**3. Results and Discussions**

*3.1. Validation of the SWHs Simulated Using the WW3 Model*

The wave fields during the four typhoon events were simulated using WW3 model. The WW3-simulated SWHs were compared with the SWH measurements of the Jason-2 altimeter statistically using root mean squared error (RMSE) and correlations (CORs). RMSE and COR were calculated as follows:

$$\text{RMSE} = \sqrt{\frac{\sum\_{i=1}^{N} \left(\lambda\_{\text{mod}}^{i} - \lambda\_{\text{obs}}^{i}\right)^{2}}{N}} \text{ and} \tag{1}$$

$$\text{COR} = \frac{\text{Cov}(\mathcal{X}\_{\text{mod}'} \mathcal{X}\_{\text{obs}})}{\sqrt{\text{Var}(\mathcal{X}\_{\text{mod}}) \text{Var}(\mathcal{X}\_{\text{obs}})}},\tag{2}$$

where N was the number of matchups, Xmod were the model-simulated results, Xobs were the measurements from the Jason-2 altimeter, Cov was the covariance, and Var was the variance.

The analysis of more than 10,000 matchups during Typhoons Tembin and Bolaven (19–30 August 2012) resulted in SWHs with an RMSE of 0.54 and a COR of 0.91 (Figure 6a). Similarly, the SWHs of Typhoons Chan-hom and Linfa (2–11 July 2015) had an RMSE of 0.50 m and a COR of 0.90 (Figure 6b). These results indicate that the WW3-simulated wave fields during typhoons were reliable, even under extreme conditions (SWH > 8). The methods used to calculate breaking waves, nonbreaking waves, radiation stress, and Stokes

drift are given in Appendix A using WW3-simulated parameters (e.g., SWH, mean wave period, wavelength, and dominant wave propagation velocity).

**Figure 6.** Comparisons of WW3-simulated SWHs with measurements from the Jason-2 altimeter in 0.5-m bins between 0 and 10 m. (**a**) 19–30 August 2012; (**b**) 2–11 July 2015.

### *3.2. Analysis of SSTs Simulated Using the sbPOM*

The four effects, which were empirically calculated based on wave parameters derived from the WW3 model, were treated as forcing fields in the sbPOM. Here, we first present the results of the sbPOM, including the individual wave-induced terms simulated using the WW3 model. When the simulated results were compared with the Argos measurements during the four typhoons, the bias in nonbreaking stress and Strokes drift terms was about 1 ◦C; the bias in the breaking and radiation stress terms was greater (Table 2).

**Table 2.** Statistical comparisons of sea surface temperatures (SSTs) generated by the sbPOM and Argos during the four typhoons.


We included Stokes drift, accounting for depth decay, in the sbPOM. The interaction between friction velocity and Stokes drift may result in Langmuir circulations in binary typhoons, and may subsequently affect SST. This is probably why Stokes drift was the least biased term.

We comparted the SSTs from the available Argos data with those simulated using the sbPOM in 2 ◦C bins between 0 and 30 ◦C during the Tembin and Bolaven typhoons (19–30 August 2012; Figure 7). Figure 7a shows SSTs simulated without the four effects induced by typhoon waves (RMSE of 1.42 ◦C and COR of 0.95), while Figure 7b shows SSTs simulated including the four effects induced by typhoon waves (RMSE of 1.07 ◦C and COR of 0.99). Statistical analyses of the Chan-hom and Linfa typhoons (2–11 July 2015) yielded similar results: the results of the analysis including the four effects induced by typhoon waves (RMSE of 1.01 ◦C and COR of 0.99; Figure 8a) were better than those not

including the four effects induced by typhoon waves (RSME of 1.37 ◦C and COR of 0.96; Figure 8b). Therefore, we concluded that the accuracy of the sbPOM SST simulation was improved when the four WW3-simulated effects induced by typhoon waves were included. The RMSE of SST was 1.40 ◦C when radiation stress was included, which was similar to the results generated without including any wave-induced effects. This suggested that radiation stress had little influence on SST cooling. Nonbreaking wave-induced mixing alone led to SST cooling in a study of individual typhoons [50]. However, our results show that effects of Stokes drift were also an important factor in SST cooling during binary typhoons.

**Figure 7.** Comparisons of the SSTs from Argos with SSTs simulated using the sbPOM for 2 ◦C bins between 0 and 30 ◦C during the period 19–30 August 2012. (**a**) Not including the four effects induced by typhoon waves. (**b**) Including the four effects induced by typhoon waves.

**Figure 8.** Comparisons of the SSTs from Argos with SSTs simulated using the sbPOM for 2 ◦C bins between 0 and 30 ◦C during the period 2–11 July 2015. (**a**) Not including the four effects induced by typhoon waves. (**b**) Including the four effects induced by typhoon waves.
