To investigate the topographic effect on heavy rainfall in Ulsan, the results of the CTL and TOPO experiments were compared. Even though the simulated typhoon track and rainfall distribution did not match the JTWC best track and the observations, the topographic effect appeared in the comparison of the CTL and TOPO simulations (Fig. 7a, b). The horizontal wind at 850 hPa decelerated over Ulsan in both CTL and TOPO due to orographic form drag. This deceleration led to low-level convergence and convection on the east of the mountain range. However, the low-level wind in TOPO was less decreased than that in CTL; therefore, the torrential precipitation on the mountain slopes (within the black dashed line box where the difference in hourly rainfall between CTL and TOPO is large in Fig. 7a, b) was slightly reduced in TOPO. In the zonal vertical cross section of the purple dashed line in Fig. 7a and b, which shows the maximum difference in the precipitation between CTL and TOPO, an upward motion appeared on the windward slope from the surface to the upper level in CTL (Fig. 7c); a downward motion was also evident on the leeward side. Additionally, the stream of water vapor over the windward side in CTL was disconnected because the orographically induced enhancement of rainfall and convection led to the consumption of water vapor (Fig. 7c, d). However, the horizontal wind in TOPO passed smoothly, and no vertical motion appeared (Fig. 7d).

Fig. 7
figure 7

Hourly rainfall (mm h−1, shading) and 850 hPa horizontal wind (m s−1, wind barbs) in a CTL and b TOPO, and vertical distribution of mixing ratio (g kg−1, shading), U-wind (m s−1, vector), and vertical velocity (m s−1, contour with 2 m s−1 interval) in c CTL and d TOPO at 2310 UTC on October 4. c, d show the zonal vertical cross section of the maximum precipitation difference point (purple dashed line in a, b) between CTL and TOPO. The black contour lines in a, b show the height difference (m, contour with 60 m interval) between CTL and TOPO, the blue lines in c, d present the pressure levels (hPa, contour), and the black dashed and solid lines in c, d indicate the downward (≤ − 2 m s−1) and upward (≥ 4 m s−1) direction of vertical velocity, respectively

The enhanced convection on the windward slope transported more water vapor upward, and this could be shown as vertical moisture flux. The orographically induced vertical moisture flux could be expressed by multiplying the water vapor mixing ratio and orographic updraft, which was written as an inner product of the horizontal wind and gradient of terrain heights (Lin et al. 2001). Figure 8 shows the orographically induced vertical moisture flux in CTL and TOPO. Similar to Witcraft et al (2005), the orographically induced vertical moisture flux was calculated at (eta =0.955) in the WRF simulations. In CTL, upward vertical moisture flux was dominant on the windward slope; downward vertical moisture flux appeared on the leeside. However, no significant signals were captured in TOPO. This means that the mountainous topography around Ulsan increased orographically induced vertical moisture flux on the windward side, which contributed to enhanced precipitation. Through TOPO, therefore, it was confirmed that the typhoon-induced heavy rainfall was possible because of Ulsan’s unique orography effect.

Fig. 8
figure 8

Orographically induced vertical moisture flux (g kg−1 m s−1, shading) of a CTL and b TOPO at (eta = 0.955), computed from the adjacent eta level. The black contour lines indicate the height difference (m, contour with 60 m interval) between CTL and TOPO

Effect of SST on Typhoon Chaba

Numerous researchers have established the correlation between SST and typhoon intensity, whereby a warmer SST contributes to maintaining typhoon intensity during the transition to the mid-latitudes. When typhoons maintain their intensity due to warmer SSTs, the possibility of stronger typhoons making landfall can increase (Park et al. 2011). Typhoon Chaba (2016) can be an example of typhoons that experienced an increase in intensity due to a warmer SST. The typhoon passed over the positive SST anomaly in the East China Sea from 1200 to 1800 UTC on October 4 (Fig. 3b). This positive SST anomaly hindered the weakening of the typhoon, as seen in the JTWC best track data (Fig. 4b, c). To examine the effect of the warm SST anomaly in the East China Sea, we compared the results between CTL and CSST. Figure 9 shows the time series of the SST, surface latent heat flux (SLHF), and water vapor at 2 m above the surface in D02 averaged within a radius of 150 km from the typhoon center. Until 1200 UTC on October 3, both the SST and SLHF were approximately the same. However, after 1200 UTC, the typhoon in CSST passed over the East China Sea, and the SST continued to decrease until the typhoon made landfall. However, in CTL, the SST slowly decreased and remained at 26 °C from 0600 to 1200 UTC on October 4 (Fig. 9a). Moreover, the intensity of the simulated typhoon in CTL marginally increased with the SST trend when it passed through the warmer SST in the East China Sea (from 0600 to 1200 UTC on October 4). After that, the difference in the typhoon intensity between CTL and CSST lasted before dissipation.

Fig. 9
figure 9

Time series of average a SST (deg C), b SLHF (W m−2), and c 2 m water vapor (g kg−1) around the typhoon’s center in CTL (red) and CSST (blue)

The SLHF on the ocean is affected by the SST, wind speed, and the vertical moisture gradient, and calculated using the following bulk formula with these variables.w

$$mathrm{LHF}= rho {L}_{mathrm{v}}{C}_{mathrm{h}}{W}_{mathrm{s}}Delta q,$$

where (rho) is the air density (kg m−3), ({L}_{mathrm{v}}) is the latent heat of vaporization (2.44 (times) 106 J kg−1), ({C}_{mathrm{h}}) is the transfer coefficient (1.3 (times) 10–3), ({W}_{mathrm{s}}) is the 10-m wind speed, and (Delta q=({q}_{mathrm{s}}-{q}_{2mathrm{m}})) is the moisture gradient between the sea surface and the air 2 m above it (Kumar et al. 2017).

The simulated typhoons entered the dry area in the mid-latitude after 1200 UTC on October 3, and then, the SST, wind speed, and ({q}_{2mathrm{m}}) started to decrease in both CTL and CSST (Figs. 4, 9). The SLHF in CSST decreased after 1200 UTC on October 3, while the decreasing SLHF in CTL was prominent after 0000 UTC on October 4 when the SST cooled notably (Fig. 9a, b). At 1200 UTC on October 4, the SST of CTL was similar to that at 0600 UTC on October 4 and ({q}_{mathrm{s}}) did not change much due to this similar SST. However, the wind speed increased and ({q}_{2mathrm{m}}) considerably decreased (Figs. 4, 9). Therefore, SLHF drastically increased at 1200 UTC due to the enhanced ({W}_{mathrm{s}}) and the increased (Delta q) in the bulk formula. However, the SST, wind speed, and ({q}_{2mathrm{m}}) in CSST decreased continuously, so a minor increase in the SLHF appeared at 1200 UTC. After leaving the area with warm SST, the SLHF in CTL decreased, and the typhoon also weakened.

The maximum difference in typhoon intensity between CTL and CSST appeared at 1200 UTC on October 4; the vertical structure of the typhoon in CTL and CSST at this time is shown in Fig. 10. Entering the upper-level westerly wind region in the mid-latitudes, the typhoon in both experiments tilted eastward, but the eye and eyewall were clearly visible. The maximum wind speed recorded in CTL and CSST was at 900 hPa, and the horizontal wind speed in CTL exceeded 70 m s−1 (Fig. 10a). However, CSST indicated a maximum wind speed of less than 65 m s−1 (Fig. 10b). In addition, the azimuthally averaged tangential wind for both experiments recorded a maximum pressure at 900 hPa; CTL showed stronger tangential winds than the CSST (Fig. 10c, d). For the radial wind of the typhoon, CTL simulated a stronger low-level inflow and upper-level outflow, as well as a wider outflow than the CSST (Fig. 10e, f). These results indicate that the low-level convergence and upper-level divergence were stronger in CTL, and the secondary circulation of the typhoon was more powerful. Similar to previous studies (Tao and Zhang 2014; Sun et al. 2017; Li and Huang 2018), our results indicate that a warm SST in typhoon tracks could play an important role in maintaining the strength of typhoons during their dissipation in the mid-latitudes.

Fig. 10
figure 10

Vertical structures of simulated typhoon at 1200 UTC on October 4. Horizontal wind (shading, m s−1) and potential temperature (contour, K with 5 K interval) in a CTL and b CSST, tangential wind (m s−1) in c CTL and d CSST, and radial wind (m s−1) in e CTL and f CSST

The change in typhoon intensity due to SST can affect moisture transport; hence, precipitation changes with typhoon intensity (Lin et al. 2015). This trend was indicated by the accumulated rainfall for the study area displayed in Figs. 5 and 6. The low-level moisture distribution of CTL and CSST at 0000 UTC on October 5 showed that moisture transport was associated with changes in typhoon intensity and SST (Fig. 11). The center of the typhoon in both experiments was located on the southwestern coast of Ulsan, and a mass of moisture covered the typhoon center. Dry air penetrated the west side of the typhoon and wrapped around the typhoon center. On the east side of the typhoon center, moisture was transported from the ocean to the land by cyclonic circulation. This moisture channel in CTL was more significant and evident because the simulated typhoon in CTL had a stronger intensity and more substantial structure than in CSST (Figs. 4b, 10, 11a). However, in CSST, the moisture transport was weaker and the air surrounding the simulated typhoon core was drier, especially in the northwest of the typhoon center. The dry air intrusion was stronger in CSST than in CTL and cut off the moisture connection with the center (Fig. 11b). We also calculated the differences in water vapor and precipitable water amounts between CTL and CSST (Fig. 11c), which flowed into the Ulsan region (blue box in Fig. 11a, b) by cyclonic circulation of Typhoon Chaba. The CTL experiment with a stronger typhoon tended to simulate a higher moisture transport. In particular, the maximum difference in the two variables between CTL and CSST appeared before heavy rainfall started. This implies that the stronger typhoon enhanced by a warmer SST conveys more moisture to the land, which leads to heavy rainfall inland.

Fig. 11
figure 11

Horizontal distribution of 850 hPa water vapor (g kg−1) in a CTL and b CSST at 0000 UTC on October 5, and c time series of difference in water vapor (g kg−1) and precipitable water (kg m−2) between CTL and CSST within the blue box in the a, b

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