1. Uncertainty of runoff flow path on a small agricultural watershed Unit of Soil and Water System Departement of Environment Science and Technology Gembloux Agro-Bio Tech – University of Liege Ouédraogo M.

2. Plan  Context  Objectives  Modeling uncertainty  Some results  Conclusion 2

3. Context Frequency of muddy floods over a 10-year period in all municipalities of the study area; data for Wallonia (1991–2000) taken from Bielders et al. (2003), data for Flanders (1995–2004) derived from a questionnaire sent to all municipalities in 2005. O. Evrard, C. Bielders, K. Vandaele, B. van Wesemael, Spatial and temporal variation of muddy floods in central Belgium, off-site impacts and potential control measures, CATENA, Volume 70, Issue 3, 1 August 2007, Pages 443-454, ISSN 0341-8162, 10.1016/j.catena.2006.11.011. Consequences:  Cleanning cost: 11000 €  Soil loss  economic impact for farmers  Stressfull for population 3

4. Context DEM GPS, Topographic cards, Aerial and Terrestrial scanning, Aerial Photogrammetry… Elevation data 4 Errors  How can we model the impact of errors?

5. Objectives  Analyze uncertainty of runoff flow path extraction on small agricultural watershed  Determine how uncertainty is depending on DEM resolution  Determine wether uncertainty is depending on the algorithm 5

6. 6 Modeling uncertainty  Test area Area:12 ha Elevations:159 -169 m Mean slope: 3.67%

7. 7 Modeling uncertainty  Digital Elevation Model (DEM) 14 stations 3 DEMs 1 m x 1 m 2 m x 2 m 4 m x 4 m

8. Modeling uncertainty 8  Monte Carlo simulation Purpose: Estimate original DEM errors, Generate equiprobable DEMs XYΔZΔZ ::: mean, variance, semivariance 1098 GCPs

9. Modeling uncertainty 9  Purpose: Estimate original DEM errors and Generate equiprobable DEMs 1.Digital error model generation  Idea: visite each pixel of terrain model and generate error value  Generation uses kriging interpolation (mean, variance, semivariance) 2.Add error model to original DEM to obtain simulated DEM + Original DEMDigital error models Simulated DEMs

10. 10 Modeling uncertainty  Apply runoff flow path extraction algorithms on simulated DEMs  Consider pixel as Bernoulli variable i.e. value=1 or 0  Compute for each pixel the number of times (nb) it has been part of runoff fow path  Define probability P=nb/N (N is the number of simulated DEMs) 0 1

11. 11 Modeling uncertainty  Define random variable D as distance from pixels (p>0) to extracted flow path  Compute cumulative distribution function i.e. P (D<=d) Objective: allow a user to define area which will contain flow path With a given probability

12. 12 Modeling uncertainty R : geoR and gstat for DEMs simulations (1000) Whitebox GAT library for runoff flow path algorithms Programming automated tasks is done in Neatbeans  Tools for modeling uncertainty

13. Some results 13 1 m x 1 m2 m x 2 m4 m x 4 m  Pixels probability increases with DEM resolution  Runoff flow path position is more variable for 1 m x 1 m Certainly due to microtopography

14. 14 Some results  Cumulative distribution function of D 1 m x 1 m

15. 15 Some results

16. 16 Conclusion  Monte Carlo is powerfull  Usefull, specially for massive data collection tools  However, very difficult to be implemented  Limitation with commercial algorithms  Need to compute automated tasks  Computing time can be very long  Next step: compare the results of different algorithms

17. Thank you 17