International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
  
12% of the unfiltered one, and in the Downstream site into 27% 
(Figure 14). This result shows that the incorporation of spatial 
dependence of elevation error reduces the estimated error of 
slope. 
—*— DownUnfilt 
-- UpUnfilt 
20 -—* - DownFilt 
-—G- UpFil 
   
   
Slope RMSE 
4 6 8 10...12 14 16 #820 22 
Initial DEM RMSE 
Figure 14. Effects of spatial dependence on slope RMSE 
5. CONCLUSION 
The increase of initial DEM uncertainty affects the increase of 
derived-slope uncertainty following a linear trend although for 
the higher resolution (5 m), the trend appears to be curvilinear, 
as the slope of the graph is smaller for the higher initial DEM 
RMSE. The slope uncertainty is larger in the Downstream site 
than in the Upstream site because the effects of similar 
magnitude of error to the original elevation variability are 
stronger in flat area than in undulating area. 
Slope RMSE increases by the increase of resolution (smaller 
cell size), which means that with a similar magnitude of error 
indicated, higher slope uncertainty occurs in higher resolution 
slope grids. This result shows the importance of choosing the 
optimum resolution so as to minimize big slope uncertainty. 
And as the result shows that higher slope uncertainty occurs in 
the flat area than in the undulating area, the decision of 
resolution is more crucial if the terrain under study is relatively 
flat than if it is undulating. 
The approach which considers that elevation error is random 
shows that initial DEM uncertainty affects derived-slope 
uncertainty in a much higher degree than if elevation error is 
considered spatially-dependent. Assuming that error is spatially- 
dependent, error propagation from DEM to the slope error 
occurs in a lower magnitude compared to the propagation when 
error is considered random. And the magnitude of the reduction 
is bigger in the undulating terrain than in the flat terrain. 
This study is still in the preliminary stage, a few points for 
further improvement are considered important to note: 
1. With the spatial dependence assumption, the relationship 
between the spatial dependence of elevation and that of the 
error is yet to be studied further. The question should be 
whether spatial dependence of elevation error is linearly 
correlated with that of the elevation. 
2. Comparison of slope RMSE obtained as the DEM-derived 
feature with that obtained from field observation may result 
in a different magnitude of uncertainty. 
3. For overall outcomes of erosion and river flow, the 
frequency distribution of slopes, and thus of the error, is 
important to assess. However for spatially-explicit 
intervention, the demand is on the location aspects of the 
error/uncertainty. 
ACKNOWLEDGEMENTS 
The overall watershed-function project by ICRAF Indonesia in 
Way Besai watershed is funded by Australian Centre for 
International Agricultural Research (ACIAR). Authors would 
like to thank Meine van Noordwijk and Sonya Dewi for their 
inputs and field staff and students who helped in data collection. 
REFERENCES 
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http://www.mercat.com/QUEST/gpstutor.htm 
Holmes, K.W., Chadwick O.A., Kyriakidis, P.C., 2000. Error in 
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terrain modeling. Journal of Hydrology, 233, pp. 154-173 
Hunter, G. and Goodchild, M., 1997. Modeling the uncertainty 
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Hunter, G., and Goodchild, M., 1995. Dealing with error in 
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Jorgensen, S E. 1994. Fundamentals of Ecological Modelling 
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