Forest Characterisation by means of TerraSAR-X and TanDEM-X (Polarimetric and) Interferometric Data

Florian Kugler(1), Irena Hajnsek(2)

(1)German Aerospace Centre (DLR), Microwave and Radar Institute, Münchner Str. 20, 82234,

Wessling, Oberpfaffenhofen, Germany, Email: florian.kugler@dlr.de (2)Institute of Environmental Engineering, ETH Zürich Schafmattstr. 6, 8093 Zürich, Switzerland,

Email: hajnsek@ifu.baug.ethz.ch

ABSTRACT

Tandem-X – successfully launched in June 2010 – forms with TerraSAR-X the first single-pass (single- dual- and quad-) polarimetric interferometer in space. This allows for the first time the acquisition and analysis of Pol-InSAR data in X-band from space without the disturbing effect of temporal decorrelation. In this paper TerraSAR-X – TanDEM-X datasets are analyzed using Pol-InSAR techniques [1][2] in order to demonstrate the potential of the TanDEM-X mission for forest parameter inversion and forest characterisation. For this purpose dual-polarimetric (HH/VV) and single-pol datasets (HH) acquired during the pursuit monostatic and the bistatic commissioning phase are used. Estimated forest heights are validated against ground and airborne LIDAR measurements.

Index Terms— X-band, TanDEM-X, Forest height, Pol-InSAR, Interferometry

1. INTRODUCTION

X-band is in general - due to its limited penetration capability into dense vegetation media - a sub-optimal frequency band for forest structure mapping in a global sense. Nevertheless airborne experiments demonstrated a - rather unexpected high - sensitivity of X-band interferometric measurements on forest vertical structure attributes [5] including the potential of Pol-InSAR data inversion at X-band for forest height estimation [4][5][7][8]. Of course the ability and the performance of forest height estimation in terms of X-band interferometry depends on the capability of X-band to penetrate into and through the forest layer that again depends on the density and dielectric properties of the volume layer.

2. INVERSION SCENARIOS

Forest height inversion is based on the random volume over ground model (RVoG) [2][3]. Accordingly, the volume

decorrelation contribution )(~ wVol

of the interferometric

coherence is given by:

m

mziw V

ZVol

1

~)exp()(~ 0

0

(1)

where 00 zZ is the phase related to the ground

topography 0z , Z is the vertical wavenumber [3] and m

the effective ground-to-volume amplitude ratio. The vector w

represents the different polarization combinations. 0~

V is

the volume decorrelation caused in the absence of the ground layer and can be modeled as described by [2][3]:

V

V

h

h

Z

V

dzz

dzz

zi

0 0

000

'cos

'2exp

'cos

'2exp)'exp(

~

(2)

where is the mean extinction coefficient and 0 the

angle of incidence. For less dense forest conditions - as it is the case for boreal forests - X-band penetrates until the ground and the Pol-InSAR signature contains a more or less significant ground contribution which is by means of Eq.1 polarization dependent. Two polarizations are in principle sufficient for a successful inversion of Eq. 1 [3]. Indeed, TanDEM-X offers a single-pass dual-pol data product as an experimental mode with the following combinations: HH/VV, HH/HV, VV/VH and HV/VH. Data quality analysis showed that the co-pol combination (HH/VV) is probably the most suitable for applying PolIn-SAR, as the cross-pol channels are characterized by a rather poor signal to noise ratio (SNR) [10][9]. Dual-pol data allow estimating the so called coherence region [1]. In case of a 2x2 polarimetric interferometric matrix Schur’s decomposition is applied describing the coherence region as an ellipse. Then the two polarizations with the lowest )(~

minwVol

and the highest )(~maxwVol

ground contribution are identified.

For the dual-pol single baseline case the inversion problem is not balanced with 5 unknowns ( 0maxmin ,,,, mmhV )

and two complex coherences [ )(~minwVol

, )(~

maxwVol

].

),,,(~),,,(~

)(~)(~

minmin0

max0

min

max

,,,, 0maxmin mh

mh

w

w

VVol

VVol

Vol

Vol

mmhV

(3)

However, a solution can be established setting 0min m . In

this way, an inversion problem with four real unknowns ( 0max ,,, mhV ) and two complex coherences

[ )(~minwVol

, )(~maxwVol

][2] is obtained:

)0,,(~

),,,(~

)(~)(~

minmin0

0max

min

max

,,, 0max mh

mh

w

w

VVol

VVol

Vol

Vol

mhV

(4)

Eq. 4 has a unique solution in terms of Vh and .

The standard mode of TanDEM-X is a single polarization either in HH or in VV acquisition. Using the interferometric coherence at a single polarization channel leads to an underdetermined inversion problem with 3 unknowns compared to only 1 (complex) observable. Fixing the ground phase (taken from an external DEM) allows obtaining a determined problem:

)0,,(~)(~min 0,

mhw DEMVVolVolhV

. (5)

3. DATA BASE

Krycklan test site is located in middle Sweden (64°10’N and 20°01’E). A description of the test site is given in [9]. For validation LIDAR tree height measurements from 2008 are used (see Figure 5 left side) divided into 216 homogeneous stands. For the following analysis a dual-pol TanDEM-X data set (HH/VV) acquired in July in a monostatic mode (see color composite in Figure 5 on the left side) and a single-pol TanDEM-X data set (HH) acquired in December in a bistatic mode is used. The monostatic acquisitons are separated by a 3sec temporal baseline; this means that temporal decorrelation can not be completely excluded [9]. A summary of the used data sets is given in Table 1. The measured interferometric coherence decreases apart from volume decorrelation Vol~ also from several other -

system induced - decorrelation processes. In [6] system induced decorrelation processes for TanDEM-X are evaluated and in [9] the importance of coherence calibration especially for the SNR decorrelation term is outlined. This means for a successful height inversion at least a compensation for SNR decorrelation is mandatory. The hilly topography in the scene induces a change of the vertical wavenumber Z varying with terrain slope. Areas

tilted towards the antenna increase Z and decrease the

height of ambiguity. Insensitive areas in the image with a height of ambiguity lower than 30m are excluded from inversion.

Table 1: TanDEM-X data base Krycklan test site

Acquisition Date 27th of July 2010 17th of December

2010

Incidenc Angle 32° 19° Vertical

wavenumber Z 0.18rad/m 0.09rad/m

Height of ambiguity 35m 69m Polarisation HH/VV HH

Mode ascending Monostatic

descending Bistatic

4. SINGLE POL INVERSION

Knowing the ground phase 0 (taken from LIDAR

measurements) allows estimating the scattering phase centre height. Plots of the phase centre heights vs LIDAR forest height of the dual-pol acquisition (27th of July) are shown in Figure 1 on the left for the HH channel and in Figure 2 on the left for the VV channel. A correlation coefficient r² of 0.54 for the HH channel and 0.65 for the VV channel denotes a relation between scattering phase centre height and total forest height. The RMSE indicates the mean penetration depths of X-band. The HH channel penetrates with a RMSE of 9.45m slightly deeper than the VV channel with a RMSE of 8.27m, indicating a higher ground contribution in the HH channel. In both cases is the phase centre height close to the half forest height which argues for a low extinction in X-band for this test site.

Figure 1: InSAR phase centre height HH polarization vs. LIDAR H100; left: acquisition from monostatic phase (27th Juli, RMSE = 9.45m), right: acquisition from bistatic phase (17th December, RMSE = 11.80m)

Figure 2: VV polarization monostatic phase (27th Juli); left: InSAR phase centre height VV polarization vs. LIDAR H100 (RMSE = 8.27m); right: Validation plot of forest height estimates obtained using Eq. 5 (LIDAR ground phase) vs. LIDAR H100 (r² = 0.91, RMSE = 1.58m)

As the VV channel seems to have less ground contribution in the signal than HH, VV is used for a single baseline inversion as described by Eq. 5. An image of the interferometric coherence in VV polarization is displayed in Figure 5 in the middle and the obtained forest height map in

Figure 6 in the middle. The validation plot for the single-pol inversion is shown in Figure 2 right hand side and results in a correlation coefficient r² of 0.91 with a root mean square error of 1.58m. One stand is clearly underestimated (see red circle in Figure 2 on the right). By taking into account the two years of time difference between the LIDAR and the RADAR measurements, there is a high probability that harvesting activities lowered the tree height in this stand between the LIDAR and the Radar acquisition. If the harvested stand is excluded, the correlation coefficient raises up to 0.93. For several pixels height inversion did not result in a unique solution. These pixels could be either affected by temporal effects or by a strong ground contribution in the signal making the inversion ambiguous. In case of the single-pol inversion in total 15% of the pixel were masked out (including Z limitations).

5. DUAL POL INVERSION

For applying the dual-pol inversion as described by Eq. 4 first the polarizations with the lowest )(~

minwVol

and the

highest ground contribution )(~maxwVol

have to be

identified. A successful implementation of Eq. 4 needs a

significant difference ))(~)(~arg( *maxmin ww VolVol

between the phase centers of the two polarizations. The plot in Figure 3 left hand side shows (in [m]), as a function

of forest height. Here increases with increasing forest

height (up to 7m), which predicts a good inversion performance and confirms the validity of the used model. With increasing forest height also the variance of

increases indicating a variation of the extinction in the different forest stands. A forest height map obtained from the dual-pol inversion is shown in Figure 6 on the left, the corresponding validation plot in Figure 4 on the left. Compared to the single-pol inversion here the validation is noisier in particular for the taller forest stands, but the correlation coefficient r² = 0.86 with a RMSE of 2.02m convinces. As already mentioned for the single-pol inversion, also in the dual-pol inversion one

stand can be clearly detected as harvested between the LIDAR and the Radar acquisition. Excluding the harvested stand the correlation coefficient becomes 0.90. For several pixels in the dual-pol inversion no unique solution could be obtained. In total 21% of the pixel were masked (including

Z limitations). Additional to the inversion problems

identified in the single-pol inversion scenario an insufficient ground contribution in all polarizations could make the inversion ambiguous and increases the number of invalid points.

Figure 3: Maximized polarimetric phase difference (minimum ground contribution, maximum ground contribution) vs LIDAR H100

Figure 4: Validation plots monostatic phase (27th of July); left: Forest height estimates obtained using Eq. 4 (dual-pol inversion) vs. LIDAR H100 (r²=0.86, RMSE = 2.02m); right: Cross validation forest heights estimates from single-pol inversion (Eq. 5) vs forest heights obtained from dual-pol inversion (Eq. 4) (r² = 0.93, RMSE = 1.44m)

Figure 5: TerraSAR-X TanDEM-X Radar images over Krycklan test site from the monostatic phase (27th of Juli); left: Radar amplitude color composite HH VV; middle: interferometric coherence (VV) scaled from 0 (black) to 1 (white); right: Maximized polarimetric phase difference (minimum ground contribution and maximum ground contribution) scaled from 0m to 6m.

Figure 6: Forest height maps Krycklan monostatic phase (27th of July); left: Radar amplitude image (grayscale) overlaid with LIDAR H100 forest height map; middle: coherence map overlaid with forest height map obtained using Eq. 4 for VV polarization (LIDAR ground phase); right: coherence map overlaid with forest height map obtained using Eq. 5 (dual-pol inversion); Height maps are scaled from 0m to 30m, see legend; Coherence is scaled from 0 (black) to 1 (white).

6. SEASONAL EFFECTS

Estimates of the phase centre height from the single-pol acquisition in December in HH polarization show, with a RMSE of 11.8m (plot in Figure 1 on the left) a significantly deeper penetration depth than the HH polarization from the dual-pol acquisition with a RMSE of 9.5m (27th of July). For the December acquisition is the phase centre height clearly below the half forest height, indicating a high ground contribution in the signal which does not allow a meaningful inversion by means of Eq. 5. Here, either the ground contribution is increased by the steeper incidence angle (19° vs. 32°) or the dielectric constant of the vegetation decreased dramatically between the two acquisitions due to the freezing weather conditions during the December acquisition. A low dielectric constant reduces backscattering from the forest canopy and raises backscattering form the ground.

7. CONCLUSIONS

TanDEM-X satellite configuration shows a good inversion performance for forest height estimation for both, the proposed single-pol method (for regions were a ground DEM is on hand) and the dual-pol (HH/VV) inversion method, which is probably limited to less dense forest conditions as found in boreal forests. The VV polarization is probably more applicable for the single-pol inversion as it had less ground scattering contribution than the HH polarization. There is still a high potential to improve inversion results especially in terms of getting more valid points when analyzing single pass acquisition scenarios. Analysis of a second single-pol data set showed a deeper penetration of the HH channel compared to the dual-pol acquisition. It was not clear whether this effect is caused by the steeper incidence angle or by the winter conditions of the second acquisition. Due to the high ground contribution in this case a successful inversion with a single polarization needs at least a second baseline (dual baseline inversion). A combined employing of different (steep / flat) incidence angle or seasonal effects (summer/winter conditions) could extend

the applicability of the presented approaches (especially the dual-pol inversion) to other (denser) forest types.

8. ACKNOWLEDGMENTS

The authors would like to thank the TanDEM-X team for the fast access to the data. They would also like to thank Pau Prats for his support in data processing issues.

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