Due to a high sensitivity of terrain analysis algorithms to local conditions, any single realisation represents only one view on terrain morphology. This is especially important for the calculation of hydrological parameters where we are more interested in the general picture of the processes. Even for the perfectly adjusted DEM, the location of the stream network can differ up to 3-4 cells from the true location (Burrough and McDonnell, 1998). A statistically robust approach to reduce the errors in terrain parameters is to average a set of possible realisations given the uncertainty in elevation values (Burrough et al., 2000; Raaflaub and Collins, 2002, Hengl et al. 2004). This methodology can now be automated by combining geostatistical and GIS tools.

R/ILWIS SCRIPTS FOR GEOSTATISTICAL SIMULATIONS

The example bellow shows results of applying error propagation techniques in geomorphometry. I used Sequential Gaussian Simulations (as implemented in gstat) to generate 50 equi-probable DEMs from point data (Baranja hill case study), then exported the DEMs to ILWIS GIS and derived slope, aspect, curvatures, northness and solar insolation 50 times. The results show that the propagated error in DEMs has different impact on calculation of various DEM parameters: (a) in the case of deriving SLOPE, the error increases with local slope; (b) in the case of deriving northness and curvatures, the error in the plain areas is much higher and (c) for some parameters such as solar insolation, SLOPE makes no impact on the precision of the output maps. A summary comparison of various land surface parameters is available here. Note that the calculation of DEM parameters in ILWIS can be time-consuming for large DEMs.

		INSTRUCTIONS: 1. Obtain and install R and ILWIS GIS. 2. Intall R packages gstat and maptools. 3. Obtain ILWIS script TP_morphometric. 4. Download and unzip the R/ILWIS script and input data. 5. First open the R script and run it line by line. This will allow you to generate multiple simulations of DEM. 6. Then open ILWIS and run the attached ILWIS script. 7. You can implement the same methodology using your own case study by adjusting the two scripts.
Figure: Simulated DEMs using conditional geostatistical simulations.	Figure: PLANC calculated by averaging up to 50 realisations.

Figure: Correlation between the local SLOPE and propagated error calculated for various land surface parameters.

REFERENCES:

Burrough, P.A., van Gaans, P.F.M. and MacMillan, R.A., 2000. High-resolution landform classification using fuzzy k-means. Fuzzy Sets and Systems, 113: 37-52.
Hengl, T., Gruber, S. and Shrestha, D.P., 2004. Reduction of errors in digital terrain parameters used in soil-landscape modelling. International Journal of Applied Earth Observation and Geoinformation (JAG), 5:97-112.
Heuvelink, G.B.M. 1998. Error Propagation in Environmental Modelling with GIS. Taylor and Francis, London (1998) 144 pp.
Heuvelink, G.B.M. 2002. Analysing uncertainty propagation in GIS: why is it not that simple?. In: G.M. Foody and P.M. Atkinson, Editors, Uncertainty in Remote Sensing and GIS, Wiley, Chichester (2002), pp. 155–165.
Raaflaub, L.D. and Collins, M.J. 2006. The effect of error in gridded digital elevation models on the estimation of topographic parameters. Environmental Modelling and Software 21: 710–732.

Author: Hengl
LAST UPDATE: 17-Oct-2007