applied sciences Article Tide-Surge-Wave Interaction in the Taiwan Strait during Typhoons Soudelor (2015) and Dujuan (2015) Li Zhang 1,2, Shaoping Shang 1,2,3,*, Feng Zhang 1,2,* and Yanshuang Xie 1,2,3 1 College of Ocean & Earth Sciences, Xiamen University, Xiamen 361005, China; [email protected] (L.Z.); [email protected] (Y.X.) 2 Key Laboratory of Underwater Acoustic Communication and Marine Information Technology, Xiamen University, Ministry of Education, Xiamen 361005, China 3 Center for Ocean Observation Technologies, Xiamen University, Xiamen 361005, China * Correspondence: [email protected] (S.S.); [email protected] (F.Z.); Tel.: +86-131-2339-3626 (S.S.) Received: 15 September 2020; Accepted: 16 October 2020; Published: 21 October 2020 Abstract: Typhoons Soudelor (2015) and Dujuan (2015) were two of the strongest storms to affect the Taiwan Strait in 2015. This study investigated the response of the waters on the western bank of the Taiwan Strait to the passage of Soudelor and Dujuan. This included an investigation of the resonant coupling between the tide and storm surge, typhoon wave variation caused by the storm tide, and wave-induced water level rise. Analyses conducted using numerical model simulations and observations from tidal stations and buoys, obtained during the passage of both Soudelor and Dujuan, revealed that resonant coupling between the astronomical tide and storm surge in the Taiwan Strait was prominent, which resulted in tidal period oscillation on the storm surge and reduced tidal range. The tide wave arrived earlier than the predicted astronomical tide because of the existence of the storm surge, which was attributable to acceleration of the tidal wave caused by the water level rise. Wave height observations showed that the storm tide predominantly affected the waves, which resulted in wave heights that oscillated within the tidal period. Numerical experiments indicated that both the current and the water level affected wave height. Waves were affected mainly by the current in the middle of the Taiwan Strait, but mostly by water level when the water level was comparable with water depth. Wave setup simulations revealed that wave setup also oscillated within the tidal period, and that local bathymetry was the most important influencing factor of wave setup distribution. Keywords: typhoon; coastal water responses; storm surge; waves; tide–surge interaction 1. Introduction The Taiwan Strait is located on the wide continental shelf of the East China Sea. The long narrow strait with average depth of nearly 60 m lies between the Chinese mainland and the island of Taiwan. Water from the North Pacific is mixed with water from the Luzon Strait in the Taiwan Strait. Regionally, the semidiurnal tide is dominant. The tidal range of 2–4 m from south to north, attributable to blocking by the island of Taiwan and the channeling effect of the Taiwan Strait, results in extremely strong tidal currents [1]. The Taiwan Strait is in an area prone to strong typhoons. Typhoons in this area often induce storm surges, high waves, and coastal inundation, which represent some of the most serious natural hazards to affect the lives and property of the regional population. During 1949–2005, 60% of the typhoons that passed through the Taiwan Strait area made landfall twice, first on the island of Taiwan and then on the western bank of the Taiwan Strait [2]. Appl. Sci. 2020, 10, 7382; doi:10.3390/app10207382 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 7382 2 of 25 The interaction between tide and storm surge has been studied since the 1980s. Both Wolf [2] and Horsburgh and Wilson [3] analyzed tidal observations and concluded that increased water depth attributable to storm surge induces acceleration of tidal wave propagation. Park and Suh [4] reported that storm surge is inversely proportional to water depth and tide, and that coupling of storm surge and tides is inevitable in coastal areas with shallow water depth and large tides. Based on study of the interaction between tides and storm surges using numerical simulations and observations, Bernier and Thompson [5] concluded that nonlinear bottom stress is an important factor. Zhang et al. [6] studied tide–surge interaction in the Taiwan Strait during the passage of Typhoon Dan (1999). They found that tide–surge interaction in the northern portion of the Taiwan Strait is intensified by the features of the strait, and that nonlinear bottom stress is an important factor that must be considered when predicting the oscillation due to tide–surge interaction. The interaction between typhoon-induced waves and sea level elevation induced by tides and storm surges has been studied previously. According to Wolf [2], the effect of tides and surges on waves must be considered in coastal areas because wave height is controlled largely by water depth, and because waves contribute to the total water level by means of the wave setup through wave radiation stress. Based on investigation of wave–tide interaction in the Yellow and East China seas, Moon [7] concluded that tides were the most influential factor with regard to modulation of regional mean wave characteristics. According to the findings of Chen et al. [8] in relation to the east coast of Taiwan, Huang et al. [9] with regard to Tampa Bay (Florida, USA), and Bertin et al. [10] in relation to the Bay of Biscay, waves should not be neglected in storm surge modeling in areas where large wave heights occur and the sea bottom slope is steep. The objective of this study was to investigate the response of the water of the Taiwan Strait (primarily on the western bank) to interactions among tides, storm surges, and typhoon-induced waves during the passage of typhoons Soudelor and Dujuan. A state-of-the-art unstructured grid storm surge–wave–tide coupled model was applied to simulate typhoon-induced storm surges for Soudelor and Dujuan. The storm surge–wave–tide coupled model is described in Sections2 and3 presents model validation for the tides, surges, and significant waves during the storms. Analysis of the interaction between water level and waves is provided in Section4. Finally, our conclusions are presented in Section5. 2. Materials and Methods 2.1. FETSWCM The tide and storm surge were simulated using the FETSWCM (finite element tide–surge–wave coupled model) model [11,12]. The FETSWCM model is a two-dimensional hydrodynamic model encompassed with a specific typhoon wind model for the Taiwan Strait [13]. FETSWCM has demonstrated satisfactory performance in storm surge forecasting along the Fujian Coast, which is on the western bank of the Taiwan Strait. Using a right-handed Cartesian coordinate system, combined GWCE (generalized wave continuity equation) [14] and VIMEs (vertically integrated momentum equations), the governing equations of FETSWCM in two-dimensional form are given as: 2 ! ! @ & @& @ @(U H) @ @(V H) ∂τ0 ∂τ0 + τ0 + · + τ0 U H + · + τ0 V H U H V H = 0, @t2 · @t @x @t · · @y @t · · − · · @x − · · @y (1) @U @U @U @(& + Ps/g/ρ0) τ τ τ + U + V f V = g + sx + wx bx , (2) @t · @x · @y − · − · @x H ρ H ρ − H ρ · 0 · 0 · 0 @V @V @V @(& + Ps/g/ρ0) τsy τwy τby + U + V + f U = g + + , (3) @t · @x · @y · − · @y H ρ H ρ − H ρ · 0 · 0 · 0 where ζ = the rise of the water level above the undisturbed sea level; Appl. Sci. 2020, 10, 7382 3 of 25 t = time; x, y = longitude (east) and latitude (north), respectively; U, V = the east and north components, respectively, of depth averaged velocity; H = the total water depth, where H = h + ζ; h = the depth of the undisturbed water; f = the Coriolis parameter; g = acceleration due to gravity; Ps = sea surface atmospheric pressure; ρa = the density of air; ρ0 = the density of sea water; W = the wind velocity vector at the height of 10 m above sea surface; τsx, τsy = the east and north components, respectively, of wind stress friction; * * τs = ρa Cs W W (4) · · · where Cs is the wind stress coefficient, which varies with wind velocity as follows: 8 * > 3 > 1.052 10− W 6 m/s > × ≤ > * * <> 3 Cs = > 0.638 + 0.069 W 10− 6 m/s W 30 m/s (5) > × ≤ ≤ > * > 3 > 2.708 10− W 30 m/s : × ≥ τbx, τby = the east and north components, respectively, of bottom friction. q τ = ρ C U (U2 + V2) (6) bx 0 · d · · q τ = ρ C V (U2 + V2) (7) by 0 · d · · where Cd is the bottom friction coefficient, which was taken as 0.0015 in this study. τwx, τwy = the east and north components, respectively of wave force (gradient of the wave radiation stress) which are calculated through SWAN model (Section 2.2) as follows: @Sxx @Sxy τwx = (8) − @x − @y @Syx @Syy τwx = (9) − @x − @y where Sxx, Sxy, Syx, Syy = the radiation stress tensor (m/s). In GWCE, the spatially differentiated momentum equation in its conservative form is combined with the temporally differentiated continuity equation, and the continuity equation is multiplied by the numerical parameter τ0, which is a constant that controls the balance of the wave equation and the primitive continuity equation. Extensive analysis of the GWCE has demonstrated that the scheme is stable [15]. 2.2. SWAN The SWAN is a wave model developed at Delft University of Technology (The Netherlands), which computes random, short-crested, wind-generated waves in coastal regions and inland waters. Appl. Sci. 2020, 10, 7382 4 of 25 SWAN has been used widely in many studies throughout the world, and is has demonstrated satisfactory performance in wave modeling in the Taiwan Strait [16–18]. SWAN uses a spectrum action balance equation to describe the generation of waves and evolution process in the near shore area as follows [19]: @N @ @ @ @ S + CxN + CyN + C N + C N = (10) @t @x @y ∂σ σ ∂θ θ σ where N = wave action density (Joule/m2/Hz); t = time (s); σ = frequency (Hz); θ = wave propagation direction; Cx, Cy = the propagation velocities of wave energy in spatial x-, y-space; " # 1 2kd σkx Cx = 1 + + U (11) 2 sinh(2kd) k2 " # 1 2kd σky Cy = 1 + + V (12) 2 sinh(2kd) k2 where U, V = the east and north components, respectively, of depth averaged velocity; d = water depth (m); k = wave number; Cσ, Cθ = the propagation velocities in spectral space σ-, θ-space; S = physical processes of generation, dissipation and non-linear wave-wave interactions, the options of these terms are list in Table1.