surface properties affected by wave noise, detailed experi- 

 ments will be needed to extend the picture of the spectral 

 energy balance derived from JONSWAP to the higher wave- 

 numbers In the Bragg scattering range. 



2 . THE RADIATIVE TRANSFER EQUATION 



It Is known that to a good approximation wind-gener- 

 ated ocean waves obey the linearized hydrodynamic wave 

 equations for Irrotational flow. Linearity Implies that the 

 wave field is closely Gaussian [21] and can be fully char- 

 acterized by its two-dimensional energy spectrum F(k) with 

 respect to horizontal wavenumber k , where 



II 



F(k)dk = mean square wave height < c,^ > 



(= wave energy/g.) 



Experimentally, wave spectra are usually determined 

 through frequency analysis of surface displacements measured 

 at a fixed position, and it is therefore convenient to intro- 

 duce also the two dimensional spectrum EaCf/Q) with 

 respect to frequency f = a3/27T and propagation direction 



, E2(f,0) dfdO = F(k) dk. The trans- 

 formation Jakoblan follows from the (deep-water) dispersion 

 relation co = (gk) ^ : dfdG = 2TTkv-^ dk , where 



V = i (gA) ^ is the modulus of the group velocity 



V = 3co/9k (a = 1,2). Integration over the propaga- 



25-7 



