anbul 2004
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asured data
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rge values,
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.
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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
glacier Nr. 4 is visible in addition. The transition from stable to
moving ice is smooth for all glaciers. The absolute value of the
line-of-sight velocities of Moscow Ice Dome varies from 0 m/a in
ice-free areas and in the center of the island up to 43 m/a near the
front of some of the outlet glaciers. The velocity of all glaciers in-
creases from the center of the island towards the glacier terminus.
The frontal part of the largest outlet glaciers suffers from strong
temporal decorrelation. Thus, processing of glaciers velocities in
the frontal parts of some glaciers was not possible.
The standard deviation of the line-of-sight velocity field is shown
in Figure 10. The parameters are again separated into two parts,
the theoretical standard deviations (Figure 10a)) and the a pos-
teriori variance factors (Figure 105)). Figure 85) and 105) are
identical. Nevertheless, the parameters are presented for the sake
of completeness. The distribution of theoretical standard devia-
tions of the estimated velocities differs from the structure of the
according topography values. This is due to the fact, that velocity
estimates are mainly defined by interferograms with short base-
lines, whereas topography is especially influenced by interfero-
grams with long baselines. In glaciated regions the real standard
Sonklar
Nr. 17
Nr. 16
a) b)
Figure 10: a) Theoretical standard deviations of the estimated
velocity field [m/a]. b) Adjusted variance factors for Hall Island.
One variance factor ist estimated for each of the 14x 14 tiles.
deviations (diagonal of Kis) of the velocity estimates vary be-
tween 0.1 m/a and 0.7 m/a and are in the range of the theoretical
values estimated in Section 3. Due to model errors the standard
deviations in mountainous terrain are larger than the simulated
ones.
43 Interpretation of the residuals
During the estimation process several gross errors and model er-
rors may occur that differ in origin and caused effect. Errors
during SAR data acquisition, processing and phase unwrapping,
wrongly determined stochastic properties, and insufficient func-
tional relations are the most prominent. Hence, the development
of a reliable estimation method, which allows to reveal gross er-
rors in the data, is one of the most important goals of system
design. The properties of the presented method regarding robust-
ness and reliability are analyzed based on several indicators. All
of them base on the equation
Aé = — (Qu — A(A" Por A)* A”) Pot = —TAD (M)
that describes how gross errors in the observations and model
errors Ab are reflected in the vector of adjusted residuals €. The
matrix Ÿ that maps Ab onto the vector of adjusted residuals is
presented in Figure 11. The structure of matrix Y entails some
convenient properties. The diagonal elements of 'Y are close to
unity, thus gross errors have a strong impact on é and are therefore
easily detectable. The off-diagonal elements are small. Hence,
an error in observation 2 only affects its associated residual and a
dispersion of errors doesn't occur.
Because of this properties of the approach the vector of residuals
€ can be consulted for analyzing gross errors in the data and the
models. An analysis of &, which results during the estimation
process indicates evidence for several error sources. These are
1009
Figure 11: Structure of matrix Y for a subset of the area of inter-
est consisting of 10x 10 pixel size.
e Phase unwrapping errors, mainly in mountainous regions
e Non-modeled changes of the glacier topography in small
isolated areas
e Errors due to an insufficient flow model in the caption of
Sonklar Glacier
e Low frequency phase variations due to atmospheric effects
5 SUMMARY
The presented approach allows an improved separation of topography-
and displacement-related contributions to the interferometric phase
by combining multi-temporal SAR interferograms in a least squares
adjustment. The interpretability of the adjusted parameters is sig-
nificantly increased by a systematic model-based quantification
of all influences on the interferometric signal. The capability of
the method to improve the accuracy of topography and displace-
ment estimates, as well as the possibility to reveal gross errors in
the observations has been demonstrated. A brief analysis of pos-
sible error sources has been presented. A validation using real
data from an island in the Russian arctic confirms the approach.
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