ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002 
  
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) $,. topography Boop glacier 
flow @ 
moi » atmospheric disturbances $,,, and noise @ 
noise 
ó = 9, + Dior + Dror x atm T noise ' (I) 
The proper selection of interferometric pairs allows the terms 
By and Gis 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 
I 
0 a +7]. (2) 
À \R-sin0 
where @ denotes the interferometric phase after the flat-terrain 
phase correction; A is the wavelength of SAR signal, B, is the 
perpendicular component of the spatial baseline, R - the slant 
range, 0 - the look angle, V - the projection of the flow vector 
on the line-of-sight direction, and T' is the temporal baseline. 
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 
À 
+2 
4c B 
es Spon Bonn] (3) 
From the equation (3) it is seen that the motion phase $,, or 2 18 
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; z 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. 
The simplest way to solve the equation (3) with regard to the 
velocity V; or V; is to assume that the glacier velocity remains 
constant over the time span covered by both interferograms, i.e. 
V; = V, = 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 V; / V; 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 the ice 
surface, normal to topographic contours and parallel to glacier 
walls. The surface parallel flow assumption is considered to be 
more or less realistic when the surface-normal velocity is small, 
which is the case only over some parts, e.g. around the 
equilibrium line, of a valley glacier (Rabus & Fatland 2000). 
Sometimes, a combination of three or more interferograms 
taken either from parallel or from opposite, i.e. ascending and 
descending orbits is used, but the necessity of performing two- 
dimensional phase unwrapping of each original interferogram in 
the case of phase noise with unavoidable error propagation is 
probably the most serious restriction to the multiple baseline 
approach in particular and to the whole DINSAR method in 
general. An essential enhancement to the multiple baseline 
technique based on stacking / averaging phase gradients was 
offered in (Sandwell & Price 1998) with the aim to decrease 
errors due to atmospheric-ionospheric disturbances and to 
improve the general quality of INSAR data for both topographic 
recovery and change detection. The phase gradient approach 
ensures serious processional advantages, e.g. it delays the 
procedure of phase unwrapping until the final step of the 
DINSAR processing, but remains, however, largely untested 
and is rarely mentioned in literature. 
3. ALGORITHMIC ALTERNATIVES TO DINSAR 
MODELLING OF GLACIER DYNAMICS 
As has been seen, obtaining several suitable INSAR pairs and 
their differential processing for studying glacier dynamics, is 
not an easy matter in the first place. There is thus a natural 
desire to try simpler techniques that do not involve complex 
process artifices such as phase unwrapping and do not require 
additional topographic reference models. 
If the length of the interferential baseline is, by lucky chance, 
very short (several meters), then the glacier motion can be 
determined directly in a single interferogram and there is no 
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