THE PENNSYLVANIA STATE UNIVERSITY THE GRADUATE SCHOOL COLLEGE OF EARTH AND MINERAL SCIENCES

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1 THE PENNSYLVANIA STATE UNIVERSITY THE GRADUATE SHOOL OLLEGE OF EARTH AND MINERAL SIENES SENSITIVITY OF TROPIAL YLONE POTENTIAL INTENSITY TO OBSERVED NEAR-SURFAE ONDITIONS A Thesis in Meteorology by Alexander Michael Kowaleski 2013 Alexander Michael Kowaleski Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science August 2013

2 The thesis of Alexander Michael Kowaleski was reviewed and approved* by the following: Jenni L. Evans Professor of Meteorology Thesis Adviser Michael E. Mann Distinguished Professor of Meteorology Kenneth J. Davis Professor of Meteorology Johannes Verlinde Professor of Meteorology and Associate Head, Graduate Program in Meteorology *Signatures are on file in the Graduate School ii

3 ABSTRAT Observed tropical cyclone (T) thermodynamic variables including temperature, humidity, moist enthalpy, and specific entropy are obtained from buoy, -MAN, and dropsonde data from 42 Atlantic hurricanes. Ocean-air energy fluxes are calculated for 31 hurricanes in the dataset for which SST data are available. Profiles constructed with these data are compared to the theoretical boundary layer profiles of Emanuel Potential Intensity (EPI) theory. It is determined that the boundary layer is not isothermal as in the idealized EPI profile, but decreases in temperature with decreasing radius between the environment and T core. Also, in the composite T profile, entropy increases more rapidly inside 2.5 times the radius of maximum winds (R max ) than pressure decreases alone can account for. This indicates that ocean-air fluxes outside of R max can play a substantial role in T entropy input. It is also determined that the scheme used in calculating spray fluxes impacts the total ocean-air turbulent energy flux, and has an even greater impact on the distribution between latent and sensible energy fluxes. In the second section of the study, the effects of environmental conditions and conditions in the storm on potential intensity (PI) are studied. Lower temperature and moisture in the unsaturated boundary layer at R max increases PI as measured by maximum sustained winds (V max ). This occurs because lower temperature and moisture at R max allow greater entropy input into the T at R max due to greater ocean-air temperature and moisture disequilibria. The PI increases from using observationally-derived profiles can be as great as 10 ms -1. This suggests that conditions within the T are of comparable importance to environmental conditions in determining PI. It also suggests that V max may be higher than EPI theory currently predicts using its idealized boundary layer profiles. A further observation is that sufficiently dense observations of T near-surface conditions may allow more accurate real-time PI calculations. iii

4 TABLE OF ONTENTS List of Figures..v List of Tables.vii List of Symbols.viii Acknowledgments x hapter 1: Introduction and motivation.1 hapter 2: Methodology of observations hapter 3: Profiles of near-surface thermodynamic scalars..27 A: Temperature..27 B: Moisture...32 : Enthalpy...38 D: Equivalent potential temperature and specific entropy.42 hapter 4: Ocean-air flux profiles...49 A: Interfacial fluxes...49 B: Spray fluxes..51 : Bowen Ratios 57 hapter 5: Methodology of FORTRAN EPI calculations.61 hapter 6: EPI test results...69 A: Sensitivity tests 69 B: EPI tests using observed conditions 75 hapter 7: Summary and onclusions...92 Appendix A: Tables of thermodynamic scalars with radius and R max...98 Appendix B: Tables of ocean-air fluxes with radius and R max 100 Appendix : Results of EPI tests for each storm.101 Appendix D: Emanuel FORTRAN subroutine for calculating PI Appendix E: Dunion (2011) mean moist tropical sounding 113 References 114 iv

5 LIST OF FIGURES Figure 1.1: arnot ycle of Emanuel Potential Intensity Theory..3 Figure 2.1: Hurricanes observed in this study compared to climatological Atlantic hurricanes ( ) 16 Figure 2.2: Tracks of storms used in this study. White circles indicate each storm s location when data were obtained 17 Figure 2.3: Tracks of storms used in this study. White circles indicate each storm s location when data were obtained 17 Figure 3.1: Near surface air temperature (T a ) with radius.27 Figure 3.2: Near surface air temperature with R max for Frances (2004), Jeanne (2005), Earl (2010), and Irene (2011) 30 Figure 3.3: Sea-Air contrast (SA) with radius and R max...32 Figure 3.4: Specific humidity (q) with radius and R max.33 Figure 3.5: Specific humidity with R max for Ophelia (2005), Jeanne (2004), and Rita (2005)...35 Figure 3.6: Relative humidity (RH) with radius and R max...36 Figure 3.7: Pressure, temperature, specific humidity and relative humidity with radius and R max 38 Figure 3.8: Sensible energy (h SEN ) with radius and R max...40 Figure 3.9: Latent energy (h LAT ) with radius and R max.41 Figure 3.10: Moist enthalpy (h) with radius and R max...42 Figure 3.11: Equivalent potential temperature (θ e ) with radius and R max..44 Figure 3.12: Specific entropy (s) with radius and R max.46 Figure 3.13: Specific entropy with R max for Irene (1999), Jeanne (2004), Rita (2005), and Earl (2010) Figure 4.1: Wind speed with radius and R max 50 Figure 4.2: Ocean-air interfacial sensible and latent energy fluxes with radius and R max.51 Figure 4.3: Ocean-air sensible and latent spray energy flux with R max using the Fairall, Andreas, and combined spray flux schemes.52 v

6 LIST OF FIGURES (ONTINUED) Figure 4.4: Total sensible and latent ocean-air turbulent energy flux with R max using the Fairall, Andreas, and combined spray flux schemes..54 Figure 4.5: Total ocean-air turbulent energy flux with R max. 56 Figure 4.6: Specific entropy with R max for all storms and for storms for which flux data are available 57 Figure 4.7: Ocean-air interfacial Bowen Ratio with R max compared to the Bowen Ratios using the Fairall, Andreas, and combined spray flux schemes.58 Figure 5.1: Schematic used for calculating APE values in EPI FORTRAN subroutine 62 Figure 5.2: EPI FORTRAN subroutine flowchart.63 Figure 6.1: PI as a function of SST using the Dunion (2011) sounding with 80% boundary layer relative humidity 70 Figure 6.2: Forms of cyclostrophic balance inside R max...74 Figure 6.3: Environmental APE values from the temperature-modified Dunion (2011) sounding, the constant Dunion sounding, and 100 observations around Atlantic hurricanes...76 Figure 6.4: Water vapor mixing ratio with R max 82 Figure 6.5: Specific entropy with R max for Gordon (2000), Frances (2004), Rita (2005), and Earl (2010)...88 vi

7 LIST OF TABLES Table 1.1: Terms used in EPI V max calculation and their descriptions 4 Table 1.2: APEs used in the FORTRAN EPI calculation and their descriptions.6 Table 2.1: Hurricanes observed in this study.14 Table 2.2: Thermodynamic variables used in this study and their formulas.18 Table 2.3: Symbols used in energy flux calculations and their formulas..20 Table 2.4: Flux calculation schemes used in this study.26 Table 5.1: Symbols used in EPI FORTRAN subroutine and their meanings 64 Table 5.2: Description of Potential Intensity tests.67 Table 6.1: EPI FORTRAN routine V max and P min sensitivity to environmental and storm conditions..74 Table 6.2: Results of Tests Table 6.3: Potential Bowen Ratios at R max for modeled composite Ts compared to Bowen Ratio values form interfacial fluxes and each of the three flux schemes 90 Table A.1: Averaged thermodynamic variables with radius.98 Table A.2: Averaged thermodynamic variables with R max 99 Table B.1: Fluxes and Bowen Ratios with radius 100 Table B.2: Fluxes and Bowen Ratios with R max..100 Table.1: Results of Modified Dunion Test (Test 1).101 Table.2: Results of the onstant Dunion Test (Test 2) 102 Table.3: Results of the Observed Sounding Test (Test 3) 103 Table.4: Results of the R max Temperature Test (Test 4)..104 Table.5: Results of the onstant Moisture Test (Test 5)..105 Table.6: Results of the Extended Temperature Test (Test 6) Table E.1: The Dunion (2011) moist tropical sounding..113 vii

8 LIST OF SYMBOLS R max : Radius of maximum winds k : oefficient of ocean-air enthalpy transfer d : Drag coefficient V max : Maximum 1-minute 10-meter sustained winds P min : Minimum central pressure V max(gradient): Maximum gradient wind γ: Reduction factor from gradient wind to V max T: Temperature SST: Sea surface temperature T s : Surface temperature T o : Outflow temperature s: Specific entropy s*: Specific entropy of a saturated air parcel T a : Near-surface air temperature. SA: Sea-air contrast (SST-T a ) e a : Vapor pressure. e s : Saturation vapor pressure r: Mixing ratio q: Specific humidity RH: Relative humidity T LL : Temperature at lifting condensation level θ: Potential temperature θ e : Equivalent potential temperature h SEN : Sensible energy h LAT : Latent energy h: Total moist enthalpy V 1min : Measured sustained wind adjusted to 1-minute sustained wind t: Time interval of measured sustained wind speed V t : Measured sustained wind speed over time interval t G 1min : Factor to adjust measured sustained wind to 1-minute sustained wind A: Altitude of measured sustained wind V A : Measured sustained wind at altitude A ρ: Density of air L v : Latent energy of vaporization V 10 : 1-minute 10-meter sustained wind speed q SST : Saturation specific humidity at T=SST H: Enthalpy transfer coefficient E: Moisture transfer coefficient viii

9 LIST OF SYMBOLS (ONTINUED) h s : Sensible energy flux from interfacial processes h l : Latent energy flux from interfacial processes Q SF : Sensible energy spray flux Q LF : Latent energy spray flux q SAT : Saturation specific humidity β(t a ): orrection term that accounts for sea spray originating at its evaporation temperature γ 10 : Adjustment factor from 10-meter sustained wind to sustained wind at significant wave height α: Fraction of sea spray that ascends above near-surface layer ρ w : Density of seawater ρ c : Specific heat capacity of seawater T eq : Equilibrium temperature of evaporating spray droplet u*: Friction velocity H s : Total sensible energy flux (interfacial + spray) H l : Total latent energy flux (interfacial + spray) APE: onvective Available Potential Energy APE A : Environmental APE APE M : Unsaturated APE at R max APE MS : Saturated APE at R max P Rmax : Sea-level pressure at R max P A : Environmental sea-level pressure TVAV: Boundary layer average virtual temperature B: onstant that determines azimuthal wind speed decay profile inside R max ix

10 AKNOWLEDGMENTS The author would like to thank Dr. Jenni Evans for her inspiration for this study, as well as her continuous assistance and encouragement on the project. He would also like to thank Dr. Michael Mann and Dr. Ken Davis, the other members of his committee, for their helpful assistance and critique. In a broader sense, he would like to thank Pennsylvania State University and the Department of Meteorology for allowing a young man to fulfill a 7-year-old boy s dream of growing up to study hurricanes. Onward! x

11 1. Introduction and motivation Understanding tropical cyclone (T) intensity and the factors that govern it remain major challenges for forecasting these intense and dangerous storms. While T track forecast errors have decreased markedly in the last twenty-five years, intensity forecast errors have decreased little if at all during this period (National Hurricane enter 2013). A better understanding of the factors that govern T intensity has the potential to contribute toward improving T intensity forecasts. Furthermore, knowledge of the maximum intensity that a T can achieve is important for the development of local building codes and emergency preparations in a particular area, as it provides a worst-case scenario for which to prepare. Kerry Emanuel s Potential Intensity (EPI) Theory (Emanuel 1986, 1988, 1991, 1995; Emanuel et al. 2004) has become the baseline from which to compare previous and contemporary potential intensity (PI) theories of maximum intensity (Miller 1958; Malkus and Riehl 1960; Holland 1997; Frisius and Schonemann 2012). Some of aspects of these theories were created or tested using observed conditions in and around the T. Holland (1997) used observed soundings as input in PI calculations, and Frisius and Schonemann (2012) adjusted EPI theory using their observation of positive slantwise convective available potential energy (APE) just outside the T eyewall. Results from EPI theory have also been compared to more sophisticated models that predict maximum T intensity (Persing and Montgomery 2003; Bell and Montgomery 2008; Bryan and Rotunno 2009; Wang and Xu 2010) and in situ hurricane intensity observations (DeMaria and Kaplan 1994; Montgomery et al. 2006). This study contributes by adjusting EPI theory with observed near-surface conditions. This is done to determine how EPI changes when observed near-surface conditions replace the idealized 1

12 conditions of EPI theory. The purpose of this study is to examine EPI sensitivity to differences between theoretical and observed thermodynamic conditions in the T and environmental nearsurface boundary layer. EPI variations among individual storms due to differences in nearsurface conditions in the T and its environment will also be explored. Emanuel (1986) developed a theoretical model of a T as a arnot heat engine (Figure 1.1). In this model PI is a function of SST, outflow temperature, environmental sea-level pressure, and environmental temperature and moisture. The T imports air from the environment and brings it to the radius of maximum winds (R max ) without ocean-air entropy input outside R max (leg A-B). R max in EPI theory is defined as the eyewall outer edge. Just inside R max, the air is brought to saturation through ocean-air entropy fluxes. The air is then lifted adiabatically and exported at the much colder tropopause (leg B-). Next, the air descends isothermally with radiational cooling cancelling adiabatic warming (leg -D). Finally, the air warms through adiabatic descent to the environmental boundary layer (leg D-A). This cycle of entropy import and export does work to maintain the storm s winds against frictional dissipation. EPI theory breaks from previous theories of T PI (Miller 1958; Ooyama 1964; harney and Eliassen 1964) by postulating that all energy that maintains a T s winds arises from oceanair latent and sensible energy fluxes. In EPI theory, PI is not dependent on pre-existing environmental convective available potential energy (APE). In fact, according to the EPI FORTRAN subroutine (hapter 5), larger values of environmental APE correspond with lower PI if the larger APE results from a warmer and/or moister environmental boundary layer. This is because a warmer, moister parcel from the environment does not gain as much entropy through ocean-air fluxes near R max when it is brought to saturation. 2

13 Figure 1.1 arnot cycle of Emanuel Potential Intensity Theory (Emanuel 2006B). R max, the radius of maximum winds, occurs at the outer edge of the eyewall (~20 km in this diagram). Emanuel (1995) revised the Emanuel (1986) theory by incorporating improved eye dynamics. Whereas Emanuel (1986) assumed that radial inflow continues to the center of the storm and that the eye (like the eyewall) is neutral to slantwise convection, Emanuel (1995) hypothesized that the azimuthal wind velocity in the eye is in cyclostrophic balance and that the ratio between the coefficient of the transfer of enthalpy ( ) and the drag coefficient ( ) greatly affects PI. As the ratio of increases, more energy is available for powering the storm s winds relative to boundary layer frictional drag. Bister and Emanuel (1998) demonstrated that the heating effect of boundary layer friction at and near the eyewall increases PI. Although friction limits maximum T intensity, including the dissipative heating caused by friction increases the boundary layer kinetic energy density by 3

14 roughly 50%. This results in a 20-25% maximum sustained wind increase in both EPI theory and a simple numerical model. The Emanuel (1995) theory, when combined with dissipative heating, is used to calculate PI in terms of the maximum 1-minute, 10-meter sustained wind (Eq. 1; Table 1.1 ). Symbol Unit Description V max ms -1 Maximum 1-minute, 10-meter sustained wind Unitless Factor to reduce gradient wind to 1-minute, 10-meter sustained wind. It is set to 0.8 for EPI calculations in this study k Unitless Ocean-air enthalpy transfer coefficient d Unitless Ocean-air drag coefficient s* Unitless. hange is measured in Jkg -1 Saturated entropy at R max s Unitless. hange is measured in Jkg -1 Entropy of an unsaturated parcel brought from the environment to R max. It has the pressure of R max and the relative humidity as the environment. T s Kelvin Entropy input temperature. Set to SST T o Kelvin Outflow temperature at or near the tropopause Table 1.1: Terms used in EPI V max calculation and their descriptions. ( ) ( ) Using this equation, knowledge of SST, outflow temperature, environmental boundary layer temperature, and environmental boundary layer moisture suffice to calculate PI in terms of V max. This equation must be solved iteratively with an equation for R max surface pressure, as s and s* in Eq. 1 depend on pressure at R max. EPI s theoretical T boundary layer profile makes two important idealizations examined in this study. First, it assumes that the boundary layer is radially isothermal; the near-surface temperature throughout the storm is equal to environmental near-surface temperature, despite adiabatic cooling from decreasing pressure between the environment and R max. Therefore, 4

15 environmental temperature determines R max temperature. Second, EPI theory assumes that relative humidity is constant at the environmental value outside R max. Although substantial ocean-air moisture fluxes occur outside R max, EPI theory assumes that these fluxes are balanced by dry air entrainment at the top of the boundary layer. Therefore relative humidity does not increase with decreasing radius outside R max. Inside R max, ocean-air fluxes overwhelm turbulent entrainment and relative humidity increases rapidly. Relative humidity is constant inside the storm s eye. Specific humidity increases slightly with decreasing radius outside R max due to falling pressure, but only increases rapidly inside R max, where fluxes input moisture into the boundary layer. This means that specific entropy is constant outside R max except for small increases from falling pressure. A FORTRAN subroutine that calculates PI using EPI theory is available from Dr. Kerry Emanuel s web site (Massachusetts Institute of Technology; Dr. Kerry Emanuel 2012; Emanuel 1986, 1994, 1995, 1997). This subroutine calculates PI as a function of SST, environmental sealevel pressure, and a single environmental sounding. The subroutine is more fully explained in hapter 5, and the full annotated code is provided in Appendix D. An environmental sounding is used in the FORTRAN EPI calculation because specific entropy change multiplied by temperature can be written as APE change. Temperature times the specific entropy that a parcel gains from ocean-air fluxes inside R max equals the difference between APE of a saturated parcel at R max (hereafter APE MS ) and APE of a parcel of air brought to R max without any input of sensible energy or moisture (hereafter APE M ). (Emanuel 1994, 1997) (Eq. 2; Table 1.2; Figure 5.1). 5

16 Type of APE Shorthand name Description APE A Environmental APE APE of a sounding taken in the tropical cyclone s environment APE M Unsaturated R max APE APE of a parcel brought to R max without input of energy or moisture. The parcel has the same temperature as the environment and a higher mixing ratio because of the lower pressure at R max. Therefore, APE M is greater than APE A. APE MS Saturated R max APE APE of a parcel brought to saturation and T=SST at R max. Table 1.2: APEs used in FORTRAN EPI calculation and their descriptions. ( ) ( ) The equation for maximum gradient wind speed can be written as (Eq. 3), where APE MS -APE M must be calculated iteratively through an equation for pressure at R max (hapter 5). ( ) ( ) ( ) PI in EPI theory depends on the entropy that a parcel gains at R max. EPI theory s idealizations of a radially isothermal boundary layer and radially-constant relative humidity outside R max affect maximum entropy input near R max and the maximum intensity that a T can achieve. If actual near-surface conditions in a T differ substantially from the idealizations of EPI theory, the storm could have a significantly different PI. For example, lower temperatures 6

17 and less moisture at R max before the parcel is brought to saturation would mean greater ocean-air entropy disequilibrium than if greater temperature and unsaturated moisture were found at R max. This would increase maximum sensible and latent energy fluxes, causing greater maximum entropy input at R max (APE MS -APE M ) and a higher PI as measured by V max. ione et al. (2000) studied observations from buoys and -MAN stations over which hurricanes passed to construct an observationally-derived composite profile of near-surface temperature, moisture, and ocean-air fluxes. Using time series of hurricanes over SST 27, ione et al. (2000) found that near-surface air temperature decreases substantially with decreasing radius outside of 140 km from the T center. (That study did not use R max measurements). Inside this radius air temperature is almost radially constant. ione et al. (2000) also showed that relative humidity and specific humidity both increase with decreasing radius as far as 200 km from the T center. This is far beyond the R max of most Ts. These data suggest that the radial thermodynamic structures of at least some observed Ts differ from the idealized profiles of EPI theory. Though EPI theory continues to be the widest-used PI theory, Holland (1997) created a separate, thermodynamically-based method to calculate PI in terms of minimum central pressure. Holland s theory uses the observation that pressure decreases and moisture increases as inflow air approaches the eyewall. This means that equivalent potential temperature (θ e ) rises as air approaches the eyewall. At the eyewall, where air ascends on a moist adiabat, this greater θ e leads to lower surface pressures under the eyewall through hydrostatic balance. Therefore, Holland s PI theory ignores non-hydrostatic effects on eyewall pressure, a potentially significant factor given the strong convection found in the eyewall. 7

18 Like EPI theory, Holland s method of calculating PI uses an environmental sounding, an environmental surface pressure, and SST as input. An environmental air parcel is brought to the eyewall, where it gains θ e from decreasing surface pressure and ocean-air fluxes. At the eyewall, the parcel is raised along its new θ e moist adiabat. This allows calculation of a new hydrostatically-determined surface pressure, which creates a new θ e value at the eyewall. This process is iterated until pressure calculations converge. If the pressure deficit is found to be greater than 20 hpa, Holland PI theory assumes that the storm has developed an eye with constant θ e. This implicitly accounts for subsidence warming within the eye, and it allows warming to contribute to a final calculation of minimum pressure. In hapter 6 the sensitivities of Holland s PI theory to environmental and storm conditions are compared to PI as calculated by the EPI FORTRAN routine. Research by Michael Montgomery and others have challenged certain thermodynamic aspects of EPI theory. Persing and Montgomery (2003) contended that ocean-air fluxes and atmospheric subsidence in the eye provide an energy source to the T for which EPI theory does not account. Persing and Montgomery (2003) used a tropical cyclone numerical model to study how intensity changed when ocean-air fluxes under the eyewall were turned off. They found that turning off fluxes under the eye substantially lowered a simulated T s maximum intensity. They concluded that fluxes under the eye cause a significant entropy buildup in the lower troposphere of the eye. This air is then advected into the eyewall, providing an additional entropy input into the T, allowing it to reach higher maximum intensities than EPI theory predicts. Studies of hurricane Isabel (2003) appear to bolster the case that entropy buildup within the eye plays a role in the maximum intensity a T can achieve. While crossing hurricane Fabian s relatively cool wake (on the order of hundreds of kilometers wide), Isabel maintained a 8

19 greater intensity than EPI theory predicted it could sustain. Montgomery et al. (2006) and Bell and Montgomery (2008) contended that Isabel maintained its super-pi intensity due to accumulation of high-entropy air in its eye. This air was advected into the eyewall at altitudes above 1 km, providing Isabel an additional source of energy. Bryan and Rotunno (2009) dissented from the hypothesis that high-entropy air in the lower-troposphere of the eye contributes significantly to T intensity. Using a more sophisticated model than Persing and Montgomery (2003), Bryan and Rotunno (2009) ran simulations of tropical cyclones with and without ocean-air entropy fluxes under the eye. Model results showed that buildup of low-level entropy in the eye contributes about 3% of the total entropy input into a tropical cyclone. In the Bryan and Rotunno (2009) model, removing highentropy air in the eye decreased maximum tangential winds by 4%, far less than the results of Montgomery s studies. Bryan and Rotunno (2009) agreed with Montgomery that ocean-air fluxes and atmospheric subsidence do increase entropy in the lower-troposphere eye and contribute to the total energy available to a T. However, they contended that eye entropy buildup affects intensity much less than Montgomery s studies had shown. Therefore, the questions of how much eye entropy affects T intensity and the extent to which a T can achieve super-pi intensities remain unsettled. It appears likely that the eye can provide an additional energy source to the T beyond the ocean-air fluxes of EPI theory. However, this source is unlikely to be large in magnitude compared to the ocean-air fluxes that occur outside the eye. Fluxes under the eye are relatively small due to the eye s weak winds, and as previous studies have noted, the eye has small surface area and volume compared to the rest of the T (Bryan and Rotunno 2009; Wang and Xu 2010; 9

20 Frisius and Schonemann 2012). While the eye likely plays a role in the T energy budget, it is unlikely that eye processes are solely responsible for super-pi intensities. Other recent studies have focused on how thermodynamic conditions outside the eyewall can affect PI, arguing that conditions and processes beyond R max have important effects on maximum T intensity. Tang and Emanuel (2010) found that vertical wind shear can ventilate a T s mid-levels, causing low-entropy downdrafts outside the eyewall. These downdrafts lower boundary layer entropy. If ocean-air fluxes do not restore boundary layer entropy before air ascends in the eyewall, the tropical cyclone may weaken. Although this effect is not a deviation from EPI theory, as EPI theory assumes no deleterious vertical wind shear, Tang and Emanuel (2010) shows that processes outside R max can play an important role in the intensity a particular T can achieve. Frisius and Schonemann (2012) contended that positive slantwise APE often exists just outside R max in both observations and numerical hurricane simulations. This contradicts EPI s assumption of slantwise convective neutrality throughout the T. This slantwise APE sharpens the eyewall radial entropy gradient, increasing maximum tangential wind speed. Frisius and Schonemann (2012) concluded that this slantwise APE plays a major role in Ts reaching intensities above those predicted by PI. They created an expanded calculation of PI that takes into account deviations from moist slantwise neutrality. Frisius and Schonemann (2012) also noted that their findings did not contradict the results of Persing and Montgomery (2004), which used a numerical model to demonstrate that environmental APE (independent of surface temperature and outflow temperature) had no effect on maximum T intensity. The APE invoked by Frisius and Schoenmann (2012) is found just outside R max, not in the T environment. 10

21 Wang and Xu (2010) showed that ocean-air fluxes outside R max can contribute to maximum T intensity. Using a numerical model, Wang and Xu found that boundary layer equivalent potential temperature under the eyewall decreased by K when ocean-air fluxes were turned off beyond 45 km from the T center. This resulted in a weaker storm; maximum sustained winds decreased by 8.8 ms -1 and minimum pressure rose by 26 hpa. Wang and Xu (2010) concluded that entropy input from ocean-air fluxes out to R max are necessary for a storm to maintain its winds against frictional dissipation, though they noted that this radius could vary among individual storms. They also noted that ocean-air latent and sensible energy input can occur beyond R max in their model simulations, but that that these fluxes cause the T inner core to increase in size without substantial intensity effects. This may happen because only fluxes inside R max affect conditions in the eyewall, whereas fluxes beyond this distance cause more convection outside the eyewall. Intensities given by EPI theory have also been compared to observed tropical cyclone intensities. Evans (1993) found that for most Ts SST is not the primary factor in determining T intensity as measured by V max, although the maximum observed V max as a function of SST increases for SST values greater than 27. DeMaria and Kaplan (1994) studied maximum observed V max of Atlantic storms as a function of SST and found that it increased substantially between 26 and 29, and increased less rapidly at SSTs above 29. They attributed the weaker V max increase with SST above 29 to the fact that the upper-troposphere temperature (T o in EPI Theory; Eq. 1) increases rapidly with increasing SST between 26 and 29, but increases less rapidly above 29. Despite challenges, EPI theory is still used in both operational forecasts and climatological studies. EPI values are used in the Statistical Hurricane Intensity Prediction 11

22 Scheme (SHIPS) model. The difference between a T s intensity and its PI is one of the inputs in the SHIPS model. However, the EPI values used in the SHIPS model are only based on SST, not environmental conditions (DeMaria et al., 2005). EPI changes due increasing greenhouse gas emissions have been analyzed as part of studies on the effects of climate change on tropical cyclone frequency and intensity (amargo et al, 2007; Vecchi and Soden, 2007; Tippet et al. 2011). EPI also serves as input in the oupled Hurricane Intensity Prediction System (HIPS) model, a two-dimensional downscaling model used to study the effects of climate change on tropical cyclones (Emanuel 2006A). PI as predicted by Emanuel Potential Intensity Theory remains a relevant predictor of maximum achievable tropical cyclone intensity from purely thermodynamic constraints. In this study, the EPI idealized boundary layer will be compared to observed nearsurface thermodynamic profiles developed from surface and dropsonde observations. After these observed thermodynamic profiles are obtained, aspects of these profiles will be used to calculate PI using observed near-surface temperature and moisture profiles. This will give a better understanding of how adjustments in the near-surface profile between theoretical and observed values affect PI. It will also show how the magnitude of intensity changes from variations of conditions inside the storm compare with the magnitude of PI changes from variations in environmental conditions. These new PI values could then contribute toward more accurate values of maximum achievable intensity in statistical hurricane intensity forecasts. They could also be used to improve understanding climatological PI patterns, giving more accurate predictions of the maximum intensity that Ts can achieve in specific regions of the globe under the current climate and future climates. 12

23 2. Methodology of observations Near-surface data are obtained from 33 Atlantic hurricanes that passed near a buoy or - MAN station and from 9 Atlantic hurricanes observed by reconnaissance aircraft dropsondes (Table 2.1). Buoy and -MAN data are obtained from the National Data Buoy enter (National Data Buoy enter 2012). Dropsonde data are obtained from the NOAA and Air Force Reconnaissance data archive available at the private web site Tropical Atlantic (Tropical Atlantic 2012). Wind and pressure data are obtained from the Best Track analysis available from the private web site Unisys Weather (Unisys Weather Hurricane/Tropical Data 2012). R max data are obtained from the Atlantic Tropical yclone Extended Best-Track Dataset (olorado State Regional and Mesoscale Meteorology Branch 2012). For buoy and -MAN observations, the T intensity recorded is the Best-Track T intensity closest to the time of lowest recorded pressure by the observing station. For dropsonde observations, T intensity is the Best-Track intensity at the middle of the observation period. Storm Buoy/Platform/Sonde Wind Pressure R max (kt) (hpa) (km) Georges* (1998) B Irene* (1999) Gordon* (2000) B Lili* (2002) B laudette* (2003) B Isabel (2003) A S Isabel* (2003) B B Alex* (2004) A B Alex* (2004) B B Frances (2004) A S Frances (2004) B Ivan (2004) A S Ivan* (2004) B B Ivan* (2004) B Jeanne (2004) A S

24 Storm Buoy/Platform/Sonde Wind Pressure R max (kt) (hpa) (km) Jeanne (2004) B Dennis* (2005) B Emily* (2005) B Katrina* (2005) A B Katrina(2005) B S Katrina* (2005) B Ophelia* (2005) A B Ophelia*(2005) B B Rita* (2005) B Wilma (2005) S Dean (2007) S Humberto* (2007) B Dolly* (2008) B Gustav* (2008) B Ike* (2008) B Kyle* (2008) B Bill* (2009) B Ida* (2009) B Earl (2010) A S Earl* (2010) B B Earl* (2010) B Igor* (2010) B Irene (2011) A S Irene* (2011) B B Irene* (2011) B Katia* (2011) B Ophelia* (2011) B Table 2.1: Hurricanes observed in this study. Wind speed and pressure are obtained from the Best Track Analysis. R max values are obtained from the Extended Best Track. Asterisks indicate cases for which SST data were available for calculating fluxes, a total of 31 cases and 1504 observations. A total of 1976 observations are obtained. Data from surface observations are obtained from 24 hours before the lowest pressure recorded by the station to 24 hours after the lowest pressure recorded. For slow-moving and/or exceptionally large storms, additional station data are obtained to give a more complete radial profile. In certain cases, data are excluded if they were recorded after a storm made landfall. For dropsonde storms, data are obtained from 14

25 multiple missions over a 12 to 48 hour period. Dropsonde data are obtained from the lowest level in which quality data are available. For almost all observations this is just above the surface (listed in the sonde data as surface), but a small number of observations (~5) are taken at 10 to 20 meters in altitude due to contaminated surface data. ertain hurricanes provide multiple observation datasets. These hurricanes passed near multiple observing stations or were observed by surface stations and aircraft at different times in their lifecycles. The hurricanes observed in this study include all Saffir-Simpson categories and vary in central pressure from 996 hpa to 902 hpa. The dataset is somewhat biased toward high-intensity hurricanes (Figure 2.1). This study has a greater fraction of category 4 and 5 hurricanes and a smaller fraction of category 1 hurricanes than are observed climatologically in the Atlantic basin. This dataset is also biased toward hurricanes relatively close to land, as this is where the largest concentration of aircraft and surface observations occurs (Figure 2.2,Figure 2.3). 15

26 Figure 2.1: Hurricanes observed in this study compared to climatological Atlantic hurricanes ( ). This study has a larger percentage of intense hurricanes and a smaller percentage of weak hurricanes than climatology. 16

27 Figure 2.2: Tracks of storms observed in this study. White circles indicate each storm's location when data were obtained. Figure 2.3: Tracks of storms observed in this study. White circles indicate storm position when data were obtained. 17

28 For each observation, air pressure, air temperature (T a ) and dew point temperature are obtained. From temperature, pressure, and dew point, mixing ratio (r), specific humidity (q), relative humidity (RH), equivalent potential temperature (θ e ), sensible energy (h Sen ), latent energy (h Lat ), moist enthalpy (h), and specific entropy (s) are calculated (Table 2.2). When available, SST and sustained wind speed are obtained. The T position at each observation time is determined. This is done by linearly interpolating vortex data messages and/or best-track positions to determine the T position at the time of each observation. Then, the distance between the T s interpolated position and the observation location is calculated. Variable Symbol Units Formula Source Vapor Pressure e a hpa [ ] Bolton 1980 Saturation Vapor e s hpa Bolton 1980 Pressure [ ] Mixing Ratio r Wallace and Hobbes 2006 Specific Humidity q Wallace and Hobbes 2006 Relative Humidity RH Percent ( ) Wallace and Hobbes 2006 LL Temperature T LL Kelvin ione et al. ( ) ( ) 2000 Equivalent Potential θ e Kelvin ( )( ) ione et al. Temperature [ ] 2000 Sensible energy h Sen kjkg -1 ( ) Massen 2010 Latent energy h Lat kjkg -1 ( ) Massen 2010 Moist Enthalpy h kjkg -1 Massen 2010 Specific Entropy s No defined unit Specific entropy changes have units of Jkg -1 ( ) Emanuel 1997 Table 2.2: Thermodynamic variables used in this study and their formulas. After all thermodynamic variables are calculated, data are divided into bins by distance between the observation and the T center. They are also divided into bins by number of R max between the observation and the T center. The number of radii of maximum winds (number of R max ) from the T center is defined as the distance from the T center divided by the T s R max 18

29 distance. Distances of 1 R max in this study range from 18 km to 166 km. R max space is used because EPI theory designates R max as the radius at which ocean-air fluxes begin to input entropy into the T. The use of R max space facilitates comparisons among storms with varying R max values. The tables of binned thermodynamic data with radius and R max are provided Appendix A. In hapter 3 these data are plotted and compared with the data from ione, which used a different dataset of storms. They are also compared to the idealized profiles of EPI Theory. To study the effect of adiabatic cooling from decreasing pressure on near-surface temperature, the dataset is divided into storms with P min 960 hpa and storms with P min < 960 hpa. This division is chosen because 960 hpa is near the average pressure cutoff between category 2 and category 3 hurricanes, and because a large number of storms in the dataset have pressures equal to or higher than 960 hpa (17) and lower than 960 hpa (25). Ocean-air fluxes are calculated for the 31 of 42 events in which SST and wind speed data are available. Of the 1976 observations used in the study, 1504 have SST and wind speed data. This allows calculation of ocean-air sensible and latent energy fluxes from interfacial and spray processes. Tables of binned interfacial and spray flux data with radius and R max are provided in Appendix B. 19

30 Symbol Unit Meaning V 1min ms -1 1-minute sustained wind speed V τ ms -1 Maximum sustained wind over observing period G 1min Unitless Factor to adjust measured sustained wind to 1-minute sustained wind τ seconds Time period of measured sustained wind A meters Height of measured wind V A ms -1 Measured sustained wind at height A ρ kgm -3 Density of near-surface air L v Jkg -1 Latent energy of vaporization of near-surface air V 10 ms meter, 1-minute sustained wind speed q SST Saturation specific humidity at sea-surface temperature q Specific humidity of near-surface air H Unitless oefficient of thermal energy exchange E Unitless oefficient of moisture exchange Q SF (F) Wm -2 Sensible energy flux from sea-spray (Fairall scheme) Q LF (F) Wm -2 Latent energy flux from sea-spray (Fairall scheme) q sat Saturation specific humidity of near-surface air β(t a ) Unitless orrection term that accounts for sea-spray droplets cooling to their equilibrium temperature rather than air temperature Unitless Adjustment term to change 10-meter sustained winds to sustained winds at the significant wave height. h s Wm -2 Sensible energy flux from interfacial processes h l Wm -2 Latent energy flux from interfacial processes H s Wm -2 Total sensible energy flux from interfacial and spray processes H l Wm -2 Total latent energy flux from interfacial and spray processes Q SF (A) Wm -2 Sensible energy flux from sea spray (Andreas scheme) α Unitless Fraction of spray latent energy flux that evaporates in the near-surface layer ρ w kgm -3 Density of seawater c w Jkg -1 K -1 Specific heat capacity of seawater T eq Kelvin Temperature of evaporating droplet u * ms -1 Friction velocity d Unitless Drag coefficient (used in calculation of friction velocity) Table 2.3: Symbols used in energy flux calculations and their formulas To calculate fluxes, all wind speeds are normalized to 1-minute, 10-meter sustained winds. First, 8.5-minute buoy sustained wind speeds and 2-minute -MAN sustained wind speeds are normalized to 1-minute sustained wind speeds. This is done by using the empiricallyderived polynomial relationship from Powell et al. (1996) (Eqs. 4, 5). Powell s relationship gives 1-minute sustained wind speed as a function of measured sustained wind speed over a different 20

31 time interval. From a conversion to 8.5-minute sustained wind (the majority of observations) to 1-minute sustained wind, this results in a multiplication factor of ( ) ( ) ( ( )) ( ( )) ( ) Next, wind speed at the altitude of each observation is normalized to a 10-meter sustained wind speed. This is done using the relationship near-surface wind speed increase with altitude over water from Hsu, Meindl, and Gilhousen (1994) (Eq. 6). For a conversion from 5-meter winds (the majority of observations) to 10-meter winds, this results in a multiplication factor of 1.08 ( ) ( ) After all wind speeds are normalized to 1-minute, 10-meter sustained wind speeds, ocean-air interfacial sensible (h s ) and latent (h l ) energy fluxes are calculated using the formulas used by and described in ione (Garratt 1977; Black et al. 1988) (Eqs. 7, 8, 9). ( ) ( ) ( ) ( ) ( ) ( ) 21

32 Sea spray also plays a potentially significant role in the ocean-air flux budget. The T s winds eject large quantities of spray droplets into the near-surface boundary layer air. These droplets transfer sensible and latent energy to the atmosphere and can increase net entropy input into the T (Andreas 1992, 2010; Fairall et al. 1994; Andreas and Emanuel 2001). To obtain more complete profiles of ocean-air fluxes, sensible (Q SF (F)) and latent (Q LF (F)) energy fluxes from sea spray are calculated from the formulas of Fairall et al. (1994), described in Wang et al. (2001) (Eqs. 10,11). is a term that adjusts 10-meter winds to winds at the significant wave height. ( ) is a term that accounts for the fact that sea spray droplets cool to equilibrium temperature rather than to air temperature (Table 2.3). ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ( ) ) ( ) ( ( ) ) (12) ( ) ( ( ) ) ( ) Observations indicate that a large fraction of spray droplets remain in the near-surface air (Fairall et al. 1994; Kepert and Fairall 1999). Fairall et al. (1994) estimates that 50% of spray evaporates in the droplet evaporation layer near the ocean surface and 50% of spray evaporates 22

33 above the droplet evaporation layer. The 50% that evaporates in the droplet evaporation layer cools the near-surface air without directly affecting energy input into the T. The 50% that evaporates above the droplet evaporation layer directly affects energy input to the T. Setting α as the fraction of spray flux that ascends above the droplet evaporation layer, formulas for net ocean-air sensible and latent energy flux are obtained (Eqs. 14, 15). These formulas are identical to the Wang et al. (2001) spray flux formulas using the Fairall scheme. ( ) ( ) ( ) ( ) In the Fairall spray flux scheme, the net spray contribution to total enthalpy flux is αq SF, a quantity two orders of magnitude less than total interfacial flux. According to the Fairall scheme, this is the only net energy input from spray fluxes because any gain in latent energy through sea spray evaporation is accompanied by an equal loss of sensible energy required to evaporate the spray drops. Therefore, according to the Fairall scheme, spray primarily redistributes atmospheric energy from sensible energy to latent energy. It also cools near-surface air due to evaporation of spray that remains in the droplet evaporation layer. The ratio of Eq. 14 to Eq. 15 is defined in this study as the Fairall Bowen Ratio. Andreas and Emanuel (2001) and Andreas (2010) contended that spray droplets can have a greater effect on net ocean-air turbulent energy exchange than the Fairall scheme gives. They argue that spray droplets that re-enter the ocean play a key role in transferring energy to the air. 23

34 According to the Andreas scheme, droplets cool rapidly to their equilibrium temperature (T eq ) before they have time to evaporate an appreciable fraction of their mass. They then re-enter the ocean at their equilibrium temperatures. This results in net ocean-air sensible energy flux. Because the drops do not have time to evaporate, they extract little sensible energy from the near-surface air. This means that in the Andreas scheme spray fluxes can potentially warm the near-surface air. Using the Andreas (2010) parameterization of flux from re-entrant spray droplets, sensible energy flux from sea spray is calculated as a function of seawater density, specific heat of seawater, friction velocity, and temperature depression from SST to 100 μm droplet equilibrium temperature (Eq. 16). Andreas (2010) estimates 100 μm as representative of spray droplets, but acknowledges that droplet size varies across a wide spectrum. ( ) ( ) ( ) Friction velocity depends on 10-meter wind speed and the surface drag coefficient (Powell 2006) (Eq. 17). Following the method of Andreas and Emanuel (2001), d is calculated from the formulas of Large and Pond (1981). However, recent observations (Powell et al., 2003; Powell 2006) indicate that d levels off at high wind speeds. Therefore, for wind speeds above 25 ms -1 the drag coefficient at 25 ms -1 from Large and Pond (1981) is used. ( ) 24

35 Equilibrium temperature depends on air temperature, humidity, droplet radius, and droplet salinity. For a 100 μm droplet the equilibrium temperature can be solved using the formula from Andreas (1995), where T a is given in elsius (Eq. 18). Per Andreas (1995), T eq values are replaced with T a when T eq > T a because equilibrium temperature cannot be above air temperature. [ ( ) ] ( ) [ ( ) ] (18) Solving Eq. 18 yields equations Eq. 19 and Eq. 20 for total sensible and latent energy fluxes using the Andreas (2010) scheme. The ratio of Eq. 19 to Eq. 20 is defined in this study as the Andreas Bowen Ratio. ( ) ( ) ( ) ( ) ( ) The Fairall spray flux scheme can be combined with the Andreas spray flux scheme to yield a combined scheme for total latent and sensible energy fluxes (Eqs. 21, 22). This combined scheme is created under the assumption that a significant fraction of spray droplets (1-α; 50% in this study) remain in the near-surface layer and re-enter the ocean before they have a chance to lose appreciable mass to evaporation. The Andreas scheme represents these droplets. The remainder (α) is lofted above the near-surface layer and input latent energy while extracting 25

36 sensible energy through evaporative cooling. The Fairall scheme represents these droplets. The ratio of Eq. 21 to Eq. 22 is defined as the ombined Bowen Ratio. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Each flux scheme (Table 2.4) gives unique profiles of sensible energy flux and latent energy flux. These schemes are compared to each other and analyzed in relation to observed surface conditions in hapter 4. Fluxes from each scheme are plotted as a function of number of R max from the T center. Spray fluxes and total fluxes are also integrated by area in R max space. This is done by weighting the average flux in each R max bin by the area of that bin in R max space. Bins near the T center (small R max ) have less area than bins far from the T center (large R max ), and so receive less weight in the integrated flux calculation. Description of flux Sensible energy flux Latent energy flux Name of Bowen Ratio Interfacial Flux H s =h s H l =h l Interfacial Bowen Ratio No spray Fairall H s =h s +αq SF (F)-αQ LF (F) H l =h l +αq LF (F) Fairall Bowen Ratio Spray scheme Andreas H s =h s +Q SF (A) H l =h l Andreas Bowen Ratio Spray scheme ombined scheme H s =h s +αq SF (F)+(1-α)Q SF (A) H l =h l +αq LF (F) ombined Bowen Ratio Table 2.4: Flux calculation schemes used in this study 26

37 3. Profiles of near-surface thermodynamic scalars A. Temperature Radial and R max temperature profiles of the composite observed T show almost constant T a beyond 450 km and 9 R max (Figure 3.1; Appendix A). Inside these distances T a decreases with decreasing radius. Between 450 and 75 km from the T center, T a falls from 28.1 to 25.7 (- 2.4 ). An equal magnitude drop occurs between 9 R max and 0.75 R max. The majority of this T a decrease occurs between 4 R max and 1.56 R max, where T a decreases by 1.5. Inside 75 km and 0.75 R max, T a increases rapidly with decreasing radius. Between 75 km and 2.5 km from the storm s center, T a increases by 1.2. A similar increase (1.3 ) is observed between 0.75 R max and R max. Figure 3.1: Near-surface air temperature (Ta) with radius and R max. Temperature decreases substantially between the environment and 75 km/0.75 R max. Inside these distances temperature increases. 27

38 These results are similar to the findings of ione et al. (2000) (hereafter ione). ione s data also shows that temperature falls with decreasing radius (Figure 3.1). ione observed that T a decreases by 1.9 between 450 km and 140 km from the T center, comparable to this study s findings. ione also found almost radially-constant temperature inside of 140 km. Data from this study shows a similar temperature decrease between 350 and 145 km. However, this study also shows a sharp temperature increase inside 50 km from the T center, a result not found in ione. This difference may be due to the greater detail in the inner-core data used in this study. ione used 37 observations inside 56 km from a hurricane s center, whereas this study uses 280 observations inside 56 km. The data used in this study give a more detailed sample of the nearsurface temperature profile in the eyewall and eye. ione also filtered out inner-core observations with less than 17.5 ms -1 sustained wind speed, causing many observations in the T eye to be excluded. In contrast, this study does not set a wind speed threshold, so observations in the eye are included. This creates a more complete radial thermodynamic profile that suggests near-surface warming inside 75 km and 0.75 R max on the order of in the composite T profile (Figure 3.1). Although this study s composite T a profile shows a similar structure to the ione T a profile outside of 50 km, there are differences in the amount of near-surface cooling with decreasing radius that can be attributed to adiabatic expansion. ione showed that only a small fraction of the T a decrease with decreasing radius in this dataset occurs due to adiabatic expansion. According to that study 0.3 of the 1.9 decrease in temperature between 360 and 140 km was caused by adiabatic cooling as pressure fell from hpa to hpa. Data from this study show more adiabatic cooling due to the larger pressure falls with decreasing 28

39 radius. Between 350 km and 140 km from the composite storm s center, T a decreases by 1.5. However, adiabatic expansion as pressure falls from hpa to hpa results in a decrease of 0.9. Both stronger (P min < 960 hpa) and weaker (P min 960 hpa) hurricanes in this study show T a decrease with decreasing radius. The composite of stronger Ts has 1.7 of near-surface cooling between 350 km and 140 km from the T center, compared to 1.2 for the composite of weaker Ts. For more intense Ts, adiabatic cooling as pressure falls from hpa to hpa accounts for the entirety of this T a change. For less intense Ts, adiabatic cooling as pressure falls from hpa to hpa accounts for 55% of the total T a change. In both cases, adiabatic cooling accounts for a greater fraction of the T a decrease than it does in ione. The combined results from ione and this study suggest that processes other than adiabatic cooling contribute to temperature falls with decreasing radius. ione suggested that this process may be cool unsaturated downdrafts from the mid-levels. In hapter 4 it is posited that spray evaporation may be responsible for some of this cooling. This study s composite T a profile also differs from EPI theory s idealized boundary layer T a profile. EPI theory assumes a radially-isothermal boundary layer with T a equal to the environmental temperature. Observational data, however, shows that T a is not radially isothermal (Figure 3.1). If the average temperature at 15 R max (28.2 ) is taken as the environmental temperature, T a decreases by 2.6 between the environment and 0.75 R max. It increases by 1.3 between 0.75 R max and R max. In nearly the entire composite observed storm, T a is lower than the environmental T a, and in the eyewall it is more than 2 lower. T a decrease with decreasing radius occurs in the majority of this study s observed Ts. Of the 30 storms with data from inside R max, 28 have R max T a lower than environmental T a. 29

40 For 25 of these storms, R max T a is at least 1.0 below environmental T a. Hurricane Frances (2004), Jeanne (2004), Earl (2010) and Irene (2011) all exhibit this temperature variation with radius (Figure 3.2). Similar to the composite storm, each of these storms has falling temperatures with decreasing radius between the environment and the core of the cyclone. Each storm profile also shows temperature increasing with decreasing radius in the innermost part of the storm. For Frances, Jeanne, and Earl, this pattern is observed in both surface-based and dropsonde data. Figure 3.2: Near-surface temperature with R max for Frances (2004), Jeanne (2005), Earl (2010), and Irene (2011). In each storm temperature decreases with decreasing radius outside the T core and increases with decreasing radius in the core. These four Ts are chosen because they offer some of the most complete radial profiles of observations. The T a decrease with decreasing radius outside the T inner core is reflected in the increase in sea-air temperature contrast (SA) with decreasing radius in the same region (Figure 30

41 3.3). SA increases inside of 450 km and 5.5 R max, reaching maximum values of 2.2 at 75 km and 2.0 at 1.25 R max. Some storms have SA as high as 4.0. The radial SA profile is similar to ione s SA profile, though in this study SA begins to increase slightly farther from the T center and increases more gradually with decreasing radius. The SA increase between the T outer region and the T core increases sensible energy fluxes in the T core and increases PI. Greater ocean-air temperature disequilibrium in the T core would increase maximum sensible fluxes due to temperature disequilibrium in this region. This would provide greater maximum entropy input into the T and increase PI. Furthermore, if lower temperatures under the eyewall are accompanied by less moisture than PI theory predicts, the ocean-air moisture disequilibrium would also increase. This would increase latent energy fluxes and provide additional entropy to the storm, further increasing PI. However, lower nearsurface temperatures also imply a more stable atmosphere. Therefore, while lower R max nearsurface temperatures can increase PI, they may also lower actual intensity if the potential for greater fluxes near R max are not manifested in greater ocean-air entropy input. 31

42 Figure 3.3: Sea-air contrast (SA) with radius and R max. In the composite storm SA increases with decreasing radius up to near R max and decreases inside 0.75 R max. B. Moisture Specific humidity (q) is almost radially-constant far from the T center, before increasing rapidly with decreasing radius in the T core (Figure 3.4). In radial space q increases monotonically inside 250 km, with the majority of this increase inside 50 km from the T center. Between 250 km and 50 km from the T center, q increases by 1.6 gkg -1 (18.4 gkg -1 to 20.0 gkg - 1 ). Between 50 km and 2.5 km, q increases by 2.9 gkg -1 to a maximum of 22.9 gkg -1. This q pattern shows reasonably good agreement with the findings of ione, which found that q increases by 1.5gkg -1 between 210 km and 40 km from the T center. However, this study 32

43 shows greater q increases occur in the innermost core of the T than ione showed. It also shows that q reaches maximum values in the eye. Much of this additional increase is due to the lower pressures and warmer temperatures found here in the eye. ione only included observations inside 85 km that had sustained wind speeds of 17.5 ms -1 or greater. This criterion excluded many observations from the T eye. This study does not use a wind speed threshold, so observations in the eye are included. The innermost bin in this study (0-5 km) has an average pressure of hpa, compared to a pressure of hpa in ione s innermost bin (0-56 km). This lower pressure contributes to higher q values. Figure 3.4: Specific humidity (q) with radius and R max. In the composite storm specific humidity begins to increase with decreasing radius at 2.5 R max. 33

44 The q profile in R max space shows a slightly different pattern. Specific humidity is nearly constant outside 5.5 R max. Between 5.5 R max and 2.5 R max q falls from 19.6 gkg -1 to 18.6 gkg -1. Inside of 2.5 R max, q rises to 19.5 gkg -1 at 1.25 R max and to a maximum of 22.8 gkg -1 at R max (Figure 3.4). This means that in the composite T profile, q begins to increase at about 2.5 R max and increases rapidly inside 1.25 R max. However, individual storms show divergent profiles (Figure 3.5). Hurricanes such as Ophelia (2005) have almost radially constant q until near R max, where q increases rapidly. This is similar to the idealized profile of EPI theory. Hurricanes like Jeanne (2004) show q increasing with decreasing radius in nearly the entire T profile. Other hurricanes such as Rita (2005) have a profile in which q falls with decreasing radius in the outer region of the storm, reaches a minimum, and increases with decreasing radius thereafter. 34

45 Figure 3.5: Specific humidity with R max for Ophelia (2005), Jeanne (2004), and Rita (2005). These three storms show varying specific humidity radial variations. Relative humidity (RH) also increases with decreasing radius (Figure 3.6). Beyond 250 km from the T center, RH changes little with radius. Between 250 km and 30 km, RH increases nearly linearly with decreasing radius, from 81.3% at 250 km to 96.5% at 30 km. Inside of 30 km, RH is nearly constant, indicating almost constant relative humidity in the composite T eye. In R max space, RH increases from 80.9% at 6 R max to 87.7% at 2 R max, 93.3% at R max, and 96.6% at R max. 35

46 Figure 3.6: Relative humidity (RH) with radius and R max. Relative humidity increases with decreasing radius inside 250 km and 10 R max. Relative humidity begins to increase with decreasing radius farther out than specific humidity increase begins. This occurs because T a decreases with decreasing radius inside 9 R max. Although specific humidity is slightly lower at 2.5 R max than 9 R max (18.6 gkg -1 versus 18.9 gkg - 1 ), RH at 2.5 R max is 4.0% higher due to a 1.4 drop in T a. Inside 2.5 R max, both q and RH increase rapidly with decreasing radius. In the eye, temperature increases moderate RH gains, while q continues to increase up to the T center due to falling pressure. The RH distributions of this study are consistent with ione, which show RH increasing from 84.9% at 210 km to 96.5% at 40 km (Figure 3.6). However, observations from this study and ione both differ from the theoretical EPI RH profile. In the EPI profile RH outside R max is radially constant at the environmental value. RH only increases inside R max (Emanuel 1986, 36

47 1995). Observations show that RH increases with decreasing radius as far as 9 R max from the T center, with rapid increases inside 2.5 R max. Much of this RH increase is due to T a decrease with decreasing radius. This is demonstrated by the composite specific humidity profile (Figure 3.4), in which q falls with decreasing radius between 5.5 R max and 2.5 R max, despite RH increases between these radii. The theoretical EPI profiles of a radially-isothermal boundary layer and constant RH outside R max combine to make the implicit assumption that q is nearly constant outside R max, with small increases from falling pressure. Observations show that this assumption is reasonably accurate for the composite storm. Specific humidity (Figure 3.4) is near radially-constant beyond 2.5 R max, and only increases rapidly inside R max. This shows that increases in relative humidity increases outside the T inner core of the composite storm are driven by temperature falls (Figure 3.7). It is posited in chapter 4 that sea spray evaporation may play a role in this falling temperature. 37

48 Figure 3.7: Pressure, temperature, specific humidity, and relative humidity with radius and R max. Temperature decreases with decreasing radius from 450 km to 75 km and from 9 R max to 0.75 R max. Temperature increases inside 75 km and 0.75 R max. Relative humidity increases with decreasing radius inside 350 km and 10 R max, while specific humidity only increases inside 2.5 R max. This indicates that relative humidity increases with decreasing radius outside 2.5 R max are driven by temperature falls.. Enthalpy Sensible energy decreases with decreasing radius between 9 R max and 0.75 R max (Figure 3.8), reflecting the temperature decrease between these radii (Figure 3.1). Latent energy (h Lat ) begins to increase with decreasing radius inside 250 km and 2.5 R max from the T center (Figure 3.9). However, the decrease in sensible energy between these radii modulates the total moist enthalpy (h) gains (Figure 3.10) caused by h Lat increases. Between 2.5 R max and 0.75 R max, h Lat increases by 4.3 kjkg -1 and h Sen decreases by 1.0 kjkg -1, resulting in a net h increase of 3.3 kjkg - 1. Inside of 0.75 R max h Lat and h Sen both rise rapidly with decreasing radius, with h Lat increases 38

49 causing the majority of the increase in h. Between 0.75 R max and the T center, h Sen increases by 1.5 kjkg -1 and h Lat increases by 6.0 kjkg -1 for a total h gain of 7.5 kjkg -1. These results agree reasonably well with the theoretical EPI profile, in which dry air entrainment at the top of the boundary layer keep boundary layer h constant outside R max, save for small increases from pressure falls. EPI theory states that inside R max, boundary layer h increases because ocean-air fluxes overwhelm turbulent fluxes and entrainment at the top of the boundary layer (Emanuel 1986, 1995) (Figure 3.10). This basic pattern is borne out by data. However, as in the composite q profile, the h increase is not as sharp as EPI theory predicts; h does not go from nearly constant outside R max to a sudden increase inside R max. Between 2.5 R max and R max, in the composite storm, h increases by 2.7 kjkg -1. Between R max and R max h increases by an additional 8.1 kjkg -1. While the majority of the h increase occurs inside R max, the increase between 2.5 R max and R max makes up about 25% of the total moist enthalpy gain inside 2.5 R max, a potentially significant amount of total moist enthalpy gain. 39

50 Figure 3.8: Sensible energy with (h SEN ) with radius and R max. The sensible energy profile is very similar to the temperature profile, as sensible energy depends primarily on temperature. 40

51 Figure 3.9: Latent energy (h LAT ) with radius and R max. The latent energy profile is similar to the specific humidity profile because latent energy depends primarily on atmospheric moisture. The slight increase inside of 0.75 R max in the EPI profile is due to pressure falls with decreasing radius in the eye. 41

52 Figure 3.10: Moist enthalpy (h) with radius and R max. Moist enthalpy increases inside 2.5 R max. However, sensible energy decreases between 2.5 R max and 0.75 R max, tempering moist enthalpy gains. D. Equivalent potential temperature and specific entropy Equivalent Potential temperature (θ e ) is nearly constant with radius outside 5.5 R max. It decreases slightly between 5.5 R max (356.7 K) and 2.5 R max (354.2 K). Inside of 2.5 R max, θ e rises with decreasing radius. Between 2.5 R max and R max θ e increases by 5.3 K and between R max and R max θ e increases an additional 13.7 K. 28% of the θ e gain inside 2.5 R max in the composite storm occurs between 2.5 R max and R max. To distinguish between θ e changes from ocean-air fluxes and θe changes from falling pressure, θ e is recalculated with pressure of each observation set to 1000 hpa. Using this pressure-independent calculation, it is found that θ e increases between 2.5 R max and R max independent of pressure changes contribute 2 K to θ e in the 42

53 T eyewall. This is comparable to the results of the Wang and Xu (2010) numerical simulation, which showed that ocean-air fluxes outside the eyewall contributed K to θ e in boundary layer air below the eyewall. ompared to ione s θ e calculations, the composite storm in this study has a sharper θ e increase near the T center, consistent with the lower pressures in the core of storms in this study. The radial composite storm shows a hint of ione s somewhat parabolic profile, in which θ e decreases with decreasing radius beyond 140 km from the T center before increasing inside this radius (Figure 3.11). ione suggested that this parabolic profile could be attributed to unsaturated convective downdrafts outside the T core, which lower near-surface temperature and moisture (Barnes et al. 1983; Powell 1990). The composite R max profile shows a more distinct parabolic profile. θ e falls from K at 5.5 R max to K at 2.5 R max, before increasing inside this radius. This pattern is observable in some but not all of the individual Ts in this study. 43

54 Figure 3.11: Equivalent potential temperature (ɵ e ) with radius and R max. Specific entropy (s) has a nearly identical radial profile as θ e because it depends directly on θ e (Table 2.2). However, s is calculated and analyzed because EPI theory uses APE changes to represent changes in s (hapter 5). Like θ e, s decreases between 5.5 R max and 2.5 R max before increasing inside 2.5 R max. Specific entropy decreases by 10.9 Jkg -1 between 5.5 R max and 2.5 R max. Between 2.5 R max and R max, s increases by 22.8, Jkg -1. Between R max and R max, s increases by an additional 54.4 Jkg -1. In the composite storm 71% of the s increase inside 2.5 R max occurs inside R max. The remaining 29% occurs between 2.5 R max and R max. This is reasonably consistent with the idealized EPI profile, in which the vast majority of s increase occurs inside R max (Emanuel 1986, 1995). Nevertheless, the s increase outside R max makes up 29% of the total gain in s, a potentially significant contribution to the ocean-air entropy input in tropical cyclones. 44

55 Like θ e, specific entropy is recalculated with constant 1000 hpa pressure at each observation to eliminate the effect of pressure changes on s. Using this calculation, the s increase between 2.5 R max and R max for the composite T makes up 26% of the total s increase inside 2.5 R max. Therefore, ocean-air fluxes, in addition to falling pressure, contribute to s increase between 2.5 R max and R max in the composite T. This indicates that for the composite storm, ocean-air fluxes out to 2.5 R max play non-negligible roles in the total entropy input into the T. For certain hurricanes such as Irene (1999), Jeanne (2004), Rita (2005), and Earl (2010) s gains outside of R max make up much more of the total s increase, sometimes greater than 50% of the total increase (Figure 3.13). This shows that ocean-air fluxes outside R max cannot be ignored in the T energy budget. However, further research is necessary to determine whether this increase in near-surface specific entropy inside 2.5 R max is reflected in specific entropy increases throughout the boundary layer or if it is confined to the lowest part of the boundary layer. This composite R max specific entropy profile accords well with the numerical model results of Wang and Xu (2010). Wang and Xu (2010) found that ocean-air fluxes inside of R max provide important contributions to the total entropy input that maintains the T s winds against frictional dissipation. Observational results show specific entropy in the composite storm begins to increase at this radius, though the radius varies among individual storms. Wang and Xu (2010) noted that some storms can have significant ocean-air entropy input beyond R max, but found that this input affects T size rather than intensity. Observations (Figure 3.13) confirm that significant entropy input can occur outside 2.5 R max in some storms, but determining whether this entropy input contributes to maximum intensity is beyond the scope of this study. 45

56 Figure 3.12: Specific entropy (s) with radius and R max. Inside 2.5 R max specific entropy increases more rapidly than pressure change alone can account for. 46

57 Figure 3.13: Specific entropy with R max for Irene (1999), Jeanne (2004), Rita (2005), and Earl (2010). In each storm specific entropy increases substantially with decreasing radius outside R max. In summary, data from the tropical cyclone near-surface layer show that the observed moisture profile has similarity to the idealized EPI moisture profile, but the observed temperature profile differs from the EPI profile. EPI s theoretical profiles of near-constant moisture and specific entropy outside R max are close to the profile of the composite observed storm. However, EPI theory states that ocean-air fluxes increase moisture and entropy inside R max, whereas observations show that the composite storm this radius is 2.5 R max. Individual T moisture and entropy profiles show large variations. Some T s have near-constant moisture and specific entropy outside of R max. In other Ts, moisture and specific entropy begin to increase with decreasing radius much more than 2.5 R max from the T center. This indicates variation among 47

58 individual storms in the number of R max that ocean-air fluxes begin to contribute to boundary layer moisture and entropy EPI theory s idealized profile of a radially-isothermal near-surface layer with temperature equal to the environmental temperature differs from observations of both this study and ione et al. (2000). Both observational studies show that temperature decreases significantly with decreasing radius between the environment and the inner core. In this study, the a temperature decrease between the environment and R max occurs in 28 of 30 storms studied, with a decrease of greater than 1 in 25 of 30 storms studied. This temperature decrease appears to occur from factors beyond adiabatic cooling alone. The differences between the EPI theoretical profile and the observed profile may play a significant role in T PI. EPI theory states that a storm s PI depends on the entropy difference between the sea surface and near-surface air at R max. This difference drives the ocean-air fluxes that power the storm. For this reason, the lower near-surface temperature at R max in the observed profile may impact PI. Furthermore, if fluxes outside of R max, play a role in the total entropy input into the T, PI is not simply a function of the ocean-air entropy disequilibrium at R max (the eyewall), but also ocean-air entropy disequilibrium beyond the eyewall. PI and observed intensity may depend ocean-air entropy input beyond the eyewall, and therefore near-surface thermodynamic conditions beyond the eyewall. This would make PI calculations more complex. 48

59 4. Ocean-air flux profiles A. Interfacial fluxes Interfacial sensible (h s ) and latent (h l ) energy fluxes increase with decreasing radius. The increase in h s with decreasing radius occurs because of increasing wind speed and increasing temperature contrast between ocean and near-surface air (Figure 3.3, 4.1; Eqs. 7, 9). The h l increase with decreasing radius is driven by the increase in wind speed (Figure 4.1; Eqs. 8, 9). The increase in near-surface specific humidity inside 2.5 R max (Figure 3.4) modulates h l increases inside this radius by reducing the term in Eq. 8. Both h s and h l increase rapidly with decreasing radius inside 2.5 R max, where wind speeds increase rapidly with decreasing radius. Between 2.5 R max and 0.75 R max, h l increases from 603 Wm -2 to 863 Wm -2 (43% increase) and h s increases from 60 Wm -2 to 172 Wm -2 (287% increase). Inside of 0.75 R max, wind speed and seaair contrast decrease, decreasing h s and h l. However, at the innermost bin (0.25 R max ), the high average wind speed (22 ms -1 ) indicates that some observations in the 0.25 R max bin are occuring in the eyewall rather than the calmer eye. This is why interfacial sensible and latent energy fluxes remain relatively high even at 0.25 R max (Figure 4.2). 49

60 Figure 4.1: Wind speed with radius and R max. Wind speed increases with decreasing radius up to 0.75 R max and decreases inside 0.75 R max. The high average wind speeds even at the innermost radius and R max values indicate that some of these observations are occurring in the eyewall rather than the eye. This study s composite interfacial flux profiles show strong similarity to ione s flux profiles. In both profiles h s and h l increase sharply with decreasing radius and reach maximum values near the T center. This similarity between profiles occurs despite ione s exclusion of observations with V < 17.5 ms -1 inside of 85 km from the T center and V < 13 ms -1 beyond 85 km. This could be why the ione profile shows a sharp increase in interfacial latent energy flux between 120 km and 40 km from the T center, whereas this study shows no major flux increases inside 75 km. This study includes eye observations with low wind speeds. This reduces average wind speeds inside 75 km (Figure 4.1). When ione s wind speed criteria are applied to this study s data, interfacial fluxes continue to increase up to 17.5 km, with h s peaking at 280 Wm -2 and h l peaking at 1141 Wm