MODELLED POLARIMETRIC BACKSCATTERING RESPONSE FROM SINGLE PINE TREES AND PINE CANOPIES. P.O. Box 3000, FIN HUT, Finland

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1 MODELLED POLARIMETRIC BACKSCATTERING RESPONSE FROM SINGLE PINE TREES AND PINE CANOPIES Jaan Praks (1), Pekka Ahtonen (1), Marcus Engdahl (1), Martti Hallikainen (1) (1) Helsinki University of Technology, Laboratory of Space Technology P.O. Box 3000, FIN HUT, Finland ABSTRACT In this work a coherent backscattering model has been employed to simulate L-band polarimetric backscattering from a single pine tree and a small pine forest stand. The recently developed 'Electromagnetic Scattering Model for Forest Remote Sensing' has been employed in calculations. The backscattering model uses the discrete particle approach and it can handle first order direct scattering, single and double ground bounce terms, and first order interaction between the trunk and branches. The model computes fully coherent polarimetric quantities for any construction made of cylinders. Tree cylinder models for simulations are created with the LIGNUM tree growth model. The polarimetric covariance matrix for the tree has been calculated as an average over tree azimuth angles. The target entropy and alpha angle are examined as a function of tree stem volume. EMISAR images from 1995 from Finland are used in comparison. Results indicate that the model can predict correctly behaviour of direct backscattering, but the ground bounce terms suffer from simplifications made as ground is modelled as a perfectly smooth surface. However, the model is able to predict correctly scattering mechanism change as a function of stem volume. 1 INTRODUCTION Simulations of polarimetric backscattering from forest canopy can provide valuable methods to find the ways to extract needed forest properties from SAR images and explain the behaviour of commonly used polarimetric parameters. The first step in the simulation is to organize the process in such a way that calculated results are comparable with SAR image parameters. Because of the coherent nature of both SAR measurement and model calculation the problem is comparing two random numbers. Comparison of absolute values of backscattering is also difficult, as the general level of backscattering is highly dependent, for example, on weather conditions. In this study we have compared entropy and alpha angles of averaged covariance matrices. These parameters reflect general polarimetric properties of the target and not depend on backscattering level. 2 SIMULATIONS 2.1 Scattering model The Electromagnetic Scattering Model for Forest Remote Sensing developed in Rolf Nevanlinna institute in Finland by Zurk et. al [1] has been used to calculate the coherent polarimetric scattering matrix from a single tree and forest stand. The model is a general cylinder model, where trees are made up of cylinders that represent its trunk and branches. The ground is modelled as an infinite plane with given complex relative dielectric constant. The model extends the discrete particle approach used previously by Chiu and Sarabandi [2] and Tsang et al. [3] to trees. The model handles first order direct scattering, single and double ground bounce terms, and first order interaction between the trunk and branches. For first order interaction between the trunk and branches the model employs computational segmentation and a local plane wave expansion to provide efficient calculation. The model computes the fully coherent polarimetric scattering matrix for general bistatic remote sensing of a forested region at microwave frequencies. In this study the model has been used for simulating monostatic remote sensing measurement.

2 2.2 Tree model The pine tree cylinder model has been generated by using the LIGNUM tree growth model described by Perttunen et al. [4]. The model is based on extensive studies of tree growth in Finland and it is able to generate photo-realistic trees. It models both the structure and the functioning of a single tree. For this study, a 66 year old and 20.3 m high pine tree was generated. The cylinder model does not involve needles. As all simulations are done for L-band, needles are not considered. The cylinder model of the used tree is shown in Fig.1 Additionally a forest stand has been built by using variations of the single tree cylinder model as shown on Fig.2. Fig 1. Cylinder model of pine tree used in simulations. Fig 2. Cylinder model of small forest stand.

3 2.3 SAR images Simulation results were compared with L-band SAR image values for pine forest area. The fully polarimetric SAR scenes were collected over the area during the EMAC-95 campaign, see Hallikainen et al. [5] for details. The measurements were carried out with the Danish EMISAR instrument at L- and C-band, incidence angle range 48 degrees to 57 degrees. The images were acquired with similar imaging geometry under almost dry snow conditions on March and during the snowmelt (wet snow) period on 2-3 May Model simulations The cylinder model of the tree was simplified for calculations by merging cylinders in same direct and decreasing amount of very small branches. By model simulations it was assured that the employed simplifications have negligible effect to the scattering properties of the cylinder model in L-band. The scattering matrix was calculated for the direct backscattering, cylinder-ground reflection, ground cylinder reflection and third order and total backscattering. Tree model was rotated and backscattering was calculated using one-degree interval. The incidence angle of monostatic measurement simulation was 50 degrees off nadir. The amplitude of HH polarized total backscattering is shown in Fig.3 as a function of tree azimuth angle. Due to coherent addition, backscattering is very sensitive to tree orientation. To get stable estimate of the covariance matrix it was calculated as an average over all calculated tree azimuth angles. The covariance matrix-related parameters attain stable values only when over 100 looks are averaged. In this work the covariance matrix is averaged over 360 tree azimuth looks. For the averaged covariance matrix target scattering mechanism (alpha angle) and target entropy were calculated. By using obtained entropy and alpha values it was possible to compare simulation results with SAR measurements over pine forests Total ba cksca tte ring amplitude azimuth angle of the model tree Fig 3. Modelled backscattering amplitude of HH polarization from pine tree for different azimuth angles of the tree. 3 RESULTS To ensure that calculated averaged covariance matrix is realistic, single look scattering matrix element probability density functions were examined. Histograms of amplitude and phase difference follow well PDF curves arising from multidimensional K-distribution. Also single look SAR data follow the same PDFs. The simulated direct scattering contribution response is in good agreement with the SAR measurements and theoretical knowledge. However the agreement is not good for ground-cylinder and cylinder-ground scattering.

4 Modeled tree scattering Z-7 D irect Ground-cyl cyl-ground 3rd Z-4order Total Z-1 Z-2 alpha Z-8 Z-5 L-band pine forest, EMISAR 1995 Z Z-9 Z-3 S tem vol=200m 3 /ha S tem vol=10m 3 /ha entropy Fig 4. Stem volume simulation results in entropy-alpha classification space. Classifications zones: Zone 1: High Entropy Multiple Scattering, Zone 2: High Entropy Vegetation Scattering, Zone 3: High Entropy Surface Scatter (not measurable), Zone 4: Medium Entropy Multiple Scattering, Zone 5: Medium Entropy Vegetation Scattering, Zone 6: Medium Entropy Surface Scatter, Zone 7: Low Entropy Multiple Scattering Events, Zone 8: Low Entropy Dipole Scattering, Zone 9: Low Entropy Surface Scatter. 1.2 M odeled tree scattering L-band pine forest, EMISAR 1995 alpha Direct Ground-cyl cyl-ground 3rd order Total S tem volume (m 3 /ha) Fig 5. Comparison of modelled scattering contributions with SAR data as a function of stem volume. Solid lines represent modelled alpha angle as a function of stem volume for different scattering contributions. Dots represent alpha angle for L-band SAR image over pine forest area as a function of stem volume.

5 This may be caused by the fact that ground is modelled as perfectly smooth surface with no roughness. This is clearly not realistic assumption. In Fig 4 is presented simulated backscattering contributions on the entropy-alpha classification space as a function of stem volume. As seen on the figure, direct backscattering contribution compares best with SAR measurements. In total backscattering, the contribution of ground-cylinder contribution is overestimated. This is probably caused by unrealistic model for ground scattering. Ground cylinder interaction is clearly too regular as entropy is low. However, if we compare only modelled alpha angle with SAR data as shown in Fig 5, good agreement between simulated backscattering scattering mechanism and measured scattering mechanism can be found. 4 CONCLUSIONS In general, our results from the model simulation and SAR image agree with each other. Deviations can be explained by simplifications made in the scattering model and the tree stand model. In reality backscattering is more random than model predicts, however scattering mechanism is estimated correctly. According to the results, the used scattering model combined with a realistic tree model provides a useful tool for further investigation of polarimetric scattering properties of forest. 5 REFERENCES 1. Zurk, L. M., P. Koistinen, J. Sarvas, L. Homström, Electromagnetic Scattering Model for Forest Remote Sensing, Rolf Nevanlinna Institute Research Reports, A38, December 2001, ISBN , Tsenchieh Chiu and K. Sarabandi. Electromagnetic scattering from short branching vegetation. IEEE Transactions on Geoscience and Remote Sensing, 38(2): , Leung Tsang, Jin Au Kong, Kung-Hau Ding, and Chi On Ao. Scattering of Electromagnetic Waves: Numerical Simulations. John Wiley & Sons, Perttunen, J., Sievänen R., Nikinmaa, E., LIGNUM: A model mombining the structure and the functioning of trees. ecological modelling 108: Hallikainen, M., Koskinen, J., Praks, J., Arslan, A., Alasalmi, H. and Makkonen, P., Mapping of snow with airborne sensors in EMAC 95, ESA EMAC 94/95 Final Results Workshop, Noordwijk, Netherlands, 1997, pp,