Impact of the Elevation Angle on CYGNSS GNSS-R Bistatic Reflectivity as a Function of Effective Surface Roughness over Land Surfaces

The Earth’s surface bistatic reflectivity ΓLHCP,CyGNSS is experimentally characterized using the novel Global Navigation Satellite Systems Reflectometry (GNSS-R) L-band passive multistatic radar technique from the Cyclone Global Navigation Satellite Systems (CyGNSS) eight-microsatellite constellation. The focus of this study is to evaluate the influence of the GNSS satellites’ elevation angle θe on ΓLHCP,CyGNSS, as a function of soil moisture content (SMC) and effective surface roughness parameter h. As the average response, the change of the scattering regime at a global scale and considering also vegetated surfaces appears at θe ≈ 55◦. This empirical observation is understood as a change on the dominant scattering term, from incoherent to coherent. Then, the correlation of ΓLHCP,CyGNSS and SMC is evaluated as a function of θe over specific sparsely vegetated target areas. The smoother the surface, the higher the angular variability of the Pearson correlation coefficients. Over croplands (e.g., Argentinian Pampas), an improved correlation coefficient is achieved over angular ranges where the coherent scattering regime becomes the dominant one. As such, this function depends on the surface roughness. The maximum correlation coefficients are found at different θe for increasing mean roughness levels: rPampas ≈ 0.78 at θe ≈ [60,70]◦, rIndia ≈ 0.72 at θe ≈ [50,60]◦, and rSudan ≈ 0.74 at θe ≈ [30,40]◦. SMC retrieval algorithms based on GNSS-R multi-angular information could benefit from these findings, so as to improve the accuracy using single-polarized signals.


Introduction
Small satellites [1] are changing the paradigm in Earth remote sensing, taking advantage of innovative payloads (e.g., References [2][3][4]).As such, the operation of constellations of these instruments has the potential to observe Earth's dynamic processes with a higher spatiotemporal sampling than traditional techniques.In particular, the so-called Global Navigation Satellite Systems Reflectometry (GNSS-R) [5] is a sort of L-band passive multi-static radar (as many transmitters as navigation satellites are in view) that provides a wide swath up to ≈1500 km [6][7][8].GNSS-R spatiotemporal sampling properties could open new process insights on mesoscale studies [6], wind speed determination [9], soil moisture content (SMC) determination [10], and vegetation water content (VWC) monitoring.There are several on-going research activities dedicated to improve the spatiotemporal sampling properties of GNSS-R.The main parameters being evaluated are the number of in-orbit receivers, the use of beam-forming strategies, and the directivity of the down-looking antennas [6].Several methods have been proposed to extract the geophysical information added to the GNSS signals in the scattering process over the Earth's surface: (a) The Passive Reflectometry and Interferometry System (PARIS) or interferometric GNSS-R (iGNSS-R) that can provide higher precision in ocean altimetry measurements, but requires the use of high-gain antennas [6,8]; (b) the conventional GNSS-R (cGNSS-R) that requires only relatively low-gain antennas for scatterometry purposes [8]; and (c) the GPS interferometric reflectometry (GPS-IR) that can determine accurately SMC with potential application to the global GNSS network [11].
At present, several small satellites have been launched into space carrying a GNSS-R payload on-board, including the United Kingdom (U.K.)-Disaster Monitoring Constellation DMC-1 [2] in 2003, the U.K.-TechDemoSat TDS-1 [3] in 2014, and the Universitat Politècnica de Catalunya UPC's 3 Cat-2 in 2016 [4].In 2012, the National Aeronautics and Space Administration (NASA) selected the CyGNSS mission led by the University of Michigan as a low cost and high science Earth Venture Space System [12].CyGNSS, an eight-microsatellite constellation, was launched on December 15, 2016 into a low Earth orbit (LEO) with an inclination angle ≈ 35 • [13].The main objective of this mission is to estimate wind speed over tropical cyclones with an unprecedented spatiotemporal sampling of the ocean [14].Each single CyGNSS microsatellite has two left-hand circular polarization (LHCP) down-looking antennas pointing to the Earth's surface with an inclination angle of ≈28 • on each side of the satellite ground track.The antennas' gain is ≈ 14.7 dB (antenna boresight), and the main payload is the so-called Delay Doppler Mapping Instrument (DDMI), which generates delay Doppler maps (DDMs) [8] on-board using a coherent integration time T c = 1 ms, and applying an incoherent average over N inc = 1000 samples.
The application of active (e.g., synthetic aperture radar (SAR)) and passive (e.g., microwave radiometry and GNSS-R) remote sensing techniques over land-surfaces is based on the variability of the dielectric properties due to changes in SMC and biomass.However, surface roughness significantly affects SMC retrieval, especially in the case of GNSS-R [15][16][17] and SAR [18][19][20].In this work, the sensitivity of GNSS-R to SMC, and the effect of surface roughness are assessed as a function of the elevation angle θ e (θ e = 90 • at the normal direction to the Earth's surface) [21].This is a first step towards SMC retrieval using GNSS-R multi-angular information [22] because the ratio of the coherent-to-incoherent scattering components [23] depends on the surface roughness through θ e .The coherent scattering component is expected to be more sensitive to SMC because of its improved spatial resolution (limited by approximately the first Fresnel zone) and its scattering properties.This smaller footprint provides an improved estimation on the actual heterogeneity of the surface.As such, the sensitivity of GNSS-R to SMC should increase with higher θ e because the size of the first Fresnel zone is lower at this geometry.On the other hand, the coherent scattering component is expected to increase with lower θ e [24] because the effective surface roughness is lower at this angular range, in agreement with the Rayleigh criterion.This trade-off is assessed over different surface types using the CyGNSS Level 1 Science Data Record [12,25].
The remainder of the paper is organized as follows.Section 2 provides an overview of approaches for studies over land.Section 3 describes bistatic scattering properties relevant to GNSS-R.Section 4 describes the methodology.Section 5 presents global-scale results.Section 6 describes the impact of θ e as a function of SMC and effective surface roughness parameter with a focus over land.Section 7 includes final discussions, and the conclusions are highlighted in Section 8.

GNSS-R Approaches for Studies over Land Surfaces
The use of different GNSS-R methods (iGNSS-R, cGNSS-R, and GPS-IR) for land-surface applications requires further research activities because the dielectric properties of this scattering medium make it more complex than the ocean surface.The first study (to the authors' knowledge) on the potential use of GNSS-R for SMC estimation was published in 2000 [26].Follow-on activities were proposed simultaneously to investigate the capabilities of GNSS-R for SMC determination using cGNSS-R [27][28][29] and GPS-IR [10,11,30,31].The use of the polarimetric ratio (ratio of the reflected signals' power at two different polarizations) on cGNSS-R data collected from two airborne experiments was further studied for biomass monitoring up to an above ground biomass (AGB) of ≈300 ton/ha, and for SMC determination because it can cancel out surface roughness effects [15,16].A GNSS dual-polarization payload [4] was successfully tested over boreal forests during two experiments from a stratospheric balloon [32].A comprehensive study over different land surface types was performed to further assess the use of dual-polarization information obtained during two airborne campaigns [33].More recently, new important conclusions were also derived, such as: (a) the use of the GPS-IR for accurate SMC estimation was validated over multiple GPS test sites including vegetated surfaces [11,34]; (b) a sensitivity to SMC of ≈38 dB/(m 3 /m 3 ) was measured over nearly bare-soil target areas using data from U.K. TDS-1 [35,36]; (c) a Pearson correlation coefficient of r ≈ −0.6 between one-year averaged polarimetric ratio from a GNSS-R experiment on-board the Soil Moisture Active Passive (SMAP) mission and SMC was measured over the complete Earth's surface [16,37]; (d) θ e should be considered for the application of the so-called Tau-Omega model in the GNSS-R case [35]; (e) the vegetation introduces short-term (volume scattering) and long-term (interference from large-size scatterers and canopy inhomogeneity) fluctuations on GNSS signals [38]; and (f) the unbiased root-mean-square difference between daily averaged CyGNSS-derived SMC and SMAP SMC is down to 0.045 cm 3 /cm 3 , after correcting for surface roughness effects [17].

Coherent and Incoherent Scattering in GNSS-R
The scattered electromagnetic field over land and ocean surfaces is composed of both a coherent and an incoherent contribution in different proportions depending on the dielectric and geometrical properties of the scattering medium, and the directions of incoming and outgoing electromagnetic waves.In the specular direction, the p-polarized bistatic scattering coefficient σ 0 p [39] can be assumed to be composed of an incoherent σ 0 p,incoh and a coherent σ 0 p,coh term as it follows [40]: The estimation of σ 0 p based on theoretical models requires several hypotheses, such as those regarding the dielectric permittivity of the lower media (land, ocean, . . .), and the distribution of the surface elevation slopes Zs = σ RMS /L [41].The root mean square (RMS) of the surface height variation σ RMS and the surface correlation length L describe the statistical variation of the random component of the surface height relative to a reference surface, which determines the degree of surface roughness.The incoherent scattering term is dominant for moderate-to-strong surface roughness conditions, while the scattering is completely coherent for a flat surface.
The power of the incident and the scattered waves is related through the reflectivity of the scattering medium.The reflectivity is a physical property of the medium.It depends on its dielectric properties and the surface roughness.The reflectivity can be indirectly linked to, e.g., the SMC, and it is used as a fundamental observable in GNSS-R.GNSS-R is a sort of bistatic radar that allows for the collection of scattered GNSS signals along the specular direction.GNSS satellites transmit relatively low-power signals, and the scattering is strong only over an area around the nominal specular point (θ e,s = θ e,i = θ e ).GNSS signals are emitted with right-hand circular polarization (RHCP), although with a certain degree of ellipticity.After scattering over a surface, they become left-HCP (LHCP) for elevation angles θ e higher than the Brewster angle, while they are mainly RHCP for lower θ e .Additionally, the scattering over biomass introduces a significant degree of depolarization.RHCP and LHCP reflected signals should be considered simultaneously in this case.The signal power collected by a GNSS reflectometer for LHCP (e.g., CyGNSS) is expressed by the so-called delay Doppler maps (DDMs), that can be derived under the bistatic radar equation as it follows [42]: where P T is the transmitted power, G T and G R are the transmitter and receiver antenna gains, χ is the Woodward ambiguity function (WAF), R T and R R are, respectively, the ranges from the transmitter and the receiver to the specular point, σ 0 LHCP is the bistatic scattering coefficient at LHCP, and ρ is the positioning vector of the scattering point.
GNSS-R LHCP-reflectivity Γ LHCP includes both coherent Γ LHCP,coh and incoherent Γ LHCP,incoh contributions in different proportions depending on satellites' elevation angle, and the biomass, topography, and surface roughness.The coherently reflected power is related with Γ LHCP,coh as in [43]: The surface roughness has a strong impact on the coherent reflectivity term Γ LHCP,coh that can be theoretically modelled as in [40]: where R LHCP is the polarized Fresnel reflection coefficient and k is the signal wavenumber.The impact of θ e on Γ LHCP,coh is twofold; on one hand it affects the Fresnel reflection coefficient, and on the other hand, it effects the exponential decaying factor.For a completely flat surface, σ RMS is zero, and Γ LHCP,coh is equal to the square of the amplitude of the Fresnel reflection coefficient.R LHCP is linked to the dielectric constant of the soil, and thus with SMC.For a given roughness and a fixed geometry, Γ LHCP,coh should increases with larger SMC.On the other hand, R LHCP is nearly constant for θ e > 40 • and it decreases significantly for lower angles.However, the exponential factor increases significantly with lower θ e .As such, Γ LHCP,coh could be expected to be higher for grazing angles, even over areas with moderate roughness levels.Figure 1 shows the theoretical relationship (Equation ( 4)) between Γ LHCP,coh and θ e for different levels of SMC.The Wang's model [44] is used to relate the SMC with the dielectric constant of the soil, assuming a soil composition of 50% clay and 20% sand.It appears Γ LHCP,coh increases for lower θ e and it decreases for higher σ RMS .On the other hand, the influence of θ e is higher as σ RMS increases.It could be expected that the coherently reflected power as collected from a spaceborne platform increases at grazing angles because it is roughly independent of the platform's height (R T >> R R ).
where T P is the transmitted power, T G and R G are the transmitter and receiver antenna gains, χ is the Woodward ambiguity function (WAF), T R and R R are, respectively, the ranges from the transmitter and the receiver to the specular point, 0 LHCP σ is the bistatic scattering coefficient at LHCP, and ρ is the positioning vector of the scattering point.
GNSS-R LHCP-reflectivity LHCP Γ includes both coherent LHCP,coh Γ and incoherent LHCP,incoh Γ contributions in different proportions depending on satellites' elevation angle, and the biomass, topography, and surface roughness.The coherently reflected power is related with LHCP,coh Γ as in [43]: The surface roughness has a strong impact on the coherent reflectivity term LHCP,coh Γ that can be theoretically modelled as in [40]: where LHCP R is the polarized Fresnel reflection coefficient and k is the signal wavenumber.Γ could be expected to be higher for grazing angles, even over areas with moderate roughness levels.The expression of LHCP,incoh Γ is quite complex and not compact.More detailed information on incoherent scattering over rough surfaces can be found in Reference [40].The effects of biomass should be also considered for modeling the incoherent scattered field over vegetated areas.A comprehensive method can be found in Reference [29].Finally, the impact of rough topography in r Y can be understood as a sort of impulse response in the delay and Doppler domains to be convolved with the WAF [45].Rough topography reduces the spreading of the DDMs, while surface roughness increases the spreading with larger roughness because more specular reflection points contribute to the total scattered field.As such, Equation ( 4) is valid in regions without rough topography.

Data and Methods
In this work, the impact of the elevation angle e θ on CyGNSS experimental reflectivity LHCP,CyGNSS Γ was empirically evaluated as a function of the effective surface roughness parameter h and SMC.CyGNSS Level 1 Science Data Record Version 2.0 [25] is used to estimate LHCP,CyGNSS Γ and SMAP Enhanced Level 3 product [46] is selected to provide h and SMC data.These observables are described here for an enhanced understanding of the experimental results. .They are computed using a coherent integration time of c T = 1 ms and 1000 samples to perform an incoherent averaging.The estimation of the CyGNSS reflectivity was obtained by applying the following algorithm:

CyGNSS experimental reflectivity
after compensating for the antennas' gain patterns versus the gain at the corresponding boresight direction [down-looking gain ≈ 14.5 dB, e θ = 62° and up-looking gain ≈ 4.7 dB, e θ = 90°], and the difference of both gains at boresight.The compensation of the antennas' gain was performed as a function of e θ , with a precision of four decimals.The half-power beamwidth (−3 dB) of each downlooking CyGNSS antenna was ≈ 30°, and the −6 dB field-of-view was ≈ 45°.On the other hand, each antenna pointed to the Earth's surface with an inclination angle of 28° (antenna boresight).As such, GNSS signals reflected at lower e θ ≈ [20,40]° could be accurately collected through the main lobe of each antenna.The expression of Γ LHCP,incoh is quite complex and not compact.More detailed information on incoherent scattering over rough surfaces can be found in Reference [40].The effects of biomass should be also considered for modeling the incoherent scattered field over vegetated areas.A comprehensive method can be found in Reference [29].Finally, the impact of rough topography in Y r can be understood as a sort of impulse response in the delay and Doppler domains to be convolved with the WAF [45].Rough topography reduces the spreading of the DDMs, while surface roughness increases the spreading with larger roughness because more specular reflection points contribute to the total scattered field.As such, Equation ( 4) is valid in regions without rough topography.

Data and Methods
In this work, the impact of the elevation angle θ e on CyGNSS experimental reflectivity Γ LHCP,CyGNSS was empirically evaluated as a function of the effective surface roughness parameter h and SMC.CyGNSS Level 1 Science Data Record Version 2.0 [25] is used to estimate Γ LHCP,CyGNSS and SMAP Enhanced Level 3 product [46] is selected to provide h and SMC data.These observables are described here for an enhanced understanding of the experimental results.
CyGNSS experimental reflectivity Γ LHCP,CyGNSS : The calibrated reflected and direct DDMs are used to estimate the power waveform peaks Y r,Peak,LHCP and Y d,Peak,RHCP .They are computed using a coherent integration time of T c = 1 ms and 1000 samples to perform an incoherent averaging.The estimation of the CyGNSS reflectivity was obtained by applying the following algorithm: after compensating for the antennas' gain patterns versus the gain at the corresponding boresight direction [down-looking gain ≈ 14.5 dB, θ e = 62 • and up-looking gain ≈ 4.7 dB, θ e = 90 • ], and the difference of both gains at boresight.The compensation of the antennas' gain was performed as a function of θ e , with a precision of four decimals.The half-power beamwidth (−3 dB) of each down-looking CyGNSS antenna was ≈30 • , and the −6 dB field-of-view was ≈ 45 • .On the other hand, each antenna pointed to the Earth's surface with an inclination angle of 28 • (antenna boresight).
As such, GNSS signals reflected at lower θ e ≈ [20,40] • could be accurately collected through the main lobe of each antenna.
Effective surface roughness parameter h: It was empirically estimated based on the Moderate Resolution Imaging Spectroradiometer (MODIS) Geosphere-Biosphere Program (IGBP) land cover classes [47,48].h is an estimation of the factor 4k 2 σ 2 RMS in the surface reflectivity term in Equation ( 4).As such, this parameterization provided an improved performance as compared to previous global constant values-based algorithms [49], because it incorporated the diversity of the land surface.h values for different land cover types are included in the SMAP Tau-Omega parameter look-up table, at a spatial scale of 9 km.
The use of physical roughness parameters, such as correlation length and RMS height, requires in situ characterization, which is time-consuming and it is not feasible at a global scale.Thus, the SMAP effective roughness parameter was selected for this study, although the ultimate accuracy of the MODIS IGBP land cover types used for the roughness parameter estimation in the SMAP algorithm needs to be further evaluated.This effective parameter accounts for the dependence of surface roughness with SMC, while physical parameters do not.A heterogeneous distribution of the water when the soil dries out more water at specific target areas creates variations in the actual roughness of the soil that is not considered by the physical parameters.Further research should also account for the effects of roughness dynamics.Over specific target areas it has been reported [50] that the actual soil roughness is slightly higher as compared to the estimation provided by physical roughness parameters.Future studies covering a large variety of areas could help to optimize the estimation of the effective roughness parameter at a global scale.
Soil Moisture Content (SMC): SMC was estimated using the single channel algorithm at V-Pol, when the optimal Earth's surface conditions are identified.Then, the corrections for surface roughness [47,48], effective soil temperature, and vegetation water content (VWC) were applied.

Global Scale Reflectivity over Land and Ocean
The focus of this work is on the study of Γ LHCP,CyGNSS over land surfaces.As a first step, the evolution of Γ LHCP,CyGNSS is shown for three different ranges of θ e over the complete coverage of the Earth's surface provided by CyGNSS (Figure 2).Reflectivity data Γ LHCP,CyGNSS were averaged over one month (from 20 September to 20 October 2017) using a 0.1 • × 0.1 • latitude/longitude grid with a moving window of 0.2 • .The spatial scale of the roughness parameter h and SMC is ≈9 km.The size of the CyGNSS's footprint under the coherent scattering regime at θ e ≈ 55 • was ≈1 km across-track, and ≈7.6 km along-track.Thus, the gridding strategy enables the analysis using different sensors with different spatial resolution.This strategy also allows to determine the evolution of Γ LHCP,CyGNSS over a wider angular range and provides good sampling density at pixel level.This gridding was found to provide an improved correlation between CyGNSS reflectivity and the SMAP microwave brightness temperature [43].Additionally, the application of this moving averaging filter minimized potential residual errors in the down-looking antenna gain pattern correction due to attitude determination and control system (ADCS) and in the estimation of the reflected Y r,Peak,LHCP and direct Y d,Peak,RHCP power waveforms peaks.Effective surface roughness parameter h : It was empirically estimated based on the Moderate Resolution Imaging Spectroradiometer (MODIS) Geosphere-Biosphere Program (IGBP) land cover classes [47,48].h is an estimation of the factor in the surface reflectivity term in Equation ( 4).As such, this parameterization provided an improved performance as compared to previous global constant values-based algorithms [49], because it incorporated the diversity of the land surface.h values for different land cover types are included in the SMAP Tau-Omega parameter look-up table, at a spatial scale of 9 km.
The use of physical roughness parameters, such as correlation length and RMS height, requires in situ characterization, which is time-consuming and it is not feasible at a global scale.Thus, the SMAP effective roughness parameter was selected for this study, although the ultimate accuracy of the MODIS IGBP land cover types used for the roughness parameter estimation in the SMAP algorithm needs to be further evaluated.This effective parameter accounts for the dependence of surface roughness with SMC, while physical parameters do not.A heterogeneous distribution of the water when the soil dries out more water at specific target areas creates variations in the actual roughness of the soil that is not considered by the physical parameters.Further research should also account for the effects of roughness dynamics.Over specific target areas it has been reported [50] that the actual soil roughness is slightly higher as compared to the estimation provided by physical roughness parameters.Future studies covering a large variety of areas could help to optimize the estimation of the effective roughness parameter at a global scale.
Soil Moisture Content (SMC): SMC was estimated using the single channel algorithm at V-Pol, when the optimal Earth's surface conditions are identified.Then, the corrections for surface roughness [47,48], effective soil temperature, and vegetation water content (VWC) were applied.

Global Scale Reflectivity over Land and Ocean
The focus of this work is on the study of LHCP,CyGNSS Γ over land surfaces.As a first step, the evolution of LHCP,CyGNSS Γ is shown for three different ranges of e θ over the complete coverage of the Earth's surface provided by CyGNSS (Figure 2).Reflectivity data LHCP,CyGNSS

Γ
were averaged over one month (from 20 September to 20 October 2017) using a 0.1° × 0.1° latitude/longitude grid with a moving window of 0.2°.The spatial scale of the roughness parameter h and SMC is ≈9 km.The size of the CyGNSS's footprint under the coherent scattering regime at e θ ≈ 55° was ≈ 1 km across-track, and ≈ 7.6 km along-track.Thus, the gridding strategy enables the analysis using different sensors with different spatial resolution.This strategy also allows to determine the evolution of LHCP,CyGNSS Γ over a wider angular range and provides good sampling density at pixel level.This gridding was found to provide an improved correlation between CyGNSS reflectivity and the SMAP microwave brightness temperature [43].Additionally, the application of this moving averaging filter minimized potential residual errors in the down-looking antenna gain pattern correction due to attitude  Additionally, the spatiotemporal variability of the permittivity over land surfaces was high.This explains the significant variability of LHCP,CyGNSS Γ (Figure 2a,c,e).Overall (Table 1), it appears Additionally it is worth noting that the Brewster angle could potentially appear in the range e θ ≈ [20,40]°.In this situation, the power of the RHCP-reflected GNSS signals would dominate that of The averaged Γ LHCP,CyGNSS is displayed over land (Figure 2a,c,e) and ocean (Figure 2b,d,f) for different elevation angles in ranges of θ e ≈ [70,90] • (Figure 2a,b), θ e ≈ [45,65] • (Figure 2c,d), and θ e ≈ [20,40] • (Figure 2e,f).Over land-surfaces (Figure 2a,c,e), there was a strong coherent scattering σ 0 LHCP,coh and the width of the waveforms was much narrower than over the ocean.In this situation, the power fluctuations of Y r,Peak,LHCP could be closely related to σ 0 LHCP,coh at some areas.Additionally, the spatiotemporal variability of the permittivity over land surfaces was high.This explains the significant variability of Γ LHCP,CyGNSS (Figure 2a,c,e).Overall (Table 1), it appears Γ LHCP,CyGNSS increased from θ e ≈ [70,90] • to θ e ≈ [20,40] 4 dB, and Γ 20 • <θe<40 • Ocean ≈ −14.1 dB.These experimental results can be explained because of the strong impact of θ e on Γ LHCP,coh .The coherent scattering was very high for grazing angle, because the effective surface roughness was low [51].As such, the reflectivity was much higher at θ e ≈ [20,40] • than at θ e ≈ [70,90] • .On the other hand, Γ LHCP,CyGNSS decreased from θ e ≈ [70,90] • to θ e ≈ [45,65] • because the incoherent scattering is dominant over the coherent one in this angular range: The incoherent or diffuse scattering was lower with decreasing θ e because this term is generated by the effective surface roughness, which in turn decreased for lower θ e .This point explains the evolution of Γ LHCP,CyGNSS along this angular range.Additionally it is worth noting that the Brewster angle could potentially appear in the range θ e ≈ [20,40] • .In this situation, the power of the RHCP-reflected GNSS signals would dominate that of LHCP-reflected ones.Γ LHCP,CyGNSS was higher at θ e ≈ [20,40] • than at θ e ≈ [70,90] • (Figure 2), although Γ LHCP,CyGNSS would decrease for lower θ e < 20 • especially over vegetated surfaces.
Table 1.Summary of the impact of the elevation angle θ e on Γ LHCP,CyGNSS over land and ocean.

[dB]
Γ 20 • <θ e <40 GNSS signals were attenuated and depolarized by the vegetation cover.This attenuation can be modeled as L canopy = e τ canopy / sin θ e , where τ canopy is the vegetation optical depth (VOD) of the vegetation layer.The attenuation is due to scattering and absorption when GNSS signals propagates through the vegetation, and thus it increases for lower θ e .The vertical stalks scatter more the vertically polarized waves than the horizontal ones.This geometrical effect contributes to the depolarization of the GNSS signals.Here, two land-cover types are selected to show different scenarios: characterized by wet biomass with high AGB ≈ 350 tons/ha that strongly attenuated GNSS signals, so that the remaining reflected power could be interpreted as a noise power floor in Y r,Peak,LHCP (areas in "white" in Figure 3b correspond to SNR lower than 3 dB).However, the increment due to the coherent scattering σ 0 LHCP,coh over soil and inland water bodies compensated this attenuation, and as a consequence, the mean Γ LHCP,CyGNSS increased by ≈3.4 dB for decreasing θ e , allowing for the detection of the hydrosphere, even at grazing angles (Figure 3b). [dB]

Results on the Surface Roughness and the Soil Moisture Effect
This section is structured in two different parts.First, the evolution of LHCP,CyGNSS Γ with e θ is studied as a function of h for different levels of SMC over the land-surface coverage enabled by

Results on the Surface Roughness and the Soil Moisture Effect
This section is structured in two different parts.First, the evolution of Γ LHCP,CyGNSS with θ e is studied as a function of h for different levels of SMC over the land-surface coverage enabled by CyGNSS.As such, this analysis allows for the evaluation of the impact of θ e at a global scale.It provides useful information for the selection of the preferred operational angular range depending on the specific application from, e.g., a small satellite.In the second part, the correlation of Γ LHCP,CyGNSS and SMC is assessed as a function of θ e over sparsely vegetated areas with differentiated h levels, so as to minimize vegetation effects.This sensitivity study focuses on the impact of h.As such, the conclusions derived from this part could help to define SMC estimation methods using multi-angular information from GNSS-R.This is an interesting approach that previously has been applied from, e.g., the Soil Moisture Ocean Salinity (SMOS) mission [22].

Global Analysis
The angular evolution of Γ LHCP,CyGNSS was studied averaging at steps of θ e = 10 • from θ e = 20 •  to θ e = 90 • using different ranges of h (Figure 4a) and SMC (Figure 4b).The averaging was performed using data from the eight satellites of the CyGNSS constellation (the maximum of eight different DDMs were used in the averaging).The rate of change of Γ LHCP,CyGNSS was larger as h increased.At the same time, the larger the roughness, the lower Γ LHCP,CyGNSS was at all the selected SMC levels (Figure 5). Figure 5 also shows two differentiated Γ LHCP,CyGNSS angular ranges: Γ LHCP,CyGNSS decreased from θ e ≈ 85 • to θ e ≈ 55 • , and it increased from θ e ≈ 55 • to θ e ≈ 25 • .Γ LHCP,CyGNSS included contributions from both coherent and incoherent scattering regimes in both angular ranges.The main difference between both scattering regimes was on the combination of the electromagnetic field vectors.σ 0 LHCP,coh came from the coherent combination of the signals scattered on the individual facets within the first Fresnel zone.σ 0 LHCP,incoh was the result of the random combination of electromagnetic waves coming from other scatterers within the glistening zone that added together at the receiving antenna.If the combination was totally coherent, Γ LHCP,coh accounted for all the reflected power.In the case of diffuse scattering, the random signs of the electric field cross-products cancelled out σ 0 LHCP,coh , and the reflected power was given by σ 0 LHCP,incoh .The changes on the angular evolution of Γ LHCP,CyGNSS depended on the dominant scattering mechanism.In the interpretation of Figure 5 it should be considered that the averaging of the reflectivity was performed over the complete land-surface coverage enabled by CyGNSS, including bare soil, deserts, rough topography areas, and highly vegetated areas such as rainforests.As such, these results provide the average response of Γ LHCP,CyGNSS as a function of θ e .

Global Analysis
The angular evolution of LHCP,CyGNSS Γ was studied averaging at steps of e θ = 10° from e θ = 20° to e θ = 90° using different ranges of h (Figure 4a) and SMC (Figure 4b).The averaging was performed using data from the eight satellites of the CyGNSS constellation (the maximum of eight different DDMs were used in the averaging).The rate of change of LHCP,CyGNSS Γ was larger as h increased.At the same time, the larger the roughness, the lower LHCP,CyGNSS Γ was at all the selected SMC levels (Figure 5). Figure 5     Γ LHCP,CyGNSS decreased in the first range (from θ e ≈ 85 • to θ e ≈ 55 • ) because the incoherent scattering was dominant over the coherent one.The coherent integration time T c is an important parameter that influences the ratio of the coherent-to-incoherent scattering components, and in this experiment it was set to T c = 1 ms.A longer T c would limit the incoherent scattering term, so as to increase the coherent-to-incoherent ratio because it would better filter out the noise and the volume scattering term [32].Previous research activities also found a transition from an incoherent to coherent scattering regime over the ocean surface [42,51], where Γ LHCP,incoh is dominant for high θ e [52].Theoretical simulations were performed in Reference [52] to study the evolution of the incoherent reflected power as a function of θ e .It was found Y r,Peak,LHCP decreased ≈ 20% when θ e reduced from θ e = 90 • to θ e = 50 • .
Γ LHCP,CyGNSS increased in the second range (from θ e ≈ 55 • to θ e ≈ 25 • ), which could be justified because the reflectivity became mostly coherent Γ LHCP,coh in regions without rough topography.σ 0 LHCP,coh was high over smooth or slightly-to-moderate rough surfaces, because it increased with a decrease in surface roughness.As such, Γ LHCP,CyGNSS increased with a decrease in θ e in the angular range θ e < 55 • because the signal coherence increased with a decrease in θ e [51], and thus σ 0 LHCP,coh became dominant for θ e < 55 • .The scattering phenomenon became more complicated in regions with a rough topography.As such, this result should be understood as the average response over the Earth's surface.For higher θ e , even in a Nadir-looking configuration, there was still a non-negligible coherent component so as to be tracked [32,53,54].
The dynamic range of Γ LHCP,CyGNSS was higher for lower roughness levels, which seemed to indicate GNSS-R loses sensitivity to SMC over rougher surfaces in a general scenario.This reduction of the dynamic range appeared to be dependent on θ e along the second angular range, where σ 0 LHCP,coh was dominant.This increment was larger for decreasing SMC levels, which meant that the effect of a higher signal coherence was more relevant over areas with low SMC.Additionally, the effect of a larger signal attenuation through the canopy layer L canopy over highly vegetated areas was larger for a lower θ e , which could contribute to this loss of sensitivity.Overall, Γ LHCP,CyGNSS increased as SMC increased for a given θ e and h (Figure 5).

Regional Case Studies
Specific target areas with little vegetation over Argentina, India, and Sudan (Figures 6-8) were selected for this section because they allowed for the evaluation of the impact of SMC and h in the angular evolution of Γ LHCP,CyGNSS , excluding the effects of rough topography and high vegetation.The coordinates of these target areas are the following ones: Argentinian Pampas (Lat = [−37,−30] • , Lon = [−65,−60] • ), India (Lat = [22,29] • , Lon = [70,77] • ) and Sudan (Lat = [4,10] • , Lon = [25,33] • ).The land cover-types were croplands (Pampas and India) and savannahs (Sudan), where the signal penetration depth was high, so as to minimize the vegetation effects.The Pearson correlation coefficient r of Γ LHCP,CyGNSS and SMC was calculated for each target area at steps of θ e = 10 • from θ e = 20 • to θ e = 90 • (Table 2).The maximum Pearson coefficients r Pampas ≈ 0.78, r India ≈ 0.72, and r Sudan ≈ 0.74 were found, respectively, at θ e ≈ [60,70] • and h Pampas ≈ 0.1, θ e ≈ [50,60] • and h India ≈ 0.11, and θ e ≈ [30,40] • and h Sudan ≈ 0.15.These coefficients were gradually achieved at lower θ e for increasing mean values of h over these target areas.As such, the angular ranges associated with an improved correlation coefficient depend on h.A lower θ e was required to increase the signal coherence with an increase in h, in agreement with the Rayleigh criterion that establishes a surface (without vegetation and without rough topography) could be considered smooth if the phase difference between two reflected electromagnetic waves was lower than π/2 rad: where λ was the signal wavelength that at the L-band was ≈20 cm.The angular dependence seemed to be lower over the Sudan target area (savannahs), which was characterized by a significantly higher effective surface roughness parameter.In this situation, σ 0 LHCP,incoh was high even for low θ e and thus the power fluctuations of Y r,Peak,LHCP were more linked to the size of the first iso-delay ellipse (much larger than that of the first Fresnel zone), which minimized the impact of θ e .Nonetheless, there was a non-negligible increment of the correlation for θ e ≈ [30,40] • .The impact of θ e was clearer over Argentinian Pampas and India (croplands).This experimental evidence was a symptom that over smoother surfaces (e.g., croplands), the correlation of Γ LHCP,CyGNSS and SMC was improved when the coherent scattering regime started to be the dominant one because: (a) A higher spatial resolution (smaller first Fresnel zone), as compared to that at lower θ e , minimized the effects of land cover heterogeneity (Table 3).(b) σ 0 LHCP,coh was mainly related to surface scattering.The use of a higher T c would improve the sensitivity of GNSS-R to SMC [16] because it would filter out the power fluctuations linked to the incoherent scattering term.The sensitivity to SMC was based on the difference between the dielectric properties of water and soil.Here, the sensitivity of Γ LHCP,CyGNSS to SMC was analyzed over these selected target areas (Figure 6a-f).In so doing, the selected θ e ranges corresponded to those with the maximum Pearson correlation coefficient between Γ LHCP,CyGNSS and SMC (Table 2).Figure 6a,c,e shows the scatter plots of Γ LHCP,CyGNSS and SMC as a function of different h levels.Land cover-types over Pampas and India were croplands with moderate mean roughness: h Pampas ≈ 0.1 (Figure 6b) and h India ≈ 0.11 (Figure 6d).The mean roughness over Sudan was higher: h Sudan ≈ 0.15 (Figure 6f).The slopes of the linear regressions were ≈26 dB/(m 3 /m 3 ), ≈37 dB/(m 3 /m 3 ), and ≈50 dB/(m 3 /m 3 ) respectively over the target areas, while the RMSE was ≈2.5 dB, ≈3 dB and ≈3.3 dB.In Sudan there was a smaller SMC variability and a significant dynamic range (Figure 6e).This explained the higher slope of the fit.On the other hand, the higher roughness h explained the higher RMSE and SD (Table 4).Overall, a good sensitivity of Γ LHCP,CyGNSS to SMC was found over the three selected target areas.Figure 6b,d,f is useful to further understand the impact of h on the sensitivity to SMC [Pampas (Figure 6a), India (Figure 6c), and Sudan (Figure 6e)].Γ LHCP,CyGNSS decreased with an increase in h for nearly constant levels of SMC, and at the same time this rate of change depended on the mean SMC level.For lower SMC levels, Γ LHCP,CyGNSS decreased significantly for a high h parameter, while Γ LHCP,CyGNSS appeared to be roughly independent of h for higher levels of SMC.useful to further understand the impact of h on the sensitivity to SMC [Pampas (Figure 6a), India (Figure 6c), and Sudan (Figure 6e)].LHCP,CyGNSS Γ decreased with an increase in h for nearly constant levels of SMC, and at the same time this rate of change depended on the mean SMC level.For lower SMC levels, LHCP,CyGNSS Γ decreased significantly for a high h parameter, while LHCP,CyGNSS Γ appeared to be roughly independent of h for higher levels of SMC.  2).The robust fit regression lines are shown in green.Γ over these target areas are displayed to complement the observations on the correlation coefficients (Figure 7).The corresponding statistics are also included  The histograms of Γ LHCP,CyGNSS over these target areas are displayed to complement the observations on the correlation coefficients (Figure 7).The corresponding statistics are also included in Table 4. Significant changes on the histograms were found from θ e ≈ [20,30] • (Figure 7a,c,e) to θ e ≈ [50,60] • (Figure 7b,d,f).The lowest mean Γ LHCP,CyGNSS and the highest standard deviation (SD) of the three target areas appeared over Sudan (Table 4).In this sense, it seems reasonable that the maximum correlation in Sudan was achieved over a significantly lower θ e as compared to the Argentinian Pampas and India.A lower angular range was required to achieve a high enough signal coherence.A bimodal distribution (Figure 7f) was found over Sudan at θ e ≈ [50,60] • , which was an additional factor that justified the lower angular variability over this particular target area (Table 2).The impact of a lower θ e was quite evident in Figure 7e where the Γ LHCP,CyGNSS distribution turned into a unimodal one with a kurtosis ≈2.5, which tended to be like a Gaussian one.This indicated the presence of a coherent component in the total scattered electromagnetic field [15], and thus it is reasonable that the maximum correlation also appeared at this angular range.Over the Argentinian Pampas, the mean Γ LHCP,CyGNSS was higher than over India, and thus the maximum correlation appeared over a slightly higher θ e .For very low θ e ≈ [20,30] • , the Pearson coefficients tended to decreases in all the selected target areas (Table 2), and this could be attributed to the lower Γ LHCP,CyGNSS dynamic range over this angular range.
Γ LHCP,CyGNSS , SMC, and h were geolocated over the specific target areas (Figure 8a-i) to further understand the effects of h on SMC estimation using GNSS-R.The averaged Γ LHCP,CyGNSS over Argentinian Pampas is shown in Figure 8a.The spatial pattern was clearly correlated with that of the SMAP-derived SMC (Figure 8b), which appeared to be the most important parameter.However, the impact of h was also relevant, especially on the upper-right side of Figure 8a-c.In this area, there was a sudden drop of h that enabled an increment of Γ LHCP,CyGNSS for nearly constant values of SMC.The spatial variability of Γ LHCP,CyGNSS was higher than radiometer data because of the higher resolution of GNSS-R, which was associated with the size of first Fresnel zone.
The target area over India was selected because this was a relatively dry region with some SMC peaks, so as to complement the information obtained from the wet Argentinian Pampas.Γ LHCP,CyGNSS increased due to a positive gradient on SMC.This effect was lower than over the Argentinian Pampas because of the reduced roughness range h < 0.13 as compared to that over the Argentinian Pampas h< 0.16.This result agrees with the conclusions derived from Figure 6b,d,f, where the effect of surface roughness was shown to be more significant for h > 0.13.
Finally, the averaged Γ LHCP,CyGNSS over Sudan showed two clearly differentiated spatial patterns that corresponded to SMC levels from moderate (0.2 < SMC < 0.3) to very high (0.4 < SMC < 0.5).The down-left side highlights the effects of h on Γ LHCP,CyGNSS over an area with moderate SMC.Here, the surface roughness was also high h > 0.13, and thus Γ LHCP,CyGNSS holds quite low ≈ −20 dB despite the increment on SMC from ≈0.

Final Discussions
Γ LHCP,CyGNSS and the sensitivity of Γ LHCP,CyGNSS to SMC appeared to have a dependence with θ e through h since the effective surface roughness was an important parameter that determined the amount of reflected power.The use of the polarimetric ratio (ratio of the reflected signals' power at two different polarizations) could provide a significant correction of h in SMC estimation, and potentially this technique could also be used in future missions, especially if daily/hourly SMC monitoring is required.On the other hand, further research is required in single-polarization missions.Multi-temporal techniques are based on change detection, under the assumption that surface roughness does not change over consecutive overpasses and thus the variability on the radar coefficient is due to SMC.However, this is partially realistic because [55]: (a) isolating SMC changes from other factors such as VWC would be difficult, and (b) the actual surface roughness has a dependence with SMC.Some different retrieval algorithms of SMC and surface roughness h are based on multi-angular information.This approach could be useful in the case of CyGNSS eight-microsatellite constellation mission.Results from this study show that GNSS-R had an optimum sensitivity to SMC at different θ e , depending on the roughness levels.As such, this relationship could be used to select the most appropriate angular range in SMC determination.On the other hand, this property can be exploited to mitigate roughness effects at an improved temporal resolution as compared to multi-temporal techniques.Additionally, the experimental results show that the coherently scattered electromagnetic field was higher than theoretical predictions.This is an important finding, which paves the way for SMC retrieval from nanosatellites because the coherent component was roughly independent of the platform's height.Thus, relatively small antennas can be sufficient to obtain accurate measurements.

Conclusions
The impact of θ e on CyGNSS GNSS-R bistatic reflectivity Γ LHCP,CyGNSS was assessed over the Earth's surface with a focus on land as a function of soil moisture content (SMC) and effective surface roughness parameter h.Global scale results show that Γ LHCP,CyGNSS decreased with decreasing θ e down to ≈55 • because of the effect of the incoherent scattering term σ 0 LHCP,incoh .On the other hand, it increased for lower θ e .This could be explained because of a higher signal coherence that increased the coherent scattering term σ 0 LHCP,coh in regions without a rough topography.This functional relationship depended on SMC and h.Also at a global scale, it appeared that the dynamic range of Γ LHCP,CyGNSS at a fixed θ e was higher as h decreased.The sensitivity of Γ LHCP,CyGNSS to SMC was then studied as a function of these two parameters for different sparsely vegetated target areas.The optimum Pearson correlation coefficients were found to be r Pampas ≈ 0.78 at θ e ≈ [60,70] • , r India ≈ 0.72 at θ e ≈ [50,60] • , and r Sudan ≈ 0.74 at θ e ≈ [30,40] • , for different mean levels of roughness h Pampas ≈ 0.1, h India ≈ 0.11, and h Sudan ≈ 0.15.At these angular ranges, the slopes of the linear regressions over these target areas were ≈26 dB/(m 3 /m 3 ), ≈37 dB/(m 3 /m 3 ), and ≈50 dB/(m 3 /m 3 ), respectively.The empirically-derived impact of θ e on the relationship of Γ LHCP,CyGNSS with SMC and h could provide useful information in the development of first order corrections of surface roughness.As a final remark, a better sensitivity of GNSS-R to SMC appeared over croplands when the coherent scattering term σ 0 LHCP,coh became dominant over the incoherent one σ 0 LHCP,incoh .Therefore, SMC retrieval using GNSS-R could benefit on the higher spatial resolution of the coherent scattering regime, limited by the first Fresnel zone.CyGNSS is a good example of how a constellation of small satellites could provide complementary information to a classical satellite such as SMAP, with a higher spatiotemporal sampling in the latitudinal band ≈ [-40,40] • .The revolution of small satellites, such as CubeSats, allowing for the provision of scientifically valuable data has just started.Future research on deployable antennas would provide a chance to elucidate whether such low-cost, small-size satellites could provide an accuracy on the same order than a classical satellite.On the other hand, passive microwave Earth observation techniques (e.g., microwave radiometry, GNSS-R) fit quite well on a single CubeSat [56], enabling the use of low power-consumption instruments that pave the way to improve the operational duty-cycle.As a matter of fact, the spatial resolution of GNSS-R is ≈1 km under the coherent scattering regime.This can clearly improve the resolution of microwave radiometry (SMAP) ≈40 km.

Figure 1
shows the theoretical relationship (Equation (4)) between LHCP,coh Γ and e θ for different levels of SMC.The Wang's model [44] is used to relate the SMC with the dielectric constant of the soil, assuming a soil composition of 50% clay and 20% sand.It appears LHCP,coh Γ increases for lower e θ and it decreases for higher RMS σ .On the other hand, the influence of e θ is higher as RMS σ increases.It could be expected that the coherently reflected power as collected from a spaceborne platform increases at grazing angles because it is roughly independent of the platform's height ( T R >> R R ).

:
The calibrated reflected and direct DDMs are used to estimate the power waveform peaks r,Peak,LHCP Y and d,Peak,RHCP Y
determination and control system (ADCS) and in the estimation of the reflected r,Peak,LHCP Y and direct d,Peak,RHCP Y power waveforms peaks.
θ ≈ [70,90]° to e θ ≈ [20,40]°: .1 dB.These experimental results can be explained because of the strong impact of e θ on LHCP,coh Γ .The coherent scattering was very high for grazing angle, because the effective surface roughness was low [51].As such, the reflectivity was much higher at e θ ≈ [20,40]° than at e θ ≈ [70,90]°.On the other hand, LHCP,CyGNSS Γ decreased from e θ ≈ [70,90]° to e θ ≈ [45,65]° because the incoherent scattering is dominant over the coherent one in this angular range: .3dB.The incoherent or diffuse scattering was lower with decreasing e θ because this term is generated by the effective surface roughness, which in turn decreased for lower e θ .This point explains the evolution of LHCP,CyGNSS Γ along this angular range.

Figure 3 .
Figure 3. Close-up of one-month (from 20 September to 20 October 2017) averaged CyGNSS bistatic reflectivity Γ LHCP,CyGNSS for a grazing angle geometry with 20 • < θ e < 40 • , over differentiated target areas over land: (a) croplands, and (b) Amazonian rainforests.At this geometry, the major axes of the Fresnel zone is ≈1.6 km.
θ ≈ 85° to e θ ≈ 55°, and it increased from e θ ≈ 55° to e θ ≈ 25°.LHCP,CyGNSS Γ included contributions from both coherent and incoherent scattering regimes in both angular ranges.The main difference between both scattering regimes was on the combination of the electromagnetic field vectors. 0LHCP,coh σ came from the coherent combination of the signals scattered on the individual facets within the first Fresnel zone. 0LHCP,incoh σ was the result of the random combination of electromagnetic waves coming from other scatterers within the glistening zone that added together at the receiving antenna.If the combination was totally coherent, LHCP,coh Γ accounted for all the reflected power.In the case of diffuse scattering, the random signs of the electric field crossproducts cancelled out 0 LHCP,coh σ , and the reflected power was given by 0 LHCP,incoh σ .The changes on the angular evolution of LHCP,CyGNSS Γ depended on the dominant scattering mechanism.In the interpretation of Figure 5 it should be considered that the averaging of the reflectivity was performed over the complete land-surface coverage enabled by CyGNSS, including bare soil, deserts, rough topography areas, and highly vegetated areas such as rainforests.As such, these results provide the average response of LHCP,CyGNSS Γ as a function of e θ .

Figure 6 .
Figure 6.Scatter plots over specific target areas [(a,b) Argentinian Pampas, (c,d) India, and (e,f) Sudan] of (a,c,e) the CyGNSS reflectivity LHCP,CyGNSS Γ vs soil moisture content (SMC) as a function of surface roughness parameter h and (b,d,f) the CyGNSS reflectivity LHCP,CyGNSS Γ vs surface roughness parameter h as a function of SMC.The selected elevation angles e θ ranges corresponded to the maximum Pearson correlation coefficient between LHCP,CyGNSS Γ and SMC (Table

Figure 6 .Figure 7 .
Figure 6.Scatter plots over specific target areas [(a,b) Argentinian Pampas, (c,d) India, and (e,f) Sudan] of (a,c,e) the CyGNSS reflectivity Γ LHCP,CyGNSS vs soil moisture content (SMC) as a function of surface roughness parameter h and (b,d,f) the CyGNSS reflectivity Γ LHCP,CyGNSS vs. surface roughness parameter h as a function of SMC.The selected elevation angles θ e ranges corresponded to the maximum Pearson correlation coefficient between Γ LHCP,CyGNSS and SMC (Table2).The robust fit regression lines are shown in green.

Table 2 .
Pearson correlation coefficients of CyGNSS reflectivity Γ LHCP,CyGNSS and SMAP-derived soil moisture content (SMC) for different elevation angles θ e , over specific target areas: Argentinian Pampas, India, and Sudan.

Table 3 .
Size of the semi-major and semi-minor axis of the first Fresnel zone for the CyGNSS scenario, as a function of the elevation angle θ e .