1. Introduction
Previous studies have revealed that various synoptic environments (Ritchie and Holland 1999; Lee et al. 2006, 2008; Dunkerton et al. 2009; Chang et al. 2010), tropical waves (Frank and Roundy 2006; Gall et al. 2010; Gall and Frank 2010; Ching et al. 2010), and mesoscale convection (Hendricks et al. 2004; Montgomery et al. 2006; Houze et al. 2009) may promote the formation of tropical cyclones (TCs). These conditions, systems, or processes can, either individually or in combination, provide a favorable environmental setting in which tropical cyclones can form. On climate scale, the number of initial disturbances and the probability of an initial disturbance intensifying into a TC are higher under such favorable conditions (Chen et al. 2018; Teng et al. 2014, 2019). However, on synoptic scale, such characteristics often make it difficult to identify the dominant mechanism responsible for the formation of a TC, especially in the western North Pacific (WNP).
Over the past few years, considerable efforts have been made to understand the mechanisms that drive TC formation in the WNP via the use of numerical sensitivity analysis (Li et al. 2014; Li and Pu 2014; Xu et al. 2014; Wu and Duan 2015; Fang and Zhang 2016). The results of these studies have demonstrated that the mechanisms inherent in the formation of TCs in the WNP can be roughly separated into three groups based on time scale: less than 3 days, 3–10 days, and more than 10 days (low frequency). Further, the influences of the interactions between different time-scale processes on TC formation were also identified in previous studies, especially the impacts of the subseasonal-to-seasonal processes on TC formation (Tsai et al. 2013; Elsberry et al. 2014; Li 2017; Lee et al. 2018).
To understand the sensitivity of the subseasonal-to-seasonal vorticity (more than 10 days, including tropical waves and oscillations) to TC formation, Hsieh et al. (2017, hereafter HS17) simulated the formation of 52 WNP TCs that occurred in the period 2008–09 using the Weather Research and Forecasting (WRF) Model with the same settings. The sensitivity of the simulation results to the cumulus schemes used was also examined in the study. TCs were classified into two groups based on the environmental 850-hPa low-frequency (more than 10 days) vorticity: HTCs, which are TCs with higher 850-hPa low-frequency vorticity and LTCs, which are TCs with lower 850-hPa low-frequency vorticity. Their results suggested that the magnitude of the 850-hPa low-frequency vorticity that occurred before the formation of the TC affected the overall results of the simulation, and that these results were not sensitive to the cumulus scheme used when TCs formed in strong low-frequency fields.
Several previous studies have addressed the relative importance of background flow (more than 20 days), Madden–Julian oscillation (MJO), and tropical waves on TC formation by removing each of these parameters in sensitivity experiments carried out as part of an investigation (Wu and Duan 2015; Fang and Zhang 2016). Their results showed that TC formation occurred only in the simulations with low-frequency fields being included in the initial conditions. These results have indicated the importance of the low-frequency fields in setting up a favorable synoptic environment for TC formation, during the positive phase of the MJO or during the positive phase of some tropical waves.
To better understand the overall influence of low-frequency fields on TC formation in the WNP, sensitivity experiments in which the low-frequency or high-frequency fields are removed from the initial conditions are conducted in this study to investigate 14 TCs. These simulations aim to analyze the evolution of the circulation on different time scales in order to address the critical role of low-frequency vorticity during the process of TC formation. The applicability of the low-level, low-frequency vorticity as an indicator by which disturbances that develop into TCs in the WNP can be differentiated from those that do not is also discussed. The setup of the model simulations and the data used in this study are described in section 2. The results of the model simulations are presented in section 3. In section 4, analysis is carried out concerning the role of 850-hPa low-frequency and high-frequency vorticity in terms of disturbances that develop versus those that do not. Finally, the discussion and the conclusions can be found in section 5.
2. Data and experimental design
To examine the characteristics of TC formation in an environment where there is low-level low-frequency vorticity, the resimulation of 14 TCs that occurred in the WNP during 2008–09 (studied in HS17) is carried out in this study. These are seven HHTCs (HTCs with the highest 850-hPa low-frequency vorticity) and seven LLTCs (LTCs with the lowest 850-hPa low-frequency vorticity). Here the vorticity is the average vorticity within a 5° radius from the disturbance center during the period 24–48 h prior to TC formation, calculated using the data from the European Centre for Medium-Range Weather Forecasts (ECMWF) Year of Tropical Convection (YOTC) on a 0.25° × 0.25° grid (Waliser et al. 2012). The HHTCs simulated were Halong, Kalmaegi, Fung-Wong, and Mekkhala from 2008 and Morakot, Dujuan, and Ketsana from 2009; the LLTCs simulated were Nakri, Nuri, TS14W, Maysak, Haishen, and Noul from 2008, and Lupit from 2009. Simulations of the 14 selected TCs are carried out using the nonhydrostatic WRF model (Skamarock et al. 2008) version 3.2 with a two-nested domain (Fig. 1). The inner domain covers the area 4°S–39°N, 103°E–173°W, with a horizontal resolution of 12 km (706 × 400 grid points). There are 31 vertical levels included in this model with the top at 50 hPa. The average thickness of the lower and upper levels is 0.07 and 1 km, respectively.
Nested model domain for WRF simulation. The horizontal resolution is 36 and 12 km for the larger and smaller domain, respectively.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
Nested model domain for WRF simulation. The horizontal resolution is 36 and 12 km for the larger and smaller domain, respectively.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
Nested model domain for WRF simulation. The horizontal resolution is 36 and 12 km for the larger and smaller domain, respectively.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
ECMWF YOTC data are used to determine the initial and lateral boundary conditions for the simulations. Four simulations initialized at 48, 72, 96, and 120 h (denoted −48, −72, −96, and −120 h) before TC formation, respectively, are performed for each TC. The TC formation time (denoted as 0 h) is defined as the first time when Vmax ≥ 25 kt based on the Joint Typhoon Warning Center (JTWC) best track data (http://www.usno.navy.mil/NOOC/nmfc-ph/RSS/jtwc/best_tracks/wpindex.php). The parameterization schemes used are the Kain and Fritsch cumulus scheme (Kain and Fritsch 1993), the Yonsei University PBL scheme (Hong et al. 2006), WRF double-moment 6-class microphysics (Lim and Hong 2010), the Rapid Radiative Transfer Model longwave radiation scheme (Mlawer et al. 1997), and the Dudhia shortwave radiation scheme (Dudhia 1989).
All model settings are identical to those used in HS17 except that the simulation runs until 11 days after TC formation and this experiment is denoted as Ctl_Exp. (Note that the simulation was done until only +24 h in HS17). The longer integration time makes it possible to apply the 10-day high-pass/low-pass filtering for the available data (i.e., the simulation results plus the data used for analysis); further details are described later in this paper.
A total of 56 simulations are performed for the Ctl_Exp (14 cases with 4 simulations for each case). The sensitivity experiment (denoted Sen_Exp) uses the same setups as those in Ctl_Exp, except that the high-frequency fields of horizontal wind, height, and temperature, are removed from the original ECMWF YOTC gridded data using a low-pass/high-pass filter with a 10-day cutoff period (Duchon 1979; Wu et al. 2013) before applying the WRF Preprocessing System to generate the initial and boundary conditions for the simulation. The method of the Sen_Exp in this study is similar to that used in Gall and Frank (2010). Note that the WRF Model itself handled the balance processes after the initial conditions and boundary conditions are altered (i.e., without the nudging processes), although some imbalances occur in the initial field in Sen_Exp. However, after 12 h of integration, the simulation results are close to the balance state in the Sen_Exp for both HHTCs and LLTCs.
For each simulation, the period considered to analyze if there is TC formation occurred is −48 to +72 h (72 h after the TC formation time). The criteria used to determine a successfully simulated TC are similar to those used in HS17, or the area-averaged vorticity (unfiltered) at 850-hPa inside 1.5° and 3° (or 5°) radius of the simulated disturbance center is greater than the threshold for more than 12 h over the period analyzed. The threshold is defined as the mean of the values for area-averaged vorticity at 0 h in all of the TC cases in 2008–09 minus one standard deviation, based on ECMWF YOTC data (or the initial fields of the WRF simulation, HS17). The threshold values are thus calculated at 7.87 × 10−5, 3.79 × 10−5, and 1.50 × 10−5 s−1 inside a radius of 1.5°, 3°, and 5°, respectively.
To analyze the 10-day low/high-pass signal from these short-range WRF simulation results, the simulation results are interpolated onto 0.25° × 0.25° grids and combined with the ECMWF YOTC data (from 30 days before the start of the simulation) to form a dataset that covers 41 days (6 hourly, 0.25° × 0.25° gridded) for each case. The schematic diagram of this data combination method is shown in Fig. 2. The same high-pass/low-pass filter is then applied to these data to calculate the high-/low-frequency wind over the period from −48 to +72 h. Even though there are some imperfections in this data combination method (such as the ECMWF YOTC analysis data used in this method is not downscaled to 12-km resolution as that of the WRF simulation results, and not all of the Lanczos weights are used for the data after the start of the simulation), the root-mean-square errors (RMSEs) of 850-hPa filtered winds are less than 6 m s−1 in the WNP for all cases before the start of the simulation. These RMSEs are smaller than those after the start of the simulation, and the filtered wind patterns are similar to those of the analysis, especially during the TC formation period (not shown). Thus, the relationship between the low- and the high-frequency signals in the simulation results during the TC formation period (from −48 to +72 h) will be presented in chapter 3.
The schematic diagram of the preprocessing data method before the Lanczos filter.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
The schematic diagram of the preprocessing data method before the Lanczos filter.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
The schematic diagram of the preprocessing data method before the Lanczos filter.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
The forecast results of three models from The Observing System Research and Predictability Experiment (THORPEX) Interactive Grand Global Ensemble (TIGGE; Bougeault et al. 2010) data are also analyzed. These three models are provide by the ECMWF, the National Centers for Environmental Prediction (NCEP), and the Bureau of Meteorology of Australia (BoM), with resolutions of 0.45°, 1°, and 1.5°, respectively. The analysis methods for the TIGGE data are the same as the methods used in WRF outputs. The forecast periods and the procedures used for analysis are the same as those used in Ctl_Exp. Note that the threshold values (vorticity) that are used to determine a TC formation are different in the different models, but the definitions of the threshold values are the same as those used in HS17 (i.e., the mean of the values for area-averaged vorticity at 0 h in all of the TC cases in 2008–09 minus one standard deviation). For example, the threshold values of vorticity inside a radius of 1.5° of three models (ECMWF, NCEP, BoM) are 7.93 × 10−5, 4.78 × 10−5, and 3.85 × 10−5 s−1, respectively.
The gridded satellite (GridSat-B1) infrared window (IR) channel data are used for determining the cloud top temperature (Knapp et al. 2011). The environmental 850-hPa vorticities of 3854 tropical cloud clusters (TCCs) in the WNP (10°S–40°N, 90°E–70°W) that occurred from June–November 1981–2009 and identified by Teng et al. (2019) are also analyzed in this study. The area-averaged low-/high-frequency vorticity inside a 5° radius is calculated for each TCC using the ECMWF interim reanalysis (ERA-Interim) data on a 0.25° × 0.25° grid (Dee et al. 2011).
3. Results of numerical simulations
a. Results of the systematic simulations of HHTCs and LLTCs
The results of Ctl_Exp (Table 1) show that the simulated disturbance meets the criteria for TC formation in all HHTC simulations. However, TC formation occurs in only 75% (21/28) of the LLTC simulations. TC formation occurs in all of the HHTC simulations in Sen_Exp, but only 35.7% of the LLTC simulations. These results indicate that the WRF model is more capable of simulating the formation of HHTCs than LLTCs, which is similar to the results shown in HS17. Furthermore, TC formation occurs in all HHTC simulations when the high-frequency fields are removed from the initial conditions.
TC formation rates of HHTCs and LLTC, as well as the average track errors in three experiments.
Table 1 also shows that larger track errors are observed in HHTCs than in LLTCs (similar to HS17). However, significantly more track errors occur in Sen_Exp than in Ctl_Exp in terms of HHTCs. As can be seen in Table 1, the mean track errors at 0 h are 163, 333, 603, and 690 km in Ctl_Exp, and 278, 434, 750, and 1246 km in Sen_Exp, for simulations initialized at −48, −72, −96, and −120 h, respectively. The average time at which the simulated disturbance first meets the criteria for TC formation (the simulated formation time) is slightly delayed in the HHTC simulations (by approximately 6 h) in Sen_Exp when compared to Ctl_Exp (as shown in Table 1), but with considerable variation (>24 h) observed in the different simulations. The average time taken for TC formation in LLTCs is 24 h longer in Sen_Exp than it is in Ctl_Exp (with a standard deviation of 22 h). Therefore, removing the high-frequency part of the initial fields not only makes it more difficult for the model to simulate the formation of an LLTC, but also delays the formation of a simulated LLTC.
The results of the three TIGGE models (with coarser resolutions) are similar. These models are also more capable of forecasting the formation of an HHTC (89.2%) than an LLTC (38.1%). TC formation occurs in all the HHTCs forecast by the TIGGE model except for Typhoon Kalmaegi in 2008 (58%). These results indicate that the environment in which a disturbance takes place, the model and resolution used, the physical processes (and the parameterization schemes) in the model, and the initial data can affect the capability of a numerical model to simulate the formation of a TC.
The simulation results for HHTCs are consistent with results of previous studies for monsoon-related cases (Nakano et al. 2015; Wu and Duan 2015), and suggest that low-level low-frequency environments play a dominant role in the formation process of TCs that formed in an environment with large low-level low-frequency vorticity. This study further indicates that TC formation can occur in such an environment whether high-frequency vorticity is present or not. However, high-frequency fields can affect the timing and location of a TC that is forming (also noted in Tory et al. 2007); thus, the track errors of HHTCs are significantly increased in Sen_Exp. These results also suggest that the probability of a pre-LLTC disturbance to develop into a TC would be greatly reduced (75% to 35.7%) if the high-frequency part of vorticity is removed in the initial conditions (Table 1).
b. The simulation results of two selected cases
To highlight the dominant role that low-frequency fields play during the formation of a TC, the simulation results of an HHTC (Tropical Storm Dujuan in 2009) and an LLTC (Typhoon Nuri in 2008) are presented. The 850-hPa low-frequency vorticity of Tropical Storm (TS) Dujuan is the largest of the 52 TCs from 2008 to 2009 that was analyzed in HS17. Typhoon (TY) Nuri involved the second-smallest 850-hPa low-frequency vorticity among the cases analyzed. Note that several studies have been carried out regarding the process by which Nuri formed, including Montgomery et al. (2010), Park et al. (2013), Li and Pu (2014), and Li et al. (2014). The results of these studies suggest that Nuri formed in an easterly wave environment and that the formation of Nuri was less predictable in numerical models because the convection that occurred near the center of the pre-Nuri disturbance was not well predicted.
Figure 3 shows the 850-hPa wind vectors and vorticity at 1800 UTC 1 September 2009 (or −48 h), and the initial conditions of Ctl_Exp and Sen_Exp, which were initialized at −48 h for the simulation of Dujuan. The total field, low-frequency field, and the high-frequency field are shown in Fig. 3. Dujuan formed in a monsoon gyre environment (Lander 1994), which is characterized by a broad and persistent 850-hPa cyclonic circulation (Figs. 3a,b). This broad cyclonic circulation can also be seen in the low-frequency part of the wind field (Figs. 3d,f). The overall initial circulation pattern in Sen_Exp (Fig. 3c) is similar to that of Ctl_Exp, except that the vorticity is greatly reduced near the center of the pre-Dujuan disturbance, as seen in Figs. 3g and 3i. Note that the high-frequency parts have been removed from the initial conditions and the initial central location of the pre-Dujuan disturbance is shifted toward the northwest in Sen_Exp.
(a) The 850-hPa wind vector (m s−1) and vorticity (shaded) at 1800 UTC 1 Sep 2009 (−48 h) in ECMWF YOTC analysis. (b),(c) As in (a), but for the initial conditions of (b) Ctl_exp and (c) Sen_exp. (d)–(i) As in (a)–(c), but for the low-/high-frequency parts as labeled. The green rectangle in (a) marks the domain of other diagrams. The blue contours indicate the convection area with the cloud top temperature lower than 210 K in (a) and the simulated maximum reflectivity greater than 15 dBZ in (b) and (c). The green cross sign indicates the center of Dujuan in ECMWF YOTC analysis, and the purple cross sign, the center of the simulated disturbance.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
(a) The 850-hPa wind vector (m s−1) and vorticity (shaded) at 1800 UTC 1 Sep 2009 (−48 h) in ECMWF YOTC analysis. (b),(c) As in (a), but for the initial conditions of (b) Ctl_exp and (c) Sen_exp. (d)–(i) As in (a)–(c), but for the low-/high-frequency parts as labeled. The green rectangle in (a) marks the domain of other diagrams. The blue contours indicate the convection area with the cloud top temperature lower than 210 K in (a) and the simulated maximum reflectivity greater than 15 dBZ in (b) and (c). The green cross sign indicates the center of Dujuan in ECMWF YOTC analysis, and the purple cross sign, the center of the simulated disturbance.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
(a) The 850-hPa wind vector (m s−1) and vorticity (shaded) at 1800 UTC 1 Sep 2009 (−48 h) in ECMWF YOTC analysis. (b),(c) As in (a), but for the initial conditions of (b) Ctl_exp and (c) Sen_exp. (d)–(i) As in (a)–(c), but for the low-/high-frequency parts as labeled. The green rectangle in (a) marks the domain of other diagrams. The blue contours indicate the convection area with the cloud top temperature lower than 210 K in (a) and the simulated maximum reflectivity greater than 15 dBZ in (b) and (c). The green cross sign indicates the center of Dujuan in ECMWF YOTC analysis, and the purple cross sign, the center of the simulated disturbance.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
Both Ctl_Exp and Sen_Exp can simulate the formation of a TC. However, the time of formation is −30 h in Ctl_Exp and −6 h in Sen_Exp. At 0 h (or 1800 UTC 1 September 2009), the low-level positive vorticity in the disturbance has increased greatly and the convection is spread over a wide area in both experiments (Fig. 4). A broad cyclonic circulation is still present in the low-frequency part of the wind field and the simulated vortex in both experiments is stronger than that found via ECMW YOTC analysis. However, a much more considerable error is apparent in the location of the center of the disturbance in Sen_Exp (Fig. 4c), which is mainly due to the shifting of the large high-frequency vorticity area (and strong convection), as seen in Fig. 4i (compared to that of Fig. 4g).
(a) The 850-hPa wind vector (m s−1) and vorticity (shaded) at 1800 UTC 3 Sep 2009 (0 h) in ECMWF YOTC analysis. (b),(c) As in (a), but for the 48-h simulation results (at 0 h) of (b) Ctl_exp and (c) Sen_exp. Others are similar to or the same as those in Fig. 3.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
(a) The 850-hPa wind vector (m s−1) and vorticity (shaded) at 1800 UTC 3 Sep 2009 (0 h) in ECMWF YOTC analysis. (b),(c) As in (a), but for the 48-h simulation results (at 0 h) of (b) Ctl_exp and (c) Sen_exp. Others are similar to or the same as those in Fig. 3.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
(a) The 850-hPa wind vector (m s−1) and vorticity (shaded) at 1800 UTC 3 Sep 2009 (0 h) in ECMWF YOTC analysis. (b),(c) As in (a), but for the 48-h simulation results (at 0 h) of (b) Ctl_exp and (c) Sen_exp. Others are similar to or the same as those in Fig. 3.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
Figure 5 shows the time series of the area-averaged 850-hPa vorticity inside a 1.5° radius that highlights the changes in vorticity that are occurring near the center of the disturbance, especially in Sen_Exp. The results demonstrate that the total vorticity increases rapidly after 36 h of simulation (at −12 h) in Sen_Exp, because of the sudden increase in the extent of the high-frequency vorticity (Fig. 5, red lines). The total vorticity increases rapidly after 18 h of simulation in Ctl_Exp (Fig. 5, blue lines); however, the high-frequency vorticity remains approximately the same during the first 18 h of simulation, only increasing rapidly after this time. Note that the vorticity of the simulated disturbance in Sen_Exp reaches a comparable magnitude to that in Ctl_Exp, but with a delay of approximately 12–24 h. It should also be noted that the low-frequency vorticity also increases during this 48-h period.
Time series of the 0°–1.5° area averages of total vorticity (solid lines), high-frequency vorticity (dashed lines), and low-frequency vorticity (dotted lines) for Ctl_Exp and Sen_Exp (as labeled) started at −48 h for Dujuan (2009). The black line indicates the 0°–1.5° area-averaged total vorticity for Dujuan based on the ECMWF YOTC data. Time 0 represents the time of TC formation.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
Time series of the 0°–1.5° area averages of total vorticity (solid lines), high-frequency vorticity (dashed lines), and low-frequency vorticity (dotted lines) for Ctl_Exp and Sen_Exp (as labeled) started at −48 h for Dujuan (2009). The black line indicates the 0°–1.5° area-averaged total vorticity for Dujuan based on the ECMWF YOTC data. Time 0 represents the time of TC formation.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
Time series of the 0°–1.5° area averages of total vorticity (solid lines), high-frequency vorticity (dashed lines), and low-frequency vorticity (dotted lines) for Ctl_Exp and Sen_Exp (as labeled) started at −48 h for Dujuan (2009). The black line indicates the 0°–1.5° area-averaged total vorticity for Dujuan based on the ECMWF YOTC data. Time 0 represents the time of TC formation.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
The evolution of the 850-hPa circulation pattern for the simulation initiated at −72, −96, or −120 h is similar to that of the simulation of Dujuan that began at −48 h (Ctl_Exp and Sen_Exp). Aside from the similarity in the pattern of evolution in the 850-hPa circulation, the formation of a TC also occurs in all eight simulations. However, the locations and intensity of the simulated disturbance in the high-frequency fields varies among the eight simulations, resulting in different TC intensities and track patterns, as illustrated in Fig. 6. Figure 6 shows the average 6-hourly 850-hPa wind field and positive high-frequency vorticity during the period from 0 to +48 h in simulations, which were initiated at different times. Note that there is no clear relationship between the intensity of the simulated TC and the time of initiation. Similar patterns in the low-level fields also occur for other HHTCs in both Ctl_Exp and Sen_Exp.
Time-averaged 850-hPa wind vector (m s−1) and positive high-frequency vorticity (shaded) during the period of 0−48 h (or 1800 UTC 3 Sep to 1800 UTC 5 Sep 2009) for (a),(c),(e),(g) Ctl_Exp and (b),(d),(f),(h) Sen_Exp initialized at different initial times as labeled.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
Time-averaged 850-hPa wind vector (m s−1) and positive high-frequency vorticity (shaded) during the period of 0−48 h (or 1800 UTC 3 Sep to 1800 UTC 5 Sep 2009) for (a),(c),(e),(g) Ctl_Exp and (b),(d),(f),(h) Sen_Exp initialized at different initial times as labeled.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
Time-averaged 850-hPa wind vector (m s−1) and positive high-frequency vorticity (shaded) during the period of 0−48 h (or 1800 UTC 3 Sep to 1800 UTC 5 Sep 2009) for (a),(c),(e),(g) Ctl_Exp and (b),(d),(f),(h) Sen_Exp initialized at different initial times as labeled.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
On the other hand, TY Nuri formed in an easterly wave environment as shown in Fig. 7a. Similar to Fig. 3, Fig. 7 shows the 850-hPa wind vectors and vorticity at 1800 UTC 14 August 2008 (or −48 h), and the initial conditions of Ctl_Exp and Sen_Exp that were initialized at −48 h for Nuri. Note that the easterly winds are prevailing in the low-frequency part of the wind field (Figs. 7d,f,h). The pre-Nuri disturbance is much weaker and smaller than the pre-Dujuan disturbance. Only a weak cyclonic circulation can be seen near the center of the disturbance, which is more apparent in the high-frequency part of the wind field (Fig. 7g). This weak cyclonic circulation is removed from the initial field in Sen_Exp, as seen in Fig. 7i.
(a) The 850-hPa wind vector (m s−1) and vorticity (shaded) at 1800 UTC 14 Aug 2008 (−48 h) in ECMWF YOTC analysis. (b),(c) As in (a), but for the initial conditions of (b) Ctl_exp and (c) Sen_exp. (d)–(i) As in (a)–(c), but for the low-/high-frequency parts as labeled. The green rectangle in (a) marks the domain of other diagrams. The blue contours indicate the convection area with the cloud top temperature lower than 210 and 240 K in (a) and the simulated maximum reflectivity greater than 10 and 20 dBZ in (b) and (c). The green cross sign indicates the center of Nuri in ECMWF YOTC analysis, and the purple cross sign, the center of the simulated disturbance.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
(a) The 850-hPa wind vector (m s−1) and vorticity (shaded) at 1800 UTC 14 Aug 2008 (−48 h) in ECMWF YOTC analysis. (b),(c) As in (a), but for the initial conditions of (b) Ctl_exp and (c) Sen_exp. (d)–(i) As in (a)–(c), but for the low-/high-frequency parts as labeled. The green rectangle in (a) marks the domain of other diagrams. The blue contours indicate the convection area with the cloud top temperature lower than 210 and 240 K in (a) and the simulated maximum reflectivity greater than 10 and 20 dBZ in (b) and (c). The green cross sign indicates the center of Nuri in ECMWF YOTC analysis, and the purple cross sign, the center of the simulated disturbance.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
(a) The 850-hPa wind vector (m s−1) and vorticity (shaded) at 1800 UTC 14 Aug 2008 (−48 h) in ECMWF YOTC analysis. (b),(c) As in (a), but for the initial conditions of (b) Ctl_exp and (c) Sen_exp. (d)–(i) As in (a)–(c), but for the low-/high-frequency parts as labeled. The green rectangle in (a) marks the domain of other diagrams. The blue contours indicate the convection area with the cloud top temperature lower than 210 and 240 K in (a) and the simulated maximum reflectivity greater than 10 and 20 dBZ in (b) and (c). The green cross sign indicates the center of Nuri in ECMWF YOTC analysis, and the purple cross sign, the center of the simulated disturbance.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
Figure 8 illustrates the same 850-hPa wind vectors and vorticity as those in Fig. 7, but at 1800 UTC 16 August (or 0 h). Results show that the 850-hPa vorticity of the simulated disturbance is smaller in Ctl_Exp (Fig. 8b) than in the ECMWF YOTC analysis (Fig. 8a) at 0 h (or the observed time of TC formation). The simulated disturbance meets the criteria for TC formation after 66 h of integration (or at 18 h). In other words, although Ctl_Exp can simulate the formation of a TC, the formation time produced by the simulation is 18 h later than that observed. Results also show that the increase in the 850-hPa vorticity associated with the disturbance is mainly due to the increase in the high-frequency vorticity (Figs. 8e,g). There is no apparent increase in the 850-hPa low-frequency vorticity during the 48-h period simulated (Fig. 8f versus Fig. 7f). This result is significantly different from that produced by the simulation of Dujuan (Fig. 4f versus Fig. 3f), in which the 850-hPa low-frequency vorticity also increased during the first 48 h of simulation (Fig. 5).
(a) The 850-hPa wind vector (m s−1) and vorticity (×10−5 s−1, shaded) at 1800 UTC 16 Aug 2008 (0 h) in ECMWF YOTC analysis. (b),(c) As in (a), but for the 48-h simulation results (at 0 h) of (b) Ctl_exp and (c) Sen_exp. Others are similar to or the same as those in Fig. 7.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
(a) The 850-hPa wind vector (m s−1) and vorticity (×10−5 s−1, shaded) at 1800 UTC 16 Aug 2008 (0 h) in ECMWF YOTC analysis. (b),(c) As in (a), but for the 48-h simulation results (at 0 h) of (b) Ctl_exp and (c) Sen_exp. Others are similar to or the same as those in Fig. 7.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
(a) The 850-hPa wind vector (m s−1) and vorticity (×10−5 s−1, shaded) at 1800 UTC 16 Aug 2008 (0 h) in ECMWF YOTC analysis. (b),(c) As in (a), but for the 48-h simulation results (at 0 h) of (b) Ctl_exp and (c) Sen_exp. Others are similar to or the same as those in Fig. 7.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
As the increase in the low-level vorticity during the formation of Nuri is attributed mainly to the increase in the high-frequency vorticity, it should be difficult for a TC to form in a simulation where the high-frequency signals have been removed in the initial conditions. Thus the magnitude of the positive high-frequency vorticity is very small (Fig. 8i) and no TC forms in the Sen_Exp of Nuri (Fig. 8c) when initialized at −48 h. In the Ctl_Exp and Sen_Exp of Nuri initialized at −72 or −96 h, the results (Figs. 9c–f) are similar to those produced when the simulation is initialized at −48 h (Figs. 9a,b). However, in simulations initialized at −120 h, the simulated disturbance does not intensify to form a TC in Ctl_Exp (Fig. 9g), but a TC does form in Sen_Exp (Fig. 9h). Further analysis of this simulation reveals that although the original disturbance is removed in the initial conditions, another disturbance forms in the easterly wind environment (not shown). The formation of this disturbance is likely due to the stochastic nature of convection and the weaker anticyclonic circulation in Sen_Exp (compared to that of Ctl_Exp). This disturbance further intensifies to form a TC during the longer simulation period (120 h). Moreover, because the vorticity of disturbances may be overpredicted in WRF Model simulation, some disturbances might have a chance to intensify and reaching the TC intensity within a longer integration time (more than half (6/10) of simulations that meet TC formation criteria are initialized at −96 and −120 h). Therefore, the percentage of all simulations with TC formation occurred is 35.7% in Sen_Exp (instead of 0%) for LLTCs.
Time-averaged 850-hPa wind vector (m s−1) and positive high-frequency vorticity (shaded) during the period of 0−48 h (or 1800 UTC 16 Aug to 1800 UTC 18 Aug 2008) for (a),(c),(e),(g) Ctl_Exp and (b),(d),(f),(h) Sen_Exp initialized at different initial times as labeled.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
Time-averaged 850-hPa wind vector (m s−1) and positive high-frequency vorticity (shaded) during the period of 0−48 h (or 1800 UTC 16 Aug to 1800 UTC 18 Aug 2008) for (a),(c),(e),(g) Ctl_Exp and (b),(d),(f),(h) Sen_Exp initialized at different initial times as labeled.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
Time-averaged 850-hPa wind vector (m s−1) and positive high-frequency vorticity (shaded) during the period of 0−48 h (or 1800 UTC 16 Aug to 1800 UTC 18 Aug 2008) for (a),(c),(e),(g) Ctl_Exp and (b),(d),(f),(h) Sen_Exp initialized at different initial times as labeled.
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
The results mentioned above are based on the simulations using the WRF Model with a 12 km grid resolution. Some studies (Park et al. 2013; Li and Pu 2014) showed that the WRF Model could simulate the formation of Typhoon Nuri if a finer grid was used. Thus, an extra experiment is performed for Nuri to highlight the importance of model resolution when using the WRF Model to simulate the formation of an LLTC. For this extra simulation, an inner domain with 706 × 400 grids and a 4 km horizontal resolution (not shown) is used, besides the original two-nested grids. This extra simulation also is initialized at −48 h. Figure 10 shows the results of the 48-h simulation (at 0 h) of this extra experiment (Fig. 10e), compared to those of Ctl_Exp (Fig. 10c). Also shown in Fig. 10 are the 850-hPa wind vectors and vorticity at 1800 UTC 16 August 2008 (0 h), based on ECMWF YOTC analysis (Fig. 10a) and the forecast results of the three TIGGE models (Figs. 10b,d,f).
(a) The 850-hPa wind vector (m s−1) and vorticity (shaded) at 1800 UTC 16 Aug 2008 (0 h) in ECMWF YOTC analysis. Other diagrams are as in (a), but for 48-h model simulations with (a) 12-km and (e) 4-km grid resolutions or forecasts by (b),(d),(f) three TIGGE models initialized at 1800 UTC 14 Aug 2008 (−48 h).
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
(a) The 850-hPa wind vector (m s−1) and vorticity (shaded) at 1800 UTC 16 Aug 2008 (0 h) in ECMWF YOTC analysis. Other diagrams are as in (a), but for 48-h model simulations with (a) 12-km and (e) 4-km grid resolutions or forecasts by (b),(d),(f) three TIGGE models initialized at 1800 UTC 14 Aug 2008 (−48 h).
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
(a) The 850-hPa wind vector (m s−1) and vorticity (shaded) at 1800 UTC 16 Aug 2008 (0 h) in ECMWF YOTC analysis. Other diagrams are as in (a), but for 48-h model simulations with (a) 12-km and (e) 4-km grid resolutions or forecasts by (b),(d),(f) three TIGGE models initialized at 1800 UTC 14 Aug 2008 (−48 h).
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
The results of this simulation indicate that the 850-hPa vorticity near the center of the pre-Nuri disturbance is higher than the 6 × 10−5 s−1 from ECMWF YOTC analysis. However, the 850-hPa vorticity near the center of the simulated disturbance is smaller than this value in most simulations (or forecasts) after 48 h of integration (including simulations with different cumulus schemes that are presented in Fig. 10 of HS17). Only the simulated disturbance with a 4 km horizontal resolution intensifies to form a TC in this extra experiment (Fig. 10e). The vorticity near the center of the simulated disturbance is the smallest among all the simulations/forecasts for the forecast results from the AMMC model (Fig. 10f), which has the coarsest grid resolution of the three TIGGE models. According to this finding and the threshold values of vorticity in three TIGGE models, which suggest that, in general, the vorticity values near the TC center in the model with a coarser resolution are lower than those in the model with a finer resolution. However, there is no clear relationship between forecasted TC number and model’s resolution. It needs further studies to address this topic.
c. Summary of the simulation/forecast results
HS17 revealed the sensitivity of simulation results to both the initial environmental conditions and the selection of the cumulus parameterization scheme. TC formation occurred in approximately 91% (204 out of 224) of all HHTC simulations carried out in HS17, but in only 25% (57 out of 224) of the simulations of LLTCs. Of the 28 simulations in HS17 that use ECMWF YOTC data as the initial conditions and the Kain–Fritch cumulus scheme, TC formation occurs in 96.4% (27 out of 28) of the simulations of HHTCs, and in 50% (14 out of 28) of the simulations of LLTCs. However, in this study, TC formation occurs in all simulations (Ctl_Exp) of HHTCs, even when the high-frequency parts are removed from the initial conditions (Sen_Exp). Note that the only difference between this study and HS17 is that the integration time is longer in this study. For LLTCs, the percentage of simulations that have a reasonable TC formation process increases from 25% in HS17 to 75% in Ctl_Exp of this study. However, this percentage drops to 35.7% in Sen_Exp.
The above results have revealed the important mechanism for TC formation in an environment with large low-level low-frequency vorticity. In such an environment, convection plays a very important role in concentrating the low-level vorticity, and TC formation is expected to occur even when the high-frequency parts are removed in the initial conditions. Removing the high-frequency vorticity only delays the strong convection and the development of the disturbance. Once strong convection occurs, the system will keep developing to almost an identical intensity. However, the stochastic nature of convection can result in a shift of the convection area, leading to larger track errors in Sen_Exp than in Ctl_Exp. Therefore, the high-frequency environment seems to play an important role in determining the time of formation and the center position of the initial disturbance, while the low-frequency environment determines whether a TC will form.
The results of this study and the TIGGE forecasts further indicate that it is important to accurately simulate the major effects of convection in order to simulate the formation of an LLTC. Therefore, the results of the simulation of an LLTC depend greatly on the selections of the numerical model, the model resolution, initial data, and the cumulus parameterization scheme. Note that the increase in the low-level positive vorticity via low-level convergence is probably not sufficient to generate a TC if the environmental low-frequency vorticity is weak. Moreover, removing the high-frequency signals in the initial conditions also weakens the disturbance, and the convection associated with the disturbance in Sen_Exp is less organized than that observed in Ctl_Exp. Therefore, it is more difficult to simulate the formation of an LLTC in Sen_Exp.
Finally, sensitivity experiments with the low-frequency environments being removed from the initial conditions are also performed for 7 HHTCs. Results show that the percentage of simulations that can simulate the formation of a TC drops from 100% (for CTL) to 46.4% (13 out of 28) in this experiment. In some simulations, the intensity of the initial disturbance cannot be maintained, and the disturbance cannot be tracked after 1–2 days of integration. These results further support the importance of low-frequency environments in the formation of HHTCs.
4. The developing ratio of TCCs
The above results suggest that the 850-hPa low-frequency vorticity could provide useful guidance for the assessment of TC formation prediction using numerical models, especially in the WNP. However, only disturbances that developed into TCs were simulated in this study. Thus, the low-level environmental vorticity for disturbances that did not develop into TCs is also analyzed to address this issue. Figure 11a shows the scatter diagram of the environmental (inside a 5° radius) time-averaged (over the TCC period) low- versus high-frequency vorticity at 850 hPa for 3854 tropical cloud clusters (TCCs) that occurred in the WNP during June–November 1981–2009 (tracked by Teng et al. 2019). TCC, the precursor to TC, has a large cold and high cloud over the ocean and can develop into a TC in a favorable environment. There are 876 developing TCCs (DTCCs) observed, which had developed into a TC by the time at which the last TCC record was made based on the JTWC best track data, and 2978 nondeveloping TCCs (NTCC). The mean of the 850-hPa low- and high-frequency vorticity of all DTCCs is 1.03 × 10−5 and 0.72 × 10−5 s−1, respectively, while the mean of the 850-hPa low- and high-frequency vorticity of all NTCCs is 0.11 × 10−5 and 0.13 × 10−5 s−1, respectively. The DTCCs are concentrated on the upper-right side and the NTCCs on the lower-left side of Fig. 11a, suggesting that DTCCs have greater total vorticity than NTCCs. Therefore, the ratio of developing TCCs to total TCCs (defined as the developing ratio) is positively correlated (with a correlation coefficient of 0.93), which is statistically significant with regards to the total environmental 850-hPa vorticity of the TCCs. Due to the sample size, the percentage shown in Fig. 11a is calculated for every 0.5 × 10−5 s−1 vorticity interval. These results further highlight the importance of low-level vorticity in differentiating between the developing and nondeveloping disturbances in the WNP, as was pointed out by Lee (1989) and Fu et al. (2012). Note that there were some NTCCs observed with considerable 850-hPa vorticity; this is because TC formation is also affected by other parameters such as vertical wind shear, 700-hPa moisture, and sea surface temperature (Gray 1998).
Scatter diagram of the time-averaged 10-day low-pass-filtered 850-hPa vorticity (abscissa) vs 10-day high-pass-filtered 850-hPa vorticity (ordinate) inside 5° radius for 3854 TCCs during June–November in 1981–2009 in the (a) ERA-Interim data and the (b) TC-removed data, respectively. Blue dots indicate the 2978 nondeveloping TCCs (NTCC), and red dots indicate the 876 developing TCCs (DTCC). The dashed line shows where the low-frequency vorticity equal to the high-frequency vorticity (x = y).
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
Scatter diagram of the time-averaged 10-day low-pass-filtered 850-hPa vorticity (abscissa) vs 10-day high-pass-filtered 850-hPa vorticity (ordinate) inside 5° radius for 3854 TCCs during June–November in 1981–2009 in the (a) ERA-Interim data and the (b) TC-removed data, respectively. Blue dots indicate the 2978 nondeveloping TCCs (NTCC), and red dots indicate the 876 developing TCCs (DTCC). The dashed line shows where the low-frequency vorticity equal to the high-frequency vorticity (x = y).
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
Scatter diagram of the time-averaged 10-day low-pass-filtered 850-hPa vorticity (abscissa) vs 10-day high-pass-filtered 850-hPa vorticity (ordinate) inside 5° radius for 3854 TCCs during June–November in 1981–2009 in the (a) ERA-Interim data and the (b) TC-removed data, respectively. Blue dots indicate the 2978 nondeveloping TCCs (NTCC), and red dots indicate the 876 developing TCCs (DTCC). The dashed line shows where the low-frequency vorticity equal to the high-frequency vorticity (x = y).
Citation: Monthly Weather Review 148, 10; 10.1175/MWR-D-19-0299.1
Results also show that approximately 61.2% of all DTCCs (536 DTCCs) are located under the dashed line in Fig. 11a, where the low-frequency vorticity is larger than the high-frequency vorticity. Thus, the developing ratio is 27.7% for TCCs with a larger 850-hPa low-frequency vorticity; this is higher than that of all TCCs (22.7%). To further assess the contribution of the variation in the low- and high-frequency vorticity to the correlation between total vorticity and the developing ratio, partial correlation is performed to exclude the impact of 10-days low- and high-frequency signals. The partial correlation coefficients between the developing ratio and the total vorticity of TCCs are 0.27 and 0.78 when the impact of the low-frequency vorticity and the high-frequency vorticity, respectively, is removed. Therefore, the correlation between the developing ratio and the total vorticity of TCCs is more sensitive to the variability in the low-frequency vorticity than that of the high-frequency vorticity.
However, the influences of the TC-related vorticity on the low- and high-frequency vorticity are not excluded in Fig. 11a. Thus, following Galarneau and Davis (2013), the TC-related vorticity and winds are removed from the ERA-Interim data for 890 TCs (when Vmax ≥ 34 kt) during 1981–2009 based on the JTWC best track data to construct a new dataset (called TC-removed data). Figure 11b is similar to Fig. 11a except that the TC-removed data are used. The results show that although the developing ratio is still higher at where the low-frequency vorticity is larger than the high-frequency vorticity (Fig. 11b), the mean of the 850-hPa low- and high-frequency vorticity are reduced greatly for DTCCs (Fig. 11b), but are changed only slightly for NTCCs. These results indicate that the TC-related vorticity affects the vorticity of DTCCs (either the low- or high-frequency vorticity) greatly, but affects only slightly the vorticity of NTCCs. Thus, for DTCCs, the correlation coefficients between the 5° area-averaged vorticity computed using the original data and that computed using the TC-removed data are only 0.45 and 0.22 for the low- and the high-frequency signals, respectively. However, for NTCCs, the correlation coefficients are 0.99 and 0.98 for the low- and the high-frequency signals, respectively.
It is reasonable that the computed low- or high-frequency vorticity becomes much smaller when the TC-removed data, instead of the original data, are used because both the TC-related vorticity and the background vorticity are removed when the method of Galarneau and Davis (2013) is used to remove TC-related vorticity (Arakane and Hsu 2020). In addition, some DTCCs are located close to a TC center or will develop into TCs, so the vorticity is greatly reduced in TC-removed data. On the other hand, the radius used to remove TC-related vorticity is fixed (500 km) in the current method, and the results would be different if a different radius is used to remove the TC-related vorticity. Therefore, it is highly desired to develop a more appropriate approach in the future to remove only the TC-related vorticity (not the background vorticity) based on the intensity and size of a TC.
5. Discussion and conclusions
Following HS17, this study further examines the impacts of high- and low-frequency vorticity on the formation of seven HHTCs and seven LLTCs that formed in 2008–09 in the WNP. In this study, the integration is carried out until 11 days after the first TC in each simulation, which allows for the analysis of both high- and low-frequency vorticity in the simulation results. Similar to HS17, the simulation results of Ctl_Exp and the forecast results of the three TIGGE models indicate that the models are more (less) capable of simulating/forecasting the TC formation process for TCs that form in an environment with higher (lower) 850-hPa low-frequency vorticity. Results of this study further show that, for HHTCs, TC formation even occurs in simulations where the high-frequency signals are removed in the initial conditions (Sen_Exp). Results of Sen_Exp also suggest that organized convection tends to occur in environments with higher low-level low-frequency vorticity, regardless of the strength of the initial disturbance. The vorticity is then concentrated by the organized convection, leading to the formation of a TC (HHTC). However, the high-frequency signals were found to affect only the time of formation and the location of the TC, which is consistent with previous studies carried out that investigated monsoon-related TCs or TCs that formed during the active phase of tropical waves (Wu and Duan 2015; Park et al. 2015; Fang and Zhang 2016).
Many previous studies have emphasized the importance of the low-level vorticity on TC formation (Lee 1989; Fu et al. 2012). This study further highlights the importance of the low-frequency part of the low-level vorticity on TC formation. A disturbance has a higher probability of developing into a TC in an environment with larger low-frequency vorticity, which is often associated with monsoons or tropical waves (Chen et al. 2018; Teng et al. 2019) in the WNP. TC formation can still occur in numerical simulations with the high-frequency parts being removed in the initial conditions (Sen_Exp) if the low-frequency vorticity is large enough. For those TCs with only limited environmental low-frequency vorticity before the formation of a TC (LLTCs), the high-frequency vorticity appears to play a critical role in the formation process.
Gray (1998) concluded that there are two dominant processes in TC formation: externally forced convergence (EFC) and internally forced convergence (IFC). EFC is the fundamental process that is associated with the genesis of an initial disturbance that is triggered by a wind–pressure imbalance on a synoptic scale, such as trade-wind surges, southwest monsoon flows, and easterly waves. EFC also sets up a favorable environment for IFC to occur, which is a self-sustaining and continuously growing convergence process that occurs in highly concentrated areas of deep convection. Based on the simulation results of both HS17 and Ctl_Exp, as well as the forecast results from TIGGE, it is suggested that EFC has a more considerable effect in an environment with larger low-frequency vorticity than in other environments. Therefore, the lead time might be longer for a numerical model to forecast the formation of a TC in an environment with larger low-frequency vorticity (or HHTC) in the WNP (Nakano et al. 2015; Wu and Duan 2015). Wang et al. (2018) also noted that the predictability of TC formation was not the same in five tropical cyclogenesis pathways in the North Atlantic. Our simulation results of the WNP agree with these results.
The results of Sen_Exp for HHTCs suggest that, under certain environmental conditions (e.g., monsoon environments, Teng et al. 2019), TC formation can be expected or may already be occurring before a well-defined initial disturbance can be observed. These environmental conditions appear to play a key role in dictating the formation of the initial disturbance and the development of the initial disturbance into a TC. Therefore, the low-frequency vorticity might be used as a parameter to evaluate the capability of a numerical model to forecast the formation of a TC as the calculations of low-frequency vorticity are not difficult for both observations and model forecasts. Thus, the objective classification of the environmental pattern (such as that in Yoshida and Ishikawa 2013; Fudeyasu and Yoshida 2018; Teng et al. 2019) might be important to the evaluation of TC formation in the WNP. However, the environments were classified into different patterns after the initial disturbance was observed in these studies. The challenge lies in how to recognize the environmental pattern before the formation of the initial disturbance (or the start of the EFC process), both in forecasts using numerical models and observations. Thus, it is highly desirable that the capability of a numerical model to forecast TC formation under different environmental conditions/processes in the WNP is further investigated, based on the forecast results of the different numerical models that have become available in recent years.
Acknowledgments
Cheng-Shang Lee and Yi-Huan Hsieh are supported by the National Taiwan University. Hsu-Feng Teng is supported by the National Center for Atmospheric Research. The authors thank Dr. Chung-Hsiung Sui and Mr. Ching-Hsuan Wu of the National Taiwan University for the help on the Lanczos filter and meaningful discussions. Furthermore, the authors also thank for the great comments from two anonymous reviewers. This research is supported by the Ministry of Science and Technology of the Republic of China (Taiwan) under Grants MOST 106-2111-M-002-009-, MOST 107-2111-M-002-012-, MOST 108-2111-M-002-010-, and MOST 109-2111-M-002-006-.
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