, and Methods

In summary, an objective size climatology of all WNP TCs between 1979 – 2014 is developed by utilizing SLP data from three reanalysis data sets. JTWC Best-Track and EBT data sets will be used to locate each storm fix per every 6 h throughout the lifetime of a particular TC. To objectively define the OCI of a TC, a new TCPR derived from the H80 WPR is introduced, which does not include any dependence on the TC’s wind field. To determine a more objective OCI, the area inside each closed contour around a TC is explicitly calculated. Next, the change in area of each adjacent contour (outward from the TC center) is examined. These results are then compared with the analytically derived solution from H80 to determine the OCI (through sensitivity testing). This procedure is then applied to the gridded reanalysis data to produce a new TC climatology. This climatology includes a frequency distribution of TC size with respect to each reanalysis data set,

an analysis of TC size versus Pc, a comparison between TC size and age, a monthly climatology, and a yearly trend of size. A final task includes analyzing TC size as a function of geographical location. Chapter 4 will discuss the overall results of the algorithm with respect to the data, definitions, and methods introduced in this chapter. The first section will present four different scenarios

54 to highlight the advantages and limitations of the algorithm. The next chapter will continue by examining the results of the statistical analysis, as well as comparing the results with existing climatologies. Finally, Chapter 4 will discuss possible environmental inﬂuences of various-sized storms. A summary and discussion of this research will be presented in Chapter 5.1, followed by the conclusions of the work in Chapter 5.2. Finally, Chapter 5.3 will suggest future work that can be conducted using this research.

55 CHAPTER 4

RESULTS

This chapter will discuss the overall results of the algorithm with respect to the data, definitions, and methods introduced in Chapter 3. The first section will present various case scenarios highlighting the advantages and limitations of the algorithm. This will be followed by the results of a climatology when the algorithm is applied to 36 years of data. Next, a comparison between this climatology and size climatologies of other research will be documented. The final section of this chapter will briefly examine the factors that impact TC size, such as environmental influences, both at formation and at the end of the TC’s life cycle.

4.1 Case Scenarios

The alternate metric of TC size introduced in this study is intended to produce more stable and objective calculations than the M84 method. Based upon the preliminary work stated in Chapter 3, as well as the definitions presented above, the detection rate of the algorithm is at least 80% for all three reanalysis databases. Many of the rejected calculations were automatically identified as such by the algorithm (defined in this study as “failed” cases), especially the storm fixes without a single closed isobar in the respective reanalysis database. The rest of these rejected cases (defined here as “unreliable” cases) were filtered out using the additional thresholds defined in the previous chapter. Accordingly, the purpose of this section is to highlight case scenarios of four different TCs, each through their entire life cycle, to discuss the overall reliability of the algorithm: 1. Tropical Storm Warren (1993): An outstanding scenario with a very high detection rate, where only one storm fix was rejected after filtering.

2. Tropical Depression 12W (1989): A poor scenario with a low detection rate, where a majority of storm ﬁxes was rejected.

3. Typhoon Omar (1992): A typical life cycle in which most of the calculations were accepted (with a few rejected calculations).

56 4. Typhoon Ian (1987): A scenario with contrasting detection rates depending upon the reanalysis data set.

Examination of this set of cases will allow one to understand both the advantages and the limitations of the algorithm, to account for and understand the reason for the rejected calculations, and to justify why storms of various sizes and intensities can result in different detection rates.

4.1.1 “Complete Storm Life Cycle” Case: Tropical Storm Warren (1984)

Tropical Storm Warren (1984) was a strong, yet relatively small tropical cyclone in the WNP that lasted for nine days between 23 October and 1 November. The algorithm performed excep- tionally well with Warren’s OCI calculations, as all 38 storm fixes within both MERRA and CFSR reanalysis data were accepted for statistical analysis. The detection rate of calculations using ERA-I was 97.4%, as only one out of 38 fixes using ERA-I was rejected. A particularly interesting aspect of Warren’s OCI calculations is the relative consistency of size between all reanalysis data sets, despite the change in OCI from development through decay (Figure 4.1a). Although incon- clusive, this scenario may hint that the temporal consistency of size calculations using SLP data has improved with this revised method. Recall from Chapter 2 that OCI values can change instantaneously, as the SLP field of a TC and the surrounding environment are both dynamic (Cocks and Gray 2002). However, since SLP is vertically integrated through the atmosphere, it should not change as quickly as with other variables such as surface wind speed. The results from Tropical Storm Warren appear to highlight the stability of OCI calculations using this alternative method.

4.1.2 “Partial Storm Life Cycle” Case: Tropical Depression 12W (1989)

Tropical Depression 12W (1989) was noticeably a very weak tropical cyclone (given its status as a tropical depression) that existed only four days between 27 – 31 July (Figure 4.1b). Accord- ingly, the algorithm attempted to calculate the OCI of 17 storm ﬁxes from 12W. However, less than 40% of the total calculations were accepted for statistical analysis, with many of these failing the

OCI – Pc threshold. The remaining rejected storm ﬁxes resulted from an area measurement being unrealistically high. The detection rate of OCI calculations using MERRA and ERA-I data was low, as only 4 and 6 out of 17 calculations were accepted, respectively. The detection rate with

57 CFSR was relatively high in comparison to the rate with MERRA and ERA-I, as 10 out of 17 cases were accepted, or 58.8% of all ﬁxes. Based upon the analysis of 12W, an apparent limitation of the algorithm is that it may not be able to resolve the size of weak TCs due to their loose pressure gradient (and therefore a very small number of closed isobars). Fortunately, this limitation plays in favor of the statistical analysis, as the size of many weak TCs is unrepresentative of the size distribution for tropical storms and typhoons due to its large variance.

4.1.3 “Expected Storm Life Cycle” Case: Typhoon Omar (1992)

The third scenario presented in this section is with Typhoon Omar (1992), a very intense hurricane that lasted from 20 August to 5 September (Figure 4.2a). Of the 69 available storm ﬁxes throughout Omar’s life cycle, 49 size calculations were accepted from MERRA (71.0%), 47 from ERA-I (68.1%), and 46 from CFSR (66.7%). Many of the rejected calculations were taken during Omar’s initial development, where either no closed contours were available, or an area ratio could not be computed due to the lack of multiple contours. The size calculations with Typhoon Omar display a rather expected case when measuring the size of any given TC. Some of these calculations are expected to be failed or unreliable cases, especially during its initial development (whereas its status as a tropical depression or invest is unrepresentative of the size distribution of TCs, as with Tropical Depression 12W), while the remaining successful calculations should be included given their well-deﬁned circulation (many isobars encompassing the TC center).

4.1.4 “Contrasting Storm Life Cycle” Case: Typhoon Ian (1987)

Typhoon Ian (1987) was an intense tropical cyclone that lasted from 21 September to 3 Octo- ber; this storm provides an interesting case in which the performance of size calculations greatly differs between data sets (see Figure 4.2b). Out of 52 storm ﬁxes, the detection rate of calculations was 55.8% with MERRA, 46.1% with CFSR, and 36.5% with ERA-I. Ian took several days to develop from formation to maturity, and appropriately, most of the rejected calculations were extracted while the TC was weak and did not contain enough closed isobars. However, the detection rate differed greatly between data sets, which is an expected consequence of the differences between the grid-spacing of each reanalysis data set. Calculations with MERRA, for example, were

58 59

(a) (b)

Figure 4.1: Time-series of OCI calculations (in hPa; top), area calculations with respect to OCI (× 106 km2; middle), and area ratio calculations with respect to both OCI and area (bottom) for (a) Tropical Storm Warren (1984), and (b) Tropical Depression 12W (1989). 60

(a) (b)

Figure 4.2: As in Figure 4.1, but with (a) Typhoon Omar (1992) and (b) Typhoon Ian (1987). somewhat reliable overall throughout the TC’s life cycle, while the majority of calculations with ERA-I throughout most of Ian’s life span were rejected. This may be partially due to the relatively coarse grid-spacing of ERA-I in relation to MERRA’s ﬁner grid-spacing (see Table 3.1). Cases like Ian justify why the statistical analysis should be done independently with respect to a particular reanalysis data set, and should only be compared with one another after the analysis is completed.

4.1.5 Summary of Storm Life Cycle Cases

All four of the time-series mentioned above display two common characteristics that are important to briefly discuss. The first is that an approximate 12 h oscillation appears in the OCI calculations, which is evident in all three of the reanalysis data sets. Preliminary work has discovered that this small oscillation is due to atmospheric tides (Chapman and Lindzen 1970; Dai and Wang 1999), and is therefore a natural occurrence that is neither a limitation of the reanalysis data, nor a limitation of the algorithm used in this study. Dai and Wang (1999) notes that these maximum (minimum) SLP anomalies occur twice daily (in the WNP) around 0000 and 1200 UTC (0600 and 1800 UTC). These respective times match with SLP anomalies found in this work. The second characteristic is that the time-series of each aforementioned case, with the exception of the partial storm life cycle case (Tropical Depression 12W), show impressive synchronization in OCI calculations between all three data sets. In other words, the OCI calculations are nearly identical between reanalysis data for most of the TC life cycles. This is rather unexpected, considering that prior studies have documented inconsistencies between reanalysis intensity of TCs (e.g., Schenkel and Hart 2012). Because the area ratio used to calculate the OCI is dependent upon Pc, given that Pc determines the magnitude of the pressure gradient, the inconsistencies in intensity estimation between data sets should result in different OCI calculations (assuming that the intensity of a particular TC varies between data sets). Further work is needed to address why and how OCI calculations correspond so well between reanalysis data sets in this study. Based upon the example cases presented above, it is clear that not all TC size calculations should be included in the statistical analysis introduced in the next section. Although the algorithm attempts to remove as many unrealistic calculations as possible, certain restrictions must also be considered to filter out the remaining inaccuracies. After removal of all failed and unreliable storm

61 fixes, 25,663 calculations out of 34,211 total storm fixes with MERRA are included for statistical analysis, or 75.0% of the total data. Regarding ERA-I, 24,889 calculations out of the same total number of fixes are retained, or a detection rate of 72.8%. Finally, 25,141 calculations out of 31,186 fixes are recorded from CFSR, or a detection rate of 80.6%. After filtering, these accepted data are hereafter assumed to be accurate, although erroneous calculations may still exist.

4.2 Climatology

The results of the statistical analysis using all accepted size calculations will now be presented. As stated in the previous section, the analysis is conducted independently with respect to each reanalysis data set, although equivalent tests using each set of data are merged into cumulative plots for comparison and to help establish conclusions.

4.2.1 Frequency Distribution of TC Size

The first set of results highlights the frequency distribution of relative TC size for all three data sets (Figure 4.3). To compare with prior research, as well as with the JTWC classifications of size (Table 3.4), each area calculation is converted from a two-dimensional size in km2 to an effective one-dimensional radius in equivalent degrees latitude. Of course, this assumes a symmetric vortex with a perfectly circular OCI; this is certainly never the case in reality, but since this is a fixed conversion for each and every calculation, it will nevertheless highlight the full size distribution of all accepted storm fixes with consistency. Statistical results (Table 4.1) show that the average and median size of TCs with respect to MERRA is 5.52◦ and 5.26◦ latitude, respectively, with a standard deviation of 1.98◦ latitude. The frequency distribution of TC size shows that the ROCI of most TCs is between 3 – 6◦ latitude with MERRA. In regards to ERA-I, the average and median TC size is 5.60◦ and 5.24◦ latitude, respectively, with a 2.00◦ standard deviation. The most common TC size with respect to ERA- I is between 3.5◦ and 4◦ latitude, with very few TCs exhibiting a size smaller than 3◦ latitude. The average and median size within CFSR data is considerably less than with MERRA or ERA- I, as these respective values are 4.78◦ and 4.08◦ latitude, with a 2.03◦ standard deviation. The frequency distribution of the CFSR cases reveals that 34.9% of all storm fixes are less than 4◦

62 (a) (b) 63

Figure 4.3: Relative frequency distributions for all accepted TC area calculations with respect to (a) MERRA data, (b) ERA-I reanalysis, (c) CFSR data, and (d) the aggregate of all three data sets. Numbers above vertical bars represent the number of cases within each respective bin. latitude in size, with the most common size being between 3 – 3.5◦ latitude. The TC SLP field of many storms within CFSR abruptly ends at a much smaller radius than its corresponding SLP field within MERRA or ERA-I, and in turn, TCs are generally smaller within CFSR. The smaller overall size of TCs within the CFSR database highlights an important constraint with the data caused by vortex relocation (Liu et al. 2000), where a TC is removed from the environmental SLP field and either re-positioned or replaced by a synthetic vortex. This process may directly impact both the

Pc and the TC’s pressure gradient (depending on how the vortex was re-positioned), and therefore may artiﬁcially modify area ratio calculations. As such, analysis with CFSR should be performed with caution.

Table 4.1: Statistical results of size for all accepted calculations with respect to each reanalysis data set, including average size (µ), standard deviation (σ), and median size. All values have been converted to a one-dimensional radius in equivalent degrees latitude.

Database µ σ Median

MERRA 5.52 1.98 5.26 ERA-I 5.60 2.00 5.24 CFSR 4.78 2.03 4.08

The aggregate frequency distribution of size with all three data sets shows a positively skewed profile, with the most common size located between 3.5 – 4◦ latitude. Since the skewed data from CFSR is included, these aggregate values are generally higher when only MERRA and ERA-I calculations are tallied. Nevertheless, the profile shows that very few TCs exhibit a size less than 2◦ latitude, primarily due to the high grid point threshold defined within the algorithm (refer to Chapter 3.3.1). A broad distribution of size exists beyond 2◦ latitude. This is rather expected, considering that the majority of TCs either maintain their initial size or expand with time, as stated by Cocks and Gray (2002) and Kossin et al. (2007a). Furthermore, the sole upper bound used to filter out erroneous data lies beyond 11.6◦ latitude (5.25 × 106 km2); in theory, the only upper bound for the size of a TC is the size of the hemisphere. However, a TC cannot be smaller than 0◦

64 latitude, which implies a lower bound for TC size even without the grid point threshold. Therefore, a positively skewed distribution results from the statistical analysis. The overall mean and median with the combined set of calculations is 5.30◦ and 4.92◦ latitude, respectively, with a standard deviation of 2.04◦ latitude.

4.2.2 Size vs. Central Pressure

To analyze the relationship between Pc and TC size, a histogram is produced that places the relative size of all accepted storm fixes into 12 separate bins between 960 – 1012 hPa, each with a bin size of 4 hPa (Figure 4.4a). A statistical analysis of OCI area versus Pc shows an apparent negative correlation among the two variables, with an approximately linear profile between all three reanalysis data sets. The conclusions of prior research generally state that TC size and intensity are no better than weakly correlated (Brand 1972; M84; Chan and Chan 2012). However, the negative correlation between size and intensity found in this study is statistically significant at the

95% conﬁdence level. This result should be expected with gridded reanalysis data, as the Pc of a TC, and therefore its pressure gradient, can only be resolved to a certain extent based upon the grid-spacing (as explained in Chapter 3.3.1). Regardless, a statistically signiﬁcant result produced by the analysis is that more intense TCs are generally larger than TCs of weaker intensity, which agrees with some prior research (e.g., Callaghan and Smith 1998) Each OCI area calculation within the analysis can also be compared with its corresponding

Pc value in the JTWC EBT database (Figure 4.4b). In this case, data were placed into one of 15 separate bins between 916 – 1012 hPa, each with a bin length of 6 hPa. Because EBT archives only date back to 2001, all TCs prior to 2001 are discarded from this part of the analysis. Results

show that a negative correlation between size and Pc continues to exist, but the trend is not statis-

tically significant with respect to the 95% confidence level. The large variance at lower Pc values somewhat explain why the negative relationship is not statistically significant. However, this investigation compares data from two partially independent databases; that said, the large variance is fairly anticipated. Although not statistically significant, the negative relationship discovered in this portion of the analysis serves as a benefit to the climatology, as it provides additional evidence of the negative correlation between TC size and intensity discussed earlier in this subsection.

65 (a)

(b)

6 2 Figure 4.4: Mean TC area (× 10 km ) versus Pc (in hPa) with respect to (a) the individual reanalysis data sets, and (b) the JTWC EBT Pc values.

4.2.3 Size vs. Age

The next step in the statistical analysis is to analyze the relationship between relative OCI area and TC age (Figure 4.5a), as Kossin et al. (2007b) showed that age can be one of the primary objective predictors for storm structure. Data are once again plotted in accordance with its relative size, and are placed into one of 10 bins between 0 – 241 h since formation. The width of each bin is 24 h, or one full day. The results show a positive relationship between size and age, with each of the three data sets displaying a roughly logarithmic profile. This trend is statistically significant at the 95% confidence level for both ERA-I and CFSR, thanks largely in part to the small variance of size just after genesis. The same analysis with MERRA, however, does not show this correlation,

66 as TC size within MERRA generally remains constant within this data set. The initial size of TCs within CFSR data is about 0.9 × 106 km2, while its maximum size (near 160 h) is approximately 1.2 × 106 km2. The analysis with ERA-I shows a much higher initial value of about 1.3 × 106 km2 and a maximum size of 1.45 × 106 km2 at approximately 130 h since genesis. The initial size of TCs within MERRA is approximately 1.3 × 106 km2, with a maximum value of about 1.4 × 106 km2 at 130 h. Because these results differ greatly between data sets, further research should be conducted in order to explain these discrepancies.

(a) (b)

Figure 4.5: (a) Mean TC area (× 106 km2) versus time since development (in h), and (b) ratio of mean TC area at the respective time since development over the mean TC area at initial formation.

The same data are plotted as a ratio with respect to the initial size (Figure 4.5b). This allows for the analysis of size change throughout a particular TC’s life cycle. Results show an average maximum size of about twice the initial value for CFSR data, roughly 1.7 times the initial value for ERA-I, and no significant increase in size throughout a TC’s life cycle with MERRA. The positive relationship is statistically significant with ERA-I and CFSR at the 95% confidence level.

4.2.4 Monthly Climatology of Size

A monthly climatology of TC size is generated to highlight the seasonal preferences of WNP TCs (Figure 4.6a). The analysis shows that the largest storms occur in either September (ERA- I and CFSR) or October (MERRA). The mean size during September for ERA-I and CFSR is

67 approximately 1.6 × 106 km2 and 1.3 × 106 km2, respectively, while the mean size during October for MERRA is about 1.6 × 106 km2. The mean TC size decreases rapidly after October for all three data sets, with the smallest average size appearing in January. The results are, once again, statistically signiﬁcant at the 95% conﬁdence level for all three data sets.

(a) (b)

Figure 4.6: Mean TC area (× 106 km2) versus (a) month and (b) year for the entire database of accepted calculations.

4.2.5 Yearly Climatology of Size

A study of TC size versus year is conducted to analyze long-term trends, if any (Figure 4.6b). MERRA, ERA-I, and CFSR data show no long-term trend in size with respect to year that is statistically significant at the 95% confidence level. The results of this analysis should nonetheless be interpreted with extreme caution, as reanalysis data is generally more accurate in more recent years due to the advancement of observations. An interesting aspect of the analysis is a somewhat erratic oscillation that is consistent between all three data sets. This could possibly be an effect of ENSO (as discussed in Chan and Yip 2003; Chan and Chan 2012), considering the interannual variability of the data. The results of Chan and Chan (2012) state that the mean TC size is larger (smaller) during El Niño (La Niña) years, when the monsoon circulation is further eastward (westward) in the Pacific basin. As discussed in the next section, the mean TC size is larger when the monsoon circulation is further eastward. Thus, there are potentially intraseasonal factors such as ENSO that

68 inﬂuence where storms form and how they change in size throughout their life cycle. This will be further discussed in Section 4.4.

4.2.6 Size vs. Location

A histogram of TC size versus latitude is constructed to evaluate the geographical preferences on various-sized storms; more speciﬁcally, this is done to see if size generally increases with latitude (Figure 4.7). An apparent maximum size exists between 15 – 25◦N for all three data sets, followed by an abrupt reduction in average size between 30 – 40◦N, and another increase beyond 40◦N. Storm ﬁxes north of 50◦N in all three data sets, and south of 5◦N in MERRA, are intentionally overlooked due to the high variance at these respective latitudes. Based on the results of Chapter 4.2.3, as well as the results of prior research (e.g., M84), TC age and latitude may be directly related in that recurving TCs are generally older, and therefore larger in size. However, recurving TCs may also be entering a more baroclinic environment that may promote TC growth. Therefore, further research is needed to address the dominant factor of size for recurving TCs.

Figure 4.7: Mean TC area (× 106 km2) versus latitude in degrees North.

69 Although the statistical analysis of TC size versus latitude presents a wealth of favorable information, the analysis can be expanded further to include a full description of geographical preferences for various-sized TCs. This procedure draws every accepted storm ﬁx onto a Cartesian grid. Each storm ﬁx is characterized by its relative size, using various-sized concentric circles, and its

relative Pc using different color values (Figure 4.8). The goal of this test is to evaluate TC size along various times, locations, and intensities based upon the aggregate results of this study.

Figure 4.8: Compilation of all accepted storm ﬁxes (MERRA) with respect to geographical location. TC size is converted from area to an approximate radius (in degrees) to classify storms in accordance with JTWC size categories.

The composite of accepted storm ﬁxes (Figure 4.8) shows that various-sized TCs exist throughout the entire WNP, and these TCs have varying intensities (regardless of location). However, the composite displays too much variance in size as a function of both TC life cycle and TC age, and

70 it is difficult to analyze results using one single composite. Therefore, the composite image must be broken down into subsets to better understand the variability of the data. Data are extracted from the compilation of storm fixes in Figure 4.8 to better investigate geographical preferences of various-sized storms. The first set of images identifies the locations of storm fixes for small TCs (2 – 3◦ latitude; Figure 4.9a) and very large TCs (> 8◦ latitude; Figure 4.9b) in accordance with the JTWC size categories. Very small TCs (< 2◦ latitude) are not analyzed in this part of the study due to the low sample size. Figure 4.9 reveals that most small TCs are located further west than very large TCs, while many of these smaller storm fixes are adjacent to terrain. Additionally, the imagery shows that more intense TCs (defined by Pc) are generally larger than TCs of lesser intensity. To better analyze the initial and final size of TCs, all data with exception of the initial and final storm fixes of all TCs are eliminated from Figure 4.8. The plot of initial storm fixes (Figure 4.10a) shows general variability of size throughout the domain, with the majority of TCs located south of 25◦N. Figure 4.10b also reveals a rather large variance of size for final storm fixes, but many storm fixes north of 25◦N are large. Smaller size values of final storm fixes are generally associated with landfall, as many of these are located near mainland China and Vietnam. In these cases, the

TC quickly decays, and the Pc – OCI difference is not large enough for the OCI calculation to be accepted by the algorithm.

4.2.7 Summary of Size Climatology

The statistical analysis of TC size using the revised OCI parameter has revealed several sig- niﬁcant aspects in regards to WNP storms. The study shows a negative correlation between size and intensity, a positive correlation between size and TC age, and a rather obvious pattern between size and latitude. It is important to compare and contrast this work with prior research in order to validate the results. Accordingly, the next section will discuss these comparisons by recalling the prior research from Chapter 2.

71 (a)

(b)

Figure 4.9: As in Figure 4.8, but with only (a) small (2 – 3◦) and (b) very large (> 8◦) storm ﬁxes.

72 (a)

(b)

Figure 4.10: As in Figure 4.8, but with only (a) the first storm fix and (b) the last storm fix per TC within the database.

73 4.3 Comparison with Prior Research

Overall, the results of the statistical analysis using the alternative TC size metric compare well with prior research. This section will serve as a means to verify these results with similar studies, especially those that use ROCI as a primary metric such as Brand (1972) and M84. By doing so, the alternative TC size metric based on M84’s definition can be validated as a stable and effective metric for operational use, or for future studies. First, the frequency distribution of size calculations is compared with the results of M84 (Figure 4.11). The peak of the frequency distribution from this study matches very closely with the highest frequency values of M84, with the most common size of TCs being about 4◦ in radius. Values less than 4◦ radius are much less common in this study than in M84, while values greater than 4◦ are more persistent in this work. Note that M84 does not include a minimum grid point threshold, and is therefore less constrained by objective methodology. Furthermore, the frequency of storm fixes greater than 8◦ latitude in this study are more prevalent than they are in M84, although it is unclear why storms larger than 8◦ are rare in M84. However, the finer contour interval used in this study (∆P = 0.5 hPa, as opposed to 2.0 hPa in M84) may explain why larger storms are more common. By using a finer contour interval, the algorithm used in this study may reveal 1 – 3 additional closed contours beyond M84’s OCI, and therefore the TC may exhibit a larger size with respect to the OCI. The mean TC size in this study (with respect to MERRA and ERA-I) does not compare well with the mean TC size of 4.4◦, as noted in M84. The mean TC size of 4.78◦ with CFSR, however, compares nicely with M84. The aggregate frequency distribution of this study also compares with the ROCI values of Liu and Chan (1999), with the most common TC size falling between 3 – 4◦. In Liu and Chan (1999), ROCI values less than 4◦ latitude are more common, and thus compare more closely with this study than those from M84. However, ROCI values greater than 5.5◦ in Liu and Chan (1999) are extremely rare, and therefore do not correspond well with this study.

The analysis of TC area versus Pc is also compared with several climatologies mentioned in Chapter 2. Recall that size is weakly correlated with intensity, according to M84 (r = 0.28), Chavas and Emanuel (2010; r = 0.36), and Chan and Chan (2012; r = 0.29). Carrasco et al. (2014), however, states that there is a negative correlation between AR17 and TC intensity, but

74 (a) (b)

Figure 4.11: (a) As in Figure 4.3d, but using a bin size of 1◦, and (b) the relative frequency distribution of size for all TCs in the WNP between 1961 – 1969. [Merrill 1984; ©American Meteorological Society. Used with permission.]

a correlation does not exist when ROCI is instead used as a size parameter. This study finds a statistically significant negative correlation between TC size and intensity, but uses Pc instead of maximum winds to define the intensity of a TC. The correlation coefficients in this study were found to be –0.30 with respect to MERRA data, –0.38 with CFSR, and –0.31 with ERA-I (all p- values are negligible due to the large number of data). Callaghan and Smith (1998) addresses the correlation between TC size and Pc and states that larger TCs have a much lower Pc than smaller TCs of similar intensity. The results found here support prior studies in that maximum wind and

Pc are generally independent from one another. The comparison of mean TC size versus age with prior research is a bit difﬁcult, as calculations with the three different reanalysis data sets produce varying results. Luckily, the results within this research do not necessarily contradict those of other studies. Chavas and Emanuel (2010) note that the R12 and R0 of a TC generally increase early in the TC’s life cycle, and usually maintain its size beyond the mature stage. The results of this study, particularly with respect to ERA-I and CFSR, follow this observation with a gradual increase in size until about 150 h after genesis, followed by a general consistency in size beyond this time. Results with MERRA, however, show a general

75 constant size from genesis until dissipation. Dean et al. (2009) supports the results with MERRA by stating that the R0 of a TC remains somewhat constant throughout the TC’s life cycle. The monthly climatology of TC size discussed in this research complements Brand (1972) very well when area values are converted to an effective radius in degrees latitude (Figure 4.12). Brand (1972) states that the mean TC size is largest in October, which aligns with results of this study using MERRA, and nearly matches that with ERA-I and CFSR. Brand (1972) theorizes that the peak size in October may be explained by the general formation and recurvature of TCs further east in the Pacific basin than those in other months. The average monthly size of TC within this work, with respect to MERRA and ERA-I, nearly matches the monthly distribution of size noted in Brand (1972), although the distribution of size prior to August is much higher in this work. Other research, such as Yuan et al. (2007), Liu and Chan (1999), and Chan and Chan (2012), agree that the mean TC size is largest in October. Because several researchers have previously analyzed the yearly trend of TC size, a comparison with this research is also warranted. Yuan et al. (2007) noted a slight increase in mean TC size (defined as the R15) from 1977 – 2004. The results of this study could not be compared with Yuan et al. (2007). Chan and Yip (2003) and Chan and Chan (2012) can be recalled to discuss the interannual variations of size, especially in regards to ENSO. Specifically, Chan and Yip (2003) note a smaller mean TC size between 1999 – 2000, followed by a larger mean size between 2001 – 2002. The results of Chan and Yip (2003) matches with the results of this work, indicating that the fluctuations of size may be an effect of ENSO variability. Chan and Chan (2012) concur that the interannual variation of TC size correlates well with ENSO, as the monsoon circulation is further eastward during El Niño years, thus promoting a larger TC size (further discussed in the next section). The statistical analysis of TC size versus latitude is very important to compare with prior research, as it may directly pertain to operations (e.g., Japan may experience larger storms overall than the Philippines). Previous work, such as Knaff et al. (2014), has noted that larger TCs are generally located at higher latitudes than smaller storms. Kimball and Mulekar (2004), as well as M84, discovered that storms usually grow in size during recurvature, or rather, as they move poleward. Figure 4.7 shows that storms at higher latitudes are larger than those at lower latitudes.

76 (a)

(b)

Figure 4.12: (a) As in Figure 4.6a, but with area values converted to approximate ROCI values, and (b) monthly distribution of size of typhoon occurrences in the WNP between 1945 – 1968. [Brand 1972]

Since Figure 4.7 conﬂates TC age, formation location, and movement, it cannot be representative of the life cycle of one storm. Thus, caution must be made when comparing the results of this work with M84 or Kimball and Mulekar (2004). Chan and Chan (2012) noted an apparent maximum size at 25◦N, globally. The results of Chan and Chan (2012) were followed-up by Chan and Chan (2015a), which explained that this maximum size is between 15 – 25◦N. The results of Chan and Chan (2015a) agree well with this research, despite the observation that the largest mean TC size is located beyond 45◦N. This apparent maximum may be due to the effect of extratropical transition, otherwise regarded as when a TC exits the tropics and either rapidly decays or intensiﬁes. This

77 portion of the work will be further discussed in the next section. The results of Brand (1972) are used to compare with the geographical preferences realized in this work. Brand (1972) observes that very small TCs are commonly found near the extreme western portion of the Pacific basin, which can be confirmed in Figure 4.9a based upon the high number of small storm fixes near the Asian continent. Brand (1972) also notes that there is a preferred geographic location for very large TCs (defined as ≥ 10◦ latitude) between 15 – 25◦N and 140 – 145◦E. Although such a specific location was not found for very large TCs in this work, a high number of very large storm fixes were found within and near this domain (Figure 4.9b). Chan and Chan (2012) states that TC size varies spatially, which may justify the seemingly random location of various-sized TCs observed in this study. This study agrees well with prior research on TC size. Although much of this previous research used differing size parameters, either in addition to or in replace of ROCI, it is rather convenient to examine a general agreement between the climatology produced here and existing climatologies. However, further exploration of the results is warranted to identify different environmental influences of various-sized storms. Accordingly, the next section will examine different subcomposites in order to explain how a TC’s environment impacts its initial size, and how changes in environment can alter the size of a TC.

4.4 Size Life Cycles and Environmental Inﬂuences

The prior analysis has shown that there are potentially several factors that influence the size of a TC. Some of these might be environmental factors separate from the storm itself. Thus, the final component of this study is to examine the potential influences of TC size by utilizing the subcomposites from Section 4.2.6. First, the composite of storm fixes from Figure 4.10a will be partitioned to include only initially small storm fixes (< 3◦ latitude), and only initially large fixes (> 8◦ latitude). The mean formation location of each set will then be compared with the concurrent mean SLP field for the entire WNP. Secondly, the mean formation location of the July and October storm fixes will be compared with its corresponding mean SLP field in the WNP. This will be done to better analyze seasonal preferences of various-sized storms based upon the synoptic setup.

78 Third, the time-series of four representative storms will be analyzed to demonstrate either TC size maintenance or changes in size, depending on their respective tracks. Finally, subcomposites will be compared with the results from Figure 4.7 in order to better explain why an apparent maximum size exists near 25◦N.

4.4.1 Subcomposites of TCs at Formation

The first set of composites includes the first storm fix for every TC that has a size of less than 3◦ latitude within the data set. CFSR-based composites will not be inspected in this part of the analysis due to potentially non-physical factors included in the data (discussed in Section 4.2.1). The mean position for initially small storm fixes within the WNP (MERRA) is located at approximately 25◦N, 130◦E. When comparing this position with the corresponding mean SLP field (using only the SLP fields coexisting with the respective storm fixes), the TC is found in between a monsoon circulation to the west and a strong subtropical high to the east (Figure 4.13a). The results align well with Harr et al. (1996), which states that three very small TCs in their study (Nathan, Ofelia, and Percy in 1993) formed in between these two synoptic features. The standard deviation of the SLP field composites do not show clear evidence that the low pressure near the mean TC position is a manifestation of the mean TC itself, which further justifies that these small TCs form from the monsoon circulation. Results with ERA-I (not discussed) compare closely with the MERRA-based results. The same task is performed for very large TCs within the database (including CFSR data, as the potential non-physical factors included in CFSR data are not an issue with larger storms). The mean position for initially large storm fixes (MERRA) is located at approximately 18◦N, 140◦E (Figure 4.13b). The comparison between the corresponding mean SLP field and the mean storm fix position shows that most of these very large storms form on the eastern edge of a large monsoon circulation, while the monsoon circulation itself is further eastward than in the very small TC case (Figure 4.13a). Figure 4.13b also shows that initially large TCs generally form in the monsoon gyre’s broad circulation, rather than the tight circulation between the monsoon and the subtropical high (as with very small TCs). Results with ERA-I and CFSR (not discussed) compare well with the MERRA-based analysis.

79 (a)

(b)

Figure 4.13: Mean formation location and mean SLP ﬁeld at formation within the MERRA database for (a) small TCs (including very small TCs; < 3◦ latitude), and (b) very large TCs (> 8◦ latitude). Shaded contours highlight the mean SLP, black contours display the standard deviation of the SLP, the black circle notes the mean formation location of TCs, and the white square depicts the formation location within the 95% conﬁdence interval.

80 4.4.2 Subcomposites by Month

To better explain the monthly climatology of TC size discussed in Section 4.2, the mean initial position of all July TCs is compared with the corresponding mean SLP field in July (Figure 4.14a). The mean initial location of July TCs is approximately 17.5◦N, 135◦E. The mean July SLP field shows that the mean TC in July forms in the gradient between the monsoon trough to the west and the subtropical high to the northeast. Based upon the existing climatologies noted in Chapter 2.4, the analysis reveals that the relatively tight gradient between the trough and the high may promote a smaller TC size at formation. Recall Harr et al. (1996), which states that these smaller TCs may form in a concentrated area of high shear vorticity between the monsoon circulation and the subtropical ridge. The same task is performed for the mean initial position of all October TCs (Figure 4.14b). The mean initial location of October TCs is approximately 15◦N, 138◦E. The mean SLP field reveals that the mean TC forms within the monsoon circulation, while the subtropical high expands through the eastern portion of Asia. The monsoon circulation is more concentrated in October, which may promote TC genesis within the monsoon gyre itself. Additionally, the mean TC does not form between the monsoon circulation and the subtropical ridge where the very small TCs generally form (Harr et al. 1996). Thus, TC size may largely be a function of the concentration of shear vorticity, given that larger TCs do not form in such a concentrated area as with smaller TCs.

4.4.3 Case Studies

To better diagnose the environmental inﬂuences of TC size change, the time-series of four different TCs are analyzed. Two of these storms recurve into the midlatitudes after maturity, while two storms maintain a westward track and therefore remain in the tropics. Prior research (e.g., M84; Knaff et al. 2014) has stated that recurving TCs generally grow in size, while those with a relatively consistent westward track maintain their initial size. M84 theorized that changes in a TC’s surrounding environment may directly inﬂuence changes in the respective TC’s size; as an example, a TC may expand in size as it moves into a more baroclinic environment. This may be the earliest indication of a TC transforming into an extratropical system (Brand and Guard 1979).

81 (a)

(b)

Figure 4.14: As in Figure 4.13, but with all initial storm ﬁxes (regardless of size) in (a) July, and (b) October.

82 Because these baroclinic features are a primary influence of recurvature, the baroclinic features themselves may be the largest influence of TC growth in general (Evans and Hart 2008). Typhoons Soulik and Utor (2013) were two medium-sized TCs that formed during the Summer months (July and August, respectively). Both of these storms formed to the east of the Philippines, where the monsoon circulation played a lesser role in the formation and movement of these TCs. As a result, both of their tracks remained westerly, and the two storms maintained their relative size throughout their respective life cycles. Typhoons Wipha and Lekima (2013) were two relatively large TCs that formed during the late season (October), where the monsoon circulation played a primary role in the formation and movement of these two TCs. Lekima, in particular, was primarily influenced by Typhoon Francisco, which developed from the monsoon circulation itself. Wipha and Lekima formed near the same general area as Soulik and Utor. However, these two storms were steered northward by the cyclonic flow of the monsoon circulation, and both grew in size as they tracked to the northwest. Accordingly, both these TCs were moving into a more baroclinic environment with recurvature, in which this change in environment likely promoted a change in TC size (Brand and Guard 1979; M84). Therefore, it is theorized that these baroclinic features do not necessarily have to be a primary influence of TC track, but they appear to be a major factor in regards to TC size. The four cases mentioned above can also be used to analyze various sizes of the last storm fix per each TC. Because Typhoons Soulik and Utor maintained a primarily westward track, they made landfall soon after formation and thus were relatively short-lived. Although intense, these two storms did not have a chance to recurve or further intensify due to their short life cycle. Ac- cordingly, their SLP fields did not expand, and their sizes remained rather constant (recall from

Chapter 4.3 that size and Pc were found to be negatively correlated). Typhoons Wipha and Lekima steered away from the Asian continent and had more time to develop into intense tropical systems. Their fate was a result of extratropical transition, in which both storms manifested into a midlatitude feature and quickly grew in size. Overall, results show two primary modes of TC size with respect to the last storm ﬁx of a TC. The ﬁrst is a rather small size as a TC makes landfall, and the other is a relatively large size as a TC undergoes extratropical transition. Other modes may also exist, and further research on this part of the study is hence warranted.

83 4.4.4 Re-examination of Size vs. Latitude

The final task of this section is to better explain the relationship between size versus latitude, as in Figure 4.7. As previously noted, an apparent maximum size exists near 25◦N, although the mean TC size is also large beyond approximately 45◦N. Figure 4.15 shows the location of initially small and initially very large storm fixes throughout the database. It is clear that the majority of very large TCs form south of 30◦N, although many small TCs can form north of this latitude. In other words, smaller TCs do not have a limited geographical preference as with very large TCs, as many are found to form between 10 – 40◦N. It was previously mentioned that TCs generally maintain their initial size or expand with time (Cocks and Gray 2002; Kossin et al. 2007a). Since a large number of TCs south of 25◦N form large, they will stay large for a longer period of time. In turn, Figure 4.7 is largely a function of initial storm fixes, and does not in any way represent the size change of any particular TC as it moves northward. The apparent maximum size near 25◦N is appropriately due to the high number of initially large storm fixes near this latitude. The large mean TC size near 45◦N, however, appears to be a consequence of extratropical transition, where the SLP field of a manifesting TC will rapidly expand.

4.4.5 Summary of Environmental Inﬂuences

This section briefly analyzed some possible environmental influences on various-sized storms. It should be noted that the mean TC position and size within the subcomposites, along with the concurrent SLP fields of these respective TCs, cannot and should not be a representation of the full database. Many of these storms form outside of these preferential zones or seasons (depending on the relative size). Furthermore, because this study composited many TCs from various locations, there may be multiple environmental modes in the composite. This implies that the mean TC location with respect to the composited environment may not be representative of all TCs. How- ever, this analysis nevertheless serves as a possible explanation on how differing environments are related to differing storm sizes. It may be interesting to analyze various-sized TCs and the corresponding SLP fields to explain additional environmental influences of all TCs, regardless of size.

84 (a)

(b)

Figure 4.15: As in Figure 4.10a, but with only (a) small (including very small) and (b) very large TCs.

85 4.5 Summary of Results

The algorithm produced in this study is a robust procedure that explicitly measures the area of isobars encompassing a TC. This alternative metric has been found to be stable and is more objective than in M84 or Cocks and Gray (2002). Overall, the algorithm had a detection rate between 72.8 – 80.6%, depending on the reanalysis data set. Although the detection rate with CFSR data was highest out of the three reanalysis data sets, one should utilize CFSR-based TC size calculations with caution, as vortex relocation may introduce bias toward smaller overall sizes. In general, the algorithm expectedly had a high detection rate with mature TCs far from terrain, and a low detection rate with newly-formed TCs. An accepted storm ﬁx was typically dependent upon whether the TC was well-resolved within the respective reanalysis data. The statistical analysis discussed in this chapter generally agrees well with prior studies, although some exceptions were found that warrant further research. In general, the smallest storms the WNP were found to form in between the monsoon circulation and the subtropical ridge (in a concentrated area of high shear vorticity). Large TCs, on the other hand, typically form farther east in the Paciﬁc basin. These larger TCs appear to form from the monsoon gyre itself due to a large concentration of curvature vorticity. Based upon the results of this study, size change is largely a function of both latitude (with a change in the synoptic environment) and age (as longer-lived TCs are generally larger). Finally, seasonal variations of environmental features were noted in this work, which can affect the mean size of TCs.

86 CHAPTER 5

CONCLUDING SUMMARY

5.1 Discussion

The purpose of this study was to develop a TC size climatology using a revised version of the ROCI parameter defined by Brand (1972); the method of calculation was later explained in detail by M84, and was therefore one foundation of this work. The concept of TC size is critical for operational forecasters and decision-makers, as it directly influences how, when, and to what extent alerts are issued for the public. The understanding of TC size also serves as a benefit for researchers, especially for how size influences the track and intensity of TCs in various environments, and also the ability for a TC to interact with its environment. According to M84, the ROCI is defined as the average radius of the OCI encompassing a TC. If the OCI is highly asymmetric and is not a favorable representation of the size of a TC, a more symmetric isobar closer to the TC center may be used instead. The ROCI is a physically meaningful parameter to approximate the full circulation of a TC because it estimates the boundary between a TC and its surrounding environment. However, M84’s method of calculation is highly subjective, and it is not clear how to apply it when the OCI is highly asymmetric. Furthermore, because both a TC and its surrounding environment are both dynamic, isobars can instantaneously open and close, which can degrade the temporal consistency of this parameter. This process can happen even in the absence of TC change due to external forcing such as atmospheric tides or environmental pattern changes (e.g., a TC moving into a subtropical ridge). From an operational standpoint, this SLP-based size parameter may be very useful for quantifying the size of a TC in the absence of wind measurements, but it is not as directly connected to the public impacts as the wind-based parameters. Historically, researchers and forecasters have largely deviated away from using the ROCI as a TC size parameter in favor of wind-based metrics. The advancement of satellite-derived wind estimations in recent years have further promoted the analysis of wind-based size parameters such

87 as R17. Although useful in an operational setting, these wind-based size parameters are not effective in describing the full TC circulation, because this circulation typically includes winds that are below gale force. Accordingly, several researchers have developed WPR models in order to describe the full TC circulation with respect to both wind and SLP. One of the most common WPRs is the H80 model due to its relative simplicity and accuracy, which has been used operationally in several different meteorological agencies. This WPR was used as the foundation of this research in order to create a more objective definition of TC size with respect to SLP observations, as SLP is a stable, base-level variable that can be used to describe the full structure of a TC. The revised method of calculating TC size developed in this work first calculates the area inside each closed contour around a TC center. After the area of each closed contour is calculated, the algorithm examines how the area changes outward from the TC center. Next, the change in area for each isobar is compared with its analytical solution derived from H80. Finally, through sensitivity testing, the algorithm objectively determines the OCI, which is the last isobar before a significant increase in the area ratio and/or a departure from the empirical area ratio. Area calculations with respect to the objectively-determined OCI can be used as a two-dimensional size calculation, or the area can be converted to a one-dimensional radius to compare with existing work (or to compare with relative size in accordance with agency-defined size categories). In order to compute the one-dimensional effective radius, the OCI is assumed to be perfectly circular. The work performed here, along with some prior studies such as Cocks and Gray (2002), have dramatically improved the original definition of ROCI. The metric developed in this research, in particular, is designed to be a more objective metric that can be applied quickly to any gridded data set. Furthermore, the metric provides a temporal consistency of TC size that is not significantly influenced by storm changes or environmental changes such as atmospheric tides. Existing metrics, especially those based upon SLP data, do not have this advantage.

5.2 Conclusions

The algorithm produced in this study was tested on all WNP TCs between 1979 – 2014 to evaluate its detection rate. Overall, the algorithm had a detection rate of 75.0% with MERRA

88 data, 72.8% with ERA-I, and 80.6% with CFSR data. The algorithm especially performed well with mature TCs that were sufficiently far from terrain. Most of the rejected cases were a result of weak TCs without a closed circulation in the respective reanalysis data set, TCs whose SLP fields interacted with terrain, or TCs whose SLP fields interacted with strong environmental features such as other nearby TCs or adjacent lows. A statistical analysis of TC size measurements for all accepted storm fixes was executed to produce a 36-year climatology for WNP TCs (1979 – 2014). First, a frequency distribution of relative TC size for all three data sets was produced, which assumes that each two-dimensional area calculation has an equivalent one-dimensional radius for comparison with existing research. Results show that the average size of TCs in the WNP is 5.52◦ latitude with MERRA, 5.60◦ latitude with ERA-I, and 4.78◦ latitude with CFSR. These results compare well with M84 and Liu and Chan (1999), although a higher bias in sizes larger than 4◦ is apparent in this work. The results of the statistical analysis also revealed that the mean TC area is negatively correlated with the TC’s Pc within the respective reanalysis data set; in other words, a more intense TC

(with respect to Pc) is generally larger. This correlation matches the observations of Callaghan and

Smith (1998), which states that large TCs have a lower Pc than smaller TCs of similar intensity. Additionally, results show that the size of a TC typically expands during the initial stage of development (with the exception of the MERRA-based results), followed by a near constant size from maturity through decay. Chavas and Emanuel (2010) agrees well with the results of this work in that TC size generally increases from genesis until the mature stage. Although the MERRA-based results in this research do not match with Chavas and Emanuel (2009), they agree well with Dean et al. (2009), which states that size remains rather constant throughout a TC’s life cycle. Nonethe- less, comparisons with these two studies should be made with caution, as this research does not utilize the wind-based size parameters that are included in both Dean et al. (2009) and Chavas and Emanuel (2010). Furthermore, it was discovered that the largest storms occur in either September or October, depending on the reanalysis data set. The monthly climatology produced in this study relates somewhat closely to prior research such as Brand (1972), Liu and Chan (1999), Yuan et al. (2007), and Chan and Chan (2012). All of these prior studies agree that WNP TCs are generally largest in

89 October. However, the mean TC size in this study prior to August is much higher than the mean TC size noted in prior research. An investigation on the yearly trend of size does not clearly illustrate whether the average size of TCs has increased or decreased over the past few decades. Interannual variability was also found in this research, which is likely an effect of ENSO as discussed by Chan and Yip (2003) and Chan and Chan (2012). An additional agenda of the statistical analysis was to evaluate the geographical preferences on various-sized storms. Chan and Chan (2012, 2015a) support the results of this research when considering the relationship between TC size and latitude. This study notes an apparent maximum TC size at 25◦N, which agrees well with Chan and Chan (2012) and with Chan and Chan (2015a). However, this study finds that even larger TCs may exist beyond 45◦N, although this may be due to modification of a TC’s SLP field due to extratropical transition. Furthermore, most of the smallest storms within the data set were found adjacent to the Asian continent, or much further west than very large storms. This somewhat agrees with the statistical analysis of Brand (1972). Finally, the analysis revealed that stronger TCs, in general, are indeed larger than weaker TCs. Subcomposites were analyzed to identify the probable environmental influences of various- sized storms. The analysis revealed that many small TCs form in between a monsoon circulation and a subtropical ridge, while very large TCs typically form within the monsoon circulation itself. The seasonal variation of TC size matches well with these synoptic patterns. In regards to size change, recurving TCs generally grow in size as they enter a more baroclinic environment, and they have the ability to further intensify without interacting with terrain. The TCs that have a primarily westward track typically remain in a barotropic environment, and they reach landfall before intensifying (reducing the probability of TC growth). The subcomposites were also used to explain an apparent maximum size at approximately 25◦N. This appears to be a function of the initial formation of TCs instead of a function of size change, as most very large TCs form south of 30◦N. It is apparent that different reanalysis data sets produce different results; accordingly, it is suggested that two or more sets of data should be used for future studies. However, this study revealed that measurements with CFSR did not compare well with measurements from MERRA

90 or ERA-I, as sizes were generally smaller than those from the other two data sets. As such, one should conduct future CFSR-based TC size calculations with caution, especially since the process of vortex relocation may modify the SLP of TCs within CFSR. MERRA and ERA-I data, on the other hand, compared relatively well with one another, and it is therefore suggested that these two respective data sets be used simultaneously for veriﬁcation. Results of the statistical analysis conclude that the alternative TC size metric produced in this study is stable and more objective than that of M84 with respect to the analysis data used, and is also relatively consistent on the temporal scale. The detection rate of the algorithm is generally high, with some erroneous measurements generally occurring as a consequence of the analysis resolution within the three databases. Some possible improvements to this algorithm will be discussed in the next section.

5.3 Future Work

The algorithm developed in this study, as well as the data set produced by it, allows for a host of other avenues to pursue scientifically with respect to TC size and beyond. As such, future work may include examining methods of improvement, testing upon other gridded data sets, and further addressing scientific questions in regards to TC size such as environmental influences. To further improve the temporal consistency of TC size measurements, calculating a 24-h mean for each storm fix may be advised in order to expand upon this climatology. It is expected that this procedure will smooth some of the large fluctuations in size caused by diurnal and semidiurnal variations, which may improve the results of this work. Additionally, testing the sensitivity of the algorithm using a finer contour interval (∆P) may be necessary. In theory, this task only depends upon the resolution of the data set used. As gridded data continues to improve, testing the algorithm’s sensitivity is certainly warranted. Supplementary work is also needed to analyze how this algorithm performs with other gridded data sets, especially those operationally in use. Accordingly, future work will involve testing this procedure with GFS operational analyses in order to evaluate its practicality with operational forecasting. Furthermore, examining this procedure with MERRA-2 reanalysis data is needed and

91 will soon be conducted. Although this algorithm relies on SLP data for this study, it may be altered to be used with satellite-derived calculations in the future, especially as these observations continue to improve. An example is to modify the algorithm to analyze TC size with respect to H*Wind data, which would allow for wind-based TC size calculations. Furthermore, with the improvement of infrared satellite imagery on both the spatial and temporal scale, estimating TC size based upon brightness temperature contours from satellite imagery may soon be possible using this algorithm. The procedure introduced in this study has already been tested on satellite imagery by Hartman (2016) to analyze mesoscale convective systems over equatorial Africa. It is hoped that this work will promote research-based studies on the initial size and size change of TCs, especially as reanalysis data continue to improve. The analysis of subcomposites for various-sized storms may be further developed to better understand the factors of initial size and size change. It is suggested that using storm relative coordinates with the SLP composites would distinguish the overlapping modes discussed in Chapter 4.4.5, and further identify factors of initial size and size change for many TCs. Additionally, this research may be utilized to verify Dean et al. (2009), which stated that TC size may be a function of the geometry of the initial disturbance. Nevertheless, given the climatological results of this study, this revised TC size metric appears to serve as a strong framework for additional SLP-based TC size applications in the future. A ﬁnal goal of this research is to make this algorithm an operational product to aid in forecasting; in particular, this may be used so that forecasters can dynamically see, in real-time, how a TC develops or changes in size. This may signiﬁcantly improve public TC forecasts, which would substantially improve resource protection overall.

92 APPENDIX A

SIZE MEASUREMENTS WITH ERA-I AND CFSR

(a)

(b)

Figure A.1: As in Figure 4.8, but with (a) ERA-I data, and (b) CFSR data (from 1979 – 2010).

93 (a)

(b)

Figure A.2: As in Figure 4.9a, but with (a) ERA-I data, and (b) CFSR data (from 1979 – 2010).

94 (a)

(b)

Figure A.3: As in Figure 4.9b, but with (a) ERA-I data, and (b) CFSR data (from 1979 – 2010).

95 (a)

(b)

Figure A.4: As in Figure 4.10a, but with (a) ERA-I data, and (b) CFSR data (from 1979 – 2010).

96 (a)

(b)

Figure A.5: As in Figure 4.10b, but with (a) ERA-I data, and (b) CFSR data (from 1979 – 2010).

97 REFERENCES

Arakawa, H., 1952: Mame-Taifu or midget typhoon. Geophys. Mag., 23 (4), 463–474.

Atkinson, G. D., and C. R. Holliday, 1977: Tropical cyclone minimum sea level pressure/maximum sustained wind relationship for the western North Paciﬁc. Mon. Wea. Rev., 105 (4), 421–427.

Brand, S., 1972: Very large and very small typhoons of the western North Paciﬁc Ocean. J. Meteor. Soc. Japan, 50 (4), 332–341.

Brand, S., and C. P. Guard, 1979: An observational study of extratropical storms evolved from tropical cyclones in the western North Paciﬁc. J. Meteor. Soc. Japan, 57 (5), 479–483.

Callaghan, J., and R. K. Smith, 1998: The relationship between maximum surface wind speeds and central pressure in tropical cyclones. Aust. Meteor. Mag., 47 (3), 191–202.

Carr, L. E., and R. L. Elsberry, 1994: Systematic and integrated approach to tropical cyclone track forecasting, Part I: Description of basic approach. Naval Postgraduate School publication NPS-MR-002. Naval Postgraduate School, Monterey, CA 93943, 65 pp.

Carr, L. E., and R. L. Elsberry, 1997: Models of tropical cyclone wind distribution and beta-effect propagation for application to tropical cyclone track forecasting. Mon. Wea. Rev., 125 (12), 3190–3209, doi:10.1175/1520-0493(1997)125<3190:MOTCWD>2.0.CO;2.

Carrasco, C. A., C. W. Landsea, and Y.-L. Lin, 2014: The inﬂuence of tropical cyclone size on its intensiﬁcation. Wea. Forecasting, 29 (3), 582–590, doi:10.1175/WAF-D-13-00092.1.

Chan, J. C. L., and C. K. M. Yip, 2003: Interannual variations of tropical cyclone size over the western North Paciﬁc. Geophys. Res. Lett., 30 (24).

Chan, K. T. F., and J. C. L. Chan, 2012: Size and strength of tropical cyclones as inferred from QuikSCAT data. Mon. Wea. Rev., 140 (3), 811–824.

Chan, K. T. F., and J. C. L. Chan, 2013: Angular momentum transports and synoptic ﬂow patterns associated with tropical cyclone size change. Mon. Wea. Rev., 141 (11), 3985–4007.

Chan, K. T. F., and J. C. L. Chan, 2014: Impacts of initial vortex size and planetary vorticity on tropical cyclone size. Quart. J. Roy. Meteor. Soc., 140 (684), 2235–2248.

Chan, K. T. F., and J. C. L. Chan, 2015a: Global climatology of tropical cyclone size as inferred from QuikSCAT data. Int. J. Climatol., 35 (15), 4843–4848.

98 Chan, K. T. F., and J. C. L. Chan, 2015b: Impacts of vortex intensity and outer winds on tropical cyclone size. Quart. J. Roy. Meteor. Soc., 141 (687), 525–537.

Chapman, S., and R. S. Lindzen, 1970: Atmospheric tides, 200 pp. D. Reidel, Norwell, Mass.

Chavas, D. R., and K. A. Emanuel, 2010: A QuikSCAT climatology of tropical cyclone size. Geophys. Res. Lett., 37 (18).

Chavas, D. R., N. Lin, W. Dong, and Y. Lin, 2016: Observed tropical cyclone size revisited. 29 (8), 2923–2939.

Chavas, D. R., N. Lin, and K. Emanuel, 2015: A model for the complete radial structure of the tropical cyclone wind ﬁeld. Part I: Comparison with observed structure. J. Atmos. Sci., 72 (9), 3647–3662.

Chu, J.-H., C. R. Sampson, A. S. Levine, and E. Fukada, 2002: The Joint Typhoon Warning Center tropical cyclone best-tracks, 1945–2000. Ref. NRL/MR/7540-02, 16.

Cocks, S. B., and W. M. Gray, 2002: Variability of the outer wind profiles of western North Pacific typhoons: Classifications and techniques for analysis and forecasting. Mon. Wea. Rev., 130 (8), 1989–2005.

Courtney, J., and J. A. Knaff, 2009: Adapting the Knaff and Zehr wind-pressure relationship for operational use in tropical cyclone warning centres. Australian Meteorological and Oceano- graphic Journal, 58 (3), 167.

Dai, A., and J. Wang, 1999: Diurnal and semidiurnal tides in global surface pressure ﬁelds. J. Atmos. Sci., 56 (22), 3874–3891.

Dean, L., K. A. Emanuel, and D. R. Chavas, 2009: On the size distribution of Atlantic tropical cyclones. Geophys. Res. Lett., 36 (14).

Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis: Conﬁguration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137 (656), 553–597.

DeMaria, M., and Coauthors, 2013: Improvements to the operational tropical cyclone wind speed probability model. Wea. Forecasting, 28 (3), 586–602.

Demuth, J. L., M. DeMaria, and J. A. Knaff, 2006: Improvement of Advanced Microwave Sound- ing Unit tropical cyclone intensity and size estimation algorithms. J. Appl. Meteor. Climatol., 45 (11), 1573–1581.

99 Demuth, J. L., M. DeMaria, J. A. Knaff, and T. H. Vonder Haar, 2004: Evaluation of Advanced Microwave Sounding Unit tropical-cyclone intensity and size estimation algorithms. J. Appl. Meteor., 43 (2), 282–296.

Depperman, C. E., 1947: Notes on the origin and structure of Philippine typhoons. Bull. Amer. Meteor. Soc., 28, 399–404.

Dunnavan, G. M., and J. W. Diercks, 1980: An analysis of Super Typhoon Tip (October 1979). Mon. Wea. Rev., 108 (11), 1915–1923, doi:10.1175/1520-0493(1980)108<1915:AAOSTT> 2.0.CO;2.

Dvorak, V. F., 1975: Tropical cyclone intensity analysis and forecasting from satellite imagery. Mon. Wea. Rev., 103 (5), 420–430, doi:10.1175/1520-0493(1975)103<0420:TCIAAF>2.0. CO;2.

Elsberry, R. L., 1995: Tropical cyclone motion. Global Perspectives on Tropical Cyclones, 106– 197.

Emanuel, K. A., 1989: The ﬁnite-amplitude nature of tropical cyclogenesis. J. Atmos. Sci., 46 (22), 3431–3456.

Emanuel, K. A., 2004: Tropical cyclone energetics and structure. Atmospheric Turbulence and Mesoscale Meteorology, (8), 165–191.

Evans, C., and R. E. Hart, 2008: Analysis of the wind ﬁeld evolution associated with the extratropical transition of Bonnie (1998). Mon. Wea. Rev., 136 (6), 2047–2065.

Figa-Saldaña, J., J. J. W. Wilson, E. Attema, R. Gelsthorpe, M. R. Drinkwater, and A. Stoffe- len, 2002: The advanced scatterometer (ASCAT) on the meteorological operational (MetOp) platform: A follow on for European wind scatterometers. Canadian Journal of Remote Sens- ing, 28 (3), 404–412.

Frank, W. M., 1977: The structure and energetics of the tropical cyclone I. Storm structure. Mon. Wea. Rev., 105, 1119–1135.

Frank, W. M., and W. M. Gray, 1980: Radius and frequency of 15 m s−1 (30 kt) winds around tropical cyclones. J. Appl. Meteor., 19 (2), 219–223.

Fujiwhara, S., 1923: On the growth and decay of vortical systems. Quart. J. Roy. Meteor. Soc., 49 (206), 75–104.

100 Goodberlet, M. A., C. T. Swift, and J. C. Wilkerson, 1989: Remote sensing of ocean surface winds with the Special Sensor Microwave/Imager. Journal of Geophysical Research: Oceans, 94 (C10), 14 547–14 555.

Harper, B. A., 2002: Tropical cyclone parameter estimation in the Australian region-wind-pressure relationships and related issues for engineering planning and design–a discussion paper. SEA Rep. No. J0106-PR003E.

Harr, P. A., M. S. Kalafsky, and R. L. Elsberry, 1996: Environmental conditions prior to formation of a midget tropical cyclone during TCM-93. Mon. Wea. Rev., 124 (8), 1693–1710, doi: 10.1175/1520-0493(1996)124<1693:ECPTFO>2.0.CO;2.

Hartman, A. T., 2016: Tracking and analysis of mesoscale convective systems over central equatorial Africa. M. S. Thesis, Florida State University, 58 pp.

Hill, K. A., and G. M. Lackmann, 2009: Inﬂuence of environmental humidity on tropical cyclone size. Mon. Wea. Rev., 137 (10), 3294–3315.

Hodge, W. T., and G. F. McKay, 1970: A computer program to select typhoon analogs and print out their descriptions including subsequent changes. Tech. rep., DTIC Document.

Holland, G., and R. T. Merrill, 1984: On the dynamics of tropical cyclone structural changes. Quart. J. Roy. Meteor. Soc., 110 (465), 723–745.

Holland, G. J., 1980: An analytic model of the wind and pressure proﬁles in hurricanes. Mon. Wea. Rev., 108 (8), 1212–1218.

Holland, G. J., J. I. Belanger, and A. Fritz, 2010: A revised model for radial proﬁles of hurricane winds. Mon. Wea. Rev., 138 (12), 4393–4401.

Hsu, S. A., and Z. Yan, 1998: A note on the radius of maximum wind for hurricanes. J. Coastal Res., 14 (2).

Hurricane Research Division, 2014: Frequently Asked Questions. [Available online at http://www. aoml.noaa.gov/hrd/tcfaq/tcfaqHED.html].

JMA, cited 2016: RSMC Best Track Data (Text). [Available online at http://www.jma.go.jp/jma/ jma-eng/jma-center/rsmc-hp-pub-eg/besttrack.html].

JTWC, cited 2017: Warning Graphic Legend. [Available online at http://www.usno.navy.mil/ JTWC/warning-graphic-legend-1].

101 Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-year reanalysis project. Bull. Amer. Me- teor. Soc., 77 (3), 437–471.

Kaplan, J., and M. DeMaria, 2003: Large-scale characteristics of rapidly intensifying tropical cyclones in the North Atlantic basin. Wea. Forecasting, 18 (6), 1093–1108.

Kepert, J. D., 2010: Tropical cyclone structure and dynamics, Vol. 4. World Scientiﬁc Series on Asia-Paciﬁc Weather and Climate.

Kidder, S. Q., W. M. Gray, and T. H. Vonder Haar, 1978: Estimating tropical cyclone central pressure and outer winds from satellite microwave data. Mon. Wea. Rev., 106 (10), 1458– 1464.

Kimball, S. K., and M. S. Mulekar, 2004: A 15-year climatology of North Atlantic tropical cyclones. Part I: Size parameters. J. Climate, 17 (18), 3555–3575, doi:10.1175/ 1520-0442(2004)017<3555:AYCONA>2.0.CO;2.

Knaff, J. A., S. P. Longmore, and D. A. Molenar, 2014: An objective satellite-based tropical cyclone size climatology. J. Climate, 27 (1), 455–476, doi:10.1175/JCLI-D-13-00096.1.

Knaff, J. A., C. R. Sampson, M. DeMaria, T. P. Marchok, J. M. Gross, and C. J. McAdie, 2007: Statistical tropical cyclone wind radii prediction using climatology and persistence. Wea. Forecasting, 22 (4), 781–791.

Knaff, J. A., and R. M. Zehr, 2007: Reexamination of tropical cyclone wind–pressure relationships. Wea. Forecasting, 22 (1), 71–88.

Knapp, K. R., and Coauthors, 2011: Globally gridded satellite observations for climate studies. Bull. Amer. Meteor. Soc., 92 (7), 893–907, doi:10.1175/2011BAMS3039.1.

Koba, H., T. Hagiwara, S. Osano, and S. Akashi, 1990: Relationship between the CI-number and central pressure and maximum wind speed in typhoons. J. Meteor. Res, 42, 59–67.

Kossin, J. P., J. A. Knaff, H. I. Berger, D. C. Herndon, T. A. Cram, C. S. Velden, R. J. Murnane, and J. D. Hawkins, 2007a: Estimating hurricane wind structure in the absence of aircraft reconnaissance. Wea. Forecasting, 22 (1), 89–101.

Kossin, J. P., K. R. Knapp, D. J. Vimont, R. J. Murnane, and B. A. Harper, 2007b: A globally consistent reanalysis of hurricane variability and trends. Geophys. Res. Lett., 34 (4).

Kozar, M. E., and V. Misra, 2014: Statistical prediction of integrated kinetic energy in North Atlantic tropical cyclones. Mon. Wea. Rev., 142 (12), 4646–4657.

102 Lajoie, F., and K. Walsh, 2008: A technique to determine the radius of maximum wind of a tropical cyclone. Wea. Forecasting, 23 (5), 1007–1015.

Lander, M. A., 1994: Description of a monsoon gyre and its effects on the tropical cyclones in the western North Paciﬁc during August 1991. Wea. Forecasting, 9 (4), 640–654, doi: 10.1175/1520-0434(1994)009<0640:DOAMGA>2.0.CO;2.

Landsea, C. W., and J. L. Franklin, 2013: Atlantic hurricane database uncertainty and pre- sentation of a new database format. Mon. Wea. Rev., 141 (10), 3576–3592, doi:10.1175/ MWR-D-12-00254.1.

Lawrence, M. B., L. A. Avila, J. L. Beven, J. L. Franklin, J. L. Guiney, and R. J. Pasch, 2001: Atlantic hurricane season of 1999. Mon. Wea. Rev., 129 (12), 3057–3084, doi: 10.1175/1520-0493(2001)129<3057:AHSO>2.0.CO;2.

Lee, C.-S., K. K. Cheung, W.-T. Fang, and R. L. Elsberry, 2010: Initial maintenance of tropical cyclone size in the western North Paciﬁc. Mon. Wea. Rev., 138 (8), 3207–3223.

Lin, Y., M. Zhao, and M. Zhang, 2015: Tropical cyclone rainfall area controlled by relative sea surface temperature. Nature Communications, 6.

Liu, K. S., and J. C. L. Chan, 1999: Size of tropical cyclones as inferred from ERS-1 and ERS- 2 data. Mon. Wea. Rev., 127 (12), 2992–3001, doi:10.1175/1520-0493(1999)127<2992: SOTCAI>2.0.CO;2.

Liu, K. S., and J. C. L. Chan, 2002: Synoptic ﬂow patterns associated with small and large tropical cyclones over the western North Paciﬁc. Mon. Wea. Rev., 130 (8), 2134–2142, doi:10.1175/ 1520-0493(2002)130<2134:SFPAWS>2.0.CO;2.

Liu, Q., T. Marchok, H.-L. Pan, M. Bender, and S. Lord, 2000: Improvements in hurricane initialization and forecasting at NCEP with global and regional (GFDL) models. US Department of Commerce, National Oceanic and Atmospheric Administration, National Weather Ser- vice, Ofﬁce of Meteorology, Science Division.

Love, G., and K. Murphy, 1985: The operational analysis of tropical cyclone wind ﬁelds in the Australian northern region. Northern Territory Region Research Papers 1984, 85, 44–51.

Manning, D. M., and R. E. Hart, 2007: Evolution of North Atlantic ERA40 tropical cyclone representation. Geophys. Res. Lett., 34 (5).

Merrill, R. T., 1984: A comparison of large and small tropical cyclones. Mon. Wea. Rev., 112 (7), 1408–1418, doi:10.1175/1520-0493(1984)112<1408:ACOLAS>2.0.CO;2.

103 Misra, V., S. DiNapoli, and M. Powell, 2013: The track integrated kinetic energy of Atlantic tropical cyclones. Mon. Wea. Rev., 141 (7), 2383–2389.

Musgrave, K. D., R. K. Taft, J. L. Vigh, B. D. McNoldy, and W. H. Schubert, 2012: Time evolution of the intensity and size of tropical cyclones. Journal of Advances in Modeling Earth Systems, 4 (3).

NHC, 2015: Introduction to storm surge. National Hurricane Center/Storm Surge Unit, 5 pp. [Available online at http://www.nhc.noaa.gov/surge/surge_intro.pdf].

NHC, cited 2017a: Glossary of NHC Terms. [Available online at http://www.nhc.noaa.gov/ aboutgloss.shtml].

NHC, cited 2017b: NHC Tropical Cyclone Advisory Archive. [Available online at http://www. nhc.noaa.gov/archive/].

NOAA, 2010: The GOES-14 science test: Imager and sounder radiance and product validations. NOAA Tech. Rep. NESDIS131, NOAA, Washington, D.C., 120 pp.

Olander, T. L., and C. S. Velden, 2007: The advanced Dvorak technique: Continued development of an objective scheme to estimate tropical cyclone intensity using geostationary infrared satellite imagery. Wea. Forecasting, 22 (2), 287–298.

Pasch, R. J., and L. A. Avila, 1999: Atlantic hurricane season of 1996. Mon. Wea. Rev., 127 (5), 581–610, doi:10.1175/1520-0493(1999)127<0581:AHSO>2.0.CO;2.

Pennington, J., M. DeMaria, and K. Williams, 2000: Development of a 10-year Atlantic basin tropical cyclone wind structure climatology. Dataset available at: http://www. bios. edu/rpi/private/pubs/2000pre/demaria/demaria. html.

Powell, M. D., and T. A. Reinhold, 2007: Tropical cyclone destructive potential by integrated kinetic energy. Bull. Amer. Meteor. Soc., 88 (4), 513–526.

Rienecker, M. M., and Coauthors, 2011: MERRA: NASA’s modern-era retrospective analysis for research and applications. J. Climate, 24 (14), 3624–3648.

Rotunno, R., and K. A. Emanuel, 1987: An air–sea interaction theory for tropical cyclones. Part II: Evolutionary study using a nonhydrostatic axisymmetric numerical model. J. Atmos. Sci., 44 (3), 542–561.

Safﬁr, H. S., and R. H. Simpson, 1971: A proposed scale for ranking hurricanes by intensity. Minutes of the eight NOAA, NWS Hurricane Conference, Miami, Florida.

104 Saha, S., and Coauthors, 2010: NCEP Climate Forecast System Reanalysis (CFSR) 6-hourly Prod- ucts, January 1979 to December 2010. Research Data Archive at the National Center for Atmospheric Research, Computational and Information Systems Laboratory, Boulder, CO.

Sampson, C. R., and J. A. Knaff, 2015: A consensus forecast for tropical cyclone gale wind radii. Wea. Forecasting, 30 (5), 1397–1403, doi:10.1175/WAF-D-15-0009.1.

Schenkel, B. A., and R. E. Hart, 2012: An examination of tropical cyclone position, intensity, and intensity life cycle within atmospheric reanalysis datasets. J. Climate, 25 (10), 3453–3475.

Schloemer, R. W., 1954: Analysis and synthesis of hurricane wind patterns over Lake Okeechobee, Florida. Hydrometeorological Report, 31, 49.

Shen, W., 2006: Does the size of hurricane eye matter with its intensity? Geophys. Res. Lett., 33 (18).

Smith, R. K., C. W. Schmidt, and M. T. Montgomery, 2011: An investigation of rotational inﬂu- ences on tropical-cyclone size and intensity. Quart. J. Roy. Meteor. Soc., 137 (660), 1841– 1855.

Smith, T. M., and R. W. Reynolds, 2003: Extended reconstruction of global sea surface tempera- tures based on COADS data (1854–1997). J. Climate, 16 (10), 1495–1510.

Torn, R. D., and C. Snyder, 2012: Uncertainty of tropical cyclone best-track information. Wea. Forecasting, 27 (3), 715–729.

Velden, C., and Coauthors, 2006: The Dvorak tropical cyclone intensity estimation technique. Bull. Amer. Meteor. Soc., 87 (9), 1195–1210.

Velden, C. S., C. M. Hayden, W. Paul Menzel, J. L. Franklin, and J. S. Lynch, 1992: The impact of satellite-derived winds on numerical hurricane track forecasting. Wea. Forecasting, 7 (1), 107–118.

Velden, C. S., T. L. Olander, and R. M. Zehr, 1998: Development of an objective scheme to estimate tropical cyclone intensity from digital geostationary satellite infrared imagery. Wea. Forecasting, 13 (1), 172–186.

Weatherford, C. L., and W. M. Gray, 1988a: Typhoon structure as revealed by aircraft reconnaissance. II: Structural variability. Mon. Wea. Rev., 116 (5), 1044–1056.

Weatherford, C. L., and W. M. Gray, 1988b: Typhoon structure as revealed by aircraft reconnaissance. Part I: Data analysis and climatology. Mon. Wea. Rev., 116 (5), 1032–1043.

105 Willoughby, H. E., 1995: Mature structure and evolution. Global Perspectives on Tropical Cy- clones, 693, 21–62.

Willoughby, H. E., R. W. R. Darling, and M. E. Rahn, 2006: Parametric representation of the primary hurricane vortex. Part II: A new family of sectionally continuous proﬁles. Mon. Wea. Rev., 134 (4), 1102–1120.

Willoughby, H. E., and M. E. Rahn, 2004: Parametric representation of the primary hurricane vortex. Part I: Observations and evaluation of the Holland (1980) model. Mon. Wea. Rev., 132 (12), 3033–3048.

World Meteorological Organization, 1970: The Beaufort Scale of wind force. WMO Commission for Maritime Meteorology, Marine Sciences Affairs Report No. 3, WMO, 22 pp.

Wu, L., W. Tian, Q. Liu, J. Cao, and J. A. Knaff, 2015: Implications of the observed relationship between tropical cyclone size and intensity over the western North Paciﬁc. J. Climate, 28 (24), 9501–9506.

Xu, J., and Y. Wang, 2015: A statistical analysis on the dependence of tropical cyclone intensiﬁ- cation rate on the storm intensity and size in the North Atlantic. Wea. Forecasting, 30 (3), 692–701.

Yuan, J., D. Wang, Q. Wan, and C. Liu, 2007: A 28-year climatological analysis of size parameters for northwestern Paciﬁc tropical cyclones. Advances in Atmospheric Sciences, 24 (1), 24–34.

106 BIOGRAPHICAL SKETCH

I was raised in Columbiana, Ohio, about 30 minutes south of my birthplace of Youngstown. I discovered an interest in meteorology when I was eight years old; specifically, I was fascinated by the media coverage of Hurricane Bonnie in 1998 and wanted to learn more about atmospheric phenomena. Upon graduation from Crestview High School, I enrolled at Ohio University and declared a major in Meteorology with a Mathematics minor. Because I was enrolled in a smaller Atmospheric Sciences program, and because I could not afford my education out-of-pocket, I decided to join Air Force ROTC and pursue an active duty career as a Weather Officer. I commissioned as a Second Lieutenant upon graduation from Ohio University in 2013, and began my Air Force career at the 21st Operational Weather Squadron in Kaiserslautern, Germany. In 2014, my supervisor persuaded me to apply for the Air Force Institute of Technology to earn my Master of Science degree, as a M. S. degree was a requirement for promotion to the rank of Major at that time. I was accepted into the AFIT’s Civilian Institution Programs shortly after applying, and I received orders to pursue my Master of Science in Meteorology at Florida State University. After graduating from FSU, I will return back to my previous unit in Kaiserslautern, Germany, and will serve as both Flight Commander and Senior Duty Officer until May of 2019. Although I will not work extensively on tropical cyclones as a forecaster in Germany, I plan to continue research in the topic and hope to publish several pieces of work; one of these pieces is currently under review. My wife and I love to travel in our spare time. I am also a die-hard Pittsburgh professional sports fan and try to make every opportunity to attend sporting events when possible. Upon return- ing to Germany, I plan on spending most of my free time traveling throughout Europe, attending German soccer games, and skiing in the Austrian Alps.

107