On ENSO-Modified Hurricane Formation in the North Atlantic
THESIS
Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in
the Graduate School of the Ohio State University
By Joshua Welty
Graduate Program in Atmospheric Science
The Ohio State University
2015
Master’s Examination Committee:
Dr. Jay S. Hobgood, Advisor
Dr. Jeffrey Rogers
Dr. Álvaro Montenegro Copyright by
Joshua Stephen Welty
2015 Abstract
A variety of statistical studies have been performed in past years identifying the variables that exhibit the greatest efficacy in determining whether or not a cloud cluster over the north Atlantic basin will form into a hurricane. An oft-used statistical model employed to assess the relative power of variables in distinguishing between cloud cluster lysis or further development into a hurricane (two simple outcomes) is linear discriminant analysis (LDA) which computes coefficients for each predictor taken from a selected predictor set. LDA maintains a wide range of applications across a breadth of disciplines.
The LDA-derived coefficients are based on the variance of each predictor correlated with the two different classifications: 1) development (into a hurricane) and 2) nondevelopment. A higher magnitude coefficient for a discrete variable indicates enhanced power in discriminating between development or nondevelopment.
The specific question addressed in this study lies at the interface between the behavior of cloud clusters and ENSO-modified (El Niño - Southern Oscillation, or colloquially, El Niño) activity over the north Atlantic. The study is designed to determine if the power of certain variables to discriminate between subsequent cloud cluster outcomes over the north Atlantic basin changes in connection to a transition in phase of
!ii ENSO. In other words, the study addresses whether or not the most effective
discriminators during El Niño years are the same as the most effective discriminators
during La Niña or neutral years. In this study, an additional model employed to
determine the maximum achievable potential intensity (MPI) of certain storms is utilized
in a variety of case studies to determine if it is a satisfactory indicator of subsequent
intensification or lack thereof.
Low-level vorticity in general is the highest-ranked discriminant across all seasons. SST and Coriolis also significantly affect cloud cluster outcomes. MPI, in nascent formation phases, is not a reliable predictor. Vorticity stretching is of highly variable significance which is dependent upon ENSO phase and the time until genesis.
Future studies examining ENSO effects on formation processes could benefit greatly by the use of dynamic models - such as shallow water primitive equation (SWPE) models - in the simulation of upper-level conditions.
!iii Dedication
To Mom, who has loved and encouraged me.
To Dad, who has inspired and led me.
To Dr. Hobgood, who has taught and guided me.
!iv Acknowledgments
I would like to extend my sincerest thanks to the Ohio State University
Department of Geography for blessing me with a Graduate Fellowship and Graduate
Teaching Associateship over the course of two years. I am humbled by the opportunity to represent the university and the department in all future endeavors.
I would also like to thank my family (Dad, Mom, Rach) and my girlfriend, Aggie, for their incessant love and patience. I love you all.
Last but certainly not least, I am very grateful for the time, efforts, and guidance provided by Dr. Hobgood, my advisor, and Dr. Rogers and Dr. Montenegro, my committee members. Thank you, Dr. Hobgood, for agreeing to be my mentor/advisor. I have learned a lot from you. Thank you, Dr. Rogers and Dr. Montenegro, for being willing to further contribute to my development as a researcher.
!v Vita
June 2008...... New Albany High School
June 2012...... (Honors) B.S. Geography/Atmospheric
Science (Spanish minor), The Ohio State
University
August 2013 - present...... Graduate Fellow, Graduate Teaching
Associate, Atmospheric Science, The Ohio
State University
Fields of Study
Major Field: Atmospheric Science
!vi Table of Contents
Abstract……………………………………………………………………………..…….ii
Dedication………………………………………………………………………………...iv
Acknowledgments…………………………………………………………………………v
Vita……………………………………………………………………………………….vi
Table of Contents………………………………………………………………………..vii
List of Tables…………………………………………………………………………….xii
List of Figures…………………………………………………………………………..xiv
Chapter 1: Introduction……………………………………………………………………1
1.1 Relevance...... 1
1.2 Forecasting...... 2
1.3 Tropical cyclogenesis (TCG)...... 3
1.4 Stochasticity...... 4
1.5 Background...... 5
1.6 Questions...... 8
Chapter 2: Literature Review...... 10
!vii 2.1 Formation Theories...... 10
2.1.1 Top-down merger…………………………………………………10
2.1.2 Top-down showerhead...... 12
2.1.3 Bottom-up...... 15
2.2 Construction………………………………………………………………..17
2.2.1 Convection...... 17
2.2.2 Shear...... 19
2.3 Intensification Theories……………………………………………………..21
2.4 Maximum Potential Intensity...... 23
2.4.1 DeMaria and Kaplan...... 24
2.4.2 Holland……………………………………………………………25
2.4.3 Emanuel…………………………………………………………..26
2.5 Climatology...... 28
2.5.1 Climatological Oscillations...... 29
2.5.2 El Niño Southern Oscillation (ENSO)...... 29
2.5.3 Future projections...... 33
2.5.4 Research questions...... 34
Chapter 3: Methods………………………………………………………………………36
3.1 Introduction to Linear Discriminant Analysis (LDA)……………………….36
3.1.1 Literature-based variable selection rationale……………………..37
!viii 3.1.2 Linear Discriminant Analysis...... 42
3.1.3 Ocean Niño Index…………………………………………………44
3.1.4 NHC Best Tracks...... 45
3.2 Cloud clusters...... 46
3.2.1 Cluster thresholds...... 46
3.2.2 Satellite imagery...... 47
3.3 Variable selection...... 52
3.3.1 Low-level vorticity...... 54
3.3.2 Upper-level vorticity...... 56
3.3.3 Coriolis (parameter, scaled)...... 56
3.3.4 Vertical wind shear...... 57
3.3.5 Vorticity stretching...... 59
3.3.5 SST...... 59
3.4 Reanalysis selection...... 60
3.4.1 NCEP/DOE AMIP-II Reanalysis (NCEPR2)……………………..60
3.4.2 NCEP Climate Forecast System Reanalysis (CFSR) ……………..61
3.4.3 ECMWF ERA-Interim Reanalysis (ERA-I)………………………62
3.5 Computation...... 62
3.5.1 NCL Computation...... 62
3.5.2 LDA in R…………………………………………………………..69
3.5.3 MPI (as delineated by BE02a)...... 71
!ix
Chapter 4: Results………………………………………………………………………..79
4.1 Linear Discriminant Coefficients...... 79
4.2 5x5° Box…………………………………………………………………….80
4.2.1 Annual analyses...... 80
4.2.2 Seasonal analyses...... 93
4.3 2° Radius…………………………………………………………………..106
4.4 Incubation period...... 111
4.5 Case Studies...... 112
4.5.1 Tropical Storms...... 114
4.5.2 Hurricanes...... 123
4.6.3 Case Study Summary (and a note on model efficacy)…………..134
Chapter 5: Discussion………………………………………………………………….141
5.1 Preeminent predictors...... 141
5.2 Figures (low-level vorticity, Coriolis)...... 143
5.3 Model efficacy…………………………………………………………….145
5.3.1 All years...... 147
5.3.2 El Niño...... 148
5.3.3 La Niña…………………………………………………………..149
5.4 Statistical analysis of Model Skill…………………………………………150
!x Chapter 6: Conclusions/Trajectory...... 157
6.1 Primary Conclusions………………………………………………………157
6.1.1 Preeminent Discriminators………………………………………157
6.1.2 ENSO Influence on Discriminators……………………………..158
6.1.3 Potential Implications Accompanying Future Climate Change…160
6.2 Model Improvement...... 161
6.3 Future Work...... 162
Bibliography……………………………………………………………………………175
!xi List of Tables
Table 1. Annual Coefficients, 5x5 Box…………………………………………………..83
Table 2. Annual Coefficient Ranks, 5x5 Box…………………………………………….83
Table 3. Annual Means, 5x5 Box…………………………….…………………………..84
Table 4. Annual Coefficients at Initial Time, 5x5 Box…………………………………..88
Table 5. Annual Means at Initial Time, 5x5 Box…………………………….…………..89
Table 6. Annual Coefficients at TTG=24Hr, 5x5 Box…………………………….……..90
Table 7. Annual Means at TTG=24Hr, 5x5 Box…………………………….…………..91
Table 8. Annual Coefficients at Genesis, 5x5 Box…………………………….………...92
Table 9. Annual Means at Genesis, 5x5 Box…………………………….………………93
Table 10. Seasonal Coefficients, 5x5 Box…………………………….…………………97
Table 11. Seasonal Coefficient Ranks, 5x5 Box…………………………….…………..97
Table 12. Seasonal Coefficients through Time, 5x5 Box…………………………….….98
Table 13. Statistical Significance, Low-level Vorticity and SST……………………….103
Table 14. Statistical Significance, Vorticity Stretching…………………………….…..104
Table 15. Annual Coefficients, 2º Radius…………………………….………………..109
Table 16. Annual Means, 2º Radius…………………………….………………………110
!xii Table 17. Annual Coefficient Ranks, 2º Radius…………………………….…………..111
Table 18. Incubation Period by Year…………………………….……………………..112
Table 19. Case Studies…………………………….……………………………….…..135
Table 20. Abridged MPI Values…………………………….………………………….138
!xiii List of Figures
Fig. 1. Vertical Wind Shear Climatology…………………………….…………………..28
Fig. 2. Hurricane Katrina…………………………….…………………………………..50
Fig. 3. Satellite Techniques…………………………….………………………………..51
Fig. 4. Color Table (<208K)…………………………….……………………………….52
Fig. 5. El Niño - Neutral Shear Anomaly…………………………….………………….58
Fig. 6. El Niño - La Niña Shear Anomaly…………………………….…………………58
Fig. 7. Read-in Code Example…………………………….……………………………..63
Fig. 8. 5x5° Vorticity Code Example…………………………….………………………64
Fig. 9. 5x5° Method for Variable Calculation…………………………….……………..65
Fig. 10. 2° Radius Vorticity Code Example…………………………….……………….67
Fig. 11. 2° Radius Method for Variable Calculation.…………………………….……..68
Fig. 12. LDA Code…………………………….……………………………….………..69
Fig. 13. LDA Output…………………………….……………………………….………71
Fig. 14. Katrina Gulf Conditions from Kafatos et al. (2006)…………………………….73
Fig. 15. Example MPI Output, SST=30ºC…………………………….…………………74
Fig. 16. Example MPI Output, SST=31ºC…………………………….…………………75
!xiv Fig. 17. MPI Variables…………………………….……………………………….…….76
Fig. 18. Absolute Value of Discriminant Coefficients at Initial HURDAT entry,
TTG=24Hr, and Genesis during WARM years.…………………………….……99
Fig. 19. Absolute Value of Discriminant Coefficients at Initial HURDAT entry,
TTG=24Hr, and Genesis during COLD years.…………………………….…….99
Fig. 20. Absolute Value of Discriminant Coefficients at Initial HURDAT entry,
TTG=24Hr, and Genesis during NADA years.…………………………….…..100
Fig. 21. Statistical significance of the absolute value of vorticity stretching through
time…………………………….…….…………………………….…………..105
Fig. 22. Inverse relationship of vorticity stretching significance (dashed lines) and low-
level vorticity coefficient absolute values (solid lines).……………………….105
Fig. 23. TS Matthew…………………………….……………………………….…….115
Fig. 24. TS Franklin…………………………….……………………………….……..117
Fig. 25. TS Danny…………………………….……………………………….……….120
Fig. 26. TS Katrina…………………………….……………………………….………127
Fig. 27. Hurricane Katrina…………………………….………………………………..127
Fig. 28. Unconventional Structure of Hurricane Sandy…………………………….…..133
Fig. 29. LDA Functions…………………………….…………………………………..142
Fig. 30. Seasonal Figures (Low-level vorticity, Coriolis)………………………………143
Fig. 31. All Years Combined (Low-level vorticity, Coriolis)…………………………..144
Fig. 32. All Year Model Separation…………………………….………………………147
!xv Fig. 33. WARM Year Model Separation…………………………….………………….148
Fig. 34. COLD Year Model Separation…………………………….…………………..149
Fig. 35. Threat Scores vs. Forecast Hour from Hennon and Hobgood (2003)…………153
Fig. 36. Threat Score vs. Incubation Period / Threat Scores for 2010, 2012…………..155
Fig. 37. Pre-Genesis cases for WARM and COLD Study Years……………………….163
Fig. 38. Vorticity Vertical Profile, GO cases…………………………….……………..164
Fig. 39. Vorticity Vertical Profile, NOGO cases…………………………….………….164
Fig. 40. RH Vertical Profile, GO cases…………………………….…………………..165
Fig. 41. Convergence Vertical Profile, GO cases…………………………….…………165
Fig. 42. Vorticity Vertical Profile for WARM Years…………………………….……..166
Fig. 43. As in Fig. 42, but for COLD years…………………………….………………166
Fig. 44. Tangential Winds Vertical Profile from McBride and Zehr (1981b)…………..167
!xvi Chapter 1: Introduction
1.1 Relevance
With increased scrutiny on the global climate system over the last decade accompanying a greater awareness of anthropogenically-induced climate change, the exigency of extreme weather forecasting and climactic clairvoyance has become an issue of paramount importance. A number of studies have addressed the potential long-term ramifications of human-governed alteration of atmospheric composition and, in such works as the Intergovernmental Panel on Climate Change Assessment Reports (IPCC
ARs), representative concentration pathways have been utilized to prognosticate the impact of various atmospheric carbon concentrations on the ‘commitment’ and degree of
‘irreversibility’. Thus, due to the unprecedented nature of humanity’s influence upon the atmosphere and earth systems over the past two centuries, scientific inquiry addressing the trajectory of climate, and in particular, climate extremes, continues to be a burgeoning field that promises to shed light on the extent to which atmospheric phenomena will deviate from conventional limits.
!1 1.2 Forecasting
Of the vast array of extreme climactic phenomena, both multifarious and complex in nature, one of the foremost in power, influence, and general cultural fixation is the tropical cyclone. Under the framework of an atmosphere and ocean that are warming steadily due to the abundance of human-generated, heat-trapping atmospheric carbon, in combination with an expanding global population, the need to augment tropical cyclone forecasting and consequent mitigation strategies is foremost. While track forecasting of tropical cyclones and beta gyre behavior in the modern literature and operational fields generated by numerical models exhibits relatively high skill, intensity forecasting is an area of study that lags slightly behind in accuracy and consensus. To perhaps an even greater degree, the topic of tropical cyclogenesis (TCG hereafter) is a more nebulous and less understood process that often proves to be problematic, especially when swelling urban areas are provided with only limited warning of an approaching high-intensity system. The disparity between maximum azimuthal winds for tropical depressions, tropical storms, and hurricanes can signify multi-billion dollar differences in damage and marked difference in hazard to human life. Thus, it is unequivocally clear that the study fields of tropical cyclone intensification and TCG require more attention in order to address the deficiency in understanding of the thermodynamic and dynamic interactions that characterize these processes.
!2 1.3 Tropical cyclogenesis (TCG)
In regard to TCG specifically, the variety of theories expounding the genesis process reflects a relative lack of consensus on what the preeminent pathway(s) to cyclogenesis actually are. However, the difficulty in reaching said consensus resides in the fact that the modes of disturbance from basin to basin across the global climatology are numerous and complex. For example, the preponderance of North Atlantic hurricanes arise as a result of tropical waves (African Easterly Waves, AEWs) propagating from the west coast of Africa westward across the Atlantic Main Development Region (MDR).
However, a lower yet relevant number of tropical cyclones form over the Northeastern
Atlantic Ocean above Sea Surface Temperatures (SSTs) that are anomalously lower than the mean and within wind shear that is anomalously high from nontropical origins such as fronts, surface lows, and other baroclinic mechanisms (Mauk and Hobgood 2012). Thus, the modes of mid-level disturbance in discrete basins, and from basin to basin, may take the form of baroclinic perturbations or a wide range of zonally-propagating waves. These waves include eastward-propagating gravity waves and Kelvin waves, and westward- propagating gravity waves, mixed Rossby-gravity waves, and both baroclinic and equivalent barotropic Rossby waves. The frequency (square root of wave equation eigenvalue) of these waves intrinsically varies based on the mode type, but generally gravity waves exhibit the highest frequency and Rossby waves exhibit lower frequencies
(Hoskins and Pearce 1983).
!3 1.4 Stochasticity
It is important that the topics of stochasticity and determinism be addressed at the outset of the study in order to clarify the rationale for applying a statistical approach to the problem of cyclone formation. Deterministic provisions in application to scientific problems are functions of both the knowledge and scale employed in addressing thematter at hand. For example, microphysics involved in cloud formation and evolution may be treated stochastically when examining a broad-scale system by virtue of limiting resolution and, consequently, expanding a region in which subgrid-scale forces (in this case, arising from a lack of focus on cloud microphysics) may play significant roles in the involved processes. However, these microphysical processes, when studied by a cloud microphysicist, may be more thoroughly understood and parameterized in a separate research project with higher resolution and subgrid-scale minimization. Thus, stochasticity is a matter of both knowledge and expertise, and to a certain degree, relativity. In this paper, due to the coarseness of reanalysis data, the relative paucity of dropsonde data for MPI calculation, and the somewhat climatological nature of the study, the examination will be classified largely as a stochastic, broad-scale endeavor in order to relegate the smaller-scale deterministic processes to the umbrella of subgrid-scale forces.
Additionally, because of the chaotic nature of convection and convective paramaterization, thermodynamic and dynamic modeling presents a difficult and persistent problem. The cyclogenetic process, as opposed to the intensification process, lacks the conditions requisite for fundamental assumptions that facilitate the construction
!4 of modeling frameworks for a myriad of intensification regimes, such as the assumption of axisymmetry. For example, the axisymmetric assumption allows for the modeling and/ or computation of azimuthal means and eddies, such as the quantification of radial mean vorticity flux and radial eddy vorticity flux during a diabatic vortex merger process
(Hendricks et al. 2004). Thus, due to the difficulty of dynamical modeling and the intrinsically chaotic, nonlinear nature of the tropical cyclone formation process, this problem will be addressed through a stochastic approach, utilizing a statistical method to examine cyclogenesis over the North Atlantic basin with the hopes of further elucidating the variables that are most salient in regard to the formation of hurricanes, as well as their interdependent relationships.
1.5 Background
The most prominent criteria necessary for cyclogenesis are as follows: i) SSTs above 26.5℃ - 27.0℃ and a relatively deep ocean mixed layer (~50m), ii) a deep layer of conditional instability (the debated importance of which will be discussed subsequently), iii) enhanced low-level vorticity, iv) persistent, organized, deep moist convection with high mid-level humidity, and v) weak to moderate wind shear (~10 ms-1)
(Briegel and Frank 1997). Upon genesis, tropical cyclones (and in the specific context of the remainder of this work, hurricanes) are large-scale phenomena constituted by a primary circulation embedded within a secondary circulation centered around the eye from which the bulk of the storm energy is derived. This primary circulation is a vortical
!5 structure which lies within the secondary, toroidal circulation that functions as a Carnot
heat engine (Emanuel 1988) entrenched around the eye. Eye diameter spans a typical
range of 20-100km and eye pressure deficit can shrink to 10% of ambient pressure,
necessitating the extension of a colossal vertical warm core through the majority of the
troposphere, and in some cases, into the stratosphere (Tory and Frank 2010). The eye and
eyewall exhibit significantly higher moist entropy (θe), and conditions in the eye are calm due to subsidence. Vigorous ascent and maximum winds occur in the eyewall and surrounding regions and represent the culmination of friction-induced inflow, latent heat release, and surface latent and sensible heat fluxes encompassed by the concept of wind- induced surface heat exchange (WISHE) (Emanuel et al. 1984). This region comprises deep, vigorous convective clouds and serves as the root of spiral rainbands that extend radially from the eye of the storm. As tropical storms reach maturity, there is (typically) a concurrent approach to virtual axisymmetry, an assumption that is necessary, as previously stated, for the facilitation of a wide range of models and analysis.
Under the overarching assumption of axisymmetry, Kepert (2010) describes the eyewall as an “amphitheatre” of constant angular momentum surfaces in near gradient wind balance. The eyewall serves as the area of concentrated ascent in the secondary, toroidal circulation that is driven by latent heat release and Ekman inflow. This secondary circulation comprises areas of boundary layer inflow, eyewall and convective rainband upflow, and upper-level anticyclonic outflow. In regard to diagnosing the potential growth and/or maturity of the secondary circulation, there are two vital
!6 parameters: the Brunt-Väisälä frequency and the inertial stability. The Brunt-Väisälä
frequency quantifies the static stability i.e. the resistance to vertical motion, and is
expressed as
! where g is the acceleration due to gravity (9.8 m/s2), and the partial derivative is the
change in the natural log of potential temperature with respect to height.
In examining the equation, it is clear that maximizing the vertical potential temperature
gradient (i.e. increasing potential temperature with height) results in a high static stability,
while the steeper the lapse rate, the greater the instability. Inertial stability, as explained
in Holland (1987), is a circulation’s resistance to horizontal displacement and is
expressed as
! .
where r is the radial distance from the circulation center, Ma is angular momentum, f0 is
the Coriolis parameter, 𝜁 is relative vorticity in (s-1), and v is the azimuthal velocity in (m/ s). As can be seen from this equation, the enhancement of Coriolis force, relative vorticity, and azimuthal velocity, in combination with reduction of circulation radius, maximizes a system’s inertial stability.
Tropical cyclone formation theories abound, from “bottom-up”, “top-down showerhead”, and “top-down merger”, yet the archetypical foundation of tropical cyclogenesis hinges upon the enhancement (or lack thereof) of lower-level vorticity
!7 spinup due to the intrinsic dependence of a burgeoning warm core on ocean sensible and latent heat fluxes, regardless of the level of the initial vorticity preponderance. The “top- down showerhead” theory is clearly delineated in Bister and Emanuel (1987), “top-down merger” in works such as Simpson et al. (1998) and Ritchie and Holland (1997), and
“bottom-up” via vortical hot tower (or other such convective pulse) generation in works like Hendricks et al. (2004) and Montgomery and Enagonio (1998). Regardless of mechanism, tropical cyclone formation requires some form of mid-level disturbance, which often arises as a result of some sort of tropical wave. The aforementioned formation theories will be described in more depth subsequently in the literature review, as well as various theories regarding intensification and the theoretical upper bounds of
TC severity, or Maximum Potential Intensity (MPI, interchangeable with PI).
1.6 Questions
The impetus behind this TCG study is the desire to examine the interface between the climatologically-rooted, stochastic processes governing TCG activity in the North
Atlantic basin and elements of the dynamic processes that are correlated with climactic oscillations (in this case, ENSO). While the general suppression of TCG activity in the
North Atlantic corresponding to El Niño - or warm phase of ENSO (WARM) - is well- known, the discrete dynamic and thermodynamic processes that coincide with this TCG suppression are less understood. In the context of the aforementioned formation theories
(“bottom-up”, “top-down merger”, “top-down showerhead”), it is also of great import to
!8 inquire if there are modifications to the formation process corresponding with changes in
ENSO phase. Foremost of the potential research questions: does the statistical effectiveness of low-level vorticity as a predictor of subsequent development or nondevelopment of cloud clusters vary seasonally (in this case, corresponding to ENSO phases)? Does upper-level vorticity become more effective in the process of discriminating whether or not a cloud cluster will develop into a hurricane due to a poleward shift in TCG tendencies during La Niña? Does the change in shear conditions cause a corresponding change in development rates and incubation periods of cloud clusters that develop into hurricanes? Do development phases become accelerated during
La Niña years, or stymied during El Niño years? A statistical process - Linear
Discriminant Analysis - will be utilized to assess whether or not the ability of certain atmospheric and oceanic variables to discriminate between subsequent hurricane formation or pre-hurricane death changes coinciding with changes in ENSO phase, hopefully elucidating modifications in the development pathway that occur coinciding with certain ENSO phases. In other words, which variables, when calculated in the proximity of a convective area, will most effectively signal whether or not the area is a hurricane seedling, and how does the discriminating power of these variables change under El Niño phases versus La Niña or neutral phases?
!9 Chapter 2: Literature Review
2.1 Formation Theories
In the following pages, the various theories underlying tropical cyclone formation will be discussed.
2.1.1 Top-down merger
In Ritchie and Holland (1997), Typhoon Irving is examined using data from a variety of sources including the Tropical Cyclone Motion (TCM-92) experiment, satellite data, and soundings and analyzed by categorizing it as a dry-adiabatic vortex dynamics problem. Thus, moist processes, diabatic forcing, and other generally baroclinic modes are not involved in the process of studying Typhoon Irving. Irving formed in late July of
1992 as it propagated as a synoptic-scale surface gyre over the western North Pacific.
The region was dominated by an upper-level anticyclone and a convectively-suppressed environment. Mesoscale Convective Systems (MCSs) formed within the tropical depression, and Irving became a tropical storm on August 2 after sustained slow development. The large-scale, or background, environment became more favorable at a relatively dampened rate, slowly allowing for the organization of persistent, deep, moist
!10 convection and resulting MCSs requisite for genesis. The stages were characterized as follows: low-level circulation propagation, tropical upper-tropospheric trough interaction
(allowing for deep convection), and the merger of multiple MCSs over a series of several days. An important caveat regarding the satellite analysis is that, even though midlevel vortex motion can be tracked utilizing cloud motion, vortices and cloud clusters may not track together as well as might be hoped, because vortices associated with MCSs may outlive post-MCS decay. The limit on the efficacy of this study, undoubtedly, arises as a result of the fact that the Typhoon Irving case was treated as a dry-adiabatic dynamics problem.
One of the pioneering works to set the trajectory for TCG study through the “top- down merger” paradigm is Simpson et al. (1998) (S98) in which TCs Daisy and Oliver are examined within such a framework. The overarching umbrella for the work is drawn from Riehl and Malkus (1958) concerning the heat balance of the equatorial trough zone and the requirement for “hot towers” as undilute nuclei to propel moist entropy upwards in the rising branch of the Hadley cell, as opposed to widespread, slower ascent. Also apparent is the necessity of background vorticity to overcome the deleterious effects of gravity wave dispersion by reducing the Rossby radius of deformation to 200-300km as opposed to the typical tropical value of 3000km. The formation environment for TCs
Oliver and Daisy were significantly different, yet the modes of intensification were similar. Initially, Oliver formed in the Australian monsoon trough as an eastward- propagating vortex. Oliver comprised two intense mesoscale convective systems
!11 (MCSs), of which the eastern and stronger vortex became the storm center and the
weaker was sheared off to become Oliver’s primary rainband. Conversely, Daisy formed
from a tropical wave propagating across the Atlantic. The authors note that the more
poleward location of Daisy may have helped the vorticity spin-up (advection of planetary
vorticity). Oliver developed in a region of much greater shear at the entrance of a
westerly jet. However, in both instances, the eye developed at the periphery of
convection with sufficient area to provide a region of subsidence resulting from the moist
entropy propulsion into the atmosphere by the hot towers. It is estimated that 20 4x4km
updrafts or “hot towers” facilitated Oliver’s construction, and that 22 hot towers
constructed Daisy. The employed model supports a couple of assertions, namely that the
hot towers that top out at 16km are effective in transferring 352K θe air upwards through the majority of the troposphere, and that eye subsidence enhances genesis probability by facilitating a significant pressure drop. Additionally, S98 utilizes electrification to examine the updraft strength, updraft development rate, and mixed phase layer extent for the purpose of assessing the strengthening of TS Oliver.
2.1.2 Top-down showerhead
An effective example for the purposes of examining the “top-down showerhead” paradigm is a case study of Hurricane Guillermo utilizing the Tropical Experiment in
Mexico (TEXMEX) analyses and a nonhydrostatic, axisymmetric model performed by
Bister and Emanuel (Bister and Emanuel 1997) (BE97). To begin with, the authors
!12 emphasize that, in reference to Rotunno and Emanuel (1987) (RE87), the suppressive
effects of low moist entropy convective downdrafts into the boundary layer must be
overcome in order for TCG to transpire. RE87 explains that a tropospheric enhancement
of θe must occur to compensate for the injection of θe into the boundary layer air through the aforementioned convective downdrafts. Hurricane Guillermo began with the development of an MCS over the eastern North Pacific. TEXMEX analyses utilized in this study consist of Doppler radar data and in situ data comprising temperature and dewpoint measurements from the NOAA WP-3D and NCAR Electra aircrafts. The
Doppler wind field is important for the purposes of determining the extent of the cold core because, under the overarching assumption that the vortex is in balance with the thermal field, wind shear is a reflection of thermal anomalies in each layer. Anticyclonic wind shear indicates that the vortex is a warm core vortex, and the reverse is true for cyclonic shear. Between the cold core and subsequent warm core phase of Guillermo’s development, a 7% increase in boundary layer relative humidity and 3K increase in θe
indicated that the primary difference in the cold to warm core transition lies in moistening
of the boundary layer. One of the foremost goals of TEXMEX was to determine if
enhanced moist entropy in the middle troposphere is a necessary and sufficient condition
for TCG. In the case of Guillermo, the midlevel θe remained constant before an
accelerated period of strengthening in the low-level winds, indicating that intensification
was independent of mid-level moist entropy augmentation. The questions then were as
follows: how did an initial disturbance with a cold-core rotation and high relative
!13 humidity germinate in the stratiform precipitation region of the MCS? Is a cold-core
vortex conducive to TCG? Is the cold-core disturbance or high relative humidity more
indispensable to the TCG process?
Before completing the numerical model simulations, BE97 call on the work of
Chen and Frank (1993) and infer that Hurricane Guillermo formed from an initial MCS
with an expansive stratiform precipitation region. The authors postulate that diabatic
heating in the upper troposphere and a corresponding cooling below generate a midlevel
vortex that, in conjunction with a moistening lower level due to evaporation of rain, leads
to a downdraft that propels vorticity downward and effectively reinitiates convection.
This amplifies the vorticity and results in a warm core vortex.
Following numerical simulations, the authors largely confirm their initial
hypothesis in regard to the formation mechanism of Hurricane Guillermo. Due to the
diabatic processes of evaporative cooling and upper-tropospheric (anvil) heating during
the lifespan of an MCS, a lower-level cold core and upper-level warm core develops.
The lower-level cold core lies above a stratum of warm and dry air resulting from
subsidence compression. During the vortex enhancement period, vorticity spirals down
to the lower levels and reignites convection in a twofold manner: increasing surface
enthalpy and latent heat fluxes, and the overlying cold core decreasing the necessary θe for convection to occur. The catalyzed convection increases boundary layer moist entropy, effectively increasing storm intensity and inhibiting evaporation of rain and, thus, downdraft destruction. Therefore, the cold-core vortex that extends to the lower
!14 levels from initial mid-levels is the vehicle by which the oft-destructive influence of convective downdrafts is overcome.
2.1.3 Bottom-up
Of the various proponents of a “bottom-up” cyclogenesis paradigm, Hendricks et al. perform (H04) a 2004 case study examining the role of vortical hot towers in the formation of Tropical Cyclone Diana utilizing a 3-km cloud-resolving numerical simulation with the PSU-NCAR MM5 version 2.0 model and initial conditions provided by NCEP-NCAR reanalysis data. H04 makes the important note that the VHTs in the simulation of TC Diana are differentiated from tropical hot towers, as expounded in Riehl and Malkus (1958), due to the intense vorticity in their cores which inhibits lateral entrainment that could enervate vigorous ascent. The powerful updrafts in hot towers cores converge and stretch embedded low-level vorticity into smaller vortex tubes, thus resulting in heat-injecting VHTs. H04 characterizes the organization process with two tiers; the first is one in which the hot towers precondition the VHT construction by augmenting low-level potential vorticity (PV) anomalies, and the second is typified by diabatic vortex merger and axisymmetrization of the PV hotspots. Dynamically, during the first phase, the dominant term in the tangential momentum budget is the mean radial vorticity flux. Vortex merger is easily identified operationally and in modeling by noting a significant increase in positive contribution to vorticity through the eddy radial vorticity flux terms (in cylindrical coordinates, -u’ζ’ ≥ 0). Via these two stages of vortex
!15 enhancement, the hot towers in combination with convergence of low-level azimuthal momentum, “cascade” vertical vorticity from hot tower to TC scale.
Another work supporting the “bottom-up” framework for TCG is Montgomery et al. (2006) (M06), in which the question of how a synoptic-scale disturbance can evolve into a surface-based, WISHE amplified vortex is addressed. M06 briefly visits the concept of hot towers, originally promulgated by Riehl and Malkus 1958, and proceeds to refer back to H04 to establish the context of a two-tiered development process comprising vortical preconditioning of the pre-TCG environment by VHTs and the competition for CAPE and tangential momentum, followed by diabatic vortex merger accompanied by axisymmetrization. In this study, numerical simulations were performed utilizing the Regional Atmospheric Modeling System (RAMS), initialized with the mean
Atlantic hurricane season sounding (Jordan 1958), a SST of 29℃, and a single mesoscale convective vortex (MCV). VHTs rotate around the MCV at approximately 0.6-0.9 times the velocity of the MCV tangential winds. Results of the experiment conveyed that the system scale spinup of low-level tangential winds was due predominantly to the mean radial influx of absolute vorticity (-ū̄ η). The study concludes that the initial MCV provides a convectively unstable and vortically-rich environment for VHTs that form as a result of tilting and stretching of preexisting vorticity tubes via hot tower updrafts. The
MCV and surrounding VHTs generate an environment that protects and enhances moist entropy and builds latent heat driven rotational energy. A resulting toroidal circulation in
!16 quasi-Sawyer-Eliassen balance collects low and mid-level vorticity of the initial MCV and associated VHTs.
2.2 Construction
An important competitive interaction that can either facilitate or enervate cloud cluster development is that which occurs between convective processes and vertical wind shear during the initial growth phases. Vertical wind shear in increasing magnitude, as has been previously stated, has a progressively suppressive effect on cloud cluster development and often prevents TCG. While in mid-latitudes shear and helicity can facilitate organization of instability, the opposite effect occurs in low latitude, equatorial bound regions. Shear can often introduce the destructive effects of dry entrainment or whisk away high moist entropy air needed to power the Carnot heat engine. Conversely, persistent, deep, organized moist convection is necessary for vorticity seedlings to germinate into tropical cyclone-scale systems.
2.2.1 Convection
Raymond and Sessions (2007) explore the dynamic convective processes that occur during the cyclogenetic process and how surface flow and fluxes change during said process. In referencing multiple sources, RS07 establishes the fundamental principle that, under typical conditions, deep, moist, persistent convection over the tropical ocean has maximum vertical mass flux in the upper troposphere, indicating that inflow is spread
!17 over a deep layer throughout the remainder of the underlying troposphere. These convective areas result in downdrafts that often cause outflow in the lowest levels. Thus, as governed by the circulation theorem, the inflow profile is characterized by preferential development of increased vertical vorticity in mid-levels. RS07 references Emanuel
(1989) to point out that, as accentuated in the “top-down showerhead” theory, that shallow and nonprecipitating convection enhances mid-level moisture content so that convective downdrafts are inhibited, allowing for unimpeded lower-level convergence and spinup-associated surface sensible and latent heat fluxes. As indicated in the
TEXMEX analysis, the level of non-divergence (transition level between inflow and outflow) did lower during this mid-level moistening, indicating a compression of the vertical extent of inflow and thus concentration of convergence. By utilizing numerical cloud models to gauge gross moist stability (GMS) as a proxy for precipitation efficiency, the authors determine that moistening of the deep convective column results in more rainfall per unit surface moist entropy flux (increased precipitation efficiency), but increasing mid-level stabilization of the column also accomplishes this and additionally concentrates inflow into a shallower layer and thus enhances low-level vorticity convergence per unit rainfall. Therefore, column stabilization wields greater efficacy in facilitating spinup of vorticity than column moisture injection. Additionally, the authors believe that the lowering of the level of nondivergence is predominantly due to column stabilization rather than moistening.
!18 2.2.2 Shear
Tory et al. (2007) complete part III of a close inspection of the Australian Bureau of Meteorology’s Tropical Cyclone Limited Area Prediction System (TC-LAPS), which is an operational numerical weather prediction (NWP) model. In this work, five storms are simulated. In parts I and II, two vortex amplification mechanisms were analyzed in a
TC-LAPS simulation of TC Chris. The primary mechanism was the construction of vortex cores in convective updrafts through horizontal and vertical propulsion of absolute vorticity. The secondary mechanism was the system-scale intensification (SSI), or the large-scale adaptation to the vigorous convective cores, with enhanced lower and mid- level absolute vorticity convergence and an augmented toroidal circulation. The former mechanism largely involves convective vortex enhancement (CVE), while the latter comprises stratiform vortex enhancement (SVE). Tory favors the pervasive use of the terms “battle” or “balance” between constructive convection and destructive shear.
Convective, vortical updrafts tend to align - or following tilting, realign - potential vorticity (PV) cores in burgeoning storms. A few notes of particular import surface in the work. One, for example, concerns the simulation of TC Erica. Tory et al. indicate that the failure to spinup a PV “monolith”, as well as the “updraft implosion” correlated with large-amplitude gravity wave dispersion, could have indicated that the system-scale cyclonic environment was too weak, thus implying that the SSI process is vital for the genesis of storms. In the simulation of extratropical cyclone Evan, an environment characterized by relatively favorable vortical conditions, including both cyclonic
!19 environmental flow and persistent deep convection, does not guarantee genesis, as shear ripped apart both individual and monolithic PV cores. Overall, the SSI intensification process will prove to be a vital part of the analysis for this experiment.
A comprehensive investigation of the spatial orientation of vertical wind shear over a developing system is completed in Rappin and Nolan 2012. This study is completed employing numerical simulations of environments of radiative-convective equilibrium (RCE). In the simulations, the wind shear vector is either aligned or counter- aligned with the mean surface wind. The three scenarios are as follows: one in which the shear is aligned with a modest surface wind, one in which shear is counter-aligned with a smaller mean surface wind, and a third in which shear is counter-aligned with a larger mean surface wind. There are no differences in the magnitude of the storm-relative flow with increasing height, but the time to genesis varies across all the cases, indicating that the alignment does have significant impact on the evolution of system intensity. Time to genesis decreases under conditions of shear and motion counter-alignment, even if surface winds exceed that of the alignment simulation. When surface wind is increased, the potential intensity decreases and the incubation period increases. The time to genesis hinges upon vortex tilt, which is most profoundly affected by the orientation of the vertical shear vector relative to mean surface flow. Under alignment conditions, the dry boundary-layer flank is entrained into the up-shear flank, which, in combination with lower and mid-level subsidence, decreases column-integrated saturation levels down- wind of the convection and, consequently, down-wind propagation of convection is
!20 stymied. Without down-wind convective development, vortex tilt becomes large, precession rate (or swirl of vortex axis orientation) decreases, and, as a result of slower precession rate, storm-scale moistening is inhibited and, thus, intensification. Under a counter-alignment regime, the aforementioned dry boundary-layer air is instead spun up into the downshear flank, where mechanically-forced convection and enhanced surface latent heat flux moistens the down-wind boundary layer. Therefore, convection propagates downwind, resulting in decreased tilt due to propagation of the mid-level vortex into the up-shear flank, unimpeded precession rate, and rapid intensification.
Additionally, the attenuated tilt allows for more downwind, up-shear moistening prior to convective vortex enhancement (CVE) due to the stratiform precipitation region of
Emanuel’s showerhead mechanism.
2.3 Intensification Theories
Two of the foremost theories behind intensification of tropical cyclones are
Conditional Instability of the Second Kind (CISK) and the Air-Sea Interaction, or more widely-known as Wind-Induced Surface Heat Exchange (WISHE). Within the last few decades, CISK has become a secondary focus in favor of augmented support of the
WISHE vehicle. CISK, for a long time, was seen as the essential vehicle of intensification in tropical cyclone regimes, as early models and studies focused almost exclusively on the dynamics of moist convection. The theoretical flaw in these models is that they grew as a result of linear instability so that the smallest disturbances in
!21 horizontal scale should intensify most rapidly, which clearly contradicts conventional
knowledge and observation of horizontal hurricane scales. Charney and Eliassen (1964)
proposed that the secondary, toroidal circulation of a nascent, large-scale vortex could
organize the microscale, randomly-dispersed cumulus clouds near the vortex center. This
coalescent convection at the vortex center would then serve as a heat source leading to
the tropical cyclone intensification. The secondary circulation would advect the
necessary moist entropy for sustained convection and, hence, intensification, ad
infinitum. In Emanuel (1986) and Rotunno and Emanuel (1987), a model of
intensification is established (the forerunner of the more recent MPI model) in which
Charney and Eliassen’s theory of CISK is discarded as the primary vehicle by which
disturbances rapidly intensify. One of the initial observations in the work is that
empirical observations have indicated that boundary layer moist entropy values are too
high for mere convergence, thus indicating that there must be another moist entropy
source. Emanuel notes that, previous to the study, the influences of CISK and air-sea
interaction had not clearly been differentiated as nearly all numerical simulations in a
variety of studies had initial conditions including some amount of preexisting conditional
instability. Emanuel demonstrates that tropical cyclones can be maintained in an intense
steady state without inputs from ambient conditional instability. The model is,
essentially, a Carnot heat engine, with thermodynamic efficiency defined as (TB - TOUT)/
TB, where TB is the temperature at the ocean surface and TOUT is the outflow temperature in the upper-levels. This seminal work served as the beginning phase of disproving the
!22 prevailing paradigm of the time that CISK was the primary mechanism of intensification in tropical cyclones by demonstrating that surface exchange of enthalpy is sufficient in maintaining an intense steady-state hurricane model. In addition to steady-state maintenance, Emanuel (1987) demonstrates that this model not only allows for the steady-state maintenance of an intense tropical cyclone without conditional instability, but also for the growth of a finite-amplitude disturbance within an environment of neutral stability to moist convection. Emanuel asserts that a mechanism of air-sea interaction instability accounts for the growth of the hurricane-like vortex in which surface fluxes of latent and sensible heat enhance boundary layer moist entropy, which is then propelled along angular momentum surfaces aloft, resulting in an intensification of the circulation and, in turn, an increase in the wind-induced surface exchanges. The essential difference between CISK and the air-sea interaction instability mechanism, as noted by the authors, is that CISK relies on the spatial organization of the conversion of latent to sensible heat through cumulus convection, whereas wind-induced surface heat exchange hinges upon the injection of heat from the ocean into the Carnot heat engine.
2.4 Maximum Potential Intensity
Maximum Potential Intensity (MPI) is the minimum achievable central pressure or maximum sustained azimuthal winds a cyclonic circulation may reach given a set of thermodynamic and/or dynamic parameters. The literature contains a number of different models utilized to calculate MPI, most of which involve a combination of
!23 thermodynamic and dynamic processes to predict the theoretical upper limit of a given tropical-cyclone scale system.
2.4.1 DeMaria and Kaplan
One of the essential areas of study and forecasting in TC development is the theoretical and/or empirical upper bounds on the intensity a storm may reach given certain initial conditions like SST, boundary layer relative humidity, surface exchange coefficients, and temperature at the level of neutral buoyancy (alternatively, the temperature at the outflow layer or the temperature at the equilibrium level). It is often calculated as a minimum achievable central pressure or maximum achievable 1-min sustained azimuthal winds. Sources refer to this upper bound as Maximum Potential
Intensity (MPI) or Potential Intensity (PI), and this limit should only grow in its forecasting power and research salience as the global climate continues to evolve in accordance with anthropogenically-induced increase in atmospheric GHG concentrations.
DeMaria and Kaplan (1994) identify an important empirical nexus between SST and the
MPI of Atlantic basin hurricanes using Emanuel’s theoretical MPI calculation (to be examined shortly). One of the first observations in the introduction to this study explains that SST is not a good predictor of the intensity a storm will achieve but, rather, the theoretical maximum the storm could approach given a combination of ideal conditions.
The authors conducted a comprehensive collection of data for the period 1962-1992, acquiring the SSTs from the Geophysical Fluid Dynamics Laboratory (GFDL) and
!24 maximum winds from the NHC archive. Maximum winds were plotted vs. the SSTs for the storms, and an exponential function involving empirically-derived constants and the difference between observed SST and an assigned initial SST was utilized to fit the resulting curve. The authors note that, while Emanuel’s theoretical MPI relied on SST, outflow layer temperature, and boundary layer relative humidity, to a first approximation,
MPI depended on SST. This approximation also requires the assumption of uniform relative humidity across the tropical atmosphere, and that the outflow temperature is estimated by the tropopause temperature and profoundly controlled by SST. The study leads one to conclude that the empirically-derived connection between intensity and SST is in relatively good agreement with the theoretical MPI drawn from Emanuel, provided that the tropopause temperature is controlled by SST.
2.4.2 Holland
Holland (1997) utilizes a thermodynamic framework to analyze and assess the primary factors influencing the maximum achievable potential intensity of a tropical cyclone. A model is formulated based on the available thermodynamic energy in the hurricane environment, including the ocean. As highlighted in the abstract, the MPI model derived in this work is very sensitive to surface relative humidity under the eyewall, height of the warm core, and to slight modifications of SST. In essence, the model utilizes the concept of the available energy for work determined by the maximum entropy difference between the storm center and the peripheral environment.
!25 Temperature, specific humidity, and pressure are evaluated at the initial level, with surface equivalent potential temperature calculated from the surface temperature and surface mixing ratio. The temperature anomaly in the eyewall is solved iteratively by utilizing a saturated column with constant saturated eyewall equivalent potential temperature equal to the surface equivalent potential temperature. The change in surface pressure due to warming aloft is calculated, and this pressure fall is the resulting MPI.
An important note is that, because surface equivalent potential temperature and surface pressure are codependent, pressure falls result in increased surface equivalent potential temperature, and subsequently additional pressure attenuation, thus comprising a cyclical development mechanism.
2.4.3 Emanuel
Emanuel delineates MPI by utilizing a Carnot cycle model that is a proxy for the secondary, toroidal circulation of TCs. The Carnot cycle within the TC framework is characterized by low-level inflow constituting the isothermal expansion phase, followed by moist adiabatic ascent in the eyewall (adiabatic expansion), upper tropospheric outflow (isothermal compression), and peripheral environmental descent on the outer edges of the storm (adiabatic compression). In the context of this model, MPI, quantified by maximum azimuthal velocity and minimum central pressure, is determined by combining the thermal wind equation and a near-eyewall boundary layer entropy equation to obtain
!26 ! .
One can see that the projected maximum wind is the square root of thermodynamic
efficiency (where Ts is the sea surface temperature and TO is the outflow temperature), the ratio of surface exchange coefficients (Ck - enthalpy, Cd - momentum/drag), and the difference between the surface saturation equivalent potential temperature and the boundary layer equivalent potential temperature. Alternatively, this equation may be expressed as
! which contains the path integral of temperature integrated over the difference in entropy at each isobaric level. Yet another way to express this computationally is
! where CAPE* is the saturation CAPE evaluated near the radius of maximum winds and
CAPE is simply the boundary layer air near the radius of maximum winds. Minimum central pressure can be calculated as follows:
!27 !
which, after simplifying, becomes
! .
The four numbered equations above were derived more fully in Bister and Emanuel
(2002a).
2.5 Climatology
!
FIG. 1. Vertical wind shear (ms-1), 2010 (La Niña) minus 2009 (El Niño), dimensionally averaged over time (June - November) in 2.5°x2.5° grid using NCEP-NCAR Reanalysis II. Red areas show the greatest positive shear disparities, while violets and dark blues reflect most negative shear disparities. Graphic created using Google Maps JavaScript API v3, OpenGIS® Web Map Service, ArcGIS 10.0, and NCL for calculations. Shown is a swath of significantly reduced shear over the upper half of the MDR extending into the Caribbean during the 2010 La Niña phase as compared to the 2009 El Niño phase.
!28
2.5.1 Climatological Oscillations
Forecasting climatologically-related trends remains one of the greater challenges in atmospheric science, as persistence, teleconnections, and the myriad of climate oscillations, in conjunction, pose a problem of unique and highly multivariate complexity.
Of the myriad of climate oscillations, there are a number of more commonly referenced ones in the United States, such as the Arctic Oscillation (AO), the North Atlantic
Oscillation (NAO), and especially El Niño-Southern Oscillation (ENSO). Other oscillations include the Pacific Decadal Oscillation (PDO), the interseasonal Madden-
Julian Oscillation (MJO), and the Atlantic Multidecadal Oscillation (AMO). Of particular import in this study is ENSO and its effects on Atlantic tropical cyclone activity and, more specifically, how it proximately affects the cyclogenetic process.
2.5.2 El Niño-Southern Oscillation (ENSO)
The effects of ENSO change are well-documented in relation to the manifestation of TCG frequency and location across the global basins, and in one study, a Genesis
Potential Index is employed to analyze ENSO effects in each of the basins. The Genesis
Potential at a point is calculated by
! ,
!29 as developed by Emanuel and Nolan (2004). It requires absolute vorticity at 850 mb (η), relative humidity at 600mb (ℋ), potential intensity (Vpot), and shear850-200mb (Vshear) as input. The climatology of the GP per basin is described in the study, and there is generally solid agreement between the calculated annual GPs and the observed quantity of TCs. In regard to the Atlantic, during El Niño (WARM) phases, there is a trend of suppressed TC activity, while the opposite occurs during La Niña (COLD) periods.
Pielke and Landsea (1999) indicates that hurricane damages are much higher in the
United States collectively during COLD as opposed to WARM, indicating an increased frequency and intensity of landfalling hurricanes during COLD. The primary indices to which the differences in TCG behavior have been attributed are vertical wind shear and the tropospheric column stability over the North Atlantic due to a disparity between advanced tropospheric warming during WARM and lagging increases in SSTs (Tang and
Neelin 2004). To examine ENSO influence on the GP index, the Niño-3.4 index is utilized in Camargo et al. (2007) to identify El Niño/La Niña events, considering the
August-September-October values. In the Atlantic, relative humidity has the strongest contribution to GP, followed closely by wind shear. Potential intensity and vorticity play more marginal roles in the GP index calculations. As far as diagnosing the GP index’s ability to forecast ENSO effects accurately across the global basins, the index performed well in reproducing the most widely-known signals such as suppression in the Atlantic
(Camargo et al. 2007).
!30 Continuing with the theme of North Atlantic TC suppression correlated with
ENSO activity, the phenomenology is tied intrinsically to the enhancement of tropospheric westerlies over the North Atlantic during WARM. The increase in magnitude of these westerlies generates a swath of augmented vertical wind shear over the Atlantic Main Development Region (MDR) which is confined to 10-20°N latitude.
Due to the statistical proclivity for the preponderance of Atlantic hurricanes to form from
African easterly waves (AEWs) generated over the Sahara and which propagate westward off the west coast of Africa, this modification of wind shear over the MDR profoundly affects the fate of cloud clusters traveling within areas of convective excitation associated with these tropical waves. Shaman et al. (2009) notes that the dynamical foundation underlying the ENSO-Atlantic TCG teleconnection has not been clearly elucidated, and that the goal of the study was to accomplish such a task. In this study, the role of the North African-Asian (NAA) jet is heavily emphasized as the
“teleconnective bridge” between different regions, and that, within this framework, observations and models indicate that intertropical convergence zone (ITCZ) convection coinciding with WARM conditions creates a vorticity signal within and just south of the
NAA jet. This vorticity modification correlates well with an increase in vertical wind shear over the north Atlantic MDR. During the Northern Hemisphere summer, convective anomalies correlated with WARM form along the ITCZ from 150°E to 80°W and in between the equator and 10°N latitude. Solutions of the linearized barotropic vorticity equation in conjunction with these Pacific convective anomalies indicate a
!31 westward-propagating barotropic Rossby wave affecting NAA jet behavior. The ENSO- governed MDR shear anomaly exhibits greatest magnitude during July, but, due to the counteractive motion of eastward-propagating barotropic Rossby waves during months later in the hurricane season cycle. The foremost conclusion reached is that ENSO- governed variability in TCG activity in the Atlantic is a product of Pacific-based, convectively-generated, competing westward- and eastward-propagating barotropic
Rossby waves. The findings are summarized as follows: 1) during hurricane season, El
Niño convective activity over the equatorial Pacific sparks westward-propagating barotropic Rossby waves that generate upper-tropospheric vorticity responses to the north, south, and interior of the NAA jet that extends over the Atlantic MDR, creating nondivergent westerly anomalies that increase shear and inhibit TCG, 2) El Niño convective activity also stimulates eastward-propagating barotropic Rossby waves
(BRWs) that, by October, create vorticity responses that interfere with the previously mentioned vorticity responses generated by westward-propagating waves, effectively neutralizing the zonal vertical shear modification by October, 3) September is most sensitive to ENSO variability due to NAA jet position on the northern edge of the MDR and LMDR, creating positive vorticity anomalies along the jet core due to the westward- propagating BRWs, effectively producing strong nondivergent westerly anomalies and inhibiting TCG, 4) October is free from ENSO variability, due to the previously mentioned counter-action of eastward-propagating BRWs and the southerly shift of the
NAA jet so that the vorticity disturbances associated with it flow south of the MDR, and
!32 5) the September to October transition of ENSO influence coincides nicely with ENSO-
related changes to upper-tropospheric vorticity, zonal winds, and zonal wind vertical
shear. The authors state that as the climate continues to change as a result of
anthropogenic activity, tropospheric changes could herald a repression of the eastward-
propagating barotropic Rossby waves, thus influencing vertical wind shear modifications
and, hypothetically, Atlantic basin TCG activity.
2.5.3 Future projections
In the wake of the IPCC’s Second Assessment Report, Henderson-Sellers et al.
(1998) (HS98) summarizes the potential ramifications accompanying IPCC-projected
greenhouse gas (GHG) concentration modifications. HS98 calls upon Holland (1997) to
comment upon changes in environmental conduciveness corresponding to the projected
atmospheric GHG changes, and that favorability may and probably will increase with an
increase in GHG concentrations. General Circulation Models (GCMs) also indicate that
large-scale circulations, including tropical monsoons and trade winds, will grow in
strength, theoretically enhancing the frequency of initial mid-level disturbances. In
regard to potential intensity, there is a projected 10-20% increase expected accompanying
-1 a doubling of CO2 in the atmosphere. Knutson et al. (1998) calculates a 3-7 ms increase in global PI with a 2.2℃ increase in global mean SST. However, there is an expected enhancement of upper-tropospheric winds, thus indicating greater shear and suppressive conditions that could counteract the potential increase in disturbance frequencies and
!33 circulation strengths. Again recalling Holland (1997), HS98 indicates that TCG will happen at higher SSTs in a GHG-modified climate due to upper-tropospheric warming that compensates for the widespread increase in ocean surface temperatures. On the changes in frequency of actual TCG on a global scale coinciding with an anthropogenically-warmed ocean-atmosphere system, the research is rather inconclusive and lacks consensus. Additionally, due to the unprecedented nature of projected future anthropogenically-induced GHG increase, many preexisting models and genesis parameters are not necessarily reliable or accurate, as they operate within the framework of precedent and current climate conditions. For example, Watterson et al. (1995) utilizesGray’s seasonal genesis parameters in a GCM to project areas and frequency of
TCG globally, and while displaying accuracy in modeling genesis regions relative to climatological observations, the model struggles to accurately recreate TCG frequency.
2.5.4 Research questions
The impetus behind this TCG study is the desire to examine the interface between the climatologically-rooted, stochastic processes governing TCG activity in the North
Atlantic basin and elements of the dynamic processes that are correlated with climactic oscillations (in this case, ENSO). In this paper, TCG, or tropical cyclogenesis, will refer to hurricane genesis, with ‘developing’, or ‘GO’ cloud clusters, as systems that will eventually reach hurricane strength and ‘nondeveloping’, or ‘NOGO’ clusters as those that do not ever reach hurricane classification in their lifecycles. While the general
!34 suppression of TCG activity in the North Atlantic corresponding to El Niño - or warm
phase of ENSO (WARM) - is well-known, the discrete dynamic and thermodynamic
processes that coincide with this TCG suppression are less understood. In the context of
the aforementioned formation theories (“bottom-up”, “top-down merger”, “top-down
showerhead”), it is also of great import to inquire if there are modifications to the
formation process corresponding with changes in ENSO phase. For example, does the
importance of low-level vorticity change in regard to its forecasting capacity as to
whether or not a cloud cluster over the North Atlantic will develop into a hurricane or
not? Does upper-level vorticity become more salient in the process of discriminating
whether or not a cloud cluster will develop into a hurricane due to a poleward shift in
TCG tendencies during La Niña (ENSO COLD)? Does increased shear over the Atlantic
MDR during WARM change the incubation period of cloud clusters (the amount of time
it takes for a tropical depression to develop into a hurricane)? A statistical process -
Linear Discriminant Analysis - will be utilized to assess whether or not the ability of
certain atmospheric and oceanic variables to discriminate between subsequent hurricane
formation or pre-hurricane death changes coinciding with changes in ENSO phase, hopefully elucidating modifications in the development pathway that occur coinciding with certain ENSO phases. In other words, which variables, when calculated in the proximity of a convective area, will most effectively signal whether or not the area is a hurricane seedling, and how does the discriminating power of these variables change under El Niño phases versus La Niña or neutral phases?
!35 Chapter 3: Methods
3.1 Introduction to Linear Discriminant Analysis (LDA)
Due to the quasi-stochastic nature of TCG, as opposed to deterministic atmospheric interactions, statistical analysis becomes paramount in assessing relative contributions from physical processes in the pre-TCG environment. This fundamental tenet is reinforced in Simpson et al. (1997) which draws from Ooyama (1982) to assert that attempts at reaching deterministic premises for tropical cyclone behavior are exercises in futility. S97 further emphasizes the lack of deterministic processes behind tropical cyclone behavior by keying in on the unequivocally stochastic facets of mesoscale vortex interactions. Thus, the mesoscale pre-conditioning of the tropical environment can be treated as a somewhat stochastic, chaotic question rather than a deterministic one. One caveat concerning the classification of the tropical cyclone formation process as quasi-stochastic is that stochastic versus deterministic designations are fluid matters with respect to both knowledge and scale. High resolution cloud studies conducted by cloud microphysics experts may be, for example, deterministic studies governed by well-defined physical models, whereas a climatologist may conduct broad- scale circulation studies with stochastic assumptions regarding cloud microphysical
!36 processes. For the sake of this study, such processes will be addressed as quasi-stochastic problems.
3.1.1 Literature-based variable selection rationale
Continuing with the previously mentioned idea of shear orientation and its effect on the incubation period of pre-TCG cloud clusters, Hennon and Hobgood (2003)
(HH03) utilize linear discriminant analysis to provide a statistical framework for the probability of formation based on a number of variables box-averaged over the areal extent of cloud clusters at 6-hour intervals during the 48 hours preceding a genesis event.
Candidate cloud clusters meeting certain areal, vertical, and temporal threshold criteria are identified through satellite imagery analysis during hurricane season for a three year period and developing cases are binned at the aforementioned 6-hr intervals according to the time to genesis together with all of the nondeveloping cases. NCEP/NCAR reanalysis data is pulled and analyzed at the certain times and locations of each of the clusters to determine box-average values of various predictors. Linear discriminant analysis is then performed on the linear system of equations to determine the coefficients of each of the predictors - that is, the relative discriminating power of each of the predictors between subsequent genesis or deterioration. Out of the analyzed predictors, HH03 find that the
Daily Genesis Potential (DGP) and the Coriolis parameter (latitude/advection of planetary vorticity/Rossby radius of deformation reduction) wield the most discriminating power between development and nondevelopment.
!37 As opposed to the Atlantic focus of HH03, Perrone and Lowe (1986) (PL86) perform a similar analysis addressing cyclone formation in the North Pacific. In this study, a variety of predictors, in combination with the gradient and the Laplacian of these predictors, are analyzed for the cloud clusters identified in the North Pacific. At 24 hours, the classification functions indicate that the Coriolis parameter, low-level vorticity
(at 2.5 and 5° box average), the local maximum of the magnitude of the gradient of the product of low-level vorticity and divergence (maximum of the gradient of the vorticity stretching term), and the Laplacian of upper-level vorticity are the best discriminators between development and nondevelopment (in the study, GO and NO GO). For the 48 hour bin preceding genesis, the preeminent discriminators are low-level vorticity, low- level divergence, the local maximum of equivalent potential temperature, and the local maximum of moist static stability (defined in the study as the difference between the equivalent potential temperature at 950mb and 500mb). Lastly, at 72 hours, the most significant predictor is low-level vorticity averaged at 5°.
Kerns and Chen (2013) (KC13) perform a similar analysis over the North Pacific with slightly different constructs. For identification of candidate cloud clusters, KC13 utilizes Multifunctional Transport Satellites (MTSAT) infrared channels to track cloud clusters through their life cycle. Utilized is a size threshold of 5000 km2 (80 km diameter) with a temperature threshold of 208 K cloud-top temperature via infrared imagery. Cloud clusters that overlap by at least half of their respective areas are assigned to the same cluster. To supplement infrared identification of candidate cloud clusters,
!38 KC13 utilizes a vorticity maximum tracking algorithm via NCEP FNL relative vorticity values at 850 hPa. If clusters were within 3 deg. radius of best track archives for a given
TC, then they are classified as TC clusters and not included in the LDA. In regard to timescale, only the 8-h minimum duration clusters are candidates for TC genesis. Among predictors, the best discriminators are low-level vorticity and low-level convergence.
Additionally, lower vertical wind shear and higher water vapor content typify conditions leading to development. SST plays little to no role in discriminating between development and nondevelopment. In regard to evolution, the environment becomes more favorable with time for developing systems. Conversely, nondeveloping clusters initially reside in more favorable conditions, after which the favorability ebbs.
Schumacher et al. (2009) (S09) perform a related analysis for 24-h probabilities of
TCG over the eastern Pacific, western Pacific, and Atlantic basins utilizing NCEP GFS analysis fields, ~6.7 micrometer wavelength water vapor imagery from multiple geostationary satellite platforms, and a resulting succession of two-step analysis comprising a screening step that removes all conditions highly deleterious to TCG and consequently an LDA step. Unlike PL86 and HH03, S09 utilize convective parameters derived from microwave imagery in combination with environmental parameters instead of limiting analysis to tropical cloud clusters. S09 argue that removing the need for subjective identification of cloud clusters facilitates the formation of an objective, spatiotemporally continuous product for the estimation of TCG probability over an enlarged domain. Over the three basin areas, 5x5 degree boxes are constructed to divide
!39 the domain into 450 boxes over which the parameters would be averaged for every 6-h observation interval. The best discriminators in this study are climatology, 850-hPa circulation, and distance from existing TC. The algorithm developed in this study is in use as the NESDIS TCFP product. In regard to future work, S09 highlight the need for expansion of the parameter set, including indices like the positions and the Dvorak intensities for invest systems supplied by NCEP/TPC Tropical Analysis and Forecast
Branch. Also, Frank and Roundy’s (2006) examination of atmospheric wave precursors introduces the need for exploration of upstream convective parameters to include in the
LDA.
In the pioneering work, McBride (1981a), a comprehensive composite data set engineered from rawinsonde data in the northwest Pacific and tropical northwest Atlantic
Oceans is utilized in order to assess various morphological processes and characteristics of non-developing cloud clusters and developing cyclones. Overall, the composited systems reside in the easterly winds, where the Atlantic systems are wholly engulfed in the easterly trades. The systems also reside near the subtropical ridge at the 200mb level.
Cloud clusters and cyclones are typified by an upper-level warm core and positive moisture anomalies. Positive vorticity and convergence exist from the surface level to
350mb level, above which the systems are characterized by divergence and anticylonic tendency. The above characteristics are mirrored in the post-procedural vertical profile analysis in chapter six. In regard to the Atlantic basin classification scheme outlined in
McBride (1981a), there is first a dichotomy comprising “non-developing” clusters and
!40 “developing” clusters or depressions, the latter of which are those that eventually develop
into hurricanes and the former those that do not reach hurricane status. Within the non-
developing cluster category, there are “N1” - “Atlantic Cloud Clusters”, “N2” - “Atlantic
Wave Trough Convection”, and “N3” - “Atlantic Non-developing Depressions: Western
Atlantic Depressions which do not Develop into Tropical Storms”. N1 are those systems
that assumed the appearance of potential development into tropical storms on satellite
-1 imagery, with a Vmax of around 10 ms or less, latitude around 20ºN, and longitude 82ºW.
N2 are systems associated with tropical wave convective episodes and had latitudes
-1 around 16ºN, longitudes around 72ºW, and Vmax around 10 ms or less. N3 mean latitude
-1 is around 21ºN, longitude around 81ºW, and Vmax around 15 ms . Developing systems
are split into four sub-categories: “D1” - “Pre-Hurricane Cloud Cluster”, “D2” - “Atlantic
Pre-Hurricane Depression”, “D3” - “Atlantic Intensifying Cyclone”, and “D4” -
“Hurricane”. D1 are characterized by values of 18ºN latitude, 72ºW longitude, and Vmax around 10 ms-1 or less. D2 exhibit latitude around 21ºN, longitude around 75ºW, and
-1 Vmax around 15 ms . D3 comprises systems with latitude around 22ºN, longitude 78ºW,
-1 and Vmax around 20 ms . Lastly, D4 exhibits latitude 23ºN, longitude 79ºW, and Vmax of
45 ms-1. In this paper, the terms ‘nondeveloping’ and ‘developing’ will be used, similar
to McBride (1981a), as umbrella terms for all cases that meet certain spatiotemporal and
intensity thresholds and either do not subsequently reach hurricane strength or do reach
hurricane strength, respectively. ‘Developing’ will be used interchangeably with ‘GO’
!41 cases and ‘nondeveloping’ with ‘NOGO’ cases. There will be no further sub- categorization as was employed by McBride.
In this study, much of the methodology for the identification of cloud clusters, candidate criteria, variable retrieval, and variable calculation will be extracted from the above works. While a significant portion of the analysis and experiment is computational, there is also a sizable portion of research within more subjective confines, particularly in regard to the satellite imagery analysis phase of this work. Thus, one caveat concerning this project is that, if it were to be improved in future iterations, there could be additional contributions from certain methodologies that may reduce subjectivity involved in qualitative analysis of satellite imagery (such as pixel counting, vorticity-tracking algorithms, filters, etc.). However, certain approaches were borrowed from these previously mentioned studies with the hopes of decreasing the level of subjectivity to an acceptable degree for Master’s research.
3.1.2 Linear Discriminant Analysis
Linear discriminant analysis is a statistical procedure utilized to determine the relative contributions of discrete predictors in linear combination to discriminate between two assigned classification outcomes. That is, LDA is typically characterized by binary classification for a system of linear equations comprising a number of predictors that are assigned coefficients based on their relative magnitudes in discriminating between the two classifications. Law and Hobgood (2007) explain that LDA, or discriminant function
!42 analysis (DFA), aids in determining which variables best discriminate between two or
more groups. Hennon and Hobgood (2003) note that, assuming normal distribution of
predictors and independence amongst the predictors, and having assigned each group
membership according to a binary classification system, that the LDA derives a function
that maximally separates the groups through a linear model of the predictors with
assigned coefficients. In other words, LDA computes the linear combination of the
predictors that best separates the two outcomes. Speaking in linear algebra terms, LDA
produces a transformation that minimizes within-class scatter and maximizes between-
class scatter. The value for the linear discriminant function is scaled so that the mean
value is 0 (i.e. centered on 0). The linear combination of predictors visualized as an
equation is
!
where Xi is a the value of a given variable at a certain time and ai is a coefficient assigned
to each variable following Gaussian elimination used to solve the system of linear
equations constituted by the pooled covariance matrix for all variables, the vector of
model coefficients to be calculated for each variable, and the vector of the differences
between the means of the variables corresponding to each class. In this specific study,
the symbolized equation is
! .
!43 The binary classification in this study comprises GO cases, or those cloud cluster cases that eventually develop into hurricanes, and NOGO cases, or those that do not reach hurricane strength (including lows, tropical depressions, tropical storms, subtropical storms, and extratropical storms that do not ever meet or exceed hurricane criteria at any point during their life cycles). Additionally, for the sake of clarity, “developing” may be used descriptively in this paper interchangeably with “GO” designation (i.e. cases that subsequently reach hurricane genesis) and “nondeveloping” is synonymous with
“NOGO” classification.
3.1.3 Ocean Niño Index
Identification of hurricane seasons suitable for representation of COLD phases,
WARM phases, and NADA (neutral) phases was achieved by referring to the National
Weather Service Climate Prediction Center’s page showing three month means of +/-
0.5°C departures from the base mean of SSTs pulled from ERSSTv3b data over the
Niño-3.4 region which extends from 5°N - 5°S latitude and 120°W - 170°W longitude.
Base means from which the three month mean anomalies are calculated is determined using 30-year base periods centered on the years of interest. For example, the set of years
1966-1970 will use the base mean from the period of 1951-1980. Or for the set of years
1951-1955, the base mean will come from the period 1936-1965. For the most recent decades, such as the 2000s, because the centered 30-year period cannot be determined, the period 1981-2000 will be used to determine the base mean from which anomalies are
!44 calculated. In 2016, the next base period will be calculated. In regard to this project, cold and warm (blue and red, respectively) phases are defined as periods of five or more consecutive three-month moving window averages less than or equal to -0.5°C anomaly or greater than or equal to 0.5°C anomaly, respectively. To represent WARM phases, the years 2004 and 2009 (an extremely TCG-suppressed year) were analyzed. For neutral conditions, the years 2005 (an extremely vigorous year for TC activity in the Atlantic) and 2012 were selected and examined. And lastly, as proxies for COLD phase TC behavior in the Atlantic, the years 2007 and 2010 were utilized.
3.1.4 NHC Best Tracks
For developing clusters, coordinates and times were drawn from the Best Track archives included in the reports for each of the storms from the six selected hurricane seasons (http://www.nhc.noaa.gov/data/#tcr). In addition to latitude, longitude, and time, these best tracks were also utilized to determine, at points throughout the research, the intensity (in wind speed, kt) and the corresponding classification of the storm (e.g.
Tropical Depression, Tropical Storm, Hurricane, Extratropical, Low, etc.). For GO cases, or in other words, developing cases, all locations and times are used from the initial observation in the best track archives up through the genesis location and time (that is, the first time at which the storm is classified as a hurricane in the best track records).
Thus, the Best Track records constitute an essential part of the research in that they describe the necessary data for the GO cases used in the linear discriminant analysis.
!45 3.2 Cloud clusters
Multiple months of research were devoted to the qualitative analysis of infrared satellite imagery in order to identify the times and coordinates of nondeveloping, or
NOGO, cloud clusters to be used subsequently in NCL programs to calculate the variable means over 5x5 box domains and 2° radius domains. These variable means would then be used in the linear discriminant analysis to identify the preeminent annual and seasonal predictors. Cloud-top temperatures are analyzed from the infrared imagery in order to identify cloud clusters that meet candidate criteria.
3.2.1 Cluster thresholds
In order to reduce the level of subjectivity inherent to much of qualitative satellite imagery analysis, certain criteria, as established by multiple sources on the cloud cluster - linear discriminant interface, were used. For example, selecting cloud clusters with accuracy may be a difficult and highly ambiguous endeavor due to the variety of shapes, variety of intensities, variety of concentrations, transient time scales, and more. Thus, cloud clusters that met candidate conditions for tropical cyclogenesis primarily exhibited
1) cloud-top temperatures equal to or less than 208K as detailed in Kerns and Chen
(2013). However, candidate cloud clusters must not merely exhibit cloud-top temperatures less than 208K, but also 2) must constitute an approximate area of 5,000 km2 or greater with temperatures equivalent to or less than 208K. Thus, these two criteria
!46 comprise the intensity and spatial thresholds for cloud clusters to meet candidacy.
Additionally, the temporal threshold, in order to eliminate highly transient convective episodes, was slightly different than the 6-hour mark used in Hennon and Hobgood
(2003). This is because the spatial and intensity thresholds were different in this study, and as such, the temporal threshold should be adjusted. Thus, the temporal threshold that cloud clusters must meet in this study is 3) 9-hour minimum persistence in infrared imagery. Perrone and Lowe (1986) utilized an 8-hour minimum for cloud clusters to meet candidate specifications, and the reason for the slight difference in this study is due to the prevailing 3-hour intervals between GOES satellite images. Therefore, candidate cloud clusters must persist through at least four consecutive satellite images, and as a result, each cloud cluster comprises, at minimum, four cases.
3.2.2 Satellite imagery
For the purposes of this study, simple constructs were created in order to make the qualitative analysis of satellite imagery for hurricane seasons (June 1 - November 30) corresponding to six years feasible within the timeframe of four to six months. In total, imagery analysis comprised approximately five months. The primary analytical tool employed in this study for the satellite imagery portion was McIDAS-V, which is the
Graphic User Interface (GUI) version of McIDAS and is the counterpart to McIDAS-X which utilizes Abstract Data Distribution Environment (ADDE) commands in order to manipulate and analyze satellite imagery. McIDAS, Open Archive, and all associated
!47 satellite data used in this project are managed, disseminated, maintained, and operated by the Space Science and Engineering Data Center at the University of Wisconsin-Madison
(http://www.ssec.wisc.edu/datacenter/). In order to gain access, a campus IP address must be registered in connection with a university-affiliated e-mail address. Throughout the years of 2004, 2005, 2007, 2009, 2010, and 2012, depending on which satellite was in operation in during each year, imagery was retrieved primarily from GOES-11,
GOES-12, GOES-13, or GOES-14, and either Meteosat-8 or Meteosat-9 occasionally in order to more clearly view and analyze cloud clusters forming of the west coast of Africa, often in areas of enhanced convection within AEWs. Satellite imagery was analyzed in three hour increments at 245 UTC, 545 UTC, 845 UTC, 1145 UTC, 1445 UTC, 1745
UTC, 2045 UTC, and 2345 UTC. Subsequently, when variables were calculated from the reanalysis datasets (which are at six hour intervals), satellite data was rounded to the nearest temporal data point. For example, if a candidate cloud cluster was located at certain latitude and longitude coordinates at 545 UTC, u- and v-wind components used in the calculation of low-level vorticity from the NCEP-NCAR Reanalysis would be calculated at the equivalent of 600 UTC of that same day. Obviously, cloud clusters located at the times of 245 UTC, 845 UTC, 1445 UTC, and 2045 UTC were not used in the reanalysis calculations, but were vital in enhancing temporal resolution to ensure that cloud clusters were meeting or exceeding the minimum threshold of nine hours, or in other words, four cases (that is, four consecutive 3-hr interval satellite images).
!48 In keeping with the aforementioned candidate cloud cluster criteria, the most important technique used in this satellite study is the creation and employment of a color table that would highlight 10.7µm (for GOES imagery) or 10.8µm (for Meteosat imagery) infrared cloud-top temperatures. In particular, it was important that a color be designated for cloud-top temperatures less than 208K, which was the intensity threshold mentioned earlier that a cloud cluster must attain in order to meet candidate specifications. Thus, within the McIDAS-V constructs, a color table was created and named 208K_1 which highlighted ~203K - ~208K a light green, followed sequentially by orange (~203K - ~200.5K), red (~200.5K - ~197K), violet (~197K - ~191K), and blue
(<~191K) for increasing intensities (i.e. lower cloud-top temperatures). Thus, the most intense convective systems exhibited greater swaths of blue and violet cloud-top temperatures. In the image below, which was drawn from GOES-12 East imagery, one can see the intensity of a burgeoning Hurricane Katrina on the border between the
Atlantic and the Gulf of Mexico at 2345 UTC 25 August 2005, right around the time of genesis. Intense vorticity, as well as green, orange, red, and violet cloud-top temperatures indicate cloud-top temperatures dropping into the 190s K.
!49 !
FIG. 2. Hurricane Katrina.
In order to determine whether or not a cloud cluster met the spatial criterion of
5,000km2 to be a candidate, a drawing tool was used to ‘Draw Freely’. This tool allowed
for free-hand circumscription of cloud clusters highlighted by the 208K_1 color table to
determine if the area of cloud-top temperatures below 208K met the minimum area. As
one can see in the snapshot below, which is a Meteosat-9 image of Tropical Storm Ana
(2009), the drawing tool may be used to circumscribe a cloud cluster and then retrieve
both the distance of the drawn line as well as the encompassed area.
!50 !
FIG. 3. Satellite Techniques.
Below is a snapshot of the window which was used to create the 208K_1 table, with a color bar that allowed for flexible manipulation of color attribution to certain cloud-top temperature ranges.
!51 !
FIG. 4. Color Table.
3.3 Variable selection
Variable averages computed in this study over the cloud cluster domains to be used subsequently in the linear discriminant analysis were selected based on the previously mentioned studies of Hennon and Hobgood (2003), Perrone and Lowe (1986), and Kerns and Chen (2013). HH03 found that, in the north Atlantic basin, Daily Genesis
Potential (DGP) and the Coriolis parameter were the most effective predictors in
!52 discriminating between development or non-development of candidate cloud clusters.
PL86 found that at the 24-hour time to genesis mark, the Coriolis parameter, low-level vorticity, the low-level maximum of the magnitude of the gradient of the product of vorticity and divergence (local maximum of low-level of the spatial derivative of vorticity stretching), and the Laplacian of upper-level vorticity were the best discriminators. At 48 hours, the primary discriminators were low-level vorticity, low- level divergence, the local maximum of equivalent potential temperature, and the local maximum of moist static stability. At 72 hours, the most notable discriminator was large- scale low-level vorticity. While not identical, the inspiration behind the variables calculated in this study was drawn from these three studies and, in particular, some of the variables that seem to be most salient in the discriminating process. By consensus, it appears that low-level vorticity and Coriolis are the most notable discriminators, and, as such, are expected to be among the primary discriminators in this study. Additionally, to pick up some upper-tropospheric behavior (using DGP from HH03 as inspiration), upper- level (200 mb) vorticity is used in this study. Additionally, due to the overwhelming relevance of vertical wind shear as it relates to ENSO-governed oscillations, particularly over the Atlantic MDR, it is included as one of the variables to be calculated over the candidate cloud cluster domains. Using PL86’s index of the local maximum of the gradient of vorticity stretching as motivation, while not identical, the maximum of low- level vorticity stretching (note: not maximum of gradient, merely maximum of magnitude), to pick up the combined effect of convergence and vorticity. And finally, in
!53 order to involve thermodynamic influence, SST is the last variable to be added to this study. SST, while perhaps not a great discriminator between development or decay due to minimal horizontal gradients in equatorial regions, is vital in the genesis process in general and is the heart of the Carnot engine that is a hurricane, particularly affecting the isothermal expansion branch of a system’s Ekman inflow. Additionally, the SST, as described in Holland’s MPI model, is vital in governing the height (temperature) of the equilibrium level, and, thus, the thermodynamic efficiency and CAPE.
3.3.1 Low-level vorticity
Low-level vorticity is of extremely great significance, as it is the focal point of numerous studies in tropical cyclone research as the mechanism of wind-induced surface heat exchange, or interchangeably, the Air-Sea Instability Interaction. In a most basic sense, it is the most closely correlated to the concept of an interface between the ocean power input and the growth of atmospheric instability following vortically-driven surface sensible and latent heat exchange, boundary layer moist entropy enhancement during the isothermal expansion phase of the Carnot engine Ekman inflow, and persistent, deep moist, organized, vigorous convection. The relative vorticity tendency, or the partial derivative of relative vorticity with respect to time, is
!
The above is from Davis and Galarneau (2009). Translated into verbal terms, the change in relative vorticity with time at a point is equal to the horizontal advection of absolute !54 vorticity plus the vertical transfer of relative vorticity plus the stretching of vorticity (the product of isobaric convergence and vorticity) plus contributions from tilting (the tilt of the vertical vorticity axis) plus the curl of subgrid-scale forces. For the purposes of this study, only relative vorticity is of interest, not the relative vorticity tendency. Relative vorticity is
! .
That is, relative vorticity is equivalent to the change in the meridional velocity with respect to the zonal direction minus the change in the zonal velocity with respect to the meridional direction. The physical root behind this is that it is equivalent to the curl of velocity
! .
As such, the components of vorticity most commonly utilized in meteorological study are orthogonal to the horizontal velocity surface, or, in other words, they are vertical.
Absolute vorticity is similar to relative vorticity except it contains the influence of the apparent force, Coriolis.
! .
Based on the abundance of literature addressing lower-level processes in the formation and intensification of both tropical and mid-latitude systems, it was expected that low- level vorticity would play a significant role in the formation processes and the linear discriminant analysis. In this study, low-level vorticity was evaluated at the 850mb isobaric level and was scaled by 105. !55 3.3.2 Upper-level vorticity
Obviously, upper-level vorticity carries many similarities to low-level vorticity, except that it is calculated at higher levels in the troposphere. For the purposes of this study, upper-level vorticity was calculated and analyzed at the 200mb level, which is close to the outflow levels of hurricane and burgeoning convective complexes. The
200mb level was selected for the sake of consistency with 850-200mb vertical wind shear, as well as congruence with the vast majority of research that analyzes flow at the
200mb level as a proxy for upper-level flow. For example, McBride and Zehr (1981) use the 200mb level as the upper level for the creation of the Daily Genesis Potential (DGP).
As was done for low-level vorticity, upper-level vorticity was also scaled in this study by
105.
3.3.3 Coriolis (parameter, scaled)
A scaled Coriolis parameter was used in this study as a proxy for latitudinal effect on the development or non-development of cloud clusters dispersed over the Atlantic.
The scaled Coriolis parameter is as follows:
!
or
! .
As noted by a variety of sources, such as Hennon and Hobgood (2003), it is also expected that Coriolis will have a marked impact on the fate of candidate cloud clusters.
!56 3.3.4 Vertical wind shear
Vertical wind shear is of particular salience because it is the proximate cause of
ENSO WARM-related TCG-suppression over the Atlantic MDR. It is correlated with the
Pacific-generated westward-propagating BRWs that cause positive upper-level vorticity
responses over the MDR and, thus, inhibit genesis. It is conventionally calculated as
! .
Below, NCL was utilized to retrieve NCEP-NCAR Reanalysis u- and v-components of wind to calculate shear for the WARM (2004, 2009) years in this study, the NADA (2005,
2012) years, and the COLD (2007, 2010) years, after which the values were dimensionally averaged over time. The first figure is the average of the WARM years minus the NADA years, and the second is WARM minus COLD. Warmer colors indicate positive, or enhanced, shear for the WARM years relative to the other sets, and cool values reflect suppressed shear for the WARM years relative to the others. In both, there is ostensible evidence of enhanced vertical wind shear during El Niño years in comparison to both neutral years and La Niña years. In fact, it seems that this tendency becomes even more entrenched / disparate in La Niña years compared to neutral years.
!57 !
FIG. 5. El Niño - Neutral Shear Anomaly.
!
FIG. 6. El Niño - La Niña Shear Anomaly.
!58 3.3.5 Vorticity stretching
The vorticity stretching term of the vorticity theorem, as indicated previously, is
the scalar product of vorticity and convergence at a specific level or point.
!
Enhanced values for vorticity stretching indicate significant contributions to the overall
relative vorticity tendency from convergent flow and vorticity resulting from vigorous
updrafts and vortical spinup at a certain level. In this study, it is evaluated at the 850mb
level, as enhanced values of low-level stretching would indicate efficient vortical spinup
of moist entropy resulting from frictional Ekman inflow and signal the development of
the Carnot heat engine. Again, as with low-level vorticity, upper-level vorticity, and
Coriolis frequency, the vorticity stretching values are scaled by 105.
3.3.6 SST
SST was a necessary inclusion in this study as a thermodynamic parameter considering the fact that the remainder of the other selected predictors are purely dynamic. Thus, SST was an indispensable element as it symbolizes the heart of the
Carnot heat engine that is a hurricane, and it is the primary source of energy for cloud clusters and tropical cyclones. Wind-induced surface heat exchange allows for the atmosphere to mine energy from the ocean mixed layer and absorb enthalpy derived from the ocean heat content. In this study, SST gridpoints were on a Gaussian latitude/ longitude grid and were retrieved from the ECMWF ERA-Interim Reanalysis accessed
!59 from the National Center for Atmospheric Research (rda.ucar.edu). SST is measured in degrees Kelvin. Due to the different spatial resolution in comparison to the NCEP/DOE
AMIP-II Reanalysis, only one coordinate selection algorithm is used for SST averages.
This algorithm averages the nine surrounding datapoints, which covers a much smaller area than that of the NCEP/DOE AMIP-II Reanalysis.
3.4 Reanalysis selection
Calculation of variables within cloud cluster vicinities for the linear discriminant analysis was achieved by gathering data from multiple reanalysis datasets. The majority of data was drawn from the NCEP/DOE AMIP-II Reanalysis (NCEPR2) (http:// www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis2.html) and SST reanalysis data was retrieved from the ECMWF ERA-Interim Reanalysis (ERA-I) (http://rda.ucar.edu/ datasets/ds627.2/).
3.4.1 NCEP/DOE AMIP-II Reanalysis (NCEPR2)
Reanalysis datasets like NCEPR2 are created by assimilating data from a variety of sources such as in-situ observations, buoys, soundings, satellite imagery, weather stations, climatology, and models. For the purposes of this study, data from the NCEPR2 reanalysis was used to calculate low-level vorticity, upper-level vorticity, shear, and vorticity stretching. Data are located on a fixed, 2.5x2.5° grid at 6-hour analysis intervals
(4x daily). U- and v-wind components were retrieved for the years 2004, 2005, 2007,
!60 2009, 2010, and 2012 in NetCDF format and further unpacked and analyzed using NCAR
Command Language (NCL). The reason for using this dataset rather than other prominent datasets such as the NCEP Climate Forecast System Reanalysis (CFSR) dataset is as follows.
3.4.2 NCEP Climate Forecast System Reanalysis (CFSR)
At the outset of the project, there was question as to which reanalysis dataset should be selected for the purposes of calculating variables. In choosing between two of the more prominent datasets, NCEPR2 and CFSR, Rachel Mauk was consulted regarding her own past experience and knowledge. After being provided with direction to multiple sources from Mauk, most notable of which was Chelliah et al. (2011), it was determined that NCEPR2 was the most accurate of the two datasets. In terms of long-term climate variability, Chelliah et al. (2011) found CFSR to be the outlier of the examined reanalysis datasets, exhibiting significantly stronger easterly trade winds, anomalously cool tropospheric temperatures, and lower geopotential heights during earlier parts of the analysis period. As a result, Chelliah et al. 2011 indicates that ENSO-related winds in the equatorial Pacific and the north Atlantic may be highly anomalous in nature and, thus, inaccurate.
!61 3.4.3 ECMWF ERA-Interim Reanalysis (ERA-I)
One of the more notable reanalysis datasets distributed by the European Center for Medium-Range Weather Forecasting is the ERA-Interim Reanalysis (ERA-I). ERA-I was utilized in this study to average SSTs in the surrounding region of cloud clusters using the various, subsequently-described coordinate selection algorithms. The default units for these SST measurements is degrees Kelvin.
3.5 Computation
NCAR Command Language (NCL) was used heavily in the computational piece of this study. Virtually all datasets were unpacked, analyzed, and visualized using NCL.
NCL is a FORTRAN-based, interpreted language that is conventionally-known to be one of the foremost tools used by meteorologists and atmospheric scientists to analyze data and visualize results. NCL contains many built-in functions for meteorological applications.
3.5.1 NCL Computation
The primary functions used in the computation of variable averages near cloud clusters were uv2vrF(), uv2dvF(), avg(), and max().
!62 !
FIG. 7. Read-in Code Example.
The above code demonstrates the typical routine used to read in data. Here, the times and coordinates for cloud clusters in the year 2009 are read in as a .csv file. Times are modified so that they correspond with the indexed times in the reanalysis data. U- and v- components, in NetCDF format, are read in from the reanalysis dataset.
!63 !
FIG. 8. 5x5° Vorticity Code Example.
The above portion of code is the latter half of the program after the data have been read in. The uv2vrF() function is then used on the u- and v-components of the read-in reanalysis data. This routine calculates vorticity on a fixed grid at the points retrieved from the .csv file, which includes not only the coordinates of cloud clusters, but also the nearest reanalysis datapoint and a 5x5° box centered on this datapoint. As mentioned before, the reanalysis data is located on a 2.5x2.5° fixed grid. Subsequently, as can be seen above, the vorticity values are then averaged at each timepoint, that is, averaged over the 5x5° box centered on the reanalysis datapoint closest to the empirically-observed
!64 cloud cluster location. Obviously, the calculation of the other variables was not identical, but the same general routine was used for the 5x5° method.
!
FIG. 9. 5x5° Method for Variable Calculation
!65 (Country boundaries/coastlines from the Detailed World Polygons shapefile from https:// hiu.state.gov/data/data.aspx).
Another method, as can be observed subsequently, was also employed to select coordinates differently than the 5x5° method. This alternate method is the 2° radius method. Instead of calculating, for example, vorticity averaged over nine points in a box roughly centered over a given cloud cluster location, this 2° radius method would calculate, in this case, vorticity averaged over the nearest four points from the reanalysis dataset 2.5x2.5° fixed grid.
!66 !
FIG. 10. 2° Radius Vorticity Code Example.
The above code demonstrates the general technique to determine the four nearest datapoints based on a cloud cluster’s coordinate position. The tointeger() function is used to round the coordinates to the nearest integer, and then, based upon the relationship of these rounded integer values to the original coordinates, a series of if_then statements is used to select the four surrounding points. If the original coordinate lied exactly on a reanalysis datapoint, then the calculation was only performed at that location.
!67 !
FIG. 11. 2° Radius Method for Variable Calculation.
Vorticity stretching calculation was achieved by multiplying the uv2vrF() and the uv2dvF() functions, effectively multiplying the vorticity by the divergence. Then, instead
!68 of subsequently averaging (avg()) over the surrounding datapoints, the max() function
was used to determine the maximum across rows (that is, within the local vicinity of an
observed cloud cluster location).
3.5.2 LDA in R
R was an indispensable part of this study, as it represents the culminating step of
the satellite imagery analysis in combination with the computation of variables in the
surrounding regions of cloud clusters. R, which is a programming language typically
associated with statistical applications, as it is in this study, was used to run a simple
linear discriminant analysis script. The function is lda() which involves a number of
options to control how the LDA is accomplished.
!
FIG. 12. LDA Code
The above snippet of code is the basic procedure that was run to accomplish the
LDA. First, library scripts were imported. Secondly, the data, that is, the calculated values of the various predictors averaged around each cloud cluster case, was read in as a .csv with six columns (one for each predictor) and an additional column classifying each case as a GO (subsequent development into a hurricane) or NOGO
(nondevelopment / cyclolysis precluding hurricane formation) case. The lda() function
!69 itself requires the equation of the desired linear model, which, in this case, is Class ~
ζ850mb + ζ200mb + Shear + Coriolis + Stretch + SST. There is an additional option,
CV=TRUE (default is CV=FALSE), that can be placed within the lda() function to utilize the cross-validation, or jackknife method to produce posterior probabilities of class assignment of each case by leaving these cases out one by one. The option na.action=na.omit signifies that any cases missing a datapoint for any of the predictors would be omitted. In this study, SST was usually the only missing data, and these cases consequently were left out of the linear model fitting.
The output of the code is below. First, it states the function that was called.
Secondly, the prior probabilities of the classes (in this study, GO and NOGO) are stated based on all of the cases. Thirdly, the means of the various predictors for both GO and
NOGO cases are printed. Lastly, and most importantly, the coefficients of the predictors are produced, which indicates the relative discriminating power of each of the variables in the provided data.
!70 !
FIG. 13. LDA Output.
3.5.3 MPI (as delineated by BE02a)
Subsequently, a number of case studies will be completed for hurricanes that formed in the north Atlantic comprising calculation of variables used in the LDA over the surrounding hurricane environments around the time of genesis, as well as the MPI for these storms determined using Emanuel’s Carnot heat engine model to see which variables are most closely tied with MPI. In order to gain greater familiarity with the methodology of the MPI model expounded in BE02a, FORTRAN subroutines calculating
Vm, pm, and CAPE were obtained from Dr. Kerry Emanuel (personal communication,
ftp://texmex.mit.edu/pub/emanuel/TCMAX/). The subroutine PCMIN was modified to
become the main program which would CALL the CAPE subroutine. The main TCMAX
!71 program, in conjunction with the CAPE subroutine iteratively calculated atmospheric/ boundary layer CAPE based on a sounding, as well as saturation CAPE and CAPE estimated at the radius of maximum wind. For the sake of experimentation, a sounding was obtained in HSA format for 1819UTC August 26, 2005 retrieved from a sonde dropped by the NOAA 49 reconnaissance aircraft into a nascent Hurricane Katrina, which had formed around 0000UTC of the same day (http://www.aoml.noaa.gov/hrd/
Storm_pages/katrina2005/sonde.html). The pressure, temperature, and mixing ratio values were manually entered as one-dimensional arrays at the beginning of the main program. The mixing ratio is only necessary at the surface level, and it was calculated using temperature, pressure, and relative humidity values retrieved for surface levels and a mixing ratio calculator provided by NOAA (http://www.srh.noaa.gov/epz/? n=wxcalc_mixingratio). The SST used for this example was 30.0℃, as sources have noted that a majority of the Gulf of Mexico region exhibited temperatures equivalent to or in excess of 30.0℃ around the time of Hurricane Katrina (Kafatos et al. 2006).
!72 FIG. 14. From Kafatos et al. (2006) with top portion indicating SST.
An important observation regarding the TCMAX model is the ability to tweak the ratio of enthalpy to momentum surface exchange coefficients (Ck/Cd). The model-
projected pressure minima and wind speed maxima are highly sensitive to the assigned
value of this ratio. Emanuel is quick to note that this sensitivity is understandable
considering the sub-cloud layer entropy budget. When the ratio is a smaller value, the
Ekman inflow is comparatively larger than the enthalpy exchange from the surface. The
attenuation of heat input results in significantly reduced intensity. However, when the
ratio is large, the enthalpy exchange at the surface is proportionally greater than the
!73 momentum exchange / drag, especially in the eyewall region, resulting in a potentially
explosive and intense storm (Emanuel 1995). To demonstrate the effect of tweaking the
ratio of exchange coefficients, the sounding from 1819 UTC August 26, 2005 for
Hurricane Katrina was used to calculate the potential minimum central pressures and
velocity maxima for varying values of the exchange coefficient ratio. A Do Loop was
inserted into the program to vary the values from ~0.5 to ~2.0 and to produce the
corresponding VMAXs and PMINs.
!
FIG. 15. Example MPI Output, SST = 30°C.
As one can see, the increase of the ratio of surface enthalpy exchange to momentum exchange drastically enhances the potential intensity of a given storm. With a ratio value of 2.0, the projected VMAX is ~79 m/s or ~154 kt and the projected PMIN is ~905 mb.
In referring to NOAA’s HURDAT2 Best Track report for Hurricane Katrina, the storm reached its greatest intensity at 1800 UTC on August 28, 2005 over the Gulf of Mexico
!74 with max winds at 150 kt and pressure minimum at 902 mb, an observation relatively
close to the projected maximum potential intensity. When adjusting the SST to 31℃, an
observed condition on August 27, and repeating the model with varying Ck/Cd, the
potential intensities drastically increase, as expected.
!
FIG. 16. Example MPI Output, SST = 31°C.
While somewhat unrealistic, both in the context of Ck/Cd values near 2.0 and SSTs ephemerally and anomalously high (31℃), the model displays the profound dependence on, again, the ratio of surface exchange coefficients and the fundamental reliance on SST as the heart of the Carnot engine, as well as the potentially explosive acceleration and expansion of this cycle with a corresponding anomalous increase of SST.
!75 !
!
!
FIG. 17. MPI Variables.
The above clippings of code (Fig. 17) convey fundamental processes occurring within the calculation of PMIN (minimum achievable central pressure) and VMAX
(maximum achievable surface wind speeds). RAT is SST(Kelvin)/TOM(temperature at the level of neutral buoyancy), CKCD is Ck/Cd, VREDUC = 0.8 to account for drag,
TVAV is the calculation of virtual temperature, CAPEA is atmospheric CAPE, CAPEM is the CAPE estimated near the radius of maximum winds, and CAPEMS is the saturation
CAPE near the radius of maximum winds (all calculated during CAPE subroutine). For
-1 the last case, with a SST of 31.0℃ and Ck/Cd = 2.0, CAPEA is ~1436 J kg , CAPEM is
~4252 J kg-1, and CAPEMS is ~8454 J kg-1. By increasing the surface exchange
coefficient radio, CAPEM and CAPEMS exhibit, intuitively, a corresponding increase, as
there is an enhancement of latent and sensible heat provided to the TC boundary layer.
Andreas and Emanuel 2001 expound an interesting study trajectory addressing the effect
of sea spray on the modeled intensity of tropical cyclones. At the outset of the work, the
!76 authors indicate the gap in understanding of hurricane intensity from low wind speeds to high wind speeds correlated with the value of the Ck/Cd ratio as systems exhibiting >25 ms-1 sustained winds, theoretically, would exist under conditions in which the surface drag coefficient is more than twice the surface enthalpy exchange coefficient, a highly deleterious process in regard to cyclone intensity maintenance. At low wind speeds, the enthalpy exchange coefficient (drag coefficient) is high (low) enough to provide a favorable exchange coefficient ratio and, thus, conditions favorable for WISHE-induced intensification. Thus, up until Andreas and Emanuel (2001), there had not been promulgated an adequate explanation for the maintenance of system intensity at high winds due to the correlated large (small) value of drag coefficient (enthalpy coefficient).
However, in this work, the authors described a process in which sea spray, as agitated by high wind speeds, becomes “re-entrant” sea spray by initially departing the sea surface at
SST, reaching a cooler airborne equilibrium temperature (releasing enthalpy to the atmosphere), then reentering the sea surface at a cooler temperature before evaporating a significant portion of its mass (which would have a suppressive effect). Additionally, large-droplet sea spray produces the effect of turbulence/drag reduction near the surface at high wind speeds. As noted by Emanuel in Emanuel (1995), a potentially interesting area of exploration is the application of surfactant technology to ocean surfaces in the path of TCs, as the dispersal of a surfactant on the ocean surface would decrease surface tension and, consequently, decrease ocean spray droplet size, which has a twofold result of inhibiting the typical lubricating effect of ocean spray at high wind speeds by
!77 suppressing spray-governed near-surface turbulence attenuation and decreasing enthalpy
flux from ocean to atmosphere because smaller droplets remain suspended and do not
return to the ocean, like larger droplets, at a temperature cooler than the initial
temperature. Thus, the ratio of the enthalpy/drag coefficients is decreased doubly by
minimizing the turbulence-reducing effect of large-droplet sea spray on the surface
momentum exchange coefficient (drag) and by attenuating the surface enthalpy exchange
coefficient (heat), thereby decreasing the overall maximum achievable potential intensity
(Andreas 2010). In the course of this study (excluding the previous Katrina didactic
example), all MPI calculations will be performed utilizing pseudoadiabatic ascent
thermodynamics (as opposed to the reversible thermodynamics option) and with activated
dissipative heating switched on. Rationale for discarding reversible thermodynamics in
favor of pseudoadiabatic thermodynamics is drawn from Wang et al. (2014) which pulls
from Bryan and Rotunno (2009a). For Pmin calculations, which will not be reported in the
case studies, the exponent b = 2.0 is used in the equation
! where rm is the radius of maximum winds, Vm is the maximum wind, and V is the azimuthal velocity at a given r.
!78 Chapter 4: Results
4.1 Linear Discriminant Coefficients
The goal of this study is to utilize LDA to compute the coefficients assigned to each predictor based on the discriminating power of these variables in distinguishing between GO and NOGO cases. Two primary algorithms were used to select the points surrounding cloud clusters, and the results of both will be discussed. It is important to note that the analyses reported first are those that include all GO cases; that is, all of the cloud cluster cases preceding genesis that eventually reach genesis (i.e. become hurricanes). Following that, the ‘Initial’, ‘TTG = 24Hr’ (Time to Genesis = 24 Hours), and ‘Genesis’ analyses will be reported in tables for each of the study years; these are the
LDAs performed with only the first cases reported in all of the Best Track records for GO clusters with tropical designation (thus excluding low phases, subtropical phases, and extratropical phases), with only the cases preceding genesis by 24 hours, and with only cases at the time of genesis, respectively. Subsequently, a table displays the LDA-derived coefficient values for each of the seasons (WARM, COLD, NADA) at the ‘Initial’,
‘TTG=24Hr’, and ‘Genesis’ stages.
!79 4.2 5x5° Box
Again, the 5x5° box method for datapoint selection utilizes averages or maxima of predictors derived from u- and v-wind component values from the NCEP/DOE AMIP
II Reanalysis at the surrounding nine datapoints.
4.2.1 Annual analyses
The initial analysis comprised discriminant coefficient calculations for the six selected variables over the previously mentioned 5x5 box domain. As stated before, the
5x5 method should pick up more of the large-scale environmental behavior and flow surrounding the peripheries of cloud clusters as opposed to the 2° radius domain, which will be explored subsequently. Relative to the latter-mentioned coordinate selection algorithm, the 5x5 method seemed to enhance the separation between the variables in their discriminating power, and this method will therefore be more heavily emphasized for the duration of the work. At the outset, there are a few trends that are readily available and may aid in the process of crystallizing some of the fundamental occurrences that are correlated with ENSO-moderated change in north Atlantic basin TCG behavior.
Primarily, as evidenced in Tables 1 and 2 displaying the linear discriminant coefficients and coefficient ranks, respectively, the preeminent broad-scale discriminator across all discrete years is low-level relative vorticity. Again, in order to ameliorate understanding and reduce confusion, it is the absolute value of a coefficient that matters (i.e. the magnitude). Thus, pervasive negative sign attached to low-level vorticity coefficients
!80 should not mislead; only the weight of the number should be taken into account. The
reason for the negative signs is the arbitrary assignment of GO cases to fall left of 0 as the
mean in the LDA equation calculations (i.e. negative assignment to GO cases) whereas
the LDA equations computed for NOGO cases are maximized to the right of 0 as the
mean (i.e. NOGO case equations arbitrarily assigned positive maximization). The year
with the highest discriminant coefficient value for ζ850 mb is 2009 with -0.7631. Both
2007 and 2012 had the lowest ζ850 mb coefficient values with -0.5385 and -0.5386, respectively. However, low-level vorticity still maintained the preponderance of discriminating power during these two years with a rank of one (highest magnitude). For the 2004 study year, the three somewhat relevant discriminators behind low-level vorticity are, in descending order, Coriolis, SST, and upper-level vorticity. However,
Stretch and Shear are both relatively indistinguishable from upper-level vorticity in discriminating power, being only slightly lower. For 2009, the second of the two El Niño years, the only other significant discriminator besides low-level vorticity is Coriolis, with a value of 0.2311. This makes sense in light of the distinct nature of TCG that year, as only three hurricanes developed, all at relatively low latitudes (low Coriolis). This is to be expected, as El Niño years exhibit the aforementioned characteristic TCG-suppression over the Atlantic MDR correlated with a NAA jet-governed positive upper-level vorticity response, thus largely attenuating TC-favorable conditions to reduced areas above and below the typical MDR. Therefore, due to the anomalous nature of TCG that year, this is
!81 a significant disparity in the meridional positioning of developing cases vs. the predominantly higher latitude positioning of the nondeveloping clusters.
Transitioning to the La Niña study years, 2007 and 2010 both exhibit, as previously stated, the salience of low-level vorticity in discriminating between development and nondevelopment of cloud clusters. Besides low-level vorticity, 2007 reflects the relative importance of SST and upper-level vorticity as the second and third ranked discriminators, respectively. SST exhibits a dramatic enhancement of discriminating power during the COLD year of 2010 with a value of 0.6009, ranking second to low-level vorticity. This increase in SST discriminatory power implicates a meridional extension of convection and cloud cluster occurrence, with a greater variance between the meridional location of developing (higher latitude, cooler SSTs) cases and nondeveloping (lower latitude, warmer SSTs, attenuated planetary vorticity advection) cases.
The neutral years (of which 2005 was extremely TCG active) also exhibit a proclivity for primary governance by low-level vorticity over the TC formation process, with secondary inputs from Coriolis and SST. 2005, which comprised Katrina, Rita,
Wilma, and a whole host of other powerful storms, exhibits SST, and Coriolis as the secondary and tertiary discriminators, respectively. Coriolis and upper-level vorticity were the second and third ranked discriminators during 2012. An enhancement of discriminatory power exercised by SST and Coriolis indicates, as previously mentioned,
!82 augmented meridional variance between GO and NOGO cases correlated with an expanded region of convective activity.
TABLE 1. ANNUAL COEFFICIENTS, DISCRIMINANT COEFFICIENTS 5x5 BOX
ζ850 mb ζ200 mb SHEAR CORIOLIS STRETCH SST
2004 -0.7160 0.1078 0.0707 -0.1629 0.0954 -0.1115 EL NIÑO (WARM) 2009 -0.7631 -0.0524 0.0460 0.2311 0.1113 -0.0012
2007 -0.5385 -0.2340 0.0110 -0.1006 -0.1195 -0.2543 LA NIÑA (COLD) 2010 -0.7110 -0.0488 0.0636 -0.0753 -0.0644 0.6009
2005 -0.6451 0.0117 0.0918 -0.2486 0.1456 -0.3288 NEUTRAL (NADA) 2012 -0.5386 -0.1265 0.0193 -0.3062 -0.0868 -0.1167
TABLE 2. ANNUAL COEFFICIENT RANKS, DISCRIMINANT COEFFICIENT RANKS 5x5 BOX
ζ850 mb ζ200 mb SHEAR CORIOLIS STRETCH SST
2004 1 4 6 2 5 3 EL NIÑO (WARM) 2009 1 4 5 2 3 6
2007 1 3 6 5 4 2 LA NIÑA (COLD) 2010 1 6 5 3 4 2
2005 1 6 5 3 4 2 NEUTRAL (NADA) 2012 1 3 6 2 5 4
!83 TABLE 3. ANNUAL MEANS, PREDICTOR MEANS 5x5 BOX
ζ850 mb ζ200 mb SHEAR CORIOLIS STRETCH SST
GO 2.1407 -1.3388 11.1966 4.6262 2.6434 300.9894 2004 NOGO 0.7423 -1.1779 12.8261 3.5934 2.2561 301.3275 EL NIÑO (WARM) GO 2.9442 -0.8045 9.7797 3.0171 2.7969 301.109 2009 NOGO 1.1535 -1.3491 13.0878 3.7616 2.2728 301.1303
GO 2.7225 -0.3646 12.3025 4.376 4.1160 301.7063 2007 NOGO 0.9576 -1.5964 12.7275 3.97 2.1886 301.5153 LA NIÑA (COLD) GO 3.0669 -0.9948 10.2107 4.2588 3.5942 301.5077 2010 NOGO 1.0563 -1.3093 11.5975 3.2435 2.8422 302.0084
GO 2.6940 -0.8091 10.1841 5.3207 1.9801 301.5325 2005 NOGO 1.1734 -1.1835 12.0977 3.916 1.4561 301.4629 NEUTRAL (NADA) GO 3.4113 -0.5049 12.6336 5.3047 2.9593 301.1247 2012 NOGO 0.8368 -1.3700 13.4139 3.6758 1.3602 301.4
Based on the annual analyses, the calculated predictor means indicate some of the fundamental processes that occur during these years and how the values diverge between
GO cases and NOGO cases (Table 3). For low-level vorticity, during the El Niño years of 2004 and 2009, there is a clear and marked difference between large-scale, environmental cyclonic flow for developing versus nondeveloping cloud clusters. In general, genesis seems to favor the nascent stages in which large-scale low-level cyclonic
!84 (positive ζ850 mb values) flow is more pronounced than in nondeveloping, indicating, perhaps, the development of convection and low-level inflow on the peripheries and within the viscera of the storms related to the isothermal expansion phase of the previously mentioned Carnot heat engine. Additionally, the ecumenical power of low- level vorticity throughout this whole study may lend credence to the “marsupial paradigm” (e.g. Wang and Hankes 2014) which asserts that TCs form over the north
Atlantic basin within tropical wave pouches that serve to engender and protect convection and vortical spinup. During 2007, a La Niña year, there are also, on average, more positive low-level vorticity values for GO cases as opposed to NOGO cases. During
2010, another La Niña year, GO cases still reflect slightly more marked cyclonic values
(3.0669 x 10-5 s-1) than NOGO cases (1.0563 x 10-5 s-1). For the neutral years of 2005 and 2012, the trend is the exact same with mean low-level vorticity values >2.5 x 10-5 s-1
for developing cases and ~1 x 10-5 s-1 for nondeveloping.
In regard to upper-level vorticity, the majority of study years are characterized by
GO cases with mean values exhibiting more positive (less negative) vorticity in comparison to NOGO cases. The lone exception to the upper-level vorticity trend is 2004
(the first of the ENSO WARM years) which exhibits slightly more negative (-1.3388 x
10-5 s-1) upper-level vorticity values for GO cases relative to NOGO cases (-1.1779 x 10-5 s-1). Excluding 2004, the tendency for GO cases to reflect less negative mean upper-level
vorticity values compared to NOGO cases must signify that developing cloud clusters are
marked by deeper layers of inflow with augmented magnitudes of vorticity, and a
!85 corresponding heightening of the levels of nondivergence, which is the approximate boundary between the updrafts and upper-level outflow and where the vertical mass flux is maximized. Additionally, if the level of non-divergence occurs at higher atmospheric strata, it can also be assumed that the outflow height / temperature (i.e. the equilibrium level, or the level of neutral buoyancy) is greater during GO cases, which is often a reliable indicator of thermodynamic efficiency and the maximum potential intensity that may be achieved. If this, in fact, is not the case, there also exists the possibility that the coordinate selection algorithm is picking up some of the cyclonic rotation occurring in the eyewall region for GO cases. Thus, if this is true, the otherwise negative vorticity resulting from a well-developed outflow region may be masked by the strongly positive positive vorticity signature transferred by the eyewall and its high velocity surroundings.
There is strong consensus among all years that average wind shear over the cloud clusters is lower for GO cases than for NOGO cases, as is expected, particularly in light of the inhibitory effect wielded by enhanced wind shear over the MDR during warm phases. For all years excluding 2009, which was a year of anomalously low TCG frequency and meridional variability of TCG, scaled Coriolis parameter values were higher for GO cases than NOGO cases and was often a discriminator displaying reasonable efficacy in predicting cloud cluster outcomes. This is to be expected, as higher latitudes signify greater Coriolis force and, thus, enhanced values of planetary vorticity advection in conjunction with the reduction of the Rossby radius of deformation.
!86 Across all study years, mean values of the local maximum of vorticity stretching were greater for GO cases than NOGO cases but it does not necessarily exhibit sufficient variance to serve as a viable discriminator between development and non-development, particularly during WARM years. In looking at 2004 and 2009, the disparity between local stretch max averages for GO and NOGO cases is significantly attenuated in comparison to the COLD and NADA years. Concerning SST, there seems to be no clear trends in mean values for GO cases and NOGO cases, probably due to the inverse relationship of the effects of the general meridional temperature gradient across the global basin climatology and Coriolis on the fate of cloud clusters. This relative absence of SST trend may support the argument promulgated by Gray asserting that, during the respective TC seasons, the majority of the north Atlantic MDR and other global basin climatologies are characterized by SSTs that are conducive to TCG and that anything above 26.5ºC is favorable for TCG and that fluctuations above this threshold have negligible effects on the ultimate fate of cloud clusters. In other words, during TC seasons, the ocean surface is virtually always thermodynamically-primed for TCG and that the environment is essentially rate-limited by the requisite atmospheric flow conditions.
!87 TABLE 4. ANNUAL COEFFICIENTS, DISCRIMINANT COEFFICIENTS, INITIAL 5x5 BOX
ζ850 mb ζ200 mb SHEAR CORIOLIS STRETCH SST
2004 -0.7088 0.0042 0.0643 -0.1208 0.0108 -0.3702 EL NIÑO (WARM) 2009 -0.8050 0.0883 -0.0157 0.2983 0.1562 0.0002
2007 -0.4931 -0.0513 0.0856 -0.0644 -0.1938 -0.2470 LA NIÑA (COLD) 2010 -0.5034 -0.1900 0.0766 -0.1347 -0.0983 0.5475
2005 -0.6031 -0.0458 0.1355 -0.1601 0.3879 -0.0674 NEUTRAL (NADA) 2012 -0.4637 -0.2842 0.0118 -0.2844 -0.0591 0.2291
As seen in Table 4, at the Initial point in the HURDAT archives, low-level vorticity is the primary discriminator across all years, but it exhibits a lower magnitude during non-WARM years. SST plays an especially important role at the Initial point during 2004 and 2010. Vorticity stretching is relevant during 2005, and Coriolis is marginally significant during 2009 and 2012. In reference to Table 5, which displays the predictor means of variables at the Initial time in the HURDAT archive, it is worth noting that low-level vorticity is not nearly as strong as it is at later times.
!88 TABLE 5. ANNUAL MEANS, PREDICTOR MEANS, INITIAL 5x5 BOX
ζ850 mb ζ200 mb SHEAR CORIOLIS STRETCH SST
GO 2.0276 -1.0198 10.3519 4.0534 2.9918 301.5044 2004 NOGO 0.7423 -1.1779 12.8261 3.5934 2.2561 301.3312 EL NIÑO (WARM) GO 2.9670 -1.7784 12.5310 2.9158 2.6607 301.2768 2009 NOGO 1.1535 -1.3491 13.0878 3.7616 2.2728 301.1343
GO 2.4694 -0.9502 9.7672 4.1144 4.0886 301.9441 2007 NOGO 0.9576 -1.5964 12.7275 3.9700 2.1886 301.5153 LA NIÑA (COLD) GO 2.7628 -0.8364 10.5300 4.0103 5.6805 301.6847 2010 NOGO 1.0563 -1.3093 11.5975 3.2435 2.8422 302.0084
GO 2.3493 -0.5690 8.7479 4.8955 1.4352 301.3009 2005 NOGO 1.1734 -1.1835 12.0977 3.9160 1.4561 301.4629 NEUTRAL (NADA) GO 2.6521 -0.2864 12.4748 4.9169 2.2092 300.7900 2012 NOGO 0.8368 -1.3700 13.4139 3.6758 1.3602 301.4034
!89 TABLE 6. ANNUAL COEFFICIENTS, DISCRIMINANT COEFFICIENTS, TTG = 24 HOURS 5x5 BOX
ζ850 mb ζ200 mb SHEAR CORIOLIS STRETCH SST
2004 -0.7058 0.0298 0.0582 -0.2025 0.0741 -0.2454 EL NIÑO (WARM) 2009 -0.8012 -0.0060 0.0259 0.2276 0.1449 -0.0524
2007 -0.5246 0.1019 0.1154 -0.0711 -0.1706 -0.0972 LA NIÑA (COLD) 2010 -0.6674 -0.1457 0.0689 -0.1079 0.0658 0.7007
2005 -0.6376 -0.0394 0.0539 -0.2048 0.0828 -0.5092 NEUTRAL (NADA) 2012 -0.2941 -0.3094 0.0037 -0.3935 -0.3323 -0.1703
At 24 hours preceding genesis, as can be seen in Table 6, low-level vorticity is the primary discriminator for 2004, 2009, 2007, and 2005, but it is the second and fourth- ranked discriminator for 2010 and 2012, respectively. During 2010, SST is the primary discriminator at TTG=24Hr, and Coriolis, vorticity stretching, and upper-level vorticity exhibit greater discriminating power during 2012. SST is also a strong discriminator during 2005.
!90 TABLE 7. ANNUAL MEANS, PREDICTOR MEANS, TTG = 24 HOURS 5x5 BOX
ζ850 mb ζ200 mb SHEAR CORIOLIS STRETCH SST
GO 2.2880 -1.1593 10.9104 4.7152 2.7921 301.1482 2004 NOGO 0.7423 -1.1779 12.8261 3.5934 2.2561 301.3312 EL NIÑO (WARM) GO 3.2498 -1.1601 10.2203 2.8826 2.7171 301.3169 2009 NOGO 1.1535 -1.3491 13.0878 3.7616 2.2728 301.1343
GO 2.2452 -1.5170 9.9116 4.4016 3.6234 301.6957 2007 NOGO 0.9576 -1.5964 12.7275 3.9700 2.1886 301.5153 LA NIÑA (COLD) GO 3.2107 -0.8746 9.7210 4.3272 3.5719 301.4720 2010 NOGO 1.0563 -1.3093 11.5975 3.2435 2.8422 302.0084
GO 3.1365 -0.5920 10.1360 5.3885 2.2077 301.8193 2005 NOGO 1.1734 -1.1835 12.0977 3.9160 1.4561 301.4629 NEUTRAL (NADA) GO 3.3031 -0.0757 12.5845 6.0203 3.2677 301.1894 2012 NOGO 0.8368 -1.3700 13.4139 3.6758 1.3602 301.4034
!91 TABLE 8. ANNUAL COEFFICIENTS, DISCRIMINANT COEFFICIENTS, GENESIS 5x5 BOX
ζ850 mb ζ200 mb SHEAR CORIOLIS STRETCH SST
2004 -0.6660 0.2597 0.0589 -0.1041 0.1786 0.0360 EL NIÑO (WARM) 2009 -0.4308 -0.0737 0.0968 0.1163 -0.1911 -0.0235
2007 -0.6166 -0.0377 -0.0666 -0.1389 -0.0673 -0.3936 LA NIÑA (COLD) 2010 -0.6343 -0.0828 0.0579 -0.1669 0.0566 0.7405
2005 -0.5840 0.1067 0.0089 -0.2307 -0.0489 -0.5475 NEUTRAL (NADA) 2012 -0.3121 -0.2330 0.0041 -0.4375 -0.2887 -0.1680
Table 8 displays the coefficient values for each discrete year including only the
GO cases at the time of hurricane classification in the Best Track archives. Relative to
Initial and TTG=24Hr times, the discriminating power of low-level vorticity during
WARM years decreases slightly, whereas the low-level vorticity coefficient values during discrete COLD and NADA years reflect similar discriminating power to that which is exhibited at TTG=24Hr (Table 6). SST plays a primary role during 2010, and a secondary role during 2005. Low-level vorticity is the first-ranked discriminator for
2004, 2009, 2007, and 2005. However, it is the second-ranked discriminator in 2010, and the second-ranked discriminator in 2012 behind Coriolis.
!92 TABLE 9. ANNUAL MEANS, PREDICTOR MEANS, GENESIS 5x5 BOX
ζ850 mb ζ200 mb SHEAR CORIOLIS STRETCH SST
GO 2.3028 -2.0883 11.3978 4.8703 2.2570 300.6915 2004 NOGO 0.7423 -1.1779 12.8261 3.5934 2.2561 301.3312 EL NIÑO (WARM) GO 2.9931 -0.5166 7.8343 3.2392 4.7187 301.1006 2009 NOGO 1.1535 -1.3491 13.0878 3.7616 2.2728 301.1343
GO 2.3005 -1.5231 14.4232 4.7071 3.4823 301.7502 2007 NOGO 0.9576 -1.5964 12.7275 3.9700 2.1886 301.5153 LA NIÑA (COLD) GO 3.3883 -1.1830 10.3945 4.7813 3.8261 301.3581 2010 NOGO 1.0563 -1.3093 11.5975 3.2435 2.8422 302.0084
GO 3.1642 -1.4624 11.8972 5.7028 2.5181 301.9184 2005 NOGO 1.1734 -1.1835 12.0977 3.9160 1.4561 301.4629 NEUTRAL (NADA) GO 3.4054 -0.6544 13.0294 6.5093 3.2850 301.1633 2012 NOGO 0.8368 -1.3700 13.4139 3.6758 1.3602 301.4034
4.2.2 Seasonal analyses
Having devoted initial examination to the linear discriminant analysis performed for each of the discrete six years, the linear discriminant analysis results for the ENSO phases will now be discussed. In performing the LDA for all of the years combined, as expected from previous investigation, the two most salient discriminators between development and non-development were low-level vorticity and Coriolis. As presented
!93 in Table 10, low-level vorticity assumed the preeminent position with a value of -0.6712, and the Coriolis parameter with a value of -0.1616. Upper-level vorticity, local maximum of vorticity stretching, and shear were, overall, marginally significant in the discrimination process of cloud cluster fate. SST remained as one of the most consistent discriminators across all of the seasonal periods; however, the magnitude of its discriminating capability was of slightly less significance than Coriolis. In Table 10, the coefficient value for SST for all of the years in combination was -0.1451. The neutral years combined, however, exhibited the highest coefficient values for SST, implying larger variance between spatial and/or temporal location between GO and NOGO cases
(as SST is a proxy for both spatial and temporal orientation). As expected, low-level vorticity occupied the highest discriminatory rank for the El Niño years with a value of
-0.7181 (Table 10). SST followed with a value of -0.1429.
The Coriolis parameter is the preeminent discriminator for the La Niña years in combination, and SST is the second highest ranked discriminator. As previously mentioned, the absence of TCG suppression mechanisms (westward-propagating Rossby waves, upper-level vorticity response, vertical wind shear) over the Atlantic MDR driven by ENSO warm phases allows for an expansion of the TCG-favorable environment, thus opening up the MDR and surrounding regions as feasible locations for TCG and inherently the Coriolis variability. It is then natural to conclude that the discriminating power of SST would increase, as there is an enhancement of meridional heterogeneity and thus temperature heterogeneity for TCG locations following the equator-pole
!94 temperature gradient, and this is indeed what is observed. Additionally, one would expect the oceanic temperature gradient during ENSO cold phases to be greater than the gradient observed during neutral years because ocean temperatures would still be in transitional phase during neutral years and temperature anomalies correlated with La Niña conditions would become more entrenched. Third in discriminating power to both low-level vorticity and SST during the COLD years, yet still of marginal significance, is upper- level vorticity with a coefficient value of -0.1256, which is displayed in Table 10.
Seasonally, La Niña exhibits the highest dependence upon upper-level vorticity relative to
WARM years, NADA years, and all years combined (Table 11). The reason behind this is unknown, but one inference is that COLD years are typified by a relative lack of the positive upper-level vorticity response that suppresses TCG during WARM years.
Theoretically, under the assumption that neutral years often serve as transitional phases between COLD and WARM years, and that the dichotomy of upper-level climatology during COLD and WARM years is not perfectly rigid or confined to these years, there could be some atmospheric lag that affects the neutral years and, thus, the TCG-inhibitory upper-level vorticity anomalies during WARM years could potentially affect parts of the
NADA years. If this is true, the relative absence of the NAA jet-mediated positive upper- level vorticity response during COLD years could allow for a greater differentiation in upper-level vorticity values for GO and NOGO cases, as GO cases may exhibit deeper levels of inflow and updrafts and a resulting higher level of nondivergence.
!95 The neutral years are characterized by significant contributions from low-level vorticity, SST, as well as the Coriolis parameter. However, Coriolis is significantly higher in discriminating magnitude than it is during other seasons, thus indicating that, as in La Niña years, the meridional extent of potentially TCG-favorable conditions is much greater in comparison to El Niño years. Low-level vorticity still plays the primary role, though, and one would always expect it to, as it is the vehicle behind the Air-Sea
Instability Interaction or Wind-Induced Surface Heat Exchange process and the intrinsic foundation of the necessary enthalpy and latent heat surface fluxes for both TCG and intensification. Again, upper-level vorticity, shear, and local max of the vorticity stretching term play a marginal role in discriminating between development and non- development. Therefore, having examined the discriminating power of certain variables in the cyclogenetic process for the years of 2004, 2005, 2007, 2009, and 2010, both discretely and seasonally, the linear discriminant analysis indicates that the most significant factors of the selected subset of variables are low-level vorticity - unequivocally - and in a secondary manner, the Coriolis parameter and SST, with the latter assuming a more salient role during ENSO warm phases, and the former exhibiting greater significance during non-warm phases in combination (NADA + COLD) corresponding with an increase in the meridional extent of the TCG-favorable environment.
!96 TABLE 10. SEASONAL DISCRIMINANT COEFFICIENTS COEFFICIENTS, 5x5 BOX
ζ850 mb ζ200 mb SHEAR CORIOLIS STRETCH SST
TOTAL -0.6712 -0.0626 0.0491 -0.1616 0.0513 -0.1451
EL NIÑO (WARM) -0.7181 0.0352 0.0739 -0.1324 0.0993 -0.1429
LA NIÑA (COLD) -0.7374 -0.1256 0.0487 -0.0362 0.0398 0.1778
NEUTRAL (NADA) -0.5775 -0.0482 0.0467 -0.2677 0.0110 -0.2698
(COLD) + (NADA) -0.6530 -0.0687 0.0482 -0.1671 0.0379 -0.1019
TABLE 11. SEASONAL DISCRIMINANT COEFFICIENT RANKS COEFFICIENT RANKS, 5x5 BOX
ζ850 mb ζ200 mb SHEAR CORIOLIS STRETCH SST
TOTAL 1 4 6 2 5 3
EL NIÑO (WARM) 1 6 5 3 4 2
LA NIÑA (COLD) 1 3 4 6 5 2
NEUTRAL (NADA) 1 4 5 3 6 2
(COLD) + (NADA) 1 4 5 2 6 3
!97 TABLE 12. SEASONAL COEFFICIENTS, DISCRIMINANT COEFFICIENTS 5x5 BOX
ζ850 mb ζ200 mb SHEAR CORIOLIS STRETCH SST
INITIAL -0.7695 0.0003 0.0474 -0.0051 0.0600 -0.2988 EL NIÑO (WARM) 24HR -0.7662 -0.0141 0.0526 -0.0873 0.1075 -0.2378
GENESIS -0.6581 0.1469 0.0856 -0.0591 0.0614 0.0016
INITIAL -0.5237 -0.1123 0.0788 -0.0552 -0.1406 0.1035 LA NIÑA (COLD) 24HR -0.7221 -0.0231 0.0832 -0.0180 0.0334 0.2735
GENESIS -0.7472 -0.0159 0.0250 -0.0757 0.0462 0.2171
INITIAL -0.5715 -0.1097 0.0788 -0.2237 0.2581 -0.0341 NEUTRAL (NADA) 24HR -0.4618 -0.1263 0.0250 -0.2969 -0.1142 -0.4735
GENESIS -0.4460 0.0012 0.0062 -0.3200 -0.1644 -0.4801
!98 FIG. 18. Absolute Value of Discriminant Coefficients at Initial HURDAT entry, TTG=24Hr, and Genesis during WARM years.
FIG. 19. Absolute Value of Discriminant Coefficients at Initial HURDAT entry, TTG=24Hr, and Genesis during COLD years.
!99 FIG. 20. Absolute Value of Discriminant Coefficients at Initial HURDAT entry, TTG=24Hr, and Genesis during NADA years.
As can be seen in the Fig. 18 of the absolute values of the seasonal 850mb low- level vorticity coefficients vs. time, there is evidence of a decrease in the relative discriminating power of low-level vorticity from the beginning of the Best Track archives to hurricane genesis for El Niño (WARM) years, whereas there is an increase in low-level vorticity discriminating power from the initial times in the Best Track archives to hurricane genesis for La Niña years (COLD) in Fig. 19. For neutral (NADA) years, there is a precipitous drop in discriminating power from initial points in the Best Track archive to the 24 hour Time to Genesis (TTG=24Hr), and a less steep decline from TTG=24Hr to genesis (Fig. 20). It is distinctly possible that the reason for the differentiation in
!100 seasonal trends is a result of the diversity of origins with respect to each season and consequent formation complexities. For example, during the WARM years, there is a very high level of homogeneity in origin; that is, the majority of hurricanes formed from tropical waves with very little influence from other genesis origins. However, COLD years comprise a much higher frequency in hurricanes that originate from other sources or tropical waves in combination with other processes (e.g. ITCZ perturbation, frontal boundary, upper-level low, lower-level cyclonic ocean gyre effect). During the two El
Niño years, 10 of the 12, or 83%, of the hurricanes formed with tropical waves as the initial and preeminent catalyst. During the two La Niña years, 13 of 18, or 72%, of the observed hurricanes originated with a tropical wave as the primary catalyst; however, two of the 13 were heavily influenced in the initial phases by interaction with other formation processes (ITCZ stationary disturbance, low pressure trough), so really 11 of 18, or 61%, of the La Niña hurricanes were results of what can be attributed to more purely tropical wave origin. In combination with different formation mechanisms is the variation in incubation periods for the developing systems corresponding to different ENSO phases.
In reference to Fig. 19 displaying the coefficient values for the different variables at the three discrete timepoints (initial, TTG=24Hr, genesis), there is seemingly an anomalous jump in SST coefficient values from Initial to TTG=24Hr and Genesis during
NADA years. It is important to take into account that 2005, one of the NADA years in this study, was characterized by anomalously high SSTs across the North Atlantic. In order to determine if the jump in coefficient values for SST is responsible for the
!101 decrease in low-level vorticity coefficient values with time, as displayed in the above figure, a Student’s t-test was performed for GO vs. NOGO case SST values throughout the years, as well as low-level vorticity values for reference, to assess the statistical significance (or lack thereof) of the respective variables. Results from the t-test are displayed in Table 13, and there is general agreement across all seasons and timepoints that low-level vorticity value differences between GO cases and NOGO cases are significant at values way below the 0.05 level, whereas statistical significance for SST values is absent across all of the data. Thus, the drop in low-level vorticity coefficient values during NADA years cannot be attributed to the variance in SSTs.
!102 TABLE 13. STUDENT’S T-TEST STATISTICAL TIME VARIABLE P-VALUE T-VALUE SIGNIFICANT SIGNIFICANCE (AT 0.05 LEVEL)?
ζ850 mb 0.0009143 3.3233 Y INITIAL SST 0.6283 0.4843 N
ζ850 mb 7.024E-05 3.9883 Y WARM TTG=24HR SST 0.8966 -0.13 N
ζ850 mb 0.0001999 3.7297 Y GENESIS SST 0.3145 -1.0063 N
ζ850 mb 1.528E-07 5.2724 Y INITIAL SST 0.8824 -0.148 N
ζ850 mb 2.671E-09 5.9843 Y COLD TTG=24HR SST 0.2481 -1.1555 N
ζ850 mb 1.766E-10 6.4218 Y GENESIS SST 0.1597 -1.4067 N
ζ850 mb 1.255E-06 4.8648 Y INITIAL SST 0.1417 -1.47 N
ζ850 mb 8.65E-13 7.2074 Y NADA TTG=24HR SST 0.612 0.5074 N
ζ850 mb 2.334E-13 7.3893 Y GENESIS SST 0.4823 0.7028 N
!103 TABLE 14. STUDENT’S T-TEST STATISTICAL TIME VARIABLE P-VALUE T-VALUE SIGNIFICANT SIGNIFICANCE (AT 0.05 LEVEL)?
INITIAL STRETCH 0.3098 1.016 N
WARM TTG=24HR | 0.4214 0.8043 N
GENESIS | 0.3143 1.0066 N
INITIAL | 0.0001 3.8101 Y
COLD TTG=24HR | 0.128 1.5227 N
GENESIS | 0.08826 1.7057 N
INITIAL | 0.2059 1.2653 N
NADA TTG=24HR | 2.176E-06 4.7532 Y
GENESIS | 5.073E-08 5.4742 Y
As previously stated, the drop in low-level vorticity discriminating power during
NADA years from the Initial timepoint to TTG=24Hr and Genesis cannot be attributed to an increase in the discriminating power of SST. However, by performing a Student’s t- test for the absolute value local max vorticity stretching (Stretch) term, the results of which are displayed in the Table 14 above, there emerges a clear trend in regard to the drop in discriminating power of low-level vorticity during NADA years throughout storm evolution. It would appear, by gauging the statistical significance (or lack thereof) of the
Stretch predictor, that the drop in low-level vorticity’s discriminating power is due to a rise in statistically significant differences between GO and NOGO Stretch values at those points. At the Initial time for NADA years, Stretch is not statistically significant at the
!104 FIG. 21. Statistical significance of the absolute value of vorticity stretching through time.
FIG. 22. Inverse relationship of vorticity stretching significance (dashed lines) and low- level vorticity coefficient absolute values (solid lines).
0.05 level. However, it is significant at TTG=24Hr, and even more so at Genesis. During
WARM years, Stretch is insignificant at all timepoints. Within COLD years, the Initial
!105 timepoint reflects that Stretch is statistically significant, but that at TTG=24Hr and
Genesis, it is not (Fig. 21). There is clear evidence in Fig. 22 that the statistical significance between GO and NOGO sample Stretch values is inversely proportional to the LDA-derived discriminating power of low-level vorticity. This relationship between low-level vorticity and the local max of the absolute value of vorticity stretching may be of some value in diagnosing some important processes occurring during tropical cyclone formation in differing ENSO phase regimes. That is, the statistical significance of low- level vorticity during WARM years and lack of significance for Stretch may indicate a decreased role in convergence maxima within the vicinity of an associated developing cluster during these years despite the continuing necessity for low-level rotation. The
Initial significance of Stretch during COLD years and insignificance at TTG=24Hr and
Genesis may indicate that the primary growth phases occur earlier on in the lifecycle of developing clusters during COLD years. The absence of Stretch significance during the
Initial phase of development during NADA years and the emergence of significance at
TTG=24Hr and Genesis may indicate that developing clusters during ENSO neutral years display a tendency toward explosive development later in their evolutions.
4.3 2° Radius
Following the LDA performed for the six distinct study years, as well as the study years in ENSO teleconnection groups, the process was repeated using the previously mentioned coordinate selection algorithm that calculated variable values within a 2°
!106 radius of the center of a cloud cluster empirically observed from the satellite imagery or the NHC Best Track archive. The purpose of such an approach is twofold: to look for further confirmation of the relative importance of each respective variable to the cyclogenetic process and how the importance of each changes seasonally, as well as to determine if one selection algorithm enhances the separation of multivariate discriminating power more than the other (i.e. cleaner results, clearer ranks in discrimination). One would assume that smaller scale processes would be picked up through this method, thus elucidating more of the mechanisms behind cyclogenesis or lack thereof. However, there exists the possibility that upper-level vorticity values may be anomalously affected by this selection algorithm, as values near the intensely-vortical eyewall region may attain more weight in the upper-level vorticity averages thus resulting in less negative / more positive upper-level vorticity for GO cases.
In initially examining the data for this method in Table 15, the numbers align relatively well with the procedure performed for the 5x5 box values. However, the data is slightly more muddled, and distinction and separation between variable discriminating powers is not as lucid as that for the 5x5 analysis. There is relative consensus that the preponderance of discriminating power during ENSO warm phases is confined to primarily low-level vorticity and the Coriolis parameter, and 2009 again is one with anomalously low meridional variation of TCG, low frequency of TCG, and, thus, markedly high coefficient value for low-level vorticity. During the ENSO cold phases, the primary discriminators are SST, low-level vorticity, upper-level vorticity, and
!107 vorticity stretching, in that order. As with the 5x5 LDA, 2007 displayed a marked
increase in upper-level vorticity discrimination relative to other years, and 2010 exhibited
a remarkably high coefficient value for SST, 0.5787. Vorticity stretching displayed
consistent discriminating power during 2007 and 2010 corresponding to a relatively large
range in between the mean local stretching max for GO cases vs. NOGO cases, with a
mean predictor value close to ~2.5 - 3.0 x 10-5 s-1 for GO cases and ~1.5 x 10-5 s-1 for
NOGOs (Table 16). Coriolis was relatively inconsistent during these two years in discriminant power with coefficient values of -0.3819 and -0.5107, respectively. The
Coriolis parameter was relatively insignificant during these years.
During neutral years, there is consensus between the two methods indicating that low-level vorticity is, again, the foremost discriminator amongst the selected six variables with values of -0.4739 and -0.4317 for the years of 2005 and 2012, respectively. SST was also relevant as the second ranked discriminator during 2005 and fourth ranked (just behind upper-level vorticity) during 2012. The importance of SST during 2005 in particular may be due to the higher frequency of developing cases over the Gulf of
Mexico which conventionally exhibits prominently elevated SSTs. Overall, if any of the methodologies in this study were to be repeated, the results seem to favor the 5x5 coordinate selection algorithm over the 2° radius method in their respective abilities to maximize separation in discriminant coefficients between these selected variables. One caveat, however, is that the utilization of a different variable set may involve processes that are more mesoscale in nature than those used here and, thus, may require or favor a
!108 different coordinate selection algorithm, such as the 2° radius, in order to augment the distinction between the variables in their power to discriminate.
TABLE 15. ANNUAL COEFFICIENTS, DISCRIMINANT COEFFICIENTS 2° RADIUS
ζ850 mb ζ200 mb SHEAR CORIOLIS STRETCH SST
2004 -0.5078 0.0231 0.0576 -0.1607 0.0872 0.0448 EL NIÑO (WARM) 2009 -0.4976 -0.1334 0.0260 0.2441 0.0141 0.0110
2007 -0.3819 -0.2385 0.0142 -0.0868 -0.1022 -0.2853 LA NIÑA (COLD) 2010 -0.5107 -0.1080 0.0434 -0.0724 0.1135 0.5787
2005 -0.4739 0.0231 0.0797 -0.1816 0.0717 -0.2988 NEUTRAL (NADA) 2012 -0.4317 -0.1473 0.0189 -0.2743 0.0569 -0.1115
!109 TABLE 16. ANNUAL MEANS, PREDICTOR MEANS 2° RADIUS
ζ850 mb ζ200 mb SHEAR CORIOLIS STRETCH SST
GO 3.0031 -1.4114 9.7974 4.6262 1.8084 300.9894 2004 NOGO 1.0687 -1.3276 12.0255 3.5934 1.2498 301.3275 EL NIÑO (WARM) GO 4.0011 -0.2732 8.121 3.0171 2.3880 301.109 2009 NOGO 1.5829 -1.5900 11.9902 3.7616 1.3594 301.1303
GO 3.8261 -0.0271 10.2237 4.376 3.1460 301.7063 2007 NOGO 1.3250 -1.7795 11.6303 3.97 1.3489 301.5153 LA NIÑA (COLD) GO 4.1495 -0.7560 8.0441 4.2588 2.6518 301.5077 2010 NOGO 1.4651 -1.4445 10.4192 3.2435 1.7016 302.0084
GO 3.9111 -0.9155 8.123 5.3207 1.6067 301.5325 2005 NOGO 1.6095 -1.2786 10.9891 3.916 0.9115 301.4629 NEUTRAL (NADA) GO 4.8164 -0.2287 10.1111 5.3047 0.5112 301.1247 2012 NOGO 1.1279 -1.6029 12.5498 3.6758 0.5568 301.4
!110 TABLE 17. ANNUAL COEFFICIENT RANKS, DISCRIMINANT COEFFICIENT RANKS 2° RADIUS
ζ850 mb ζ200 mb SHEAR CORIOLIS STRETCH SST
2004 1 6 4 2 3 5 EL NIÑO (WARM) 2009 1 3 4 2 5 6
2007 1 3 6 5 4 2 LA NIÑA (COLD) 2010 2 4 6 5 3 1
2005 1 6 4 3 5 2 NEUTRAL (NADA) 2012 1 3 6 2 5 4
4.4 Incubation period
Table 18 was created to communicate the average incubation period for hurricanes during each study year, beginning with the initial times recorded in the Best Track archives up until the time of genesis. Storms that developed on timescales outside of one standard deviation of the initial mean were not included in the final mean. Overall, the
WARM years exhibit a tendency towards shorter incubation periods compared to the
NADA and COLD years, whereas the NADA years display a significant trend of longer incubation periods.
!111 TABLE 18. ANNUAL INCUBATION PERIOD BY YEAR INCUBATION PERIODS
TIME FROM TD TO HURRICANE (HURDAT, HOURS)
2004 51 EL NIÑO (WARM) 2009 34
2007 44.4 LA NIÑA (COLD) 2010 72
2005 58.2857 NEUTRAL (NADA) 2012 75.4286
4.5 Case studies
Case studies have been performed for the purpose of examining the large-scale dynamics and thermodynamics in place around developing systems that eventually reach either TS or hurricane strength. The goal is to determine if there are clear harbingers of subsequent periods of strong intensification in the earliest stages of cloud cluster development by analyzing eventual TS clusters and eventual hurricane clusters up until
TS designation to determine if there is a marked dichotomy between the two in dynamic and thermodynamic nature. Another salient area of research addressing the tropical cyclogenetic process involved the calculation of MPI for a number of tropical storms and hurricanes employing dropsonde data from around the time of Tropical Storm designation
!112 in the Best Track Archives for the various storms. Hopefully, by analyzing each of the storms up until the aforementioned TS designation, as opposed to analyzing up to
Tropical Storm designation for TSs and up to Hurricane designation for hurricanes, the data would be normalized to a certain degree in order to determine if incipient tropical storms and hurricanes, both preceding and at tropical storm stage, exhibit significant similarities or deviation in behavior. Additionally, by calculating MPI for each of these storms, the purpose is to assess whether or not MPI, at TS stage, is a reliable proxy for the subsequent intensity outcome of the storms. It is expected that, due to the disorganization and inchoate conditions often characteristic of incipient systems at the outset of Best Track archives, there may not be clear distinction in trends within TSs vs. eventual hurricanes.
Eight tropical storms were analyzed with at least one storm for each of the study years. The predictor values were averaged using the data from the 5x5° method calculated for the LDAs for each year. The values were averaged from the initial observations/entries of the Best Track archives up until the approximate time of the dropsonde data retrievals used for the MPI calculation for each TS, which, in most cases, was either the 6-hr interval time of TS designation or within one or two 6-hr intervals of the TS designation. As indicated in the methodology, dropsonde data was pulled from
NOAA’s Hurricane Research Division (http://www.aoml.noaa.gov/hrd/data_sub/ dropsonde.html). SSTs used in the FORTRAN subroutines were taken from the averaged values extracted from the LDA analysis originating in the ERA-Interim Reanalysis.
!113 Reported MPI values are those with a surface enthalpy exchange / drag coefficient ratio
(Ck/Cd) equal to 1.0. As stated in Chapter 3, MPI was calculated utilizing pseudoadiabitic thermodynamics and dissipative heating. The factor used to reduce the gradient wind to the 10 m wind (function of drag) was 0.8. At the end of the hurricane case studies, some of the LDA-derived posterior probabilities will be reported, and model efficacy will be addressed later in the paper. For the sake of succinctness, not every storm numerically analyzed in the table will be described at length in the body of text. Detailed descriptions of storms and their evolutions are drawn from the National Hurricane Center’s Tropical
Cyclone Reports (http://www.nhc.noaa.gov/data/tcr/index.php?).
4.5.1 Tropical Storms
TS Matthew
The first tropical storm case was drawn from 2004, an ENSO WARM year. This tropical storm was TS Matthew. Matthew originated from a tropical wave that departed from the west coast of Africa on 19 September. It was difficult to track in between Africa and the Lesser Antilles due to its proximity to Tropical Storm Lisa and another disturbance. Upon reaching the Lesser Antilles, Matthew interacted with a westward- propagating upper-level low and a corresponding increase in convection and precipitation occurred. Subsequently, an upper-level ridge developed over the convection with a corresponding drop in pressure as Matthew reached tropical depression classification.
!114 Matthew continued to strengthen over the Gulf, eventually reaching tropical storm strength, and was steered northeastward by an upper-level low hovering over west Texas.
Matthew made landfall near Cocodrie, Louisiana and subsequently degraded.
Matthew was classified in the “best track” data as a TS at 1800 UTC 8 October.
Dropsonde data was retrieved from US Air Force reconnaissance at 1730 UTC of said day. The variable values, as averaged up until the TS designation, reside in the table above. The calculated MPI utilizing Emanuel’s method was ~30 m/s. Low-level vorticity exhibited relatively high positive values, and shear was also remarkably high
(21.140 m/s). Upper-level vorticity indicated immense anticyclonic tendencies, perhaps due to the interaction with an upper-level ridge around the time of TD designation.
!
FIG. 23. TS Matthew.
!115 TS Franklin
One tropical storm was selected from the neutral year of 2005, and that was TS
Franklin. Franklin emerged as the eventual result of a tropical wave that left Africa on 10
July. After passing the Cape Verde Islands, convection began to develop within this tropical wave, and upon reaching the halfway point between these islands and the Lesser
Antilles, there was a large swath of convection, albeit poorly organized. Upon arriving in the Caribbean, deep moist convection had abated due to wind shear associated with an upper-level trough over the Caribbean. The southern region of the of the wave generated
TS Gert over the SW portion of the Gulf of Mexico, and the aforementioned upper-level trough decayed permitting the development of upper-level anticyclonic outflow.
Convection reinitiated over the area north of Hispaniola associated with the upper-level outflow. Eventually the convection exhibited banding and a prominent mid-level circulation followed by a closed low-level circulation. The storm then reached TD and
TS intensities but was somewhat suppressed in intensification for a time due to shear associated with TS Gert’s upper-level outflow. As Gert moved westward and Franklin translated to higher latitudes, the shear dissipated and Franklin reached peak winds of 60 kt at 2100 UTC 23 July.
MPI was calculated from dropsonde #034113081 data taken at 1932 UTC 22 July.
The best track archive records initial TS intensity at 0000 UTC 22 July. The calculated
MPI was an impressive ~74 m/s, indicating significant thermodynamic efficiency and available boundary layer moist entropy. Averaged variable values exhibit a couple of
!116 notable trends: only slight low-level cyclonic flow, slight upper-level anticyclonic
outflow, and low to modest shear.
!
FIG. 24. TS Franklin.
TS Gabrielle
TS Gabrielle is an example of deviation from the most common mechanism of TS and Hurricane development - that is, the tropical wave. A low pressure area developed over the Georgia coast on 3 September 2007 along a frontal boundary that initially departed from the coast on 1 September. The low transitioned eastward in the following days and remained nontropical. A mid- to upper-level cut-off low moved over the low and recatalyzed a surface low. Surface circulation became more apparent in satellite analyses on 7 September and the system gained subtropical storm classification at 0000
UTC 8 September. Satellite imagery indicated that the system remained subtropical during the next half-day as the primary thunderstorm development occurred markedly
!117 north of the circulation center. This swath weakened and fresh convection grew in proximity just northwest of center. This process aided the transition to TS. Before arriving at the east coast, the center reformed closer to the thunderstorm activity leading to subsequent intensification. After landfall, Gabrielle dissipated from shear and land influences.
Dropsonde data for Gabrielle was retrieved at 0438 UTC 9 September and the estimated MPI was ~37 m/s. Mean low-level vorticity values display marked cyclonic behavior. Upper-level vorticity value reflects slightly cyclonic upper-level flow. The relatively positive (most of the storms and hurricanes reflect clear negative upper-level vorticity) upper-level vorticity values may be indicative of the formation mechanism.
Rather than the typical mechanism of tropical wave excitation, a mid- to upper-level low interacted with a surface low off the eastern US seaboard. Thus, also due to the unconventional nature of TS formation, Coriolis values are high owing to the relatively poleward meridional location.
TS Danny
Danny formed from a tropical wave that left Africa on 18 August 2009. Showers showed some semblance of organization on 22 August, which was halted by shear, and again on 24 August due to interaction with an upper-level trough. Satellite imagery and
QuikSCAT information showed that a closed circulation formed around 0900 UTC 26
August. TS-force winds were already established at this point, and Danny strengthened
!118 through the rest of 26 August and reached 50 kt the following day. Southwesterly vertical wind shear and a low pressure area near North Carolina enervated Danny, after which it was absorbed by a frontal zone.
Dropsonde data for Danny was obtained at 0232 UTC 26 August. Danny was classified as a TS at 0900 UTC 26 August. Calculated MPI value for Danny at 0232
UTC was very high with a value of ~64 m/s. This may be due to the pre-existent TS- force winds and thus high values of WISHE-induced boundary layer moist entropy.
Average predictor values up to this point indicated intense low-level cyclonic rotation, and anomalously positive upper-level vorticity values displayed remarkably cyclonic behavior. Stretch values were also extremely high, indicating that, if it were to continue unfettered, that TS Danny would develop a well-structured isothermal expansion branch of the Carnot heat engine. These anomalously high values may be due to the relatively rapid formation of TS Danny, thus reflecting the initial upscale energy cascade mechanism and a lack of developed upper-level outflow.
!119 !
FIG. 25. TS Danny.
TS Bonnie
TS Bonnie eventually spawned from a tropical wave that departed the African coast on 10 August of 2010. Convection did not thoroughly develop until the wave’s approach to the Leeward Islands on 18 July facilitated an interaction with an upper-level trough situated over Hispaniola. Despite southwesterly shear, a weak surface low developed on the northern portion of the wave axis at approximately 0000 UTC 22 July.
As the low passed the upper-level low, shear diminished and backed from southwesterly to southerly. This upper-level flow allowed for the generation of deep convection near the low-level circulation center. As the upper-level low moved south of the depression, the cyclone translated into an upper-level col area between the upper-level low and an expansive trough to the north. Within the col, vertical shear was heavily attenuated and
!120 further enhanced deep convection near the center. The system then reached TS intensity before upper-level flow increased and sheared off Bonnie’s top.
Dropsonde data was taken from NOAA 49’s Sonde # 082029096 at 2116 UTC 22
July. Bonnie was classified as a TS at 0000 UTC 23 July. MPI was estimated at ~60 m/s, which is quite prominent. Low-level vorticity values reflect cyclonic behavior, and upper-level vorticity values indicate slight upper-level anticyclone development. This may be due to the influence of the aforementioned col region between a northward trough region and a southward upper-level low. This col region, which would be characterized by a meridional-oriented wave with a ridge oriented westward due to no wind shift between the two low pressure areas, would enhance upper-level anticyclonic flow and thus facilitate outflow.
TS Colin
Colin’s seedling stages began with the interaction of a surface low and a tropical wave over the eastern Atlantic. The trough was originally formed by a previous passage of a slow-moving tropical wave that had detached. A larger and swifter tropical wave came off Africa and on 31 July of 2010 the two interacted to form a broad area of low pressure. Thunderstorm activity associated with this low pressure area exhibited increasing organization despite a lack of clearly-delineated circulation. On 2 August, the
Advanced Scatterometer (ASCAT) indicated that the circulation had become more prominent and it was thus assigned TD status. The depression translated WNW to the
!121 southern fringe of a deep subtropical ridge over the central Atlantic. Thunderstorm activity underwent another period of organization and the storm attained TS strength at
0600 UTC 3 August. The system accelerated to 25-30 kt from a precedent 15 kt, thus preventing the maintenance of a closed low-level circulation. Colin degenerated into a trough, yet maintained TS-force winds for a time. As the trough approached a weakness in the subtropical ridge on 5 August, it decelerated, the system slowed, and a well-defined surface circulation formed at 1200 UTC 5 August, thus regaining TS status.
Subsequently, stiff upper-level westerlies sheared off thunderstorm activity to the east of the surface circulation nucleus.
MPI was calculated using vertical data from sonde #095139445 at 2142 UTC 5
August, approximately ten hours after Colin had regained TS status after an initial weakening following a primary TS phase. The estimated MPI was ~40 m/s, and the averaged variable values over 5x5 domains up to that point indicated an cyclonic low- level tendency and anticyclonic flow in the upper levels.
TS Patty
A weak mid-level disturbance left the southeastern US coast in October 2012 and gravitated toward a mid-level anticyclone situated over the western Atlantic. This disturbance combined with a front on 3 and 4 October, and this front moved southward and became quasi-stationary to the north of the Leeward Islands by 6 October. A weak surface trough detached from the tail of the front which then generated deep convection
!122 as it moved westward, then northward, ahead of a cold front that sat east of Florida. The trough developed a closed circulation and, thus, became a low at 1800 UTC 10 October.
Subsequently, it evolved into a TD and thunderstorm activity became adequately organized close to the circulation center. The TD then strengthened to a TS at 0600 UTC
11 October. TS Patty was situated in a weak steering flow and moved very little.
Intensification was suppressed by an inchoate low-level ridge north of the cyclone and strong southwesterly winds aloft, creating shear and bringing dry stable air behind a front to the west into the center of circulation. Patty was degraded to a trough of low pressure and lost all deep convection by 1200 UTC 13 October.
MPI estimated for TS Patty was ~47 m/s from a dropsonde deployed by a US Air
Force Hurricane Hunter (USAF 308 (0116A)) at 1300 UTC 12 October, a little over a day after Patty was classified as a TS. Mean predictor values indicate that low-level was cyclonic in nature and upper-level vorticity was very prominently anticyclonic in nature.
Shear values of ~15 m/s also indicate the deleterious influence of shear destruction.
4.5.2 Hurricanes
Alex
Alex formed as the result of interaction between three discrete weather systems: a weak surface trough of mid-latitude origin, the diffluent portion of an upper-level low, and an approaching tropical wave. A broad area of surface low pressure developed on 30
July of 2004 NE of the central Bahamas. The low translated northwestward and,
!123 subsequently, the circulation became more coalescent and was classified as a TD. The
TD was characterized by poor organization initially due to shear and dry subsidence.
Following the approach of an upper-level trough from the west, the northeasterly shear over the circulation began to loosen and the TD became a TS on 1800 UTC 1 August. TS
Alex began to translate northeastward on 2 August and northeasterly shear continued its attenuation pattern. Deep convection previously contained in the SW quadrant of the circulation was then able to organize in spiral bands to the east, resulting in intensification and hurricane force at approximately 0600 UTC 3 August. Warm Gulf
Stream waters and reduced shear allowed for the continuation of intensification. After passing the Outer Banks, Alex steered away from the coast and accelerated within a deep layer of WSW flow. Alex then became a major hurricane and dropped to a minimum pressure of 957 mb. Eventually, Alex departed from the Gulf Stream and decayed.
Dropsonde data was drawn from a US Air Force flight at 1737 UTC 1 August. TS status was initially reached only slightly after that time, at 1800 UTC 1 August. MPI was estimated at ~28 m/s. Low-level and upper-level vorticity values averaged up until that point were only moderately positive and negative, respectively. Coriolis, however, was moderately high owing to the relatively high latitudinal positioning of Alex during inchoate phases. In regard to the forecasting capabilities of the discriminant function calculated for all data, including all temporal GO bins, the average posterior development probability calculated by the model for all Alex cases is 0.52, with an average probability of development of 0.58 from TTG=24Hr through Genesis.
!124 Katrina
Katrina formed as a consequence of the interaction of a tropical wave, the mid- tropospheric remnants of TD Ten, and an upper-level trough in 2005. This trough dismantled TD Ten, and the associated low-level circulation from TD Ten dissipated despite the continuation of its mid-level skeleton. A tropical wave departing from Africa on 11 August merged with these remnants on 19 August and produced thunderstorm activity north of Puerto Rico. The activity moved past Hispaniola and coalesced east of
Turks and Caicos. The upper-level trough weakened as it moved westward toward
Florida and the shear relaxed allowing for the formation of a TD by 1800 UTC 23
August. This TD was called TD Twelve, not Ten, because the originating tropical waves were separate entities. The TD became more organized over the Bahamas and deep convection grew overnight on 23 August. Convection began to wrap around the north side of the circulation center early on 24 August. The circulation became TS Katrina at
1200 UTC 24 August. It then moved northwestward within a weak region of the low- level subtropical ridge. The system developed an inner core and grew in intensity on 24
August, after which it was affected by a mid- to upper-level ridge over the northern Gulf, steering Katrina westward. Katrina experienced a period of deep convection over the low-level circulation center on 25 August and was declared a hurricane around 2100
UTC. Katrina crossed over the Florida peninsula and was briefly downgraded to a TS before traveling back over water into the Gulf. A markedly large upper-level anticyclone was the dominant feature over the whole of the Gulf of Mexico with a consequent drastic
!125 shear reduction and significant upper-level anticyclonic outflow allowing for enhanced thermodynamic efficiency. The strong mid- to upper-level ridge that steered Katrina west began to shift eastward, and a mid-latitude trough grew over the north-central US. This pulled Katrina westward then followed by a northwest turn. Katrina underwent an eyewall replacement cycle over 27 August, and it intensified from a Category 3 to
Category 5 hurricane in less than 12 hrs. SSTs over the Gulf at this time were anomalously high, which added to the remarkable strength of Katrina. It made landfall on 29 August over Louisiana.
The data used for the MPI calculation came from a dropsonde deployed at 1829
UTC 24 August 2005 by the NOAA 49 reconnaissance within 7 hrs after it was classified as a TS. MPI was ~62 m/s at this time. Low-level vorticity values reflect that the flow was primarily cyclonic, and upper-level vorticity was slightly positive, perhaps indicative of a higher level of nondivergence at upper levels and thus a more intense and deep layer of inflow and moist convection. Shear exhibited anomalously low values, indicative of the TCG-favorable conditions of the environment. Additionally, relatively high Coriolis values indicate the salience of planetary vorticity advection in aiding the formation process. LDA-derived average posterior development predictions for all Katrina cases is
0.51, with a heightened 0.59 of predicted development from TTG=24Hr through Genesis.
!126 !
FIG. 26. TS Katrina.
!
FIG. 27. Hurricane Katrina.
Felix
Felix developed from a tropical wave that left the African coast on 24 August
2007. The associated shower activity did not show signs of organization until 29 August
!127 corresponding with an increase in low-level vorticity when it formed into a TD around
1200 UTC 31 August east of Barbados. The TD moved westward, then made a WNW leap due to possible center reformation. The TD became a TS at approximately 0000
UTC 1 September ~60 nautical miles south of Barbados. TS Felix moved across the southern region of the Caribbean Sea in the midst of deep-layer easterly flow and subsequently reached hurricane intensity at 0000 UTC 2 September. After an eyewall replacement cycle, a corresponding intensification cycle, and landfall over Nicaragua,
Felix dissipated.
Data from sonde #054066012 dropped from a US Air Force Hurricane Hunter at
1626 UTC 31 August, approximately six hrs before TS designation, was utilized to calculate an estimate MPI of ~30 m/s. Pre-TS Felix exhibited moderate cyclonic low- level flow, anticyclonic upper-level flow, and low scaled Coriolis values. The model performed very poorly for Felix development cases, exhibiting predicted posterior development probability of 0.22 averaged across all cases.
Ida
Ida formed from the interaction of a poorly-demarcated tropical wave that reached the western Caribbean on 1 November 2009 and a broad low-level cyclonic gyre over the
SW Caribbean and transecting Central America over into the eastern North Pacific. This low moved only slightly for a period of days as deep, persistent convection developed, as well as an upper-level anticyclone over the western Caribbean. This engendered a light
!128 shear environment. Surface pressure continued to drop and convection became organized around the low center, and the circulation became a TD. The storm continued to crystallize as convective bands became clearly defined, and it became a TS at 1200 UTC
4 November as it progressed toward the Nicaraguan coast. Sustained light shear and warm SSTs augmented the intensification, and Ida became a hurricane at 0600 UTC 5
November before moving over Nicaragua and Honduras. After passing over the terrain,
Ida restrengthened over the northwestern Caribbean and reached a peak intensity of 90 kt winds. Over the eastern Gulf, strong shear disjointed the convection from the low-level circulation center and Ida weakened to a TS. Subsequently, convection regrew around the center and Ida reached hurricane strength again before passing over cool waters and undergoing another period of strong shear associated with a short wave trough. Ida became extratropical before making landfall on the Alabama coast.
Dropsonde data was retrieved from sonde #053716187 at 1806 UTC 4 November, approximately 6 hrs after initially reaching TS strength. Estimated MPI for TS Ida was
~43 m/s. Averaged low-level vorticity indicated cyclonic development and moderate upper-level anticyclonic flow. Shear was moderate. With respect to the efficacy, the discriminant model performed particularly poorly for Ida, with an average predicted posterior development probability of 0.24.
!129 Karl
Karl developed as a result of a broad low pressure system created by the interplay of a westward-propagating tropical wave and an extended trough protruding northeastward across northern South American into the southwestern North Atlantic in
2010. The tropical wave departed from the African coast on 1 September and produced little convection during its passage over the Atlantic. Upon approaching the Windward
Islands on 8 September, the wave slowed and thunderstorm activity burgeoned in proximity to the wave axis. The wave then emerged from the South American trough and these systems combined to form the aforementioned large low pressure system. The combined low then moved over the Caribbean Sea and generated small bands of deep convection at a sizable distance from the low center. Convection remained disorganized but the vertical structure became more distinct. On 13 September, research flights observed that the surface low did not remain but that the mid-level circulation was ostensibly present. Later that day, convection was reinvigorated, curved banding formed, and a closed low-level circulation redeveloped. It formed into a TD around 1200 UTC 14
September. Convective construction continued to coalesce and the TD met TS strength 6 hrs later. The TS moved toward the eastern Yucatan and, with the influence of a broad subtropical high pressure system over the Gulf and SE US, began to move WNW across the Yucatan into the Bay of Campeche. Karl traveled over land for 18 hrs and its intensity decrease; however, satellite imagery actually indicated that the convective organization and vertical structure improved, with a corresponding eye-like feature and
!130 enhanced convective banding. Low shear, warm SSTs, and significant mid-level moisture led to rapid intensification and the expansion of the subtropical high cause the storm to turn WSW. Karl reached hurricane strength at 0600 UTC 17 September. Before hitting the Mexican coast, Karl underwent high NE shear and dry air entrainment, resulting in weakening.
Dropsonde data for Karl was retrieved from sonde #092329043 at 1730 UTC 14
September deployed by a US Air Force flight, and MPI was calculated to be ~36 m/s.
This comes about 30 mins before Karl was classified as a TS. Variable values averaged up until that point indicated cyclonic low-level flow, anticyclonic upper-level flow, and low shear values below 10 m/s. SSTs were very high, bordering on 30ºC. Model-derived average posterior probability of development for Karl cases is 0.37, with an enhanced probability of 0.48 from TTG=24Hr through Genesis.
Sandy
Sandy emerged as a result of a tropical wave that departed the African coast on 11
October 2012 and interacted with a large upper-level trough over the eastern Atlantic creating an expanse of thunderstorm activity that was limited by shear for a time.
Subsequently, minimal convection occurred near the wave axis for the next few days, probably due to upper-level convergence over the Atlantic associated with Hurricane
Rafael to the east. The wave propagated past a pre-existing disturbance in the ITCZ and coalesced to the point of minimal distinction. The wave entered the Caribbean on 18
!131 October with disorganized convection that would subsequently grow in intensity. The environmental favorability grew in the proximity of the wave with corresponding pressure falls over the central Caribbean Sea due to a clearly-demarcated rising branch of the Madden-Julian Oscillation. Incipient banding formed on 20 October and deep moist convection intensified. This convection probably contributed to the generation of a broad area of low pressure that moved to the west and southwest on 21 October during a period of high pressure build-up over the Gulf of Mexico. The southwest translation of the low heralded a period of reduced shear associated with an upper-level anticyclone over the
SW Caribbean Sea. Convective banding was organized sufficiently to warrant TD classification by 1200 UTC on 22 October. Thunderstorm activity increased near and north of the center, and an Air Force Hurricane Hunter flight indicated TS conditions by 6 hrs after TD-strength was reached. Subsequently, the growth of Sandy was slow during the initial stages, but by late 23 October, Sandy began to intensify at a greater rate. A mid- to upper-level trough over the NW Caribbean and Gulf drove Sandy N/NEward, and
Sandy became a hurricane at 1200 UTC 24 October 80 nautical miles south of Kingston.
Sandy would then pass over Jamaica, the Bahamas, and would grow in horizontal extent considerably correlated with the upper-level trough that brought warm advection aloft and augmented upper-level divergence. Sandy then turned NEward and grew in translational speed ahead of a mid-tropospheric trough over the central US. The structure of Sandy became unconventional, with strongest winds in the western portion of the cyclone with an associated stationary frontal boundary to the NW of the center. The front
!132 weakened on 28 October as Sandy departed from the upper-level trough. On 29 October,
Sandy approached an anomalous blocking pattern over the north Atlantic that kept it from
departing to sea. The large mid-tropospheric high grew into the NE parts of North
America, while the mid-tropospheric trough in the central US deepened, protruded into
the SE, and generated baroclinic forcing for Sandy.
!
FIG. 28. The unconventional appearance of Sandy at 1145 UTC 27 October with a stationary front and enhanced convection confined to the quadrant NW of center. The convection deviates from the classic pattern of convective concentration located to the storm-relative right side.
Dropsonde data for the MPI calculation came from sonde #122725076 at 2247
UTC 23 October dropped from USAF 302 (0318A). This was about 24-30 hrs after reaching TD status and 12-18 hrs before reaching hurricane strength. MPI was calculated to be ~43 m/s. Low-level vorticity exhibited, on average, markedly positive values, whereas upper-level vorticity was characterized by anticyclonic flow. Out of all the hurricane case studies, the discriminant function performed the best in forecasting !133 capabilities, with an average posterior probability development prediction of 0.57, with an augmented posterior probability of 0.82 from TTG=24Hr through Genesis.
4.6.3 Case Study Summary (and a note on model efficacy)
Variable values for each of the respective case studies are presented on the subsequent page in table format. An important note: the efficacy (or lack thereof) of the
LDA model-derived posterior probabilities reported in the hurricane (developing/GO) case studies will be explored and assessed in the following chapter (5.2 and 5.3).
!134 TABLE 19. CASE CASE STUDIES STUDIES
MPI ζ850 mb ζ200 mb SHEAR COR STRE SST (VMX)
TS
2004 MATTHEW 30.485 2.594 -4.630 21.140 5.943 3.441 302.166
2005 FRANKLIN 73.661 0.590 -0.470 10.328 6.244 0.938 302.260
2007 GABRIELLE 37.009 2.853 0.299 11.019 7.484 2.792 301.242
2009 DANNY 63.724 4.161 1.386 10.547 6.071 9.580 302.184
2010 BONNIE 60.169 2.945 -0.557 14.158 5.492 1.797 301.955
COLIN 39.824 1.933 -1.379 10.124 4.145 2.097 301.725
2012 HELENE 26.602 1.784 -0.956 8.715 3.846 1.649 301.626
PATTY 46.957 1.893 -3.520 14.902 6.267 1.245 301.825
HURRICANE
2004 ALEX 28.381 2.854 -2.256 12.071 7.555 3.069 301.884
2005 KATRINA 62.098 1.916 0.443 5.791 5.862 1.215 303.169
RITA 35.650 2.375 -1.147 11.206 5.404 2.373 302.491
WILMA 32.540 3.125 -1.261 9.175 4.368 2.147 302.771
2007 FELIX 30.184 2.196 -1.137 8.772 2.957 3.395 302.032
2009 IDA 43.325 2.660 -2.037 10.569 2.833 3.964 302.216
2010 KARL 35.931 2.331 -1.822 8.462 4.293 2.249 303.264
2012 SANDY 42.820 2.921 -2.007 10.084 3.404 3.459 302.550
P-VALUE 3.1E-05 0.742 0.106 0.781 0.026 1.2E-13
!135 In looking macroscopically at the results from the variety of storm case studies in
Table 19, there are a few trends that emerge, with a few exhibiting robust consensus.
Some of the clearest trends are that all cases exhibit low-level cyclonic development,
typically anticyclonic upper-level behavior, and shear is, on average, lower surrounding
the cases that eventually develop into hurricanes (9.507 m/s) in comparison to the
systems that only reach TS strength (10.636 m/s). Another trend is that hurricane (GO)
cases display slightly higher low-level vorticity values (2.613x10-5 s-1 vs. 1.983x10-5 s-1) and slightly more negative upper-level vorticity values. Across all cases, the majority exhibit negative upper-level vorticity values indicating that there is a deep layer of convergence overlaid by an outflow stratum that signifies thermodynamic efficiency. The average upper-level vorticity for the nondeveloping cases (-1.306x10-5 s-1) here is slightly more positive than that for the hurricane cases (-1.416x10-5 s-1), indicating that the level of nondivergence is higher for nondeveloping TS cases than the developing hurricane cases. Although potentially somewhat surprising, this slight disparity 1) may not be reliable due to a very small sample size here but 2) if it is representative of a more wide- ranging trend, it may be indicative of the fact that, in comparison to nondeveloping cases, developing cases often initiate in conditions of low favorability but expand in favorability over time. Coriolis is slightly attenuated during the TS case studies (4.676x10-5 s-1 vs.
4.755x10-5 s-1), as well as vorticity stretching maxima (1.915x10-5 s-2 vs. 2.611x10-5 s-2)
and SST (301.713K vs. 302.602K). The bottom row of Table 19 reflects the p-values for
!136 the constituent variables (excluding MPI) which indicate that only low-level vorticity, stretch, and SST are significant at the 0.05 level for this small case study sample set.
In regard to MPI, the average value is actually higher, on average, for the nondeveloping TS cases than the developing TS cases. This implies that MPI, particularly in the earliest stages of development, is not a reliable proxy for projecting subsequently-realized intensification. As alluded to by Hennon and Hobgood (2003), which references McBride and Zehr (1981), the thermodynamic environment is usually very similar surrounding cloud clusters throughout the entirety of the Atlantic hurricane season, indicating that changes in MPI should not significantly affect the projected outcome of a given cloud cluster. Additionally, Kerns and Chen (2013) convey that developing systems grow in favorability over time (as previously stated), whereas nondeveloping systems may initially reflect highly favorable conditions yet taper off in potential intensity with time. In regard to the lack of robust consensus concerning the low-level and upper-level vorticity values for the developing cases vs. the nondeveloping cases, HH03 also indicate that low-level vorticity by itself (or upper-level vorticity) is not adequate in determining the outcomes of cloud clusters, but rather, the change in vertical vorticity as encapsulated in the Daily Genesis Potential (DGP).
!137 TABLE 20. MAXIMUM POTENTIAL INTENSITY ABRIDGED MPI (SUB-500MB CAPE) VALUES
MPI (VMAX) AVE 𝜎
TS 31.193 5.019
2004 MATTHEW 30.405
2005 FRANKLIN 35.703
2007 GABRIELLE 30.005
2009 DANNY 30.985
2010 BONNIE 29.508
COLIN 32.024
2012 HELENE 21.815
PATTY 39.095
HURRICANE 29.823 1.748
2004 ALEX 28.330
2005 KATRINA 31.722
RITA 30.554
WILMA 30.002
2007 FELIX 27.105
2009 IDA 31.583
2010 KARL 28.151
2012 SANDY 31.133
!138 A caveat in regard to the previous case studies and the calculation of MPI utilizing the delineated dropsondes at the respective times near TS designation for each of the storms is that there is a relative lack of consistency in the vertical extent of the recorded values for the dropsondes; that is, minimum pressure level (maximum altitude) at which measurements are recorded is often different between the distinct dropsondes. This is dependent upon which aircraft type/model is deploying a given dropsonde and is a function of its typical flight altitude. For example, one dropsonde may take readings up to a level of 189.0mb, whereas another dropsonde may only retrieve data for levels up to
410.0mb. The dropsondes reflecting data up to higher levels in the atmosphere will therefore typically exhibit much higher CAPE and, consequently, VMAX values. Thus, there exists the need to introduce a normalizing factor to the data so as to not mislead.
Therefore, by employing the same data used previously, but instead only lifting the parcel to a level of 500mb during CAPE calculation within the CAPE subroutine (because all reported dropsondes extend above the 500mb level, at least), the MPI is calculated and displayed in the Table 20. A drawback of this method is that, obviously, only the MPI values involving the lower to mid-level CAPE integrations are represented while the upper-level CAPE extending to the level of neutral buoyancy is absent. Thus, the method is far from perfect. However, as previously stated, it is important to account for the varying vertical extents of dropsonde data for the case studies. In looking at the results, the trends appear similar to those summarized in the case studies. There is no clear distinction between the calculated MPI values for TSs as opposed to hurricanes, but TSs
!139 appear to exhibit slightly higher mean MPI values around the time of TS designation with higher variance, as evidenced by a higher standard deviation (5.019) than that of the hurricane case studies (1.748).
!140 Chapter 5: Discussion
5.1 Preeminent predictors
In Fig. 28 below are the summarized results for the primary output of the study.
The two top rows contain the LDA-derived linear model of the six predictors with respective coefficients as calculated using the 5x5° box method with the top row including data from all years and the second row utilizing data only from the WARM years - 2004 and 2009. The bottom two rows are of the same vein except they employ the predictors averaged using the 2° radius method (smaller scale). A few basic trends are clearly manifest in juxtaposing these equations for the two aforementioned methodologies. There emerges a clear trend that for all years combined, across both methodologies, the two preeminent predictors are 1) low-level vorticity and 2) interchangeably the Coriolis parameter and SST. There exists no great disparity between the discriminating power of low-level vorticity during WARM years vs. all years combined. SST, as well as Coriolis and upper-level vorticity, are slightly less powerful predictors during El Niño in comparison to the LDA performed including all study years.
Shear exhibits a slight increase in discriminating power during El Niño years vs. all years. Thus, one of the primary questions at the outset of the study regarding the change
!141 in discriminating power of certain variables correlated with distinction between ENSO
phases is satisfied by the fact that it appears that the discriminatory power of the
predictors remains relatively unchanged interseasonally. That is, it seems that the upper-
level pattern that affects TCG-suppression during WARM years over the Atlantic MDR
does not significantly affect the discriminators of the formation process relative to each
other (in regard to the variables described here). However, when analyzing the predictors
discretely, it is clear that the behavior of each does differ at least slightly when addressed
in one ENSO phase vs. another.
5x5° BOX METHOD
ALL YEARS
EL NIÑO
2° RADIUS METHOD
ALL YEARS
EL NIÑO
FIG. 29. LDA Functions.
Due to the preponderance of power assumed by low-level vorticity and the scaled
Coriolis parameter, it was deemed necessary to attempt to visualize and further analyze the relationship between these predictors and how said relationship behaves interseasonally. A series of three figures were created to graphically represent the spatial distribution of all of the cloud cluster cases included in this study relative to each one’s class (GO or NOGO), low-level vorticity value, and scaled Coriolis value (effectively,
!142 latitude). All cases for the La Niña years combined, the El Niño years combined, and all study years combined were scatterplotted sequentially in the following three figures.
Coriolis lies on the y-axis to convey a sense of the latitudinal / meridional spatial extent of the cases, and low-level vorticity lies on the x-axis. GO cases are represented by open circles with a red hue and NOGO cases are symbolized with the same open circles but of a powder-blue hue. For the discrete years, each graph included a linear best-fit model for just the GO cases (a desert hue) as well as all cases combined (GO + NOGO, violet hue).
For the combined-year / seasonal graphs, an additional line of best fit was added for the
NOGO cases (seafoam hue). Considering the format of these figures, the lines of best fit then effectively indicate the meridional gradient of low-level vorticity for each of the respective datasets they fit.
5.2 Figures (low-level vorticity, Coriolis)
FIG. 30. Seasonal Figures.
!143
FIG. 31. All Years Combined.
Analysis of the previous three figures leads one to a number of very elementary conclusions regarding the relationship of the scaled Coriolis parameter and low-level vorticity across all ENSO phases. Primarily, there appears to be little difference in the relationship, as evidenced by the lines of best fit, between ENSO WARM, COLD, and neutral phases. Secondly, the general trend across all three figures is that developing cases lie predominantly on the right side of the cloud cluster scatterplots, indicating that
!144 low-level vorticity exhibits notable amplification around GO cases in comparison to
NOGO cases. Additionally there seems to be an enhanced concentration of GO cases
around 3 x 10-5 s-1 value of low-level vorticity in each graph, Coriolis values around 4
rad/s in COLD years, and around 2.5 rad/s in WARM years. Thus, it seems that low-level
vorticity is the most consistent across all study years, and that there is a slight
modification of the Coriolis parameter favored for GO cases from one ENSO phase to
another. The modification of the Coriolis parameter is to be expected, as the TCG
suppression over the Atlantic MDR constricts and wedges the areas of favorability to
above and below 10-20ºN. Lastly, the figure representing COLD year cases indicates a
higher incidence of GO cases with significantly increased values of low-level vorticity
between 4 and 6 x 10-5 s-1.
5.3 Model efficacy
Histograms were plotted using R in order to visually assess the separation achieved by the LDA-derived model for all study years combined, WARM years combined, and COLD years combined using the 5x5° averaging method. The first set of figures indicates the separation achieved by the model for GO and NOGO cases for all study years combined. In regard to the LDA-derived model for all of the study years combined, as evidenced in Fig. 31, the distribution of LDA values for NOGO cases is slightly more normal, with center falling somewhere in between near +1. The GO cases are distributed relatively normal, with peak density in between -0.5 and -1 and the
!145 majority remainder of values residing in between 0 and -2. There is moderate separation, but overall, there is clearly significant potential for a more effective means of separating and achieving maximal separation.
!146 5.3.1 All Years
FIG. 32. All-Year Model Separation.
WARM year separation produced by the model indicates, again, a slightly bimodal distribution of NOGO cases with peak density between 0 and +1, whereas LDA values for GO cases skew left and are predominantly negative, with most prominent range of 0 to -0.5. As in the case of All years, there is significant overlap in the
!147 normalized mean region around 0, but, overall, there is generous separation achieved by
the LDA model for WARM years.
5.3.2 El Niño
FIG. 33. WARM-year Model Separation.
COLD year GO cases look slightly different than in the previous two models, with a wider dispersion of equation values throughout the negative domain. Peak density
!148 lies between 0 and -1.5, with the maximum density in between 0 and -0.5 in particular.
NOGO case equation values are distributed normally across the positive domain with maximum counts between +1 and +1.5 As with the other two models (all years and
WARM years), the separation achieved by the linear discriminate analysis reflects slight success in producing a statistically effective model.
5.3.3 La Niña
FIG. 34. COLD-year Model Separation.
!149 The appearance of visual separation (alternatively, overlap) between LDA- computed case values for GO and NOGO cases is tangible affirmation that the model constructed in this study has significant accuracy in predicting the outcomes of cloud clusters, but there remains room for improvement in regard to its ability to clearly demarcate and distinguish between developing and nondeveloping cloud cluster cases.
As with virtually any model, the results are not perfect, but are satisfactory for the scope of this study. Because there is slight overlap in GO and NOGO case equation values for each model set, there exists a variety of potential remedies that could be employed in order to enhance the separating power of the model further so that the probabilities of development or decay for north Atlantic tropical cloud clusters can be assigned more confident and higher magnitude values with a higher degree of accuracy.
5.4 Statistical analysis of Model Skill
For the sake of supplementing the previous visualization of model efficacy, statistical measures will be used to assess the predictive skill achieved by the model.
Statistical analysis of model efficacy will be performed for the LDA involving all pre- genesis GO cases (as opposed to only selecting the ‘Initial’, ‘TTG=24Hr’, or ‘Genesis’ cases). In order to numerically quantify the relative skill of this LDA in discriminating between development and nondevelopment cases, two conventional statistical scores were employed based on the discriminant function computed including all years’ data with the 5x5º Method. Overall, model efficacy reflects the accuracy (or lack thereof) in
!150 reforecasting the outcomes (GO or NOGO). For example, if an LDA is run for all of the
study years combined, the prior probabilities of GO or NOGO ([ΣGO/ΣTOTALCASES]x100% and [ΣNOGO/ΣTOTALCASES]x100%) and data for all cases are used in LDA computation to train (create) the linear model, and then said model may be used to reforecast/predict the posterior probabilities of GO and NOGO for each case (satellite image). Then, statistical measures may be used to assess how effectively the model recreates the past empirical reality (e.g. how often observed GO or NOGO cases are actually predicted by the model subsequently). One of these statistical measures of skill is the Brier Score.
The Brier Score calculated for this study is 0.097. Essentially, a Brier Score is the mean squared error between the probability of development and actual development (assigned a value of 1 if development occurred). Thus, the observed value for each case (0 for nondevelopment/NOGO, 1 for development/GO) is subtracted from the LDA-generated posterior probability calculated for each case, after which the difference is squared.
These squared differences are summed and subsequently divided by the sample size, which is, in this instance, 5,221 cloud cluster cases. Theoretically, a Brier Score of 0 signifies perfect statistical skill and, thus, the lower the number, the greater the model efficacy.
!151 A second statistical procedure used to analyze the skill of the LDA derived from all study years’ data is the Threat Score, which is displayed above and involves three simple quantities - A, B, and C. C signifies the amount of development cases correctly predicted/forecasted by the model, A reflects the quantity of development forecasts made by the model, and B represents the amount of empirically observed development cases.
A, B, and C values were computed utilizing data from all of the study years with the broad-scale 5x5º Method for variable calculation and a 0.5 probability threshold, which is lower than the 0.65 threshold from Perrone and Lowe (1986). The value of A - the quantity of forecasted development cases - is 338. The B value, or quantity of observed development cases, is 756. And the value of C, or the cases in which development is both forecasted and observed, is 182. Thus, the Threat Score is equal to
which, following calculation, produces a value of 0.22. As stated by Hennon and
Hobgood (2003), Threat Scores above 0.5 reflect high model skill, and, thus, there is significant room for improvement in the model used in this study. The previously mentioned p>0.65 threshold from PL86 refers to the probability boundary between development and nondevelopment; that is, if a posterior prediction generated by the model for a certain case comprises higher than a 0.65 probability of development, then such forecasts are classified as developing. In the case of the Threat calculation presented here, the utilized threshold is the lower value of p>0.5 (which is the default
!152 used in R). Therefore, A is the quantity of these ascribed development classifications, and C is the amount of said development forecasts coinciding with observed development cases. A perfect Threat Score would exhibit a value of 1, meaning that every posterior probability forecast is accurate when compared to the empirical observations.
The inevitable question then is this: why is there model deficiency? First and foremost, it is important to take into account that the purpose of this study was more so to identify the most powerful discriminators in the process of distinguishing between the two outcomes of hurricane development or nondevelopment. In this way, it is more of a heuristic model rather than one meant for forecasting capabilities. Secondly, and very importantly, the statistical measures of skill are not wholly uncharacteristic of these types
FIG. 35. Threat scores vs. Forecast hour from Hennon and Hobgood (2003).
of studies based on precedent. Hennon and Hobgood (2003) reported values of Brier scores and Threat scores with respect to each of the temporal bins (up to 48 hours
!153 preceding genesis) as shown in the line graph. Taking into account that the scores reported in the present study include all data (that is, all developing cases regardless of the temporal bin), the Brier score would fall closer to the more skilled side of the spectrum in HH03’s, and the Threat score falls around the middle of the range of Threat scores from HH03. Due to the fact that all forecast hours are included in the scores calculated for this study, it can be assumed that both scores would reflect higher model skill at the forecast hours more immediately preceding (closer) to genesis, and potentially lower skill at much earlier bins (such as 48 hours preceding genesis). As indicated in the hurricane case studies, the predicted posterior probability of development increased in the
24 hours leading up to genesis relative to the average of the developing cases from the initial point up to genesis. However, it is very important to keep in mind that the p>0.5 threshold is used in the Threat score computation for this study (as opposed to the p>0.7 threshold used in HH03) due to its different nature relative to the design of HH03, therefore inflating the value of the Threat score. The model in this study achieved a
Threat score of 0.11 when utilizing the p>0.7 threshold employed in HH03.
!154 FIG. 36. (left) Threat score achieved by six discrete yearly LDA runs including all GO cases vs. incubation (gestation) period of GO systems averaged discretely over each year. (right) Threat scores of predictions from LDAs run discretely for 2010 and 2012 - the years of highest statistical skill - for each temporal bin from 6Hr TTG to 48Hr TTG.
Another extremely important caveat regarding model skill, as alluded to in the one of the previous sentences, is the fact that the design, methodology, and implementation of this study is glaringly different from those presented in Perrone and
Lowe (1986), as well as HH03. The goal in PL86 was to produce a discriminant function based on the two outcomes of development into a tropical storm or nondevelopment, which, intuitively, is very different than differentiating between hurricane development or nondevelopment. In HH03, the primary focus was to generate discriminate functions based on the outcomes of tropical depression development or nondevelopment. Thus, both of these studies present statistical analyses based on fundamentally disparate processes. With the increasing magnitude in the systems being studied from tropical depression < tropical storm < hurricane, the disparities between outcomes of
!155 development and nondevelopment become proportionally smaller relative to overall intensity and more statistically problematic. For example, a system that hovers at 60 kt max-sustained 1-min winds for a significant amount of time, which is just below the 64 kt necessary for category 1 hurricane classification, may exhibit very little structural and behavioral differences from a system that reaches 65 kt (and hurricane categorization) at only one 6 hour interval. Inevitably, in this study a significant number of strong tropical storms were present and, by virtue of the methodology, were classified as NOGO systems. Thus, the intrinsic nature of a binary classification system such as this is that it is, perhaps, too rigid to be effective when discriminating between outcomes at such high intensities. When tweaking and reclassifying the LDA performed for all cases such that
GO signifies TS development and NOGO signifies decay preceding TS development
(nondevelopment), there was a slight improvement in Brier score (0.079) and in Threat score (0.23), potentially lending credence to the idea that LDA loses its effectiveness for
TCG forecasting at higher intensity thresholds like hurricane development.
!156 Chapter 6: Conclusions/Trajectory
6.1 Primary Conclusions
In order to reiterate the foremost goals of the study, the most salient results will be summarized in the following sections so that a framework may be established to support a future direction of research regarding the tropical cyclogenetic process. As alluded to previously, there is significant room for model improvement, enhanced variable inclusion, and methodology modifications that would markedly ameliorate any of the present shortcomings.
6.1.1 Preeminent Discriminators
As previously expounded, the predictors exhibiting the highest magnitudes of discriminating power are low-level vorticity (rotation), the scaled Coriolis parameter, and
SST. This observation is in alignment with a significant portion of the literature addressing LDA applications to the TCG processes in various ocean basins. In general, there is consensus across both of the methods - 5x5° Box and 2° Radius - that low-level vorticity, Coriolis, and SST are the primary discriminators. However, the results are more clearly demarcated using the broader-scale 5x5° method than the smaller-scale 2° radius method. This could potentially indicate that the larger, system-scale intensification
!157 (SSI) mechanism described in Tory et al. (2007) and its associated conditions is a greater discriminator (not necessarily more important) of cloud clusters‘ outcomes than the initial primary mechanism of VHT-driven vorticity enhancement. In other words, it seems that a plausible conclusion is that the SSI is a rate-limiting step in the cyclogenesis process and that the initial construction of vortical cores is necessary but not sufficient to guarantee TCG.
6.1.2 ENSO Influence on Discriminators
ENSO’s most profound effect on the north Atlantic, as highlighted by the literature, is a swath of TCG-suppressive conditions associated with a positive upper- level vorticity response over the Atlantic MDR. Thus, the TCG-favorable environment is significantly constricted during El Niño (ENSO WARM) phases as opposed to COLD and NADA years. In addition to the constriction, there exists a sort of wedging effect in that the TC-favorable areas are pushed to the meridional regions north and south of the
MDR. However, this affects the frequency of TCG, as the region south of the MDR possesses little vortical augmentation in the form of Coriolis-driven planetary vorticity advection (and associated Rossby radius of deformation reduction), and the region north of the MDR is often characterized by cooler SSTs and the absence of tropical wave propagation. As a result, there is less meridional variability in TCG over the north
Atlantic during El Niño years with an accompanying decrease in Coriolis discriminating power and, consequently, increase in low-level vorticity discriminating efficacy. In
!158 general, developing cases reflect a tendency toward markedly more positive ζ850 mb values, indicating that these cloud clusters possess enhanced vortical scaffolding throughout the lower-levels of the troposphere.
As evidenced in the case studies at the terminus of the results section, MPI, calculated around the time of TS-strength classification, is not an effective predictor of whether or not a TS will develop into a hurricane. In fact, some of the highest MPI values aligned with cases that never developed past TS designation (nondevelopment). In regard to these case studies, the developing cases, on average, exhibited more negative upper-level vorticity values, indicating that these cases differed from the nondeveloping counterparts in that they were constituted by a shallower layers of tropospheric inflow, lower levels of nondivergence, and less elevated outflow heights at the inchoate outset of storm development. This is in alignment with the previous discussion about favorability evolution throughout the course of storm life cycles, as GO cases typically start out with less favorable characteristics and grow in favorability through time, whereas NOGO cases can often initiate with the appearance of a “bomb” but subsequently degrade in favorability. Developing cases also exhibit preference for environments of suppressed vertical wind shear, which is to be expected. Additionally, the local maximum of the magnitude of vorticity stretching around cloud clusters is typically higher for developing cases across the majority of years.
!159 6.1.3 Potential Implications Accompanying Future Climate Change
The Atlantic MDR comprises an area of simultaneously favorable SSTs and
Coriolis values for TCG. North of the MDR, SSTs are often too cool for genesis to be supported, and conditions below the MDR, in many cases, do not favor development due to relatively low Coriolis-driven planetary vorticity advection. Thus, the MDR represents a belt of favorability arising from the combined effects of warm SSTs and sufficient
Rossby deformation radius reduction. However, if SSTs continue to rise corresponding with an increase in human-induced global mean temperature, then, based on thermodynamic theory and some of the MPI models discussed previously such as
Holland’s, the potential severity of TCs globally will increase (however, one caveat is that these same authors indicate that TCG will occur at higher SSTs in a warmer world).
While the atmosphere in some locations may adjust to the potential increase in SSTs with elevated geopotential heights and upper-level tropospheric temperatures (which would mean that TC severity should not increase significantly), some areas that experience heavy influence from interannual or interseasonal teleconnections that cause transient decoupling or lagging between ocean and atmosphere may have windows of anomalous favorability for TCG due to the higher SSTs. More specifically, if SSTs increase in the
Atlantic, would the lagging that occurs with cooler SSTs relative to a warmer, more stable tropospheric column become more attenuated? That is, would the anomalously cool
SSTs and stable atmospheric column during WARM years be characterized by warmer
SSTs and less stable atmospheric columns in a warmer world? In other words, would
!160 WARM years be less TCG-suppressed? Would the meridional extent of TCG favorability expand over the Atlantic with warmer SSTs reaching poleward? Is there a legitimate possibility that human-induced climate change may eventually shut down the Atlantic
Meridional Overturning Circulation? If so, how would that affect TCG?
6.2 Model Improvement
One of the most controllable elements of this study is the acquisition and analysis of data, and tweaking or alteration of the methodology could drastically augment the efficacy of the LDA model. As visually delineated previously, the separation achieved by the model between the two classification outcomes was apparent, but there remains significant room for improvement. While there was some separation, there was still a small degree of overlap between the LDA equation values calculated for the GO and
NOGO cases. One of the most intuitive remedies would be possibly the inclusion of more variables or substitution of some variables with others. Some variables that could potentially be included are DGP (McBride and Zehr 1981), level of nondivergence, or mid-level or low-level specific humidity.
Another potential remedy addresses how the variables are collected spatially. In this study, the two spatial methods used were the 5x5° box method and 2° radius method around cloud clusters. Potentially, the application of an interpolation technique - such as cubic spline approximation - to calculate the values of variables on a 5x5° box centered
!161 on the specific cloud cluster location could enhance the separation achieved by the derived linear model.
Thirdly, the threshold criteria for cloud cluster candidacy could be altered or improved to yield greater predictive power. That is, the size, areal, and intensity thresholds identified via IR brightness temperatures could be changed, or a different type of satellite imagery with a different threshold set could be utilized.
6.3 Future Work
There exist a number of potential future directions for research founded on the basic tenets of this study. It still seems appropriate that the tropical cyclone formation be treated as a stochastic problem, so the continued application of statistical models appears to be quite fitting. One of the more obvious potential enhancements of this study is drastic expansion of the original dataset to include many more study years in order to further highlight differences in tropical cyclogenesis from one ENSO phase to another.
Additionally, as stated above, the inclusion of more/different predictors or a modification of how these predictors are calculated spatially could significantly improve the quality of the LDA model. A third potential study enhancement would be the utilization of dynamic numerical modeling in order to tweak certain environmental variables (f, relative humidity, SST, tropospheric environmental temperature profiles) surrounding a convective pulse and observe how the modifications affect low-level vorticity, cold- to warm-core transition, and intensification. Fourth, there exists the potential for
!162 completing future statistical iterations utilizing Emanuel and Nolan’s Genesis Potential, which involves four very important variables: low-level vorticity, mid-level relative humidity, shear, and PI. Particularly, the quality of this study could have been dramatically improved by the inclusion of an atmospheric thermodynamic variable such as mid-level relative humidity instead of the mere inclusion of SST. As previously stated, the ocean is thermodynamically primed for TCG throughout the majority of hurricane season and probably does not provide significant covariance with respect to GO or
NOGO cloud clusters. Conversely, the inclusion of mid-level humidity could be very effective in signaling either subsequent amplification or decay of atmospheric disturbances.
FIG. 37. Locations of pre-genesis GO cases for 2004 (orange), 2007 (purple), 2009 (red), and 2010 (blue).
!163 FIG. 38. Vertical Vorticity Profile for GO cases, 5x5° Method (orange - 2004, purple - 2007, red - 2009, blue - 2010).
FIG. 39. Vertical vorticity profile for NOGO cases, 5x5° Method.
!164 FIG. 40. Vertical RH profile for GO cases at the closest reanalysis point.
FIG. 41. Convergence profile calculated at closest reanalysis point.
!165 FIG. 42. Vertical vorticity profile for WARM year GO (thick lines) cases vs. NOGO (thin lines).
FIG. 43. The same as the previous figure, but for COLD years.
!166 FIG. 44. Tangential winds at 2, 4, and 6º radius for Atlantic developing and nondeveloping clusters.
Fig. 44 is from McBride and Zehr (1981b), which displays the tangential wind
(which is directly related to vorticity) for ‘developing’ and ‘non-developing’ cloud clusters in the Atlantic composited over a 2, 4, and 6º radius. There is general agreement between the figures above and the vertical profiles created previously.
Within the context of dynamic modeling and tropospheric vertical profiles, there remains a vast area of potential future examination concerning the vertical structure of the pre-TCG environment. Due to persistent widespread atmospheric warming as a result of human activity, the vertical structure of developing cloud clusters and subsequent hurricanes will become even more relevant, as warming ocean temperatures will affect surface interface fluxes and planetary boundary layer flow structure significantly, as well as tropopause heights and thermodynamic efficiencies. In addition to vertical variable
!167 profile changes of developing cases accompanying human-induced climate modifications, there may be some value in assessing the varying vertical structures interseasonally (from El Niño to La Niña).
The previous six figures are an attempt to provide a preliminary perspective on the vertical structure of burgeoning GO cases and nondeveloping NOGO cases. The first of the six figures (Fig. 38) conveys the vertical profile of developing cases based on vorticity calculated using the 5x5º Box Method. Thus, this figure should capture the vertical vorticity structure at both proximate and broad-scale locations around developing cloud clusters. The warm-colored lines (orange and red) represent the calculated vorticity values for the WARM years, 2004 and 2009. Purple and blue represent GO cases averaged during 2007 and 2010, respectively. In regard to overall trends, the most apparent is the enhancement of positive vorticity throughout the majority of the troposphere, which reaches its maximum around 850mb, and the superposition of a layer of anticyclonic outflow above the deep inflow layer (at approximately 250mb). Within the lower layers of the planetary boundary layer, there is an attenuation in positive vorticity from the maximum residing at the layer surrounding 850mb. This reduction in vorticity is due to the effects of friction-induced turbulent mixing, sub-grid scale forces, as well as convective downdrafts. In comparing the vertical structures of vorticity for
WARM years vs. COLD years, there are no clear disparities in the developing broad- scale environment.
!168 Fig. 39 reflects the general structure for nondeveloping cases during the four discrete ENSO COLD and WARM years. Vertical vorticity is characterized by a layer of cyclonic flow throughout the low to mid troposphere, and, generally, anticyclonic behavior between the 400mb to 100mb levels. There is little disparity between the vertical structure of the WARM years in comparison to the COLD years, but as in the first figure displaying a vertical profile of GO cases, the stratospheric behavior is somewhat erratic and inconclusive. The one trend that was hoped to be evident was the positive upper-level vorticity response governed by NAA jet behavior over the Atlantic
MDR. While there is a slight tendency for, in both developing and nondeveloping circumstances, positive vorticity in the upper levels of the troposphere and lower levels of the stratosphere, the evidence is not conclusive. Interestingly, 2007 indicates the opposite stratospheric behavior, with negative vorticity at upper-tropopsheric / lower-stratospheric levels, and no positive vorticity development above. However, 2010 aligns with the trend of the WARM years, comprising a layer of positive vorticity above the upper- tropospheric, negatively vortical outflow. Still, it differs from the WARM years in that this positive upper-level vorticity occurs at more elevated levels in the atmosphere, at approx. 70mb for COLD NOGO cases as opposed to approx. 100-125mb for WARM
NOGO cases.
Fig. 40 displays the vertical relative humidity profile for developing cases for the aforementioned years, but utilizing data from the reanalysis datapoint closest to the developing cloud clusters in contrast to the previously employed 5x5º Method. Thus, the
!169 visualization will reflect smaller scale behavior as opposed to the broader scale activity captured more effectively by the 5x5º Method. There are two noteworthy trends that emerge from this figure: 1) 2009 is a generally anomalous year, as has been discussed throughout the duration of the paper, with enhanced RH values throughout the majority of the troposphere up to the 200mb level and 2) the WARM years exhibit augmented RH in between the 300-200mb layer particularly. The reasoning for this is unknown to the author, but one inference is that the thermodynamic efficiency may be slightly lower for the WARM years than during the COLD years, and, thus, the moist entropy that is propelled into the upper levels of the atmosphere may not be as effectively funneled into the outflow in order to ossify the adiabatic expansion to isothermal compression transition. This vertical profile image provides further support for the fact that the study could be dramatically improved by inclusion of an atmospheric thermodynamic variable such as mid- to upper-level RH instead of merely utilizing an ocean thermodynamic variable (SST). As opposed to the inclusion of a 600mb RH variable, such as in Emanuel and Nolan’s Genesis Potential index, perhaps the 300mb or 250mb RH could be more telling in regard to seasonal differentiation in the cyclogenetic process.
Fig. 41 is of significant import, as it reflects a salient trend regarding divergent behavior in the upper levels. This figure is constituted by the vertical profile of convergence for developing cases for the two WARM years and the two COLD years.
The lowest levels of the troposphere indicate that there is no deviation between the
WARM and COLD years, with all of the data representing, as expected a well-developed
!170 layer of broad-scale Ekman inflow (the “in” segment of the “in-up-out” structure of tropical cyclones). Tropospheric mid-levels exhibit virtually no convergence (if any, slightly positive) as this region comprises maximum vertical mass flux associated with updraft development and moist entropy flux. The transition to divergent outflow begins in the 400-300mb layer for the majority of cases, and the disparity in outflow behavior for the WARM years vs. the COLD years emerges at approximately the 200mb level. At this point, it appears that, up to the approximate level of 100mb, the WARM years exhibit much less intense divergence (outflow), perhaps reinforcing the concept that developing cases during these years may be characterized by attenuated thermodynamic efficiency.
In vertically integrating the divergence from the 400mb level to the 70mb level, the values for the years are as follows: 1) WARM years (2004 and 2009): -94.6mb/s and
-87.9mb/s and 2) COLD years (2007 and 2010): -147.1mb/s and -92.2mb/s. Integrating instead from the 200mb level as the lower limit, the point at which the divergence profile significantly deviates for the WARM years in comparison to the COLD years, the values for the WARM years become -31.0mb/s and -16.5mb/s, whereas for the COLD years they are -58.2mb/s and -48.0mb/s. Clearly, there is a tendency for the COLD years’ developing cases to exhibit higher magnitude divergence at upper-tropospheric levels as evidenced in greater absolute value divergent numbers for 2007 and 2010 relative to 2004 and 2009. This trend may result from the relative meridional positions of the developing cases for WARM years vs. COLD years. For example, the one year that seems to be an outlier frequently in this study, due to the nature of TCG frequency and meridional
!171 homogeneity, is 2009. Interestingly, it exhibits marked differences in vorticity, divergence, and relative humidity profiles, even in comparison to the other WARM year of 2004. In the case of divergence, 2009 exhibits a marked attenuation of divergence at the 150mb level which could be indicative of the lack of Coriolis force correlated with a relative equatorward TCG tendency during that year. The low latitudes, and, thus, the lack of Coriolis force resulting in a relatively unreduced Rossby radius of deformation, would theoretically result in a higher incidence of gravity wave dispersion in the upper- troposphere / lower stratosphere, therefore preventing the extensive development of a well-entrenched outflow layer. One caveat that should be taken into account is that, due to the small sample size (four discrete years) used to reach a number of these conclusions, the ideas presented here are merely heuristic in nature with the hopes of fomenting future exploration and may be highly variable from year to year. In order to strengthen the merit of these ideas, there would need to be a requisite expansion of the study years in order to reach greater consensus, an endeavor that is well beyond the scope and time constraints of this study. Therefore, inferences should be received with caution and without a stamp of authoritative truth.
The last two of the six figures (Figs. 42 and 43) communicate one of the simple yet foundational precepts governing the cyclogenetic vs. cyclolytic processes. Both of these figures contain the vertical vorticity profiles of the broad-scale environment around
GO cases vs. NOGO cases during the two WARM years and, subsequently, the two
COLD years. The rationale for presenting these two figures last is that they combine data
!172 in such a way that some of the foremost trends of this study are readily accessible. One of the trends is that cloud clusters as convective entities exhibit deep tropospheric layers of positive vorticity which reaches its maximum around the 850mb level and becomes less positive with height. In the upper levels of the troposphere, vortical flow transitions from positive to negative values, indicating the formation of an incipient upper level divergent outflow. For developing cloud clusters, the divergence max occurs at about the
150mb level; for nondeveloping clusters, the divergence max emerges at a lower level, at approximately 200mb. In regard to the deep layer of cyclonic flow through the majority of the troposphere, GO cases in both WARM and COLD years have higher maxima of positive vorticity, and amplified positive vorticity throughout. Generally, in the upper- level outflow layer, developing cases also display a tendency to have less negative divergence values than NOGO cases. Additionally, corresponding with enhanced positive vorticity in the low to mid-levels of the troposphere for GO cases, these developing clusters also exhibit much more elevated levels at which anticyclonic outflow begins.
In transition, one of the most apparent shortcomings of this study, as well as virtually all empirical studies addressing tropical cyclones and their formation periods, is the relative paucity of data over ocean basins. Due to the magnitude, scale, and danger of tropical cyclones, observational data is at a premium, especially within the context of a changing global climate. Thus, the idea of expanding buoy networks would be vital for the advancement of research and would constitute a landmark initiative in tropical
!173 cyclone research. Expanding and enhancing the spatial resolution of a buoy network would increase the accuracy of empirically-observed data. By looking at the National
Data Buoy Center’s homepage (http://www.ndbc.noaa.gov/), it becomes apparent that the network is sparse over the eastern North Atlantic, which is of concern, especially in regard to monitoring the nascent phases of convection within AEWs. Obviously, this is way beyond the scope of this project or any individual’s sole efforts, but the paucity of data is a glaring shortcoming and one that could be mitigated by the combined efforts and funding of multiple groups.
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