Tropical cyclones (TCs) with spatially compact and well-formed vortex structures are one of the major extreme meteorological events that can generate large and potentially destructive ocean surface waves (Moon et al., 2003). The highest recorded significant wave heights (maximum crest-to-trough wave heights) resulting from TCs are 23.9 m (32.3 m) in the western North Pacific and 17.9 m (27.7 m) in the North Atlantic (Wang et al., 2005; Liu et al., 2008; Moon et al., 2016), observed during Typhoon Korosa (2007) and Hurricane Ivan (2004), respectively. With regard to TC disaster prevention, improving the forecasts of TC-generated high waves is an essential step toward minimizing the damage caused by TCs to coastal settlements and economic activities in the nearshore zone. In particular, it is important to accurately predict the maximum significant wave height ( H s m a x ) caused by TCs and to understand its generation mechanism, as it is a major factor that determines design waves, which are widely used in the engineering field (Kim et al., 2008; Lee and Kim, 2015).

Since TC wind fields can be parameterized in a relatively simple form, many studies have attempted to describe the wave field in a similarly parametric form (Young, 1988; Young and Burchell, 1996; Alves et al., 2004; Young and Vinoth, 2013; Hwang, 2016; Young, 2017; Hwang and Walsh, 2018). These attempts can help elucidate the mechanism of H s m a x occurrence caused by TCs. Several studies have introduced the concept of “extended (or trapped) fetch” in developing parametric models (King and Shemdin, 1978; Young, 1988; Young and Burchell, 1996; Alves et al., 2004; Bowyer and MacAfee, 2005; MacAfee and Bowyer, 2005; Young and Vinoth, 2013; Hwang, 2016; Hwang and Fan, 2017; Lee et al., 2017; Hwang and Walsh, 2018). King and Shemdin (1978) first proposed the key concept of extended fetch within TCs using aircraft-based NASA Scanning Radar Altimeter observation data. They showed that to the right of the storm center (in the Northern Hemisphere), the wind direction approximately aligns with the direction of propagation of the storm; in this region, the waves propagate forward with the storm and consequently remain within the intense wind regions of the storm for an extended period, which leads to an “extended” fetch. If the propagation speed of the waves (i.e., group velocity) is comparable to the velocity of the forward movement of the storm, the waves remain “locked” to the TC, which results in extended or trapped fetch (Young, 2017).

Based on these concepts, Young (1988) proposed a parametric model to estimate the TC-induced H s m a x that has been widely used as a guideline for emergency management (Alves et al., 2004). Using a synthetic database created by numerical model runs, Young defined the equivalent fetch for typical TCs, which is a function of the maximum wind speed (MWS) and the translation speed of the storm (V _fm ). The equivalent fetch is normalized by a scaling parameter that is related to the radius of maximum wind (RMW) representing the size of the TC system (Alves et al., 2004; Young, 2017). With the equivalent fetch defined, Young (1988) used the JONSWAP relationship (Hasselmann et al., 1973) to determine the H s m a x within the TC. The parametric model of Young (1988) has been adopted in many engineering studies because it successfully captures the important physics of TCs. Recently, Alves et al. (2004) proposed an advanced parametric model based on wave simulations using a moving-grid version of the WAVEWATCH III model, a third-generation wave model. The model included RMW as an additional parameter in defining the equivalent fetch, along with MWS and storm translation speed (V _fm ), unlike Young (1988), who used RMW as a scaling parameter. This idea is based on the fact that wind field curvature affects the effective fetch. That is, if RMW is small, the wind field curvature is large, which produces a smaller equivalent fetch since waves propagate in straight lines.

Besides RMW, there are various TC size parameters, such as wind radii at 34 knots (R34), 50 knots (R50), and 64 knots (R64) (see Figure 1 ; Sampson et al., 2018). Among the parameters, most studies used RMW as a scaling parameter or a proxy representing the curvature of the TC wind field without questioning whether RMW is an optimal representative TC size parameter that influences extended fetch for TCs. The use of RMW basically assumes that larger RMW values result in higher H s m a x values within the TC due to longer “accumulated fetches” (Young, 2017). However, in many cases, this assumption does not hold true. For example, for the two TCs (Cases A and B) in Figure 1 , RMW is greater in A than in B, but the resulting H s m a x is less in A than in B. This result occurred because although A has a larger RMW, it has smaller R64, R50, and R34 values than B and thus a smaller total cumulative wind (see Figure 1 ; this will be discussed in detail in a later section). This simple example suggests that the TC size parameter that most strongly influences H s m a x for translating TCs may not be RMW.

This study aims to investigate the TC size parameter that best fits the extended fetch concept and is most closely related to the H s m a x induced by TCs. To this end, an empirical TC wind field was constructed using TC size information observed in the North Atlantic from 1988 to 2017, and the H s m a x for each TC was calculated using a third-generation wave model. The calculated H s m a x values were classified and compared according to various TC size parameters to find the optimal parameter that affects H s m a x . The data and design of the ideal numerical experiments are described in Section 2. Section 3 examines the relationship between TC-induced H s m a x and TC size parameters. A summary and conclusion are presented in Section 4.

To determine the TC size parameter that has the greatest influence on H s m a x within TCs, ideal numerical experiments were designed using the size information of TCs that occurred in the Atlantic Ocean. First, an empirical parametric wind model was used to produce TC wind fields based on the collected TC size, intensity, and track information (Bender and Ginis, 2000; Moon et al., 2003; Kim and Moon, 2021). TC winds were used to simulate H s m a x using a third-generation wave model. TC size and track information were obtained from the Extended Best-Track (EBT) data provided by the Regional and Mesoscale Meteorology Branch every six hours (Demuth et al., 2006). The EBT data include the MWS and its radius, the radii with wind speeds of 34, 50, and 64 knots in all four quadrants of the hurricane, and the central pressure and location of the TC center. All storm parameters in the EBT data were first interpolated in time to the model time step (30 min). Radial wind profiles were then calculated along the northeast (NE), southeast (SE), northwest (NW), and southwest (SW) directions, correspondingly, using the following formula (Moon et al., 2003):

where V _max , R34, R50, and RMW are the TC’s MWS and the radii with wind speeds of 34 knots, 50 knots, and MWS, respectively (see dotted lines in Figure 1 ). The radial wind profile was constructed such that wind speed increased linearly in proportion to the ratio of V _max and RMW within RMW and decreased exponentially, depending on the average values of R34 and R50 outside RMW. The two-dimensional wind field was generated via spatial interpolation of the above radial profiles azimuthally.

The current parametric wind model can produce an asymmetric TC wind field based on the size information of the fourth quadrant of the TC (Kim and Moon, 2021). However, to make the results easier to interpret, a symmetrical wind field produced by averaging the TC information across the four quadrants was used in the experiment. The numerical experiments were designed using 12,830 TC data points obtained at six-hour intervals from a total of 642 TCs that occurred in the North Atlantic from 1988 to 2017. Numerical experiments for all TC intensities require substantial computational time. Thus, in this study, only the following two TC intensities were tested: 55 knots (517 points) and 105 knots (105 points). For the TC translation speed, only the basin-mean value (5.6 m s^-1) and the 75th percentile value (7.875 m s^-1) were applied. All experiments were designed to move a TC with a symmetrical wind field from west to east at a constant speed.

Wave simulations were performed using WAVEWATCH III v5.16, developed by the National Centers for Environmental Prediction Environmental Modeling Center. This model has been validated in many previous studies and has been shown to realistically simulate the mean wave parameters and wave spectrum, especially under various TC conditions (Moon et al., 2003; Tolman et al., 2005; Fan et al., 2009; Montoya et al., 2013; Moon et al., 2016; Liu et al., 2017; Abdolali et al., 2020; Wang et al., 2020; Zieger et al., 2021). The spatial resolution of the current model was set to 1/12° x 1/12° (541 x 481), and the basic source term ST2 was used as the physics package (Tolman and Chalikov, 1996). The water depth was uniformly set to 200 m. The H s m a x values within the TC were extracted after the waves had fully developed and reached a steady state.

This study investigated whether RMW, which has been widely used in previous studies for the extended fetch by TCs, is the optimal TC size parameter for determining TC-induced H s m a x through an idealized numerical experiment using actual TC size information in the North Atlantic from 1988 to 2017. Based on the collected TC size, intensity, and track information, translating TC wind fields were produced using an empirical parametric wind model. The TC winds were then used to simulate H s m a x using a WAVEWATCH III model. Finally, for TCs with two translation speeds and intensities, the correlation between simulated H s m a x and three TC size parameters (RMW, R34, and R50) was investigated.

The numerical experiments revealed that the RMW had the lowest correlation with H s m a x in all experiments ( Figures 3A, D ), while R34 had the highest correlation with H s m a x . We also further examined how the three TC size parameters correlated with the total accumulated wind component aligned with the direction of propagation of the storm, which had a significant impact on H s m a x , and found that RMW had the lowest correlation with the accumulated wind, while R34 had the highest correlation, followed by R50. This explains why R34, rather than RMW, is the TC size parameter most closely related to H s m a x . In a case study of two TCs with the same intensity and translation speed but different TC size parameters, we found that TCs with large RMWs can have lower H s m a x values than TCs with small RMWs due to the relatively small wind component affecting wave development. Figures 3A , 4A , 7A reveal that there could be many actual examples of this.

The low correlation of RMW with H s m a x is fundamentally related to the negative correlation of RMW with TC intensity. Figure 10 implies that RMW tends to decrease as the intensity of TC increases, which contrasts with the tendency of R34 and R50 to increase as the TC gets stronger. This explains why cases where the RMW is small but the other TC parameters are large, such as in Case B in Figure 1 , often occur in reality. In many cases, therefore, the TC-induced H s m a x is more affected by the region containing moderately strong winds outside the TC than by the region of maximum wind speed near the RMW. These findings provide additional insights into the mechanisms by which TC-induced extreme waves occur. Finally, our paper suggests the need to change the RMW used in the traditional “extended fetch” concept to a more appropriate TC size parameter, such as R34, and to re-parameterize the corresponding equivalent fetch based on extensive experiments for TCs with more diverse translation speeds and intensities.

The original contributions presented in the study are included in the article/supplementary material. Further inquiries can be directed to the corresponding author.

Conceptualization, YO and I-JM. Methodology, YO. Validation, YO. Formal analysis, SMO and P-HC. Data curation, YO and I-JM. Writing-original draft preparation, YO. Writing-review and editing, YO and I-JM. Supervision, YO, I-JM, SMO, and P-HC. All authors contributed to the article and approved the submitted version.