## 2 Dataset and Methods
### GNSS-R Data Processing  
The GLORI processing chain comprises eight main steps and makes use of the raw data stream, and the GPS ephemeris and flight ancillary data as inputs [30,31]:  
1. GNSS processing of the raw data stream
2. Acquisition and tracking of the modulated signal to compute correlation waveforms \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Date (dd/mm/yy)** & **Soil Moisture (m\({}^{3}\)/m\({}^{3}\))** & **LAI (m\({}^{2}\)/m\({}^{2}\))** & **VH (cm)** \\ \hline
22/06/2015 & [0.04–0.23] & [0–5.5] & [0–104] \\
25/06/2015 & [0.1–0.22] & - & - \\
29/06/2015 & [0.04–0.24] & [0–6.5] & [0–203] \\
01/07/2015 & [0.08–0.21] & [0–6.18] & - \\
06/07/2015 & [0.09–0.23] & [0–6.8] & [0–257] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Range of variation in soil moisture, leaf area index (LAI) and vegetation height (VH) during GLORI campaigns. Time tagging and extraction of waveform maxima as described in [32]
* Processing of the navigation message to recover the transmission time, and extraction of the correlation power
* Instrument corrections and incoherent averaging
* Correction for antenna gain and instrumental noise, incoherent averaging and reflectivity computation
* Geo-location and merging of individual files
* Computation of the location and surface shape of each footprint, merging of individual measurements into a consolidated file  
Three observables were considered in our analysis of the GNSS-R sensitivity to the land surface parameters: the apparent reflectivity, the processing signal-to-noise-ratio (SNR) of the reflected signal and the polarimetric ratio. The apparent reflectivity is related to the fraction of power reflected by the ground [16]. For a polarization \(pq\) (\(p\) and \(q\) denote the incident and the scattered, respectively), the apparent reflectivity \(\Gamma_{pq}\) can be expressed as the ratio of the reflected \(Y_{ref,q}\) to the direct waveform \(Y_{dir,p}\). In the case of GNSS-R, the right-right (\(RR\)) and right-left (\(RL\)) ratios represent the co- and cross-polarization reflection coefficients, \(\Gamma_{RR}\) and \(\Gamma_{RL}\):  
\[\Gamma_{pq}=\frac{\left|\left\langle Y_{ref,q}\right\rangle\right|^{2}}{\left| \left\langle Y_{dir,p}\right\rangle\right|^{2}} \tag{1}\]  
The processing signal-to-noise-ratio (\(SNR\)) of the reflected signal defined as the signal power (above the noise floor), divided by the noise level:  
\[SNR=(|Y_{r,max}|-B_{r})/B_{r} \tag{2}\]  
where \(B_{r}\) is the waveform noise floor and \(Y_{r,max}\) is the maximum of the reflected waveform. The polarimetric ratio (\(PR\)) is defined as the ratio of both apparent reflectivities \(\Gamma_{RR}\) and \(\Gamma_{RL}\):  
\[PR=\Gamma_{RL}/\Gamma_{RR} \tag{3}\]  
The scattered signal consists of two components, the coherent and incoherent terms. The first of these is related to the Fresnel zone, whereas the second covers an area much larger than the Fresnel zone, the so-called glistening zone. The latter component is reduced in the calculation of apparent reflectivity. The values of apparent reflectivity \(\Gamma_{pq}\) are thus associated with the Fresnel zone, which is elliptical and has a semi-major axis defined by:  
\[ra=\sqrt{\lambda h\sin\ \theta}/\sin^{2}\ \theta \tag{4}\]  
where \(\lambda\) is the signal's wavelength, \(h\) is the aircraft's height above the ground, and \(\theta\) is the elevation angle. In the present case, the aircraft flew at an altitude of 600 m, such that for an elevation angle equal to 60\({}^{\circ}\), \(ra\) was approximately 13 m for the L1 signal. These dimensions show that it should be possible to analyze the behavior of GNSS-R signals scattered by reference fields a few hectares in size. For the purpose of spatial co-location, all of the 240 ms incoherently averaged GNSS-R measurements were mapped onto ellipses, defined according to the size of their first Fresnel zone, and elongated in the flight direction.