! 2004 
——— 
N Site, 
in the 
im site 
6 and 
spatial 
obtain 
slope 
ifects 
ire 8). 
to be 
higher 
E and 
m site 
n has 
vation 
E 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
  
[n this case study, taking the RMSE of 10 m, for the Upstream 
site (undulating terrain), the slope uncertainty is 9? (for 20 m 
cell size ) up to 22? (for 5m cell size), and for the Downstream 
site (flat terrain) 11? (for 20 m cell size) up to 35? (for 5 m 
resolution ). 
4.3 Effects of Resolution on Slope RMSE 
Slope RMSE decreases with increase of cell size following a 
negative power trend (Figure 9) but less strong than expected if 
all effects are due to the large number of random variables 
involved. 
Because in this case error is assumed to be randomly 
distributed, more slope variability occurs for the surface with 
smaller cell size than that with bigger cell size. The increase of 
cell size to some extent brings smoothing effects and with 
similar error of the elevation, the slope RMSE is lower. 
  
40 1 mt T 
| *  DownlO 
s  Upl0 
35 
Slope RMSE (degree) 
  
+ T 1 t + T - i 
4 6 8 10 12 14 16 18 020. 22 
Cell Size (m) 
Figure 9. Effects of resolution on slope RMSE, example of 
initial DEM RMSE = 10 m 
4.4 Effects of Spatial-dependence 
44.1 Perturbation layer - unfiltered and filtered. An 
example of unfiltered layer for perturbation (Figure 10a) shows 
randomly distributed error. In the filtered layers (Figure 10b and 
10c), clustered values are seen, with “decreasing” values as the 
function of distance. This effect is more clearly seen in the 
Upstream site (Figure 10b), because the distance of spatial 
dependence is bigger in this site than in Downstream site 
(Figure 10c). 
x a 
a 
= Du Te 
o m 
aes ve Eros 
ds 
Unfiltered Filtered (upstream) Filtered (downstream) 
[7] -36.6- -27.2 -4.2--3 L..1:98--72 
]-27.2 - -17.8 I. i73--19 fo] 
28 
Ri 
Eu 
RES 
EN 
  
  
  
      
s 
  
     
"8.3 - 1.1 
1.1- 10.5 
10.5 - 19.9 
19.9 - 29.4 
29.4 - 38.8 
(a) 
  
   
  
  
Figure 10. Perturbation layer (a) unfiltered; (b) filtered for 
Upstream site: (c) filtered for Downstream site 
4.4.2 Effects of spatial dependence on the slope grids. The 
final average slope grids by the end of simulations, both the 
unfiltered and. filtered and in comparison with the original one 
are shown in Figure 11. Frequency distributions are shown in 
Figures 12 & 13. From the unfiltered approach, there is an 
increase of low slopes into steeper slopes, which is the effect of 
“added” error. With the incorporation of spatial dependence, 
slopes are less eicvated and the distribution is closer to that of 
the original slope grid. 
  
  
    
   
  
   
  
  
  
  
  
Upstream original 
  
Slope (deg ee] 
(1:0 
[7] 10.20 
[7] 0.3 
  
  
  
  
Downstream unfiltered 
  
  
Downstream original 
  
  
      
Hog 
CE rtm "e Downstream filtered 
  
  
  
  
  
  
Figure 11. Original slope grids and the resulting slope grids 
—*— Origin | 
—* - Unfilterred | 
*^ Filterred 
Fifonency 
  
  
0 10 20 30 40 50 60 
Slope (degree) 
Figure 12. Frequency distribution of original slope, and slopes 
of unfiltered and filtered approaches in the Upstream site 
900 , 
850 | —*— Origin 
800 ; —* - Unfilterred 
750 F +++: Filterred 
650 | A 
600 | 
550 | 
ts 
4 
, A 
© 
dede 
ve“ 
Lilo Un 
S 
  
  
Slope (degree) 
Figure 13. Frequency distribution of original slope, and slopes 
of unfiltered and filtered approaches in the Downstream site 
Despite the different magnitude, both perturbations create a 
larger frequency of steep slopes. However, the slopes of 
filtered-perturbed DEM stay closer to the original slopes than 
the unfiltered-perturbed ones. The shape of frequency 
distribution of slopes is maintained, i.e. normal for Upstream 
site and left-skewed for the Downstream one 
4.4.3 Effects of spatial dependence on the slope RMSE. The 
incorporation of spatial dependence, i.c. by applying weighted- 
mean filter, decreases slope RMSE in the Upstream site into 
1017