STUDIES OF PHASE CENTER AND EXTINCTION COEFFICIENT OF BOREAL FOREST USING X- AND L-BAND POLARIMETRIC INTERFEROMETRY COMBINED WITH LIDAR MEASUREMENTS

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1 STUDIES OF PHASE CENTER AND EXTINCTION COEFFICIENT OF BOREAL FOREST USING X- AND L-BAND POLARIMETRIC INTERFEROMETRY COMBINED WITH LIDAR MEASUREMENTS Jaan Praks, Martti Hallikainen, and Xiaowei Yu Department of Radio Science and Engineering, Helsinki University of Technology PL 3, TKK, Finland Finnish Geodetic Institute FIN-43, Masala, Finland ABSTRACT In this work we study L-band and X-band interferometric phase center location in boreal forest in order to assist height retrieval with POLinSAR methods. We complement interferometric L-band and X-band dataset with an accurate LIDAR measured terrain and canopy height model. The LIDAR measured model allows to calculate ground and treetop phase estimates and reveal the radar measured phase center location inside the canopy We show that for X-band, the interferometric phase center is mostly in the upper quarter of the canopy as predicted by Random Volume over Ground model, indicating that ground is not visible but attenuation is still rather low. We show that tree height estimation is feasible with one polarization X-band (TanDEM-X ) interferometry with simple methods when an accurate digital terrain model is available. At L- band the phase center is around half way of the canopy height and often lower, indicating that ground contribution is significant and attenuation is low. The phase center height follows well the treetop line, except for sparse forest. Key words: SAR, POLinSAR, forest height, boreal forest, phase center, X-band, L-band.. INTRODUCTION SAR polarimetric interferometry (POLInSAR) has been successful in forest remote sensing by utilizing Random Volume over Ground (RVoG) model []. Inversion of the RVoG model can provide an estimate of forest height [] which has been shown in several studies for different forest types [], [3], [4], [6]. The model inversion allows to study also extinction and ground-to-volume scattering ratio. The RVoG model inversion is applicable to fully polarimetric data, because for single-pol data the inversion problem is under-determined. However, our results from the FINSAR campaign show [6] that X-band single polarization interferometric coherence can be successfully used to retrieve forest height. In this work we continue our study of the forest height retrieval by POLinSAR and focus this time to the phase center height in boreal forest. With the help of complementary LIDAR measurements of ground topography and canopy model, it is possible to determine accurately the location of the phase center and the average properties of boreal forest. We show that the X-band ground is not often visible and the RVoG model can be simplified and inverted for tree height and extinction coefficient for single polarization data when ground topography is known. This can lead to an important application for the future TanDEM-X mission. We determine the phase center location for also L-band and discuss the results by using the RVoG model as a theoretical framework.. MATERIAL.. Airborne SAR images The SAR data used in our study was collected during FINSAR campaign [6], carried out in autumn 3 in Finland. The main instruments of the campaign were E-SAR and the HUTSCAT ranging scatterometer. The main campaign took place on 9 September 3 over the test site in southern Finland (N 6, E 4 9 ). The German E-SAR collected from 3 km altitude five L-band (.3 GHz) repeat pass fully polarimetric images ( m, m, m and m baselines) and an X-band (9.6 GHz) single-pass single-pol (VV) interferometric image pair. The forest in the area is heterogeneous and consists of small stands, fields and lakes. Most forested areas are located on top of small hills. The dominant tree species are Scotch pine, Norwegian spruce, birch and alder. Stem volume can be at maximum m 3 /ha and tree height up to 3 m... LIDAR measurements Laser scanning over part of the FINSAR test site was performed on July using laser scanner Optech Proc. of 4th Int. Workshop on Science and Applications of SAR Polarimetry and Polarimetric Interferometry PolInSAR 9, 6 3 January 9, Frascati, Italy (ESA SP-668, April 9)

2 ALTM 3 with khz PRF and km flight altitude and providing 3-4 pts/m point density on the object. The strip adjustment (matching adjacent slight strip data) was made using TerraMatch. Ground hits were classified using TerraScan [7]. Digital Surface Model (DSM) relevant to treetops was obtained by taking the highest point within a -m grid and missing points were interpolated by Delaunay triangulation. The canopy height model (CHM) was then obtained by subtracting the Digital Elevetion Model DEM from the corresponding DSM. The crown DSM was calculated by means of the first pulse echo and the DEM with the last pulse echo. The accuracy of the obtained DEM is better than cm for forested terrain. The CHM includes a -7 cm bias in obtained tree heights and about. m std error. Information at individual tree level can be derived from CHM using methods depicted in [8]. 3. METHODS 3.. Producing ground phase estimate from DEM The DEM and CHM were transferred to slant range coordinates by using E-SAR range and azimuth geocoding tables. The missing pixels in slant range maps were recovered by two dimensional interpolation. In order to get ground phase, we wrapped the LIDAR measured DEM to interferometric SAR phase. The ground phase φ DEM can be represented in terms of SAR vertical wavenumber κ z and terrain elevation h DEM as φ DEM = κ z (h DEM + h f ) + φ f () where h f and φ f are unknown parameters. These two parameters were recovered by fitting the DEM generated ground phase to the SAR measured ground phase for open areas. The open areas were chosen by a simple coherence value threshold (γ >.97) and the cost function E = e iφ DEM e iφγ () was minimized for h f and φ f by the Nelder-Mead simplex method. where h is height of volume layer, φ is ground phase, M is ground-to-volume amplitude ratio and γ V is volume only caused coherence, defined as γ V = e h(σm+iκz) ( + iκ z σ m )(e hσm ). (4) where κ z is the vertical wavenumber, depending on imaging parameters. σ m = σ/ cosθ is defined by mean extinction σ and local incidence angle θ. We assume that ground phase φ is known and we can calculate the phase center height relative to ground φ = φ γ φ. Let us study the γ phase center height against the tree height. There are three special cases when it is possible to simplify the model to the extreme: Ground is not visible (M = ) and extinction is infinite (σ m = ). In this case we see that φ = κ z h which means that the scattering center is at the top of the forest. Ground is not visible (M = ) and extinction is insignificant (σ m = ). In this case we see that δφ =.κ z h, the scattering center is halfway of the forest height. Note that the scattering center cannot be lower than in halfway when ground contribution is missing, according to the RVoG model. Ground reflection is strong (M >> ). In this case phase height is always near zero, regardless of the values we choose for h and σ. Of course, the RVoG model sets conditions also to coherence magnitude correspondingly to every phase value, but magnitude does not change the phase center location. In the following discussion we will deal with the special case of the RVoG model where ground contribution is missing, entitled the Random Volume (RV) model, although the model accounts also the ground phase. According to the RV model, all polarizations have the same penetration depth and the tree height and extinction coefficient can be calculated even with one polarization coherence and phase when ground phase is known. The validity region for the RV model can be determined for a given coherence phase and amplitude when ground phase and tree height are known. In the following section we use this technique to calculate extinction coefficients for X-band and L-band. 3.. Phase center height according to RVOG model In order to interpret phase center location inside the canopy, we use Random Volume over Ground (RVoG) model as a theoretical framework. The RVoG model states that polarization dependent complex coherence γ( w) for a volume above the ground can be modeled as [] γ( w) = e (iφ) [ (γ V )( + M( w)e hσm ) + ], (3) 4. RESULTS AND DISCUSSION 4.. X-band coherence phase center location Figure shows a part of X-band coherence amplitude image and phase image together with the ground phase, calculated according to LIDAR measured DEM and LIDAR measured canopy height map for the same region. The line in the image shows the transect, to be presented in

3 X VV coherence amplitude X VV coherence phase Ground phase estimated by laser Tree height map measured by laser Figure. X-band VV polarization coherence amplitude, coherence phase, ground phase estimate based on LIDAR measured DEM and LIDAR measured canopy height. The dotted line indicates the transect used in Figure. Phase angle (rad) Elevation (m) index Ground phase (lidar) Treetop phase (lidar) M= condition E SAR X band interferometric phase RV inversion area index Ground (lidar) Treetop (lidar) Treetop from restricted RVOG inversion Treetop from RV inversion Figure. X-band VV polarization coherence phase along the range with ground and canopy top phase estimate based on LIDAR measurement. Below is the same transect track with elevation and tree height measurement. The dots represent tree height estimates based on RV of RVoG(M<<) model inversion.

4 3 8 X VV phase center height Tree height Figure 3. A two dimensional histogram showing the relation between X-band relative phase height and LIDAR measured tree height. The green solid line indicates treetop phase and dotted cyan line indicates phase height at halfway of the canopy height, which is also the lower limit for zero ground contribution condition, according to RVoG model. Unit on color bar is samples X VV extinction(db/m) [RV inversion] Figure 4. X-band extinction values retrieved from RV model inversion for areas where ground contribution is zero. detail in Figure. Figure shows the X-band VV polarization coherence phase across the range together with LIDAR measurement based ground phase estimate and tree height estimate. The range index on x axis refers to E-SAR range coordinate for slant range image. The ground phase fit is good, following well the X-band coherence phase for open areas. In most areas, the X-band coherence phase is located in the upper quarter of the forest canopy. For highest canopies also the RV applicability condition is satisfied; these coherence values are marked with blue circle. The LIDAR measured forest height is not filtered in any way and has therefore quite much dynamics. However, X-band coherence phase follows this line rather well, although without sudden jumps due to coherence window averaging. The relation of the scattering center height and LIDAR measured tree height is presented in more detail in a two dimensional histogram in Figure 3. The figure shows that the phase center height correlates with LIDAR measured tree height very well, however, it is located approximately % lower than tree top line (green line). Therefore it is probable that the ground contribution to the signal is very small or missing. This is also found by more detailed inspection by taking into account also the coherence amplitude. Significant changes to this trend are seen only for canopies less than m high. The phase center drops towards the ground, indicating that below this height the X-band coherence starts to have significant ground contribution. For areas, where it as possible to assume zero ground contribution, we made RV model inversion for forest height and extinction coefficient. In this way it was possible to get some reference about the extinction coefficient value range for boreal forest at X-band. When interpreting the results, one should keep in mind that the sample is probably biased toward higher extinction where ground is less visible. Figure 4 shows the histogram of extinction values x Tree height (m)[x band RV inversion] Figure. Tree height values retrieved from RV model inversion for areas where ground contribution is zero. Tree height (m) [Xvv RV model inversion] 3 3 Tree height (m) [lidar] Figure 6. Scatterplot between tree height values retrieved from X-band RV model inversion for areas where ground contribution is zero and tree height measured by LIDAR.

5 retrieved by RV model inversion for areas with no ground contribution. The histogram is evenly distributed with a mean value close to.4 db/m. The highest values are almost.8 db/m. Corresponding height values are presented in Figure. The histogram shows that the main amount of the forests meeting the RV criteria, tend to be over m high and the criteria is never met by canopy height smaller than m. Figure shows a pixel by pixel scatterplot between tree height retrieved by RV model inversion and unfiltered LIDAR measured tree height. The correlation is good and there is no systematic error between these two measurements. This indicates that the RV model assumption for X-band is in good agreement with reality. Encouraged by the good correlation, we implemented a simple two stage inversion scheme for single channel X- band data when the ground topography is known. The first stage of the inversion is made with the RV model for the areas where ground contribution is negligible. For the rest of the heights we apply restricted RVoG model inversion, where M is fixed to a very small value. The forest height map generated in such a way is presented in Figure 4 with LIDAR canopy height measurement and extinction coefficient (only areas where M=) for comparison. 4.. L-band coherence phase center location Figure 7 shows a part of L-band HV polarization coherence amplitude image and phase image together with the ground phase, calculated according to LIDAR measured DEM and LIDAR measured canopy height map. The transect, presented in the figure below, is shown with dotted line. Figure 8 is shown the L-band polarizations coherence phase across the range together with LIDAR measurement based ground phase estimate and tree height estimate. Even refers to HH-VV polarization, Odd to HH+VV polarization and x-pol refers to HV polarization. The ground phase fit is not as good as for L-band. In most areas, the L-band coherence phase is located near the middle line of the forest height, but the variability is significantly larger than it is for X-band. Phase location differences between polarizations are surprisingly small. The RV applicability condition is satisfied for only few pixels for very high canopy on the negative slope area, near range index. The scattering center height and LIDAR measured tree height relation is presented in more detail in two dimensional histograms in Figures 4. and. The best phase center height correlation with LIDAR measured tree height is obtained for HV polarization; it is much worse for HH-VV polarization. The variability is substantially larger than for the X-band case, indicating a larger influence of ground. The phase center is around the mid line of the three height or below that and therefore ground is probably visible. This is supported by a more detailed condition which takes into account also the coherence amplitude. However, high and dense forest in steep slopes in the direction of incident SAR pulse satis- L HV phase center height 3 3 Tree height Figure 9. A two dimensional histogram showing the relation between L-band HV polarization relative phase height and LIDAR measured tree height. The green solid line indicates treetop phase and dotted cyan line indicates phase height at halfway of the canopy height, which is also the lower limit for zero ground contribution condition, according to RVoG model. Unit on color bar is samples. fies in some places RV model conditions. For those areas we made RV model inversion for forest height and extinction coefficient to get some indication about extinction coefficient value range for boreal forest at L-band, however with some bias to higher values. Figure shows the histogram of extinction values retrieved by RV model inversion for a small area on the slopes with no ground contribution. The histogram is evenly distributed, indicating stable inversion, with a mean value of.8 db/m. The highest values are near.6 db/m. Corresponding height values for the same inversion are presented in Figure. The histogram main body is closer to high values than for X-band. Figure 3 shows a pixel by pixel scatterplot between tree height retrieved by RV model inversion and LIDAR measured tree height. The correlation is good and there is no systematic error between these two measurements. This indicates that the RV model assumption is in good agreement with measurements. We implemented the simple two stage inversion scheme also for L-band HV. The ground contribution was fixed to a slightly higher value than it was for X-band. Resulting tree height can be seen in Figure 8 tree height transect. Together with restricted RVoG (M<<) inversion we also present a simple phase based height calculation, which assumes that ground contribution and extinction are both zero. The result is not as good as for X-band but the results indicate clearly that phase height contains a significant amount of tree height information.. CONCLUSIONS In this study we combined LIDAR measurements and X- band and L-band interferometric measurements to show

6 L HV coherence amplitude L HV coherence phase Ground phase estimated by laser Tree height map measured by laser Figure 7. L-band HV polarization coherence amplitude, coherence phase, ground phase estimate based on LIDAR measured DEM and LIDAR measured canopy height. The dotted line indicates the transect used in Figure Phase angle(rad) index Ground phase (lidar) Treetop phase (lidar) M= condition L band, odd L band, even L band, x pol Elevation (m) Treetop (lidar) Ground (lidar) Tree height from restricted RVoG inversion Treetop from phase only index Figure 8. L-band coherence phases for different polarizations (Odd=HH+VV, Even=HH-VV, X=HV) along the range with ground and canopy top phase estimate based on LIDAR measurement. Lower image shows the same transect track in terms of elevation and tree height measurement. The dots represent tree height estimates based on RV of RVoG(M ) model inversion.

7 L HH VV phase center height 3 3 Tree height Figure. A two dimensional histogram showing the relation between L-band HH-VV polarization relative phase height and LIDAR measured tree height. The green solid line indicates treetop phase and dotted cyan line indicates phase height at halfway of the canopy height, which is also the lower limit for zero ground contribution condition, according to RVoG model. Unit on color bar is samples L HV extinction(db/m) Figure. L-band HV polarization extinction values retrieved from RV model inversion for areas where ground contribution is zero Tree height (m) [L band RV inversion areas] Figure. Tree height values retrieved from L-band HV polarization coherence by RV model inversion for areas where ground contribution is zero Tree height (m) [L HV RV model inversion] 3 3 Tree height (m) [lidar] Figure 3. Scatterplot between tree height values retrieved from L-band by RV model inversion for areas where ground contribution is zero and tree height measured by LIDAR. the location of the interferometric phase center in boreal forest. We showed that for X-band the scattering center is approximately at 7% of the height of the tree top. The X-band does not normally see the ground if the forest is higher than m. By using ground phase and tree height from LIDAR measurement, we selected areas where ground contribution in X-band signal was minimal and inverted Random Volume model for extinction and height. Inversion results are stable and consistent and therefore we assume that RV approximation for X-band is mostly valid. The mean extinction coefficient for the X- band in boreal forest according to our results is around.4 db/m. We showed also that RV model can be used successfully for accurate forest height retrieval when ground phase is known. This indicates that forest height retrieval should be feasible also for the TanDEM-X mission, if accurate digital model of underlying ground is available. We applied the same techniques to L-band and found that at the L-band the scattering center is approximately at % of the height of the tree top. This indicates that L-band sees the ground for all types of boreal forests, the only exceptions are some dense forests on slopes in the incidence direction. By applying RV model inversion for these areas without ground contribution, we were able to calculate the mean extinction coefficient also for L-band. The mean extinction coefficient for L-band HV polarization in boreal forest according to our results is around.8 db/m and the highest values are around.7 db/m. Phase center height seems to contain a significant amount of tree height information and, therefore, ground phase estimation is essential for good tree height estimation with POLinSAR methods. ACKNOWLEDGMENTS We would like to thank the German Aerospace Center Microwaves and Radar Institute team for support.

8 Tree height (lidar) Tree height (Xvv interferometry) Xvv band extinction (db/m) Figure 4. Canopy height model measured by LIDAR and estimated by E-SAR X-VV interferometry by using supplemental ground phase estimate. The height estimate is derived by RV model inversion and RVoG model inversion where ground contribution was fixed to %. On the right estimated values for extinction coefficient. REFERENCES [] K.P. Papathanassiou and S.R. Cloude, Single Baseline Polarimetric SAR Interferometry, IEEE Transactions on Geoscience and Remote Sensing, vol. 39, no., pp ,. [] S.R. Cloude and K.P., Papathanassiou, Three-stage inversion process for polarimetric SAR interferometry, IEE Proceedings - Radar Sonar and Navigation, vol., no. 3, pp. -34, 3. [3] T. Mette, K.P Papathanassiou, I Hajnsek, Biomass estimation from polarimetric SAR interferometry over heterogeneous forest terrain, Proceedings of IEEE Geoscience and Remote Sensing Symposium (IGARSS 4), vol., pp. -4, -4 Sept. 4. [4] M. Brandfass, C. Hofmann, J.C. Mura, K.P Papathanassiou, Polarimetric SAR interferometry as applied to fully polarimetric rain forest data, Proceedings of IEEE Geoscience and Remote Sensing Symposium (IGARSS ), vol. 6, pp. 7-77, 9-3 July. [] F. Kugler, F. N. Koudogbo, K. Gutjahr, K. P. Papathanassiou, Frequency effects in Pol-InSAR Forest Height Estimation. 6th European Conference on Synthetic Aperture Radar, EUSAR 6, 6-8 May, Dresden, Proceedings of EUSAR 6, CDROM. 6 [6] J. Praks, F. Kugler, K. Papathanassiou, I. Hajnsek, M. Hallikainen Height estimation of boreal Forest: interferometric model based inversion at L- and X- band vs. HUTSCAT profiling scatterometer IEEE Geoscience and Remote Sensing Letters, no. 3, pp. vol. 4, , July 7. [7] P. Axelsson, DEM generation from laser scanner data using adaptive TIN models, In International Archives of Photogrammetry and Remote Sensing, 33, Part B4, pp. -7,. [8] J. Hyyppä, Inkinen, M., Detecting and estimating attributes for single trees using laser scanner, The Photogrammetric Journal of Finland, 6, pp. 7-4, 999.