A total of 163 tropical cyclones (TCs) occurred in the eastern China seas during 1979–2011 with four types of tracks: left turning, right turning, straight moving, and irregular. The left-turning type is unusual and hard to predict. In this paper, 133 TCs from the first three types have been investigated. A generalized beta–advection model (GBAM) is derived by decomposing a meteorological field into climatic and anomalous components. The ability of the GBAM to predict tracks 1–2 days in advance is compared with three classical beta–advection models (BAMs). For both normal and unusual tracks, the GBAM apparently outperformed the BAMs. The GBAM’s ability to predict unusual TC tracks is particularly encouraging, while the BAMs have no ability to predict the left-turning and right-turning TC tracks. The GBAM was also used to understand unusual TC tracks because it can be separated into two forms: a climatic-flow BAM (CBAM) and an anomalous-flow BAM (ABAM). In the CBAM a TC vortex is steered by the large-scale climatic background flow, while in the ABAM, a TC vortex interacts with the surrounding anomalous flows. This decomposition approach can be used to examine the climatic and anomalous flows separately. It is found that neither the climatic nor the anomalous flow alone can explain unusual tracks. Sensitivity experiments show that two anomalous highs as well as a nearby TC played the major roles in the unusual left turn of Typhoon Aere (2004). This study demonstrates that a simple model can work well if key factors are properly included.
Tremendous progress has been made in tropical cyclone (TC) track forecasts over the past 20 years as a result of significant improvements in numerical model guidance and the use of consensus forecasts. For example, current 5-day track forecasts are often as accurate as 3-day forecasts were a decade ago (Elsberry 2014). Every year, about seven typhoons or TCs hit the mainland of China from either the southern or eastern coasts (Xue et al. 2012). Over the past five years (2007–11), the average typhoon track forecast errors at the National Meteorological Center of China are 114, 190, and 287 km for 24-, 48-, and 72-h forecasts, respectively (Qian et al. 2012). Similar progress has been made for TCs in the North Atlantic basin at the National Hurricane Center, where TC position forecasts have gained approximately 1 day in skill; for example, 48-h position errors during 2000–08 are comparable to 24-h position errors during 1970–89, at about 100 km (Rappaport et al. 2009). Much of the increase in forecast skill can be attributed to improvements in model physics, increases in model resolution, and the availability of aircraft and satellite observations (e.g., Aberson 2010), as well as new data assimilation techniques (e.g., Hamill et al. 2011). For the infamous Atlantic-based Hurricane Sandy (2012), the European Centre for Medium-Range Weather Forecasts (ECMWF) global model accurately predicted its landfall location one week ahead of time (Bassill 2014).
Statistically, all typhoons that make landfall on mainland China must reach the offshore area to the north of 15°N and west of 130°E during their lifetimes. From 1979 to 2011, there were a total of 330 typhoons over the two ocean basins [South China Sea (SCS) and eastern China seas (ECS)] that reached or passed through this area (Qian et al. 2014a). Among those 330 TCs, most of them had smooth tracks and only a few had abrupt turns. It is those smooth-track (normal) TCs that contribute to the high accuracy in track forecasts, while false predictions are often associated with the rapid-turning TCs. Most TCs move westward from the northwestern (NW) Pacific into the SCS (normal track) but a few of them swerve to the north with a sudden right-turning track (Deng et al. 2010). With such sudden right-turning typhoons, their landfall locations are very difficult to accurately predict with currently available methods even at 24–48-h lead times. A well-known case is Supertyphoon Megi in 2010, which made a sharp turn to the north and failed to be predicted by any of the major operational prediction centers worldwide (C. H. Qian et al. 2013; Qian et al. 2014b). To investigate these unusual typhoon tracks, we recently developed a generalized beta–advection model (GBAM) by decomposing an atmospheric variable into climatic and anomalous components. Fifteen cases of sudden right-turning typhoons, including Supertyphoon Megi (2010), which occurred in the SCS from 1979 to 2011, were studied using the GBAM. The results are very encouraging. All 15 right-turning, as well as 10 straight-moving, typhoon tracks were successfully forecasted by the GBAM 2–3 days in advance (Qian et al. 2014b).
Given the success of the GBAM in predicting unusual TC tracks in the SCS, the GBAM method is extended to study unusual typhoon tracks in the ECS in this study. A sudden north-turning (right turning) TC is unusual in the SCS, while a sudden west-turning (left turning) TC is unusual in the ECS (Wu et al. 2013). It is these unusual tracks that cause the most property damage and loss of life in China. Unfortunately, there are no causes unanimously agreed upon by researchers for these unusual TC tracks. For example, Typhoon Aere in 2004 (Fig. 3a, described in greater detail below) is such a case with an unusual left-turning track. It was investigated in several studies that resulted in different conclusions (Wei et al. 2006; Li et al. 2006; Duan et al. 2014). Among them, four different causes were mentioned: (i) anticlockwise motion due to interaction with another typhoon in the tropical NW Pacific, (ii) impact of two subtropical high systems over the continent and ocean, (iii) intensification of east-northeasterly winds on its northwestern side, and (iv) terrain. All of these studies admitted the difficulty of this forecast. Therefore, it is critical to know the correct causes and to understand the interaction between the TC and its surrounding environment for further improving TC track forecasts, which is the motivation of this study.
By decomposing atmospheric variables, we are trying to isolate environmental and disturbed flows in order to understand the underlying causes. All TCs that occurred in the ECS from 1979 to 2011 (163 TCs) were used in the study. This paper is organized as follows. Section 2 describes the data and methods, including the classification of the 163 TCs, the variable decomposition method, and different beta–advection models. Section 3 focuses on the four unusual left-turning TCs, including their spatial structures and track predictions from different beta–advection models. Section 4 focuses on the normal tracks (smoothly right-turning and straight-moving TCs), using composite analysis and beta–advection model predictions. Conclusions and a discussion are given in section 5.
2. Data and methods
a. Data and typhoon track classification
Two datasets are used in this paper. The first is the ERA-Interim dataset from the ECMWF website (http://apps.ecmwf.int/datasets/data/interim_full_daily), with a horizontal 0.75° × 0.75° latitude–longitude grid interval and at standard pressure levels from 1000 to 50 hPa (Dee et al. 2011). The second dataset is the best tracks derived from the Joint Typhoon Warning Center (Chu et al. 2002). Since the observations of the modern satellite era began in 1979, the dataset from that year onward is used.
During the period 1979–2011, a total of 163 TCs occurred in the ECS and reached typhoon strength [74 mi h−1, 64 knots (kt; 1 kt = 0.51 m s−1), or 33 m s−1]. The ECS includes the Bohai Sea, the Yellow Sea, the East China Sea, and Taiwan Island, as shown in Fig. 1a. Their tracks are classified into four types (Table 1). Right turning and straight moving are the two most common tracks. One hundred and thirteen TCs have a right-turning track. Their initial, peak intensity, and dissipating positions are indicated by open circles, solid circles, and plus signs, respectively, in Fig. 1a. As shown by the fitted lines, the initial positions of these right-turning TCs are located in the lower latitudes, mostly in the tropical NW Pacific, and the dissipating positions are in the midlatitudes. The peak intensity positions are observed mostly in the subtropical NW Pacific near the ECS. Thirty-three TCs have straight-moving tracks (Fig. 1b); their initial, peak intensity, and dissipating positions are mostly located in the tropical NW Pacific, in the ECS, and over inland eastern China, respectively. From the initial to peak intensity and dissipating positions, the general directions of movement are illustrated by the arrows in Figs. 1a and 1b.
Figure 2 shows the three representative groups of tracks in the ECS. The first group shows five TCs with a single right-turn point near the box (24°–26°N, 124°–126°E) located to the northeast of Taiwan (Fig. 2a). Most right-turning TCs reached their maximum intensity near the turning point (Dare and Davidson 2004; Zeng et al. 2007). The second group shows four TCs with multiple (two or more) right-turn points (Fig. 2b). The third group shows seven TCs with a straight-moving track and an initial landfall on Taiwan (Fig. 2c). In total, there were 33 straight-moving TCs with 29 of them making landfall on mainland China, one making landfall on Japan, and three dissipating over the open sea. Among the 29 landfalling TCs, 20 of them made their initial landfalls on Taiwan. The seven selected cases in Fig. 2c show that they moved straight toward Taiwan and made first landfall on the island within the box (23°–24.5°N, 121°–122°E) during the last 48 hours of their life cycles.
The four typhoons with an unusual left-turning track are shown in Fig. 3. The five pairs of arrows indicate a direction change exceeding 40° between the postturning point and the track 48 hours prior to the turn. After their final left turns, all four of the TCs made landfall on the eastern coast of China. Although the occurrence of left-turning TCs is rare (4 out of 163 or about 2.5%), they caused severe damage after their unexpected landfalls and were woefully difficult to predict in current operations.
Thirteen TCs (Table 1) experienced complex irregular paths, as shown in Fig. 4. Six of them had at least one stationary circular movement for 2–3 days. TC number 14 in 2002 originated on 20 July 2002 in the tropical NW Pacific and moved westward for 2 days (Fig. 4a, dotted line). It experienced a circular movement for 3 days and then turned northwestward, heading for southwestern Japan. TC number 13 in 1996 originated on 28 July 1996 in the equatorial central Pacific and moved northwestward for 7 days (Fig. 4a, dashed line). It experienced a stationary circular movement for about 8 days in the southern Sea of Japan and then turned northeastward along the Japanese coast with increasing speed. TC number 20 in 2001 originated on 5 September 2001 in the eastern sea of Taiwan and moved northeastward for only 1 day (Fig. 4a, solid line). Its track experienced two quasi-stationary circles to the northeast of Taiwan, each with a duration of about 9 days. Finally, the TC moved southwestward and made landfalls in Taiwan and on the southern coast of China. Similarly, the three TC tracks illustrated in Fig. 4b also had a stationary circular movement. Seven other TCs showed a serpentine movement, with two moving northeastward (Fig. 4c) and five moving northwestward (Fig. 4d). The 13 complex TC tracks, 3 dissipated TCs, and 14 multiple turning-point tracks are not investigated in this study, which leaves the total number of TCs to be investigated in this study at 133. A summary of these 163 TCs is given in Table 1.
b. Decomposition methodology
Traditionally, a TC vortex is considered to be embedded in and steered by large-scale environmental flow (Chen and Ding 1979; Chan and Gray 1982; Deng et al. 2010; Roy and Kovordanyi 2012). Theoretically, this steering flow can be obtained by removing the TC vortex from the total circulation on the scale of a thousand kilometers. However, since an actual weather circulation is complex and contributed to by both the TC vortex (internal forcing) and the surrounding flow (external forcing), as well as their interactions, it is difficult to define a TC vortex. Therefore, separating a TC vortex from its surrounding flow remains a challenge.
On the other hand, the relationship between TC movement and large-scale environmental flow usually varies depending on the definition of an environmental flow. Previous works attempted to extract a steering flow from the total flow by spatially filtering the TC vortex and other small-scale disturbances. George and Gray (1976) suggested that the flow near 700 hPa or the average flow in the 700–500-hPa layer is the best representation of the environmental steering flow in the tropics, while Holland (1984) suggested the use of the vertical mean steering flow between 850 and 300 hPa. Some others suggested the use of a deep-layer mean from 1000 to 150 or 100 hPa to approximate a TC’s motion (Sanders et al. 1980; Dong and Neumann 1986; Franklin 1990; Velden and Leslie 1991). Recently, Galarneau and Davis (2013) defined an optimal environmental steering flow with variable vertical extent. At all levels from 850 to 200 hPa, at an increment of 50 hPa, TC vorticity and divergence are removed within a predetermined radius to obtain the environmental steering flow for a TC (Davis et al. 2008; Galarneau and Davis 2013). However, there is a large uncertainty in defining the radius of a TC vortex in this method. Therefore, it is difficult to obtain a realistic steering flow and TC vortex from all of the existing methods.
A new objective approach is used to separate large-scale background flow and weather disturbances in this study. The new approach can avoid the ambiguities involved with defining steering flow, the TC vortex, and surrounding small-scale disturbances. This method decomposes a total meteorological field into instantaneous (hourly time resolution at present) climatic and anomalous components. Any atmospheric field F such as geopotential height, temperature, and wind at diurnal time t (24 hours per day), say 0000 UTC, on calendar day d in year y at a spatial point of latitude , longitude , and pressure level p, can be decomposed into a climatic field and an anomalous field following Qian (2012a,b) and Qian et al. (2014b):
The climatic field is estimated by averaging over 30 years (1981–2010) based on the reanalysis data for a given calendar day and diurnal time:
where y covers 1981–2010. It is assumed that the positive and negative anomalies of atmospheric variables at a specific grid point cancel each other out during the 30-yr period to approximate the quasi-static climatic state. The climate defined by Eq. (2) varies from hour to hour and from day to day.
As a matter of fact, the method of decomposing a total field into instantaneous climatic and anomalous components was proposed and used in anomaly forecasting in early 2000 (Grumm and Hart 2001; Hart and Grumm 2001) and gained popularity for high-impact weather forecasts in recent years (Junker et al. 2008, 2009; Graham and Grumm 2010; Grumm 2011a,b; Graham et al. 2013). Du et al. (2014) further expanded this concept into “ensemble anomaly forecasting” by combining anomaly forecasting with ensemble forecasts to not only identify abnormal events but to also quantify the confidence of an anomaly forecast itself. Similar to ensemble anomaly forecasting, an “extreme forecast index” is used at the ECMWF (Lalaurette 2003; Zsoter 2006). To be suitable for all climate zones, the standardized anomaly is used in an anomaly forecast. In recent years Qian and his colleagues found that a nonnormalized anomaly is also useful in short-, medium-, and extended-range forecasts of many extreme weather events, such as freezing rain (Qian and Zhang 2012), heat waves (Ding and Qian 2012), heavy rain (W. H. Qian et al. 2013), and typhoon tracks (Qian et al. 2014b).
All of these previous anomaly-related methods [except for Qian et al. (2014b)] are used for analyzing either analysis data or model outputs but not for initializing a model. In this study, the decomposed climatic and anomalous components will be directly used to initialize simple prediction models.
c. Model descriptions
The barotropic vorticity equation thought to approximately govern the horizontal flow under consideration is written in a planar coordinate system as
where t is time, x (y) is the distance in the west–east (south–north) direction, β is the meridional variation of Coriolis parameter f, , , and (rad s−1) is the angular speed of the earth’s rotation. We use a and as the mean radius of the earth and geographical latitude, respectively. Here, F is a generic forcing term that includes forces at all scales and dissipation such as divergence, friction, and diabatic processes. For nondivergent, frictionless and adiabatic atmospheric motion, Eq. (3) can be simplified as
Equation (4) indicates that the movement of a vortex such as a typhoon is primarily controlled by the advection of relative vorticity and the earth rotation beta effect. This is the classical two-dimensional beta–advection model (BAM).
Holland (1983) and Marks (1992) applied this BAM to hurricane track forecasting. The dynamics of advection and the beta effect of TC motion have been described in more detail by Chan (2005). There are several versions of the BAM (Velden and Leslie 1991; Marks 1992; Simpson 2003): the BAM Shallow (BAMS) applied to the 850–700-hPa layer, the BAM Medium (BAMM) for the 850–400-hPa layer, and the BAM Deep (BAMD) for the 850–200-hPa layer. In the early days, the BAM was initialized using the vertically averaged horizontal wind predictions from the National Meteorological Center (NMC; the predecessor of NCEP) spectral model (Marks 1992) and also included the beta effect (i.e., variations of the Coriolis force with latitude) (Holland 1983). Roy and Kovordányi (2012) found that the BAM’s performance is poor in the NW Pacific basin compared to the North Atlantic basin, while in the North Atlantic basin the BAMD and BAMM performed slightly better than the BAMS.
Which layer (shallow, medium, or deep) to apply is an issue for the classical BAM. In our previous study with a generalized BAM (Qian et al. 2014b), we found that there is an optimal level for a BAM-type model to apply for short-term TC track predictions. This level is close to the levels of the maximum vorticity anomaly VAmax and minimum divergence anomaly DAmin. The VAmax and DAmin levels can be estimated between 850 and 200 hPa over the TC center at model initialization time. The generalized BAM can be derived as follows.
According to the decomposition of Eq. (1), total wind (vorticity) can be decomposed into climatic and anomalous wind (vorticity) as
Taking the climatic average of Eq. (6), we can obtain a pure climatic vorticity equation driven by climatic vorticity advection, the climatic-flow beta effect, the climatic averaged forcing from anomalous weather systems (transient eddies, X and Y), and other climatic averaged generic forcings:
Based on our estimations of many TCs, it is found that
Based on the 30-yr ERA-Interim dataset, it is also found that can be neglected because it is on the order of 10−10 s−3, an order of magnitude smaller than the daily anomalous vorticity advection by total wind (on the order of 10−9 s−3), that is,
Therefore, under the nondivergent, frictionless, and adiabatic condition , Eq. (8) can be simplified as
Equation (11) is the GBAM used in our recent work (Qian et al. 2014b). The GBAM basically describes the advection of a TC disturbance (anomaly) by the total flow, which is the sum of the climatic and anomalous flows. To examine the different roles of the climatic and anomalous flow, a climatic-flow beta–advection model (CBAM1) and an anomalous-flow beta–advection model (ABAM) can be analogously defined by
respectively, where the vorticity anomaly is . The CBAM can be viewed as the steering process of a TC vortex by climatic flow, while ABAM explicitly describes the interaction between a TC vortex and other surrounding anomalous weather disturbances. The separate descriptions of the impacts from large-scale background flow and the anomalous systems by the CBAM and the ABAM are an advantage over the traditional total-field-based BAM. In operation, the CBAM might be similar to the classical BAM with differences in the definition of flows, that is, climatic (temporally anomalous) versus large-scale environment (residual) flow. Note that there is a typographical error for the beta effect term in both the GBAM and CBAM equations of Qian et al. (2014b) (misprinted as and ). The climatic vorticity equation in Qian et al. (2014b) has also been corrected here by adding two climatic-averaged eddy feedback terms (but the term was purposely not included over there) [see Eq. (7)].
All the integrations in Eqs. (4) and (11)–(13) are written in planar coordinates for ease of understanding and simplicity. In our actual calculations, these equations are written and calculated in spherical coordinates. For example, the GBAM is in the form of
where the anomalous vorticity is .
Below is a brief description of the computational methods used to integrate our models forward in time. For further details, readers are referred to Qian et al. (2014b). Model integration is done in spherical coordinates with 0.75° × 7.5° latitude–longitude grid spacing at every pressure level. The ERA-Interim is used as initial conditions, where the global climate and the anomaly are obtained through Eqs. (2) and (1). The time step for the model integration is 10 minutes and the climate is updated every 6 hours (since the reanalysis is available 6 hourly) through Eq. (2). At each time step, a new vorticity anomaly is calculated using Eqs. (11)–(13) from the GBAM, CBAM, and ABAM. Then, new wind anomalies are derived from the new vorticity anomaly via a spherical harmonic expansion, and climatic wind is linearly interpolated between two climatic winds that are 6 hours apart (ideally climatic winds are needed at every time step, i.e., every 10 minutes). Since the vorticity anomaly tends to grow too strong and causes numerical instability during integration, the model-derived new vorticity anomaly field is smoothed by performing a triangular truncation on the spherical harmonic coefficients to make the model computationally stable. This technique makes the computation stable but also has a side effect: the vorticity anomaly amplitude decreases steadily with time and becomes weaker than the observations after 2 days. The spherical harmonic expansion and triangular truncation technique are described online (http://dx.doi.org/10.5065/D6WD3XH5).
3. Unusual left-turning tracks
a. Typhoon Aere (TC number 20 in 2004)
Historical cases have shown that unusual TC tracks are difficult to predict even 24–48 hours in advance (Chen et al. 2002). Typhoon Aere (Fig. 3a) formed in the equatorial NW Pacific at 1700 UTC 17 August 2004, reached typhoon intensity on 21 August, and then moved northwestward. Its intensity peaked at 1800 UTC 24 August off the northeastern shore of Taiwan and then in an unusual move, turned to the west-southwest. It landed on the southeastern coast of China (Shishi City, Fujian Province) at 1330 UTC 25 August and dissipated in Guangdong Province at 1200 UTC 26 August 2004. From 24 to 26 August, it caused severe flooding in both southeastern Fujian Province and northern Taiwan. As indicated by Fig. 3a, the left turn is quite sharp with a turning angle of about 65°.
To have an initial look at Typhoon Aere’s structure and its surrounding environment, Fig. 5 shows the vertical–meridional cross sections of some related fields through the TC center at various stages of the typhoon. In Fig. 5a, the difference in the total temperature from the climate is somewhat noticeable and the difference in the total height is also barely noticeable over the TC area (indicated by the letter T) and subtropical region (indicated by the letter S). But no detailed structures are revealed because of the too large contour intervals used. To enlarge these difference signals, anomalous fields are displayed in the remainder of Fig. 5. Figures 5b–d are the height and temperature anomalies 48, 24, and 0 hours prior to the turning point, from which a well-defined TC structure as well as an anomalous extratropical cyclone and an anomalous anticyclone to the north of Typhoon Aere can be observed in both the height and temperature fields. This vertical structure of the TC and extratropical cyclone is similar to that seen by Hart (2003), who calculated a spatial height departure relative to a zonal mean height. The interaction among these anomalous systems should be described by the ABAM [Eq. (13)]. The vorticity and divergence anomalies 24 hours before the turning are separately shown in Figs. 5e and 5f. In Fig. 5e an axis of positive vorticity anomaly extends from the surface to about 200 hPa over the TC area, indicating the vertical depth of Typhoon Aere. In Fig. 5f an axis of convergent anomaly extends from the surface to about 300 hPa and an axis of divergent anomaly extends from 400 to 200 hPa over the TC. The transition from convergence to divergence resulted in a minimum divergence anomaly around the 350-hPa level. A maximum vorticity anomaly is also observed approximately at 350 hPa. Later results will show that the optimal level for GBAM performance is close to the levels of DAmin and VAmax (see Table 2).
In addition to the vertical structures shown in Fig. 5, Fig. 6 shows a two-dimensional view of Typhoon Aere at the optimal level of 350 hPa at 0600 UTC 23 August 2004 (24 hours before the turning). From the total fields (Fig. 6a), Typhoon Aere is intuitively expected to continue its northwestward or northward path because it is located on the western edge of a strong subtropical NW Pacific high. Since it turned toward the southwest in reality, there must be other stronger impacts acting upon the typhoon. Li et al. (2006) and Wei et al. (2006) argued that the northeasterly wind of a high pressure system over land to the west of the TC, as well as the interaction with a nearby typhoon, contributed to this unusual southwestward turn. The climatically easterly wind (Fig. 6b) suggests that it should be steered to the west. In the anomalous fields (Fig. 6c) two positive (anticyclonic; A1 and A2) and two negative (cyclonic; V1 and V2) centers of height anomaly surrounded Typhoon Aere (indicated by the hurricane symbol). Vortex V2 is another TC, which is used to explain the interaction with Typhoon Aere in some early studies (Lin et al. 2005; Wei et al. 2006; Li et al. 2006). From Fig. 6c, both V1 and A2 seem to pull the typhoon north-northeastward. At the turning point (Fig. 6d), two positive and two negative height-anomaly centers still surrounded Typhoon Aere. It had approached anticyclonic system A1 and could be directly influenced by A1 to make a southwestward turn. These speculations will be examined by the GBAM, CBAM, and ABAM below to quantitatively assess the roles played by the total, climatic, and anomalous flows in causing this unusual left-turning movement.
Nine experiments (Table 2) were carried out for the four left-turning typhoons, which are shown in Fig. 3. For each of the experiments an optimal level for the GBAM to predict a TC track, which ranges from 850 to 300 hPa (Table 2), is first detected. The corresponding VAmax and DAmin levels of the nine experiments were also located and listed in Table 2.2 For locating VAmax and DAmin levels, two-dimensional divergence and vorticity anomalies are first obtained at each pressure level from 850 to 200 hPa. They can then be found by manually comparing the central values at all levels over a typhoon center. Table 2 shows that the optimal level is in the neighborhood of the VAmax and DAmin levels but especially closer to the DAmin level, which is probably consistent with the zero divergence assumption used in deriving Eq. (4). Therefore, the GBAM could be operated at the DAmin level in a real-time prediction since the optimal level is not known beforehand. Figure 7a shows the 48-h predictions of Typhoon Aere by the six models initialized at 0600 UTC 23 August 2004. The GBAM, CBAM, and ABAM are integrated at the optimal level of 350 hPa. The TC turns left (westward) immediately if just the climatic flow is considered (CBAM), while it turns right (northeastward) rapidly if just anomalous flow is considered (ABAM). The prediction is the best and is closest to the best track if both climatic and anomalous flows are considered together by the GBAM. To compare with the classical BAM [i.e., Eq. (4) using the full wind and full vorticity with no decomposition], all three versions (BAMS, BAMM, and BAMD) were also employed to predict Typhoon Aere’s track. By definition, the mean wind and vorticity of the 850–700-, 850–400-, and 850–200-hPa layers were used for the BAMS, BAMM, and BAMD, respectively. Unfortunately, all three classical BAMs incorrectly predicted a straight-moving track (Fig. 7a). To better understand the above result, we compared the differences in the three controlling factors between the GBAM and the three BAMs: advection flow, vorticity itself, and the beta effect. It is seen that the largest difference is in the advection flow with smaller differences in the vorticity and beta terms (not shown). By replacing the advection flows in the BAMS, BAMM, and BAMD with that of the GBAM, the three BAMs, especially BAMD, yield slightly improved track forecasts but were still much worse than the GBAM and far away from the best track (not shown). Even when we initiated the BAM with the full wind and full vorticity from the optimal level of the GBAM, the BAM still incorrectly predicted a locally circular track for Typhoon Aere (not shown). By repeating the same experiment for the other three left-turning TCs (Walt, Herb, and Todd), all the results showed that the BAM prediction is much worse than the GBAM prediction in terms of both position and speed. This indicates that the TC vortex structure and intensity modified by the decomposition method are also important in determining the track. The beta term plays the smallest role in track prediction.
To investigate the relative impacts of the four anomalous systems in Fig. 6c, another four 48-h track forecasts of Typhoon Aere are made by the GBAM, each of them with one particular anomalous system being removed. The results are compared in Fig. 7b. To remove an anomalous system such as V2, total wind u, υ are replaced by the corresponding climatic wind , within the area covered by the positive vorticity anomaly. New anomalous wind u′, υ′ and vorticity can then be obtained by integrating the GBAM [Eq. (11)]. By removing the nearby TC vortex (V2), the GBAM prediction has an immediate deviation from the originally predicted track and then moves in a straight line to the northwest. By removing the midlatitude vortex V1, the GBAM follows the original track closely in the first 24 hours but makes a sharp left turn to noticeably deviate from the original track in the second 24 hours, although the direction trend is still close. However, by removing either the A1 or A2 anomalous highs, the predicted Typhoon Aere continues to move northwestward with no left turns at all during the entire 48 hours, similar to the tracks predicted by the BAMs. These results suggest that the left-turning motion of Typhoon Aere is greatly influenced by the two anomalous highs (A1 and A2) as well as the nearby TC and is less influenced by the midlatitude cyclone.
Figures 8a and 8b show a detailed snapshot comparison between the analyzed and predicted Typhoon Aere vortex (vorticity anomaly) at the turning point. We can see that the GBAM predicts a very nice left curve along the best track at 24-h lead time. However, the predicted TC moves faster than the observed TC. Moving too fast for a TC vortex seems to be a common feature for the GBAM since it happened in most of the cases, including right-turning (Figs. 8c,d) and straight-moving (Figs. 8e,f) TCs (note that the classical BAMs tend to move TCs even faster). The relatively fast trajectories predicted by GBAM and BAM could be a subject of further study. Although the predicted intensities are comparable to the observed ones for these three typhoon cases, intensity prediction is certainly beyond the capability of the GBAM since the GBAM is merely a simple dynamical model with no physics.
b. The other three left-turning cases
The same experiment was repeated for the other three left-turning TCs. Their optimal, VAmax, and DAmin levels are all listed in Table 2. Figure 9a shows the model track predictions of Typhoon Walt (TC number 17 in 1994) initiated at 0600 UTC 9 August 1994 (48 hours prior to the left turn). The CBAM predicts a right-turning track under the influence of climatic southwesterly steering flow, the ABAM predicts an immediate left-turning track, and only the GBAM prediction is more consistent with the best track: moving northeastward initially followed by a sharp left turn, although the direction is to the west instead of the southwest. All three classical BAMs (BAMS, BAMM, and BAMD) predict tracks in the wrong direction (two to the northeast and one to the northwest). When initiated 24 hours prior to the left turn (Fig. 9b), the GBAM correctly predicts a left-turning track after 24 hours and the ABAM predicts an immediate left turn while the CBAM track continues to move northeastward under the climatic steering flow. The other three models (BAMS, BAMM, and BAMD) all incorrectly predict some kind of circular track.
Typhoon Todd (TC number 10 in 1998) experienced a continuous left-turn loop and even a returning movement after its landfall on eastern China. Experiments were carried out for the two turning points: a left turn to the north near 20°N and a left turn to the west with a surprising northeastward return after landfall near 30°N. Figures 10a and 10b are the two 48-h forecasts for the first turn, where the GBAM obviously outperformed all other models, the CBAM, ABAM, and the three classical BAMs. Initiated at 1200 UTC 18 September (24 hours before the landfall; Fig. 10c), both GBAM and especially ABAM give the correct direction, while the CBAM goes in an opposite direction. The BAMS predicts a northwestward motion, and the BAMM and BAMD predict two stagnating motions wandering locally. Initiated at 1200 UTC 19 September (12 hours before the returning movement; Fig. 10d), the GBAM correctly predicts the returning movement but the ABAM keeps its southwestward movement and the CBAM predicts a northeastward movement steered by the climatic flow. The BAMS, BAMM, and BAMD wrongly predict northwestward, northeastwards and eastward motions, respectively.
Typhoon Herb (TC number 10 in 1996; Fig. 11) experienced a long 14-day path with several left and right turns. After a left turn to the southeast of Taiwan, it made an initial landfall on Taiwan and then a second landfall on the southeastern coast of China. Finally, it continued to move northwestward and dissipated in central China. Initiated at 1800 UTC 28 July 1996 (72 hours before the first landfall; Fig. 11a), the GBAM correctly predicts a left-turning track closely following the best track and landfall on Taiwan at the 48-h lead time, while the CBAM moves too far north in position and is too slow in speed and the ABAM departs too far south. For the three classical BAMs, the BAMS predicts a very fast straight track instead of a left-turning path initially, although the overall track accidently matches with the best track pretty well, while both the BAMM and BAMD predict straight tracks too far to the south. Initiated at 1800 UTC 29 July 1996 (48 hours before the second landfall; Fig. 11b), the GBAM correctly predicts landfall on an area close to the observed on the southeastern coast of China 48 hours in advance (unfortunately the landfall on Taiwan is missed in this prediction); the ABAM prediction is too slow in speed and too far north in position, and the CBAM predicts a straight westward track that is completely off the best track. All three classical BAMs maintain a northwestward track with a speed about 18 hours too fast and make their landfalls too far north of the observed.
4. Normal tracks
Section 3 clearly demonstrates that the GBAM noticeably outperformed the classical BAM in predicting the unusual left-turning TC tracks in the ECS. This section will examine if that is also true for normal tracks (i.e., right turning and straight moving). The two representative groups of TCs shown in Figs. 2a and 2c will be used for demonstration although all 99 right-turning and 30 straight-moving cases listed in Table 1 had been examined.
a. The right-turning tracks
As with the left-turning TCs, we first visually examine the climatic and anomalous systems associated with right-turning TCs. From Fig. 2a, we see that the five right-turning TCs reached their maximum strength within the box covering 24°–26°N, 124°–126°E. This box is used to define the TC turning point. The composite vertical–meridional cross sections of the height and temperature anomalies of the five TCs were constructed through the TC center 48 hours before and at the turning point, respectively (Fig. 12). Compared to the left-turning TC (Fig. 5), an apparent difference is in the anomalous system distribution to the north of the TC: from lower to high latitudes, we find a low–high–low pattern (an anomalous high to the north of the TC) for the right-turning TCs, while there is a low–low–high pattern (an anomalous low to the north of the TC) for the left-turning TCs.
Consistent with the vertical structure, this anomalous high located to the north of the TC is clearly visible in the horizontal composites at 350 hPa before and after the turn (Figs. 13e–h). In the temperature anomaly, two warm centers are collocated with the TC vortex and the anomalous high center. The climatic system at different stages is shown in Figs. 13a–d. The TC is initially located on the southern side of the subtropical high ridgeline with easterly steering flow (Fig. 13a); 24 hours before the right turn, the TC is near the northern edge of the ridgeline (Fig. 13b); at the moment it turns right, the TC is located on the northern side of the ridge (Fig. 13c); and 24 hours after the turn, the TC has entered the climatic westerly flow region (Fig. 13d).
Figure 14 shows the 48-h track forecasts of the five right-turning TCs by the GBAM and the three classical BAMs (the CBAM and ABAM are no longer shown for clarity) initiated 24 hours before the turn. The superiority of the GBAM over the three classical BAMs is evident: the GBAM successfully predicts right-turning tracks closely following the best track for all five cases, while the classical BAMs fail in all cases (moving straight in the northwest direction), except for one occasion when the BAMD predicts a right-turning track for TC number 23 in 1980 (Fig. 14d).
To assess the overall forecast capability of the GBAM, the model is applied to all 99 right-turning TCs and their track errors are calculated. Note that since the GBAM-predicted speed is faster than the best track in most cases, speed error is not considered in the following calculation but only the distance between a predicted position and the best track is measured. An example is shown in Fig. 14a, where the two short black lines indicate the 24- and 48-h forecast track distance errors. Since all the forecasts were initiated 24 hours before the right turn, the 24- and 48-h forecasts represent the track errors before and after the turning point. Averaged over the 99 right-turning TCs, the distance errors are 122 and 215 km for the 24- and 48-h forecasts, respectively, which is slightly worse than or comparable to the total track errors (speed error was also included) in current operational forecasts based on state-of-the-art numerical weather prediction (NWP) models. The TC track forecast errors are on the order of 100 and 200 km for 24- and 48-h lead times in current operational forecasts, which include all easy and difficult tracks [Xu et al. (2010) for China, and http://www.nhc.noaa.gov/verification for the United States]. Considering such a simple dynamics-only model, the GBAM’s performance is amazingly good. However, it needs to be pointed out that an analysis used to initialize a real-time NWP model is different from a reanalysis and contains fewer observations than a reanalysis does.
b. The straight-moving tracks
For straight-moving TCs, their landfalls are used as a reference point because of the significance. Figure 15 shows the composite vertical–meridional cross sections of height and temperature anomalies through the TC center 48 hours before and at the landfall point, based on the seven straight-line TCs shown in Fig. 2c. Comparing Fig. 15 with Fig. 12, we can see that the anomalous vertical structure of the straight-moving TCs is similar to that of the right-turning TCs but with a weaker and much broader anomalous high on its northern side. This can be further seen from the composite horizontal fields at 350 hPa, where both the anomalous and climatic subtropical highs are quite spatially extensive (Fig. 16). The TC remains in the climatic easterly flow zone on the southern side of the climatic subtropical high ridge at all stages (Figs. 16a–c). In the anomalous fields, the TC is located in the southeasterly to easterly zone under the influence of anomalous highs (Figs. 16d–f). Unlike the left- and right-turning situations where opposite forcing is often seen between climatic and anomalous fields, in the straight-track situation forcing is generally in a similar direction from both climatic and anomalous flows. Therefore, a northwestward straight-moving track is probably a relatively easier one to predict, which is indeed confirmed by the results shown in Fig. 17.
Figure 17 shows 48-h track forecasts of the seven straight-moving TCs by the four models initiated 48 hours before landfall. The GBAM predicts the tracks quite well in all seven cases. As expected, this is the best group to predict among the classical BAMs: all three of the BAMs have skill similar to the GBAM for two cases (TC number 13 in 2005 in Fig. 17d and TC number 15 in 1980 in Fig. 17e), slightly worse than the GBAM for three cases (TC number 9 in 2007 in Fig. 17b, TC number 17 in 1990 in Fig. 17f, and TC number 18 in 2000 in Fig. 17g), and much worse than the GBAM for two cases (TC number 8 in 1994 in Fig. 17a and TC number 9 in 2009 in Fig. 17c). To assess the overall forecast capability, the GBAM is applied to all 30 of the northwestward straight-moving TCs that made landfall either on mainland China or Japan. The 48- and 24-h track forecasts were made separately by initializing the GBAM 48 and 24 hours before landfall. Landfall location errors were then also measured separately for the 24- and 48-h forecasts. Averaged over the 33 TCs, the mean landfall location errors of the GBAM are 33 and 101 km for 24- and 48-h forecasts, respectively. Again, this performance is surprisingly impressive for such a simple model compared to the current operational forecasts involving models with state-of-the-art complexity (Powell and Aberson 2001).
5. Conclusions and discussion
During the last 33 years (1979–2011), a total of 163 TCs arrived in or passed through the ECS. These TCs can be classified into four groups. The right-turning group has 113 TCs, including 99 with a single turning point and 14 with multiple turning points. The northwestward straight-moving group has 33 TCs, including 29 that made landfall on mainland China, one that made landfall on Japan, and 3 that dissipated over the open sea. Four left-turning cases with a turning angle greater than 40° form another group that occurred in the ECS and then made landfall on the eastern coast of China. The left-turning track is unusual, hard to predict, and has the biggest impact when it occurs. Therefore, understanding the causes of left-turning TCs is important. There are 13 TCs that experienced complex tracks. Among them, six experienced from one to two circles and quasi-stationary movement persisting for 2–3 days, two exhibited northeastward serpentine movements and five had northwestward serpentine movements. From the first three groups, 133 TCs were investigated in this study (Table 1).
A generalized beta–advection model (GBAM) is derived by decomposing a meteorological variable into climatic and anomalous components. Its ability to predict TC tracks for 1–2 days is compared with three versions of the classical beta–advection model (BAM): BAMS, BAMM, and BAMD. For all the three types of TC tracks tested (left turning, single right turning, and straight moving), the GBAM apparently outperforms the BAMS, BAMM, and BAMD. The ability of GBAM to predict unusual tracks is particularly encouraging. The classical BAMs have no skill in track forecasts for the left- and right-turning groups (only the BAMD predicted a correct right-turn for one case—TC number 23 in 1980; Fig. 14d) and exhibit any skill only for the straight-moving cases (seemingly the easiest type to predict). On the other hand, the GBAM is skillful for most cases although the predicted storm speed is generally too fast.
For the right-turning group (99 cases), the average track distance errors (distance to the best track only with the speed error not considered) are 122 km for 24-h forecasts (predicting the turn) and 215 km for the 48-h (predicting the movement after the turning point) forecasts. For the straight-moving TCs (30 cases), the average landfall location errors are 33 and 101 km for 24- and 48-h forecasts, respectively. Compared to the order of track forecast errors in current operational forecasts, which are based on complex NWP models, the GBAM performance is amazingly good for such a simple dynamic model. This demonstrates that as long as key controlling factors are properly included in a method, even a very simple tool like GBAM can do a good job.
Not only does the GBAM have high track forecast skill, but it can also be used to understand possible causes of unusual TC tracks (the left-turning tracks in this study). The GBAM can be separated into two forms according to the flow decomposition: a climatic-flow BAM (CBAM) and an anomalous-flow BAM (ABAM). In the CBAM a TC vortex is steered by large-scale climatic background flow, while in the ABAM a TC vortex interacts with surrounding anomalous flows or weather systems. It is found that neither CBAM nor ABAM alone can explain left-turning tracks, but only the GBAM, where the total flow (climatic plus anomalous) is considered. This suggests that the total flow must be considered for a model to accurately predict TC tracks although the TC vortex itself can be described by anomalous flow alone.
Another benefit of the flow decomposition approach is that it makes it easier to identify the area of an anomalous system, which can then be objectively removed for sensitivity experiments. Four sensitivity tests were conducted with the GBAM by removing each of the four anomalous systems associated with Typhoon Aere to determine which anomaly system might cause the TC’s left-turning track. It is found that the two anomalous highs played an important role; the subtropical high over the ocean leads Typhoon Aere to move northwestward initially and then the midlatitude high over land leads it to turn left to the southwest. Interaction with another existing TC vortex is also important.
Although the GBAM has the basic capability to predict both normal and unusual TC tracks in the short range, as demonstrated by this study as well as by Qian et al. (2014b), our purpose here is not to promote the GBAM to be used in real-time operations or to compete with any NWP models but to gain scientific insights, test new approaches, and compare them with traditional same-type models. The GBAM is only a simple dynamical model with no physics, baroclinic structure, ocean, and land forcing, etc., included, so it certainly cannot simulate storm intensity changes. For real-world prediction, a more complex model such as a baroclinic model or a full-physics NWP model is obviously needed. In this study, the GBAM is applied to an optimal level that needs to be determined before model integration. However, the optimal level varies with the situation, influenced by typhoon intensity and other surrounding anomalous systems, and is not known to us beforehand. Therefore, it will be interesting to evaluate how sensitive a track forecast will be if we use the VAmax or DAmin level to approximate the optimal level in a future study. The VAmax and DAmin levels are found to be close to the optimal level in this study (Table 2).
The authors wish to thank the editor and three anonymous reviewers for their constructive suggestions, which greatly improved our revised manuscript. This work is supported by the National Natural Science Foundation of China (41375073) and the Key Technologies R&D Program (201306032), as well as the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA0509400). Ms. Mary Hart of NCEP is appreciated for improving the readability of the manuscript.
The inclusion of β in the CBAM was not found to affect the typhoon trajectory in a number of random test cases, despite having the potential to modify the vorticity anomaly that defines the shape and position of a typhoon.
The levels of DAmin and VAmax could be sensitive to the vertical resolution of the data. A few cases have been found to be in the mid- to upper troposphere in this study (Table 2), while Rogers et al. (2013) reported that the max relative vorticity of an intense TC is typically seen in the lower troposphere. However, this discrepancy could also be simply due to the difference between the vorticity anomaly and the vorticity itself.