The Pennsylvania State University
The Graduate School
Department of Meteorology and Atmospheric Science
ANALYZING TROPICAL CYCLONE STRUCTURES DURING SECONDARY
EYEWALL FORMATION USING AIRCRAFT IN-SITU OBSERVATIONS
A Thesis in
Meteorology
by
Katharine Wunsch
2018 Katharine Wunsch
Submitted in Partial Fulfillment of the Requirements for the Degree of
Master of Science
May 2018
The thesis of Katharine Wunsch was reviewed and approved* by the following:
Anthony C. Didlake, Jr. Assistant Professor of Meteorology Thesis Advisor
Fuqing Zhang Professor of Meteorology Director, Center for Advanced Data Assimilation and Predictability Techniques
George Young Professor of Meteorology
Hans Verlinde Professor of Meteorology Associate Head, Graduate Program in Meteorology
*Signatures are on file in the Graduate School
iii
ABSTRACT
In the evolution of mature tropical cyclones (TCs), intensity and structural changes can occur due to a process called an eyewall replacement cycle (ERC). Secondary eyewall formation
(SEF) is the initial phase of an ERC, in which a ring of convection forms outside of the pre- existing primary eyewall of the TC. The dynamical mechanisms for SEF remain unclear, but most hypotheses rely on the early presence of persistent and widespread rainband convection outside of the primary eyewall. The evolving rainband convection has both axisymmetric and asymmetric structures that play a role in SEF processes. This project uses aircraft reconnaissance observations from the FLIGHT+ dataset to examine the evolution of these structures. We create composites from this dataset which includes USAF C-130 and NOAA P-3 aircraft observations of Atlantic basin TCs from 1999-2015. The axisymmetric structures of TCs undergoing SEF are first compared to intensifying TCs that did not experience an ERC. Tangential wind and angular momentum profiles show a broadening of the outer wind field prior to SEF, while thermodynamic observations indicate features consistent with strengthening eyewall convection.
Next, the ERC TCs are analyzed in quadrants relative to the deep-layer environmental wind shear to examine the evolution of asymmetric kinematic and thermodynamic structures. We utilize a new normalization technique based on the radii of both eyewalls to isolate structures that surround the secondary eyewall before and during SEF. We found that the kinematic structures of the developing secondary eyewall were most prominent in the storm half left of the wind shear vector. The thermodynamic structures of the secondary eyewall became more axisymmetric over time during SEF, but those of the primary eyewall became more asymmetric as it began to weaken prior to being fully replaced. Analyzing observations from Hurricane Earl as a case study illustrates variations in convective coverage that are captured in the composite study.
Understanding the structures observed by aircraft reconnaissance and their relation to
iv mechanisms that lead to SEF will improve our ability to predict the resultant changes in TC intensity and structure.
v
TABLE OF CONTENTS
List of Figures ...... v
List of Tables ...... vi
Acknowledgements ...... vii
Chapter 1 Introduction ...... 1
Chapter 2 Data and Methodology ...... 8
Chapter 3 Axisymmetric composite structures of ERC and non-ERC TCs ...... 19
Axisymmetric composite-mean kinematic structures ...... 19 Axisymmetric composite-mean thermodynamic structures ...... 22
Chapter 4 Asymmetric composite structures of TCs undergoing secondary eyewall formation ...... 26
Quadrant-averaged kinematic structures ...... 26 Quadrant-averaged thermodynamic structures...... 31
Chapter 5 Case Study: Hurricane Earl (2010) ...... 37
Kinematic profiles ...... 37 Thermodynamic profiles ...... 41
Chapter 6 Conclusions ...... 44
References ...... 48
vi
LIST OF FIGURES
Figure 1. Schematic illustrating the typical organization of TC convection during an eyewall replacement cycle. From Houze (2010)...... 2
Figure 2. Normalization methdology applied to flights from Hurricane Earl...... 11
Figure 3. Box and whisker plot of eyewall and moat radii for major hurricanes and anchor sets for each ERC event...... 17
Figure 4. Radial distribution of data coverage for axisymmetric mean profiles and individual flight legs...... 17
Figure 5. Axisymmetric composite-mean radial profiles and statistical significance test results for tangential wind (m s-1), relative vorticity (s-1), and nondimensional angular momentum in major hurricanes...... 20
Figure 6. As in Figure 5, for temperature (°C), specific humidity (kg kg-1), relative humidity (%), and equivalent potential temperature (K)...... 25
Figure 7. Quadrant mean profiles and statitical significance test results for tangential wind for all shear environments...... 27
Figure 8. As in Figure 7, but for shear magnitude greater than 5 m s-1 only...... 29
Figure 9. Mean quadrant profiles and statistical significance test results for relative vorticity (s-1) and nondimensional absolute angular momentum in moderate and high shear environments...... 31
Figure 10. As in Figure 9, but for temperature and specific humidity...... 33
Figure 11. As in Figure 9, but for relative humidity and equivalent potential temperature .... 36
Figure 12. Quadrant distribution of tangential wind (m s-1) for selected flights from Hurricane Earl (2010)...... 39
Figure 13. As in Figure 12, but for nondimensional absolute angular momentum...... 41
Figure 14. As in Figure 12, but for temperature (°C)...... 42
Figure 15. As in Figure 11, but for relative humidity (%)...... 43
vii
LIST OF TABLES
Table 1. Parameters and values used in the algorithm for tangential wind speed maximum identification ...... 10
Table 2. Eyewall replacement cycle events in Atlantic TCs from 1999-2015 ...... 11
Table 3. Intensifying, non-eyewall replacement cycle Atlantic TCs from 1999-2012 ...... 14
viii
ACKNOWLEDGEMENTS
I would like to thank my advisor, Dr. Anthony Didlake Jr., for giving me the opportunity to participate in this research and for providing guidance and assistance along the way. In addition, I want to thank my committee members, Dr. Fuqing Zhang, and Dr. George Young for providing valuable feedback in the construction of this thesis. I also want to thank Jonathan Vigh from NCAR, and his collaborators who developed the FLIGHT+ dataset, which was fundamental in the design of this study. Finally, I wish to thank my family and friends for all of their support and encouragement along this journey.
1
Chapter 1
Introduction
The ability to forecast tropical cyclone (TC) intensity accurately is valuable for coastal areas susceptible to landfalling storms. However, intensity forecasts – particularly in short-term forecasts (12-48h) – have not improved significantly over the past ten years (Cangialosi and
Franklin 2017). The difficulty with intensity forecasts is that a number a factors play a role in modulating the intensity. Certain large-scale environmental conditions are necessary for intensifying a storm, such as warm sea surface temperatures, high mid-level relative humidity, and low environmental wind shear (Gray 1968). TC intensity changes are also tied to the evolution of the “inner core” features – including the eye, eyewall, and inner rainbands.
The inner core region of a storm is largely dynamically isolated from the environment because it is dominated by the TC vortex circulation (Houze 2010). Figure 1 shows a typical schematic of the inner core features in a mature TC that can affect storm intensity. The primary eyewall contains the strongest winds and heaviest precipitation of a TC, and intensification is generally associated with contraction of the eyewall convection ring (Shapiro and Willoughby
1982). In some cases, particular changes in eyewall convection can lead to rapid intensification where the maximum sustained wind speed increases by at least 30 knots in 24 hours or less. Most storms that undergo rapid intensification experience convective bursts just inward of the radius of maximum winds (RMW), suggesting they may be important triggers for rapid intensification
(Rogers et al. 2013, 2015; Guimond et al. 2016).
2
Figure 1. Schematic illustrating the typical organization of TC convection during an eyewall replacement cycle. Inner core convection is composed of the primary eyewall, secondary eyewall, and the principal and secondary rainbands. The environment is characterized by outer rainbands.
From Houze 2010.
In some strong TCs, the rainbands in the inner core can coalesce and form into another eyewall outside of the pre-existing eyewall. This secondary eyewall (notated in Figure 1) has an associated tangential wind maximum (Willoughby 1990). The formation of a secondary eyewall triggers an eyewall replacement cycle (ERC) where the outer (secondary) eyewall contracts, while the inner (pre-existing primary) eyewall decays and eventually dissipates. As the primary eyewall dissipates, the secondary eyewall replaces it and becomes the new singular eyewall.
During an ERC, TC intensity typically fluctuates in a three phases: intensification, weakening, and re-intensification (Sitkowski et al. 2011, 2012). The intensification stage is marked by
3 strengthening of the primary eyewall and ends when the secondary wind maximum emerges.
During the weakening phase, the primary eyewall weakens, while the secondary wind maximum intensifies and contracts, similar to the contraction observed in a single eyewall TC (Willoughby et al. 1984). At some point during the weakening phase the strength of the secondary wind maximum surpasses that of the primary eyewall maximum, which marks the beginning of the reintensification phase. The gradual decay of the original primary eyewall and continued strengthening of the secondary wind maximum characterize this phase. The entire ERC process takes an average of 36 hours, with a standard deviation of 13 hours (Sitkowski et al. 2011).
Observations and modeling studies regularly find that prior to secondary eyewall formation (SEF), the outer wind field of the TC expands (Sitkowski et al. 2011, 2012; Rozoff et al. 2012; Didlake and Houze 2013a,b; Qiu and Tan 2013; Sun et al. 2013; Wang et al. 2016; Tang et al. 2017; Zhang et al. 2017). In this expansion, the wind speed in the rainband regions strengthens and the radii of tropical storm-force and hurricane-force winds increase. This larger wind field also brings a corresponding increase in the total kinetic energy of the storm, which can lead to increased socioeconomic risk if the TC is near land (Irish et al. 2008; Maclay et al. 2008;
Sitkowski et al. 2011, 2012).
As they have a significant impact on TC intensity and size, it is important that ERCs are well predicted. Despite their importance, we currently are limited in our prediction capabilities for ERCs. This limitation is in part due to our lack of understanding of the SEF process, which initiates an ERC. Typically, SEF tends to occur more frequently in stronger TCs, often following a period of intensification (Hawkins and Helveston 2008; Zhang et al. 2017). However, not all intensifying TCs undergo eyewall replacement. Martinez et al. (2017) examined distinguishing characteristics of intensifying TCs using a composite analysis of flight-level data from reconnaissance aircraft. In comparison to steady state and weakening TCs, they found that intensifying TCs were characterized by sharper radial gradients of tangential wind inward of the
4 primary eyewall, which created a ring-like structure of relative vorticity. Intensifying storms also had drier eyes and more moisture in the outer core than steady state or weakening TCs. Rogers et al. (2013) also compared the composite characteristics of intensifying TCs to steady-state TCs, but used airborne radar data. Their analysis also found the ring-like vorticity structure in intensifying TCs, as well as lower vorticity in the outer core. Intensifying TCs also exhibited stronger axisymmetric upward vertical motion in the eyewall, and greater precipitation coverage in the eyewall and outer core. Both of these composite analyses excluded cases with a developing or mature secondary eyewall and thus excluded the characteristic changes in TC intensity and structure associated with ERCs. The current study will explore a composite analysis approach to understanding ERCs using observations – specifically, observations of the initiating SEF process.
The exact processes that cause SEF are not yet clear, but several theories describe potential formation mechanisms. One theory is the generation of vortex Rossby waves in the primary eyewall that propagate outwards and reach a stagnation radius, at which point they increase the local wind speeds through momentum convergence and lead to the development of a secondary wind maximum (Montgomery and Kallenbach 1997). In conjunction with vortex
Rossby waves, other studies have suggested that relaxing the radial gradient of tangential wind allows for vorticity anomalies associated with rainband convection to cascade upscale and axisymmetrize into the secondary eyewall (Terwey and Montgomery 2008). Another source of uncertainty in the SEF process is the role of the boundary layer. Some studies invoke balanced boundary layer dynamics (i.e., gradient wind balance) in which an axisymmetric gradient wind vorticity anomaly can spin up a secondary wind maximum through a feedback between frictional convergence, convection, and radial vorticity (Kepert 2013; Zhang et al. 2017). Others invoke unbalanced boundary layer dynamics as a necessary component for SEF, where axisymmetric supergradient flow develops in response to a broadening tangential wind field, causing outward acceleration and a persistent updraft that also leads to a secondary wind maximum (Abarca and
5 Montgomery 2013, 2014; Abarca et al. 2016). Sun et al. (2013) found that both unbalanced and balanced dynamics contribute significantly to developing a secondary eyewall. The aforementioned broadened tangential wind field may also be critical for SEF (Rozoff et al. 2006;
Fang and Zhang 2012). However, it is not clear if this wind field expansion is a catalyst for SEF, or if it is a result of SEF processes that have already begun.
Despite the debate regarding underlying dynamics behind SEF, most theories indicate that the rainbands are crucial for SEF. Specifically, there must be adequate coverage of rainband convection such that the associated convective heating and vorticity structures are sufficiently apparent on an azimuthal mean of the TC. Prior to a sufficient axisymmetric projection of rainbands, rainband convection can have asymmetric structures that may have an earlier impact on eventual SEF. Under environmental wind shear, the rainband complex (i.e., the primary and secondary rainbands in Fig. 1) tends to be oriented such that active convective cells inhabit the
TC half that lies to the right of the deep-layer environmental wind shear vector. Meanwhile, slowly falling ice crystals are advected downwind and fall out as stratiform precipitation in the left-of-shear half of the storm (Black et al. 2002; Hence and Houze 2012b; Didlake and Houze
2013a,b). The downwind stratiform portions of the rainband complex have recently been considered instrumental in the formation of the secondary eyewall (Fang and Zhang 2012;
Didlake and Houze 2013b; Dai et al. 2017; Zhang et al. 2017; Didlake et al. 2018). These rainband features project more strongly onto the axisymmetric structure than do the convective rainbands upwind given both the mesoscale, homogenous nature of stratiform precipitation and the fact that these features occur at a smaller radius on the downwind end of an inward spiraling complex.
In their modeling study, Fang and Zhang (2012) pointed to rainband stratiform processes as a catalyst for a “top-down” pathway to SEF. Midlevel latent heating associated with the stratiform mesoscale updraft begins in the middle levels, and later extends into the low levels.
6 Here, interaction with the boundary layer leads to a deep overturning circulation that ultimately develops the secondary eyewall. Zhang et al. (2017) found similar results in their ensemble modeling analysis. They proposed that the rainband complex had to occur at a sufficient distance away from the primary eyewall in order to facilitate coupling with the boundary layer, or SEF would not occur.
The aforementioned studies on SEF primarily focused on processes occurring in the azimuthal mean. Dai et al. (2017) examined how the interaction between TCs and an upper-level mid-latitude jet can result in SEF. They found that the jet increased the upper-level eddy momentum flux convergence at the early stages of SEF, and this interaction enhanced the upper- level outflow of the TC, resulting in an asymmetric stratiform rainband region. This stratiform region also interacted with the boundary layer and triggered sustained convection that led to a secondary eyewall. An idealized simulation of SEF by Qiu and Tan (2013) found that an inward contracting rainband induced radial inflow that descended to the surface, increased convergence, and led to supergradient winds in the low-levels, which resulted in upward vertical motion and promoted deep convection.
Didlake and Houze (2013b) found that mesoscale descending inflow occurred in the stratiform region of a rainband complex, and they postulated that this flow pattern may have an effect on SEF in a manner similar to Qiu and Tan (2013). In their findings, latent heating from a mesoscale updraft at smaller radii and latent cooling from melting, sublimation, and evaporation at larger radii generated horizontal buoyancy gradients across the stratiform rainband. This created a descending inflow pattern similar to that of the trailing stratiform region of a mesoscale convective system (Parker and Johnson 2000; Houze 2004). As the air flowed inward through the rainband, it descended sharply and produced a downdraft extending into the boundary layer.
Didlake et al. (2018) argued that this downdraft air spreads along the surface and interacts with the strong tangential flow to create persistent convergence and deep convection that ultimately
7 lead to SEF. Since stratiform rainband precipitation is preferred in the left-of-shear half of the storm, the mesoscale descending inflow and nascent secondary eyewall convection are also expected in this storm region (Didlake et al. 2017). Although the exact dynamics of this process remain an active area of research, these studies demonstrate that rainband asymmetries are crucial to SEF.
These SEF theories all describe an evolution of characteristics that are distinguishable traits of storms developing a secondary eyewall. However, the initial stages of these theories involve characteristics, such as vortex-Rossby wave propagation or ample rainband activity, which can exist in storms that do not undergo SEF. The extent to which these evolving features become unambiguous indicators of SEF is not clear in the current literature. The current study explores this problem by investigating storm composites to seek structural characteristics, both axisymmetric and asymmetric, that typify and can help explain SEF processes. The data used in this study are 700-mb level observations collected from reconnaissance aircraft. We first compare axisymmetric structures of non-ERC storms to that of ERC storms to determine the earliest characteristics that are distinguishable for SEF processes. We then further analyze the evolution of asymmetric structures in ERC storms to identify distinguishing asymmetric features for SEF.
The kinematic and thermodynamic characteristics identified in this two-part study will be examined in the context of hypothesized SEF mechanisms.
8
Chapter 2
Data and Methodology
The primary data source for this study is the Extended Flight-level Dataset for Tropical
Cyclones (FLIGHT+; Vigh et al. 2016). This dataset contains flight-level in situ observations of
TCs from all National Oceanic and Atmospheric Administration WP-3D and U.S. Air Force C-
130 reconnaissance missions during 1999-2015. These aircraft mostly fly in figure-4 or butterfly patterns to gather multiple transects across the storm. The FLIGHT+ dataset organizes these observations into radial legs using the storm centers determined by the Willoughby and Chelmow
(1982) method. For this analysis, we included radial legs where the aircraft flew within 25 km of the storm center of the TC and that had a radial extent of at least 45 km (these are the “good radial legs” in the FLIGHT+ dataset). Only flight legs that occurred at the 700 hPa level were considered in this study. Data from the radial legs were first interpolated to a radial grid with a resolution of 0.5 km and extending out to 350 km. To reduce noise in the observations, a 10-km
Lanczos filter was applied (Duchon 1979), following the methodology of Martinez et al. (2017).
Next, radial legs from each flight were organized into “sets” of 4-7 consecutive legs such that each set had adequate azimuthal coverage to produce an azimuthal mean representative of the axisymmetric storm structure. This means that, for example, a flight with only 3 radial legs would not have been included; a flight with 5 radial legs constituted a set, and a flight with 8 radial legs was divided into 2 sets, where each set included 4 consecutive legs. Each azimuthal mean averages a given variable along all azimuths at a specified radius. To correct for instrument wetting, the method described by Zipser et al. (1981) was applied to reduce errors in temperature
9 and dew point observations; this method is consistent with previous studies using aircraft observations of TCs.
Eyewall replacement cycle (ERC) “events” in the North Atlantic were identified by first examining the tangential velocity azimuthal mean of each set. We applied an algorithm that located local maxima in the set mean wind field. This MATLAB algorithm (“findpeaks”) took into account the width and relative magnitude of each peak to capture the primary eyewall peak and meaningful signals of potential secondary eyewall formation. The specific parameters and values used in the algorithm are presented in Table 1. The value of each parameter was adjusted subjectively to ensure that the maxima being captured were associated with the eyewalls; moderate changes in these parameters did not yield changes in the overall conclusions of this study. Next, we used a combination of datasets to confirm that each set of flight legs with an identified secondary wind maximum was actually part of an ERC event observed over time.
These datasets included microwave satellite imagery, airborne radar imagery, National Hurricane
Center (NHC) storm reports, and the current FLIGHT+ tangential wind mean profiles. We examined the potential cases for specific indicators of an ERC: a contracting axisymmetric secondary ring of convection, a contracting axisymmetric secondary wind maximum, or the decay of inner eyewall convection. If any of these features were identified, then these cases were confirmed to be an ERC event.
Table 1. Parameters and values used in the MATLAB “findpeaks” algorithm to identify the peaks associated with the primary eyewall for ERC and non-ERC TCs, and the developing secondary eyewall for ERC events.
Parameter Values Peak Width 2.5 km Prominence 2.5 m s-1 Distance to other peaks 20 km
10 Figure 1a shows an example of two consecutive sets from a confirmed ERC in Hurricane
Earl (2010). In the first set, only the primary wind maximum was identified and is labeled as r1, while the next set had the first appearance of a secondary wind maximum, which is labeled as r2.
The set with the first appearance of the secondary wind maximum is called the “anchor” set of the event. The next step was to define the time span of each ERC event. Particularly, we identified the beginning time of each event to determine those sets that preceded the anchor set and capture the secondary eyewall formation process. To do this, we examined the evolution of the storm’s central pressure during each event using the NHC Best Track dataset. An ERC is typically accompanied by a fluctuation in the central pressure. For each event, we identified the local minimum pressure that occurred near the time of the anchor set, and this time of the minimum pressure was noted. The beginning time of each event was defined as 36 hours prior to the time of the minimum pressure. Flight missions (and their associated sets) that took place within 36 hours of the minimum pressure time initially defined an ERC event. Those events were then refined based on the other datasets (i.e. satellite and radar imagery), and any overlap between successive
ERC events was removed (discussed further later in this chapter).
Atlantic basin storms that undergo an ERC tend to be major hurricanes (i.e., Category 3 or higher; Hawkins et al. 2006; Kossin and Sitkowski 2009). In this study, less than 10% of identified ERC events occurred in storms below major hurricane status. We, therefore, only focus on sets when the maximum wind speed of the storm reached a minimum of 96 kts in the NHC
Best Track dataset at some point during the set time span. Weaker intensities may have an unknown impact on the structural evolution of the storm during ERCs; effects due to this possibility are now avoided. This methodology resulted in 32 ERC events in 21 North Atlantic
TCs listed in Table 2. The identified ERC events included all of the events analyzed by Sitkowski et al. (2011, 2012) that are in the FLIGHT+ database. Table 2 also shows the minimum pressure time, the flight IDs for each mission, and the number of radial legs in each mission.
11
Figure 2. Set mean tangential wind profiles from flight missions 20100830U1 and 20100830U2 into Hurricane Earl. a) Profiles in actual radius (km). The radius of maximum winds is denoted by black and cyan dots for 20100830U1 and 20100830U2, respectively. The radius of the secondary eyewall is noted by a gray dot in 20100830U2. b) Set mean tangential wind in normalized space relative to the radius of the primary eyewall in each set. c) Set mean tangential wind profiles for
20100830U1 and 20100830U2 in normalized space relative to the radii of both the primary and secondary eyewalls at the time when the secondary eyewall is first observed.
Table 2. List of identified ERC events in the Atlantic from 1999-2015. TC name is followed by
ERC event number, year, ID of flight reconnaissance during ERC timeframe, number of radial legs in each mission, and number of sets in the pre-SEF and post-SEF groups for each event.
Storm Year Flight ID (total number of radial legs) Pre-SEF group name- ERC set counts, Post event SEF group number counts Floyd-1 1999 19990910U2 (7), 19990911U1 (8), 19990911U2 2, 1 (4), 19990912U1 (8), 19990912U2 (10) Floyd-2 1999 19990912U1 (8), 19990912U2 (10), 6, 2 19990913U1 (8), 19990913I1 (8), 19990914U1 (6), 19990914U2 (9), 19990914U3 (7) Gert-1 1999 19990916U1 (4), 19990916U2 (4) 1,1 Erin-1 2001 20010909_AF980_0706A (8), 1,1 20010909_AF985_0806A (7) Michelle-1 2001 20011103_AF966_1015A (7), 0,1
12
20011103_AF861_1115A (5), 20011103H1 (10), 20011104H1 (10), 20011104H2 (6) Isidore-1 2002 20020920U1 (7), 20020920U2 (10), 0,1 20020921U1 (8), 20020922U1 (7) Fabian-1 2003 20030902I1 (5), 20030902H1 (5), 20030903U1 2,2 (4), 20030903U2 (4), 20030904U3 (4), 20030905U1 (8) Isabel-1 2003 20030916U2 (8), 20030917U1 (7), 20030917U2 0,0 (6), 20030917U3 (9), 20030918U1 (7) Frances-1 2004 20040830u1 (4), 20040830I1 (6), 20040831u1 0,1 (8), 20040831I1 (4), 20040831u2 (7), 20040901u1 (7) Frances-2 2004 20040830I1 (6), 20040831u1 (8), 20040831I1 5,1 (4), 20040831u2 (7), 20040901u1 (7), 20040901I1 (6), 20040901u2 (10), 20040902u1 (10), 20040902u2 (6) Frances-3 2004 20040831I1 (4), 20040831u2 (7), 20040901u1 2,1 (7), 20040901I1 (6), 20040901u2 (10), 20040902u1 (10), 20040902u2 (6), 20040902u3 (9), 20040903u1 (4), 20040903I1 (5), 20040903u2 (4) Frances-4 2004 20040902u2 (6), 20040902u3 (9), 20040903u1 1,1 (4), 20040903I1 (5), 20040903u2 (8), 20040903u3 (10), 20040904u1 (9), 20040904u2 (8) Ivan-1 2004 20040908u1 (7), 20040908u2 (8), 20040909u1 3, 1 (9), 20040909I1 (6), 20040909u2 (8), 20040910u1 (10), 20040910u2 (9) Ivan-2 2004 20040909I1 (6), 20040909u2 (8), 20040910u1 1,1 (10), 20040910u2 (9), 20040911u1 (6), 20040911u2 (6), 20040912u1 (8), 20040912I1 (6), 20040912u2 (6), 20040912H1 (4) Ivan-3 2004 20040910u2 (9), 20040911u1 (6), 20040911u2 0,1 (10), 20040912u1 (8), 20040912I1 (6), 20040912u2 (6), 20040912H1 (8), 20040912u2 (6) Ivan-4 2004 20040912u1 (4), 20040912I1 (6), 20040912u2 1,1 (6), 20040912H1 (8), 20040913u1 (7), 20040913u2 (5), 20040913H1 (7), 20040913I1 (4), 20040913u3 (4), 20040914u1 (10), 20040914H1 (13), 20040914u3 (5), 20040914I1 (9), 20040915u2 (4) Katrina-1 2005 20050826U1 (10), 20050827U1 (10), 3,1 20050827I1 (5), 20050827U2 (6), 20050827U3 (8), 20050828U1 (10), 20050828I1 (10) Katrina-2 2005 20050827U1 (10), 20050827I1 (5), 20050827U2 1,3 (6), 20050827U3 (8), 20050828U1 (10), 20050828I1 (10), 20050829U2 (11),
13
20050829U3 (9) Rita-1 2005 20050920U1 (8), 20050920U2 (10), 2,1 20050921U1 (8), 20050922U1 (8), 20050922I1 (10), 20050922U2 (7), 20050923U1 (8) Wilma-1 2005 20051019U2 (5), 20051020U1 (7), 20051020H1 0,1 (8) Dean-1 2007 20070817U1 (9), 20070817U2 (6), 20070818U1 3,1 (10), 20070818U2 (11), 20070819U2 (7) Dean-2 2007 20070817U2 (6), 20070818U1 (10), 1,1 20070818U2 (11), 20070819U2 (7), 20070819U3 (8), 20070820U2 (6) Felix-1 2007 20070902U1 (5), 20070902U2 (4), 20070903U1 3,2 (4), 20070903U3 (6), 20070904U1 (6) Ike-1 2008 20080909U2 (5), 20080910U1 (10), 1,2 20080910U2 (7), 20080911U1 (8), 20080911U2 (8), 20080912U1 (10), 20080912U2 (4) Bill-1 2009 20090820U1 (4), 20090820U2 (4), 20090821U1 2,1 (4), 20090821U2 (4), 20090822U1 (4) Danielle-1 2010 20100827U1 (4), 20100828U1 (4) 0, 1 Earl-1 2010 20100829U2 (6), 20100830U1 (7), 20100830U2 2,1 (9), 20100831U1 (5), 20100901U1 (4) Earl-2 2010 20100901U1 (4), 20100902U1 (7), 20100902U2 1,1 (8), 20100902U3 (8), 20100903U2 (7) Igor-1 2010 20100916U2 (4), 20100917U2 (4) 1,0 Irene-1 2011 20110823U2 (4), 20110823U3 (6), 20110824U1 3,1 (8), 20110824U2 (8), 20110825U1 (8), 20110825U2 (7), 20110826U1 (8), 20110826U2 (8) Irene-2 2011 20110824U2 (8), 20110825U1 (8), 20110825U2 3,1 (7), 20110826U1 (4), 20110826U2 (8), 20110826U3 (8), 20110827U1 (8), 20110827U2 (4) Gonzalo-1 2014 20141014U2 (8), 20141014U3 (6), 20141015U1 3,1 (6), 20141015U3 (6)
The sets of flight legs in each ERC event were categorized into two “groups” that best capture the evolution of structures leading up to secondary eyewall formation. The post-SEF group consisted of all anchor sets and any set that occurred during the same flight as an anchor set and had a secondary tangential wind maximum. The pre-SEF group consisted of all other sets that occurred before the anchor set and after the beginning time of the event. The beginning time of the final leg of each set was used for this time comparison. Some TCs had successive ERC
14 events, which affected some sets in the pre-SEF group. For these ERC events, the beginning time of an event often extended into the ending stage of the previous event. Therefore, the end of an event was marked by the decay of an inner eyewall wind maximum. To account for this overlap, we removed sets from the pre-SEF group that had local maxima in the tangential wind profile radially inward of the maximum wind. The final total in each group was 33 pre-SEF sets and 30 post-SEF sets during major hurricane ERC events. Table 2 lists the number of sets from each event that were part of each group.
We also analyzed storms that did not go through ERCs for comparison with the storms that did. The non-ERC sets were those from the FLIGHT+ dataset that were not included in the
ERC events. Using the NHC Best Track dataset, we identified how the TC intensity changed over a 12-hr period that encompassed the time of the set of flight legs. When the intensity increased by at least 10 kts, those sets were selected for the IN group. This is the same criterion used in
Martinez et al. (2017). As with the two ERC groups, only major hurricanes were considered for the IN group. The resultant storms, flight numbers, and number of sets from the IN group are listed in Table 3.
Table 3. Atlantic intensifying TCs from 1999-2012 that did not have ERCs. Storm name is followed by year, ID from reconnaissance flights during intensification, total number of radial legs during each flight, and the number of sets for each storm.
Storm Year Flight ID (total number of radial legs) Number of sets name Bret 1999 19990821U2 (6), 19990822U1 (9), 19990822U2 5 (10) Dennis 1999 19990827U5 (6), 19990828U1 (10), 9 19990828U2 (7), 19990829U2 (8), 19990828U3 (8), 19990829U1 (7) Lenny 1999 19991116U2 (5), 19991117U1 (6), 19991117U3 4 (8) Debby 2000 20000822U1 (11) 2 Keith 2000 20001001U1 (6) 1
15
Humberto 2001 20010923_AF861_0410A (4) 1 Lili 2002 20020930U2 (8), 20021002U1 (10) 4 Claudette 2003 20030710U2 (6) 1 Alex 2004 20040803u2 (4) 1 Charley 2004 20040812u3 (9), 20040812u2 (10) 4 Jeanne 2004 20040924u2 (8), 20040925I1 (8), 20040924u3 7 (4), 20040925u1 (9) Dennis 2005 20050707U1 (6), 20050707U2 (11), 7 20050709U2 (9), 20050709U3 (11) Emily 2005 20050714U1 (8), 20050714U2 (7), 20050715U1 13 (10), 20050716U1 (8), 20050718U1 (10), 20050719U1 (8), 20050719U2 (10) Nate 2005 20050908U1 (4) 1 Ophelia 2005 20050910U1 (4), 20050910U2 (10) 3 Philippe 2005 20050918U3 (4) 1 Beta 2005 20051029U1 (4) 1 Ernesto 2006 20060827U1 (5) 1 Florence 2006 20060910U2 (10), 20060911U1 (8) 4 Gustav 2008 20080826U1 (8), 20080830U1 (11) 4 Omar 2008 20081015U2 (7) 1 Paloma 2008 20081107U2 (8), 20081108U1 (6) 3 Ida 2009 20091108U1 (4), 20091108U2 (8) 3 Paula 2010 20101013U1 (5) 1 Rina 2011 20111026U2 (6) 1 Rafael 2012 20121016U1 (7) 1 Sandy 2012 20121026U1 (5), 20121027U3 (6) 2
With such a wide variety of storm sizes and structures, the storm data must be analyzed in a way that highlights fundamental structures across all storms. To do this, we normalize the radial dimension of the set profiles using two distinct methods. The first method follows Martinez et al. (2017) and previous studies by using the radius of maximum wind (r1) from the azimuthal mean of each set. The radial axis is then incremented by r1/50 for each set and extended out to 8 times r1. Figure 1b shows our example sets in this normalized radius coordinate that we call the r* coordinate space. The r* coordinate normalization is applied to the pre-SEF, post-SEF, and IN groups in Chapter 3. Figure 2 displays the distribution of the r1 values for these three groups.
In addition to variation with the radius of maximum wind, the radius of the secondary wind maximum can vary widely as well. Of particular interest is the distance between r1 and r2,
16 known as the moat region, which increasingly exhibits characteristics of an eye during ERCs
(Houze et al. 2007). Figure 2 also shows the distributions of r1, r2, and the moat width (distance between r1 and r2; m) for the ERC anchor sets. Values of m range from 40-120 km, with a median of 92 km. One goal of this study is to examine structures that lead up to SEF. Given the large variance of m, the r* coordinate space would not be effective for the pre-SEF and post-SEF groups because a composite could obscure those signatures in individual sets that occur on either side of the secondary wind maximum at r2. We, therefore, apply a new normalization technique based on both r1 and r2, hereafter referred to as r**. In this r** coordinate space, the normalization points along the radial axis begin with r1 and r2 from each anchor set. The normalization points continue out from the secondary wind maximum (r2) at distances equal to m and 2 times m. Thus, we are creating a radial coordinate system that first goes from 0 to r1 in increments of r1/50. Continuing outward, the radial coordinate then is uniformly spaced from r1 to r2, r2 to r2+m, and r2+m to r2+2m, with increments of m/50. The same normalized radius coordinate for the anchor set was used for all sets within that event to track the ERC evolution.
Figure 1c shows our example of pre- and post-SEF sets normalized into r** space for two sets during Hurricane Earl. This normalization scheme is utilized for the analysis in Chapters 4 and 5.
Figure 1. Box and whisker plot showing the radius of maximum winds (km) associated with the primary eyewall for the pre-SEF, post-SEF, and IN groups. The radius of the primary eyewall,
17 secondary eyewall, and moat are shown for the anchor sets, when the secondary eyewall is first observed in each event.
Also in Chapter 4, we examine each radial leg relative to the large-scale environmental wind shear. The wind shear used in this study is the 850-200 hPa shear from the SHIPS analysis database (DeMaria et al. 2005). These 6-hourly shear vectors are linearly interpolated to the center time of each radial leg. An average azimuth is then calculated for each radial leg, and assigned to the shear quadrant (downshear-left [DL], downshear-right [DR], upshear-left [UL], and upshear-right [UR]) based on the shear direction at that time.
Finally, the radial legs may not have data at all radii. Figure 3 shows the number of sets with data at each radius in r* space and the number of legs in each quadrant in r** space. To avoid unrepresentative mean profiles, a minimum data count threshold was implemented at each radius. Each group must have data for at least 3 sets in r* space and each quadrant must have data for at least 10 legs in r** space. This threshold cuts off some data in the eye and at outer radii, as indicated in Fig. 4.
Figure 4. a) Data counts at each radius for the axisymmetric composite groups in r* space, where the thick vertical black line marks the threshold radius where each group contained at least three
18 axisymmetric means. b) Data counts at each normalized radius in r** space for the shear-relative quadrants in the pre-SEF group. The thick vertical black lines mark the threshold radii where each quadrant contained at least 10 radial leg profiles. c) As in b, for the post-SEF group.
19 Chapter 3
Axisymmetric composite structures of ERC and non-ERC TCs
The first analysis compares the kinematic and thermodynamic structures of storms that underwent an ERC to those that did not. Specifically, we examine the mean of the azimuthal set means from the pre-SEF, post-SEF, and intensifying (IN) storm groups in the r* coordinate framework. By comparing the axisymmetric radial profiles of TCs that went through ERCs to those that did not, we can gain an understanding of critical differences between the two storm types and the resulting implications on differences in storm structure. Given that SEF often occurs during or after the intensification of a TC, we can consider the three groups (pre-SEF, post-SEF, IN) as consecutive moments along the timeline of an evolving storm. 29 of our 33 pre-
SEF sets were intensifying or steady state during the observation time span. Comparing the evolution of these profiles can highlight the earliest differences between ERC and non-ERC storms. At each normalized radius, the distributions representing each group were compared using a two-tailed Wilcoxon-Mann-Whitney rank-sum test; the colored boxes at the bottom of
Figure 5 denote radii where the differences among the distributions are statistically significant at the 95% confidence interval.
Axisymmetric composite-mean kinematic structures
The most prominent differences in the axisymmetric tangential wind profiles occur outside of 2r* (Fig. 5a). The pre-SEF composite mean has a statistically significantly higher tangential wind speed than the IN composite mean between 2r* and 6r*, while the post-SEF group is statistically significantly higher than both the pre-SEF and IN groups outside of 2r*.
These signals in the pre-and post-SEF groups reflect the broadening of the outer wind field which
20 previous studies indicate is a precursor to secondary eyewall formation (Fudeyasu and Wang
2011; Fang and Zhang 2012; Rozoff et al. 2012; Didlake and Houze 2013b). As shown in Figure
2, the radius of the secondary eyewall (r2) occurs anywhere from 40-120 km. The radius of the secondary eyewall emerges between 2r* and 8r* in more than 85% of cases analyzed here; this is a wider range than that observed by Sitkowski et al. (2011) and Rogers et al. (2013). For the pre-
SEF group, this region is where the earliest broadening of the wind field occurred. For the post-
SEF group, this region demonstrates the continued broadening of the outer wind field and the emergence of the secondary eyewall. This region also corresponds with the stagnation radius for vortex Rossby waves, which propagate outward from the TC center (Montgomery and
Kallenbach 1997; Chen and Yau 2001; Wang 2002a,b; Corbosiero et al. 2006). Though significant differences among the profiles are apparent, no clear secondary eyewall wind maximum is visible in the r* framework, as noted in Chapter 2.
Figure 5. Composite-mean radial profiles for pre-SEF, post-SEF and IN groups in normalized space relative to the primary eyewall for major hurricanes for a) tangential wind, b) relative vorticity, and c) nondimensional angular momentum. Statistically significant differences between each group pair are plotted along the bottom of each plot with colors corresponding to each group.
21 The vertical vorticity composite-mean profiles reveal a ring-like structure of vorticity radially inward of the primary eyewall (1r*) of all three groups (Fig. 5b). For the IN cases, this signature is consistent with Martinez et al. (2017), and characterizes a dynamically unstable structure and a thermodynamically isolated eye (Kossin and Eastin 2001; Braun et al. 2006;
Houze 2010; Martinez et al. 2017). The pre-SEF composite mean profile is statistically significantly lower than both the post-SEF and IN composite means inside the primary eyewall, as well as between 1r* and 2r*. Martinez et al. (2017) found that both intensifying and weakening major hurricanes had a vorticity ring, but that the weakening TCs had smaller vorticity magnitudes. Meanwhile, steady-state storms did not have a vorticity ring in the eyewall but rather a flatter vorticity profile, which they attributed to differing TC regimes as described in Kossin and
Eastin (2001). Utilizing the intensity change definitions from Martinez et al. (2017), 45% (37%) of TCs in the pre-SEF (post-SEF) group meet the criteria for intensifying, 3% (27%) are weakening, while 42% (27%) fall are steady state (the remaining ~10% in each group spanned more than one intensity change classification during the observation time span). Martinez et al.
(2017) found that steady state TCs exhibited smaller vorticity magnitudes than intensifying and weakening TCs; the larger proportion of steady state TCs in the pre-SEF group may account for its smaller vorticity magnitude compared to the post-SEF group. However, we have not precisely quantified the effects of the weakening TCs on the magnitude of the vorticity in each group. The vorticity differences outside of the primary eyewall are small, but it is clear that the post-SEF group has statistically significant higher vorticity between much of 1r* to 4r*. This increased vorticity corresponds to the expanded wind field from Figure 5 and the associated increase in curvature vorticity.
The axisymmetric angular momentum was calculated in cylindrical coordinates, given by:
1 푀 = 푟푣 + 푓푟2 (1) 2
22 where r is the radius, v is the tangential wind, and f is the Coriolis parameter. To account for the strong radial dependence of absolute angular momentum, we normalized each leg by the value of
M at 1r* to calculate the nondimensional angular momentum (M*) as done by Martinez et al.
(2017). We then composited the resulting set means and determined the radii with statistically significant differences (Fig. 5c). Inside 1r*, the differences among the groups are small, which was also the case for dimensional M (not shown). Outside of 1r*, the M* profiles are consistent with their corresponding tangential wind profiles. The pre-SEF group had higher M* values than the IN group between 2r* and 6r*, which corresponds with the radii where the broadening of the outer wind field was observed (Fig. 5a). Outside of 2r*, the post-SEF composite mean profile was statistically significantly higher than the other groups consistent with the observed higher tangential wind speeds. The differences between groups suggest that M surfaces are advected radially inward over time during SEF, consistent with the findings of Bell et al. (2012). The IN profile also exhibited the smallest M* in the outer core in Martinez et al. (2017), which they theorized was due to the characteristically lower latitude of IN TCs compared to steady-state and weakening storms. In our analysis, IN TCs were found between either 14-20° N or 25-28° N. The
ERC TCs were observed at a larger latitudinal range (12-33° N), which may also influence the elevated M* in the outer radii.
Axisymmetric composite-mean thermodynamic structures
The kinematic variables showed a clear progression from IN to pre-SEF to post-SEF groups outside of 2r* that is expected with structural changes during SEF. We now examine the thermodynamic variables for signatures that also indicate some progression leading up to SEF.
The composite mean temperature profiles were similar among the three groups (Figure
6a). We find maximum temperatures in the eyewall cloud at 1r*. The eyewall also has the
23 greatest negative radial temperature gradient, which is consistent with the maintenance of thermal wind balance for the strongest TC winds in the low levels. The post-SEF group has a higher composite-mean temperature than the pre-SEF and IN groups from the center to 4r*, but this difference was statistically significant only near 1-1.5r*. This region could be experiencing adiabatic warming associated with increased subsidence between the two concentric eyewalls, or it could be experiencing diabatic heating due to a possible increase in the convection at flight- level. Next, we examine moisture to assess these conjectures.
A comparison of the composite mean specific humidity profiles reveals that the post-SEF group has a larger amount of moisture present between 2r* and 4r* (Fig. 6b). This difference compared to the pre-SEF group is statistically significant, and a smaller stretch of statistically significant differences occur compared to the IN group. Based on the distributions of eyewall radii, this region corresponds with frequent emergence of the secondary eyewall, which would explain the moisture differences at these radii. In the eyewall cloud, specific humidity decreases rapidly in all three groups; the post-SEF group had the highest amount of moisture here as well.
The difference between the pre-SEF and post-SEF composite-mean specific humidity profiles is statistically significant between 4r* and 6r*. Rainband activity at these radii may explain this difference. Didlake and Houze (2013b) illustrated that the appearance of drier air tends to occur preferentially in the stratiform portion of the rainband complex prior to secondary eyewall formation. To assess the importance of this signature and its location in the rainband complex, we employ the framework relative to both eyewalls in Chapter 4.
Comparing relative humidity (RH) profiles, the IN composite mean has higher RH values than the ERC composite means throughout much of the radial profile (Fig. 6c). The differences between the IN and both ERC profiles are statistically significant just outside of 1r*, possibly indicating fewer clouds in this region for ERC storms. The lower RH values here would then be indicative of a moat appearing outside of the eyewall. The RH in IN storms is also statistically
24 significantly higher than the pre-SEF profile between 5r* and 6r*. The post-SEF group coincides with the first emergence of the secondary eyewall. Thus a moat would indeed be developing at this time which likely explains the clear dip in RH just outside of 1r* for post-SEF storms. To assess the structural significance of this result, we will examine the ERC storms relative to the radius of the secondary eyewall in addition to the primary eyewall in Chapter 4.
The composite mean equivalent potential temperature (θe) profiles contain a maximum of
θe within the eyewall cloud (Fig. 6d). θe decreases with increasing radius as temperature and specific humidity both decrease. The difference between the pre and post-SEF groups is statistically significant at nearly all radii between 1r* and 7r*, primarily because of higher moisture content in the post-SEF group. This finding is consistent with several studies that show an increase in θe in the inner core of a storm undergoing SEF (e.g. Fang and Zhang 2012; Rozoff et al. 2012). The post-SEF group has a statistically significantly higher θe composite mean than the IN group between 2r* and 3r* corresponding with an increase in specific humidity likely associated with the emerging secondary eyewall.
Overall, the thermodynamic variables do not have a widespread structural progression from IN to post-SEF groups as that seen in the kinematic variables. Compared to the ERC storms, the IN storms only had notable differences in moisture at the primary eyewall, secondary eyewall, and moat. However, going from pre- to post-SEF, the composite storm had a clear increase in θe throughout most radii.
25
Figure 6. As in Figure 5, but for a) temperature (°C), b) specific humidity (kg kg-1), c) relative humidity (%), and d) equivalent potential temperature (K).
26
Chapter 4
Asymmetric composite structures of TCs undergoing secondary eyewall formation
Using a normalization based on the radii of both the primary and secondary eyewalls, we are able to composite the ERC events in a way that highlights the importance of structures near the developing secondary eyewall. We analyze observed asymmetric structures that occur prior to and during SEF. Specifically, we focus on the region surrounding r2, where the secondary eyewall ultimately forms. As discussed in Chapter 2, we classify each flight leg into a quadrant based on the deep-layer environmental wind shear at the time of the flight leg to account for the role of shear in ERC evolution asymmetries.
Quadrant-averaged kinematic structures
First, using all flight legs, we assess the mean tangential winds within each quadrant
(Figure 7). In the pre-SEF group, all quadrants exhibit the primary tangential wind maximum at r1 (Fig. 7a). Outside of r1, the highest wind speeds are in the downshear quadrants. In particular, the downshear-right (DR) quadrant has higher wind speeds than the upshear quadrants between r1 and r2. After SEF, the highest tangential wind speeds are observed in the downshear-left (DL) and DR quadrants throughout the entire profile (Figure 7b), with the DL being statistically significantly higher than the upshear-right (UR) inward of r2. In the post-SEF group, a clear local maximum of tangential wind at r2 emerges, demonstrating that secondary eyewall formation has occurred. This maximum is clearly visible in the normalization relative to both eyewall radii; it
27 was indistinguishable in the normalization relative to only the primary eyewall discussed in
Chapter 3.
Wavenumber-1 asymmetries in tropical cyclones can result from both deep-layer environmental wind shear and storm motion. Corbosiero and Molinari (2003) found that for both inner and outer regions of TCs, the wavenumber-1 asymmetry aligns with the motion vector when the shear magnitude is weak (< 5 m s-1). With moderate and high shear magnitudes, the shear-induced asymmetry dominates the motion-induced asymmetry. To focus our quadrant analyses more on shear-related asymmetries, we present data from TCs experiencing shear greater than 5 m s-1 only.
Figure 7. a) Quadrant mean profiles of all shear magnitudes for the pre-SEF group. Statistically significant differences between each quadrant pair are plotted along the bottom with colors corresponding to each quadrant. b) As in a for the post-SEF group. c) The change in tangential wind speed by quadrant from the pre-SEF group to the post-SEF. Statistically significant differences for the change in each quadrant are plotted along the bottom.
28 Figure 8 shows the same variables as Figure 7, but only for flight legs that occurred during moderate and high shear magnitudes. These results are similar to those of all shear magnitudes, but with some notable exceptions. The differences between both downshear quadrants and both upshear quadrants are statistically significant between r1 and r2 in the pre-SEF group (Fig. 8a). Such downshear enhancement of tangential winds is different from previous composite studies who show a left-of-shear enhancement (Reasor et al. 2013; Rogers et al. 2013;
Zhang et al. 2013), albeit these studies did not exclusively focus on SEF cases. Based on Figure
3, there is significant variation of the radius of the secondary eyewall, particularly in the r* framework. However, the lack of statistically significant differences outside of r1 in the r** framework suggests the axisymmetric broadening of the outer wind field observed in Figure 5 is not specific to a certain quadrant.
For the post-SEF group, the extent of statistically significant differences between DL and
UR decreases outside r1, underscoring a reduction in the asymmetry inward of the secondary eyewall. We also note subtle differences in the wind profiles near r2. Both DL and upshear-left
(UL) quadrants have peaks that are more prominent in their profiles. These are the only quadrants with statistically significant changes at r2 from the pre to post-SEF group (Fig. 8c). This clear increase in peakedness suggests that SEF involves preferred strengthening of the 700-mb tangential winds in the left-of-shear quadrants. In an observational study of Hurricane Earl,
Didlake et al. (2018) also found that the left-of-shear quadrants developed a clear secondary wind maximum first, which is consistent with the current composite analysis. Previous studies point to a left-of-shear preference for enhanced convective activity in developing and mature secondary eyewalls (Hence and Houze 2012a; Didlake et al. 2017). In comparison, the primary eyewall experiences the greatest change in tangential winds in the downshear quadrants, which is upwind of the observed secondary eyewall asymmetries. These differences in the arrangement of the two eyewalls are also consistent with previous studies (Hence and Houze 2012a; Didlake et al. 2017).
29
Figure 8. As in Figure 7, but for shear magnitudes greater than 5 m s-1 only.
An assessment of relative vorticity shows a broad vorticity maximum in all quadrants in the eye and primary eyewall (Fig 9a, b). The small regions suggesting statistical significance outside of the primary eyewall are likely false positive test results that can occur when applying statistical significance testing over a large number of radial points. In several of these regions, we have no a priori reason for differences to occur, and so we do not interpret the statistical significance signals as having implications on the TC structure.
In the post-SEF group, a secondary vorticity maximum is associated with the developing secondary eyewall. This maximum is less than one fourth of the magnitude of the maximum in the primary eyewall, which is consistent with observations of Hurricane Rita documented in Bell et al. (2012). The secondary eyewall vorticity peak is the most prominent in the left-of-shear quadrants (Fig. 9b), and at this radius, the left-of-shear quadrants have statistically significant increases going from pre- to post-SEF groups (Fig. 9c). The differences between the left-of-shear and right-of-shear secondary vorticity maxima suggest a wavenumber-1 structure in the secondary eyewall circulation as it develops, consistent with the asymmetry in peakedness
30 observed in tangential wind. The greatest change in the primary eyewall vorticity from pre-SEF to post-SEF is found in the downshear quadrants, again consistent with the changes found in tangential wind.
The nondimensional angular momentum shows increasing momentum with radius in all quadrants, and an increase in momentum in the outer core in all quadrants from the pre-SEF to post-SEF group, as seen in the axisymmetric profiles (Fig. 9d, e). In the pre-SEF group, the DL quadrant has higher angular momentum than the upshear quadrants between r1 and r2. While the broadening of the wind field between r1 and r2 was most notable in the DR and DL quadrants for tangential wind (Fig. 8a), a corresponding profile of enhanced angular momentum only appears in the DL quadrant. Though this enhancement is slight, its statistical significance through much of the region between r1 and r2 is unique to the pre-SEF group and could be dynamically important.
The presence of a broad stratiform rainband may explain this signal; this explanation would be consistent with Didlake and Houze (2013b), Qiu and Tan (2013), and Didlake et al. (2017, 2018).
These previous studies found that the stratiform rainband, primarily located in the DL quadrant, induces mesoscale descending inflow that advects high angular momentum air inward from the surrounding environment. This inward advection could result in enhanced angular momentum values seen in the current observations. These studies also suggest that the mesoscale descending inflow in the stratiform portion of the rainband in the DL quadrant is crucial for SEF. As the mesoscale descending inflow reaches the lower levels, this flow perturbs the boundary layer and produces persistent updrafts that lead to the development of a local tangential wind maximum.
This tangential wind maximum then strengthens and axisymmetrizes into the wind maximum associated with the secondary eyewall seen in the post-SEF group.
After SEF, the similarity of the quadrant momentum values between r1 and r2 suggests that axisymmetrization has occurred (Fig. 9e). The momentum increased in all quadrants from the
31 pre to post-SEF group (Fig 9f), indicative of the locally increased tangential wind speeds associated with the secondary eyewall and broadened outer wind field.
Figure 9. As in Fig. 8, but for (a-c) vertical vorticity and for (d-f) nondimensional absolute angular momentum.
Quadrant-averaged thermodynamic structures
Next, we analyze the thermodynamic mean quadrant profiles in the pre-SEF and post-
SEF groups. The temperature profiles reveal a maximum in the eye and eyewall cloud, consistent with the presence of subsidence in the eye, and deep convection in the eyewall cloud (Houze
2010). Outside of r1, the profiles decrease in a gradual quasi-linear fashion in both groups. The
UR quadrant is statistically significantly warmer than the DL quadrant through much of r1 to r2+m in the pre-SEF group (Fig. 10a), consistent with previous studies (Frank and Ritchie 1999;
Zhang et al. 2013). They theorized the difference between the UR and DL quadrants is due to precipitation and evaporative cooling in DL, which would be reasonable at the 700-mb flight level as well.
32 In the post-SEF group (Fig. 10b), the quadrant temperatures are relatively uniform. In particular, the DL is no longer cooler than UR throughout most of the profile, perhaps due to latent heating resulting from enhanced convection. There are slight statistically significant differences near r1 where the UR quadrant is slightly warmer than the other quadrants following
SEF. This may be a result of more adiabatic warming from descent and the absence of cooling from evaporating precipitation in this quadrant (Reasor et al. 2013; DeHart et al. 2014). The only statistically significant changes in temperature over time were between r1 and r2, where an increase (decrease) in the DL (DR) temperature occurred. The increase in the DL quadrant just outside the primary eyewall could be due to increasing subsidence as the moat forms, as this is also the quadrant with the most robust strengthening transverse circulation of the secondary eyewall (Didlake et al. 2017). The decrease in temperature at r1 is likely a result of the contraction as higher temperatures associated with the DR eyewall convection moving inward to smaller radii.
As in the axisymmetric profile, the specific humidity is at its maximum in the eyewall cloud and then decreases radially outward (Fig. 10d, e). An examination of pre-SEF specific humidity reveals no significant differences among the quadrants (Fig. 10d). Zhang et al. (2013) found that the UR quadrant tends to have the lowest specific humidity at 1.5 km altitude due to the relative lack of convection in this region. We did not find this result outside of r1; perhaps the specific humidity asymmetries observed in Zhang et al. (2013) do not extend up to the 700-mb flight level or that storms leading up to SEF have more symmetric specific humidity distributions.
Going to post-SEF, the only post-SEF significant differences are between DL and UR in the eyewall cloud (Fig. 10e), which corresponds to a significant increase in DL specific humidity.
This change may indicate an increased asymmetry in the primary eyewall convection and circulation as the secondary eyewall takes shape. The axisymmetric analysis showed an increase in specific humidity going from pre- to post-SEF throughout the profile. The quadrant composite
33 analysis shows that the DL quadrant drives this increase for the inner eyewall, but the outer eyewall and rainband regions do not indicate that a specific quadrant dominates this increase.
Figure 10. As in Figure 8, but for (a-c) temperature, and (d-f) specific humidity.
The relative humidity (RH) mean quadrant profiles have more statistically significant differences than all other thermodynamic variables (Fig. 11a, 11b), where higher RH regions likely indicate increased clouds at flight-level. In the pre-SEF group, the UL quadrant has higher
RH radially inward of r1, which indicates inward spiraling of the inner eyewall cloud in this quadrant. Radially outward, the UR quadrant is statistically significantly lower than the other quadrants at various points throughout the profile, which suggests decreased convection in this region. Between r1 and r2, axisymmetric RH analysis indicates possible moat development compared to non-ERC storms, and this decreasing cloud coverage appears to be most prevalent in the UR quadrant. Outside of r2, lower RH in the UR indicates decreased rainband activity. This finding is generally consistent with several studies (e.g., Chen et al. 2006; Hence and Houze
34 2012b). In particular, Zawislak et al. (2016) found lower RH values and decreased cloud coverage in the UR quadrant of Hurricane Edouard with dropsonde and satellite observations.
The differences between UR and UL are statistically significant at many more radii than the differences between UR and the other quadrants. From this, we can infer that the rainband complex ends abruptly between the UL and UR quadrants. This RH structure is consistent with broad cloud coverage transitioning to a dry, clear region. This suggestion is in line with the downwind end of a rainband complex comprising of broad, stratiform precipitation and thus consistent cloud coverage in the UL quadrant (Didlake and Houze 2013b).
Immediately following SEF, DL consistently has the highest RH values throughout the profile. This difference is statistically significant compared to the upshear quadrants, especially in the primary eyewall cloud where observations suggest the presence of a wavenumber-1 asymmetry in RH between the downshear and upshear regions of the storm. This wavenumber-1 structure could be a manifestation of the effect that a sheared environment has on vertical motions in the upshear and downshear sides of an inner eyewall. Updrafts typically predominate the downshear quadrants, and downdrafts predominate the upshear quadrants (Jones 1995; Black et al. 2002; Eastin et al. 2005; Reasor et al. 2013; DeHart et al. 2014). This asymmetry manifests as higher (lower) relative humidity values in the downshear (upshear) quadrants. Zawislak et al.
(2016) found that subsidence was omnipresent in the upshear quadrants where lower RH values predominated. In addition, following SEF, the secondary eyewall tends to act as a barrier that hinders low-level inflow of high- θe air from reaching the primary eyewall. Didlake et al. (2017) showed how this barrier effect occurs more in upshear quadrants, which may also contribute to the observed enhanced asymmetry in the primary eyewall. The enhanced asymmetry of the inner eyewall following SEF is consistent with that found in specific humidity.
Between r1 and r2, the reduction of RH becomes more apparent in the downshear profiles.
The statistically significant differences between these quadrants and the UR quadrant become less
35 apparent, which suggests that clearing of the moat region is reaching all quadrants. Outside of r2, the UL quadrant no longer has a higher RH than the UR quadrant. This drying in UL is the most apparent RH change during SEF, as seen in statistically significant differences outside the secondary eyewall (Fig. 11c). As a result, the region outside r2 has decreased symmetry in cloud coverage, just as in the inner eyewall. The transverse circulation of the strengthening secondary eyewall likely triggered subsidence radially outward in the UL quadrant and decreased the RH here. Overall, the axisymmetric RH changes very little going from pre- to post-SEF, but the quadrant analysis shows that the asymmetry of this RH structure increases in both the inner eyewall and outside of the secondary eyewall, while the reduced RH in the moat becomes more axisymmetric.
An inspection of equivalent potential temperature (θe) reveals a maximum in the eye and eyewall cloud (Fig 11d, 11e) and a sharp decrease in the eyewall cloud similar to that observed in specific humidity. The decrease slows and is quasi-linear outside of r1, consistent with the behavior of the T and q profiles. Despite differences in the temperature and RH profiles, there are no broad regions of statistically significant differences in either the pre or the post-SEF group.
The axisymmetric analysis showed a clear increase in θe going from pre- to post-SEF in all regions of the TC, but the quadrant analysis shows that this increase is not particular to a specific quadrant.
36
Figure 11. As in Figure 8, but for (a-c) relative humidity, and (d-f) equivalent potential temperature.
Analyzing the asymmetries of both kinematic and thermodynamic fields during SEF provides insight into structural changes during TC evolution that axisymmetric means may average out. In addition, using a normalization technique that takes into account the radii of both eyewalls highlights the role of these structures in SEF, and enables us to perform a composite analysis. We have observed several asymmetries and statistically significant differences in both space and time that appear to play a role in SEF. The next chapter will further examine the role of these structures in a case study of the first ERC in Hurricane Earl (2010).
37
Chapter 5
Case Study: Hurricane Earl (2010)
Employing a normalization technique based on the radii of both eyewalls enables us not only to perform a composite analysis of the importance of storm-scale structures prior to SEF, but to do so for a case study as well. This case study will focus on the timeframe leading up to the first eyewall replacement cycle of Hurricane Earl in 2010. Several aircraft as part of field campaigns and regular reconnaissance, as well as the land-based radar in San Juan, Puerto Rico, extensively observed Hurricane Earl. It is due to this abundance of various observations that we chose this event for case study. Three U.S. Air Force reconnaissance flights occurred during the period of interest: 20100829U2, 20100830U1, and 20100830U2. The first two flight missions represent the pre-SEF structures of Hurricane Earl, while 20100830U2 is representative of post-
SEF structures as a secondary wind maximum is clear in the azimuthal mean radial profile
(Figure 2). As discussed in Chapter 2, we partitioned radial flight legs from each mission into quadrants based on the deep-layer environmental wind shear. For flights with multiple legs in one quadrant, we examine a leg representative of the mean. Since most quadrants only contain one leg during each flight, we cannot test for statistical significance. Nevertheless, based on the analysis of the previous two chapters, we can assess the importance of observed structures and compare to studies that analyze other concurrent data sets.
Kinematic profiles
In the tangential wind of the first pre-SEF flight, the primary eyewall maximum is most prominent in the downshear quadrants, particularly DR (Figure 12a). In the second flight, the DR
38 has the most prominent primary eyewall maximum (Figure 12b). Through both of these flights, the DL and UL contain a persistent secondary wind maximum just outside of r2. This is consistent with radar observations of Hurricane Earl presented in Didlake et al. (2018). The local wind maximum was associated with the stratiform end of the spiral rainband complex and a concurrent mesoscale descending inflow outside of r2. Figures 12a and b also illustrate that the UL secondary maximum begins radially inward of the maximum in DL, which is consistent with the inward spiral of the rainband complex. The enhanced tangential winds near r2 in UL have a much larger radial extent than that of DL. The mesoscale descending inflow, which acts to increase the tangential winds, was strongest in the DL quadrant (Didlake et al. 2018). However, the bulk of this enhanced flow is advected downwind into the UL, resulting in the broader signal seen here.
After SEF occurred (Fig. 12c), the DL and UL secondary wind maxima are collocated and have peaks that are more prominent than the local maxima in the right-of-shear quadrants, consistent with the composite analysis presented in Chapter 4, as well as with previous studies
(Didlake et al. 2017; Didlake et al. 2018). The primary eyewall maximum is again located in DR following SEF, consistent with the composite analysis of the previous chapter and previous studies.
During the SEF process, several changes to the tangential wind field structure take place.
Figure 12d shows the changes in tangential wind from 20100829U2 to 20100830U2. The tangential wind strengthened in the primary eyewall in all quadrants as Earl intensified. The tangential wind speed increased at r2 where the secondary eyewall formed. Limited increases in tangential wind between r1 and r2 illustrate that the processes occurring are restricted to the eyewalls, rather than uniformly occurring throughout the radial profile. The broadening outer wind field is also particularly visible in DL outside of r2.
The vorticity radial profiles (not shown) correspond with the tangential wind profiles, consistent with the analysis presented in Chapter 4. The magnitude of the vorticity maximum
39 associated with the primary eyewall increased as Earl strengthened prior to SEF. The secondary vorticity maximum was most clearly visible in the left-of-shear quadrants, collocated with the most prominent secondary eyewall tangential wind maximum.
Figure 12. Quadrant distribution of tangential wind (m s-1) for a) 20100829U2, b) 20100830U1, and c) 20100830U2. The change in each quadrant from 20100829U2 and 20100830U2 is shown in d).
The nondimensional angular momentum (M*; divided by the set mean angular momentum at the radius of maximum winds for each set, as in Chapters 3 and 4), is similar to the results of the composite study. The quadrant distribution of M* in Hurricane Earl (Figure 13) shows that, prior to SEF, higher angular momentum was found in the UL quadrant, with the DL reaching a clear peak during each mission. These signals reflect the corresponding tangential
40 wind profiles in that region (Figure 12). During SEF, the momentum increases in all quadrants, consistent with the composite observations in Chapter 4. This increase is a result of the broadening of the outer wind field and formation of the secondary eyewall. The similarity between all quadrants from the center to r2 suggests that axisymmetrization has occurred inward of the secondary eyewall. At r2 and outward, the largest increase occurs in the DL quadrant, which leads to the DL having the largest M* values. This exact evolution of the DL quadrant was not seen in the composite profiles, where the DL quadrant exhibited higher M* values prior to
SEF. Nevertheless, the left-of-shear quadrants overall are shown to be preferred quadrants for higher tangential wind and angular momentum leading up to and during SEF. To explore the processes observed here further, we next assess the thermodynamic structures observed during these flight missions into Hurricane Earl.
41 Figure 13. As in Figure 12, but for nondimensional absolute angular momentum.
Thermodynamic profiles
Radial profiles of temperature show lower temperatures in the DL before SEF outside of r1 (Figure 14a, b), consistent with the composite analysis presented in Chapter 4. The decreased temperatures DL are likely a result of evaporative cooling due to widespread precipitation observed in this region prior to SEF (Didlake et al. 2018). A strong temperature gradient between the eye and primary eyewall indicate that the eye of Earl was thermodynamically isolated from the rest of the inner core.
The left-of-shear quadrants featured prominent changes in temperature during SEF
(Figure 14d). Significant warming, reaching ~5°C in UL, occurred between the two eyewalls as the secondary eyewall formed. This warming is likely associated with subsidence and moat formation; examining the corresponding change in moisture will provide further insight into this process. The left-of-shear quadrants also warmed outside of r2, which may be a result of compensating subsidence due to the strengthening transverse circulation of the secondary eyewall, which is most prominent DL and UL. Much of the DR radial profile cooled, though possible reasons for this cooling are not yet apparent.
42
Figure 24. As in Figure 12, but for temperature (°C).
An assessment of moisture highlights the changes in the spatial and temporal variability of convection and cloud structures at flight-level during SEF. The composite analysis presented in
Chapter 4 showed that relative humidity had the largest variability of all moisture variables among the TC quadrants. Thus, RH is the only moisture variable we present in this chapter. The
20100829U2 profile reveals that the relative humidity (RH) at 700 hPa varied throughout the radial profiles of all quadrants (Figure 15a). Meanwhile, 20100830U1 displays a large spread in
RH, with more saturated conditions in the primary eyewall of the DL quadrant that then decreases significantly in the UL quadrant (Fig. 15b). At the same time, RH values near r2+m are consistently unsaturated; this result suggests that cloud cover is reduced in all quadrants.
43 In the post-SEF flight mission, a notable minimum in relative humidity is evident in all quadrants between r1 and r2 (Figure 15c). Comparing the change in RH from pre- to post-SEF indicates that the cloud cover decreased in all quadrants between r1 and r2, particularly in UL and
UR. In conjunction with the simultaneously observed warming, this signal indicates moat formation. Compensating subsidence strengthened to counteract the strengthening transverse circulation of the developing secondary eyewall. As SEF occurred, the moat began to take on characteristics of the TC eye – that is, it warmed and dried – consistent with observations by
Sitkowski et al. (2012). Outside of r2, the RH in the UL quadrant increased, which contradicts the composite results presented in Chapter 4, where RH decreased in radii beyond the secondary eyewall (Fig. 11c). Variability in this individual case may be a reason for this dissimilarity. While temperature and moisture both influence the equivalent potential temperature (θe), the quadrant radial profiles of θe (not shown) largely follow the patterns shown in Figures 14 and 15.
Figure 35. As in Figure 11, but for relative humidity (%).
44
Chapter 6
Conclusions
Aircraft in-situ observations at the 700 hPa level from the FLIGHT+ dataset (Vigh et al.
2016) were compiled and analyzed to assess the composite axisymmetric and asymmetric structures that are characteristic of secondary eyewall formation (SEF). We first examined the quasi-evolution of axisymmetric TCs by comparing intensifying (IN) storms that did not undergo
SEF to storms just prior to SEF (pre-SEF) and just after SEF (post-SEF). This axisymmetric composite analysis uses a radial framework that is normalized relative to the radius of the maximum wind (RMW) in the primary eyewall. The SEF groups exhibit broadening of the wind field in both tangential wind (v) and nondimensional absolute angular momentum (M*) profiles that is not seen in the IN TCs, which was an expected structural change leading into SEF. In the pre-SEF group, the broadening begins with an enhancement of v and M* just outside the primary eyewall (near the radii of the eventual secondary wind maxima) and then in the post-SEF group stretches to even farther radii. Compared to IN TCs, the SEF groups develop distinct and expected thermodynamic differences that are characteristic of a concentric eyewall structure. The
SEF groups have higher θe at the radii of both eyewalls that is associated with strengthening convection, and lower relative humidity at the moat between the eyewalls that indicate decreasing clouds.
In our analysis using an RMW-relative normalization framework (the r* framework), features related to the secondary eyewall were smeared since the radii of the secondary eyewall varied widely and was unrelated to the RMW in each ERC. We therefore employed a different normalization technique, the r** normalization, which takes into account the radii of both the primary eyewall (r1) and the secondary eyewall (r2). This framework successfully captured the
45 axisymmetric secondary wind maximum and the expected secondary vorticity maximum. Both of these signals did not emerge in the often-used RMW-based normalization. With this new framework, we were able to do a more thorough examination of features that are associated with secondary eyewall formation. This included an analysis of asymmetric features relative to the
850-200 hPa environmental wind shear.
In the pre-SEF group, kinematic and thermodynamic signatures corresponded well with the expected asymmetry of a mature rainband complex. Previous studies found that a rainband complex typically begins in the upshear-right (UR) quadrant and stretches around the TC to the upshear-left (UL) quadrant (Willoughby et al. 1984; Corbosiero and Molinari 2002; Hence and
Houze 2008, 2012b). Convection generally consists of actively convective cells in the right-of- shear half and transitions to broader stratiform precipitation in the left-of-shear half (Black et al.
2002; Hence and Houze 2012b; Didlake and Houze 2013a,b). The expansion of the wind field seen in the axisymmetric analysis between r1 and r2 was a result of downshear enhancement of v and downshear-left (DL) enhancement of M*. The enhanced M* coincides with the mesoscale descending inflow typically seen in DL stratiform rainband precipitation. This broad inflow pattern locally increases angular momentum by advecting higher angular momentum air radially inward (Didlake and Houze 2013b). Compared to the UR quadrant, temperatures radially outward of r2 were lower in the DL quadrant due to latent cooling beneath the broad stratiform cloud. In the UR quadrant, temperatures were higher and relative humidity (RH) was lower, which is consistent with large-scale subsidence and limited rainband activity expected in this quadrant.
The RH in the UR quadrant was also significantly lower than the upshear-left (UL) quadrant, suggesting that clouds at 700 hPa significantly decreased as the circulating air travelled across this quadrant border. This finding is consistent with the expected decline of broad stratiform clouds near the UL downwind end of the mature rainband complex. A dynamically active and well-organized rainband complex is apparent in this composite analysis prior to SEF.
46
In the post-SEF group, a clear secondary wind maximum emerged at r2. This wind maximum is particularly prominent in the left-of-shear quadrants, as a result of significant increases in the tangential winds at this radius during SEF. The vorticity signals are consistent with the tangential wind profiles, with prominent secondary maxima in the left-of-shear quadrants. The left-of-shear occurrence of these wind and vorticity peaks coincides with the dynamically important stratiform rainband precipitation in the pre-SEF group. Such coincidence is consistent with Didlake et al. (2018) who hypothesized that the mesoscale descending inflow in stratiform rainband precipitation plays a primary role in spinning up an incipient secondary eyewall wind maximum in the left-of-shear half. Going from pre-SEF to post-SEF, the inner eyewall does not display the same alignment in tangential wind increases as at r2. Rather there is a downwind shift in the asymmetry going from the inner to outer eyewall. This composite result is consistent with concentric eyewall differences seen in Hence and Houze (2012a) and Didlake et al. (2017). These studies suggest that while the inner eyewall directly dynamically interacts with the wind shear and yields a downshear asymmetry alignment, the outer eyewall asymmetry likely results from interaction with the rainband complex and yields a left-of-shear asymmetry alignment.
Also going from pre-SEF to post-SEF, the inner eyewall became more asymmetric in its thermodynamic structure. The clearest indicator of this enhancing asymmetry is the drying and warming of the UR inner eyewall and a corresponding moistening of the DL in the composite results. This finding follows the expected asymmetry of vertical motion in the inner eyewall cloud, where updrafts dominate the downshear quadrants and downdrafts dominate upshear
(Jones 1995; Black et al. 2002; Corbosiero and Molinari 2002, 2003; DeHart et al. 2014). It is also consistent with inevitable weakening of the inner eyewall during an ERC, possibly due to the secondary eyewall preventing sufficient low-level high θe air from reaching the inner eyewall, as discussed in Didlake et al. (2017). While the relative humidity axisymmetric profiles were similar
47 between the pre- and post-SEF groups, the quadrant analysis of RH revealed that drying in the moat region appears first in the UR, and then becomes more symmetrical, a signal classically associated with concentric eyewalls.
A case study analysis of the observations of Hurricane Earl (2010) showed both similarities and variances with the composite structures. Consistent with the composites, enhanced v and M* in the left-of-shear quadrants prior to SEF illustrated a broadening outer wind field and local wind maxima near r2. Lower temperatures in the DL and lower RH in the UR were also present. Unlike in the composites, there was more saturated air and likely cloud cover outside r2 following SEF. Such variation from the composite is expected, given that Earl was a single case study.
Our results highlight the TC features and evolving structures that are ubiquitous during
SEF. Additional work must be performed to analyze these kinematic and thermodynamic structures to determine their specific contribution to SEF in the context of proposed SEF theories.
Additional reconnaissance and radar observations of ERCs will be useful in this endeavor. In addition, continued use of numerical models to examine the axisymmetric and asymmetric features leading to SEF will help us to gain a better understanding of the processes and thus improvement in forecasts of subsequent eyewall replacement cycles.
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