Roles of the Inner Eyewall Structure in the Secondary Eyewall Formation of Simulated Tropical Cyclones

Abstract. It has been suggested that the inner eyewall structure may play an important role in the secondary eyewall formation (SEF) of tropical cyclones (TCs). This study is to further examine the role of the inner eyewall structure by comparing two numerical experiments, which were conducted with the same large-scale environment and initial and boundary conditions but different grid sizes. The SEF was simulated in the experiment with the finer grid spacing, but not in the other.Comparing the eyewall structure in the simulated TCs with and without the SEF indicates that the eyewall structure can play an important role in the SEF. For the simulated TC with the SEF, the eyewall is more upright with stronger updrafts, accompanied by a wide eyewall anvil at a higher altitude. Compared to the simulated TC without the SEF, diagnostic analysis reveals that the cooling outside the inner eyewall is induced by the sublimation, melting and evaporation of hydrometeors falling from the eyewall anvil. The cooling also induces upper-level dry, cool inflow below the anvil, prompting the subsidence and moat formation between the inner eyewall and the spiral rainband. In the simulated TC without the SEF, the cooling induced by the falling hydrometeors is significantly reduced and offset by the diabatic warming. There is no upper-level dry inflow below the anvil and no moat formation between the inner eyewall and the spiral rainband. This study suggests that a realistic simulation of the intense eyewall convection is important to the prediction of the SEF in the numerical forecasting model.



eyewall.
169 4 Differences in the vertical structures of the eyewall 170 One of the major differences in the eyewall between NSEF and CTL is the magnitude and the 171 vertical distribution of the vertical motion, which can be examined with the azimuthally averaged 172 vertical motion within the radius of 100 km (Fig. 4) and the contoured frequency by altitude 173 diagram (CFAD) of the vertical motion (Fig. 5a). The CFAD illustrates the frequency distribution 174 of the vertical motion of the indicated values at each altitude in the region of the 10-km radially 175 inside and outside of the radius of the maximum tangential wind (RMW) for two simulations. The upward motion between 45-to 75-km radii is associated with the broad rainbands (Figs. 4a and 180 4b). In contrast, the maximum upward motion in CTL is 12 and 14 m s -1 for the 0.1 % and 0.05% 181 percentiles (Fig. 5a). The stronger upward motion in CTL indicates that a higher resolution in the 182 model simulation can resolve more intense eyewall updrafts (Yau et al., 2004). Moreover, the 183 eyewall with strong updrafts in CTL is more upright in the vertical direction. 184 Another important difference in the eyewall between NSEF and CTL is the feature of the 185 upper-level outflow layer. Figure 5b compares the upper-level outflow in the two simulations by 186 showing the 0.1% and 0.05% contoured frequency of the radial wind in the region of a radial 187 distance of 60 km starting from the radius of 10-km outside the eyewall. In NSEF, the upper-level 188 outflow peaks around the 11-km height with maxima of 28 and 26 m s -1 for the 0.05% and 0.1% 189 percentages, respectively. The outflow layer is deep with a magnitude of over 15 m s -1 extending 190 downward to 8 km. In CTL, the maximum outflow with values of over 29 m s -1 is located around 191 the 14-km height. The outflow layer at the higher altitude in CTL is associated with the strong 192 upward motion in the eyewall that can lift the hydrometeors much higher.

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The different eyewall structures can also be seen in the horizontal distribution of the cloud-194 top temperature (Fig. 6). In NSEF, the eyewall is wider and possesses relatively weaker convection 195 as indicated by the cloud-top temperature of above -75 0 C (Fig. 6a). In CTL, the cloud associated 196 with the eyewall is deeper since the coldest cloud-top temperature is below -75 0 C (Fig. 6b). The 197 coldest cloud-top temperature is located at the downshear-and upshear-right region due to the 198 influence of the southeastward VWS. The strong eyewall convection is accompanied by the strong and high-altitude outflow compared to that in NSEF.  Many studies indicated that buoyance, which is determined by temperature perturbation, affects 206 the vertical motion tendency (e.g., Zhang et al., 2000;Braun, 2002;Miller et al., 2015). It is 207 intended to examine how the buoyancy changes when the SEF fails in NSEF with a different 208 eyewall structure. Following the method used by Braun (2002), the perturbation associated with 209 the buoyance calculation is defined as ′ ( , , ) = ( , , ) − 0 ( ) − 0,1 ( , , ) , where A 210 represents any variable in a cylindrical coordinate ( , , ), , r, z are the azimuthal angle, the 211 radius from the TC center, and the vertical height axis, respectively, 0 is averaged over the whole 212 area of the 1-km domain, 0,1 are the wavenumber-0 and -1 components of the perturbation field 213 from 0 . 0 + 0,1 denotes the reference state for the buoyance analysis. Following Houze (1993) 214 and Braun (2002), buoyancy (B) is defined as:

Subsidence in response to the diabatic cooing
286 where = 1/ and is the potential temperature, is the density, b is the buoyancy term, is a 287 stream function, = 2 / + is the local Coriolis parameter and f is the Coriolis parameter, below the strong outflow layer (Fig. 12e). These results suggest that the formation of the moat is 303 sensitive to the diabatic heating, especially the diabatic cooling beneath the eyewall anvil.

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Although the diabatic cooling caused by phase changes usually occurs in TCs, the magnitude 305 of the diabatic cooling, especially the cooling due to the sublimation of ice particles, matters much 306 in the formation of the moat (Figs. 12c and 12g). The cooling due to the sublimation process is 307 much less outside the primary eyewall in NSEF compared to that in CTL (cf. Figs. 12c and 12g).

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In NSEF, the diabatic warming released by the low-to middle-level convection outside the primary 309 eyewall exceeds the cooling, resulting in net diabatic warming (Fig. 12a). Thus, a wider eyewall 310 with warming-forced upward motion prevails due to the positive feedback among the diabatic 311 heating and the convection (Fig. 12a). In addition, the warming-forced upward motion is 312 accompanied by the deep-layer outflow (Fig. 13a), under which the low-level inflow appears 313 below the 8-km height (Fig. 13a), which brings moist air enhancing the convection in NSEF. In