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GRAPES_TYM is a regional model for predicting the tracks and intensities of TCs in Northwest Pacific and the South China Sea. It was developed by the National Meteorological Center of the CMA and has been in operation since 2012. The model has been improved in terms of the model dynamics and physics as well as the vortex initialization scheme (Zhang et al., 2017; Ma et al., 2018). GRAPES_TYM uses a terrainfollowing height coordinate in the vertical direction and an ArakawaC grid in the horizontal direction. The model physics include the singlemoment 6class microphysics scheme (WMS6), the scaleaware Simplified Arakawa–Schubert cumulus convection scheme, the Yonsei University planetary boundary layer scheme, the Goddard shortwave radiation scheme, and the rapid radiative transfer model longwave radiation scheme. The horizontal grid space is 0.09° with 75 levels in the vertical direction.

GRAPES_TYM uses the forecast fields of the NCEPGFS as its initial and boundary conditions. The resolution of the NCEPGFS input is 0.5° × 0.5° in the horizontal direction and 26 levels in the vertical direction. No relocation is performed in GRAPES_TYM because it has no positive effect on the prediction of the mean track of TCs in the first 48 hours (Ma et al., 2018, 2019).
Correction of the initial intensity of TC was only applied if the minimum sealevel pressure around the center of TC (p_{min}) in the initial field was greater than the central pressure from the objective analysis of the forecaster (p_{obs}). The difference between p_{min} and p_{obs} is Δp (Δp = p_{min} − p_{obs}) and the corrections to the initial field from NCEPGFS (U_{org}, V_{org}, H_{org}, and T_{org}) are ΔU, ΔV, ΔH, and ΔT. The function used to calculate the tangential wind is defined by:
$${V_T}\left( {r,\sigma } \right) = \left\{ \begin{array}{l} {V_{\rm{m}}}\left( {\dfrac{r}{{{r_{\rm{m}}}}}} \right)\left[ {\exp \left\{ {\dfrac{1}{b}\left[ {1  {{\left( {\dfrac{r}{{{r_{\rm{m}}}}}} \right)}^b}} \right]} \right\}  \left {\dfrac{{r  {r_{\rm{m}}}}}{{{r_0}  {r_{\rm{m}}}}}} \right\exp \left\{ {\dfrac{1}{b}\left[ {1  {{\left( {\dfrac{r}{{{r_{\rm{m}}}}}} \right)}^b}} \right]} \right\}} \right]\sin \left( {\dfrac{\pi }{2}\sigma } \right),\;\;r < \;{r_0};\;\;\;\\ 0,\;\;r \geqslant {r_0}, \end{array} \right.$$ (1) where V_{m} is the velocity of the maximum wind at 10m height, r_{m} is the radius of the maximum wind, r is the radius from the center of the vortex, r_{0} is the outermost radius of the wind (set to r_{0} = 4° in this study), and b is a parameter determining the horizontal shape of the wind profile, which is related to the radius of 15 m s^{−1}. The vertical profile of the tangential wind is given as a sine function of the vertical coordinate σ. The parameter σ is calculated by:
$$\sigma = \frac{{p  {p_{{\rm{top}}}}}}{{p  {p_{{\rm{bas}}}}}},$$ (2) where p_{top} = 100 hPa and p_{bas} = 1010 hPa.
The VIC was calculated at each pressure level and the result was interpolated into the terrainfollowing height coordinate. The parameters Δp, ΔU, ΔV, ΔH, and ΔT were calculated by using the following steps:
1) Calculate V_{T} (ΔU, ΔV) using Eq. (1) starting from a smaller value of V_{m} such as 0.5 m s ^{−1}.
2) Obtain the sealevel pressure (p_{sea}) using a nonlinear balance equation through Poisson iteration and calculating Δp1 as p_{bas} − p_{sea}.
3) If Δp1 < Δp, then add a small increment ΔV_{m} to V_{m}: V_{m} = V_{m} + ΔV_{m} (0 < ΔV_{m} < 1) and repeat steps 1–3 until Δp1 ≥ Δp.
4) Calculate ΔU and ΔV based on V_{m}.
5) Obtain the geopotential height (ΔH) using a nonlinear balance equation.
6) Obtain the temperature (ΔT) using a hydrostatic balance equation.
The initial U, V, H, and T are calculated by: U = U_{org} + ΔU; V = V_{org} + ΔV; H = H_{org} +ΔH; and T = T_{org} + ΔT. TC1822 (Super Typhoon Mangkhut in 2018) was used as an example to show the modification to the initial fields from the NCEPGFS using this process. Mangkhut was classified as a tropical depression at 1200 UTC 7 September 2018 and ended at 0900 UTC 17 September 2018. The peak intensity was 65 m s^{–1} at 1800 UTC 12 September 2018 and lasted for 60 h (Fig. 1).
Figure 2 shows profiles of the mean sealevel pressure across the center of TC1822 along 162.5°E with and without VIC at the initial time 0000 UTC 8 September 2018. The minimum sealevel pressure decreased from 1004 to 997.5 hPa after VIC, close to the pressure in the besttrack data (998 hPa).
Figure 2. Mean sealevel pressure profile along 162.5°E without/with vortex intensity correction (red/black). Valid at 0000 UTC 8 September 2018.
The Uwind latitude–height crosssections along 162.5°E before (Fig. 3a) and after (Fig. 3b) VIC show that the Uwind increased and there was no change in the location of V_{max}, which was located at about 900 hPa. The difference in U between before and after intensity correction (ΔU) (Fig. 3c) shows that the maximum ΔU is 14 m s^{–1} at 1000 hPa with a symmetrical structure and no boundary layer. This may cause the sudden initial change in the central pressure of the tropical cyclone and maximum wind speed at 10 m (Wang, 1998).
Figure 3. Uwind latitude–height crosssections along 162.5°E. Initial time is 0000 UTC 8 September 2018. (a) Before vortex intensity correction, (b) after vortex intensity correction, and (c) increment/adjustment (m s^{−1}) from the vortex intensity correction.
The temperature crosssections before and after VIC are plotted in Figs. 4a, b. There is a warm core at the midlevel at about 400 hPa before VIC (Fig. 4a) and at about 450 hPa after VIC (Fig. 4b). The maximum ΔT after VIC is about 1.1 K within 500–600 hPa (figure omitted).
2.1. GRAPES_TYM
2.2. Vortex intensity correction scheme

Two experiments were carried out for major TCs in 2018. One used the NCEPGFS forecast fields as the initial condition of the model (hereafter referred to as ORG) and the other used the NCEPGFS forecast fields modified by VIC within the inner core region as the initial condition (hereafter VIC). The integration time was 120 h with 12h intervals at 0000 and 1200 UTC. Fourteen TCs (TC 1808, 1810, 1812, 1814, 1816, 1817, 1818, 1819, 1820, 1821, 1822, 1824, 1825, and 1826) were studied, all with lifetimes > 72 h. There were 150, 143, 130, 111, 96, and 64 samples at 0, 24, 48, 72, 96, and 120 h, respectively.
The track and intensity errors were calculated against the besttrack data from the Shanghai Typhoon Institute of the China Meteorological Administration. The analysis included the mean track and intensity errors for all samples and for the stratified samples by different initial intensities and different stages of intensity. The TCs in the Northwest Pacific Ocean are divided into six categories: tropical depression (TD), tropical storm (TS), severe tropical storm (STS), typhoon (TY), severe typhoon (STY), and super typhoon (SUTY). The samples with the same intensity category at the initial time (TSIN, STSIN, TYIN, STYIN, and SUTYIN) are shown as Table 1. Stratified analysis provided a clear picture of how the VIC affected the prediction of the track and intensity of TC by GRAPES_TYM. Because there were only three samples for the category of tropical depression, this category was removed from the statistical analysis (Table 1).
Category V_{max} (m s^{−1}) Scale of wind No. of samples TSIN 17.2–24.4 8–9 45 STSIN 24.5–32.6 10–11 20 TYIN 32.7–41.4 12–13 17 STYIN 41.5–50.9 14–15 25 SUTYIN ≥ 51.0 ≥ 16 43 Table 1. Categories of tropical cyclone in the Northwest Pacific Ocean
The relative skill and positive population rate (percentage of samples of VIC with smaller errors than ORG to the total samples) were calculated by using the following equation:
$${\rm{Skill}} = \frac{{{\rm{error}}_{\rm{VIC}}  {\rm{error}}_{\rm{{ORG}}}}}{{{\rm{error}}_{\rm{{ORG}}}}}.$$ (3)