1 Introduction

Tropical cyclones (TCs) are probably the world’s most deadly and destructive natural hazards, which pose a disastrous threat to life and property (Tonkin et al., 1997; Henderson-Sellers et al., 1998). At present, global warming has been an undoubted fact (Cox et al., 2000; Webster et al., 2005; Knutson, 2010; Camargo, 2013), and changes in sea surface temperature (SST) have contributed greatly to global warming since a fairly large part of the earth’s surface is covered by the oceans (Lau and Weng, 1999). Many previous studies have indicated that exchanges of latent and sensible heat fluxes in the lower atmosphere provide important energy for the genesis and development of TCs. SST apparently is a critical factor affecting TC activities (Emanuel, 1986, 2000; Holland, 1997; Bell and Montgomery, 2008). In addition, TC intensity in response to SST increase has been quantitatively described in many previous studies based on both observations and numerical simulations, and the important impact of SST warming on TC activities has been identified (Elsner et al., 2012; Strazzo et al., 2013a). However, little is known about TC track change under warmer SST condition, which is not only a scientific issue, but also of public concern.

Kossin et al. (2014, 2016) explored climatological changes in TC tracks based on observations under the background of global warming. They found that the mean latitude where TCs reach their lifetime-maximum intensity (LMI) systematically migrates poleward in the past 30 years in both the Southern and Northern Hemispheres, and this phenomenon is especially prominent in the western North Pacific (WNP). However, this poleward migration of TC tracks can be attributed to not only SST impact, but also impacts of other nature variabilities and factors. Thereby, the results of Kossin et al. (2014, 2016) cannot determine the contribution of SST alone to TC track. Sun et al. (2017a) conducted a few semi-idealized numerical experiments, in which SST is the only exter-nal forcing that is varied and the increases in the underlying SST in all domains are respectively set to 0, 1, 2, and 4°C, to investigate the impacts of increased SST on tracks of two TC cases [i.e., TCs Songda (2004) and Megi (2010)]. The results show that increased SST led to in earlier northward turning of both the two TCs. Although this study was performed to investigate sensitivity of TC track to SST change, the results are solely based on two specific TC cases and perhaps it is not quite certain whether this phenomenon is universal for more TCs. Thus, the climate simulations with a large amount of TCs are needed to explain SST impact on climatological TC tracks. Moreover, the change of TC tracks is also closely related to the shift of the areas of heavy TC disaster, and thus, such an investigation can also provide evidence for the government strategy on TC disaster prevention.

Based on the above mentioned, the present study aims to conduct climate simulations of idealized TC cases and to explore the impact of warmer SST on TC track and TC destructive potential related to TC track change in the WNP. Idealized experiments are designed with manually varied SST to simulate TC tracks using the high-resolution Weather Research and Forecasting (WRF) model. This paper is organized as follows. Section 2 introduces data and experiment design. Model simulations are analyzed in Section 3. Results and discussion are presented in Section 4.

2 Data and experiment design 2.1 Data

The Data used in this study include TC best-track dataset and the NCEP final (FNL) global analysis data.

The observed TC track data are extracted from the International Best Track Archive for Climate Stewardship (IBTrACS) v03r09, which provides a homogeneous and comprehensive global TC best track dataset based on the World Meteorological Organization (WMO) sanctioned forecast agencies. Central positions and intensities of TCs at 6-h intervals are provided by this dataset (Knapp et al., 2010). In the present study, the 36-yr observations during 1980–2015 are used, which can be downloaded from https://www.ncdc.noaa.gov/ibtracs.

The NCEP 1° × 1° global FNL analysis product at 6-h intervals during 2001–10 is used to provide initial and boundary conditions for WRF simulation. The SST data are derived from NCEP-FNL analysis data and manually changed for idealized WRF experiments. The NCEP-FNL data can be downloaded from http://rda.ucar.edu.

2.2 Model configuration and experiment design

Long-term climate simulation is conducted by using WRF model version 3.3 (WRFv3.3). The model domain is centered at 30°N, 140°E with a total grid number of 400 × 300. The model resolution is 0.2° in horizontal on latitude–longitude projection and 36 layers in vertical, the simulation period covers the typhoon season from 1 May to 1 November 2001–10. Important physical parameterization schemes include the WRF single-moment (WSM) 3-class simple ice scheme (Hong et al., 1998), the Grell–Devenyi ensemble cumulus scheme (Grell and Devenyi, 2002), the Yonsei University (YSU) planetary boundary scheme (Hong et al., 2006; Hong, 2010), the rapid radiative transfer model (RRTM) longwave radiation scheme (Mlawer et al., 1997), and Dudhia shortwave radiation scheme (Dudhia, 1989).

Sensitivity experiments of climate simulation are conducted with a resolution of 0.2° to investigate the response of TC activities, especially TC tracks, to increased SST. These sensitivity experiments cover all the typhoon seasons of the 10 years from 2001–10 over the WNP (0°–60°N, 100°E–180°). Same atmospheric initial and lateral boundary conditions are applied for these simulations but SST distributions are modified. In the control experiment (Exp_CTL), SST comes from NCEP-FNL analysis data; in the sensitivity experiment (Exp_DBCO2), SST is manually increased following the approach of Lau et al. (2016), i.e., mean SST anomalies derived from double CO₂ experiments of 33 Coupled Model Intercomparison Project Phase 5 (CMIP5) models are added to SST in Exp_CTL to obtain future scenario of SST used in Exp_DBCO2. In another two sensitivity experiments (Exp_SST+), SST is uniformly increased by 1 and 2°C, respectively. Exp_SST+1 (Exp_SST+2) represents the experiment in which SST is increased by 1°C (2°C). Note that all TCs in the WNP are considered except those originated in the South China Sea in the present study, since the mechanism controlling the TCs’ track over the South China Sea is substantially different from that controlling the TCs’ track over the WNP.

The number of simulated TCs during the 10-yr period (2001–10) in Exp_CTL (52 simulated TCs in the WNP) is notably less than the observation (132 WNP TCs). It should be pointed out that the underestimation of TC frequency is attributed to the relatively coarser spatial resolution, which would make the simulated vortex fail to reach the standard of TC.

Despite of the notable difference in TC number between Exp_CTL and the observation, the interannual variability of TC number in Exp_CTL is quite similar to that in the observations, and their correlation coefficient is 0.67, which is significant at 95% confidence level (see Fig. 1). In addition, the 500-hPa geopotential height of Exp_CTL is also consistent with that of observation, and the averaged WNP TC tracks in Exp_CTL and the observation both present northwestward moving, despite of some differences in TC genesis positions and the length of TC tracks (see Figs. 2a, b). Moreover, by comparing the TC track density of Exp_CTL with that of observation, it is found that their large values of track densities all appear in the sea area to the east of Taiwan Island, and their overall distributions of TC track density are all characterized by a northwestward-to-northeastward turning, which is related to the prevailing large-scale environmental flow varying with the latitude. Furthermore, the spatial correlation coefficient of TC track density between the observation and Exp_CTL is 0.45, which is significant above the 99% confidence level. As for the types of TC tracks, despite of notable difference in the percentage of the three TC types between Exp_CTL and the observation, in both Exp_CTL and the observation, the percentage of westward TCs is the largest among three TC types and there is no significant difference in the percentages of northwestward TCs and recurving TCs (see Table 1). Besides, two metrics of TC track are also calculated to compare the observation and Exp_CTL. The values of one metric (i.e., φ_LMI and φ_DP, which will be introduced in Section 3.4) show a relatively large difference but the values of another metric are similar between the observation and Exp_CTL (see Table 1).

Note that, in this study, it is not necessary to precisely reproduce TCs. Our conclusions are based on the comparisons between sensitivity experiments and less dependent on absolute and precise simulation results. Thus, the simulated TC activities can still be employed in analysis for their track characteristics.

3 Results 3.1 Climatological mean TC track

To investigate the impact of ocean warming on the changes of large-scale circulation and TC tracks, 500-hPa geopotential height averaged over the integration period, and TC tracks simulated by each experiment are displayed in Fig. 2. Besides, the climatological averaged TC tracks are also shown in Fig. 2. The calculated method is illustrated as follows. First, separate averagely the time length of each TC life-time to 40 points-in-time in chronological order. Second, interpolate the central position data (latitude and longitude) of each TC during its life-time to the aforementioned 40 points-in-time, and get the time series with the length of 40 of each TC about the latitude and longitude. Third, average the time series, got in the last step, of multiple simulated TCs in each experiment, and the formula is expressed as:

${\rm {AC}}_k^t = \mathop \sum \limits_1^N {C_i}/N,$

(1)

where k represents the name of each experiment (e.g., Exp_CTL), N represents the total TC number of each experiment, C_i represents the latitude or longitude of the ith TC, and ${\rm {AC}}_{\rm k}^t$ represents the average latitude or longitude of all TCs in each experiment at tth point-in-time. It is obvious that as the increase of SST, more TCs generate and the averaged simulated TC tracks tend to recurve gradually from northwest to northeast in the WNP; meanwhile, the western Pacific subtropical high (WPSH) tends to retreat eastward. The averaged TC tracks basically follow the flank of the WPSH. This is because TC tracks almost always follow large-scale steering flow that is closely related to the WPSH. These results are consistent with that conducted by Sun et al. (2017a) for a case study.

3.2 Distribution of TC track density

TC track density is widely used to reflect the characteristics of TC tracks (Camargo et al., 2005; Kim et al., 2012; Strazzo et al., 2013b) since it contains information on TC frequency, position, and lifecycle. TC track density distributions in the WNP are presented in Fig. 3, which show that the TC track density becomes larger as SST increasing. One reason is that more TCs occur in the WNP with increasing SST (Table 1). This kind of change in TC frequency is contrary to those in some previous studies indicating that TC frequency would decrease in the WNP in the context of global warming (e.g., Emanuel et al., 2008; Sugi et al., 2009; Li et al., 2010). The possible reasons are relatively complex. First, regional variation of TC frequency in the global warming experiments depends largely on the SST spatial patterns (Yoshimura et al., 2006). The SST patterns in other studies are different from those in our experiments, which lead to the difference in the simulated TC frequency and its trend. Second, many studies found strong sensitivity of model TC frequency to changes in convective parameterization (Vitart et al., 2001), a relative humidity threshold (Tsutsui and Kasahara, 2000), radiative processes (Ueno and Yoshimura, 2002), and so on. The difference in the parameterization schemes also contributes to the TC number difference. Third, global warming includes not only higher SST, but also changes in large-scale environmental background (e.g., Cox et al., 2000). In the present study, we only investigate the impact of unvaried SST on climatological WNP TC tracks, and do not consider the role of large-scale environmental background that affects the simulated TC number. Therefore, the result of the present study does not really conflict with that of the previous studies. Instead, it may raise the possibility that SST warming can indeed lead to more TCs, whereas effects of other factors (e.g., large-scale circulation influenced by the other factors that are beyond the scope of ocean warming but include in the scope of global warming) probably offset the effect of SST warming on TC frequency (i.e., leading to less TCs), which will be further investigated in our next work.

To facilitate further comparison of the control and sensitivity experiments, differences between simulations in these experiments and regions where the differences are significant at the 90% confidence level, based on a two-sided Student’s t test, are presented in Fig. 4. It is found that under the condition of warmer SST (Figs. 4a, b), the TC tracks as whole tend to shift eastward and northward, especially over the oceans to the east of Taiwan Island and the Philippines, where the TC occurrence tends to decrease. On the contrary, the TC track density significantly increases in the midlatitudes to the east of Japan and over the Pacific in mid- to low-latitude regions near 160°E. Comparing Exp_SST+2 with Exp_SST+1 (figure omitted), the TC track density tends to decrease in the low-latitudes but increase in the midlatitudes to the east of 140°E. This indicates that the northward and eastward shifts of TC track become more distinct with larger SST increase. Note that the overall northward and eastward shifts of TC track do not change with SST increase linearly. For Exp_DBCO2, the simulated TC track also demonstrates a tendency of eastward and northward shifts compared to that simulated in Exp_CTL (Fig. 4c).

It is well known that the impacts of stronger and weaker TCs are quite different when they pass over the same place. To consider the effects of TC destructive potential, the conventional TC track density is weighed by the Power Dissipation Index (PDI) proposed by Emanuel in 2005 to further study the poleward movement of TCs under the influence of warming SST. The algorithm of computation is expressed as:

$ X (i) = \sum\limits_1^N {V_{{\text{max}}}^3} (i, j) , $

(2)

where X (i) denotes the weighed track density in a specific grid (i), V_max (i, j) is the maximum wind speed of a specific TC that moves into the grid (i) at a specific time (j). TC track data at 6-h intervals are used in the present study. For any TC, its occurrence frequency in a specific grid is counted as the time (6-h interval) when it stays in that grid. N represents the sum of occurrence frequencies of all TCs in the grid.

Zonal summation of the weighted TC track densities yield the zonal distribution curves as shown in Fig. 5. It is obvious that the curves of Exp_CTL and observation all show a characteristics of normal distribution, and their curves coincide in low latitude despite of some differences in midlatitude. In addition, the correlation coefficient between the curves of Exp_CTL and observation is 0.87, which is significant at 95% confidence level. Comparison among the simulation experiments indicates that the latitude where the maximum weighted TC track density occurs gradually migrates northward with increasing SST (Exp_CTL: 21.32°N, Exp_SST+1: 22.72°N, Exp_SST+2: 26.08°N, Exp_DBCO2: 25.8°N), suggesting that when considering the TC destructive potential, areas where TCs may have the largest impact would migrate northward. Note that the ratio of maximum weighted TC track density to total density decreases with increasing SST, indicating that the largest impact of TC may weaken under warmer SST condition. Overall, the weighted TC track densities simulated in the three sensitivity experiments all decrease in the low latitudes. In Exp_SST+1, the weighted TC track density is similar to that in Exp_CTL near 30^oN, but gradually becomes larger than that in Exp_CTL and the difference reaches the largest near 48^oN. Those simulated in Exp_SST+2show distinct northward shift compared to those in Exp_CTL, i.e., to the south of 24°N, the weighted TC track density in Exp_SST+2 is less than that in Exp_CTL and to the north of 24°N, the result is opposite. For Exp_DBCO2, the change trend is similar to that in Exp_SST+2, that is, the weighted TC track density becomes larger than that in Exp_CTL from 26° to 53°N. This shows that the areas influenced by TCs gradually migrate northward under warmer SST condition.

3.3 Changes in the type of TC track

The geographical property is an important feature of TC tracks. In order to further explore the SST impact on TC tracks, the simulated TCs are classified based on their tracks. The K-means cluster method is implemented first to classify observed TCs (V_max ≥ 35 knot) in 36 yr from 1980 to 2016 in the IBTrACS (International Best Track Archive for Climate Stewardship) dataset (Macqueen, 1967; Elsner, 2003; Nakamura et al., 2009, 2017). The mass moment that contains five elements, i.e., the latitude and longitude of the TC centroid, and the variances of the TC centroid along the latitude, longitude, and diagonal directions, is used to describe the geographical property of a full TC track like its pattern and trajectory length in each of the clusters determined by the K-means method. Detailed description of the method can be found in Nakamura et al. (2009). The five track moment elements are normalized first. The weight of the two elements associated with the centroid and that of the three elements associated with the variances at different directions are set to 1/3 and 1/9 respectively to relatively weaken the effects of TC track length, pattern, and direction represented by the variances, and the Cosine Distance Metric is chosen as our distance metric.

The observed TCs are classified into three types (K = 3) based on their tracks (Fig. 6), which is different from that in Yu et al. (2016) who used a “silhouette” value to define seven types of TC track in WNP. We chose K = 3 for three reasons: first, the three patterns of TC track are quite simple and straightforward; second, other studies have classified TC tracks into three track types, i.e., westward, northwestward, and recurving (Elsner, 2003; Wu and Wang, 2004; Wu et al., 2005; Ying et al., 2011); and third, for some models, which only simulate a low number of TCs, three types of TC tracks may be more appropriate than a higher number of clusters. Simulated TCs are then classified by using the same method. A model TC track is set to belong to a specific cluster whose distance metric is the closest to the observed cluster centroid.

Table 1 clearly shows that corresponding to 1°C increase of SST, the percentage of TCs with westward tracks (Exp_SST+1: 26.04%) decreases pronouncedly compared to that in Exp_CTL (36.54%), whereas the percentage of TCs with northwestward tracks increases significant (Exp_CTL: 30.77%, Exp_SST+1: 40.63%), and there is little change for TCs with recurving tracks (Exp_CTL: 32.69%, Exp_SST+1: 33.33%). When SST increasing from 1 to 2°C, the percentage changes for TCs with westward and northwestward tracks are opposite to that for 1°C increase of SST compared with Exp_CTL. However, compared to the results in Exp_CTL, the percentage of TCs with westward tracks (Exp_SST+2: 33.64%) still decreases, while that of TCs with northward tracks (Exp_SST+2: 36.36%) increases. Moreover, little change is found for TCs with recurving tracks (Exp_SST+2: 30%). The results in Exp_DBCO2 are similar to that in Exp_SST+2, it shows that, compared to the results in Exp_CTL, the percentage of TCs with westward tracks slightly decreases (Exp_DBCO2: 33.04%), while that of TCs with northwestward tracks increases (Exp_DBCO2: 35.71%). The percentage of recurving TCs still shows no obvious change (Exp_DBCO2: 31.25%). Overall, sensitivity experiments in the present study (i.e., Exp_SST+1, Exp_SST+2, and E_DBCO2) imply that SST change has more significant impacts on TCs with westward and northwestward tracks compared to those with recurving tracks. With specific SST distribution (i.e., warmer SST relative to that in control experiment), the percentage of TCs with westward tracks will decrease (2.9%–10.5%), while the percentage of TCs with northwestward tracks will increase distinctly (4.94%–9.86%). This result is consistent with the change of climatological TC track discussed previously, which will turn from northwestward to northeastward.

3.4 Features of the TC poleward migration index

In order to disclose the possible TC track change under warmer SST condition in a more straightforward way, the average latitude where TCs achieve their lifetime-maximum intensity (φ_LMI) (Kossin et al., 2014) is calculated. The Kossin algorithm is implemented to calculate φ_LMI for TCs simulated in control experiments and sensitivity experiments. Table 1 indicates that φ_LMI tends to migrate poleward with increasing SST (Exp_CTL: φ_LMI = 25.83, Exp_SST+1: φ_LMI = 26.07, Exp_SST+2: φ_LMI = 28.96), and this tendency can also be found in φ_LMI calculated from 30-yr TC observations (Kossin et al., 2014). This feature suggests that warmer SST contributes to the northward migration of the overall TC track to a certain degree.

For a single TC, φ_LMI contains the information only on the specific moment when TC reaches its LMI. However, latitudes where TC is located at other times in its lifetimes are not considered at all. In addition, strong and weak TCs are treated in the same way, whereas the impact of a strong TC can be much more significant than that of a weak one. Based on the above consideration, a new index, i.e., the lifetime-averaged latitude weighted by TC destructive potential (φ_DP), is introduced in the present study. The TC destructive potential at various stage of the TC lifetime is taken as the weighting factor, which is multiplied by the latitude where the TC is located at the corresponding time to yield the comprehensive latitude. Algorithms for computation of φ_DP and its annual average are expressed as:

${\varphi _{{\rm{DP}}}} = \frac{{\int_0^\tau {\varphi V_{\max }^3{\rm d}t} }}{{\int_0^\tau {V_{\max }^3{\rm d}t} }}{\rm{ = }}\frac{{\int_0^\tau {\varphi V_{\max }^3{\rm d}t} }}{{{\rm{PDI}}}},\qquad\qquad\quad\,\,$

(3)

${\varphi _{{\rm{DP - annual}}}} = \displaystyle\frac{{\sum\limits_1^N {\left( {{\varphi _{{\rm{DP}}}} \cdot {\rm{PDI}}} \right)} }}{\textstyle{\sum\limits_1^N {{\rm{PDI}}} }}{\rm{ = }}\frac{{\sum\limits_1^N {\int_0^\tau {\varphi V{_{\max }^3}{\rm{d}}t} } }}{{\sum\limits_1^N {\int_0^\tau {V_{\max }^3{\rm{d}}t} } }}, \,\,\,\,\,\,$

(4)

where τ denotes the length of the TC lifetime, and φ is the latitude of the TC centroid. Table 1 shows clearly that φ_DP also presents a poleward migration trend, which is quite similar to φ_LMI but more pronounced. Compared with that in Exp_CTL (φ_DP = 24.99), the latitude of φ_DP shifts poleward. This poleward migration becomes more distinct following larger SST increase (Exp_SST+1: φ_DP = 28.01, Exp_SST+2: φ_DP = 29.04).

3.5 The possible reason of TC track change

In the study of Kossin et al. (2014), the poleward shift of TC track in the WNP was attributed to the so-called “tropical expansion” caused by global warming. However, there exists no study in the literature to explain in detail the mechanism associated with the above argument. In recent years, Sun et al. (2017a, b) quantitatively evaluated the TC track change via case studies. They found that earlier TC recurvature with increasing SST might be related to changes in TC size. The surface tangential wind profile can reflect the storm size because the value of the tangential wind is strongly associated with the density of the isobars (Sun et al., 2017b). Figure 7 illustrates the tangential wind profiles at 10 m, and the climatological TC size in terms of the climatological average radius of gale force wind (AGW; 17 m s^–1) is also calculated in Table 1. It is obvious that as the SST increases, the outer tangential wind, the maximum wind speed, and the radius of maximum wind increase, which results in the expansion of the storm size. In addition, comparison of experiments results (Table 1) reveals that the AGW obviously becomes larger under warmer SST. The TC size increases more significantly corresponding to larger SST increase (Exp_CTL: 0.55, Exp_SST+1: 0.96, Exp_SST+2: 3.75, Exp_DBCO2: 1.33; unit: 10⁵m²), which is significant at the 90% confidence level based on Mann–Whitney U test (Mann and Whitney, 1947). This provides further evidence to support the impact of ocean warming on TC size proposed by Sun et al. (2015a, b).

Previous studies suggested that the inflow mass flux entering the TC region will increase with the increase of the storm size, leading to a significant decrease in 500-hPa geopotential height in the TC outer region. As a result, the intensity of WPSH over its fringe close to the TC decreases notably when the WPSH edge is within the TC outer region and such a decrease leads to a break of WPSH. Subsequently, the TCs are forced to turn northward toward the break of the subtropical high (e.g., Sun et al., 2015a; Wang et al., 2017). Consistent with the results of previous studies, the increase in TC size caused by the ocean warming leads to the decrease in 500-hPa geopotential height in TC main activity region, which eventually results in the eastward withdrawal of the WPSH and thus the movement northward of the TC (see Fig. 2).

4 Conclusions and discussion

Long-term climate simulation of TC track in the present study reveals possible TC track change in the future under warmer SST conditions. Comparison of control and sensitivity experiments indicates that the climatological TC track systematically migrates poleward with increasing SST due to the eastward withdrawal of the WPSH caused by the expansion of TC size (AGW). The TC track tends to recurve northward earlier. Classification of TC tracks implies the possibility that the percentage of westward moving TCs decreases while the percentage of northwestward moving TCs increases. The two quantitative indexes used to evaluate characteristic TC track, φ_LMI and φ_DP, both show a poleward migration tendency.

In the present study, changes in climatological TC track are investigated based on two sets of ideal numerical experiments. However, the mechanisms for TC track response to SST have not been discussed in detail and the responses of various TC elements to SST change have not been examined yet. These issues will be addressed in our future study.