4.2 Estimation results 
The preprocessed data sets form the vector of observations b in 
the estimation approach. Within the adjustment the unknown to- 
pography and motion parameters are estimated in the nodes of the 
chosen spatial model (see Section 2.3.3). To reduce the compu- 
tational load the area of interest is separated into 14x14 tiles, 
which are evaluated separately and re-merged afterwards. Fi- 
nally, topography and motion values in all resolution cells (i, j) 
are interpolated from the estimated unknowns in the bilinear gird 
based on the mapping function of the spatial model. Thus, an 
area-wide DSM and velocity field is available after the process. 
4.2.1 Digital surface model of Hall Island Figure 7 shows 
the DSM of Hall Island derived from the interferometric phase 
using the proposed method. The topographic height values shown 
Sonklar 
     
Nr. 17 
Nr. 16 
Figure 7: DSM of Hall Island derived from the interferometric 
phase. The black arrow indicates the viewing direction of the 
sensor. The positions of the largest outlet glaciers are indicated. 
in Figure 7 are referenced to the WGS84 ellipsoid and vary within 
Om-500m. The topography gradient is small in the glaciated 
terrain. Rough terrain only appears in the mountainous regions in 
tne south-western and eastern parts of the island. 
Standard deviations for the height values are extracted from the 
covariance matrix K zz, which is estimated within the adjustment. 
Ks is defined by 
AD s 
Kaz = 00022 — 00 (AT PA) with 62 = res 
5 00) 
Equation (10) shows that the standard deviations of the adjusted 
unknowns are a function of the a priori defined functional and 
stochastic model as well as of the variance factor a2 which is 
estimated within the adjustment. ó$ may be interpreted as link 
between the implemented models and the real data. Its values 
indicate how far the chosen functional and stochastic model fit 
the measured data sets. In the adjustment the a priori value of o2 
is set to 1. Significant deviations of 63 from 1 indicate errors in 
the models or gross errors in the data. A separate variance factor 
is estimated for each of the 14 x 14 tiles. 
The standard deviations of the adjusted topographic heights are 
presented in Figure 8, split into the theoretical standard deviations 
(diagonal elements of matrix Q;;) and the estimated variance 
factors for each of the 14x14 tiles. The parted representation 
entails several advantages. The theoretical standard deviations 
offer an insight into the properties of the adjustment's configura- 
tion (compare Figure 8a)). They illustrate the spatial distribution 
of the achievable height accuracy assuming a precise functional 
1008 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
a) b) 
Figure 8: a) Theoretical standard deviations of the estimated 
DSM [m]. 5) Adjusted variance factors for Hall Island. One 
variance factor ist estimated for each of the 14x 14 tiles. 
and stochastic model. Figure 8a) shows that the design of the 
adjustment allows to estimate topography with high accuracy all 
over the island. The estimated variance factors presented in Fig- 
ure 85) indicate, in which parts of the island the measured data 
sets are sufficiently described by the implemented models. Low 
values for 6$ appearing in large parts of the Moscow Ice Dome 
depict good agreement between model and data. Large values, 
which are visible in mountainous areas and in the catchment of 
the glaciers Sonklar, Nr. 7 and Nr. 8, indicate model errors. In 
the mountainous areas this errors are due to phase unwrapping 
problems. In the glacier catchments this errors are caused by an 
insufficient flow model. 
The real standard deviations of the estimated topographic heights 
(diagonal of Kz) reach oy, = 1m to on = 2m in the glaciated 
terrain and lie between o, = 2m and op = 8m in mountainous 
areas. In glaciated regions the standard deviations are in the range 
of the theoretical values estimated in Section 3 on the basis of 
theoretical data. Due to model errors the standard deviations in 
mountainous terrain are larger than the simulated ones. 
4.2.2 Velocity field of Moscow Ice Dome To the best of the 
author’s knowledge no detailed velocity map of the glaciers on 
Hall Island has been published up to now. Thus, the results of 
these study provide a new insight into the rheology and the phys- 
ical properties of the ice masses on Hall Island. The estimates for 
the line-of-sight velocity components of the Moscow Ice Dome 
are presented in Figure 9. The surface velocity is given in m/a. 
As expected mainly the glaciers Sonklar, Nr. 7, Nr. 8, Nr. 12, Nr. 
Sonklar 
     
   
Nr. 17 
Nr. 16 
Figure 9: Velocity field of Hall Island derived from the interfer- 
ometric phase. The black arrow indicates the viewing direction 
of the sensor. The positions of the largest outlet glacier are indi- 
cated. 
16 and Nr. 17 are reflected in the interferometric phase. This is 
because the flowing direction of these glaciers is approximately 
directed in the sensor’s line-of-sight. Besides, the movement of 
   
  
  
  
  
  
  
  
  
   
   
    
   
    
   
   
  
  
  
  
  
     
    
  
   
   
   
   
   
   
    
    
   
  
  
  
  
  
  
  
  
  
  
   
   
   
   
    
    
   
   
  
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