METHODICAL ALTERNATIVES TO THE GLACIER MOTION MEASUREMENT FROM DIFFERENTIAL SAR INTERFEROMETRY

Algorithmic variations to the glacier motion estimation from differential SAR interferometry are discussed in the present paper. Two efficient albeit relatively simple algorithms for modelling glacier dynamics using spaceborne INSAR data have been devised and tested as alternatives to the conventional DINSAR approach. Neither of the algorithms involves the procedure of interferometric phase unwrapping, thus excluding the areal error propagation and improving the modelling accuracy. In general, they remain feasible even under significant phase noise. An original gradient approach (GINSAR) to differential processing of repeat-pass SAR interferograms based on the calculation of interferometric phase gradients, the generation of glacier slope maps and the analysis of differences between multitemporal slope maps provides global and fast solutions to unsupervised glacier change detection and ice motion estimation. A transferential approach is based on the interferometric measurement of the fast-ice translation forced by the glacier flow and provides good reference values on the glacier frontal velocity and velocity gradients for the GINSAR technique. A comparative analysis of the results obtained by different techniques was performed and algorithmic singularities were discussed. The revealed differences of up to 40% between the GINSAR velocities and those surveyed in the field are explained. 1. PRELIMINARY REMARKS The high level of scientific and industrial interest in satellite radar interferometry (INSAR) has not been extinguished over the past 10 years. The INSAR method is greatly valued by experts studying glacier dynamics, because of its notable data availability and astonishing sensitivity to ice motion / deformation. Spectacular results using multitemporal repeatpass interferograms from ERS-1/2 and RADARSAT satellites for glacier-flow measurement, strain rate estimation and detection of rapid glacier changes are reported every year (Bamler & Hartl, 1998; Forster et al., 1999; Rabus & Fatland, 2000) Differential interferometry (DINSAR), the methodological variant based on differencing between two SAR interferograms obtained at different times over the same glacier, became especially popular among glaciologists investigating glacier mass flux and mass balance. Although the theory of conventional DINSAR is well established (Gabriel et al., 1989; Joughin et al., 1996), the technological perfection in converting differential SAR interferograms to a surface-velocity vector field has yet to be completed. There are several approaches to solving the principal task of differential interferometry, i.e. distinguishing between the impacts of surface topography and surface displacement on the interferometric phase. A concise classification and characterisation of algorithmic variations to differential interferometric processing of SAR imagery can be found in (Wegmüller & Strozzi, 1998). Generally speaking, all known DINSAR algorithms are based on practically the same complement of operations including coregistration of interferograms, phase scaling and subtraction and, inevitably, the procedure of interferometric phase unwrapping; the latter is reputed to be the most sophisticated and problematic calculus in interferometric signal processing. Apart from the algorithmic complexity and computational load, this integral procedure is error-prone and frequently becomes impossible, at least locally, because of complex glacier topography and significant phase noise at glacier fronts, walls and tops. Moreover, in conventional DINSAR the operation of phase integration has to be performed twice, i.e. in each of two original interferograms. This leads to error propagation. In our experience, none of the available phase-unwrapping algorithms such as branch-cut, least squares or minimum-cost flow techniques, provide reliable and detailed surface models of test glaciers, even if high-quality interferograms are used. The procedure of phase unwrapping is currently reputed by experts to be a break-point in the INSAR technology; the quality of consecutive products cannot be guaranteed (H.Raggam, personal communication 2002). Our recent research has thus been focused on designing and testing alternative algorithms for glacier motion estimation and variational analysis of ice velocities without phase unwrapping. Several alternative algorithms using • transferential approach to the ice motion interpretation in single interferograms and • gradient approach to the glacier surface modelling and glacier velocity measurement were developed and tested using the ERS-1/2-INSAR data obtained over large tidewater glaciers in the European Arctic. The present paper describes these new algorithms and their singularities, and provides the most interesting results of tests and validations. The tachometric accuracy was verified by mutual comparison of models obtained by alternative techniques and compared with results of geodetic observations from the field campaign 2001. 2. STANDARD DINSAR TECHNIQUE FOR THE GLACIER MOTION ESTIMATION AND ITS LIMITATIONS Compared to other remote sensing techniques, the DINSAR method has the one wonderful advantage: it allows quite small glacier changes / motions in the centimetre range to be detected and measured from satellite SAR images with a nominal ground resolution of several tens of meters. A full separation between the impacts of glacier topography and glacier motion on the interferometric phase is a prerequisite for attaining such a high performance. Although the non-linear behaviour of the SAR interferometer with regard to the phase may not be excluded, especially when it comes to INSAR modelling of active glaciers, for the sake of simplicity, the unwrapped interferometric phase is usually treated as a linear combination of several phase terms. For example, in (Bamler & Hartl, 1998), the interferometric phase is presented as a sum of independent contributions from imaging geometry (the flat earth phase) o φ , topography topo φ , glacier flow mot φ , atmospheric disturbances atm φ and noise noise φ noise atm mot topo o φ φ φ φ φ φ + + + + = . (1) The proper selection of interferometric pairs allows the terms atm φ and noise φ to be kept small (Sharov & Gutjahr 2002), and, after the flat earth correction is performed, the equation (1) can be rewritten as a function of only the topographic phase and the motion phase       ⋅ + ⋅ ⋅ ⋅ ≅ ⊥ T V R h B θ λ π φ sin 4 , (2) where φ denotes the interferometric phase after the flat-terrain phase correction; λ is the wavelength of SAR signal, is the perpendicular component of the spatial baseline, R the slant range, θ the look angle, V the projection of the flow vector on the line-of-sight direction, and T is the temporal baseline. ⊥ B Theoretically, the isolation of the motion phase from the topographic phase can be performed by differencing between two SAR interferograms of the same glacier, one of which does not contain the phase term related to the ice motion. In practice, however, it is nearly impossible to find out the real interferometric model of a living glacier without motion fringes. This holds good especially for the study of fast-moving polar glaciers, such as large tidewater glaciers. Their velocities reach tens of centimetres a day and more. Thus, in general, glaciologists must deal with a pair of SAR interferograms, each containing both topographic and motion phases. Interferograms in processing have different spatial baselines. Therefore, one of the interferograms must be scaled before the subtraction in order to account for different surveying geometry and to compensate the topographic phase. The procedure of scaling is usually applied to the unwrapped phase picture because scaling of the wrapped phase provides reasonable results only for integer scaling factors (Wegmüller & Strozzi 1998). After phase unwrapping and co-registering both pictures can be combined and subtracted one from the other. This is generally considered to be a somewhat complicated technique, since it involves up to ten obligatory processing steps. Furthermore there are several major limitations to conventional DINSAR impeding its application to glacier motion estimation. In the differential interferogram, the topographic phase is compensated and the equation for differential phase is given as follows       ⋅ ⋅ − ⋅ ⋅ ≅ ⊥ ⊥ 2 2 2 1 1 1 4 T V B B T V d λ π φ . (3) From the equation (3) it is seen that the motion phase mot φ 2 is also scaled, and the direct estimation of the glacier motion is still impossible because only the difference between two motion phases is given. The proper selection of interferograms with different temporal baselines T does not help much in this case because of the decorrelation noise that increases drastically with time between surveys. Practically, only SAR interferograms with a temporal interval of 1 day and 3 days can be applied to glacier modelling. 2 1 T ≠ The simplest way to solve the equation (3) with regard to the velocity V1 or V2 is to assume that the glacier velocity remains constant over the time span covered by both interferograms, i.e. V1 = V2 = V. Although applicable to modelling in the accumulation area of large ice domes, the stationary flow assumption has often proved to be incorrect in fast moving areas of outlet glaciers (Fatland & Lingle, 1998). A more reliable constraint has been offered in (Meyer & Hellwich, 2001), who supposed that the velocity ratio V1 / V2 remains constant over the whole glacier area. Still, the validity of such an assumption has not been confirmed empirically. Another serious limitation to DINSAR is that only the velocity component in satellite look direction can be derived from differential SAR interferograms. Hence, some additional constraints are necessary for estimating the horizontal and vertical components of the ice-velocity vector. A common way to proceed is to assume that the glacier flow is parallel to