water Article Simulation of Typhoon-Induced Storm Tides and Wind Waves for the Northeastern Coast of Taiwan Using a Tide–Surge–Wave Coupled Model Wei-Bo Chen 1,* ID , Lee-Yaw Lin 1, Jiun-Huei Jang 2 and Chih-Hsin Chang 1 1 National Science and Technology Center for Disaster Reduction, New Taipei City 23143, Taiwan; [email protected] (L.-Y.L.); [email protected] (C.-H.C.) 2 Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan City 70101, Taiwan; [email protected] * Correspondence: [email protected]; Tel.: +886-81958612 Received: 13 June 2017; Accepted: 19 July 2017; Published: 21 July 2017 Abstract: The storm tide is a combination of the astronomical tide and storm surge, which is the actual sea water level leading to flooding in low-lying coastal areas. A full coupled modeling system (Semi-implicit Eulerian-Lagrangian Finite-Element model coupled with Wind Wave Model II, SELFE-WWM-II) for simulating the interaction of tide, surge and waves based on an unstructured grid is applied to simulate the storm tide and wind waves for the northeastern coast of Taiwan. The coupled model was driven by the astronomical tide and consisted of main eight tidal constituents and the meteorological forcings (air pressure and wind stress) of typhoons. SELFE computes the depth-averaged current and water surface elevation passed to WWM-II, while WWM-II passes the radiation stress to SELFE by solving the wave action equation. Hindcasts of wind waves and storm tides for five typhoon events were developed to validate the coupled model. The detailed comparisons generally show good agreement between the simulations and measurements. The contributions of surge induced by wave and meteorological forcings to the storm tide were investigated for Typhoon Soudelor (2015) at three tide gauge stations. The results reveal that the surge contributed by wave radiation stress was 0.55 m at Suao Port due to the giant offshore wind wave (exceeding 16.0 m) caused by Typhoon Soudelor (2015) and the steep sea-bottom slope. The air pressure resulted in a 0.6 m surge at Hualien Port because of an inverted barometer effect. The wind stress effect was only slightly significant at Keelung Port, contributing 0.22 m to the storm tide. We conclude that wind waves should not be neglected when modeling typhoon-induced storm tides, especially in regions with steep sea-bottom slopes. In addition, accurate tidal and meteorological forces are also required for storm tide modeling. Keywords: storm tide; radiation stress; wave-induced surge; tide–surge–wave coupled model 1. Introduction Typhoon-induced storm surge and wind waves are major forces that pose a potential hazard in the form of coastal inundation and to shipping routes. Storm surge is classified as long gravity waves, whereas wind wave are short-period waves. Only long gravity waves can ascend to land, causing inundation that leads to severe loss of life and substantial damage to infrastructure in low-lying areas near the coast. Although short-period wind waves could be dangerous over the ocean, they would break at shallow waters and cannot climb land. Storm tide is the actual level of the water in the sea and adjacent tidal waterways during a typhoon event. The storm tide level results from the additive combination of the normal astronomical tide and the increase in water level due to the storm surge. The total surge depends on the interaction of wave forcing, wind stress, inverted barometer Water 2017, 9, 549; doi:10.3390/w9070549 www.mdpi.com/journal/water Water 2017, 9, 549 2 of 24 Water 2017, 9, 549 2 of 24 effects,wave-induced tidal stage radiation and bathymetry stress was in theusually path ofneglected the typhoon in early [1–7 ].storm The wave-inducedsurge modeling radiation [8–16]. stress The wascontributions usually neglected of wind waves in early to storm the momentum surge modeling equation [8–16 were]. The replaced contributions by adding of wind an additional waves to thedrag momentum coefficient equationto the wind were stress replaced equation. by adding Although an additional this simple drag method coefficient is convenient to the wind in storm stress equation.surge modeling, Although the this momentum simple method transf iser convenientrate from wave in storm breaking surge modeling,is highly dependent the momentum on the transfer slope rateand fromdepth wave of the breaking sea-bottom is highly [17]. dependent Fully coupled on the wave–current slope and depth models of the based sea-bottom on structured [17]. Fully or coupledunstructured wave–current grids have models been based recently on structured developed or unstructured for storm gridstide havemodeling been recentlydespite developedthe high forcomputational storm tide modeling cost [6,7,18–22]. despite the high computational cost [6,7,18–22]. To betterbetter understandunderstand thethe wavewave effectseffects onon stormstorm tidetide modeling,modeling, thethe tide–surge–wavetide–surge–wave coupledcoupled modeling system based on unstructured grids wa wass implemented for for the the Taiwan Waters in this study, andand fullyfully coupledcoupled simulationssimulations were conductedconducted for storm tides and wind waves using an unstructured-grid finite-elementfinite-element model. This This pape paperr is organized as follows.follows. The The study site and unstructured grid system for the numericalnumerical modelmodel areare describeddescribed inin SectionSection2 .2. AA briefbrief outlineoutline ofof models used in the present study is givengiven inin SectionSection3 3.. SectionSection4 4describes describes the the model model validation validation for for typhoon-induced storm tides and waves.waves. In In Sectio Sectionn 55,, numericalnumerical experimentsexperiments werewere conductedconducted toto investigate the contributions of wave-, wind wind stress stress-- and and air pressure-induced surge surge to to storm storm tides. tides. The conclusions areare summarizedsummarized inin thethe lastlast section.section. 2. Description of Study Area ◦ The computational domain in the present study coverscovers the region within a longitude of 114114° to ◦ ◦ ◦ 130130° E and latitude of 1919° to 2929° N. This area isis composedcomposed of the western PacificPacific Ocean, the Taiwan Strait, the South China Sea and the East China Sea, which are located in the east, the west, the south and the north of Taiwan,Taiwan, respectivelyrespectively (Figure(Figure1 1a).a). TheThe bathymetricbathymetric datadata usedused inin thethe presentpresent studystudy were obtained from coastal digital elevation models (DEMs) and ETOPO1 [23], [23], a global relief relief model. model. ETOPO1 integratesintegrates land land topography topography and theand ocean the bathymetryocean bathymetry of Earth’s of surface Earth’s with surface a 1-arc-minute with a resolution.1-arc-minute It isresolution. quite clear It in is Figurequite clear1a that in theFigure sea-bottom 1a that elevationsthe sea-bottom along elevations the eastern along coast the of Taiwaneastern arecoast very of steep.Taiwan The are bottom very steep. elevations The bottom vary rapidly elevatio fromns vary tens ofrapidly meters from at the tens shoreline of meters to several at the thousandshoreline metersto several at 10 thousand km off the meters coast. Withat 10 respectkm off to the the coast. north With coast, respect the slopes to ofthe the north sea-bottom coast, the are relativelyslopes of flatter.the sea-bottom A total of are 278,630 relatively non-overlapping flatter. A total unstructured of 278,630 triangular non-overlapping cells and 142,041unstructured nodes weretriangular used cells in the and horizontal 142,041 nodes to fit were the complex used in the shoreline horizontal of Taiwan to fit the and complex its adjacent shoreline small of Taiwan islands. Theand resolutionsits adjacent ofsmall the meshislands. range The from resolutions 30 km toof 300 the m. mesh The range fine meshes from 30 are km along to 300 the m. coastline The fine of Taiwanmeshes andare along small the offshore coastline islands, of Taiwan while theand coarse small meshesoffshoreare islands, along while the open the coarse ocean boundariesmeshes are (Figurealong the1b). open ocean boundaries (Figure 1b). Figure 1. Cont. Water 2017, 9, 549 3 of 24 Water 2017, 9, 549 3 of 24 Water 2017, 9, 549 3 of 24 Figure 1. (a) Bathymetry and (b) unstructured grids for the computational domain. Figure 1. (a) Bathymetry and (b) unstructured grids for the computational domain. Figure 1. (a) Bathymetry and (b) unstructured grids for the computational domain. 3. Methodology 3. Methodology3. Methodology The effects of the wave forcing and meteorological forcing induced by typhoons on storm tide The effectsThe effects of theof the wave wave forcing forcing and and meteorologicalmeteorological forcing forcing induced induced by bytyphoons typhoons on storm on storm tide tide modeling are taken into account using the coupled modeling system for wind waves, tide and modelingmodeling are taken are taken into account into account using theusing coupled the coupled modeling modeling system system for wind for waves,wind waves, tide and tide storm and surge. storm surge. The numerical tide–surge–wave modeling system used in the present study consists of The numericalstorm surge. tide–surge–wave The numerical tide–surge–wave modeling system modeling used in system the present used in study the pr consistsesent study of a consists hydrodynamic of a hydrodynamic model (Semi-implicit Eulerian-Lagrangian Finite-Element