## 2 Procedure
As for the formation of whitecaps, [18] provides a number of local parameters, and in particular it provides a \"dynamic indicator\" based on the value of the vertical acceleration of the surface particles. Negative (_i.e._, downward) values of the acceleration below a certain threshold are likely to induce wave breaking. Thus the \"birth\" of foam covered areas can be simulated for a given instantaneous realization of the sea surface. [PERSON] _et al._[14] have successfully applied this technique to the simulation of SAR images of the sea. After its birth, floating foam decays, and this process has also been the object of much research work; to our purposes the results are summarized as in [19] where it is assumed that foam thickness grows and then decays according to two characteristic times \(\tau^{*}\) and \(\tau^{\prime}\) (Equation (2) and Figure 4). This approach recalls Monahan distinction between \"A\" and \"B\" foam. \[\delta(t)= \begin{cases}\beta t,t\leq\tau^{*}\\ (\beta\tau^{*})exp\left(-\frac{t-\tau^{\prime}}{\tau^{\prime}}\right),t>\tau^ {*}\end{cases}  \tag{2}\]  
For the purpose of present work the formation time of whitecaps \(\tau^{*}\) is negligible [20], so the only parameter left is the decay time \(\tau^{\prime}\). A connection between the thickness of the foam layer and the microwave properties is provided in [11, 21]. According to these results, it can be assumed that \(\sigma_{f}\) is equal to a constant, and very low, backscattering value; as it is very well known for very strong winds, when the sea surface is entirely covered by foam, the vertical average backscattering coefficient reduces to a very low value, which obviously coincides with the local backscattering of the foam. The next step is the calculation of the vertical distribution \(\sigma_{\!f}(\eta,\,X)\) of the local vertical backscattering coefficient; as stated above, \(\sigma_{\!f}(\eta,\,X)\) turns out to be a simple \(\sigma_{\!f}(\eta)\) if average horizontal uniformity is assumed. The calculations are carried out through a pseudo-code outlined in Figure 5.  
Sea surface realizations \(\eta(X,\,t)\) are generated by Inverse Fast Fourier Transform (IFFT) of directional JONSWAP sea spectra and random phase values; particle velocity and acceleration components are similarly computed according to a procedure which has been developed and tested in [13], and reported for example in [22]. The trajectories of foam particles are then calculated from their birth to their disappearance by considering the surface velocity values and the time evolution laws described above. Figure 6 yields a graphical example. Figure 4: Time evolution foam-layer thickness (after [19], modified). Figure 5: Simulation procedure for fractional foam surface pseudo-code (comments in italic). Applying the standard procedure to extract the sea parameters from the waveforms, two different set of values are thus obtained, one of which represents the conventional \"constant backscattering\" point of view, the other--presumably--more realistic. The best candidate for this kind of test is SSL, since the accuracy required for this parameter is very high: Figure 9 shows some results. The waveforms for a given sea state (_Hs_) is calculated by taking into account the presence of foam (red line) or by ignoring it (\(F(\eta)=0\) in Equation (1), blue line). Neglecting foam effect--as it is generally assumed--provides a SSL lower than the \"real\" one. This difference is one of the components of the so-called Sea State Bias (SSB) [1, 23], _i.e._, the error in the SSL evaluation induced by the wave agitation. The following Table 1 and Figure 10 illustrate the trend of Foam Induced Sea Surface Bias (FISSB) as function of H\({}_{\mathrm{s}}\) and wind speed U\({}_{10}\). Even though a proper calibration of the procedure cannot be carried out since no universally valid procedure to model SSB exists to date, it makes however sense to compare the results against a classical set of experimental data such as those provided by [PERSON] _et al._[24] reported by [PERSON] _et al._[23].