Uncertainty of runoff flow path on a small agricultural watershed

Unit of Soil and Water SystemDepartement of Environment Science and Technology

Gembloux Agro-Bio Tech – University of Liege

Ouédraogo M.

Plan

ContextObjectivesModeling uncertaintySome resultsConclusion

2

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

Context

DEM

GPS, Topographic cards, Aerial and Terrestrial scanning, Aerial

Photogrammetry…

Elevation data

Errors

How can we model the impact of errors?

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

Modeling uncertainty Test area

Area:12 ha

Elevations:159 -169 m

Mean slope: 3.67%

7

Modeling uncertainty Digital Elevation Model (DEM)

14 stations

3 DEMs

1 m x 1 m2 m x 2 m

4 m x 4 m

Modeling uncertainty

8

Monte Carlo simulation

Purpose: Estimate original DEM errors , Generate equiprobable DEMs

X Y ΔZ : : :

2mean , variance , semivariance

1098 GCPs

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 DEM Digital error modelsSimulated DEMs

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

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

Modeling uncertainty

R : geoR and gstat for DEMs simulations (1000)

Whitebox GAT library for runoff flow path algorithmsProgramming automated tasks is done in Neatbeans

Tools for modeling uncertainty

Some results

13

1 m x 1 m 2 m x 2 m 4 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

Some results

Cumulative distribution function of D

1 m x 1 m

15

Some results

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

Thank you

17