Four methods for determining the extratropical transition (ET) onset and completion times of Typhoons Mindulle (2004) and Yagi (2006) were compared using four numerically analyzed datasets. The open-wave and scalar frontogenesis parameter methods failed to smoothly and consistently determine the ET completion from the four data sources, because some dependent factors associated with these two methods significantly impacted the results. Although the cyclone phase space technique succeeded in determining the ET onset and completion times, the ET onset and completion times of Yagi identified by this method exhibited a large distinction across the datasets, agreeing with prior studies. The isentropic potential vorticity method was also able to identify the ET onset times of both Mindulle and Yagi using all the datasets, whereas the ET onset time of Yagi determined by such a method differed markedly from that by the cyclone phase space technique, which may create forecast uncertainty.
The process of extratropical transition (ET) occurs when a tropical cyclone (TC) moves poleward into the midlatitudes from its genesis region in the tropics, accompanied by environmental changes including the increasing Coriolis force, decreasing sea surface temperatures, and the ambient atmosphere of increased baroclinicity and vertical wind shear. On average, 46% of Atlantic TCs (Hart and Evans 2001), 27% of western North Pacific storms (Klein et al. 2000), 33% in the southwest Pacific basin (Sinclair 2002), and about 10% of TCs in the South Indian Ocean (Foley and Hanstrum 1994) experience ET. During ET the TC structure is replaced by extratropical features, with a hybrid period due to the complex interaction between the cyclone and the midlatitude systems. Several characteristics of this interaction include asymmetries in wind, thermal structure, moisture field, precipitation, cloud, and convection (Sekioka 1970; Jones et al. 2003), as well as the dispersal of the upper-level tropical cyclone warm core (Ritchie and Elsberry 2001).
A TC undergoing ET frequently reintensifies and evolves into a fast-moving and rapidly developing extratropical cyclone (EC), which may produce torrential rainfall resulting in catastrophic inland flooding (DiMego and Bosart 1982a,b), damaging winds (Merrill 1993; Evans and Hart 2008), and hazardous seas (Sekioka 1956; Sinclair 2002). A review of the cyclone structure change due to ET, associated disaster threats to land communities and maritime activities, and challenges to forecasters can be found in Jones et al. (2003). Forecasting when an ET process starts and finishes thus becomes important for forecasters and is still one of many challenging issues related to ET due to our incomplete understanding of the interaction between TCs and midlatitude systems. As pointed out by Jones et al. (2003), to specify a precise time at which a TC has become extratropical and propose a universal definition that is based on tools available to a forecaster would be desirable from an operational viewpoint.
Klein et al. (2000) proposed a two-stage definition for ET in the western North Pacific from an observational perspective. With the loss of symmetric features of the cloud field, a TC is in the transformation stage, which completes when the storm becomes embedded in the baroclinic zone. The second stage of ET is called the reintensification stage, in which the transformed TC either reintensifies as a baroclinic system or else dissipates. In the present study, the beginning (ending) of the transformation stage of ET is defined as the ET onset (completion) time. At present, forecasters mostly rely on subjective assessments of the asymmetry of the storm’s cloud shield, its travel over colder waters, and the intrusion of cold air into the central storm circulation to discern the onset and completion of ET (Evans and Hart 2003). However, those TCs that weaken or recurve may also have these traits. Several diagnostic criteria for ET onset and completion times have been suggested in previous studies from different perspectives. Through investigating the frontal characteristics of the ET process (Keyser et al. 1988; Schultz and Doswell 1999), Harr and Elsberry (2000) deemed that values of the scalar frontogenesis function could be used for describing the ET of TCs. Another tool that can be used to determine ET onset and completion times is the cyclone phase space (CPS), which is a combination of parameters of the storm-motion-relative thickness symmetry and thermal wind (Hart 2003; Evans and Hart 2003; Hart et al. 2006). Demirci et al. (2007) proposed the ET completion time when an open-wave (OW) pattern at 500-hPa geopotential height occurs. More recently, Kofron et al. (2010a) analyzed the applicability of the above-mentioned criteria for the ET time using the Navy Operational Global Assimilation and Prediction System (NOGAPS) gridded analyses and found that the OW and scalar frontogenesis diagnosis both failed to discriminate between transitioning ET and recurving non-ET cases, and all of the above-mentioned methods were found to have disadvantages that preclude them from providing consistent guidance for the time when extratropical transition of a poleward-recurving TC is occurring. They also suggested that isentropic potential vorticity (IPV) can be utilized to define ET onset and completion times and, more importantly, further determine whether a cyclone will reintensify after ET (Kofron et al. 2010b).
Operational forecasters commonly employ a variety of numerically analyzed datasets of differing resolutions with which to determine the ET onset and completion times of a TC. To provide more detailed guidance to forecasters, this study will compare the utility of these different methods for determining ET onset and completion times on four numerically analyzed datasets of different horizontal resolutions. Evans and Hart (2003) used the CPS diagnostic to examine the ET onset and completion times of several storms with the operational National Centers for Environmental Prediction (NCEP) Aviation Model and NOGAPS numerical analyses, which have comparable resolutions, and found that the diagnosis of ET onset or completion of some cases differed between the two data sources. Nevertheless, intercomparisons of operational feasibility of the aforementioned ET onset and completion diagnostic techniques across datasets of differing horizontal resolution are still lacking. Therefore, as the first step, we will evaluate in this study the existing methods of defining ET onset and completion times with two typical ET cases in the northwestern Pacific using distinct reanalysis data and numerical simulation results. The two TCs chosen in this study are Typhoons Mindulle (2004) and Yagi (2006), with the former reintensifying slightly and the latter undergoing rapid reintensification after ET in terms of the reports of the best-track data. The data and methodology employed in this study are described in section 2, followed by the analysis results in section 3. Finally, a summary and discussion are represented in section 4.
2. Data and methodology
a. Typhoons Mindulle (2004) and Yagi (2006)
The best-track data from the Shanghai Typhoon Institute of China Meteorology Administration (STI/CMA) shows Typhoon Mindulle formed near Guam at 1800 UTC 21 June 2004 as a tropical depression and then moved west-northwestward (Fig. 1a). It developed into a tropical storm after 36 h and was updated to a typhoon at 0600 UTC 27 June 2004 (Fig. 1b). This typhoon peaked at 1200 UTC 28 June 2004 with a minimum sea level pressure (MSLP) of 950 hPa (Fig. 1b). Mindulle made its first landfall at the eastern coast of Taiwan (about 20 km south to Hualien) as a severe tropical storm around 1500 UTC 1 July 2004 (Fig. 1a). After 15 h, it made its second landfall in the city of Yueqing in China’s Zhejiang Province with tropical storm intensity. Henceforth, Mindulle accelerated north-northeastward toward the East China Sea (Fig. 1a). During this period it underwent an ET process. The STI/CMA best-track data reported the ET completion time of Mindulle as 0000 UTC 4 July 2004. The MSLP of Mindulle dropped 2 hPa from 1200 UTC 3 July to 1200 UTC 4 July 2004 (Fig. 1b).
Typhoon Yagi originated from a tropical depression about 1200 km east-northeast of Guam and had a clockwise loop in its track afterward (Fig. 1c). Yagi reached its peak intensity on 21 September 2006 with an MSLP of 920 hPa (Fig. 1d); the storm then recurved northeastward (Fig. 1c). With the increasing wind shear in midlatitudes, Yagi began to weaken and underwent ET. This storm was identified as an EC at 0600 UTC 25 September 2006 by the CMA. The STI/CMA best-track data indicated a reintensification, with a 22-hPa decrease in MSLP during next 30 h beginning at 0000 UTC 25 September 2006 (Fig. 1d).
As noted above, Mindulle (2004) and Yagi (2006) both underwent ET processes. The former only slightly reintensified while the later exhibited a striking reintensification after ET. These two cases, which experienced distinct intensity change after the ET, are chosen to investigate the ET processes in the present study.
To examine the possible influences of different data sources on determining the ET onset and completion times, three reanalysis datasets with different horizontal resolutions ranging from 20 km to 1.25° in longitude and simulation results from the mesoscale Weather Research and Forecasting Model (WRF) are examined. Two global reanalysis datasets, the Japan Meteorological Agency’s (JMA) 25-yr Reanalysis Project (JRA-25) data (Hatsushika et al. 2006; Onogi et al. 2007; Song et al. 2011) with 1.25° × 1.25° resolution and the National Center for Atmospheric Research (NCAR)-archived National Centers for Environmental Prediction (NCEP) Global Final (FNL; Wang et al. 2009) analysis data with 1.0° × 1.0° horizontal resolution at 6-h intervals, are used in this study. In addition to these two relatively coarser datasets, JMA Regional Spectral Model 20-km reanalysis data (RSM-20km; NPD/JMA 1997) are employed to investigate the ET evolution of the two typhoons. It should be noted that assimilated data, assimilation techniques, model dynamic codes, physics packages, and reanalysis methods also evidently differ among the above datasets, and these differences must cause uncertainty and discrepancies in determining ET onset and completion times. However, an evaluation of the influences of these differences is not possible. Nevertheless, the possible impact of data resolution on the identification of ET onset and completion times can be at least qualitatively examined, as is discussed below.
Because it is often difficult for authors to gain access to higher-resolution (e.g., grid spacing of ~10 km or less) reanalysis data, an alternative is to investigate results of high-resolution mesoscale numerical simulations. Also, high-resolution mesoscale regional numerical models have been widely employed for operational TC forecasting, and forecasters may diagnose ET processes using mesoscale numerical forecast results. It is expected that the evaluation of the determination techniques of ET times based on high-resolution mesoscale numerical model results enables us to provide more operational guidance for forecasters. Therefore, the addition of high-resolution numerical model results is employed in this study. Simulations of Typhoons Mindulle and Yagi were conducted with WRF version 3.1 (Skamarock et al. 2008). Here, two grids nesting down to 10-km horizontal resolution are employed in the simulations of these two storms. The outer domains both have a grid length of 50 km and contain 150 × 150 grid points in the x and y directions. A 10-km nested mesh is used with grid dimensions of 320 × 320 and 400 × 400 in the simulations of Mindulle and Yagi, respectively, and is large enough to include the regions where the typhoons moved during their ET processes. Corresponding domains used in the simulations are illustrated in Figs. 1a and 1c, respectively. All meshes have 57 vertical levels with the top level at 10 hPa. The two simulations employ the same physics options, including the Yonsei University boundary layer scheme (Noh et al. 2003; Hong et al. 2006), the Noah land surface model (Chen and Dudhia 2001), a simple cloud-interactive shortwave radiation scheme (Dudhia 1989), the Rapid Radiative Transfer Model (RRTM) longwave radiation (Mlawer et al. 1997) scheme, the Betts–Miller–Janjić cumulus scheme (Betts 1986; Betts and Miller 1986; Janjić 1994) on the 50-km grids, and the Lin microphysics scheme (Lin et al. 1983) on all grids. The NCEP FNL gridded analyses are used as the initial and lateral boundary conditions for the simulations. The starting times of the simulations are 0000 UTC 3 July 2004 with an integration length of 48 h for Mindulle and 0000 UTC 23 September 2006 with an integration length of 72 h for Yagi, respectively. The simulation periods covered the respective ET processes of Typhoons Mindulle and Yagi as discussed below.
Figure 1 shows that the simulated tracks of Mindulle and Yagi approximate well the observations, and the simulated storm intensities are fairly reasonable, particularly with the slight (rapid) reintensification of Mindulle (Yagi) being reproduced well. Because model verification is not the focus of this study, only preliminary model verification was conducted. For instance, in comparison with the National Aeronautics and Space Administration Quick Scatterometer (QuikSCAT) surface winds (Fig. 2), the asymmetric surface wind distributions associated with both Mindulle and Yagi were captured well in the simulations. Around 1000 UTC 4 July 2004, Typhoon Mindulle triggered higher surface winds (>25 m s−1) near the northeastern coasts of the Korean Peninsula (Fig. 2a), a trend that was found in the modeling results as well (Fig. 2b). For Yagi, a wavenumber-2 asymmetry of surface winds was noted in the core region with elevated wind velocities in the northwest and southeast at 1855 UTC 24 September 2006 (Fig. 2c). The WRF model successfully simulated this asymmetric feature, with the peak surface wind velocity greater than 30 m s−1 (Fig. 2d). The cloud features (e.g., cloud shapes and occurrence of active convection) indicated by the model-derived topcloud temperatures of the two storms (not shown) appear similar to the observations from the infrared satellite imagery as well. Therefore, the simulations are believed to have reproduced reasonably well the structures of these two typhoons.
c. Methodology in determining ET onset and completion times
Four methods employed to determine the ET onset and completion times will be discussed in this section.
Harr et al. (2000), as well as Ritchie and Elsberry (2003), indicated that ET was dependent primarily on midlatitude structures. Demirci et al. (2007) proposed that the occurrence when the TC became an OW on the 500-hPa map (contoured every 20 m) denoted the completion of ET. At that time, the cyclone was properly embedded in the baroclinic zone. In addition, the OW method provided an objective way to define the ET time that can be viewed using gridded datasets by nonexperts (Kofron et al. 2010a).
A number of previous studies found that the ET process could be considered to be an interaction between a vortex and a baroclinic zone (Doswell 1984, 1985; Davies-Jones 1985; Keyser et al. 1988), accompanied by the development of midlatitude frontal boundaries. Harr and Elsberry (2000) demonstrated that the development of frontal characteristics manifested various complex physical processes associated with ET, and proposed that the rate of the increase in frontogenesis peaked at a time that may be defined as the ET completion time. The three-dimensional scalar frontogenesis parameter [SFP; see Eq. (A1) in the appendix] calculated in this study follows Schultz and Doswell (1999) and Harr and Elsberry (2000). More specifically, Harr and Elsberry (2000) suggested that the time when the sum of the scalar frontogenesis in the northeast and southwest quadrants of the cyclone within the 500-km radius shows a distinct increase could potentially indicate the ET completion time.
Another method for analyzing the process of ET is the use of phase-space diagrams (Hart 2003; Evans and Hart 2003; Hart et al. 2006; Kitabatake 2011). The CPS (Hart 2003) is a continuum describing the broad evolution of all synoptic-scale cyclones. Three parameters (i.e., B, and ) are calculated in the CPS method as indicated in the appendix [Eqs. (A2)–(A4)]. Parameter B reflects the 900–600-hPa thickness asymmetry relative to the moving direction of the storm.1 Parameters and indicate the 900–600- and 600–300-hPa thermal winds, respectively. These CPS parameters are computed within a 500-km radius from the storm center based on the geopotential height field. Positive (negative) values of or indicate a warm- (cold-) core structure according to the thermal wind relationship. Large positive values of B reveal a highly asymmetric (frontal) structure while near-zero values of B indicate the symmetry. The start of an ET event is decided when |B| becomes greater than 10 m, and the ET completion is determined as and both change from positive to negative (Hart and Evans 2001; Hart 2003; Evans and Hart 2003; Hart et al. 2006; Song et al. 2011).
Potential vorticity (PV) has been used to describe the structure of the cyclone and the surrounded balanced atmospheric flow related to ET events (Bosart and Lackmann 1995; Thorncroft and Jones 2000; McTaggart-Cowan et al. 2001), and has recently been considered to be a potentially useful tool for determining ET onset and completion times (Kofron et al. 2010b). Because TCs have higher PV values at lower levels with high PV gradients confined to the inner core (Jones et al. 2003; Shapiro and Franklin 1995) and the preexisting trough interacting with the TC has higher PV values in upper levels associated with the upper-level jet, the interaction of the TC and the trough may be described by the evolving midlevel isentropic PV [IPV; Eq. (A5) in the appendix; Kofron et al. (2010b)]. Using the Navy Operational Global Atmospheric Prediction System analyses on a 1° latitude–longitude grid, Kofron et al. (2010b) found that the time when the TC-centered circular average IPV on the 330-K potential temperature isentropic surface shows a minimum is a good indicator of ET onset. Moreover, the completion of ET for reintensifying cases is defined as occurring when the storm exceeds an IPV threshold value of 1.6 PVU (1 PVU = 10−6 K m2 kg−1 s−1) at the 330-K potential temperature isentropic level.
a. Open-wave features in the 500-hPa geopotential height fields
Demirci et al. (2007) found that the time when the last closed contour of the 500-hPa geopotential height fields related to the cyclone becomes open (namely OW structure) seemingly coincides with the end of the transformation stage defined in Klein et al. (2000), when the storm has the characteristics of a baroclinic cyclone in both satellite imagery and numerical weather prediction analyses, and the center of the storm is embedded in cold, descending air. Demirci et al. (2007) proposed that such time is thus potentially taken as the ET completion time. The ET completion times of Typhoon Mindulle and Yagi are examined in this section using the three reanalysis data and WRF simulation results, based on the OW criterion.
Figure 3 depicts the 500-hPa geopotential height fields associated with Typhoon Mindulle. Mindulle was located to the southeast of a weak trough at 0600 UTC 4 July 2004 (Figs. 3a, 3d, 3g, and 3j). The coarser-resolution data (JRA-25 and FNL) show the occurrence of OW structures both at 1200 UTC 4 July 2004 (Figs. 3b and 3e), which is 12 h later than the completion time in the STI/CMA best-track data. Note that, although the cyclone tended to slightly intensify, a closed-contour feature only recurred in the FNL analyses at 1800 UTC 4 July 2004. The 500-hPa geopotential height fields from RSM-20km do not exhibit the open-wave feature during the period shown in Figs. 3g–i, although a typical EC feature was seen with the lower-level center of the cyclone significantly separating from the midlevel one (e.g., Fig. 3i). Additionally, the absence of open-wave features was also found throughout the whole simulation of Mindulle (seen in Figs. 3j–l), suggesting that it is unable to ascertain the ET completion time of Mindulle based on the simulated 500-hPa geopotential height fields.
For the rapidly reintensifying case of Yagi, all datasets show the presence of open-wave features (Fig. 4), but the corresponding ET completion times are distinct. At 0000 UTC 24 September 2006, a pattern with a closed 500-hPa geopotential height contour associated with Yagi lays in the south of a deep trough in the JRA-25 data (Fig. 4a). An open-wave feature was present 6 h later (Fig. 4b), indicating the ET completion. This OW figure still existed at 1200 UTC 24 September 2006 (Fig. 4c), with pronounced cyclone tilting. The ET completion time determined with FNL data was 6 h earlier than that in JRA-25, with the OW structure found at 0000 UTC 24 September 2006 (Fig. 4e). For the RSM-20km dataset, the ending time of ET based on the OW method was much later than those with JRA-25 and FNL data, with the open-wave feature occurring at 0600 UTC 25 September 2006 (Fig. 4i). The ET completion time based on WRF simulation results is about the same as that in RSM-20km. Figure 4k illustrates an OW signal at 0100 UTC 25 September 2006.
The above-mentioned analyses suggest that the OW method seems not to be a feasible operational tool for determining the ET completion time, and it is at least sensitive to data sources. The presence of OW structure is also dependent on other factors, such as model resolution, storm translation speed, and the latitude where the storm is located. As grid spacing becomes smaller, it becomes easier to find a closed contour on the 500-hPa geopotential height map. As a storm encounters a strong pressure gradient and accelerates, the OW signal may occur. These dependent factors complicate the identification of the ET completion time using the OW method. As a result, we could obtain relatively consistent ET completion times of these two typhoons with the JRA-25 and FNL datasets, which have coarser resolutions, whereas the ending time of the ET of Mindulle could not be determined with the RSM-20km and WRF simulation results and the achieved ET times of Yagi with the RSM-20km and WRF simulation results obviously lag those with JRA-25 and FNL data.
Harr and Elsberry (2000) examined the frontogenesis of cyclones interacting with a preexisting trough to the northwest and northeast, and they hypothesized that scalar frontogenesis could be used to describe the ET of TCs. More specifically, the addition of the SFP in the northeastern and southwestern quadrants of the cyclone at 500 hPa and averaged within the 500-km radius would show a distinct increase, which could indicate the ET completion time. The SFPs are calculated from Eq. (A1) in the appendix by using all of the three reanalysis data and the WRF simulation results, revealing that the tilting term dominates positive frontogenesis at all times for the two cases during the period of interest, consistent with the finding of Schultz and Doswell (1999).
The horizontal distribution of scalar frontogenesis and the evolution of potential temperature indicated that there existed obvious warm frontogenesis in the northeastern quadrant of Mindulle, which was related with the frontal cloud feature (not shown). Additionally, a T-bone feature in the frontogenesis horizontal distribution was found in Mindulle (not shown), which was generally observed in warm seclusion ET cases (Shapiro and Keyser 1990; Kitabatake 2008).
Figure 5 shows the evolution of scalar frontogenesis in four quadrants within the 500-km radius from the center of Typhoon Mindulle. It seems that frontogenesis dominated at the mid- and upper levels in the case of Mindulle. However, different data sources represented distinct particulars in different quadrants. The low-resolution data (i.e., JRA-25 and FNL) show similar patterns; however, the frontolysis in the northwestern quadrant and frontogenesis in the northeastern quadrant from FNL are both more striking than those from JRA-25 (Figs. 5a, 5b, 5e, and 5f). RSM-20km also suggests the presence of significant frontogenesis in the mid- and upper layers in its northeastern quadrant (Fig. 5j), but the frontogenesis features in other quadrants are different from those found with the JRA-25 and FNL data. In particular, pronounced frontogenesis was observed in the northwestern and southwestern quadrants (Figs. 5i and 5k). WRF simulation results of Mindulle reflected relatively noisy signals of the SFP (Figs. 5m–p), resulting from the calculation of scalar frontogenesis magnitude that is dependent on the horizontal gradients of potential temperature and wind fields and thus is highly dependent on the resolutions of the datasets. In the northwestern quadrant, weak frontogenesis occurred in the mid- and upper troposphere prior to 0600 UTC 4 July 2004 (Fig. 5m). Relatively intense frontogenesis in the mid- and upper levels was found in the northeastern quadrant, whereas notable frontolysis existed in the lower troposphere at the same time (Fig. 5n). It is noted that marked frontolysis was found throughout the troposphere in the southeastern quadrant before 0000 UTC 4 July 2004 (Fig. 5p), while the evidence of weak frontogenesis was found from FNL (Fig. 5h).
The temporal evolution of the addition of the 500–300-hPa SFP of Mindulle in the northeastern and southwestern quadrants is depicted later (Fig. 7a), showing clearly that frontogenesis was found in the middle and upper troposphere (Fig. 5). JRA-25, FNL, and the WRF simulation results show the peak increasing rates of the sum of the SFP around 0000 UTC 4 July 2004, suggesting that the ET completion time of Mindulle determined using these data is 0000 UTC 4 July 2004. However, it is difficult to obtain the ET completion time using RSM-20km data due to there being no continuously growing summed SFP (Fig. 7a), although striking frontogenesis was found in the mid- to upper troposphere (Figs. 5i–l).
The SFPs associated with Typhoon Yagi and calculated with the different data sources are portrayed in Fig. 6, showing distinct distribution features. Despite the comparable horizontal resolutions, the SFP details of JRA-25 and FNL somewhat differed. Significant frontogenesis existed in the northeastern quadrant with peak SFPs at 1800 UTC 23 September and 1800 UTC 24 September 2006 for FNL and JRA-25 (Figs. 6b and 6f), respectively. Figures 6d and 6h suggest weak frontogenesis in the southeastern quadrant, with maximum SFPs at 0000 UTC 23 September and 0600 UTC 24 September 2006 for FNL and JRA-25, respectively. Furthermore, the distributions of the SFPs derived from RSM-20km and the WRF simulation results were strikingly different from those from the JRA-25 and FNL data, and the SFPs computed from the WRF results were relatively noisy again. Note that Figs. 6i–l only show the SFP distributions derived from RSM-20km in the 48-h period prior to 0000 UTC 25 September 2006 after which the storm circulation partly moved beyond the coverage range of the data. The RSM-20km and WRF simulation results represent visible frontogenesis below the midtroposphere in the northwestern quadrant (Figs. 6i and 6m). Unlike the frontogenesis revealed from JRA-25 and FNL in the northeastern quadrant, the RSM-20km and WRF simulations indicated that frontolysis was dominant in that quadrant (Figs. 6j and 6n). Additional distinction of frontogenesis characteristics among these data sources occurred in the southeastern quadrant, with frontolysis in the mid- and upper troposphere for the RSM-20km data (Fig. 6l) and frontolysis prevailing before 0000 UTC 25 September 2006 for the WRF simulation (Fig. 5p).
For the rapidly reintensifying case of Yagi, it seems that only the JRA-25 data represented an obvious increase in the addition of the SFP in the northeastern and southwestern quadrants around 1800 UTC 24 September 2006 (Fig. 7b), indicative of the completion of ET according to the SFP method. Other data failed to determine the end of ET via the addition of the SFP, even with frontolysis for the RSM-20km and WRF results during most of the period of interest (Fig. 7b).
c. CPS parameters
Phase-space diagrams can be used to illustrate the ET, subtropical and tropical transitions, and the development of warm seclusions within ECs (Hart 2003). As represented previously in the literature (Hart 2003; Evans and Hart 2003; Hart et al. 2006), a TC should start with a relatively symmetric warm-core structure, reflected by the thickness asymmetry parameter B close to 0 m, and the thermal wind parameters and show positive values. Accompanying poleward movement of the cyclone and the interaction with midlatitude westerlies, B will begin to rise and the thermal wind parameters will decrease; with B greater than 10 m indicative of the ET onset; and with both and negative along with B > 10 m showing the end of ET.
Figure 8 shows the time series of B, , and values corresponding to Mindulle (Figs. 8a–c) and Yagi (Figs. 8d–f) during the periods of interest. The values of the B parameters computed from all four data sources were accordantly greater than 10 m around 1200 UTC 3 July 2004 (Fig. 8a), indicating the ET onset time of Mindulle. The consistent ET onset time indicated across the datasets results partly from the areal averaging employed to calculate the B parameter in the CPS method. Around 1200 UTC 3 July 2004, the upper-level thermal wind parameters () derived from the JRA-25, FNL, and RSM-20km data became negative, which revealed that a cold-core structure occurred. In contrast, the upper-level thermal wind parameter of the WRF simulation result was not negative until 0600 UTC 4 July 2004 (Fig. 8c). On the other hand, the lower-level thermal wind parameters () computed from FNL and JRA-25 turned out to be negative at approximately 1800 UTC 4 July 2004 (Fig. 8b), while the values from the RSM-20km and WRF simulation results became negative about 6 and 8 h before that time, respectively, suggesting that the lower-level vortex was featured a cold core and thus the ET ended. The aforementioned phase-space parameters associated with Typhoon Mindulle showed that it was likely a warm seclusion ET case (Shapiro and Keyser 1990; Kofron et al. 2010a).
For the rapidly reintensifying case of Yagi, the B parameters from all data tended to rise starting at 0000 UTC 23 through 1200 UTC 25 September 2006 (Fig. 8d). Note that, because the circulation of Yagi moved beyond the coverage range of RSM-20km after 0000 UTC 25 September 2006, only part of the CPS parameter’s evolution was shown in Fig. 8. The determined ET onset times of Yagi based on FNL, JRA-25, and RSM-20km data, as well as the WRF simulation results, were about 0900, 1200, 2000, and 1500 UTC 23 September 2006, respectively, with the B parameters greater than 10 m (Fig. 8d). Like Mindulle, all data deemed that the upper-level core of Yagi got cold in advance of the lower-level core. The FNL data show that the upper core of the storm turned cold at about 1000 UTC 23 September 2006 (Fig. 8f), and the ET finished 8 h later when the associated became negative (Fig. 8e). JRA-25 represented a relatively late process, with the upper- (lower-) level core turning cold at 1800 UTC 23 September (1500 UTC 24 September) 2006. Figure 8f illustrates that the values computed from RSM-20km and the WRF simulation became negative around 1500 UTC 24 September 2006. The WRF simulation results showed the latest ET completion time at 0200 UTC 25 September 2006 (Fig. 8e).
The PV can be used to depict TC structure and interaction between the TC and surrounding environments and has been used to describe the evolution of TCs undergoing ET (Bosart and Lackmann 1995; McTaggart-Cowan et al. 2001; Thorncroft and Jones 2000), thus being a potentially useful tool for determining the ET time (Kofron et al. 2010b). Kofron et al. (2010b) demonstrated that the evolving IPV might reflect the interaction of the TC and the preexisting trough during ET. As introduced in section 2, Kofron et al. (2010b) found that the local minimum value of 330-K IPV averaged within the 500-km radius apart from the storm center occurs when ET begins, and the ET completion time appears to be well defined by the 330-K IPV threshold value of 1.6 PVU. Whether the ET onset and completion times of Typhoons Mindulle (2004) and Yagi (2006) can be successfully determined or not with the IPV method proposed by Kofron et al. (2010b) based on JRA-25, FNL, and RSM-20km data and WRF simulation results will be examined in this section. Another issue of interest is the sensitivity of the radius used to average the results, which is also investigated herein.
The calculated IPV of Mindulle and Yagi is shown in Figs. 9 and 10, respectively. Figure 9 shows the average IPV of Mindulle with the value at the initial time (0000 UTC 3 July 2004) removed during the period 0000 UTC 3 July–0000 UTC 5 July 2004. The 300-, 400-, and 500-km average results consistently suggest that there exist lower PV values around the 330-K isentropic surface for all data, with higher PV values above and below, respectively. Therefore, following the method in Kofron et al. (2010b), the 330-K IPVs averaged within the radii of 300, 400, and 500 km are drawn in Figs. 11a–c to determine the ET onset of Mindulle. The 330-K IPVs averaged within the 500-km radius from JRA-25, FNL, and RSM-20km data were characterized by a very similar pattern, with the minima present at 1200 UTC 3 July 2004 (Fig. 11a). This time was the ET onset time of Mindulle as suggested in Kofron et al. (2010b). The minimum 330-K IPV value averaged within the 500-km radius from the WRF results was seen at 0800 UTC 3 July 2004 (Fig. 11a). It is noted that the 330-K IPV patterns were somewhat changed when averaged within the 300-km radius (Fig. 11c), although they were similar to those in Fig. 11a when averaged within the 400-km radius (Fig. 11b). Figure 11c indicates that the values of the 330-K IPV from FNL and JRA-25 were still minimized at about 1200 UTC 3 July 2004, while the lowest values from RSM-20km and the WRF simulation appeared at 1200 UTC 3 July and 0600 UTC 4 July 2004, respectively. This suggests that different average radii used to calculate the mean PV value possibly lead to different IPV patterns.
Figure 10 depicts the average IPV of Typhoon Yagi with the values at the initial time (0000 UTC 23 September 2006) removed. Note that the IPV distributions from RSM-20km were shown in Fig. 10 only through 0000 UTC 25 September 2006 due to the storm circulation beyond the coverage range of the data, and we do not analyze them in depth herein. The distributions of IPV associated with Yagi differed from those of Mindulle. JRA-25, FNL, and the WRF results notably represented relatively low IPV values on the 325–350-K isentropic surfaces prior to 0600 UTC 25 September 2006 (Fig. 10), with the lowest values found in the 300-km-radius calculation. As a result, the 330-K IPV associated with Yagi was featured by a rapid increase after 1200 UTC 25 September 2006 (Figs. 11d–f). The ET onset time could be clearly defined at 0000 UTC 25 September 2006 in the light of the 500-km-radius average 330-K IPVs from JRA-25 and FNL, and such a time was about 3 h earlier according to the WRF simulation result (Fig. 11d). If IPV was averaged within a 400-km radius (Fig. 11e), the minimum 330-K IPV from FNL and the WRF results was still at 0000 UTC 25 September and 2100 UTC 24 September 2006, respectively, while the minimum 330-K IPV from JRA-25 occurred at 0600 UTC 25 September 2006. In contrast, considering the IPV averaged within a 300-km radius, the ET onset times defined from FNL data and the WRF simulation result were shifted to 0000 and 1200 UTC 25 September 2006 (Fig. 11f), respectively.
4. Concluding discussion
During ET a decaying TC frequently reintensifies as an intense EC that may produce intense rainfall, strong winds, and hazardous seas. Therefore, determination of ET onset and completion times is important, and is a challenge to forecasters. In the present study, we examine four methods for determining the ET onset and completion times of two representative storms (i.e., Typhoons Mindulle and Yagi) with four datasets (i.e., JRA-25, FNL, and RSM-20km, as well as WRF simulations) that have different horizontal resolutions. Note that, although it is impossible to quantitatively evaluate the influence of the difference of data resolution on the identification of the times, the probable role of resolution was qualitatively investigated in this study. A summarized schematic diagram of the determined ET onset and completion times of the two typhoons is displayed in Fig. 12.
It was proposed that the OW and SPF methods had potential for determining the ET completion time (Demirci et al. 2007; Harr and Elsberry 2000). The OW method could determine the ET completion time of the rapidly reintensifying case of Typhoon Yagi (2006) based on all datasets (Fig. 12b), while it failed to indicate the ET completion time of the slightly reintensifying case of Typhoon Mindulle (2004) using RSM-20km and the WRF simulation results (Fig. 12a), which have finer resolutions. In contrast, the SFP technique was able to identify the ET completion time of Mindulle across the four datasets (Fig. 12a), whereas this method was successful in only determining the ET completion time of Yagi using the two coarser datasets (i.e., JRA-25 and FNL; Fig. 12b).
With the exception of RSM-20km for Typhoon Yagi, CPS succeeded in determining the ET onset and completion times of Mindulle and Yagi (Figs. 12a and 12b). Also with the exception of RSM-20km for Yagi, the IPV method enabled us to suggest the ET onset times of the two storms (Figs. 12a and 12b). However, the ET onset times of Yagi determined by the IPV method were much later than those by CPS. Kofron et al. (2010b) proposed that the ET completion time may be defined as the time when the 330-K IPV exceeds the threshold value of 1.6 PVU. Only the 330-K IPV calculated from the 10-km WRF simulation result met the above threshold for Typhoon Mindulle (2004), with the determined ET completion time of around 1200 UTC 4 July 2004 (Fig. 12a). For Typhoon Yagi, the values of average 330-K IPV calculated from JRA-25, FNL, and the WRF simulation result exceeded 1.6 PVU, suggesting the end of the ET according to the IPV method (Fig. 12b).
Of interest is that the ET onset times of Mindulle suggested by the CPS and IPV methods using the four datasets were quite consistent, around 1200 UTC 3 July 2004 (Fig. 12a). The ET completion times of Mindulle determined by OW, CPS, and IPV were around 1200 UTC 4 July 2004, while the SFP method indicated the ET completion time of 0000 UTC 4 July 2004 (Fig. 12a).
The four methods seem not to be sensitive to the data sources for the slightly reintensifying case of Mindulle (Fig. 12a), whereas they become strikingly sensitive to the distinct datasets for the rapidly reintensifying case of Yagi (Fig. 12b). For instance, the ET completion times of Yagi determined by OW using JRA-25 and FNL, which have coarser horizontal resolutions, were around 0000 UTC 24 September 2006, while the completion times based on high-resolution RSM-20km and the WRF simulation results were about 24 h later (Fig. 12b). Only JRA-25 data succeeded in determining the ET completion time of Yagi. The ET onset times indicated by the CPS method using JRA-25 and FNL were approximately around 1200 UTC 23 September 2006. However, these two datasets with comparable horizontal resolutions obviously indicated different completion times, with the ET process determined based on JRA-25 data ending about 24 h later than that suggested using FNL. Figure 12b shows the much longer ET course of Yagi determined by CPS using the WRF simulation result that lasts for about 36 h.
Kofron et al. (2010a) pointed out that the OW and SFP methods appeared not to be feasible operational tools for determining the ET completion time. In this study we also find that the ET completion times of the two distinct ET cases were not smoothly obtained with the OW and SFP methods based on the four data sources. For the OW method, whether the 20-m contour intervals utilized on the 500-hPa geopotential height map are appropriate for data having different resolutions is still questionable. On the other hand, it is sometimes difficult to illustrate the complex circulation features associated with the storm and thus the OW structure, when the cyclone interacts with ambient midlatitude systems. Furthermore, the presence of OW structure appears to be dependent on a variety of factors, such as data resolution, storm translation speed, and the latitude where the storm is located. As grid spacing becomes smaller, it tends to become easier to see a closed contour as suggested in this study. As a storm becomes superimposed on a strong pressure gradient and accelerates, the OW signal may occur. These factors complicate the identification of the ET completion time using the OW method. Additionally, an objective technique for determining the occurrence of the OW structure is hard to achieve as well. SFP may be used to dynamically characterize the TC–trough interaction, but it is seemingly difficult to be used for practically finding the ET completion time, because of the lack of reasonable thresholds for scalar frontogenesis to determine an ET completion time. Harr and Elsberry (2000) suggested that the time when the 500-hPa scalar frontogenesis averaged in the northeastern and southwestern quadrants within the 500-km radius shows a distinct increase could potentially indicate the ET completion time. However, reasonable thresholds for the scalar frontogenesis increase are not obtained in operational forecasting. Additionally, scalar frontogenesis features represent case-to-case variability. Because of the magnitude of scalar frontogenesis dependent on horizontal gradients of the variables, noisy patterns associated with scalar frontogenesis are generally found in high-resolution data analysis, resulting in the lack of continuity in scalar frontogenesis evolution (e.g., Fig. 7b). CPS parameters give quantitative thresholds and succeed in determining the ET times when applied to the two cases in this study. However, there are still several problems to be discussed further. Since the result from the CPS method appeared to be sensitive to the data sources in the case of Yagi (2006), as shown in Fig. 11b, forecasters need to take into account the dependence of the data source as they make use of the CPS technique to predict the ET onset and completion times of such a rapidly reintensifying storm. Moreover, more rapidly reinforcing cases after ET should be further examined to document whether the sensitivity to data sources is ordinary. In addition, the corresponding thresholds for the parameters (i.e., B, , and ) may vary over different ocean basins (Hart 2003), which needs to be investigated in depth. As a method proposed more recently, the IPV method successfully determined the ET onset times of Mindulle and Yagi using all the datasets. However, it is difficult to suggest the ET completion times according to the present threshold [averaged 330-K IPV > 1.6 PVU; Kofron et al. (2010b)]. Therefore, the threshold of IPV for determining the ET completion time based on different data sources of different resolutions needs to be analyzed further. As indicated in Fig. 11, the average range of IPV seems to more or less influence the pattern of IPV and thus the result. Hart (2003) and Tapiador et al. (2007) demonstrated that sensitivity to radius also existed for the CPS method, particularly for TCs with differing sizes. These sensitivities should be taken into account in practical forecasting. It is also noted that the ET onset times of Typhoon Yagi indicated by the CPS and IPV methods differ markedly from each other (Fig. 12b), which may create forecast uncertainty.
As a specific case study, the present paper examined only two representative cases undergoing distinct intensification processes after ET. Factors affecting the ET process are highly complicated they involve unique synoptic and TC environments. Therefore, comprehensive studies of a large number of ET cases may provide further insight into the operational applicability of these methods across different data sources. Additionally, it is impossible to absolutely examine the role of resolution in determining ET onset and completion times based on datasets from differing models. Sensitive numerical experiments with a certain model may be an alternative approach to this problem. Corresponding results will be represented in future publications.
The authors are grateful to two anonymous reviewers for their helpful comments. This study was supported through the National Basic Research Program of China (2009CB421504), and the National Natural Science Foundation of China under Grants 40775060, 41005033, 40905029, and 40921160381. G. Fu was partly supported by the Chinese Meteorological Agency under Grants GYHY200706031 and GYHY GYHY200906002, and the Chinese Government Program of Introducing Talents of Discipline to Universities (B07036). We also thank the Key Laboratory of Mesoscale Severe Weather (MOE) of Nanjing University for furnishing the Japanese Meteorology Agency Regional Spectral Model 20-km reanalysis.
Related Formulas Used in the Determination Techniques of ET Times
where θ is the potential temperature. Positive (negative) −Fn corresponds to the frontogenesis (frontolysis).
In the cyclone phase-space method (Hart 2003), parameter B is related to the 900–600-hPa thickness asymmetry relative to the moving direction of the storm. In the Northern Hemisphere, it is computed as
where Z is the isobaric height, R indicates right of current storm motion, L indicates left of storm motion, and the overbar denotes the areal mean over a semicircle of the 500-km radius. Parameters and indicate the 900–600- and 600–300-hPa thermal winds, respectively,
in which is the pressure.
As in Kofron et al. (2010b), the IPV used herein is
where is the gravitational constant, is the relative vorticity along a constant potential temperature surface, and is the Coriolis parameter.
Sinclair (2004) deemed that calculations based on the method of Evans and Hart (2003) yielded fluctuating B values for the TCs whose moving directions were varying, and proposed referencing B to the area-averaged thermal wind vector. The method used in Sinclair (2004) produced smoothly varying values of B for the southwest Pacific TCs. We have also employed the method of Sinclair (2004) to calculate the B values of Typhoons Mindulle and Yagi, and found that the B values (not shown) often seemed to be larger than those calculated with the method of Evans and Hart (2003), with the exception of the WRF results for Mindulle. In addition, whether using 10 m as the B threshold is reasonable for western North Pacific TCs, still needs to be considered further if B is calculated as in Sinclair (2004). Therefore, considering the smooth motion of Mindulle and Yagi, we still used the method of Evans and Hart (2003) for the calculation of B in the current study.