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  • View in gallery

    Photographs inside the eye of TC Trami taken from an aircraft flying at 13.8 km MSL at (a) 0447 UTC 25 Sep, (b) 0728 UTC 26 Sep, (c) 0550 UTC 27 Sep, and (d) 0433 UTC 28 Sep 2018. The clouds at a red arrowhead in (b) and inside a broken red ellipse in (c) are DECs.

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    The horizontal distribution of SSTs created using microwave satellite data on (a) 23, (b) 24, (c) 25, (d) 26, (e) 27, and (f) 28 Sep. Red crosses indicate the positions of the TC centers from 22 Sep to each date.

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    Radius–pressure cross sections of the paths of dropsondes in the inner core on (a) 25, (b) 26, (c) 27, and (d) 28 Sep. The paths of each dropsonde are drawn in reddish and bluish colors at smaller and larger radii, respectively, with few exceptions. The numerals indicate the launch time in a unit of UTC.

  • View in gallery

    A time series of (a) the central pressure and (b) maximum wind speed in the best track data from the JMA (black solid curves) and JTWC (black broken curves), the coupled atmosphere–ocean model (blue curves), and the noncoupled atmospheric model (red curves). The best track data are provided every 6 (3) h before (after) 0000 UTC 28 Sep for the JMA and every 6 h for the JTWC. The central pressures and maximum wind speeds in the models are plotted every 1 h. Crosses indicate estimated values from the dropsonde data deployed in the eye region. Note that the maximum wind speeds provided by the best track data from the JMA and JTWC are 10- and 1-min averages, respectively. The maximum wind speeds in the best track data from the JTWC are shown in (b). This maximum wind speed is multiplied by 0.93 following Harper et al. (2010). Note also that the maximum wind speeds in the coupled and noncoupled models are instantaneous values.

  • View in gallery

    The positions of the TC centers from 22 to 29 Sep in the best track data from the JMA (black solid curve) and JTWC (black broken curve), the coupled atmosphere–ocean model (a blue curve), and the noncoupled atmospheric model (a red curve). As in Fig. 4, the best track data are provided every 6 (3) h before (after) 0000 UTC 28 Sep for the JMA and every 6 h for the JTWC, while the TC positions in the models are plotted every 1 h. Crosses indicate the TC positions at 0000 UTC on each date.

  • View in gallery

    Visible satellite images from the Himawari-8 at (a) 0447 UTC 25 Sep, (b) 0727 UTC 26 Sep, (c) 0550 UTC 27 Sep, and (d) 0432 UTC 28 Sep. Red stars indicate the storm center estimated from the best track. Red broken circles indicate 50- and 100-km radii from the storm center. The clouds in green broken ellipses in (b) and (c) correspond to the convective clouds in Figs. 1b and 1c, respectively. The clouds are taken from the northwest direction in both Figs. 1b and 1c. (e)–(h) As in (a)–(d), but for infrared satellite images.

  • View in gallery

    Hovmöller diagram of the ARCHER ring score. The image is sourced from http://tropic.ssec.wisc.edu/real-time/archerOnline/web/index.shtml. The dates on the vertical axis indicate 0000 UTC on each date.

  • View in gallery

    Radius–pressure cross sections of RH based on the dropsonde data during the time periods of (a) 0347–0540 UTC 25 Sep, (b) 0505–0816 UTC 26 Sep, (c) 0341–0655 UTC 27 Sep, and (d) 0418–0514 UTC 28 Sep.

  • View in gallery

    Radius–pressure cross sections of storm-relative tangential wind in the dropsonde data during the time periods of (a) 0435–0458 UTC 25 Sep and (b) 0505–0746 UTC 26 Sep.

  • View in gallery

    A radius–time cross section of frequency of total (liquid and ice) cloud water content > 1 mg kg−1 at 500 hPa in the coupled atmosphere–ocean model.

  • View in gallery

    Total (liquid and ice) cloud water content at 500 hPa at (a) 2100, (b) 2200, and (c) 2300 UTC 26 Sep, and (d) 0000 UTC 27 Sep.

  • View in gallery

    Radius–pressure cross sections of frequency of total (liquid and ice) cloud water content > 1 mg kg−1 at (a) 2100, (b) 2200, and (c) 2300 UTC 26 Sep, and (d) 0000 UTC 27 Sep.

  • View in gallery

    (top) Skew T–logp diagrams of dropsondes in the eye region launched at (a) 0452 UTC 25 Sep and (b) 0722 UTC 26 Sep. The paths of each dropsonde are drawn in Figs. 3a and 3b. Vertically averaged distances from the TC center of the dropsondes at 0452 UTC 25 Sep and 0722 UTC 26 Sep are 5.8 and 25.3 km, respectively, as indicated at the upper right of each panel. Red solid, red dashed, and blue solid curves denote temperature, dewpoint temperature, and air parcel temperature, respectively. Horizontal dashed lines in (a) and (b) indicate the LCL. (bottom) Radius–pressure cross sections of θ anomaly from that at r = 400 km in the dropsonde data during the time periods of (c) 0435–0458 UTC 25 Sep and (d) 0505–0746 UTC 26 Sep.

  • View in gallery

    Vertical profiles of θe (a) in the eye region on 25 Sep and (b) in the radial range of 10–30 km, where the sporadic formation of DECs is observed, on 26 Sep. Numerals indicate launch time in a unit of UTC. Dropsondes launched at smaller and larger radii are drawn in reddish and bluish colors, respectively.

  • View in gallery

    (top) Skew T–logp diagrams of azimuthal-mean fields at r = 20 km in the coupled model in (a) period 1 and (b) period 2. The meanings of the three curves are as in Fig. 13. Three horizontal dashed lines in (a) and (b) indicate the LNB, LFC, and LCL from top to bottom. (bottom) Radius–pressure cross sections of azimuthal-mean θ anomaly from that at r = 400 km in the coupled model in (c) period 1 and (d) period 2.

  • View in gallery

    A histogram of vertical velocity in the pressure range of 600–400 hPa at r < 20 km in period 1 (a blue curve) and at r < 35 km in period 2 (a red curve). These radial ranges are chosen to exclude updraft in the eyewall.

  • View in gallery

    (a),(b) Radius–pressure cross sections of azimuthal-mean diabatic heating rate in the coupled atmosphere–ocean model in period 1 and period 2, respectively. (c),(d) As in (a) and (b), but for the local λR.

  • View in gallery

    Radius–pressure cross sections of azimuthal-mean vertical velocity induced by diabatic heating rate > 10 K h−1 in the coupled atmosphere–ocean model in (a) period 1 and (b) period 2.

  • View in gallery

    A time–pressure cross section of azimuthal-mean θ advection due to vertical velocity w¯θ¯z induced by diabatic heating rate >10 K h−1 averaged at 10 < r < 30 km in the coupled atmosphere–ocean model.

  • View in gallery

    A radius–pressure cross section of azimuthal-mean horizontal divergence in the coupled atmosphere–ocean model in period 2.

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Deep Eye Clouds in Tropical Cyclone Trami (2018) during T-PARCII Dropsonde Observations

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  • 1 aDepartment of Physics and Earth Sciences, University of the Ryukyus, Okinawa, Japan
  • | 2 bMeteorological Research Institute, Tsukuba, Japan
  • | 3 cInstitute for Space-Earth Environmental Research, Nagoya University, Aichi, Japan
  • | 4 dDepartment of Atmospheric Sciences, National Taiwan University, Taipei, Taiwan
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Abstract

The sporadic formation of short-lived convective clouds in the eye of Tropical Cyclone (TC) Trami (2018) is investigated using dropsonde data and simulation results from a coupled atmosphere–ocean model. According to the satellite data, top height of the convective clouds exceeds 9 km above mean sea level, considerably taller than that of typical hub clouds (2–3 km). These clouds are located 10–30 km away from the TC center. Hence, these convective clouds are called deep eye clouds (DECs) in this study. The dropsonde data reveal an increase in relative humidity in the eye region during the formation of DECs. Short-lived convective clouds are simulated up to the middle troposphere in the eye region in the coupled model. Investigation of thermodynamic conditions shows a weakened low-level warm core and associated favorable conditions for convection in the eye region during the formation of DECs. DECs are formed after the weakening and outward displacement of convective heating within the eyewall. To elucidate the influence of the changes in convective heating within the eyewall on the formation of DECs, we calculate secondary circulation and associated adiabatic warming induced by convective heating within the eyewall using the Sawyer–Eliassen equation. In the eye region, weakening of subsidence and associated vertical potential temperature advection is observed as DECs are formed. This suggests that the weakening and outward displacement of convective heating within the eyewall create favorable conditions for the sporadic formation of DECs.

This article is licensed under a Creative Commons Attribution 4.0 license (http://creativecommons.org/licenses/by/4.0/).

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Soichiro Hirano, soichiro@sci.u-ryukyu.ac.jp

Abstract

The sporadic formation of short-lived convective clouds in the eye of Tropical Cyclone (TC) Trami (2018) is investigated using dropsonde data and simulation results from a coupled atmosphere–ocean model. According to the satellite data, top height of the convective clouds exceeds 9 km above mean sea level, considerably taller than that of typical hub clouds (2–3 km). These clouds are located 10–30 km away from the TC center. Hence, these convective clouds are called deep eye clouds (DECs) in this study. The dropsonde data reveal an increase in relative humidity in the eye region during the formation of DECs. Short-lived convective clouds are simulated up to the middle troposphere in the eye region in the coupled model. Investigation of thermodynamic conditions shows a weakened low-level warm core and associated favorable conditions for convection in the eye region during the formation of DECs. DECs are formed after the weakening and outward displacement of convective heating within the eyewall. To elucidate the influence of the changes in convective heating within the eyewall on the formation of DECs, we calculate secondary circulation and associated adiabatic warming induced by convective heating within the eyewall using the Sawyer–Eliassen equation. In the eye region, weakening of subsidence and associated vertical potential temperature advection is observed as DECs are formed. This suggests that the weakening and outward displacement of convective heating within the eyewall create favorable conditions for the sporadic formation of DECs.

This article is licensed under a Creative Commons Attribution 4.0 license (http://creativecommons.org/licenses/by/4.0/).

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Soichiro Hirano, soichiro@sci.u-ryukyu.ac.jp

1. Introduction

The air in the eyes of typical intense tropical cyclones (TCs) is separated by a temperature inversion (Jordan 1952; Franklin et al. 1988; Halverson et al. 2006). The air near the surface is moist and usually cloudy, whereas the air aloft is clear, warm, and dry (Willoughby 1998). Near-surface conditions in the eye region are favorable for formation of a cloud-topped mixed layer due to the presence of a stable layer at the top of the mixed layer (Bretherton et al. 2004; Houze 2010). Formation of warm and dry air above the inversion, which is generally referred to as a warm core, has been investigated in the literature, because strength and structure of warm cores are closely related to the TC intensity (Stern and Nolan 2012; Zhang and Chen 2012; Chen and Zhang 2013; Wang and Wang 2014; Wang and Jiang 2019). Although warm cores are mainly created by subsidence, Stern and Zhang (2013) and Tsujino et al. (2021a) found by performing a potential temperature (θ) budget analysis that, at a certain life stage of TCs, maintenance and/or intensification of warm cores are also contributed by horizontal advection of θ due to nonaxisymmetric components, which is suggested to stem from dynamical instability.

Simpson and Starrett (1955) pointed out that the TC eye often contains low-level stratocumulus called a hub cloud at its center. A hub cloud is surrounded by an inner moat of clear air or thin stratocumulus near the outer edge of the eye (Simpson 1952; 1955; Jordan 1961; Aberson et al. 2006). Schubert et al. (2007) analytically solved the Sawyer–Eliassen (SE) equation (Eliassen 1951; Shapiro and Willoughby 1982) by assuming piecewise constant form of the Rossby radius of deformation (λR) and a barotropic vortex to derive the radial distribution of vertical velocity in the eye. They demonstrated that a larger radius of the eye and smaller λR in the eye region lead to concentration of subsidence at the edge of the eye, and hence provide favorable conditions for the formation of hub clouds at the center of the eye. Although clouds developing in the eye region have been investigated by the aforementioned studies, environmental conditions of cloud development are still not elucidated well, especially based on observational evidence.

Aircraft reconnaissance was conducted for TC Trami (2018) from 25 to 28 September 2018 as a part of the Tropical Cyclones–Pacific Asian Research Campaign for the Improvement of Intensity Estimations/Forecasts (T-PARCII; Ito et al. 2018; Yamada et al. 2021). Dropsondes were deployed in the inner-core region, including the eye region, as well as in surrounding regions, from an altitude of 13.8 km above mean sea level (MSL; 43 000 ft). The datasets obtained from these observations are valuable because airborne observations in the eye region have been performed in limited cases in the western North Pacific Ocean since the termination of regular airborne observations of TCs by the U.S. Air Force in 1987 (Elsberry and Harr 2008; Chan et al. 2018). The T-PARCII aircraft reconnaissance is noteworthy in that the eye region of the middle and upper troposphere was observed by penetration flights at z = 13.8 km MSL, while aircraft surveillances have been conducted in the western North Pacific Ocean by several observation campaigns such as the Tropical Cyclone Motion (TCM-90) in 1990 (Elsberry 1990), the Dropwindsonde Observations for Typhoon Surveillance near the Taiwan Region (DOTSTAR) since 2003 (Wu et al. 2005), The Observing System Research and Predictability Experiment (THORPEX)–Pacific Asian Regional Campaign (T-PARC) in 2008 (Elsberry and Harr 2008), the Impacts of Typhoons on the Ocean in the Pacific (ITOP) in 2010 (D’Asaro et al. 2014), and the dropsonde observation by the Hong Kong Observatory in 2016 (Chan et al. 2018). Figure 1 shows photographs of the eye region taken from the aircraft flying over it. On 25 September, there were only low-level clouds inside the eye (Fig. 1a). This characteristic is typical of intense TCs. In contrast, short-lived convective clouds extending into the middle troposphere were formed in the eye region on 26 and 27 September (the clouds at the red arrowhead in Fig. 1b and inside the broken red ellipse in Fig. 1c). According to infrared satellite images, brightness temperature is <−20°C, which approximately corresponds to the altitude of <300 hPa (>9 km MSL),1 where the convective clouds were observed on 26 September (Fig. 6f). This is considerably higher than top height of conventional hub clouds, which is approximately 2–3 km (Simpson and Starrett 1955; Fletcher et al. 1961; Schubert et al. 2007). Moreover, visible satellite images show that the convective clouds are apparently located in the radial range of 10–30 km, i.e., outside the TC center (Figs. 6b,c). In contrast, hub clouds are usually observed at the circulation center (Simpson and Starrett 1955; Willoughby 1998; Schubert et al. 2007). Hence, the convective clouds observed in the eye of TC Trami (2018) are hereafter referred to as deep eye clouds (DECs) to distinguish them from the conventional hub clouds. The short-lived convective clouds vanished on 28 September and the sea surface was visible from the aircraft (Fig. 1d).

Fig. 1.
Fig. 1.

Photographs inside the eye of TC Trami taken from an aircraft flying at 13.8 km MSL at (a) 0447 UTC 25 Sep, (b) 0728 UTC 26 Sep, (c) 0550 UTC 27 Sep, and (d) 0433 UTC 28 Sep 2018. The clouds at a red arrowhead in (b) and inside a broken red ellipse in (c) are DECs.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

Almost no previous studies identified DECs and investigated favorable conditions for their formation. The present study clarifies favorable conditions for the sporadic formation of DECs using data from the T-PARCII dropsondes and model simulation results. Although the dropsonde data provide a general picture of the eye and surrounding regions, model simulations provide gridded data with higher temporal resolution and physical quantities such as vertical velocity and diabatic heating, which cannot be directly obtained from dropsonde observations. We employ a coupled atmosphere–ocean model because substantial TC–ocean interaction presumably occurs during the formation of DECs. According to the TC best track data from the Japan Meteorological Agency (JMA), Trami had peak intensity with its central pressure of 915 hPa during the time period of 1800 UTC 24 September to 0600 UTC 25 September (Fig. 4a). The translation speed of Trami was <3 m s−1 from 25 to 27 September (Fig. 5). Figure 2 shows the horizontal distribution of sea surface temperature (SST) created using the microwave Optimally Interpolated (OI) SST daily product. SST starts to decrease behind the TC center on 25 September (Fig. 2c). Significant SST cooling is observed behind the TC center and to the right of the TC track on 27 and 28 September (Figs. 2e,f).2 This SST cooling is caused by the slow translation speed and strong wind of Trami (Wada 2019; Kanada et al. 2021). Generally speaking, SST cooling caused by TCs is divided into one- and three-dimensional (3D) processes, which mainly correspond to shear-induced mixing and upwelling, respectively (Ginis 2002; Shay 2010). Yablonsky and Ginis (2009) indicated that SST cooling induced by TCs translating at <2 m s−1 is mainly related to the 3D process, i.e., upwelling. Hence, it is reasonable to use a three-dimensionally coupled atmosphere–ocean model to investigate the cause and environmental conditions for the sporadic formation of DECs from 26 to 27 September, when Trami translated at a slow pace (Fig. 5).

Fig. 2.
Fig. 2.

The horizontal distribution of SSTs created using microwave satellite data on (a) 23, (b) 24, (c) 25, (d) 26, (e) 27, and (f) 28 Sep. Red crosses indicate the positions of the TC centers from 22 Sep to each date.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

The following section describes data and methods used in this study. Section 3 gives an overview of the intensity and track of Trami based on the best track and dropsonde data. These are compared to the intensity and track of simulated Trami in the coupled atmosphere–ocean model. In section 4, the sporadic formation of DECs is described using the satellite and dropsonde data. We also mention the eyewall replacement cycle (ERC) which occurs before the formation of DECs. Thereafter, we examine reproduction of the formation of DECs and ERC in the coupled model simulation. In section 5, thermodynamic conditions in the eye region are investigated using the dropsonde data and simulation results to clarify whether the eye region is favorable for convection. Vertical motion is also examined to reveal convective activity in the eye region. In section 6, we calculate vertical velocity and associated θ advection induced by convective heating within the eyewall by numerically solving the SE equation. This calculation enables one to estimate the influence of changes in the strength and location of convective heating within the eyewall on vertical velocity and associated adiabatic warming in the eye region. Concluding remarks are given in section 7.

2. Data and methods

a. Dropsonde data

During the T-PARCII observations, the aircraft succeeded in penetrating the eye six times: twice on 26 and 27 September, and once on 25 and 28 September. Figure 3 shows the paths of dropsondes in the inner core region relative to the storm center. Dropsondes were deployed inside the eye daily, which enables one to estimate the central pressure of Trami, as shown in Fig. 4a. Dropsonde data were densely obtained, especially on 26 September (Fig. 3b). Observed variables of dropsondes were pressure, horizontal winds, temperature, relative humidity (RH), and 3D GPS positions. They were sampled at a frequency of 1 Hz. Temperature above 300 hPa is not used because it may be affected by temperature of the aircraft cabin. A detailed description of the aircraft structure and dropsondes used in the reconnaissance flight is given in Yamada et al. (2021).

Fig. 3.
Fig. 3.

Radius–pressure cross sections of the paths of dropsondes in the inner core on (a) 25, (b) 26, (c) 27, and (d) 28 Sep. The paths of each dropsonde are drawn in reddish and bluish colors at smaller and larger radii, respectively, with few exceptions. The numerals indicate the launch time in a unit of UTC.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

Fig. 4.
Fig. 4.

A time series of (a) the central pressure and (b) maximum wind speed in the best track data from the JMA (black solid curves) and JTWC (black broken curves), the coupled atmosphere–ocean model (blue curves), and the noncoupled atmospheric model (red curves). The best track data are provided every 6 (3) h before (after) 0000 UTC 28 Sep for the JMA and every 6 h for the JTWC. The central pressures and maximum wind speeds in the models are plotted every 1 h. Crosses indicate estimated values from the dropsonde data deployed in the eye region. Note that the maximum wind speeds provided by the best track data from the JMA and JTWC are 10- and 1-min averages, respectively. The maximum wind speeds in the best track data from the JTWC are shown in (b). This maximum wind speed is multiplied by 0.93 following Harper et al. (2010). Note also that the maximum wind speeds in the coupled and noncoupled models are instantaneous values.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

In the following analysis, these dropsonde data are projected onto radius–pressure cross sections based on GPS positions of the dropsondes and the best track data from the JMA. The analysis is mainly focused on axisymmetric features because the dropsonde observations are not sufficient to discuss nonaxisymmetric structures.

b. Satellite data

The OI SST daily product version 5 is created by Remote Sensing Systems using microwave satellite data. The horizontal grid spacing is 0.25°.

We use visible and infrared images with central wavelength of 0.64 and 10.4 μm, respectively. They are scanned every 150 s by the Himawari-8 geostationary satellite. The horizontal grid spacings are 0.005° and 0.02° for visible and infrared images, respectively.

c. Model description

Our coupled model employs the Japan Meteorological Agency Nonhydrostatic Model (JMA-NHM; Saito et al. 2006; Saito 2012) and Meteorological Research Institute Community Ocean Model (MRI.COM; Tsujino et al. 2017) as atmospheric and oceanic components, respectively. The settings of each component and the coupling procedure are briefly described below.

The JMA-NHM is a nonhydrostatic model developed by the JMA. In this study, the advection scheme is flux form fourth order with a flux limiter advection correction scheme (Kato 1998). We employ a dynamical core with six-category bulk microphysics (Ikawa and Saito 1991) and the modified Kain–Fritsch convective scheme (Kain and Fritsch 1990; Saito 2012). Boundary layer turbulence is solved by the Mellor–Yamada–Nakanishi–Niino level-2.5 closure model (Nakanishi and Niino 2004). Surface fluxes are calculated using the Beljaars and Holtslag (1991) scheme, with the maximum drag coefficient capped at 0.0018 for strong wind conditions over the ocean (Powell et al. 2003; Takagaki et al. 2012). A clear-sky radiation scheme (Yabu et al. 2005) and a cloud radiation scheme (Kitagawa 2000) explicitly treat radiation processes.

The MRI.COM is a hydrostatic model developed by the JMA for both operational and research work. The MRI.COM uses the finite volume method on structured mesh to discretize governing equations. In the current experiment, we employ the Quadratic Upstream Interpolation for Convective Kinematics for advection (Leonard 1979), the biharmonic operator for both horizontal viscosity and diffusion, and the Noh and Kim scheme for turbulent closure in the oceanic boundary layer (Noh and Kim 1999). The shortwave radiation flux penetrates the ocean interior and we consider the effect of insolation angle on the shortwave radiation flux in the oceanic interior (Ishizaki and Yamanaka 2010).

The JMA-NHM is coupled to the MRI.COM using a coupler, Jcup3, developed by Arakawa et al. (2020). The JMA-NHM provides the following components to the MRI.COM: surface stress, shortwave radiation, longwave radiation, latent heat flux, sensible heat flux, precipitation, surface air temperature, and surface pressure. Conversely, the MRI.COM provides updated SST to the JMA-NHM. The coupling interval between the JMA-NHM and MRI.COM is 600 s.

d. Experimental design

The domain size of our calculation is 8.425°–30.784°N, 120.037°–143.963°E for the atmospheric component, and 9.5°–29.9°N, 121.2°–142.8°E for the oceanic component. A 7-day simulation is conducted from 0000 UTC 22 September 2018, following a spinup period for oceanic components, which will be explained later in this subsection.

For the atmospheric component, the horizontal grid spacing is 0.023 93° in longitude and 0.022 36° in latitude on a Mercator projection plane, which correspond to 2.5 km at 20°N. There are 30 vertical layers from the surface up to 21 km. The vertical grid spacings are <0.5 km below 3 km, 0.5–1 km in the altitude range of 3–11 km, and 1–1.5 km above 11 km. The main conclusions do not change with 50 vertical layers. A time step is 10 s. Leapfrog integration is employed for time integration. The initial condition is given by a posteriori JMA Global Analysis with the horizontal grid spacing of 0.5° (JMA 2013). Because the intensity of Trami is not sufficiently strong at the initial time of the main experiment (0000 UTC 22 September), the vortex initialization scheme of Nguyen and Chen (2011) is used to spin up the TC vortex with the best track data from the JMA. The boundary condition for the atmospheric component is also taken from the JMA Global Analysis.

For the oceanic component, the horizontal grid spacing is 0.1° on a Mercator projection plane, with a vertical representation of 54 layers to a depth of 6000 m in zσ coordinates. A time step is 300 s with a barotropic component integrated with a time step of 30 s. The initial condition is created from the JMA operational analysis of the North Pacific Ocean with the horizontal grid spacing of 0.5°, based on the JMA–MRI Multivariate Ocean Variational Estimation system (Usui et al. 2006). To set up the initial condition of the main experiment, we conduct a 21-day spinup run, from 0000 UTC 1 September to 0000 UTC 22 September. During the spinup run, oceanic temperature and salinity are relaxed toward the analysis value with a time scale of 0.25 day. To provide realistic surface wind forcing, the atmospheric component is coupled during the spinup run. The settings of the atmospheric component are the same as in the main calculation, except that the horizontal grid spacing is doubled, and that the coupling time interval between the atmospheric and oceanic components is 1800 s. The boundary condition for the oceanic component is also given by the JMA operational analysis.

We also conduct a simulation without the oceanic component for comparison. Experimental settings are the same as in the coupled experiment, except that the initial SST in the noncoupled experiment is fixed to SST at the end of the ocean spinup run.

e. The SE equation

In section 6, we use the SE equation to estimate the influence of the magnitude and location of diabatic heating within the eyewall on downward motion and associated θ advection in the eye region. The SE equation is expressed as
(N2ρ0rψ¯r+γρ0rψ¯z)r+(γρ0rψ¯r+I2ρ0rψ¯z)z=[(2υ¯r+f0)(F¯(ϕ)uξ¯wυz¯)]z+gθ¯(Q¯uθr¯υrθϕ¯wθz¯)r,
where r is the radius; ϕ is the azimuth; z is the isentropic pseudoheight; u, υ, and w are the radial, tangential, and vertical components of wind, respectively; ξ is the vertical component of relative vorticity; Q is the diabatic heating rate; ψ is streamfunction; F(ϕ) is the tangential component of unspecified friction or other nonconservative mechanical forcings; ρ0 is the basic density; f0 is the Coriolis parameter at a given latitude; g is the acceleration due to gravity; the overbar and prime denote azimuthal average and deviation from the azimuthal average, respectively; the subscripts refer to derivatives with respect to a given variable; N2=(g/θ¯)θ¯z is the static stability; γ=(2υ¯/r+f0)υ¯z is the baroclinicity; I2=(2υ¯/r+f0)(f0+ξ¯) is the inertial stability; and θ=T(p0/p)R/cp, where T is temperature; p is the pressure; p0 is a reference pressure (1000 hPa); cP is the specific heat at constant pressure; and R is the gas constant (Bui et al. 2009; Abarca and Montgomery 2014). The SE equation is derived based on the assumptions of the gradient wind balance υ¯2/r+f0υ¯=Φ¯r and hydrostatic balance Φ¯z=g, where Φ is geopotential. Streamfunction ψ is defined as u¯=ψ¯z/(ρ0r) and w¯=ψ¯r/(ρ0r), based on the continuity equation for the axisymmetric component (1/r)(ru¯)r+(1/ρ0)(ρ0w¯)z=0. The isentropic pseudoheight z is expressed as z=[1(p/p0)R/cp]cpθ0/g, where θo is a reference potential temperature (300 K) (Hoskins and Bretherton 1972; White and Beare 2005). By using the continuity equation for the nonaxisymmetric component (1/r)(ru)r+(1/r)υϕ+(1/ρ0)(ρow)z=0, the terms corresponding to θ advection due to nonaxisymmetric components on the right-hand side of Eq. (1), uθr¯(υ/r)θϕ¯wθz¯, can be written in terms of convergence of eddy heat flux: (1/r)(ruθ¯)r(1/ρ0)(ρ0wθ¯)z (Stern and Zhang 2013; Ohno and Satoh 2015).
The left-hand side of Eq. (1) may be written in the form of
Aψ¯rr+2Bψ¯rz+Cψ¯zz,
where A=N2/(ρ0r), B=γ/(ρ0r), and C=I2/(ρ0r). The partial differential Eq. (2) is elliptic, and a unique solution for ψ¯ can be obtained if the discriminant of Eq. (2)
Δ=ACB2=gθ0r(2υ¯r+f0)q¯, 
where q is the potential vorticity, is positive everywhere (Shapiro and Willoughby 1982; Shapiro and Montgomery 1993; Fudeyasu and Wang 2011). Regions with Δ > 0 correspond to where the flow is symmetrically stable. To guarantee the solvability condition Δ > 0, the SE Eq. (1) is regularized in a way similar to Wang and Smith (2019): regions of C < 0 are replaced by |0.001C|, and then B2 is replaced by 0.95AC. Wang and Smith (2019) suggested that a regularization procedure introduces uncertainty in the integrity of the balance solutions, and that the dynamical structure of TCs, within and near regions where the coefficients of the SE equation are regularized, must be discussed with considerable caution. Our calculation demonstrates that regions with Δ < 0 are seen in the boundary layer outside the eye region and in the outflow region, and that regions with C < 0 are found in the outflow region during the time period analyzed in this study. It should be emphasized that the eye region, which is featured in the present study, is not regularized.

After the regularization, Eq. (1) is solved numerically using a successive overrelaxation method (Press et al. 1992; Hendricks et al. 2004; Montgomery et al. 2006). Boundary conditions are ψ¯=0 at the axis of rotation, and at the upper and lower boundaries (0 and 14.5 km, respectively), and ψ¯r=0 at the outer radius (400 km; Fudeyasu and Wang 2011; Abarca and Montgomery 2014). The radial and vertical grid spacings are 5 and 0.5 km, respectively.

3. An overview of TC Trami (2018)

a. Best track and dropsonde data

This subsection gives an overview of the intensity and track of Trami based on the best track data from the JMA and Joint Typhoon Warning Center (JTWC), and dropsonde data. Figure 4a shows a time series of the central pressures of Trami. According to the best track data from the JMA, the central pressure of Trami gradually decreased from 0600 UTC 22 September until Trami had the peak intensity of 915 hPa from 1800 UTC 24 September to 0600 UTC 25 September. Thereafter, there was sudden increase in the central pressure, followed by constant central pressure until 0000 UTC 29 September. Qualitatively similar temporal changes in the central pressure are also observed in the best track data from the JTWC. Estimations from the dropsonde data also show the sudden weakening of the TC intensity from 25 to 26 September as in the best track data. Then gradual increase in the central pressure was observed from 26 to 28 September. The maximum wind speed is shown in Fig. 4b. Temporal changes corresponding to those of the central pressure are observed in the maximum wind speed. Figure 5 shows the positions of the TC centers. According to the best track data from the JMA and JTWC, Trami moved west-northwestward until it slowed down and became quasi stationary near 130°E and 20°N at 0000 UTC 25 September. The translation speed of Trami was <3 m s−1 from 25 to 27 September. Thereafter, Trami approached the Okinawa Islands.

Fig. 5.
Fig. 5.

The positions of the TC centers from 22 to 29 Sep in the best track data from the JMA (black solid curve) and JTWC (black broken curve), the coupled atmosphere–ocean model (a blue curve), and the noncoupled atmospheric model (a red curve). As in Fig. 4, the best track data are provided every 6 (3) h before (after) 0000 UTC 28 Sep for the JMA and every 6 h for the JTWC, while the TC positions in the models are plotted every 1 h. Crosses indicate the TC positions at 0000 UTC on each date.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

b. Simulation results

The best track and dropsonde data are used for verification of the center position and intensity of Trami in the coupled atmosphere–ocean model. Simulated storm centers in the coupled model are determined using a method proposed by Braun (2002). The track of Trami in the coupled model is almost identical to that in the noncoupled model. A maximum difference in the positions of the TC centers between the best track and the simulation is approximately 200 km at 0000 UTC 25 September, i.e., 72 h after the initial time of the simulations (Fig. 5). This is comparable with an average difference between the best track and forecasts by the JMA with forecast time of 72 h.

Next, the intensity of the simulated TC is examined. The gradual intensification of Trami is reproduced in the coupled model simulation (Fig. 4a). The central pressure in the coupled model attains a minimum 6–18 and 6 h earlier than in the best track data of the JMA and JTWC, respectively. The minimum central pressure in the coupled model is 7–8 hPa higher than in the best track data of the JMA and JTWC. We speculate that these differences do not largely exceed uncertainties contained in the TC intensity of the best track data (Torn and Snyder 2012; Ito et al. 2018). The increase in the central pressure shortly after the peak intensity of Trami is gentler in the coupled model than in the dropsonde and best track data. This is probably because of the weaker ocean cooling which results from the slightly faster translation speed of a simulated TC in the coupled model than in the best track data (Fig. 5). The gradual increase in the central pressure after 26 September in the coupled model is qualitatively similar to that in the dropsonde data. On the other hand, in the noncoupled model, although the gradual intensification of Trami before 24 September is reproduced, the central pressure continues to decrease down to 890 hPa on 25 September, thereafter remaining almost constant. The higher central pressure in the coupled model than the noncoupled model after the slow translation of Trami is due to coupling between the atmospheric and oceanic components, as already shown by previous studies (e.g., Wu et al. 2007; Lin et al. 2008; 2009; Blair et al. 2017).

Although several quantitative discrepancies are found, the intensity and track of Trami are qualitatively reproduced in the coupled model. In the next section, we describe convective activity in the eye region and structural changes in the eyewall during the T-PARCII dropsonde observations, and check whether these are reproduced in the coupled model.

4. Sporadic formation of DECs and the REC

a. Satellite observations

In this subsection, we examine visible and infrared images from the geostationary satellite Himawari-8. Figure 6 shows visible and infrared satellite images when photographs are taken from the aircraft in the eye region (Fig. 1). On 25 September, low-level clouds are mainly seen and DECs are not observed in the eye region (Fig. 6a). Brightness temperature is approximately 15°C (Fig. 6e). On 26 September, the sporadic formation of DECs is observed at 10 < r < 30 km in the southeast quadrant (the green broken ellipses in Fig. 6b). Brightness temperature is <−20°C where DECs are formed (Fig. 6f). It appears from visible satellite images that DECs sporadically develop in the eye region and that their lifespan is a few hours (not shown). DECs are also observed in the same radial range on 27 September (Figs. 6d,h). Note that regions where brightness temperature is <−50°C are observed in the eye region on 26 and 27 September (Figs. 6f,g). These regions probably correspond to those where upper-level clouds emerge (Figs. 6b,c). On 28 September, low-level clouds are sparsely observed in the eye region (Fig. 6d), and brightness temperature is approximately 15°C (Fig. 6h).

Fig. 6.
Fig. 6.

Visible satellite images from the Himawari-8 at (a) 0447 UTC 25 Sep, (b) 0727 UTC 26 Sep, (c) 0550 UTC 27 Sep, and (d) 0432 UTC 28 Sep. Red stars indicate the storm center estimated from the best track. Red broken circles indicate 50- and 100-km radii from the storm center. The clouds in green broken ellipses in (b) and (c) correspond to the convective clouds in Figs. 1b and 1c, respectively. The clouds are taken from the northwest direction in both Figs. 1b and 1c. (e)–(h) As in (a)–(d), but for infrared satellite images.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

Figure 7 shows a Hovmöller diagram of the ARCHER ring score for Trami. The ARCHER ring score is an index for ring structures of TCs and is defined based on microwave satellite data (Wimmers and Velden 2016; Wimmers et al. 2017). Trami likely experiences the ERC from 0800 UTC 24 September to 1800 UTC 25 September. Tsujino et al. (2021b) showed that Trami has concentric eyewall structure at 0427 and 1638 UTC 25 September based on microwave satellite images and the criterion of Yang et al. (2013; see their Figs. 2b,c). A radius of the eye is apparently larger on 26–28 September than on 25 September after the ERC (Fig. 6). The sporadic formation of DECs is observed after the increase in a radius of the eye.

Fig. 7.
Fig. 7.

Hovmöller diagram of the ARCHER ring score. The image is sourced from http://tropic.ssec.wisc.edu/real-time/archerOnline/web/index.shtml. The dates on the vertical axis indicate 0000 UTC on each date.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

b. Dropsonde observations

Figure 8 shows radius–pressure cross sections of RH from 25 to 28 September in the dropsonde data. On 25 September, RH gradually decreases from r = 30 to 10 km above 800 hPa, whereas RH is >90% below 800 hPa at r < 30 km (Fig. 8a). This is the distribution of RH in typical intense TCs. RH is higher above 800 hPa on 26 and 27 September than on 25 September at r < 30 km (Figs. 8a–c). This increase in RH in the eye region is likely caused by the sporadic formation of DECs (Figs. 1b,c and 6b,c,f,g). RH is slightly lower at r < 50 km in the pressure range of 800–500 hPa on 28 September than on 27 September (Figs. 8c,d). This is probably related to the decrease in cloud amount in the eye region (Figs. 1d and 6d,h).

Fig. 8.
Fig. 8.

Radius–pressure cross sections of RH based on the dropsonde data during the time periods of (a) 0347–0540 UTC 25 Sep, (b) 0505–0816 UTC 26 Sep, (c) 0341–0655 UTC 27 Sep, and (d) 0418–0514 UTC 28 Sep.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

Figure 9 shows storm-relative tangential wind on 25 and 26 September from the dropsonde data. The radius of maximum wind (RMW) at 850 hPa is approximately 40 and 95 km on 25 and 26 September, respectively. The larger RMW on 26 September results from the ERC. Moreover, tangential wind at the RMW is weaker on 26 September than on 25 September (Fig. 9). This is consistent with the sudden increase in the central pressure of Trami from 25 to 26 September observed in the dropsonde and best track data (Fig. 4a). The RH increase in the eye region occurs after the increase in the RMW and weakening of the TC intensity. This is reminiscent of the RH increase in the eye region of Hurricane Rita (2005) in the lower troposphere during the ERC (Houze et al. 2007). They showed a vertical profile of RH in the eye region below 2 km MSL using dropsonde data. In contrast, aircraft reconnaissance during the T-PARCII observations enables one to identify the significant RH increase from 25 to 26 September in the pressure range of 800–300 hPa (Figs. 8a,b).

Fig. 9.
Fig. 9.

Radius–pressure cross sections of storm-relative tangential wind in the dropsonde data during the time periods of (a) 0435–0458 UTC 25 Sep and (b) 0505–0746 UTC 26 Sep.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

c. Coupled model simulation

Simulation results from the coupled atmosphere–ocean model are validated by examining the characteristics of clouds in the eye region. Figure 10 shows frequency of total (liquid and ice) cloud water content (TCWC) > 1 mg kg−1 at 500 hPa in the coupled model. In the eye region, occurrence of high TCWC is rare before 1400 UTC 25 September in the middle troposphere. This corresponds to suppressed convection in the eye region. In contrast, occurrence of high TCWC is sporadically observed at 10 < r < 30 km thereafter. To examine nonaxisymmetric features of TCWC, Fig. 11 shows the horizontal distribution of TCWC at 500 hPa from 2100 UTC 26 September to 0000 UTC 27 September as an example. Regions with high TCWC sporadically appear in the eye. Moreover, to clarify the vertical structure of TCWC in the eye region, TCWC is shown in radius–pressure cross sections in Fig. 12. It can be seen that convective clouds develop vertically in the eye on a time scale of hours. For example, a convective cloud suddenly emerges at r = 10 km at 2300 UTC: however, it is not observed at 2200 UTC (Figs. 12b,c). Thereafter, the convective cloud at r = 10 km disappears at 0000 UTC (Fig. 12d). A convective cloud at r = 30 km observed at 2300 and 0000 UTC appears to grow over a time period of a few hours from 2100 UTC. These features are qualitatively similar to observed DECs. The short-lived convective clouds are mainly observed after 1400 UTC 25 September, while high TCWC is observed only in the lower troposphere before this time (not shown). In the following, time periods of 2300 UTC 23 September–1300 UTC 24 September and 0800–2200 UTC 26 September are referred to as periods 1 and 2, respectively. Periods 1 and 2 represent time periods with dry air above the middle troposphere and during the formation of the short-lived convective clouds, respectively.

Fig. 10.
Fig. 10.

A radius–time cross section of frequency of total (liquid and ice) cloud water content > 1 mg kg−1 at 500 hPa in the coupled atmosphere–ocean model.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

Fig. 11.
Fig. 11.

Total (liquid and ice) cloud water content at 500 hPa at (a) 2100, (b) 2200, and (c) 2300 UTC 26 Sep, and (d) 0000 UTC 27 Sep.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

Fig. 12.
Fig. 12.

Radius–pressure cross sections of frequency of total (liquid and ice) cloud water content > 1 mg kg−1 at (a) 2100, (b) 2200, and (c) 2300 UTC 26 Sep, and (d) 0000 UTC 27 Sep.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

Moreover, we pay attention to the radial maximum of frequency of TCWC > 1 mg kg−1, which corresponds to the eyewall. Clear concentric eyewall structure is observed from 0600 to 1900 UTC 24 September (Fig. 10). The ERC starts slightly earlier and ends approximately 24 h earlier in the coupled model than in observations (Fig. 7; Tsujino et al. 2021b). However, one of the essential elements for the formation of DECs is the location of the eyewall, as will be shown later. The eyewall is located at a larger radius in period 2 than in period 1 (Fig. 10). Note that DECs do not apparently correspond to a remnant of the inner eyewall in the coupled model (Fig. 10). Simulation results of the coupled model are used to investigate the sporadic formation of DECs in the following sections.

5. Thermodynamic conditions and vertical motion in the eye region

a. Dropsonde observations

Thermodynamic conditions in the eye region are compared between 25 and 26 September to examine whether the eye region is favorable for convection. Skew T–logp diagrams of individual dropsondes launched in the eye region are shown in Figs. 13a and 13b. On 25 September, a temperature inversion is found near 800 hPa (Fig. 13a). Temperature and dewpoint temperature are almost equal below the temperature inversion, whereas dewpoint temperature is lower than temperature above the inversion (Fig. 13a). In other words, the air below the inversion is humid while the air above the inversion is dry, as shown in Fig. 8a. Temperature which an air parcel would have if it were lifted from the surface by buoyancy, which is simply called air parcel temperature in the following, is almost identical with temperature below the inversion, and the lifting condensation level (LCL) is located just above the surface (Fig. 13a). Hence, the air below the inversion is probably cloudy. In contrast, air parcel temperature is lower than ambient temperature, especially in the pressure range of 800–500 hPa (Fig. 13a). This large negative buoyancy inhibits ascent of an air parcel and development of convective clouds above the inversion. This is a thermodynamic profile observed in the eyes of typical intense TCs (Willoughby 1998). Qualitatively similar characteristics are also found in another dropsonde launched at 0446 UTC 25 September in the eye region (Fig. 3a).

Fig. 13.
Fig. 13.

(top) Skew T–logp diagrams of dropsondes in the eye region launched at (a) 0452 UTC 25 Sep and (b) 0722 UTC 26 Sep. The paths of each dropsonde are drawn in Figs. 3a and 3b. Vertically averaged distances from the TC center of the dropsondes at 0452 UTC 25 Sep and 0722 UTC 26 Sep are 5.8 and 25.3 km, respectively, as indicated at the upper right of each panel. Red solid, red dashed, and blue solid curves denote temperature, dewpoint temperature, and air parcel temperature, respectively. Horizontal dashed lines in (a) and (b) indicate the LCL. (bottom) Radius–pressure cross sections of θ anomaly from that at r = 400 km in the dropsonde data during the time periods of (c) 0435–0458 UTC 25 Sep and (d) 0505–0746 UTC 26 Sep.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

On 26 September, there are temperature decrease and increase in dewpoint temperature above 800 hPa (Fig. 13b). Dewpoint temperature is almost equal to temperature below 600 hPa and very close to temperature in the pressure range of 600–400 hPa. Namely, the air becomes humid above 800 hPa in the eye region. Moreover, air parcel temperature and ambient temperature are almost identical below 400 hPa down to the sea surface (Fig. 13b). The large negative buoyancy in the lower troposphere on 25 September is not observed. The LCL is located near the surface, as on 25 September. These features correspond to favorable conditions for convection and are consistent with the formation of DECs on 26 September. Qualitatively similar characteristics are also found in other dropsondes launched in the eye region (Fig. 3b).

To examine warm cores in the dropsonde data, θ anomaly from that at r = 400 km is shown in Figs. 13c and 13d. The radius of 400 km is chosen because an average taken at least several hundred kilometers from the TC center is recommended for environmental temperature by previous studies, such as Stern and Nolan (2012) and Durden (2013), and dropsondes are densely deployed at r < 400 km (Fig. 3). Weakening of a warm core is observed from 25 to 26 September above 800 hPa (Figs. 13c,d). This weakening of the low-level warm core leads to the disappearance of the large negative buoyancy in the lower and middle troposphere.

Although vertical velocity cannot be measured by the dropsondes, occurrence tendency of vertical motion is estimated from the vertical distribution of equivalent potential temperature (θe) because θe is conserved for a parcel during dry adiabatic and pseudoadiabatic displacements. Figure 14 shows vertical profiles of θe on 25 and 26 September from the dropsonde data. Vertical profiles in the eye region are drawn for 25 September, while those in the radial range of 10–30 km, where the sporadic formation of DECs is observed, are drawn for 26 September. On 25 September, there is a local minimum of θe at 550 hPa (Fig. 14a). The higher θe in the lower troposphere is due to the higher RH near the surface (Fig. 8a). Decrease in θe is distinct below 800 hPa and the local minimum in the middle troposphere is obscured on 26 September (Fig. 14b). This decrease in θe in the lower troposphere is probably due to the weakening of the low-level warm core and SST cooling caused by the slow-translating TC. The decrease in lower tropospheric θe leads to decrease in the vertical variation of θe in the eye region. This suggests that vertical motion tends to occur in the eye region on 26 September.

Fig. 14.
Fig. 14.

Vertical profiles of θe (a) in the eye region on 25 Sep and (b) in the radial range of 10–30 km, where the sporadic formation of DECs is observed, on 26 Sep. Numerals indicate launch time in a unit of UTC. Dropsondes launched at smaller and larger radii are drawn in reddish and bluish colors, respectively.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

b. Coupled model simulation

We also examine thermodynamic conditions in the eye region in the coupled model. Figures 15a and 15b show skew T–logp diagrams of azimuthal-mean fields at r = 20 km in the coupled model. The radius of 20 km is chosen because high TCWC is observed in period 2 around this radius (Fig. 10). In period 1, temperature and dewpoint temperature are almost equal below 800 hPa, whereas dewpoint temperature is lower than temperature above 800 hPa, as observed on 25 September in the dropsonde data (Figs. 13a and 15a). The LCL and level of free convection (LFC) are near the surface, while the level of neutral buoyancy (LNB) is located just above 700 hPa (Fig. 15a). The convective inhibition (CIN) is approximately 2 J kg−1. These features indicate that development of clouds by buoyancy is limited to the lower troposphere, as on 25 September in the dropsonde data.

Fig. 15.
Fig. 15.

(top) Skew T–logp diagrams of azimuthal-mean fields at r = 20 km in the coupled model in (a) period 1 and (b) period 2. The meanings of the three curves are as in Fig. 13. Three horizontal dashed lines in (a) and (b) indicate the LNB, LFC, and LCL from top to bottom. (bottom) Radius–pressure cross sections of azimuthal-mean θ anomaly from that at r = 400 km in the coupled model in (c) period 1 and (d) period 2.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

In period 2, a difference between temperature and dewpoint temperature is smaller than in period 1, especially in the pressure range of 700–250 hPa (Figs. 15a,b), i.e., the air in this pressure range becomes more humid. Temperature decreases in the pressure range of 700–400 hPa (Figs. 15a,b). Consequently, a layer with negative buoyancy disappears and the LNB is located considerably higher in period 2 than in period 1 (Figs. 15a,b). The LCL and LFC are located near the surface, as in period 1 (Figs. 15a,b). The convective available potential energy (CAPE) changes from 57.8 J kg−1 in period 1 to 1036.9 J kg−1 in period 2. Bogner et al. (2000) revealed the radial distribution of the CAPE using dropwindsondes deployed in six TCs in the North Atlantic Ocean. They showed that the CAPE at r < 30 km is <200 J kg−1, regardless of the TC intensity. Hence, the CAPE during the formation of DECs is expected to be considerably higher than that in the eye of typical TCs. It is also noteworthy that the CAPE during the formation of DECs is comparable to climatological CAPE in the tropics (1000–2000 J kg−1; Riemann-Campe et al. 2009). In contrast, the CIN is ∼2 J kg−1, as in period 1. These thermodynamic conditions are favorable for convection, and convective clouds can spontaneously develop up to the middle and upper troposphere in period 2.

As examined using the dropsonde data, we investigate changes in warm cores in the coupled model. Figures 15c and 15d show θ anomaly from that at r = 400 km. A double warm-core structure is found at r < 30 km in period 1 (Fig. 15c). The double warm-core structure is frequently observed in intense TCs (Hawkins and Imbembo 1976; Schwartz et al. 1996; Yamada et al. 2021; Rotunno and Emanuel 1987; Stern and Zhang 2013; Kieu et al. 2016). A peak of θ anomaly at 450 hPa is not observed in the dropsonde data, probably because warming tendency at the altitude is slightly overestimated in the coupled model (Fig. 13c). Note that existence of an upper-level warm core cannot be confirmed from the dropsonde data because temperature above 300 hPa is probably affected by temperature inside the aircraft, as mentioned in section 2a. Anomaly of θ decreases at r < 30 km from period 1 to period 2, especially in the pressure range of 700–400 hPa (Figs. 15c,d). This weakening of a low-level warm core corresponds to favorable thermodynamic conditions for convection in the eye region.

We examine vertical velocity, which cannot be obtained from the dropsonde observations, in the eye region. Figure 16 shows a histogram of updraft in the eye region of the middle troposphere in the coupled model. Frequency of updraft and the maximum value of updraft are larger in period 2 than in period 1. This indicates that convective activity is larger in the eye region in period 2 than in period 1. Note that vertical variation of simulated θe in the eye region is smaller in period 2 than in period 1 (not shown), as in the dropsonde data.

Fig. 16.
Fig. 16.

A histogram of vertical velocity in the pressure range of 600–400 hPa at r < 20 km in period 1 (a blue curve) and at r < 35 km in period 2 (a red curve). These radial ranges are chosen to exclude updraft in the eyewall.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

6. Influence of convective heating within the eyewall on the sporadic formation of DECs

a. Weakening and outward displacement of diabatic heating within the eyewall

As mentioned in section 1, the air in the eye is separated by moist and cloudy air near the surface and warm and dry air (warm cores) above the temperature inversion. While the former results from frictionally induced ascent caused by cyclonic airflow in the eye near the surface, the latter is primarily maintained by mechanically forced subsidence. Hence, the height of clouds in the eye region generally reflects the relative dominance of the mechanically forced subsidence and the frictionally induced ascent (Emanuel 2019). Several previous studies confirmed using the SE Eq. (1) that the strengths of subsidence and associated adiabatic warming in the eye region are related to the magnitude and location of diabatic heating within the eyewall. Schubert et al. (2007) showed that subsidence and associated vertical temperature advection in the eye region induced by diabatic heating within the eyewall are proportional to the diabatic heating within the eyewall for a barotropic vortex if the location of the eyewall and λR are constant. Pendergrass and Willoughby (2009) calculated SE responses to prescribed diabatic heating within the eyewall for a vortex with prescribed vertical shear of tangential wind. They showed that warming tendency in the eye region increases for greater intensity of vortices and smaller radius of the eye.

The sporadic formation of DECs is observed after the weakening of the TC intensity and outward displacement of the eyewall, which occur after the ERC, as mentioned in section 4. We compare the magnitude and location of diabatic heating within the eyewall before and after its weakening and outward displacement. Figures 17a and 17b show diabatic heating rates in periods 1 and 2, respectively. Diabatic heating is generally smaller within the eyewall in period 2 than in period 1 (Figs. 17a,b). This is consistent with the weaker TC intensity in period 2 than in period 1 (Fig. 4). Moreover, the eyewall is located at a larger radius in period 2 than in period 1 (Figs. 17a,b). These weakening and outward displacement of diabatic heating within the eyewall are expected to lead to weakening of subsidence and associated adiabatic warming in the eye region. Hence, we estimate the influence of the weakening and outward displacement of diabatic heating within the eyewall on the magnitude of subsidence and associated adiabatic warming in the eye region using the SE Eq. (1) in the next subsection. Note that the ERC may not be always necessary for the formation of DECs. It should be emphasized that the weakening and outward displacement of diabatic heating within the eyewall create favorable conditions for the sporadic formation of DECs, as will be shown in section 6b.

Fig. 17.
Fig. 17.

(a),(b) Radius–pressure cross sections of azimuthal-mean diabatic heating rate in the coupled atmosphere–ocean model in period 1 and period 2, respectively. (c),(d) As in (a) and (b), but for the local λR.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

b. Subsidence and adiabatic warming in the eye region

Diabatic heating rate > 10 K h−1 is chosen as convective heating within the eyewall (see Figs. 17a,b). Using this heating as forcing in the SE Eq. (1), we calculate secondary circulation and associated θ advection induced by convective heating within the eyewall. Note that the coefficients on the left-hand side of Eq. (1) and terms on the right-hand side are averaged for 15 h to ensure the gradient wind balance. Figure 18 shows vertical velocity induced by diabatic heating within the eyewall in periods 1 and 2. Downward motion is <−10 cm s−1 around the TC center in the pressure range of 800–300 hPa in period 1 (Fig. 18a). In particular, downward motion at 20 < r < 30 km, i.e., just inside the eyewall is <−15 cm s−1. In period 2, the eyewall is located at a larger radius than in period 1, and the strong downward motion just inside the eyewall is observed at 35 < r < 45 km (Fig. 18b). Moreover, downward motion is weaker around the TC center than in period 1 (Figs. 18a,b). Thus, downward motion at 10 < r < 30 km is weaker after the weakening and outward displacement of convective heating within the eyewall than before. This weakening of downward motion probably helps frictionally induced ascent reach the middle troposphere and contributes to the formation of DECs.3

Fig. 18.
Fig. 18.

Radius–pressure cross sections of azimuthal-mean vertical velocity induced by diabatic heating rate > 10 K h−1 in the coupled atmosphere–ocean model in (a) period 1 and (b) period 2.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

Next, we calculate θ advection at 10 < r < 30 km due to vertical velocity w¯θ¯z induced by diabatic heating within the eyewall to examine the weakening of the low-level warm core (Figs. 15c,d). The result is shown in Fig. 19. Distinct vertical advection of θ is observed below 400 hPa. Large vertical advection of θ is observed before 1200 UTC 24 September when Trami intensifies (Figs. 4 and 19). The largest vertical advection of θ is observed just before period 1 (Fig. 19). On the other hand, vertical advection of θ is weaker after 1800 UTC 24 September when the intensity of Trami decays (Figs. 4 and 19). Vertical advection of θ is <2.25 K h−1 several hours before period 2 (Fig. 19). Hence, this decrease in θ advection due to vertical velocity induced by convective heating within the eyewall likely leads to the weakening of the low-level warm core. Note that θ advection due to radial velocity is one or two orders of magnitude smaller than that due to vertical velocity in the eye region (not shown). Note also that vertical velocities and associated θ advections induced by diabatic heating rate < 10 K h−1 and nonaxisymmetric components are one order of magnitude smaller than those induced by diabatic heating rate > 10 K h−1 in the eye region in the lower and middle troposphere (not shown).

Fig. 19.
Fig. 19.

A time–pressure cross section of azimuthal-mean θ advection due to vertical velocity w¯θ¯z induced by diabatic heating rate >10 K h−1 averaged at 10 < r < 30 km in the coupled atmosphere–ocean model.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

Previous studies found that factors other than magnitude and location of diabatic heating within the eyewall also contribute to decrease in warming tendency in the eye region. Schubert et al. (2007) demonstrated that smaller λR in the eye region as well as a larger radius of the eye leads to decreases in downward motion and associated vertical temperature advection near the center of the eye, as mentioned in section 1. To examine the influence of λR on the decrease in vertical advection of θ in the eye region, the local λR are shown in Figs. 17c and 17d. The local λR is calculated as NH/I, where H, the typical depth scale of secondary circulation, is set to 15 km. The local λR increases around the boundary between the eyewall and eye because of decrease in I2 in this area. This increase in the local λR should contribute to increases in subsidence and warming tendency near the center of the eye. However, Pendergrass and Willoughby (2009) showed that the contribution of changes in I2 to warming tendency in the eye region is smaller by a few factors than that of changes in the TC intensity and location of the eyewall. The influence of the increase in the local λR is probably smaller than that of the weakening and outward displacement of diabatic heating within the eyewall. Thus, it is suggested that the weakening and outward displacement of convective heating within the eyewall contribute to the weakening of subsidence and the low-level warm core, which correspond to favorable conditions for the sporadic formation of DECs. Hence, the formation of DECs is important because it is expected to be related to weakening of the TC intensity.

7. Discussion regarding hub clouds

Schubert et al. (2007) suggested that weakening of downward motion at the TC center creates favorable conditions for the formation of hub clouds. As already mentioned in section 6b, the SE solutions show weaker downward motion at the TC center in period 2 than in period 1 (Fig. 18). This corresponds to favorable conditions for the formation of hub clouds, according to Schubert et al. (2007). However, hub clouds are not observed during the aircraft reconnaissance for Trami (Figs. 1b,c; compare with Fig. 9 in Schubert et al. 2007). Neither are hub clouds reproduced in the coupled model. To investigate the reason for this, azimuthal-mean horizontal divergence in period 2 is shown in Fig. 20. Near the surface of the eye region, convergence due to frictional inflow is smaller at r = 5 km than at 10 < r < 30 km, where DECs are formed in the coupled model (Fig. 10). This feature implies that the neighborhood of the TC center is less favorable for cloud formation than r = 20 km. This is probably the reason why hub clouds are not formed at the TC center in period 2.

Fig. 20.
Fig. 20.

A radius–pressure cross section of azimuthal-mean horizontal divergence in the coupled atmosphere–ocean model in period 2.

Citation: Journal of the Atmospheric Sciences 79, 3; 10.1175/JAS-D-21-0192.1

8. Concluding remarks

The present study investigates the sporadic formation of DECs observed in the eye of TC Trami (2018) and clarifies favorable conditions for their formation using the T-PARCII dropsonde data and simulation results from the coupled atmosphere–ocean model. The coupled model is employed because Trami translates at a slow pace, and resultant TC–ocean interaction causes SST cooling and weakening of the TC intensity during the formation of DECs. It is shown that observed characteristics of DECs are different from those of conventional hub clouds. One is the cloud-top height. Top height of DECs exceeds 9 km MSL whereas that of hub clouds is 2–3 km (Simpson and Starrett 1955; Fletcher et al. 1961; Schubert et al. 2007). Another different feature is the location. DECs are located at 10 < r < 30 km while hub clouds are usually observed at the TC center (Simpson and Starrett 1955; Willoughby 1998; Schubert et al. 2007). Our main results are as follows:

  • The dropsonde data show the increase in RH in the eye region of the middle troposphere from 25 to 26 September. This is probably caused by the sporadic formation of DECs.

  • Investigation of thermodynamic conditions reveals the weakened low-level warm core and favorable conditions for convection in the eye region during the sporadic formation of DECs. Decrease in the vertical variation of θe is found in the eye region. This suggests that vertical motion tends to occur in the eye region during the formation of DECs. More frequent and stronger updraft is observed in the eye region in the coupled model when DECs are formed.

  • The sporadic formation of DECs is observed after the weakening of the TC intensity and outward displacement of the eyewall. We estimate the influence of weakening and outward displacement of convective heating within the eyewall on the formation of DECs by calculating subsidence and associated adiabatic warming induced by convective heating within the eyewall using the SE equation. Subsidence and associated θ advection decrease when convective heating within the eyewall weakens and displaces outward. This suggests that the weakening and outward displacement of convective heating within the eyewall contribute to the weakening of subsidence and the low-level warm core, which correspond to favorable conditions for the sporadic formation of DECs.

1

Although the cloud-top height data are available by the High-Resolution Cloud Analysis Information using the Himawari-8 geostationary satellite data, it turns out that the cloud-top height in the eye region is estimated to be too large during the formation of DECs (K. Mouri and M. Hayashi 2021, personal communications). This is probably partly due to high sensitivity to upper-level thin clouds over the eye region rather than DECs. Hence, we estimated the cloud-top height using temperature measured by dropsondes instead.

2

Note that SSTs under deep convections cannot be obtained by microwaves and are optimally interpolated in time and space in the OI SST daily product. The SST cooling observed in the OI SST daily product is probably less pronounced than actual SST cooling.

3

Azimuthal-mean upward motion in the eye region is more pronounced in period 2 than in period 1 (not shown). This is consistent with the larger updraft frequency and larger maximum updraft value in the eye region of the middle troposphere in period 2 (Fig. 16).

Acknowledgments.

We thank Kouki Mouri and Masahiro Hayashi for their advice on the cloud-top height provided by the High-resolution Cloud Analysis Information. This work was supported by the University of the Ryukyus Research Project Promotion Grant (Strategic Research Grant 18SP01302), JSPS KAKENHI Grants 16H06311, 18H01283, and 21H04992, and the Understanding Lightning and Thunderstorms (ULAT) and the Science and Technology Research Partnership for Sustainable Development (SATREPS) Project JPMJSA1612. This research used computational resources of the Fujitsu PRIMERGY CX600M1/CX1640M1 (Oakforest-PACS) in the Information Technology Center, The University of Tokyo (ID: hp200128) supported by the MEXT (JPMXP1020200305) as “Program for Promoting Researches on the Supercomputer Fugaku” (Large Ensemble Atmospheric and Environmental Prediction for Disaster Prevention and Mitigation).

Data availability statement.

The best track data from the JMA are sourced from http://www.jma.go.jp/jma/jma-eng/jma-center/rsmc-hp-pub-eg/besttrack.html. The data from the Himawari-8 geostationary satellite and JMA Global Analysis are sourced from http://www.jmbsc.or.jp/en/meteo-data.html. The microwave OI SST daily product is produced by Remote Sensing Systems and sponsored by National Oceanographic Partnership Program (NOPP) and the NASA Earth Science Physical Oceanography Program. Data are available at www.remss.com. The dropsonde data are available upon request. Please contact the fifth coauthor (tsuboki@nagoya-u.jp), if necessary.

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