Formation and Replacement Mechanism of the Concentric Eyewall of Super Typhoon Muifa (1109)

In 2009, Kuo et al. ^[1] studied the changes in typhoon intensity before and after the formation of concentric eyewall. The typhoons occurred in Northwestern Pacific from 1997 to 2006 were analyzed and the results showed that the intensity of 49% of the typhoons increased before the outer eyewall formation and decreased after the outer eyewall formation. For 22% of the typhoons, the outer eyewall reduced the growth rate of their intensity. The intensity of 4% of them decreased before the outer eyewall formation and increased after the formation. Their research indicates that the changing trend of typhoon intensity after the outer eyewall formation is debatable. Even if the generation of the concentric eyewall can be predicted accurately, predicting the future change in typhoon intensity is also difficult. At present, since the understanding of the concentric eyewall replacement process is not clear enough, it is difficult for forecasters to accurately predict the intensity change caused by the concentric eyewall replacement (Zhou and Wang ^[2]).

Moreover, Zhu and Yu ^[3] categorized concentric eyewall typhoons into Typical Eyewall Replacement Cycle (T-ERC) ones and No Eyewall Replacement Cycle (N-ERC) ones. Statistical analysis also found that the N-ERC concentric eyewall typhoons were strongly influenced by the environment, while the T-ERC concentric eyewall typhoons occurred in a relatively calm environmental field. Kossin and Sitkowski (Sitkowski et al. ^[4]; Kossin and Sitkowski ^[5]; Kossin ^[6]) analyzed 19 ERC cases with dense aircraft observations, and divided the ERC process into three stages according to typhoon intensity changes: enhancement, weakening, and re-enhancement. Some statistical results showed that the secondary eyewall formation (SEF) generally occurs in the vertical wind shear (VWS) with moderate strength (6 m s^-1) (Kossin and Sitkowski ^[7]; Yang et al. ^[8]; Zhang et al. ^[9]; Dai et al. ^[10]). Dougherty et al. ^[11] used aircraft reports, radar data, dropsonde data, and satellite microwave image data to analyze Hurricane Bonnie (1998) and found that under strong VWS (12-16 m s^-1), the SEF of Hurricane Bonnie remained, and its intensity did not weaken during the ERC.

Through an ideal experiment based on a simple numerical model, Molinari and Dudek ^[12] found that the formation of the concentric eyewall might be related to the angular momentum flux of the vortex. When there is a low trough in the upper layer, an upper trough can deliver positive eddy angular momentum to a typhoon, the delivered angular momentum flux can enhance the convection in the lower troposphere, and the enhanced convection will gradually develop into an outer eyewall in the concentric eyewall of the typhoon under favorable conditions. Nong and Emanuel ^[13] were the pioneers to conduct the test using a two-layer equilibrium model, pointing out that a concentric eyewall can always be formed when there is sufficient water vapor in the middle layer of the troposphere. Without adequate water vapor, an initial disturbance is needed to generate a concentric eyewall. A symmetrical model with full physical processes was used to simulate the typhoon concentric eyewall, and the results showed that the initial disturbance with specific amplitude was the basis of the formation of the concentric eyewall. However, the study results from Terwey and Montgomery ^[14] differed from the conclusions of Nong and Emanuel ^[13]. Terwey and Montgomery ^[14] used a complex model with full physical processes to simulate a typhoon and discovered that the concentric eyewall and its replacement process could still occur without initial disturbance.

Sun et al. ^[15] added a sensitivity test based on the successful simulation of the concentric eyewall of Typhoon Sinlaku (2008). In the sensitivity test, the cumulus convection parameterization scheme outside the typhoon was turned off. Since there was no cumulus convection scheme and the peripheral resolution was low, the simulated peripheral convection was relatively weak, preventing the formation of a concentric eyewall. Therefore, it is proposed that the peripheral environmental conditions had a significant impact on the formation of the concentric eyewall, and it was necessary to emphasize the environmental conditions outside the typhoon when forecasting the concentric eyewall. Hill and Lackmann ^[16] designed four ideal experiments to study the impact of environmental humidity on a typhoon, finding that the typhoon with high relative humidity showed the characteristics of a concentric eyewall, but they failed to further their study. By analyzing the numerical simulation results of Hurricanes Katrina (without concentric eyewall) and Rita (with concentric eyewall), and probing into dropsonde data, Ortt and Chen ^[17] found a big difference between the relative humidity of the two typhoons. The relative humidity near the top of the boundary layer for Rita was about 10% higher than that for Katrina, so the authors believed that sufficient environmental water vapor was conducive to the formation of concentric eyewall. While exploring the factors affecting the size of the outer eyewall, Zhou and Wang ^[18] found that the size of the outer eyewall was inversely proportional to typhoon intensity and the vorticity in the lower layer of the environment: the large-scale outer eyewall often appeared in the relatively weak typhoon, the small-scale outer eyewall usually appeared during the rapid reinforcement, and the large-scale outer eyewall was often found under conditions of high latitude, high relative humidity, and low environment pressure.

In many ideal tests of the stationary atmosphere, the typhoon concentric eyewall can be simulated (Terwey and Montgomery ^[19]; Zhu and Zhu ^[20]; Tyner et al. ^[21]). The balance dynamic response for diabatic heating (Shapiro and Willoughby ^[22]; Wang ^[23]; Rozoff et al. ^[24]; Menelaou et al. ^[25]; Zhu and Zhu ^[26]; Wang et al. ^[27]), or the nonequilibrium kinetic mechanism of the boundary layer (Sun et al. ^[15]; Huang et al. ^[28-29]; Wang et al. ^[30]; Wang et al. ^[31]), asymmetric stratus and rain band heating effect (Tyner et al. ^[21]; Chen ^[32]; Didlake Jr et al. ^[33-34]; Zhang and Perrie ^[35]; Wang and Tan ^[36]), the diurnal changes of solar radiation (Tang et al. ^[37]), or the typhoon initial vortex structure (Ge et al. ^[38]) are thought to have a significant impact on the SEF process. Sun et al. ^[15] believed that the contribution from the vortex Rossby wave to SEF is actually very limited.

Tyner et al. ^[21] indicated that the asymmetric stratus triggered a "top-down" process and adjusted the position and intensity of the stratus precipitation cooling by changing the falling velocity of the solid particles in the cloud, further confirming that SEF was formed through "top-down" propagation. This "top-down" way, however, did not exist independently, and triggered SEF together with the boundary layer process. Recently, the triggering effect of asymmetric stratus heating (or precipitation cooling) on the SEF was confirmed by Yu and Didlake Jr ^[39] and Wang et al. ^[27]. Cheng and Wu ^[40] conducted the stratus precipitation cooling sensitive tests with different strengths, and the results further emphasized the importance of negatively buoyant downflow.

Didlake Jr et al. ^[34] related the asymmetric stratus to the initial perturbations required for axisymmetric SEF theory. In particular, the "top-down" SEF formation mechanism proposed by previous numerical simulation was confirmed from an observational perspective (Zhang et al. ^[9]; Tyner et al. ^[21]; Fang and Zhang ^[41]; Qiu and Tan ^[42]).

It has been shown in some studies (Zhou and Wang ^[2]; Willoughby et al. ^[43]; Samsury and Zipser ^[44]; Rozoff et al. ^[45]) that after the concentric eyewall formation, the boundary layer inflow and the radial transport of water vapor into the inner eyewall would be cut off, and the inner eyewall would collapse due to the decrease of water vapor transport. Furthermore, Willoughby et al. ^[43] pointed out that the divergent downdraft generated in the upper layer could also restrain the development of convection in the inner eyewall, and finally reduce the strength of the inner eyewall. However, Rozoff et al. ^[45] held the opposite view. He pointed out the descending motion caused by the outer eyewall mainly occurs in the eye area and the moat area.

Shapiro and Willoughby ^[22] and Barnes et al. ^[46] found that in the moat region, the descending motion caused by the outer eyewall could transport the air in the middle layer with relatively low potential temperature to the inflow zone of the boundary layer, thus inhibiting the convection development in the inner eyewall. Zhou and Wang ^[2] attempted to study the physical process of the concentric wall formation and replacement through sensitivity numerical experiments. In the sensitivity test, they increased the concentration of ice particles by modifying the parameterization scheme of the microphysical process. The simulation results showed that when the concentration of ice particles increased, the radius of the outer eyewall became larger, the radius of the new eyewall after replacement was also larger, the replacement time of the concentric wall became longer, and the intensity of the typhoon varied more greatly. It was also showed that when the concentration of ice particles was larger, the content of ice particles in the descending motion would increase, and the cooling effect of ice particles after melting would be larger. This change led to a larger width of the moat region and a larger radius of the outer eyewall. When the inner eyewall disappeared, the moat area with relatively low potential temperature would become a part of the eye area, and the intensity of the typhoon would decrease. Nonetheless, the typhoon intensity would increase when the new eyewall was developed to maintain the previous warm core. The lower equivalent potential temperature in the moat region increased the variation range of the typhoon intensity. They also pointed out that the blocking effect of the outer eyewall was the main reason for the decrease of the inner eyewall strength. The larger the radius of the outer eyewall, the smaller the blocking effect of the outer eyewall. They concluded that the capability to predict typhoon intensity change caused by concentric eyewall replacement could be improved through monitoring the structural characteristics of the moat area and the outer eyewall.

Based on the Tropical Rainfall Measuring Mission (TRMM) 2A12 and 2A25 satellite data, Zhou and Wang ^[2] compared some cases in which the typhoon intensity changed significantly due to the outer eyewall formation with those in which the intensity did not change. The results showed that the typhoon intensity decreased obviously when the outer eyewall was heated by stratus, while the typhoon intensity did not decrease and was even strengthened when the outer eyewall was heated by convection. They also set up a set of sensitivity tests to further demonstrate their conclusions.

In previous research (Dai et al. ^[10]; Chen ^[32]; Cheng and Wu ^[40]; Abarca and Montgomery ^[47-48]; Chih and Wu ^[49]), there were many discussions on the formation and replacement mechanism of concentric wall. Early research (Zhu and Zhu ^{[20, 26]}; Menelaou et al. ^[25]; Wang et al. ^{[27, 31]}) on the concentric wall mostly adopted ideal models or ideal tests. It needs to be further studied whether the conclusions can be applied to real typhoons. In recent years, most studies (Dai et al. ^[10]; Chen ^[32]; Cheng and Wu ^[40]; Abarca and Montgomery ^[47-48]; Chih and Wu ^[49]) focused on the observation and numerical simulation analysis of real cases, and the conclusions might not be generally applicable.

According to the above studies, the formation of a typhoon concentric eyewall is still debatable. Whether the results can be applied to real typhoons remains to be further explored. Moreover, we are still not sure whether the secondary eyewall is developed from the upper levels (top-down) or the lower boundary layer (bottom-up). Therefore, it is important to explore the physical processes during SEF. To better understand the formation and replacement mechanism of concentric eyewall, the Weather Research and Forecast (WRF) model was used in this study to numerically simulate Super Typhoon Muifa, and the numerical simulation data with high spatio-temporal resolution was used to analyze the main formation and replacement mechanism of the outer eyewall.

In the following sections, Section 2 introduces the model and data which were used to simulate Super Typhoon Muifa. The track and intensity of Typhoon Muifa and the cycle of its concentric eyewall are simulated and verified in Section 3. In Section 4, we study the important effect of water vapor condition on concentric eyewall formation. Some analysis on the potential vorticity (PV) forcing items is also conducted. In Section 5, we analyze the replacement and impact mechanism of the inner eyewall after the outer eyewall formation from the angles of dynamics and thermodynamics. In Section 6, to obtain more general conclusions, we set up some sensitivity tests to further study the influence of water vapor conditions on the outer eyewall formation. Section 7 presents the conclusions.

Due to limited spatial and temporal observations of Super Typhoon Muifa, it is difficult to carry out a detailed analysis of the formation, development, and replacement processes of the concentric eyewall. In this study, a numerical simulation was conducted to investigate the physical characteristics of the formation and replacement of the concentric eyewall of Super Typhoon Muifa, which formed to the east of the Philippines in 2011. Hawkins ^[50] suggested that the concentric eyewalls of some typhoons were caused by topographic forcing. The eyewall replacement of Muifa occurred over the sea surface, avoiding the topographic influence.

In 2011, Typhoon Muifa (1109) formed on the east ocean surface to the Philippines at 0600 UTC on July 28, and the center was located at 11.7°N, 135.0°E. On July 30, it rapidly intensified from a tropical storm into a super typhoon. At 1800 UTC on July 30, the typhoon intensity reached its maximum. After that, the intensity of the typhoon decreased, and at 0000 UTC on August 1, the typhoon weakened into a strong typhoon. After August 4, Muifa began to move to the northwest, and weakened into a strong tropical storm. On August 8, it landed on the northern part of the west coast of Democratic People's Republic of Korea, and soon weakened into a tropical depression in the northeastern part of China.

In this study, the WRF model was used with the two-way quadruple nesting meshes. The outermost coarse grid domain (D1) was centered at (132°E, 20°N), and the centers of the second (D2) and the third (D3) coarse grid domain and the fine grid domain (D4) were the same as the center of the typhoon at 0600 UTC on July 29 and moved with the typhoon. The horizontal resolutions of D01, D02, D03, and D04 were 45 km, 15 km, 5 km, and 1.667 km, respectively, with the numbers of grid points being 110 × 100, 103 × 97, 184 × 169, and 298 × 298, respectively. They were simulated from 0600 UTC on July 29 to 1600 UTC on August 4. As pointed out by Emanuel ^[51] and Yang et al. ^[65], the surface heat flux is the main source of energy for typhoons. The "ventilation flow" that occurs in the upper troposphere (about 15-18 km) determines the intensity of the typhoon secondary circulation. According to Kimball and Dougherty ^[52], a simulated typhoon will be more realistic if the vertical resolution is finer. Therefore, the nonuniform grid was used with 50 layers in the vertical direction, and there were finer resolutions in the boundary layer and the tropopause. The top pressure of the model was 50 hPa. Molinari and Dudek ^[12] pointed out that when the horizontal resolution is smaller than 5 km, the grid can resolve the cumulus convection. Thus, the Tiedtke cumulus parameterization scheme (Kain and Fritsch ^[53]) was applied for D01 and D02, while the scheme was turned off for D03 and D04. The other physical process parameterization schemes for all domains were the same, with WSM6 (Hong et al. ^[54]) being the microphysical scheme, RRTM (Mlawer et al. ^[55]) being the long wave radiation scheme, Dudhia ^[56] being the short wave radiation scheme and YSU (Hong et al. ^[54]) being the scheme for the boundary layer.

The initial field and lateral boundaries of the numerical model were derived from the Final Operational Global Analysis (FNL) data of the National Centers for Environmental Prediction (NCEP) with a time interval of six hours and a horizontal resolution of 0.5° × 0.5°. The observed typhoon track and intensity were extracted from the tropical cyclone best track dataset of the Shanghai Typhoon Institute of China Meteorological Administration (Ying et al. ^[57]), which were compared with the simulation results to verify the simulation of the model. The observed precipitation rates were taken from the TRMM 2A12 dataset (http://trmm.gsfc.nasa.gov/publications_dir/multi_resource_tropical.html).

To verify the reliability of the model results, the typhoon track and intensity and the cycle of the concentric eyewall simulated by the model were analyzed. Then the high-resolution numerical simulation results were used to analyze the characters of the concentric eyewall during its formation and replacement processes.

Figure 1 shows the simulated and real tracks of Typhoon Muifa from 0600 UTC on July 29 to 1200 UTC on August 4. Here, the shading denotes the sea surface temperature (SST) at the initial time, which kept constant throughout the entire integration process.

Figure 1.  Simulated and real typhoon tracks from 0600 UTC on July 29 to 1200 UTC on August 4, with the time interval being 6 hours. ● denotes the simulated track, Δ represents the real track, and the shading stands for the SST (units: K).

It can be seen that Typhoon Muifa was initially in the region of higher SST, where there were sufficient water vapors for its development. After Muifa passed through the cold tongue from 20°N-30°N, 130°E-140°E, the simulated track kept going north, which was essentially the same as the observed track. From 1200 UTC on August 1, the typhoon intensity began to reduce, perhaps because Muifa moved to the region with lower SST. At 1800 UTC on August 2, the typhoon turned from the north to the west, and then moved westward, which was essentially the same as the observed track. In general, this model well simulated the typhoon track from 0600 UTC on July 29 to 1200 UTC on August 4, indicating that the model accurately simulated the large-scale weather pattern by which the typhoon track was dominated (Goerss ^[58]). This result provided a more realistic large-scale environmental field for further discussion on the intensity and structural characteristics of the typhoon.

Figure 2 shows the change of 10 m maximal wind speed (MWS) provided by the Shanghai Typhoon Institute of China Meteorological Administration and the simulated MWS with time.

Figure 2.  (a) Changes in the simulated and observed 10 m MWS (units: m s^-1) with time and (b) changes in the simulated MWS radius (units: km) with time.

As shown in Fig. 2, from 1800 UTC on July 29 to 1800 UTC on July 30, the rapidly increasing trend of the simulated MWS from 30 m s^-1 up to 50 m s^-1 was close to that of the observed MWS from 30 m s^-1 to 65 m s^-1. The observed MWS roughly decreased by 15 m s^-1 in the next 72 hours, and stayed at around 50 m s^-1 from 0600 UTC on August 1 to 0600 UTC on August 3. The simulated typhoon intensity continued to increase after 1800 UTC on July 30, and the MWS reached 57 m s^-1 at 1200 UTC on July 31. Within 18 hours after 0600 UTC on August 3, the observed MWS decreased again with a reduction of about 9 m s^-1. The MWS simulated from 0000 UTC on August 3 to 1800 UTC on August 3 increased slightly. The MWS increased significantly after 1800 UTC on August 3, while the observed intensity at this stage was maintained at around 45 m s^-1. It can be seen from Fig. 1 that after 1800 UTC on August 3, the typhoon center began to enter the region with SST greater than 302 K. Wu and Duan ^[59] used the WRF model to study the effects of the SST with different time resolutions on Typhoon Muifa. The results indicated that the SST with different time resolutions had a great influence on the simulated intensity of Typhoon Muifa. As shown in Fig. 2b, from 0800 UTC on July 30 to 1800 UTC on August 3, the MWS radius was maintained at around 50 km, while from 1800 UTC on August 3, the MWS radius increased to about 90 km.

The concentric eyewall appeared again after the first concentric eyewall replacement was completed. Starting from 0000 UTC on August 3, the secondary radar reflectivity maximum began to appear within the radius of 140 km to 160 km. As the tangential wind extended obviously outward, the secondary wind maximum obviously appeared, indicating that the outer eyewall was formed within a radius of 140 km to 160 km. At this time, the echo intensity of the outer eyewall was slightly smaller than that of the inner eyewall. The echo intensity of the moat region was significantly weaker than that at the first time, and the width was significantly larger than that of the moat region at the first time. At 1200 UTC on August 3, the echo of the inner eyewall was slightly enhanced, and the echo of the outer eyewall was also enhanced and inwardly contracted. Afterwards, the echo intensity of the inner eyewall continued to increase slightly for 12 hours before being weakened and contracting slightly inward, while the echo of the outer eyewall continued to increase and contract inward. According to the real-time ground precipitation rate (in Fig. 3a2 and 3b2), the inner eyewall was replaced by the outer eyewall at 1300 UTC on August 3, and the simulated inner wall was still clearly visible. At 1200 UTC on August 4, the simulated inner eyewall almost disappeared (in Fig. 3b3), the outer eyewall replaced the inner eyewall, and the real-time ground precipitation rate (in Fig. 3a3) implied that the third concentric eyewall of the typhoon had been formed at this time. The radius, width, and intensity of the new eyewall formed by the second replacement were obviously larger than those by the first replacement.

Figure 3.  The TRMM 2A12 surface precipitation rate (left column) (the units of the color bar are mm h^-1) and the simulated radar reflectivity at z=500 m (right column) (the units of the color bar are dBZ), at 1300 UTC on August 1(top row), 1300 UTC on August 3 (middle row), and 1200 UTC on August 4 (bottom row).

In summary, the main changes in the typhoon intensity were successfully simulated, thus providing reliable high-resolution simulation results for the follow-up analysis.

There is no formal unified standard for the definition of SEF (Kossin and Sitkowski ^[7]; Dougherty et al. ^[11]), and different studies adopted different standards to determine the formation of the external eyewall. For example, Dougherty et al. ^[11] said that the secondary eyewall formed when the secondary maximum of the azimuthal mean tangential wind existed outside the inner eyewall; Miyamoto et al. ^[60] thought that the concentric eyewall rose when the maximum of the outer eyewall wind speed exceeded the maximum of the inner eyewall wind speed. The definition of the concentric eyewall adopted in this study was based on one given by Willoughby et al. ^[43]. Around an eyewall, there is a strong precipitation ring accompanied by the secondary wind maximum. Such inner and outer convection rings are called as the concentric eyewall of typhoons. The following section describes characteristics during the formation and replacement processes of the concentric eyewall.

Figure 4 shows the evolution of the radial radar reflectivity and tangential wind speed with time at the height of 3 km during the simulation. It can be seen from the figure that before July 30, the vertical convection was weak and the radar echo was scattered. After that, the convection began to be organized, forming an obvious eyewall and spiral rain bands. The eyewall with strong radar reflectivity was gradually strengthened and contracted. At 0000 UTC on July 31, the eyewall was retracted to a radius of about 40 to 60 kilometers, the corresponding tangential wind speed slowly increased, and gradually expanded outward. At 0000 UTC on August 1, within a radius of about 100 kilometers to 120 kilometers, the radar reflectivity began to form a secondary maximum, the tangential wind expanded obviously outward, the range of the secondary wind speed maximum gradually expanded, and the first concentric eyewall was formed. The secondary wind speed maximum was not obvious enough because the distance between the two eyewalls was too small. There was a weak echo between the two eyewalls, which was the moat area. At this time, the echo intensity of the outer eyewall was significantly smaller than that of the inner eyewall. After that, the echo of the inner eyewall gradually weakened, with the corresponding typhoon intensity decreasing as well. The outer eyewall gradually shrank inward, and the corresponding echo intensity first increased slightly and then decreased slightly, but the wind speed increases slowly. The moat area gradually became narrower. At 0000 UTC on August 3, the inner eyewall with strong echoes was nearly disappearing, the outer eyewall replaced the inner eyewall, and its radius was about 50 to 70 km. The entire process from the formation of the concentric eyewall to the replacement of the concentric eyewall lasted for 48 hours.

Figure 4.  The averaged radial radar reflectivity at z=3 km (represented by the shading, units: dBZ) as well as the averaged tangential wind speeds at z=3 km (represented by the contours, units: m s^-1) simulated along the azimuth with time.

It can be seen from Fig. 5 that before July 30, due to the weak intensity, the vertical motion in the typhoon was not obvious. After July 30, with the organization of the convection, there was a significantly strong ascending motion in the eyewall. From July 30 to August 1, the strong ascending motion was primarily concentrated in the inner side of the region. Starting from around August 1, the secondary ascending motion maximum began to appear within a radius of 70 km to 100 km in the outer rain band. There was a descending motion between the two strong ascending motions. The features of the vertical motion illustrated the characters of the first outer eyewall. After 1200 UTC on August 1, the ascending motion of the inner eyewall decreased significantly and the corresponding typhoon intensity decreased. The area with the strong ascending motion of the outer eyewall gradually moved toward the typhoon eye and its intensity had a slight decrease after a slight increase for two days. As the outer eyewall contracted, the area with the weak descending motion was gradually reduced. At 0000 UTC on August 3, the strong ascending motion of the inner eyewall disappeared, the outer eyewall gradually contracted, and the outer eyewall replaced the inner eyewall.

Figure 5.  The average radial vertical velocity at z=1 km (units: m s^-1) simulated along the azimuth with time.

At around 0000 UTC on August 3, the secondary hydrometeors maximum began to appear within a radius of 140 km to 160 km. There was a strong ascending motion on the inner side. This further explains the fact that the concentric eyewall appeared again after the first replacement of the concentric eyewall. Within the following 24 hours, the strong ascending motion of the inner eyewall was slightly enhanced, while the outer eyewall significantly developed and contracted. At 0000 UTC on August 4, the strong ascending motion of the inner eyewall began to weaken and the outer eyewall continued to develop. At 1200 UTC on August 4, the simulated inner eyewall almost disappeared and the outer eyewall replaced the inner eyewall.

The PV can show the total effect of the thermal and dynamic processes. Wen ^[61] believed that the significant increase of PV in the outer rainband showed the formation of typhoon outer eyewall. Then we will explain the main mechanism of the formation of typhoon outer eyewall by discussing the abnormal local vorticity.

The PV tendency equation is the same as that given by Judt and Chen ^[62], and is averaged along the azimuth. The equation is as follows:

where P indicates a PV, ∇_h is a horizontal gradient operator, V is a horizontal wind vector, w is a vertical velocity, and the overbar and the prime indicates the average and disturbance variable, respectively. ∇₃ is a three-dimensional gradient operator. Q shows the diabatic heating, and ζa is absolute vorticity. The left-hand side of the equation indicates the local variation term of the azimuth average PV. The PV forcing terms are on right-hand side of the equation. The first term of the right-hand side is the averaged PV horizontal flux term; the second term is the azimuth averaged PV vertical flux term; the third term is the disturbance PV horizontal flux term; the fourth term is the perturbed PV vertical flux one, and the fifth term is the diabatic heating term or the latent heat term. The diabatic heating during the typhoon development mainly comes from the latent heat release of water vapor condensation. The friction dissipative term is small and thus ignored (Wang ^[63]). Compared with the outer rainband of the typhoon, in the core region, the vertical mass transport is larger, and the PV and its growth rate are also larger. Therefore, the core region and the rainband region will be discussed respectively as two parts below.

Figure 6 shows the radial distribution of the PV and its forcing items before, during, and after the first and secondary outer eyewall formation at 0000 UTC on August 1. From the figure we can see that before the first outer eyewall formation at the height of 1 km, the PV in the radius range of 60 to 120 km gradually decreased from 4 PVU to 2 PVU, and in the outer rainband with a radius greater than 120 km, the PV is about 2 PVU. And those PV forcing are very small in the area with a radius greater than 60 km of outer rainband.

Figure 6.  Radial distribution of latent heat (a1, b1), averaged PV horizontal flux (a2, b2), azimuth averaged PV vertical flux (a3, b3), perturbed PV horizontal flux (a4, b4), perturbed PV vertical flux (a5, b5), and the PV (units: PVU) (a6, b6) in the rainband at the height of 1 km in the first outer eyewall formation (left column) and the secondary outer eyewall formation (right column), respectively. In the left column the black curve represents the average value from 0000 UTC to 0600 UTC on July 31, the green curve represents the average value from 0000 UTC to 0600 UTC on August 1, and the purple curve represents the average value from 0000 UTC to 0600 UTC on August 2. In the right column the black curve represents the average value from 0000 UTC to 0600 UTC on August 2, the green curve represents the average value from 0000 UTC to 0600 UTC on August 3, the orange curve represents the average value from 1800 UTC on August 3 to 0000 UTC on August 4, and the purple curve indicates the average value from 0600 UTC to 1200 UTC on August 4.

When the first outer eyewall began to form at 0000 UTC on August 1, the PV in the outer rainband increased, in particularly, in the radius from 60 to 100 km. The PV maximum with about 6 PVU appeared at the radius of about 70 km. In the area where the PV was enhanced, the condensation latent heat in the PV tendency equation had positive values, and its maximum was above 3 PVU. It indicated that amounts of condensation latent heat release made the PV increase. The averaged PV horizontal flux was positive, and its maximum was about 1 PVU, namely, the PV flux was convergent. Given the distribution characteristics of the horizontal wind field, it was mainly caused by the PV inward transport in the lower layer of the outer rainband. The azimuth averaged PV vertical flux was negative, and the absolute maximum was 1.5 PVU, suggesting the PV flux was divergent. Combined with the distribution characteristics of the vertical motion, it was mainly caused by the ascending motion transporting the low-level PV to the upper level and resulting in the decrease of the low-level PV. The perturbed PV horizontal flux was still small. The perturbed PV vertical flux was negative, and the absolute maximum was about 0.5 PVU. Generally speaking, if the net PV forcing was positive, the PV was enhanced. Comparison of PV forcing with each other shows that the PV enhancement in the radius of 60 to 100 km was mainly from the condensation latent heat release, and secondly from the PV transport of the horizontal basic flow.

After the first outer eyewall formation, the PV inside the outer eyewall further increased with the enhancement of the outer eyewall intensity, and the location of the PV maximum moved toward the typhoon center with the contraction of the outer eyewall. With the increase of the outer eyewall intensity, the condensation latent heat in the outer eyewall was further enhanced and the horizontal PV flux of the outer eyewall was further convergent. There was obvious divergence of the PV flux inside the outer eyewall. It could be seen that with the enhancement of the outer eyewall intensity and the convergence of the PV flux, the airflow inside the outer eyewall transported the PV from the inside of the outer eyewall to the outer eyewall. The transport would reduce the PV inside the outer eyewall. The divergence of the PV vertical flux in the outer eyewall had no obvious change, but there was obvious convergence of the PV flux inside the outer eyewall. Combined with the distribution characteristics of the vertical wind field, this was mainly caused by the descending motion inside the outer eyewall. It transported the PV from the middle layer to the lower layer. The disturbance PV horizontal flux was still small, while the perturbed PV vertical flux increased obviously. It indicated that the effect of wave disturbance on the PV transport increased with the enhancement of the outer eyewall intensity.

Similarly, before the secondary outer eyewall formation, in the outer rainband with the radius of more than 90 km, the PV mainly ranged from 3 to 4 PVU, and the other forcing was very small. When the outer eyewall began to form, the PV maximum appeared in the area with radius of 90 to 130 km, and was about 5 PVU. There was condensation latent heat release in the region where the PV maximum appeared, the averaged PV horizontal flux had weak convergence, and other forcing still kept small. The net PV budget was positive, so the PV was enhanced. Comparison of the forcings with each other shows that the PV enhancement mainly came from the condensation latent heat release, and secondly from the PV transport of the horizontal base flow. After that, with the contraction and development of the outer eyewall, the location of the increasing PV maximum inside the outer eyewall moved toward the typhoon center. The change of each forcing was the same as that after the first outer eyewall formation.

It can be seen that the condensation latent heat release contributed most to the PV enhancement in the outer rainband, followed by the PV transport of the horizontal basic flow. During the first outer eyewall formation, the effect of the condensation latent heat release was less than that of the second time, so the PV intensity of the first outer eyewall was less than that of the second.

Further analyzing each PV forcing in the rainband at an altitude of 8 km (Fig. 7), we find that the PV in the rainband increased during both the first and second outer eyewall formation. And the PV enhancement in this region was mainly from the condensation latent heat release, followed by the PV transport of the horizontal base flow.

Figure 7.  The same as Fig. 6 but at the height of 8 km.

Through all the above analysis we conclude that the PV enhancement in the rainband mainly comes from the condensation latent heat release. The effect of the condensation latent heat release during the first outer eyewall formation is less than that during the second one, so the intensity of the first is less than that of the second. It shows that the condensation latent heat release is the main reason for the outer eyewall formation.

The contraction phenomenon often occurs after the outer eyewall formation. With the contraction of the outer eyewall, the typhoon intensity characterized by the inner eyewall decreases gradually. When the inner eyewall disappears, the concentric eyewall replacement will be completed. The replacement time of the concentric eyewall lasts for a few hours to more than a day. Next, we will discuss how the inner eyewall changes after the outer eyewall formation. We focus on the change of dynamic structure, thermal structure, and sea surface heat flux.

The inertial stability refers to the measure of whether the air mass can return to the original equilibrium position when it leaves the initial position.

The inertial stability I is obtained as follows,

here f₀ is the Coriolis parameter of the typhoon center, V_t is the tangential wind speed, and r is the distance from typhoon center.

Figure 8 shows the change of the inertia stability before and after the outer eyewall formation. As the figure shows, before the formation, the eyewall located in the strong inertial stability area, and the inertial stability outside the eyewall was relatively weaker. After the outer eyewall was formed, the inertial stability outside the eyewall augmented, especially in the lower troposphere. This indicates that the convergence maximum in the lower troposphere gradually moved from the inner eyewall to the outer eyewall. With the outward movement of the convergence maximum, the water vapor which was horizontally transported to the inner eyewall decreased, while the water vapor which was transported to the outer eyewall increased. The condensation latent heat which the rising water vapor rreleased further enhanced the convergence in the lower layer of the outer eyewall. Therefore, we conclude that the outer eyewall formation will change the dynamic characteristics of the typhoon, and it is one of the reasons for the decrease of the inner eyewall intensity.

Figure 8.  Vertical profile of the inertial stability along the radius at 0600 UTC on July 31 (top left panel), 1200 UTC on August 1 (top right panel), 0400 UTC on August 3 (bottom left panel), and 0000 UTC on August 4 (bottom right panel).

As Fig. 9 shows, with the formation and development of the secondary outer eyewall, there is an obvious airflow outside the inner eyewall in the upper layer of the moat area. Seen from the overall flow, the airflow inwards mainly came from the divergent airflow in the upper layer of the outer eyewall. This divergent airflow corresponded to the weak descending motion, and they both increased with the increase of the outer eyewall intensity. This would restrain the development of the inner eyewall. Therefore, the weakening of the secondary inner eyewall intensity was associated with the descending motion caused by the divergent airflow in the upper layer of the outer eyewall. This conclusion is the same as that of Willoughby et al. ^[43]. However, according to the characteristics of the vertical movement and radial wind in the formation and replacement process of the first outer eyewall, the divergent airflow in the upper layer of the outer eyewall was not obvious. This could be attributed to the small radius and weak intensity of the first outer eyewall. Therefore, only when the moat area is wide and the intensity of the outer eyewall is large, the weakening effect of the divergent descending motion in the upper layer of the outer eyewall on the inner eyewall intensity is relatively obvious.

Figure 9.  Cross-section of the radial wind speed (represented with shadow, units: m s^-1) and vertical velocity (represented with isoline, units: m s^-1) along the radius at 0500 UTC on August 1 (top left panel), 2200 UTC on August 1 (top middle panel), 1400 UTC on August 2 (top right panel), 1300 UTC on August 3 (bottom left panel), 2200 UTC on August 3 (bottom middle panel), and 0900 UTC on August 4 (bottom right panel).

As shown in Fig. 10, after the first outer eyewall formation, the potential temperature increased in the moat area and the outer eyewall outside the inner eyewall. The increase of the potential temperature in the outer eyewall area was mainly due to the amounts of condensation latent heat (Fig. 11). The increase of the potential temperature in the moat area mainly attributed to the warming effect of the descending motion of dry air. Similarly, after the secondary outer eyewall formation, the potential temperature in the moat area and the outer eyewall outside the inner eyewall also increased. Also, the warming effect of dry air descending motion and the condensation latent heat contributed most to the potential temperature increase in the two areas respectively. According to the hydrostatic adjustment theory proposed by Wang ^[64], the condensation latent heat can reduce the pressure of the air column, and the decrease of the surface air pressure will reduce the pressure gradient at the radius of the MWS. As shown in Fig. 12, the pressure gradient of the inner eyewall decreased during the first concentric eyewall replacement and at the later stage of the secondary replacement. The decrease of the pressure gradient at the inner eyewall would reduce the wind speed maximum, so the intensity of the inner eyewall characterized by the wind speed maximum decreased. In the early stage of the secondary concentric eyewall replacement, although the potential temperature increased outside the inner eyewall, the intensity of the inner eyewall was still increasing. There were some other factors to enhance the intensity of the inner eyewall, which will be discussed later.

Figure 10.  Cross-section of the simulated azimuth average potential temperature difference in each period (units: K) along the radius.

Figure 11.  Cross-section of the simulated azimuth average condensation latent heat rate (units: K h^-1) along the radius.

Figure 12.  Simulated azimuth average radial sea surface pressure gradient (units: hPa km^-1h^-1) with time.

As shown in Fig. 13, the differences between the sea surface heat flux at 1000 UTC on August 1 and one at 0000 UTC on August 1 were almost all negative within the radius of the inner eyewall. It indicated that after the first outer eyewall formation, the sea surface heat flux in the inner eyewall decreased. Therefore, during the first concentric eyewall replacement, the weakening of the inner eyewall intensity was related to the decrease of sea surface heat flux. The differences between the sea surface heat flux at 1000 UTC on August 3 and one at 0000 UTC on August 3 were mainly positive in the inner eyewall, and the larger value was mainly concentrated on the west side of the typhoon center. It indicated that after the secondary outer eyewall formation, the sea surface heat flux in the inner eyewall increased. Thus, during the early stage of the secondary concentric eyewall replacement process, the enhancement of the inner eyewall intensity was related to the increase of sea surface heat flux.

Figure 13.  The difference between the sea surface heat flux (units: W m^-2) at 1000 UTC on August 1 and one at 0000 UTC on August 1 (left panel), one at 1000 UTC on August 3 and one at 0000 UTC on August 3 (right panel).

The change of sea surface heat flux was closely related to that of the sea surface temperature. As the figure shows, after the secondary outer eyewall formation, the typhoon center gradually moved to the area with high sea surface temperature. The higher sea surface temperature would provide a warmer surface and amounts of water vapor for the typhoon, so the eyewall would be strengthened for some time during the early stage of the secondary outer eyewall replacement. It should be noted that in the later stage of the secondary concentric eyewall replacement, the intensity of the inner eyewall did not continue to increase but decreased, indicating that the increase of sea surface heat flux in the concentric eyewall replacement process may prolong the concentric replacement time.

In the literatures (Zhang et al. ^[9]; Tyner et al. ^[21]; Cheng and Wu ^[40]; Chih and Wu ^[49]; Yang et al. ^[65]), through a large number of observations and numerical experiments, it has been verified that the amount of large-scale water vapor transport has a great influence on typhoon intensity and structure. Sun et al. ^[15] pointed out that the external environment, including water vapor conditions, had a significant influence on the formation of typhoon concentric wall, and more attentions were paid to the external environmental conditions when predicting typhoon concentric wall. Ortt and Chen ^[17] found that sufficient environmental water vapor was beneficial to the formation of concentric eyewall through the diagnostic analysis of two typhoon cases. Zhou and Wang ^[18] found that the radius of the outer eyewall was closely related to the environmental relative humidity. The research results of Emanuel ^[66] and Holland ^[67] showed that the change of typhoon intensity was positively correlated with the environmental humidity. Hu et al. ^[68], Guan ^[69] and Yuan ^[70] analyzed the large-scale water vapor transport of a specific typhoon with rapidly weakening and strengthening progress. They found that when the typhoon strengthened rapidly, the water vapor flux around the typhoon suddenly increased, and vice versa. The research on hurricane named "Frances and Jeanne (2004)" by Matyas and Cartaya ^[71] showed that the convection in the rainband around the typhoon determined the distribution of the typhoon precipitation, and the convective level was related to the environmental humidity. In the following part, we will conduct a sensitivity test to further explain the influence of water vapor on the formation of the concentric eyewall.

We carried out numerical experiments utilizing WRF model. The setup of the experiment was as follows:

(1) Control experiment: no change was made to the environmental water vapor of the typhoon, which was the same as that in the numerical simulation test given in Section 2.2.

(2) Sensitivity test: we reduced 30% of the sea surface water vapor flux in the whole integral process and 30% relative humidity except for the D02 domain in the initial field (Fig. 14). Other parameters were consistent with the control experiment. Reducing the sea surface water vapor flux was purposed to further reduce the amount of water vapor transported from the ocean to the air. Many studies (Cheng and Wu ^[40]; Chih and Wu ^[49]) showed that the formation of the outer eyewall was closely related to typhoon intensity. Thus, to make the simulated typhoon develop rapidly and reduce the influence of the typhoon intensity on the formation of the concentric eyewall, we did not reduce the relative humidity of the D02 domain in the initial field.

Figure 14.  Initial relative humidity distribution in the control test (left panel) and the sensitive test (right panel) at the height of 850 hPa.

As shown in Fig. 15, in the sensitivity test, starting from 1800 UTC on August 2, the isotach expanded outwards obviously, and the secondary ascending motion maximum began to appear in the rainband region within a radius of 80 to 100 km, as well as the secondary PV maximum. It indicated that the outer eyewall began to form in the radius of 80 km to 100 km. In the control test, the outer eyewall began to form at 0000 UTC on August 1, 42 hours earlier than that in the sensitivity test. Comparing the typhoon intensity simulated in the control test with that in the sensitivity test (Fig. 16), we found there was little difference for the typhoon intensity simulated by the two tests at 0000 UTC on August 1. Therefore, compared with the typhoon intensity, the decrease of water vapor had a greater influence on the typhoon structure, especially on the formation of the concentric eyewall.

Figure 15.  Azimuth average radial distribution of the horizontal wind speed (units: m s^-1) (left panel), vertical velocity (units: m s^-1) (middle panel), and PV (units: PVU) (right panel) with time at z=1 km.

Figure 16.  The wind speed maximum (upper panel, units: m s^-1) and maximal wind speed radius (lower panel, units: km) simulated by the control test (CNTL) and the sensitivity test (RR30) with time.

Figure 16 shows the change of the wind speed maximum and its radius with time in the control test and sensitivity test. Comparison of the two groups of experiments shows that before 0600 UTC on July 30, the typhoon intensity simulated by the sensitivity test was greater than that by the control test. From 0600 UTC on July 30 to 0000 UTC on August 2, the typhoon intensity simulated by the sensitivity test was less than that by the control test. From 0000 UTC on August 2 to 0000 UTC on August 3, the wind speed maximums simulated by the control test and sensitivity test decreased with time, but the decrease in the control test was greater than that in the sensitivity test. Before 0000 UTC on August 3, the variation trend of the wind speed maximum simulated by the two groups was the same. After 0000 UTC on August 3, the wind speed maximum simulated by the control test increased with time, while in the sensitivity test, it continued to decrease. Before 1800 UTC on August 3, the maximal wind speed radius simulated by the two groups and its variation trend with time were similar. But from 1800 UTC on August 3, the maximal wind speed radius simulated by the two groups changed abruptly. The maximal wind speed radius simulated by the control test was larger than that by the sensitivity test. Generally speaking, the different typhoon structure simulated by the two groups of experiments was the main reason for the difference of typhoon intensity between the two groups.

In this subsection, the characteristics of typhoon water vapor content in the early stage of the concentric eyewall formation in the two groups of experiments are analyzed. Fig. 17 shows the cross section of the 12-hour average water vapor mixing ratio. It can be seen that the water vapor content in the boundary layer had greater value before the outer eyewall formation both in the control test and the sensitivity test. And the water vapor content in the the boundary layer of the outer rainband was higher than 18g kg^-1. Comparing the 12-hour average water vapor content between the two groups from 1300 UTC on July 31 to 0000 UTC on August 1, we found that the water vapor content in the sensitivity test was less than that in the control test, especially in the boundary layer of the outer rainband. This further showed that the difference in water vapor conditions had a great influence on the outer eyewall formation.

Figure 17.  Cross section of 12-hour average water-vapor mixing ratio (units: g kg^-1) along the radius in the control test (top row) and in the RR30 (bottom row).

Therefore, the environmental water vapor condition has a great influence on the structure of the typhoon, especially on the concentric eyewall of the typhoon. When the water vapor is sufficient, the condensation latent heat is conducive to the formation of the outer eyewall, and the outer eyewall further affects the intensity of the typhoon.

In this paper, the WRF model was employed to conduct the numerical simulation for the Super Typhoon Muifa (1109). Combining observational data with the sensitivity test, we studied the main formation mechanism of the typhoon concentric eyewall structure and how the intensity of the inner eyewall is affected. A sensitivity test was employed to further prove our conclusions. The main conclusions are as follows:

(1) Utilizing the PV tendency equation, we analyze the reasons for the elevated PV increase in the outer rainband. Based on the analysis, we explain the main mechanism of the outer eyewall formation. Analyzing the PV forcings during the outer eyewall formation, we found that the elevated PV increase in the rainband mainly comes from the condensation latent heat, and its effect during the first outer eyewall formation is less than that of the second, so the intensity of the first outer eyewall is less than that of the second. It shows that the condensation latent heat is the main reason for the outer eyewall formation. In the typhoon vortex system, the sufficient water vapor condition is beneficial to the outer eyewall formation, which is consistent with the conclusion of Hill and Lackmann ^[16] in the ideal experiment, and when the environmental water vapor content is higher, the intensity of the outer eyewall will be larger.

(2) When the typhoon outer eyewall is formed, the increase of the inertial stability in the outer eyewall is one of the reasons for the decrease of the inner eyewall intensity. With the increase of the inertial stability in the outer eyewall, the convergence maximum moves from the inner eyewall to the outer eyewall gradually. With the outward movement of the convergence maximum, the horizontal transport of water vapor to the inner eyewall will decrease, while the water vapor transported to the outer eyewall increases, and the condensation latent heat further enhances the convergence of the lower layer in the outer eyewall, which is consistent with the conclusion of Wang et al. ^[27]. The weakening of the inner eyewall intensity is related to the descending motion caused by the divergent airflow in the upper layer of the outer eyewall. When the intensity of the outer eyewall is large, the divergent descending motion in the upper layer of the outer eyewall weakens the intensity of the inner eyewall more greatly. After the outer eyewall formation, the change of the thermal structure outside the inner eyewall is one of the reasons for the weakening of the inner eyewall intensity. When the outer eyewall is formed, the potential temperature outside the inner eyewall increases. And the increase of the potential temperature in the outer eyewall is mainly caused by the condensation latent heat and the warming effect of the dry air descending motion in the moat area. The surface air pressure decrease in the heated area will reduce the pressure gradient at the radius of the surface wind speed maximum, then reduce the pressure gradient in the lower layer of the inner eyewall, and finally reduce the wind speed maximum which denotes the inner eyewall intensity.

(3) We find that the increase of the sea surface heat flux can prolong the time of the concentric replacement. In the early stage of the secondary concentric eyewall replacement process, the sea surface heat flux in the inner eyewall increases, which can provide sufficient heat and water vapor for the inner eyewall. Therefore, the inner eyewall does not die out rapidly in the secondary concentric eyewall replacement process. However, it begins to weaken after a certain period of enhancement.

(4) Using the environmental water vapor as the control factor, we reduce the water vapor content in the control test to take the sensitivity test. Comparing the simulation results of the two groups of experiments, we find that the water vapor condition plays an important role in the outer eyewall formation, which is consistent with the conclusion of Ortt and Chen ^[17].