2 Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao 266071, China;
3 University of Chinese Academy of Sciences, Beijing 100049, China;
4 Laboratory for Ocean and Climate Dynamics, Qingdao National Laboratory for Marine Science and Technology, Qingdao 266237, China;
5 Numerical Simulation Division, North China Sea Marine Forecasting Center of Ministry of Natural Resources, Qingdao 266000, China
The Yellow Sea (YS) and East China Sea (ECS) are located in the western Pacific Ocean. Due to its location, China has become one of the countries experiencing the largest number of tropical cyclones (typhoons) and their effects in the world. Strong atmospheric disturbances, such as typhoon, temperate cyclone, and strong cold wind, often lift ships at sea, destroy marine and coastal constructions, cause huge disasters, and pose threats to the safety of life and property of people living along the coast. Typhoon waves are one of the major marine disasters that affect China. Therefore, it is of great practical and theoretical significance to study typhoon waves and further improve the technology and accuracy of typhoon wave prediction.
Numerical simulation has become an indispensable tool for studying waves. A simulating waves nearshore model (SWAN) is a third-generation wave model, developed at Delft University of Technology, that computes random, short-crested wind-generated waves in coastal regions and inland waters. Booij et al. (1999) compared the calculated results of the SWAN model with measurements; they found that SWAN simulated accurately the wave field under terrain and wind field environments and was applicable to the simulation and prediction of wind, swell and mixed waves. Ris et al. (1999) simulated the wave field of Haringvliet, Norderneyer Seegat, and Friesche Zeegat, and the results show that SWAN calculation results were stable and reliable. Padilla-Hernández and Monbaliu (2001) simulated the wave field of Lake George (Australia); the results show that the SWAN model could simulate offshore wave fields quite well under moderate wind speed conditions.
Many efforts have been devoted to the numerical study of typhoon waves. He et al. (2015) simulated waves during Typhoon Damrey off the Jiangsu coast in 2012 using the SWAN model, driven by the Jelesnianski typhoon model and NCEP winds, and the simulation results are highly correlated with observational data, showing that the distribution and variation of wind-wave elements in offshore platforms are more complicated than in the sea. He et al. (He and Xu, 2016; He et al., 2018a) implemented a third-generation wave model (WaveWatch-Ⅲ) and performed long-term wind-wave hindcast in the Yellow Sea and the Bohai Sea from 1988 to 2002, and then analyzed the regional wave climate. Comparisons between model results and satellite data are generally consistent on monthly mean significant wave height. Qi et al. (2015) used a wave mode (MIKE-SW) driven by a wind field simulated by the Jelesnianski atmospheric model to simulate the wave growth process during Damrey in 2012 off Lianyungang; the results show that the typhoon parameter and wave models are validated. Tan et al. (2012) simulated the wind of Typhoon Wipha using a mesoscale atmospheric model (WRF) to force the SWAN model for wave simulation. The results show that using the WRF and SWAN models simulate typhoon wind and waves quite well. He et al. (2018b) examined the effects of surface waves and sea spray on air-sea fluxes during the passage of Typhoon Hagupit. Xu et al. (2017) used Buoy-based observations of surface waves during three typhoons in the South China Sea to obtain the wave characteristics. The results show that with the local wind speeds stayed below 35 m/s, and the surface waves over an area with a radius 5 times that of the area where the maximum sustained wind was found, were mainly dominated by wind-wave components. In addition, swells dominated the surface waves at the front of and outside the central typhoon region.
This study aimed to simulate typhoon waves more accurately and provide a better understanding of typhoon wave characteristics. It is well known that there are variable parameters in typhoon wind parametric models, as well as different choices of source schemes in the SWAN model, which may have significant influences on the simulation of typhoon waves. Thus, they need to be carefully tested. Furthermore, the characteristics of typhoon waves are still not fully understood.2 METHOD
In this study, wind forcing is constructed by combining NCEP-reanalyzed wind data with the Holland typhoon wind model. Three typhoons, Damrey (1210), Fung-wong (1416), and Chan-hom (1509), that entered the Yellow Sea and East China Sea are used (Fig. 1).2.1 Wind model
The wind field is constructed by combining NCEP-reanalyzed wind data with the Holland wind parametric model (Holland, 1980). This model is expressed as:
where P∞ and P0 are external and central pressure, respectively; r is the distance to the typhoon center; f is a Coriolis force parameter; ρa is air density; B is the Holland fitting parameter; and R is the maximum wind radius of typhoon. Moreover, θ is the position angle of the calculated point relative to the center of the typhoon; and umove and vmove are the components of the velocity of the center of the typhoon.
Some studies suggest that the Holland fitting parameter (B) and the maximum wind radius (R) are possibly related to the central pressure (P0) or the pressure difference (Δp), latitude (lat) and the moving speed of the typhoon (V). Several different formulations of B and R have been proposed (Table 1).
The typhoon wind field was derived from a weighted sum of the NCEP-reanalyzed wind field and Holland wind:
SWAN is a third-generation wave model that computes random, short-crested wind-generated waves in coastal regions and inland waters. However, SWAN can be used on any scales relevant to wind-generated surface gravity waves. The model is based on the wave action balance equation with sources and sinks. All information about the sea surface is contained in the wave variance spectrum or energy density E(σ, θ). Usually, wave models determine the evolution of the action density N(σ, θ). The action density is defined as:
where σ represents wave energy over (radian) frequencies and θ represent propagation directions. The evolution of the action density N is governed by the action balance equation (Mei, 1983; Komen et al., 1994; Booij et al., 1999):
where Cσ and Cθ are the propagation velocities in spectral space(σ, θ). The second and third terms denote the propagation of wave energy in two-dimensional geographical x-y space. The fourth term represents the effect of shifting radian frequency due to variations in depth and mean currents. The fifth term represents the depth and current-induced refraction. The symbol S is the nonconservative source/sink term, representing all physical processes that generate, dissipate, or redistribute wave energy.
The dissipation of wave energy is represented by the sum of three different contributions: whitecapping Sds, w, bottom friction Sds, b and depth-induced breaking Sds, br. Whitecapping is primarily controlled by the steepness of the waves:
where Г is a steepness-dependent coefficient, κ is the wave number, and
where Cd is the bottom friction coefficient. Considering the large variation in bottom conditions, such as the material, roughness, length and ripple height, in coastal areas, there is no field data that provide evidence for a particular friction model. For this reason, the simplest of each of these types of friction models was implemented in SWAN: the empirical JONSWAP model of Hasselmann, the drag law model of Collins and the eddy-viscosity model of Madsen (SWAN Team, 2018).
The three calculation methods (JONSWAP, Collins, and Madsen) were adopted for the dissipation of bottom friction. The JONSWAP model is the default option for SWAN and the default parameters for JONSWAP, Collins, and Madsen were 0.038, 0.015, and 0.050, respectively.
Moreover, in this study, the SWAN mode adopted a rectangular grid with a mesh resolution of 0.083°×0.083° and a time step of 30 min for calculation.2.3 Wind-produced wave calculation
Different expressions have been proposed for the full growth of wind-sea interactions. This study was based on the WAM model (Deng et al., 2007):
The swell index was defined as:
where Hf denotes the significant wave height under the full growth state and Hm is the wave height calculated from the model output. If SWI > 1, swell waves are dominant, otherwise wind-induced waves are dominant.2.4 Error metrics
Taylor diagrams were used to evaluate the model output based on the correlation coefficient (CC), standard deviation (STD), and root-mean-square deviation (RMSD). In addition, the scatter index (SI), relative bias (RB), maximum error (MAXE), mean error (MAE) and normalized standard deviation (NSTD) are as follows:
where Xcal and Xobs are the mean values of the data sets Xcal and Xobs, respectively, in a sample of size n, and σXcal and σXobs are the corresponding standard deviations. In this study, Xobs denotes the observed wind speed and significant wave height and Xcal is the corresponding value from model input or output.3 SIMULATION ANALYSIS 3.1 Wind simulation sensitivity analysis
Table 2 lists the different combinations of Holland B and R values, which were used to simulate the typhoon wind fields in the Holland model.
The comparison of various wind fields from the Holland model and the measured data are shown in Figs. 2–4. The wind speeds determined from each combination of Holland B and R values scatter around the line of perfect agreement, whereas the combination of e winds yielded superior statistical scores for RB, SI, CC, and RMSD for all buoy stations.3.2 Wind data verification
The wind fields of the three typhoons were constructed by combining NCEP-reanalyzed wind data with the Holland typhoon wind field model with B and R values taken from the Powell and Jiang formulas, respectively.3.3 Wave simulation sensitivity analysis 3.3.1 Wind input and whitecapping
Under deep-water conditions, the impact of the seabed is negligible. Wind input and whitecapping play a key role. Buoy D, located in deep water, was the appropriate station from which the wind input and whitecapping source schemes (Janssen, Komen, and Westhuysen) could be tested.
Figure 10 and Table 3 show that the simulation produced by the Janssen scheme underestimated the peak significant wave height. The results from Komen and Westhuysen are close with the simulation results of Komen slightly better in comparison with the measured data.3.3.2 Bottom friction
Under shallow water conditions, the influence of bottom friction cannot be neglected. Using wave measurements (buoys B and C) in shallow waters, the three schemes for the dissipation of bottom friction (JONSWAP, Collins, and Madsen) were evaluated. The wind input and whitecapping used the Komen scheme, as that was shown to produce the best results.
Figure 11 and Table 4 show that the variations in wave height simulated by the three bottom friction schemes were qualitatively consistent. The wave heights from the Madsen method were obviously smaller than the other two methods during the high wave period. For waves with significant heights > 3 m, the simulation effects of JONSWAP and Collins were better than the Madsen method. The simulation results of JONSWAP were in better agreement overall with measured data than with the results from the Collins scheme.4 DISCUSSION
We compared wind speed and significant wave height (Fig. 12a), and found that the wind speed is relatively faster on the right front quadrant than on the left rear quadrant. The distribution of significant wave height was similar to wind speed; the significant wave height was larger (smaller) in correspondence with faster (slower) wind speed. We also noted that the contours of significant wave height were nearly parallel to depth rather than wind speed in shallow water. These features highlight the importance of bottom-induced wave dissipation on wave energy.
Figure 12b shows that there were clear misalignments in a direction between winds and waves; the wave direction tended to be parallel to the direction of the typhoon, resulting from the contribution of the swell. In shallow water conditions, the waves moved nearly perpendicular to the depth contours because of depth-induced refraction.
The maximum R values, calculated by the Jiang formula, were 57.44 km, 83.85 km, and 96.48 km (Fig. 12c). With the distance of R to the eye of the typhoon, the swell was the dominant wave pattern. The wind-sea appears to dominate in the outer region that extends about six to eight times the value of R beyond which swell waves dominate (Fig. 12c). The wind-sea interaction area appears to be more significant and widely distributed, which has been confirmed previously by Shao et al. (2017) using satellite observations. As previously shown, directional misalignment between winds and waves prevailed, even in the wind-sea dominant region. This can be attributed to nonlinear wave-wave interactions (Young, 2006); strong nonlinear wave-wave interactions can be significant during typhoons with energy exchange between the waves in high and low frequencies. Thus, the waves exhibited wind-sea interaction features.5 CONCLUSION
In this study, wind fields are constructed by combining NCEP-reanalyzed wind data with a Holland typhoon wind model. The variable parameters (B and R) in the Holland model are verified by comparing the simulated wind data with in-situ measurements. The wind fields were used to force a third-generation wave model (SWAN) to simulate the effects from the typhoons Damrey, Fung-wong, and Chan-hom in the Yellow Sea and East China Sea. The simulation results are validated by comparison with measured data from three buoys. The validity of the source schemes for wind input and whitecap dissipation are tested by comparing wave simulation results with data from a deep water buoy, and the source schemes for bottom friction are tested by comparing wave simulations with buoy data from shallow water. Overall, the simulations reproduced the significant wave heights during the typhoons. A preliminary analysis of the wave characteristics in terms of wind-sea interactions and swell waves was carried out and the results indicate that the swell dominates within the values of R, while wind-sea interactions prevail in the outer region. There was a clear misalignment between winds and waves, but the results confirm the importance of nonlinear wave-wave interactions in the formation of wave characteristics.
These results improve both the accurate simulation of typhoon waves and our understanding of typhoon wave characteristics and dynamics. Further study should include more in-situ measurements to improve the model skills, including the proper choice of source schemes and optimization of model parameters, as well as detailed analysis of the wave dynamics, especially with respect to nonlinear wave-wave interactions.6 DATA AVAILABILITY STATEMENT
The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.7 ACKNOWLEDGMENT
The data set is provided by marine scientific data center, IOCAS, China. The numerical work is supported by the High-Performance Computing Center, IOCAS, China.
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