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Topic 2.6

INTENSITY CHANGE: INTERNAL INFLUENCES Rapporteur: Daniel Stern National Center for Atmospheric Research 3450 Mitchell Lane, Boulder, CO 80301 Email: dstern@ucar.edu Phone: +1+443+465 1921 Rapporteur: Jason Dunion NOAA/AOML/HRD University of Miami/RSMAS/CIMAS, 4600 Rickenbacker Causeway, Miami, FL 33149 Email: Jason.dunion@noaa.gov Phone: +1+305+720 3060 Working group: Michael Bell (University of Hawaii), Eric Hendricks (Naval Research Laboratory), Yi-Hsuan Huang (National Taiwan University), Haiyan Jiang (Florida International University), James Kossin (NOAA National Climatic Data Center), Jeff Kepert (The Centre for Australian Weather and Climate Research), Yoshiaki Miyamoto (RIKEN Advanced Institute for Computational Science), Yuqing Wang (University of Hawaii) Abstract: Significant advances have been made in our understanding of internal influences on tropical cyclone (TC) intensity change, particularly regarding rapid intensification (RI) and the effects of eyewall replacement cycles (ERCs) on intensity. Recent observational studies have identified structural characteristics of the TC vortex and associated convection that are conducive for RI. The typical lifecycle of ERCs as they relate to TC intensity has been documented observationally, a number of studies have successfully simulated ERCs, and progress has been made towards understanding the mechanism by which outer eyewalls lead to weakening of the inner eyewall. Recent studies have identified diurnal (or quasi-diurnal) oscillations in rainbands that may influence intensity. Idealized studies of barotropic instability have increased in realism, examining the effects of diabatic heating and surface friction, as well as extending analyses to three dimensions. The effect of surface fluxes of heat and momentum on intensity continues to be somewhat uncertain, due in part to difficulties in determining the magnitude of exchange coefficients at high wind speeds. Nevertheless, recent observational estimates continue to suggest that these coefficients do not vary substantially with wind speed beyond minimal hurricane-strength, and a long-lived discrepancy between observations and theory in this respect may have been resolved. Finally, differing viewpoints regarding the fundamental mechanisms by which TCs intensify remain. This debate is discussed, with the hopes of guiding future research that makes progress towards resolving these issues. 2.6.0 Introduction The goal of this report is to summarize the progress of research on internal influences on tropical cyclone (TC) intensity change since IWTC-VII. In order to properly put the recent studies in the context of our existing knowledge, we have also included discussion of some earlier studies as background. While the scope of this topic is itself relatively narrow, there are close connections between internal influences on intensity change with several other topics in IWTC-VIII. Specifically, intensity change is intrinsically tied to structure change (Topic 4.1), the boundary layer (Topic 4.5), and air-sea interaction (Topic 4.4). For the purposes of this report, we have attempted

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to minimize duplication with these other topics as much as possible, but there is inevitably some overlap. We encourage readers to consult these other chapters, as internal influences on intensity change are best understood in the context of these related topics. There have been many recent studies that relate at least tangentially to internal influences on intensity change, and it is not possible to adequately cover all of them. Here, we attempt to summarize the most important and relevant recent studies in this subject. This summary is organized into 6 subsections: 1. Rapid Intensification 2. Eyewall Replacement Cycles 3. Relation of Rainbands to Intensity Change 4. Eyewall Instability and Inner-Core Mixing 5. Relationship between Surface Fluxes and Intensity Change 6. Mechanisms of Tropical Cyclone Intensification 2.6.1 Rapid Intensification 2.6.1.1 Relationship between Convection and Rapid Intensification Rapid intensification (RI) remains a challenging issue, both from a research and forecasting perspective. Many tropical cyclones (including nearly all Category 4 (59-69 m s-1) and 5 hurricanes (≥70 m s-1)) experience one or more periods of RI (most often defined as a 24-h intensity increase ≥ 30 kt (15.4 m s-1), Kaplan and DeMaria 2003; Kaplan et al. 2010) during their lifetime. The physical processes associated with these events remain incompletely understood, and predicting the onset of RI is one of the most challenging aspects for TC forecasters. TC intensification mechanisms that have been proposed in the past several decades include the symmetric intensification mechanism and the asymmetric intensification mechanism (discussed in 2.6.6). Convective and precipitation properties in the inner core are closely related to latent heat release, which is crucial for storm development. Earlier studies (e.g., Kelly et al. 2004; Reasor et al. 2009) have shown some relationships between TC intensification and inner-core rainfall and convective properties. An asymmetric paradigm of TC intensification has been proposed by Montgomery and Smith (2014), who summarized previous studies advocating the importance of “vortical hot towers” (VHTs) (i.e., deep convective updrafts that are nearly collocated with cyclonic vorticity anomalies). However, relatively few studies have documented the relationship between VHTs and RI. Case studies by Guimond et al. (2010) and Rogers (2010) have shown evidence of hot towers and convective bursts near the eye during RI events. Vigh and Schubert (2009) found that the warm core in TCs may rapidly develop if a portion of the deep convection occurs in the inner core region. Using an 11-yr NASA Tropical Rainfall Measuring Mission (TRMM) satellite-based Tropical Cyclone Precipitation Feature (TCPF) database (Jiang et al. 2011), Jiang (2012) found that the (global) probability of RI increases slightly from the climatological mean of 6.3% to 9.6 % when one or more hot towers exist in the inner core. Tao and Jiang (2013) found that the percentage of inner-core precipitation features classified as hot towers is the highest for RI storms (17%), followed by slowly intensifying (11%), neutral (9%), and weakening (8%) storms. However, the probability of RI (slowly intensifying) is still 4.9% (28%) for samples without hot towers. Therefore, Jiang (2012) argued that hot towers are neither a necessary nor a sufficient condition for RI. In contrast to the asymmetric intensification mechanism, many theoretical studies have found that a TC intensifies as the symmetric overturning circulation draws air from outer radii above the boundary layer while conserving absolute angular momentum (e.g., Ooyama 1969, Shapiro and Willoughby 1982, Schubert and Hack 1982). Nolan et al. (2007) found that the symmetric response to asymmetric forcing was much smaller than the symmetric response to the azimuthally averaged heating. Recently, Kieper and Jiang (2012) demonstrated that a precipitation

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ring pattern around the TC center, detectable using 37 GHz passive microwave imagery, can be a robust predictor of RI. This ring is a low- to mid-level feature that is commonly found in TCs and becomes more symmetric in storms that are undergoing RI. During RI events, the inner edge of the ring is nearly 100% closed surrounding the TC center and mainly consists of shallow convection/precipitation from near or below the freezing level to the surface. The outer edge of the ring sometimes includes asymmetric intense convection (i.e., hot towers) embedded within the ring, but for about 50% of the RI cases, the ring only contains shallow convection/precipitation. The results of Kieper and Jiang (2012) support the idea that the symmetric component of heating is more efficient at intensifying a cyclone than is asymmetric heating. Jiang and Ramirez (2013) showed that storms undergoing RI do not necessarily have more extremely intense convection in the inner core than non-RI storms. Instead, a minimum threshold of raining area, total volumetric rain, and convective intensity in the inner core was determined from the RI cases examined using the 11-yr TRMM dataset. The box and whisker plots in Figure 1 represent the distributions of maximum near surface reflectivity and maximum heights of 20 and 40 dBZ radar echo in the inner core for different 24-h future intensity change categories including rapidly intensifying (RI, ≥30 kt), slowly intensifying (SI, 10 to 30 kt), neutral (N, -10 to 10 kt), and weakening (W, ≤-10 kt). The distributions in Figure 1 are much narrower for RI storms than those for storms in other intensity change categories. For RI storms, the maximum near surface reflectivity in the inner core never goes below 40 dBZ, and the maximum heights of 20 and 40 dBZ radar echo in the inner core never go lower than 8 and 4 km, respectively. Jiang and Ramirez (2013) concluded that these are therefore “necessary conditions” for RI. Zagrodnik and Jiang (2014) further sub-divided the RI category into an initial (RI-initial) and continuing (RI-continuing) category based on whether the storm was near the beginning of an RI event or had already been undergoing RI for 12 or more hours. As shown in Figure 2, they found that rainfall frequency (defined as the shear-relative occurrence of TRMM precipitation-radar near-surface reflectivity >20 dBZ) is most strongly correlated with future intensity change. They also found that moderate to deep convection only increases significantly after RI has already been underway for at least 12 hours. The additional precipitation in rapidly intensifying TCs is composed primarily of a mixture of weak convective and stratiform rain, especially in the upshear quadrants. The rainfall frequency and latent heating distributions are more symmetric near the onset of RI and continue to become more symmetric as RI continues and the rainfall coverage expands upshear.

Figure 1. Box and whisker plots of (a) maximum near surface radar reflectivity, (b) maximum height of 20 dBZ radar echo, and (c) maximum height of 40 dBZ radar echo in the inner core of TCs in different intensity change stages. The top of the

box represents the 75th percentile, the center line the median, and the bottom the 25th percentile. The whiskers extend out to the maximum or minimum value of the data, or to 1.5 times the 75th and 25th percentiles, if there is data beyond this

range. Outliers are plotted individually with circles. Taken from Jiang and Ramirez (2013).

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Figure 2. Composite shear-relative distribution of the percent occurrence of near-surface reflectivity > 20 dBZ for (a)

Weakening, (b) Neutral, (c) Slowly Intensifying, (d) RI (Initial), and (e) RI (Continuing) tropical cyclones observed by the TRMM precipitation radar during 1998-2011. The black arrow represents the orientation of the vertical wind shear vector.

Taken from Zagrodnik and Jiang (2014). Several studies have investigated possible relationships between lightning activity and RI. Using the World Wide Lightning Location Network (WWLLN), DeMaria et al. (2012) found that intensifying TCs generally have a greater lightning density than do weakening storms. However, the inner-core lightning density is on average greater in rapidly weakening storms than in storms undergoing RI. In the outer rainband region (200-300 km), lightning density was found to be much greater in RI cases. Using 11 years of TRMM Lightning Imaging Sensor (LIS) data, Jiang and Ramirez (2013) found a similar relationship between intensity change and lightning activity. The percentage of TRMM observations with lightning in the inner core decreases with increasing intensification rate. The percentage is lowest for storms undergoing RI and highest for weakening storms. Consistent with DeMaria et al. (2012), Jiang and Ramirez (2013) found that for the outer rainband region, lightning activity is greater for storms undergoing RI. As discussed in DeMaria et al. (2012), lightning activity in TCs tends to be very episodic (particularly within the inner core), with long periods of little activity interspersed with outbreaks. While DeMaria et al. (2012) found that such outbreaks “are often a signal that an intensification phase is coming to an end”, Stevenson et al. (2014) found that an outbreak of inner-core lightning preceded the RI of Hurricane Earl (2010). Finally, Fierro et al. (2011) presented evidence that the height of lightning discharges increased during the RI of Hurricane Rita (2005), followed by a rapid decrease in those heights near the end of RI.

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2.6.1.2 The Onset of Rapid Intensification Recently, the conditions associated with the onset and maintenance of RI have been intensively studied, both in observations and simulations. Barnes and Fuentes (2010) found from dropsonde data in Hurricane Lili (2002) that the equivalent potential temperature increased inside the radius of maximum winds (RMW) prior to the onset of RI. Rogers (2010) found that in a simulation of Hurricane Dennis (2005), the inner-core low-level (1.5 km) vertical mass flux increased significantly 3-6 h prior to the onset of RI, and that this increase was dominated by relatively weak (1-2 m s-1) updrafts. On the other hand, McFarquhar et al. (2012) examined a period of RI within a simulation of Hurricane Dennis (2005), and found that an increase in the most extreme (99.9th percentile) updrafts preceded the onset of RI. They contrasted this result with the simulation of Dennis by Rogers (2010), who did not find this relationship. Miyamoto and Takemi (2013) examined the initiating process of RI for simulated TCs in idealized experiments, and proposed a transition mechanism for RI as follows. A TC needs to be nearly axisymmetric and sufficiently strong prior to the onset of RI, which results in the enhancement of inertial stability in the inner-core region. Fluid parcels within the inner core have longer residence times within the boundary layer than do parcels at times prior to the axisymmetrization, and hence obtain more enthalpy from the underlying ocean. This increases convective available potential energy (CAPE) inwards of the RMW. An eyewall forms that utilizes this enhanced CAPE, and RI subsequently begins. Wang and Wang (2014) also found that a build up of CAPE or slantwise CAPE in the eye preceded RI. Miyamoto and Takemi (2014, in revision) found that the RI of TCs in both idealized and real-data simulations is triggered by eyewall formation, and that TCs with greater maximum tangential winds, smaller RMW, and/or a smaller Coriolis parameter are more likely to experience RI. Their result that a smaller Coriolis parameter is favourable for the onset of RI is consistent with Li et al. (2012), who also examined idealized numerical simulations. 2.6.1.3 Relationship of Vortex Structure to Rapid Intensification Rogers et al. (2013) used Doppler radar composites of a number of TCs to investigate whether or not there are significant convective- and vortex-scale differences between intensifying (>20 kt increase in 24 h) and steady-state (<10 kt increase or decrease in 24 h) TCs. They found that as compared to steady-state storms, intensifying TCs had a stronger azimuthal mean eyewall updraft, a deeper low-level inflow layer, and a more ringlike radial profile of vertical vorticity. Additionally, the azimuthal extent of eyewall precipitation was greater in the intensifying composite. Significant differences in the distribution of vertical velocity were only found for the most extreme updrafts, which were stronger in the intensifying TCs. Finally, convective bursts were preferentially found inwards of the RMW in the intensifying composite, whereas the bursts tended to occur outwards of the RMW in the steady-state composite. Brown and Hakim (2014, submitted) examined a set of WRF ensemble analyses and forecasts for 5 rapidly intensifying or nearly-rapidly intensifying TCs, in order to determine the sensitivity of intensification to vortex structure. They found that a stronger primary circulation, secondary circulation, and warm core were all associated with greater intensification. They found that enhanced moisture beyond the RMW was also conducive for intensification. Separately evaluating the sensitivity to moisture variables (e.g., water vapour, cloud water, etc.) and “dry” variables (horizontal and vertical velocity, pressure, and potential temperature), the authors found consistently that the latter had a greater effect. Finally, for perturbations that led to increased intensification, the most extreme updrafts were significantly enhanced. Several recent studies have investigated the relationship between the RMW and RI. In a simulation of Typhoon Sinlaku (2008), Leroux et al (2013) found that the intensification rate during RI was sensitive to the initial size of the RMW. In particular, they found that the minimum pressure

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at the end of RI decreased with increasing initial RMW. In contrast, using a suite of idealized simulations, Stern and Nolan (2011) found no systematic dependence of the intensification rate or final intensity on initial RMW. Carrasco et al. (2014) examined the relationship between RMW and intensification in the Extended Best Track dataset, and found that among non-weakening TCs, those with a smaller RMW are more likely to undergo RI. Finally, Stern et al. (2014, in review) showed that in both idealized simulations and observations, the contraction of the RMW tends to cease during the middle of RI, with most intensification occurring after the storm has achieved a quasi-steady size. 2.6.2 Eyewall Replacement Cycles 2.6.2.1 Observations of Eyewall Replacement Cycles Eyewall replacement cycles (ERCs) are commonly observed in strong TCs and are well known to cause fluctuations in intensity and wind structure (e.g., Willoughby et al. 1982, Willoughby 1990, Black and Willoughby 1992). These fluctuations are often large and rapid and pose a significant additional challenge to intensity forecasting because they constitute a transient anomalous behavior that is generally not captured well by the present suite of operational intensity forecast guidance. Consequently, when the formation of a secondary (outer) concentric eyewall signals a likely impending ERC in an operational setting, forecasters must rely on expert judgment based on experience to subjectively modify the intensity forecasts provided by the available objective guidance. Willoughby et al. (1982) were among the first to quantify intensity and wind-structure changes during an ERC. They used low-level aircraft reconnaissance data collected in three Atlantic hurricanes and five western North Pacific typhoons to identify changes in minimum sea-level pressure and eye diameter, which serves as a proxy for the RMW. More recently, Sitkowski et al. (2011) expanded on previous results by compiling low-level aircraft data capturing 24 complete ERC events in the North Atlantic, and formed a climatology of associated intensity and RMW changes. They found that the typical ERC can be naturally divided into 3 distinct phases: 1) intensification (nearly half of the cases were rapidly intensifying at the time outer wind maxima were first observed, with an average increase of 14 kt during the intensifying phase), 2) weakening (all cases exhibited a period of weakening during the ERC, by 20 kt on average), and 3) re-intensification (all but 2 cases exhibited an intersection in intensities of the inner and outer maxima, followed by continued intensification of the outer maximum, by on average 8 kt). The climatology of each phase is summarized in Figure 3. The mean total duration from point (a) to (d) is about 37 h. At point (d) in the evolution of the ERC, the mean intensity is roughly equal to where it was at point (a), but the mean RMW has roughly doubled and the intensification rate reduced by half. Some of the variance found in the changes shown in Figure 3 can be explained by factors such as storm structure and various environmental conditions, which provides a means to construct operational forecasting tools for predicting the onset of ERCs (Kossin and Sitkowski 2012). Structural changes associated with ERCs can affect intensification even after the inner eyewall has decayed. For example, Sitkowski et al. (2013) found that following the demise of the inner eyewall convection, a relict inner eyewall circulation remained, characterized by a distinct air-mass with high inertial stability that was isolated from the rest of the (now larger) eye. As an apparent consequence, subsidence over this relict circulation was suppressed, pressure falls were concentrated just inwards of the outer eyewall, and vorticity became peaked in the outer eyewall. The lack of inner-eye subsidence (and associated reduced warming) can manifest as a rise in minimum pressure, resulting in highly anomalous wind-pressure relationships. Finally, the sharpening of the eyewall vorticity maximum can result in barotropic instability, leading to eye/eyewall mixing, and further intensity changes.

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Figure 3. Mean evolution of an ERC. Here the beginning of the ERC [point (a)] is identified by a persistent coherent

secondary wind maximum observed at flight-level. This marks the beginning of the intensification phase (I) of the ERC. During this phase, both the primary (inner) and secondary (outer) wind maxima are increasing and contracting. During the

weakening phase (II), the primary wind maximum decreases while the secondary maximum increases as it contracts inward. The end of the weakening phase [point (c)] is identified when both wind maxima are equal. Beyond point (c), the

outer wind maximum has exceeded the inner, and is now the primary maximum. During the re-intensification phase (III), the outer wind maximum continues to contract inwards while intensifying. The three inset figures represent typical radial

profiles of flight-level tangential wind observed during the three phases. The mean intensity changes and their standard deviations, and the mean durations are also shown for each phase. The ERC is completed [point (d)] when there is no

longer an observed inner wind (local) maximum. At this time, the mean intensification rate is about half that observed at the start of the ERC [at point (a)]. The mean radius of maximum wind (RMW) at point (b) and (d) is 28 km and 50 km,

respectively. Adapted from Kossin and Sitkowski (2012). Bell et al. (2012b) conducted a detailed observational study of intensity change during an ERC in Hurricane Rita (2005) using aircraft, radar, and satellite observations from the NSF/RAINEX and NOAA/IFEX field experiments. Their observations (Figure 4) are consistent with numerical simulations (e.g., Rozoff et al. 2012, Huang et al. 2012) and composite studies that indicate a broadening of the tangential wind field during ERCs, followed by the formation of a distinct secondary wind maximum and decay of the primary wind maximum. While the peak intensity of Rita decreased during the ERC, the area of hurricane force winds (≥33 m s-1) increased by 125%, and the integrated kinetic energy increased by 19% over the analysis domain.

Figure 4. Radial time series of mesoscale-filtered axisymmetric absolute vertical vorticity (colour, 10-4 s-1), tangential wind (white contour, m s-1), and absolute angular momentum (thick yellow contours, 106m2s-1) at 700-hPa flight level from 1830

UTC 21 Sep to 1830 UTC 22 Sep in Hurricane Rita (2005). Aircraft passes corresponding to analysis times are shown on the right ordinate. Dashed contours indicate linearly interpolated data between aircraft missions.

Taken from Bell et al. (2012b).

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Unlike in the Atlantic basin, aircraft observations are relatively lacking in the western North Pacific, where intense typhoons have a high probability of experiencing secondary eyewall formation (e.g., Hawkins and Helveston 2008; Kuo et al. 2009). Passive microwave satellite imagery thus serves as the primary means to study the associated intensity and structure changes for ERCs in the western North Pacific. Yang et al. (2013) developed an objective method to identify concentric eyewall typhoons using passive microwave imagery. They categorized concentric eyewalls (CE) into three different types, depending on whether the typhoon undergoes an ERC, and whether the double eyewall structure is maintained for more than 20 hours. Based on satellite data from 1997 to 2011, they found that 53% of typhoons with concentric eyewalls in the western North Pacific complete an ERC within 20 hours after the secondary eyewall forms (categorized as ERC cases), and 23% maintain the double eyewall structure for more than 20 hours (categorized as “concentric eyewall maintained” (CEM) cases). The remainder of the cases, covering 24% of the identified typhoons with concentric eyewalls, do not experience an ERC (categorized as “no replacement cycle” (NRC) cases). In terms of the average intensity, intensification in all three types continues for a few hours after secondary eyewall formation. While the ERC and NRC typhoons subsequently weaken, the intensity of the CEM cases can be maintained for another 24 hours, followed by a decrease at a distinctly slower rate. On average, the NRC typhoons experience the most pronounced weakening after secondary eyewall formation. While Yang et al. (2013) found that their three types of concentric eyewall typhoons are embedded within different environments, they also found evidence of internal influences on CE behavior (and storm intensity), as the typhoons with longer-lasting double eyewalls (i.e., CEM) exhibited a greater distance between the inner and outer eyewalls. This study speculated that the internal dynamics and ambient conditions might be equally important for the CEM typhoons. The authors suggested that the NRC cases might be more influenced by environmental conditions than internal dynamics. In contrast, it was suggested that the ERC typhoons could be more closely connected to intrinsic dynamics of the storm. The structural and intensity changes of a CEM case were further examined for Typhoon Soulik (2013), which had two anomalously long-lived CE periods of 25 h and 34 h, respectively (Yang et al. 2014). These results highlight the importance and complicated nature of different CE types, other than the classical ERC, in typhoon structural and intensity variability. 2.6.2.2 Simulations of Eyewall Replacement Cycles Concentric eyewalls have been documented as a relatively common phenomenon in intense TCs, but relevant numerical studies on these storms had been relatively limited until recently. However, with the increase in computational power that now allows for horizontal grid spacing on the order of 1-3 km, there have been a number of studies that have successfully simulated ERCs. Hurricane Rita (2005) and Typhoon Sinlaku (2008) are perhaps the most discussed cases with concentric eyewalls. The observed weakening during their ERCs, as well as their re-intensification associated with the contraction of the new eyewall have been captured in the numerical simulations of different studies (Rita: Judt and Chen 2010; Abarca and Corbosiero 2011. Sinlaku: Wu et al. 2012; Huang et al. 2012; Sun et al. 2013). More comparisons between observations and numerical simulations are needed to assess the model capability of capturing intensity and structure changes associated with concentric eyewalls and ERCs. The intensity and structure changes associated with ERCs appear to share similarities among different idealized simulations constructed in a quiescent environment using numerical models with sophisticated physical processes (e.g., Terwey and Montgomery 2008; Wang 2009; Zhou and Wang 2011; Rozoff et al. 2012; Wang et al. 2013; Qiu and Tan 2013; Nolan et al. 2013; Zhu and Zhu 2014). These simulated storms all produced concentric eyewalls and underwent an ERC. The storms weakened during or after the ERC and expanded in size following the ERC. In the absence of environmental conditions that are inhibitive for TC intensification, these storms re-

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intensify as the outer eyewall contracts following the ERC. Different from the aforementioned idealized studies, Fang and Zhang (2012) carried out one of their simulations on a beta-plane (very similar to the simulation of Rozoff et al. 2012), and obtained a concentric eyewall storm that did not decrease in intensity following secondary eyewall formation. However, this is not necessarily inconsistent with observations, as Kuo et al. (2009) analyzed ERCs for western North Pacific typhoons using satellite data, and found that not all ERCs were characterized by weakening after secondary eyewall formation. 2.6.2.3 Why Does the Inner Eyewall Weaken? In most cases, the formation of a secondary eyewall eventually leads to the decay of the primary eyewall and a decrease in storm intensity. A key question is how the outer eyewall development acts to weaken the inner eyewall. Rozoff et al. (2008) proposed four different hypotheses regarding the mechanism of inner-eyewall weakening: (1) subsidence associated with the outer eyewall directly weakens the inner eyewall’s convection, (2) the outer eyewall intercepts and consumes the boundary layer supply of moist entropy and angular momentum, “effectively choking off convection” in the inner eyewall, (3) the increased static stability in the inner eyewall associated with the warm core preferentially suppresses convection relative to the outer eyewall, and (4) subsidence inwards of (and induced by) the outer eyewall weakens convective instability by warming and drying. Using a Sawyer-Eliassen model, Rozoff et al. (2008) examined the plausibility of some of these hypotheses, and determined that (1) is unlikely, as the subsidence induced by each eyewall on the other is “quite small”. Partially investigating (2) and (3), they found that as diabatic heating increases (decreases) in the outer (inner) eyewall, the subsidence warming of the eye (and the moat) is substantially weakened. On the other hand, the contraction and intensification of the outer wind maximum greatly increases inertial stability, resulting in an increased warming tendency of the eye, and therefore an increase in overall intensity of the storm itself. These competing effects may offset one another regarding TC intensity. Due to the lack of a boundary layer in the Sawyer-Eliassen model, Rozoff et al. (2008) were unable to examine hypothesis (2), that the outer eyewall “chokes off” the supply of entropy to the inner eyewall. Using diagnostic boundary layer models Kepert (2013) investigated this hypothesis. Kepert (2013) found that as the outer eyewall strengthens it removes mass from the inflow layer, which weakens the frictionally-induced updraft of the inner eyewall. Therefore he proposed that it is not simply the entropy supply that matters, but also the radial flow itself. Additionally, Kepert (2013) showed theoretically that for equally strong tangential wind maxima, the frictional updraft of the outer maximum is substantially stronger. This will likely affect the relative strength of the inner and outer eyewall convective heating, and may lead to a positive feedback process that acts to destroy the inner eyewall. 2.6.3 Relation of Rainbands to Intensity Change 2.6.3.1 Introduction Mature TCs typically consist of a precipitation-free eye surrounded by an eyewall with deep convection, and spiral rainbands outside of the eyewall. Spiral rainbands can be classified into inner and outer rainbands, according to their dynamical and thermodynamic characteristics and locations (Guinn and Schubert 1993; Wang 2009). Inner rainbands (as defined in Wang 2009) occur in the inner-core region inside a radius of about three times the RMW. Inner rainbands are usually invisible on satellite imagery, but are often evident on radar reflectivity. Outer spiral rainbands are defined as those rainbands that occur outside of the inner core. They generally have larger horizontal scales but with convection less organized than the inner rainbands. Although rainbands are distinct features of a TC, they may interact with the eyewall in ways that can modulate TC structure and intensity (May and Holland 1999; Franklin et al. 2006; Wang 2009; Wang and Xu 2010; Xu and Wang 2010a, b). Rainband activity is controlled in part by the TC

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internal dynamics (Li and Wang 2012a,b), but may also be greatly affected by different large-scale environmental forcings (Willoughby et al. 1984; Guinn and Schubert 1993). Wang (2008) found that the rapid filamentation zone (Rozoff et al. 2006) where shearing deformation dominates over vorticity provides a favorable environment for the organization of inner spiral rainbands. These inner rainbands are closely related to convectively coupled vortex Rossby waves (VRWs, or potential vorticity waves) whose restoring force is the radial gradient of potential vorticity (PV) of the axisymmetric TC vortex, namely, the so-called vortex beta effect (Guinn and Schubert 1993; Montgomery and Kallenbach 1997; Wang 2002a, b; Chen and Yau 2001; Schecter and Montgomery 2007). Outer spiral rainbands usually propagate radially outward (Kurihara 1976; Willoughby 1978; Wang 2009) and are generally characterized by extensive stratiform rainfall regions with embedded convective elements having varied degrees of organization (Barnes et al. 1983; Barnes et al. 1991; May 1996; Hence and Houze 2008). Although earlier studies predominantly viewed outer spiral rainbands as inertia-gravity waves (Diercks and Anthes 1976; Kurihara 1976; Willoughby 1978), recent model simulation and observational studies (Sawada and Iwasaki 2010a,b; Yu and Tsai 2010; Li and Wang 2012a,b) suggest that outer rainbands propagate radially outward with a much slower speed than inertia-gravity waves and thus could not be attributed to the activity of inertia-gravity waves. The movement of the outer rainbands is found to follow the low-level vector winds associated with the azimuthally averaged low-level flow and the radially outward cross-band flow caused by the downdraft-induced cold pool in the boundary layer. Several recent studies have investigated various aspects of spiral rainbands. They are introduced below. 2.6.3.2 Formation and Quasi-Periodic Behavior of Outer Spiral Rainbands In the study of Wang (2009), it was noticed that there was a quasi-periodic development of outer spiral rainbands near a radius of 60 km (or about three times the RMW) in the simulated TC with a period of about 22-26 h, even though no diurnal radiative forcing was considered in the model simulation. The detailed formation mechanism of these outer rainbands, their quasi-periodic nature, and their preferred radial location were later investigated by Li and Wang (2012a). After initiation, outer spiral rainbands generally propagate radially outward with a mean speed of ~5 m s-

1. The formation of outer spiral rainbands was shown to be triggered by the inner-rainband remnants immediately outside of the rapid filamentation zone, as well as inertial instability in the upper troposphere. The preferred radial location of initiation of outer spiral rainbands is a balance between the suppression of deep convection by rapid filamentation and the favorable dynamical and thermodynamic conditions for initiation of deep convection. Li and Wang (2012a) found that the quasi-periodic occurrence of outer spiral rainbands was associated with the boundary layer recovery from the effect of convective downdrafts, and the consumption of convective available potential energy (CAPE) by convection in the previous outer spiral rainbands. Specifically, once convection is initiated and organized in the form of outer spiral rainbands, it will produce strong downdrafts and consume CAPE. These effects weaken convection near its initiation location. As the rainband propagates further outward, the boundary layer air near the original location of convective initiation takes about 10 h to recover by extracting energy from the underlying ocean. Convection and thus new outer spiral rainbands will be initiated near a radius of about three times the RMW. This will be followed by a similar outward propagation and the subsequent boundary layer recovery, leading to a quasi-periodic occurrence of outer spiral rainbands. In response to the quasi-periodic appearance of outer spiral rainbands, the storm intensity experiences a similar quasi-periodic oscillation with its intensity or intensification rate starting to decrease about 4 h after the initiation of an outer spiral rainband. The results of Li and Wang (2012a) provide an alternative mechanism for the quasi-periodic (quasi-diurnal) variation in the intensity and in the area of outflow-layer cloud canopy of observed tropical cyclones.

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Note that Wang (2009) and Li and Wang (2012a) simulated the quasi-periodic occurrence of outer spiral rainbands under idealized conditions on an f-plane in a quiescent environment. Since the storm was quasi-stationary during the simulation, the effect of downdrafts and the recovery of the boundary layer may be applicable only to those storms in the real atmosphere that are quasi-stationary or slow-moving. In a future study, it will be interesting to compare the activity of outer spiral rainbands in slow-moving storms with that in fast moving storms from both observations and numerical simulations. The results from Li and Wang (2012a) provide plausible mechanisms for the initiation and evolution of outer spiral rainbands in real TCs. Many other factors may considerably affect the activity of outer spiral rainbands in real TCs, such as radiation, the beta-effect, environmental flow, and vertical wind shear. Tang et al. (2014) suggest that the interaction between a cold pool and vertical wind shear played an important role in maintaining a very intense, nearly stationary primary rainband in Typhoon Hagupit (2008) via a mechanism similar to that seen in mid-latitude squall lines. In Li and Wang (2012a), the quasi-periodic behavior of outer spiral rainbands and the associated storm intensity change coincidentally matches the observed strong quasi-diurnal variation in the horizontal areal extent of the upper-level cirrus canopy (Browner et al. 1977; Muramatsu 1983; Lajoie and Butterworth 1984; Hobgood 1986; Kossin 2002) without consideration of radiation or cloud-radiative feedbacks in the simulation. Therefore, the results from this study may provide an alternative explanation for one of the mechanisms that are responsible for the quasi-diurnal variation in the observed TCs. Relatedly, Dunion et al. (2014) describe an observed phenomenon called the TC diurnal cycle that is characterized by a radially propagating feature in the cloud field that they refer to as a “diurnal pulse”. These diurnal pulses are trackable though a deep layer of the troposphere and begin propagating away from the storm near sunset each day, reaching peripheral radii (R=400-500 km) the following afternoon. Diurnal pulses are highly predictable in time and space when local standard time is used as a reference point and may be linked to the outwardly propagating spiral bands that have been previously documented in the literature. 2.6.3.3 Effects of Diabatic Heating/Cooling in the Rapid Filamentation Zone The effects of diabatic heating and cooling in the rapid filamentation zone (where inner rainbands are often active) on TC structure and intensity were recently investigated by Li and Wang (2014), who employed several idealized numerical experiments using a cloud-permitting model - TCM4. Removal of both diabatic heating and cooling greatly suppresses the activity of inner rainbands, but leads to the quasi-periodic development of a convective ring immediately outside of the inner core. A similar convective ring also developed in an experiment with the removal of diabatic heating only. Diabatic heating in the convective ring can accelerate low-level tangential winds, forming a low-level jet at the top of the inflow boundary layer. With diabatic cooling removed only in the filamentation zone, inner rainbands become inactive likely due to the considerable filamentation effect. In this case, an eyewall replacement occurred, leading to a broader and more outwardly tilted eyewall. Diabatic heating in the rapid filamentation zone plays an important role in increasing the inner-core size. The results also show that removal of heating (cooling) in the rapid filamentation zone reduce (increase) the storm intensity. This is in sharp contrast to diabatic heating/cooling in the outer spiral rainband where the increase in diabatic heating (cooling) in outer rainbands leads to a weaker (stronger) storm (Wang 2009). 2.6.4 Eyewall Instability and Inner-Core Mixing The hurricane eyewall satisfies the necessary condition for barotropic instability by having a ring-like structure in relative vorticity, with a maximum away from the center (Kossin and Eastin 2001; Mallen et al 2005). If the vorticity ring is thin enough, the counter-propagating vortex Rossby waves that exist at the inner and outer edges may interact, leading to a breakdown of the ring, and formation of polygonal eyewalls and eye mesovortices (Schubert et al. 1999). Prior work has

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examined this problem in adiabatic and nearly inviscid scenarios (e.g., Schubert et al. 1999; Kossin and Schubert 2001; Hendricks et al. 2009; Martinez et al. 2010). However, fewer studies have been devoted to understanding this problem in more complicated scenarios with diabatic heating and friction. Here we summarize progress on this topic during the past four years. Building upon previous two-dimensional studies, Hendricks and Schubert (2010) examined the nonlinear evolution of three-dimensional unstable baroclinic vortices in an adiabatic, inviscid framework. Unstable potential vorticity (PV) waves were found to grow fastest at lower levels, leading to inner-core PV mixing there. The PV mixing produced a “bridge” of elevated PV across the eye (Figure 5) and associated warmer temperatures at approximately 850 hPa (not shown). Thus, in certain instances, it is possible that the hurricane eye inversion can be dynamically controlled as a result of PV mixing. This may have implications for intensity change, as changes in the height of the eye inversion are often associated with changes in TC intensity (Willoughby 1998).

Figure 5. Comparison of initial conditions (left) and t=12 h (right) for the unstable hollow PV tower. During the break down,

PV mixing occurs preferentially at lower levels, creating a tilted PV structure and “PV bridge” across the eye. In each panel, the top left is the azimuthal mean PV, the top right is the azimuthal mean tangential velocity (with isolines of

absolute angular momentum), the bottom left is a plan view of the PV near the surface, and the bottom right is a plan view of the PV at mid-levels.

Recent studies have examined the interaction of diabatic heating and barotropic instability. Nguyen et al. (2011) and Hankinson et al (2014) found (using a full-physics numerical simulation of Hurricane Katrina (2005)) that the eyewall often vacillates between symmetric and asymmetric states, with a period of approximately 13 h. The symmetric-to-asymmetric transition was triggered by a combination of barotropic and convective instability, yielding an asymmetric eyewall (with vortical hot towers (VHTs) forming at the polygonal eyewall vertices), and weaker intensification rates. In contrast, intensification was favoured when the eyewall was more symmetric. These full-physics simulation results are supported by the observational study of Rogers et al. (2013), who found that intensifying TCs were more symmetric than steady-state TCs, with a ring-like vorticity structure. The interaction of convective and barotropic instability has also been examined in idealized frameworks. Building on the work of Rozoff et al. (2009), Hendricks et al. (2014) examined the generation, maintenance and break down of the eyewall using a forced shallow water model, where diabatic heating was parameterized as a radially and temporally varying annular mass sink. Diabatic heating was found to produce a strengthening and thinning PV ring in time, which became unstable if it was thin enough. The thinning PV ring is due to the induced radial divergent

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circulation, which erodes the PV at the outer edge of the heating region. In a sensitivity test where the heating was made to be proportional to the relative vorticity, universal intensification (increase in maximum wind and decrease in minimum central pressure) was shown to occur during barotropic instability. In this case, the convective/dynamic instability causes the rollup of the ring into convective mesovortices (similar to VHTs in the real atmosphere). This is a fundamental difference between barotropic instability in adiabatic simulations (where both the pressure and wind decrease), and consistent with observations of Hurricane Dolly (2008) (Hendricks et al. 2012) and some full-physics modeling studies (Menelaou et al. 2013) depicting intensification during barotropic instability. With regard to the effects of friction and turbulent mixing, Hendricks et al. (2014) found that friction helps stabilize the PV ring during initial symmetric growth in response to the annular diabatic heating. In a full-physics study of Hurricane Isabel (2003), Zhu et al. (2013) found that barotropic instability was sensitive to the vertical turbulent mixing scheme. Different schemes affected both the eyewall mean radial PV profile and the perturbations, which led to variability in the onset and nature of barotropic instability, which in turn affected variations in TC intensity. 2.6.5 Relationship between Surface Fluxes and Intensity Change Some theoretical models of intensification (e.g., Emanuel 1995) have assumed that the enthalpy exchange coefficient (CK) must increase with wind speed, such that the ratio of CK/CD (where CD is the drag coefficient) is much larger for strong TCs. However, the magnitudes of the wind-speed-dependent bulk exchange coefficients are largely unknown at major hurricane wind speeds (≥50 m s-1). Since direct turbulent flux measurements in these conditions are extremely difficult, Bell et al. (2012a) deduced the momentum and enthalpy fluxes via absolute angular momentum and total energy budgets, respectively. An analysis of six missions from the 2003 CBLAST field program in major Hurricanes Fabian and Isabel was conducted using a new variational technique called SAMURAI (Spline Analysis at Mesoscale Utilizing Radar and Aircraft Instrumentation). The results (Figure 6) suggest that there is no significant change in the magnitude of the bulk exchange coefficients at major hurricane wind speeds from those estimated at minimal hurricane wind speeds.

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Figure 6. Wind speed dependence of CK/CD from Bell et al. (2012a) (green squares) compared with previous studies. ASIST laboratory results (blue circles) and CBLAST (red triangles) measurements shown with HEXOS results (gray x's) adapted

from Haus et al. (2010). The mean and 95% confidence intervals are shown in black.

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Richter and Stern (2014) used GPS dropsondes to calculate surface enthalpy fluxes and CK, and found no significant dependence of CK on wind speed between about 20 and 50 m s-1, generally consistent with Bell et al. (2012a), as well as the recent laboratory study of Jeong et al. (2012). However, Richter and Stern (2014) also found that the enthalpy flux itself scales super-linearly with wind speed, in agreement with the data of Bell et al. (2012a) and the data of Zhang et al. (2008), but inconsistent with Jeong et al. (2012), whose data indicates a sub-linear scaling. From this, Richter and Stern (2014) concluded that sea spray is likely to be a dominant source of surface enthalpy in TCs, and that the ambient laboratory conditions are perhaps too dry to capture this effect. The results of all of the above observational studies regarding the magnitudes of the surface exchange coefficients (and their dependencies on wind speed) further suggest that the ratio CK/CD is less than one and does not significantly increase with wind speed, such that a high ratio is not required for TCs to reach major hurricane intensity. This is supported by Bryan (2012), who compared the intensity and structure of axisymmetric (and some three-dimensional) simulations to observations in order to determine the most “reasonable” values of the exchange coefficients as well as turbulence length scales. He concluded that the ratio of CK/CD that is most consistent with observed structure and intensity is 0.5. Bryan (2012) also attributed the conclusion of Emanuel (1995) that the ratio needed to be greater than 0.75 to the use of unrealistically large horizontal diffusion. Recent research by Soloviev et al. (2014) suggests that above minimal hurricane strength (≥33 m s-1), the drag coefficient may decrease with increasing wind speed due to reduced wave form drag, but then increase at still higher speeds (≥60 m s-1) due to small-scale roughness elements formed through shear instabilities. They propose that this behavior (a change in sign of the CK/CD dependence on wind speed) may play a role in allowing storms to more rapidly intensify. Recent work has suggested that wind-speed dependent flux feedbacks are not essential to intensification (Montgomery and Smith 2013), and that intensification may depend more on the radial location of convection and its associated diabatic heating (Rogers et al. 2013) and the aggregate effects of asymmetric convection (Menalou et al. 2014; Sanger et al. 2014). However, intensity change in numerical simulations can be sensitive to the magnitude of parameterized surface fluxes (Green and Zhang 2013; Green and Zhang 2014; Smith et al. 2014). Further research is required to reduce the uncertainty in CK and CD, improve the parameterization of surface fluxes in numerical models, and improve our understanding of the role of wind-speed dependent fluxes on TC intensification. 2.6.6 Mechanisms of Tropical Cyclone Intensification 2.6.6.1 Introduction The conventional paradigm of TC intensification has long been based on axisymmetric dynamics. Essentially, an axisymmetric vortex of sufficient intensity1 will (in the absence of prohibitive environmental forcing) spontaneously intensify through a self-induced positive feedback between surface enthalpy fluxes and the tangential wind field. This idea, termed WISHE (Wind-                                                                                                                          

1 Recently, it has been suggested that a pre-existing vortex may not be necessary, at least within an axisymmetric framework. Hakim (2011) used an axisymmetric model to simulate TCs in radiative-convective equilibrium, and as TCs formed spontaneously from a state of rest, he concluded that the “undisturbed tropical atmosphere is unstable to axisymmetric hurricanes.”

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Induced Surface Heat Exchange), was first proposed by Emanuel (1986), and has subsequently formed the basis for much of our contemporary understanding of TC intensity change. A related paradigm is the convective ring model (Shapiro and Willoughby 1982; Willoughby et al. 1982; Willoughby 1990), which predicts that intensification of the maximum winds occurs as the symmetric response to the azimuthal mean eyewall heating. Essentially, unbalanced diabatic heating from convection drives a secondary circulation that brings the vortex back towards thermal wind balance. The associated deep layer of inflow spins up the maximum winds through radial advection of absolute angular momentum. Though distinct, the convective ring model and WISHE can be considered to be complementary perspectives on TC intensification, with the increased surface fluxes being manifest as increases in eyewall heating, which in turn yields intensification of the maximum winds. While WISHE and the convective ring model remain the dominant paradigms of intensification, they have been challenged to varying degrees within the last decade. In particular, it has been argued that TC intensification is fundamentally asymmetric, and that intensification of the maximum winds is not due to a deep layer of heating-forced inflow. In the remainder of this section, we summarize relevant recent studies related to these debates. 2.6.6.2 Is Intensification Fundamentally Symmetric or Asymmetric? A series of idealized numerical studies (Van Sang 2008; Bui et al. 2009; Persing et al. 2013) have advocated the idea that TC spin-up is fundamentally asymmetric, because the vorticity and vertical velocity structure tends to be dominated by small-scale localized updrafts (VHTs). In the framework of these studies, these rotating updrafts amplify vorticity locally, and the aggregation and merger of cyclonic vortices resulting from the asymmetric convection leads to the intensification of the TC. At the same time, this theory acknowledges that the azimuthal mean inflow forced by the net eyewall heating also contributes to the spinup of the tangential wind field. However, because the convective elements that contribute to the symmetric heating are themselves localized, these studies view the intensification process as intrinsically asymmetric. The idea that convection is often localized and asymmetric during intensification is not itself controversial. The relevant question seems to be whether or not the intensification of the azimuthal mean wind field is well represented by the response to the azimuthal mean forcing, regardless of whether that forcing is localized. In contrast to the above studies, Nolan et al. (2007) found that the symmetric response to the purely asymmetric component of localized heating is much smaller in magnitude than the response to the symmetric component. The study of Moon and Nolan (2010) supports this finding, in the context of the dynamics of rainband heating. In a study of secondary eyewall formation, Rozoff et al. (2012) found that the secondary circulation of a simulated TC could largely be reproduced by a linear vortex model forced by the symmetric components of diabatic heating and friction. In a budget analysis of an idealized simulation, Fudeyasu and Wang (2011) found that the spinup of the eyewall was dominated by advection from the azimuthal mean secondary circulation. Using a Sawyer-Eliassen balanced model, they further found that the secondary circulation was dominated by the response to symmetric forcing. Even though Bui et al. (2009) are of the viewpoint that intensification is fundamentally an asymmetric process, they found (also using a Sawyer-Eliassen model) that above the boundary layer, spinup of the TC is largely in response to azimuthal mean heating. Therefore, it seems that at least above the boundary layer, the idea that the symmetric component of heating drives most intensification is generally accepted. Part of the remaining disagreement seems to be semantic, related to what exactly is meant by “asymmetric”. Within the boundary layer itself (where the maximum winds are found), there is a more fundamental disagreement about the mechanisms of intensification.

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2.6.6.3 What Leads to the Spin-up of the Maximum Winds? The convective ring model predicts that a deep layer of inflow leads to the spin-up of the inner core, through conservation of absolute angular momentum (M). Based on idealized simulations, Smith et al. (2009) advocated the idea that there are in fact two distinct (and “largely independent”) spin-up mechanisms: (1) the aforementioned eyewall heating, which increases the winds above the boundary layer and spins up the outer-core circulation, and (2) convergence within the boundary layer, which spins up the inner-core circulation. As the winds within the boundary layer are unbalanced, it was suggested that the convective ring model of intensification may not be fully applicable, as it assumes thermal wind balance. Relatedly, Bui et al. (2009) found that within the boundary layer, the Sawyer-Eliassen calculation substantially underestimated the magnitude of the actual simulated inflow, and therefore the balanced model similarly underestimated the rate of intensification. As a result, the authors of these studies concluded that unbalanced dynamics are essential to understanding intensification. These conclusions were supported by and elaborated upon by subsequent companion studies using similar simulations, including Montgomery et al. (2010), Abarca and Montgomery (2014a, b), and Smith et al. (2014). These studies further concluded that intensification of the inner core is actually largely due to unbalanced boundary layer processes (in addition to heating and convergence of angular momentum above the boundary layer), as the frictional inflow can advect M surfaces inwards at a fast enough rate to more than offset the negative tendency of friction itself. Very recently, Stern et al. (2014, in review) found that in contrast to Bui et al. (2009), the secondary circulation within the boundary layer can indeed be largely represented as the balanced response to symmetric forcing. They further found that a substantial percentage of the inflow within the boundary layer is a response to eyewall heating, comparable to the response due to friction. The large role of heating in driving boundary layer inflow would imply that it is not necessarily the case that friction drives intensification, as the advection of M due to friction might not offset the direct spin-down by friction. Indeed, Stern et al. (2014) found that the positive tendency on tangential winds due to frictional inflow is less than the negative tendency due to friction itself. Therefore, they concluded that while the spin-up of the inner core does occur within the boundary layer, it is due to eyewall heating, and can be represented in a balanced framework. 2.6.7 Summary In this report, we have attempted to summarize recent studies that have advanced our understanding of internal influences on intensity change. Substantial progress has been made in all aspects of this subject, though important questions remain unanswered, and some unresolved debates persist. Perhaps the most important aspect of internal influences on intensity change, in terms of potential impact, is rapid intensification (RI). A number of recent studies have investigated the relationship between convection and RI, from both observational and numerical perspectives. While there is some relationship between isolated strong convection (i.e., “hot towers” or “vortical hot towers”) and RI, there is increasing observational evidence that this relationship is relatively weak. In contrast, a number of recent studies suggest that RI might instead be more related to the symmetric distribution of weaker convection, and that such convection becoming more widespread and wrapping more completely around the vortex is a key feature of TCs that undergo RI. Numerical studies remain somewhat mixed in their findings, as some studies have found that the onset of RI is preceded by an increase in mass flux by relatively weak updrafts, whereas others have found that the onset of RI is instead preceded by an increase in magnitude of only the most extreme updrafts (which is consistent with some recent observations). Observations also indicate that storms that are undergoing RI have a systematically stronger secondary circulation as compared to steady-state TCs of similar intensity, as well as a more ringlike profile of vertical vorticity. An interesting new observational result is that the “convective bursts” in intensifying storms are preferentially found inwards of the RMW, whereas

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those in steady-state storms tend to occur more outwards of the RMW. The apparent importance of the radial location of convection relative to the RMW is consistent with numerous theoretical studies of intensification. Whereas RI is most common in storms that are relatively weak, the prevalence of eyewall replacement cycles (ERCs) is well known to increase with increasing intensity. The mechanism(s) for the formation of secondary eyewalls remains hotly debated and incompletely understood. We left this important debate to Topic 4.1. Instead, we focused on the effect that ERCs have on TC intensity. Substantial progress has been made in characterizing the typical observed tendency of intensity with respect to the lifecycle of secondary eyewalls. Almost half of all TCs are undergoing RI at the start of ERCs, and so ERCs are a common mechanism for bringing RI to a halt. There is a large amount of variability in both the behavior of the concentric eyewalls and their effect on intensity, and this variability is believed to have contributions from both the environment and internal forcing. Recent studies have found that perhaps a quarter of all concentric eyewalls are maintained for at least 20 hours, and these events are characterized by a slower than average weakening of intensity. Successful numerical simulations (both idealized and real data) of ERCs have now become relatively common (note that this is distinct from the ability to successfully forecast ERCs). These simulations generally reproduce the typical lifecycle of ERCs, with a weakening of intensity associated with the demise of the inner eyewall, followed by a re-intensification as the outer eyewall contracts and strengthens. The precise mechanism by which the inner eyewall decays remains uncertain. Theoretical analysis using a Sawyer-Eliassen model has shown that it is unlikely that subsidence driven by the outer eyewall directly weakens the inner eyewall. Another theoretical study has found that as the outer eyewall strengthens, it extracts mass from the inflow layer, and this ultimately reduces the strength of the inner eyewall frictional updraft. Further research is necessary to investigate these processes in more complex numerical models. While spiral rainbands can be forced by environmental flow in addition to internal processes, once such rainbands form, they can be considered as an internal influence on intensity change. Previous studies have generally found that outer rainbands have a net negative effect on TC intensity. A recent numerical study has found that in contrast to outer rainbands, the heating associated with inner rainbands may have a net positive effect on intensity. Recently, it has been found in idealized simulations that outer rainbands can exhibit quasi-diurnal oscillations in the absence of radiative forcing, and there is evidence that these oscillations in turn modulate TC intensity, with a weakening tendency found a few hours after the initiation of outer rainbands. As these simulations were performed in a quiescent environment, it is unclear to what extent this variability is representative of processes in observed TCs. Recent observational work has identified a consistent and predictable diurnal oscillation in infrared brightness temperatures in major hurricanes. This cycle manifests as a ring of convection that initiates near local sunset and propagates outward throughout the overnight and into the following afternoon. There is some evidence that this diurnal cycle is associated with changes in the surface wind field and perhaps TC intensity. Currently, the mechanism for driving this cycle is unknown, and it is also unclear how (and whether) this cycle relates to the aforementioned oscillations in outer rainbands seen in idealized simulations. Recent numerical studies have advanced our understanding of the effects of barotropic instability and associated eye/eyewall mixing on TC intensity. Extending previous two-dimensional studies of barotropic instability to three dimensions, it has been found that instability is manifested preferentially at low-levels, resulting in enhanced mixing at these heights. Recent studies using a shallow-water model have found that diabatic heating generally acts to destabilize the vortex, whereas friction tends to inhibit such barotropic instability. Previous idealized adiabatic studies

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have generally found that while barotropic instability acts to lower the minimum pressure, it also weakens the maximum winds. In contrast, the presence of diabatic heating (that is proportional to vorticity) during barotropic instability events yields “universal intensification.” Recent real-data simulations indicate oscillations between symmetric and asymmetric eyewalls, apparently associated with convective and barotropic instability. Notably, weakening or a slowing of intensification occurred during the transition to asymmetric states. Efforts continue to improve our estimates of the surface exchange coefficients of both momentum and heat, using a variety of direct and indirect observational methods. These studies generally find that there is no significant change of these coefficients with wind speed above hurricane force, although the uncertainty remains quite large. All observational studies find that the ratio of enthalpy to drag coefficients CK/CD is well below the threshold suggested by previous theoretical studies to be necessary for TCs to achieve observed intensities. A recent idealized numerical study has possibly resolved this disagreement, finding that horizontal diffusion has a substantial effect on the necessary value of CK/CD, and that the previous theoretical threshold was based on an unrealistically large amount of diffusion. Despite substantial progress in our understanding of internal influences on intensity change, the fundamental processes by which TCs intensify are still a matter of debate. A number of idealized numerical studies have concluded that the primary TC intensification mechanism is intrinsically asymmetric, and that isolated deep convective elements are essential to spin-up. This is in contrast to the long-held paradigm that TC intensification is fundamentally an axisymmetric phenomenon (also supported by other recent studies), with spin-up largely explained as the symmetric response of a vortex to azimuthal mean eyewall heating. There are some elements of these two disparate viewpoints that are actually in common, as both theories accept that the secondary circulation induced by eyewall heating does indeed act to intensify the tangential wind field. The primary difference between these paradigms is whether or not the fact that convection is discrete and asymmetric is important for TC intensification. Within the boundary layer, there is another disagreement, as the same studies that conclude that intensification is asymmetric also conclude that friction can contribute to intensification, and that unbalanced processes are critical. This is in contrast to the widely accepted convective ring model, as well as other recent studies that have found that intensification can indeed be represented as a balanced response to symmetric forcing, and that friction opposes intensification. Given the continued debates regarding fundamental mechanisms of TC intensification, this is a key area in which continued research is necessary to help resolve these questions. Acronyms used in the report TC - Tropical Cyclone RI - Rapid Intensification VHT - Vortical Hot Tower TRMM - Tropical Rainfall Measuring Mission TCPF - Tropical Cyclone Precipitation Feature WWLLN - World-Wide Lightning Location Network RMW - Radius of Maximum Wind CAPE - Convective Available Potential Energy WRF - Weather Research and Forecasting Model ERC - Eyewall Replacement Cycle CE - Concentric Eyewall CEM - Concentric Eyewall Maintained NRC - No Replacement Cycle VRW - Vortex-Rossby Wave PV - Potential Vorticity

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