## 3 Simulations and Discussion
### Higher-Resolution Forecast Results with the DVI  
The above experiments were conducted using the resolution of 60-15 km for MPAS forecasts. For the sensitivity tests on model resolution, the higher resolution of 60-15-3 km is used for MPAS forecasts in both the hybrid DA and free forecasts. The same static B is utilized at the DA for the higher-resolution experiments because DA still uses the same resolution settings. Since the BND experiment exhibits better performance on track forecast, we focused on the BND experiment for the investigation with higher resolution. At the end of DA, the mean differences and standard deviations for O\(-\)B and O\(-\)A during DA with RO data are shown in Figure 12; the mean differences are the average of the differences over the verification area as shown in Figure 3a. The vertical variations in O\(-\)B (Figure 12a) and O\(-\)A (Figure 12b) are similar in the experiment BND_H (similar to BND but with the resolution of 60-15-3 km), while the differences and standard deviations of the BND are relatively smaller with about half reduction in the troposphere compared to those of the BND_H. Compared to the DA results with 60-15 km resolution in Figure 3, use of the 60-15-3 km resolution appears to further reduce the magnitudes of O\(-\)A from the larger mean differences and standard deviations (Figure 12a vs. Figure 3a) but maintain similar variations and magnitudes. The horizontal distributions of the induced temperature and specific humidity increments at 850 hPa after the DA for BND and BND_H are quite similar (figures not shown). Figure 13 shows the track and intensity forecast for BND and the higher-resolution experiments, BND_H, BND_RPH, and BND_RVH. Note that the DVI in BND_H, BND_RPH, and BND_RVH reaches the best track pressure and wind intensity after 40 and 39 cycles. The track for BND_H agrees best with the best track (Figure 13a), showing a slightly southward deviation after 48 h but a less northward deviation after 84 h than the other experiments. Indeed, the track errors for BND_H are less than 100 km at 96 h and only about 300 km at 120 h. For BND_RPH and BND_RVH, the track errors are close to BND_H in the first three days, but with a much larger growth rate afterward (Figure 13b). Use of the higher resolution for BND resulted in an improved track forecast in BND_H, which, however, is not further improved by the complementary DVI at the end of DA for enhancing the inner typhoon. Comparing the track and intensity forecasts for BND_H, the two-way system produces a faster and more consistent deepening rate in days 2-4 than using the one-way system in [PERSON] et al. ([22], Figure 18). The two-way system also gives the smallest track error (about 50 km on average) in day 3 as seen in Figure 13b. Despite this noted improvement in track and intensity forecasts in day 3 for BND_H, both the systems perform about equally for this typhoon. Figure 12: The vertical profiles of mean fractional differences (red) in bending angle and their standard deviations (blue) between (**a**) the observation (O) and the first guess (B) during the data assimilation for BND_H (i.e., (O\(-\)B)/B in %) (similar to BND but with the resolution of 60-15-3 km), and (**b**) as in (**a**) but for the observation (O) and the analysis (A), i.e., (O\(-\)A)/A. The black dashed line indicates the number of all GPS RO soundings used in the verification area (see Figure 2) during the data assimilation. The vertical profiles are shown as impact height (km). The intensity forecasts with the higher resolution also exhibit similar benefits from the DVI as shown in Figure 13c where both BND_RPH and BND_RVH obtain more deepening in the first four days and a consistent decaying in the last day, in better agreement with the best track data than BND and BND_H (without the DVI). It can be attributed to the initial spin up of the typhoon vortex core by a deepening of about 10 hPa for both DVI experiments. It is noted that BND_H obtained a much faster deepening roughly after day 3 before landfall in Taiwan than BND.