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
A- 325