*2.3.2 Evaluation of different source functions in tropical cyclones*

These input/dissipation source packages are evaluated in many studies and for different locations and scenarios. Using Hurricane Ivan (2004) as the test case, Liu et al. [30] conducted the first comprehensive evaluation of the relative strengths/weaknesses of all WAWEWATCH III source functions but ST1 under tropical cyclone conditions. Through the comparison of bulk wave parameters (i.e., significant wave height, mean wave direction and period) derived from SRA spectra measurements, satellite observations, and NDBC buoy data, the authors found that ST3, ST4, and ST6 have comparable skills on wave predictions under extreme wind conditions and significant outperformed the ST2 source package. Their comparisons with the SRA data are given in **Figure 3** for illustration. We can see that while ST2 has similar skills as other sources functions on wave direction predictions, it under predicts the significant wave height and mean wave period. One possible explanation for this is because the upper limiter on *C*d adopted by ST2 (*C*d*,* max = 2*.*5 × 10−3) starts being active when *U*10 is far below the hurricane wind forcing (*U*<sup>10</sup> ∼ 15 ms−1), which will influence the well-tuned wind wave growth behavior under low to moderate winds [47] and may influence the high wave predictions by ST2.

Another important feature to be noticed in **Figure 3** is the underprediction of wave period by ST2, a model bias reported by Fan et al. [11] as well (we can easily relate wave period to wave length through the dispersion relations), while good prediction skills on the wave period are found using ST3/4/6. This has suggested that more physical based new input/dissipation source functions were able to correct this bias efficiently.

Another wave model evaluated in Liu et al. [30] is the University of Miami Wave Model (UMWM) [4]. It was devised as an efficient wave model to provide full atmosphere-wave-ocean coupling in hurricane forecasting systems [29]. Thus, the physics-based but time-consuming nonlinear interaction source term *S*nl (e.g., [66–68]) was treated parametrically in such a way that wave breaking was assumed to be the primary cause of the shift of energy to the longer waves. Based on the comparisons between model results and measurements from various platforms, such as the comparison with the SAR measurements in **Figure 3**, the authors concluded that UMWM shows less accuracy than WAVEWATCH III in specification of bulk wave parameters. This is possibly because (i) UMWMestimated drag coefficient does not clearly show a saturation trend when wind

### **Figure 3.**

*Comparison of model results (colored lines: Blue for ST2, yellow for ST3, green for ST4, red for ST6 and gray for UMWM) and SRA observations (black dot •) acquired on September (a–c) 9, (d–f) 12 and (g–l) 14–15. For clarity, the SRA measurements on September 14–15 is divided into two parts. One (the first 300 records) is plotted in panels (g–i) and the other (the remaining 300 records) in panels (j–l). Three bulk parameters are taken into account: (a, d, g, j) significant wave height* Hs*, (b, e, h, k) mean wave direction* θw *(oceanographic convention: the direction towards which waves are propagating, measured clockwise from geographic north) and (c, f, i, l) mean wave period* T*02. The purple dashed lines in panel (a–c) represent the results from the ST6 + WRT experiment.*

speeds are beyond ∼35 ms−1 and (ii) the four-wave interaction term of UMWM disagrees evidently with the full solution of the Boltzmann integral in detail.
