MEASURING SURFACE ROUGHNESS ON BASE OF THE CIRCULAR POLARIZATION COHERENCE AS AN INPUT FOR A SIMPLE INVERSION OF THE IEM MODEL

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1 MEASURIG SURFACE ROUGHESS O BASE OF THE CIRCULAR POLARIZATIO COHERECE AS A IPUT FOR A SIMPLE IVERSIO OF THE IEM MODEL Christian Thiel Frierich-Schiller-University Jena, Institute of Geography, Jena, Loebergraben 32, Germany c5thch@geogr.uni-jena.e ABSTRACT/RESUME In this paper a simple inversion approach is applie at the integral equation metho moel for single scattering (IEM). The inversion of the raar backscatter into soil moisture was accomplishe with an iterative metho. To ate most inversion approaches with use of the IEM try to etermine both the surface roughness an the soil moisture on base of two copolarize raar channels. Because there are a number of possible combinations of roughness an moisture parameters to reach the same values for the raar backscatter, these approaches always contain a fragment of uncertainty an inaccurateness. Therefore this work follows the iea of arising the number of input variables to reuce the inaccurateness an ambiguity of the inversion results. For this reason the surface roughness parameters are eclare as input variables an were calculate externally of the IEM. The base for computing the rms-height values (s) is the circular polarization coherence of the copolarize channels. The real part of this coherence was foun to be a goo measure for this surface roughness parameter. For agricultural surfaces the correlation length of the autocorrelation function was foun to correlate with the rms-heights. Because of the fact, that the autocorrelation length is not the most eciing parameter, this contiguity was use to calculate the autocorrelation length from the s. The final result in the form of a soil moisture map seems quite promising. Goo correlations between measure an moelle values were realise. The arrangement of the soil moisture outsie the test areas is rather realistic, which means higher values in epresse areas an lower values on hilltops. 1 ITRODUCTIO Base on the fact, that raar backscatter is epenent on the ielectric properties of the objects within the resolution cell, the raar signal must contain information on soil moisture. However, the backscattere signal is also affecte by the geometric properties of the scatterers. For bare soil surfaces the surface roughness is the riving parameter. With one single polarisation an no roughness information it is impossible to isolate the ielectric properties of the groun from the SAR signal. However, the availability of polarimetric ata leas to techniques which aim at the ecomposition of the raar signal into ielectric an geometric properties of the illuminate surface. This ecomposition may be one in a more empirical manner [1, 2] or on a rather theoretical basis (Small Perturbation Moel - SPM, Geometric Optics Moel - GOM, Physic Optics Moel - POM) within the limitations of these algorithms. The IEM Moel evelope by [3] combines the theoretical approaches. Some generalisation le to a nearly unrestricte applicability. While the forwar results with IEM are quite promising, the inversion seems to be rather complicate. Because no applicable numerical solution has been foun yet, other solutions like neural networks [4] or lookup tables [5] are use for the inversion. However, such solutions are arguable because several combinations of surface parameters can result in the same backscattering coefficients. In this work that ambiguity in the inversion process is avoie by using the surface roughness parameters as moel input. Hence, the only output of the IEM inversion process is the ielectric constant. As SAR input only one like polarisation is neee. The other like polarisation shoul provie the same results for the ielectric constant an coul be use for roughness accuracy assessment. The base for computing the rms-height (s) is the circular polarization coherence (ρrrll) as propose in [6]. These values where calculate before the inversion of the IEM. The real part of the circular polarization coherence Re[ρRRLL] was foun by [6] to be a goo measure for s. During this work the correlation length of the autocorrelation function was foun to correlate with s for agricultural surfaces. Because of the fact, that the autocorrelation length is not the most eciing moel parameter, this contiguity was use to calculate the autocorrelation length from the rms-heights.

2 2 TEST SITE AD DATA DESCRIPTIO The test site of the stuy is place within the catchment of the rinking water reservoir Zeulenroa, Germany. This reservoir suffers from intensive nutrient leaching from agricultural areas, which ominate the site. It is therefore object of many remote sensing base water balance stuies. The catchment, which is 139 km² in size, is situate in the foothills of the low mountain range Thueringer Schiefergebirge. The terrain is hilly with a maximum ifference in height of about 200 metres. An impression of the lan use is given by Fig.1. In this stuy quapol airborne L-ban ata (E-SAR) from the German Aerospace Centre (DLR) are use. The geometrical resolution is about 2 by 2 metres. The recore stripe lies within the escribe catchment. Its groun imensions are about 10 by 3 kilometres. The ata were recore in March 1999, just before the growing season. Most fiels were free from vegetation. Only few fiels were covere with sparse vegetation like winter-rapesee or winter-cereals. The soil was not frozen anymore. Fig.1. RGB Composite of L-ban intensities VV, HH, HV Simultaneous to the flight campaign intensive groun truth measurements were accomplishe. Fig.2 shows the spatial arrangement of the various measure parameters. Soil moisture was acquire both volumetric (in situ measurements with TDR) an gravimetric (soil samples). The surface roughness was evaluate parallel an perpenicular to the flight irection, whereby the rms-height values for both measuring irections are strongly correlate (r = 0,91). For each measuring a 5 metre profile was photographe with a metal plate as backgroun. Then the soil surface was igitise manually an the roughness parameters s an l were calculate. vegetation measurements roughness measurements volumetric soil moisture measurements gravimetric soil moisture measurements fiel borers Meters Fig.2. Groun truth ata

3 3 ROUGHESS ESTIMATIO FROM POLARIMETRIC DATA The circular polarisation coherence (ρrrll) was foun by [6] to be a potential estimator of s. With an increasing ks value a ecreasing of the circular polarisation coherence was etecte. The computation of ρrrll is epicte in Eq.1. * S RRS LL ρ RRLL (1) * * S S RR S S LL RR LL This polarimetric parameter prove to be inepenent of the ielectric properties of the soil. Furthermore [6] state that the real part of the circular polarisation coherence Re[ρRRLL] is especially preferable for vegetate areas. Moreover it seeme to be more sensitive for roughness estimation for small ks values (ks 0,5). Finally [6] foun an exponential relationship between ks an ρrrll. In this work Re[ρRRLL] was use for roughness estimation. This parameter is irectly proportional to ks. Contrary to [6] in this work ρrrll as well as Re[ρRRLL] seeme to be inepenent of the local incience angle an the topography. Thus, no topographic normalisation of these parameters before roughness estimation was necessary. After polarimetric basis transformation from the linear to the circular basis ρrrll was compute accoringly to Eq.1. A first visual interpretation of the result (see Fig.3 ) seeme to approve the assumption that Re[ρRRLL] coul be use as roughness estimator. The coherence pattern reflects the roughness of the various fiels. Whereas rough areas are epicte in light tones, smooth fiels appear in ark grey. The only important exception was foun for very smooth regions like water boies or harrowe fiels, which o not appear in black but in shaes of grey. For such areas the backscattere signal is obviously too weak to contain useful phase information, it is rather ominate by noise. Fig.3. Re[ρRRLL] with fiel borers - forests, settlements an water boies are maske out (black) The assumption, that the polarimetric phase for low backscatter areas is strongly noise isturbe is also evient in Fig.4. For the smoothest surfaces one woul expect the highest polarimetric coherence (which means the lowest values for Re[ρRRLL]). Inee, this is not the case in this work. For very smooth fiels with s between 0.5 an 1.0 cm the Re[ρRRLL] values lie within 0.2 an 0.1. With an increasing surface roughness the circular polarisation coherence increases as well (the real part ecreases). ot until a further increasing of s Re[ρRRLL] also starts to increase. In this work the rms-height of ~0.9 cm seems to be a kin of threshol for reliable phase information.

4 However, this value is of course strongly epenent on the local incience angle (lia). A more useful criterion for the reliability of the measure phase is the intensity of the backscattere signal. Therefore the cross polarisation HV was chosen to mark areas with a low backscatter intensity. All regions with an HV-intensity value below 30 B (this number was acquire empirically) were maske out an thus not consiere in the roughness computation. The surface roughness computation was sorte out on the base of the linear relation between Re[ρRRLL] an s. For etermining this linear relation the rms-height values below 1.0 were exclue. 3,5 3,0 rms-heights [cm] 2,5 2,0 1,5 1,0 0,5 0,0-0,4-0,3-0,2-0,1 0,0 0,1 Re[ρRRLL] Fig.4. Re[ρRRLL] versus rms-height [cm] 4 IVERSIO OF THE IEM MODEL The promising results of the forwar moelling with the single scattering IEM le to the aim of the inversion of this moel. For this goal a simple an easy applicable approach with unambiguous results was aspire. Furthermore this approach shoul not suffer from a weak relative calibration of the like polarise channels. Therefore one of the rather output variables of the inversion, namely the surface roughness, was use as input parameter. The rms-height estimation is escribe in chapter 3. The other roughness parameter that is require for moelling with IEM is the autocorrelation length. This parameter was also chosen as input for the inversion proceure. For simplicity this variable was calculate linearly from s. Two reasons mae this step feasible. Firstly, both roughness parameters correlate moerately. That was also reporte in [7]. For roughness measurements on agricultural forme an thus artificial surfaces, especially if the measures are taken perpenicular to the till irections, this behaviour woul be expecte. Seconly, as shown in Fig.5, within the measure ranges for s an l (0.5 cm s 3.5 cm, 4 cm l 11 cm) l has minor effects on the moelling results. The graph shows the behaviour of L-HH in epenence of s an l. An equivalent performance is evient for L-VV. The inversion of the IEM Moel was conucte by an iterative ajustment of the ielectric constant. All other parameters (s, l, lia) where kept constant. This proceure was repeate until the ifference between moelle an measure like polarize intensity falls below a efine threshol. This inversion can be one for both like polarisations separately. If the backscatter effective roughness is estimate properly an the absolute as well as the relative SAR calibration is accurate, the results for both like polarisations shoul be equal. For well calibrate SAR ata the ifferences in both results coul ientify errors in roughness estimation. Unfortunately the SAR calibration was not goo enough to figure this out. Only the L-VV channel coul be use for the inversion.

5 -10,0-15,0-20,0-25,0-30,0-35,0 s0 L-HH [B] 3,4-45,0 2,6 1,8 s[cm] 1,0 0,2 0,5 2,0 Fig.5. Sensitivity of [s] an [l] for s 0 L-HH, erive with IEM (soil moisture m v = 25%) The outcome of the inversion are maps of the real (ε ) an the imaginary (ε ) part of the ielectric constant. The ε chart is shown in Fig.6. With knowlege of the eciing soil properties (porosity, salinity, mineral composition etc.) one coul easily compute the soil moisture from the erive ielectric constant. If these soil properties are constant all over the test site, which is the case for this stuy, the ε pattern is in accorance with the soil moisture pattern. A visual interpretation of the spatial arrangement of real part of the ielectric constant clarifies a more or less natural istribution of the soil moisture. Contrary to the surface roughness the soil moisture values o not change necessarily vary from fiel to fiel. In fact, the soil moisture is variable within the fiels. The estimate moisture pattern reflects the fiel measurements quite well. The correlation between both ata sets is about 0.7. Uncertainties of the inversion result may be ue to the sparse vegetation cover on a few fiels. Furthermore SAR calibration problems show up as an overestimation of the soil moisture in near range (top of the figures). 3,5 5,0 6,5 8,0 l [cm] 9,5-40,0 Fig.6. Map of the real part (ε ) of the ielectric constant erive with IEM inversion (low values in yellow, high values in blue) - forests, settlements, water boies an areas with no roughness information are maske out (black)

6 5 COCLUSIO A simple inversion of the IEM moel was carrie out. For this purpose the surface roughness was eclare as input parameter. The only output of the inversion is the ielectric constant. For estimating the surface roughness the empirical relationship between rms-height (s) an the polarimetric parameter circular polarisation coherence was utilise. Especially the real part of the coherence prove to be very sensitive to s. The autocorrelation length (l) was compute from s. For regions with a very low backscatter (very smooth regions) the phase information is ominate by noise. Therefore no roughness values coul be acquire for such areas. Because of insufficient phase information for very smooth surfaces this problem obviously can not be solve by means of polarimetric parameters alone. The raar backscattering intensity has to be inclue. The final results of the inversion are quite promising. Due to the roughness calculation externally the IEM any ambiguities of the resulting parameters are eliminate. Owing to the possibility of calculating the ielectric constant on base of both like polarisations separately, the roughness estimates are uner supervision. If the roughness input was figure out correctly, both separately calculate maps of the ielectric constant shoul be equal. Due to SAR calibration errors this step coul not be performe in this work. Further investigations shoul inclue this step. 6 ACKOWLEDGEMETS This stuy is foune by the German Research Association (DFG) uner contract HO 1840/ REFERECES 1. Dubois, P.C. an van Zyl, J.J. An Empirical Soil Moisture Algorithm using Imaging Raar, Proceeings of IGARSS 94, , Oh, Y. / Sarabani, K & Ulaby, F.T. An Empirical Moel an an Inversion technique for Raar Scattering from Bare Soil Surfaces, IEEE Transactions on Geoscience an Remote Sensing, Vol. 30, , Fung, A.K. Microwave Scattering an Emission Moels an their Applications, Artech House, orwoo, Satalino, G., Pasquariello, G., Mattia, F., Davison, M., Le Toan, T., an Borgeau, M. A Methoological Stuy on Soil Moisture Retrieval Using SAR Data, Proc. of CEOS SAR Workshop 2001, , van Oevelen P.J. an Hoekman, D.H. Raar backscatter inversion techniques for estimation of surface soil moisture: EFEDA-Spain an HAPEX-Sahel case stuies, IEEE Transactions on Geoscience an Remote Sensing, Vol. 37/1, , Schuler, D.L., Lee, J.-S., Kasilingam, D. an esti, G. Surface Roughness an Slope Measurements Using Polarimetric SAR Data, IEEE Transactions on Geoscience an Remote Sensing, Vol. 40, , Davison, M.W.J., Le Toan, T., Mattia, F., Satalino, G., Mannier, T., & Borgeau, M., On the characterisation of agricultural soil roughness for raar remote sensing stuies, IEEE Transactions on Geoscience an Remote Sensing, Vol. 38, o. 2, , 2000.