Remote Sensing for Agriculture, Ecosystems, and Hydrology V, edited by Manfred Owe, Guido D Urso, Jose F. Moreno, Alfonso Calera, Proceedings of SPIE

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1 Electromagnetic model of rice crops for wideband POLINSAR J. Fortuny-Guasch and A. Martinez-Vazquez a, J.M. Lopez-Sanchez and J.D. Ballester-Berman b a DG Joint Research Centre of the European Commission I-22 Ispra (Va), Italy b DFISTS, University of Alicante P.O. Box 99, E-38 Alicante, Spain ABSTRACT A coherent electromagnetic model developed for estimating the radar backscatter from rice crops is presented. This model is based on the first order solution of the polarimetric backscatter response as a function of the sensor parameters and the physical description of the rice plants. This paper presents a comparison between simulations obtained by the model and experimental data collected at the European Microwave Signature Laboratory (EMSL). This laboratory is currently carrying out several campaigns of measurements over different growing stages of a rice crop sample. For the first stage of growing, simulated and measured backscattering coefficients, at HH, HV and VV channels, show a reasonable agreement. The sensitivity and dependence of the radar signal with respect to the input parameters (incidence angle, frequency and morphological characteristics of the rice plants) has been studied in order to achieve a future parameter inversion. The final aim of this work is to establish a reliable inverse algorithm to retrieve biophysical parameters of rice crops from radar measurements. Keywords: Electromagnetic models, radar remote sensing, rice crops, parameters inversion 1. INTRODUCTION Remote sensing of crops is of prime interest for socio-economic and global environmental aspects. Rice is a vital world food crop and forms the basis of the economy inmany countries, as it happens in the south-east of Asia. In this sense, the existence of rice crops monitoring programs provides an important way to guarantee an efficient management of resources applied to them. With regard to environmental aspects, it is also necessary to control the rice production, since it is directly related to the processes of generation of methane, which is the second most important gas in the greenhouse effect. 1 Despite the clear interest in the development of monitoring systems for this kind of crop, the results presented by the remote sensing community during the last years have been successful only to a partial extent. In the case of radar remote sensing, the main limitation of the proposed monitoring schemes originates from the unavailability ofcomplete and accurate models to predict the radar response of rice. In general, the characterization of the electromagnetic behaviour of vegetation is achieved by two different kinds of models: incoherent and coherent. The incoherent approximation is based on the Radiative Transfer Theory, 2, 3 and it estimates the second order statistics of the scattered field. The most important works of this kind of model were presented at the end of ninety's. 4, Nevertheless, these first attempts did not take into account the effects that the vegetation morphology induces on the global electromagnetic response, i.e., they were not able to preserve information about the phase of the scattered fields. This fact introduces two limitations 6 : 1) The phase interferences among elements are neglected, and 2) Impossibility of using the model in an interferometric SAR system. A first approximation to the coherent scattering from vegetation was presented in. 7 Later on, a two-scale branching model 8 for soybean plant was implemented in order to demonstrate the importance of vegetation structure. In this context, the main objective of the present work is the development of an electromagnetic model with sufficient features to represent a natural rice crop in a realistic way from the point of view of radar remote sensing. The number of biophysical parameters considered in the model should be large enough to simulate accurately Further author information: (Send correspondence to J.D.B-B.) J.M.L-S. and J.D.B-B.: fjuanma,davidbg@dfists.ua.es, Telephone: J.F-G. and A.M-V.: fjoaquim.fortuny,alberto.martinezg@jrc.it, Telephone: Remote Sensing for Agriculture, Ecosystems, and Hydrology V, edited by Manfred Owe, Guido D Urso, Jose F. Moreno, Alfonso Calera, Proceedings of SPIE Vol. 232 (SPIE, Bellingham, WA, 24) X/4/$1 doi:.1117/

2 the plants. However, it is also important to take into account the dimensionality of the inverse problem (i.e. the retrieval of physical parameters from the radar measurements). Consequently, the parameters included in the model must demonstrate their meaningful influence on the final backscatter response. Since the construction of such a model is not straightforward, the electromagnetic formulation is being validated with experimental measurements obtained in controlled laboratory conditions. It is known that the European Microwave Signature Laboratory (EMSL) 9 at the Joint Research Centre of the European Commission (JRC), Ispra, Italy, is an unique facility for such experiments. Recently, this laboratory has been carrying out a campaign of measurements in order to characterize completely a rice variety called selenio, with round grain and fast growing. Three samples with different densities have been studied. The paper is organized as follows. The electromagnetic model that simulates a natural scene with a rice crop is detailed in Section 2. In Section 3 we examine the validity of the formulated model through comparing the simulated data and measured responses for the first growing stage. Then, we illustrate the dependence of the polarimetric backscattering coefficients on rice biophysical parameters and radar configuration. Finally, some conclusions and the ongoing and future work are summarized in Section COHERENT ELECTROMAGNETIC MODEL FOR RICE CROPS In this section a simplified first order coherent scattering model for rice crops is presented. The model considers the rice as an arrangement of plants over a flooded soil. Plants are modeled as clusters of stems, without branches, since they contribute much more importantly to the total microwave scattering of a real rice plant. The stems are modeled as dielectric cylinders. More details about the geometry and architecture of the simulated plants can be found in Section 3.1. The scattering model takes into account the coherent sum of several basic contributions to the total scattering field. 6, 8 Firstly, we assume a first order scattering solution, i.e., the trunk-ground interaction dominates the electromagnetic response of the model, considering multiple interaction between cylinders negligible in this 6, approach. Fig. 1 shows all the contributions included in this interaction. S t Sgt Stg Sgtg Figure 1. Contributions considered in the scattering model. In order to calculate the total scattering in the far field region it is previously necessary to obtain the scattering by a single cylinder-ground set. The dielectric cylinder response is computed by applying the infinite cylinder approximation 6 (semiexact solution). The addition of all four contributions represented in Fig. 1 is obtained by considering the ground as a infinite dielectric half-space. Once a cylinder-ground set is characterized, the scattering matrix of a single stem is expressed as» n Svv S n vh ; (1) S n hv S n hh so it is possible to write the total scattered field from the rice plants as» E s v E s h =[^v s ^hs ] ψ NX n=1» S n vv S n hv S n vh S n hh e jk(^k i^k s)! rn!» E i v E i h e jk ^k s! r ; (2) where N is the number of stems, k is the free space wavenumber, ^k i y ^k s are the directions of propagation of the incident and scattered waves, respectively,! r n is the position of n-th stem and! r is the observation point at far range. 636 Proc. of SPIE Vol. 232

3 Figure 2. Photograph of the low density rice sample. Equation (2) defines mathematically the simplest approximation to model the electromagnetic response of the rice crop. An additional effect that also must be taken into account is the scattering introduced by the soil flooded with water. For simplicity, this contribution is modeled as a perfectly conducting square plate, and it has been computed by means of the Physical Optics approximation. 11 For the backscattering case it can be written as S water = iab (^n g ^k i ) sin(k a^k i ^x) k a^k i ^x sin(k b^k i ^y) ; (3) k b^k i ^y where ^n g is the normal unit vector to the surface and ^x and ^y are the X and Y axis unit vectors. This effect only modifies the co-polar contributions, since the cross-polar term becomes zero for the backscattering direction. It mustbepointed out that the lossy medium below the rice plants becomes important only within a certain incidence angle interval around the vertical direction, and it depends on the plate area and on the frequency of the signal. This effect is incorporated into the model by applying superposition. As a result, the global scattering for a rice crop yields» E s v E s h =[^v s ^hs ] ψ NX n=1» S n vv S n hv S n vh S n hh» e jk(^k i^k s)! rn +» S water S water E i v E i h e jk ^k s! r (4) Depending on the characteristics of each scene, it could be necessary to include the attenuation effect caused by the medium 3, 8 on the wave when it travels through the vegetation cover. It can be calculated by means of 3, 12 Forward Scattering Theorem. Simulations have shown that its influence is negligible when the rice is short and the stems density islow, as it happens in our case. 3. RESULTS The rice sample employed in the experimental validation of the proposed model consists of an 1m 1m square region enclosing plants uniformly distributed. A photograph of the sample is shown in Fig. 2. The simulations are divided in two stages. First, the polarimetric backscattering coefficients are computed in order to compare them with those provided by the experimental data. In a second stage, a dependence study on biophysical parameters and radar configuration is performed Comparison With Experimental Data Table 1 shows the parameters used in the simulation. Cylinders parameters are random: their length and elevation orientation angle follow a gaussian distribution, while the birth position and azimuth orientation angle are uniformly distributed within a cluster. The simulated scene is displayed in Fig. 3. Proc. of SPIE Vol

4 Figure 3. Simulated scene: top view and perspective The calculation of polarimetric backscattering coefficients has been carried out in the incidence range from to 6 degrees, for frequencies ranging from 2 to 8 GHz. Table 1. Simulation parameters PARAMETER VALUE Frequency GHz Illuminated area 1m 2 Mean height 1 cm Height StDev 2. cm Elevation orientation StDev ffi Stem radius 3mm Stems per cluster Number of clusters Stem dielectric constant 26+j8 Water dielectric constant 74+j Observation in azimuth ffi - 36 ffi Points in azimuth 72 Simulated backscattering coefficients are shown in Fig. 4, and a comparison with measurements can be performed by observing Fig.. From both simulations and experiments, it can be noticed that the electromagnetic response is dominated by co-polar contributions. The model approximates the trends shown in the experimental measurements, however, both the VV and HH channels are overestimated. This fact is more evident in the VV channel, as it could be expected from the simple vegetation structure that has been modeled (mainly composed by nearly vertical cylinders). The simulated HH channel, on the other hand, shows a good agreement with experimental data. Nevertheless, the absence of horizontal structures, not considered yet in the model, generates a lower extinction 638 Proc. of SPIE Vol. 232

5 Figure 4. Backscattering coefficients: Simulations results Figure. Backscattering coefficients: Experimental results coefficient, which in turn leads to an overestimation of this contribution at high frequencies. It is important to note that although extinction has been considered, its effect is minimum due to the small size of the plants considered, since they are in the first stage of growing. The measured HV backscattering coefficient is always between -1 and -2 db for all frequencies. The simulated response for the cross-polar channel exhibits a very similar behaviour compared with measurements, obtaining the best results at 4 GHz. This is because of the similarity between simulated and real scenes in the first stage of growing, where stems are practically straight (only with the extreme bent down). In later stages of growing, the rice plants exhibit a more complicated structure, then it would be necessary to model better the plant morphology and to consider multiple scattering in order to avoid an underestimation of the cross-polar channel Dependence on Parameters Several simulations have been performed in order to study the dependence of the polarimetric backscattering coefficients on the biophysical parameters, such as stems and water permitivity, length and radius of stems and standard deviation of stems' length and their elevation angle. Monte Carlo simulations have been performed with realizations and using a 4 degrees elevation incidence angle. The results as a function of water perimitivity and standard deviation of stems' length and elevation angle are shown in Figs. 6, 7 and 8. The model predicts a low variation of the backscattering coefficients as a function of all these parameters. However, for the standard deviation of the cylinders' elevation angle, the crosspolar contribution increases almost linearly, starting from a null value corresponding to a zero degrees elevation standard deviation. In addition, it is interesting to note in the three plots that the VV channel level decreases drastically at 8 GHz and it approaches the HH channel values. This specific reduction in the VV backscatter Proc. of SPIE Vol

6 Water ε 2GHz Water ε 4GHz Water ε 8GHz Figure 6. Backscattering coefficients as a function of real part of water permitivity: Simulations results Length std. dev. (cm) 2GHz Length std. dev. (cm) 4GHz Length std. dev. (cm) 8GHz Figure 7. Backscattering coefficients as a function of standard deviation of stems' length: Simulations results response is due to the variation of the signal level as a function of the stems' radius, which is analyzed later in the text (see Fig. 11(c)). Figs. 9, and 11 present the simulated backscatter responses as a function of the permitivity, the average length and the radius of the stems. In Figs. 9 and, it can be observed that backscattering coefficients show a quasi-linear behaviour. Moreover, the average levels increase with frequency, except for the VV channel at 8 GHz, where it decreases down to the Elevation std. dev. (degrees) 2GHz Elevation std. dev. (degrees) 4GHz Elevation std. dev. (degrees) 8GHz Figure 8. Backscattering coefficients as a function of standard deviation of elevation angle: Simulations results 64 Proc. of SPIE Vol. 232

7 Cylinders ε 2GHz Cylinders ε 4GHz Cylinders ε 8GHz Figure 9. Backscattering coefficients as a function of real part of stems' permitivity: Simulations results Cylinders length (cm) 2GHz Cylinders length (cm) 4GHz Cylinders length (cm) 8GHz Figure. Backscattering coefficients as a function of stems' average length: Simulations results HH level. This is due to the particular response of the cylinder model around k a ß :, where the function has a local minimum, as displayed in Fig.11(c). With regard to the dependence on the stems' radius, Fig. 11 shows that the model predicts a parabolic variation for low frequencies and some oscillations as the frequency increases. It is also important to note that the VV channel results decrease at 8 GHz because of using the same radius for all cylinders. As it can be observed in Fig. 11(c), this fact generates the electromagnetic response to be around the local minimum with value k a ß :. If different radii values were used to model the stems, the scattering would correspond to different values of k a, thus providing a higher average scattered field. Finally, it must be pointed out that the cross-polar contribution reaches a saturation level and it remains almost constant. Nevertheless the model underestimates this component. 4. DISCUSSION A simplified coherent first order electromagnetic model for rice crops has been presented. The global trends shown in the simulated backscatter data are similar to the experimental ones. However, the co-polar contributions are overestimated, and the cross-polar term is underestimated. The HH response exhibits a good agreement with the measurements, although it yields higher values than experiments, specially at higher frequencies. The inclusion of horizontal structures, as bent stems, would produce a higher extinction coefficient, which would improve the estimation of the HH channel scattering. As demonstrated in other previous works, the consideration of multiple scattering would provide a better estimation of the cross-polar scattering. It has been performed a study about the dependence of the results on the biophysical parameters of the rice scene. Standard deviation of stems' length and elevation angle affect slightly the polarimetric backscattering response. Only the cross-polar component has a stronger linear variation as a function of elevation angle standard Proc. of SPIE Vol

8 k.a 2GHz k.a 4GHz k.a 8GHz Figure 11. Backscattering coefficients as a function of stems' radius: Simulations results z (m).2 z (m) y (m) x (m) (a) First stage of growing.2 y (m). 2 (b) Advanced growing x (m) Figure 12. Advanced geometrical models for the rice crop at two growing stages deviation. On the other hand, stems' permitivity and average length, as well as stems' radius, present a strong influence on the final electromagnetic response. Future work will include an accurate measurement and model of all geometrical and biophysical rice parameters, in order to eliminate possible error sources on the input parameters to the direct model. In this line, Fig. 12 illustrates a new geometrical model of the rice crop that is under development. Stems are modeled by ellipsoids and the architecture and shapes of the plants are simulated better than only with cylinders. Once the direct electromagnetic model is sufficiently accurate, it is possible to design and test a parameter inversion. In principle, the following algorithms are candidates for solving the retrieval problem: 1. Single-polarization interferometric coherence, which has been found to be linearly dependent on the crop height during the growing season. 2. Frequency correlation function (FCF) of the radar backscatter. 3. Polarimetric SAR interferometry, since it has shown promising results with crops presenting pronounced orientation characteristics. 642 Proc. of SPIE Vol. 232

9 ACKNOWLEDGMENTS This work has been supported by the Spanish Ministry of Science and Technology (MCYT) and FEDER, under Projects TIC C3-2 and TIC C2-2. REFERENCES 1. T. L. Toan, F. Ribbes, L.-F. Wang, N. Floury, K.-H. Ding, J. A. Kong, M. Fujita, and T. Kurosu, Rice crop mapping and monitoring using ERS-1 data based on experiment and modeling results," IEEE Transactions on Geoscience and Remote Sensing 3, pp. 416, January S. Chandrasekhar, Radiative Transfer, Dover, L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing, John Wiley and Sons, F. T. Ulaby, K. Sarabandi, K. C. McDonald, M. W. Whitt, and M. C. Dobson, Michigan microwave canopy scattering model," Int. J. Remote Sensing 11(7), pp , M. A. Karam and A. K. Fung, Electromagnetic scattering from a layer of finite length, randomly oriented, dielectric, circular cylinders over a rough interface with application to vegetation," Int. J. Remote Sensing 9(6), pp , Y. C. Lin and K. Sarabandi, Electromagnetic scattering model for a tree trunk above a tilted ground plane," IEEE Transactions on Geoscience and Remote Sensing 33, pp. 637, July N. S. Chauhan, R. H. Lang, and K. J. Ranson, Radar modeling of a boreal forest," IEEE Transactions on Geoscience and Remote Sensing 29, pp , July S. H. Yueh, J. A. Kong, J. K. Jao, R. T. Shin, and T. Le Toan, Branching model for vegetation," IEEE Transactions on Geoscience and Remote Sensing 3, pp. 3942, March G. Nesti, A. J. Sieber, G. De Grandi, J. Fortuny, and E. Ohlmer, Recent advances at the European Microwave Signature Laboratory," in SPIE, Microwave Instrumentation and Satellite Photogrammetry for Remote Sensing of the Earth, 2313, pp. 663, (Roma, Italia), J. M. Lopez-Sanchez, H. Esteban-Gonzalez, M. Baquero-Escudero, and J. Fortuny, An electromagnetic scattering model for multiple tree trunks above a tilted rough ground plane," IEEE Transactions on Geoscience and Remote Sensing 37, pp , March F. T. Ulaby and C. Elachi, eds., Radar Polarimetry for Geoscience Applications, Artech House, L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications, Wiley Interscience, 2. Proc. of SPIE Vol