Reflectometry using GNSS signals of opportunity (GNSS-R) has stood as a powerful technique for ocean remote sensing. Particularly, the use of these techniques has been proposed to retrieve sea state information (i.e. sea surface roughness) among other applications. Precise knowledge of the sea state is a key issue to process L-band radiometric measurements for sea surface salinity retrieval. It has been recently shown that GNSS-R data can be directly linked to the brightness temperature variations caused by the sea state effect, without the use of emission/scattering models or sea spectra models. In this study, this approach is applied to CoSMOS 2007 flights data. Firstly, the radiometric and GNSS-R data sets are presented. Secondly, measured brightness temperature is corrected using the collocated GNSS-R data. In particular, the area under the normalized waveforms is used to directly compute the required brightness temperature correction. Thirdly, the salinity retrievals are presented (achieving an error reduction from 2.8 psu for the raw measurements down to 0.51 psu). Finally, the obtained results are compared with the WISE correction approach, based on the wind speed correction, and the conclusions of this work are presented.
 Sea surface salinity (SSS) is a key parameter for oceanography and climatology. The difficulty to regularly sample the SSS at a global scale by taking in-situ measurements makes remote sensing the single alternative. The best technique for measuring SSS is L-band microwave radiometry and, with this objective, the Soil Moisture and Ocean Salinity Mission (SMOS) of the European Space Agency (ESA) was launched in 2009 [Font et al., 2004, 2010]. Moreover, other space missions, such as Aquarius of NASA/CONAE [Le Vine et al., 2010], are planned to be launched in the near future for SSS measuring as well.
 The ocean brightness temperature at L-band is a function of the SSS and sea surface temperature (SST), but also of the incidence angle (θ), and the sea state (i.e. sea surface roughness). As the brightness temperature (TB) sensitivity to SSS is low (0.5 K/psu for warm open ocean conditions and decreasing with SST; see Figure 1), all the other parameters affecting TB must be properly accounted for. From these parameters, the one that has the largest impact in the final SSS retrievals is the sea state, as it is difficult to obtain well collocated information. If sea state is not taken into account, the salinity signature can even be totally masked [Font et al., 2004]. To study this impact of sea surface roughness on the sea emissivity, the WISE experiments were conducted [Camps et al., 2004]. One of the main conclusions was that the TB increment induced by sea state at L-band, is not well parameterizable by the available significant wave height (SWH) and wind speed (WS) measurements.
 Meanwhile, reflectometry of opportunity signals such as Global Navigation Satellite Systems' (GNSS-R) was proposed by Martin-Neira  for ocean altimetry. Since then, GNSS-R has stood as a powerful remote sensing technique and in recent years has been proposed for many applications such as ocean scatterometry [e.g., Zavorotny and Voronovich, 2000; Garrison et al., 2002] or soil moisture [e.g., Masters et al., 2000; Rodriguez-Alvarez et al., 2011]. Using opportunity signals makes possible to implement instruments with a low mass and power budgets so they are very suitable to be used as secondary payloads in other missions. With the aim of studying the benefits of jointly using L-band radiometry and GNSS-R for improving SSS retrievals, the Passive Advanced Unit (PAU) project was proposed in 2003 to the European Science Foundation (ESF) within the frame of the European Young Investigator (EURYI) Awards program, and granted in 2004 [Camps, 2004].
 The PAU sensor [Camps et al., 2009] is a suite of three instruments: an L-band radiometer (either real aperture with digital beam-forming or synthetic aperture) with polarization synthesis, a GPS reflectometer (sharing the RF front-end with the radiometer), and an infrared radiometer to measure the sea surface temperature. One of the main scientific goals of this project was to explore the possibility of directly relating the TB variations induced by the sea state effect with some GNSS-R observable without using emissivity/scattering models. The volume of the normalized delay-Doppler Map (DDM) is the GNSS-R direct observable proposed within the PAU project framework to describe sea state [see Marchan-Hernandez et al., 2008]. Conceptually, as the sea surface gets rougher the glistening zone is larger, so the measured DDM is contributed from a larger region in the delay-Doppler domain although its peak amplitude is reduced. After normalization, the integral of the DDM is a measurement of its widening caused by the increase of sea surface roughness.
 To explore the validity of these assumptions, the Advanced L-Band Emissivity and Reflectivity Observations of the Sea Surface (ALBATROSS) 2008 and 2009 field experiments were performed. The ALBATROSS 2008 experiment served to prove the feasibility of using the volume of the normalized DDM (VDDM) to directly describe the sea state [see Marchan-Hernandez et al., 2010]. During the ALBATROSS 2009 experiment, perfectly collocated (time and space) radiometric and GNSS-R data were collected. These data sets were used to prove that it was possible to directly link the measured TB variations induced by sea state to GNSS-R observables such as VDDM [see Valencia et al., 2009, 2010a, 2010b].However, due to TB calibration issues (mainly non-controlled contributions of the cliff through the antenna secondary lobes), absolute TB was not used for salinity retrievals.
 To further study the relationship of the ocean TB variations induced by sea state with GNSS-R measurements, the data gathered during ESA's CoSMOS-OS 2007 air-borne experiment [Delwart et al., 2008] is used in this work. In that experiment, different instruments were deployed on-board the Helsinki University of Technology (TKK) Skyvan aircraft to assess the feasibility of SSS retrieval using L-band microwave radiometry: the HUT-2D [Rautiainen et al., 2008] and EMIRAD [Rotbøll et al., 2003] L-band radiometers, the GOLD-RTR GPS reflectometer [Nogues-Correig et al., 2007], and others such as an infrared radiometer for SST measurements. The HUT-2D data were used by Talone et al.  for SSS retrieval and by Kainulainen et al.  to test different approaches to correct TB for the sea state effect. One of the approaches by Kainulainen et al.  is based on parameterizing the measured TB by the sea surface mean square slopes (MSS) derived from the GOLD-RTR data. In this work, an improved approach is followed to reduce the SSS retrieval errors from the EMIRAD measurements, but directly using the GOLD-RTR data without the use of emission/scattering models in line with the concepts developed in the PAU project and the ALBATROSS experiments. Improvements in the final SSS retrievals from 2.8 to 0.51 psu are achieved by applying the proposed correction and a simple TB inversion method with respect to the uncorrected measurements.
 In section 2 the different data sets used are described. Section 3 explores the correction of the measured TB for the sea state effect using the area under the waveform as an integrated collocated GNSS-R observable. After the TB correction, its impact on the SSS retrieval is assessed in section 4. Finally, the main conclusions of this work are wrapped up in section 6.
2. Available Radiometric, GNSS-R and Ground-Truth Data
 The ESA-sponsored CoSMOS-2007 field experiment [Delwart et al., 2008] consisted of two flights performed over the Gulf of Finland. The aim of these flights was to test the ability of different instruments to measure SSS gradients, so the flight tracks were planned to pass above an estuary area and open sea (Figure 2). This track is referred to as the “test line” and it presents a SSS gradient from nearly 0 psu inside the estuary to approximately 4 psu in the open sea area. While the aircraft passed several times over the test line (around 20 passes), a vessel was collecting in-situ SSS, SST and sea state measurements along it. To avoid the Sun glint effect in the measurements, flights were performed in the evening, from 19:00 to 21:00 approximately.
 The aircraft flew different instruments. In this study the data sets of three of them were used: the EMIRAD L-band radiometer [Rotbøll et al., 2003], the GOLD-RTR GPS reflectometer [Nogues-Correig et al., 2007], and a standard thermal infrared radiometer (TIR).
2.1. Radiometric Data
 The EMIRAD data set contains calibrated polarimetric L-band measurements of the observed scenario. The raw data files provide the brightness temperature values for basic integration periods of 8 ms which have been further integrated up to 1 s so as to be time-collocated with the GNSS-R measurements from the GOLD-RTR instrument. With this 1 s integration time, the radiometric sensitivity is specified to be ΔT = 0.1 K and the thermal stability is within ±0.1 K. The EMIRAD's antenna is a horn with a 30° half-power beam width, and side-lobes below −17 dB with respect to the antenna's boresight gain. The data files also contain information regarding the aircraft position and attitude.
 To minimize the impact of the aircraft attitude on the radiometric data, in this work only the nadir-looking measurements were processed from the two antennas on-board the aircraft (nominal incidence angles of 0° and 40°). Moreover, the chosen radiometric observable was the first Stokes parameter divided by two (I/2) as it presents a very low sensitivity to attitude variations for low incidence angles. This parameter is defined as the mean of the horizontally and vertically polarized brightness temperatures (see equation (1)).
2.2. GNSS-R Data
 The main product of the GOLD-RTR instrument are the so-called waveforms (see equation (2)) which are computed by correlating received signal (s(t)) with a local replica of the GPS L1 (fL1 = 1575.42 MHz) coarse acquisition (C/A) pseudo-random noise (PRN) code (a(t)), after compensating for the Doppler frequency shift (fD) during a coherent integration time (Tc), as defined by Zavorotny and Voronovich . This coherent integration process takes into account the phase of the complex correlation.
 However, the coherent integration time is limited by the coherence time of the scattered signal which depends on the scattering surface and the observation scenario's dynamics. For an airborne experiment as the one presented here, this time has shown to be of the order of a few milliseconds [You et al., 2006]. The coherently integrated waveforms (Y(τ)) can be further integrated incoherently during an incoherent integration time Ti = N · Tc in order to improve the resulting signal-to-noise ratio (SNR):
 For this experiment, waveforms were acquired in different ways (i.e. different PRNs and Doppler shifts) according to a established measuring cycle. This work uses the incoherently integrated 1 s waveforms computed for the highest elevation satellite present at each time, as the reflection is closer to nadir and, thus, the specular reflection point is closer to the radiometer antenna footprint. The considered reflections present a local incidence angle uniformly distributed between 5° and 40°.
 In the absence of the complete DDMs, to study the sea surface roughness a parameter analogue to VDDM [see Marchan-Hernandez et al., 2008] was defined for the waveform in this work. It is the area of the normalized waveform (AWF) computed by integrating the area below the measured waveform in the delay domain. As for the case of the VDDM, an empirically-determined threshold of 0.2 was used to minimize the impact of noise. The rationale of using this observable to parameterize the ocean surface roughness is that, for a very calm sea, the scattered signal will only be contributed from a small region close to the specular point while, for rougher surfaces, it will be contributed from larger surface regions which present larger physical delays. Thus, the power of the scattered signal will spread along the delay domain as the surface gets rougher. After normalization of the waveforms' peak value, the area below them is then a function of the surface roughness. As the waveforms are normalized, the unity of AWF is the same as for the delay domain. In this work, the C/A code chip length (0.97 microseconds) is used.
 To better show the concept of “waveform spreading” described by the AWF parameter, the area of the ideal non-spread waveform was computed from the direct signal and subtracted from the area of the measured waveforms (i.e. the waveform cannot be thinner than the autocorrelation function of the C/A code, thus the area of this function acts as an offset). Although for direct signal its value should be theoretically equal to the area of the squared triangle (shape of the ideal autocorrelation function of the C/A code in the delay domain), it is actually a little larger due to the limited bandwidth of the system. This value is 0.63 chips and was subtracted from the AWF for the reflected signal, to define a new parameter ΔAWF. For a very calm sea, ΔAWF should tend to 0, while it should increase for rougher seas.
 Although waveforms from different PRNs and elevations were used, a high consistency among the derived AWF was observed (i.e. AWF showed to be independent of the different PRNs and elevation), as it was observed for the VDDM in previous experiments such as the ones presented by Marchan-Hernandez et al.  and Valencia et al. [2010a].
2.3. Ground-Truth Data
 The ground-truth data set that was used in this work is formed by the SSS measurements taken by the vessel along the test line (Figure 3), and the SST collocated measurements taken by the on-board TIR averaged up to 1 s. To obtain the SSS ground-truth measurements, TKK personnel took water samples (in bottles) that were post-analyzed in an specialized laboratory. The SST measurements from the vessel were not used as they were not collocated in time with the radiometric data and did not reflect the water cooling effect along the evening, which leads to errors when trying to model the sea brightness temperature or to perform SSS retrievals. Due to the thermal cycle along the day, the parameter whose variations affect the most the measured brightness temperature is SST. For the presented experiment, it ranged from 23.5°C to 20°C considering the different measurement spatial region and time. This variability was the reason to use the on-board instantaneous TIR SST measurements, and not the vessel ones. However, the SSS spatial distribution changed less than 0.5 psu in 24 h [Talone et al., 2010], so it can be considered constant during the 2.5 hour flights.
 There is not any available well collocated (neither in time, nor in space) sea state ground truth data. However, the vessel measurements (obtained by processing the data of two GPS-equipped buoys pulled by the vessel) showed a relatively calm sea during the flights (mss < 0.025; SWH < 30 cm). Moreover, the closest wind speed (WS) measurements in time and space (measurements at 18:00 UTC with a resolution of 0.25°), provided by QuickScat and ECMWF, were also low and very similar for both flights (QuickScat around 3.5 m/s and ECMWF around 2.5 m/s).
3. Brightness Temperature Correction Using GNSS-R Data
 As seen in equation (4), the ocean measured brightness temperature (after correction for the external contributions such as galactic, cosmic and atmospheric) can be divided into two contributions: TB,flat, the flat sea term, and ΔTB, the increment introduced by the sea surface roughness.
 The flat sea contribution is computed from the Fresnel reflection coefficient Γ (equation (5)) using, for example, the sea water dielectric constant model of Klein and Swift , since the emissivity can be assumed to be the complimentary value of the reflectivity:
where p is the desired polarization, θ is the incidence angle, and ε is the dielectric constant of the sea water, which is a function of SSS and SST. Using the available ground truth data, the flat sea contribution was computed for each measurement taking into account the collocated SST and SSS measurements. Figure 4 shows the resulting flat sea contribution modeled for the first Stokes parameter I/2, for the first flight. It can be observed how I/2 changes according to SST, SSS and surface roughness variations as the aircraft performed the different passes over the test line.
 At this point, since the SSS and SST effects were modeled, the contribution of the sea state to the total brightness temperature could be estimated by subtracting the modeled flat sea term from the actual measurements. The spatial distribution of the final estimated ΔTB is presented in Figure 5, where the different aircraft passes have been plotted in different colors. It can be seen that ΔTB presents a dispersion larger than the radiometric resolution of the instrument and that it is a function of time. This ΔTB is actually related to the instantaneous sea state, except for the errors introduced by the model used to compute TB,flat, and the ground-truth errors.
 In Figure 5 some spatial features appear as spikes in the computed ΔTB. These phenomena occur in the region where the aircraft track passed closest to land (transition from estuary to open waters) and, according to their magnitude of a few kelvin, were thought to be caused by land contribution to the overall measured brightness temperature which was collected through the antenna secondary lobes (roughly, a 300 K brightness temperature of the land, attenuated 17 dB results in a 6 K contribution). Moreover, this transition area is also the one that presented a larger SSS gradient. Due to the sparse SSS ground truth sampling, the final error among the interpolated ground-truth and the actual SSS may be larger, resulting also in a larger error in the modeling of the flat-sea contribution to the total brightness temperature. These errors (land contribution and ground-truth error) can mask the roughness effects and bias the final results, thus this region was discarded for processing.
 In order to directly perform the sea-state correction, the derived ΔTB needed to be parameterized as a function of a sea state descriptor. As mentioned above, in this work the sea state descriptor chosen was the area of the normalized waveforms which was obtained from the quasi-collocated GNSS-R measurements, and is conceptually similar to the volume under the normalized DDM [Marchan-Hernandez et al., 2008]. The time evolution of ΔTB is plotted in Figure 6a along with the time evolution of AWF. It is observed that both are highly correlated in time: both measurements present oscillations which are perfectly in-phase, as well as a slight decrease in their mean. This oscillation is attributed to the roughness variation observed as the plane flew over the two different roughness areas (estuary and open sea). This fact further supports the hypothesis that both are related to sea state.
 Collocated measurements of ΔTB are plotted as a function of the corresponding ΔAWF in Figure 7 along with the resulting regression line. These measurements present a Pearson correlation coefficient of r = 0.41. The polynomial coefficients of the performed geometric regression [see Leng et al., 2007] were used to compute an estimation of the actual ΔTB from the AWF. By subtracting this estimation from the TB measurements, the sea state contribution was then corrected, better approaching to the desired TB,flat term. In Figure 8 the computed ΔTB correction for all the aircraft passes is plotted as a function of the measurement longitude and with different colors depending on the measurement time. It can be seen that the needed correction is lower in the inner waters part of the test line than in the open sea areas. The required ΔTB correction also decreases with time as the sea got calmer at the end of the day.
 To assess the performance of the proposed sea surface roughness correction, it was applied to the first flight data. The resulting corrected first Stokes parameter is shown in Figure 9 along with the raw radiometric measurements and the modeled flat sea contribution. The RMSE with respect to the modeled first Stokes parameter TB,flat is reduced from 0.70 K to 0.30 K by applying the proposed correction. Spatial averaging can be performed to reduce the final brightness temperature error. In Figure 10 the result of spatially averaging the raw and the corrected I/2 measurements with a cell size of 0.002° (approximately 100 m at the flight latitude) are shown. In this case, the sea state effect correction reduces the RMSE from 0.63 K to 0.12 K.
 Although the correction needed for this data set is not large (in the order of 0.5 K) due to the relatively low sea surface roughness conditions present during the flight (mss < 0.025; SWH < 30 cm), larger ΔTB will be introduced by rougher sea conditions. However, the final error after correction is expected to be similar to the one achieved in this example as this error is mainly due to the dispersion of the radiometric measurements around the corresponding regression line (see Figure 7), which is not dependent of the sea state.
4. Sea Surface Salinity Retrieval
 After applying the sea state correction to the measured I/2, its benefits to the final SSS product can be assessed. To do so, the inversion of the flat sea model (equation (5)) was used as a first approximation to the problem. Retrievals were performed for both raw and corrected radiometric measurements, and the derived SSS products are shown in Figure 11. As a reference for the error introduced by the retrieval algorithm, also the SSS retrieved from the flat sea model itself and the ground-truth measurements have been plotted in Figure 11. As it can be seen, the corrected values for the I/2 better match the in-situ SSS measurements. It has to be noticed that the highest I/2 values, that should correspond to non-real negative SSS, saturate down to 0.2 psu (the lowest salinity value that the used method can output). This fact will lead to overestimation of the SSS retrieval mean for the lowest salinity regions.
 To further assess the benefits of the proposed correction, the SSS retrievals were also spatially averaged in longitude cells of 0.002° (approximately 100 m at the flight latitude). The averaged SSS retrievals are shown in Figure 12, along with the values retrieved from the model itself and the ground-truth. As can be observed, in the highest salinity part of the test line, the retrieval from the corrected I/2 matches the in-situ measurements significantly better than the SSS retrieved from the raw radiometric measurements (RMSE of 0.51 psu and 2.8 psu respectively). However, for the lowest salinity region, the retrieval mean appears to be overestimated due to the aforementioned saturation effect. This is why the retrievals from the uncorrected I/2 measurements seem to match the ground-truth data better. For this reason, the quality of the retrieval was not assessed in this region as the introduced bias resulted in misleading conclusions.
5. Comparison With the WISE Correction Approach
 In order to have a more complete picture of the brightness temperature correction process, the sea surface roughness correction problem was also approached by using the currently existing WISE model for the ΔTB correction. Concretely, the ΔTB correction was computed from the QuickScat and the ECMWF WS measurements using the I/2 sensitivity to WS derived in the WISE experiment [Camps et al., 2004]. This sensitivity is 0.25 K/(m/s) for the measurements' incidence angle. However, a single WS measurement was available for the flight time along the test line. For both QuickScat and ECMWF WS measurements, ΔTB appears overestimated (10). The I/2 RMSE with respect to the flat sea model for the different correction approaches are shown in Table 1.
Table 1. Brightness Temperature and SSS RMSE for the Different Correction Approaches (Spatially Averaged)
WISE correction (ECMWF)
WISE correction (QuickScat)
 SSS was also retrieved after applying the WISE correction for the two available WS data. For both WS data, the retrieved SSS is higher than when using the collocated GNSS-R data to perform the sea state correction. The derived RMSE is 2.33 psu when using QuickScat and 1.14 psu when using ECMWF, also computed only for the highest salinity part of the test line to avoid the model inversion saturation that affects the lowest salinity region. The SSS RMSE for the different correction approaches are summarizes in Table 1.
 Even though the WISE corrections do improve the final results with respect to the raw data (reduction of the error at the brightness temperature and SSS levels), these results show the benefits of using collocated GNSS-R data to parameterize the sea surface roughness contribution to the measured brightness temperature.
 Previous ground-based studies linked the sea state and the brightness temperature variations caused by the sea state effect. In this work the CoSMOS-OS 2007 experiment data were used to extend those studies to the airborne case and to analyze the feasibility of improving the retrieval of SSS by jointly using collocated L-band radiometry and GNSS-R measurements. The GOLD-RTR measured waveforms were used directly, through their area after normalization of the peak amplitude, to compute the required brightness instantaneous temperature correction.
 The first step of this process was to study the relationship among the ΔTB induced by the sea state effect and the area of the normalized waveforms. This was done by subtracting the modeled TB,flat from the radiometric measurements to compute an estimation of ΔTB. The first parameter of Stokes divided by two (I/2) has been used as it is nearly independent of the aircraft attitude for low incidence angles. The time evolution of both ΔTB and AWF shows an instantaneous correspondence. When plotted one versus the other, both parameters present a Pearson correlation coefficient of r = 0.41. The AWF was then used to compute the instantaneous brightness correction needed. After applying this correction, the error with respect to the TB,flat model was significantly reduced (RMSE from 0.63 K (raw measurements) down to 0.12 K when TB was spatially averaged in approximately 100 m cells along the test line). This correction appeared to be robust in spite of the noise level of the used GNSS-R observable.
 Once the corrected TB were derived, the Fresnel-based brightness temperature model was inverted for SSS retrieval. A final improvement in the RMSE from 2.8 psu (raw measurements) down to 0.51 psu was achieved when applying the proposed correction prior to the SSS retrieval process, even though a simple retrieval method based in model inversion was used. These results should improve when using more refined retrieval algorithms and further time and space averaging as is done within the SMOS processor.
 Moreover, the currently existing WISE model for the ΔTB as a function of the WS was also applied to the data set. It was concluded that the final brightness temperature errors were further reduced by using time and space collocated GNSS-R data to parameterize the sea surface roughness, rather than when considering a single low-resolution WS measurement.
 The results achieved in this work, as a follow-on to prior ground-based experiments, provide further encouragement for the development of a joint L-band radiometry/GNSS-R mission (e.g. for future SMOS follow-on missions). As GNSS-R are passive remote sensing systems, a relatively low extra power and mass budget would be required to accommodate this kind of system as a secondary payload in an L-band radiometry mission such as SMOS or Aquarius. Moreover, the GNSS-R system would not interfere with the radiometer system, either in its operation, or in its performance.
 Authors acknowledge the European Space Agency (ESA) for the provision of data from the 2007 CoSMOS field campaign. The campaign was funded under ESA contract number 19686/06/NL/FF. The authors also acknowledge the IEEC members F. Fabra, O. Nogues-Correig and A. Rius for their effort to make the GOLD-RTR data publicly available and their support at working with it; the Helsinki University of Technology (TKK) for providing the logistics to perform this experiment; and the Danish Technical University (DTU) for the EMIRAD radiometer development and operation. This work has been supported by funds from the Spanish National Plan project AYA2008-05906-C02-01/ESP.