## 1 Introduction  
Radar altimeters such as fitted in many satellite constellations (_i.e._, TOPEX/Poseidon, Jason-1 and -2, ERS-1 and 2, Envisat, CryoSat-2, SARAL) have carried out systematic measurements of SSL (Sea Surface Level) and H\({}_{\text{s}}\) (Significant Wave Height) over the oceans for many years. The theory, as well as the practice of radar altimeter is fully consolidated, and it is reported in many classical works. Briefly summarizing, an electromagnetic impulse of very short duration (typical effective pulse duration after pulse compression technique is about 3 n-s) is sent from the antenna to the sea surface and the reflected signal (waveform) after preliminary processing to correct errors of electromagnetic origin, is analyzed to extract the required parameters. A schematic waveform is illustrated in Figure 1. The algorithms and the values of the gates follow [PERSON] _et al._[1]. Total reflected energy (segment \(P\)), integrated over the whole radar footprint is strictly correlated to the NRCS (Normalized Radar Cross Section, in the following \(\sigma_{0}\)) and it provides an estimate of the wind velocity, since both wind induced ripples and sea foam decrease the local surface reflectivity. Calibration of the link between \(\sigma_{0}\) and wind speed has been carried out by many researchers with different techniques over many years of data so that various empirical or semi-empirical correlation functions are now available. A description of radar techniques is reported in [2]. Signal processing also provides the delay of the central point (epoch at middle height in Figure 1) and the curve slope: these two measures are related to two extremely important geophysical  
Figure 1: Typical altimeter waveform over sea surface. \(P_{0}\) is the thermal noise; \(P\) the useful signal amplitude (related to wind speed); \(E\) the epoch at mid-height (related to SSL) and \(S\) the leading edge slope (related to \(H_{\text{s}}\)). parameters, respectively the Mean Sea Level (MSL), _i.e._, the long term average of SSL, and \(H_{s}\)[3, 4, 5]. The retrieval of those parameters is far from trivial and implies many aspects of the physical processes of the sea surface and of its modeling techniques. Conceptually at least, most techniques to extract \(\mathrm{H_{s}}\) from radar altimeters data originate from the so called [PERSON]'s model and successive variants. According to such models, the only relevant information on the sea state is the statistical distribution \(P(\eta)\), _i.e._, the percentage of the area at height \(\eta\) where a free surface is present water, since the local backscattering coefficient \(\sigma\) is assumed to be uniformly distributed over the wave surface. Under such assumptions, SSL derives immediately from the position of the \(P(\eta)\) mean, _i.e._, \"epoch at mid-height\" of the signal in Figure 1. A normal distribution is the most common hypothesis for \(P(\eta)\), but skewed distributions [6] have also been considered to account for the difference between crest and trough heights. Things become more complicated if the effects of floating foam are taken into consideration. The mechanics of foam over the sea surface is still an active subject of research, and the terminology is not totally uniform. Following, for instance, [PERSON] _et al._[7], we define as \"whitecap\" the breaking crest of a wave ([PERSON]'s \"A\" stage), \"floating foam\" the bubble layer which keeps floating after the breaking has terminated ([PERSON]'s \"B\" stage) and \"foam\" for the two effects together. We do not take into account the ocean-atmosphere interface made up of foam, spray and bubble emulsion, sometimes called \"spray and foam\" or \"foam\", which forms for very high winds (\(>\)30 m/s). Foam backscatters electromagnetic waves very differently from blue water, and in particular the reflection at nearly-vertical incidence angle, as it occurs in altimeters, is much lower.