**2. Data and methodology**

**1. Introduction**

172 Recent Developments in Tropical Cyclone Dynamics, Prediction, and Detection

moisture inflow to the inner eyewall (e.g., [12]).

structural and intensity changes of CE by an objective method.

Tropical cyclones (TCs), and particularly strong TCs, are observed with a concentric eyewall (CE) structure that has an inner eyewall and an outer eyewall separated by a convective minimum region [1]. A local tangential wind maximum is associated with the outer eyewall and the most rapid increase in wind speed lies on the inside of the wind maximum [1]. The outer wind maximum thus contracts and intensifies, and then the inner eyewall weakens and eventually vanishes during eyewall replacement cycle (ERC). One of the great challenges associated with TC prediction is the large variability in structure and intensity changes, and the CE formation and the ERC is a mechanism to produce such variability [1–4]. Many theories allude to the influences of both synoptic scale environmental conditions and mesoscale processes in the CE formation. Nong and Emanuel [5] showed that the CE may form due to favorable environmental condition or external forcing and wind-induced surface heat exchange instability. Examples of internal dynamics include propagating vortex Rossby waves (VRWs) that interact with a critical radius [6, 7] and axisymmetrization during a binary vortex interaction [8, 9]. Terwey and Montgomery [10] employed idealized full physics hurricane to demonstrate the secondary eyewall form at region of sufficient low-level radial potential vorticity gradient. The result highlights the VRW energy accumulation in the critical radius with a wind-moisture feedback process at the air-sea interface. Huang et al. [11] suggested that the broadening of the radial tangential wind profile above the boundary layer (BL) in a symmetric fashion can lead to BL convergence and inflow. The progressive strengthening of the BL inflow and the unbalanced BL response may lead to secondary eyewall formation. Previous observational studies indicate that the secondary eyewall can act as a barrier to the

Sitkowski et al. [4] used flight-level data to study the ERC process in the Atlantic (ATL) basin. They suggested that large variances are in the ERC time requirement, the intensity, and the change in radii because CEs are not only associated with intensity but also structural changes. Maclay et al. [13] used the low-level area-integrated kinetic energy to show that while the intensity weakens during the ERC, the integrated kinetic energy and the TC size increase. Their results suggest that CE formation and ERC are dominated by internal dynamical processes. The passive microwave data can more clearly reveal the CE structure in TCs. Using microwave data between 1997 and 2002, Hawkins and Helveston [14] suggested that CEs exist with a much higher percentage (80 and 40%) in intense TCs (maximum wind > 120 kts) than previously realized in the western North Pacific (WNP) and ATL basin. As further noted by Hawkins et al. [15], there were more CE cases with large radius in the WNP than in other basins. Hawkins and Helveston [16] provided examples of different modes of CE structure, including the ERC, triple eyewalls [17], ERCs that are repeated multiple times, ERCs that are interrupted by vertical shear and landfall, and cases where an outer eyewall forms at a large radius and remains in a CE structure for a long duration. The different CE modes appear to have profound impacts on intensity and structural forecasts. This study quantitatively examines these

The passive Special Sensor Microwave/Imager (SSM/I) 85 GHz horizontal polarized orbital imagery and Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) data from the polar-orbiting TRMM satellite [27] are used in this study. These data were obtained from the website of Naval Research Laboratory (NRL) Marine Meteorology Division [15, 28]. The microwave satellite images are available and online since 1997, and the TRMM satellite ended collecting data from April 15, 2015. We use the microwave satellite data to examine the characteristics of TCs with CEs in the WNP and ATL basins between 1997 and 2014 for consistent data. The National Centers for Environmental Prediction (NCEP) warm and cold episode data are based on a threshold of ±0.5°C for the Oceanic Niño Index (ONI) in the Niño 3.4 region (5°N-5°S, 120°170°W). The ONI data are a product of three-month time running mean of SST in the Niño 3.4 region and they are used to classify the environmental condition of CE formation. The Niño 3.4 SST anomaly is used because it is better correlated with overall tropical storm activity [21].

The microwave satellite images are reprocessed using the Backus-Gilbert theory of reference [29] to create high-resolution (1–2 km) products that can assist in defining inner storm structural details [14, 15]. These images are stored as 800 × 800 pixel color jpeg files that are composed with red (R), green (G), and blue (B) colors. The pixels of R, G, and B components are converted into the high-resolution brightness temperature (*T*B) based on the color table in the picture. To identify CE typhoons, the *T*B dataset is transformed from Cartesian to polar coordinates with the TC center as the origin. The TC center is determined based on the Joint Typhoon Warning Center (JTWC) best track data at the time closest to satellite observation as the TC center. To further smooth the data and also to be consistent with the center position uncertainty of 10 km, we employ 5 pixel averages in the radial direction and a 45-degree sector average of *T*B to obtain eight radial profiles for the bin data. In each bin of the radial profile, the *T*B mean value and the standard deviation (*σ*) within each 45-degree sector were calculated. An objective method is developed to identify the CE structure from the eight radial profiles. The method involves the following five sequential steps:

**Figure 1.** Color-enhanced microwave CE imageries of typhoons (a) Oliwa (1997), (b) Vamco (2009), and (c) Soulik (2013). The averaged *T*<sup>B</sup> profiles of eight radial directions for Typhoon Oliwa are conformed to the CE-determined criteria. The secondary *T*<sup>B</sup> minimum for Typhoon Vamco only identified spiral outer rainband. One-half symmetry of Typhoon Soulik identified CE structure (solid green: WNW; solid yellow: WSW; solid red: SSW; solid blue: NNW; dash green: ENE; dash yellow: ESE; dash red: SSE; and dash blue: NNE). Figures (a) and (b) from Yang et al. [26], courtesy of American Meteorological Society.


composed with red (R), green (G), and blue (B) colors. The pixels of R, G, and B components are converted into the high-resolution brightness temperature (*T*B) based on the color table in the picture. To identify CE typhoons, the *T*B dataset is transformed from Cartesian to polar coordinates with the TC center as the origin. The TC center is determined based on the Joint Typhoon Warning Center (JTWC) best track data at the time closest to satellite observation as the TC center. To further smooth the data and also to be consistent with the center position uncertainty of 10 km, we employ 5 pixel averages in the radial direction and a 45-degree sector average of *T*B to obtain eight radial profiles for the bin data. In each bin of the radial profile, the *T*B mean value and the standard deviation (*σ*) within each 45-degree sector were calculated. An objective method is developed to identify the CE structure from the eight radial profiles.

**Figure 1.** Color-enhanced microwave CE imageries of typhoons (a) Oliwa (1997), (b) Vamco (2009), and (c) Soulik (2013). The averaged *T*<sup>B</sup> profiles of eight radial directions for Typhoon Oliwa are conformed to the CE-determined criteria. The secondary *T*<sup>B</sup> minimum for Typhoon Vamco only identified spiral outer rainband. One-half symmetry of Typhoon Soulik identified CE structure (solid green: WNW; solid yellow: WSW; solid red: SSW; solid blue: NNW; dash green: ENE; dash yellow: ESE; dash red: SSE; and dash blue: NNE). Figures (a) and (b) from Yang et al. [26], courtesy

The method involves the following five sequential steps:

174 Recent Developments in Tropical Cyclone Dynamics, Prediction, and Detection

of American Meteorological Society.



**Table 1.** The numbers of CE cases when we use criterion (3) by making outer eyewall convection criterion 10 K weaker and stronger (240 and 220 K) than 230 K, use criterion (4) by making 4/8 and 6/8 symmetry to identified CE structure, and do not use criterion (5).

Criterion (1) identifies the existence of the structure that resembles the moat and the double eyewall in each of the eight radial profiles. Criterion (2) ensures that the moat is significant and criterion (3) ensures that the outer eyewall has strong convection. Criterion (4) ensures axisymmetry of double eyewall structure and criterion (5) ensures that the outer eyewall identified is not a spiral band. **Figure 1** provides an example of the CE TC and the no-CE TC and their associated *T*<sup>B</sup> radial profiles. Three examples that have the *T*<sup>B</sup> profiles of two local minima (double eyewalls) and one maximum in between the minima (the moat) are presented in **Figure 1**. The no-CE Typhoon Vamco (2009) is not classified as a CE typhoon based on our criterion (5), with the convection in the outer eyewall identified as a spiral band. Compare with CE Typhoon Oliwa (1997), Typhoon Soulik (2013) is not classified as a CE typhoon at this time based on criteria (3) and (4). If we relax criterion (3) from 230 to 240 K, or relax criterion (4) from five to four out of eight sectors, it can be considered a CE typhoon. The objective method allows us to systematically identify CE typhoons from dataset. We examined 29,785 (19,001) SSM/I and TMI satellite images in the WNP (ATL) basin from the NRL website. Out of these, 113 (50) CE cases were identified, including 17 (11) cases of multiple CE formation. There are 91 (33) CE typhoons identified in the WNP (ATL) basin. **Table 1** shows the numbers of CE cases with sensitivities in criterion (3) by making outer eyewall convection 10 K weaker and stronger (240 and 220 K) than 230 K, in criterion (4) by making 4/8 and 6/8 symmetry, and no criterion (5). Consistent with the subjective work of Kuo et al. [3], the five criteria of reference [26] ensure that the CE typhoons identified are axisymmetric with a significant moat and a strong outer eyewall while retaining enough cases for statistics. The inner eyewall radius was determined as the distance between the typhoon center to the point where *T*<sup>B</sup> = 0.5 × *σ*inner + *T*Binner. The moat width was determined by the distance between the points of *T*<sup>B</sup> ≧ 0.5 × *σ*outer + *T*Bouter and *T*<sup>B</sup> ≧ 0.5 × *σ*inner + *T*Binner. Finally, the outer eyewall width was determined by the distance of the region that satisfies *T*<sup>B</sup> < 0.5 × *σ*outer + *T*Bouter in the outer eyewall region. The inner eyewall radius, the moat, and the outer eyewall width were calculated by averaging the radial profiles of the eight sections as shown in **Figure 1**.
