ABSTRACT. Index terms compact polarimetry, Faraday rotation, bare soil surfaces, soil moisture.

Transcription

1 COPARION BETWEEN THE CONFORITY COEFFICIENT AND PREVIOU CLAIFICATION TECHNIQUE FOR BARE URFACE DICRIINATION AND APPLICATION TO COPACT POLARIETRY ODE y-linh Truong-Loï 13, A. Freeman, P. Dubois-Fernandez 1 and E Pottier 1. ONERA, DER, Centre de alon de Provence, BA701, alon Air cedex, France y-linh.truong-loi@onera.fr, Pascale.Dubois-Fernandez@onera.fr,. Jet Propulsion Laboratory, California Institute of Technology, 800 Oak Grove Drive, Pasadena, CA 91109, UA, Anthony.freeman@jpl.nasa.gov 3. CNE, Centre de Toulouse, 18 Avenue Edouard Belin Toulouse, France. Université de Rennes1, 63 Avenue Général Leclerc, Rennes, France, eric.pottier@univ-rennes1.fr ABTRACT In a previous paper [1], we have investigated the potential of the compact polarimetry mode at longer wavelengths in a space environment for soil moisture estimation. At longer wavelengths, one of the main challenges in recovering the information content in the measured scattering signatures, is Faraday rotation estimation and correction. In order to do that, we have introduced a parameter, the conformity coefficient, computed from compact polarimetry measurements. This criterion was observed to provide similar results to the Freeman-Durden model. In this paper, the study is pursued to include a more theoretical approach to the comparison. Furthermore, other published classifications as the one proposed by Cloude and Pottier [] known as the entropy-alpha and Freeman- Durden [3] classifications are explored and the conformity coefficient is benchmarked against those techniques. The comparison between these classification techniques is first performed theoretically and the effect of noise is investigated. The next step is then to apply all techniques to existing datasets coming from various sources, airborne sensors as RAE [] and space borne sensors as PALAR [5] data. The Faraday rotation angle can be estimated from full polarimetric data as was proposed by both Freeman [6] and Bikel & Bates [7]. From compact polarimetry data, this estimation is more difficult but we have shown in a previous paper how bare surface behavior can be used to perform this estimation. In this paper, the performance of this estimation is evaluated on PALAR data and on RAE data where a constant ionosphere is simulated. The results are confronted to the estimation issued from full polarimetric data. Index terms compact polarimetry, Faraday rotation, bare soil surfaces, soil moisture. INTRODUCTION The compact polarimetric (CP) mode which consists on transmitting only one polarisation is subject to constant discussion. Indeed it allows acquiring data over larger swaths and higher incidence angles than conventional full-pol data from space, but the main drawback when transmitting at low frequencies is the interaction with the ionosphere which induces a rotation of the wave plane, called the Faraday rotation (FR). However, transmitting a circularly polarised wave solves the problem for the emission as the electromagnetic wave illuminating the scattering element will be the same independently of the FR. To correct for the FR on the way back, we need to estimate this angle. This can be done over bare surfaces for which we can use some assumptions as the reflection symmetry. The selection of bare surfaces is made via the conformity coefficient introduced in a previous paper. This criterion which is FR invariant is evaluated against Freeman-Durden [3] and Cloude- Pottier [] classifications. Once the bare surfaces are selected we can then estimate the FR using CP data with three methods. For the first and the second ones, we use two linearly polarised waves on reception (H & V). For the third one the estimation is performed using two circularly polarised waves on reception (R & L). These estimates are compared to the ones computed with Freeman method using FP data linearly polarised [6], and Bickel and Bates theory based on the transformation of the measured scattering matrix to a circular basis [7]. The performance of the bare surfaces selection and FR estimation is evaluated on PALAR L-band data and RAE P-band data. Finally, we demonstrate that CP and FP signatures are equivalent over bare surfaces. o, by directly applying CP data in Dubois et al. algorithm [8], we compare the result of soil moisture inversion in CP mode vs FP mode. Proc. of th Int. Workshop on cience and Applications of AR Polarimetry and Polarimetric Interferometry PolInAR 009, 6 30 January 009, Frascati, Italy (EA P-668, April 009)

2 1. THE CONFORITY COEFFICIENT Consider the / mode suggested in [9-10] where a right circular polarised wave is transmitted and two orthogonal polarised waves are recorded in the reception channels. The measured vector r [10], subject to FR, can be written as: hh vv hh vv hv = f s v 3 = f + f s = f β + f α + f s d d d + f = f β + f α + f v v 3 v (3) = 1 cosω = sin Ω sin Ω cosω VH cosω sin Ω sin Ω 1 cosω j (1) We introduce the conformity coefficient µ with Eq.. It can be shown that this coefficient is FR independent. Furthermore, this coefficient can be expressed simply in the linear basis as long as the reflexion symmetry is met ( 0 ) [1]: µ = µ = Im Re( + ) ( + + ) () Note that this coefficient can be used to discriminate the different scattering types. Indeed, the denominator allows to differentiate the surface scattering from the double-bounce and from the vegetation through the correlation between the co-pol channels and the behaviour of the cross-pol. Normalization is done by the lower part of the ratio which is the span. Two thresholds have to be set to separate the different scattering types as : -surface : t 1 <µ<1 -volume : t <µ<t 1 -double-bounce : -1<µ<t. a. FREEAN-DURDEN ODEL [3] The Freeman-Durden model, based on a threecomponent scattering mechanism, includes volume scattering (f v ) modeled by a radar return from a cloud of randomly oriented dipoles, surface (f s ) and doublebounce (f d ) scatter [3]. For the volume scattering, some assumptions are made as the return from cylinder scatterers so that h equals one and v zero, and a uniform orientation distribution. The double-bounce component ressembles the scattering from a dihedral corner reflector. Then, the surface element is represented by a first-order Bragg model with second-order statistics. The model is: b. CLOUDE-POTTIER CLAIFICATION [] Using the eigenvalue of the coherency matrix and a three-level Bernouilli statistical model, Cloude and Pottier get an estimate of the average target scattering matrix parameters. The entropy which is the degree of randomness is defined from the eigenvalues and allows to know if one or more mechanism are presents in the pixel. The alpha angle is invariant by rotation around the radar line of sight and signs the type of mechanism existing in the pixel. Then, the H/α plane enables the classification of the different scattering types into nine regions. c. COPARION OF THE CONFORITY COEFFICIENT WITH THEE TWO PUBLIHED CLAIFICATION. i. Over Ramses data To evaluate this new coefficient, it is compared to the output of the Freeman-Durden [3] classification. In fact, we have adapted the model as a classification by pointed up the most important contribution. Indeed, if Ps (surface contribution) is bigger than Pv (volume contribution) and than Pd (double-bounce contribution), we display Ps, etc For every models the different scattering types are separated by a color table as : -scattering from surface in blue -scattering from volume in green -scattering from double-bounce in red. We set t 1 =0.35 and t =-0. for the conformity coefficient. These thresholds have been set by using confusion matrices between conformity coefficient, and Freeman-Durden and Cloude-Pottier classifications. These confusion matrices are written below % H/α 6.93% µ 5.50% 57.5% FD 35.38% 7.1% 1.1% 3.0% The element (0,0) of these matrices is the percentage of pixels identified as surface scattering µ

3 with both criteria, the element (1,1) pixels that are not identified as surfaces with both criteria. The elements which are in the off-diagonal are percentage of pixels that are identified as surface with one criterion and not a surface with the other. We can see here that we have a very good agreement between µ and H/α as 87,5% of the pixels are identified with the same way with both classifications. Also the elements in the off-diagonal are very close from each other, which is good. In 00, ONERA s airborne AR system, known as RAE [], was flown over an area around aint Germain d Esteuil in France and acquired a FP P- band dataset. This data set was used to evaluate the conformity coefficient, as shown in Fig. 1. In Fig.1 we see that most of the areas identified as bare soils with the two known classifications appear also as bare soils with the conformity coefficient. These three classifications show obviously that all the bare surfaces identified with the conformity coefficient are the same with the Freeman-Durden and the Cloude-Pottier classifications. Besides, the doublebounce (and volume) scattering of the conformity coefficient seems to better match with the Cloude- Pottier classification than the Freeman-Durden one, where there are more double-bounce than volume scattering. The solution could be to set other thresholds as maybe Ps > β(pv+pd), with some β. We can conclude here that the bare soils are well estimated with the conformity coefficient compared to the published classifications. The remaining task is to adjust the threshold to better differentiate the double-bounce and the volume scattering. Then, a more theoretical comparison (performing the pdf of µ over several areas) will allow to verify the thresholds. t 1 = 0.35 t = t t 1 1 Conformity coefficient Cloude-Pottierclassification P s >P d & P s >P v surface P d >P s & P d >P v Double-Bounce P v >P d & P v >P s volume Freeman-Durden classification ii. Figure.1 : Comparison of the conformity coefficient with Cloude-Pottier and Freman-Durden classifications over Ramses data. Over PALAR L-band data We assess the conformity coefficient against Cloude-Pottier and Freeman-Durden classifications over PALAR L-band data, provided by JAXA and AF. The results are displayed below with the confusion matrices. H/α µ 96.9% 0.39% 0.1%.6% µ 96.66% 0.88% FD 0.67% 1.79% In fig., the three classifications seem to be in good agreement over these data, which is also proved by the confusion matrices. As these data are overall mostly composed of water bodies, we can say that with

4 the three classifications, oceans are identified as surface scattering. -1 t t 1 1 Conformity coefficient Cloude-Pottier classification Freeman-Durden classification Figure. : Comparison of the conformity coefficient with Cloude-Pottier and Freeman-Durden classifications over PALAR L-band data.. FARADAY ROTATION ETIATE Two following methods are presented using FP data (Freeman method and Bickel & Bates) and three others with CP data (two with circular transmission and linear receptions and the other with circular transmission and receptions). a. FREEAN ETHOD This method uses reciprocity hypothesis for scattering coefficient without FR ( = VH ), but does not use this same assumption between the measured scattering coefficient with FR ( VH ), then noting Z =0.5( - VH ), it follows that the FR can be computed by [6]: 1 Ω = tan 1 Z Z ( + + Re b. BICKEL & BATE ETHOD Bickel and Bates theory is based on the transformation of the measured scattering matrix in linear basis [] to a circular basis as followed: ) Z LL Z LR 1 j VH 1 j = (5) Z RL Z RR j 1 j 1 Then the FR is calculated by [7]: 1 Ω = arg RL LR (6) c. ETHOD TO ETIATE FR FRO CP DATA The first approach using CP data with a circular transmission and two linear receptions is to estimate the FR angle by correcting the received CP data with all values of FR angle possible between 0 and 180, and to perform the correction until we have: Arg ~ ~ = 90. Indeed, CP data are related to FP data by: = = VH j j (7) It can readily be shown, under the reflection symmetry hypothesis and the bare surface assumption, that the

5 phase between these two measurements is: Arg = j = 90 (8). Then, from this first method, we can also introduce an other one, applicable directly to the measured received data in CP mode as followed. The FR angle is estimated from a CP mode with a right circular transmission and two linear receptions: Ω = 1 Arc tan Re( ) ( ) (9) Then, the last method presented here uses CP mode where the receptions are circular (right and left): Ω = 1 Arg < RL > RR (10) Note that the two methods using FP data and the one using the CP data with linear receptions are usable within 5. o, the FR has to be less than 5 to be measured with this method. If it is more than 5, it will have an error of 90. The method by correcting the data, even if it take long time to implement, is within 180 as the one using circular receptions in CP mode. Also, observe that these CP methods are usable under reflection symmetry and bare soils assumptions, this is why we needed to select bare soils first. We tested these methods over space borne and air borne data, simulating CP data from FP data and adding a FR of respectively and 110. d. REULT OF THE FR ETIATE i. Over PALAR data From PALAR data, provided by the Alaska atellite Facility and JAXA [5], the FR is estimated using the previous methods (Eq., Eq.6, Eq. 8, Eq. 9 and Eq. 10). From FP data, we synthesized CP data and add a FR of. Then, we select bare surfaces using the conformity coefficient and we estimate the FR using the three methods introduced previously. For the FP method (Freeman and Bickel&Bates) we added the same FR value () and the estimate of FR is performing directly over the full scene. The results are shown below. (a) (b) (c) (d)

6 n (e) Figure.3: FR estimate over PALAR data. (a) Freeman method, using FP data in linear basis. (b) Bickel & Bates theory using FP data in a circular basis. (c) FR estimate from CP simulated data using linearly polarised receptions and estimating the FR by correcting the data and performing the phase between the cross-pol scattering coefficient with all values of Ω between 0 and 180 until it reaches the value of 90.. (d) FR estimate from CP simulated data using linearly polarised receptions. (e) FR estimate from CP simulated data using circularly polarised receptions In fig. 3, we can see that the estimation of the FR using the five methods leads to a FR angle as expected. The estimation using FP data (Eq. and Eq. 6) is more precise but if we have bare surfaces, the estimation is possible and is good using CP mode (Eq. 8, Eq. 9 and Eq. 10). Then, we evaluate the five methods over RAE data with a simulated FR of (a) (b) (c) 119 (d) n (e)

7 Figure.: FR estimate over RAE data. (a) Freeman method, using FP data in linear basis. (b) Bickel & Bates theory using FP data in a circular basis. (c) FR estimate from CP simulated data using linearly polarised receptions and estimating the FR by correcting the data and performing the phase between the cross-pol scattering coefficient with all values of Ω between 0 and 180 until it reaches the value of 90. (d) FR estimate from CP simulated data using linearly polarised receptions. (e) FR estimate from CP simulated data using circularly polarised receptions As expected, for both FP methods (Eq. and Eq. 6), and the CP method using linear receptions (Eq. 9), we have an error of 90 for Eq. and Eq. 6 methods and an error of 91 for Eq. 9 method, whereas for the two others CP methods Eq. 8 and Eq. 10, the FR is well estimate with an error of 1. We can say that if we have FR and bare soils, we can estimate the FR using assumptions: reflection symmetry and bare soils hypothesis. Then, if we compare the results using PALAR (space borne data) and RAE (air borne data) data, the estimates are better over PALAR data. Actually, this is because PALAR data are mostly made of water bodies. o if we are interesting by doing FR imaging over oceans, it could be attractive to consider CP methods. 3. OIL OITURE INVERION a. COPARION BETWEEN CP AND FP IGNATURE In the / CP mode, once the Faraday rotation has been corrected, the measurement vector can be written as: ~ ~ VH j j (11) Assuming that the scattering is small over bare surfaces, we have: ~ ~ j (1) The following histogram shows the comparison between FP and CP signatures over bare surfaces with horizontal reception first and then vertical reception. 10 (db) 0 σ Hh 10 (db) 0 σ Vv 10% oil moisture FP -30 (db) σ 10 (db) (db) Rv 0% oil moisture CP (db) (a) (b) (c) 0 σ Rh 10% Figure. 5 : Once bare surfaces have been selected and FR corrected, we display the comparison between FP and CP signatures.(a) Hh vs Rh, (b) Vv vs Rv and (c) oil moisture FP vs oil moisture CP. A very good agreement between these signatures is noted, with an R deviation of less than 1dB for a window size of 7x7 and less than db for a window size of 3x3. o, bigger the window size, better the correlation. Now, we adapt the CP data directly in Dubois et al. algorithm [8] to estimate the soil moisture. b. OIL OITURE INVERION As CP data are very close to FP data, the Dubois et al algorithm [8] is directly applied to CP data. Fig. 5 (c) shows the soil moisture estimate using FP data versus CP data over a 7x7 window. This estimate is performed over the same areas identified earlier as bare soil surfaces using the conformity coefficient as a discriminator for CP data and 0 0 σ σ ratio for FP data. Overall very good agreement is observed between the soil moisture estimate from CP data and the one from FP data, to within a standard deviation of about %. CONCLUION The simulated results presented in this paper lead to the following major conclusion: we can use CP data, even in the presence of Faraday rotation and apply the Dubois et al algorithm to retrieve the soil moisture estimates with a residual error of only %. These results are relevant to the design of future

8 spaceborne AR systems, since CP has the advantage over FP in that it can achieve larger swaths, and can accommodate the higher incidence angles necessary for soil moisture retrievals. The process starts with the identification of bare surfaces based on the conformity coefficient µ, which has the advantage of being FR independent over surfaces for which the reflection symmetry hypothesis holds (which is the case for most natural surfaces, except where there is a preferred orientation in the along-track direction). Furthermore, we have shown that µ can be used as an indicator of dominant scattering types (surface, double-bounce, volume). This new coefficient was validated against the Freeman- Durden and the Cloude-Pottier classifications. Once µ has been used to discriminate bare surfaces, any Faraday rotation present can be estimated using three possible equations and then corrected for over the full scene. Once the data are corrected for FR, the co-pol measurements can be closely approximated by the CP measurements (as σ o is close to 0) over bare surfaces. The standard Dubois et al. algorithm, applied directly to the CP data provides soil moisture estimates equivalent to those computed from the FP data. An R error of about % is found, indicating that the proposed procedure has very similar performance relative to the initial algorithm. This opens an interesting perspective in soil moisture mapping from space as CP has the advantage over FP of much larger swath coverage, especially at higher incidence angles. In conclusion, the approach described in this paper offers a simplified radar mode of operation (only two scattering measurements required; robust separation of areas where surface, volume or doublebounce scattering is dominant; built-in estimation and correction of Faraday rotation). oil moisture results estimated using our techniques were shown to be in good agreement with standard techniques which uses FP data. On the basis of these results, we recommend evaluation of compact-polarimetry as a viable alternative mode of operation for future spaceborne ARs targeting soil moisture such as NAA/JPL s DEDynI [11] and AP [1] missions, the Argentinian aocom [13] mission. [3] A Three-Component cattering odel for Polarimetric AR Data, A. Freeman and. L. Durden, IEEE Transactions on Geoscience and Remote ensing, vol. 36, no. 3, pp , ay [] The ONERA RAE AR : status in 00, P. Dubois-Fernandez et al, Proc. RADAR 00 symposium, Toulouse, October 00. [5] [Online] and courtesy to AF for providing the data. [6] Calibration of Linearly Polarized Polarimetric AR Data ubject to Faraday Rotation, A. Freeman, IEEE Transactions on Geoscience and Remote ensing, vol., no. 8, pp , August 00. [7] Effects of magneto-ionic propagation on the polarization scattering matrix,. H. Bickel and R. H. T. Bates, Proc. IRE, vol. 53, pp , [8] easuring oil oisture with Imaging Radars, P. Dubois, J. van Zyl and T. Engman, IEEE Trans. Geosci. Remote ens., vol. 33, no., pp , July [9] Compact Polarimetry Based on ymmetry Properties of Geophysical edia : The ode, J- C. ouyris, P. Imbo, R. FjØrtoft,. ingot and J- Lee, IEEE Transactions on Geoscience and Remote ensing, vol. 3, no. 3, pp , arch 005. [10] The Compact Polarimetry for paceborne AR at Low Frequency, P.C. Dubois-Fernandez, J-C. ouyris,. Angelliaume and F. Garestier, IEEE Transactions on Geoscience and Remote ensing, vol. 6, no. 10, October 008. [11] [Online] [1] [Online] [13] [Online] REFERENCE [1] Compact Polarimetry at Longer Wavelengths - Calibration, A. Freeman, -L Truong-Loï and P. Dubois-Fernandez, EuAR08. [] An Entropy Based Classification cheme for Land Applications of Polarimetric AR,.R. Cloude and E. Pottier, IEEE TGR, vol. 35, no. 1, pp , January 1997.