## 1 Introduction: Principles of L-Band Microwave Radiometry and GNSS-R over the Ocean  
Sea Surface Salinity (SSS) is a key climatologic and oceanographic parameter. It has a significant influence on ocean currents (thermo-haline circulation), it is related to the evaporation minus precipitation, is responsible for El Nino Southern Oscillation (ENSO) events, and determines the life conditions of some species...  
Sea surface salinity can be determined by means of microwave radiometry. The largest sensitivity is found at P-band [1], but at L-band (1.400-1.427 MHz) there is a quiet frequency band where the sensitivity to SSS is still relatively \"high\" (\(\sim\)0.5 K/psu at 15 \({}^{\circ}\)C). However, the sea emission in the L-band depends on other parameters, such as the Sea Surface Temperature (SST) and mainly, the sea state (surface roughness) [2]. Furthermore, the relationship between the brightness temperature changes and the sea state is very complex, since the sea emission is not dominated either by capillary waves, nor by the long waves, and even swell effects have an influence. Experimental activities conducted in the frame of the SMOS mission have shown that regressions in terms of the geophysical variables usually measured such as the wind speed (WS) and/or the significant wave height (SWH), exhibit too high a scattering (Figure 1) to provide a satisfactory correction to perform the sea state correction for the salinity retrieval, and that it is advisable to retrieve an \"effective\" wind speed as well, that can compensate for modeling errors [3]. Within the frame of the EURYI program, in 2003 the _PAU_ (_Passive Advanced Unit for ocean monitoring_) project was proposed to the European Science Foundation to test the feasibility of using GNSS-R over the sea surface to make sea state measurements and, jointly with IR observations to obtain the SST, perform the corrections of the L-band brightness temperature [4]. GNSS-R was originally devised for altimetry applications [5], and here it is extended to try to obtain a direct correction for the sea state, without having to rely neither in numerical sea surface spectra models, nor in scattering and emission models. The concept is simple: when the electromagnetic wave is scattered over the sea surface, the scattered signal changes its polarization (from RHCP to mostly LHCP) and arrives at the receiver mainly from the specular reflection point, determined by the shortest distance between the transmitting GPS satellite and the receiver, but when the sea is roughed, the scattered signals come from a wider region (known as \"glistening zone\") that enlarges with increasing sea state, in a similar manner as the Sun reflecting over the sea (Figure 2). Figure 1: Derivation of the brightness temperature sensitivity to wind speed. Scatter plots of the brightness temperature change at (a) horizontal (\(\Delta\)T\({}_{\rm B\;\;h}\)) and (b) vertical (\(\Delta\)T\({}_{\rm B\;\;v}\)) polarizations _vs._ the 10-m height wind speed (U\({}_{10}\)). Solid line: linear fit, and dashed lines: percentile 50% as a function of U\({}_{10}\) for incidence angles from 25\({}^{\circ}\) to 65\({}^{\circ}\). (c) Derived T\({}_{\rm B\,\,h,v}\) sensitivity to wind speed as a function of (solid line) polarization and incidence angle, associated \(\pm\)1 \(\sigma\) error bars, and (dashed lines) linear fit. All data points used (Figure 6 from [3]). When observing the GNSS reflected signals, two points over the sea surface correspond to the same delay and Doppler coordinates, with minimum delay corresponding to the specular reflection point (Figure 3). In _PAU_ it was proposed to measure the complete Doppler-Delay Maps (DDMs) to make the sea state correction of the brightness temperature required for the salinity retrieval.