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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
A local discrepancy between simulated and observed ERS 
heights is the sign of a potential anomaly in the DEM. 
A systematic shift between both height is the sign of a 
systematic shift error on DEM. 
6. ERS ERROR ANALYSIS ON NON-FLAT TERRAIN. 
We investigated the ERS elevation data error on rougher 
terrain, using a 30-meter digital elevation model considered as a 
reference. Two different study areas with different relief 
characteristics were selected. We derived parameters from this 
DEM. Errors between ERS data and DEM and also between 
the simulated responses obtained with the DEM were 
calculated. Finally, their correlation with the terrain parameters 
were analysed. 
6.1 Study areas description 
The first geographical area, located at the south-west of France, 
includes landforms ranging from extensive floodplains to low 
relief foothills, and high relief, long mountains slopes to the 
east. The other area, located in the North, is less rough but 
contained larger urban area, which can distort the altimeter 
response. The field areas are approximately 150 km. 
6.2 Elevation data 
ERS elevation data : we collected all data obtained after the 
retracking step in both areas. There were 5679 and 8634 
elevation points over each area. 
30-m DEM : the DEM is a level 1 data (DTEDI) acquired by 
photogrammetric method from remote sensing images such as 
Spot, or by contour digitising from existing 25,000 scale maps. 
A root mean square errors (RMSE) is provided to express its 
quality . The RMSE is reported as 30 m for horizontal 
coordinates, and 5 m for height, relative to the WGS 84 datum. 
We extracted elevation at each ERS elevation positions using a 
bilinear interpolation method. 
ERS simulated elevation data : at each ERS elevation position, 
we use the DEM to obtain a simulated ERS height based on the 
method described in previous section . 
  
  
  
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distance (km) 
Figure 6. Height profiles from DEM and ERS altimeter 
63 Exploratory data anaiysis 
63.1 Errors statistical distribution 
Fig 7 shows the different data sets with their histograms. They 
seem similar for the three data sets. On the north area, they 
show a roughly normal distribution of the elevations. On the 
389 
second sites they are broader, showing the various relief. The 
errors were calculated by subtracting the interpolated DEM 
elevation and the simulated elevation from the ERS measured 
elevation. The spatial distribution of these absolute error values 
and their histograms are plotted in fig.8. 
first study area 
  
  
  
  
  
  
    
    
min :0 min 15 
2500 2500 2500 ee 
mean: 114 mean: 129 mean: 137 
2000 std: 45 i 2000 std: 31 2000 sid: 26 | 
max :254 i max :354 max :252 i 
min :10 min :17 min :32 i 
1500} + 1500: 1 1800: 1 
1000 ; 1000 ; 000: | 
i | 
i i | 
500 500; 500 | 
0: 3 0- X ge és 
0 100 200 300 0 100 200 300 0 100 200 300 
elevation (rn) elevation (m) elevation (m) 
second study area 
800 . - 273549007: - r . 800 r 
mean: 102 mean: 112 mean: 131 | 
std: 57 i sid: 65 | 
600: max301  ; 600 max :366 | 
| 
  
0 { — 0 
0 100 200 300 0 100 200 300 0 100 200 300 
elevation (mj alevation (m) elevation (m) 
Figure.7, Elevation histograms in both study areas. 
first study area 
  
  
  
7000 = — — — —MÀÀ 7000 € 
6000 | mean : 15 | 
S std: 24 $000 
5000 mm d 5000 
min: 0 
4000 | 4000 
3000 { 3000 
2000 2000 
1000 1000 
0 sean sre st ens 0 —J 
0 So 100 150 200 0 50 100 150 200 
Bbs(DEM-ERS) (m) abs(SIM-ERS) (m) 
second study area 
3000 777 ome 30008 — ^ 
mean : 29 mean : 22 
2500 std: 29 2500 std: 28 
max:163 max:257 
2000 min: 0 2000 mino 
1500 1500 
1000 1000 
500 500 ] 
| 
0 eat suut eat 0 eruere ro. 
0 50 100 150 200 250 0 50 100 150 200 250 
abs(DEM-ERS) tm) abs(SIM-ERS) (m) 
Figure.8. Absolute errors, DEM and simulated ERS elevations 
versus ERS measured elevation. 
The histograms indicate that on average the altimeter gives a 
coherent elevation value over the study areas. However, the 
maximum absolute errors values show there are significant 
differences in some areas. The distribution error is narrower, 
particularly in the place with low roughness. 
6.3.[2 Terrain parameters influence. 
To understand the altimeter behaviour, we derived some 
parameters from the DEM reflecting the local topographic 
roughness around each elevation position within a moving 
window (a 20-cell or 10 km circle). The parameters are the 
following : 
P1 and P2: the slope mean and standard deviation. 
P3 and P4: the mean and standard deviation of elevations. 
The next table shows the coefficient for correlation between the 
errors and the different parameters over both study area.