1 Introduction

Studies concerning climate changes have confirmed that the global climate has varied significantly in the past, and more profound changes are expected in the future (IPCC 2021). As a typical mesoscale meteorological event, tropical cyclones are certainly affected by climate changes. A number of previous studies have focused on the alteration in extreme winds, occurrence rates and tracks of tropical cyclones due to climate changes, and subsequently have forecast the tropical cyclone hazards in the future. Some studies have revealed that both the occurrence rates and intensities of Atlantic hurricanes and tropical storms could be reduced, driven by the increasing sea surface temperatures (SST) (Knutson et al. 2008; Bender et al. 2010). Other studies claimed that there is no significant relationship between SST and tropical cyclone activities (Chan and Liu 2004; Ren et al. 2011). A considerable number of studies supported the view that wind hazards from tropical cyclones are likely to increase in a warmer climate (Mudd et al. 2015; Chen et al. 2020). Since extreme weather conditions brought by tropical cyclones cause severe damage to coastal zones, such as Hong Kong, and put the majority of the population living along coastlines at risk, a quantitative assessment of climate change impact on regional hazards is necessary from the perspectives of both urban planning and structural design.

The sea–land transition zone is the region where there are abrupt changes in the roughness conditions of the underlying terrain across the sea–land interface (Gao et al. 2011). It is important as around 38% of the world’s population live by and depend on coastal regions, where the sea–land transition of the atmospheric boundary layer wind field plays an important role (Seibert et al. 2020). A proper description of the boundary layer wind fields in the sea–land transition zone is therefore of significance in studies concerning ocean and atmosphere sciences, such as the construction of the hurricane wind field model (Vickery et al. 2000), the investigation of air pollutant transport and dispersion in coastal areas (Xie et al. 2019), and the study of the formation of sea–land breezes (Xu et al. 2021), among others. The Tropical Cyclone Boundary Layer (TCBL), on the other hand, is important since it poses the most severe threats to the safety of the buildings and infrastructures within the coastal area during the visit of a tropical cyclone (Kloetzke 2019). Given the importance of the sea–land transition and the TCBL, an in-depth study of the sea–land transition of the TCBL wind field is valuable. Specifically, the underlying surface roughness length (\({z}_{0}\)) of complex land topography is the reason for the wind speed to reduce at lower altitudes in the TCBL. Therefore, a modular model that considers abrupt changes in underlying roughness determines, in part, the performance of a regional-scale model used to estimate the near-surface wind speed in the coastal region (Yeung et al. 2018; Shen et al. 2020; Li et al. 2022). In recent years, a series of studies have illustrated the impact of the \({z}_{0}\) value on the estimation of the TCBL wind field. For example, Vickery, Wadhera et al. (2009b) applied the empirical roughness model to estimate the surface wind of a hurricane, which reveals that the parameterization of sea surface roughness influences the estimation of wind speeds in the TCBL. Li et al. (2015) investigated turbulent wind characteristics in the TCBL based on observations, and discussed the influences derived from the underlying terrains. Fernández-Cabán and Masters (2017) analyzed the observed hurricane wind data and wind-tunnel measurements to reveal that the near-surface wind statistics of the TCBL deviate from the Gaussian probability distribution as the surface roughness increases. In conclusion, a realistic and reliable sea–land transition model is an important supplement to the existing TCBL wind field models as it takes into consideration the differences in the underlying terrain roughness corresponding to the sea and land (Powell 1982).

Various wind field models have already been established to depict the TCBL wind field onshore and offshore (Meng et al. 1995; Vickery et al. 2000; Huang and Xu 2012). Considering the relatively narrow width of most sea–land transition zones, the impacts of sea–land transitions on the dynamic behavior of the TCBL across the sea–land interface are rarely targeted in previous studies concerning the tropical cyclone meteorology (Powell et al. 2005; Vickery, Masters et al. 2009a). Studies in the wind engineering field, on the other hand, which are focused on the transition of the boundary layer wind field caused by the abrupt changes in the underlying terrain roughness, do not consider the particularity of the TCBL wind field (Vickery, Masters et al. 2009a). Consequently, there is a gap in existing models pertaining to the surface wind field within the sea–land transition zone when a tropical cyclone approaches the coastline. Furthermore, global climate changes certainly affect the formation, intensification, and decay of tropical cyclones and influence the TCBL wind field (Wang et al. 2022a; Wang et al. 2022b). Such influences, in theory, ultimately pass on to its sea–land transition. In this study, the sea (land) equilibrium wind speed profiles calculated by the improved TCBL wind field model are used as the starting point from which to provide the boundary conditions for the ESDU (Engineering Sciences Data Unit) roughness transition model (ESDU 1982a). Given that the calculations of the equilibrium wind profile inside the TCBL over land and over the sea take into account the influence of climate changes predicted by the Shared Socioeconomic Pathways 1-26 (SSP1-26, sustainable pathway with low challenges to mitigation and adaptation), 2-45 (SSP2-45, moderate pathway, medium challenges to mitigation and adaptation), and 5-85 (SSP5-85, the severe pathway, ongoing fossil-fuel development), such a transition model is useful in terms of putting forward guidance on building designs and urban planning for coastal cities in typhoon-prone regions.

In detail, this study investigates the influences of climate changes on the sea–land transition of the TCBL wind field through an integration of a TCBL wind field model, a transition model showing the influence of abrupt changes in underlying terrains on the boundary layer wind field, and predictions on the key parameters defining the TCBL wind field under the influence of climate changes. In formulating the transition model, the required roughness length \({z}_{0}\) is estimated using the mean height of buildings and structures in Hong Kong, which sheds light on urban planning in terms of mitigating typhoon hazards under the influence of climate change.

Based on the integration of these well-accepted theoretical and empirical models from different fields, this study reveals how global climate changes affect the sea–land transition in the TCBL wind field, and ultimately influence structural designs within the coastal region. In order to be illustrative, this study analyzes the wind statistics in the Hong Kong urban area by using the integrated model that considers the city’s vulnerability to tropical cyclones. In the illustration, the SSP1-26, SSP2-45, and SSP5-85 scenarios are employed to predict the future increase in SSTs near Hong Kong. Subsequently, the variations in the six key parameters defining the TCBL wind field are statistically predicted. Meanwhile, the mean building heights in different zones of Hong Kong are calculated and used to estimate the roughness lengths \({z}_{0}\). The modified key parameters that reflect climate changes and roughness length reveal three typical underlying terrains (city center, suburban, and rural areas). These archetypes are then input into the TCBL wind field model suggested by Huang and Xu (2012) to provide the start and end points for the ESDU model, which shows the gradual transition of the wind profile from the sea surface to different types of urban areas. Such a process is repeated following the Monte-Carlo simulation philosophy to provide estimates of probabilistic descriptions along the coastline of Hong Kong. Based on the Monte-Carlo simulation results, which correspond to the SSP1-26, SSP2-45, and SSP5-85 Pathways, the vertical variations in design wind speeds with a 50-year return period are compared to the reference values given in the Hong Kong Wind Code of Practice (Buildings Department 2004a, 2004b, 2019a, 2019b), which leads to possible improvements of the wind-resistance structural designs and guidance for urban planning targeting the coastal areas of Hong Kong.

Section 2 of this article presents the methodology for predicting the wind speed field inside the TCBL within the sea–land transition zone under the influence of climate changes. Section 3 articulates the prediction of the wind field in the sea–land transition zone in Hong Kong. The predictions of the design wind speeds considering climate changes are compared to the recommended values obtained from the Hong Kong wind code in Sect. 4. Concluding remarks are given in Sect. 5.

2 Methodology

Generally, the wind field model is the core for estimating the sea–land transition in the TCBL wind fields with climate change effects. The climate change description, which predicts the future SST variations, supplies the mesoscale key parameters to the wind field model. The roughness model provides the underlying boundary conditions over land and sea for the wind field model. Given the equilibrium wind profiles corresponding to the surface roughness of the sea and of land, the sea–land transition model is then used to calculate the variations in wind profiles within the sea–land transition zone along the coastline.

2.1 The Tropical Cyclone Boundary Layer (TCBL) Wind Field Model

The wind field inside the TCBL can be described by the simplified three-dimensional Navier-Stokes equations expressed in Huang and Xu (2012). Two boundary conditions, namely, the upper condition corresponding to the free atmosphere and the lower condition corresponding to the underlying terrain are applied to constrain the wind field model (Wang et al. 2022b). In order to be comprehensive, the main content of the wind field model suggested by Huang and Xu (2012) are shown in Eqs. 1 to 4. In the equations, \({v}_{\theta f}\) and \({v}_{rf}\) are friction-induced wind velocity components in the tangential and radial directions at the surface level; \(z\) is the height above the sea level; \({D}_{1}\), \({D}_{2}\), \(\xi\), \(\lambda\), and \(\chi\) are parameters calculating the friction-induced wind velocity, which can be estimated according to the formulas proposed by Meng et al. (1995). \({C}_{d}\) is the drag coefficient; \(\kappa\) is the von Kármán constant; \({z}_{10}\) is 10 m above the mean height of roughness elements; \(h\) is the mean height of roughness element; \(d\) is the zero-plane displacement; \({z}_{0}\) is the equivalent roughness length; \({k}_{m}\) is the vertical coefficient of eddy viscosity; \({v}_{s}\) is the horizontal wind velocity near the ground surface; \({v}_{\theta s}\) and \({v}_{rs}\) are the tangential and radial components of \({v}_{s}.\)

$${v}_{\theta f}={e}^{-\lambda z}\left[{D}_{1}\mathrm{cos}\left(\lambda z\right)+{D}_{2}\mathrm{sin}(\lambda z)\right]$$
(1)
$${v}_{rf}=-\xi {e}^{-\lambda z}\left[{D}_{2}\mathrm{cos}\left(\lambda z\right)-{D}_{1}\mathrm{sin}(\lambda z)\right]$$
(2)
$${C}_{d}={\kappa }^{2}/{\left\{ln\left[{(z}_{10}+h-d)/{z}_{0}\right]\right\}}^{2}$$
(3)
$$\chi =\frac{{c}_{d}}{{k}_{m}\lambda }\left|{v}_{s}\right|=\frac{{c}_{d}}{{k}_{m}\lambda }\sqrt{{v}_{\theta s}^{2}+{v}_{rs}^{2}}$$
(4)

Such friction-induced wind velocities are combined with the gradient wind velocities in association with the horizontal pressure profile to show the total wind velocities in the TCBL. The gradient wind velocities, on the other hand, rely on the translation velocities and approaching angles of a tropical cyclone as shown in Eqs. 5 and 6. \({v}_{\theta g}\) and \({v}_{rg}\) are the tangential and radial components of wind speed at the gradient level; \(c\) means the translation velocity of the tropical cyclone; \({\theta }_{r}\) is the angle between the typhoon translation direction and the vector from the center of the pressure field to the site of interest; \(f\) is the Coriolis parameter; \(r\) is the radial distance from the typhoon center. It is noted that the calculation of the gradient wind velocity relies on the pressure gradients in the radial direction, and therefore relies on the parameters defining the horizontal pressure profile of a tropical cyclone. In the present study, the pressure profile model is adopted as shown in Eq. 7, in which \(p\) is atmospheric pressure; \({p}_{c0}\) is the central pressure of a typhoon at the sea surface; \(\Delta {p}_{0}\) is central pressure difference of the tropical cyclone; \(RMW\) is the radius to the maximum wind; \(B\) is Holland’s radial profile parameter, in this study \(B\) is 1.0 (Georgiou 1986; Meng et al. 1995); \(g\) is the gravitation acceleration; \(\theta\) is the potential temperature and taken as a constant in this study; \({c}_{p}\) is the specific heat capacity of the air; \(R\) is the ideal gas constant.

$${v}_{\theta g}=\frac{1}{2}\left(csin{\theta }_{r}-fr\right)+{\left[{\left(\frac{csin{\theta }_{r}-fr}{2}\right)}^{2}+\frac{r}{p}\frac{\partial p}{\partial r}\right]}^\frac{1}{2}$$
(5)
$${v}_{rg}=-\frac{1}{r}{\int }_{0}^{r}\frac{\partial {v}_{\theta g}}{\partial r}dr$$
(6)
$$p=\left\{{p}_{c0}+\Delta {p}_{0}exp{\left[-\left(\frac{RMW}{r}\right)\right]}^{B}\right\}{\left(1-\frac{gz}{\theta {c}_{p}}\right)}^{\frac{{c}_{p}}{R}}$$
(7)

2.2 Climate Change Model

The assessment reports of the Intergovernmental Panel on Climate Change provide comprehensive evaluations of climate change. These reports have presented a number of well-accepted models helping scientists to understand how the climate may change in the future (Eyring et al. 2016). The latest generation of the assessment reports was published in 2021 with a new climate change scenariothe Shared Socioeconomic Pathways (SSPs). The SSPs consider not only the greenhouse gas emission, but also the socioeconomic influences associated with a series of climate-related policies. Five SSPs have been designed to comprehensively capture different levels of socioeconomic challenges, varying from SSP5 (ongoing fossil-fuel development with high challenges to mitigation) to SSP1 (sustainability with low challenges to mitigation and adaptation) in order to quantify the global warming degrees, and then to describe the evolution of society and ecosystems until the end of this century (O’Neill et al. 2017; IPCC 2021).

The climate change model predicts the variations in SSTs, which is a key parameter influencing the TCBL wind field (Slangen et al. 2017). For SSP5-85, the global SST is expected to rise at 0.39℃ per decade (Sung et al. 2021). In this study, the variations in SSTs dictate the changes in the probability distributions of six key parameters defining the TCBL wind field model. Specifically, it is postulated that the variations in the SSTs lead to the changes in the mean and standard deviations of the six key parameters in modeling the TCBL wind field. When randomly drawn from the probability distributions modified according to the variations in SSTs, the pseudo stochastic key parameters are input into the TCBL wind field model to estimate the equilibrium wind profiles over the sea and land. The six key parameters and associated probability distributions adopted in the present study to define the TCBL wind field are the Lognormal distribution of the translation velocity (\({V}_{t}\)), the Normal distribution of the approach angle (\(\theta\)), the Lognormal distribution of the central pressure deficit (\(\Delta {p}_{0}\)), the Lognormal distribution of the \(RMW\)(radius to maximum wind), the Trapezoidal distribution of the distance of closest approach (\({d}_{min}\)), and the Weibull distribution of the annual occurrence rate (\(\lambda\)). Details of the climate change model and its influences on the key parameters defining the TCBL wind field are found in the study of Wang et al. (2022b).

2.3 Sea–Land Transition Model

When a tropical cyclone approaches the coastline, a sea–land transition zone appears inside the TCBL due to the abrupt changes in the underlying surface roughness, and the wind field adjusts to accommodate the two equilibrium states corresponding to the two different underlying terrains. More specifically, an internal boundary layer develops inside the TCBL within the sea–land transition zone. In the wind engineering field, the wind profile transition due to the changes in the underlying roughness has been studied for common applications (ESDU 1982a; Barthelmie et al. 1993; Verkaik and Holtslag 2007; Giammanco et al. 2012). According to Deaves (1981) and ESDU (1982a), the transition can be taken as a process in which the internal boundary layer develops from the initial equilibrium state to another state accommodated with the changed underlying terrain roughness, and such a process can be described by Eqs. 8 to 14.

$$\begin{array}{c}{V}_{zx}={K}_{x}{u}_{\ast}{K}_{z^{\ast}} \left(z\le {h}_{i}\right)\\ {V}_{zx}={u}_{{\ast}1}{K}_{z^{\ast}1} (z>{h}_{i})\end{array}$$
(8)
$${h}_{i}=exp\left[\frac{{K}_{x}\left({u}_{{\ast}}/{u}_{{\ast}1}\right)ln{z}_{0}-ln{z}_{01}}{{K}_{x}\left({u}_{{\ast}}/{u}_{{\ast}1}\right)-1}\right]$$
(9)
$${K}_{x}=1+0.67{\left\{\frac{\left|ln\left({z}_{0}/{z}_{01}\right)\right|}{{\left[{u}_{{\ast}}/\left(f{z}_{0}\right)\right]}^{n}}\right\}}^{0.85}\bullet {f}_{sr}$$
(10)
$$\begin{array}{c}{f}_{sr}=0.1143{X}^{2}-1.372X+4.087 \left(X\le 5.5\right)\\ {f}_{sr}=0 \left(X>5.5\right)\end{array}$$
(11)
$$\begin{array}{c}{u}_{{\ast}}=\left[\frac{{V}_{r}}{2.5ln\left(\frac{{z}_{r}}{{z}_{0r}}\right)}\right]\left[\frac{{K}_{N}}{{K}_{Nr}}\right]\left[\frac{ln\left(\frac{{10}^{5}}{{z}_{0r}}\right)}{ln\left(\frac{{10}^{5}}{{z}_{0}}\right)}\right]\\ {u}_{{\ast}1}=\left[\frac{{V}_{r}}{2.5ln\left(\frac{{z}_{r}}{{z}_{0r}}\right)}\right]\left[\frac{{K}_{N}}{{K}_{Nr}}\right]\left[\frac{ln\left(\frac{{10}^{5}}{{z}_{0r}}\right)}{ln\left(\frac{{10}^{5}}{{z}_{01}}\right)}\right]\end{array}$$
(12)
$${K}_{N}={\left\{\frac{5+lnN-ln\left[-\mathit{ln}\left(1-{P}_{N}\right)\right]}{8.901}\right\}}^{0.5}$$
(13)
$$\begin{array}{c}{K}_{z^{\ast}}=2.5\left[ln\left(\frac{z}{{z}_{0}}\right)+\frac{34.5fz}{{u}_{{\ast}}}\right]\\ {K}_{z^{\ast}1}=2.5\left[ln\left(\frac{z}{{z}_{01}}\right)+\frac{34.5fz}{{u}_{{\ast}1}}\right]\end{array}$$
(14)

where \({V}_{zx}\) is the mean-hourly wind speed at height \(z\) above the ground level at the in-fetch distance of \(x\) (the distance that the new terrain extends or the distance that the internal boundary develops); \({K}_{x}\) is the fetch factor accounting for the sudden change in terrain roughness; \({u}_{{\ast}}\) and \({u}_{{\ast}1}\) are the friction velocity corresponding to different terrain roughness; \({K}_{z^{\ast}}\) and \({K}_{z^{\ast}1}\) are the height factors for corresponding terrains; \({h}_{i}\) is the height of the internal layer at the in-fetch distance of \(x\); \({z}_{0}\) and \({z}_{01}\) are the roughness lengths corresponding to the land and sea terrain, respectively; \(f\) is the Coriolis parameter; \(h\) is the gradient height; \(n=0.23\) for smooth-to-rough terrain change; \(X={log}_{10}x\); \({V}_{r}\) is the reference wind speed at height \({z}_{r}\) (normally 10 m) for reference terrain roughness \({z}_{0r}\); \({K}_{N}\) and \({K}_{Nr}\) are the correction for the risk of exceedance and exposure period from the reference wind speed; \({P}_{N}\) is the probability of exceeding the typical wind speed for a return period of \(N\) years. Given knowledge of the necessary empirical parameters, the gradual change in wind profile can be estimated according to the in-fetch distance of \(x\) from Eq. 8.

2.4 Roughness Model

Both the TCBL wind field model and the sea–land transition model require the roughness conditions for the sea surface and the land. According to Raupach (1994), Grimmond and Oke (1999), and Liu et al. (2016), the urban roughness length can be estimated as a function of the frontal area index and mean height of the roughness elements as shown in Eqs. 15 to 17. In Eqs. 15 to 17, \({z}_{d}\) is the zero-plane displacement; \({z}_{0}\) is the roughness length; \(\overline{{z }_{H}}\) is the mean height of roughness elements in the area; \({c}_{d1}\) is assumed as 7.5; \({\lambda }_{F}\) is the ratio of the windward area of a building per unit of land, also known as the frontal area index; \(U\) is the mean wind speed at reference height; \({u}_{{\ast}}\) is the friction velocity; \({\psi }_{h}\) is the sublayer influence function of the roughness; \({c}_{s}\) is the drag coefficient at height \(\overline{{z }_{H}}\) without considering the roughness elements; \({c}_{R}\) is the drag coefficient of an isolated roughness element.

$$\frac{{z}_{d}}{\overline{{z }_{H}}}=1+\left\{\frac{exp\left[{-\left({2c}_{d1}{\lambda }_{F}\right)}^{0.5}-1\right]}{{\left({2c}_{d1}{\lambda }_{F}\right)}^{0.5}}\right\}$$
(15)
$$\frac{{z}_{0}}{\overline{{z }_{H}}}=\left(1-\frac{{z}_{d}}{\overline{{z }_{H}}}\right)exp\left(-k\frac{U}{{u}_{{\ast}}}+{\psi }_{h}\right)$$
(16)
$$\frac{{u}_{{\ast}}}{U}=min\left[{\left({c}_{s}+{c}_{R}{\lambda }_{F}\right)}^{0.5},{\left(\frac{{u}_{{\ast}}}{U}\right)}_{max}\right]$$
(17)

According to Eqs. 15 to 17, \({\lambda }_{F}\), the ratio of the windward area of a building per unit of land, also known as the frontal area index, is the key parameter determining the roughness length \({z}_{0}\) in this roughness model. The frontal area index is a complex variable involving multiple factors, and it is closely related to the roughness area density \({\lambda }_{P}\). Grimmond and Oke (1999) illustrated that for the majority of urban areas, the value of \({\lambda }_{P}\) is between 0.3 to 0.4 corresponding to the peak value of height-normalized \({z}_{0}/\overline{{z }_{H}}\), and the value of \({\lambda }_{p}\) is concentrated at around 0.35. Therefore, this study adopts 0.35 as \({\lambda }_{P}\), and assumes that the relationship between \({\lambda }_{F}\) and \({\lambda }_{P}\) is: \({\lambda }_{F}=0.8{\lambda }_{p}\) according to Liu et al. (2016). Subsequently, the roughness length \({z}_{0}\) in relation with different building heights can be estimated via Eqs. 15 to 17.

2.5 Topographic Model

This study adopts a simplified method given by the ESDU for estimating topographic factors required for the calculation of the mean wind speed, shown as Eqs. 18 to 20 (ESDU 1982b). In Eqs. 18 to 20, \({K}_{L}\) is the speed-up factor on mean wind speed; \(\Delta {K}_{L2d}\) and \(\Delta {K}_{L3d}\) are the values of \({\Delta K}_{L}\) for two-dimensional and three-dimensional topography, respectively; \({f}_{ar}\) is the correction factor; \(H\) is the height of topography and \({L}_{u}\) is effective length scale of a topographic feature, which can be found in Fig. 1; \({s}_{z}\) and \({s}_{z=0}\) are the incremental speed-up parameter at height \(z\) and at the ground surface, respectively; \(a\) is the adjustment parameter that gives the variation of \({s}_{z}\) with height; \(z\) is the height above the ground surface.

Fig. 1
figure 1

Equivalent embankment for a hill in the topographic model. H is the height of topography and Lu is effective length scale of topographic feature.

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$${K}_{L}=1+\Delta {K}_{L2d}{f}_{ar}+\Delta {K}_{L3d}$$
(18)
$${K}_{L2d}=1+2\times \frac{H}{{L}_{u}}\times {s}_{z}$$
(19)
$$\frac{{s}_{z}}{{s}_{z=0}}=\frac{1}{1+a\left|{s}_{z=0}\right|{\left(\frac{z}{{L}_{u}}\right)}^{0.8}}$$
(20)

2.6 Calculation Process

The process of estimating the sea–land transition of the TCBL wind field under the influence of climate changes following the Monte-Carlo simulation philosophy can be divided into four steps:

Formulate the probability distributions of the key parameters to input into the TCBL wind field model (for example, the translation velocity, approach angle, central pressure deficit, radius to the maximum wind, minimum of closest distance, and occurrence rate) according to the increase in the SST projected by the climate change model. The six key parameters are assumed to be independent random variables, and the formulated probability distributions provide the base to randomly draw the key parameters defining the TCBL wind field in a series of Monte-Carlo simulations;

Adapt the roughness model to calculate the roughness lengths corresponding to various underlying terrains. More specifically, the mean height of structures located in the sea–land transition zone corresponding to different urban morphology types is obtained and brought into the roughness model to calculate the regional roughness length z0

Employ the wind field model, which uses the key parameters randomly drawn, the roughness lengths suggested by the roughness model, and the topographic factor estimated according to the topographic features around the site of interest, to provide the boundary layer equilibrium states of the wind profiles; and

Apply the sea–land transition model to show the gradual transition in wind profiles along the coastal areas according to the regional roughness length obtained from the previous step.

The above-articulated Monte-Carlo simulation yields the wind statistics of the sea–land transition inside the TCBL. The flowchart of a single Monte-Carlo simulation run is shown in Fig. 2.

Fig. 2
figure 2

Flowchart of the proposed integrated semiempirical model. ESDU = Engineering Sciences Data Unit

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3 Sea–Land Transition of the Tropical Cyclone Boundary Layer (TCBL) Wind Field in Hong Kong

In this study, we choose Hong Kong to illustrate the proposed methodology because the sea–land transition zone is particularly important for both policymakers and structural designers in Hong Kong. More specifically, tropical cyclones generated from the Northwest Pacific Ocean pose threats to Hong Kong buildings in the coastal area. According to Tse et al. (2013), 12 tropical cyclones typically pass through the South China Sea annually, and more than half move close to or across Hong Kong.

3.1 Topography in Hong Kong

Based on the category map of land use provided by the Planning Department of Hong KongFootnote 1 (Fig. 3), Hong Kong has various types of terrains, including commercial centers, open spaces, grassland, water areas, and so on. As a case study illustrating our proposed methodology, the wind profile transition in close proximity to Tsim Sha Tsui (TST) is modeled in the present study. Tsim Sha Tsui is located on the Kowloon Peninsula, with the longitude and latitude range from 114°10′00″E to 114°11′00″E, and 22°18′00″N to 22°19′00″N. As one of the major commercial centers in Hong Kong, TST corresponds to the city center terrain type according to the Planning Department of Hong Kong as shown in Fig. 3. Five 200 m × 200 m rectangles within the TST area are chosen to calculate the mean structure heights. The average building heights are then obtained from the Google Earth Pro 3DFootnote 2 for each of the rectangles and the corresponding roughness length \({z}_{0}\) is generated using the method presented in Sect. 2.4. For this case study the topographic factor can be ignored since there are no significant hills, ridges, cliffs, or escarpments within the TST region. However, for other types of terrains that are surrounded by significant topographic features, the topographic factor is required to calculate the equilibrium wind profiles onshore in modeling the sea–land transition of the TCBL wind flow.

Fig. 3
figure 3

Source https://www.pland.gov.hk/pland_tc/info_serv/open_data/landu/index.html#!

Hong Kong land use map and the typical place of interest (Tsim Sha Tsui, TST) in this study.

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3.2 Monte-Carlo Simulation Process

In order to conduct a series of Monte-Carlo simulations, the probabilistic models of the typhoon key parameters, including the translation velocity, the approach angle, the central pressure deficit, and the \(RMW\) (radius to maximum wind) of future tropical cyclones are required. As mentioned in Sect. 2.2, the mean and standard deviation values of four key typhoon parameters are calculated as a function of sea surface temperature (SST). Figure 4 illustrates the annual averaged SST in the past (historical, from 1961 to 2014) and in the future (SSP1-26, SSP2-45, and SSP5-85, from 2021 to 2080). The averaged SST is obtained through different climate models (the details are illustrated in Table 1) under the “all-forcing simulation of the recent past” condition detected by the Coupled Model Intercomparison Project Phase 6 (CMIP6). The relationships between SST and the key parameters of the TCBL wind field are specified according to the models listed in Table 2 and the detailed estimation method can be found in Wang et al. (2022b).

Fig. 4
figure 4

Past and future sea surface temperature (SST) records and predictions for Hong Kong. Note: “Historical” represents the annual mean sea surface temperature (SST) data in Hong Kong from 1961 to 2014, while the “SSP1-26,” “SSP2-45,” and “SSP5-85” predictions are the annual mean SST of the SSP1-26, SSP2-45, and SSP5-85 climate scenarios from 2021 to 2080

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Table 1 Availability of sea surface temperature (SST) models in historical mode, SSP1-26, SSP2-45, and SSP5-85
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Table 2 The relationships between sea surface temperature (SST) and key parameters of typhoons in Hong Kong
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With the probability distributions modified according to increases in the SSTs, the key parameters defining the TCBL wind field are randomly drawn. Given the equilibrium wind profiles over the sea and land calculated by the TCBL wind field model, the sea–land transition model is applied to show the gradual transition in TCBL wind profiles from sea surface to city center in Hong Kong. The estimation of the sea–land transited wind profile is repeated 10,000 times to predict the variations in extreme wind speeds with a 50-year return period. In other words, this study generated 10,000 virtual tropical cyclones impacting Hong Kong, and then estimated the influence of climate changes on the extreme wind speeds within the sea–land transition zones.

3.3 Sea–Land Transitions of the Tropical Cyclone Boundary Layer (TCBL) Wind Speeds

The Monte-Carlo simulation results of the wind profiles inside the sea–land transition zone of the TCBL are illustrated in Fig. 5 when compared to the wind profiles estimated by ignoring the climate change effect. The transition fetch (\(x\)) is assumed to be 20 km in the present study, and the results corresponding to in-fetch distances of \(0.01x, 0.1x, x\) (0.2 km, 2 km, 20 km), are shown in Fig. 5. Specifically, Fig. 5 presents the resulting wind profile in the sea–land zone of the TCBL in the past (therefore without the climate change impacts) and in the future (considering the SSP5-85 climate scenario) at locations TST in Hong Kong. Figures 5a and b show the results without the climate change effects at the in-fetch distance \(x\), and the wind profile under the SSP5-85 scenario at the in-fetch distance of \(x\), respectively. Figure 5c and d show the same comparisons at the in-fetch distance of \(0.1x\), and Fig. 5e and f show the same comparison at the in-fetch distance of \(0.01x\).

Fig. 5
figure 5

The Tsim Sha Tsui (TST) city center area typhoon sea–land transition wind profiles with and without climate change effects at different Fetch lengths. Key symbols for “v_sea,” “v_land,” and “v_trans” present the equilibrium wind speed from the sea and from the land, as well as the transition wind speed from sea to land

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4 Discussion

Based on the findings obtained from analyzing the wind profiles in the sea–land transition zone of the TCBL produced by a series of Monte-Carlo simulations, this study examined the influences of climate changes, underlying roughness, topographic effects, and comparisons with the recommendations from the wind load code of Hong Kong.

4.1 Impacts of Climate Change Effects

It is apparent from Fig. 5 that increases in SSTs change the shape of the wind profiles at different in-fetch distances. In other words, the climate changes adjust the Hellmann exponent of the wind profile in the sea–land transition zone of the TCBL. The Hellmann exponent is a parameter reflecting the wind profile shape and hence correlating the wind speeds at two different heights (Charki et al. 2018), as shown in Eq. 21. In order to quantitatively assess the influence, the Hellmann exponent \(\alpha\) is calculated according to Heier (2014), Okorie et al. (2017), and Simiu and Yeo (2019) as:

$$\alpha =\frac{ln\left({V}_{h}/{V}_{10}\right)}{ln\left(h/{h}_{10}\right)}$$
(21)

where \({V}_{h}\) and \({V}_{10}\) are the wind speeds at heights \(h\) (300 m is chosen in this study according to DeMarrais (1959), Tse et al. (2013), and Liu et al. (2017)) and 10 m, respectively. It is concluded from Fig. 5 that the wind speeds increase with the SST regardless of the transition fetch, and the increasing trend of global warming will induce a greater wind speed in the TCBL affecting Hong Kong. In Table 3, the hourly mean wind speed above the sea at 10 m for three typical transition fetches under historical climate conditions is 21.31 m/s. This is 8.1% smaller than that under the SSP5-85 climate scenario (23.20 m/s), and the mean wind speeds under the SSP1-26 and SSP2-45 scenarios, which are 21.33 m/s and 21.62 m/s, respectively. On the other hand, the mean wind speed during typhoon sea–land transition processes at 10 m for three transition fetches under the historical scenario is 8.44 m/s, which is slightly greater than the wind speed corresponding to SSP1-26 and lower than the value of SSP2-45. The mean wind speed corresponding to SSP5-85 at the same condition is 8.59 m/s, and therefore 1.8% greater than the historical value. Similar comparison results for wind speeds at 90 m are shown in Table 3.

Table 3 Hourly mean wind speeds above the sea and during the typhoon sea–land transition processes at 10 m and 90 m in Tsim Sha Tsui (TST) of Hong Kong under historical climate condition, SSP1-26, SSP2-45, and SSP5-85 climate scenarios
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4.2 Comparison of 50-Year Return Period Wind Profile in Hong Kong

The design of wind speed is one of the keys to the wind codes or standards (Architectural Institute of Japan 2015; Buildings Department 2019a; Standards Australia/Standards New Zealand 2021). In the Hong Kong Wind Code of Practice 2004 (Buildings Department 2004a, 2004b, 2019a, 2019b), a simplified power-law model is adopted to calculate the vertical variation in design wind speeds. The model assumes that the wind speeds below the gradient height follow the power-law model and remain constant above the gradient height. Also, the Hong Kong Wind Code of Practice 2004 (Buildings Department 2004a, 2004b, 2019a, 2019b) recommends a magnification of 5% based on the wind speeds with the 50-year return period considering the uncertainties in estimating the design wind speeds. The power-law model is shown in Eq. 22:

$$\overline{{v }_{z}}=1.05\overline{{v }_{g}}{\left(\frac{z}{{z}_{g}}\right)}^{\alpha }$$
(22)

where \(\overline{{v }_{z}}\) is the design wind speed at height z, \(\overline{{v }_{g}}\) is the gradient wind speed, \({z}_{g}\) is the gradient height, \(\alpha\) means the power exponent value. According to Simiu et al. (2001), Huang et al. (2011), and Sarkar et al. (2011), the Fisher–Tippett probability distribution function can be used as the probabilistic model for describing extreme wind speeds. The function is shown in Eq. 23:

$$F\left(v\right)=exp\left[exp\left(-\alpha \left(v-\mu \right)\right)\right]$$
(23)

where \(\alpha\) and \(\mu\) are called the dispersion and mode, respectively. \(v\) is the annual maximum wind speed. In this study, 10,000 Monte-Carlo simulation runs are carried out to predict the 50-year return period design wind speed under the influence of the SSP5-85 climate scenario in Hong Kong. Tsim Sha Tsui, the city center, is selected as the site of interest in the evaluation of the recommendation from the Hong Kong wind code since the city center is most prone to damage induced by tropical cyclones. In the comparisons, the wind profiles that correspond to the three different climate scenarios (SSP1-26, SSP2-45, and SSP5-85) are used to discern the differences between the simulated and code-recommended wind field in the development of the internal boundary layer.

Figure 6 illustrates the comparison between the predicted 50-year return period wind speed obtained from the Monte-Carlo simulation and the design wind speed recommended by the Hong Kong Wind Code of Practice (Buildings Department 2004b, 2004a, 2019a, 2019b). The figure shows that, when the TCBL sea–land transition completes (in-fetch distance of 20 km) under three different climate change pathways, the wind speeds obtained from the Monte-Carlo simulation do not exceed the recommendations at the lower level where the majority of buildings are found. Especially at the 10 m height, the code-recommended design wind speed is higher than the predictions provided by over 100%. Such findings demonstrate an over-conservative value adopted in the code currently practiced in Hong Kong. For the wind profiles above 480 m, the wind speeds under the SSP5-85 scenario show exceeding values compared with the code recommendations. When normalized by the design wind speeds recommended by the wind code, the maximum exceedance is found around 3% (around 1.77 m/s) near a height of 690 m. Consequently, the magnification of the design wind speed by 5% is required for estimating the wind loads above 400 m if the climate changes ultimately induce the increases in SSTs as predicted in the SSP1-26, SSP2-45, and SSP5-85 scenarios. Even after the magnification, the design wind speeds recommended by the code are still slightly lower than the wind speeds with 50-year return period obtained from the Monte-Carlo simulation under the SSP5-85 scenario. This result implies that a moderate modification procedure should be initialized when the climate change effect is commonly acknowledged within the wind engineering community in Hong Kong.

Fig. 6
figure 6

Mean wind profiles in Hong Kong by code and prediction scenario. Note: “HK code” presents the basic design wind speed given by the Hong Kong Wind Code of Practice 2004. “Not Magnified” means the design hourly mean wind speed without considering the uncertainties of 50-year return period. “SSP5-85,” “SSP2-45,” and “SSP1-26” are the different climate scenarios used in this study

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Figure 7 presents the normalized profiles of the design wind speeds recommended by the Hong Kong wind code and obtained from the Monte-Carlo simulation (across the sea). It is apparent from the figure that the simulated wind profile above the sea reaches a peak at around 500 m, while the code-recommended design wind speed remains constant above the gradient height. Additionally, Fig. 7 shows the Hellmann exponents calculated from the profiles under 300 m. The exponent values estimated above the sea, based on the Monte-Carlo simulation results under SSP1-26, SSP2-45, and SSP5-85, are 0.037, 0.039, and 0.048, respectively, which are smaller than the value suggested by the Hong Kong Wind Code of Practice (0.110). Such a difference indicates that the future climate change effects cannot be ignored in the design of low- to high-rise buildings on the shoreline where the TCBL wind field over the sea dominates the wind loads.

Fig. 7
figure 7

Comparison of the normalized wind profiles for Hong Kong. Note: “HK code” presents the normalized hourly mean wind speed given by the Hong Kong wind code; “SSP1-26,” “SSP2-45,” and “SSP5-85” are the estimated normalized hourly design wind speeds above the sea under SSP1-26, SSP2-45, and SSP5-85 climate change scenarios; \({U}_{z}\) and \({U}_{10}\) are the wind speeds at heights z and 10 m; and \(\alpha\) is the Hellmann exponent value

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4.3 Design Wind Speed with Topographic Effect

In the present study, TST is chosen as a case study to show the sea–land transition of the TCBL wind profile under climate change influences. Since there is no obvious topography feature nearby, the topographic effect is ignored in the case study. Hong Kong, however, is a densely populated, mountainous metropolis. The effects of topography (such as hills) cannot be ignored for other areas, such as Hong Kong Island. Therefore, the present study considers the sea–land transition of the TCBL wind profile around the highest mountain located on Hong Kong Island (Victoria Peak, 552 m). More specifically, the topographic factors articulated in Sect. 2.4 are adopted to estimate the onshore equilibrium wind profile at Hong Kong Island in a series of Monte-Carlo simulations. The simulated wind profile is then compared to the code-recommended wind profile by integrating the topographic multiplier suggested by the Hong Kong wind code. These multipliers are calculated according to Eqs. 24 to 26. In Eqs. 24 to 26, \({S}_{t}\) is the topographic multiplier; \({\psi }_{e}\) is the minimum of maximum slope for a quarter of the hill-height or 0.3; \(s\) is the topographic location factor; \({K}_{u1}\) and \({K}_{u2}\) are two parameters related to \(\frac{z{\psi }_{e}}{{H}_{t}}\); \(z\) is the structure height; \({H}_{t}\) is the height of topography; \({z}_{t}\) is the location of the structure above the ground surface; \({I}_{v,z}\) is the turbulence intensity; and \({z}_{e}\) is the effective height.

$${S}_{t}=\left[1+\frac{2{\psi }_{e}s}{1+3.7{I}_{v,z}}\right]$$
(24)
$$s={K}_{u1}\bullet {e}^{\left[-{K}_{u2}\left(1-\frac{{z}_{t}}{{H}_{t}}\right)\right]}$$
(25)
$${I}_{v,z}=0.087{\left(\frac{{z}_{e}}{500}\right)}^{-0.11}$$
(26)

In comparisons, the wind speeds at the 10 m height found at the mountain foot (\(z=0\)), half-height (\(z=H/2\)), and the peak (\(z=H)\) from the Monte-Carlo simulation and code suggestions are calculated. In the Monte-Carlo simulation, the transition process is assumed to be complete as the Victoria Peak can be considered located in the center of the Hong Kong Island. Table 4 shows such comparisons. It is obviously that the topographic factors estimated according to the proposed methodology decrease due to the height increase, while the topographic multipliers suggested by the Hong Kong wind code increase with height. More importantly, the wind speeds extracted from the Monte-Carlo simulations under three climate change pathways are significantly lower than those recommended by the Hong Kong wind code. It can be concluded that the topographic effect is influential in giving suggestions for the design wind speeds in Hong Kong, and the recommended wind speed indicated by the current code at the lower part of TCBL is significantly conservative, even considering the influence of global warming.

Table 4 The topographic factor obtained from the Engineering Sciences Data Unit (ESDU) and the Hong Kong wind code, and the estimated design wind speeds at 10 m
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5 Conclusion

The influence of climate changes on the sea–land transition in the TCBL wind field is evaluated by combining the refined TCBL wind field model, the SSPs climate change description, the roughness length dataset corresponding to sea surface and land topographies, and the sea–land transition model. Following the Monte-Carlo simulation philosophy, the wind statistics within the sea–land transition zone of the TCBL wind field in Hong Kong are estimated to quantitatively assess the impact of climate change on the design wind speeds and tropical cyclone hazard assessment in the coastal area. Using the proposed methodology, the wind profiles are simulated in sea–land transition zones connecting the sea surface and the city center terrains of Hong Kong. The results illustrate that the likely warmer climate of the future will raise wind speeds at various heights. Furthermore, the predicted wind speeds are compared with the design wind speeds given by the Hong Kong building standards (Buildings Department 2004a, 2004b, 2019a, 2019b), and exceedances are noted at greater heights (above 400 m). The comparisons indicate that the code-recommended wind speed is noticeably higher than the wind speeds derived from the Monte-Carlo simulation in the lower part of the TCBL. Such differences imply that modification or alteration of the Code of Practice in Hong Kong is needed, given that the increases in SSTs gradually will become commonly accepted among the wind engineering community in Hong Kong.

This study presents and utilizes an integrated semiempirical methodology to estimate a sea–land transition wind profile inside the TCBL that considers the impacts of climate change. Although the validity of the individual module suggested by the methodology has been independently checked in previous studies, the integration of such individual components should be further examined. Due to the scarcity of three-dimensional wind measurements of the TCBL in the sea–land transition zone, it is suggested that observations taken at a few selected sites in Hong Kong and other parts of the Asia Continent could be employed to systematically verify the proposed framework. Such verification is the next step of the work reported here. Furthermore, the roughness length of the sea surface is assumed constant in this study, and the changes in sea surface roughness with surface wind speed/friction velocity should be considered for further analysis. Additionally, a more precise fetch for each estimation point could be adopted to improve the predictions, and multiple roughness change steps due to variations in underlying terrains (for example, sea-rural-urban) can be generated to represent more realistic conditions.