ISPRS Commission II, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002 
  
need for the DINSAR approach at all. Sometimes, essential ice 
flow is recorded in relatively flat glacier areas. If the 
interferential baseline is not long (several tens of meters), the 
topographic phase vanishes in such areas, and the glacier 
motion also can be evaluated (locally) from a single SAR 
interferogram. From a practical point of view, however, such 
cases should be treated as an exception to the rule, and we thus 
applied such interferograms to the verification of results 
obtained by other DINSAR techniques. In the next chapter, we 
present an original and simple approach to measuring frontal 
velocities of tidewater glaciers from single SAR interferograms. 
3.1 Transferential approach 
For most tidewater glaciers, the longitudinal strain rate and the 
ice velocity attain their maximum at the glacier front. There are 
many crevasses at the front part of the glacier tongue, the 
surface is very rough and the block-wise ice motion is 
incoherent (Forster et al., 1999). Both, the amplitude and the 
coherence of the interferometric signal from the glacier surface 
is usually quite low near the glacier face, and the interferential 
picture of glacier exteriors is characterised by poor quality. This 
explains why reports on using INSAR data for the measurement 
of frontal glacier velocities are quite few in number. 
In contrast to the glacier surface, the area of fast sea ice attached 
to the glacier face is often reproduced with quite good 
coherence and demonstrates good visibility of interferential 
fringes. Vast plane floes of young coastal ice with a very small 
elevation above sea level thus represent an ideal surface for the 
interferometric analysis of small motions, such as translation, 
tilting and rotation. There is no need for topographic reference 
in this case. This factor makes it possible to accurately measure 
frontal glacier velocities in single SAR interferograms by 
analysing the fast-ice motion forced by the glacier flow. 
In winter interferograms, the effect of lateral displacement of 
young coastal ice pushed by moving glacier manifests itself as a 
zone of concentric hemispherical or hemi-elliptical fringes 
converging at the tips of the glacier front (Fig. 1). Such 
interferential features called “outflows” are permanently found 
at fronts of nearly all active tidewater glaciers. The orientation 
of outflows mostly coincides with the cross-track direction that 
indicates the lateral character of corresponding motions. Tilting 
and bending of ice floes due to the atmospheric/oceanic forcing, 
e.g. tidal effects, would produce fringes in any orientation. 
Rotation produces fringes parallel to the track direction. Also 
regions of high deformation are characterised by high local 
fringe rates and increased phase noise. But usually we did not 
observe any significant phase noise in the area of outflows and 
did not detect the presence of significant deformation features 
(cracks, ridges) in the young sea-ice cover by jointly 
interpreting corresponding amplitude, coherence and fringe 
images. Thus, the origin of “outflows” is believed to be related 
primarily to the horizontal displacement of the coastal ice. 
It is reasonable to assume that in the immediate proximity of the 
glacier face and under calm weather conditions, the local speed 
of the fast-ice translation is equal to the frontal velocity of 
gently sloping tongues of tidewater glaciers. Then, in the tide- 
coordinated INSAR data without significant tidal effects, the 
horizontal (frontal) glacier velocity in the SAR-range direction 
can be simply determined by counting the (real) number of 
interferential fringes k within the “outflow” as follows 
V, =0.51-k-(T-sin@-cos 6), 4) 
A - 326 
where A = 5.66 cm is the wavelength, 6 - the look angle 
measured from the vertical, B - the flow direction angle 
measured from the cross-track direction, and 7 is the temporal 
baseline of the interferogram. 
An application of an approach of this kind known as 
transferential [from Latin transferre: trans-across, change 7 ferre 
to carry] to ERS-1/2-INSAR data processing allowed the frontal 
velocities of 52 large Eurasian tidewater glaciers oriented in the 
SAR-range direction to be determined for the first time in the 
history of their exploration (Sharov & Gutjahr 2002). 
Transverse variations of the frontal velocity along the glacier 
face can be evaluated by analysing the shape of outflows. The 
fringe rate within outflows decreases offshore and vanishes with 
the distance from the glacier front that corresponds to the 
localised and decelerated mode of displacement. The amount of 
displacement usually increases along the ice coast from zero at 
the tips of the glacier front to its maximum in the mid point at 
the glacier snout. 
The lateral extension of an “outflow” and the number of 
interferometric fringes within increases with the time interval 
between SAR surveys, though the local fringe rate remains 
nearly unchanged. For example, Figure 1 shows a typical 
“outflow” at the front of Impetuous Glacier, Russian Arctic as 
shown in the interferograms generated from ERS-1/2-SAR 
images taken at 1 (a) and 3 (b) day intervals. The sea ice 
thickness grows through time and sea-ice deformation features 
become noticeable in  late-winter  interferograms, but, 
nevertheless, the transferential technique remains feasible up to 
the time of melting and disintegration of the coastal ice. The 
main drawback to the transferential technique is that it is not 
suited for the velocity measurement / representation over the 
whole glacier area. For the reliable separation between the 
topographic and the motion phase and the accurate 
determination of the velocity field over the whole glacier area 
we devised (independently of the publication by D.Sandwell & 
E.Price) an original gradient approach, which is presented below. 
  
Figure 1. “Outflows” in interferograms of 17/18 December, 
1995 ( B, = - 41 m, a) and 23/25 February 1994 ( B, — -34 m, b) 
3.2 Gradient Approach 
Gradient approach to differential processing of SAR 
interferometric data (GINSAR) is based on the calculation of 
interferometric phase gradients, the generation of glacier slope 
maps without interferometric phase unwrapping and the 
analysis of differences between slope maps generated from 
multitemporal INSAR sets. The underlying concept of the 
GINSAR technique is to make use of the fact that, for the great 
majority of points in the interferential picture, partial derivatives 
of the wrapped interferential phase are equal to partial 
derivatives of the unwrapped phase, i.e.