Is the tropical cyclone surge in Shanghai more sensitive to landfall location or intensity change?

It has been shown that the proportion of intense tropical cyclones (TCs) has been increasing together with a poleward migration of TC track. However, their relative importance to TC surge at landfall remains unknown. Here we examine the sensitivity of TC surge in Shanghai to landfall location and intensity with a new dynamical modelling framework. We find a surge sensitivity of 0.8 m (°N)−1 to landfall location, and 0.1 m (m s−1)−1 to wind speed in Shanghai during landfall. The landfall location and intensity are comparably important to surge variation. However, based on a plausible range of reported trends of TC poleward migration and intensity, the potential surge hazard due to poleward migration is estimated to be about three times larger than that by intensity change. The long‐term surge risk in Shanghai is therefore substantially more sensitive to changes of TC track and landfall location than intensity. This may also be true elsewhere and in the future.

world in terms of population and assets exposed to coastal flooding (Hanson et al., 2011). On average there is less than one landfalling TC directly influencing Shanghai per year (Fogarty et al., 2006), and yet it can come at significant cost. Typhoon Winnie (1997), for example, caused a loss of $91 million to the city due to the concurrence of strong surge and high astronomical tide at landfall (Wang et al., 2018).
Extreme winds and storm tide happen concurrently during TC landfall. The storm tide is a nonlinear combination of astronomical tide and storm surge, which is challenging to assess due to the nonlinear interactions between the atmosphere, ocean and bottom topography (Anthes, 1982). Storm surge depends on ocean depth/shelf width combined with TC characteristics, for example, the landfall location, intensity (Harris, 1963), size (Irish et al., 2008), approaching speed (Rego and Li, 2009) and angle (Weisberg and Zheng, 2006). The dependence of surge on wind more than pressure closer to land is predominantly a function of ocean depth. For open ocean islands with a narrow continental shelf the pressure component can end up being a more important factor of surge (Joyce et al., 2019). For marginal and shelf seas positive surge occurs where winds are blowing onshore (Wong and Toumi, 2016b). In the North Hemisphere, this requests the region of interest locating on the right-hand side of landfall location along the TC track. The magnitude of positive surge is then driven primarily by wind stress and atmospheric pressure gradient (Jelesnianski, 1966;Anthes, 1982), with the dependence on wind much stronger than pressure when moving close to land (Wong and Toumi, 2016a). Therefore, the maximum surge at landfall commonly happens to the right-hand side (in the North Hemisphere) of landfall location close to the radius of maximum surface wind.
The surge induced by landfall TCs may be modulated by the climatic changes of TC intensity and/or geographical distribution of TC tracks. Emanuel (2005) showed that the destructive potential of TCs has been rising since the 1970s due to the increase in the sea surface temperature (SST). The poleward migration of the location of TC lifetime maximum intensity (LMI) (Kossin et al., 2014), probably driven by tropical expansion (Sharmila and Walsh, 2018), may also potentially increase TC-related hazards in the regions at higher latitudes (Kossin et al., 2016). The poleward migration is particularly well observed in the western North Pacific (Knutson et al., 2019). This change may shift TC activity from the South China Sea to the East China Sea (Knutson et al., 2020) and the surge risk at Shanghai may consequently increase.
The prediction and planning for TC surge is crucial for preventing casualties and economic damage. The prediction of TC surge involves statistical and dynamical approaches. Conner et al. (1957) developed an empirical method for maximum surge forecasting with TC intensity as a singular input. The Sea, Lake, and Overland Surges for Hurricanes (SLOSH) model (Jelesnianski, 1992), developed by the National Weather Service back to the 1970s, is a widely used dynamical surge model and remains in operation at the National Hurricane Center. The SLOSH model applies a parametric TC surface wind field constructed with a few readily obtained TC characteristics, which is a compromise between the operational efficiency and the accuracy of TC wind field. Bruyère et al. (2019) emphasised the importance of dynamical representation of TC landfall scenarios to risk assessment and developed a hybrid cyclone model with idealised atmospheric configuration and realistic topography and coastlines. However, their hybrid model was not coupled with a hydrodynamical component to simulate TC surge which we are doing here for the first time for Shanghai. With such an integration of full-physics atmospheric and hydrodynamic models the TC surface wind field can evolve more realistically during landfall, and therefore the storm surge in Shanghai can be simulated more accurately in difference TC landfall scenarios.
The objective of this study is to (i) develop a dynamical modelling framework for TC surge with a flexiblemesh hydrodynamical model forced by a full-physics atmospheric model, and (ii) evaluate the relative importance of TC landfall location and intensity to surge in Shanghai. The following section will introduce the model setup and experiment design. Section 3 will show the results of the simulated surge and surge sensitivity to landfall location and intensity. The last two sections will discuss the results and summarise the study.

| Atmospheric model setup
The TC simulation is conducted with the Weather Research and Forecasting (WRF) Model (Skamarock et al., 2008, version 4.1). Three square nested domains (800 Â 800 grids), each with 41 σ levels in the vertical, are implemented with a horizontal grid spacing of 12, 4 and 1.33 km, respectively, on an f plane (20 N) with horizontally uniform SST. Three domains are two-way interactive with the inner two domains following the TC centre. Full-physics parameterisation is used as in Wang and Toumi (2019) to account for radiation, microphysics, planetary boundary layer and surface layer processes. Considering that the innermost domain with 1.33-km grid resolution (about 1,000 Â 1,000 km) is large enough to cover the main convection region in a TC, the cumulus scheme is not applied in any domain.
The TC simulation is initiated on an idealised aquaplanet in a stationary environment. The initial bogus vortex is specified from an analytic wind profile model (Wang and Toumi, 2016). The initial atmospheric sounding profiles for different SSTs are adopted from Wang and Toumi (2018b). Note that the initial soundings are adjusted to the underlying SST to reach the radiativeconvection equilibrium before any storm simulation. The model is integrated for 5 days to have the TC fully developed, that is, the intensity reaches the LMI. In the second stage of simulation, we restart the simulation and add in a vertically uniform steering flow to convey the TC towards the Northwest. The background steering flow is added via the boundary condition and fixed at 4 m s À1 (2.83 m s À1 of easterly and poleward winds) at the lateral boundary throughout the landfall simulation. Nudging technique is not applied and there is no horizontal relaxation distance specified. At the start of the second stage of simulation, we also add in the topography and coastlines within the radius of 1,000 km around Shanghai to the northwest of the TC. At the beginning of the restart run, Shanghai is about 1700 km away from the TC centre. The simulated TCs make landfall around Shanghai in the fifth simulation day of the second-stage simulation. The second-stage simulation lasts for 7 days so that a complete intensity decay after landfall can be properly simulated.

| Hydrodynamical model setup
Once a WRF simulation is completed, the model surface wind, pressure and rainfall are used to force the Delft3D D-Flow Flexible Mesh hydrodynamical model. It is a newly developed shallow water solver using unstructured grid (De Goede, 2020). The governing equations include continuity equation and momentum equations (Kernkamp et al., 2011). The finite volume numerical scheme is applied to compute hydrodynamics, and substance transport in river, estuary and coastal waters (Kernkamp et al., 2011;Martyr-Koller et al., 2017). The model has been calibrated and validated with observed surge and tidal levels at 10 stations around Shanghai during Typhoon Winnie in 1997 (Ke et al., 2021). Surge level is calculated as the difference between total water levels with and without forcings by a TC in the hydrodynamical model.

| Experiment design
A suite of experiments is conducted by varying the SST and landfall location around Shanghai (Table S1). The purpose of the SST experiments is to vary the TC intensity at landfall in a physically plausible way so that a linear sensitivity of surge to landfall intensity can be derived. In this sense the SST in the control experiment (CTRL_0), set as 27.0 C, does not has to accurately reflect the mean climatological SST around Shanghai. Based on CTRL_0 five more simulations are conducted to simulate TCs making landfall to the north and south of Shanghai by only tuning the background steering flow. These six simulations are then reproduced by increasing the SST by 1 C and 2 C, respectively. This approach generates 18 cases.

| Observations
The TC best track data are from the China Meteorological Administration. The maximum surface wind speed and latitude of TC landfall are calculated along China's coastline (31.2 N to 27.0 N) for the period 1949-2018. The Wusong tide gauge station is located at the estuary of the Huangpu River. Any extreme surge reaching this station may severely raise the water level in the upstream of the river and then potentially lead to dike breach and flooding in the downtown region ( Figure S1).

| RESULTS
The tracks of CTRL_0, SST1_0 and SST2_0 pass through Shanghai with Wusong station to the right-hand side of the TC eyewall where the onshore wind is expected to be the strongest (Figure 1a). Wusong station is exposed to easterly (onshore) wind in 12 simulations with the landfall location to the south of the station, and westerly (offshore) wind in the other 6 simulations in which the landfall is to the north.
The all cases mean TC intensity-measured by the maximum surface wind speed-stabilises above 50 m s À1 as a category-3 TC for simulation hour 24-96 (Figure 1b). During this period, the mean intensity is 51 m s À1 for the experiments with an SST at 27 C, 53 m s À1 at 28 C and 57 m s À1 at 29 C, respectively. This gives a sensitivity of about 6% of intensity increase per degree SST increase. TC intensity decays rapidly post landfall after hour 96 with a mean rate of 15 m s À1 per day. With the dynamical atmospheric model the complexity of TC intensity evolution can be physically simulated during landfall. Figure 2a shows that the maximum surge is to the right of the track where the wind is stronger due to the combination of swirling and transition. This asymmetric surge pattern is clearer when a TC approaches land. A more intense TC under higher SST leads to a higher surge as expected (Figure 2b).
When landfall location moves from the south to north towards Shanghai (31.2 N), the maximum wind during landfall increases at Wusong station, and consequently, the local surge rises (Figure 3). For the same landfall location, Figure 3 also shows a slight reduction of surge height for the same local wind speed when the SST increment changes from +1 to +2 C. This may be due to a smaller TC size with higher SST (Figure S2), which is consistent with recent observations (Lavender and McBride, 2020). The important point is that these size effects are much smaller than the range of wind speeds we examine here. When the landfall location shifts to the north of Shanghai, the maximum surface wind at Wusong station remains around the hurricane-force level (33 m s À1 ), but the local surge height is reduced to less than 1 m (not shown in Figure 3). This is because of the change in offshore wind direction at Wusong station when Shanghai is located on the left of the track. The relationships in Figure 3 are significant (p ≤ .05) between surge and wind speed/landfall location. The surge To convert these sensitivities to potential changes of surge hazard over recent decades, we need to know the historical trends of intensity and landfall location. The reported trends depend on the data and analysis procedure. Rather than fix on one trend estimate here we will use a range of plausible values. This is sufficient to allow us to compare the different potential contributions of intensity and landfall location to surge variation. Park et al. (2014) showed a range of annual trend in TC landfall intensity of 0.6-1.8 m s À1 per decade in East Asia. The reported range of poleward migration of TC lifetime maximum intensity is 0.4-1.0 N per decade (Kossin et al., 2014(Kossin et al., , 2016Sun et al., 2019). Combining these observed trends with the surge sensitivity in our simulations, we find a potential surge trend of 0.1-0.2 m per decade due to TC intensity change, but a much larger 0.3-0.8 m per decade due to poleward migration of TC locations. If we take the central value as the best estimate, landfall location change is at least three times more important than wind speed change. Therefore, the longterm change in potential surge hazard in Shanghai is much more sensitive to the change in TC track than intensity.

| DISCUSSION
The atmospheric configuration of our hybrid TC-surge model is similar to Bruyère et al. (2019). Such a semiidealised setup with real topography is a useful tool of exploring the worst-case scenario of hazard impact induced by landfalling TCs. Our improvement here is to integrate this atmospheric modelling setup with a stateof-the-art hydrodynamical model for surge investigation. Previous studies have combined WRF with other hydrodynamical models (e.g., Mori et al., 2014), but they are all designed for real TC case studies and therefore constrained by specific environmental conditions during the TC passage. Our new hybrid TC-surge modelling framework can produce realistic physical scenarios for wind and surge during a TC landfall, which can be used to explore worst-case scenarios for the location of interest.
We find the surge sensitivity to intensity of 0.10 ± 0.02 m (m s À1 ) À1 . A similar sensitivity can be obtained with the Saffir-Simpson Hurricane Scale warning system (Simpson and Saffir, 1974), which estimates the surge height for five TC intensity categories. By linearly interpolating surge level with 1 m s À1 intervals of all the categories, we obtain a surge sensitivity of 0.13 ± 0.01 m (m s À1 ) À1 . Wong and Toumi (2016b) showed that a TC with a maximum wind speed of 77 m s À1 can generate a surge of 5.4 m at landfall in an idealised modelling framework. This implies a linear surge sensitivity to wind intensity of about 0.07 m (m s À1 ) À1 , which is also close to the sensitivity in our simulations. The possibility of size changes under warming (Xu and Wang, 2010;Sun et al., 2017;Wang and Toumi, 2018b;Bruneau et al., 2020) also does not change the sensitivity markedly. The local wind speed is the dominant source of surge height-wind sensitivity. It is noteworthy that the discussion here does not consider the surge dependence on ocean depth and continental shelf width. The consistency between our results and previous studies suggests general applicability of our surge-to-wind sensitivity.
We also find the surge sensitivity to landfall location of 0.82 ± 0.22 m ( N) À1 . This can be understood in term of the radial TC wind profile. Chan and Chan (2015) and Wang and Toumi (2018a) find a global mean wind radii of gale-force wind (18 m s À1 ) and damaging-force wind (26 m s À1 ) of about 200 and 100 km, respectively. This change implies the surface wind at the location of interest may be increased by about 8 m s À1 (from gale-force to damaging-force) due to a poleward migration of TC landfall by 1 latitude towards this location from the South, that is, 8 m s À1 ( N) À1 . This sensitivity is confirmed by our analysis (Figure 3). Combining the surge sensitivity to wind of 0.1 m (m s À1 ) À1 , we obtain a surge sensitivity to poleward migration of TC landfall of 0.8 m per degree latitude change, which agrees well with our simulations. Two inferences may then be made. Firstly, our simulated surge sensitivity to landfall location and intensity can be applied in Shanghai, but may also be true elsewhere. Secondly, the important role of landfall location is due in part to the radial reduction of wind outwards from TC centre.
We now consider case-by-case variations. The standard deviation of landfall latitude and intensity in our Shanghai region (Section 2.4) is 1 N and 11 m s À1 , respectively, and they are independent (r = À0.16, p = .37). By multiplying the sensitivities [0.8 m ( N) À1 for location and 0.1 m (m s À1 ) À1 for intensity] by the variations, the surge variability is estimated to be 0.8 m and 1.1 m due to landfall location and intensity variations, respectively. Thus, the landfall intensity is as important as the landfall location to case-by-case surge variability. However, for long-term change in potential surge hazard, our results have shown that the historical poleward migration of TC locations is at least three times more important to surge than the increase of TC intensity.
Our simulation shows a relatively weak dependence of TC maximum intensity on SST change. This is consistent with previous studies showing that the sensitivity of TC maximum intensity to SST is only about 3-4% C À1 under the radiative-convective equilibrium (Knutson and Tuleya, 2004;Knutson et al., 2015;Yoshida et al., 2017;Wang and Toumi, 2018b). The global mean SST has increased by half a degree in the past half-century and perhaps another 1 by 2050. Under equilibrium assumption this would lead to only 3-4% of increase in TC maximum wind speed (about 2 m s À1 increase for a category-3 TC). This change in intensity would yield a small change in surge (only about 0.2 m). On the other hand, Kossin et al. (2014) showed that the poleward migration in the western North Pacific has been about 0.3 N per decade. If we assume the landfall location shares the same trend from 27 N to the latitude of Shanghai and continues in the future, the poleward migration of landfall location to 2050 would be about 1 latitude northward. This latitudinal shift of TC tracks may lead to a dramatic potential change of surge by 0.8 m, about four times larger than the change induced by the intensity increase of a category-3 TC. This suggests the possible future relative importance of poleward migration of TC location to surge hazard in Shanghai.
The main uncertainties in this study arise due to uncertain trends of TC poleward migration. This is why we focus on a range of values. We assume the whole TC track shifts to higher latitudes. However, a robust and significant poleward migration of TC lifetime maximum intensity and genesis location has been only confirmed in the western North Pacific (Kossin et al., 2014;Daloz and Camargo, 2018). Murakami et al. (2020) showed a clear poleward shift of TC frequency along the east China coast for 1980-2018. Liu and Chan (2019) found that the mean landfall intensity is increasing at the east coast of China due to more frequent landfalls by intense typhoons.

| CONCLUSIONS
In this study, we develop a new dynamical modelling framework for TC surge with a full-physics atmospheric model forcing a hydrodynamical model. We find a surge sensitivity of 0.8 m ( N) À1 to TC landfall location, and 0.1 m (m s À1 ) À1 to wind speed in Shanghai during landfall. Considering the case-by-case variation of TC surge, the landfall location and intensity contribute comparably to the variation of surge in Shanghai. However, based on a plausible range of reported past trends the long-term surge level in Shanghai is at least three times more sensitive to changes of TC landfall location than intensity. The landfall location change therefore likely plays a dominant role in the future climatic change of TC surge risk in Shanghai, and this may also be true elsewhere. ORCID Shuai Wang https://orcid.org/0000-0002-0413-081X Zhan Tian https://orcid.org/0000-0002-4520-0036