A Simulation Study of GNSS-R Polarimetric Scattering from...

Research ArticleA Simulation Study of GNSS-R Polarimetric Scattering from theBare Soil Surface Based on the AIEM

Xuerui Wu 123 and Shuanggen Jin123

1Shanghai Astronomical Observatory Chinese Academy of Sciences Shanghai 200030 China2Key Laboratory of Space Navigation and Position Technology Shanghai 200030 China3School of Remote Sensing and Geomatics Engineering Nanjing University of Information Science and TechnologyNanjing 210044 China

Correspondence should be addressed to Xuerui Wu xrwushaoaccn

Received 29 November 2018 Revised 20 March 2019 Accepted 7 April 2019 Published 8 May 2019

Academic Editor Anthony R Lupo

Copyright copy 2019 Xuerui Wu and Shuanggen Jin is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

In the past two decades global navigation satellite system-reflectometry (GNSS-R) has emerged as a new remote sensing techniquefor soil moisture monitoring Some experiments showed that the antenna of V polarization is more favorable to receive thereflected signals and the interference pattern technique (IPT) was used for soil moisture and retrieval of other geophysicalparameters Meanwhile the lower satellite elevation angles are most impacted by the multipath However electromagnetictheoretical properties are not clear for GNSS-R soil moisture retrieval In this paper the advanced integral equationmodel (AIEM)is employed using the wave-synthesis technique to simulate different polarimetric scatterings in the specular directions Resultsshow when the incident angles are larger than 70deg scattering at RR polarization (the transmitted signal is right-hand circularpolarization (RHCP) while the received one is also RHCP) is larger than that at LR polarization (the transmitted signal is RHCPwhile the received one is left-hand circular polarization (LHCP)) while scattering at LR polarization is larger than that at RRpolarization for the other incident angles (1degsim70deg) ere is an apparent dip for VV and VR scatterings due to the Brewster anglewhich will result in the notch in the final receiving power and this phenomenon can be used for soil moisture retrieval orvegetation corrections e volumetric soil moisture (vms) effects on their scattering are also presented e larger soil moisturewill result in lower scattering at RR polarization and this is very different from the scattering of the other polarizations It isinteresting to note that the surface correlation function only affects the amplitudes of the scattering coefficients at much less levelbut it has no effects on the angular trends of RR and LR polarizations

1 Introduction

Soil moisture is the link between surface water andgroundwater which plays an important role in terrestrialecosystems and water cycle systems As one of the de-terminants in the status of the terrestrial hydrosphere soilmoisture largely controls the evapotranspiration watermigration and carbon cycle on the land surface Soilmoisture is also important for understanding and fore-casting climate change solving global water cycle waterresources management and basin hydrological modelingMeanwhile it is also one of the necessary conditions formonitoring crop growth droughts and floods

Soil moisture has strong spatial and temporal variationheterogeneity e traditional ground and meteorologicalmonitoring is difficult to meet the requirements e de-velopment of satellite remote sensing technology provides anew method for monitoring In the past two decades GNSS-R has emerged as a new promising remote sensing techniquedue to its unique advantages [1] Its applications extend frommesoscale ocean remote sensing to the remote sensing ofsnow ice and land surface parameters [2ndash4] As for the landscenario the most important application is soil moisturemonitoring GNSS-R is an effective complement to existingradars and radiometers and can be a potential efficienttechnique for the validation of the L-band soil moisture

HindawiAdvances in MeteorologyVolume 2019 Article ID 3647473 9 pageshttpsdoiorg10115520193647473

satellites such as SMOS (soil moisture satellite) [5] andSMAP (soil moisture active passive) mission [6] Howeveras an emerging means of earth observation there are manyopen problems that need to be solved such as the polari-zation properties of the reflected signals

Polarization is one of the most important properties ofthe electromagnetic waves e polarization of a planewave describes the shape and direction of the space tra-jectory formed by the end of the electric field vector as afunction of time However different from the traditionallinear polarizations of the microwave remote sensing thetransmitted polarization of GNSS (global navigation sat-ellite system) is RHCP (right-hand circular polarization)When the GNSS signals reflect from the surface theirpolarizations will change Kavak et al [7] pointed out thatthe reflected signals consisted of two parts the circularpolarization and the perpendicular polarization which aredependent on the elevation angles Several experimentshave paid attention to the polarization study of GNSSreflected signals In [7] the modified GPS receiver wasused and a horizontal-positioned antenna of LHCP (left-hand circular polarization) was used to collect the coherentenergy of the direct signals and the reflected signals In theSMEX 0203 (soil moisture experiment 20022003) [8] theantennas of the global position system-reflectometry (GPS-R) receiver were different An airborne GPS-R receiverknown as DMR (delay-Doppler maps receiver) was usedwith two antennase standard zenith RHCP antenna wasused to collect the direct signal and the nadir LHCPantenna was used for the collection of the surface-reflectedsignals Meanwhile the incident angles were from 15deg to35deg [4]

As early as in 2000 Zavorotny and Voronovich haveused the GO (geophysical optics) scattering model [2] tostudy the reflection polarizations of soil moisture [9] eysimulated the sensitivity of polarization ratios (LRRR andHRVR) to the soil moisture at larger incident angles (60degand 70deg) and concluded theoretically that the polarizationratios can be used for soil moisture measurement Here LR RR HR and VR present the polarization of transmittedsignal as RHCP while the received polarizations are LHCPRHCP horizontal (H) and vertical (V) respectively In theBAO-tower (Boulder Atmospheric Observatory-tower) ex-periment [10] a multipolarization receiver provided by theNASA Langley Research Center was used In order to collectthe surface reflected signals a low-gain LHCP and four high-gain antennas (V and H polarizations LHCP and RHCP)were used e incidence angle was 35deg and the incidentazimuthal angle was 245deg However the BAO-tower ex-periment did not support their original theoretical hy-pothesis [9]

At present the interference pattern technique (IPT)was used for soil moisture and vegetation retrieval [11] Anantenna of V polarization was employed since the angularinformation would be masked due to Brewsterrsquos angle if anantenna of LHCP was used [12] LEiMON (Land Moni-toring with Navigation Signals) was a long-term GNSS-Rexperimental campaign which was funded by the Euro-pean Space Agency (ESA) e experiment was conducted

in 2009 using a SAM sensor antenna of RHCP was used tocollect the direct signals and antenna of RHCP or LHCPwas used to collect the reflected signals e elevationangles were from 40deg to 80deg However their theoretical andexperimental results indicated that the reflectivity of bothRR and LR was increasing with the increase of the in-cidence angle (0sim80deg) which was very different from thecommonly used Fresnel theory of circular polarization inthe GNSS-R study [2 4] Different from the speciallydesigned GNSS-R receiver the multipath information ofthe geodetic-quality GPS receivers could be used to re-motely sense the soil moisture in the top 5 cm of soil[13ndash15] e in situ measurements showed that the ele-vation angels with 5degsim30deg were most impacted by themultipath [13ndash15]

In general most of the GNSS-R soil moisture monitoringis based on the experimental study [4 8 10 11 13ndash15] esimple combination of geometry is commonly used toproceed from linear polarization to circular polarization[2 4 13ndash15] RR polarization reflection increases with theincidence angle increase while LR reflection decreases etrend is very different from the LEiMON experimental re-port It should be highlighted that only the amplitudechanges are considered [2 4 13ndash15] while phase differencesare not considered as calculations from linear to circular[16] However with the development of GNSS-R moreattention should be paid to theoretical models since they canassist in the data interpretation sensitivity analysis exper-iment design and others [17] In this paper we focus on thepolarization (especially circular polarization) dependence ofbare soil scattering using an AIEM [18 19] wave-synthesistechnique is used for arbitrary polarizations calculation inSection 2 Reflectivity of XR polarization and linear polar-izations versus incident angles is presented in Section 3 XRpolarization means that the transmitted signal is RHCP andany polarization that is circularly polarized (RHCP andLHCP) or linearly polarized (V vertical or H horizontal) isreceived From the Mueller matrix the effects of volumetricsoil moisture and surface roughness for different polariza-tions are evaluated in Section 4 Finally a conclusion is givenin Section 5

2 AIEM

To overcome the ionospheric effects the transmitted signalsare RHCP while the polarizations of the transmitted signalschanged after reflected from the soil surface As shown inSection 1 since the polarizations of the reflected signals aredifferent the linear (vertical and horizontal) and circular(RHCP and LHCP) antennas are used to receive the reflectedsignals erefore different combinations of polarizationsneed further study in theory In this section the commonlyused random rough-surface bistatic scattering model ofAIEM has been employed By using the method of wave-synthesis technique the model can calculate the bistaticscattering coefficient of arbitrary polarization combination(both linear and circular) In this way the developed bistaticscattering model can be used to study the full polarizationcharacteristics of soil moisture

2 Advances in Meteorology

e traditional electromagnetic scattering models fromrandom rough surfaces [17] are the Kirchhoff model (KA)and the small perturbation model (SPM) e former issuitable for surfaces with small curvatures or high frequencylimit while the latter is applicable to slightly rough surfacesor low frequency e popular integral equation model(IEM) is developed to bridge the gap between the SPM andKA However its several assumptions limit the accuracyespecially for bistatic scattering e subsequently developedAIEM is an improvement of the IEM [18 20] Here we focuson the polarization study using the developed surfacescattering model for GNSS-R applications It is pointed outthat the received power is mainly coming from the first

Fresnel zone [21] and therefore only the coherent scatteringis considered in our scattering properties study

e bistatic scattering coefficient is related to themodified Mueller matrix asfollows [17]

σdegqp 4πA

M q p h v (1)

where σdegqp is the bistatic scattering coefficient subscripts q

and p are the polarizations of the received and transmittedsignals respectively A is the illuminated area and themodified Mueller matrix M can be written in terms of theelements of the scattering matrix S

M

lang Svv

111386811138681113868111386811138681113868111386811138682rang lang Svh

111386811138681113868111386811138681113868111386811138682rang RelangSvvSlowastvhrang minusImlangSvvSlowastvhrang

lang Shv

111386811138681113868111386811138681113868111386811138682rang lang Shh

111386811138681113868111386811138681113868111386811138682rang RelangShvSlowasthhrang minusImlangShvSlowasthhrang

2RelangSvvSlowasthvrang 2RelangSvhSlowasthhrang RelangSvvSlowasthh + SvhSlowasthvrang ImlangSvhSlowasthv minus SvvSlowasthhrang

2ImlangSvvSlowasthvrang 2ImlangSvhSlowasthhrang ImlangSvvSlowasthh + SvhSlowasthvrang RelangSvvSlowasthh minus SvhSlowasthvrang

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(2)

For more information of the AIEM model see reference[20]

According to wave-synthesis technique [22] the scat-tering coefficient for a general transmitted and receivedantenna polarization can be written as

σdegqp ψq τqψq τq1113872 1113873 4πA

Iq middot Q middot M middot Ip1113872 1113873 (3)

where subscripts q and p are the polarizations of the receivedand transmitted signals respectively I is the normalizedStokes vectors with unit amplitude and Q is a rotatingmatrix e normalized Stokes vectors can be expressed interms of the ellipticity angle χ and orientation angle ψ

Iq

05 1 + cos 2τq cos 2ψq1113872 1113873

05 1minus cos 2τq cos 2ψq1113872 1113873

cos 2τq sin 2ψq

sin 2τq

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Ip

05 1 + cos 2τp cos 2ψp1113872 1113873

05 1minus cos 2τp cos 2ψp1113872 1113873

cos 2τp sin 2ψp

sin 2τp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)

e first element of I describes the intensity of theelectromagnetic wave in the horizontal direction and thevertical direction the second one is the intensity differencebetween the horizontal and vertical directions of the wavevector the third one is the linear polarization intensity at theazimuth angle of plusmn45deg in the polarization ellipse and thefourth one indicates the degree of circular polarization Inthis way the phase information in scattering matrix S can becalculated through I

For like polarization τq τp and ψq ψp + π and for across polarization ψq ψp minus π2 and τq minusτp Any polar-izations of transmitted and received signals can be obtainedby setting the ellipticity χ and orientation angle ψ ac-cordingly For GNSS-R it is necessary to study the scatteringcharacteristics of σdegXR Subscript XR polarization means thatthe transmitted signal is RHCP and any polarization that iscircularly polarized (RHCP and LHCP) or linearly polarized(V vertical or H horizontal) is received

3 Reflectivity of Different Polarizations versusIncident Angles

When a plane wave is transmitted through a plane boundaryamong the nondestructive media there is an angle at whichthe vertical polarization broadcasts a full projection whichbecomes the Brewster angle e IPT method expressed inSection 1 uses the position and number information of thenotches in the direct signal and the reflected signals co-herent waveform to perform the geophysical parameterretrieval In fact the notch in the waveform is the result ofthe Brewster angle Due to its particularity Brewsterrsquos angleis a phenomenon that needs attention as for GNSS-R remotesensing inversion Table 1 presents the corresponding di-electric constants and the Brewster angles for different soilmoistures e vms is a way of expressing soil moisture thatis the percentage of soil moisture volume is kind ofrepresentation can reflect the degree of water filling of soilvoids and can calculate the three ratios of soil solid liquidand gas Figure 1 shows the Fresnel reflectivity of rv and rh

polarization for different vms here r means Fresnelreflectivity while subscripts v and h mean the polarizationstate v stands for vertical polarization and h stands forhorizontal e corresponding Brewster angles in Table 1 areapparent at V polarization (left panel) As we can see if the

Advances in Meteorology 3

vms is certain the rv decreases with the incidence angleincrease (before the Brewster angle) and the rv increasesafter the Brewster angle As for the different vms the rv islarger if the vms is larger (before 59deg) but the rv is smaller ifthe vms is larger (after 82deg) However the rh is larger if thevms is larger

e real parts of the rv and rh (Re[rv] Re[rh]) play animportant role in the calculations of XR and linear polar-ization scattering coefficients So their changes with theincident angles are presented in Figure 2 Before hitting theBrewster angle the Re[rv] is positive while it becomesnegative if the incident angle is lower than the Brewster angleand the Re[rv] increases with the incident angles increaseWhile Re[rh] is negative for the whole angles with Re[rh]

decrease as vms increasesFigure 3 is reproduced from [23] and it shows the

scattering coefficients of linear polarization and XR po-larization versus the incident angles As we can see forsmaller incident angles (1deg lt θ lt 70deg) the scattering of LRpolarization is larger than that of RR polarization(RR lt LR) Here LR and RR polarizations mean thetransmitted signals are RHCP while the received ones areLHCP and RHCP respectively However for larger in-cident angles (70deg lt θlt 85deg) the trend is just opposite thatis to say the scattering coefficients of RR polarization are

larger than the ones of LR polarization e scatteringcoefficients of RR polarization is larger than that of VRpolarization for larger incident angles (70deg lt θlt 85deg) hereVR polarization means the transmitted signal is RHCPwhile the received one is vertical polarization e scat-tering coefficients of RR polarization increase as the in-cident angles increase (1deg lt θ lt 55deg) but for the otherincident angles the scattering coefficient of RR polariza-tion decreases However the scattering coefficients of LRpolarization decrease as the incident angle increases etrends of scattering coefficient of VV VR HH and HRversus incident angles are the same Here VR and HRmeans the transmitted signals are RHCP while the re-ceived signals are vertical and horizontal polarizationsrespectively VV and HH mean the same polarization ofvertical and horizontal respectivelye reason is that theyare only related to M(1 1) and M(2 2) respectively(equations (2) and (5)) As the incident angles increase thescattering coefficients of HH and HR polarizations de-crease Scattering coefficients of VV and VR polarizationshave dips at about 70deg because of the Brewster angle de-fined in equation (8) [17] the scattering coefficients de-crease at first (before the Brewster angle) and then increasewith the incidence angle increase (after the Brewsterangle)

55 60 65 70 75 80 85ndash25

ndash20

ndash15

ndash10

ndash5

0

Incident angle (degree)

r v

vms = 001vms = 005vms = 025

vms = 045vms = 060

(a)

55 60 65 70 75 80 85ndash4

ndash35

ndash3

ndash25

ndash2

ndash15

ndash1

ndash05

0


r h

vms = 001vms = 005vms = 025

vms = 045vms = 060

(b)

Figure 1 Fresnel reflectivity vs incident angles (a) rv (b) rh

Table 1 Dielectric constants and the Brewster angles for different vms

vms Dielectric constant Brewster angle001 2814ndash0127i 592005 3965ndash0241i 6333025 13175ndash1021i 74597045 2699ndash219i 791046060 40ndash33i 81015


4 Effects of Volumetric Soil Moisture andSurface Roughness on Polarizations

41 Effects of Volumetric Soil Moisture on PolarizationsFigure 4 gives the linear and circular polarization scatteringcoefficients at different soil moisture (vms) versus the in-cident angles e scattering trends of HR polarization arevery similar to that of HH polarization while VR polari-zation is very similar to VV polarization as shown in Fig-ure 1 e dips at VV and VR polarization are related to thevms and this is due to the Brewster angles (Table 1) If thevms is larger the position of dip is at the position of largerincident angle It should be noted that the scattering co-efficients of RR polarization are larger if the vms is smallerFor the other polarizations (LR HR and HH) larger vmscorresponds to larger scattering coefficients But for VV and

VR polarizations if the vms is larger the scattering co-efficients are larger if the incident angles are lower than theBrewster angles While if the incident angles are larger thanthe Brewster angles the lower vms corresponds to largerscattering coefficients

42 Effects of Surface Roughness on Different PolarizationsSince the soil moisture affects the GNSS reflection signal thegeometric characteristics of the soil that is the surfaceroughness will also affect the GNSS reflection signalerefore in the soil moisture inversion how to remove thesurface roughness is a difficult problem e surfaceroughness can be represented by two parameters the rootmean square height (s) and the surface correlation length (l)which respectively define the surface roughness from thevertical and horizontal scales Another way to describe thedegree of random surface roughness is the surface auto-correlation function which can be described by a Gaussianautocorrelation function or an exponential autocorrelationfunction

In this section surface roughness effects on the finalscattering at RR and LR polarizations are presented Figure 5shows the roughness effects on different correlation func-tions As we can see if root square height (s) is fixed largercorrelation length (l) corresponds to larger scattering co-efficients (both RR and LR) if l is fixed larger s correspondsto larger scattering coefficients (both RR and LR) k is thewave number

e scattering of exponential correlation function islarger than the one of Gaussian function (both RR and LR)(Figure 6) It is interesting to note that unlike in back-scattering direction the surface correlation function onlyaffects the amplitudes of the scattering coefficients while theangular trend is at much less level

0 10 20 30 40 50 60 70 80 90

ndash50

ndash40

ndash30

ndash20

ndash10

0

Incident angles (degree) ϕs = 0deg

Scat

terin

g co

effic

ient

s (dB

)

RRLRHR

VRHHVV

Figure 3 Scattering coefficients of linear polarization and RXpolarization vs incident angles (vms 015)

55 60 65 70 75 80 85ndash08

ndash06

ndash04

ndash02

0

02

04

06


Re (r

v)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(a)

55 60 65 70 75 80 85ndash1

ndash09

ndash08

ndash07

ndash06

ndash05


Re (r

h)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(b)

Figure 2 Real parts of the Fresnel reflectivity vs the incident angles (a) Re[rv] (b) Re[rh]


60 70 80 90ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5


AIEM rms = 045cm cl = 1875cm Gaussian

RR sc

atte

ring

coef

ficie

nts (

dB)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(a)

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10


LR sc

atte

ring

coef

ficie

nts (

dB)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(b)


Incident angles (degree) ϕs = 0deg60 70 80 90

ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

HR

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(c)


ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

VR

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(d)

Figure 4 Continued


5 Conclusions

As for GNSS-R remote sensing the polarization of trans-mitted signals is RHCP which is commonly thought that thereceived power is coming from the first Fresnel zone Herethe coherent scattering of different polarizations is simulatedby the modified AIEM using the wave-synthesis techniqueResults show that the scattering at RR polarization is lowerthan that at LR polarization as for incident angles lower than

70deg when the incident angles are between 70deg and 80deg thescattering at LR polarization is larger than that at RR po-larization As for larger incident angles there are dips at VVand VR polarizations due to the Brewster angles which arerelated to the soil moisture erefore the antenna of Vpolarization is suggested to be used because the informationof dips caused by the Brewster angle at different soilmoistures is useful for soil moisture monitoring and thescattering dynamic ranges of VR polarization are larger than



ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

HH

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(e)


vms = 001vms = 005vms = 025

vms = 045vms = 060

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

VV

scat

terin

g co

effic

ient

s (dB

)(f )

Figure 4 Scattering coefficients of different vms vs the incident angles

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

θdeg (θs = θi ϕs = 0deg)

AIEM rms = 045cm cl = 1875cm vms = 015

σ RR

(dB)

ks = 02 kl = 2ks = 02 kl = 4ks = 04 kl = 4

(a)


σ LR

(dB)

ks = 02 kl = 2ks = 02 kl = 4ks = 04 kl = 4

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

(b)

Figure 5 Surface roughness effects on the RR and LR scattering


those of the other polarizations Meanwhile VR polarizationwill provide efficient information for vegetation correctionsIt should be noted that larger soil moisture corresponds tolower scattering at RR polarization while the trend is just theopposite as for the other XR (LR HR VR HH and VV)polarizations Meanwhile it is interesting to note that unlikein backscattering direction the surface correlation functiononly affects the amplitudes of the scattering coefficients but ithas no effects on the angular trend

Abbreviations

AIEM Advanced integral equation modelDDM Delay-Doppler mapsDMR Delay Doppler maps receiverGNSS Global navigation satellite SystemGNSS-R GNSS-reflectometryGO Geophysical optics modelGPS Global positioning systemHR VR +45R andminus45R polarizations

e polarization of the transmittedsignals is RHCP with the receivedonesH (horizontal) V (vertical) +45(+45deg linear) and minus45 (minus45deg linear)polarizations respectively

IEM Integral equation modelIPT Interference pattern techniqueKA Kirchhoff modelLEiMON Land Monitoring with Navigation

SignalsLHCP Left-hand circular polarizationLR e polarization of the transmitted

signal is RHCP while the receivedone is LHCP

RHCP Right-hand circular polarization

RR e polarization of the transmittedsignal is RHCP while the receivedone is also RHCP

SMAP Soil moisture active passiveSMEX Soil moisture experimentsSMIGOL Soil moisture interference pattern

GNSS observations at L-bandreflectometer

SMOS Soil moisture and ocean salinitymission

SPM Small perturbation modelZ-V model ZavorotnyndashVoronovich model

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was supported by the National Natural ScienceFoundation of China (NSFC) Project (Grant no 41501384)and the Strategic Priority Research Program Project of theChinese Academy of Sciences (Grant no XDA23040100)

References

[1] S Jin and A Komjathy ldquoGNSS reflectometry and remotesensing new objectives and resultsrdquo Advances in Space Re-search vol 46 no 2 pp 111ndash117 2010

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

RR sc

atte

ring

coef

ficie

nts (

dB)

GaussianExponential



(a)

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0


LR sc

atte

ring

coef

ficie

nts (

dB)

GaussianExponential

(b)

Figure 6 Correlation functions on the RR and LR scattering


[2] V U Zavorotny and A G Voronovich ldquoScattering of GPSsignals from the ocean with wind remote sensing applicationrdquoIEEE Transactions on Geoscience and Remote Sensing vol 38no 2 pp 951ndash964 2000

[3] E Cardellach F Fabra A Rius S Pettinato and S DrsquoAddioldquoCharacterization of dry-snowsub-structure using GNSS re-flected signalsrdquo Remote Sensing of Environment vol 124pp 122ndash134 2012

[4] D Masters P Axelrad and S Katzberg ldquoInitial results ofland-reflected GPS bistatic radar measurements in SMEX02rdquoRemote Sensing of Environment vol 92 no 4 pp 507ndash5202004

[5] M Berger A Camps J Font et al ldquoMeasuring ocean salinitywith ESArsquos SMOS missionrdquo ESA Bulletin Journal vol 111no 113 pp 113ndash121 2002

[6] D Entekhabi E Njoku P OrsquoNeill et al ldquoe soil moistureactive passive (SMAP) missionrdquo Proceedings of the IEEEvol 98 no 5 pp 704ndash716 2010

[7] A Kavak G Xu and W J Vogel ldquoGPS multipath fademeasurements to determine L-band ground reflectivitypropertiesrdquo in Proceedings of the 20th NASA PropagationExperimenters Meeting Fairbanks AK USA 1996

[8] D Masters SMEX02 Airborne GPS Bistatic Radar Data IowaUniversity of Colorado Colorado Center for AstrodynamicsResearch Boulder CO USA 2005

[9] V U Zavorotny and A G Voronovich ldquoBistatic GPS signalreflections at various polarizations from rough land surfacewith moisture contentrdquo in Proceedings of the IEEE In-ternational Geoscience Remote Sensing Symposium vol 7pp 2852ndash2854 Honolulu HI USA July 2000

[10] V Zavorotny D Masters A Gasiewski et al ldquoSeasonalpolarimetric measurements of soil moisture using tower-based gps bistatic radarrdquo in Proceedings of the 2003 IEEEInternational Geoscience and Remote Sensing Symposium(IGARSSrsquo03) vol 2 pp 781ndash783 Toulouse France July 2003

[11] N Rodriguez-Alvarez A Camps M Vall-llosera et al ldquoLandgeophysical parameters retrieval using the interference pat-tern GNSS-R techniquerdquo IEEE Transactions on Geoscienceand Remote Sensing vol 49 no 1 pp 71ndash84 2011

[12] N Rodriguez-Alvarez X Bosch-Lluis A Camps et al ldquoSoilmoisture retrieval using GNSS-R techniques experimentalresults over a bare soil fieldrdquo IEEE Transactions on Geoscienceand Remote Sensing vol 47 no 11 pp 3616ndash3624 2009

[13] K M Larson E E Small E D Gutmann A L BilichJ J Braun and V U Zavorotny ldquoUse of GPS receivers as asoil moisture network for water cycle studiesrdquo GeophysicalResearch Letters vol 35 no 24 article L24405 2008

[14] K M Larson J J Braun E E Small V U ZavorotnyE D Gutmann and A L Bilich ldquoGPS multipath and itsrelation to near-surface soil moisture contentrdquo IEEE Journalof Selected Topics in Applied Earth Observations and RemoteSensing vol 3 no 1 pp 91ndash99 2010

[15] C C Chew E D Small K M Larson and V ZavorotnyldquoEffects of near-surface soil moisture on GPS SNR datadevelopment of a retrieval algorithm for soil moisturerdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 1pp 537ndash543 2013

[16] G Ruck D Barrick W Stuart et al Radar Cross SectionHandbook Plenum Vol 2 New York NY USA 1970

[17] A K Fung Microwave Scattering and Emission Models andAeir Applications Artech House Norwood MA USA 1994

[18] K S Chen T-D Wu L Tsang Q Li S Shi and A K FungldquoEmission of rough surfaces calculated by the integralequation method with comparison to three-dimensional

moment method simulationsrdquo IEEE Transactions on Geo-science and Remote Sensing vol 41 no 1 pp 90ndash101 2003

[19] X Wu and S Jin ldquoCharacteristics of GNSS-R bare soil basedon advanced integral equation model (AIEM) and in-terference patternsrdquo in Proceedings of the General Assembly ampScientific Symposium IEEE Beijing China August 2014

[20] T D Wu K S Chen J C Shi H W Lee and A K Fung ldquoAstudy of AIEM model for bistatic scattering from randomlysurfacesrdquo IEEE Transactions on Geoscience and RemoteSensing vol 46 no 9 pp 2584ndash2598 2008

[21] P Beckmann and A Spizzichino Ae Scattering of Electro-magnetic Waves from Rough Surfaces Artech House Nor-wood MA USA 1963

[22] F T Ulaby and C Elachi Radar Polarimetry for GeoscienceApplications Artech House Publishers Norwood MA USA1990

[23] X Wu and S Jin Sensing Bare Soil and Vegetation UsingGNSS-RmdashAeoretical Modeling Satellite PositioningMethods Models and Applications InTech-Publisher RijekaCroatia 2015


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Submit your manuscripts atwwwhindawicom

satellites such as SMOS (soil moisture satellite) [5] andSMAP (soil moisture active passive) mission [6] Howeveras an emerging means of earth observation there are manyopen problems that need to be solved such as the polari-zation properties of the reflected signals

Polarization is one of the most important properties ofthe electromagnetic waves e polarization of a planewave describes the shape and direction of the space tra-jectory formed by the end of the electric field vector as afunction of time However different from the traditionallinear polarizations of the microwave remote sensing thetransmitted polarization of GNSS (global navigation sat-ellite system) is RHCP (right-hand circular polarization)When the GNSS signals reflect from the surface theirpolarizations will change Kavak et al [7] pointed out thatthe reflected signals consisted of two parts the circularpolarization and the perpendicular polarization which aredependent on the elevation angles Several experimentshave paid attention to the polarization study of GNSSreflected signals In [7] the modified GPS receiver wasused and a horizontal-positioned antenna of LHCP (left-hand circular polarization) was used to collect the coherentenergy of the direct signals and the reflected signals In theSMEX 0203 (soil moisture experiment 20022003) [8] theantennas of the global position system-reflectometry (GPS-R) receiver were different An airborne GPS-R receiverknown as DMR (delay-Doppler maps receiver) was usedwith two antennase standard zenith RHCP antenna wasused to collect the direct signal and the nadir LHCPantenna was used for the collection of the surface-reflectedsignals Meanwhile the incident angles were from 15deg to35deg [4]

As early as in 2000 Zavorotny and Voronovich haveused the GO (geophysical optics) scattering model [2] tostudy the reflection polarizations of soil moisture [9] eysimulated the sensitivity of polarization ratios (LRRR andHRVR) to the soil moisture at larger incident angles (60degand 70deg) and concluded theoretically that the polarizationratios can be used for soil moisture measurement Here LR RR HR and VR present the polarization of transmittedsignal as RHCP while the received polarizations are LHCPRHCP horizontal (H) and vertical (V) respectively In theBAO-tower (Boulder Atmospheric Observatory-tower) ex-periment [10] a multipolarization receiver provided by theNASA Langley Research Center was used In order to collectthe surface reflected signals a low-gain LHCP and four high-gain antennas (V and H polarizations LHCP and RHCP)were used e incidence angle was 35deg and the incidentazimuthal angle was 245deg However the BAO-tower ex-periment did not support their original theoretical hy-pothesis [9]

At present the interference pattern technique (IPT)was used for soil moisture and vegetation retrieval [11] Anantenna of V polarization was employed since the angularinformation would be masked due to Brewsterrsquos angle if anantenna of LHCP was used [12] LEiMON (Land Moni-toring with Navigation Signals) was a long-term GNSS-Rexperimental campaign which was funded by the Euro-pean Space Agency (ESA) e experiment was conducted

in 2009 using a SAM sensor antenna of RHCP was used tocollect the direct signals and antenna of RHCP or LHCPwas used to collect the reflected signals e elevationangles were from 40deg to 80deg However their theoretical andexperimental results indicated that the reflectivity of bothRR and LR was increasing with the increase of the in-cidence angle (0sim80deg) which was very different from thecommonly used Fresnel theory of circular polarization inthe GNSS-R study [2 4] Different from the speciallydesigned GNSS-R receiver the multipath information ofthe geodetic-quality GPS receivers could be used to re-motely sense the soil moisture in the top 5 cm of soil[13ndash15] e in situ measurements showed that the ele-vation angels with 5degsim30deg were most impacted by themultipath [13ndash15]

In general most of the GNSS-R soil moisture monitoringis based on the experimental study [4 8 10 11 13ndash15] esimple combination of geometry is commonly used toproceed from linear polarization to circular polarization[2 4 13ndash15] RR polarization reflection increases with theincidence angle increase while LR reflection decreases etrend is very different from the LEiMON experimental re-port It should be highlighted that only the amplitudechanges are considered [2 4 13ndash15] while phase differencesare not considered as calculations from linear to circular[16] However with the development of GNSS-R moreattention should be paid to theoretical models since they canassist in the data interpretation sensitivity analysis exper-iment design and others [17] In this paper we focus on thepolarization (especially circular polarization) dependence ofbare soil scattering using an AIEM [18 19] wave-synthesistechnique is used for arbitrary polarizations calculation inSection 2 Reflectivity of XR polarization and linear polar-izations versus incident angles is presented in Section 3 XRpolarization means that the transmitted signal is RHCP andany polarization that is circularly polarized (RHCP andLHCP) or linearly polarized (V vertical or H horizontal) isreceived From the Mueller matrix the effects of volumetricsoil moisture and surface roughness for different polariza-tions are evaluated in Section 4 Finally a conclusion is givenin Section 5

2 AIEM

To overcome the ionospheric effects the transmitted signalsare RHCP while the polarizations of the transmitted signalschanged after reflected from the soil surface As shown inSection 1 since the polarizations of the reflected signals aredifferent the linear (vertical and horizontal) and circular(RHCP and LHCP) antennas are used to receive the reflectedsignals erefore different combinations of polarizationsneed further study in theory In this section the commonlyused random rough-surface bistatic scattering model ofAIEM has been employed By using the method of wave-synthesis technique the model can calculate the bistaticscattering coefficient of arbitrary polarization combination(both linear and circular) In this way the developed bistaticscattering model can be used to study the full polarizationcharacteristics of soil moisture





σdegqp 4πA

M q p h v (1)



M

lang Svv

111386811138681113868111386811138681113868111386811138682rang lang Svh


lang Shv

111386811138681113868111386811138681113868111386811138682rang lang Shh




⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(2)






Iq

05 1 + cos 2τq cos 2ψq1113872 1113873


cos 2τq sin 2ψq

sin 2τq

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Ip

05 1 + cos 2τp cos 2ψp1113872 1113873


cos 2τp sin 2ψp

sin 2τp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)












55 60 65 70 75 80 85ndash25

ndash20

ndash15

ndash10

ndash5

0


r v

vms = 001vms = 005vms = 025

vms = 045vms = 060

(a)

55 60 65 70 75 80 85ndash4

ndash35

ndash3

ndash25

ndash2

ndash15

ndash1

ndash05

0


r h

vms = 001vms = 005vms = 025

vms = 045vms = 060

(b)











0 10 20 30 40 50 60 70 80 90

ndash50

ndash40

ndash30

ndash20

ndash10

0


Scat

terin

g co

effic

ient

s (dB

)

RRLRHR

VRHHVV


55 60 65 70 75 80 85ndash08

ndash06

ndash04

ndash02

0

02

04

06


Re (r

v)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(a)

55 60 65 70 75 80 85ndash1

ndash09

ndash08

ndash07

ndash06

ndash05


Re (r

h)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(b)



60 70 80 90ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5



RR sc

atte

ring

coef

ficie

nts (

dB)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(a)

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10


LR sc

atte

ring

coef

ficie

nts (

dB)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(b)



ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

HR

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(c)


ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

VR

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(d)

Figure 4 Continued


5 Conclusions





ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

HH

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(e)


vms = 001vms = 005vms = 025

vms = 045vms = 060

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

VV

scat

terin

g co

effic

ient

s (dB

)(f )


60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0



σ RR

(dB)

ks = 02 kl = 2ks = 02 kl = 4ks = 04 kl = 4

(a)


σ LR

(dB)

ks = 02 kl = 2ks = 02 kl = 4ks = 04 kl = 4

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

(b)




Abbreviations












Data Availability




Acknowledgments


References


60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

RR sc

atte

ring

coef

ficie

nts (

dB)

GaussianExponential



(a)

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0


LR sc

atte

ring

coef

ficie

nts (

dB)

GaussianExponential

(b)




























Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy


















σdegqp 4πA

M q p h v (1)



M

lang Svv

111386811138681113868111386811138681113868111386811138682rang lang Svh


lang Shv

111386811138681113868111386811138681113868111386811138682rang lang Shh




⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(2)






Iq

05 1 + cos 2τq cos 2ψq1113872 1113873


cos 2τq sin 2ψq

sin 2τq

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Ip

05 1 + cos 2τp cos 2ψp1113872 1113873


cos 2τp sin 2ψp

sin 2τp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)












55 60 65 70 75 80 85ndash25

ndash20

ndash15

ndash10

ndash5

0


r v

vms = 001vms = 005vms = 025

vms = 045vms = 060

(a)

55 60 65 70 75 80 85ndash4

ndash35

ndash3

ndash25

ndash2

ndash15

ndash1

ndash05

0


r h

vms = 001vms = 005vms = 025

vms = 045vms = 060

(b)











0 10 20 30 40 50 60 70 80 90

ndash50

ndash40

ndash30

ndash20

ndash10

0


Scat

terin

g co

effic

ient

s (dB

)

RRLRHR

VRHHVV


55 60 65 70 75 80 85ndash08

ndash06

ndash04

ndash02

0

02

04

06


Re (r

v)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(a)

55 60 65 70 75 80 85ndash1

ndash09

ndash08

ndash07

ndash06

ndash05


Re (r

h)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(b)



60 70 80 90ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5



RR sc

atte

ring

coef

ficie

nts (

dB)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(a)

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10


LR sc

atte

ring

coef

ficie

nts (

dB)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(b)



ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

HR

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(c)


ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

VR

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(d)

Figure 4 Continued


5 Conclusions





ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

HH

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(e)


vms = 001vms = 005vms = 025

vms = 045vms = 060

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

VV

scat

terin

g co

effic

ient

s (dB

)(f )


60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0



σ RR

(dB)

ks = 02 kl = 2ks = 02 kl = 4ks = 04 kl = 4

(a)


σ LR

(dB)

ks = 02 kl = 2ks = 02 kl = 4ks = 04 kl = 4

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

(b)




Abbreviations












Data Availability




Acknowledgments


References


60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

RR sc

atte

ring

coef

ficie

nts (

dB)

GaussianExponential



(a)

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0


LR sc

atte

ring

coef

ficie

nts (

dB)

GaussianExponential

(b)




























Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy




















55 60 65 70 75 80 85ndash25

ndash20

ndash15

ndash10

ndash5

0


r v

vms = 001vms = 005vms = 025

vms = 045vms = 060

(a)

55 60 65 70 75 80 85ndash4

ndash35

ndash3

ndash25

ndash2

ndash15

ndash1

ndash05

0


r h

vms = 001vms = 005vms = 025

vms = 045vms = 060

(b)











0 10 20 30 40 50 60 70 80 90

ndash50

ndash40

ndash30

ndash20

ndash10

0


Scat

terin

g co

effic

ient

s (dB

)

RRLRHR

VRHHVV


55 60 65 70 75 80 85ndash08

ndash06

ndash04

ndash02

0

02

04

06


Re (r

v)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(a)

55 60 65 70 75 80 85ndash1

ndash09

ndash08

ndash07

ndash06

ndash05


Re (r

h)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(b)



60 70 80 90ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5



RR sc

atte

ring

coef

ficie

nts (

dB)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(a)

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10


LR sc

atte

ring

coef

ficie

nts (

dB)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(b)



ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

HR

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(c)


ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

VR

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(d)

Figure 4 Continued


5 Conclusions





ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

HH

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(e)


vms = 001vms = 005vms = 025

vms = 045vms = 060

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

VV

scat

terin

g co

effic

ient

s (dB

)(f )


60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0



σ RR

(dB)

ks = 02 kl = 2ks = 02 kl = 4ks = 04 kl = 4

(a)


σ LR

(dB)

ks = 02 kl = 2ks = 02 kl = 4ks = 04 kl = 4

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

(b)




Abbreviations












Data Availability




Acknowledgments


References


60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

RR sc

atte

ring

coef

ficie

nts (

dB)

GaussianExponential



(a)

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0


LR sc

atte

ring

coef

ficie

nts (

dB)

GaussianExponential

(b)




























Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy





















0 10 20 30 40 50 60 70 80 90

ndash50

ndash40

ndash30

ndash20

ndash10

0


Scat

terin

g co

effic

ient

s (dB

)

RRLRHR

VRHHVV


55 60 65 70 75 80 85ndash08

ndash06

ndash04

ndash02

0

02

04

06


Re (r

v)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(a)

55 60 65 70 75 80 85ndash1

ndash09

ndash08

ndash07

ndash06

ndash05


Re (r

h)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(b)



60 70 80 90ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5



RR sc

atte

ring

coef

ficie

nts (

dB)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(a)

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10


LR sc

atte

ring

coef

ficie

nts (

dB)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(b)



ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

HR

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(c)


ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

VR

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(d)

Figure 4 Continued


5 Conclusions





ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

HH

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(e)


vms = 001vms = 005vms = 025

vms = 045vms = 060

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

VV

scat

terin

g co

effic

ient

s (dB

)(f )


60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0



σ RR

(dB)

ks = 02 kl = 2ks = 02 kl = 4ks = 04 kl = 4

(a)


σ LR

(dB)

ks = 02 kl = 2ks = 02 kl = 4ks = 04 kl = 4

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

(b)




Abbreviations












Data Availability




Acknowledgments


References


60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

RR sc

atte

ring

coef

ficie

nts (

dB)

GaussianExponential



(a)

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0


LR sc

atte

ring

coef

ficie

nts (

dB)

GaussianExponential

(b)




























Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















60 70 80 90ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5



RR sc

atte

ring

coef

ficie

nts (

dB)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(a)

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10


LR sc

atte

ring

coef

ficie

nts (

dB)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(b)



ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

HR

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(c)


ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

VR

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(d)

Figure 4 Continued


5 Conclusions





ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

HH

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(e)


vms = 001vms = 005vms = 025

vms = 045vms = 060

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

VV

scat

terin

g co

effic

ient

s (dB

)(f )


60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0



σ RR

(dB)

ks = 02 kl = 2ks = 02 kl = 4ks = 04 kl = 4

(a)


σ LR

(dB)

ks = 02 kl = 2ks = 02 kl = 4ks = 04 kl = 4

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

(b)




Abbreviations












Data Availability




Acknowledgments


References


60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

RR sc

atte

ring

coef

ficie

nts (

dB)

GaussianExponential



(a)

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0


LR sc

atte

ring

coef

ficie

nts (

dB)

GaussianExponential

(b)




























Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















5 Conclusions





ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

HH

scat

terin

g co

effic

ient

s (dB

)

vms = 001vms = 005vms = 025

vms = 045vms = 060

(e)


vms = 001vms = 005vms = 025

vms = 045vms = 060

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

VV

scat

terin

g co

effic

ient

s (dB

)(f )


60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0



σ RR

(dB)

ks = 02 kl = 2ks = 02 kl = 4ks = 04 kl = 4

(a)


σ LR

(dB)

ks = 02 kl = 2ks = 02 kl = 4ks = 04 kl = 4

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

(b)




Abbreviations












Data Availability




Acknowledgments


References


60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

RR sc

atte

ring

coef

ficie

nts (

dB)

GaussianExponential



(a)

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0


LR sc

atte

ring

coef

ficie

nts (

dB)

GaussianExponential

(b)




























Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy
















Abbreviations












Data Availability




Acknowledgments


References


60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

RR sc

atte

ring

coef

ficie

nts (

dB)

GaussianExponential



(a)

60 70 80 90ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0


LR sc

atte

ring

coef

ficie

nts (

dB)

GaussianExponential

(b)




























Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy








































Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















A Simulation Study of GNSS-R Polarimetric Scattering from...

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