**Theoretical expression of radiation stress:**

The components of radiation stress Sxx, Syy, and Sxy are calculated as follows:

$$\mathbf{S}\_{\infty} = \mathbf{k} \mathbf{E} (\frac{\mathbf{k}\_{\mathbf{x}} \mathbf{k}\_{\mathbf{x}}}{\mathbf{k}\_{\mathbf{x}}^2 + \mathbf{k}\_{\mathbf{y}}^2} \mathbf{F}\_{\text{CS}} \mathbf{F}\_{\text{CC}} - \mathbf{F}\_{\text{SC}} \mathbf{F}\_{\text{SS}}) + \mathbf{E}\_{\text{D}\prime} \tag{A10}$$

$$\mathbf{S}\_{\rm yy} = \mathbf{k} \mathbf{E} (\frac{\mathbf{k}\_{\rm y} \mathbf{k}\_{\rm y}}{\mathbf{k}\_{\rm x}^2 + \mathbf{k}\_{\rm y}^2} \mathbf{F}\_{\rm CS} \mathbf{F}\_{\rm CC} - \mathbf{F}\_{\rm SC} \mathbf{F}\_{\rm SS}) + \mathbf{E}\_{\rm D'} \tag{A11}$$

$$\mathbf{S}\_{\mathbf{x}\mathbf{y}} = \mathbf{S}\_{\mathbf{y}\mathbf{x}} = \sqrt{\mathbf{k}\_{\mathbf{x}}^{2} + \mathbf{k}\_{\mathbf{y}}^{2}} \mathbf{E} \frac{\mathbf{k}\_{\mathbf{x}} \mathbf{k}\_{\mathbf{y}}}{\mathbf{k}^{2}} \mathbf{F}\_{\text{CS}} \mathbf{F}\_{\text{CC}} \tag{A12}$$

where

$$\mathbf{F\_{SC}} = \frac{\sin \mathbf{hk(z+h)}}{\cos \mathbf{hkD}},\\\mathbf{F\_{CC}} = \frac{\cos \mathbf{hk(z+h)}}{\cos \mathbf{hkD}},\tag{A13}$$

$$\mathbf{F\_{SS}} = \frac{\sin \mathbf{hk(z+h)}}{\sin \mathbf{hkD}},\\\mathbf{F\_{CS}} = \frac{\cos \mathbf{hk(z+h)}}{\sin \mathbf{hkD}},\tag{A14}$$

$$\mathbf{E} = \frac{1}{16} \rho\_{\mathbf{w}} \mathbf{g} \mathbf{H}\_{\mathbf{s}'}^2 \tag{A15}$$

where ρw is the seawater density; Hs is the significant wave height; g = 9.8 m/s2; kx and ky are the wave numbers in the x and y dimensions, respectively; D = H + η, where h is the seabed topography and η is the sea surface undulation; and η+−h EDdz = E/2 when z = η and Ed = 0.
