Assessment of the forecasting potential of WAVEWATCH III model under different Indian Ocean wave conditions

Abstract

This study assesses the performance of different source term packages of WAVEWATCH III (WWIII, V-6.07) wave model for various wave conditions in the Indian Ocean (IO). Eight simulations of WWIII were made for the year 2017, four using default source term packages (ST2, ST3, ST4, and ST6) and another four by tuning the wind–wave interaction parameter (β) in the ST4 and ST6 schemes. The simulated wave outputs are compared with in-situ and altimeter wave fields over a wide range of weather conditions. All wave simulations have significant errors in low wind speeds (e.g., in pre-monsoon season) compared to medium (e.g., post-monsoon) and strong (e.g., monsoon season) winds which is independent of the error in the forecast wind. Overall, the ST4 scheme reproduces well the wave characteristics in all seasons and different conditions of IO, while the ST6 scheme is best suited for cyclonic weather conditions for wave simulation. Changing the WWIII parameterization schemes based on wind conditions is not a practical option for a timely wave prediction for a basin like the IO, where varied wave patterns exist year-round, owing to the full spectrum of wind conditions. Instead, this study advocates selecting a scheme that works well in all conditions, like ST4, and tuning it to suit well in cyclonic conditions.

Appendix

1.1 A.1 Notes on WAVEWATCH III source term parameterizations of the selected packages

Among all the packages included in WWIII, the following four switches are considered in this study.

1.1.1 A.1.1 ST2

This package is based on the (Tolman and Chalikov 1996) parameterization, as updated by (Tolman 2002). This scheme combines a wind input adjusted to the numerical model of air-flow above waves by Chalikov and Belevich (1993) and a dissipation consisting of two separate terms, one for low-frequency waves and the other for the high-frequency tail of the spectrum. The model is tuned and tested using standard fetch-limited growth conditions.

The input source term is given as:

$$S\left(k,\theta \right)=\sigma \beta N\left(k,\theta \right),$$

where β is a non-dimensional wind–wave interaction parameter whose value depends on non-dimensional frequency and drag coefficient at a height equal to the ‘apparent’ wavelength.

Energy flux from waves to the wind is not present in previous parametrizations of Sin (i.e., negative input source terms are introduced in this scheme).

1.1.2 A.1.2 ST3

ST3 is a WAM cycle 4 (ECWAM) scheme. This parameterization scheme combines the wind input term initially based on the wave growth theory of Miles (1957) with the feedback on the wind profile parameterized by Janssen (1991). A linear swell dissipation component due to stress variations in phase with orbital velocity was introduced by Janssen (2004). The input source term is expressed as follows:

$$S\left(k,\theta \right)=\frac{{\rho }_{a}}{{\rho }_{w}}\frac{{\beta }_{\mathrm{max}}}{{K}^{2}}{e}^{Z}{Z}^{4}{\left(\frac{u}{c}+{z}_{\alpha }\right)}^{2} \times {\text {cos}}^{{P}_{\mathrm{in}}}\left(\theta -{\theta }_{u}\right)\sigma N\left(k,\theta \right)+{S}_{\mathrm{out}}\left(k,\theta \right),$$

where ${\rho }_{a}$ and ${\rho }_{w}$ are the air and water densities. ${\beta }_{\mathrm{max}}$ is a non-dimensional growth parameter (constant). ${u}_{*}$ is the wind friction velocity and $K$ is the von Karman constant. $Z$ is a function of roughness length given by Janssen (1991) and corrected for intermediate depths. ${z}_{\alpha }$ is a wave age parameter. ${P}_{in}$ is a constant that controls the directional distribution and ${S}_{\mathrm{out}}\left(k,\theta \right)$ is a linear decrease in swell included following Janssen (2004).

${z}_{\alpha }$ is not well described in ST3 documentation; it has an important effect on wave growth. Essentially it shifts the wave age of the long waves, which typically increases the growth, and even generates waves that travel faster than the wind. This accounts for some gustiness in the wind and should possibly be resolution-dependent.

1.1.3 A.1.3 ST4

Parameterization with switch ST4 is built around a saturation-based dissipation, provided by Ardhuin et al. (2010), closely following Banner and Morison (2010), a cumulative effect that dissipates short waves due to the breaking of long waves and a swell dissipation that transitions from non-linear in turbulent conditions, to linear in the viscous regime (Ardhuin et al. 2009). The main advance of this scheme is an adjustment of the dissipation function without any predefined spectral shape. The wind input is loosely adapted from the (Janssen 1991) formulation, with an important reduction of input at high frequencies necessary to achieve a balance with the white capping term. This modification reduced the unrealistic large drag coefficients under high winds, but it removed the wave age dependence on the wind stress, which is not realistic (Rascle and Ardhuin 2013). The wind input term gives the flux of energy from atmospheric non-wave motion to wave motion, is the sum of ${S}_{\mathrm{in}}$ (wave generation) and ${S}_{\mathrm{out}}$ (wind generation term or −ve wind input term). The full wind input source term is as follows:

$$S\left(k,\theta \right)=\frac{{\rho }_{a}}{{\rho }_{w}}\frac{{\beta }_{\text{max}}}{{K}^{2}}{e}^{Z}{Z}^{4}\left(\frac{u}{c}\right) \times \text{max}{\left[\text{cos}\left(\theta -{\theta }_{u}\right),0\right]}^{P}\sigma F\left(k,\theta \right),$$

where ${\rho }_{a}$ and ${\rho }_{w}$ are the air and water densities. ${\beta }_{\mathrm{max}}$ is a non-dimensional growth parameter (constant). ${u}_{*}$ is the wind friction velocity and $K$ is von Karman constant. $Z$ is defined as effective wave age. The power of cosine is taken constant, P = 2.

For younger seas, the wind input is weaker than that given by Janssen (1991) (ST3), but stronger than that given by Tolman and Chalikov (1996) (ST2). However, the dissipation at the peak is generally stronger because it is essentially based on a local steepness and these dominant waves are the steepest in the sea state. As a result, the short fetch growth is relatively weaker than that with the source term combination proposed by Bidlot et al. (2007).

1.1.4 A.1.4 ST6

ST6 is an input-dissipation source term based on measurements from laboratory experiments carried out during AUSWEX at Lake Georgia, Australia. The wind input used is non-linear that relaxes under conditions of steep waves and strong winds to represent detachment of air-flow. The wind input function represents the energy flux transferred from the wind to waves. This term is due to form drag. AUSWEX data analysis and the wind input parameterization reported by Donelan et al. (2006, 2005) and (Babanin et al. 2007) show dependencies that have not been reported in previous experiments. Donelan et al. (2006) described the effect of full air-flow separation in which the wind detaches from the flow, skipping the wave troughs before it re-attaches on the windward side of the wave crest. The effect was parameterized by Donelan et al. (2006) and included in the new wind input term based on the observations. The input term is proposed as:

$$S\left(k,\theta \right)=\frac{{\rho }_{a}}{{\rho }_{w}} \sigma \gamma \left(k,\theta \right)N\left(k,\theta \right),$$

$$\gamma \left(k,\theta \right)=G\sqrt{{B}_{n}\left(k\right)}W,$$

$$G=2.8-\left[1+\text{tanh}\left(10\sqrt{{B}_{n}}W-11\right)\right],$$

$${B}_{n}=A(k)N(k) \sigma {k}^{3},$$

and

$$W={\left(\frac{U}{c}-1\right)}^{2},$$

where ${\rho }_{a}$ and ${\rho }_{w}$ are densities of air and water, $U$ is wind speed, $c$ is phase speed of wave, $\sigma$ is radian frequency and $k$ is the wavenumber. The parameterization of wave steepness $ak$ is replaced by the spectral saturation $\sqrt{{B}_{n}}$ following Phillips (1984). The omni-directional action density is obtained by integration over all directions $N(k) =\int N(k,\theta )d\theta$.

Drag coefficient parameterization proposed by Hwang (2011) is used, which accounts for saturation and decrease in magnitude for extreme winds.

$${C}_{d}\times {10}^{4}=8.058+0.967{U}_{10}-0.016{U}_{10}^{2}.$$

Source term yields faster wave growth for young seas than ST2 and ST4 source terms. As the wave field develops, the value of the wind input term near the spectral peak reduces. Compared to previous schemes, input and dissipation are stronger at high frequencies.