Modeling of Subsurface Scattering from Ice Sheets for Pol-InSAR Applications

Remote sensing is a fundamental tool to measure the dynamics of ice sheets and provides valuable information for ice sheet projections under a changing climate. There is, however, the potential to further reduce the uncertainties in these projections by developing innovative remote sensing methods. One of these remote sensing techniques, the polarimetric synthetic aperture radar interferometry (Pol-InSAR), is known since decades to have the potential to assess the geophysical properties below the surface of ice sheets, because of the penetration of microwave signals into dry snow, firn, and ice. Despite this, only very few studies have addressed this topic and the development of robust Pol-InSAR applications is at an early stage. Two potential Pol-InSAR applications are identified as the motivation for this thesis. First, the estimation and compensation of the penetration bias in digital elevation models derived with SAR interferometry. This bias can lead to errors of several meters or even tens of meters in surface elevation measurements. Second, the estimation of geophysical properties of the subsurface of glaciers and ice sheets using Pol-InSAR techniques. There is indeed potential to derive information about melt-refreeze processes within the firn, which are related to density and affect the mass balance. Such Pol-InSAR applications can be a valuable information source with the potential for monthly ice sheet wide coverage and high spatial resolution provided by the next generation of SAR satellites. However, the required models to link the Pol-InSAR measurements to the subsurface properties are not yet established. The aim of this thesis is to improve the modeling of the vertical backscattering distribution in the subsurface of ice sheets and its effect on polarimetric interferometric SAR measurements at different frequencies. In order to achieve this, polarimetric interferometric multi-baseline SAR data at different frequencies and from two different test sites on the Greenland ice sheet are investigated. This thesis contributes with three concepts to a better understanding and to a more accurate modeling of the vertical backscattering distribution in the subsurface of ice sheets. First, the integration of scattering from distinct subsurface layers. These are formed by refrozen melt water in the upper percolation zone and cause an interesting coherence undulation pattern, which cannot be explained with previously existing models. This represents a first link between Pol-InSAR data and geophysical subsurface properties. The second step is the improved modeling of the general vertical backscattering distribution of the subsurface volume. The advantages of more flexible volume models are demonstrated, but interestingly, the simple modification of a previously existing model with a vertical shift parameter lead to the best agreement between model and data. The third contribution is the model based compensation of the penetration bias, which is experimentally validated. At the investigated test sites, it becomes evident that the model based estimates of the surface elevations are more accurate than the interferometric phase center locations, which are conventionally used to derive surface elevations of ice sheets. This thesis therefore improves the state of the art of subsurface scattering modeling for Pol-InSAR applications, demonstrates the model-based penetration bias compensation, and makes a further research step towards the retrieval of geophysical subsurface information with Pol-InSAR

Modeling the Vertical Backscattering Distribution in the Percolation Zone of the Greenland Ice Sheet with SAR Tomography

The penetration of microwave signals into snow and ice, especially in dry conditions, introduces a bias in digital elevation models generated by means of synthetic aperture radar (SAR) interferometry. This bias depends directly on the vertical backscattering distribution in the subsurface. At the same time, the sensitivity of interferometric SAR measurements on the vertical backscattering distribution provides the potential to derive information about the subsurface of glaciers and ice sheets from SAR data, which could support the assessment of their dynamics. The aim of this paper is to improve the interferometric modeling of the vertical backscattering distribution in order to support subsurface structure retrieval and penetration bias estimation. Vertical backscattering distributions are investigated at different frequencies and polarizations on two test sites in the percolation zone of Greenland using fully polarimetric X-, C-, L-, and P-band SAR data. The vertical backscattering distributions were reconstructed by means of SAR tomography and compared to different vertical structure models. The tomographic assessment indicated that the subsurface in the upper percolation zone is dominated by scattering layers at specific depths, while a more homogeneous scattering structure appears in the lower percolation zone. The performance of the evaluated structure models, namely an exponential function with a vertical shift, a Gaussian function and a Weibull function, was evaluated. The proposed models improve the representation of the data compared to existing models while the complexity is still low to enable potential model inversion approaches. The tomographic analysis and the model assessment is therefore a step forward towards subsurface structure information and penetration bias estimation from SAR data

Towards a Pol-InSAR Firn Density Retrieval

Polarimetric and (multi-baseline) interferometric SAR techniques are promising tools to investigate the subsurface properties of glaciers and ice sheets, due to the signal penetration of up to several tens of meters into dry snow, firn, and ice. Two different lines of research were addressed in recent years. The first is based on PolSAR, which provides not only information about the scattering mechanisms, but also has the uniqueness of being sensitive to anisotropic signal propagation in non-scattering layers of snow and firn. The second line of research is related to the use of Pol-InSAR and TomoSAR to retrieve the 3D location of scatterers within the subsurface. So far, the different SAR techniques were mainly assessed separately. In the field of PolSAR modeling efforts have been dedicated to establish a link between the co-polarization HH-VV phase difference (CPD) and the structural properties of firn [1]. CPDs have then been interpreted as the result of propagation effects due to the dielectric anisotropy of the firn volume. This modeling approach establishes a relationship between the measured CPD and firn density, firn anisotropy and the vertical backscattering distribution in the subsurface of the glacier or ice sheet. By assuming bulk values for density and anisotropy and employing a constant signal extinction for the vertical backscattering function, i.e. a uniform volume, a first attempt to retrieve firn thickness from PolSAR data was presented [1]. In the fields of Pol-InSAR and TomoSAR for the investigation of the subsurface scattering structure of glaciers and ice sheets, recent studies were concerned with the estimation of the vertical backscatter distribution, either model-based or through tomographic imaging techniques. The complexity of (Pol-)InSAR models for the retrieval of subsurface structure information is mainly limited by the available observation space. Thus, constant signal extinction volumes [2], with additional Dirac deltas to represent refrozen melt layers [3] and variable extinction volumes [4] have been modelled and used to retrieve information about the subsurface. With TomoSAR, the imaging of subsurface features in glaciers [5], and ice sheets [4][6][7] was demonstrated and the effect of subsurface layers, different ice types, firn bodies, crevasses, and bed rock was recognized in the tomograms. Those studies on PolSAR, Pol-InSAR and TomoSAR techniques made promising steps towards a subsurface structure information retrieval on glaciers and ice sheets, but the direct relationship to geophysical parameters, which are useful for the glaciological community, is only limited. The most promising way to achieve this goal is the combination of PolSAR and Pol-InSAR/TomoSAR techniques in order to exploit the synergies between the individual methods and by integrating the models and algorithms into one common framework. A first experiment in this direction was the integration of TomoSAR vertical scattering profiles into the PolSAR firn anisotropy model [8]. This allowed the inversion of the firn density from experimental airborne F-SAR data over Greenland, which would be a promising geophysical information product. However, this experiment enabled only the inversion of a single bulk density value for the entire penetration depth and was based on hundreds of samples of CPD measurements and TomoSAR profiles across a wide range of incidence angles, which is of limited applicability. Therefore, this study will continue this investigation, assessing to which degree an inversion is possible on reduced and more feasible observation spaces. Open questions are, which number and range of incidence angles as well as which and how many baselines are required, and whether depth-varying densities could be retrieved. The results should give an indication if such an approach might be feasible with future spaceborne SAR systems. [1] G. Parrella, I. Hajnsek, and K. P. Papathanassiou, “Retrieval of Firn Thickness by Means of Polarisation Phase Differences in L-Band SAR Data,” Remote Sensing, vol. 13, no. 21, p. 4448, Nov. 2021, doi: 10.3390/rs13214448. [2] E. W. Hoen and H. Zebker, “Penetration depths inferred from interferometric volume decorrelation observed over the Greenland ice sheet,” IEEE Transactions on Geoscience and Remote Sensing, vol. 38, no. 6, pp. 2571–2583, 2000. [3] G. Fischer, K. P. Papathanassiou and I. Hajnsek, "Modeling Multifrequency Pol-InSAR Data from the Percolation Zone of the Greenland Ice Sheet," IEEE Transactions on Geoscience and Remote Sensing, vol. 57, no. 4, pp. 1963-1976, 2019. [4] G. Fischer, M. Jäger, K. P. Papathanassiou and I. Hajnsek, "Modeling the Vertical Backscattering Distribution in the Percolation Zone of the Greenland Ice Sheet with SAR Tomography," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 12, no. 11, pp. 4389-4405, 2019. [5] S. Tebaldini, T. Nagler, H. Rott, and A. Heilig, “Imaging the Internal Structure of an Alpine Glacier via L-Band Airborne SAR Tomography,” IEEE Transactions on Geoscience and Remote Sensing, vol. 54, no. 12, pp. 7197–7209, 2016. [6] F. Banda, J. Dall, and S. Tebaldini, “Single and Multipolarimetric P-Band SAR Tomography of Subsurface Ice Structure,” IEEE Transactions on Geoscience and Remote Sensing, vol. 54, no. 5, pp. 2832–2845, 2016. [7] M. Pardini, G. Parrella, G. Fischer, and K. Papathanassiou, “A Multi-Frequency SAR Tomographic Characterization of Sub-Surface Ice Volumes,” in Proceedings of EUSAR, Hamburg, Germany, 2016. [8] G. Fischer, K. Papathanassiou, I. Hajnsek, and G. Parrella, “Combining PolSAR, Pol-InSAR and TomoSAR for Snow and Ice Subsurface Characterization,” in Proceedings of the ESA POLinSAR Workshop, Online, Apr. 2021

Combining PolSAR, Pol-InSAR and TomoSAR for Snow and Ice Subsurface Characterization

Polarimetric and (multi-baseline) interferometric techniques are promising tools to investigate the subsurface properties of glaciers and ice sheets, due to the signal penetration of up to several tens of meters into dry snow, firn, and ice. Two different lines of research were addressed in recent years. The first is based on PolSAR, which provides not only information about the scattering mechanisms, but also has the uniqueness of being sensitive to anisotropic signal propagation in non-scattering layers of snow and firn. The second line of research is related to the use of Pol-InSAR and TomoSAR to retrieve the 3D location of scatterers within the subsurface. So far, the potential of the different SAR techniques was only assessed separately. In the field of PolSAR, modeling efforts have been dedicated to establish a link between co-polarization HH-VV phase differences (CPDs) and the structural properties of snow and firn [1][2]. CPDs have then been interpreted as the result of propagation effects due to the dielectric anisotropy of such materials. In the simplest case of snow-covered terrain, the volume scattering from the snowpack can be neglected and the total backscattered signal can be attributed to the underlying ground. The measured CPD arises then from the radar signal propagation through the entire snow layer and can be used to retrieve snow depth [1]. In the case of firn, i.e. in a glacier scenario, the relation between depth and CPD involves also the vertical distribution of backscattering generated by ice inclusions, such as layers and lenses. These scatterers are distributed along depth and influence the signal propagation in the firn volume. The CPD contributions corresponding to the location of the different scatterers have then to be integrated along depth. Up to now, only a simple constant vertical backscattering distribution was considered [2] to attempt the inversion of firn thickness. In the fields of Pol-InSAR and TomoSAR for the investigation of the subsurface scattering structure of ice sheets, recent studies are mainly concerned with the estimation of the vertical backscatter distribution, either model-based or through tomographic imaging techniques. Pol-InSAR models exploit the dependence of the interferometric volume decorrelation on the vertical distribution of backscattering. By modeling the subsurface as a homogeneous, lossy, and infinitely deep scattering volume, a relation between InSAR coherence magnitudes and the constant extinction coefficient of the microwave signals in the subsurface of ice sheets was established in [3]. This approach approximates the vertical backscattering distribution as an exponential function and allows the estimation of the signal extinction parameter, which is a first, yet simplified, indicator of subsurface properties. Recent improvements in subsurface scattering distribution modeling [4], [5] showed the potential to account for refrozen melt layers and variable extinctions, which could provide geophysical information about melt-refreeze processes and subsurface density. With TomoSAR, the imaging of subsurface features in glaciers [6], and ice sheets [5][7][8] was demonstrated. Depending on the study, the effect of subsurface layers, different ice types, firn bodies, crevasses, and the bed rock was recognized in the tomograms. This verified that the subsurface of glaciers and ice sheets can have a more complex backscattering structure than what is accounted for in current models. SAR tomography plays, therefore, a major role for investigating and improving subsurface scattering modeling of ice sheets. This study will address a promising line for future research, which is the combination of PolSAR and Pol-InSAR/TomoSAR approaches to fully exploit their complementarity and mitigate their weaknesses. As described above, on the one hand, polarimetry is sensitive to the signal propagation in snow and firn and thus to the non-scattering part of the subsurface, but provides no vertical information. On the other hand, Pol-InSAR (models) and TomoSAR allow assessing the 3-D distribution of scatterers in the subsurface, but provide no information on the anisotropic propagation effects of snow and firn. This study will investigate the synergies between the individual methods by integrating the models and algorithms into one common framework. Accordingly, the first step will be an integration of Pol-InSAR/TomoSAR vertical scattering profiles into the depth-integral of the CPD for the estimation of firn thickness with PolSAR. This will resemble a more realistic model setup and is expected to improve the estimation. Furthermore, the added information from the CPDs could act as a regularization when inverting Pol-InSAR models, opening up further potential for subsurface structure estimation. [1] S. Leinss, G. Parrella and I. Hajnsek, "Snow Height Determination by Polarimetric Phase Differences in X-band SAR Data," in IEEE JSTARS, vol. 7, no. 9, pp. 3794-3810, 2014. [2] G. Parrella, I. Hajnsek and K. P. Papathanassiou, "On the Interpretation of Polarimetric Phase Differences in SAR Data Over Land Ice," in IEEE Geoscience and Remote Sensing Letters, vol. 13, no. 2, pp. 192-196, 2016. [3] E. W. Hoen and H. Zebker, “Penetration depths inferred from interferometric volume decorrelation observed over the Greenland ice sheet,” IEEE Transactions on Geoscience and Remote Sensing, vol. 38, no. 6, pp. 2571–2583, 2000. [4] G. Fischer, K. P. Papathanassiou and I. Hajnsek, "Modeling Multifrequency Pol-InSAR Data from the Percolation Zone of the Greenland Ice Sheet," IEEE Transactions on Geoscience and Remote Sensing, vol. 57, no. 4, pp. 1963-1976, 2019. [5] G. Fischer, M. Jäger, K. P. Papathanassiou and I. Hajnsek, "Modeling the Vertical Backscattering Distribution in the Percolation Zone of the Greenland Ice Sheet with SAR Tomography," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 12, no. 11, pp. 4389-4405, 2019. [6] S. Tebaldini, T. Nagler, H. Rott, and A. Heilig, “Imaging the Internal Structure of an Alpine Glacier via L-Band Airborne SAR Tomography,” IEEE Transactions on Geoscience and Remote Sensing, vol. 54, no. 12, pp. 7197–7209, 2016. [7] F. Banda, J. Dall, and S. Tebaldini, “Single and Multipolarimetric P-Band SAR Tomography of Subsurface Ice Structure,” IEEE Transactions on Geoscience and Remote Sensing, vol. 54, no. 5, pp. 2832–2845, 2016. [8] M. Pardini, G. Parrella, G. Fischer, and K. Papathanassiou, “A Multi-Frequency SAR Tomographic Characterization of Sub-Surface Ice Volumes,” in Proceedings of EUSAR, Hamburg, Germany, 2016

Ice Sheet Subsurface Density from Polarimetric and Interferometric SAR

Information about ice sheet subsurface properties is crucial for understanding and reducing related uncertainties in mass balance estimations. Key parameters like the firn density, stratigraphy, and the amount of refrozen melt water are conventionally derived from in situ measurements or airborne radar sounders. Both types of measurements provide a great amount of detail, but are very limited in their spatial and temporal coverage and resolution. Synthetic Aperture Radars (SAR) can overcome these limitations due to their capability to provide day-and-night, all-weather acquisitions with resolutions on the order of meters and swath widths of hundreds of kilometers. Long-wavelength SAR systems (e.g. at L- and P-band) are promising tools to investigate the subsurface properties of glaciers and ice sheets due to the signal penetration of up to several tens of meters into dry snow, firn, and ice. Understanding the relationship between geophysical subsurface properties and the backscattered signals measured by a SAR is ongoing research. Two different lines of research were addressed in recent years. The first is based on Polarimetric SAR (PolSAR), which provides not only information about the scattering mechanisms, but also has the uniqueness of being sensitive to anisotropic signal propagation in snow and firn. The second is related to the use of interferometric SAR (InSAR) to retrieve the 3D location of scatterers within the subsurface. Particularly multi-baseline InSAR allows for tomographic imaging (TomoSAR) of the 3D subsurface scattering structure. So far, the potential of the different SAR techniques was only assessed separately. In the field of PolSAR, modeling efforts have been dedicated to establish a link between co-polarization (HH-VV) phase differences (CPDs) and the structural properties of firn [1]. CPDs have then been interpreted as the result of birefringence due to the dielectric anisotropy of firn originating from temperature gradient metamorphism. Moreover, the relation between the anisotropic signal propagation and measured CPDs depends on the vertical distribution of backscattering in the subsurface, e.g. generated by ice layers and lenses, which defines how the CPD contributions are integrated along depth. Up to now, assumptions of density, firn anisotropy, and the vertical backscattering distribution were necessary to invert the model, e.g. for the estimation of firn thickness [2]. However, the need for such assumptions can be overcome by integrating InSAR/TomoSAR techniques. In the fields of InSAR and TomoSAR for the investigation of the ice sheet subsurface, recent studies are mainly concerned with the estimation of the vertical backscatter distribution, either model-based or through tomographic imaging techniques. InSAR models exploit the dependence of the interferometric volume decorrelation on the vertical distribution of backscattering. By modeling the subsurface as a homogeneous, lossy, and infinitely deep scattering volume, a relation between InSAR coherence and the constant extinction coefficient of the microwave signals in the subsurface of ice sheets was established in [3]. This approach approximates the vertical backscattering distribution as an exponential function and allows the estimation of the signal extinction, which is a first, yet simplified, indicator of subsurface properties. Recent improvements in subsurface scattering modeling [4], [5] showed the potential to account for refrozen melt layers and variable extinctions, which could provide information about melt-refreeze processes and subsurface density. With TomoSAR, the imaging of subsurface features in glaciers [6], and ice sheets [5][7][8] was demonstrated. Depending on the study, the effect of subsurface layers, different ice types, firn bodies, crevasses, and the bed rock (of alpine glaciers) was recognized in the tomograms. This verified that the subsurface structure of glaciers and ice sheets can result in more complex backscattering structures than what is accounted for in current InSAR models. SAR tomography does not rely on model assumptions and can, therefore, provide more realistic estimates of subsurface scattering distributions. This study will address a promising line for future research, which is the combination of PolSAR and InSAR/TomoSAR approaches to fully exploit their complementarity and mitigate their weaknesses. As described above, on the one hand, PolSAR is sensitive to the anisotropic signal propagation in snow and firn, even in the absence of scattering, but provides no vertical information. On the other hand, InSAR (models) and TomoSAR allow assessing the 3-D distribution of scatterers in the subsurface, but provide no information on the propagation through the non-scattering parts of firn. In a first step, an estimation of firn density was achieved by integrating TomoSAR vertical scattering profiles into the depth-integral of the PolSAR CPD model [9]. This approach is in an early experimental stage with certain limitations. The density inversion can only provide a bulk value for the depth range of the signal penetration and measurements at several incidence angles are required to achieve a non-ambiguous solution. Furthermore, multi-baseline SAR data for TomoSAR are currently only available from a few experimental airborne campaigns. Finally, the density estimates have to be interpreted carefully, since the underlying models are (strong) approximations of the real firn structure. This could be addressed in the future by an integration with firn densification models. Nevertheless, this combination of polarimetric and interferometric SAR techniques provides a direct link to ice sheet subsurface density, without parameter assumptions or a priori knowledge, and the first density inversion results show a promising agreement with ice core data [9]. This contribution will present first results of the density inversion, discuss its limitations and will show investigations towards a more robust and wider applicability. One aspect will be the use of InSAR model-based vertical scattering profiles instead of TomoSAR profiles, which reduces the requirements on the observation space and increases the (theoretical) feasibility with upcoming spaceborne SAR missions. [1] G. Parrella, I. Hajnsek and K. P. Papathanassiou, "On the Interpretation of Polarimetric Phase Differences in SAR Data Over Land Ice," in IEEE Geoscience and Remote Sensing Letters, vol. 13, no. 2, pp. 192-196, 2016. [2] G. Parrella, I. Hajnsek, and K. P. Papathanassiou, “Retrieval of Firn Thickness by Means of Polarisation Phase Differences in L-Band SAR Data,” Remote Sensing, vol. 13, no. 21, p. 4448, Nov. 2021, doi: 10.3390/rs13214448. [3] E. W. Hoen and H. Zebker, “Penetration depths inferred from interferometric volume decorrelation observed over the Greenland ice sheet,” IEEE Transactions on Geoscience and Remote Sensing, vol. 38, no. 6, pp. 2571–2583, 2000. [4] G. Fischer, K. P. Papathanassiou and I. Hajnsek, "Modeling Multifrequency Pol-InSAR Data from the Percolation Zone of the Greenland Ice Sheet," IEEE Transactions on Geoscience and Remote Sensing, vol. 57, no. 4, pp. 1963-1976, 2019. [5] G. Fischer, M. Jäger, K. P. Papathanassiou and I. Hajnsek, "Modeling the Vertical Backscattering Distribution in the Percolation Zone of the Greenland Ice Sheet with SAR Tomography," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 12, no. 11, pp. 4389-4405, 2019. [6] S. Tebaldini, T. Nagler, H. Rott, and A. Heilig, “Imaging the Internal Structure of an Alpine Glacier via L-Band Airborne SAR Tomography,” IEEE Transactions on Geoscience and Remote Sensing, vol. 54, no. 12, pp. 7197–7209, 2016. [7] F. Banda, J. Dall, and S. Tebaldini, “Single and Multipolarimetric P-Band SAR Tomography of Subsurface Ice Structure,” IEEE Transactions on Geoscience and Remote Sensing, vol. 54, no. 5, pp. 2832–2845, 2016. [8] M. Pardini, G. Parrella, G. Fischer, and K. Papathanassiou, “A Multi-Frequency SAR Tomographic Characterization of Sub-Surface Ice Volumes,” in Proceedings of EUSAR, Hamburg, Germany, 2016. [9] G. Fischer, K. Papathanassiou, I. Hajnsek, and G. Parrella, “Combining PolSAR, Pol-InSAR and TomoSAR for Snow and Ice Subsurface Characterization,” presented at the ESA POLinSAR Workshop, Online, Apr. 2021