Journal of Marine Science and Engineering

Article An Efficient Method for Simulating Typhoon Waves Based on a Modified Holland Vortex Model

Lvqing Wang 1,2,3, Zhaozi Zhang 1,*, Bingchen Liang 1,2,*, Dongyoung Lee 4 and Shaoyang Luo 3

1 Shandong Province Key Laboratory of Ocean Engineering, Ocean University of China, 238 Songling Road, Qingdao 266100, China; [email protected] 2 College of Engineering, Ocean University of China, 238 Songling Road, Qingdao 266100, China 3 NAVAL Research Academy, Beijing 100070, China; [email protected] 4 Korea Institute of Ocean, Science and Technology, Busan 600-011, Korea; [email protected] * Correspondence: [email protected] (Z.Z.); [email protected] (B.L.)



Received: 20 January 2020; Accepted: 23 February 2020; Published: 6 March 2020


Abstract: A combination of the WAVEWATCH III (WW3) model and a modified Holland vortex model is developed and studied in the present work. The Holland 2010 model is modified with two improvements: the first is a new scaling parameter, bs, that is formulated with information about the maximum wind speed (vms) and the typhoon’s forward movement velocity (vt); the second is the introduction of an asymmetric typhoon structure. In order to convert the wind speed, as reconstructed by the modified Holland model, from 1-min averaged wind inputs into 10-min averaged wind inputs to force the WW3 model, a gust factor (gf) is fitted in accordance with practical test cases. Validation against wave buoy data proves that the combination of the two models through the gust factor is robust for the estimation of typhoon waves. The proposed method can simulate typhoon waves efficiently based on easily accessible data sources.

Keywords: Holland vortex model; WAVEWATCH III; scaling parameter; gust factor; typhoon waves

1. Introduction Tropical cyclones, hurricanes, or typhoons (hereafter referred to simply as typhoons) are intensive ocean forces that can destroy coastal properties or offshore engineering structures, leading to significant economic losses [1]. Generally, the ocean waves induced by typhoons are characterized by extreme heights [2] and are critical inputs for the design of offshore or coastal structures. Historical typhoon waves are often used as fundamental samples to predict the possible wave loads that shore-based or floating structures will bear in the future [3–5]. In order to simulate typhoon waves, researchers have adopted numerical wave models [6,7], used empirical formulas [8], and given a parameterization of the nearshore wave front slope [9]. Machine-learning methods, such as artificial neural networks, have gradually been introduced to predict wave parameters [10–12]. To study typhoons, researchers have calculated the ultra-long return level of wind speed based on a deductive method [13], carried out systematic numerical experiments in an idealized continental shelf–beach–land system to identify the role of waves in storm surge and inundation under different storm characteristics [14], simulated 39 years of wave data with high temporal and spatial resolutions [15], and proposed a formula for blended tropical cyclone wind fields that combines two datasets and shows a good capacity to simulate a tropical cyclone’s wind field [16]. For all of the abovementioned methods, a realistic typhoon wind field should first be reconstructed as the input force. In other words, the accuracy of the typhoon wind field determines the quality of a model of typhoon waves [17].

J. Mar. Sci. Eng. 2020, 8, 177; doi:10.3390/jmse8030177 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2020, 8, 177 2 of 21

There are three basic approaches to reconstructing typhoon wind fields. The first is to use atmospheric models, such as MM5 and WRF, to simulate typhoons [18–20]. The second is to adopt wind reanalysis products to reconstruct a typhoon’s wind field [6,21]. The third approach is to use parametric vortex models to reconstruct a typhoon’s wind field following typhoon track data. A typical parametric model is that created by Holland in 1980 [22], hereafter known as H80. Since its release, H80 has been extensively utilized in various types of applications with different modifications that agree well with researchers’ observations [23–26]. In particular, due to the typhoon track data that have been available since the 1940s and can be easily accessed via meteorological service websites, a parametric vortex model can be used to obtain wave samples that are more than 60 years old. Holland (2008) developed a new parametric equation to formulate the scaling parameter b, which makes the H80 model more flexible. During its 30th anniversary in 2010, H80 was improved by a new analytic representation of the radial profile, which ensuring that the model has lower sensitivity to external parameters, such as the radius of maximum wind (RMW) and external winds (Holland et al., 2010 [27], hereafter known as H80H10). Some researchers have coupled the Holland model with a third-generation wave model [28,29], such as WAVEWATCH III (WW3), to simulate typhoon waves. Practical applications show that the H10 model may be further improved, and, in this paper, we present two improvements: the introduction of an asymmetric typhoon structure and a robust Holland scaling parameter bs. In the remainder of this paper, the modified H10 model will be abbreviated as MH10. WW3 is a state-of-the-art third-generation wave model [10,30] widely used to forecast and hindcast ocean waves [31–33]. Considering its high efficiency and accuracy, we used the WW3 model to simulate typhoon waves in this study. Generally, the WW3 model is forced by the 10-min averaged 10-m 10’ surface wind U10 , where the subscript refers to the surface height of 10 m and the superscript refers to the 10-min average. However, in the cyclone research community, it is usual to use the 1’ 1-min averaged wind U10 [26]. In order to use the Holland wind to force the WW3 model, it is 1’ 10’ necessary to convert U10 into U10 . Although some researchers have proposed a range of gust 10’ 1’ factors (U10 /U10 ) to achieve this conversion [26], it is difficult to find a universal gust factor that applies to all typhoons [34,35]. With the aim of coupling the Holland wind and the WW3 model, we 1’ 10’ formulate a gust factor to convert U10 into U10 in accordance with test cases. Furthermore, MH10 uses an empirical formula to define the RMW, since it is not always available in the track data distributed by different meteorological organizations. With the adoption of an RMW formula, the MH10 model is more flexible. In this study, we used a Chinese website http://www.wztf121.com/ (accessed on July 2017) (hereafter, WZTF) as a reference for the track data. Details about the RMW can be found in Section 3.4. This article is structured as follows. Section2 describes the wave dataset. Section3 presents the standard H10 model and the modified H10 model. Section4 validates the combination of the two models. Sections5 and6 present a discussion and our conclusions, respectively. AppendixA provides diagrams of the wave–time series, and AppendixB provides a table of results with all involved test cases.

2. Data sources

2.1. Typhoon Track Data The track data that are distributed through the website WZTF are characterized by different temporal intervals (6 h, 3 h, and 1 h) and gradually become finer from east longitudes to west longitudes in the Northwest Pacific Ocean. The finest time resolution of the typhoon track data from WZTF is 1 h. The track data from WZTF are structured by date, time, longitude, latitude, maximum wind speed (BS), maximum surface wind speed (m/s), central pressure (hPa), velocity of forward movement (km/h), moving dir., radius of BS-7 wind speed (km), and radius of BS-10 wind speed (km). However, the RMW is not explicitly provided. J. Mar.J. Mar. Sci. Sci. Eng. Eng.2020 2020, 8,, 8 177, 177 3 of3 23 of 21

2.2. Wave Data 2.2. Wave Data An open source of buoy wave data, released by the Central Weather Bureau of Taiwan (CWBT), is adoptedAn open to source validate of the buoy model. wave More data, detailed released information by the Central about Weather the buoys Bureau can be ofaccessed Taiwan through (CWBT), is adoptedthe website: to validate http://www.cwb.gov.tw/ the model. More (access detailed date: information July 2017). about Another the buoysset of buoy can bedata accessed is from throughthree thebuoys website: moored http: in// www.cwb.gov.twthe northern South/ China(access Sea date: (SCS), July as 2017).seen in Another Figure 1. set All of three buoy buoys data are is frommoored three buoysin open moored ocean, in where the northern the water South depth China is approximately Sea (SCS), as seen30‒50 in m. Figure The buoys1. All are three 50 buoys‒85 km are from moored the incoastline. open ocean, Wave where heights the waterand wave depth periods is approximately will be verified 30–50 in accordance m. The buoys with are the 50–85 data from km from these the coastline.buoys. Wave heights and wave periods will be verified in accordance with the data from these buoys.

Figure 1. Geographical location of wave buoys for model verification (QF301–QF303 are from some Figure 1. Geographical location of wave buoys for model verification (QF301‒QF303 are from some discontinuous scientific projects; others are from the Central Weather Bureau of Taiwan (CWBT) discontinuous scientific projects; others are from the Central Weather Bureau of Taiwan (CWBT) 3. Standard and Modified H10 Models 3. Standard and Modified H10 Models 3.1. Standard H10 3.1. Standard H10 Based on the radial surface pressure profile, approximated by a rectangular hyperbola as suggested Based on the radial surface pressure profile, approximated by a rectangular hyperbola as by [36], H80 introduced an upgraded pressure profile formulated as in Equation (1), where ps is the suggested by [36], H80 introduced an upgraded pressure profile formulated as in Equation (1), where surface pressure at radius r, pcs is the central surface pressure, ∆ps = pns pcs is the pressure drop from 𝑝 is the surface pressure at radius r, 𝑝 is the central surface pressure,− ∆𝑝 =𝑝 −𝑝 is the an external pns to a central pressure (in hPa), rv is the radius of the maximum surface wind speed, pressure drop from an external 𝑝 to a centralms pressure (in hPa), 𝑟 is the radius of the maximum and e is the base of nature logarithms [22]. Parameter b is a scaling parameter defining the proportion surface wind speed, and e is the base of nature logarithms [22]. Parameter b is a scaling parameter of pressure gradient near the RMW. In the last few decades, it has been proven that the introduction of defining the proportion of pressure gradient near the RMW. In the last few decades, it has been parameter b is successful for the estimation of typhoon wind vortex profiles. proven that the introduction of parameter b is successful for the estimation of typhoon wind vortex

profiles. b ( rvm ) = + r ps pcs ∆pse− (1) ( ) 𝑝 =𝑝 +∆𝑝𝑒 (1) With Equation (1) as the basic form of the radial pressure variation, H10 proposed a new formula for With Equation (1) as the basic form of the radial pressure variation, H10 proposed a new formula for wind profile as in Equation (2), where vs is the surface typhoon wind at a 10-m height, vms is the surface wind profile as in Equation (2), where 𝑣 is the surface typhoon wind at a 10-m height, 𝑣 is the maximum wind in m/s, bs is the surface scaling parameter kept constant in a typhoon, and ρs is the air surface maximum wind in m/s, 𝑏 is the surface scaling parameter kept constant in a typhoon, and density.ρs is the Notably, air density. all of Notably, the variables all of the in Equationvariables (2)in Equa shouldtion be (2) observations should be observations at a height at of a 10 height m, where of the10 variable m, wherex can the bevariable defined x can as inbe Equationdefined as (6). in Equation (6).

𝑟   b x 100𝑏∆𝑝(rvms ) s 100bs∆ps 𝑟r  𝑣 =[ ] v =  ( )  s  r bs   𝜌𝑒( vm )  ρse r or or ( )x  bs r bs rvms [ ( vms ) ] v = v e 1 r (2) s ms r − J. Mar. Sci. Eng. 2020, 8, 177 4 of 21

Once the maximum surface wind and central pressure are known, bs can be estimated following H80 through Equation (3), where ρms is the air density at a radius of surface maximum wind.

2 vmsρmse bs = (3) 100∆ps

Another method to derive the surface scaling parameter bs is proposed by Holland as in Equation (4) [37], where vt is the velocity of the forward movement of typhoons in m/s.

5 2 ∂pcs n bs = 4.4 10− ∆p + 0.01∆ps + 0.03 0.014ϕ + 0.15v + 1.0 − × s ∂t − t ! ∆ps n = 0.6 1 − 215 !0.5 100bs vms = ∆ps (4) ρmse 1 1 The surface air density can be derived from Equation (5), where R = 286.9 J kg− K− , Tvs is the 1 virtual surface temperature in K, qs is the surface moisture in gkg− , Ts is the surface temperature, and SST is the sea surface temperature. 100ps ρs = RTvs

Tvs = (Ts + 273.15)(1 + 0.61qs) ! 17.67Ts 3.802 243.5+Ts qs = RHs 100ps

Ts = SST 1 (5) − The exponent x in Equation (2) can be defined as in Equation (6), where xn is an adjusted exponent that is fitted in accordance with the peripheral observations at a radius of rn.

 =  x 0.5 r rvms  xn 0.5 ≤ (6)  x = 0.5 + (r r ) − r > r vms rn rv vms − − ms Equations (1)–(6) define the H10 model. In H10, the scaling parameter b formulated in Equation (4) is more feasible and flexible than in H80, and the exponent x in Equation (2) varies with different radiuses. Among these inputs of H10, the air density “is not critical and constant value of density can be used if preferred” [27]. Alternatively, if there is a good estimation for the maximum wind (vms), the air density will be disregarded, and Equation (2) can be used to get vs directly.

3.2. Modifications of Standard H10

3.2.1. A More Informative Scaling Parameter

As a key parameter of the Holland model, scaling parameter b (in H80) or bs (in H10) plays a major role in the accurate prediction of a radial wind profile. Two different types of empirical formulas for parameter b are provided in H80 and H08 [22,37]. There are also some statistical models fitted according to realistic typhoons to estimate parameter b [38,39]. J. Mar. Sci. Eng. 2020, 8, 177 5 of 21

In the H80 model, the gradient wind speed is defined as in Equation (7), where vg is the gradient wind speed at the location with distance r from the typhoon center, fc is the Coriolis parameter, ρa is the air density, pc is the central pressure, and pn is the ambient air pressure.

1  A  2 b 2 2 Ab(pn pc)e− r r f  r fc v =  − + c  (7) g  b   ρar 4  − 2

There is a relationship between the parameters A, b, and RMW formulated as in Equation (8) [22].

The maximum wind speed of the typhoon occurs at r = rvms , where the Coriolis force can be negligible. Then, the surface maximum wind speed can be estimated through Equation (9) [8].

1 b rvms = A (8)

1 ! 2 b(pn pc) vt vms = 0.8 − + (9) ρae 2

Following Equation (9), once vm, vt, and pc are known, bs can be explicitly defined as in Equation (10). Physically, bs as in Equation (10) should be the gradient level value. However, according to repeated calibrations against the buoy data, parameter b deduced from Equation (9) can be directly used as the surface level bs formulated in Equation (10), which is perhaps caused by the uncertainty of reducing factors, as revealed by Vickery et al. [40]. Differently from the initial formulas about the scaling parameter, our modification involves both vm and vt, leading to the new formula, Equation (10), which is more informative than Equation (3) and Equation (4). It will be proven that this deduction of Equation (10) is robust to improve the performance of the Holland model.

h  i2 vt vms 2 1.25 ρae bs = − × (10) pn pc −

In the typhoon track data distributed by WZTF, vm, vt, and pc have been provided hour by hour. The parameter pn can be approximately estimated with a constant, such as 1005 hPa [27]. Consequently, Equation (10) can be easily utilized to calculate parameter bs. Compared with other RMW-dependent methods [38], Equation (10) tends to be more independent, feasible, and simple.

3.2.2. Asymmetric Typhoon Structure Plotting the realistic evolution of a typhoon is a very complicated process [41–43]. The actual structure of the typhoon is asymmetric, with the maximum wind possibly located in the rear-right quadrant or in the front-right quadrant [44,45]. An asymmetric structure is helpful for accurate estimations of coastal risks, such as the surge [46]. In order to convert the axis-symmetric H10 into an asymmetric model, an asymmetric term caused by typhoon forward movement can be superimposed [25,46–48]. Equation (11) is one type of an asymmetric term, where Vadd is the component of the asymmetric wind speed, vt is the forward movement velocity of the typhoon, β is the angle from the typhoon moving direction [47] 1, and C and n are positive constants. In the present work, C and n are determined to be 0.4 and 1, respectively, according to some tentative tuning. The final asymmetric wind is formulated in Equation (12) [25], where vas is the asymmetry surface wind and vs is the Holland surface wind calculated in Equation (2). The forward movement velocity, vt, is explicitly provided in the WZTF track data. Even if vt is not available in the typhoon track data,

1 The original definition by Georgiou (1986) is the trigonometric angle where 0◦ = East and 90◦ = North, assuming a northward typhoon motion. In order to be consistent with the following formulas in the present work, this is converted into the angle from the typhoon’s moving direction. J. Mar. Sci. Eng. 2020, 8, 177 6 of 21 it can be approximately estimated by referring to the geographical coordinates of typhoon centers at different times. n Vadd = C vt sinβ (11) J. Mar. Sci. Eng. 2020, 8, 177 · · 6 of 23 vas = vs + Vadd = vs + 0.4vtsinβ (12) 𝑣 =𝑣 +𝑉 =𝑣 +0.4𝑣𝑠𝑖𝑛𝛽 (12) 3.3. A New Gust Factor

1’ 3.3.As A mentioned New Gust Factor above, the wind in Equation (2) is 1-min averaged U10 [8], which is not suitable for the numericalAs mentioned wave above, models the [ 49wind]. The in Equation wind field (2) from is 1-min Equation averaged (2) shouldU101’ [8], be which converted is not suitable into 10-min 10’ averagedfor theU numerical10 for furtherwave models forcing [49]. WW3. The wind field from Equation (2) should be converted into 10- minWe averaged accomplish U1010’ this for further conversion forcing with WW3. the following sequence of steps. First, we find out the maximumWe wind accomplish speed andthis itsconversion occurrence with time the from following a track sequence data file. of Second, steps. First, we utilize we find this out maximum the windmaximum speed to wind normalize speed and 48-h its occurrence wind speeds time before from a thetrack maximum data file. Second, wind hourwe utilize and this get maximum the standard deviationwind speed of the to normalizednormalize 48-h wind wind speed. speeds Thirdly, before the the maximum gust factors wind can hour be and estimated get the basedstandard on the deviation of the normalized wind speed. Thirdly, the gust factors can be estimated based on the standard deviations of normalized wind speed following Equation (13), where gf is the gust factor standard deviations of normalized wind speed following Equation (13), where gf is the gust factor and std is the standard deviation of the normalized wind speed in the 48 h before the wind peak. and std is the standard deviation of the normalized wind speed in the 48 h before the wind peak. A A gust factor curve is fitted as in Figure2. According to Figure2, the gust factor decreases while the gust factor curve is fitted as in Figure 2. According to Figure 2, the gust factor decreases while the standardstandard deviation deviation increases, increases, meaning meaning that that a sharply a sharply fluctuating fluctuating typhoon typhoon should should be be reduced reduced in in a largera proportion.larger proportion. A detailed A detailed discussion discussion of Equation of Equation (13) is (13) presented is presented in Section in Section 5.1. 5.1. 𝑈100 𝑔 = U10 = 0.827 − 0.036 × ln (𝑠 ) (13) = = ( ) g f 𝑈 0.827 0.036 ln std (13) 10 − × U10

Figure 2. Fitted curve of the gust factor and the manually adjusted gust factors. Figure 2. Fitted curve of the gust factor and the manually adjusted gust factors. 3.4. Approximation of RMW 3.4. Approximation of RMW Although the H10 model shows little sensitivity to the RMW, and even errors of up to 50% in Although the H10 model shows little sensitivity to the RMW, and even errors of up to 50% in this radius result in relatively small errors in the overall wind profile [27], RMW is a mandatory input this radius result in relatively small errors in the overall wind profile [27], RMW is a mandatory input parameter.parameter. For For universalization universalization ofof thethe Holland model, model, it itisis helpful helpful to tofind find an aneffective effective method method to to approximateapproximate RMW. RMW. ThereThere have have been been some some statistical statistical RMWRMW models fitt fitteded regionally regionally [39] [39 for] for local local predictions, predictions, but but therethere is not is not a model a model available available for for the the SCS. SCS. In In this this paper, paper, aa classicalclassical method of of empirical empirical formula formula [50] [50 ] is adoptedis adopted to approximate to approximate RMW RMW following following Equation Equation (14), (14), where whereϕ is 𝜑 the is the latitude latitude of theof the typhoon typhoon center. center.  pcs 1013.2  ( .− ) rv = 28.52th 0.0873 (ϕ 28) + 12.22e 33.86 + 0.2vt + 37.2 (14) ms . (14) 𝑟 = 28.52𝑡ℎ[0.0873× × (𝜑− − 28) + 12.22𝑒 +0.2𝑣 +37.2] It isIt di isffi difficultcult for for Equation Equation (14) (14) to to provide provide accurateaccurate estimations estimations for for every every typhoon. typhoon. In order In order to to verifyverify the the accuracy accuracy of Equationof Equation (14), (14), IBTrACS IBTrACS data data [51 [51]] are are adopted adopted toto extractextract realistic RMW RMW values values for for typhoons in the Northwest Pacific. A virtual benchmark is utilized to check the sensitivity of H10

J. Mar. Sci. Eng. 2020, 8, 177 7 of 21

J. Mar. Sci. Eng. 2020, 8, 177 7 of 23 typhoons in the Northwest Pacific. A virtual benchmark is utilized to check the sensitivity of H10 to RMW, where r = 180 km and v = 40 m/s in Equation (2). Several typhoons in the Northwest Pacific to RMW, where r = 180 km andms vms = 40 m/s in Equation (2). Several typhoons in the Northwest Pacific indexedindexed from from 022015 022015 (Typhoon (Typhoon NO. NO. andand YYYY)YYYY) to to 132015 132015 (Typhoon (Typhoon NO. NO. and and YYYY) YYYY) are are investigated. investigated. RMWsRMWs from from Equation Equation (14) (14) areare distributeddistributed in a narrow range range from from 40 40 to to 60 60 km. km. Contrarily, Contrarily, the the RMWsRMWs extracted extracted from from IBTrACS IBTrACS are are widely widely distributeddistributed fromfrom 9 to to 90 90 km, km, as as seen seen in in Figure Figure 3.3 Although. Although therethere some some distinct distinct di differencesfferences in in the thetwo two datasetsdatasets of the the RMWs, RMWs, the the wind wind speed, speed, reconstructed reconstructed based based onon the the RMWs, RMWs, show show small small di differences,fferences, as as inin TableTable1 1.. RMW extracted from IBTrACS (km) IBTrACS from extracted RMW 10 15 20 25 Wind speed with RMW of IBTrACS(m/S) 20 40 60 80

18.5 19.0 19.5 20.0 20.5 21.0 40 42 44 46 48 50 Wind speed with RMW by Eq. (14) (m/s) RMW by Eq. (14) (km) Figure 3. Comparison of the radius of maximum winds (RMW) by Equation (14) against RMW from Figure 3. Comparison of the radius of maximum winds (RMW) by Equation (14) against RMW from IBTrACS (left) and comparison of wind speed deduced from the two RMWs (right). IBTrACS (left) and comparison of wind speed deduced from the two RMWs (right). Table 1. Quantile statistics of the radius of maximum winds (RMWs) and relevant wind speed reconstructedTable 1. Quantile by H10. statistics WSP: wind of the speed. radius of maximum winds (RMWs) and relevant wind speed reconstructed by H10. WSP: wind speed. RMW by Equation RMW from WSP with RMW by WSP with RMW from RMW by Equation RMW from IBTrACS WSP with RMW by WSP with RMW (14) (km) IBTrACS (km) Equation (14) (m/s) IBTrACS (m/s) (14) (km) (km) Equation (14) (m/s) from IBTrACS (m/s) Min. 40.4 9.3 18.3 6.9 0.05Min. 40.4 41.09.3 18.5 18.3 18.56.9 11.1 0.250.05 41.0 42.518.5 27.818.5 18.911.1 14.5 0.500.25 42.5 44.027.8 37.018.9 19.314.5 17.4 0.75 45.5 64.8 19.7 24.0 0.50 44.0 37.0 19.3 17.4 0.90 47.9 74.1 20.3 25.8 Max.0.75 45.5 50.664.8 92.619.7 20.924.0 28.8 0.90 47.9 74.1 20.3 25.8 Max. 50.6 92.6 20.9 28.8 3.5. Descriptions of Model Input 3.5.The Descriptions final MH10 of Model model Input consists of Equations (2), (6), (10), (12), and (13). If the RMWs of typhoons are notThe available, final MH10 Equation model (14) consists can be of adoptedEquations to (2), approximate (6), (10), (12), RMWs. and (13). Input If the variables RMWs of to typhoons run MH10 areare listed not available, in Table2 .Equation The model (14) MH10can be canadopted be easily to approximate utilized based RMWs. on Input the tracking variables data to run distributed MH10 throughare listed WZTF. in Table 2. The model MH10 can be easily utilized based on the tracking data distributed throughBesides WZTF. the easily accessible typhoon track data resources, both the MH10 model and the WW3 model canBesides perform the easily reliable accessible simulations typhoon of typhoon track da wavesta resources, with high both effi theciency MH10 on model a desktop and workstationthe WW3 ensuringmodel thatcan aperform researcher reliable can gainsimulations insight intoof typh typhoonoon waves waves. with For example,high efficiency a simulation on a desktop from 1949 toworkstation 2017 with more ensuring than that 200 typhoonsa researcher takes can about gain 40insight h at ainto workstation typhoon waves. computer For withexample, two Intela E5-2650simulation processors. from 1949 to 2017 with more than 200 typhoons takes about 40 h at a workstation computer with two Intel E5-2650 processors.

Table 2. Variables to run modified H10 (MH10).

Variable Description Unit (IS) Definition p cs Typhoon central pressure hPa Available in distributed track data

J. Mar. Sci. Eng. 2020, 8, 177 8 of 21

Table 2. Variables to run modified H10 (MH10).

Variable Description Unit (IS) Definition

pcs Typhoon central pressure hPa Available in distributed track data vt Typhoon translation speed m/s Available in distributed track data vns Peripheral wind speed m/s Defined as BS-7 wind speed rn Radius of peripheral wind km Radius of BS-7 wind ϕ Latitude of typhoon center degree Available in the distributed track data β Angle from the typhoon moving direction degree Determined according to actual track pns Peripheral pressure hPa Constant at 1005 3 ρa Air density kg/m Constant at 1.15

4. Test of Model Performance

4.1. Basic Setup of WW3 WW3 (V4.18) code is compiled to establish a regional hindcasting wave model covering latitudes of 5 –45 N and longitudes of 100 –145 E, with a grid resolution of 10 10 . A numeric obstacle ◦ ◦ ◦ ◦ 0 × 0 technique has been embedded to simulate the effect of numerous islands [30]. The classical source term package of Tolman and Chalikov (T&C package) [52] is adopted to simulate wave physics, including wave generation and wave dissipation with quaternate timesteps set up as 1800 s, 900 s, 180 s, and 45 s. The compiling option FLX3 is switched on, since the option is purposely designed for hurricane winds to alleviate the problem of an unrealistically high drag coefficient leading to unrealistically high wave growth rates. Though some researchers have found that the classical T&C package (or the ST2 switch) frequently underestimates typhoon waves [28,29], this paper will demonstrate that the T&C package performs well in the SCS.

4.2. Setup of Input Wind The wind fields reconstructed by MH10 and H10 are both gridded as 15 15 with a temporal 0 × 0 interval of 1 h. Practical simulations have proven that the wind field with one-quarter degree is precise enough to force the WW3 model with grids of 10 10 . The reconstructed wind field covers 0 × 0 the same area as in the WW3 model, covering latitudes of 5◦–45◦ N and longitudes of 100–145◦ E. The reconstructed wind field will be reduced by the gust factor before it works to force the WW3 model.

4.3. Explanations of Test Cases In order to verify the combination of the MH10 model and WW3, 12 typhoons tracking in the Northwest Pacific are investigated in this study. All of these typhoons have been reconstructed through three models: the standard H10 model, indexed as B2-A1-A1; the varying scale parameter bs without asymmetric typhoon structure, indexed as B3-A1-A1; and the modified parameter bs with asymmetric typhoon structure, i.e., the MH10 model, indexed as B3-A1-A2. All three models will be reduced by a gust factor that is calculated separately for different typhoons following Equation (13). Due to the limited length of this paper, seven representative typhoons, seen in Figure4, will be selected and discussed, with explanatory illustrations to gain insight into the simulation capability of the combination. All simulation results of the 12 typhoons are listed in Table A1. J. Mar. Sci. Eng. 2020, 8, 177 9 of 21 J. Mar. Sci. Eng. 2020, 8, 177 9 of 23

Figure 4. Tracks of seven representative typhoons in the Northwest Pacific. Figure 4. Tracks of seven representative typhoons in the Northwest Pacific. 4.4. Model Verification 4.4. Model Verification The wave time series comparisons between the buoy data and the modeling results, as seen in FiguresThe A1 wave–A10 time, show series that comparisons the wave series between created the bybuoy MH10 data isand characterized the modeling by results, swifter as feedback seen in toFigures wind A1 input‒10, than show by that the the standard wave series H10. Allcreated of the by waveMH10 series is characterized figures in Appendix by swifterA feedbackshow that to thewind introduction input than ofby an the asymmetric standard H10. structure All of enhances the wave the series model’s figures ability in Appendix to capture A extremeshow that wave the parameters.introduction Generally, of an asymmetric MH10 created structure a more enhanc realistices wavethe model’s time series ability than to standard capture H10.extreme wave parameters.An error Generally, analysis ofMH10 the resultscreated in a Tablemore realA1 isticis conducted wave time for series the absolutethan standard value H10. error and the percentageAn error error, analysis which of are the summarized results in Table in Table A1 is3. conducted According for to the Table absolute3, the RMSEs value error (root and mean the squarepercentage errors) error, of Hwhichs (Hs isare significant summarized wave in height)Table 3. induced According by standardto Table H103, the and RMSEs MH10 (root wind mean are 1.14square m anderrors) 0.86 of m, Hs respectively.(Hs is significant The wave MAEs height) (mean induced absolute by errors) standard of HH10s induced and MH10 by standard wind are H101.14 andm and MH10 0.86 wind m, respectively. are 1.36 m and The 0.78 MAEs m, respectively,(mean absolute and errors) the SDs of (standard Hs induced deviations) by standard of equivalent H10 and variablesMH10 wind are 1.05are 1.36 m and m 0.67and m.0.78 For m, those respectively, percentage and errors, the SDs the mean(standard error deviations) of Hs forced of by equivalent standard H10variables is 20%, are and 1.05 the m equivalentand 0.67 m. error For those of MH10 percentage is 10%. errors, Additionally, the mean the error maximum of Hs forced error isby decreased standard fromH10 is 75% 20%, (standard and the equivalent H10) to 31% error (MH10), of MH10 and is the 10%. standard Additionally, deviation the of maximum errors is reduced error is decreased from 19% (standardfrom 75% H10)(standard to 9% H10) (MH10), to 31% showing (MH10), that and MH10 the standard has a more deviation stable of simulating errors is reduced ability thanfrom H10.19% All(standard of the errorH10) resultsto 9% (MH10), demonstrate showing that that MH10 MH10 generally has a more performs stable better simulating than standard ability than H10. H10. From All Tableof the3 ,error it can results be concluded demonstrate that thethat new MH10 scaling generall parametery performsbs and better the asymmetricthan standard structure H10. From both Table lead to3, improvedit can be concluded performance. that the new scaling parameter bs and the asymmetric structure both lead to improved performance. In general, the three parametricTable 3. typhoonError analysis wind of models the three show models. equal performances to the force wave model in capturing peak wave periods. Table 3 shows that the three kinds of models tested B2-A1-A1 B3-A1-A1 B3-A1-A2 have a similar ability in the simulationError Type of wave periods whose mean errors are 13% (Standard H10) and 11% (MH10). Both the error analysis and theHs wave(m) series Tr (s)comparisonsHs (m) reveal Tr (s) thatHs the(m) wave Tr period (s) is Errormore analysis difficult in to absolute simulate accuratelyRMSE than the wave 1.14 height. 1.12 Especially 1.08 after 1.04 the peak 0.86 time, the 1.00 wave values (error = |X MAE 1.36 1.26 1.23 1.07 0.78 1.01 period will decreasemodel sharply,− which is mainly attributed to the absence of an external background Xbuoy|) Sd 1.05 1.14 0.87 0.92 0.67 0.94 wind field. Considering that the restructured wind model is often adopted to estimate extreme sea Error analysis in percentage Mean percentage 20% 13% 16% 12% 10% 11% states(error and= |X the model/X results1| canMax give percentage a good estimation 75% of 51%the typhoon 49% waves, 41% the disagreement 31% 46% after model buoy − × the100%) peak time is not a significantSd. concern. of Error 19% 12% 12% 10% 9% 10% In most of the test cases, both the wave height and wave period at the peak time can be simulated well. However, the WW3 model, forced by a reconstructed wind field, will perhaps generate more In general, the three parametric typhoon wind models show equal performances to the force wave swells than in a natural ocean setting, and the swells may propagate unrealistically far away. The model in capturing peak wave periods. Table3 shows that the three kinds of models tested have a major reason for this may be that the reconstructed wind field fails to represent the ambient wind similar ability in the simulation of wave periods whose mean errors are 13% (Standard H10) and 11% field. The ambient wind field may influence the swell dissipation and induce local sea winds, which (MH10). Both the error analysis and the wave series comparisons reveal that the wave period is more can reduce the wave periods. This is what happened at Taitung Open Ocean during typhoon 012016 difficult to simulate accurately than the wave height. Especially after the peak time, the wave period (Nepartak) and at Pratas during typhoon 142016 (Meranti), as seen in Figures A6 and Figure A10; will decrease sharply, which is mainly attributed to the absence of an external background wind field. there is an obvious difference between the buoy-measured wave periods and the WW3 wave Considering that the restructured wind model is often adopted to estimate extreme sea states and the periods.( Hs is significant wave height; Tr is average period) model results can give a good estimation of the typhoon waves, the disagreement after the peak time is not a significant concern. Table 3. Error analysis of the three models.

J. Mar. Sci. Eng. 2020, 8, 177 10 of 21

In most of the test cases, both the wave height and wave period at the peak time can be simulated well. However, the WW3 model, forced by a reconstructed wind field, will perhaps generate more swells than in a natural ocean setting, and the swells may propagate unrealistically far away. The major reason for this may be that the reconstructed wind field fails to represent the ambient wind field. The ambient wind field may influence the swell dissipation and induce local sea winds, which can reduce the wave periods. This is what happened at Taitung Open Ocean during typhoon 012016 (Nepartak) and at Pratas during typhoon 142016 (Meranti), as seen in Figures A6 and A10; there is an obvious difference between the buoy-measured wave periods and the WW3 wave periods (Hs is significant wave height; Tr is average period).

5. Discussion

5.1. Gust Factor Literature reviews indicate that there has been no definitive conclusion regarding the gust factors for tropical cyclones and extratropical winds. It is revealed that the gust factor is sensitive to surface roughness, and the gust reduction in typhoon winds can be higher than in extratropical winds [35]. In the WW3 model, the wave growth rate is determined by both an effective roughness ze and the friction velocity u* [30,53]. However, WW3 is prone to overestimating the drag coefficient for hurricane winds, leading to unrealistically high wave growth [30], since the WW3 model is supported by wave data measured in low-to-moderate wind conditions [29,53]. According to in situ measurements, the drag coefficient decreases as the wind speed increases [54]. Fetch is another important influence for the sea surface roughness [55], and the fetch can be approximately estimated by the pre-peak time. In short, there are many unknown conditions that weaken the WW3 model’s performance at simulating intense typhoon waves. Physically, the gust factor defined in this paper is purposely utilized to convert different time-scale wind speeds. However, the practical applications proved that the gust factor can act as an external adjustor to alleviate some uncertainties caused by various unknown factors, such as the surface roughness, drag coefficient, fluctuation of wind speed, and other unresolved physical parameters. In general, Equation (13) works well for typhoons with smooth tracks and for those buoys that are moderately far away from the typhoon centers. While a typhoon track shows sharp changes when the buoys are in the typhoon centers, Equation (13) is incapable of making a good estimation of gust factors. For example, the center of Typhoon Vicente (082012) turned sharply away from its preceding track path (see Figure4), and QF302 is almost overlapping with the center. The gust factor extrapolated by Equation (13) is 0.88, and the best manually adjusted factor is 0.96, as seen in Figure5. Figure5 presents several other cases where the two gust factors are di fferent. Statistics of their difference show that the wave height biases between buoy peak and modeling peak vary between 0.5 and 1.4 m, with the gust factor difference varying between 0.03 and 0.08. For a sharply turbulent typhoon wave series, this magnitude of peak wave difference may be negligible considering that the error ratio of all cases is about 10%, as in Table3 (TC is the abbreviation of tropical cyclones). J. Mar.J. Mar. Sci. Sci. Eng. Eng.2020 2020, ,8 8,, 177 177 11 of11 23 of 21

TC INDEX=222016, Buoy=Pratas TC INDEX=142016, Buoy=Taitung Open Oc.

Buoy Hs Buoy Hs GF=0.92 GF=0.98 GF=0.88 GF=0.93 Hs (m) Hs Hs (m) Hs 24681012 2468101214

0 10203040 0 20406080

Time Series(hour) Time Series(hour)

TC INDEX=192013, Buoy=Eluanbi TC INDEX=082012, Buoy=QF302 Buoy Hs GF=0.97 GF=0.94 Buoy Hs GF=0.96 GF=0.88 Hs (m) Hs Hs (m) Hs 51015 246810

0 1020304050 0 5 10 15 20 25 30

Time Series(hour) Time Series(hour)

FigureFigure 5. 5.Influence Influence ofof gust factors on on the the simulate simulatedd wave wave height height series. series. GF: GF: gust gust factor. factor. 5.2. Scaling Parameter 5.2. Scaling Parameter DuringDuring Typhoon Typhoon MerantiMeranti (142016),(142016), four buoys’ buoys’ da datata were were available available simultaneously. simultaneously. This This case case providedprovided a a good good chance chance toto investigateinvestigate the models’ models’ ability ability to to reconstruct reconstruct a wind a wind field field across across a large a large geographicalgeographical range. range. FollowingFollowing Equation Equation (13),(13), thethe gust factor of of Meranti Meranti is is defined defined as as gfg =f =0.918.0.918. Both Both MH10 MH10 and and the the standardstandard H10 H10 have have successfullysuccessfully captured the the extr extremeeme waves waves at at the the Eluanbi Eluanbi buoy buoy with with a maximum a maximum HsHofs of approximatelyapproximately 18 18 m m (Figure (Figure A7). A7 However,). However, H10 poorly H10 poorlysimulates simulates the other thethree other buoys three (Figures buoys (FiguresA8‒10), A8 whereas–A10), the whereas MH10 themodel MH10 works model well. works well. InIn accordance accordance with with Figure Figure6, in which6, in which wind fieldwind contours field contours are mapped, are andmapped, the wind and reconstructedthe wind byreconstructed standard H10 byis standard obviously H10 di isff obviouslyerent from differen that oft MH10.from that The of MH10. wave fieldsThe wave induced fields by induced winds by from threewinds kinds from of three models kinds are of depicted models inare Figures depicted7–9 .in All Figures the figures 7‒9. All indicate the figures that the indicate maximum that the wave heightmaximum occurs wave at the height front-right occurs at quadrant the front-right of the typhoonquadrant motion,of the typhoon and the motion, waves and at the the right waves side at are usuallythe right severer side are than usually at the severer left side. than at Obviously, the left side. the Obviously, standard the H10 standard overestimates H10 overestimates the wind speed,the leadingwind speed, to too-large leading a to wave too-large height a inwave the height ambient in the oceans. ambient oceans.

J. Mar. Sci. Eng. 2020, 8, 177 12 of 21 J. Mar. Sci. Eng. 2020, 8, 177 12 of 23 J. Mar. Sci. Eng. 2020, 8, 177 12 of 23

Figure 6. Wind fields (unit as m/s) restructured by MH10 (asymmetric structure as solid line, B3-A1- FigureFigure 6. 6.Wind Wind fields fields (unit (unit as as m m/s)/s) restructured restructured by by MH10 MH10 (asymmetric (asymmetric structure structure as as solid solid line, line, B3-A1-A2); B3-A1- A2); standard H10 (axis-symmetric structure as a dashed line, B2-A1-A1); and the varying scaling standardA2); standard H10 (axis-symmetric H10 (axis-symmetric structure structure as a dashed as a line,dashed B2-A1-A1); line, B2-A1-A1); and the varyingand the scalingvarying parameter scaling parameter bs without asymmetric structure (depicted with the dashed‒dotted line, B3-A1-A1) at bsparameterwithout asymmetric bs without structureasymmetric (depicted structur withe (depicted the dashed–dotted with the dashed line, B3-A1-A1)‒dotted line, at EluanbiB3-A1-A1) Station at Eluanbi Station peak wave time during Typhoon Meranti (142016). peakEluanbi wave Station time duringpeak wave Typhoon time during Meranti Typhoon (142016). Meranti (142016).

Figure 7. A wave field (unit: cm) induced by the wind field from the standard H10 (B2-A1-A1) at Figure 7. A wave field (unit: cm) induced by the wind field from the standard H10 (B2-A1-A1) at EluanbiFigure Station7. A wave peak field wave (unit: time cm) during induced Typhoon by the Meranti wind field (142016), from the where standard the bigger H10 black(B2-A1-A1) dot is at the Eluanbi Station peak wave time during Typhoon Meranti (142016), where the bigger black dot is the locationEluanbi of Station the typhoon’s peak wave center. time during Typhoon Meranti (142016), where the bigger black dot is the location of the typhoon’s center. location of the typhoon’s center.

J. Mar. Sci. Eng. 2020, 8, 177 13 of 23 J. Mar. Sci. Eng. 2020, 8, 177 13 of 21 J. Mar. Sci. Eng. 2020, 8, 177 13 of 23

Figure 8. A wave field (unit: cm) induced by the wind field from the model with a varying parameter Figure 8. A wave field (unit: cm) induced by the wind field from the model with a varying parameter bFigure but without 8. A wave an asymmetric field (unit: cm)structure induced (B3-A1-A1) by the wind at Eluanbi field from Station the peakmodel wave with time a varying during parameter Typhoon b but without an asymmetric structure (B3-A1-A1) at Eluanbi Station peak wave time during Typhoon Merantib but without (142016), an asymmetric where the bigger structure black (B3-A1-A1) dot is the at location Eluanbi of Station the typhoon’s peak wave center. time during Typhoon Meranti (142016), where the bigger black dot is the location of the typhoon’s center. Meranti (142016), where the bigger black dot is the location of the typhoon’s center.

Figure 9. A wave field (unit: cm) induced by the wind field from MH10 (B3-A1-A2) at Eluanbi Station Figure 9. A wave field (unit: cm) induced by the wind field from MH10 (B3-A1-A2) at Eluanbi Station peak wave time during Typhoon Meranti (142016), where the bigger black dot is the location of the peakFigure wave 9. A timewave during field (unit: Typhoon cm) induced Meranti by (142016), the wind wh fieldere fromthe bigger MH10 black (B3-A1-A2) dot is the at Eluanbi location Station of the typhoon’s center. typhoon’speak wave center. time during Typhoon Meranti (142016), where the bigger black dot is the location of the 5.3. Asymmetrictyphoon’s center. Structure of Typhoon 5.3. Asymmetric Structure of Typhoon 5.3.In Asymmetric Table3, the Structure mean of error Typhoon percentage of B3-A1-A1 when the asymmetric typhoon structure is excludedIn Table is 16%,3, the andmean the error error percentage of B3-A1-A2 of B3-A when1-A1 the when asymmetric the asymmetric structure typhoon is included structure is 10%. is In Table 3, the mean error percentage of B3-A1-A1 when the asymmetric typhoon structure is Theexcluded model verificationis 16%, and hasthe shownerror of that B3-A1-A2 the introduction when the ofasymmetric the empirical structure asymmetric is included structure is 10%. is helpful The modelexcluded verification is 16%, and has the shown error that of B3-A1-A2 the introduction when the of theasymmetric empirical structure asymmetric is included structure is is10%. helpful The to enable the model to capture wave extremes. Similar conclusions can be visually drawn from the tomodel enable verification the model has to showncapture that wave the extremes. introduction Similar of the conclusions empirical canasymmetric be visually structure drawn isfrom helpful the figures in AppendixA. figuresto enable in theAppendix model A.to capture wave extremes. Similar conclusions can be visually drawn from the Another example is typhoon 172011 (Nesat). During this typhoon, three buoys QF301–QF303 figuresAnother in Appendix example A. is typhoon 172011 (Nesat). During this typhoon, three buoys QF301‒QF303 worked well; their track is depicted in Figure 10, where the wind structure at the peak wave time is workedAnother well; theirexample track is is typhoon depicted 172011 in Figure (Nesat). 10, wh Duringere the this wind typhoon, structure three at the buoys peak QF301 wave‒ timeQF303 is plotted. With this asymmetric wind field, higher wind speed is formulated in the right half of the plotted.worked well;With theirthis asymmetrictrack is depicted wind in field, Figure higher 10, wh windere speedthe wind is formulated structure at in the the peak right wave half time of the is typhoon track than in the left half, leading to an appropriate simulation of all three buoys in Figure 11 typhoonplotted. Withtrack thisthan asymmetric in the left half, wind leading field, higherto an appropriate wind speed simulation is formulated of all in three the rightbuoys half in Figureof the (QF301 and QF303) and Figure A3 (QF302). Though it is hypothetically triggered by the typhoon 11typhoon (QF301 track and thanQF303) in theand left Figure half, A3 leading (QF302). to an Though appropriate it is hypothetically simulation of triggered all three buoysby the intyphoon Figure motion11 (QF301 only, and the QF303) asymmetric and Figure structure A3 is(QF302). indeed Though helpful toit is improve hypothetically the accuracy triggered of reconstructing by the typhoon the wind field.

J.J. Mar. Mar. Sci. Sci. Eng. Eng. 2020 2020, 8, 8, 177, 177 1414 of of 23 23

J. Mar.motionmotion Sci. Eng.only, only,2020 the the, 8 ,asymmetric 177asymmetric structure structure is is indeed indeed he helpfullpful to to improve improve the the accuracy accuracy of of reconstructing reconstructing14 of 21 thethe wind wind field. field.

FigureFigureFigure 10. 10. 10.Wind Wind Wind fields fields fields (unit: (unit: (unit: m m/s) m/s)/s) restructured restructured restructured byby by MH10MH10 MH10 (asymmetric(asymmetric (asymmetric structurestructure structure asas as solidsolid solid line,line, line, B3-A1-A2)B3-A1- B3-A1- andA2)A2) the and and model the the model model with awith with varying a a varying varying parameter parameter parameter b but b withoutb but but without without an asymmetric an an asymmetric asymmetric structure structure structure (B3-A1-A1) (B3-A1-A1) (B3-A1-A1) at QF301 at at StationQF301QF301 peak Station Station wave peak peak time wave wave during time time during Typhoon during Typhoon Typhoon Nesat (172011).Nesat Nesat (172011). (172011).

BuoyBuoy Hs Hs BuoyBuoy Hs Hs B3-A1-A2B3-A1-A2 B3-A1-A2B3-A1-A2 B3-A1-A1B3-A1-A1 B3-A1-A1B3-A1-A1 B2-A1-A1B2-A1-A1 B2-A1-A1B2-A1-A1 Hs (m) Hs Hs (m) Hs Hs (m) Hs Hs (m) Hs 2468 2468 2468 2468

00 20 20 40 40 60 60 80 80 100 100 020406080100020406080100

TimeTime Series Series(hour(hour) ) TimeTime Series(hour) Series(hour)

FigureFigureFigure 11. 11. 11.Simulation Simulation Simulation ofof of wavewave wave height height at at buoys buoys QF301 QF301QF301 (l (left)(left)eft) and and QF303 QF303 QF303 (right) (right) (right) during during during typhoon typhoon typhoon Nesat Nesat Nesat (172011):(172011):(172011): the the the standard standard standard H10H10 H10 isis is indexedindexed indexed as as as B2-A1-A1, B2-A1-A1,B2-A1-A1, the the model model with with with varying varying varying parameter parameter parameter b b without bwithout without an an an asymmetricasymmetricasymmetric typhoon typhoon typhoon structure structure structure isis is indexedindexed indexed as as B3-A1-A1, B3-A1-A1, and and MH10 MH10 is is is indexed indexed indexed as as as B3-A1-A2. B3-A1-A2. B3-A1-A2.

5.4.5.4.5.4. Limitations Limitations Limitations of of of the the the ModelModel Model CombinationCombination Combination

5.4.1.5.4.1.5.4.1. Variability Variability Variability of of of Gust Gust Gust FactorFactor Factor AsAsAs a statisticala a statistical statistical model model model for for for gust gust gust factor, factor, factor, Equation Equation Equation (13) (13) (13) can can becan furtherbe be further further optimized optimized optimized based based based on more on on more more studies ofstudies thestudies typhoon ofof the thewave typhoontyphoon simulations. wavewave simulations.simulations. If the samples IfIf thethe utilized samplessamples for utilized utilized fitting Equation forfor fittingfitting (13) Equation Equation can be (13) increased,(13) cancan bebe the empiricalincreased,increased, formula the the empirical empirical may be formula formula givenwith may may morebe be given given confidence. with with more more confidence. confidence.

5.4.2.5.4.2.5.4.2. E Effectiveff Effectiveective Radius Radius Radius

ThoughThoughThough the the the new new new formulated formulated formulated scalingscaling scaling parameter parameter b bbs ssenhances enhances its its its reconstructing reconstructing reconstructing ability ability ability both both both in in time intime time seriesseriesseries and and and geographical geographical geographical covering, covering, covering, MH10 MH10 MH10 fails fails fails to to correctlyto co correctlyrrectly restructure restructure restructure the the the wind wind wind field field field in oceansinin oceans oceans far far awayfar fromawayaway the from from typhoon the the typhoon typhoon centers. centers. centers. The standard The The standard standard H10 hasH10 H10 a has similarlyhas a a similarly similarly limited limited limited performance. performance. performance. For For For instance, instance, instance, with buoy QF301 during the Nock-ten (082011), buoy QF303 during the Usagi (192013), and buoy Pratas during the Sarika (212016), the model results show large bias compared to the buoy data. In fact, it is difficult for a typhoon to induce destructive ocean waves further from its track path than about 400 km. J. Mar. Sci. Eng. 2020, 8, 177 15 of 21

In general, the parametric MH10 vortex wind model is more efficient in oceans within 3.5–4.0◦ of the typhoon’s center.

6. Conclusions A combination of a modified Holland vortex model (MH10) and the WW3 wave model is suggested in this paper and expected to lead to more accurate predictions of typhoon waves. Validation against buoy data and altimeter data proved that the combination of the two models works well. With these improvements, the MH10 typhoon vortex model shows a robust ability to reconstruct a typhoon wind field. Practical testing cases indicate that the new formula of scaling parameter bs tends to reproduce a more realistic wind field in both temporal and spatial contexts. Furthermore, the asymmetric typhoon structure proves to be helpful to capture extreme wave parameters. The gust factor fitted in this paper bridges the gap between the Holland vortex model and the WW3 model. With the gust factor, the WW3 model performs much more realistically in the typhoon wave simulation, avoiding unrealistic wave growth. The introduction of an effective empirical formula to estimate RMW universalizes the utilization of MH10. However, the combination of the models should be limited to estimating the sea state in those oceans located within a radius of 3.5–4.0 geographical degrees from the typhoon centers. For oceans too far away from the typhoon center, vortex wind models, including both H10 and MH10, are not able to accurately estimate wind speeds.

Author Contributions: Data curation, formal analysis, investigation, software, validation, and writing were contributed by L.W. Formal analysis, investigation, and writing were contributed by Z.Z. Formal analysis, funding acquisition, methodology, supervision, and review and editing were contributed by B.L. Formal analysis, investigation, and writing were contributed by D.L. Investigation and English editing were contributed by S.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Science Fund (grant numbers 51739010 and 51679223) and 111 Project (grant number B14028). Acknowledgments: The authors would like to acknowledge the support of the National Science Fund of China (grant numbers 51739010 and 51679223), Shandong Provincial Natural Science Key Basic Program (grant number ZR2017ZA0202), and a grant from the 7th Generation Ultra-Deep-water Drilling Rig Innovation Project. Conflicts of Interest: The authors declare no conflict of interest. J. Mar. Sci. Eng. 2020, 8, 177 16 of 23 Appendix A

Buoy Hs Buoy Tr B3-A1-A2 B3-A1-A2 B3-A1-A1 B3-A1-A1 B2-A1-A1 B2-A1-A1 Tr (s) Tr Hs (m) Hs 4681012 12345678

0 20406080100 0 20406080100

Time Series(hour) Time Series(hour)

Figure A1. Comparison of typhoon waves induced by Typhoon Chanthu (03-2010) at buoy QF303: the Figure A1. Comparison of typhoon waves induced by Typhoon Chanthu (03-2010) at buoy QF303: standard H10 is indexed as B2-A1-A1, the model with varying parameter b without an asymmetric the standard H10 is indexed as B2-A1-A1, the model with varying parameter b without an asymmetric typhoontyphoon structure structure is is indexed indexed asas B3-A1-A1,B3-A1-A1, and MH10 MH10 is is indexed indexed as as B3-A1-A2. B3-A1-A2.

Buoy Tr Buoy Hs B3-A1-A2 B3-A1-A2 B3-A1-A1 B3-A1-A1 B2-A1-A1 B2-A1-A1 Tr (s) Tr Hs (m) Hs 4681012 123456

0 20406080 020406080

Time Series(hour) Time Series(hour)

Figure A2. Comparison of typhoon waves induced by Typhoon Nock-ten (08-2011) at buoy QF302: the standard H10 is indexed as B2-A1-A1, the model with varying parameter b without an asymmetric typhoon structure is indexed as B3-A1-A1, and MH10 is indexed as B3-A1-A2.

J. Mar. Sci. Eng. 2020, 8, 177 16 of 23

Buoy Hs Buoy Tr B3-A1-A2 B3-A1-A2 B3-A1-A1 B3-A1-A1 B2-A1-A1 B2-A1-A1 Tr (s) Tr Hs (m) Hs 4681012 12345678

0 20406080100 0 20406080100

Time Series(hour) Time Series(hour)

Figure A1. Comparison of typhoon waves induced by Typhoon Chanthu (03-2010) at buoy QF303: the standard H10 is indexed as B2-A1-A1, the model with varying parameter b without an asymmetric J. Mar. Sci.typhoon Eng. 2020 structure, 8, 177 is indexed as B3-A1-A1, and MH10 is indexed as B3-A1-A2. 16 of 21

Buoy Tr Buoy Hs B3-A1-A2 B3-A1-A2 B3-A1-A1 B3-A1-A1 B2-A1-A1 B2-A1-A1 Tr (s) Tr Hs (m) Hs 4681012 123456

0 20406080 020406080

Time Series(hour) Time Series(hour) J. Mar. Sci. Eng. 2020, 8, 177 17 of 23 FigureFigure A2. A2.Comparison Comparison of of typhoon typhoon waves waves induced induced by by Typhoon Typhoon Nock-ten Nock-ten (08-2011) (08-2011) at at buoy buoy QF302: QF302: the J. Mar.standardthe Sci. standard Eng. H10 2020 is,H10 8, indexed 177 is indexed as B2-A1-A1, as B2-A1-A1, the the model model with with varying varying parameterparameter b b without without an an asymmetric asymmetric17 of 23 typhoontyphoon structure structure is is indexed indexed as as B3-A1-A1, B3-A1-A1, andand MH10MH10 is indexed as as B3-A1-A2. B3-A1-A2.

Buoy Hs Buoy Tr B3-A1-A2 B3-A1-A2 B3-A1-A1 B3-A1-A1 Buoy Tr Buoy Hs B2-A1-A1 B3-A1-A2B2-A1-A1 B3-A1-A2 B3-A1-A1 B3-A1-A1 B2-A1-A1 B2-A1-A1 Tr (s) Tr Hs (m) Hs Tr (s) Tr Hs (m) Hs 2468 468101214 2468

468101214 0 20406080100 0 20 40 60 80 100

0 20406080100Time Series(hour) 0 20Time 40 Series(hour) 60 80 100 Time Series(hour) Time Series(hour) Figure A3. Comparison of typhoon waves induced by Typhoon Nesat (17-2011) at buoy QF302: the Figurestandard A3. ComparisonH10 is indexed of as typhoon B2-A1-A1, waves the model induced with by varying Typhoon parameter Nesat (17-2011) b without at an buoy asymmetric QF302: the Figure A3. Comparison of typhoon waves induced by Typhoon Nesat (17-2011) at buoy QF302: the typhoon structure is indexed as B3-A1-A1, and MH10 is indexed as B3-A1-A2. standardstandard H10 H10 is is indexed indexed as as B2-A1-A1, B2-A1-A1, the model with with varying varying parameter parameter b without b without an asymmetric an asymmetric typhoontyphoon structure structure is is indexed indexed as as B3-A1-A1, B3-A1-A1, and MH10 MH10 is is indexed indexed as as B3-A1-A2. B3-A1-A2.

Buoy Hs B3-A1-A2 BuoyB3-A1-A1 Hs B3-A1-A2B2-A1-A1 B3-A1-A1 B2-A1-A1 Tr (s) Tr Hs (m) Hs Tr (s) Tr Hs (m) Hs 4681012 12345678 4681012 12345678 0 102030405060 0 102030405060

0 102030405060Time Series(hour) 0 102030405060Time Series(hour) Figure A4. ComparisonTime of Series(hour) typhoon waves induced by Typhoon Vicente (08-2012)Time Series(hour) at buoy QF301: the Figure A4. Comparison of typhoon waves induced by Typhoon Vicente (08-2012) at buoy QF301: the standardstandard H10 H10 is is indexed indexed as as B2-A1-A1, B2-A1-A1, thethe model with with varying varying parameter parameter b without b without an anasymmetric asymmetric Figure A4. Comparison of typhoon waves induced by Typhoon Vicente (08-2012) at buoy QF301: the typhoontyphoon structure structure is is indexed indexed as as B3-A1-A1, B3-A1-A1, andand MH10 is is indexed indexed as as B3-A1-A2. B3-A1-A2. standard H10 is indexed as B2-A1-A1, the model with varying parameter b without an asymmetric typhoon structure is indexed as B3-A1-A1, and MH10 is indexed as B3-A1-A2.

J. Mar. Sci. Eng. 2020, 8, 177 18 of 23

J. Mar.J. Mar. Sci. Sci. Eng. Eng.2020 2020, 8,, 8 177, 177 18 of 1723 of 21

Buoy Hs Buoy Tr B3-A1-A2 B3-A1-A2 BuoyB3-A1-A1 Hs BuoyB3-A1-A1 Tr B3-A1-A2B2-A1-A1 B3-A1-A2B2-A1-A1 B3-A1-A1 B3-A1-A1 B2-A1-A1 B2-A1-A1 Tr (s) Tr Hs (m) Hs Tr (s) Tr Hs (m) Hs 51015 51015 468101214

0 50 100 150 468101214 0 50 100 150

0 50Time Series(hour 100) 150 0 50Time Series(hour) 100 150

Time Series(hour) Time Series(hour) Figure A5. Comparison of typhoon waves induced by Typhoon Soudelor (13-2015) at buoy FigureFigureGuishandao: A5. A5.Comparison Comparison the standard of typhoon ofH10 typhoon is indexed waves waves induced as B2-A induced1-A1, by Typhoon theby modelTyphoon Soudelor with Soudelor varying (13-2015) parameter (13-2015) at buoy b Guishandao:at without buoy theGuishandao:an standard asymmetric H10 the typhoon is standard indexed structure H10 as B2-A1-A1, is indexed is indexed theas B2-Aas model B3-A1-A1,1-A1, with the varyingand model MH10 with parameter is varying indexed b parameter withoutas B3-A1-A2. an b without asymmetric typhoonan asymmetric structure typhoon is indexed structure as B3-A1-A1, is indexed and as B3-A1-A1, MH10 is indexed and MH10 as is B3-A1-A2. indexed as B3-A1-A2.

Buoy Hs Buoy Tr B3-A1-A2 B3-A1-A2 B3-A1-A1 Buoy Hs BuoyB3-A1-A1 Tr B2-A1-A1 B3-A1-A2 B3-A1-A2B2-A1-A1 B3-A1-A1 B3-A1-A1 B2-A1-A1 B2-A1-A1 Tr (s) Tr Hs (m) Hs Tr (s) Tr Hs (m) Hs 51015 51015 4 6 8 101214

0 20 40 60 80 100 4 6 8 101214 0 20 40 60 80 100

0 20Time 40 Series(hour) 60 80 100 0 20Time 40 Series(hour) 60 80 100 Time Series(hour) Time Series(hour) FigureFigure A6. A6.Comparison Comparison of of typhoon typhoon waveswaves induced by by Typhoon Typhoon Nepartak Nepartak (01-2016) (01-2016) at buoy at buoy Taitung Taitung J. Mar.Open Sci. Ocean: Eng. 2020 the, 8, standard177 H10 is indexed as B2-A1-A1, the model with varying parameter b without19 of 23 FigureOpen Ocean: A6. Comparison the standard of typhoonH10 is indexed waves asinduced B2-A1-A1, by Typhoon the model Nepartak with varying (01-2016) parameter at buoy b Taitungwithout an asymmetric typhoon structure is indexed as B3-A1-A1, and MH10 is indexed as B3-A1-A2. Openan asymmetric Ocean: the typhoon standard structure H10 is indexed is indexed as B2-Aas B3-A1-A1,1-A1, the and model MH10 with is varying indexed parameter as B3-A1-A2. b without an asymmetric typhoon structure is indexed as B3-A1-A1, and MH10 is indexed as B3-A1-A2.

Buoy Hs Buoy Tr B3-A1-A2 B3-A1-A2 B3-A1-A1 B3-A1-A1 B2-A1-A1 B2-A1-A1 Tr (s) Tr Hs (m) Hs 51015 4 6 8 101214

0 20406080100 0 20 40 60 80 100 Time Series(hour) Time Series(hour)

Figure A7. Comparison of typhoon waves induced by Typhoon Meranti (14-2016) at buoy Eluanbi: the Figure A7. Comparison of typhoon waves induced by Typhoon Meranti (14-2016) at buoy Eluanbi: standardthe standard H10is H10 indexed is indexed as B2-A1-A1, as B2-A1-A1, the the model model with with varyingvarying parameter parameter b bwithout without an asymmetric an asymmetric typhoontyphoon structure structure is is indexed indexed as as B3-A1-A1, B3-A1-A1, andand MH10 is is indexed indexed as as B3-A1-A2. B3-A1-A2.

Buoy Hs Buoy Tr B3-A1-A2 B3-A1-A2 B3-A1-A1 B3-A1-A1 B2-A1-A1 B2-A1-A1 Tr (s) Tr Hs (m) Hs 5101520 4 6 8 101214

0 20 40 60 80 100 0 20406080100

Time Series(hour) Time Series(hour)

Figure A8. Comparison of typhoon waves induced by Typhoon Meranti (14-2016) at buoy Taitung Open Ocean: the standard H10 is indexed as B2-A1-A1, the model with varying parameter b without an asymmetric typhoon structure is indexed as B3-A1-A1, and MH10 is indexed as B3-A1-A2.

J. Mar. Sci. Eng. 2020, 8, 177 19 of 23

Buoy Hs Buoy Tr B3-A1-A2 B3-A1-A2 B3-A1-A1 B3-A1-A1 B2-A1-A1 B2-A1-A1 Tr (s) Tr Hs (m) Hs 51015 4 6 8 101214

0 20406080100 0 20 40 60 80 100 Time Series(hour) Time Series(hour)

Figure A7. Comparison of typhoon waves induced by Typhoon Meranti (14-2016) at buoy Eluanbi: the standard H10 is indexed as B2-A1-A1, the model with varying parameter b without an asymmetric J. Mar. Sci.typhoon Eng. 2020 structure, 8, 177 is indexed as B3-A1-A1, and MH10 is indexed as B3-A1-A2. 18 of 21

Buoy Hs Buoy Tr B3-A1-A2 B3-A1-A2 B3-A1-A1 B3-A1-A1 B2-A1-A1 B2-A1-A1 Tr (s) Tr Hs (m) Hs 5101520 4 6 8 101214

0 20 40 60 80 100 0 20406080100

Time Series(hour) Time Series(hour) J. Mar. Sci. Eng. 2020, 8, 177 20 of 23 FigureFigure A8. A8.Comparison Comparison of oftyphoon typhoon waves induced induced by by Typhoon Typhoon Meranti Meranti (14-2016) (14-2016) at buoy at buoy Taitung Taitung J. Mar.OpenOpen Sci. Ocean: Eng. Ocean: 2020 the, the8, standard177 standard H10 H10 isis indexedindexed as B2-A B2-A1-A1,1-A1, the the model model with with varying varying parameter parameter b without b without20 of 23 an asymmetrican asymmetric typhoon typhoon structure structure is is indexedindexed as B3-A1-A1, and and MH10 MH10 is isindexed indexed as asB3-A1-A2. B3-A1-A2.

Buoy Hs Buoy Tr B3-A1-A2 B3-A1-A2 BuoyB3-A1-A1 Hs B3-A1-A1 B2-A1-A1 Buoy Tr B3-A1-A2 B3-A1-A2B2-A1-A1 B3-A1-A1 B3-A1-A1 B2-A1-A1 B2-A1-A1 Tr (s) Tr Hs (m) Hs Tr (s) Tr Hs (m) Hs 5101520 5101520 468101214

0 20406080100 468101214 0 20406080100

Time Series(hour) 0 20406080100 0 20406080100Time Series(hour)

Time Series(hour) Time Series(hour) Figure A9. Comparison of typhoon waves induced by Typhoon Meranti (14-2016) at buoy Taitung: Figurethe standard A9. Comparison H10 is indexed of typhoon as B2-A1-A1, waves the induced model bywith Typhoon varying Merantiparameter (14-2016) b without at an buoy asymmetric Taitung: the Figure A9. Comparison of typhoon waves induced by Typhoon Meranti (14-2016) at buoy Taitung: standardtyphoon H10 structure is indexed is indexed as B2-A1-A1, as B3-A1-A1, the modeland MH10 with is varyingindexed as parameter B3-A1-A2. b without an asymmetric the standard H10 is indexed as B2-A1-A1, the model with varying parameter b without an asymmetric typhoontyphoon structure structure is is indexed indexed as as B3-A1-A1, B3-A1-A1, and MH10 MH10 is is indexed indexed as as B3-A1-A2. B3-A1-A2.

Buoy Hs Buoy Tr B3-A1-A2 B3-A1-A2 BuoyB3-A1-A1 Hs BuoyB3-A1-A1 Tr B3-A1-A2B2-A1-A1 B3-A1-A2B2-A1-A1 B3-A1-A1 B3-A1-A1 B2-A1-A1 B2-A1-A1 Tr (s) Tr Hs (m) Hs Tr (s) Tr Hs (m) Hs 24681012 4 6 8 101214 24681012

0 20406080100 4 6 8 101214 0 20 40 60 80 100

0 20406080100Time Series(hour) 0 20Time 40 Series(hour) 60 80 100 Figure A10. ComparisonTime ofSeries(hour) typhoon waves induced by Typhoon Meranti (14-2016)Time Series(hour) at buoy Pratas: the Figure A10. Comparison of typhoon waves induced by Typhoon Meranti (14-2016) at buoy Pratas: standardthe standard H10 is H10 indexed is indexed as B2-A1-A1, as B2-A1-A1, the the model model with with varyingvarying parameter parameter b bwithout without an anasymmetric asymmetric Figure A10. Comparison of typhoon waves induced by Typhoon Meranti (14-2016) at buoy Pratas: typhoontyphoon structure structure is is indexed indexed as as B3-A1-A1, B3-A1-A1, andand MH10 is is indexed indexed as as B3-A1-A2. B3-A1-A2. the standard H10 is indexed as B2-A1-A1, the model with varying parameter b without an asymmetric typhoon structure is indexed as B3-A1-A1, and MH10 is indexed as B3-A1-A2. Appendix B. Appendix B. Table A1. Paired peak-value of buoy extremes and simulated extremes in every case.

Table A1. Paired peak-value of buoyMeasured extremes and simulated extremesSimulated in Extremes every case. Case ID of Index of Typhoon Extremes B2-A1-A1 B3-A1-A1 B3-A1-A2 No. Buoy Measured Simulated Extremes Case ID of Hs (m) Tr (s) Hs (m) Tr (s) Hs (m) Tr (s) Hs (m) Tr (s) Index of Typhoon Extremes B2-A1-A1 B3-A1-A1 B3-A1-A2 032010 Chanthu 1No. QF303Buoy 6.50 9.00 5.93 8.54 6.67 8.86 6.42 8.79 2 QF301 Hs2.90 (m) Tr7.70 (s) Hs1.98 (m) Tr6.26 (s) Hs1.99 (m) Tr6.31 (s) Hs2.97 (m) Tr7.30 (s) 032010082011 ChanthuNock-ten 13 QF303QF302 6.504.00 9.008.20 5.933.45 8.547.67 6.673.38 8.867.84 6.423.98 8.798.34 24 QF301QF303 2.905.60 10.107.70 1.984.24 6.268.02 1.994.37 6.318.05 2.974.94 7.308.35 082011 Nock-ten 35 QF302QF301 4.005.60 11.408.20 3.455.25 7.679.46 3.384.71 7.849.56 3.985.56 8.349.83 172011 Nesat 46 QF303QF302 5.60 8.00 10.1010.70 4.247.57 10.678.02 4.377.14 10.428.05 4.947.85 10.848.35 57 QF301QF303 5.60 8.70 11.4010.70 5.258.61 10.979.46 4.718.22 10.849.56 5.569.01 11.109.83 172011082012 VicenteNesat 68 QF302QF301 8.007.50 10.709.40 7.575.66 10.678.82 7.146.17 10.428.97 7.856.72 10.849.16 7 QF303 8.70 10.70 8.61 10.97 8.22 10.84 9.01 11.10

082012 Vicente 8 QF301 7.50 9.40 5.66 8.82 6.17 8.97 6.72 9.16

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Appendix B

Table A1. Paired peak-value of buoy extremes and simulated extremes in every case.

Measured Simulated Extremes Extremes Index of Typhoon Case ID of Buoy B2-A1-A1 B3-A1-A1 B3-A1-A2 No. Hs Hs Hs Hs Tr (s) Tr (s) Tr (s) Tr (s) (m) (m) (m) (m) 032010 Chanthu 1 QF303 6.50 9.00 5.93 8.54 6.67 8.86 6.42 8.79 2 QF301 2.90 7.70 1.98 6.26 1.99 6.31 2.97 7.30 082011 Nock-ten 3 QF302 4.00 8.20 3.45 7.67 3.38 7.84 3.98 8.34 4 QF303 5.60 10.10 4.24 8.02 4.37 8.05 4.94 8.35 5 QF301 5.60 11.40 5.25 9.46 4.71 9.56 5.56 9.83 172011 Nesat 6 QF302 8.00 10.70 7.57 10.67 7.14 10.42 7.85 10.84 7 QF303 8.70 10.70 8.61 10.97 8.22 10.84 9.01 11.10 8 QF301 7.50 9.40 5.66 8.82 6.17 8.97 6.72 9.16 082012 Vicente 9 QF302 8.10 8.90 6.06 8.2 6.35 8.28 6.47 8.66 10 QF301 6.20 8.60 7.68 8.1 6.62 7.67 6.10 7.51 11 QF303 1.90 12.50 3.32 9.32 2.41 10.13 2.49 11.08 192013 Usagi 12 Pratas 13.40 11.67 12.09 11.18 11.75 11.05 12.13 11.37 13 Eluanbi 14.10 11.62 11.33 11.10 11.27 11.80 11.22 132015 Soudelor 14 Guishandao 12.60 10.80 12.52 12.26 12.34 12.10 13.28 12.44 012016 Nepartak 15 Taitung Open Oce. 14.20 9.60 16.12 12.98 14.59 12.19 15.43 12.21 16 Eluanbi 17.80 11.00 17.81 12.83 16.85 12.50 17.66 12.74 17 Taitung Open Oce. 13.10 11.80 15.35 13.32 11.01 12.32 11.72 12.82 142016 Meranti 18 Taitung 12.80 10.60 12.93 11.74 11.27 11.34 12.02 11.56 19 Pratas 6.60 8.70 10.04 13.12 6.90 12.28 7.20 12.70 172016 Megi 20 Guishandao 12.29 11.30 11.54 12.03 11.09 11.84 11.90 12.10 192016 Aere 21 Pratas 6.00 7.70 3.28 6.22 3.04 6.14 4.16 7.06 212016 Sarika 22 Pratas 4.70 7.40 3.06 7.82 2.80 7.79 3.60 8.10 222016 Haima 23 Pratas 10.60 10.10 7.08 10.47 7.79 10.85 8.80 11.24

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